Harold E. Saunders. Hydrodynamics In Ship Design. Volume Two

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Marine

Biological

Woods

Hole,

Laborolory Library

MossQchusetls

VOL

HYDRODYNAMICS IN SHIP DESIGN VOLUME TWO by

HAROLD Captain, U.

E. S.

SAUNDERS

Navy, (Retired)

Honorary Vice-President, The Society of Naval Architects and Marine Engineers David

W.

Taylor Medalist

Published by

The

Society of Naval Architects and Marine Engineers 74 Trinity Place, New York 6, N. Y. 1957

Copyright,

l'.)')?

by The Society of Naval Architects and Marine Engineers

If

man permits

it,

the water of the seas does things for him

A

surf canoe riding

an incoming wave toward Waikiki

Beach.

Photograph by courtesy

of

Photo Hawaii, Honolulu.

Acknowledgements This section supplements a corresponding secAcknowledgements in Volume I, to be

Dott. Ing. Emilio Castagneto, Superintendent the

Rome Model

Basin

(Vasca

Navale;

tion on

of

found on pages vii-xi of that volume. The author takes this occasion to express his

Instituto Nazionale per Studi ed Esperienze di

number

appreciation to a

of his associates

and

friends

who have been most helpful in the prepara-

tion of

Volume

II.

Listing their

names and accom-

plishments briefly

Mrs.

Claudette

author's

Leveque

Horwitz,

of

the

in preparing the three sets of indexes for each of

Volumes I and II Mr. W. C. Suthard and the staff members of the Photographic and Reproduction Division of the David Taylor Model Basin for taking the model and flow photographs of TMB models reproduced throughout this volume; Mr. G. R. Stuntz, Jr. and Mr. M. S. Harper of the Ship Powering Division of the TMB Hydromechanics Laboratory for finding them among the vast assortment on hand at Carderock Mr. Werner B. Hinterthan, of the TMB staff,

who

translated

many

of the titles in the

German

references listed in the present volume,

and who

many German

technical

helped the author find references

Margaret M. Montgomery, for her and ever-ready help in finding books for the author and in guiding him around the TMB Miss

cheerful

library

Mrs. Ruby S. Craven, head of the Aeromechanics Laboratory library at the David Taylor

Model Basin,

for her assistance in looking

many references in aerodynamics and

up

aeronautical

engineering

Mr. C. A.

information concerning models tested in that basin.

In particular, the author wishes to express his appreciation for the useful ideas and information

especially for her invaluable help

staff,

Architettura Navale), for assistance in furnishing

Ryman and

other

members

of the

and Shafting, Bureau of Ships, Navy Department, for calculating the

staff of Propellers

U. S. weight of the screw propeller designed for the

ABC

ship in Chap. 70 of this volume Dr. Hans F. Mueller, for his help in furnishing valuable information in the rather limited field of rotating-blade propellers

Mr. William H. Taylor, managing editor of Yachting magazine, who has gone out of his way to render as.sistance to the author where information from small craft would be of value

found in a number written during the titles and Russian listed throughout references are

made

of Russian technical

past decade.

books

The Russian

authors of these books are the

text

wherever

direct

to them.

In over four decades of experience while working with others, the present author has been blessed with constant and heart-warming cooperation to an unexpected degree. Nevertheless, he is compelled to take this occasion to express his admiration and gratitude for a superlative measure of cooperation in the printing and engraving projects on this book. Mr. Richmond Maury, Mr. W. W. Tompkins, Mr. David G. Wilson, Captain Horace F. Webb, Mrs. Janet Jones, Mr. Orvrille W. Harrell, Mr. Henry F. Drake, Jr., Mr. John L. Moore, Mr. Stuart M. Holmes, Mr. Raymond C. Jones, and other staff members of The William Byrd Press, Inc., of Richmond, Virginia, designers and printers of the book, as well as Mr. Jay R. Golden, of the staff of the Industrial Engraving Company, Easton, Pennsylvania, have contributed with their efforts and their talents a friendship that will always be treasured. Every reference inserted in the text of the book "is intended as a tacit acknowledgement of assistance rendered by the author, book, publisher, or organization mentioned in that reference. The present author and The Society of Naval Architects and Marine Engineers are grateful for permission to make quotations from and adaptations of material developed by others, whether published or unpublished. Specific acknowledgements are made in the cases listed hereunder. The reproductions in Sees. 18.3 and 18.4 of Chapter 18 in Volume I, of John Scott Russell's admirable drawings of a boat running in confined waters, from the Transactions of the Royal

ACKNOWLEDGEMENTS Society of

lAliiiliurgli,

ns wvll ns the (luoUtion in

See. 48. rj on page 182 of

by

vohuno, arc made

(iiis

Hrpriut-s

CJ.

lished in the

of papers by William Bottomiey, originally pub-

portions

of

and

II.

1870 1S71 and

l'.»:{.")

Proceeding.s.

respectively, of the Institution of Civil Engineers in

Cin^at

Volume

I

Britain

and

and included

in

Sec.

37.4 of

Sec. 71.7 of \'olume II, arc repro-

duced by courtesy of the Institution. The adaptation in Fig. 32. D on page 450 of Volume I, and the fiuotation on page 557 of that volume, arc made by permission of E. and F. N. Spoil, Limited, publishers of the book "Marine Propellers," by Sydney W. Barnaby, 4th edition.

I'JOO.

The drawings

fouling-resLstance graphs of E. Y. Lewis,

are embotlied in

pormiiision of the Council of that Society.

I'roiuic

The

adapted from the

of the magnetic lines of force in

Figs. LB and I.C of the Introduction to Volume I, on page xxvi, are reproduced from the publication

"Mo
volume by permission

of

and

45. L

The

LOG

following books, copyrighted on the dates indicated,

are

by permission

New

Sons, Inc., of

Durand. W.

F.,

of

"Resistance and Propulsion of

Pcabody, C. IL, "Naval .Uchitecture," IU04 Rou.se, IL,

"Elementary Mechanics of Fluids,"

194f.

The quotation from the Reports and Memoranda of the (British) Aeronautical Research Committee, in Sec. 49.8 on page 195 of the present volume, is reproduced by permission of Majesty's the Controller of Her Britannic

lishers, Limitefl, of

I'iuiei

.Mechanics,"

edition, 1947

Rouse, H., editor, "Engineering Hydraulics,"

The

firm of Hutchinson

and Company, Pub-

178-202 Great Portland Street, London, W.l, England, in generously granting permi.ssioii for the use of material from books

by them, advises that the book on by Juan Baader of Buenos Aires (in Spanish) is to be i.ssued by them in an English edition in 1957. It is to be an improved and enlarged version of "Cruceros y Lanchas Veloces," published in 1951; the Enghsh title will be I)ul)li.shed

Stationery Office.

The c|uotation in Sec. 30.5, on page 127
publication rights to the book "Sail

John Wiley and

Y'ork:

Ships," 1903

1950.

,

(now Marine

1950 cnlition of "TheoHydrodynamics" are by permission of The Macmillan Company of New York, publishers of the American edition, and of Macmillan and Company, Limited, publishers of London, for the British and other world markets. The quotations and adaptations from the

Vennaril,.!. K., "l-^icnicatary 1

Ixjg,

of this

(Quotations from the

bridge Philosophical Socictj'.

©

of

The

i.ssuc

K

retical

2Md

1

The

1948 45.

Engineering/ Ixig).

on page 299 of The quotation in Sec. 20. Volume I, is from the Proceedings of the Cam-

Renewal

May Figs.

and

iiiotorboats

Power," by UlTa Fox, are held by Peter Davies, Limited, of London. The quotation in Sec. 40.3, on page 3 of this volume, is published with their permis-sion. Rcjidei-s will be interested to know' that this firm maintains a stock of the I'fTa Fox

"Cruisers and Speetlboats."

books on jachting.

the text.

Mr. Thomas D. Bowes, consulting naval archiand engineer of Philadelphia, made it possible to embody the photograph of the fircboat in

tect

action, reproduced as Fig. 7G.II on page 775 of

Table of Contents INTRODUCTION SOURCE ABBREVIATIONS FOR REFERENCES

xix

xx

PART 3— PREDICTION PROCEDURES AND REFERENCE DATA CHAPTER 40— BASIC CONCEPTS UNDERLYING ALL CALCULATIONS AND PREDICTIONS 40.1

40.2

Calculation of Ship-Design and Performance Data Useful Formulas Embodied in Theoretical

The

Hydrodynamics 40.3

1

2

40.4 40.5 40.6 40.7

Present Limitations of Mathematical Meth-

The

Principles of Similitude

Dimensions

of Physical Quantities

....

3 4

Terms

5

Double or Multiple Solutions to the Equations of Motion

6

The Derivation and Use

of "Specific"

2

ods

CHAPTER 41— GENERAL FORMULAS RELATING TO LIQUID FLOW 41.1 41.2

The Use of Pure Formulas The Quantitative Use of Dimensionless Numbers; The Mach and Cauchy NumThe Euler and the Cavitation Numbers The Froude Number and the Taylor Quotient Calculation of the Reynolds Numbers .

Application of the Strouhal

The

Number

Planing, Boussinesq, and

.

.

.

.

.

.

.

Weber Num-

bers

41.8

Derivation of Stream-Function and Velocity-

Formulas

for

Typical

Two-

Diniensional Flows

41.9 7

bers

41.3 41.4 41.5 41.6 41.7

Potential

7

8 11

17

Velocity-Potential and Stream-Function Formulas for Three-Dimensional Flows The Determination of Liquid Velocity .

41.10

Around Any Body

20

Conformal Transformation

24 25

Quantitative Relationship Between Velocity and Pressure in Irrotational Potential Flow

25

Tables of Velocity Ratios, Pressure Coefficients,

Ram Pressures and Heads ....

30

r.ONTENI'S

viii

C'HArTKU 43.6

43.7

The

DKl.lNKAlluN

»;{

Construclion

ol'

SolUCK-SIXK FI.oW OlAt iKAMS

Two-Dimensional Stream Piitterns from

of

Stronm Forms iiikI Liiu* Sources and Sinks Flow Pattern for tlie T\vo-Dimeniiionnl Doublet and the Circular Stream Form Graphic Const met ion of Three-Dimensional Stream Forms and Flow Patterns .... Variety of Stream Forms Produced liy Sources and Sinks Source-Sink Flow Patterns by Colored Liquid and Kleetric Analogy .

43.8 43.9 43.10

CH.-VPTEH 44— FORCE,

.

MOMENT. AND

4:i

11

Cuntimifd

I'ormulas for the Calculation of Stream-Form

Shapes and the Flow Patterns .Vround

Them

51) •13.

12

67

The Forces Exerted by or on Bodies .\round Sources and Sinks in a Stream; Lagally's

CI

Theorem 13

()2

-13.

(')7

43.14

G8

Partial Ribliography on Sources

and Sinks 70

and Their .\pplieation Selected Heferences on I.Kigally'3

FT.OW DATA Fni; TIvnUOFOTT.S

Theorem

AXO

71

EQI'IV-

ALENT FORMS 44.1 44.2

44.3

General; Scope of Chapter Formulas for Calculating Circulation, Lift, Drag, and Other Factors Test Data from Typical Simple .Mrfoll.-* and Hydrofoils

44.4 44.5 44.6 44.7

Polar Diagrams for Simple Hydrofoils

Test Data from

Flow Patterns Pitching

Compound

.-Vroiind

Moment;

Hydrofoils

.

N'floi'ity

aiul

Pressure

Fields

.\round

a

2

It. 10

Spanwise Distribution of Circulation and

3

44.11

Kffective .\.spect Ratio for Equivalent Ship

Lift

.

75 5

.

.

75 5

.

78 8

Typical Hydrofoils

14.9

Hydrofoil

.

Hydrofoils 44 12

44.13

Center-of-Prcssure Loca-

tion

44.8

2

10 80

Design Notes and Drag Data on Hydrofoil Planforms and Sections Quantitative Data on Cascade and Interference Effects

Distribution of Velocity and Pressure on a

Hydrofoil

80

CHAPTER 45— VISCOUS-FLOW DATA AND FRICTION-RESISTANCE CALCULATIONS 45.1

82 83 8.3

83 84

CONTENTS CHAPTER 46— REFERENCE DATA ON SEPARATION, EDDYING, AND VORTEX MOTION— Continued 46.6 46.7 46.8

Phenomena Around Geometric and Non-Ship Forms Vortex Streets and Rehited Phenomena Vortex Streets and Vibrating Bodies

Separation

.

CHAPTER

46 10

ber to Singing and Resonant Vibration References on Eddy Systems, Vortex Trails,

.

141

.

.

141

.

.

.

and Singing

143

144

AND EFFECT OF CAVITATION ON

-THE INCEPTION

47-

Practical Applications of the Strouhal

.

.

Num-

46 9 140

SHIPS

AND

PRO-

PELLERS 47.1 47.2

47.3 47.4

of This Chapter General Rules for the Occurrence of Cavitation on Ships and Appendages Vapor-Pressure Data for Water

Scope

Numbers The Prediction 47.6

Nomogram

Tables of and

for

145

146

Cavitation

147

47.9 47.10

on Hydrofoils

of Cavitation

and Blades Cavitation Data for Bodies and Other Bodies

47.7

145

The

Effect of Cavitation on Screw-Propeller Performance Photographing the Cavitation on Model and FuU-Scale Propellers Propeller Cavitation Criteria

Hub

Predicting

of Revolution

47.11 47.12

151

153 154

Cavitation and

Hub

Vor-

texes or Swirl Cores

149

152

155

Prediction of Cavitation Erosion

156

Under Supercavita-

Propeller Performance

156 157

tion

Selected Cavitation Bibliography

CHAPTER 48— DATA ON THEORETICAL SURFACE WAVES AND SHIP WAVES 48.1 48.2

Purpose of This Chapter Theoretical

Wave

Patterns

Surface

48.3

Hogner's Contribution to the Kelvin

Summary of the Trochoidal-Wave Theory

Standard Simple and Complex Waves for Design Purposes

160

48

Delineation of a Synthetic Three-Component

161

48 48 48

161

Elevations and Slopes of the Trochoidal

Wave 48.6

48

Wave

System 48.4 48.5

160

on a Water

Complex Sea Tabulated Data for Actual Wind Waves

Tabulated Data on Length, Period, Velocity, and Frequency of Deep- Water Trochoidal

Waves

166

Orbital

48.8

Water Waves Data on Steepness Ratios and Wave Heights

Velocities

for

Trochoidal

for Design Purposes Formulas for Sinusoidal Waves

48 48

166

48 169

170

.

Bibliography on Subsurface

48

175

176

Wind- Wave Patterns and Profiles by Modern Methods Comparison Between Waves in Shallow Water and in Deep Water Shallow- Water Wave Data General Data for Miscellaneous Waves; The Tsunami or Earthquake Wave Bibliography of Historic Items and References on Geometric Waves

48

Deep-

48.7

172 .

The Zimmermann Wave

163

171

Waves

....

177

180 181 181 182

185

CHAPTER 49—MATHEMATICAL METHODS FOR DELINEATING BODIES AND SHIP FORMS Scope

This Chapter; Definitions

....

49.1 49.2

The Usefulness of Mathematical Ship

49 3

Existing Mathematical Formulas for Deline-

49.4

Mathematical and Dimensionless Represen-

.

of

Lines

.

ating Ship Lines

Summary

49.9

....

of Dimensionless General

tions for Ship

49.7 49.8

199

49 14

by Mathematical Methods Example for Fairing the Designed

199

191

Illustrative

192

49. 15

Practical

49.16 49.17

The Geometric Variation

.

Application of the Dimensionless Surface

Equation to Ship-Shaped Forms 49.6

....

189

Section-Area Curve Longitudinal Flowplane Curvature Checking and Establishing Fairness of Lines

198

49.12 49.13

49 10

187

tation of a Ship Surface

49.5

49.11

Graphic Determination of the Dimensionless Longitudinal Curvature of any Ship Line Mathematic Delineation and Fairing of a

186 186

Equa-

Forms

Limitations of Mathematical Lines

.

....

Value and Relationship of Fairness and Curvature Notes on Longitudinal Curvature Analysis .

Waterline of the

193

of

ABC

200

Ship

Mathematical Formulas for

Faired Principal Lines

192

195

Use

Selected

196

References

of Ship

Relating

matical Lines for Ships

Forms to Mathe.

.

203 204

204

CONTENTS

X

CIIAPTKU 50-MArili:MAII("AI, MI'miODS OF CALCULATIXC TIIK PUKSSlIiK KESISTANCK OF SHIPS

50.4

General &irly KfTorta to Analyze and Calculate Ship Resistance Mo
50.5

Presenf-Day Calculations Formulation of the Velocity-Potential Ex-

60.1 oO 2

50 3

.

pression

50.6 50.7

The Calculation of Wavemaking ComjKinents of the Calculated Wavemaking Resistance

.

C'llAl'li;i;

51.2 51.3

51.4

I'ltol'oiM'lOXS

.-.1

50.8

Compiirison of Calculated and Experimental Resistances ._

207

50.9

Other Features Derived from Analytic Ship-

210

50.10

Ship Forms Suitable for Wave-Resistance

212

50.11

N'ocessarj'

211 215

50.12

Practical Benefits of Calculating Ship Per-

Wave

AM)

.

Improveraenta

210 in Analytical

and

formance 50. Ki

223 223

223 228

DATA 51.5 51.6 51.7 51.8 51.9 51.10

Hofercncc Material on Theoretical Rcsistanrc Calculations

l-'oR

2115

217

Mathematical Methods

SIIAI'E

General Comments Parent Form of the Taylor Standard Series References to Tabulated Data on Principal Dimensions, Proportions, Coefficients, and Performance of Ships References to Tabulated Data on Yachts and Small Craft

Relations

Calculations

2IG

Retii.st:incc

51.1

200

219 220 221

rVPR'Ar> SHU'S

Designed Waterline Shapes and Coefficients Reference Data for Drawing Section-.\rea Curves "Standard" Body Plans Single-Screw Body Plans Twin-Screw Body Plans Multiple-Screw Sterns

228 230 231

234 236 236

CHAPTER 52— ANALYSIS OF FLOW DIAGRAMS AND PREDICTION OF SHIP FLOW P.VTTERNS 52.1 52.2 52.3 52.4 52.5

52.6 52.7

Scope of Chapter Typical Ship- Wave Profiles Wave Profiles Alongside Models

239 239 241

General Rules for Wave Interference Alongside a Ship Estimate of Bow-W'ave and Stern- W'ave Heights and Positions Prediction of the Surface- Wave Profile

Typical

Lines-of-Flow

Diagrams

for

.

.

52.10 52.11

244 246

Ship

Models 52.8 52.9

243

Analysis of Model Surface-Flow Diagrams

.

Observation and Interpretation of OfT-theSurface Flow Data on Models Elstimating the Ship Flow Pattern on the Body Plan Prediction of the Ship Flow Pattern at the

218 250 254

255

52.

CONTENTS

CHAPTER 54— ESTIMATING THE AIR AND WIND RESISTANCE OF SHIPS— Continued 54.5

Notes

on

Wind-Resistance

Models

and

54.6

Bibliography Tests

54.7

Drag

of

Model

Wind-Resistance

Coefficients for Typical

Hulls and Upper

Abovewater

Works

54.8

Comments Concerning Wind-Friction Re-

64.9

Drag and Resistance with Wind on the Bow

sistance of

64.10

278

Testing Techiniques

an Abovewater Hull

CONTENTS

xii

CIlAITICll 58 4 58.5

oS— UrNMXC.-ATTrn

AND SHIP-MOTIUN DIAGRAMS— CoiUimu-d

1)K

DatA on Sinkngo and Change of Trim iu Shallow and Restricted Waters ChanRis of Attitude and Trim of Sliips with

CHAPTER 59-PREDICTIX{; 59 2 59 3

59.5 59.6 69.7 59 8

Open-Water Test Data

i>;i:2

.

References to Published Uat^i

Craft with Spceii and Other Factors

.

.

.

:J29

SM

Performance Devices

59.11

.\rea Hntios,

333

Performance Data from Scrcw-PropcUer Design Charts Performance Dat:i on Puddlcwheels and Sternwheels Bibliography on Puddlewheels Test Results on Rotating-Blade Propellers Available Performance Data on HydraulicJet, Pump-Jet, and Gas-Jet Propulsion Performance Data on Controllable and Re-

59.12

335 59.13

335 335 337

of

Miscellaneous

Propul.sion .339

Blade Widths, and Blade-Heli.x .\nglesof Screw Propellers Pertinent Data on Flow Into PropulsionDevice Positions Data on Induced Velocities and Differential Pressures

59.11 59.15 59.10

337 338

OF PROPULSION DEVICES

10

.j'.l

332

Model Screw

for

Devices

59.9

58.7

:i!I(>l!MA\CE

Relationship to Other Chaptor.i I'^timatvof Propulsion-Dcvioc KITioienoics Propellers

59.4

Variation of Attitude and Position of Planing

320

Fat Hulls

59.1

58

328

59.17

versible Propellers

The Thrust-Load Factor and Derived Data of Screw-Propeller Thrust from Insuflicienl Data Relation Between Thrust at the Propeller and at the Thrust Bearing Estimates of Thrust and Torque Variation per Revolution for Screw Propellers

341)

341

343 345

.•\pi)ro.>;imation

.

.

.

346 347

348

CHAPTER 60—SHIP-POWERIXG DATA FOR STEADY AHEAD MOTION 60.1 60.2

General Estimation or Calculation of Effective and

60.3

Effect of Displacement and

60.4

on Effective Power Methods and Factors Involved

Friction

Power

tXJ.9

tJO.lO

Merit Factors for Predicting Shaft Power Shaft-Power Estimates by the Ideal-Effi-

358

00.15

358 300

00.10

Estimating Sliaft Power for a Fouled- or Rough-Hull Condition IiiiTcasing the Power and Speed of an

Three-Dimensional Wake-Survey Diagrams Interpretation and Analysis of the

.

.

.... .

(il— THE

.

.

ciency

TMB

Three-Dimensional Wake Diagram Estimating the Ship-Wake Fraction Prediction of the Thrust^Deduction Fraction Finding the Relative Rotative Efruiency

.

Ships and Propellers

Axial-Component W'ake-Fraction Diagrams

CHAPTER 61

355

60.13 60.14

in Predicting

.

60.8

Determination of the Propulsive Coefficient Data from Self-Propulsion Tests of Model

354

at Propulsion-Device Positions

60.6 60.7

60.11 00.12

Trim Changes

Shaft I'ower

60.5

354

00 17

302

308 370 374

OU.IS

.

Method

Existing Ship Powering for Two or More Distinct Operating Conditions Backing I'ower from Self-Propelled Model Tests

PREDiCTIOX OF SHIP RE1IA\ lOR IX COXFIXED WATERS

375 377 380 383

385 387

388

388

CONTENTS CHAPTER 61— THE PREDICTION OF SHIP BEHAVIOR IN CONFINED WATERS— Continued

Data on Power and Pro-

61.16

Lack

61 17

Data on Confined- Water Operation

of Reliable

pulsion-Device Performance .

critical

61.18

Data on

Running

and

Positions

Steering in a Channel

61 19 .

Unexplained

61.21

Summary

Restricted

412

Speeds Offset

61.20 411

at Super-

Prediction of Ship Resistance in Canal Locks

Anamolies in Shallow and Water Performance and Restricted- Water

Effects

414

Partial Bibliography on the Effects of

61 22 .

413 413

fined

414

of Shallow-

Con-

...

Waters on Models and Ships

415

CHAPTER 62—ESTIMATING THE ADDED MASS OF WATER AROUND A SHIP IN UNSTEADY MOTION 62.1 62.2

62.4

General Added-Liquid Masses for Some Geometric Shapes and for Selected Modes of Motion Comparison of a Vibrating Ship with a Vibrating Geometric Shape The Change of Added Mass Near a Large

Boundary

417

62.5

419

62.6

423

62.7

432

62.8

Estimating the Added-Mass Coefficients of Vibrating Ships in Confined Waters Estimating the Added-Mass Coefficients for Vibrating Propulsion Devices .

.

.

Added-Mass Data for Water Surrounding Ship Skegs and Appendages Partial Bibliography on Added-Mass and

Damping

Effects

433

436 438 439

PART 4— HYDRODYNAMICS APPLIED TO THE DESIGN OF A SHIP CHAPTER 63—BASIC FACTORS IN SHIP DESIGN 63.1

Definition of Ship Design

63.2 63.3

Application and Scope of Part 4 General Assumptions as to

63.4

The Fundamental Requirements

442 442 Propelling

Machinery

443 for

63.5 63.6 63.7 63.8

Every

Ship

Design as a Compromise

444

The Essence of Design The Design Schedule for a Ship The Field for Future Improvements

444 444

De-

in

444

sign

443

CHAPTER 64— FORMULATION OF THE DESIGN SPECIFICATIONS INVOLVING HYDRODYNAMICS 64.1

General

64.2 64.3

The

First

Task

446 446

of the Designer

Statement of the Principal Design Requirements

64.4

Absolute Size as a Factor in Maneuvering

64.5

Requirements Tabulation of the Secondary Requirements

.

452 452

446

CHAPTER 65— GENERAL PROBLEMS OF THE SHIP DESIGNER 65.1

65 2 .

Interpretation of Ready-Made Design Requirements Departures from the Letter of the Specifieations

65 3 65 4 65 5 .

.

.

Design and Performance Allowances

....

Basis for the Selection of Ship Dimensions

.

Determination of the General Hull Features

65.6

Limits for Wavegoing Conditions to be Encountered

65 65.8 65

The Bracketing Design Technique

454 .

454 454 457 457

.

.

.

.

•

.

.

Adherence to Design Details in Construction Guaranteeing the Performance of a New Ship Design

458 458 459 459

CHAPTER 66—STEPS IN THE PRELIMINARY DESIGN 66 1 66 2 66 3 66.4 .

.

.

General Considerations Analysis of the Hydrodynamic Requirements

Probable Variable- Weight Conditions First Weight Estimate

.

.

.

460 460 463 463

66

.

Approximation to Principal DimenThe Waterline Length and Fatness Ratio

First

sions;

66.6

The Longitudinal Prismatic

Coefficient

.

.

.

464 467

COXTIXTS

xiv

CHAPTER 6C— STEPS

IN

Maximum-Section

rill-:

66.7

The

608

Draft Hiid lU-nm Finit K»tini;itc of Hull Volume

66.9 06.10 00.11

l'i;i:i.l

Tlio

Coefliciont;

First Approxlniiilion to Shaft I'ower Secoiiil l'>tim:itv of

l'rin('i|>:il Wi'iglitjt

Second Approximution to

Ml \ M; V

.

.

.

.

.

.

Dimen-

I'rinoipiil

Proportions

sioiiM uiul

66.12 00.13

Selection of Hull Shape

00. 14

First llstimnte lU-hiting to Motuccntric Sta-

06.15 00.10 00.17

First Skeloh of Designed Wiiterline

Layout

Contour

of Mu.xinuim-Scction

.

.

.

bility

66.18 06.19 66.20 60.21 66.22

I'j!timiitfd

Shape

.

Draft Variations

Sketching

Section-Area

the

The

Curve;

Miuximum-Area Position Middlebody Bulb-Bow Panimeters Transom-Stern Parameters P:irallcl

The Preliminary Section-Area Curve I/ongitudinal

Position

of

the

.

Center

.

.

of

Buoyancy 66.23

Preparation S<MMi()nM

of

Small-Scale

Profiles

and

DESIGN— Continued

CONTENTS CHAPTER 68— LAYOUT OF THE ABOVEWATER FORM— Continued 68.14 68.15

Shaping and Positioning of Superstructure and Upper Works Design of Facilities for Abovewater Smoke and Gas Discharge

68.16

Reducing the Wind Drag Spars, and Rigging

68.17

Consideration of Increased Draft Through the Years Preparation of Hull Lines for Model Tests

561

563

68.18

of

Masts,

the

566

.

566 566

CHAPTER 69— THE GENERAL DESIGN OP THE PROPULSION DEVICES 69 1 69.2 69 3 69.4 .

.

69 5 69 6 69.7 .

.

Introductory

Comment

Type and Number of Propulsion Devices Positions and Limiting Dimensions

.

.

....

Type and Design of Propelling Machinery and Number Position of the Engines Use of Systematic Wake Variations .... Rate and Direction of Rotation of Propul-

69 9 .

69.10

Graphic Representation of Powering Allowances and Reserves

576

69.11

Selection of Feathering, Adjustable, Reversible, or Controllable Features

578

69 12

Propulsion Devices to be Used with ContraVanes, Contra-Guide Sterns, and Contra-

69 13

Disadvantages of Unbalanced PropulsionDevice Torque Propulsion-Device Design to Meet Maneuvering Requirements Relation of Propulsion-Device and HullVibration Frequencies

580

....

612

Calculating the Thrust-Load Factors and the Advance Coefficients

613

Effect of

.

.

.

sion Devices

69.8

567 667 568

570 570 572

.

Rudders .

572

Design to Equalize or to Apportion the Powers of Multiple Propellers Powering Allowances

69.14 573 574

69.15

579 579 580

CHAPTER 70—SCREW-PROPELLER DESIGN 70 1 70 2 70.3 .

.

General Considerations Design Requirements for a Screw Propeller Comments on Available Design Methods and Procedures

70.4

Requirements

70.5

Comments on and Comparison

for.

Availability

Listing of Propeller-Series Charts

.

70.7

70.8 70.9 70.10 70.11

70.12 70.13 70.14 70.15 70.16 70.17

....

Preliminary-Design Procedure, Employing Series Charts Modification of Series-Chart Procedure for Other Design Problems Preliminary Comments on Propeller-Design Features Selection of Propeller Diameter

Determining the Rate of Rotation .... The Proper Pitch-Diameter Ratio; Pitch Variation with Radius Choice of Number of Blades Use of Raked Blades Propeller-Hub Diameter; Hub Fairing Determination of Expanded-Area Ratio; Choice of Blade Profile Selecting and Applying Skew-Back .... Design Considerations Governing Blade .

.

.

70.21

Type of Blade Section .... Shaping of Blade Edges and Root Fillets Partial Bibliography on Screw-Propeller Design Design of a Wake-Adapted Propeller by

70.22

ABC

70. 19

70.20

Selection of

.

the Circulation Theory

70.23

70.24

Ship Propeller Designed by Lerbs' 1954 Method Choice of the Number of Blades for the ABC Design Determination of Rake for the ABC Propeller

583

70.27

First Appro.ximation of the

70.28

Second Approximation of /3, and the Radial Thrust Distribution Determination of the Lift-Coefficient Product and the Hydrodynamic Pitch-Diameter Ratio Finding the Blade-Thickness Distribution Blade-Section Shaping by Cavitation Cri-

Hydrodynamic

Pitch Angle and the Radial Thrust Dis-

584

615

tribution

589

Width 70.18

Propeller-Disc and

of Propeller-

Series Charts

70.6

70.25 70.26

and

of,

Hub Diameters

582 583

592 596

.

596 597 597

617 620 621

teria

Procedure

616

When

Cavitation in

Not Involved

625

Corrections for Flow Curvature and Viscous

Flow 598 599 600

625

Final Blade-Section

ABC

Shapes for the

Design by Lerbs' Method

627

Introducing Skew-Back in the

601

ABC

Blade

Profile

Drawing the Propeller Calculating the Expected Propeller Efficiency

627 629 629

602 603

Summary

630

605

Method; Schoenherr's Combination Avoiding Air Leakage with Inadequate Sub-

605 606

mersion Design Comments on

631

606

Design of Bow Propellers, Free-Running

609

Open- Water and Self-Propelled Model Testa Mechanical Construction; Tjrpe of Hub; Shaping and Finish of Blades Blade Strength and Deformation Propeller Materials and Coatings to Resist

of

Design Steps for Lerbs' Short .

Supercavitating

611

612 612

70 46 .

Propellers

for

.

.

the

Range

631

Coupled and

Erosion Prevention of Singing and Vibration

....

632 632 633 634 635 636

CONII.NIS

xvi

CHAPTKK 71

71

TllK 1)KSU;N Ol' xMlSL"KLLANKt)r.S ruoi'l

1,S1(JX

DIOVICKS

CONTENTS CHAPTER 74— THE DESIGN OF THE MOVABLE APPENDAGES AND CONTROL SURFACES 74.1 74 2 .

706 706 708

General Positioning Rudders and Planes

74.3 74.4

Single or Multiple Rudders?

74.5 74 6 74.7

Design Procedure for Conflicting Steering Requirements First Appro.ximation to Control-Surface Area Determining the Proper Areas of Various

715

74.8

Control Surfaces Positioning the Stock Axis Relative to the Blade; Degree of Balance and Proportioning of Chord wise

720

74.9

Selection

.

Sections Structural Control-Surface Design as Affected

722

74 10 74 1 1 74.12

Design Notes for Motorboat Rudders Design of Close-Coupled and Compound

.

the Rudder Portion of the Ship

Shaping

and

the

Adjacent 709

by Hydrodynamics .

.

Rudders

.

.

713 713

723 724 726

74.

c:()N rr;\ IS

niAi'iiiK 1

2 3

Tin:

iivDitonvNAMic" dksicn of a MontiiUoAT

l'l;l•;I.I.\ll^Ali^

Scope of This Chapter General Considcmtions Rcluting to Motorboat DesiRn S|)oci!il ncsinn Features for Small-Cnift

-I

Ppsikh Notes for Displacemcnt-Tj'pe Motor-

5

Scmi-rinniiig and Planing Small Cnift

6

Operating Requirements for Planing Forms Gcncril Notes on the Powering of Small Craft Principal llequirementa for a Preliminary

l>0!its

7

8

... .

Design Study ".I

in

1

.Viialysis of

the Principal Requirements

.

.

.

Tentative Selection of the Tj-po and Proportions of the Hull First Space I.,ayout of the 24-Knot Planing Hull

12

13 .14

Weight Estimate; Weight-Estimating Procedure Second Weight E.stimato First .\pproximation to Shaft and Brake

.15

Selecting the Hull Features; Section Shapes

.

.16

Risc-of-Floor Magnitude and Variation

.

.17

Chine Shape, Proportions, and Dimensions Buttock Shapes; The Mean Buttock .... Trim .\nglc and Center-of-Gravity Position; Useof Trim-Control Devices Spray Strips Stem Shape

.

19

.20 .21

78 3 78.4

.

.

C'll.\l'li:i;

78.1 78 2

77.25 77.26

Design Check on a Basis of Chine Dimensions Second Estimate of Shaft Power, Ba»c
823 823 824 824

77.28

825 826

77.29 77.30

Effective Power Running Attitude and Fore-and-Aft Position of the Heavy Weights First Space T^ayout of the 18-Knot RoundBottom Hull First Weight Estimate for the 18-Kiiot Hull First Power Estimate for the 18-Knot and

820

7S

.

.

Interdependence of Hull-Design Features I.,ayout of the Lines for the ABC Planing.

.

Type Tender

14-Knot Conditions the 18-Knot

827

Selecting

827

Layout

828

77.33

831

832 835 83C 837 839

77.34 77.35 77.36 77.37 77.38 77.39 77.40

840 841

77.41

843 846 847

850 852 853

and 854

of the Lines for the

ABC

Round-

Bottom Tender Example of a Modern Round-Bottom UtilityBoat Design Design for a Motorboat of Limited Draft .

.

Estimate of Screw-Propeller Characteristics Propeller Tip Clearances; Hull Vibration .

Still-Air

842 843

853

Shape

Hull

Characteristics

First

Power

18

Deep Keel and Skeg; Other .\ppendage8

822

Hulls .

77.22 77.23 77.24

819

Dnigand Wind Resistance

.

....

Design of Control Surfaces and Appendages Third Weight Estimate Self-Propellod Tests for Models with Dynamic Lift Partial Bibliographj' on Motorboats .

....

855

858 858 859 859 862 862 863 864 865

842

MoDEI^TESTING PROGRAM FOR A LARGE SHIP

Preliminary

Model-Test Data Desired for a Major-Ship Design Model-Test Notes for Preliminary ABC Designs Use of Stock Model Propellers for First Self-

78 5 78 6 78.7 78.8

Displacement and Draft Conditions Resistjinee Tests

78 9

Sclf-Proi)elled Tests

78 10

Open-Water Propeller Tests

78.11

Neutral Tests

868

78.12 78.13 78.14

Controllability Tests in Shallow

869

78. 15

870

Propulsion Tests

....

Wave

Profiles and Lines of Flow Flow Observations with Tufts; Sinkage and Trim; Wake Vectors

Rudder

8G8

871

78.16 78.17

872 873

78.18

874 875 876

Wavegoing Model

.\ngli'

iind

Maneuvering

Water

.

.

Testes

Vibratory Forres Induced by the Propeller . Reporting and Presenting .Mwlel-Test Data Test Results for Models of the ABC Ship Comments on Model Tests and Analysis of .

.

876 876 877 877 877 879

Data

78.19

Proposed Changes in Final Design of ABC Ship Comments on Illustrative Preliminary-Design Procedures of Part 4

APPENDIX

1

Symbols and Their

Al'i'KNDIX

:i

Mcchanieal Properties of Water, Air,

APPENDIX

4

Uaoful Data for Analysis and Comparison

898

900

Titles

aiui

Other Media

915

926

PERSONAI^NAME INDEX

933

SHIP-NAME INDEX

911

SL'HJECT

INDEX

918

Introduction Taking

for

granted a knowledge of the material

in

Volume

it

aside temporarily

a reader or user

I,

calculations for

is

enabled to lay

and make the estimates or the preliminary hydrodynamic

Scott Russell, Rankine, and other contemporaries in stretching to the

of

hydrodynamics

architecture.

utmost our existing knowledge in

its

They made

application

to

naval

incorrect assumptions

tours, graphs, diagrams, tables,

some instances, and arrived at solutions which had to be corrected, but there is no doubt that in doing so they advanced both the analytical and applied phases of the art. A good measure of care is called for in the application of data derived from past practice and observations, in both ship operation and model experiment. As Sydney W. Barnaby observed in his book "Marine Propellers," written

makes

in 1900,

design of a ship, or the parts thereof, as well as to carry through such a design, solely

to

Volume

II.

The

by reference

latter is to be considered a

reference or design volume, containing

little

or

no

theory or exposition and only sketchy descriptions

phenomena

of the

or physical laws involved.

The

publication of these experimental and reference

data in a separate volume, in the shape of conit

and other aids, from Volume I much of quantitative data which would have

possible to omit

the strictly

interfered greatly with the continuity of its story.

Many

of

the aspects

hydrodynamics as

of

in

later

"No

table can supply the place of judg-

ment and experience." By a generous practical examples, in ulas, graphs,

insertion of

which the use of the form-

and procedures

is

illustrated in the

applied to ship design have not yet been investi-

preliminary hydrodynamic design of a hypothet-

gated analytically, or else only the easiest and simplest of the problems have been solved. In

ical ship,

these cases

it

is

necessary to

fall

back upon

derived.

experimental results and empirical data. It must

be admitted that in some respects our knowledge of naval architecture has not expanded greatly its position of nearly a century ago. At that time the renowned hydrodynamicist, naval archi-

from

Wilham John Macquorn

and engineer,

tect,

Rankine, was moved to observe that: "Owing

principally to the great antiquity of the art

and the immense number of practical experiments of which it has been the subject, that part of it which related to the forms of water-Unas has in many cases attained a high degree of excellence through purely empirical means. Excellence attained in that manner is of an uncertain and unstable kind; for as it does not of shipbuilding,

spring from a knowledge of general principles,

it can be perpetuated by mere imitation only" ["On Plane WaterLines in Two Dimensions," Phil. Trans., Roy. Soc,

London, 1864, Vol. 154,

Nevertheless,

p. 386].

when

necessity demanded,

kine himself was forced to data, as

is

fall

evidenced in his

Ran-

back upon empirical book "Shipbuilding:

In general,

made with primary units of pounds, feet, and seconds. Ship speeds may be given in knots in the statement of the problem but are entered as feet per second in the calculations. Wherever practicable, curves and graphs are supplemented by simple diagrams illustrating the coordinates or parameters. It is pointed out in the Introduction to I,

and repeated

relationships equalities,

every possible instance, an effort

is

made

Volume

that the formulas and

used in this book for expressing and the like are, with very

ratios,

certainty as to units, physical concepts,

A

as, in

here,

few stated exceptions, in what is known as pure form. That is, they involve only physical concepts and basic relationships between these concepts. The units expressing them are kept entirely separate, to be selected by the one using the relationship. This procedure leaves no un-

No

volume, especially

calculations in examples incor-

English

factors

apologies are therefore offered for following

all

porated in this volume of the book are

Theoretical and Practical," published in 1866. this procedure in the present

embodied in Part 4, the reader may see what sort of answers and solutions are

for himself

which

may

and other

be hidden in a mixed equation.

case in point is the former use of 1.00 for 0.5p

in salt water, in the English pound-foot- second

system.

The pure form

also facilitates checking

to tie in these data with physical laws governing

for dimensionality because all physical quantities

the motion of liquids.

stand out clearly. Furthermore, the relationships are dimensionally consistent, so that equalities

Nor

are any apologies offered for following J.

ABBRl

SC)1 RC.l.

have

pliysioal

Kjinu'

till*

\

A

I

aro

nititts

iliinoiisioiis,

lONs lOR Rl

1

tunipio iiuiitlH>n<, niui mi on.

any systoni

l'mploy^^^ witli

Ih»

with any i-onthinations of

may

tlierffort'

of inwusuriMnont or

unit.s in

I.

SIS horses.

as follows:

The

(a)

EfToctive

-

(h)

Fatness mtio

=

=

»-'

(O.IO/,)'

tion

of

-

\

To

(water

times

gravity) gh.

indicate

that

or

*,

example

=

= L

veliH'ity

times (distance))"

The

is

=

*

*

=

L.t.

elimination of mixeti quantities in power

0. 15I>5

no nuxlern application.

lias practically

necessitates the use of

It

and 550, the use the term horse as a puir unit, and strict con-

arbitrary figures such as

formity of numerical

I^^.IXH)

vniits

short ton of 2,(KH) (Hiuniis freiiuoiu-y in

with tho.se

lijiuivs.

naval

A

simple solution

is

to use the large

A

and nnich handier unit, for the system at least, would bo KHH) pouiul-

of a metric ton.

volumes the author has introduced some historical highlights where they seemed to be appropriate, and has mentioned the

names

often

of

The

Finally, throughout both

done by a horse served conveniently as a it

could iw

weight unit of structural mechanics, the kip, or kilopound, equal to 1,(K)0 pounds. It is O.o of a

Witli

point of r»'ferenco a contviry ago;

much ambiguity

of a standard lar^e weight unit.

short ton, O.lUVl of a long ton of 2,211) pounds,

((acceleration)

((L//')L)"

to

conu' in

architecture and shipbuilding on inland lakes and

formulas represents somewhat of a ilepartm-e fron> standanl practice. The rate at which work could Ih'

u.se

appearing with incn^ising

and

= "Vgh =

t

may

is

dimeiisionally ctinsistent c

kind

((accelera-

depth))"

this

this

long ton o{ 2,JI() pounds and the metric ton pounds are of the sjxme order of maKiiiludo

waterways.

wave =

SihhhI of a shallow-water

(c)

by the

but are not equal.

voliuno dividinl by (a con-

decimal .simplicity

and equivalent

J,'Jt)5

times sjMvd, or

RV

stant times IcngllO'

c

of rt'sistaniv

change of

.\

its

kilowatt

the meantime,

In siveil

/•«

similar in

the futunv

a particular

sysloni. Brii'f oxaniplos of thosi- applications arc

power =

Rl \t;i:s

1

the well-known

to

T\\v purv' foriuula.s uiul oquiitiuns

1

fool-.>i«'coiul units,

of pioneers in various hues of endeavor.

many developments now

tiiken for granted,

(he people responsible for originating

them are

the words of an

unknown when

forgotten.

eiiitorial

In

writer of

some

three decades ago,

discussing an article about the originator of the set of Simpson's rules: 'AVo

wi.sh

iireliiUvtun'

vastly simpler

!uliln>.ss

F^nglish

;i.i

well

.'iiul

iux

on

tliiit our futuri' :ulv;inci'portion, on nu'u !.•;«•.<

I

oiilighti'ii tliii\>'.'<"

(SUSli,

l.'i

Nov

I'.C'a,

pp. O00-4i01|.

SOURCE .\BRREVI.VriONS lOR REFERENCES The

soun^e abbreviations employe*.! through-

.Ml.\

out the text and listed here are formetl by combining the first letters of the principal wonis

composing the the

like,

titles

or of the

of books,

names

groups wliich have publishetl ceodings,

The

and reports

re.sulting

alphabetic

one

of

tniiisiictii>ns,

tion, AS of 19511, to citetl

ics,"

and and pri>-

kiiui or another.

abbreviations an> set

orvler, ttigether

the references

periiniicals,

of organizations

down

Ilill.

in

.\M

permit the reader to look up or to get in touch with the

nue,

York. 1934 Motorship, Diesel

New York

I\il)-

Ave-

N. Y. Research Committee, 16,

ARC

.\eronautical

.\SCE

.Vmerican Siniety of Civil Engineers,

threat Hritain

"Aerotlynamic Drag," by S. F. Iloerner, 11)51 publi.sheil by the author, lis Uusteiil, Midlan.i Park. X. J.

X\ West ;59th Stn>et, IS,

;

AKW

New

(.\mericaii)

lications. Inc., 192 Ix'xington

with suHicient informa-

organizations concerneti.

AD

Hydro- and .\eromwhaiiby L. Prandtl and O. G. Tietjens, translatetl by J. P. Den Ilartog (substantially an English translation of II.\M). Enginwring Societies Monographs, Mctlraw-

".\pplitxl

.\dminilty KxiH'riment Works, lar, (IiKsport,

IIsus-

Ham|islure, England

.V.sJME

New York

N. Y.

.\merican

Sm-iety

Engintvrs, Xi

New York

IS,

of

\\\M N. Y.

Mechanical ;t9tli

Stre»
SOIIRCF, AHI5KKVIA ASNl'l

American

ASTM

BuildinK,

1012

14Lh

Street,

by Dr.

FD

"Fluid Dynamics," by Dr. Victor L.

son Street, Iloboken, N.

FIIA

1936 (formerly

BEG

Bassin

neering

FMTM

cenus,

Germany des

6,

HPSA

Kempf and

Scientific

British Shipbuilding Research Assoc-

Chesterfield

iation,

5,

Curzon

Street,

jjj)

q

USVA

land

C and R

Bureau

of

(prior to 1940)

jj'p

Comptes

CIT

California Institute of Tcclmology,

Academic

Rendus,

U. D. C.

Office,

25,

Hamburgische

Pasadena

Schiffbau

Navy,

S.

Versuch-

EAAT

"Elements of Aerofoil and Airscrew Theory," by H. Glauert, Cambridge

7,

ICSTS

University

2nd

Press,

Cam-

edition, 1948

by a conference 2nd ICSTS

Ship

of

held at

The

"Congrfes

in

London

in 1934.

International des

Direc-

teurs de Bassins, Paris, Octobre

"Engineering Hydraulics," edited by Dr. H. Rouse, Wiley, New York,

1935" (Published by the Imprimerie Nationale, Paris, 1935)

1950

Experimental Model Basin, Washington (prior to 1941)

"Elementary Mechanics

Conference

Hague, Holland, 1933. This conference was preceded by a preliminary meeting of the superintendents of European model basins in Hamburg in 1932, and followed

D. C.

bridge, England,

International

Tank Superintendents

4, California

David Taylor Model Basin, Wash-

SNAME,

Transactions,

1943 1st

DTMB

ington

Historical

des

Sciences, Paris

EMF

Hydrographic Washington

(Hamburg Shipbuilding Experimental Establishment), Hamburg, Germany (prior to 1945)

Construction and Repair,

OR

EMB

"Hydro- und Aeromechanik," Vols. I and II, by L. Prandtl and 0. G. German), Julius (in Tietjens, Springer, Vienna, 1934 and 1931 "Hydrodynamics," by Sir Horace Lamb, Dover Publications, New

sanstalt

Navy Department, Washington

EH

Hamburg,

York, Gth edition, 1945 fj

Gardens,

London, W.l, Eng-

E. Foerster,

des

G.

Editors,

1932

HAM

York, 1953

Barnaby, Hutchinson's

Probleme

"Hydromechanische Schil'fsantriebs,"

"Basic Naval Architecture," by K. C.

and Technical Publications, London and New York, 1948. A new edition was published in 1954.

BSRA

by Prof. George F. WisliMcGraw-Hill, New York,

1947 Car&nes,

Mechanics of Fluids," by Hunter Rouse and J. W. Howe,

New

Monographs,

Societies

"Fluid Mechanics of Turbomachinery,"

"Basic

Wiley,

BNA

Hydro- and AeroPrandtl and

of

McGraw-Hill, 1934

Boulevard Victor, Paris (15me), France

BMF

"Fundamentals

O. G. Tietjens, (in English), Engi-

only

Paris, France American Towing Tank Conference Versuchsanstalt, Aerodynamische

d'Essais

New

mechanics," by L.

ATTC AVA

Volkenrode,

Publica-

York, 1948

lioulevard Haussmann,

1,

McGraw-Hill

J.

tions in Aeronautical Science,

Association Technique Maritime et

ATM),

New

Wiley,

ETT

Streetcr,

A6ronautique

Rons(!,

IT.

York, 1940 Experimental Towing Tank, Stevens Institute of Technology, 71 1 Hud-

Pa.

ii,

"Aerodynamic Theory," by Dr. W. F. Durand, series of six volumes (in English), Julius Springer, Rerlin,

ATMA

IONS K)R RKFERENCES

I

lOiifri-

N.W., WaHlihiKton 5, D.C. American Society for Testing MatePhilarials, 19l() Race Street, delpliia

AT

NiiviU

Suite lOO'l, (JoniiiuMi-

neci's, Inc.,

tal

of

Hooioi.y

3rd

ICSTS

"Internationale

der of Fluids,"

Tagung der

Leiter

Schleppversuchsanstalten,"

Berlin, 1937

SOURCE .\BHRL\1\I •Ith

ICSTS M'STS

lOR

(This conferoiico was to liave been

Home

held in r,tl.

li)\s

in 19;?9)

Intoniafional Conference of

"Fifdi

9,

MKSR MESA

Tank Superintendents," London, I'JIS (Piil)lishetl by H. M. Stiitionery Odicc,

ICSTS

London, 1949) Conference

International

"Sixtli

Tank Superintendents,"

of Sliip

1951 (Published by SNAMl-:. 1953) "Seventh International Conference on Sliip Ilydrodj'namics," Scandinavia, 1954 (Published by SSPA, 1955, Rep. 34) WatihiiiRton,

7tli

ICSII

ICT

International

Graw-Hill,

ME

I

lESS

Critical

New

PT

abbreviation

of

is

for

this

"I.E.S."

Hydraulic

Iowa City, Iowa Institution of Naval Architects, 10, Upper Belgrave Street, London, S.W.I, England Instituto de Pesquisas Tecnol6gicas,

MU

neering,

Ann

NA NACA

NBS

National

Bureau

Standards,

of

Wa.siiington 25, D. C.

NECI

Coast

Xortli-East

Institution

of

SSo Paulo, Brazil

Hall, Newcastle-upon-Tyne,

Towing Tank Confer-

ence, formerly of

ASME, York

ICSTC and ICSH

Applied

NN

Towing Tank, Hydraulic Laboratory, Newport News Shipbuilding and Dry Dock Company, Newport

NPL

National Phy.sical Laboratory, Ted-

NSP

Nederlandsch

Mechanics,

33 West 39th Street,

18,

New

News, Virginia

N. Y.

Journal of Research, National Bu-

D. C.

dington, Middle.sex, England

Aktiebolaget Karlstads Mekaniska

Developments in Fluid Dynamics," Vols. I and II, edited by Dr. S. Goldstein, Oxford Uni-

Whitehall Te.lini<:il

Pn-.s,s,

(Netherlands

Exijcrimcnt

Ship-

Establish-

ment), Wageningen, Holland

NW

Model

Ba-sin,

The Technological

In-

Northwestern University, Evanston, Illinois Office of Naval Research, Navy Department, Wiushington 25, D. C. On nance Research Laboratory, Pennsylvania State University, stitute,

ONR

versity Press, 1938

"Marine Engineering," Vols. I and II, e
building

KaMeWa)

"Modern

Scheepsbouwkiindig

Proefstation

Werkstad, Kristinehamn, Sweden (.sometimes called

Eng-

land

reau of Standards, Washington 25,

MENA

Langley Air Force

Laboratories,

Base, \'irginia.

Engineers and Shipbuilders, Bolbec

Journal

ME

University of Michigan,

Arbor, Michigan

Pra9a Cel. Fernando Prestcr, 110,

lAM

MI>11>

and Shipping Age, Marine Engineering, and more recently Marine Engineeruig/l.,og, 30 Church Street, New York 7, N.Y. Massachusetts Institute of Technology, Cambridge 39, Mass. ".\ Manual of Naval Architecture," by Sir William H. Wiite, Van Nostrand, New York, 1900 "The Modern System of Naval Arcliitecture," by J. Scott Russell, 3 vols., London, 1805 (out of print) Naval Tank, Department of Naval Arcliitecture and Marine Engi-

basins at the Langley Aeronautical

Institute

International

KMW

Ma-

York, formerly

Re-

Iowa

riTC

.Ill

New

search, State University of Iowa,

official

Institution in Great Britain

i

Review,

"Naval Architecture," by C. H. Peabody, Wiley, New York, 1904 National Advisory Committee for Aeronautics, 1512 H Street, N. W., Washington 25, D. C. Also model

The

\A

MSXA

Elmbank

Crescent, Glasgow, C.2, Scotland

I

MNA

York, 1926

Marine Engineers, 85, Minories, London, E.C.3, England Institution of Engineers and Ship-

Institute of

builders in Scotland, 39,

IIIIR

MIT

Mc-

Tables,

Catherine Place, S.W.I, Lundun EnRincering and Shipping

.Marine

rine Engineering

Sliip

Gth

kl 11 Ri;Nt:K.S

ORL

I

University Park, State College, Pa.

OTT

llyilraniic

Labiinitory,

Division

of

SOURCE ABBREVIATIONS FOR REFERENCES Mechanical Engineering, National Research Council, Ottawa, Canada

PD

Model

Propeller

Data

sheets,

SNAME

RandM

Naval Architecture," by H. E. Rossell and L. B. Chapman, SNAME, 1939, Vols. I and II Reports and Memoranda of the "Principles of

ARC, Great

RD

SBMEB

Builder,

33,

Street,

STP

"Shipbuilding: Theoretical and Prac-

many tical,"

SD

"S.

&

S.

TABLAS

Vols. I

SEE

SH

and

II,

by

G.

S.

Baker,

"Theory

adjective only) of

Prof. A.

and

Naval Architecture," by

M. Robb,

Charles Griffin

USNI

London, 1952 Taylor Standard Series of models United States Naval Institute, An-

WRH

napohs, Maryland Werft-Reederei-Hafen; combined

Co., Ltd.,

with Schiffbau und Schiffahrt into

Liverpool, 1933

und Hafen, C. D. C. Heydorns Buchdruckerei, Uetersen bei Ham-

1866

TNA

"Ship Efficiency and Economy," by G. S. Baker, Liverpool, 1946 Schiff

M. Rankine,

TMB

TH

"Ship Design, Resistance, and Screw Propulsion,"

J.

"Semejanza Mecanica y Experimentacion con Modelos de Buques, Tablas, Canal de Experiencias Hidrodinamicas, Madrid, Spain, 1943 "Theoretical Hydrodynamics," by L. M. Milne-Thomson, Macmillan, New York, 1950. A third edition was issued in 1955. Taylor Model Basin (used as an

TSS

R."

by W.

(out of print)

The customary contraction for the name of this periodical in Great Britain is

Gote-

STG

Westminster,

London, S.W.I, England

Establishment),

Sweden Schiff bautechnischen Gesellschaft, Albert Ballinhaus, Hamburg, Ger-

House, 10, Terrace, Newcastle-

Tothill

sheets,

borg,

Townsville

Shipbuilding and Shipping Record,

Data

Seamanship, and SmallBoat Handling," by C. F. Chapman, Motor Boating, 572 Madison

periment

Cartington on-Tyne, 6, England

SBSR

N. Y.

6,

Self-Propulsion

Avenue, New York, 1951 edition Statens Skeppsprovningsanstalt (Swedish State Shipbuilding Ex-

ing of Ships," by

RS SandP

New York

Trinity

SSPA

"Resistance, Propulsion and Steer-

W. P. A. van Lammeren, L. Troost, and J. G. Koning, Amsterdam, 1948 Royal Society, London "The Speed and Power of Ships," by D. W. Taylor, 3rd edition, U. S. Govt. Printing Office, Washington, D. C, 1943 Shipbuilder and Marine Engine-

74

"Piloting,

and Propulsion of by W. F. Durand, Wiley,

York, 1903

and

Architects

SSBH

"Resistance

New RPSS

Model

Naval

Engineers,

SNAME

Britain

Model Resistance Data and Expanded Resistance Data sheets,

Ships,"

of

Place,

SPD

SNAME RPS

Society

Marine

edited

36,

Germany

SNAME PNA

Hamburg

burg, Neuerwall 32,

und Werft in und Hafen Journal of Zosen Kiokai, The Society of Naval Architects of Japan. the periodical Schiff 1943; see

ZK

SH,

Schiff

PART

3

Prediction Procedures and Reference Data

CHAPTER

40

Basic Concepts Underlying All Calculations

and Predictions 40

.

The

1

Calculation of Ship-Design and Perform-

ance Data Useful Formulas Embodied in Theoretical

40.2

Hydrodynamics

40.4

The

40.5 40.6 40 7

The Derivation and Use

.

Present Limitations of Mathematical Methods

40 3 .

The

40.1

Calculation

Performance Data.

The

of

Ship-Design

reader

who

and

first

part

The second

part

is

5

Double or Multiple Solutions to the Equations of Motion

6

of "Specific"

how much and how many. Nor will a how explicit, point the

story alone, no matter

way

out of the hydrodynamic tangles that

may

be expected to confront the naval architect and marine engineer of tomorrow. He must have better

and sharper tools with which more puzzhng problems.

in general form, considering a

is

simple or schematic ship.

3 4

Terms

answers of

progresses

this far in a consecutive perusal of the book has found a word and a graphic picture of the flow phenomena associated with the motion of a ship.

The

Principles of Similitude

Dimensions of Physical Quantities

in

more detailed form, having to do

newer and

to face

derivations, processes,

This third part of the book, therefore, is devoted to an exposition of the methods whereby flow and its phenomena may be deflned in graphical, mathematical, and numerical terms. It gives a description of the methods, formulas,

omitted from the

procedures, and other aids whereby the influences

successively

with the behavior and

and

its

To

effect of

an actual ship

many components.

avoid breaking up the story, mathematical

and formulas are purposely two parts, except in a few The reader has been asked to take

special cases.

first

and

the story largely on faith, with copious references if

his faith appears to

There

is

waver at any

second of D.

m

W.

when

Indeed,

Manifestly,

it is

the ultimate aim of

architecture, to develop

be

all

those

who

and to

refine

methods

of

computation and calculation by which any aspect of the performance of a ship or any of its parts may be predicted on paper and in the design stage. The modern hydrographer can not afford to wait on the spot to see what the height of the tide and the strength of the tidal current will be at Point ten years hence; he has designed and

p. 246]:

"... The problems of stream-line motion have hitherto been almost out of the reach of everybody except practical mathematicians; not because all such problems are too abstruse for anyone but a practical mathematician to understand, but rather, because all treatises dealing with those subjects have been condensed and written, so to say, in a language which no one but practised technical mathematicians can understand."

ship, nor

may

take a deep interest in these phases of naval

discussing the

Taylor's papers on stream forms

1895 [INA, Vol. 36,

and 2

the ship designer.

point.

another reason for this procedure, well

expressed by R. E. Froude

effects described in Parts 1

predicted or calculated in quantities useful to

X

machine that predicts it for him. The modern owner, operator, and naval architect, by the same token, can not wait, with a ten-million built a

a story alone can not design a

meet those modern needs which demand

dollar ship at stake, until it runs sea trials to 1

HYHROnYNAMICS fiiul

out whether

tjpitil

of the twentietli centurj' at his

»io wontii-rs

eommand,

this respect, especially

in

the help of model tests. However,

it is

with

not wise

much on nunlel results that analytic and prediction procedure sufTer by con-

to rely so ability

sequence.

Useful Formulas Embodied in TheoHydrodynamics. The amazingly large

40.2 retical

grouj) of naval architects, engineers, scientists,

and mathematicians, manj" of them of great renown, who devoted their thoughts, energies, and talents to a study of the mechanics of fluids, have tackled the problems confronting them along two general lines. Some have conducted experiments, analyzed data, and evolved theories explaining the fluid action obser\'ed. Others have started with certain basic assumptions and premises, like the principles of continuity and conser\'ation of energj- and the laws of mechanics, and have succeeded, bj' reasoning and intuitive processes, in deriving fundamental mathematical expressions for the behavior and flow of ideal liquids.

By

is

lines of endeavor, there

can be derived

in

too

known where

of the well-

kinetic-energj- formula for solid

E =

ii.bmV^, and

maintains the

sum

energies constant,

ram pressure

is

tliird

sure 7 = O.opf/". The modern engineer uses this formula, as he does many others like it, without

a moment's hesitation as to certainly without requiring

its its

accuracy and experimental

confirmation.

hydrodynamics

The

by the mathematics of classical hydrcxlynaniicsare to the mfKJern naval architect and marine engineer ju.st HO many u.seful tools. This is the reason why the chaptirrs which follow are given over to a presentation of formulas gathered from many .s<jurce«, without including the mathematical proofs or derivations

among them. The

may

upon the mathematics as a

continue to

mearm

to

an

|(M)k

end,

without

rendering

engineer iiimself

of

them can best be

architect

himself.

The

them

or to

of the ship.

who

reader

wishes to familiarize himself

with the mathematical theoiy and processes of

hydrodynamics is referred to a number of textbooks and other publications. The authors, titles, and other data on these books, listed in Sec. 1.3 of the Introduction to

Volume

I,

are repeated

here for convenience: R. C, "Fluid Mechanics," Prcntice-llall, York, 1947. A third edition appeareti in 1955. Vennard, J. K., "Elementary Fluid Mechanics," Wiley, New York, 2nd edition, 1917. A third edition appeared in 1951. Rouse, II., and Howe, J. W., "Basic Mechanics of Fluids," Wiley, New York, 1953 Rouse, H., "Elementary Mechanics of Fluids," Wiley, New York, 194G Prandtl, L., and Tietjens, O. G., "Applied Hydroand Aeromechanics," McGraw-Hill, New York, Binder,

New

(2)

(4)

(5)

1934 Rouse,

New (7)

II., ICtlitor,

"Engineering Hydraulics," Wiley,

York, 1950

Dryden, H. L., Murnaghan, F. D., Bateman, H., "Hydrodynamics," National Research Council, Wasliington, 1932

(S) Slrceter,

V.

L.,

"Fluid

DynainicM," McGraw-Hill,

New

(9)

York, 194S Binder, R. C, "Advance*! Fluid Dynamics and Fluid Machinery," Prentice-Hall, New York, 1951

(10) Goldstein,

In this respect, the everyday formulas derived

many

naval

formulate better ones can be omitted from the knowledge of one who aims to specialize in the

(C)

a body of revolution. Here the Uquid-strcam velocity is zero, and the ram pres-

the

mathematical derivations in this part should not be taken, therefore, as an

at the stagnation point in the center

of the nose of

to say that

bj'

indication that the ability to derive

of the potential it

mean.

the}'

omi-ssion of the

bodies,

by the tlieorem which and kinetic possible to deduce the

much

derived

(3)

numerical tenns.

work. However,

Furthermore, as the science of ship propulsion and ship motions progresses, more and more new formulas are needed. Many of them can be derived only through mathematical processes. It is not

a surpri.sing store of mathematical

For example, by the application

know what

engineer shoulii

expressions by which data on the flow of real licjuids

ilaiiy

to apply these or other formulas intelligently, the

(1)

aviiilablt!

exjircssions, like the ram-pressure

formula, that help him in his

a judicious combination of the results

stemming from these two

Src. 40.2

vulnerable, as long as .someone cLso continues to

work out new methods

nuHlerii t^hip designer, with all the

and data can

mniiitnin a reasonable

stomiy weather.

ill

The

will

it

1\ SHIP Dl.SlGN

S.,

"Modern

Developments

in

Fluid

Mechanics," Vols. I and II. Oxford Prcts, 1938 (U) Milne-Thomson, L. M., "Theoretical Hydrodynamics," .Macmillan, New York, 2nd edition, 1950 (12) Lamb, Sir Horace, "Hydrodynamics," Dover, New York, 0th

40.3

rcvisetl e
Present

Methods.

Limitations

of

Mathematical

.Matlicmutical and jiiialytical nicduxis

in their present state,

even though stretched to the

utmost, can by no means .supply all the an.swers wanted l.v llif nindrrn marine nrcliitecl. Thi-y

BASIC CONCEPTS FOR CALCULATIONS

Sec. 40.4

can not, in fact, supply any but incomplete answers in cases where the physical phenomena are not as yet fully understood. Friction-drag formulas for ship plating are a case in point. Despite an enormous amount of time and energy

expended on the problem of friction flow, both in air and in water, the mechanism of fluid friction is still incompletely understood. Formulas much better than those now in use can not be expected until this knowledge is achieved. Heretical as it may seem to mathematicians, the use of mathematics, in both science and engineering, must always be tempered by good judgment. In fact, it is a generous gift of this same good judgment that makes a good engineer

(as for the lapt foot of the 50-foot plank) throughout the last 250 feet of the surface, or to cease entirely after 50 feet; while it is perfectly certain that the truth must lie

somewhere between these assumptions."

According to E. V. Telfer and F. H. Todd, as described in the reference cited: ". believing the truth to lie between them, but unable to decide on which was nearer to the absolute truth, he (Froude) compromised by taking an exact mean curve." .

.

A more modern example might arise architect were called

upon

if

a marine

to estimate the hydro-

conditions,

dynamic resistance of the balsa-log raft of South American design, called Kon-Tiki and used by Thor Heyerdahl and his companions in their voyage from Peru to the South Pacific Islands in 1947 [Heyerdahl, T., "Kon-Tiki," Rand-McNally, 1950]. Assuming that he could approximate the drag of one log, moving end on, he would with

always

reasonable certainty estimate that the total drag

any line of work. must be recognized that mathematics is always based on some kind of assumptions and in

It

which the mathematician hopes are complete and correct. They may be neither. This is Avhere judgment enters, in advance as well as in the wake of the mathematics. It may be interesting to quote here the comments of one well-known designer on this phase of the subject [Fox, Uffa, "Sail and Power,"

New

York, 1937,

person who has the sense to use the right formula and start with the true value. Too many mathematicians today multiply an unknown quantity by an illogical factor, and arrive at proportions that a man with discerning eyes can see are wrong, even though the mathematicians believe the answer to be correct if the mathematics are correctly worked." It

must be

of value to the

said in defense of mathematicians

that they are by no means the only people

"multiply an unknown quantity by an

who

illogical

was

less

than nine times

know

that the drag was more than that of a box-shaped

body having the same planform,

the

same

general dimensions, and the same volume dis-

placement.

p. 20]:

"Mathematics are only

of the nine logs abreast

the drag of one log. Similarly, he would

By

a series of approximations of this

kind he could narrow the probable resistance to within rather close limits.

The

diversion in this section

as a caution,

and

is in

as a discouragement.

space

is

no sense

The

is

intended partly

to be looked

upon

fact that considerable

devoted in the chapters following to

means for deriving quantitative data should serve as an indicator of its importance in this line of work.

For an intelUgent and proper use

of the data,

the reason for inserting some

however, a certain amount of preliminary knowl-

mathematical cautions in a design book for naval architects and marine engineers. Nevertheless, it becomes necessary at times to venture far afield in one's need for arriving at some kind of numerical

edge is necessary, and a few specific rules are to be observed. These are described briefly in the

factor." This

is

answer.

A

example

of this

by William Froude

kind was well de-

in his reports of the

early 1870's to the British Association [Todd,

SNAME,

F. H.,

1951, p. 316],

when

discussing

the means of extrapolating his 50-ft plank friction

The

Principles of Similitude.

comments

of similitude,

The

dynamic

similarity of flow

in parentheses are those of the present

utilizing

the dimensional-analysis methods ex-

data to ship lengths of 300

ft

or more.

author: "...

A knowlforming the basis of all model-testing procedures, is not necessary for an understanding of the calculation, prediction, and ship-design methods described in Parts 3 and 4 of this book. However, for the marine architect who is interested in knowing the conditions for 40.4

edge of the theory

classic

scribed

sections following.

it will

make no very great difference in our

estimate

of the total resistance of a surface 300 feet long, whether

we assume such

decrease to continue at the same rate

and motions, and in

pounded by Lord Rayleigh, the n Theorem of Riabouchinsky, and elaborations upon them by R. C. Tolman, E. Buckingham, P. W. Bridgman, and others, a background of general knowledge of

HYDRODYNAMICS \\\c

thion- ami principles of similiUuie

IN SlllP Dl-.SKiN

assuredly

is

iiecessan'.

who

refresh his

method, menmry, or look up doubtful points, a

partial

of references

Fur

reader

tlie

list

wishes to study

is

lliis

-to.

(Princeton Univ. Press, 1950, pp. 182-183| I,., "Dimensional Analysis and Theorj'

(24) I.,!inghaar, H.

New York, 1951 "Dimensional Analysis," Macdonald,

of Mmiels," Wiley, (25) Huntley, H. E.,

given:

Sec.

accompany a chapter on modeling and dimensional analysis in his book "Hydrodynamics" subject, to

Ivondon, 1952 il)

(2)

(3)

HiBbourhinsky, D., "M^-thodc den Variables dc Dimcndion Zero ct son Application en Af rodynamiquc (DimensionleRR \'arial>los and Their Uso in

AiToilynamics\" A6rophilo, 1 Sep 1911 Rayli-igh, IajmI, Brit. Adv. t'omm. Aero., Ann. Rop., 1::JS. 1010: 2:20, 1911; 3:30, 1912 Tolmnn, U. C, "The Principle of Similitude," Phys.

BuckinRliam, Iv, "On Phy.sically Similar Syplems," Phys. Rev., 1914, Vol. IV, p. :}45 (5) Tolman, R. C, "The Principle of Similitude and the Principle of Dimensional Homogeneity," Phys. Rev., 1915, Vol. VI, p. 219 (4)

Buckingham, of

(7)

(8)

E.,

"Model

E.\i)eriment8

Empirical Equations," Trans.

(11)

Slocum,

S. E.,

SNAME,

102-106, from Buckingham's

pp.

(4) of this series

ref.

Discussion of

of the basic

(10) of this series,

ref.

Dryden, H. L., Muriiaghan, F. D., Bateman, H., "Hydrodynamics," Nat. Res. Council, Wa.shington, 19:J2, pp. 4-6 (13) Buckingham, E., "Dimensional Analysis of M(mI(I

ASNE, May

Pages 107-198 of this paper

1936, pp. 147-19S.

list

24 references on

the subject.

"Dimensional Analysis,"

Bridgman, P. W., University

(15) Rouse, H.,

Pre.ss, rev. edition,

Mechanics

"Fluiil

PNA,

Yale

19;J7

for

1

architects

O.

Applie
1939, Vol. II, pp. 67-58,

(10)

"Experimental

Fluid

60, pp.

Dynamics

NECI, 1943-

to I'^ngincering Practice,"

HM4, Vol. (IS)

A.,

24-25

or a

(20) Vcnnjird,

Wiley,

No. 1 Mechanics,"

19-16, Vol. 13,

"Elementary Fluid York, 2nd e«Jitiori, 1947, pp. 142 153

K.,

J.

New

(21) C1inrp(^nticr,

ASME,

H.,

"Introduction

aiix

NK'thodes Di-

merurionnelloK (Intrmluclion to Dimensional

O.U)."

ATMA,

UM7.

and engineers are derived

may

list

Better

still,

(22) Roiwc. H., i;il, IBM), Appx., pp. 1MI5 WS. 1001 lOW (23) O. BirkhofT givoo a lint of cightMn references on this

bj' relatively

be kept handy for ready reference. may be derived each time they

they

(lix 2.

and tangents

X;itural sines, cosines,

of angles

are perhaps the simplest examples of dimensionless

Others are pitch

ratios.

and aspect

engineer, or so he

ratio.

may

blade-thickne.ss

ratio,

Unfortunately for the

think, there are no limits

to the coni])iexity or intricacy of other dimensionless

Among

combinations.

the particular 0-diml

exprc.'^sions of interest to the

na^al architect are

the comijlete set of hull-form and ])ropcller-form

Froude luimber /•'„ the Reynolds and the cavitation index (^(sigma). All of these are important, and they arc in constant use in one form or another. coetficients, the

number

The sions

//„

,

,

opposite sides of

(House,

EH,

II.,

all

etiviations involving

must have the 10.50,

pp.

.sjune

dimen-

i)'.l.'-)-!)!)8).

A

formula for a (luantity must have the dimensions

Take

of that (luantity.

the familiar

V

=

2gh.

g is an acceleration having the dimensions of a length // divided by a time I is 0-
and the height h has the dimensions of = (L/l'){L) = // l' = /.. Hence (/y//)' = v. Another example is the formula for lift force /., which is L = r',.(()..'ip).t f '', where .1 is the |)rojected area of lui airfoil or hydrofoil and f/

stiuared,

a length

Mcth-

Vol. 46, p. 156

of

are needed by the procedure described in .Vppen-

Here 2

Rouw, H., EMF, 10^16, Appx., pp. 'AhX'ATA Van Driest, Iv R., "On Dimensional .'Vnalysis and Prc!(«,-ntatinn of Data in Fluid Flow Problems," Jour. Appl. Mcch.,

The dimensions

simple processes and are tabulated in full in Appendix 2 of Volume I. They may he memorized

physical (]uantitie.s

00-61 (17) Hnnkins,

terms

dimensions of length, mass, and time,

described elsewhere and employed constantly in

Hydraulic Engi-

neers," McGraw-Hill, 1938, Chap. (10) Davidson, K. S. M.,

Quantities.

not versed in dimensional

needs to be clearly visualized. Only in this way can the dimensionless (0-diml) relationships

(12)

(14)

is

analysis or the theory of similitude, the concept

ratio,

1923, pp. R0-S7

Proi«-ller Tests,"

or

is

York, 1953.

Physical

of

the various physical quantities in general use by

pp. 99-106, which include the deduction of the

n Theorem on

Wliellier one

New

Martin's Press,

Dimensions

40.5

the book be well understood.

1915,

Phys. Rev., 1910, Vol. VIII, p. 423 (9) Buckingham, E., "Notes on the Methml of Dimensions," Phil. Mag., 1921, Vol. 52, p. ti<)6 (10) Tavlor, D. W., "Propeller Design Based upon Model E.\i)eriments," SNAME, 1923, pp. 57-109: csp.

paper,

"Physical Similarity and Dimensional

ASME,

W., "Tolman's Principle of Similitude,"

P.

J.,

.\n:ily»i8," St.

and the Forms

Vol. 37. pp. 263-296 Tolman, R. C, "Note on the Homogeneity of Physical Equations," Phvs. Rev., 1916, Vol. VIII (Ser. II), p. 8 Bridgman,

Duncan, W.

of the dimensions of a physical ciuantity, in

Rev., 1914, Vol. Ill, p. 244

(6)

(26)

is

the fluid velocity

tilt!

V

pa.st

it.

Since

(",. is

0-
reasons given in the section following, with

the dimensions of unity.

BASIC CONCEPTS

Sec. 40.6

Force

L =

FOR CALCULATIONS in simple numerical form, the ratio of (1)

the drag force on a given body, moving at a relative speed U, at a certain attitude and under given conditions in a liquid, to (2) the force that would be exerted on the body if the ram pressure

(1)(0.5)

niL

L'f

The

last expression

has the dimensions of a force.

The Derivation and Use of Terms. The term "specific" as now 40.6

ship resistances of various kinds to marine architects

come

is

"Specific"

q (or 0.5pU^) acted uniformly over projected area A. Here

applied to

not a

Drag ^ ^

new term

by any means but

it

has

into extended use only during recent years.

be encountered more frequently in The term expresses, in 0-diml numbers or as a ratio, the relationship between some quantity under consideration and a quantity having the same characteristics which is taken as a standard or reference. The best-known use of this term is in the

Still

It will surely

the years to come.

another familiar specific resistance

Here the specific gravity of any liquid is represented by the 0-diml ratio of (1) the weight of unit volume of liquid to (2) the weight of unit volume of standard fresh water. In this case, is

taken as a reference because

readily available, widely used,

and

its

it is

weight per

coeflGicient

that for friction resistance, expressed by Cf This 0-diml coefficient is again the ratio of (1) the is

Rp

friction resistance

to (2) a ram-pressure force,

but the reference area in

S

surface area.

of the

this case is the

body rather than

its

wetted

projected

Hence

expression specific gravity, as applied to a liquid.

fresh water

entire

its

Rf

=

Cf

SU' Provided the flows around two bodies are in respects dynamically similar, and the bodies are geosims (geometrically similar), it is possible to determine from model tests and to tabulate for ready reference the drag coefficients of objects having many different forms and running at all

volume is easily determined. Another familiar but unfortunate term is the one known as specific weight; unfortunate because it is not truly dimensionless. It signifies the weight of a substance per unit volume and is expressed by the symbol w. While it does have a reference

in the specific-coefficient formula. Similarly, the

basis of sorts, it has nevertheless the dimensions

coefficients

a weight divided by a volume. Broken down into its dimensional elements, explained in

When

unit

of

Appendix

2,

and with a weight given the dimenw = Force/L^ = {mL/f)/L^ =

sions of a force,

m/{LH-). Practically

all

the customary specific resistance

terms now employed in naval architecture and marine engineering are dimensionless. An example is

various attitudes,

as

in

Fig.

55. B.

The

tests

may

be made, furthermore, in any convenient medium by using the proper mass-density value apply to motion in any other medium.

and using specificmost important that the reference length, area, or volume be carefully understood and defined. For example, in the devising, calculating,

resistance terms,

it is

expression for the

lift

coefficient of

a hydrofoil or

a rudder, Cl = L/(0.5pAU^), the area A is that of the projected or lift-producing area. In other

words,

it is

the area of the planform or the lateral

the specific pressure coefficient, often called

area of the blade bounded by the profile, as

This expresses

projected on the plane of the base chords. In the

simply the pressure

coefficient.

Cd =

the ratio between (1) a pressure difference Ap (or an absolute pressure) at a given point on a body

expression for hydrofoil drag coefficient,

and (2) the ram pressure q developed at the forward stagnation point of that body at the relative speed U. In the form Ap/(0.5pC/^) the pressure coefficient is also known as the Euler number E^ In the form (p„ — e)/(0.5pf7^), where e is the vapor pressure of the liquid, it is the

projected area as before, notwithstanding that

.

cavitation ^

number

Another example

Cd

,

o-(sigma). is

the specific drag coefficient

or simply the drag coefficient. This expresses.

D/{0.5pAU^), the area this area is projected

A

usually remains the

on a plane Ijdng generally

at right angles to the direction in which the drag force

is

exerted. In the expression for the specific

friction-resistance coefficient of either rudder or

hydrofoil,

Cf

=

where

tangential forces are involved,

Rf/(0.5pSU^). Here

S

is

the superficial or

wetted area of both sides of the rudder blade or hydrofoil.

IIVDRODNX VMICs Double or Multiple Solutions

40.7

Equations of Motion.

pos.-jiMc for

is

It

to travel from one port to luiothor

more

and

under

Kest

its

own

S1(;N

,

10.:

.ship

lie

the

particular comiiina-

Double lightning

paths to qroun*

found that nature, in her role as a canscr\er of enerRj-, cau.ses water and other liquids to flow b}- difTerent paths from one point to another whenever there is a good reason for doing so. Speaking in terms of mathematics this means that there may he two or more solutions to the ecjuations of motion which govern tion of circumstances. It

1)1

two or

l)j'

may

which

difTerent routes, each of

easiest

i\

1\ Mill'

the

to

is

Position

1

Time A

the action of the liquids or the bodies in (juestion,

two solutions

just as there are

^f-

to the ordinary

quadratic equations in algebra.

Nature does

not

these

select

solutions

at

random but chooses them in strict accordance witii some secondary' or lesser cause, which maj' appear only after the most careful examination or extended study. A case in point, although admittedly not pertaining to liquid flow, is the

Flow pattern

changes

^

(^

to

form large vortexes on alternate sides

multiple paths taken by high-voltage discharges

and by lightning to another.

A

encountered

---«-~-^ '^////////yy,,..

darting from one fixed point pattern frequently

that which takes place around

is

and behind a

in

shifting flow

which

cylindrical stick

is

^T7^7777777777777777777777

Ce&el

drawn

rapidly through the water at right angles to its

^-

40.A depicts the manner in which a double row of vortexes known as the B(5nard or KirmAn vortex trail or vortex street is formed in the wake of a 2-diml rod, when drawn through a liquid in a direction normal to its axis. Here large vortexes roll up, first behind one quarter and then behind the other quarter of the rod as

separation on alternote

mey occur sides

Fig.

axis.

moves along. The lowest diagram manner in which a jet it

nozzle with a flared

shows the of water i.ssuing from a exit cone clings to one side the

in

figure

or the other of the cone, as the nozzle

is

flicked

Fin. 40.A

Taken from Xaturb DoCBLE SOLUTIONS OK THE Egt'ATIONS OF Flow

Sevbrai. Exampi.ks

iM-f.STRATlNG

In the top diagriim clectririty flows through the two paths simultaneously. In the middle iiiid bottom diagrnms the schematic flow patterns change with time or other

circumstances; these illustrations are indicate that the flow patterns can and

intended only to

do change while the

surroiMulings remain the same.

quickly from side to side. IjOss familiar cases

mf)dcl

Ijasins

in

are those encountered by

the transition region between

laminar and turbulent flow, where the nature of the flow may and does change with position and time. Similar situations often occur

when investiThe water

gating the flow around ship models.

passing through a given region on the model at timcfl

follows

one

without reason,

|)ath

anrl

suddeiily

path, finly to return to the BH

it

been

then,

changes first

ai)parently to

another

as unexpectedly

from it. This phenomenon has often upon as a matter of instability in the

cleparl<-d l(Mike
flow but

it

can ju»t aa well be regarded ob a uhifling

flow condition causcil

li,\'

two suiulions

to

the

equations of motion.

As a consequence of this situation it may be expected that any of the real solutions to a set of equations of motion may be encountere
will

it

Would turn

in

;i

loose circle or a tight ipmc

CHAPTER

41

General Formulas Relating

41.3 41.4 41.5 41.6 41.7 41.8

The Use of Pure Formulas The Quantitative Use of Dimensionless Numbers; The Mach and Cauchy Numbers The Euler and the Cavitation Numbers The Froude Number and the Taylor Quotient Calculation of the Reynolds Numbers Application of the Strouhal Number The Planing, Boussinesq, and Weber Numbers

Formulas for Typical TwoDimensional Flows Stream-Function and Velocity-Potential Formulas for Three-Dimenaional Flows ... The Determination of Liquid Velocity Potential

7 7

41.9

8

.

.

.

.

.

15

.

.

.

16

11

41.10

Around Any Body Conformal Transformation

24 25

Quantitative Relationship Between Velocity and Pressure in Irrotational Potential Flow

25

41 13

Tables of Velocity Ratios, Pressure Coeffi-

16

The Use of Pure Formulas. The ahnost employment of pure mathematical

20

41 12

.

cients,

41.1

17

41.11 .

Derivation of Stream-Function and Velocity-

Liquid Flow

to

in

Ram

Pressures and

...

Heads

which they are generally used. Table

30

2. a is

exclusive

repeated as Table 4 La in this volume for the

formulas in this book, described in Sec. 1.7 of the Introduction to Volume I, is emphasized here.

convenience of the reader.

Unless specific exceptions are mentioned, these formulas contain only symbols representing

interest in the analysis of underwater-explosion

physical concepts and dimensionless ratios, and

cially in

they are dimensionally consistent. They may be used as given, with consistent units belonging to any system of meas urement.

explosion.

Examples are velocity

h

of

a

=

y/gLw/^Tz for the celerity or trochoidal surface wave, and

c

= kw{Bx/LE){Vy2g)

for the predicted height

of the bow-wave crest on a ship. Substituting the dimensions of the physical quantities in the first,

The Mach number phenomena

may

ilf „

in liquids is of

primary

or high-order impact studies, espe-

the immediate vicinity of the impact or

The Cauchy number C„

,

related to

it,

eventually be found of interest in studies of

cavitation erosion on propeller blades objects.

Taking account

and similar and mass

of the elasticity

density of the material,

it

may

be useful in

analyzing shock-wave erosion on different propeller materials.

As a study

of high-order impact and of the shock-wave erosion is somewhat beyond the scope of this book, the treatment of the Mach

details of

f=[Hr=

or

There

no

whatever upon the units used in these and other formulas like them, is

restriction

provided they are consistent.

example,

may

are in

The wave

be in mi per

hr,

celerity, for

kt, ft

per sec,

what not, so long as g and Lw the same units. The examples in the sec-

meters per

Cauchy numbers

in this section is limited to

examples giving the derivation of the shock-wave velocities in salt water and propeller bronze. For the first of these examples it is assumed that salt ocean water at an average temperature of 60

For the second,

sec, or

tions following illustrate the use of pure formulas.

deg

F

possesses an elastic

temperature, from Table

wave

The Quantitative Use of Dimensionless Numbers; The Mach and Cauchy Numbers. The ten dimensionless numbers or relationships hydrodynamics, previously described in Sec. and listed in Table 2.a, are expressed briefly here in quantitative terms to illustrate the manner

K

of Sec.

at that

X3.7

of

Appendix 3, of 340,000 psi, or 144(340,000) lb per ft^. The mass density of salt ocean water, for the examples quoted here, may be taken as 1.9903 slugs per ft^. The celerity c of an elastic shock in ocean water

is

41.2

=

of

2.22

modulus

X3.m

4,960

ft

then

["

144(340,000)

L

1.9903

1°" J

per sec, approx.

is the speed of sound in the ocean water under the conditions described.

This

FIVDROnYNAMICS

8

For a propeller hroiize of 519 lb per

ft',

=

liaviiiK a

10. 13 slugs

E

the elastic nuxhilus

that

per

of

ft'.

this

2.33:

bronze

is

wave

in

The Euler and the Cavitation Numbers. The Euler number K„ «>r the prc.s.sine cocliicient,

[E.

\p

=

1

=

r i5(10")144

l,.")7l ft

41. a

is

a relationship between

Ap

Ap

P y2

q

^n =

(2.xviii)

Sum.nhkv of D.\ta on Dimensionless Relatio.vships

a duplicate of Table 2.a

is

pres-sures of

T

known, the fonn

also

per sec.

TABLE This table

The

,

is

it

J

1(3.13

L

1.

41.3

as

^

Srr. -//J

between the two values of as a matter of interest, is 1 1,574 4,960 =

reiation.ship

celerity,

is

"

DESIGN

Assuming

15(10*) psi, the celerity r of a shock

bronze

The

weinht density the mass density p(rho) at sea

level is 5 H), 32.174

IN SHIP

down

in

Volume

I,

inserted here for the convenience of the reader.

by J. K. Vennard |"Elemcntary Fluid Meclianica," York, 1947, pp. 144-145] and by H. Rouse (E.MF, 1946, pp. 02, 104, 322, 344). The forces mentioned are unit forces in each case, and the inertia force is the same as the inertia! reaction. Wiley,

ratios of the forces set

in this table follow the listing

New

Name of

Symbol

Relationship

Mathematical

Relationship between Physical Quantities

Expression

Mach

U

Af.

Ratio of

Cauchy

C.

Velocity -— r^

of

— —

phenomenon

;;

in

:

Velocity of compression

Cb

„

.

,

Ratio of

s

—

Inertial reaction

.

in

wave

any medium

any given medium

Elasticity force

Ap Euler

Accelerative or pressure force

E.

Ratio of Inertial reaction

—

p»

e

Accelerative or pressure force

Cavitation

Ratio of

(sigma)

Inertial reaction

Froude

VJl

Reynolds

R.

UL

V^

'

VL

Ratio of

—

—Inertia force ; :

in

a deep, unlimited body of liquid

Gravity force

UD

Inertia force

Ratio of Viscosity force

Drag

Planing

Dynamic-lift force

Stroubal

Ratio of

u Wil•IH-T j

force or resistance

Ratio of

Ln

Longitudinal vorte.K spacin g in a vortex stree t

Body diameter

Inertial reaction to

W,

transverse to flow

an accolerative force

Ratio of Surface (tension) force

ylfi Inert ial reaction lkMtininfac|

ih

VgR„

Ratio of '

VgRii

Gravity force

within bnundiirioit of dimincl of hydraulic

rmhua

liu

GENERAL LIQUID-FLOW FORMULAS

Sec. 41.3

rh

V

E„

-Pressure at Stagnation Point Q

Pressure Indicator

I

Rom P ressure -

O.SyoV^

Atmospheric

plus Hydrostatic Pressure Due to Head h

^^

Po,r^

-f

phe Pressure

-5.58

= Ap

= -0.3455

16.15

If a model of the ship, with a scale ratio of 25 and a corresponding speed ratio of 5, were being run in an endeavor to obtain dynamically similar flow, the Euler number E„ would be the same but the ram pressure q would be, as indicated in diagram 3 of Fig. 41. B,

Pressure Dio

?Mod'"

-

=

fj

2 I

(gship)/25

Fig. 41. a

Schematic Layout and Pressure Diagram for Pressure Observation on a Ship

0.646 psi.

Rudder Overall Lencjth for Calculating

and

R,-,

F^ of

I

As applied

to the rudder section of Fig.

4LA, and

Rudder

as an

Independent

Bod-^

I

specifically to

conditions at the orifice P, the Chord Lenqlh for Rud der as

measured pressure at that point is p, with the ship underway at the speed V. Assume that, at rest in fresh water at a temperature of 59 deg F, the submergence h of the orifice is 8 ft, and that the atmospheric pressure Pa at the time

is

Subm e

a!

14.69

psi absolute.

To find the hydrostatic pressure at the orifice, with the ship at rest, it is noted from Table X3.a of Appendix 3 that the weight density w of the fresh water is 62.366 lb per ft^, equivalent to a pressure of 62.366/144 = 0.433 psi. At a depth of 8 ft the corresponding hydrostatic pressure

Ph Pa

8(0.433)

is

-h

3.464

=

Ph = P^

=

3.464 psi.

The ambient

at the orifice

is

pressure

then 14.69

+

=

i^^ (48.98)'

p-po^^ -Ap=-5.58

=

I

2,325 lb per

^

—^^

p'

Vapor ---.>. ^ -.^ E 0.25 .^k"' Pressure-^t^ _

Absolute Zer&

psi a r

2 —S:-,^

llllllllllllllTlTlllllllllllllllllMlllllllhllllllllllNllllll!

FOR

MODEL Ram

Hydrostatic

y-'

p

I

then

=

,o-l2.57 psia

I

Neoative Differential Pressure,

18.15 psi absolute.

Assume next that the vessel of Fig. 41.A is underway at a speed of 29 kt, or 48.98 ft per sec. From Table X3.a the mass density p of the fresh water is 1.9384 slugs per ft^. The ram pressure is

5

r

1

Observed Pressure at Orifice. Absolute

Atmos-l

TotaV"^

T"

p^tPH +

15.475

psia

Pressure <\^^ 0.64-6 ps

plus AttnospherJc

^Pa^Phhi

T-

pheric-

ft'

k

T~ 0.084 psi .

~T^I'*-606 "^ psia

Negative Differentia

=

A

16.147 psi,

Pressure p-po^

say 16.15 psi.

small pressure diaphragm back of the orifice

P on

the rudder,

connected to an indicating of the rudder stock,

mechanism at the top shows a pressure drop

--Ap'-Q223

psi

Ordinate for Atmospheric

Pressure is Compressed to 0.22 of its Proper Heiqhl Compared to Other Ordinates on this Diaqram

of 2.12 psi helow atmospheric

when running. The negative differential pressure — Ap below the ambient pressure p^ at rest is then -3.464 - 2.12 = -5.58 psi. The absolute pressure at the orifice

is

14.69

—

2.12

=

Vapor Pressure^

12.57 psi.

These values are shown on the pressure diagram 2 in the middle of Fig. 41. B. The Euler number E„ or the pressure coefficient at the orifice P, when underway, is

Zei ''Absolute A bsolute .Lero

^ X. llllllIlllllllllllllllTlTllMlllllllllllllllMlltllllllllllMII '

Fig. 41. B

Details and Pressure Diagrams for a Pressure Measurement on a Rudder

HVDRODVN \MICS

10

IN SHIP DESIGN

Sec.

Multiplying this by tlu- luilcr numher E, = —0.3455 gives -0.223 psi ns the - ^p to be

of the

expect
readily calculated from the expression

tl>e

rudder section at the point

number

ff(sigma)

model rudder. The submergence of the orifice, S/2o = 0.32 ft, and the

=

witli tlie nuKJel at rest, is

hydrostatic pressure there

3.404/25

is

—

Hence, from the equaUty p

psi.

(14.69

-

y)

-

(14.G9

+

=

0.139)

1',

-t

the captation

the flow at that level

for

1.3

P--« _E:

is

(2.xix)

= 0.139 = —^p,

p, -0.223, as

from which y = (0.223 - 0.139) = 0.084 below atmospheric pressure at the orifice.

Here the ambient pressure p.

befor«,

or

14.69

psi

vapor pressure

-f-

=

3.464

18.15

is

3.464 psi gage

psi absolute.

The

the pressure indicator on the model, on the basis

water at 59 deg F, with a small amount of dissolved air, may be taken from Table 47.a as about 0.25 psi absolute. The

that the flow

dynamic pressure q

This

is tlie

pressure that should be registered by

is

djniamically similar.

Another way of expressing the state of pressure at the orifice P on the ship (or on the model) is to say that it is equivalent to — 0.3455g. Assuming that the test medium is the same, and that the nature of the dynamic flow does not change (it would change if cavitation set in on the ship but not on the model), this pressure coefficient is independent of the stream velocity. If a different

medium

test

is

used, of a greater

mass density

in

order to obtain greater pressure differences, the

value of the pressure coefficient E„

would

still

= — 0.3455g

be the same, for dj'^namically similar

In the same way, tests to determine the

flow.

pressure coefiicients over a series of points along

the section contour of a model rudder,

by

itself,

could be

made

in air or

mounted

they could be

mercury, whichever was most convenient. when tests are run in a different medium, to set the speed at such a value that the

run

in

It is customarj',

dynamic pressure of the test is the same numerically as the dynamic pressure in the medium in which the full-scale body is to run. As the mass density of mercury is about 13.60 times that of fresh water, the velocity-squared term C/J would have to be decreased by this ratio to keep the dynamic pressure the same. This w ould involve a red uction

in velocity to

a value of

V2, 399/ 13. 60

V

= 170.4 = 13.28 ft per sec, corresponding to a ship speed of 7.86 kt for mercury instead of 29 kt for water. For a scale ratio of 25, and a corresponding speed ratio of 5, the test speed for the model would be 7.80/5 If,

=

1.57 kt.

as maj' be expected, the pressure coefficient

changes with rudder angle {(delta) and with the thickness ratio

t.x/c

of the section, it is convenient

and for design purposes to plot the prciwure CKcflicicnt for any desired point or points on a basis of rudder angle and of thickness ratio. A Himilnr procedure i.s followed for other variables. for teating

If

the liability of cavitation nrima in a study

psi.

The

e of fresh

the

is

cavitation index

i:

This index

as before, 16.15

now

-

18.15

_E=

same

is

0.25

=

1.108

16.15

7'

a measure of the pressure avail-

is

able to create a gradient which will (or will not)

cause the water to follow the rudder section. Since

it

exceeds numerically the negative-pressure

—Ap/q =

coefficient

there

is

0.3455 at the orifice P,

more than enough pressure

create a gradient which

toward the rudder.

No

\vill

cavitation

therefore at the point P, nor

at

somewhat higher

A

is

available to

turn the water in

any

is

taking place

to be expected

speeds.

look at pressure diagram 2 of Fig. 41.B,

plotted to scale in psi absolute, explains is so.

The numerator p expression

coefficient

negative distance from

— 5.58 the

—

psi.

The

terra

expression

for

p^

is

—

represented

P to H,

p„ the

—

or 12.57

e in

is

this

—

by

the

18.15

=

the numerator of

cavitation

represented by the distance from tation

why

A73 in the pressure-

H

number

is

to E. Cavi-

not to be expected until the absolute P drops to E, at which time both

pressure at

numerators would be equal. Therefore, as long as p — p„ is smaller numerically for a given speed than p„ — c, cavitation does not occur at that speed. This is also evident directly from the fact that the absolute pressure p at the orifice P, 14.69 — 2.12 = 12.57 psi absolute, is far above the vapor pressure e of the water, taken as 0.25 psi absolute.

Unless one

is

working constantly

in this field,

the calculation and use of pressure cix-fficicnts and

numbers can become confusing and is recommended that, in these cases, the calculations be supplemented by graphic diagrams drawn ap|)roximatoly to scale, corresponding to those at 2 nud 3 in I'^ig. 11, B. cavitation

exasperating. It

GENERAL LIQUID-FLOW FORMULAS

Sec. 41.4

a help to remember that the -pressure is a function of body shape, because it embodies the pressure p which is found or measured on a body under given flow conditions. The It is also

coefficient

E„

cavitation

number

is

a function of the flow conditions

trim by the bow, due possibly to damage, the

topmost rudder sections in Fig. 41. A lie at the surface of the water instead of below it, then wavemaking and gravity effects come into play and the Froude number is appHcable. Here

of the liquid in the stream; this can be re-

and

membered because it embodies the vapor pressure The critical cavitation number (tcr occurs e. when the cavitation number of the flow drops

Assuming the length of these rudder sections ft, and the reduced speed as 12 kt, or 20.27 ft per sec, the Froude number for the rudder

same numerical value as the pressure coefficient of the body at the point of lowest

as 14.6

absolute pressure on the body.

only

the

to

11

is

customary in some quarters, when con-

It is

F„

venience dictates the change, to derive the Euler

number E„ and the

number a by using pressure. The expression

20.27

=

cavitation

values of head instead of

-En

h

=

The corresponding Taylor quotient

h^ (41. i)

the dynamic or velocity head

is

undisturbed liquid. With a vapor-pressure

head hv

the cavitation

,

number

h„

the

ft, is

-

r„

=

2g

in the

for

rudder only, based upon speed in kt and length in

becomes

for the former then

where Ul/(2g)

0.935

V32. 174(14.6)

12

\/14.6

=

The Froude number F„ and

3.14

the Taylor quotient

Tj are related to each other by the constant ratio

is

„ ^»

—

V

VL

=

—^

1.6889 .„. (-f

and

J

T =

^

(F)

1.6889^

"'^

fey

(41. ii)

where 29

per

Employing the same data as

for the preceding

is 1.6889 ft per sec. If g is 32.174 ft as in the example given, then F„ =

kt

1

sec',

0.2978r, and T,

=

3.358F„

For mental calculamay be taken

.

examples, and taking g as 32.174 ft per sec^, the

tions or rough approximations, F„

dynamic

and T, as (10/3)F„ There are certain applications, such as in planing craft, in which the conventional Froude number is modified by using the beam B as the length dimension rather than the length L, or in which ¥^'^ is used for L as the length dimension.

or velocity

hu

head

2,399

= 2g

as 0.3T,

is

=

37.28

ft.

2(32.174)

The measured gage

pressure at the orifice

P

of 2.12 psi below atmospheric corresponds to a

= -4.896

negative head of -2.12/0.433 pressure coefficient

Ap

-8.00

-

is

The head

4.896

=

—0.346, as before. F,

is

14.69/0.433 is

=

33.93

ft.

based upon a vapor

head of 0.25/0.433 or 0.57 index is then

ft

(33.93 -f 8.0)

-

of

water.

0..57

=

The

1.109

37.28

2g This

is

41.4

equal to the value previously derived.

The Froude Number and

Quotient.

derivation of the numerical values for the

modified F^ and

Fv numbers

=

V

and

corresponding to the atmospheric

cavitation index a

h^

The

is

obvious from the

corresponding expressions

pressure of 14.69 psi

The

The

then:

37.28

g

ft.

.

If it is

the Taylor

assumed that at an excessive

Fy =

V

VgV

There are set down in Table 41. b a series of Froude numbers F„ covering a range of speed from 2 through 100 ft per sec, equivalent to 1.18 through 59.21 kt, and embracing a range of model and ship lengths from 5 through 1000 ft. A first approximation to the Froude number for a given speed and length, based upon a standard g-value of 32.174 ft per sec', is obtained by inspection from this table. More accurate values are calculated by using the formulas in preceding ,

paragraphs of this section.

]i\

12

TABLE Velocity

41.b

DRODN

\ \\li(

s

|\ sllil-

1)1

M(.\

Proudb Numbers for Ship and Model Speeds and Lenoths

.SV(

.

11. -f

GENERAL LIQUID FLOW FORMULAS

Sec. 41.4

TABLE Velocity

41.b

^Feoudb

Numbers for Ship and Model Speeds and Lengths

13

—Continued

IIMiRonVN XMICS

14

TABLE Velocity

l\ sllll' 1)1SI(;\

41.b— Froudb Nuubbrs fob Ship and Modbl Spbbds and Lbnotiis—Condu/M

Sec.-fl.-f

GENERAL LIOUID-FLOW FORMULAS

Sec. 41.5

Calculation of the Reynolds

41.5

many

Although

rudders

partly

lie

Numbers. or

within the boundary layer of the main hull,

wholly it

be assumed in Fig. 41. A that the point

may P is

At the orifice position assumed to be that due to

outside (below) that layer.

the boundary layer

is

flow over the rudder alone.

For a ship speed of 29 kt, the velocity U in the Reynolds-number expression UL/v{rm) for the rudder only is again 48.98 ft per sec and the

L of the rudder section, at 8 ft below the at-rest WL, is 10.2 ft. From Table X3.h the kinematic viscosity v of fresh water at 59 deg F is 1.2285(10"') ft' per sec. Hence, for the rudder section as a whole, sketched in diagram

B

or

body diameter

15

D

=

48.98(10.2)

41.

D

of Sec. 41.6 it is the

say 1.72

1.2285(10"')

is

The

ft.

D

diameter

of the head,

relationship so formed

is

called

the rf-Reynolds number, represented by

Rd For a ship speed

= UD

(2.xxii)

of 14 kt, or 23.64 ft per sec,

this is

Rd

=

L

flow encountered. For this reason, a dimension transverse to the flow rather than one parallel to the flow is used as the space dimension in the numerator of the Reynolds number. For the case of the underwater sound head of Fig.

41.B,

Rn

length

its

viscous

significant length

1 of Fig.

rather than

the determining factor in the type and nature of

= UD ^

23.64(1.72)

V

1.2285(10"')

40.66(10")

=

3.3(10')

There are several other Reynolds numbers in

As the Reynolds number

rarely

needs to be

its value for a speed of about 49 ft per sec, and for a length of 10.2 ft, may be taken by inspection from Table 45. a. This gives about 40(10**), almost exactly the same as by computation. If the flow at the orifice position P is to be studied, the significant Reynolds number is the x-Reynolds number R^ at that point, indicated in Fig. 41. B. It is customary, in asymmetrical as well as symmetrical shapes of this kind, to measure the x-distance from the leading edge along the base chord or other convenient dimension parallel to the direction of flow. In this case it is measured along the meanline. It is customary, also, when the velocity of the hquid along the boundary is not accurately known, to consider it equal to the undisturbed stream velocity. Here Ua, = V. If the orifice at P lies opposite a point 2.84 ft downstream from the leading edge, then the

expressed in exact terms,

29

kt, or

a;-Reynolds

number

use by hydrodynamicists, such as the 5-Reynolds

number Rs

In this case the thickness 8 of the boundary layer replaces L as the space dimension in the expression UL/v. One of great importance is the blade-Reynolds number R^ for the blade sections of screw and rotating-blade built

up

R.

Vix) V

^ ~

propellers.

in the

This

expression

manner shown by

Chord Length at 0.7

Blode

is

Fig. 41. C. It

R=

c q.yr

Section Qt 0.7 Rodiusl

\-

Blade Rev/nolds Number Reiode ^/.[2rrn(0.7R)]t-^(co.,,)

Tonqential

V

Velocitij

Nominal Blode Velocity {v/t[a^n(o.7R)]2)0-5

2-rrn(0.7R)

is

Lonqitudmal

=

.

48.98(2.84)

=

11.32(10''')

Fig. 41. C

by

the leading edge, the a;-Reynolds

number

is

VA

^

Effect

of

Small

Angle of Attack is

1.2285(10"')

calculation or 11.2(10') from inspection of Table 45.a. For the 1/25 scale model, run at a speed equal to 48.98/5 = 9.79 ft per sec with the test point 2.82/25 = 0.113 ft downstream from

Velocity

Nei^lected

Definition Sketch and Formula fob

Blade Reynolds Number

utihzes as the length dimension the chord length c of

a typical blade section, at 0.7i2 on a screw proand a nominal velocity generally parallel to

peller,

R.

=

9.79(0.113)

1.2285(10"')

0.09(10')

the base chord of the blade. For

In the case of flow around a body of short length, broadside to the stream, the

body beam

TMB

model pro2294 shown in Fig. 78. L, where the chord length c at 0.7R is 2.682 inches or 0.2235 ft, the value of 0.7R is 3.378 inches or 0.2815 ft, Va is peller

innuoDNA

16 (lAstinml as

rpm

ft.

or 10. S.}

07

ft

t\)!>.

Ci'A)

and the Strouhal numi)er S, a sonu'wiiat lower range of

=

a J-value of l'^/ (nD)

l.l.i

kt, aiid u as

0.80 works out as

diagram ...^

f

+

1(6.97)'

=

0.371(10')

of Fig.

1942, Fig. 8, p.

17).

sponding S, value I

|6.2832( 10.83)0.28151'

°

'(0.2235)

;

is

L.,

l/.f,

this is available for

the left-hand

fi^ in

[House. H.,

4().('i

Landweber,

i:U);

94, p.

^^_ \Vl+[2M0.7R)]r\c...,) ^

Srr.

liladr-Ht-ynolds lumilitT for

prr sec or

'I'lic

\Mi(.s i\ Mill' ni su.x

EH,

19.50, Fig.

TMIJ Rep.

485, Jul

Assuming that the corre0.0, and using Kq. (2.xxiii)

of See. 2.22,

1.228,5(10-*)

41.6

For

Application

.sound m'ar .show

tlio rc'triU'taliif

Number.

Strouhal

the

of

II

in

{'"ig.

I

Direction of

=

0.0

y

wlicrc the ciidy frc(|uency

I.I),

r

/ = O.G

M Motion]

^=

=

S,

23 01

=

D J-

'

(0.0)

=

14.8 cycles per sec.

0.90

|-^

Ke el of Vesse j^

I

I

I

I

the frequency of resonant transverse vibra-

If

tion

the

of

sound-gear

cylindrical

assemblj',

taking the added ma.ss of the entrained water into account,

is

close to this value, the vibration caused

by the periodic alternating transverse force accompanying the eddy pattern in the vortex

To avoid resonance diameter of the .sound gear, the extension below the hull may have to be diminished, or the maximum speed reduced. 41.7 The Planing, Boussinesq, and Weber be greatly magnified.

trail will

without a change

Numbers.

in

Tlie planing

application. It

D

Definition Sketch a.vd Foiimi

Eddy Fiu:giEN'cv

in a

liead

(or total resistance

hhi

of

ment

^'ortex trails of eddie.s having fore-

b, and bj on each side are behind the two parts of the device.

and-aft spacings of

left

A (delta)

is certain to be encountered at some speed, and the Strouhal number .S'„ is of interest in this phenomenon. Tlu; situation depicted in Fig. 4 .D is complicated by a neck and head of dilTerent diameter, so for the jiurpose of this example it is assumed that the head diameter A>, is reduce
to the neck diameter

/->,

.

This

of the (/-Reynolds

at Hay 14 kt or 23.04

ft

is

taken as

number

O.'JO ft.

lij is

numerical

in

the

is

supported

l\v

the

becomes

P„

=

expression

values

for

a

given

case

harilly

example here. The Houssinesci number, similar to the Froude an

illustrative

number with

tlu>

waterway as

its

length dimension,

R.

=

hydraulic radius Ri, of a conlined is

expressed by

u__

(2.XXV)

\ <jR„

The radius

method is

of

The Weber number As

it is

calculating

described and illustrated

the

hydraulic

in See. 01.14.

\\\ is described in Sec. 2.22.

not employed in anj' of the chapters

this volvmie,

in

an illustrative example of the metho
computing and applying it is omitted. again emphasi/ed that, although normal engineering computations of the various dimensionle.ss numbers would not take account of all of

23.64(0.96) 1.8.5(10")

1.228.5(10 It

or weight IT

Dr;]V. Expressing the planing nunil)er

then,

per sec in standard fresh

water.

It is

')

Hum been found by experiment that here between the HeynoIdH iiumber

n-lutiuiMihip

planing speed,

full

Dt/^ =

1

UD

at

zero and the entire displace-

lift,

Vibration of the neck and head in a transverse

H. -

is

dj'namic

reciuires

plane

The value

B

of liniilcd

,

occurs around the after sides of both the neck

and the head,

the buoyancy

is

(1) the total drag Dt Rr) of a planing fonn and Lg produced by that form.

(2) the dynamic lift When, as usually occurs

Tkaii.

diameter D, ami a of diameter D^ .separation

having a cylindrical neck cylindrical

Vortex

i.a

/-"„

between

2.22, as the ratio Fio. 41.

number

expressed, as described in Sec.

is

I

is

a

/{j

tlu!

signilicant ligurcs in the preceding examples,

GENERAL LIQUID-FLOW FORMULAS

Sec. 41.S

they are retained here to insure that the same answer is obtained by different methods of

2"-Diml

f-^

Source

calculation.

q\

In view of the dimensionless character of the

'i

parameters described in this section they have the same numerical values when derived by consistent units in the metric or any other system of

two liquid flows is discussed briefly in Sees. 2.11 and 2.14. To illustrate how this procedure is employed in analytic hydrodynamics a brief outline is given of the of

the

equations for

the

resultant

stream functions and velocity potentials for flow

about the following simple forms: (a)

Single-ended 2-diinl body with a single source

body

in the nose;

Combination of these two

--Uoo V <-m9°-U ooRsir ^~~-Reference Axis

Definition Sketch and Formulas for Stream Function and Velocity Potential of Combination of Uniform Flow and Single Source

of

respectively, of

formation

V-q for

Fig. 41. E

Stream-Function and Velocity-Potential Formulas for Typical TwoDimensional Flows. The combination of the stream functions '/'(psi) and the velocity potentials Derivation

<^(phi),

Smijle E-DimI

f<"-

'^SO

0s= -U„xtmlo(5gR= -UooRco5e*mloijeR

measurement. 41.8

17

l^u for Uniform Flo

axis parallel to the flow.

partial longitudinal section

shown by the heavy

through this body

is

line in Fig. 43. B.

,

Adding the two gives the stream function combined flow ^s

+

me = - U„R

sin 6

function for

+ mB =

^,5

for the

(41.ivx

outlines

a single-ended body, of which a portion of one half pictured in Fig. 43. B.

The values

of ^.9

= — 1,

— 2,

—3, and so on, produce resultant streamlines around the body.

similar section

through such a body is drawn in Fig. 43. D. (c) Two-dimensional circular cyhnder or rod, with its axis normal to the flow, illustrated in diagram 1 of Fig. 41.G (d) Two-dimensional circular cylinder with its axis normal to the flow, and about which circulation is taking place, corresponding to diagram 3 of Fig. 14.E in Volume I.

= - U^y

The 2-diml stream is

Two-dimensional Rankine stream form developed around a 2-dinil source-sink pair whose

A

,

A

(b)

axis is parallel to the flow.

stream of velocity — U„ listed under (a) of the preceding tabulation. The liquid in the stream is moving from right to left, as in Fig. 4 I.E. Here the 2-diml stream function fso for the single source is m9 (theta.) from Eq. (3.xi). The 2-diml stream function ^pu for the uniform flow is — U^y.

The 2-diml

velocity potential

m loge

<j)s

o for

the single

That for the uniform flow is — U^x. Adding the two gives the velocity potential for the combined flow source

is

4>s

R, from Eq.

= — U^x

+m

= - Ua.R

COS e

(3.xii).

log,

R

+m

log,

R

(41. v)

of

Take next the case of the 2-diml Rankine stream form, produced by a source-sink pair, lying in a uniform stream having a direction of

these five classes of bodies enable the coordinates

flow parallel to the stream-form axis, as listed

The formulas given

for the

and ^-values

yp-

for their potential-flow streamline patterns to

determined

and

the

resultant

velocities

pressures at selected points to be calculated.

methods

be

and

The

of developing the formulas in the text

may

be followed for formulas applying to bodies shapes. For all of these bodies, the mathematical expressions characterizing the contours and the flow can be manipulated with mathematical operators to derive other useful of varied

purely mathematic steps in the derivations

of this section

from the I.

It

is

under (b) preceding. the stream function )

convenient to take

in Fig. 41.F.

the case of a

m

in a

The stream

diagrammed obtained by the source and

function

is

adding the stream functions of sink. For the source, ypso = fn tan"' [y/{x for the sink, ypsK

= —in

tan~' [y/(x

-(- s)],

—

s)];

where

the origin of the cartesian coordinates

the midlength of the source-sink axis and

is

at

s is

the stream function for the source and sink gives:

= m first

(and the velocity potential

for the source-sink combination,

and the one following are omitted

text.

single 2-diml source of strength

It is necessary first to derive \f/

the half-distance between the two. Combining

data, practical as well as analytical.

The

II.

uniform

tan

= m tan

y

—

tan

L-.^^]

in

18

Satnt-ond- Sink

\

I1R()|)^

AMKs

k«

IN Mill'

= —

.i

sK.N

1)1

['-X

Sec. 11.

+ Jm

log.

l(x

+

+

ay

(11. ix) j/'J

For the 2-diml circular cj'linder diagrammed 41.0 and tabulated in (c) preceding, it is shown in Fig. '.i.M that this form can be represented by the resultant flow from a 2-
Reference Axis ." Sourte.

Adding th% SUtotn Function ¥-y

^5K--mlogeRsK

ftirSinh,

fcrSooree-SmW

Riir,

A<Jdinq th« Velocity

j^c "

-

•

-U^y

JJjo"

for the

inlfln'-jf?j-

Uniform Row,

-05mloq« jjx.s)'*/]

7

T'^'^^e

(t

Moitiol ^u'-Ua>^

'e""

i

the Uniform

Flow,

>[l^]

*3--U»>.*-Z-"'l'

at

1

in Fig.

doublet

F Definition Sketcfi and Formulas voh Stream Function and Velocity Potential ok CoMBrNATION OF UNIFOR.M FlOW AND SoORCE-SiNK

Fifi. 41.

the limit as s diminishes to an infini-

is

tesimally small distance in Eq. (41.vi), the stream

function of a source-and-sink pair. Expressed in .sjTiibols,

Pair J/D

Ailding the stream function

uniform flow

^,/

= —U„y

=

lim

tan

HI

,

in the direction of the sourcc-sinlv

^n

-U.y+ wtim-

=

r , J'-'! Lx + 2/

-

s

,1 (41.vii) '

Adding

J

The ova! body shape for a value of ^.,- = 0, and the streamlines for ^., = —2, —4, and so on,

\l/u

To

M.V

+

X-

= m

(t>so

log.

for a sink

=

-m

Rso = \m

-

sY

+

Setting

ny + x' -i + y'

\l's

=

-\m

log. [(x

+

sY

+

is its

L(x

+

sY

+

(41.viii)

soliij 'J-dinil

rod,

-T^ X + y

(41.xii)

Hence the flow takes place around /?„ where /?,, = 'Vti^l\,

radius

The J-diml

a cylinder of

.

.stream function

it-s

yf/s

cylinder

circular

axis

can

of the flow in

a

around a stream

uniform

be written

in

several

alternative forms:

v'j

the velocity potential

i,

= —f

'...x

for a uiiifurin utrcam, the velocity potential for 2-dinil miiirce-siiik pair lying in a

parallel to the source-sink axis is

value at the reference

;/]

nomial to

thi.M

which

U.y =

^c = \m log" to

0,

(41.xi)

if]

where the relationship of the coordinates is as shown in Fig. 41. H of Sec. 41.9. Adding the two Rvalues, the velocity potential for the field set up by the source-sink pair is

Adding

=

surface, in this case that of the

is

log. /?.,K

stream function

becomes

-V~y

log. [{x

(n.x)

y-

the function of the coinliiacd flow

determine the velocity potential for the

2-diml source-sink pair of Fig. 41.F, that for a source is

That

=

to this the uiiiform-flow

— —U^y,

are delineated in Fig. 43. D.

a

J

Sim

2-diml combination

iiK

s

2msy

=

5

+r -

Lx-

gives for the stream function of the entire

a.xis

^.

"•-

'

of the

unifonn stream

^. = -r..,/

+

f

= -I'Ju -

=-f.«(i-^;)

S'')^*" «

(41.xiii)

GENERAL LIQUID-FLOW FORMULAS

Sec.41.R y^-n

/yi

*•

^.

of Doublet

whe where

»

R'X^

p

is

^

';

y-y for Uniform Flow

I

•^

H e nce

,

the doublet strength

is

is

^

-Ua

l^s-- U<»V^^^^

Plane of Paper

15

^r^ Plane

throuqh Reference Axis >!-Dfor 3-Biml Doublet /jsin^6

V-U ' -0.5 Uqo R^sin^e where yr for this Cose is Q 3-Diml Axisymetric Function

Then

Sphere

-i/r'

11

51

-Reference Axis

n ^6

-0,5U„R^3in'^e+^^^-f^ /Licos9

i=

-U„Rcos6--=S;?

G Definition Sketch and Formulas for Stream Functions and Velocity Potentials for 2-Diml Rod and 3-Diml Sphere

Fig. 41.

The

velocity potential

whose strength

ix

/,

= 2ms

limit of Eq. (4Lvui) as s

of a 2-diml

doublet

found by taking the approaches zero. This

is

gives ^1

cos 6

.

in polar coordinates

R

(41.xiv)

IXX

X-

The

+

y'

in cartesian coordinates (41.xiva)

velocity potential of a uniform flow from

right to left in

diagram 4>u

1

of Fig. 41.

G

is

= — U^x

Combining the two algebraically

gives, for the

resultant flow around the rod,

=

(4Lxv)

(41.xva)

(41.xvb)

HYDRODYNAMICS

20

In a similar manner, the velocity potential

is

the

ol)taine«l Ity adding; tlie velocity potentials of

separate flows. For circulation alone,

^^ =

f

i\

+J

tUi

~e

=

r,}{ de

(ii.x.x)

IN

derived

potential,

+ ^e

1^') cas

(U.xxi)

either the velocity potential or the stream

function, the velocity at the surface of the cylinder is ol)tainetl

from the relationships

4+1).

U,

in e

Hence, at the surface, where

/?

+

=

.T

/?„

streamline

licjuid,

The

e

+

,

by

is,

Ec].

the present section carries out

the

same derivation

(a)

A A

for the flow around:

3-diral sphere

Dioqram os Droivn

(2.xvi),

2r.

=

'<-

V"

sin d

-

1

velocity

pressure in

and hydrofoil flows around a its axis normal to a uniform

diagrammed

is

1^

k»^ *

for the 2-Dimensionol

the 3-DimensionQl Cose

in Fig. 41. H,

[*

!

—s...

Cose It Serves Also for b>( Rototmq It to on^

Ilesired Anqle About the

"^^slr^^" ~---

—

|"~-

Souae-Sinh Axis

,

^I§S!i"=t«) ftint

I

V

local

(ll.xxii) 27r/f„

pressure at any point on the surface of the

2-diml cylinder

function,

and

velocity,

spherical coordinates,

U = 2r. sin

ran
3-diml bodj' with a head of ovoid shape, formed by placing a single .3-diml source in a uniform stream. A partial longitudinal section of such a bod}' is illustrated in Fig. G7.II. Only that flow is considered which is symmetrical about an assumed x-axis through the center of the sphere and of the body described. By using

= U,

Rdd

the stream

for

2-diml rod with

(b)

1^

t

11.11.

local

stream of

From

Sec

41.9 Stream-Function and Velocity-Potential Formulas for Three-Dimensional Flows. Paralleling the expositicjn uf Sec. ll.S, where formulas

the

+

i„ = -{•.(/<

"irc.-il.O

other section shajjcs by confoniial dcscribeil in

are

For the comliinetl hydrofoil How,

D1.S1(;N

Sllll'

+

VI (41.xxiii)

Upon

over the sur-

integration of this pressure

Source Axis

face to obtain the resultant force in the //-direction, the lift

// is

obtained. Fin. 41.

=

sin -fvR. Jo

= pr„r

e (le

As a matter of iiif(jnn;ition, llio npproximalc value for the stream function in the case of a 2-diml cylinder of radius R„ in the middle of a 2-diml water passage of width .1, as workcil out by

II.

I^mb,

where the

"'"

.Rl 17-

through the

A

,

2tt/

—^ —

cosh

A

cos

2x1 r-

—A

is

IXA,

1808, Vol. XI., p. 28).

I

he

text

appar-

A

plot

is given by Ilele20 on Plate XI of the reference'. Knowledge of the stream function or velocity

need be used to

and

axis,

any one longitudinal plane

parallel

to

the direction

of

|)iii|inscs

this sei-li(in, as for use in

ciT

and reference books, the

(liuiiitity

^

is

3-diinl

stream

l/(27r)

rate of flow

in

with a uniform velocity of ^Blok..

a "rod" of radius

— ('„

,

ij,

is

= -V^Ttf

in Fig.

potential

great

A'

times the Stokes stream function described in the concluding paragraphs of Sec. 2.12, on page 32 of \'oluine I. Hence the

fimction

of the streamlines for this ca.se

Shaw

coordinates

liie

for a selected point in

most

origin of cartesian coordinates

II. S.,

only

define the flow, although the cartesian coordinates

l''or

A

ently taken at the center of the cylinder [Ilclc-

Shaw,

Definition Sketch for Cartesian and Coordinates ok Source-Sink Pair

uniform flow, are shown for convenience.

is

2irx

^ =

H

Spiikuicai.

fii.xxiv)

the

for

value

in

2-
circular s<'ction

deriving corrcspondinn

is

dat.'i

of for

However,

for the 3-diml

stream function used here

GENERAL LIQUID-FLOW FORMULAS

Sec. 41.9

The first case considered The relationships between I.

is

that of the sphere.

the stream function,

the velocity potential, the radial velocity

and the tangential velocity

Ub

are,

for

Ur

,

the

axisjonmetric case in spherical coordinates [Milne-

Thomson,

L. M.,

TH,

^=

1950, pp. 403-404],

-U,R sin

e

21

To

obtain the doublet,

niul

/i',,A

—

/^,<,

—

HVDROUVNAMiCs O^o — Osk —* 6.

—

s

DISIGN

1\ sll||>

Sec. 11.9

0.

»

1

—

=

4>

/I

cos (ll.xxxa)

= -MX

I

-

Tlicii. for llic :>-(liinl (i..ul)li't,

• It.

COS

(ll.xxxiv)

siir

1

M

,

II.

For the case of the :5-diinl bodj' of ovoid formed by placing a 3-diml source of

shape,

(U.xxxb)

strength

rn in

a uniform stream of velocity

— f/.

,

as in Fig. 07. H, the .3-diml velocity potential and Coml)ii>iiig tlie cloul)let and the uniformstream veloeity potentials and stream functions gives, for the streamline flow around a sphere in

—U„

a uniform stream of velocity

,

depicted in

the

stream

3-diml

function

are

obtained

as

by adding the values of and respectivcl.v, for the two flows. Then, from Eqs. (41.xx'via) and (U.xxviia), previouslj' explained,



}f/,

diagram 2 of Fig. 41.G,

-U^R

4>

- U^R

«.

1

= -o

^3.d.=.i

,-,o

,,

.

n cos 8

-

cos 8

R-.

f^/?"sm-

„

8

+ ,

-

cose

(41.xx.xva)

j^

(U.xxxia)

From

u sin' 8

,

...

,

,

i/-

(41.xxxib)

^

Iv|.-;.

(41.xxvib) and (4l.xx\iib),

= — .Jf/„/2"sin"

- m

cos B

(41.xxxvb)

whence Setting

^ =

at the .spherical .surface, /I

I l\R' sin=

72'

= 1^ =

"'- RdB

= (1^)"'

ii-o

To where Ro

is

the radius of the sphere about which

the flow takes place. Stated in another way, the flow around a sphere of radius Ro

adding a uniform doublet of strength

=

Substituting m for

(f>

and ^

«a.din..

\^3-dllI>l

=

— 1/„

\U,.,R\

is al.so

Ur

and

equal to zero since the nose

[/»

the stagnation point.

a

to

IB-diml

-

7^

§t/„/?o into the expressions

Hence the nose cos 8\R

[/. sin' 8

{Rl

= -

+ -

^j

(41 .xxxiia)

R')

(li.xxxiil))

=

[/„ sin

=

Ro =

0,

The 3-diml stream

nates, '

8 dfi

at

the surface of the .sphere,

tlic (I Illation of

the surface

Ro

is

08

ft

,

Uk =

0,

8

—

cas

U„ sin'

6)

(11 .xxxviii)

8

For the points abreast the source, where = and sin 8=1, whence 90 dcg, cos

=

local velocity is

U = The

R =

^

function value which passes

through the stagnation point is ^ = — ;». But this stream function is also the surface of the body. Hence, in axisymmetric spherical coordi-

1

R sin

=

is

R-

whence the

Then

i/„ cos e

2?/i(l

On

(41.xxxvii)

the coordinates of the nose of the

find

body, set

[/„sin 8

.

Eqs. (41.xxA-a) and (41.xxvd),

f/,

(41.xxx-A-i)

obtained by

is

2ft

From

fLcosO

gives:

= - 1/. —

stream /x

=^-

=f|

R or

7?^

t/«

sin^ 6

If/.sin e

prcKHure cocilicicnt at any point

jnirfncc of the Hphere

Im,

by

F'lq.

Rio

(41.xxxiii)

(2.xvi),

on

l!ic

From Till'

=

2m

or

Rt

V

2. it appears that Ron = /?o Inmsvcr.se radius of a 3-dinil ovoid such as

this

GENERAL LIQUID-FLOW FORMULAS

Sec. 41.9

To

23

satisfy the condition that the ovoid is to

a transverse "base" radius distance of 10 ft abaft

its

Rb

Yj

Rb

of 6.5

have

ft,

at a

nose.

—

cos 63

10

and

Rb

=

sin Ob

6.5

where Rb and 63 are the coordinates the ovoid at

of

Rb

foregoing for

in

of the

rim

Substituting in the

base.

its

terms of 6b and m, gives

-

2m(l

1

tan 6b

cos

61b)

=

10

(7.

and 2m(l

—

cos Qb)

4 From

=

6.5

the second equation, 42.25C7, 2(1

Resultant

Velocitij

Point

at

P

Ship Speed

j<{^a2^

in

Plane of Poqe

'

^

that in Fig. 41.1 or Fig. 67. H, formed by placing

a single 3-diml source in a uniform stream, approaches as an asymptote a limiting value of

4.596

ft

abaft the nose

it is

ft

per

-

10

=

error gives 6b

135

cos 6b)

=

428.4

ft'

per sec.

(2) (1.707)

The equation R'

=

of the desired ovoid is

(2)(428.4)(1

-

34.62 sin'

The

6.5

coordinate origin is

and

trial

(42.25) (34.62)

that the ovoid shape have a transverse radius of Fig. 41.1

=

42.25(7. 2(1

desired

ft.

in the first

Then

suppose that it is desired to develop the coordinates of an ovoid shape for the bulb bow of the ABC ship of Part 4, resembling the ovoid for

the designed ship speed of 20.5 kt or 34.62

6.5

tan 6b

cos 6b

Solving for 6b by deg.

2Rq at an infinite distance downstream. As an example of the use of the formulas,

which a fore-and-aft section is drawn in Fig. 67. H. Assume that the stream velocity U„ is equal to

m

equation gives

Vl -

and that at 10

cos Bb)

Substituting this expression for

Construction of 3-Diml Ovoid by Inserting Single 3-Diml Source in Uniform Stream

Fig. 41.1

sec,

-

U,

i

cos 6

6)

_

24.75(1

sm"

cos

6)

6

distance of the nose of the ovoid from the is

a longitudinal section through the

axisymmetric ovoid of this example, indicating the initial dimensions given and including the ovoid shape derived by the methods described here.

The equation of the ovoid, from Eq.

R'

=

2m(I

-

cos

(41.xxxviii),

B)

C/„ sin^ d

'

R =

sin 6

2m(l

4

-

cos

e)

Knowing the value of the 3-diml source strength m, the radial and tangential velocity components for any point P in the field, beyond the ovoid surface, at a radius R from the source and an angle 6 from the axis, are found by substituting the proper values of m, R, cos 6, and sin 6 in Eqs. (41.xxxvi) and (41.xxxvii), with the fixed Combining these radial and axial [/co components vectorially gives the velocity and

value of

.

ll^ i)R()i)>

HI ninRiiitiHlf

i>i

ilir rc.-iilliiiit

For pxamplr. assume the volofity

P

point

r_ of

or 34.tV2

.

P

are 9

is

it

=

ft

per sec.

The

85 deg and

7?

1'.

roqniriMl to find

cos e

W The

U,

=

The

re.'^ultant

34.7

ft

17- sin 6

velocity

per sec.

resolve themselves, directly or indirectly, into the

the liquid velocity at any or

ft.

Then from

ft

(34 .62) (0.0872)

from Eq.

(4

=

34.02(0.9962)

33.49

ft

is 1(3:^.49)'

1

.x.xxvii),

"Doubtless

+

(8.88)']"

*

=

of tan"' (8.88/33.49) is

and sink are both involved, as shown in Fig. 43.J, the stream function of each, and of the combination,

has a value of zero at the source-sink

axis.

WTien representing 3-diml sources and sinks

of

apply only to motion in ideal

flow, as in

through the center of

The

The

sources and sinks are

Sec. 2.20

sitik.

axi.sj-mmet ric with respect to the j-axis for either

methcKi of representation but in the latter case the characteristics of the flow can be represented

by the two spherical coordinates R and B. As far as the shape of the streamline pattern and the evaluation of liquid velocities at any point are concenied, it makes no difference where the reference line or plane is chosen. Hut changing the reference of a source or sink changes the stream-function value of a given streamline. Thi.s is the reas<^>n

why

the stream-function value

which represents the surface of the in Fig. 07.11 is zero,

while

representation of the

same

in

3-(linil

flow, K(|. (41.xxxvb), I

he ovoid

of Liquid

Velocity

the Mlreain function at the surface of hft.s

a value of

41.10

ovoid

the mathematical

—m.

The Determination

lifiuids.

Fortunately,

it,

explained in Sec. 5.15. Potential

an ideal liquid, is then a.ssumed to exist around this expanded form, in the manner depicted by Figs. 7.1, IS.A, and 18.0.

(or the source-sink axi.s)

the source or

whereas most formulas

procedures and

some adjustment is possible by expanding the body or ship form so that it includes the displacement thickness 5* (delta star) of the boundary layer around

a plane perpendicular to the x-axis

the naval architect,

their parts involve real liquids,

the mathematical

forms of and the flow around axi.s^Ttimetric bodies, it is much more convenient to take as the refer-

=

come when

Analytic and design problems concerning ships

and

mathematically, e.specially when developing the

ence for ^

will

surface.

actual ships."

0-valued stream function coinciding positive x-axis. If a 3-diml source

day

That day is not yet, but the present knowledge of the mechanics of fluid motion is such that we can determine completely, under certain conditions, the pressure and velocity in a perfect fluid flowing past botiies whose lines closely resemble tho.se of immersed

In Fig. 67.H of Sec. 07.7 the 3-diml source used as a means of constructing the ovoid shown its

tlic

given the lines and speed of a ship, will be able to ralculato the pressure and velocity of the water at everj- point of the

the point P.

the

on the

[p. 38.51:

per sec.

state of our

with

point.s,

Taylor, in his paper "On Ship-Shaped Stream Forms," for which he was awarded a gold medal by the Institution of Xaval .Architects in London in 1894, prefaced his remarks i>y the following

about 14.9 deg. This means that the direction of the resultant velocity makes an angle of (90 - 14.9) = 7.5.1 deg with the radiu.s R to

there has

all

Once the velocity is known, the pressures, forces, moments, and other factors are derived by relatively simple and expeditious methods. Xaval Constructor David

W.

per sec.

= The value

of the problems arising around a IkmIv or ship

surface and in the vicinity.

S.SS is,

of iicpiid

determination of the magnitude and direction of

0.0

=

'

from the flow

=

^^ -

(

Many

Around Any Body.

spherical coordinates

=

tangential velocity

StT.H.lO

ni si(.\

1'

the

for

(41.xxvsi'> the radial velocity

Eq.

11

speed equal to

and diroction

niaRiiitinlo

\\ii( s i\ SI

vclocii y at llic|niiiii

tliat

Fig. 41.1. at a ship

in

\

flow net for 2-diml bodies, described in

and constructed by graphical, electrical, is one way of finding the velocity. Another method is to .shape the body by a combination of radial and uniform flow, employing sources and sinks. Then by cal-

or other convenient procedure,

culation or graphic procedures the velocities in

the surrounding

field

are derived.

Methods

of

following the latter procedure arc described in

and 41.9. The steps for obtaining the by the second method are described in Chap. 43. Both methods give the velocity throughout the field as well as at the body surface. Sees. 41.8

desired data

If

a velocity jjotential



for the field

amund

any body or ship form is a.ssumed or can be set up, by the methoils outlin<'d in Sees. 41.8 and 41.9, or by any other methods, expres-sions for the comi)onent velocities u, v, and «• are derived by partial difTcrentiation of

4>

^^ith

respect to

GENERAL LIQUID-FLOW FORMULAS

Sec. 41.12 X,

and

y,

z,

respectively.

Substituting selected

values for the coordinates in the region being

25

geometric figure that preserves geometric similarity of infinitesimal parts of the figure. This

investigated, the

component velocity values are comments apply equally to the stream function f, and to 3-diml as well

means

readily calculated. These

responding lines are the same in the original figure and in its conformal representation"

as 2-diml forms.

[Wislicenus, G. F.,

Data on

velocity

and pressure

fields,

already

calculated or otherwise available for a considerable

number

of typical

body shapes, are referenced

in

several of the sections of Chap. 42.

FMTM,

M. Milne-Thomson

L.

all

angles between cor-

1947, p. 582].

gives an excellent illus-

tration of conformal transformation, or conformal mapping, as it is sometimes called [TH, 1950, p. 140]. This:

Baker and J. L. Kent give an example of D. W. Taylor's method of using line sources and sinks to delineate a 2-diml ship-shaped body and to determine the magnitude and distribution of pressure around it in an ideal liquid [IN A, 1913, Vol. 55, Part II, pp. 50-54]. They describe an adaptation of this method to a determination of the same features around a ship-shaped form in a G.

in particular that

S.

afforded by an ordinary map on Mercator's is well known that the angle between two measured on the map is equal to the angle at which the two corresponding lines intersect on the earth's surface; in fact, it is this property which renders the map ".

.

is

.

projection. It lines as

useful in navigation.

"In particular the lines on the map which represent the meridians and parallels of latitude are at right angles. If

we

confine our attention to a small portion of the map,

know

that distances measured

on the

map

we

restricted channel with straight walls parallel to

also

and equidistant from the ship axis. A. F. Zahm, in NACA Report 253 of 1926, entitled "Flow and Drag Formulas for Simple Quadrics," gives calculated and obsei-ved pres-

represent to scale the corresponding distances on the globe, but that the scale changes as the latitude increases."

sures for a series of geometric forms, including a

an elliptic cylinder, prolate and oblate spheroids, and a circular disc. He also gives diagrams of isobars and isotachyls about some of these forms, and discusses velocity and pressure in oblique flow. 4L11 Conformal Transformation. An ingenious mathematical process, involving complex variables, was utilized by W. Kutta in the early sphere, a circular cylinder,

determine the flow characteristics around typical or schematic airfoils [Kutta, W., 111. Aeronaut. Mitt., 1902; AHA, 1934, p. 173]. 1900's

to

Knowing the flow characteristics in the region surrounding some simple geometric form such as a circular rod, by the doublet construction illustrated in Figs. 3.M and 43. J, the circular form and the flow pattern are transformed simultaneously into the form and pattern desired. However, the nature of Kutta's method restricts its

is

effected

by

retaining the

blunt nose and a somewhat pointed flow pattern

determined.

Stated

mathematically,

the

modified

same general laws irrotational flow, namely

picture obeys the

and

for

du dv — +—= dx

„

,

dv

,

and

dx

dij

du Tdy

=

as the original flow picture from which

derived [Wishcenus, G. F.,

FMTM,

flow

for continuity

it

was

1947, p. 193].

Wislicenus gives a brief discussion of conformal transformation in Sec. 44 of the reference, pages 211-218. H. Rouse gives a more complete treatin Chap.

draulic

V

of "Fluid

Engineers"

Mechanics

[McGraw-Hill,

for

New

Hy-

York,

pp. 96-124]. excellent presentation of this subject is the

one by A. Betz, entitled "Konforme Abbildung (Conformal Representation)," pubhshed by Juhus Springer in Germany.

in

or

conformal

Quantitative Relationship Between Veand Pressure in Irrotational Potential Flow. Having determined the magnitudes and directions

defined "as a distortion of a

of the velocity at selected (or at all) points in the

as conformal transformation.

way,

conformal is

The

Put

of the flow net is reduced, the process is

known

representation

tail.

or transformed with

for the transformed pattern are fully

teristics

An

"mesh"

flattened

is

the rod so that the velocity and pressure charac-

19.38,

presei'vation of angles in each small area as the

mapping it is possible, and the accompan}dng

to flatten the rod into a hydrofoil section with a

the flow net around the typical body as the size

from visible to infinitesimal dimensions. Taking its name from the

of

2-diml flow pattern of Fig. 3.M, depicting a field in which the velocities and pressures are known,

essential shape of the "curvilinear squares" in

of these squares is reduced

method

this

starting with a circular rod

ment

use to 2-dunl problems.

The transformation

By

will

transformation

another

41.12

locity

HYDRODYNAMICS

26

motion

field of rvlnlive liquid

next practical step

is

aroiiiui

ii

luKiy. the

usually to determine the

pressures at thtvse points. For irrotntional potential flow in an ideal liquid without viscosity, at a depth where the hydrostatic pressure remains sensibly constant, this is a rather simple, straight-

fonvard process.

From

the basic assumption, explained in Sec.

any stream tube

which the flow is steady and continuous the total pressure remains constant along the tube, the relationship between the dynamic pressure q and the pumping pressure p at two reference points 1 and 2 is expressed bj2.7, that in

Pi

+

I

V\

=

Pi

If the point

undisturbed infinity,

+

V\

or

+

p,

from the point

li(inid

then the preceding equation

p.

+

=

?,

I

VI =

P,

+

1

2, i.s

+

p,

taken at a great distance

is

1

I

in

in

9,

IN

HI

SI1I1»

Assume

SIGN

Sec. -11.12

that for the 2-diml flow net around the

blunt-ended 2-
.section of Fig. 41. J

(adapted

from Rou.se, H., E.MF, 1940, Fig. 21), p. 50), the stream-tube width An. is 0.25 in. .\nd that at the point A on the fonvard shoulder the width An is narrowed to 0.20 in. Then An,/An is 0.25/0.20 = 1.25, whence (An^/An)^ = 1.5G25. The pressure coefficient or Euler

-

thus 1.000

The values

number E, at

1.5()25 or

thus derived for any selected

down

of points are laid

is

number

graphically in several

ways, depending upon what

by the

this point

-0.5625.

is

to be represented

and negative diiTerential pressures + Ap and — Ap are to be emphasized the scheme followed in diagnini 2 of Fig. 41. J is plot. If the positive

the

say at

written as

c/^

Transposing,

v.-v^ = livl-v^ =

l(x-^

whence, omitting the subscripts "2,"

= ^P =

^r <'-^)

This gives the relationship derived in Eq. (2.xvi) of Sec. 2.20,

namely

-^ = :^= The

1

expressed

equalities

--^ in

Eq.

(2.xvi)

(2.xvi)

are

mast important and useful. They can with profit be memorized by everyone who works with this subject. The left-hand and middle terms in this equation are expressions for the pressure expressing the cient or Euler number 7?, ,

coeffi-

difTer-

encc in pressures between that at any select<>d point 2 and that at infinity, as a proportion of the ram pres.sure O.TypUl which could be set uj) in the unlimited, undisturbed stream.

The ratio U/U.. is exactly that given l)y the ^n./^n in the 2-diml How net described in

ratio

Sec. 2.20.

Hence

and subtracting

sf|unring the fraction

it

An. /An

from unity gives directly the

pressure c
U

IM

larger in

coefficient

'I'his

ratio

is

larger than I.O

magnitude than l\

^p/q

is

then negative.

.

The

t

In-

when

pressure

F"io.

41.J

Bbtween Veixjcitv and Pressure OK AN Ideal LiguiD .\koi:nd a Body

Uki.ation

IN Fixjw

preferable.

Here the normal vectors representing

the combination of atmospheric and diiTerential l)re.ssures

are laid

as a reference

o)T

line,

from the solid-surface contour

with the

-f

Ap

vectors directed

toward the surface and the

— Ap ones away from

However, the practice

drawing vectors inside

the

.solid

is

of

not recommended for general

it.

u.sjige

crowded together in n-gions of sharp cur\'ature and the solid may be too narrow to lay them down at a conveniently large scale. becau.se they are

GENERAL LIQUID-FLOW FORMULAS

Sec. 4 1.1

27

the total pressures on the sohd surface are to be emphasized the preferred method is to draw a hue outside the solid surface, everywhere equidistant from it at a distance which represents conveniently the ambient pressure p„ or that of the undisturbed liquid at infinity. A variation of this method is illustrated in diagram 2 of Fig. 2.B, where the atmospheric pressure Pa on the hydrofoil section corresponds to the ambient

as in the right-liand portion of diagram 2 of

pressure p„ of Fig. 41. J.

customary pressure is sometimes used when investigating the proper location for a pitot-type velocity indicator or a speed meter. As the entire velocity head in the liquid is converted to pressure head at the nose orifice of the pitot tube, this velocity is measured as a pressure when the region under consideration is being

If

,

using the length along the x-axis of the body as

the a;-coordinate. This method 2.V,

illustrated in

is

depicting the velocity and

pressure

A

variation at a stem section on a ship.

third

method is to use the developed distance along the boundary or contour of the body (or an expansion of

it)

as the distance basis, erecting the velocity

and pressure vectors normal to

TABLE The data given

The

this

41. c

contour

line,

pressure relationships are frequently ex-

pressed and plotted as fractions or as multiples of the

ram

pressure 0.5p[/J

— Ap

at the point

coefficient

of

or Euler

the

number

By relating (1) the pitot pressure observed at any selected point in the field, as

surveyed.

registered

on an instrument mounted in a fixed

1

(^)'

T^Ul for potential flow in

u

an

ideal liquid.

They apply

The dynamic

A is — 0.5625?.

variation

Velocity Ratios and Pressure Coefficients

_ Ap =

q.

motion are then referred to as so many "q's," plus or minus. For the previous example the

here are plotted from Eq. (2.xvi),

Ap

=

caused by body or liquid

pressure variations

This

In addition, of course, the pressure coefficients may be plotted on the usual x-y coordinates,

Fig.

Fig. 41. J.

to a liquid (or a fluid) of

any mass

density.

iiM)R()i)\ \

28

wiK

s

i\ Mill' nrsir.N

Sec. -11.12

Oi^^Mrt»'3t*OiOOCO^

o«<e
3B

S.i

oo

S—n

U3

i»

o

5

3e

CO

3C

Q

-r

o

I- I-

* M X

"5

m « »

'C ci

—

c;

o o _ M -

"5

o

i~ _ _ CO "I r<

_

o

-J" i>-

Q

"ft

'400a>aoi^t^to>0'4a>aor>c8>o>a'Ttao

O O — — ?» C7 m cs (N e^ N M N e*

OpQOQQOQ©©OOOOQQOQQPOOOOQQOQpp

Ml. 2 ZC *jS.^ PC **>

Z.

5

•»

')>«oooooowr-e<30ii^or-©"-'rt'Oiot^C3e<50>incoMe^^

6

cscccococc*^'r^"5»-'5icco©t*h-oooocoC5C500-^c^c*<Mrc-?'*r»o

-^^ 5 •< ^ t^ 2

»>

5

" «

©oe>Ju5ooe>j»^«e^05ffl«'oomo©« -^cO'^iooodc5-^c^^ipr^Oi^cO'i'eooooco»ot>-C5C^'t*t>-OM-ft>'

u

Ei

lO

=

S

~

S.C-

-

—

c5

-,.

— — —

00 C^ "3

»

CO

o

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°

'r^b^^odojoc>^co'l^ccooc^M"»>«5t£iocic>

..l

-5-s S

ag

li:

-

^2fS

=

6"3

— -^ < = -

-3

_5

S

£

e<'<»'OcoQN'»'!Soop5ig;©ooQe>'»'«oop v^">"'»">5'OiO'SS5oo«©3r-i~i~r^i-ooao<»(»o6oososao90

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oc>doodb^-H«^^c^co«^5^^ou5»^^cooc>^*u5o6o"cj'*

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— »i"N— ff^'OCOMCitoooior-.tpocoMM c^ooo-rcoM-rioo — — c«c<5"riotoooc3-<«cixi-i-oo 3

a.

ddddddoc>ddO'-<'^'--">-'"e>4C>iMc<5W'S'>oo

b

&^

cot«>OMOi>oo>oora«aoo>-i>M<--ine4a>e<3U3

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t-wSS

— i-«Slo — i-SS'* —

I—

NoooN'*«ooa>-He<5u5h-

III

H

e<W'»'0»t^or)Oo-"C«coT'0!or»<»o>Ofj'i"sRWQ2<3C2«©

GENERAL LIOUID FLOW FORMULAS

Sec. 41.12

T3 -*

2

t;

O o

f-T'i-^

lO

a.

03

o

29

nVDRODVNAMlCS

30 position ship,

t*>

ami (2)

at a lixinl nttitinie tlu-

on

Ixxly or

tlie

nnn prrssure which would

lie

registered in tlie direction of motion at an infinite distiince, a

simple relationship q,./q

is

established

which greatly facilitates plotting experimental data. Contours of pitot-pressure coeflicient of 1.00, with allowable limits on each side, indicate the regions where the pitot orifice of the instru-

ment can be

located

to give accurate

under the coiulitions established. If the flow remains steady and free

of rotation,

hold regardless of scale, velocity, liquid density,

upon the sj'stem. A pressure determination from known velocity magnitudes and direction is much less determinate when the flow is complicated by viscosity overall pressure

41.13

variation in velocity are plotted for the potential flow of an ideal li(|uid around ll.c

gives

the variation

pre.ssure coeflicient

Tables

of

Ram

Velocity

Ratios,

Pressure

and Heads. To facilitate the preparation of diagrams in which the distribution of dilTercntial pressure and the Pressures

of

any body. Table Euler number or

with velocity ratio as deter-

mined by the following relationship derived from the Bernoulli Theorem:

Ap

-^='-^ = '-(^)"

'--'

This relationship applies to liquids of any mass density p, provided the values on both sides of the equality sign are for the same liquid.

The ram calculated

pressures corresponding to 0.5p6'i for

=

q,

both standard fresh water and

standard salt water, are set down in Tables 4l.d and 41.e, respectively. These are given in both

supplemented by the noted that the laller value is the same for water (or other liquid or fluid) of any mass density. The range of velocities covers those normally encountered in model tests and ship design. lb per ft^

and

lb per in',

velocity head in

effects.

Coefficients,

Srr. 11.13

results

and if vi.scosity effects are neglected, the pressure and velocity relationships are dimcnsionlcss and and

IN sniP i)tsic;.\

ft.

It is to be

CHAPTER

42

Potential-Flow Patterns, Velocity and Pressure Diagrams 42.1

42.2

Around Various Bodies

Various Methods of Drawing Streamlines Around Bodies Flow Patterns Around Geometric and Other

31

Shapes; Published Streamhne Diagrams

31

.

42.5

a

42

Constructing a flow net

made up

of streana-

lines

Determining the streamlines mathematically construction, if the body shape is one that may be formed by placing one or more sources or sinks, or source-sink pairs, in a uniform stream

by graphic

(c)

Plotting the equip otential-line pattern in an

electrolytic

tank and constructing the streamline

pattern from

it

(d) Plotting

the streamline pattern as an equi-

potential-hne pattern in an electrolytic tank (e)

Placing

the

body

in

a

circulating-water

channel and observing the streamline pattern by one of several methods (f)

By

irrotational,

a flow net for

potential flow in

two

dimensions in an ideal liquid can be constructed for a great variety of boundary shapes, channel boundaries, or both. Flow nets are reproduced in Figs. 2.0, 2.P,

Fig. 2.X;

and

2.W; in diagrams in Fig. 41.J.

They

1, 2, 3,

and 4

of

are to be found

frequently in the literature, as hsted in Table 42.a. 31

47 48

limitation to

an

49 for

50

ideal liquid, the

practical usefulness in applied hydrodynamics. There are many instances in the course of ship design or in the analysis of ship behavior where an approximation to the flow pattern by this method is most illuminating. For example, before surface wavemaking has become pronounced, the flow around the uppermost waterlines of a ship is predominantly 2-diml in character, expecially

abreast the forward part of the vessel. Several

examples are to be found in Figs. 2.S and 4. A. Other examples are the 2-diml flow patterns around a sharp 2-diml bend in a duct, illustrated in diagram 2 of Fig. 2.X, and around the stem bar of a ship, shown without the equipotential lines in diagram 1 of Fig. 2.V. Three-dimensional flow nets can be constructed [Rouse, H., EH, 1950, Fig. 26 (lower), p. 33] but the technique becomes complicated, as described

them

following the relatively simple sketching

continuous,

its

46

2-diml flow-net technique has a rather extensive

in Sec. 2.21. Practical

Utilizing conformal transformation.

process described in Sec. 2.20,

Despite

43

48

Studies

43

.

(b)

or

11

40

.

the streamline pattern. Listed briefly, these are:

and equipotential

.

.

of Revolution

42.1 Various Methods of Drawing Streamlines Around Bodies. For 2-diml potential flow around a body of any shape, at any orientation with the stream, there are several methods of determining

(a)

Analogy BibUography on the Electric Analogy Flow Patterns

39 40

Two- and Three-Dimensional Bodies

lines

42.14

42.10

Velocity and Pressure Diagrams for Various

42.7

Delineation of Flow Patterns by Electric

39

Velocity and Pressure Distribution Around

Body

42 13

.

Ideal Liquid

42.6

42. 12

Distribution of Velocity and Pressure About an Asymmetric Body Flow, Velocity, and Pressure Around Special Forms Velocity and Pressure Distribution Around Schematic Ship Forms Pressure Distribution Along a Vee Entrance Use of Doubly Refracting Solutions for Flow

42 9

.

Flow Patterns in Ducts and Channels ... Flow Patterns for an Ideal Liquid Around Simple Ship Forms Flow Patterns About Yawed Bodies in an

42 3 42.4

The

42.8

methods

for constructing

are not considered here.

It is important to note, as mentioned on page 44 of Sec. 2.20, that since the flow in a separation zone is not potential in character, it can not be represented in a flow net. Furthermore, this technique does not take account of centrifugalforce effects as the liquid changes direction around bends and corners in channels and ducts. These

forces

42.2

may

be appreciable at high velocities.

Flow Patterns Around Geometric and

lI^llR()l)^

S2

TABLE

Type or

of

Body

Shape

\

wiK

s

i\ Mill"

1)1

si(;n

Data kor Line Diww is
42.ft— IlErKRESCE

Src. 12.2

POTENTIAL-FLOW PATTERNS

Sec. 42.2

TABLE Type or

of

Body

Shape

42.a— (Continued)

33

IIM)R<)in \ \MI(

S4

TABLE

Type of Body orShapo

s

IN

Sllll'

l)ISI(;\

42.b— IlKFEiuiNcE Data »x)h riioTuiauriis ok Flow Patterns Abound GeOUBTRIC AND OrilKli Sl.Mfl.K SlIAI'liS

Sec. 42.2

POTENTIAL-FLOW PATTERNS

Sec. 42.2

TABLE Type

of

Body

or Shape

42.b— (Continued)

35

in

.S«i

DKODN

UJI.K •rj.r— Ukkkhkncb

Tvpo

of PtiMaRO

Data

\

WIU

s

I\ sllir

koii Ligi'ii>-Fu)W

1)1

Pattkhnk

sl(.\ in IJiu-rs anii

Set. 12.2

Ciianneui

Sec. 42.2

POTENTIAL FLOW PATTERNS TABLE

Type

of Passage

42.C— (Continued)

37

nvnRonYN.\Mic:s

38 1931,

\i.l.

I,

pp.

;i;n

:«31.

Tli.-

contains oxcoUent photogruplis of

hitter

'J-tlintl

paper

i.\ 3.

objectij

moving through glycerin with alununum powder on the surface to show the flow patterns. The Ueynoltls number in Tietjens' experinjents paper points out

251).

tliat

The

discussion of the

vortex

1907 and first

or street,

trail liy

R<5nard in

paper on

The

now

calletl

Wagner, O. Flamm, and F. Gebers, also made in Germany. The results were embodied in the following papers and books: by those

1.

of R.

Wagnor,

R.,

"Versuche mit

Schifrsschrftul)oii utul litTon

praktisohe Ergcbnisse

(Tests with Ship Propellers

and Their

Results),"

Practical

STG,

lOOG,

pp.

2&4-366, esp. pp. 293-295, 302, 310-323. This paper embodies many flow diagrams and flow patterns

around propeller blades and propellers. 2.

Flamm,

O., "Beitrag zur

der

wcise

peller),"

opp.

p.

STG,

TABLE of

Body

(Contribution

to

the

Ship Pro1908, pp. 427-438, esp. Figs. 1-12

Gebers,

F.,

EfTectivene.ss of the

Tests)," p.

758,

42.d

"N'euc Proi>ellerversuchc (New Pro|)cllcr 1910, pp. 729-7S1, esp. Fig. 12, opp.

STG, and

Figs.

1,

2,

and 3 on

p.

782; also

INA,

1910, pp. 69-70.

In the course of the last half-century, since

most

of the foregoing references appeared, a multitude of flow-pattern photographs have been

taken, a large number of flowiine diagrams have been drawn, and a great many of i)oth have been published. Reference data on some of these are

presented in two groups in this section, and in other groups in the sections to follow:

Table

432

or Shape

Entwicklung der Wirkungs-

SchifTsschrauben

Development of the

Type

5.

this subject in 1911.

34ti.

".Vbwehr der Kcmpfschcn AngrilTo und einiges mehr iilx-r seine und meine Propellerversuche (Defense of Kempf's Method of .-Vtt.'ii'k and .\dditional Information on His Projvller Tests and Mine)," SchilTbau, 28 Feb 1912, pp. 388-396. On pp. 390 and 391 there are a.xial views of model propellers showing some of the flow paths over the widths of the blades, on both faces and backs. F.,

the

Some of the Flamm pliotngraplis STG, 1909, Vol. 10, Figs. 1 through

1909.

page

7, opjxisitc

Gebers,

was noted by Mallock in 190S, prior to von Kiirmiin's

and flow diagrams were supplemented a few years later

Berlin,

4.

propeller photographs

of Alill)orn

<)., "Die .SchilT,s.si'liraubc uiid iliru Wirkung auf daa Wnsser (The Screw Propeller and Ifa .\clion in Water)," published by R. OldenlKJurg, in .Munich

arc published in

the double row of vortexes

leaving the blunt-ondetl bodies,

Sec. -12.2

Flanim,

and

sprinkletl

varied from 0.25 to

ship dksign

Rekkrknce Data for Fixjw Patterns

42. a

.\Rot:.Nn

Reference data for line drawings of

Simple

Siiapi-:.s

When Yawed

POTENTIAL-FLOW PATTERNS

Sec. 42.4

data for photographs of flow patterns around geometric and other simple

b.

42. b Reference

To

M

save space in Tables 42. a and 42. b of this

Table 42.c of Sec. 42.3, and in Table

d.

been made with reflecting particles sprinkled on the liquid surface or suspended within the Uquid

marked "Al. Powder," regardless of whether aluminum powder was used in every case. "Normal" means that the long dimension of the section or body was across the flow, normal to it. "In line" means that the long dimension was are

or not

parallel to the flow.

Of the streamline diagrams derived by analytic methods, among the first to be published were those of W. J. M. Rankine, appearing in the

Naval Architects

literature of the Institution of

Great Britain), in the period 1862-1872. Stemming from the work of Rankine were the analytic streamlines about ship-shaped and other bodies pubUshed by D. W. Taylor in the references Usted in Sees. 3.8 and

and

of the

Royal Society

(of

Volume II "The Speed and Power

43.6 of the present book, and in

of

the 1910 edition of

of

Ships."

Many more source-sink

streamline diagrams evolved from combinations have been pubUshed

Among the references, America, may be hsted:

since then. in (i)

not well known

ATMA,

1933,

Vol.

pp. of flow nets 37,

number and diagrams giving streamline and equipotential395-410. This paper contains a line patterns for (ii)

a series of flow conditions.

Brard, R., "Les M6thodes pour

le Trace des Lignes de Courant dans les Ecoulements Thfeoriques ou Reels. Leur Role en Hydrodynamique (The Tracing of Streamlines in Theory and Practice. Their Role in Hydrodynamics)," ATMA, 1938, Vol. 42, pp. 65-83. So far as known this paper is not translated into EngUsh. A full understanding of it involves a working knowledge of complex variables and con-

formal transformation.

and

airship models were

in the technical Uterature. a.

inverted position.

T. B. Abell published some unusual photographs of the wakes abaft simple ship-shaped bodies, using filaments of colored Uquid and air bubbles as indicators ["A Contribution to the Photographic Study of the Mechanism of the Wake," INA, 1933, pp. 145-152 and Pis. XVII,

XVIII].

N. W. Akimoff pubUshed the results of some and wave studies about vertical circular-section rods and elongated forms suspended in a moving current of water ["tJber das Wesen des Mitstroms (On 'the Behavior of the Wake)," STG, 1934, pp. 149-163]. 42.3 Flow Patterns In Ducts and Chaimels. The naval architect and marine engineer are flow-pattern

interested in the details of liquid flow within pipes, ducts,

and channels, as well as

of the flow

Flow-net diagrams for the motion of an ideal Uquid within typical open and obstructed passages

shown

are

in Fig.

2.X

of Sec. 2.20.

Table 42. c Usts reference data for what might be termed "inside" Uquid-flow patterns, subject to the notes in Sec. 42.2 applying to Tables 42.

and

42.b.

A

paper by H. S. Fowler and V. Walker, "Fluid Flow in Turbo-Machinery"

entitled

[lESS, 1953-1954, Vol. 97, pp. 113-152], contains informative diagrams of air flow through

many

ducts, bends,

and

axial-flow turbine

and blower

blades.

In the early 1910's, representations of the wake patterns and streamHnes alongside and abaft surface-ship

M

e.

outside of bodies and objects of varied shape.

Legendre, R., "Hydrodynamique Graphique (Graphic

Hydrodynamics),"

Methods of the Flow Past Plates and Models," ARC, R and 58, Mar 1912, pp. 97-99 Baker, G. S., "Methodical Experiments with Merchant Ship Forms," INA, 1913, Part I, pp. 162-180, esp. pp. 167-168 and PI. XVIII. This plate shows four photographs made at the stern of totally submerged models, each composed of the underwater body of a ship form with its mirror image superposed, in graphic

42.d of Sec. 42.4, the authors' names in the references are omitted. All photographs which have

in

M

c.

section, in

and Models

M

shapes

Table

39

a Current of Water," ARC, R and 31, Mar 1911, pp. 48-49 Booth, H., and Eden, C. G., "The Wind Resistance of Some Aeroplane Struts and an Examination of Their Relative Merits," ARC, R and 49, 1912, pp. 95-96 Bairstow, L., and Eden, C. G., "Experiments on Airship Models," ARC, R and 55, 1912, pp. 48-51 Eden, C. G., "Investigation by Visual and PhotoPlates

flow patterns around geometric and other simple

A

pubUshed

brief Ust follows:

Eden, C. G., "Apparatus for the Visual and Photographic Study of the Distribution of the Flow Round

42.4 Flow Patterns for an Ideal Liquid Around Simple Ship Forms. Available flow diagrams around forms resembUng those of ships are relatively scarce. Such as do exist are limited to the more-or-less 2-diml flow about the designed waterline, and that in an ideal Uquid only. Other than those embodied in Figs. 2.S and 4.A

Volume

of

book thiTc mny be

of this

I

listed the

following: (»)

Two-dimensional ship h.'iviiiR n li-titiciihir form of walorlinc, for which the flow puttcrn was derived and publiiihiHl l>y D. \V. Taylor in: (1) (2)

INA. isoi, Vol. S and P, 1933,

35, Fig. 14, PI.

LXXI

Fig. 4, p. 4; practically the

sanio figure aa in (1) (3)

same (b)

S and

P,

1943, Fig.

4,

0; practically the

p.

figure aa in (1).

How anJ

forward shoulder waterlines of a 2-diml ship generated by a uniform line source in a uniform

stream. Derived and published by H. Futtinger in

STG, 4S,

1924, Vol. 25, Fig. 11,

May

Same

(c)

as

p.

306;

TMB

Transl.

1952, p. 14.

preceding e.\cept that the line source

(b)

increases linearly in strength from the stem. lished in

48, (d)

(e)

May

STG,

1924, Fig. 12, p. 307;

TMB

Transl.

1952, p. 15.

Complete 2-diml ship with waterlines generated by the combination of a bow line source and a stern line sink, each of constant and equal strength. Generally similar to (c) preceding. Published by F. Horn in "Theorie des SchifTcs," Vol. V. Reproduced in RPSS, 194S, Fig. 2, p. 15, including diagrams giving the variation of p and U along and beyond the .ship a.\is. Three-dimensional ship having a lenticular form of lateral plane, for which a schematic flow pattern was pubUshed by D. W. Taylor in: (i) INA, 1895, Vol. 36, Fig. 0, PI. XVI. It is to

axis. (ii)

S and

figure as in (iii)

as for

P, 1933, Fig. 5, p. 4; practically

(i)

same

(i)

S and P, 1943, Fig.

5, p. 6;

.\ii

same comments

preceding.

Ship-shaped forebody, 2-diml in character, introduced a uniform stream flon-ing parallel to the ship a-xis. S. Baker and J. L. Kent give a plot of 2-diml streamlines ahead of and abreast this forebody, when there is no limitation on the extent of the surrounding water ["Effect of Form and Size on the Resistance of Ships," IXA, 1913, Part II, pp. 37-60, and Pis. Ill, IV, especially Fig. 5 on the latter plate). The lower portion of Fig. 5 gives graphs of pressure variation with distance along the longitudinal axis for two stream surfaces fairly close to in

G.

More recent data, applying to pressures rather than streamlines around a yawed body, may be found in Admiralty Research Laboratory (Great Report ARL/Rl/G/HY/19/1 of April Campbell and R. G. Lewis, entitled "Pressure Distributions: Axially Symmetric Bodies in Oblique Flow." A copy of this report is in the Britain)

1954 by

I. J.

TMB library. 42.6

and

Velocity

Aroimd a Body

of

having

revolution

same as

Pressure

Revolution. appreciable

Distribution

For bodies of diameters,

for ships with appreciable

Flow Patterns About Yawed Bodies

42.5

Liquid.

pattern.s

'Iho

about yawed

itJcaI-lif|ui(i

in

an

potential-llow

bodie.s in a stream, avail-

able in the publi.Hhcd literature,

amount

to only

worked out for axial flow. A partial list of references embodying these patterns is presented in Table 42. d. One HUch patt«:rn is that around the incUncd flat plate in diagram of Fin. 3.IJ in Volume I. a very small fraction of those

1

the it is

part of the book.

AVhen working with 3-diml rather than 2-diml around a body of revolution, it is important that the nature of the 3-diml flow pattern be clearly understood. In a number of pubhshed diagrams in standard works of reference the streamUnes approaching and leaving the 3-diml bodies of revolution have, apparently as a matter of convenience in drafting, equidistant radial spacing from the principal body axis. This flow, as with that

is

equivalent to equidistant transverse

.-ipacing

when a longitudinal section through the body axis is diagrammed [Prandtl, L., and Tietjens, 0. G.,

AHA,

1934, Fig. 58 on p. 109, Fig. 59 on p. 110,

and 64 on

p. 120,

and

Fig. 65

Taylor, D. W., S and P, 1910, Vol. Ideal

beams,

customary to plot velocity and pressure distributions on a basis of body or ship length along the principal or x-a.\is. This scheme is followed in Figs. 4.C and 4.D of Volume L However, when the diameter is large in proportion to the length, or when one end or the other is blunt, the velocity and pressure distributions are plotted to much better advantage on a base of length along the section contour, as in diagram 2 of Fig. 2.B of Volume I or in the diagram of Fig. 4LJ of this

Figs. G3

the ship.

Sfc.-f:^

excellent source of analytic information in

this particular field is the work of A. F. Zahm, embodied in NACA Report 253, 1927, entitled "Flow and Drag Formulas for Simple Quadric.-*," pages 517-537. Fig. 3.C of Volume I of this book is adapted from Fig. 23 of the Zahm report.

Pub-

be noted in this figure that the streamlines are not spaced from the body a-xis at distances corresponding to cquidifTerent stream functions in tubes about the

(f)

DKSIGN

HVl)R()l)V.\A.MIC:s IN Mill'

•10

on

II,

p. 122;

Fig. 20;

S and P, 1943, Fig. 5 on p. 6). The streamlines so depicted do not correspond to cquidifTerent 3-diml stream functions, as do the traces in diagram 2 of Fig. 2.M of Volume I, and those of Figs. 42.A, 42.B, 43.M, and 43.0. Consider the symmetrical 3-diml flow of an ideal liquid along a solid rod of circular section of

radius Ro

,

with

of flow, in a

its

axis parallel to the direction

stream whose undisturbed uniform

POTENTIAL-FLOW PATTERNS

Sec. 42.6

41

mean

in proportion to the increase in its

radius,

to maintain the relationship of Eq. (42.i).

When

the flow takes place around some body

of revolution

which has a varied section along the

axis of flow, such as the sphere in Fig. 42.B, the

elocity

in all

tubes

Schematic Diagram of Uniform ThreeDlMENSIONAL FlOW AeOUND A STRAIGHT CIRCULAR Rod With Equidifferent Stream Functions

Varying liquid velocity at different rad

Fig. 42.A

Longitudinal Section Through ThreeDlMBNSIONAL FlOW ArOUND A SPHERE, WiTH Equidifferent Stream Functions

Fig. 42.B

velocity

42.A,

is

is

?/„

.

This situation, pictured in Fig.

derived immediately from the 3-diml

diagram 2 of Fig. 2.M an operation which does not change the flow pattern around it. The immovable quantity of frozen liquid, extending out to radius Rq is then subtracted from the whole. It is convenient in stream-function

by

lA(psi) in

freezing the hquid within the central rod,

,

this process to retain the rod axis as the reference

axis for measuring the 3-diml stream functions. If

the thickness of the

first,

second, or

any other

is no longer constant but changes with distance along the x-axis. In

velocity in each stream tube

fact,

there are three variables in the stream-

x, namely R, measured normal to the axis of the uniform stream flow. It then becomes necessary to make use of some rather involved procedures to dehneate the stream surfaces. For

function expression which vary with

An, and U, where

R

is

tube of hquid is represented by An, and its mean radius from the axis by R, then the increment of

two 3-diml bodies

hquid volume AF passing tlurough it in the time At is represented approximately by

nates are worked out in Sec. 41.9.

A¥ =

-U„{2ivR)An

(42. i)

including the

of revolution,

sphere, the stream functions in spherical coordi-

A

3-diml stream form, especially one derived

from a

single

source-sink pair,

lends

to

itself

graphic construction of the flow pattern around

where the velocity the tubes. If cyhndrical

Ra

[/„ is constant is

throughout

all

the radius to any selected

stream surface,

function of that surface

the

3-diml

stream

is

The

is

—

Ro)

zero.

subdivision of the uniform liquid flow into

stream tubes of equal area means that the normal spacing between the tube-wall traces in any longitudinal plane through the axis is no longer a direct measure of the velocity in each tube, or

even of the relative velocity, as it was in the case. For equidifferent values of the volume increment per unit time or of the stream function, the tube thickness diminishes inversely 2-diml

When so constructed, the radii -Ri

and the stream-tube thicknesses An^

Eq.

the soUd cylindrical surface of radius Ro the

3-diml stream function

pattern.

U

,

R2

,

AUi

,

.

.

,

.

are

are determined,

and the accompanying pressures p derived from (42. ii)

At

as well as to calculation of the elements of this

measured, the local velocities

= \~){-u:)-k{ri-r^:) {Ra

it,

(2.xvia).

The graphic

scribed in Sec. 43.8

and

construction

is

de-

illustrated in Figs. 43.L,

43.M, 43.N, and 43.0. The formulas for a 3-diml sphere are set down in Sec. 41.9 and in diagram 2 of Fig. 41. G.

Fortunately for the physicist, marine architect,

and others, certain staff members of the Aerodynamische Versuchsanstalt (AVA) at Gottmgen, Germany, have worked out the pressure distributions over 12 forebodies and 59 fuU bodies of revolution, of a great variety of shapes and proportions. These bodies were created by placing various combinations of point and hne sources and sinks along an axis, and then superposing upon this combination a uniform flow of ideal

IlVDROnVNAAflCS IN SHIP DESIGN

•12

A

liquid parallel to the axis.

streamlines adjacent

the

to

also given in their Report

December

few of the 3-diml 12

available in

1944,

I-nglish

Translation 220, issued in April

AVA

forebcKlies

11)47.

VU

Report

English

by

3106,

of

Riegels and

M. Brand, mentioned on page

Reference 2 on page 7 of

lation 220,

i.><

on

library at the

file

T.MB

as

An

translation

listed as

are

I'M 320G, dated 30

TMB

1

F.

and

Trans-

in the AercMlynainics Divi.sion

David Taylor Motlel Basin.

L Source- Strength SinW-Strenglh

I

.

Distribution

,

\

1

Distribution

---.^miniTMl^

I

Ratio of x/L from Nose 1.0

ai

0.9

0.8

a?

ae

o.s

0.4

0.3

0.2

qi

I

-0.1

-02 Fio. 42.C SouHCB-SiNK Strength Distmbution, AXISTMMETRIC BODT FoR.M, AND DISTRIBUTION OF Pressure CoEFnciENT Around an Aircraft Fuselage

Srr. 42.6

POTENTIAL-FLOW PATTERNS

Sec. 42.8

Flow About Elongated Bodies of Revolution,"

TMB Rep. 761, Aug 1951. On pp. 59-61 the author (14)

lists 28 references, some of which are given here. Campbell, I. J., and Lewis, R. G., "Pressure Distributions About Axially Symmetric Bodies in Oblique Flow," ARL (Admiralty Research Laboratory) Report (ACSIL/ADM/54/254) of Apr 1954.

Velocity

42.7

Various

When

and Pressure

Diagrams

for

Two- and Three-Dimensional Bodies.

the body shape, form, and contour can not

by some type of mathematical when the liquid flow around a body

be expressed equation, or

can not be expressed in the form of a given stream function

\}/

or velocity potential

sions for the velocity

<^,

analytic expres-

and pressure can rarely be

established or derived. It becomes necessary, as

back upon experimental observaupon data previously derived, assembled, and pubhshed by other workers. a

rule, to fall

tions, or

Some

references

containing

these

data

for

various 2-diml and 3-diml bodies, usually with

graphs of both velocity and pressure, are given under the appropriate categories in Table 42.e. Could this list be made complete, for all published works, the marine architect might find readily

hand a great amount of data that would be directly useful and occasionally most valuable. 42.8 The Distribution of Velocity and Pressure About an As3mimetric Body. Many underwater craft, such as submersibles and submarines, have shapes resembUng roughly a body of revolution at

43

1, with a uniform flow of velocity C/„ taking place parallel to the longest axis, has been investigated by H. Chu, P. C. Chu,

axes in the ratio of 6 2 :

:

and V. L. Streeter [Illinois Inst. Tech., Report on Project 4955, sponsored by ONR Contract 47onr-32905, dated 15 Mar 1950]. They found that around the elUptic midsection periphery the surface velocity parallel to the stream axis had a constant value of 1.0714f7»

,

At the

quarter-

lengths the velocity around the girth of the body

by only about one per cent from the mean. The uniformity of tangential surface velocity

varied

the undisturbed

at the midlength,

parallel

stream direction,

a sign that the surface pres-

is

to

around the midsection girth is hkewise everywhere the same. However, at a constant given distance from the body surface, in the plane of the midsection, the velocity and pressure do vary around the girth. This variation has been investigated by R. K. Reber for the elhptic ellipsoid having axes in the ratio of 6 2 1 [unpubl. memo of 13 Apr 1950 to HES], lying with its sure

:

Circular

:

A,'^

stream-tube boundarvj

Port streamline

but they almost invariably possess transverse asymmetry, at least above and below the principal longitudinal axis. Submerged bodies, and craft of the type mentioned, usually possess asymmetry in a fore-and-aft direction as well, reckoned about the midlength.

However, considering first the geometric forms having asymmetry about the principal axis, it so happens that formulas are available for computing the velocity and pressure distribution about

may be termed

elUptic elhpsoids.

the profiles, planforms, and sections are elliptic

first,

all

of

shape, as in diagram 2 of Fig. 42. D. Indeed,

this particular

form

is

in that the flow of

special in

an

Typical Schematic Flow Abound AxiSYMMETRIC AND ELLIPTIC ELLIPSOIDS

Fig. 42.D

what

For these bodies,

two

ideal fluid

respects;

around

it

longest axis parallel to the uniform stream. results are

shown

in Fig. 42.E.

Here

it is

that, in the plane of the midsection, the isotachyls

lends itself to computation, and second, in that,

or loci of constant velocity (parallel to the

when placed with one

axis

axis in the direction of

uniform flow, the velocity at the surface is constant everywhere around the girth of the midsection.

The

latter

feature

appears to be

inherent in these elliptic shapes only.

The

flow around an elhptic ellipsoid having

The

noted

and

body

to the stream direction) he closer than

the average distance to those portions of the transverse midsection having the sharpest curvature. Opposite the portions of least curvature they are farther from the body. The transverse

velocity gradient

is

therefore greater in

way

of

u

]\\

TABLE The Type

— RltrERENCKS -m

42.0

DRODN

\ WIK.s 1\ Mill'

1>I

^1(.\

iiijsiu;i> Data on Vki/»ity am> Tukssi hk Two- AND Timr.K-DlMKVBIOSAI, BoDIKS

I'l

Src. f2.S

I

•isiiium ih.n

direction of How. 2-diml bodiea liatod have conitant aoctiona along an axia normal to the

of

Body

or Sliapo

k.k Vahioi's

POTENTIAL-FLOW PATTERNS

Sec. 42.8

TABLE Type

of

Body

or Shape

42.6— (Continued)

45

11M)R()I)VX A.MICS IN SHIP DESIGN

•16

asymmetric hcxlies of tin- kind shown by Fig. 42.F. Nothing lias as yet been lieveloped to take its place. For the time being it appears useful to retain the enveloping stream surfaces, such as those of diagrams 1 and 2 of Fig. 42. D, along which the direction of flow is everywhere tlie

caw

of

tangent to the direction of those surfaces.

They

are qualified, however, as surfaces for which the

tangent velocity

ponent

— not

necessarilj' the axial

of that velocity

—

is

com-

constant around the

trace of the stream surface in

any transverse

plane of the body. For any such section, these traces form what are describetl in Sec. 1.4 and illustrated in Fig. l.B of

Volume

I as isotachyls,

or contours of equal velocity. Unfortunately, they

do not define the flow completely because the direction of the constant-velocity vector must also

be specified for every point around

the

some by adding vectors alongside the

periphery. This can be done, at the expense of

complication,

Direction ond Moonilode of Uniform- Flow Velocity,

Asymmetric

Bod>^

Um^

Scr. 12.9

component in the plane of the contour diagram, as is done in the wake-survey diagrams of Sees. 11. G and 11.7 of ^'^olume I and Sees. 60.0 and 60.7 of this volume. 42.9 Flow, Velocity, and Pressure Around contours

representing

Special Forms.

It

is

the

certain that the toclmical

much more data on

literature contains

the flow

patterns and the velocity and pressure distribution

around bodies of special shape than are referenced in this book and in others on hydrodynamics and hydraulics. Moreover, it appears reasonable to expect that, in the course of time, data field

which arc now

da.ssificd will

in this

becume available

for general distribution.

Among

the special forms in this category arc

the planing surfaces on the bottoms of flying-boat hulls

and

A

fast motorboats.

considerable

amount

work on flow patterns under these surfaces has been carried out by the National Advisory Committee for Aeronautics and the of experimental

FISH-EYE VIEW

whose Sections ore shown

here IS formed bvy J>locinQ Three Sources ond One Sink in Q Uniform Streom Eoch Source of Slrenqth m-l ot Stotion Zero is Offset

3

Lencjth

Units or Stotion

Intervals

The Source m-3 The Sink tn--5 is ot Sto 10.

Centerplone

is

from the

ol Sto. -5.

cole for Stations

Alono the X-Akis TVie

and

in

Numerals on the Diagram the Table

Represent the

Maqnitudes of the Tonqentiol Velocities at the

as Multiples or Fractions the Uniform- Stream Velocity l^

Expressed of

Streomllne at nisition of

8Urn

12

Points Indicoted.

POTENTIAL-FLOW PATTERNS

Sec. 42.10

Towing

Experimental

Institute of Technology.

Tank at The following

"A New Method

Studying the Flow of the Water Along the Bottom of a Flying-Boat Hull," NACA Tech. Note 749, Feb 1940 Sutherland, W. H., "Underwater Photographs of Flow Patterns," ETT Tech. Memo 86, May 1948.

(2)

E.,

mathematical terms, Uke those of bodies of revolution or thin, deep planks, theoretical hydrodynamics in its present stage of development offers little that is of practical value to the ship designer or even to the flow analyst. There are definite indications, however, that the theoretical work on wavemaking resistance and on analytic ship-wave relations, described in Chap. 50, may in time lead to reasonable in

convenient

and

its

its

local direction

lished

der

illustrating,

1952, pp. 14-15].

by

Horn ["Theorie des Schiffes," Handbuch und Technischen Mechanik, 1930, Vol. V; reproduced in RPSS, 1948, F.

Physikalischen

Leipzig, p. 15].

Three-dimensional ship having a lenticular form of waterplane, developed by D. W. Taylor [INA, 1895, Vol. 36, Fig. 7, PI. XVI]. Reproduced later

(f)

in

S and P, on p.

1933, Fig. 7 on p. 4,

Fig. 7

and S and P, 1943,

6.

Three-dimensional model of a merchant ship of normal form, on which local pressure measurements were made by W. Laute ["Untersuchungen iiber Druck-

(g)

und

an einem Schiffsmodell Flow and Pressure on a Ship

Stromungsverlauf

(Investigations of

TMB

Model)," STG, 1933, Vol. 34, pp. 402-460; Mar 1939]. There is a bibliography of 19 items at the end of this paper; some of them are quoted here. Eggert, E. F., "Form Resistance Experiments," SNAME, 1935, pp. 139-150 Eggert, E. F., "Further Form Resistance Experiments," SNAME, 1939, pp. 303-330; abstracted in SBMEB, Apr 1940, pp. 162-164. Simultaneous pressure measurements were made with a multitude of orifices in the hull of a battleship model having a very large bulb bow. Transl. 53,

(h)

(1)

literature.

Diagrams

2-diml ships generated

Complete 2-diml ship with waterlines generated by bow and stern line sources in a uniform stream. Curves of, Ap and At/ along the ship axis are pub-

(e)

surface configura-

below the surface. Until that time comes the marine architect has recourse only to non-classified data available at testing establishments and in the technical tion

the streamlines at

TMB

May

Transl. 48,

predictions of the characteristics of the flow sur-

rounding a ship, other than

for

in a uniform stream. Curves of velocity and velocity head on a basis of ship distance along the axis are published by H. Fottinger [STG, 1924, Vol. 25, pp. 306-307;

of

Pressure Distribution 42.10 Velocity and Around Schematic Ship Forms. For the determination of velocity and pressure around ship forms whose shapes do not lend themselves to expression

bow

Bows and forward shoulders of by line sources (and sinks)

(d)

Ward, K.

the

increasing lateral distance from the form.

references

pertain to this work: (1)

47

x-distance from

Stevens

the

for simple ship forms,

the changes in and distribution of velocity or pressure, or both, are to be found in the papers listed hereunder.

Methods

References which illustrate flow

for determining the velocity at

patterns as well as velocity and pressure distri-

point in the potential

bution are duplicated from earlier sections of the

ship form are described by:

present chapter: (a)

(b)

Two-dimensional ships having lenticular forms of waterhne [Taylor, D. W., INA, 1894, Vol. 35, Figs. 24 and 25 on PI. LXXV]. Adaptations of these original diagrams are to be found in S and P, 1933, p. 4 and in S and P, 1943, p. 6. In the original diagrams the plots are in terms of pressure heads for fixed speeds, on a basis of distance along and beyond the ship axis. Five 2-diml forebodies of ship-shaped stream forms, with waterlines delineated by the use of line sources and sinks in a uniform stream, are given by W. McEntee [SNAME, 1909, Vol. 17, pp. 185-187 and Figs. 5 and 6, Pis. 114, 115]. These figures

embody curves and (c)

A

of velocity ratio

(f/co+

AC/)/C/„,

of pressure head.

any

around a schematic

1894, Vol. 35, pp. 396-399 "Die Verteilung der Verdrangungs Stromung neben der Schiffswand (The Distribution of the Displacement (potential) Flow Around the

(1)

Taylor, D. W.,

(2)

Lerbs, H.

W.

INA,

E.,

Hull of a Ship)," Transl. 85,

Feb

WRH,

7 Jul 1928,

Both these methods require rather cations

Method Method

of

the

p.

263;

TMB

1944.

actual

drastic simplifi-

conditions

for

a

ship.

2-diml flow throughout. (2) requires that the ship form be considered as a body of revolution generated by multiple sources and sinks, having a lateral plane (1)

calls

for

corresponding to the ship waterplane. Neither of wave formation at the

method takes account

flow diagram for a 2-diml ship-shaped form midway between two walls, with an ideal liquid streaming is given by G. S. Baker and J. L. Kent [INA, 1913, Vol. 55, Part II, Fig. 5, PI. IV]. It is supple-

by,

mented by curves

field

of

pressure

coefficients

with

boundary and other factors. S. Yokota, T. Yamamoto, A. Shigemitsu, and Togino describe the "Pressure Distribution over

surface, displacement thickness of the layer, possible separation zones,

S.

IIM)R()|)N \ WIK.S IN Mill'

•J8

the Surfaoc of the Ship ami

its

mi lu^isi-

1;iT«mI

anco" ill Paper 789, presented before the World Engineering Congress in Tokyo in 1929. The complete paper is published in the Proceedings of this Congress, Vol. XXIX, Part 1, issued in Tokyo in 1931. The text in question is found on pages 293-318; Figs. 1 througli 30, accompanying the paper, are published on pages 319-341. These experimenters rneasureil the distribution of pressure on tlie Inill and the magnitude of the thrust at the tiirust bearing on a self-propelled steel steam launch having a length between perpendiculars of 39.37 ft, an extreme beam of 9.79 ft, and a depth of 5.7-i ft. The draft was about 3.99 ft, the trim was zero, and the depth of water for the test with the underwater propeller varied from 12.8 ft to 13.8 ft.

The well

total

number

distributed

of pressure orifices

was

DKSIGN

the

bai>is

Srr. 12.11

by conformal transformation on

HMilts, dirive
that the flow leaves the trailing edges

of the plates tangentiallj-, are

and

"Cavitation

Forms

Pressure

shown

Yaw"

at Zero Angle of

in their

paper

Head

Distribution:

[State Univ. of

Iowa, Studies in Eng'g., Bull. 32, 1948, pp. 2C-28).

These data, supplemented by

McXown

J. S.

iticluded angles of the order of those

on actual ships, are diagrammed

for

encountered Fig.

in

42. G.

289,

over the entire length of the

Each orifice had a diameter of 1 mm and was connected by flexible tubing to one glass tube of a multiple-tube manometer which was photographed during the tests. However, it was found that those orifices lying above and in the vicinity of the actual wave profile when underway could not be used. The speed of the launch was measured bj' a launch.

(0.04 in),

10

pressure speed log in the form of a standard pitot

tube mounted forward of the bow, with 2.23 ft below the at-rest waterline ft

and about 2.83

Kio.

The launch could be driven by screw

Q8

a?

0.6

05

a^

Qz

as

ai

Orapiis of Pressure Coefficient for Fi.ow Ai-ONO A Two-Dimensional

12.0

luiOAi, I,ujun>

forward of the stem. its

\'i;e

own

propeller

Entii.\nce

single,

underwater propeller could be removed and the launch be pushed by an engine-driven airscrew mounted above the deck. A d^'iiamometer served to record 3-l)laded

0.9

its orifice

the

or

the thrust in each case.

The

varialiuii

A/j


iVdiii

the vertex aft serves

the forward portion of the entrance of a simple ship,

Attempts were made to photograph the wave

ol'

as an indication of the pressure distribution along

It

is

about as

far aft as the

forward neutral point.

expected that these data

may

eventually

profile

be combined with others, possibly those derived

the hull.

from the Guilioton method, for a prediction or determination of the pressure distribution along the 2-(linil waterline area of a ship hull of normal

from another boat running alongside but the actual wave-surface inter.section at the IniU was partly oiwcured by the wave crests beyond

The wave

profiles given in the report are

thase recorded in a model basin on a one-third

model of the launch. Tables accompanying the

report

give

the

individual pressure readings for a scries of several Hpeed.s.

42.11

Pressure

Entrance.

The

flow along

two

Distribution

pre.s.sure

flat plates,

Along

coeflicients

for

a

Vee

2-diml

disposed .s3'mmetrically

a stream, like those on each side stem of a shij), have been calculated an
of the

design.

This

scale

i)roblem

Thomson (TH,

(rcaU'd

is

iiy

M.

.Milne-

who

obtains

L.

1950, pp. 309-310),

an exi)rcssion for the drag on the pair of plates, with a cavity behind them. H. I.anib [HD, 194'), l)p.

104-10")) describes the analytic solutions of

Rethy and

HobylelT, of 1879-1881, and gives a

convenient table of pressure ratios for this system for

entrance slopes from

42.12

Use

Flow Studies.

of

In 170

dcj:;.

Doubly Refracting Solutions I<\'

ii

lOMiiiiiiatinn

of

for

]>oiari/,(Ml

POTENTIAL-FLOW PATTERNS

Sec. 42.13

and doubly refracting colloidal solutions, mentioned in Sec. 5.6, it is possible to observe certain interesting and useful types of flow phenomena. The solution most commonly used in the past has been water with a finely ground light

49

equipotential hues everywhere at right angles.

Diagram 2

of Fig. 42.

H

shows how

this

method

used to trace the streamlines directly. This is accomplished by passing the current across the is

1948, p. 52].

and shaping the body out of a conducting rather than a non-conducting material. Three-dimensional axisymmetric flow is repre-

Report 617, issued in March 1952, goes into the fundamentals as well

sented by using a tank having a cross section corresponding to one sector of the axisymmetric

as the procedure. In this report there are 45 references on the subject.

flow

clay called bentonite; the procedure briefly

by C. H. Hancock [SNAME,

TMB

B. Rosenberg, in

One

described

is

listed

of these references, plus three others not

Dewey, Davis

R., II, "Visual Studies of Fluid

MIT, (2)

Chem.

a narrow sector cut out of a log. illustrates such an arrange-

3 of Fig. 42.

H

ment, with the current passed in the direction of flow and the body a nonconductor.

Flow

Patterns Resulting from Streaming Double Refraction," Dr. of Sci. Thesis, Dept. of

field, like

Diagram

in the hst, are given here: (1)

flow, as it were,

[Electrodes

Eng'g.,

1941

Takahashi,

Double

W.

and Rawlins, T. E., "The Streaming of Tobacco Mosaic Virus,"

N.,

Refraction

Science, 1937, Vol. 85, pp. 103-104 (3)

Flow

Ullyott, Phillip, "Investigation of

Use

Pento.xide," Trans.

A

ASME, Apr

of 23 references

list

is

F. N., Garber, H.

(4) Peebles,

by Vanadium

in Liquids

of Birefringent, Colloidal Solutions of

1947, pp. 245-251.

given on pp. 248-249. J., and Jury, S. H., "Pre-

liminary Studies of Flow

Phenomena

Doubly Refractive Liquid,"

[Third

Utilizing a

Midwestern

Conf. on Fluid Mech., Univ. of Minn., Jun 1953, pp. 441-454]. These authors describe similar tests

made

with an organic dye. On pp. 26 references on this subject, Dewey, Ullyott, and Rosenberg

successfully

451-452 they including

list

the

references mentioned previously.

Delineation of Flow Patterns by Electric

42.13

The

Analogy. Sec.

2.13

story

discusses

on velocity potential in rather

briefly

between velocity potential and

Diagram

1

of Fig.

the parallel

electric potential.

2.P illustrates in schematic

fashion the use of an electrolytic tank for deUneat-

ing the equipotential Unes around any

or

surface in 2-diml streamline flow.

of

Fig. 42.

H indicates

body Diagram 1

the essentials of the setup for

delineating the flow around a 2-diml lenticular shape, utilizing a

and

weak liquid

direct current passing

body

of

electrolyte

between the rows

electrodes at the ends of the tank. If the latter of area sufficiently large

compared to that

body around which the flow

is

of is

of the

being studied,

it is

possible to replace the separate electrodes, con-

nected to resistances so as to pass equal amounts of current,

by

single-plate electrodes.

equipotential lines are delineated

When

the

by the probe

method it is necessary to sketch in the streamUnes by hand, utilizing the principles of the flow net. This means that the streamlines must cross the

Broken Lines ore \ True Equipotential Lines for Flow from Right

to

Left

MYDRODYNAMK-S

50

opposite plato plus that being fed into the foil, between the plates. In diagram 4 of Fig. 42. H, traced from one published by H. Fottingcr [STG, 1924, Fig. 43, p. 338], the

foil

IN SHIP

amount

auxiliary direct current of the proper

done by connecting it to the source that supplies the row of positive electrodes, and interposing a variable is

fed into the body. This

easily

is

The

resistance in the circuit of the body.

(0)

current

from the botly flows in the manner shown toward the row of negative electrodes. It pushes aside, as it were, the current paths from the row of positive electrodes. This setup produces equi-

now

electrolytic-tank technique has

The authors go

give

In the same volume, in a paper by iRonet, Plate 3 on p. 551, there

(7)

unearthed, in generally chronological order, and

Comments are appended

to

some

by

himself.

of the references.

42.14 Bibliography on the Electric Analogy for Flow Patterns. In tlii.s section there arc listed a number of the principal references to the rather extensive literature on the employment of the electric

(S)

(9)

analogy for delineating streamline, equi-

potential,

and other flow patterns.

E. F., "An Electrical Method of Tracing Streamlines for the Two-Dimensional Motion of a Perfect Fluid," Phil. MaR., Sep 1924, Vol. 48, pp. al.so

ARC,

R

M

and

Aero., 1943 (10)

905, 1924

M

1195,

(2h) Taylor, O.

a

F.,

I.,

"The Flow Round a Body MovinR Fluid,"

Pror. Third

Appl. Mcch., Stockholm, 1930, Vol. cap. pp. (3)

Koch,

J.

I,

in

(11)

ConR. pp. 203 275,

"Fine Expcrimcntcllo Methotic zur Masse dcs Mit-

Wasscrs Dei SchilTsschwingunRcn {Exfwrimcntjil Metho
(12)

schwinRenden

Maw)

for

Cjsrillations

of

Ships),"

1033, Vol. IV, Part 2, pp. 103-109;

225 of (4)

May

lnR.-.\rchiv,

TMH

Transl.

10-19

rh6o61ectrique do

dv*

problemcs


propulsive

rhf'liie

grilles

ind^fmics de prolils quclconquea

(On a Method of Study of llnderined Flow Nets Around any Profde)," Cong. Nat. Aviat. Franfftise, Apr 1945 (13) Malavard, L., "Application afrodynamique de ejdcul oxp^rimontal tion

of

analoRique

ExiHirinientid

(.\erodynamic .\nal
Applica-

t'alrulalions),"

Cong. Nat. Aviat. Franc^aiw, Apr 1945

dyiinmic (A|iplicatiun of Eleclriral AnuloRicji to

Some Ilydrodynaniic ProWcms),"

solution

(On a Rheo-Electric Method of Solution of ScrewPropeller Problema)," Comptcs-Rcndua, Acad. Sci., Paris, Sep 1914 Malavard, L., and Sicstrunck, R., "Sur unc melhodo dY-tude des

Malavard, I.., "Application dea analogies ^Icctriquea h lu iHihitiun do (|Uclr|u<-fl prold^mes dc I'liydrothe Solution of

la

.Application to the

<''lcrlri
205-272 J.,

"Sur

Conformal Representation Theory of Wing Profiles)," Compte.s-Rendus, .\cad. Sci., Paris, Jan 1944 Sicstninck, R., "Sur un mode de solution rhfo-

and

Int.

Bcxtimmung der Reduziertcn

L.,

Solulioii of Questions of

AuR 1928

Comprc-f-silile

Malavard,

questions dc representation conforme et application ,^ la th^'oric des prolils d'ailcs (On the Rhco-Electric

'Troblcma of (2a) Taylor, G. I., Flow in Compressible Fluids," Proc. Roy. Soc, Ix)ndon, Scries A, 1928, Vol. 121; also ARC, R and

and Sharman, C.

Malavard, L., "fitude de quelque probl6mes reU'vant de la thforie dcs ailcs. .\pplication ii Icur solution de la mcthode rh6o61cctrique (Study of Problems Relevant to the Theory of Wings. Application of (he Rheo-Electric Method to Their Solution)," Publ. Sci. et Tech., Min. de I'Air, Paris, No. 153, 1939 Peres, J., and Malavard, L., "Rlieographic and Rheometric Analog Methods," (in French), Bull. Soc. Fr. Elec, 1939, Vol. 8, pp. 715-744 Malavard, L., and P^ri^s, J., "Tables numfiriques pour Ic caloul de la rtpartition des charges aCro(lynumiqucs sur I'envcrRurc d'uiie aile (Numerical Tables for the Calculation of the Distribution of .\crodynamic I^oada On the Span of a Wing)," Tech. Rep. 9, Group. Frangais pour les Rtcherches

(1) Relf,

535-539; sec

shown a group of equiRankine ellipsoid.

is

potcntial spots for a 3-diml

a hst of the principal references so far

leave the reader to further study

into the question of the use of

circulation.

ex-

panded and developed to the point where it needs its own book. All that can be done here is to

No. 57,

the electrolytic tank for flow problems involving

body and a streamline flow from Figs. 14. E and 14. F.

flow around the

The

Paris,

"D6tennination dcs pointcs do tension dans lea arbrca de revolution sourais ii torsion au moyen d'un module 6lcctrique (Determination of Tcn.sile Stress in RevolvinR Shii/ts under a Torsional Load, by Means of an Electric Model)," .VTMA, 1930, Vol. 40, pp. 341-351. Thia paper illustrates and describes an electrolytic tank which is, in effect, a 3-diml affair, inasmuch as the body in the tank hits varied depths of electrolyte over it. P6r&i, J., and Malavard, L., ".\pplication du bassin flectrique i\ quelques questions de mecanique dcs fluidos (The .\pplication of Electric Flow in Liquids to Some Questions of the Mechanics of Fluids)," ATMA, 1938, Vol. 42, pp. 529-541. This paper, so far as known, is not translated into English. A number of references are listed on pp. 529, 531, G.,

and 534.

potential lines which are actually the streamlines of a combination of counter-clockwise circulatory

(he right; see

I'.Vir,

1934

small heart-shaped botly and the flow resembles (hat delineatetl for the Magnus Effect in Fig. 14. E.

An

Sec. 42.14

Publ. Sci. et Tech., Min. de (5) Salct,

replaced by a

i.s

DESIGN

(14)

.Malavard,

L.,

"Calculatcur

d'aiica

ul

rOscau

do

POTENTIAL-FLOW PATTERNS

Sec. 42.14 resistances

pouvant

lineaire

certaines questions, tions of Linear

le

remplacer,

dans

Analogy

(22) Surugue, J.,

Paris, Jul 1945 (15) Siestrunck, R., essais

Laboratory),"

"Sur

d'hfelices

de parois dans

les

(On Wall-Effect Corrections

in

les corrections

Sep 1945 Siestrunck, R., "Sur le calcul des hfilices ventilateurs (On the Calculation of Propeller-Type Fans)," Comptes-Rendus, Acad. Sci., Paris, Sep 1945 Peres, J., and Malavard, L., "Sur la determination des corrections de soufHerie (On the Determination of Blowing-Pressure Corrections)," Comptes-Rendus, Acad. Sci., Paris, Sep 1945 Marchet, P., "Determination des lignes de jet dans

(16)

(17)

(18)

les mouvements plans et de revolution (Determination of Streamlines in Two- and ThreeDimensional Flow)," Probleme D359A, Travaux du Laboratoire de Calcul Experimental Analogique, under the direction of L. Malavard (19) Peres, J., Malavard, L., and Romani, L., "Problemes non lineaires de la theorie de I'aile. Application k la determination du maximum de portance (Non-Linear Problems of the Theory of Wings. Application to the Determination of Maximum Load)," Rep. Tech. Group. Frangais pour les Recherches Aero. (20) Malavard, L., "The Use of Rheo-Electrical Analogies in Certain Aerodynamic Problems," Jour. Roy. Aero. Soc, Sep 1947, Vol. 51, No. 441, pp. 739-756. This is an excellent paper, with many photographs and diagrams illustrating the technique and the

Hubbard,

(24)

(25)

A

P.

G.,

"Application

of

the

Electrical

of

CNRS,

Paris,

1950,

II.

concise

but

comprehensive

treatment

of

Methods" is given by T. J. Higgins, covering many methods other than the "Electroanalogic

electrical-tank

analogue described

Mech. Rev., Jan 1956, pp.

1-4].

here

[Appl.

Part I of this

paper, devoted to "Solution of Electrical Prob-

lems

by Continuous-Type Conductive Proce-

its end a huge array of 111 few of which are to be found in the preceding list. Part II of this paper, entitled "Solution of Continuum-Mechanics Problem by Continuous-Type Conductive Procedures," is supplemented by an even more massive list of 203 references, some of which are also to be found

dures," carries at

references, a

in the preceding list [Appl.

results.

(21)

(23)

edition

Chap. 15 contains a discussion by L. Malavard on "Les Techniques des Analogies Electriques (Electric Analogy Technique)." Rouse, H., EH, 1950, pp. 20-22 and Figs. 17, 18 Markland, E., and Hay, N., "The Potential Flow Tank," Engineering, London, 7 Mar 1952, pp. 292-294 Borden, A., Shelton, G. L., Jr., and Ball, W. E., Jr., "An Electrolytic Tank Developed for Obtaining Velocity and Pressure Distributions About Hydrodynamic Forms," TMB Rep. 824, Apr 1953. Vol.

Sorew-Propeller Tests)," Comptes-Rendus, Acad. Sci., Paris,

Sci.

Inst.,

Resistances

which can be Performed, in Certain Cases, in the Electrolytic Tank)," Comptes-Rendus, Acad. Sci.,

Mechanics Research," Rev.

Nov 1949, Vol. 20, pp. 802-807; also State Univ. Iowa, Reprints in Eng'g., Reprint 82 "Techniques gen^rales du laboratoire de physique (General Techniques of the Physics

bassin 61ectrique (Calcula-

Wing and Network

51

in Fluid

pp. 49-55].

Mech. Rev., Feb 1956,

cuAPiER

i:;

Delineation of Source-Sink Flow DiaoTams 43 1 43.2

General

.

52

Two-Uimensional StreamForm Contours and Streamlines Around a Single Source in a Stream Graphic Construction of a Two-Diniensional Flow Pattern .\round a Source and a Sink Graphic Determination of Velocity .\round Two-Dimensional Stream Forms .... Laying Out the Two- Dimensional Flow Pattern .\round Two Pairs of Sources and Sinks in a Uniform Stream The Const ruct ion of Two-Dimensional Stream Forms and Stream Patterns from Line Sources and Sinks Flow Pattern for IheTwo-Dimensioniil Doublet and the Circular Stream Form Delineation

43.3 43.4 43.5

43 6 .

43.7

.

43.1

43. S

of

General.

.

.

43.9 52

43.10 51

43.11

57 43. 12

Graphic Construction of Three-Dimensional

Stream Forms and Flow Patterns .... of Stream Forms I'roduced by Sources and Sinks Source-Sink Flow Patterns by Colored Liquid and Electric .\nalog_v Formulas for the Calculation of Stream-Form Shapes and the Flow Patterns .\round Them The Forces E.xcrtcd by or on Bodies Around Sources and Sinks in a Stream; Lagally's Partial Bibliography on Sources

43.14

Selected References on Lagally's

and Their

70

who

architect

source-sink

and other features

Theorem

of

illustrate

forms

stream

Frequent application

of

know how

and

flow

"know how"

this

knowledge

uniform and of radial flow. The present chapter contains instructions for drawing manj' kinds of stream forms and for delineating graphically the

Form Contours and Streamlines Around

there are a few typical formulas for calculating

some simple stream forms them graphically. Both sets how these constructions and

coordinates of

rather than plotting

draw will

greatly expand the usefulness of source-sink or radial-flow

flow patterns around them. In Sees. 41.8 and 41.9

to

patterns.

a variety of simple stream forms resulting from a graphic combination of the stream functions of

the

71

.

knowledge of hydro-

expects a

the source and sink, the radial stream function

3.M through 3.P

and Sinks

01

Sees. 3.8 through 3. L3 contain

potential,

67

.\pplication

dj'namics to serve him should

and velocity

G7

08

43.13

a description and discussion of radial flow and

source-sink flow. Figs.

fi7

Theorem

58

59

C2

\'ariety

43.2

in his

work.

Delineation of Two-Dimensional Streama Single

Source in a Stream. Notwithstanding that for every source there must theoretically be a corresponding sink of ecjual strength, the plotting of the flow around a single 2-diml source in a uniform stream is first described as a preliminary to subsequent operations. For the time being it may be assumed that the companion sink

formulas lead to a determination of the velocities and pressures around the forms. It has been true in the past, and perhaps may be for some time to come, that the stream forms

lies at an downstream. The plotting method is a single-step combination of the "radial" stream functions for the soiu'ce and the "parallel" functions for the uniform stream.

and streamline patterns created found and will And infrctjuent

stream-f miction lines for the source. It

of

sections

tell

in this u.se

in

infinite distance

Lay down

way have practical

naval architecture, as contrasted to their frctiuent occurrence in analytic investigations and their

first

a set of radial equidiflerent

con-

have two of these radial lines lie on the customary and //-axes, and to jilace the imiform stream

use in the development of underwater non-ship forms. Nevertheless, a knowledge of the mechanics

X-

drawing source-sink flow patterns and some experience in drawing them gives one an insight into and a working knowledge of certain phases of hydro<Jyiiainics that can not be obtained in any other way. A parallel ca.se is experience in the

(juadrants

^ao(p«i))

coiutruclion of flow neta. Literally, the marine

set of positive numlicr.s, in

of

is

venient, for reasons which appear presently, to

parallel to the z-axis, as in Fig. 43. .V.

around

source

the

divided into a suitable

number

are

The

then

four

each

of equal arcs

the remaining radial streani-function lines.

by

The

stream functions from tht; source, identified aa then marked with any convenient 'ii"*-'

tliis

cxse

1

through 28,

DELINEATION OF SOURCE SINK DIAGRAMS

Sec. 43.2

Unifoi'm-

-2.0-

flow stream function

_|g_

by the

53

vectors beyond B. It then goes

full-line

through a gap where the algebraic sum of the and uniform-stream functions is equal to

radial

—4. Such a gap 4'so

= +4

is

that portion of the radial hne

represented by the segment BF, lying

between the parallel horizontal lines whose stream functions 4/u are —4 and —8, respectively.

The Reference avis

+oo

original four units of liquid in the parallel

up through this gap and cross the line BF. At the point F, therefore, the stream function ^s of the combined flow is equal to —4. The four units of liquid in the radial flow turn upward flow turn

Fig. 43. a

Uniform-Flow and Radial-Flow Stream Functions for a 2-Diml Soubce

starting with at the positive x-axis and going around both ways to 32 at the negative x-axis. Only those hnes above the a;-axis are shown in

inside the point B.

the figure.

barrier at F, turn

draw the stream comb

Off to the right

for the

The second

=

\pu

—4^ and

the point J

uniform flow and assign suitable equidifferent values, marked from i/'^ = through ^c = ~20 in Fig. 43. A. The negative signs for the uniform

four units of uniform flow, between

~8, now approaching a new up between F and J, whereupon on the new streamline ^s = —8.

ypu =^

lies

the procedure just described

If

followed for

is

flow signify liquid moving opposite to the positive

The stream comb

direction of the .T-axis.

extended

the

to

to

left

form

the

43. B.

straight-line portions of Fig.

is

then

horizontal

In this and

succeeding layouts the lower half of the diagram, that

the mirror image of the upper half,

is,

is

omitted to save space.

The horizontal hne extending from — » through the source to

+

<»

,

coinciding with the

a;-axis,

Combination of Uniform Flow With Radial Flow Feom a 2-Diml Source

Fig. 43.B

represents the trace of the reference plane for the

flow diagram to be constructed. If four radial

vectors are

drawn from SO, between the

lines

=

^ and 4/so = +4, they represent schematically the four units of the quantity rate of 4'so

flow from the source in that sector. If four parallel vectors

drawn between the trace of the and the horizontal - 4, they represent in the same manner

are

reference plane, in the x-axis, line

^p

=

the quantity rate of flow in that part of the

stream. These eight vectors are drawn in broken lines in the figure.

The two

which the

flows, in

quantity rates are each numerically equal to 4, buck each other along the region AB in Fig. 43. B.

At

the intersection

and the horizontal

B

of the radial line

line

stream function value

moment

^^

is

= —4,

zero.

the resultant

Assuming

that the reference plane

is

= +4

^so

for the

impenetrable,

the uniform flow between the x-axis and

^pu

= ~^

There is estabhshed a line and B, across which no liquid

deflected upward.

is

^s

=

between

A

passes.

The

liquid in the uniform stream

tity rate equal to

\}/v

,

in

quan-

—4, turns upward as indicated

groups of eight liquid units instead of four, a

C is = +8

point

established

and ^u

at

the

intersection

of

= ~8

where the resultant stream function value \{/s is again zero. There is also found a point G where the stream function of a new series is lAs = —4 and a point K where ^s = —8. i^so

A

whole pattern of intersections

is

thus quickly

determined, at which the stream functions

xf/g

of

the third series are equal to the algebraic sums of those of the

example, at 4'so

At

E

second and the it is

= +16, so this = —20 and

L, xpu

point on the streamhne

The various

first

found that i/'p point is on the 4'so 4's

= +12, = —8.

series.

For

= —16 and line \ps = 0. so this is a

points so determined are

all inter-

sections of radial stream-function lines having

values greater than the uniform stream-function lines by increments equal to the value of the new stream function 4's This means that the parallel stream flow that lay below 4'u = —4 at infinity

IIVDRODVN

51

\MK:.S IN SUIT DI-SIGN

now flows across the radial sogincnls BF, CG, DH, and so on. A fair line joining the points

E becomes the streamline or bound= 0. Another line through F, G, H,

B, C, D, and ary where 4^3

and corresponding points becomes the streamline where 4's = —4. A line joining J, K, L becomes the streamline yps = —8. If the same construction is followed inside the line

BODE,

tlie

= — 4 and ^so = +8, where= -fSplusi^y = —4 becomes^/ = -|-4. at N, ipso = +12 and fpu = —8, = +4. A streamline representing

point

M, where

upon

(^Ao

Similarly,

whence

=

^/

radial flow preponderates at the ^t;

rff,

4, for inlernal flow, is

source through

M, N,

series of intersections.

then drawn from the

P, and a corresponding

The

four radial broken-line

vectors, each representing unitj' quantity rate of

below the

Uquiil, originally lying

turn upward and to the tlie

^i

boundary

=

BCDE

left

line \pso

= +4,

as they pass between

and the

inside streamline

4.

from the source SO and boundary BCDE freezes into ice, or is otherwise suddenly solidified, the flow outside that boundary remains exactly If all the lii|uid issuing

doubling

back

inside

the

the same as defined by the streamlines of the

^s-system. Bj' following this extremely simple

and straight-

forward construction in both quadrants above the reference plane, and then adding its mirror image

bounding surface ABODE ... is extended to any desired limit downstream. All the streamlines around it can be sketched through the respective series of intersections by the process of adding the stream functions algebraically and joining the points having equal ^s values, as in Fig. 43. B. As few or as many radial and parallel stream function Unes are drawn as may be desired. The more are drawn, the more intersections arc found and the more accurately is the body defined and the resulting stream pattern delineated. Filling in streambelow

that

the

plane,

ovoid-sliaped

function lines at intervals of unit quantity rate in Fig. 43.

B

instead of in increments of four units

would give sixteen time^ as many intersections and four tim&s as

many

streamlines as are

shown

there.

The width

is

chosen with a radial stream function

at 90 deg,

of

the is

ovoid-shaped

boundary

equal to the uniform-stream-

function position for a value corresponding to the radial-.streatn-function

number

at

'JO

deg from the

Hlream direction. Therefore, to make the solid boun
of

in.stoad

=

^.^o

-|-1G

= +8

\l/so

as shown.

Similarly, the uniform-fiow stream function ^j; if

only half as wide. It in

,

given values twice as great, produces a body

and

this

other

is

to be noted particularly,

applications

suh-socjuenlly

described, that the velocity of the uniform flow

can be increased without changing the shape of the form represented by velocitj' is increased

=

^.s

in

if

same

the

the radial-flow ratio.

equivalent to multiplying or dividing functions in Fig. 43. B by the

same

all

This

is

stream

factor; the

form contour and the various streamlines in the diagram remain the same. The solid boundarj' around a single source in a uniform stream in 2-diml flow continues to widen with distance downstream so that it is of limited

application

practical

to

ship

design.

However, Sees. 41.9 and 07. 7 tell how a 3-diml single source in a uniform stream may be used to delineate an underwater bulb shape for the bow of a ship. The solid boundary' around a source and adjacent sink in uniform flow is closed and of oval shape, resembling some parts of a ship. Because of the ea.se with which 2-diml streamlines are constructed around it, tliis bodj' serves well as a simple ship form, by which to explain and depict many kinds of flow phenomena. Graphic Construction of a Two-Dimen-

43.3

Flow Pattern Around a Source and a Sink. The construction of a solid boundary surface and a streamline diagram for a 2-diml source and a sional

2-diml sink placed in a uniform stream involves

one more step than the procedure described for a single source. It

is

convenient, as before, to

They are when once

take up each of the steps separately. simple

graphic

operations

which,

and rapidly performed. line from — oo to -|- <» in Fig. 43. C, pa.ssing through the source and the sink and coinciding with the x-axis, represent the learned, are easily

Let the horizontal

trace of the reference plane for the 2-iliml uniform-

stream flow. The tracing

midway between the Using separate sheets of

y-ax'is is

source and the sink.

suitable

transparent

down orthogonal axes

in the center

cloth,

material, lay

opposite the source

Srr. 43.3

or

other

of each sheet. In each of the four ((uadrants

an equal number of uniformly

draw

sijaceil radial lines,

representing equidifl'erent radial stream functions. Series of

numbers

difi"ering

by 2 or 4 are used

generally in the present ch.'ipter but any series licrmissible.

is

Sec.

DELINEATION OF SOURCE-SINK DIAGRAMS

433

Fig. 43.C

Radial Stream Functions foe a 2-Diml Source-Sink Pair and the Resultant Stream Functions

Leave a clear space at the center of each sheet where the lines would otherwise be crowded together.

55

One way

is

to use large circles for the

source and sink. Extend the radial lines as far

The

as the drawing area permits or requires.

^/so-

from the source is designated as the or ^o-system; that from the sink as the

^SK-

or

pattern representing the liquid

the

it is

more

convenient to start from the axis between the source and sink instead of from the axis stretching to the right from the source.

radial flow

Number

movement from

the source to the sink. For this purpose

Considering four units

from the source

of

in the sector

liquid emanating between the hori-

around both source and sink, starting with zero at the reference Hne in the positive x-axis on the right and increasing numerically hoth ways to the negative x-axis. This applies both to the diagram shown and its mirror image. As previously men-

zontal reference line and the radial- stream-function hne \po = +28, represented by the four brokenUne vectors, these units must enter the sink between the reference line and the radial line ^K = —4. Where the stream-function hne fo = +28 crosses the hne \pK = —4, at the point

tioned, any convenient set of equidifferent numerical values may represent the outflowing

i^c

\^K-system.

radial

lines

and inflowing stream functions, but the sets must be identical. The lines i^o = and ^^ = — both he over the reference trace and point toward the source of the uniform-stream flow and opposite to its velocity vectors. The hnes radiating from the source are marked with positive signs to indicate positive stream functions, while those

pointing toward the sink are marked with negative signs.

With the reference-plane trace as a base, superpose these separate radial-flow diagrams with their

centers

at the selected

positions. Fasten the source

source and sink

and sink sheets

in

then over both diagrams lay a third sheet paper or cloth, or other transparent material, upon which the straight reference line

Y, the value of the resultant^ stream function

= +28 (-4) = +24. The numerical stream-function values of the fc system are distinguished by single bars over the numerals. However, the four liquid units flowing out

of the

source and into the sink, corresponding to the

curved vectors shown, actually pass between the point Z, where rf/c = +28, and the fuU-hne

Whereas the streamline \pc = +28 tangent to the radial line ^o = +28 at the source and to ^^ = — 4 at the sink, this streamhne moves downward or inward, away from those reference trace.

is

hnes, as the distance increases.

through

The

place,

of tracing

+

along

from the source or sink

In other words,

Y it

instead

of

passing

passes through Z.

intersections of other parts of radial Hnes

a

perpendicular

to

the

reference

hne,

is

midway between the source and smk, occur at the points m^ked_Y, X, and_W, where the values

as the straight-line portions of Fig. 43. C.

other

drawn and the source-sink positions are marked. The hnes visible through the top sheet then appear

The next

step

is

the construction of the flow

of

if/c

^c are +24, +20, and +16, respectively. Two points, and N, on the streamline = +16, are given by the intersection of

M

1IM)K()I)\

56

.\

\.\IK:s IN Mill'

^o = +20 plus \fiK = — t'<|ual.s 4>r = +><», as well as bv 4'o = +'-S plus ^^ = —12 equals = +1G ^f. = +1(5. These permit the streamline ^c J

to be drawn, rememheriiip that, like the descrilMxl,

it is

tangent to

at the source and the line ^k

= —16

How between

Actually, for 2-iliml

first

radial linc^o

(lie

one

= +1C

at the sink.

a source-sink

pair, all the streamlines of the

^c series are drcics which pass through the source and sink centers. These circles have a radius of s cosec 0(thcta), where s is the half-tlistaiice between source and is the angle between (1) the radial sink, and stream function at the sourer for which the circle is drawn and (2) the reference axis. Considering the radial source streamline or 90 deg and_cosec 6

=

ypo

= +1G,

is ir/2

the radius of the circle

\;

^c = +16 is therefore s, half the distance from the source to the sink. This particular circle has its center on the reference line and is tangent to the radial strcamhncs if/o — +H> and

for

^K = —16 at the source-sink axis. When cxteiidetl below the source-sink axis in the diagraraj_thiri n circle becomes the stream function ^^ = -flfi •

that side. Similarlj',

all

other circles extended

below the axis become what might be termed supplementary streamlines in that region. For example, the streamline ioTjpc = +4 above the reference line and tpc = +28 below it are parts of the same circle. Numerically, the stream function for these two parts of any complete circle total 32, the

same value

the source or the sink. streamlines

fall

The

as for half of either

centers of the circular

on intersections

alreadj' given liy

the radial-flow lines in the diagram, because

if

the

quadrants are divided into a whole number of

1)1

sU.\

Sec.

(jJ

always a radial stream-function from the source at right angles to another line from the sink. For example, since the circular streamline \pc = +12 is tangent to rpo = +12 at the source, its center lies on the line rpo = +28, where 12 -|- 16 (for one quadrant) = 28. On this basis, and with the additional intersections on the diagram, the remainder of the circular streamlines are drawn. AVhereas these lines are approximately equidistant from each other at the source and sink centers, they become increasingly farther apart at greater and greater distances from the source and sink, bccau.-je of the slowing down of the liquid in the widening crescent-shaped sectors. However, once drawn by subdividing each quadrant into a given number of sectors, the circular stream pattern nerer changes for any change in source-sink strength or spacing. Once carefully drawn, it can be enlarged or reduced photographicallj^ to suit the sourcesink spacing. The numbers on it are altered to sectors, there is line

.suit

the source-sink strengths.

This completes the

The second

step

source-to-sink

is

first

step in the operation.

the combination of this circular

flow

with

pattern

uniform-flow pattern parallel to plane.

The uppermost

the the

2-diml

reference

sheet of tracing cloth or

paper containing the circular-streamline pattern of the \{/c S3'stcm is now transferred and superposed

on a sheet which has parallel streamlines of the uniform flow drawn on it. Following this, the i^f/ flow is combined with the ^c flow by adding the ipc and the i^y stream functions algebraically where the strcamhncs cross each other. For example, in the right-hand portion of Fig. 43. D, \

Uiiifomi-flow

v stream

tuifclions^'^''

aurtace

Fi'i.

'l-'t.!)

Uankink. Stiikam Form and Simnoit.VDi.vo Stiikam Vuiw Uesi'i.tino Fmni Inskhtion or a Soi;k(;k-Sink 1'aiii i\ a U.\ih-oiiM Stiikam

'.J-Himi.

DELINEATION OF SOURCE-SINK DIAGRAMS

Sec. 43.4

new form

at the intersectioii_B of the circular stream-function Una ypc = +4 and the uniform-flow stream

hand, a

function Hne ^v = —4, the resultant flow is zero. Therefore B is a point on the boundary of the

The shape

Rankine body to be formed. There and corresponding point B for iZ-^ =

is

a second, at the left

At the intersections of the circles +8, +12, and 4-16 with the parallel-flow lines ^f/ = —8, —12, and —16, respectively, the pairs of points C, D, and E are found, all on the of the sink.

\pc

=

stream-form boundary. A streamline through the lettered points where yps = 0, passing through the stagnation points Q and embracing the lower or mirror image as

of the stream form is preserved while changing its velocity relative to the uniform stream by the simple expedient of increasing or decreasing all the velocities and stream functions by the same factor. The oval "ship" thus retains its

form while changing

43.4 Graphic Determination of Velocity Around Two-Dimensional Stream Forms. The magnitude and direction of the resultant velocity in the streamUne field ^s is determined in a simple

manner,

graphic

By

an oval-shaped stream form or Rankine body. The flow pattern around this body is constructed by drawing the streamlines for the functions ^s = —2, —4, —6, and so on, using the method

the separate flows

The

resulting

speed through the

its

liquid.

Rankine.

body shape and flow patterns are illustrated by the heavy lines of Fig. 43. D. Points near amidships along the body boundary are determined by drawing intermediate streamlines which are radial, circular, and parallel, or they may be determined by calculation, whichever may be found most convenient. The necessary formulas

57

as quickly sketched, using

different relative strengths for the several flows.

well as the upper half of the flow diagram, forms

described for the single source.

is

this

W.

with

originating

M.

J.

method the velocity vectors of are combined to give a resultant

The

velocity vector of the streamline flow.

inter-

between the composition of stream functions and Uquid velocities for 2-diml flow is explained in Sees. 2.11 and 2.14 and illustrated in Figs. 2.L and 2.Q of Volume I. Fig. 43. E diagrams relation

are listed in Sec. 41.8.

Flow from the source

to the sink also takes

place within the boundary of the Rankine body,

depicted by the stream-function line ^/ = +2 in the figure. This inside liquid can be considered

Diagram Illustrating Graphic Method Determining Resultant Velocities for

Fig. 43.E

and the flow neglected. The length of the oval-shaped form is partly adjusted but not wholly controlled by the spacing 2s between the source and the sink. Its length-

the graphic method for the example of Fig. 43. D,

beam

as applied to several points around the body.

as solidified

or fineness ratio

is

a function of the relative

oj'

2-DiML Flow

Take

strength of the source-sink flow and the uniform-

stream flow. The absolute largely a function of

diagram

With

is

form is the scale upon which the size

of the

laid out.

relatively simple radial-

first

the

B

body point

in Fig. 43.E.

— (7„

uniform-flow velocity vector

is

A

laid off at

OiB, parallel to the reference axis. From B a line drawn toward A, tangent to the circular or source-sink streamline of the ^c system passing is

and uniform-flow

diagrams made up beforehand on translucent or transparent material, the delineation of a stream form and its surrounding 2-diml flow pattern is a much shorter and easier task than might appear from the detailed description just given. In fact, with a httle practice, the freehand sketching of the form and the flow pattern is the work of only an hour or two. Figs. 3.0 of Sec. 3.11 in Volume I and 43. G of Sec. 43.5 are examples of this procedure. If the stream-form shape and proportions are not suitable for

the

work

in

through B. The latter is shown by the light circular arc in the diagram. From B a hne BC is drawn, tangent to the body surface at B. From Oj a line

OiA

is

drawn

parallel to the body-surface

tangent BC, cutting the hne from tangent

to

velocity

Ub

the

circular-arc

at the point

B

is

B

which

streamline.

is

The

then defined by the

vector OiA. For any point on a streamline in the field away from the body, the procedure is exactly the same, considering the streamline as the surface of a

new body.

HYDROOVNAMICS

58

When

IN SHIP DESIGN

Ub is known at a Ap is found by uniform

the resultant velocity

8olcct«l point, the corresponding

Ap =

the rclationsliips

—

0.bp{l'\

Ul) and

—

(i'g/U.Y], described previously in Sec. 41.12. Values of the pressure coefficient corresponding to various combinations of velocities squared, in English units, for liquids of any mass

^p/q

c=

(1

flow with the "circular" flow between

one source-.sink pair

axis, placed farther

INA,

Nb

point

occurs at a

represented by the vector OjN in Fig. 43. E, U,v equals in magnitude the uniform velocity — U. ,

,

By

represented by the vector OjH.

arc on 0, as a center, using the radius it

is

lies

known

striking an

0,H =

f/.

that the extremity of the vector

HM.

somewhere on the arc

It is also

,

OjN

known

The

(1)

NbL

body

at the

is

parallel

HN

which represents a portion

NflK,

circular-arc

^c-system through Nb the body boundary.

By

streamline

source-sink

a process of

,

same

strength (Rankine,

The

W. J. M.,

construction of the body

method, using a main source-sink pair, each having a total quantity rate of flow of 128 units, and an auxiliary pair, each having a flow of 32 units.

stream-flow diagram representing the

source and sink

of

the

constructed.

When drawn by

in Sec. 43.3

and

illustrated

has the appearance of diagram 2 of Fig. 43.F. Second, a stream-flow in Fig. 43. C, one-quarter of

it

the

— S2

the

of

is

method described

where that arc crosses

Half of source-alnK

— distance V'C2" System

and error a point Nb on found where the necessary

trial

the body surface

is

met [Rankine, W.

conditions are

even

shape and the flow pattern involves four steps as compared to the two of the previous section, but the procedure for each is equallj- straightforward. An example is worked out here to illustrate the

surface, at the

proper location of the neutral point Nb is parallel to a tangent to the (2) The vector arc

of a ship,

modified by the

"circular" ^ci-systcm flow between the primary

OjN

streamline-velocity vector

to the tangent

is

apart than the main pair, and

less

1870, p. 178].

First, a

that:

bow

addition of a second source-sink pair on the

having somewhat

neutral

often too blunt to represent

schematically. This bluntness

41.13, on page 27.

point in the surface where the streamline velocity

is

the no.se of a body or the

density p(rho), arc given in Table 41.c of Sec.

The forward

0.5

Sec.

stream form resulting from the combination of

M., Phil.

J.

Trans. Roy. Soc, 1871, Vol. IGl, p. 305, where Rankine calls the neutral point "the point of no disturbance of pressure"]. The U.SC of Rankinc's graphic method gives a neat solution for the conditions at the stagnation where it is known that the points Qb and Qs ,

resultant velocity surface.

function

At Qb

for

,

of

lines

body

directed normal to the

is

example, the circular-stream^c-sj'stem

the

are

directed

ahead, opposite to the uniform-flow line rpa = 0. Therefore, at this point the circular-stream velocity vector

Qb03

magnitude but

is

resultant velocity at

equal to the vector

is

of

opposite sign,

Qn

U„

in

hence the

zero.

is

At the midsection of the stream form or Rankine bfxiy, and abreast it, the grapliic method describo
uniform-flow vectors and

the

intersection

n-Hpoiifiing to

E

indetfrminate.

.\

in Fig.

13.

i.s

cor-

Laying Out the Two-Dimensional Flow Pattern Around Two Pairs of Sources and Sinks 43.5

in

a

Uniform

Stream.

The

2-diml

Rankine

Half of aourca-»ink di»tsnca *] 5,

M:ircular »tr«A
funcLOn

h

Fin.

-13.

F-"

Soi'iir-K-SiNK SriiKAMi.iNr..s

t-t>n

Two

SoUHCE-SlSK PaIIW OK DlF«:RKNT OuTPlT AND DiF>xRt.sT .VxiAL Spacing

DELINEATION OF SOURCE-SINK DIAGRAMS

Sec. 43.6

diagram representing the ^c2-systena flow between the secondary source and sink

When

the same method.

is

prepared, by

completed, one-quarter

down

the

is

special

\i/c2

diagrams must be drawn with lines sufficiently heavy to make them visible through each other and through the sheet carrying the ^cz diagram, subsequently to be placed on top of them. When the ^ci and i/'c2 diagrams of the primary and secondary

source-sink

are

flows

and

finished

superposed, with the sources and sinks at the distances Si and Sa respectively, from the origin, is

constructed by adding

the two sets of "circular" stream functions to form a composite diagram for the two pairs, called for convenience the ^C3

system. It

is

stream-function

shown by the curved broken

lines

different

such a form and the streamline pattern around it, involving as it does the six steps listed hereunder,

admittedly tedious but

These

(2) (3) (4)

it is

readily done for

the results are worth while.

if

six steps are:

Combination Combination

(5) (6)

iu

studies

Flow between primary source and sink, \(/ci Flow between secondary source and sink, if/ci Flow between tertiary source and sink, \j/c3 Combination of flows ^d and \pc2 = 4'ct

(1)

,

a third flow diagram

in

To make the bow and stern even more pointed a tertiary source-sink system may be added near the extreme ends. The graphic construction of

function values. However, both the ^ci and

it

59 diagrams

radial

positions along the source-sink axis.

appears hke diagram 1 of Fig. 43. F. It is possible to use the same basic radial diagrams for constructing tlie circular streamlines associated with the two sets of sources and sinks by assigning to them different radial streamof

inked

=

of flow

\]/c4

with flow xj/cs = 4'cs with uniform flow

of flow rpcs

iPs

Regardless of the combination of stream-function values used in this operation the ends retain

any reasonable number of sets and sinks. A solution to problem, developed by D. W. Taylor, is

some bluntness

for

or pairs of point sources

of the freehand sketch of Fig. 43. G, radiating

this

from the two sources.

described in the section to follow. It is pointed out here, as

W.

M. Rankine

J.

did in his classic treatise of 1866 on "Shipbuilding:

Theoretical and Practical," that

it is

not strictly

necessary to limit a ship curve, for analysis or design, to the contour of the Rankuie body or -64

stream form defined by the stream function = 0. Parts of the lines of ships may be represented by streamlines which lie at some distance rps

Stream function "^

-Sttejm functions

from what is considered as the solid boundary of the stream form, described in Sec. 4.2 on page 72

Jiijj

G Freehand Sketch of Source-Sink Streamlines for Two 2-Diml Source-Sink Pairs, Form of Body When Inserted in Uniform Flow, and Resultant Streamlines

of

Fig. 43.

Volume

I.

This

final step,

the i/'c3-system

in

accordance with the any stream

by a without changing the flow pattern

surface in an ideal liquid can be replaced solid surface

on the other side

As a fourth and

is

principle previously enunciated that

is

combined with the uniform flow i^crsystem to produce a stream form yj/s = 0, indicated by the heavy line of Fig. 43. G. This has definitely more pointed ends than the 2-diml body which would be produced by either primary pair alone. The exact shape of the ends of a body such as that delineated in Fig. 43. G depends upon the strengths of the secondary source and sink and the relative locations selected for them. A great variety of body shapes can be drawn in a surprisingly short time, simply by assigning different stream functions to the radial and parallel flows and changing the source-sink spacing by tacking

of

it.

The Construction of Two-Dimensional Stream Forms and Stream Patterns from Line 43.6

Sources and Sinks. It is possible to construct stream forms with the sharp ends customary in ship waterlines, and with practically any desired shape and degree of fineness or fullness, by an ingenious method devised by D. W. Taylor many years ago ["On Ship-Shaped Stream Forms," INA, 1894, pp. 385-406; "On Sohd Stream

Forms, and the Depth of Water Necessary to Avoid Abnormal Resistance of Ships," INA, 1895, pp. 234-247]. This involves the use of what are called line sources and sinks. In its simplest form this procedure embodies the

HVDROnVNAMICS

t;u

use uf n niultituile of nuinite sources and sinks, not

nt>ccs!«irily

of

all

infinitciiimal spacing,

siuno strength,

tlio

crowilixl

willi

togetlier along a

line representing the longitudinal axis of a Innly

The

or ship.

sources are groupetl along the en-

the sinks along

trance;

minute strength

the

each

of

run.

source

Despite or

sink,

IN SHIP DESIGN

Sec. -13.6

distributed along the sinks

tlistributwl

XO-part

along

the

of the line to the

t)Xi-part,

ceding.

When

the flow pattern of the resultant

the

source-sink stream function

the

bined with the uniform-flow function

is

found,

it is

com-

^t/

along

combineil strength of ench group of them along

the reference

the line

form, defined by the streamline where

[-

is finite.

—

Line

Streom

Form-^^^sr

the line

0^__l,-t-^T:urve of Strength

X,OX

DEnsTTiON Sketch kor AND Line Sink

Li.ne

Source

.

vector

perpendicular

the

to

source-sink

above the

off

A

and

all

the

line joining

curve. If

each source or sink occupies a space of line,

is

is

due_to any dx^BVljOg

5ource-intensily curve

then the total strength of all times the average

the length

OX

strength or ordinate. Similady, the total strength of all the .sinks

is

the length (JXi times the average

negative ordinate.

The line

strength of any source or sink along the

XOX, may

be a.ssigncd at

will,

upon the shape

of the Ixxly or ship

desired to form.

The only

limitation

depending which it is is

that the

area below the curve of source ordinates, in V\g. 43.11,

AXO

representing the total source output,

be ixaclbj (t/ual to the area

sink ordinates

(JDX,

,

above the

curve; of

representing the total sink

input. Otherwi.s*' there will be

some

liiiuid

lacking

and the resulting stream furni will not \)C bounded by a closed curve. In practice, when working with line .sources and sinks, it is convenient to plot a grajili of ituurcc and sink strengths as in diagram 1 of Fig. -13.1. The problem then is to find the stream function of the combined llnw from the sources or

left

,

measured counter-clockwise from the reference plane. The stream function at G due to any rfx-sink, such as at F, is — rf.r(CF)fl;, Plotting these values as a separate graph, diagram 2 of Fig. 43.1, the source stream function is laid off as the ordinate EH above E, and the sink stream function as FJ below F. Proceeding in similar fashion for all the rf.r-sources between X is

the source-sink, strength-distribution

is

the sources

G

line.

line

ordinates

dx along the

0.

.

represented by the height of a velocity

Source strengths are laid sink strengths below it.

=

'

Fig. 43.H depicts schematically such a line, marked X,OX, with a row of sources from X to O and a row of sinks from to X, The strength is

^.,-

as the trace of the reference plane,

infinitesimal (/x-source, such as at E,

Distribution

where 0^

of each

to give the outline of the ship

as before, the stream function at

-Line of Source9-»j

Fio. 43.11

a.\is

Other values of the stream function ^., give the 2-diml flow pattern around the ship form, at a distance from the boundary. At any selected point G in diagram 1 of Fig. 43.1 it is necessary to determine first, the flow from all the dx sources; second, the flow into all the dx sinks; and then to combine them. Taking

of Sinks-*-!

of 2-diml

lOutline r^

corre-

sponding to the "circular" stream flow for the simple l2-diml sourcc>-«ink pair of Sec. 43.3 pre-

over,

Fio. 43.1

DEKiNrnoN Sketch

nm the Stream

Ki'NrrioN AT A Point in a Linb Souhck-Link

Sink

I''iei.1)

DELINEATION OF SOURCE-SINK DIAGRAMS

Sec. 43.7

and X, and OJR are produced. Subtracting the area under the first from the area above the second, both measured to the XOXj axis, gives the net value of the combined sourceand 0, and

all

the curves

KHO

the dx-sinks between

3-diml

,

sink stream function at the point G. It

is

repre-

for all points in the

G

the

the source-and-sink lines

XO

and

was done by Taylor. The method is explained and used in a practical example by him on pages 392-396 and

LXX-LXXIII

of his 1894

INA

paper.

Shortening the lines of sources and sinks to cover only hmited intervals or portions of the (b)

(c)

bow and

zero.

curves by straight

fines; in

other words, making

the strengths constant along the source-and-sink latter

in producing the simple 2-diml ship

forms described in Sees. 2.17 and 4.3 and

the

source-sink

When this distance is reduced to an extremely

and the

left in

illus-

and 4.C of Volume I. They used by Brand and others in producing

because the

is

^ ^.-^•^^-n where

now

at the

doublet position which

axis,

common position for both. When the source and sink

n

=

in

effect,

a

are brought together

of the doublet is then indicated

m

by

are increased

The

strength

/i(mu),

where

2m(s).

When

the double-circular flow pattern around

a doublet

combined with a uniform flow

is

in the

direction of the doublet axis the resulting 2-diml

stream form, is

down

la

depicted

circular.

The

in Sec. 41.8. It

the Value

V4 of

'Ji^u

in

half-section

in

Fig.

derivation of this form is

is

convenient, for reasons

/

at the

Point M,

Sink^

Fig. 43.J

crosses the axis is,

to hold the product m(2s) constant.

-6 -;n

tangent to the

forming the locus of their

fine

normal to the

set

Other Half Below Axis Identical

lie

centers,

were also

to

now

source-sink axis, regardless of their radius. This

43. J,

)^-5yslem Equol

Furthermore, the visible streamlines

sink.

of the circular pattern

trated in Figs. 2.S

Rodii of

their

decreased toward

is

small value, the only circular streamhnes

uniformly varying in those regions. The

two steps were adopted by H. Fottinger

and F. Horn

as

size

to form a doublet their strengths

stern

Replacing the general source-and-sink strength

lines or

in

distance 2s along the axis

equal length and the source-and-sink

length near the

diminish

sink

retain

However, the between the source and

as in Fig. 43. C.

sight are the outer ones, beyond both the source

distribution symmetrical about 0, as

Plates

streamlines

source-sink

inner streamline circles

immensely by:

of

The

II.

circular shape,

UM

Making

1952, pp. 14-15].

43.7 Flow Pattern for the Two-Dimensional Doublet and the Circular Stream Form. A source and sink, both 2-diml, when placed infinitely close to each other along a given axis, form a doublet, described in Sec. 3.10 and illustrated in Fig. 3.M of Volume I and in Fig. 43.J of Volume

Taylor in the references cited. Nevertheless, it can be and has been done, as witness the works of the AVA, Gottingen, on 3-diml line sources and sinks in their report 3206, mentioned in Sec. 42.6. The general problem is simplified

(a)

is

TMB

May

Transl. 48,

and carrying through the remainder of the operation is a tedious and laborious task, despite the systematic method of calculation outUned and described by D. W.

OX,

one of which

revolution,

(d) Using a calculating machine developed by H. Fottinger [STG, 1924, pp. 295-344;

figure.

Repeating this procedure

of

illustrated in Fig. 42.C.

sented by the hatched area in diagram 2 of the

entire field other than

bodies

61

Construction Diagram for 2-Diml Doublet

n^b^

IIYDRODYNAMICS

f.2

pxplainod

presently,

aicuratcly

tiie

to

he

able

to

delineate

potential flow of an ideal liquid

IN

DKSK.N

SIIIl'

speak, to suit the

Src. -f^.S

new contour. Sections

of hydro-

around this circular form. This is accomplishetl by combining the circular doublet streamlines of the ^o-system with the parallel streamlines of llie ^^systcm, as described for other graphic constructions in the sections preceding. However, the ^o-system is constructed in quite different

and control surfaces, even transverse sections and watcrlines of ships, are the end result of this procedure, complete with data for the flow around them. However, because of the discontinuity at tlie trailing edge of a hydrofoil which is definitely sharp, the method breaks down for the region in

fashion.

this vicinity.

Selecting the desired radius

R

of the circular

stream form, the stream functions of the uniform flow arc laid off at intervals of say tenths of the

R on

a.\is. This is illustrated one side only. The innermost circular streamline of the doublet system, not shown in the figure, has a radius of R/2. Its geometric center, as for all other centers of the system, lies on a line normal to the doublet a.\is at the doublet position 0. If this innermost circle

radius

each side of the

in Fig. 43.J,

drawn

for

were drawn from the center P it would be tangent and to the uniform-flow to the doublet a.\is at is a streamhne for iu = —10 at M. Since point on the stream form where \f/s = 0, this circle has a stream-function value ^o = -f-lO. The next circle representing a doublet stream and has a function ^o is tangent to the a.xis at radius (7?/2)(10/9). The remaining circles of

M

the

have the radii (/?,'2)(10/8), .so on to (ft/2)(10/l) for the ^o = +1- Expressed in another

i^c-system

(/<:/2)(10/7),

and

outermost circle, way, at the top of Fig. 43.J, the radii of the \^/)-systcm maj' be taken as A-/1, fc/2, k/3,

where n has the numerical value point M, and k = nR/2.

The

algebraic addition of the

.

.

.

k/n,

of ^,; at the

4'd

and the ^u

stream functions produces points in the resultant ^s-isystem.

is a function for ^., = Other stream functions such as and so on define the streamlines

The stream

circle of radius R. ^fl

=

1,

2,

depicted in Fig. as large a

43..J for

the ^.,-systcm, covering

may

be desired for analysis. Both by this graphic construction and b^' pure field

as

propeller

foils,

rudders

blades,

Graphic Construction of Three-DimenStream Forms and Flow Patterns. The manner in which an oval 2-diml body is formed by 43.8

sional

inserting a 2-diml source-sink pair into a uniform

stream, flowing in a direction parallel to the sourcesink axis,

much

described in Sec. 43.3. It

is

source-sink axis.

For the mathematical formulations of Sec. 41.8 and the spherical coordinates employed there, it was convenient to use a zero stream-function reference for the 3-diml source (and sink) in the

form

of

center,

a transverse plane through the source normal to the source-sink axis. For the

graphic construction, however,

and more straightforward for

itself.

from the source-sink axis. Using the same zero reference for the 3-diml flow out of the source and into the sink, the radial flow is split up into a cone-and-funnel pattern symmetrical about the source-sink axis rather than into a "pyramidal" pattern uniformly distributed in

all

directions around

(or sink) as a center.

of the radial 3-diml flow t-akes

radial flow

is

the source

This means that the inner-

the velocity potential, the flow pattern, the

so to

representation

radially

the source-sink axis, as at

it,

The

stream flow is the same in both cases. It is depicted in diagram 2 of Fig. 2.M of Sec. 2.12, on page 31 of Volume I, where the 3-diml stream function ^[/ corresponds to — U^y'/'l, with y measured

possible to determine easily the stream function,

variuu.H flow characteristics along with

simpler

of the stream function \pv for the 3-diml uniform-

the form of a cone whose axis

and other flow characteristics around the circular stream form. Bj' the proccjvs of confornial transformation, mentioned in Sec. 41.11, the circular boundary of Xhi' 2-diml doublet Htrcam form is transformed into almost any dceired Hha()e, taking the flow pattern and the

much

both source-and-sink flow and uniform-stream

flow the source-sink axis

most subdivision

»ures, the velocities,

it is

to use as a zero reference

calculation, using the formulas of Sec. 41.8 for

pre.s-

possible,

the

flow about a 2-diml rod of circular section,

it is

is

same way, to form an axisymmetric 3-diml body by inserting a 3-diml source-sink pair into a uniform stream moving parallel to the in

assumed

B

is

coincident with

in Fig. 43. K.

The

to pass through the circular-

contour spherical base of this cone, notwithstanding that

it

is

shown

closed at

B

in the figure.

A

similar cone lies diametrically opposite the source

or sink, also

The next

shown at B.

subdivision of the 3-diml radial flow,

reckoned outward from the source-sink axis and out of (or into) which a unit (|uiinlity rate of

DELINEATION OF SOURCE-SINK DIAGRAMS

Sec. 43.S

63

Cones of inflow for unity stream function between -p^A and fi-^ =0 Funnels of outfiow for unity stream function

between

liquid flows,

the cone.

V'q'Z

and

TiQ'\

Definition Sketch foe 3-Diml Soubcb-and-Sink Stream Functions for Graphic Construction OF Body Shapes and Flow Patterns

Fig. 43.K

is

a conical "funnel," surrounding

The same quantity

rate of liquid

is

equal parts corresponding to the selected stream of the radial

functions for each "hemisphere"

such as k

=

When

perpendiculars are

assumed to pass through the annular spherical

flow,

surface at the base of the "funnel." This funnel

is

erected on this radius at the spacing h

it

the intersections of these perpendiculars with a

K

diagrammed at A stand out more

clearly,

source-sink axis

omitted. Diametrically opposite

one funnel

is

is

in Fig. 43.

where, to

make

the cone around the

an identical one, drawn at the

side of the 3-diml source in the figure.

left

With a

3-diml stream function ^o = at the source-sink axis, this stream function has a value of unity (1.0) at

the outer surface of the cone and the inner

surface of the funnel. It has a value of 2 at the

outer surface of the funnel,

indicated

in

the

Surrounding the inner funnels are a series of other larger funnels, also concentric with the source-sink axis, terminating in zones of area equal to the first, through which unit quantity rates of Hquid flow in and out. figure.

For a given spherical radius and radial velocity at the source and sink, the quantity rates of liquid flowing through the cones and funnels are directly proportional to the areas of their spherical

bases and zones, respectively. For the construction of the 3-diml

stream forms to be described, the

surface of each source or sink "sphere"

is

divided

an integral number of zones of equal area, all symmetrical about the axis. The area of a spherical segment or zone is expressed by the formula 4s = 2irRb, where R is the radius of the sphere and h is the height of the segment or zone in the direction of the polar axis, normal to the planes dividing the zones. In into

circle representing

10.

=

R/k,

the spherical surface give the

limits for the bases of the cones

and the funnels

through which equal quantities of liquid move out from the source and in toward the sink. The radial-flow diagram for a 3-diml source (or sink),

as projected on a page to represent the

any plane passed through the source-sink the form indicated in diagram 1 Fig. 43.L, where only one-quarter of the pattern shown. That for the sink is the same, with

traces on axis,

of is

takes

negative signs.

The uniform

flow approaching from a distance

assumed to be made up tubes, circular and annular is

of

stream rods and

in section

and con-

centric about the extended source-sink axis, as

shown in diagram 2 of Fig. 2.M of Volume I and in Fig. 42.A. The inner stream "rod" of Fig. 2.M has the form of a cylinder of any selected radius, depending upon the value of the 3-diml uniform-stream function assigned. The outer stream "tubes" have radial thicknesses such that the quantity rate of flow through each of them equals that through the center "rod." Their divisional surfaces therefore have equidLfferent stream functions, based upon their common axis

this case the polar axis corresponds to the source-

prospective inner and outer and the annular stream tubes are determined graphically by laying down a secondorder parabola y' = ex, with its vertex on the

Hence a

source-sink axis. Perpendiculars are then erected

sink axis, and to the direction of flow.

selected or convenient spherical radius along the

direction of flow

is

divided into a

number

of

as a reference.

The

radii of the rod

at uniform intervals along the source-sink axis in the

manner indicated

at 2 in Fig. 43.L [Taylor,

IIVDRODYN AMIC.S

64

TAULB

43.n

IN

SIIII' 111

Data roK CoNSTKCcTisr. Tmhkk-Dimi. This tablo applies to (iingram

k

I

of

SICN

1{mihi-I'

Pii;.

i:i.I,.

Sec. -fJ.S

I

)i

m;k\\is

DELINEATION OF SOURCE-SINK DIAGRAMS

Sec. 43.ft 22

2

0.10

Source-

or sinK ^-20

0.20

0.30

0.40

0.5O

R"^^

0.60

O.TO

H

080

0.90

"-^O

1.00 I

fiS

Curbed streamlines correspoodmq to 32 plus the inward radial stream function values are tanqenl to each other at the sink center Ifc

Fig. 43.N

The curved streamlines are tanqenl to the Outward raoial flow lines havinq the same numerical stream function

WO'>>rtW V^

Stream-Function Pattern for a 3-Diml Source-Sink Pair

the 3-diml siiigiosource-and-uniforin-flow combi-

nation described picviou.slj' in illustrated in Fig. 43. M.

The

tliis

section

and

result, indicated in

a plane longitudinal section through the a.\is of a 3-diml stream form of revolution of oval shape and the 3-diml flow pattern around it. Fig. 43.0,

is

This form may be called, following the lead of D. W. Taylor, a solid stream form; it may also be called a solid liankine body. The streamlines lying outside

-?4

it

are the traces of varied-radius

Curvad source-sink streamlines

PlO. 43.0

AxiBTUMBTIUf

Ik)l)Y

at the source center

(2^)

of

Fiq.

stream tubes, formed by the intersection of the circular-section .stream surfaces with the plane of the page. If

the solid axisj'mmetric stream forms resulting

from

anj' of these

combinations are too blunt,

pairs of 3-diml secondary or tertiarj' sources

sinks

may

and

be added, following the scheme de-

scribed in Sec. 43.5 for 2-diml radial flows of this kind.

The methods

of constructing graphically

the

43Ji

SlUrK rOR C'dMIIISATION oy 3-DlMI. SotmCF.-SiNK TaIU and

:t-niMI.

HSIMIIIM

Flow

DELINEATION OF SOURCE-SINK DIAGRAMS

Sec. 43.11

flow patterns around source-and-sink combinations in uniform flow is described here at some

length as an aid in the visuaUzation of this type of flow and in understanding the nature and the

combination of stream functions. The more famihar this action becomes to the marine architect, the more frequently is it recognized around

67

The number of forms which can be developed by source-sink combinations is in fact limited only by the ingenuity, imagination, and talent put to work on them. The reward offered by this work is

the ability to calculate the characteristics of the

flow around these forms, under a great variety of

The

initial conditions.

and practical

useful

results

a ship form and the more interesting and useful

of these enterprising endeavors are described in

become in practice. Forms Produced by Sources and Sinks. Thanks to Taylor's line sources and sinks, and to mathematical methods which have been developed in the three-quarters

somewhat greater

is this

knowledge

likely to

Variety of Stream

43.9

of a century since Rankine's time,

to produce stream functions

it is

now possible

and velocity poten-

forms and combinations hitherto undreamed of. This applies not only to the 2-diml source-sink combinations of Sees. 43.2 to 43.7 but to the 3-diml source-sink combinations of Sec. 43.8. Examples of these apphcations are: tials

(i)

for

source-sink

Line sources and sinks along a longitudinal

axis parallel to the direction of uniform flow, to

form a large number of bodies of revolution, having a great variety of shapes and proportions [AVA, Gottingen, Rep. 3206, dated 30 Dec

UM

1944; available in English as

Apr (ii)

TMB

Transl. 220,

1947]

Sources and sinks offset from the longitudinal

axis to produce a rather blunt stern

on a de-

stroyer form, pictured in Fig. 3.Q on page 69 of

Volume

I

[Lunde,

J.

K.,

INA,

1949, Figs.

1

and

2,

pp. 186-187]

doublets

of

introduced

in

been done by Sir Thomas Havelock (iv) Ring sources in a plane normal to a uniform stream of relatively high velocity, to form duct or pipe entrances with streamlined outer and inner walls. Longitudinal traces through some of the 3-diml bodies worked out in this fashion by the Ilhnois Institute of Technology on Project 4955, ONR Contract N7onr-32905, under V. L. Streeter, are illustrated in the First Phase Report of this project, dated 1 February 1949, entitled "Axially Symmetric Flow Through Annular

Bodies." (v)

Infinitesimal

dA

sources spread over the after

dA

sinks spread over

the forward area to reproduce the velocity and pressure effects of a screw propeller, following

H. Dickmann. this fashion is

43.10

A

group

shown

of five pairs

in Fig. I5.F.

arranged in

a dis-

Source-Sink Flow Patterns by Colored In Sec. 2.13, on

pages 34 and 35 of Volume

I,

there are explained,

somewhat general terms, the means by which radial-flow patterns around sources and sinks, singly or in combination, are determined by in

plotting traces of equal electric potential in a

weak electrolyte. The use of colored flowing into

and

sinks,

actual

is

hquids, emanating from and holes

representing

mentioned in Sec.

3.8.

sources

Excellent

source-sink flow patterns for practical use, capable

manual diagramming or photographing, are by this relatively simple, expeditious, and economical technique [Moore, A. D., "Fields from Fluid Flow Mappers," Jour. Appl. Phys., of

delineated

Aug

1949, Vol. 20, pp. 790-804]. Colored hquid orifice(s) to the sink

moves from the source

orifice (s) through a thin horizontal space between a light-colored slab containing the orifice (s) and a sheet of plate glass just above it. Streamlines of sorts are indicated by colored streaks left on the

Motion pictures may be made

liquid while

it is

of the colored

flowing.

This method lends itself to the quick solution, not only of 2-diml flow problems but to the delineation of axisymmetric flow in three dimensions. Further, fine sources and sinks may be represented, using slots instead of holes.

The

width

slot

is

varied to correspond to the strength distribution

along that axis. Flow from or into relatively largearea sources and sinks is represented by running colored Hquid through small sand beds within the boundaries of the sources and sinks. Similar representations, employing a liquid flow

the

of constant

utiUzed by

area of a propeller disc and

50, in

Liquid and Electric Analogy.

slab.

Assembhes

a uniform stream to produce special forms, as has (iii)

Chap.

detail in

cussion of calculated ship resistance.

patterns

depth over a broad-crested weir, were Harvey to approximate heat-flow

J. F.

in

boilers

[SNAME,

1950,

Vol.

58,

pp. 252-257]. 43. 11

Formulas

StreamFlow Patterns Around

for the Calculation of

Form Shapes and Them. The shapes

the

of all the

stream forms con-

structed graphically in the preceding sections^of

IIM)R()1)\ \

G8 the

the

prt-stMit rliiiptor, tlu> Iriict's of

nroiiiitl tlu-iii, iiiul tlu' local

How

AMICs

patterns

stream veliuitifs ami

DISICN

I\ Mill' Body ~'~

M CTo'»cd~Ji Ver^

Sic ond

Loni).

— "•~-^~"

"*

i4 1

calcuiatetl

l)e

formulas. This metluxl

is

Sink ol

J.

12

Unif orm Flow -

me LtU tno-

by mathematical the most conveiiient anil advantageous, depending upon the eipiipment and facilities available and the use to which the deriveil data are to be put. Specific eaii

presjiiiri-s,

Synmetixol

About

-I

often

a few selected and 41.9 and are (pioted on Figs. 41. E, 41. F, and 41. CI accompanying them. These formula.s, and others, are found in many mixlern te.xt and reference books, but more often than not they are without adetiuatc explanation as to the symbols and notation employed. Some additional formulas were dcNclopi'd iiy

formulas for accomplishing

this, in

cases, are derivtnl in Sees. 41.8

\V. J.

M. Rankine

Roy Soc,

[Phil. Trans.,

such as those to establish the

loci

1871],

of points of

ma.ximum and minimum velocity around stream them are not readily available and the notation in which forms, but the references which contain

they were exprcs.sed threc-{|uartcrs of a century ago re(|uires conversion to nKxlern Mt)tatioii. 43.12 The Forces Exerted by or on Bodies Around Sources and Sinks in a Stream; Lagally's Theorem. If a i-loscd body is formed by a stream surface around sources and sinks, as for the bodies around the source-sink pairs dcscrilied

previously in this chapter, there

is a resultant hydrfxiynamic force acting on the stream surface bounding the body. It is explained presently that

a uiiifonn stream the resultant force is zero, conforming to the fl'.Memliert paradox, but in an unsteady or non-uniform flow the force is finite. in

It

can be evaluated very neatly by the use of is known as the Lagalbj Throrrm. The

what

derivation of Lagally's theorem .scope of this book,

is

beyond the Diagrams Ii.lustratino the Factors IN' TUB Lacai.i.v Tiikorkm

i'A.Y'

I'"iG.

but at the expense of stretching

InVOI.VKD

the mathematical truth temporarily, the physical basLs for

it

is

rather easily explained.

what happens inside the 2-dLml ov(>id-shape
Hource or up.stream singularity in the leading end of .such a brxly, formed

aroimd a source and a

sink at a gnat dixlancc frinn rnrh nihrr. In diagram I

of Fig.

13.1',

dei)i(ting the nose of this body,

lying in a uniform flow of velocity

—l\,

all

the

emanating from the after part of the .source flows more or le.ss directly toward the left, away from the oncoming stream. That from the forward lifiuid

part

of

reverses

the source it.s

toward the

«lirection, left.

and also to flow downstream

turn.s

rather

sharply

Regardlesw of the direct ion

in

emanated from the source, it.s is downstream. As the "inside" li(|uid moves farther and farther from the source the railial component of its velocity |)rogre.ssivel}' diminishes. At a great distance downstream, on its way to the sink, this which the

li(|uid

ultimate direction

li<|uid acfiuires

to

— f/o.

volume time,

.so

,

a velocity

—U

essentially etjual

that of the uniform stream.

If a certain from the source in unit the volume or (|uanlit,y rate of

of li(iuid i.ssues

that

Q

is

this (low, then the

unit time

the source

is fA). it

mass

.Fust

of li(|uid (lowing

before the

had no compniiciit

o\it

litpiid i.ssued

in

from

of mulioii p;ir;dlel

DELINEATION OF SOURCE-SINK DIAGRAMS

Sec. 43.12

to the uniform stream.

At a

large distance

has a velocity Therefore the augment of

stream, half-way to the sink,

— U„

approximating

.

down-

velocity AC/ imparted to

it

the process of

in

it

flowing around inside the ovoid-shaped stream-

form boundary is — C/„ Its downstream is its mass times — pQUo, assuming that .

momentum its

—U=

,

also its increase in

momentum

of mechanics, is a

measure

to impart that increase.

acting downstream,

is

far

or

velocity,

—U„

.

This

is

which, by the laws

of the force necessary

The

force in question,

balanced by an equal and

opposite force acting on the body surrounding

The

the source to shove the body upstream.

may be likened to a thrust which is producing the relative motion depicted between latter force

the source boundary and the stream. signs for the

The

two terms of the equality F

different

= —pQUa,

indicate that the direction of

F is

U^ indicated At the left

of Fig. 43. P.

,

"opposite"

in

diagram

1

opposite that of

or trailing end of the body, an

situation

exists,

depicted

at

the

diagram 3 of Fig. 43. P. As the velocity in the uniform stream is every^vhere — U„ the net thrust or drag on the body is obviously zero. When the forces on both source and sink are taken into account, the expression left in

,

f

—

Bodv

/

,oU^

+

kU.

a simplified form of the Lagally Theorem, for the special case considered, in which Fsody is zero. is

The

and extremely useful applications theorem embody situations in which the flow is unsteady and non-uniform and in which the closed body may be 2-diml or 3-diml, formed by any desired number and combination of sources and sinks. Leaving the schematic physical explanation and turning to one that has hydrodynamic rigor, a simplified form of the theorem is the expression practical

of the

—

F where Qi

is

J(Q.C/0

the output of the source or sink

within the body, expressed as a volume rate of flow,

positive for a source

sink.

The symbol

C/;

and negative

for a

represents the velocity of

the stream, at the position of the source or sink

under consideration, which would occur if the body, and hence all the sources and sinks forming the body, were removed from the stream. For each source or sink the line of action of the individual force

is

through the singularity under

consideration and in the direction opposite to

that of Ui

body

is

.

The

69

net hydrodynamic force on the

the vector summation of the individual

forces, evaluated for

each source and sink within

the body. If the body is placed in a uniform stream, Ui at each singularity equals the uniform-stream

And since, for any closed body U„ formed by a stream surface, the source outputs must equal the sink inputs, and the mass density p is constant, the net hydrodynamic force acting on the body is zero, which simply confirms velocity

.

d'Alembert's paradox.

The complete theorem developed by M. Lagally ["Berechnung der Krafte und Momente, die stromende Fliissigkeiten auf ihre Begrenzung (Calculation of Forces and Moments which Streaming Liquids Exert on Their Boundary)," Zeit. fiir Ang. Math. Mech., Dec 1922, Vol. 2, pp. 409-422 (in vector notation); MUneThomson, L. M., TH, 1950, pp. 208-211] permits the determination of both forces and moments acting on a body in both steady and unsteady flow [Cummins, W. E., "The Forces and Moments Acting on a Body Moving in an Arbitrary Potential Stream," TMB Rep. 780, Sep 1952]. For example, if the uniform flow at the right of diagram 1 of Fig. 43. P is replaced by a single outside source on the x-axis, the flow from the latter is radial rather than parallel and uniform.

ansiiben

The

momentum

velocity C/„ in the

equation

is

then replaced by an array of radial velocities, varying with distance from the outside source. If

the outside source

is offset

a source-sink body, there

is

a

from the

moment

a;-axis of

as well as a

force exerted on the ovoid-shaped boundary.

architect

who

wishes

further into this subject

may

flnd a

The marine

to

delve

paper by

A. Betz of Gottingen somewhat more readable

than the references cited in the preceding paragraph. This paper is entitled "The Method of Singularities for the Determination of Forces and Moments Acting on a Body in Potential Flow"

[TMB In

Transl. 241,

all

Nov

1950].

applications of Lagally' s

Theorem

it is

important to remember that, although the line of action of the force on a body, formed by placing a source-sink system in a stream, passes through the source or sink, the force is not to be taken as acting on the source or sink proper but

on some type of surface or body boundary surrounding each. However, in the conventionaUzed Translation diagrams published by Betz in 241, he apparently employed a schematic short-

TMB

I1M)R()|1VN \MI(:s IN

70 with no nttciiipl to

\\i\w\,

from

rosultiiip

tlie

surfare

iloliiicatc tlic

system

sourcos,

of

sinks,

diagrams the result ing forces are shown as emanating directly from the singularities. There are indications tliat an important future u.se of the I Jigally Theorem may be in the solution of the problem of determining the forces and the moments exerted on ships when pa.'vsing or meeting

and

doublets,

each other

vortexes.

In

his

in confinetl waters. Thi.s will involve

a

and

the application of the radial-flow characteristics

and sinks to problems in hydrodj'namics extremely extensive. There are listed here a few of the most important references, with which of sources

is

groups or arrays, and placed

in

another aspect of the forces involved for one or

two simple hypothetical conditions. Assume first that two sources of equal strength, lying opposite each other, are enclosed by two large bo
Runkino,

(3)

282-288 Rankine, W.

M., "On Piano Wator-lincs in

Two

J.

M., "Shipbuilding: Theoretical and

Practical," 1866, p. 106 (4)

W.

Rankine,

"On Stream-Line

M.,

J.

Surfaces,"

IN.\, 1S70, Vol. XI, pp. 175-181 (5) Rankine, W. J. M., "On the Mathematical Especi.iliy

and Upwards,"

Phil. Trans.,

Roy. See, Ix)ndon,

IJaulc, A.,

(7)

Pollard,

(8)

Taylor, D. W.,

1885

Rrus.'icls,

is

and Dudcbout, .V., "Thfiorie du Naviro (Theory of the ShipX" 1S02, Vol. Ill, pp. 401-410, 417-418, especially Fig. 135 on p. 408

INA,

J.,

"On

Ship-Sha[>ed Stream Forms,"

1894, pp. 38.5-106

"On Solid Stream Forms and the Water Necessary to Avoid Abnormal Resistance of Ships," INA, 1895, pp. 234-247 and

Taylor, D.

Depth l>ls.

(10)

XV

"Note sur les Lignes d'eau Propo.sic8 par M. le Profefsseur Rankine (Note on the Waterlines Proposed by Professor Rimkine)," Ann. Soc. Sci.,

(6)

(9)

Theory

those with Four Foci

of Streamline.'!,

1S71, Vol. 161, pp. 267-300; alsoPI.

surfaces

between them, as at 2 in Fig. 43. P. As no superposed stream flow in this case, the liquirl flowing from each source toward the adjacent flat portion of body surface Ls deflected anfi pu.shetl backward. For the 2-diml case, the flow from each source is pictured graphicallj' by combining the stream functions of the two .sources, indicated by the light radial lines in the diagram. Because of the momentum imparted to the suiromiding liquid, in a direction opposite to that in which the other source lies, away from the adjacent flat body surface, a reactive force is created on each body, directed toward the adjacent body and the other source. While the analogy' Ls by no means a perfect or a valid one, it can be said that, unlike the similar poles of electromagnets, the two adjacent sources give the appearance of attracting each other. If a .source and a sink lie near each other in a unifonn stream who.se direction of motion is parallel to the source-sink axis, as in diagram 3

J.

\V. J. M., "Summary of Proportios of Certain Stroam-Linc)," Phil. Mag., Oct ISCt, pp.

(2)

place
there

in

DimpiisionB," Phil. Trans., Roy. Sor.. 1S03

surfaces adjacent to the sources take the form of

a pair of parallel but independent

W.

Rank-ine,

non-uniform and

connection to consider

pursue his studies

this fascinating field:

unsteady flow. It is interesting in this

may

the marine architect

by the boundaries arounrl nearby

sinks, arranged cither singly or in

n.n

43.13 Partial Bibliography on Sources and Sinks and Their Application. The literature on

(1)

forces exerted

Stc.

phenomenon, where unlike

poles attract each other.

knowletigc of the nature and direction of the .sources

DESIGN

SIIII'

of the electromagnetic

\V,,

of

XV-XVIII

Fuhrraann, O., "Widerstands- und Druckmessungen (Resistance and Pressure an Ballonmodellen Mea.surcmenta on Balloon Models)," Zeit. fiir Flugtcchnik und Motorluft-schiffahrt, 15 Jul 1911, Vol. II, pp. lG.5-106

(11)

A

French by van Meerten |ATMA, and PI. I: 1904, pp. 275-293; 1905, 209-289 and Pis. III-VIj. These discuss the pp. application of hydrodynamic studies of the theory of sources and sinks in both two and three dimensions. They contain diagrams of a variety of sourceseries of papers in

1903, pp. 51-60

sink flows, including several involving line sources

perpondlrular to a uniform How. .\ st.'irt is made 1905 paper to utilize this method of analysis

in the

of Fig.

'13. P,

the action of the "inside"

lifpiid is

such that equal arul opposite reactive forces are

away from

and the source positions, respectively, and act outward on the upstream and the downstream ends of the IxmIv. .Mthongh the analog,v here i.s perhaps less valid

directed

than

it

the sink

wa.s in the ca.se of the adjac<>nt .sources,

for predicting the resistance of

(12)

11.,

TMH

(13) AcnMlynainisc-he Versui-li.Mjuistalt (AV.\), rK'ittingen,

Report

UM

lOnglish

a.s

repelling each other. This

Sec. 42.0

again the opposite

ship.

"Fort.schnitte der Striimungslehro

STfi, 1924, Vol. 25, pp. 295-311; lOnglish version ill Transl. IS, May 1952

the source and the sink give the appearance of is

an actual

im Maschinenbau und Schiffbau (/\(lvance8 in the .Shipbuilding)," Theory of Flow in Fngineering and

Fdltingor,

32(M(, dat«-
TMH

30 Dc- 1911; available

in

Transl. 220, .\pr 1947; sec also

DELINEATION OF SOURCE-SINK DIAGRAMS

Sec. 4 3.

Lamb, H., "Hydrodynamics," 6th

(14)

ed.,

Dover,

New

York, 1945, pp. 57-71 "The Elements of Aerofoil and Airscrew Theory," 2nd ed., Cambridge, England, 1948, pp. 21-32

(6)

(15) Glauert, H.,

R., "Cas d' Equivalence entre CarSnes et Distributions de Sources and de Puits (Similarities

(16) Brard,

Milne-Thomson, namics," 2nd pp. 194-223

(17)

(18)

(19)

vector notation) L. ed.,

M

(7)

Street

Lab.,

Yale Univ., Tech. Memo.

14,

15

Selected References on Lagally's TheoFor the reader who wishes to investigate further the application of the Lagally Theorem, 43.14

rem.

the following references should prove useful: (1)

Kelvin, Lord,

Liquid

(2)

"On the Motion

NACARep.

Irrotationally

ausiiben

(4)

(5)

(Calculation

of

Forces

and

Moments

which Streaming Liquids Exert on Their Boundary)," Zeit. fur Ang. Math, und Meoh., Dec 1922, Vol. 2, pp. 409-422 Taylor, G. I., "The Forces on a Body Placed in a Curved or Converging Stream of Fluid," Proc. Roy. Soc, London, 1928, Series A, Vol. 120 Taylor, G. I., "The Force Acting on a Body Placed in a Curved and Converging Stream of Fluid,"

Converging or Diverging Stream," ARC, R and 1164, May 1928, Vol. 33, pp. 114-117 Mohr, E., "tJber die Krafte und Momente, welche Singularitaten

auf

eine

stationare

Fliissigkeits-

Mathematik

(Crelle's Jour.), 1940, Vol. 182 "Forze e momenti in una corrente leggermente curva convergente (Forces and Moments in a Slowly Coverging Curved Stream)," Commentations, Pont. Acad. Sci., 1944, Vol. 8 (10) Brard, R., "Cas d'Equivalence entre Carenes et Distributions de Sources et de Puita (The Equivalence of Ship Hulls and Distributions of Sources and Sinks)," ATMA, 19.50, Vol. 49, pp. 189-230 (9)

Pistolesi,

(in

(11)

(12)

114, 1921

M., "Berechung der Krafte und Momente, die stromende Fliissigkeiten auf ihre Begrenzung

(3) Lagally,

"Note on the Forces Experienced by

stromung iibertragen (On the Force and Moment which Singularities Transfer upon Stationary Liquid Flow)," Jour, fiir die reine und angewandte

of Rigid Solids in a

through Perforations in Them or in a Fixed Sohd," Phil. Mag., May 1873, Vol. 45 Munk, M., "Some New Aerodynamical Relations," Circulating

H.,

M

(8)

Sep 1952.

Lamb,

Ellipsoidal Bodies Placed Unsymmetrioally in a

M., "Theoretical HydrodyMacmillan, New York, 1950,

Cummins, W. E., "The Forces and Moments Acting on a Body Moving in an Arbitrary Potential Stream," TMB Rep. 780, Sep 1952 Hellerman, L., and Van Zandt, T. E., "Rankine Solids," Harbor Protection Project, Edwards

and 1166, 1928-1929, Vol. 33, p. 104ff Glauert, H., "The Effect of the Static Pressure Gradient on the Drag of a Body Tested in a Wind Tunnel," ARC, R and 1158, 1928-1929, Vol. 33, pp. 81-113

Between Ship Hulls and Distributions of Sources and Sinks)," ATMA, 1950, Vol. 49, pp. 189-230 (in

71

M

R

ARC,

E.,

vector notation)

Milne-Thomson,

L. M., "Theoretical namics," Macmillan, New York, 2nd 208-211 pp.

Hydrodyed.,

1950,

ToUmien, W., "Uber Krafte und Momente in schwach gekriimmten oder konvergenten Stromungen (On the Force and Moment in Flows which are Weakly Curved or Convergent)," Ing.-Archiv., 1938, Vol. 9; translated in ETT, Stevens, Rep. 363, Sep 1950

(13) Betz,

A.,

"Singularitatenverfahren zur Ermittlung

Momente auf Korper in Potentialstromungen (The Method of Singularities for the Determination of Forces and Moments Acting on a Body in Potential Flow)," Ing.-Archiv, 1932, Vol. 3, pp. 454-462; Transl. 241, Nov 1950 (14) Weinblum, G. P., MIT Hydrodyn. Symp., 1951, pp. 91-92 der Krafte und

TMB

(15)

E., "The Forces and Moments Acting on a Body Moving in an Arbitrary Potential Stream," TMB Rep. 780, Sep 1952.

Cummins, W.

c;ilAl'

General; Scope of Chapter

72

rolar Diagrams for Simple Hydrofoils

Test Data from

.

Compound

.

Hydrofoils

Pitching

Moment;

ami

data are

44

11

Effective Aspect Ratio for Equivalent Ship

44.12

Design Notes and Drag Data on Hydrofoil Planforms and Sections Quantitative Data on Cascade and Inter-

75

.

75

.

78

Distribution

of

83 83

Hydrofoils

44.13

80

83

84

ference Effects

80

I'lu'

k'vcii in this

intendi'il for the

submerged lift,

in a lit|uid.

The manner

of

lift

wlien

producing

in a ilircctioii generally at right angles to

and performance data on them,

classed as hydrofoils

is

it

if

and water,

flow around the two, in air

similar. In other words, data

airfoils

known

from

generally

tests in air are

perfectly valid for applii'ation to the design

performance of hydrofoils

in

water

if it is

and

known

that air-water surface effects and cavitation are

As a

rule,

sejiaration effects

around botlies wholly submerged in air and in water are similar; this applies also to the correlalion of the.se effects between niiKlel and full scale, Since whole books are insufficient to list the airfoil and hydrofoil data presently available design purpases,

(195.")) for

sible, in this

chapter, to do

it is

to present

certain data which the marine architect

may

find

ship and appendage ilesign. The.se and

uwful

in

other

data

in

the

technical

literature

almost

32.11 on the

Sees. 3r).2, 37.2,

and movable appendages. 44.2

Formulas

for Calculating Circulation, Lift,

Drag, and Other Factors. There are no simple formulas wliirli will permit the computation of lift, ilrag, pitching moment, ami other factors on hydrofoils of given shape and on botlies of random shape acting as hyilrofoils. There are given here only a few of the basic fornuilas and procedures for the calculation and prediction t)f tlicse quantitles. In practice it is necessary to rely on experi-

mental data for the determination of design and other factors. The volume of these data is now very large; some of the

priiici|)al

As

is

customary

for

groups

the shape,

to other fields,

an'

and

given

in

0-diml

ratios,

coellicients,

and

expressions.

The

lift

force

L developed on

hydrofoils,

circulation

violently with time.

of fornuilas relating

characleristics,

performance of hydrofoils and e(|uivalent bodies

hydrofoil or similar bod^' in a

may change

sources are listed

in Sec. 44.3 following.

invariably a|)ply to steady-stnte con
uttuek

of

and 37.3 and the accompanyand 37.D on fi.xed

control .surfaces

and other ship parts restMubling the relative .speeds and angles of

geometry

ing Figs. 37.A, 37. B, 37.C,

manifestly impo.s-

more than

Fig. 14. .\

the screw propeller

may

that the

is

and

Figs. 32.F, 32.G,

(c)

concerned, including

is

and the accompanying

32.8 and 32.9 and the accompanying

is

described in Chap. 14. Insofar as their behavior

Sec. 14.2

(a)

for hvdrofoils are

!\'inl)ols

in:

(b) Sees.

production of dynamic

nonexistent.

found

chapter embrace plates and

the flow or to the direction of body motion,

1)6

Nomenclature and

hyilro-

0(|iiivaleiit foini.s for wliich pi'rfonnaiu'o

bodies, irrespective of shape or size, which are

to

82 Circulation and

73

Ccntcr-of-Prcssure Loca-

General; Scope of Chapter.

44.1

1)6

a

Spanw-iso

.

Hydrofoil

test

Around

Fields

44.10

.

tion

this

Pressure

Distribution of Velocity and Pressure on a

44.8

foils

and

Velocity

72

.

Flow Patterns Around Typical Hydrofoils

44.9

Lift

Hydrofoilii

44.4 44 5 44.6 44.7

1

Hydrofoil

Formulas for CnlculafinR Circulation, Lift, Drag, ami (Hhor Factors Test Data from Typical Simple Airfoils and

44.3

I'.R

Moment, and Flow Data for Hydrofoils and Equivalent Forms

Force,

41.1 14.2

1

span of a

stn-am,

when

by an effective angle of attack means, is represenleil by

is .set uj)

or other suit.able

72

unit

lii|uid

FORCE AND FLOW DATA FOR HYDROFOILS

Sec. 14.3

L

= pU^T

per unit span

(44.i)

and moment

drag,

where

73

wealth of published data on the

ture, a great

coefficients

and other factors

of a great variety of airfoil shapes,

p (rho)

is

the mass density of the liquid in the

stream [/„

is

the velocity of the uniform stream relative

Some

lift,

when

tested

data are in tabular form but most are in graphic form, corresponding somewhat to the information in Figs. 44. A and 44. B. Here,

in air.

of these

to the hydrofoil

r

(capital

gamma)

is

the strength of the circu-

Moment

lation in a plane parallel to the stream

motion and normal to the body

0.1

Coefficient 0.3

O.a

C^

04

axis.

For a hydrofoil of span or breadth h, measured normal to the stream direction and to the plane of circulation, the total lift force

L = bpU^T The

required

circulation

leaves

liquid

(44. ii)

to insure that the

the hydrofoil tangentially at

its

edge is approximated by [Rouse, H., 1946, Eq. (192), p. 279]

trailing

EMF,

r

=

xct/oo sin

(44.iii)

where a(alpha) is the geometric angle of attack of an equivalent flat plate and c is the chord. Expressed in terms of the Uft coefficient Cl and the drag coefficient Cd the overall Uft and drag are ,

L =

Lift

Ci^^ Ulhc

=

CA UlA„

(44.iva;

Fig. 44.A

Lift-Coefficient, Drag-Coefficient,

AND Moment-Coefficient Graphs for Gottingen

Drag

D =

For the

CoT) Ulhc

= Co^ UlA„

special case of

an

infinitely thin flat

plate lying at an angle of attack a in a uniform

when

stream,

with

the plate

also of infinite span,

infinite aspect ratio, the

Lift coefficient

W.

[Durand, Vol.

is

I,

F.,

Cl

=

2x

sin

a

(44.V)

"Aerodynamic Theory," 1935,

Div. B].

By making an

arbitrary assumption as to the

distribution of the intensity of

lift

over a hydrofoil

an approximate induced-drag coCdi = Cl/[T{b''/A„)], where 67 A „ is

of finite span, efficient is

the aspect ratio [Rouse, H.,

By

the

EMF,

Profile 409 op Aspect Ratio 1.00

(44.ivb)

1946, p. 285].

same reasoning the downwash angle

e(epsilon) is approximately C/,/[T(?>V^ff)l.

The magnitude of the lift by the Magnus Effect on a rotating cylinder in a stream is given by the simple expression L = p[/„r for unit length of the cyhnder along its axis. 44.3 Test Data from Typical Simple Airfoils and Hydrofoils. There is, in the technical litera-

as in

many

cases in the literature, the geometric

or the nominal angle of attack

is the independent For the data in Figs. 44.A and 44.B, adapted from the work of H. Winter at Danzig on Gottingen section 409 ["Flow Phenomena on Plates and Airfoils of Short Span," NACA Tech. Memo 798, Jul 1936, Figs. 16 and 17, respectively], the values of the angle of attack a are spotted along the Cl and Co curves. To use these graphs, follow along the proper curve until a mark is found for the particular value of the angle of attack that has been selected. Then the abscissa and the ordinate of this mark are the values of drag and lift coefficient, respectively. For example, for the full-line graph of Fig. 44.A, take the point where the angle of attack a is 17.8 deg, at which partial breakdown or preUminary stalling occurs. The corresponding value of Cl is about 0.592 and of Co about 0.12. The lift-drag ratio at this hydrofoil position is 0.592/0.12 or about

variable.

4.93.

HVDRonvx AMirs Moment 0.0

O.Z

0.1

DroqCoefft.,

Coefficient

C^

a4

0.3

IN SHIP nrsiGX D«KMihofT, A.

0.5

i:.,

Sec.

and

Stivers, L. S.. Jr.,

H.3

NACA

Rep. 824, 1945]. This report contain.s, in addition to the usual information on airfoil shape and the customary experimental data, a considerable

Side EcJoe! f?bund Side Eaqc Flo't

amount

of information on pressure distribution

over the

airfoils illustrated.

For the

specific

needs of the marine architect

in

predicting the behavior of simple movable hydro-

the

of

foils

shapes,

sections,

and proportions

required in ship design there are several useful

sources of information. These appl^' principally to hydrofoils of sj'mmetric section

and to aspect

ratios in the smaller ranges. I.

Data on Thin Rectangular Plates of Aspect 5.0, 1.0, and 0.20. In PXA, 1039, Vol. II,

Ratio

page 204, K. E. Schocnhcrr gives curves and ratio of (1) distance of center of pressure CP from leading edge to (2) chord length of plate, on a base of nominal Fig. 6 on

04

Q2.

0.0

Drag

0.6 Coefficient

of normal-force coefficient

08 Cd

^"Z^ Fia. 41. B

angle of attack in degrees, for three

Lift-Coefficient, Drag-Coefficient,

AND Moment-Coefficient Graphs for GOttingen Profile 409 of Aspect Ratio 0.5

To

prevent confusion, mo.st of the marks for

omitted from Figs. 44.A and 44.B. In Figs. IG and 17 of NACA Technical Note 798 there are small circles along the moment-coefBcient graphs but no numerals to indicate the numerical values of a. Tables of coordinates for the symmetric Gottingen section 409, as well as for Gottingen specific angles of attack are

and 640, and moment coefficients, are given by W. P. A. van Lammcren, L. Troost, and J. G. Koning in Tables 3 and 4 on pages 324 and 325 of RPSS, 1948. It is pointed out here, and it will again be sections

with

410, 411, 443, 429, 539, 639,

lift,

drag,

pointed out in later portions of this chapter, that the behavior of a influenced section.

No

foil in

critically

by

water or in air small

is

changes

often

in

its

performance data are acceptable for

design and other purpo.ses in practice, therefore, unless accompanied by a delineation (and pref-

erably

al.so

a table of coordinates) of the section,

in sufTicicnt detail to

permit

it

to be reproduced

1932, Vol. 4, p.

who

is

Included are graphs for one

9GfT].

of the test plates of Joessel,

but with no informa-

tion as to its aspect ratio. II.

NACA

Data on

Symmetrical

Airfoil Sections

with tx/c Ratios of 0.06, 0.12, 0.18, 0.25, and Aspect Ratio 6. In PNA, 1939, Vol. II, pages 205-206, K. E. Schoenherr gives curves of lift coefficient,

drag

coefficient,

and

ratio of

CP

from

leading edge to chord length of the hydrofoil.

The

section ordinatcs are given, together with a

procedure (explained

in

the text) for converting

the given data to that which would be expected for aspect ratios other than 6. The data are taken from a report by E. N. Jacobs and R. E. Anderson ["Large Scale Characteristics of Airfoils as Tested in the Variable Density Wiiul Tunnel," NACA

Rep. 352, 1930]. Additional data are given Ijv E. N. Jacobs, K. E. Ward, and R. M. Pinlierton in NACA Report 460, publi-shed in 1933 (pages 299-354 of the volume for that year), entitled "The Characteristics of

to large scale.

For the physicist, engineer, or architect

flat plates

"Mcssungen an ebenen und gewolbten Platten (Measurements on Flat and Curved Plates)," Ergebnisse der Aerodynamischen Versuchsanstalt zu Gottingen, tested at Gottingen [Flach.sbart, 0.,

in the

78 Relatetl Airfoil Sections from Teats Wind Tunnel."

Variable-Density

Data

Hydrofoils

on

Having

Symmetric

looking for a comprehensive compilation of airfoil

III.

form tliere is available a summary of airfoil data prepared and published by the National Advi.sory Cfimniittce for Aero-

Sections and Outlines Suitable for Ship Rudders, with Aspect Ratios of 0.5, 1.0, 1.5, and 2.0. In the

data

in

nautics

systt-inatic

in

Washington

[.Mtbott,

1.

11.,

Von

early 1930's there

Mcxlcl

Ha.siii

ill

was tested at the Experimental Wa.shingloii a scries of twelve

FORCE AND FLOW DATA FOR HYDROFOILS

Sec. 44.5

hydrofoils of symmetric section,

having varied

The results of by R. C. Darnell ["Hydrodynamic Characteristics of Twelve Sym-

aspect ratios and blade outlines. these

tests

were reported

metrical Hydrofoils,"

The

EMB

Rep. 341,

Nov

1932].

hydrofoils were towed beneath a special flat-

bottomed float which carried a dynamometer to measure the lift, the drag, and the torque. The angle of attack was varied from to 45 deg and the gap between the top of the hydrofoil and the bottom of the float was varied from to 2 inches. The report gives the 0-diml lift, drag, and moment coefficients for tion, together

each hydrofoil in each test condiwith the positions of the center of

pressure with respect to the leading edge.

The

running the hydrofoils with their trailing edges foremost was also studied.

effect of

For hydrofoils having raked or swept-back leading (and trailing) edges and

some

taper,

it is

customary to assume a nominal chord length equal to the mean chord length, neglecting local rounding of the outlines at the corners. Although not clearly stated in Report 341, this

EMB

scheme was followed for the 12 hydrofoils reported upon in that publication. For fixing the fore-and-aft position of the center of pressure

moment,

pitching

CP

or of the point of zero

this distance is

reckoned along

the direction-of-motion chord at midspan. For a

blade

outline

with rake and taper but with and trailing edges, the chord at

75

one of the four in Figs. 44. A and 44.B serves also as a so-called -polar diagram, which is useful in

determining the Cl/Cd ratio at one aspect ratio when the Cl/Cd ratio at another aspect ratio is

known

When

[Rouse,

H.,

EMF,

the ordinate scale of

abscissa scale of

Co

,

pp. 285-286].

1946,

C^

same as the the slope of a line (with is

the

drawn from the origin a along the graph is the value of the hft-drag ratio CJCd A line from the respect to the horizontal) to

any

origin

selected value of

of

coordinates,

represents the foil;

tangent

maximum

the

graph,

ratio

of the

to

lift-drag

the corresponding angle of attack

is

indicated

at the point of tangency. lists a number of references to pubdiagrams for representative airfoils. Diagrams of this type are of little use for practical and design purposes, however, unless the section

Table 44. a

lished polar

contours of the hydrofoils or

airfoils are

defined

by a rather complete set of coordinates. 44.5 Test Data from Compound Hydrofoils. Figs. 37.A, 37.B, 37.C, and 37.D of Sees. 37.2 and 37.3 indicate that

compound

hydrofoil

is

for boats and ships the used as extensively as the

simple hydrofoil for movable appendages and control surfaces. Included in this category are

and tabs as well as hydrofoils placed abaft fixed leading-edge portions and abaft hydrofoils with flaps

and

For steering rudders, fins, and other movable appendages the hydrofoils and hydrofoil

fixed horns, fins,

skegs.

diving planes, active roll-resisting

straight leading

midspan

is

PNA,

also the

mean

chord.

and pages 206-207, K. E. Schoenherr summarized the results of selected tests on five of the twelve symmetrical hydrofoils tested by Darnell, involving those with varied rudder outlines but with the aspect ratio limited to 1.0. In the figure cited he gave graphs of lift coefficient C^ and of the ratio of CP position from the leading edge to the mean chord length In

1939, Vol. II, Fig. 9

of the hydrofoil for the five blade outlines dia-

grammed

in the figure.

IV. Data on Tests of Wageningen Rudders A and B, with Symmetric Sections and Different Outlines. The results of open-water tests on two model spade-type rudders of orthodox shape, outline, and proportions are described by W. P. A. van Lammeren, L. Troost, and J. G. Koning [RPSS, 1948, Figs. 210-214 and pp. 319-322].

44.4

A

Polar Diagrams for Simple Hydrofoils.

Hft-coefficient,

drag-coefficient graph such as

Graphs of Lift Coefficient for Compound Hydrofoils Having Varied Proportions AND Varied Angles of Attack of the Movabm; Blade

Fig. 44.C

ll^MR()|)^ \ VMics IN SHIP nisi{;N

76

TABLE

Sec.

H.5

—Bnoir Lwr of RcrcHKNccii Illl'stiutinc; Pui.kk DuniiAMti and Lirr/DRAa Ratios roR Airfoils

44jk

AND IlrDROFOIlA

Type of Section

FORCE AND FLOW DATA FOR HYDROFOILS

Sec. 44.5

and

0.227, 0.329,

0.453, respectively.

between the two

tions

sets of ratios

The

varia-

were due to

the rounded ends of the planform of the assembly.

For rudders and planes having aspect ratios materially less than 4, stalling should occur at flap angles greater than those shown in Fig. 44. C. On page 105 of the Gottingen reference there are given some data for a flap-type compound hydrofoil in which the fixed leading portion lies at an angle of attack a to the stream, and flap angle ^(ksi)

applied to

augment the

lift,

as in

In the late 1940's the National Advisory

Com-

is

diagram 2 of Fig. 14.U. mittee for Aeronautics conducted an extensive investigation

control-surface

of

characteristics.

purpose was to provide experimental data for designers and to determine the section characIts

of

teristics

various

airfoil-and-flap)

types of fin-and-flap (or combinations suitable for use as

control surfaces.

Two

of the reports describing the results of

these tests are listed hereunder: (1)

J. M., and Church, O., "Medium and Large Aerodynamic Balances of Two Nose Shapes and a Plane Overhang Used with a 0.40-Airfoil-Chord Flap on an NACA 0009 Airfoil," ARR L5 COl, March

Riebe,

1945. This appears to be Part

XXI

of the report

complete investigation. M., and McKinney, E. G., "Medium and Large Aerodynamic Balances of Two Nose Shapes and a Plane Overhang Used with a 0.20-AirfoilChord Flap on an NACA 0009 Airfoil," ARR L5 F06 of June 1945. This is Part XXII of the comseries covering the

(2)

Riebe,

J.

plete series.

As applying

to combinations of fixed plates or

and movable control surfaces abaft them, K. E. Schoenherr gives a graphic summary [PNA, 1939, Vol. II, pp. 207-208] of data derived by experimenters abroad and published in the fins

following references: (a)

W. L., Simmons, L. F. G., and Coales, J. D., "The Effect of Balancing a Rudder, by Placing the Rudder Axis Behind the Leading Edge, upon the

Cowley,

Moment of Comm. for Aero.,

Controlling

the Motion," Tech. Rep.

Adv.

R

and

M

253, 1916-1917,

p. 154ff

(b)

Munk, M. M., "Systematische Versuche an

Leit-

werkmodellen (Systematic Tests on Models of Control Surfaces)," Technische Berichte der Flugzeugmeisterei, 1917, p. 168ff.

Fig. 44.D,

adapted from Fig. 10 on page 208 of covers a number of

the Schoenherr reference,

cases of this kind, in sufficient detail to indicate

about what

pound

may

be expected of elementary com-

assembfies.

77

The results of somewhat similar experiments made by T. B. Abell are to be found in his paper "Some Model Experiments on Rudders Placed Behind a Plane Deadwood" [INA, 1936, pp. 137-144]. The results of these experiments are summarized by W. P. A. van Lammeren, L. Troost,

and

J.

G.

327-328].

"ImoWp,

Koning [RPSS,

1948,

pp.

ll\l)RenJ\.\A.\lR„s

78

TABLE AU

\\.\i

l.\

Mill'

SU,.\

Sec. 11.6

— List ok IIcfcrences Containing FijOw Diauiuus About AiBtx>iLs and IIyuuofoils

diagruna roproecnt flow with circulation unless othcrwiao indirntcd.

Tj'pp or Shape of Hydrofoil

1)1

FORCE AND FLOW DATA FOR HYDROFOILS

Sec. 44.6

TABLE Type

or

44.C

Shape

of Hydrofoil

List op References Containing Photographs of

Flow About Airfoils and Hydrofoils

79

innRoinx

80 Tlio roador

is

riuitiniicd

ii>

ninfmlxT

How

pnttoms inailo on a plate lieKl lirmly anainst tlio pad of n hydrofoil, iioriual to its axis, are liahle to

niisleadiiig. Tliere is

Im?

indennite thickness over

on

tlepiite*!

tliis

is jilTettcHl

it

to

of attack

applied

may

it

liy

change its angle be well-nigh useless. The torque in s«'rvice to

hydrmlynamic action on the blades

of

controllable jiropellers and on rudders

and the pattern some extent by (low

efTectivc center of pressure on the entire under-

plate,

Flow Almut an NAt'A 2:«)1") Airfoil at an lllTective Reynolds Nnniher of ISO.IMMI," 'IMH Hep.

Apr

Srr. 11.7

can not be rotated

n hoiiiulary layer of

ut the l)otton» of this layer ["Photographs of the

..'i7,

disk.x

\Mi(.s i\ siin"

that

knowledge

Ciutsehe has published a series of

The

location of the

water bixly of a turning ship, considered as a hydrofoil, is a major factor in its maneuvering

and

characteristics

Most

I'.MC.].

for their design.

necessary

is

the heel while turning.

in

moment

of the

(and other) data relating

graphs which show the flow traces over hydrofoils which comprise the blades of experimental model

and available for engineering use apply to airfoils. For these a fore-and-aft aerodynamic center is usually assumed, about which the

screw propellers. These show the i)aths taken bj' the surrounding liquid when passing over and

(pitching)

moment

ditions

relatively

!•'.

jjlioto-

to foils

is

coefTicient

for

constant.

various con-

This

center

is

between the blades, as viewed generally normal to the projectttl area of the blade ("Versuche an umlaufenden riiigelschnitten mit abgerisscner Striinuing (Kxperiments on Rotating lilade Sections with Hrcakawaj' Flow)," Report, of the Berlin Ahnlel liasin, published in S'R!, HMO,

sometimes taken on the chord of the meanline, at a distance of c/4 from the nose, but usually it lies on the ba.se chord, at the same distance from

Vol. 41. pp. 1S8-22G].

center

44.7

Pitching

Location.

Moment;

.Vs a rule,

Center-of -Pressure

information

a.s

to the ])itch-

ing-nioment coenicient and location of the center of pressure

on a hydrofoil to be used on a ship is lift and drag

as important as that relating to the

Indeed,

eoenicienl.s them.solves.

if

the hydrofoil

the nose.

As an

indication

of

Flow

CP

pressure

with varying angle of

and

cally for a flat, rectangular plate (diagram 1)

for

an

gram

of not-unusual .shape (dia-

airfoil section

2).

Sonie (luanlitative didii on this item, for simple hydrofoils and others suitable for ship rudders, tlinnigh

I.

I\'.

of Sec.

-1

\.'.\.

Distribution of Velocity and Pressure on

44.8 of

of chord wi.se shift of the

attack, Fig. 44. F illustrates this feature graphi-

arc given in items

Direction

what may normally be

of

way

expected in the

a Hydrofoil,

'i'lie

distribution of

and

velocity

for l)rc.>isure

&oth Oiograms

on an

airfoil

or hyilrofoil, discussed in

that occurring on and meas-

the jHcsent section,

is

ured
external surface. This

its

is

to be

distinguished from the velocity and pressure fields

around

it,

are tho.sc external

described in Sec. 44.9 following, which existing

foil

outside of and

surface.

occurring on the

foil

In general,

beyond the the pressures

surface determine the

drag, and other forces exert<^d on or

by

pres.sures occurring in the adjacent field

Smoll Circles Poftitions

Indicate Center-of -Pressure for Nominol Anolee of AttocU

Hydrofoils

06

0.0

Kio. 44. K

0.4

Length from

D1AORAM8

or-l'iiKjuii'iiK

ion A

'-2 0I~" Leadmo Edqe

Ii.i.i/HTiiATi.Nii

Position

l''l.AT

determine

of

symmetric section arc widely

used in ship tlesign and construction. Figs. 44.G, 44.11, and 44.1, adapted from Volume II of the

Section U5A5 Aspect Rotio 6

Chord

lift,

The

the forces on adjacent objects.

Airfoil

1.0

it.

Hmrr or

'"

Cf.ntkk-

With Anoi.k ok Attack,

P1.ATK ASI> A

HyDKOPOM.

book "Modern Developments in Fluid Dynamics," eiliteil by S. CJoldstein, Oxford Press, 1938 (Fig. 179 on page 455, Fig. 180 on page 4tV2, and Fig. 139 on page 404, respectively), give the chorilwi.se distribution of pressure coi'fTicient on eight typical .symmetric .s<'ction8, covering a wide range of thickness ratios tx/c. The angle of attack is zero, so the pressures on both sides are the same.

FORCE AND FLOW DATA FOR HYDROFOILS

Sec. it.S

08

06

OZ

04

X-Diatonce from LE, Froction of Chord c

Fig. 44.G Typical Chordwise Pressure Distribution ON Face and Back op a Symmetric Hydrofoil AT AN Angle of Attack

At the nose the dynamic

pressure equals the

pressure 0.5pC/« or LOOg.

On

ram

the back of a sym-

metric section working at a small angle of attack, the pressure coefficient usually drops very rapidly

with distance abaft the nose, to a value of 0.0 at 2 or 3 per cent of the chord. Within from 5 to 20 per cent of the chord length from the leading edge it increases numerically to a large negative value. Then it diminishes with distance abaft the nose, until at about 0.9 or more of the chord length the pressure coefficient

may

reach zero

a small positive value. On the face of the section, in a typical case with a small angle of attack, the pressure coefficient drops from its or have

value of LOO at the nose to a small positive value,

Hydrofoil

81

HYDRODYNAMICS

82 l>nck of the ncvenil nootions

oxtn-mc vmIuci of

for tho in the

shows wide

vtiri:iti
M

pp. 97-lO.S

Norton, F. H., and Bacon, D. L., "Pressure Distribution over Thick Airfoils— Model Tests," NACA Rep. 150, 1922, pp. -I.'il-ITI. On pp. 451-J52 there is a list of a numlicr of prior references on pressure

(5)

255, 1926 (6)

"The Flow

and

an Inviscid Fluid .\round an EUiptic Cylinder and an Aerofoil of Infinite Span, Especially in the Region of the Forward Stagnation Point," Tech. Rep. Aero. Res. Comm. (England), 1927-1928, Vol. I, R and 1097, Jul 1926, pp. 61-80

Fage, A.,

of Air

of

M

W. G. A., "The Theoretical Pressure Distribution Around Joukowski Aerofoils," Tech. Rep. Aero. Res. Comm. (England), 1927-1928, Vol. I,

(7) Perring,

R and M (S) Perring,

1

106,

W. G.

May

1927, pp. 209-221

A., Discussion,

INA,

1928, Fig.

B

on

253 (9) Knight, M., and Loc.ser, O., Jr., "Pressure Distribution over a Rectangular Monoplane Wing Model Up to 90 Degrees Angle of Attack," N.\CA Rep. 288, 1928 (10) Gutsche, F., "Versuchc an Propellerblattschnittcn (Tests on Propeller Blade Sections)," Schiffbau, 1 Aug 1933, pp. 267-270; 15 Aug 1933, pp. 286-289. The latter group of pages contains many graphs of pres-sure distribution on airfoil section.^. (11) Schoenhcrr, K. E., SXAMi;, 1934, p. 90. Contours p.

for

minima

pressure

and

sections,

airfoil

terms of

in

thickness ratio, and (3)

lift

(1)

Ap/g,

arc

respectively,

given

and 20, pp. 109-112. (12) Winter, H., "Flow Phenomena on Plates and

K.

p. 176. Thiti

E.,

PNA,

diagram

give.n

19.39,

Vol.

11,

Fig.

29,

p.

of Propcllors,"

SNAME,

151.

F. Riegels, Technische Berichtc,

of Calculating Pressure Distributions

Profilen,'

TMB

Aero.

Memo

28,

Velocity and Pressure Fields

Mar

1955.

Around a

In Fig. 44. E of Sec. 44. G there are

two flow

iiiotric airfoil

pattern.s

around a

tj'pical

sym-

or hydrofoil, one corresponding to

the flow of an ideal lifiuid and one of a real liquid. Tables 44. b and 44. c of that section list references

diagrams and flow patterns around other and hydrofoils, made up generally of streamlines. However, the designer can often use to advantage a chart or plot embodying isobars and isotachj'ls, to show the essential characteristics of the pressure and velocity fields around the foil. Unfortunately, the published data on this particular item are very meager and there appear to be no distribution plots that can be taken as typical. Most of the data apply to airfoils, of the customary asymmetric .sections used for airplane wings. Thej' were taken usually to indicate to

airfoils

acceptable positions for the pitot tubes of air-

speed meters, and so do not cover the

fields sur-

rountiing the airfoil as a whole.

A

few references indicate sources of some of the

published results for projects of this kind: (1)

N. A. V., and Richardson, E. G., "On the Flow of Air Adjacent to the Surface of an .\erofoil," ARC, R and 1224, Dec 1928, pp. 32f.-34S Tanner, T., "The Two-Dimcnsional Flow of Air Around an .\crofoil of Symmetrical Section," ARC, R and M l.!.">3, Jul 1930, pp. 100-116 Parsons, J. F., "Full-Scale Wind-Tunnel Tests to Determine a Satisfactory Location for a Service Pitol-Stalic Tube on a Low-Wing Monoplane," NACA Tech. Note 501, Mar 1936 Gates, S. B., and Cohen, J., "Note on the Standardisation of Pilot-Static Head Position on Monoplanes," ARC, R and M 177S, Jan 1937, pp. 1238-1251 Crablw, E. R., and Diproso, K. V., "Calculated Pri'».sures /Vhcad of Struts and Wings," R..\.E., Farnborough (Engliiiun, Ti'chiii.-al Note .Xero 1510, Oct 1944 Piercy,

M

(2)

(3)

(4)

(5)

airfoil) wrction

at nn K.6Hlegre<.- angle of attack. (15) Goodttll, Sir Sliinli-y V., "Sir Charles Parsons and the Royal Navy," INA, Apr 1942, pp. 1-10, esp. Fig. 6, p.|3; SCO also HBHR, 23 Apr 1942, p. 451

104,

by

])ii'Uirp(i

the pre.Hsure distribuliun

along the chord of a hydrofoil (or

Fig.

tion of 'l;ber die

44.9

of Short Span,"

(14) Schoenhcrr,

1948,

Over Shape (Including a TranslaBerechnung der Druckvertcilung

Hydrofoil.

in

.\irfoils

11,

1943, Vol. 10),"

Figs. 19

NACA Tech. Memo 798, Jul 1930, pp. 7-9 and Figs. 21-24 Arnold, R. N., "Statistical and Shannon, and J. F., (13) on tho Singing Invostigalions Experimental Propeller Problem," lESS, 193H-1939, Vol. 82, pp. 255-374, esp. pp. 270-285, 326

lU'SS,

Profiles of Arbitrary

(2)

coefficient, for ogival

A.,

"Tho Design

Fig.

Method

.\.,

M

P.

This diagram shows the graphs of pressure coclTicient Ap/7, on a base of from cent of chord the leading edge, for tho per backs of two N.\C.\ sections with two difTereot camber ratios and two angles of attack. (18) Reed, T. G., and Ormsby, R. B., Jr., "The AVA 1949,

von

and Howard, R. G., "A Consideration of .Virscrcw Theory in the Lisht of Data Derived from an Experimental Investigation of the Distribution of Pressure over the Entire Surface of an Airscrew Blade, and also Over .Verofoils of Appro6S1, Mar 1921, pp. priate Shapes," .\RC, R and 264-357. Pres-sure measurements were taken on a full-size airscrew, one point at a time. Briggs, L. J., and Dryden, H. L., "Pressure Distribution Over Airfoils at High Speeds," NACA Rep.

Src. -14.9 \V.

p. 101

distribution over airfoils.

Fage,

SKiX

(17) Hill, J. G.,

ti-st.

M., nml Piitenion, C. J., "InvostiRation of the Diiitribution of Pressure over the Entire Surface of an Aerofoil," Teeh. Rep. Adv. Comm. for Aero for 1912-1913 (Kngland), R and 73, Mar 1913,

(4)

1)1

Liiinimrrii,

Villi

real-slip nitio roprescnte*!

(2) Jones, B.

(3)

1\ Mill' .11..

(6)

Kuethr, A.

.M.,

M.K.-.-,

P.

U.,

.•m.l

Curry,

U

.

II.,

"Measurements in the Boundary Ijiycr of a Vawcil Wing," NACA Tech. Note 1946, Sep 1949.

FORCE AND FLOW DATA FOR HYDROFOILS

Sec. 44.12

44.10

and

Spanwise

Distribution

Sees. 14.8

Lift.

and

may

Fig.s. 14.1

may

14.J illustrate the variations that

that

Circulation

of

and

14.9

and

occur, or

be planned in the spanwise distribution

of circulation

and

across a hydrofoil. These

lift

diagrams, plus Figs. 14. L and 14.0, show about

where the principal

vortexes

trailing

may

be

expected for certain circulation distributions. In particular

practice,

and

circulation (a)

in

spanwise

distributions

of

are desired for the purpose of:

lift

Reducing the tip-vortex strength and severity, an effort to reduce the force and energy losses

there, as well as the induced drag

Eliminating almost entirely the root vortexes

(b)

may

be done at the roots of screw-propeller blades to reduce the strength and harmful effects of the swirl core.

in a cantilevered hydrofoil. This

Applying the greater part

(c)

of the

lift

load at a

given point or in a given region across the span,

and lift that actually obtains, and is by no means an independent function of the geometric planform shape and proportions. This of circulation

because the effectiveness of the end plate depends upon the magnitude of the overall pressure differential between the +Ap and the is

— Ap

ments (d) Reducing the magnitude of the — Ap values in a region where air is liable to be sucked down from the surface. An example is the top of a rudder which has only a thin layer of water above it.

Distributing

(e)

the

lift

load

achieve

to

the

greatest efficiency for the hydrofoil as a whole.

surfaces. If the pressure differential at the

desired circulation distribution

is

generally

obtained by changing the nominal angle of attack

with respect to the probable

across the span,

direction of the inflow velocity. In this connection, it is

to be

remembered

reduced,

is

the

that, as the angle of attack

circulation,

induced velocity diminish with

the it.

lift,

and the

A large induced

velocity results in a large actual angle of attack,

which compensation must be shaping the hydrofoil. for

Another method the

lift is

made when

of reducing the circulation

to diminish the

camber

and

of the sections

must usually be done without changing the section thickness, since the latter is

in question. This

it

(if

No

general procedure

is

known

hydrofoil

when

surfaces which in Sees.

lie

close to

act as the end plates described

and 14.8 and illustrated in Figs. and 14.M. Indeed, the effective aspect

14.7

14.H, 14.1, ratio

either or both ends

may

depends largely on the spanwise distribution

is

no

were practical) would create an effective

At one

limit it is probably sufficiently accurate

for engineering purposes to say that a

gap parallel

to the span, equal to the adjacent chord length,

has the same effect as one of great width. A tip or an end next to such a gap may be considered

beyond the influence

of the adjacent structure

acting as an end plate.

At the other construction

limit the

customary working or mechanical

clearance used in

tip

enough to prevent the adjacent and the hydrofoil from behaving as one of infinite length and aspect ratio. Furthermore, an end plate attached to a tip with zero gap is probably not design

is

large

structure from serving as an end plate,

such unless

it

extends for at least one

around the section. The hub surface of a screw propeller, as one example, is almost never adequate for this purpose, when considered as a combined inner end plate for all chord length

all

the blades.

Design Notes and Drag Data on HydroPlanforms and Sections. This section is intended to cover hydrofoils designed and fitted for general and special purposes. The design of control-surface hydrofoils is discussed in Chap. 74 44.12

foil

and

of screw-propeller blades in

Chap. 70.

Aside from the influence of planform on the aspect ratio, the principal features in the selection of hydrofoil

planforms and section shapes involve:

Increasing the chord length and thickness at

points

Ship Hydrofoils.

there

geometric ratio.

siderations.

for determining the effective aspect ratio of a

tip,

aspect ratio roughly twice that of the actual

(a)

Effective Aspect Ratio for Equivalent

this differential increases at

need for an end plate. With a large pressure differential at the tip, an end plate of adequate area

required for strength, rigidity, and other con44.11

if

only a slow rate inboard from the

effective as

The

and

tip is zero,

free,

because of strength, rigidity, or other require-

83

where the

member

or

foil

structure

attaches to some fixed and where the end-plate

effect is sufficient to

Ap

(b)

tip

prevent loss of overall Diminishing the chord length at the because of the low strength needed there and reduction in tip-vortex loss which normally companies the use of a short tip. Values of

the ac-

the

taper ratio Ct/cr

may

range from 0.3 or

fixed fins to 1.0 or

more

for screw-propeller blades.

less for

in

84 If rnkc or .xwoop-lmck in the leading

edge

OROm \

edpe of a hydrofoil, and

SHIP DESIGN

\MI(.S 1\

Sec.

H.13

or licsirahlc

is lu'Ci-ssjiry

if

the trailing

raked in the opposite direction so that the hydrofoil has a taper ratio less than 1.0, the is

may

behavior and characteristics the basis of a

number

liaving small spans If

be estimated on

of chordwisc eiomcnts

Sh and varying chord lengths.

the raked or swept-back hydrofoil has ajjpioxi-

mately constant chord over the span, it.s performance may be predicted on a basis of (1) a span normal to the relative-flow direction cc|ual to the diagonal length of the hydrofoil,

and

K Variation OF Total-Drao, FrictionDrag, AND Residuary-Drag CkjEKKiciENTs of a JorKOWSKI .\lRFOIL WiTII THICKNESS RaTIO

Fio. 44.

(2) a

rciativc-flow velocitj" equal to the dircction-of-

motion speed times the cosine of the angle of sweep-back. This corresponds to the situation depicted in diagram 1 of Fig. 17. D on page 2G5

adapted from Fig. 138 on page 138 of Volume II

of \'olume

values

I.

The appropriate chapters and

III describe

ship

hydrofoils.

Of

still

and

act

as

in

which

whose design

is

discussed

73. IG, especially the

forward

the

for

book,

representative

gives

and

friction-drag,

total-drag,

rcsiduary-tlrag coefficients, on a base of thickness ratio, for

low-aspcct-ratio

smaller aspect ratio are the

fbced roll-resisting keels in Sees. 73.15

manner

illustrate the

themselves

hulls

of Part 5 in ^'olu^le

referenced

the

of

Joukowski

airfoil siH'tioiis.

Quantitative Data on Cascade and In-

44.13

On

terference Effects. effects foils

ill)

exist

the basis that interference

between the flows around hydro-

placed abreast or in cascade, despite the

portions which run at varying angles of attack

qualifying statement in the last paragraph

as the ship pitches and

Sec. 14.15 on page 228 of

The ma.ximum ness ratios

rolls.

/.v and thickmore often than not, fi.xed by strength and stiflne.ss. Xevcr-

section thickness

/.v/c arc,

requirements for theles.s, it is

well for the designer to

know some-

allowing

many

for

predicting

or

difficulties.

reasonably

Volume

So

simple

far as

or

of

the matter of

I,

these

poses

effects

known, there are no

straightforward

rules

or

may

procedures by which the marine architect

thing of the effect of thickness ratio upon hydro-

execute a proper new design or even estimate the

adapted from "Modern Developments in Fluid Dynamics," edited by S. Goldstein (Fig. 137 on page 402 of Volume II), indicates the variation in drag coefficient with thickness ratio to be expected on a Joukowski type of airfoil section at low /?, values. Fig. 44. K,

behavior of an existing design involving two or

foil

drag.

Fig.

44.J,

more hydrofoils approximately abreast each In every screw propeller, even though

a Reynolds Number Uc/k

of

has

only two blades, there arc some small radii where the stagger between blade sections

small with

is

However, the interference the case of an analytic design

respect to the gap. here,

effects

in

based upon the circulation or vortex theory, are taken care of by other portions of the design

Data Are for Joukowshc Airfoil Sections ot

other. it

4 (lO*)

procedure, as described in Chap. 70. It

Drag Coefficients ore Based on Chord Lenqth per Unit Span

easy Jifl2

to

transfer

the

is

procedure

correction

another problem, such as to that of twin or

not to

triple

steering rudders, side by side.

Problems involving the use spaced vOOl

hydrofoils

in

cascade

occurrence in the design of fluitls

of ratlier closely

are

pumps

of all kinds. Allliough there

is

literature in this field, the symbols, ''ioniinor

Flow on o Fiol Plote

m

55 Thici
Fifi. 'll-J

analysis,

—r—

Rolio

35

-^

Vaiiiatiom in ReHiDUARY-Diun Cokkkiciknt

ov J0UKOW8K1 Aiiiron. Skctionh With Tiiickncss IIatio

and design procedures

of

common

for handling

an extensive

methods

for

of

hydraulic

machinery' are so different from those customary in

marine proi>ulsion and

relateii fieUls

that they

are not in a form readily usjible by naval architects

and marine engineers.

FORCE AND FLOW Dy\TA FOR HYDROFOILS

Sec. 44.13

Nevertheless,

a few of these references are

quoted here: Gutsohe,

F.,

85

recent reference, written entirely in readable,

straightforward English,

"Versuche an Propellerblattschnitten (Tests on Propeller Blade Sections)," Schiffbau, 1 Aug 1933, pp. 267-270; 15 Aug 1933, pp. 286-289; 1 Sep 1933, pp. 303-306. Some of these original data are worked over and adapted bjf K. E. Sohoenherr ISNAME, 1934, pp. 105-107, esp. Fig. 15 on p. 106]. (b) Spannhake, W., "Centrifugal Pumps, Turbines and Propellers," MIT Press, Cambridge (Mass.), 1934 (c) Wislieenus, G. F., FMTM, McGraw-Hill, 1947 (d) Rouse, H., EH, 1950, Chap. XIII, pp. 858-992. A list of 54 references is given on pp. 990-992. (a)

A

analytic

is

the description of the

and experimental work undertaken by

Commander W.

T. Sawyer,

USN,

as his doctorate

dissertation at the Federal Technical Institute in

Zurich, Switzerland. It

is

entitled "Experimental

Investigation of a Stationary Cascade of Aero-

dynamic Profiles," Mitteilungen aus dem Institut fiir Aerodynamik, No. 17, an der Eidgenossichen Technischen Hochschule in

Leeman, Zurich (copy

in

Ziirich, 1949,

TMB

Ubrary).

Verlag

C;11A1'1LR

IJ

Data and Friction-Resistance

Viscx)us-Fl()\v

Calculations 45 1 45 2

General Refcnnice Data on Mass Density, Dynamic Viseosity, anil Kinematic Viscosity ...

45 3

Representative Internal Shearing Stresses in Water Alongside Models and Ships ...

45 5

I.,ayer

Characteristics

45.7

The Development

45. 5

List of Principal Friction-Resistance

of

Formulas

Smooth Plate

in

Practical Definitions of Surface

97

45.19

Factors Affecting Fouling Resistance on Ship

99

45.20

The

I.aminar Sublayer Thicknesses in Turbulent

45.11

Friction

ATTC

herr or

1947

Flow for

Water Flow

in

45.24 45.25 45.20

Internal

GeneraL

of the

Wetted Surface

Cliap.s. 5, G,

of a Ship

and 22

of

100

\'olume

flow in a real liquid along flat

and curved plate

useful a

somewhat

Selected Bibliography on Friction Resistance

128

for

of

ship and

some

of its parts.

The method

is

of

Superintendents,

mcnt.s for u satisfactory and acceptable cojjy of this pajjer

o'

f

in

using

the

variations

is

subseciuent .sections

The Reynolds number

not only as a flow parameter but as an

model rather than the

may

Rej'nolds

in ship

nmnbers

is

of inti-rest in

work, becau.se most of

for

minlels

are

in

the

low ranges.

One other fcaliu'e invohing the u.se of the Reynolds number in practice does require mention. It is cuslomary in many (juarters, when

available in

I

and

conditions. This latter feature

rid ion

'IhcTc are a«s
41..")

and

several

it*!

be exi)ected aroimd a IkkIv imder a given set of

library.

furnuilaM, c(|untiunH,

calculating

indicator of the type of viscous flow which

in

lield

of

the present chapter.

.serves

September, 1948. It gives a brief re.sumd of the development of the various friction formulas, a most elaborate comi)ari.son of the re.Hultw obtained from each, and a set of re(|uire-

A

and

L.

in

'1MB

various

by Senor M.

by Senor Acevedo at the Fifth International Con-

Ihr-

[jrodiftiiig

different exposition

described in Sec.

formulation.

or

(.stiinatiiig

in a

45.A convenience and the

an am()li(ied version contribution actually presented

Tank

127

128 128

Friction Resistance." This

London

Moored

Stream

of a Craft

Hej'nolds inunber antl

ference of Shiji

120

.

Drag

Acevedo, .Superintendent of the M(k1c1 Basin at E\ Pardo, near Madrid, Spain, entitled "Shii) (in KnglLsh; of tlur

of a

summarizes these data for subsequent sections of this chapter explain how they are used to derive numerical answers for a

referred to a paper

is

125

Drag

ships, including the friction resistance. Fig.

and around the e.xternal boundaries of an underwater ship hull. The reader who may friction

120

Calculation of the Friction

Friction

rccniircd

surfaces,

find

117

Prediction of Fouling Effects on Ship

features of the viscous flow around bodies

give a general physical picture of the viscous

14

115

Ship Allowances for Friction Drag on StraightElement and Discontinuous-Section Hulls The Friction Resistance of a Planing Hull

45.23

105

Computation

1

.

Ship Propulsion

The

45.22

104

Data

113

Roughness the Allowances for Rough-

References Relating to Fouling as Affecting

15 21

104

Passages

112

Resistance

Schoen-

MeanHne

110

Sand Roughness

Determination of

102

45. 10

109

.

Smooth

Surfaces

Turbulent

Specific Friction Coefficients for the

45.1

E(|uivalent

95

45.10 45.17 45.18

Form-

45.9

I

94

.

for Calculat-

Flow

45.12

Criterion for a Mydrodynamically

ness

ing Ship Friction Resistance

ulas for a Flat,

45.15

Surface

Typical Velocity Profiles in Ship Boundary layers

45.0

94

94

Tables of Reynolds Numbers for Various Ship Lengths and Speeds Data on and Prediction of Ship Boundary-

45.4

45. 14

Wetted-Surfaco and Boundary-Layer Calculations for the Transom-vStern ABC Ship of Part 4 Estimating the .MIowanccs for Curvature

45.13

80

lie

and other qnanlitalivc data

cnnsidcring only

8G

the

visctnis-flow

situation

for

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.1

r~~

—

^

a-l-:— Transition —>4-<:

Flow

Turbulent

87 Laminar Flow

Logarithmic

-. I

Tr\i

FOR

mA

Equation

Profile,

of

U-Cyf

Equation

|

U-Clogy

or U = U„f^)^|

6 - 0.38

^{^^'^

Enerqiy

H

= -|- -

Thickness

where

0*-

to

1.3

Enerqy Thickness

Shear . ."^

0.5/0

,

U^ ,

B

or C,

symbol R„

.

L

When

signifies that the

number studies

of

-

0.074 R^

it

°"^

of

a body or ship, to use the done it almost invariably

space dimension in the Reynolds flow

and

many

boundary-layer

becomes necessary to consider

the body or ship which has an x-distance less

than the length L. In these cases the Reynolds number for the situation under study is the with the x-Reynolds number, expressed as R^ x-distance from the leading edge or stem stated in each case. For example, in the formulas of Figs. 5.R and 45.A, the symbol R^ is used in connection with values averaged for the whole ,

situations

R^ is used for local values, or for where the x-distance is itself a factor

in the formula.

in

This Case)

2. 6, obt.

(Not Applicable

Velocity

\Jt-(^)°-^

Local Frictionol-Droq Coefficient at

Clf" 0.66

the situation at or ahead of a certain point along

length, while

Laminar)

Any

~3~

Point A,

R.£°-5

Mean Drag Coefficient for x-Distance Cf- 1.33 Rx'"

this is

viscous

development

C,

x-rDistance

that entire length. However, in

is

ond

©*=

is

0.133(5, abt.

to A,

Summary op Viscous-Flow Formulas for Laminar and Turbulent Flow

Fig. 45.A

the entire length

Cf

1

B

l.73x R^'^ = 0.55S,abt.

Shearing-Stress Coefficient (^r~ oJoU ^ "

- -?-

Local Frictional-Drag Coefficient at Points Clf = 0.059 Rx""'*

to

6*=

6l- (Entire Loijer

Shear Stress at Plate To=CLF-q- 0.66q-R^°-^

^t'{-^)°'''

Mean Drog Coefficient for

Sublayer Thickness

6* Shape Factor H = -q-"

1.5

Ct ^^ -

Lo^er ot ony Point A,

5.(-^)''== 5.Ri°-=

Momentum Thickness 9=

Shear Stress at Plote TQ-CLp-q -0.059q-Rx°"^ Sheor Velocity

of

6 =

Displocement Thickness

ll.6-i k*: IS.6

0.175 5, abt.

Shearinq-Stress Coefficient ^

^«:?~T6 ^~~^-^_ U ? I

Equation of Profile, U„-U-a(6-y)^or U=U^--^(6-y)2

R^"''^

0.146, obt. ,

Leodii 1^

Edqft

Nominol Thickness

C,

6- 0.097 6

Momentum Thickness Shape Factor

k-^

S^_-

—

FOR LAMINAR FLOW

U-U„-|^

B and

- 0.38 X

6*=

Thickness

5ublQx;er Thickness

to Leading

Profile,

or

Nominal Thickness of La\/er ot Points

Displacement

I

X

of

I

I

TURBULENT FLOW

U^-

|_

Parobolol V/?T?/y>,

rorabolio Approximation

I

I

It

seems almost certain that there are factors

in viscous flow not taken into account

by the

Reynolds number, but until more is known of them, they can not well be considered in any quantitative treatment of friction resistance. Friction-resistance

calculations

are

necessary

Froude method of predicting ship resistance, in which the residuary resistance derived from tests of a model of the same proportions and shape is added to the friction resistance deduced from resistance tests of flat, smooth surfaces in the form of thin planks or friction planes. Because of the limitations of model-testing equipment it is still necessary to extrapolate the flat, smooth-plate data well beyond the experimental range, especially for large, fast vessels. It has not been possible to check this extrapolation in the latter range by full-scale ship measurements for the

IIVDRODVX AMIC.S

88

TABLE 4&a— Rbtnouw Nuubebs Velocity

IN SHIP

DtSIGN

raa Vabious Ship Lenothb and Spkeos in

Sir. -15.1

STANDARD FRESH WATER

Sec. 45.1

FRlC'llON-RESISTANCE CALCULATIONS TABLE

Velocity

45.a— (Continued)

89

90

IIMIRODN \

\MI(;s l\

sllll'

l>|s|(,\

Sec. -15.1

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.1

TABLE

45.b-

91

11M)R()^^ \ \MI(;s l\

92

TABLK Velocity

-JS.l)

-Hkvnou.8 Nimbkils

in

sllll'

IIF.SIGN

.STANDAKD SALT WATER

Srr.

(Continuod)

If. I

Sec.4'i.l

FRICTION-RESISTANCE CALCULATIONS

93

HYDRODYNAMICS

«M in

which the

can be segregated

friction resistance

with reasonahle accuracy.

Adequate

are not yet avaihible for prwHctions of the effects of

and

transverse

from the

when making the

smooth plate to the

flat,

and

curvature

longitudinal

pressure gradients,

of

transition

niotlel or ship

Limited

from

data derived

full-scale

thrust

measurements enalile a reasonably reliable assessment of combined smooth-plate and rough-ship friction resistances for certain types and conditions of ship-bottom surface.

Reference Data on Mass Density, Dy45.2 namic Viscosity, and Kinematic Viscosity. Tables X3.d thri)Uij;h X:^.i of Api)x. 3 of this volume give values of the ma.ss density p(rho) and the kinematic vi.scosity v(\\n) of "standard" fresh and salt water, the latter of 3.5

per cent salinity, for

a range of latitudes and temperatures sufficient to meet the usual needs of the ship designer and

marine architect. Tables X3.j and X3.k of Appx. 3 give values of these characteristics, plus values of the M(niu),

dynamic

over a rather wide range in

temperature, for a number of well-known li((uids encountered at times in ship-design work. The original

which

from

data,

(a)

Rouse,

(b)

Rouse, H.,

IT.,

EMF, EH,

were

tables

these

adapted, are listed .somewhat differently

in:

1940, Appx., pp. 3.J7-3G.5 Appx., pp. KIUI 1013,

19.50,

including the references listed

Rouse, n., and Howe, Appx., PI). 231-238.

(c)

W.,

J.

Water Alongside Models and

rcl:itionsliii)S

BMF,

1953,

given

in

Chap.

Ships. 5

of

From the Volume I,

particularly in Fig. o.R, the shearing stress r(tau)

any point in a li(|uid undergoing viscous action = nidU/dy) where y is measured normal to the flow, in the direction in which U is varying. At a solid surface under a viscous liquid flow the

at i.s

T

shearing stress at the wall

is

[Rouse, H.,

KMF,

HUG, pp. 185-180]

where area

to ha.s

or

specific

•

any designated point along the solid surface may be found by the formulas of J'ig. 45.A and of the preceding paragraph. The numerical examples of Sees. 5.12 and 45.15 give value for

a

in/Li'.

The

friction

resistance coefficient

Cir

namely

water:

(a)

Ship 500

=

ft^. To

speed 20.72

ft long,

1.797 lb per

ft'

kt,

5 =

45,000

as an average value for

the whole ship, calculated at the end of Sec. 5.12

Ship 400

(b)

=

To

2.504 lb per

Ship 190.5

(c)

speed 30

long,

ft

on a point 200

calculations

ft

kt,

but basing

abaft the FP,

at that point

ft"

ft long,

speed 12

kt, to

=

0.485

kt, t„

=

1.051

lb per ft' for a point at the stern

Slup 510

(d)

speed 20.5

ft long,

lb per ft' for a jioint near the stern, TjOO

the

bow

(c)

Model 20

To

=

ft

on

calculations

ft'

10

from

ft

10 kt, but basing

long, speed

a point

0.G093 lb per

ft

abaft

FP,

the

at that point.

Tables of Reynolds Numbers for Various

45.4

Ship Lengths and Speeds.

and

Sec. 2.22 of X'olume 1

in

is

pointed out in

many

of the standard

It

works on hj-drodynainics, that the Reynolds number is a logical and a practical parameter for representing quantitatively the analytical and experimental evidence on viscous reference

flow, involving friction resistance.

This

regard-

is

the type of viscous flow, whether laminar

or turbulent, or of the degree to which surface

roughness effects enter into the picture. In the latter case there are, however, certain (|ualifications

as

to

the

separate

influences

liquid

of

and distance from the leading edge. As such the Reynolds number enters into many of the present-day calculations and predictions, not velocity

only with

the

space dimension x representing

length from the leading edge, as in a ship form,

but with the space dimension representing the width b or the diameter i) of a body. To facilitate calculations involving its wide-

and "standard"

the dimensions of a force per unit

pressure,

Siilt

spread use. Tables 45. a and 45. b give calculatecl values of /f„ = VL/v for both "standard" fresh

'^"'" '(f) L. - '^"(i)"- -

'•

calculateii average t„ for a whole solid surface found simply by dividing the wetted area S into the calculated friction drag Rr Its local

less of

45.3 Representative Internal Shearing Stresses in

A

the following representative values for "standard"

surface.

viscositj'

Sec. 45.2

is

nielliotls

ninking accurate

IN SHIP DESIGN

local is

as

given in the wvcral formulas of Figs. 5.R and •t.')..\, for the condilions existing or assumed.

The range

sjilt

water, as defined in .Vppx. 3.

of lengths L, or j:-<listances,

enough to span both model and ship the range of speed, expressed in both

and

is

sizes, ft

large

as

per

is

.sec

kt.

The


in

Table

l.").!i

are caiculatrd bv the

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.5

usual formula

72„

=

VL/v, where

V

the ship

is

speed in ft per sec, L is the length or space dimension in ft, and v is the kinematic viscosity for standard fresh water at a temperature of 59 deg F, 15 deg C, namely 1.2285(10"') ft' per sec.

The data in Table 45. b are calculated in same way for standard salt water, having a

fouling in service.

A velocity traverse with a

at a given point on a model of the ship gives

3.5

indication of the thickness but this

To

R^

facilitate calculations of

lengths not covered

by these

The

of the art.

principal reasons for the uncer-

tainties are: (a)

The boundary-layer

point on a model

is

thickness

a

at

given

greater in proportion than at

the corresponding point on a hydrodynamically

are in millions, or /?„(10"°).

/?„

some method is

tedious and uncertain, at least in the present state

Values of x~ or d-Reynolds numbers are taken from these tables simply by substituting x or D forL. Values of

cylindrical pitot tube

the

1.2817(10"'^) ft' per sec.

is

in the water. This

new surfaces and those roughened by uneven paint coatings and by

Under these conditions the kinematic

viscosity v

is

applies to both clean,

per cent salinity and a temperature of 59 deg F, 15 deg C.

95

long before the ship

hull,

smooth ship, for the reasons explained in Sec. 6.8

and

for speeds

of

Volume

I

tables:

and

illustrated in Fig.

6.E of that

section (a)

Speeds in

ft

per sec corresponding to integral

values of kt, from

1

through 100

kt, are

Table X4.b (b)

The

The

is

0.8140(10')

S.

reciprocal of 1.2817(10"')

is

0.7802(10')

the

and

for lengths of 50 to 1000 ft [INA,

Data on and Prediction

of

R„

Apr

on a model, or on a

for a

from the

inch.

1952, p. 61].

of Ship

F. M. Richardson, J. K. Ferrell, H. A. Lamonds, and K. 0. Beatty, Jr., in a paper entitled "How Radiotracers are Used in Measuring Fluid Velocity

Boundary-

Profiles"

describe

6=5xRx,"'° in 8.14(1 0*")

ship, at distances

surface of the order of a few thousandths of an

and

Layer Characteristics. A number of detail shipdesign problems require, for their proper solution, a good estimate of the boundary-layer thickness 5 (delta) at any given point around the underwater

,R^=

as

traverses in the vicinity of the laminar sublayer

Baker gives a small table

y-value of 1.29(10"') for speeds of 2 to 35 kt,

4S.5

to

1955)

(in

action in thickening the boundary layer, over and above what it would be on a hydrodynamically smooth surface (c) The difficulties in making accurate velocity

or 0.07802(10').

G.

uncertainty

its

reciprocal of 1.2285(10^')

or 0.08140(10') (c)

Existing

effective roughness of the actual ship surface,

(b)

given in

[Nucleonics,

new

Jul

1955,

tracer techniques

for Laminar

221-223],

pp.

by which

liquid

Flov

Standard Fresh Water

Broken Lines Indicate Regions of Extrapolation for the Formula Given 0.09.: 0.08ii

0.03IQ

30 £8

26 24 22 20 18 16 x-Distonce from Leadino

Fig. 45.B

in

le

10

8

6

4

2

0"""

Edae, ft

6 with s-Distance from Leading Edge, for Laminar Fresh Water

Vaeiation of Boundary-Layer Thickness

Flow

14

IIVDRODVNAMKLS

96 velocities

nmy

l>e

within 0.002 inch

lieteriniiied

of the inner wall of a tube of circular section. Fig. 3

on page 23 of the reference is a plot of V on distance from the inner wall,

local velocity

embodying observations taken within 0.0006 inch of the solid surface in a regime

which

is

distinctly

laminar in character. Despite the difficulties and drawbacks mentioned, the velocities at a series of

normal

dis-

tances from the hull surface can be and have been

measured on both ship and model, and the velocity profiles plottetl.

Two

sets of typical ship profiles

arc reproducctl in Sec. 45.6, are quoted there on

many

and reference data Despite the

others.

shortcomings of the observed data, anj' information at all is considered l)etter than none.

A

designer's need for boundarj'-layer data

be sufficienth' pressing

— for instance,

may

in selecting

propeller-tip clearances alongside the hull on a

large

and important passenger extensive

rather project.

However,

model- or it

is

—

to justify a ship-measurement

liner

well for the designer to

no matter how extensive are the measurements projected, they will almost surely be found insufficient when the time comes to plot, analyze, and use the results. This is not intended to discourage the designer before he begins but to broaden the scope of the measure-

know beforehand

that,

ments.

As an

illustrative

example there

may

be men-

tioned the investigation carried out on a cruiser

model

in the early 1940's, to

400 360

960

340

320

300

determine the proper

260

260

240 I-

Fio. 45.C'

IN Mill'

DKSIGX

Flow

in

It

is customary' for these instruments, an acceptable pasition was found only after exploring the boundarj' layer under a model

the entrance, as

from the stem to a position far aft, under the after engine room. When the isotachyl representing 100 per cent of ship speed was drawn on the outboard profile it was found that, at the position originally proposed for the log, the isotachyl lay more than 6 ft below the keel. of the ship

This distance was about twice as great as the contemplated log extension beyond the hull. On the basis previously' mentioned, that some indication of 6-valucs are better than none. Figs.

4o.B and 45.C show plots of boundary-layer thicknesses for laminar and turbulent flow, respectively, derived from the space-velocity relationships of Sec. 5.13 of ^'olume I and Eqs. (o.vii)

and

(5.viii)

for

flat,

smooth

plates.

In

plotting these graphs, the data have been extra-

polated to ranges far beyond those justified by the manner in which the formulas were derived.

The

plots are therefore to be considered as indi-

cators of the 5-values, nothing more.

A

graph illustrating the values of

160 140 120 180 220 200 Distance from Leodinq Edqe, ft

Vaiuatki.n uv HorsDAnY-LAVKii Thic-knkk.h

Sec. -(5.5

was necessary to know the position, both fore and aft and relative to the surface of the underwater hull, of the cloak of the boundary layer where, at the designed speed, the relative water velocity was within one per cent plus or minus of the ship speed through undisturbed water. Although it was expected that the log would be installed under location for a pitot^type speed log.

i with j-1)i.stanck Fkuii Watek

kiu)M

100

5

for the

eo

Lkadino

Kiiok, fxju Trniiiii.ENT

FRICTION-RESISTANCE CALCULATIONS

Sec. 45/,

ABC

97

Values of the displacement thickness 6* (delta

Freeman entitled "Measurements of Flow in the Boundary Layer of a 1/40-Scale Model of the U. S. Airship Akron" [NACA Rep. 430, 1932,

are even more difficult to predict because they depend upon the shape of the velocity

pp. 567-579]. This paper contains a considerable number of boundary-layer velocity profiles of

ship designed in Part 4, calculated

method,

is

by

this

given as Fig. 45.1 in Sec. 45.13.

star)

within

profile 5* is

of

=

the

boundary

layer.

The

ratio

0.145 for turbulent flow, given in Fig. 45. A,

an acceptable engineering more definite data. It

is

available, described in the references listed here-

regrettable that the technical

problems involved in the measurement of boundary-layer profiles on ships, or even on models, are of such magnitude that complete and accurate observed profiles are almost nonexistent. For an indication

of

the

enormous amount

labor

of

involved in a comprehensive study of this kind the reader has only to study a report

Bottom Scale for Local in

In the cases where ship (or model) profiles are

figure in the absence

Typical Velocity Profiles in Ship Bound-

45.6

ary Layers.

the type which should be available to naval architects for typical ship models.

by H. B.

under, either: (a)

The

velocity traverse

the small values of

was not

variation in the range of

about 0.6 or 0.5 1/„ (b)

The

enough, at

U

(or

V)

less

than

(or V), or

velocity traverse

extended only to a

value of y where U (or V) was approximately equal to U^ (or F), despite indications that at a greater transverse distance

U

would exceed

[/„

Hull PlQti nq.pf^ShJR Velocit'j

Percentooe

of

U

100

Ship Speed

Boundorvj- Lo\;er

"1

1

Relative

Profiles

Velocitij

1

Velocitvj

1

U

for

a

1

1

Small Destrovjtr Zero Point 118.5 ft Abaft FP, /6.10 ft below At-Rest WL

•

in

PercentQoe of Ship Speed

-Bottom^ Hull^PlQtintf, Fig. 45.D

fine

to follow the velocity

y,

of

Ship (rnvertedj

Typical Boundary-Latek Velocity Profiles for Several Operating Conditions on

Two

Ships

,

HYDROnYN WIK

98 because of expecteil

tlio

+At"

nugmeiit of velocity

to

Ijc

the potential flow abreast the wide

itt

This lack of essential data makes it impossible, not, to determine the boundary-

more often than

by the

tiiifkncss

(5.5

this situation is

found

diagram of

method

delta-velocity

of \"olumc

described in Sec.

in the

I. An example of upper right-lmnil

Fig. 45. D, giving three partial velocity

data kindly

by

furni.'shed

J.

Both high-speetl deep-water profiles on Fig. D show a characteristic flatness almost a hollowness at a ratio U/Um of about 0.90. The Laute and Gruschwitz profiles of Fig. 22.C in

are the: Hindcnburg,

(1)

The

TMB

ship velocity profile comparison by E. A. Wright

(S\.\ME,

case only suflicient to obtain readings of local

bottom and

23. G kt, with clean

The in

V

deep water, indicate greater

local velocities

(4)

diagrammed

for a

considerabl}' thicker laj'er, as

22.H

Fig.

in

of Sec.

22.13.

Again the

pp. 107-174).

full

boundarj'-laycr thickness could not be explored

(0)

The

is

thicker, as

Swedish ]Vrangcl), shown inverted in Fig. 45. D, are taken from tho.se published by II. F. Nordstrom [SSPA Rep. 27, 1953,

pp.

II.

F,

Xordstrom and assistants ["Full-Scale Tests with the Wrangcl and Comparative Model Testa,"

SSPA Victory

(8)

Rep. 27, 1953). ship,

APS,

Observations by

Tcrvacle.

G.

Aertsscn and his assistants [IN.V, 1953, pp. J21-J5G]. Fig. 3 on p. J25 and Fig. 22 on p. J52 (a revision of Fig. 3) show velocity profiles made with a rodmetor speed log under various conditions. Lucy Ashlon. Pilot traverses were made by a Pitometer

boundary-laj'er velocity profiles for the

small destroj-er

.also

Wrangcl, Swedish destroyer. Observations by

(7)

should be.

it

pp. 8:5-100 and Pis. III-V;

141-140).

but taking the reduced speed into

possibly be higher rather than lower. In anj' case,

XLVI,

Vol.

account, indicates that the local velocities should the boundary layer

STG,

Snaifell and Ashworth, British cross<-hannel steamers. Observations by G. S. Baker [NECI, 1929-1930.

are less than for the higher

speed with clean bottom in deep water. Consideration of backflow in the shallow water, plus surface roughness,

transl. available;

1951, Vol. 45, pp. 228-243).

For the test at 18.85 kt, with a dirty bottom and in a depth of water of 2.24 times the draft,

U

TMB

1952, Fig. 7A;

200,

because of the limited log-tube extension.

the local velocities

Some

Sanln Elena, merchant ship, 1951. V'^elocity profiles for both rough and smooth hull surfaces were measured amidships, 72 meters (236.2 ft) from the stem and 4 meters (13.1 ft) below the at-rest wat«rlinc [Kempf, G., and Karhan, IC, HSV.\ Rep.

(5)

typical foul-bottom boundar3--layer velocity profile

The

boundury-laycr profiles were measured on this ship but they were not published |WRH, 1.5 Jun 1939,

U

and a

p. 393).

TMB

observations at 23.G kt, with dirty bottom

in the inner portion of the l>oundary laj'cr

1940, Fig. 24,

U. S. merchant vessel, 1933-1934. data are unpublished. Tannenberg, German merchant ship, 1938.

Ctairton,

(3)

at

deep water.

in

German merchant vessel, early 1920's. by W. Dnhlmann, II. Hoppe,

as reported

Hamilton, U. S. destroyer (DD 141), 1933-19.34. The data are unpublished except for one model-

(2)

Unfortunately, the log-tube extension was in this

speed

(lata,

and O. Schafor |\\TIH, 7 Sep 1920, pp. 415-4191, were taken witli a resistance log towed abeam from a boom, and are rather sketchy.

are from observations with a Pitometer speed log.

ecjual to the ship

upon which velocity-profile observahave been made, including the Wrangcl,

(Jthcr ships tions

Comstock and

P.

News Shipbuilding and Dry Dock Company. The data in all cases

U

—

Sec. 22.(5 are actually hollow.

C. H. Hancock of the Newport

relative velocity

Sec. 45.6

45.

taken from unpublished

profiles for a large liner,

DESIGN

I\ SHIP

—

portion of the body or ship.

layer

S

(the

(9)

log (INA, 1955, Vol. 97, pp. 14).

No

velocity profiles

543-545 and Figs.

show

U >

Ua,

13,

.

Fig. 39, p. 85], with the horizontal scale modified

to

the

suit

being

features

measurements were,

velocity

large liner,

made below

illustrated.

These I'ur llie

like

those on the

the ship but fortunately

the pitot-tube extension was greatly in excess of the j/-distance where relatively small

U ~ U^ = Wrangcl,

it is

Mar 1939. This paper covers flow testj<, velocity measurements, and pressure observations on a

possible that

cargo-ship model.

some wave wake being measured with

is

the friction wake. Indeed,

wave action itself felt

bottom

With the

Volume I are repeated here, along with a few others. These, however, apply to tests on models only: (a) Laute, \V., STG, 1933, pp. 402-460; T.MB Transl. 53,

submergence of the pitot-tube

orifice in the case of the

there

V.

U.H

it is

possible that the

in the ca.se of the large liner

not only well.

down

makes

the side but under the

sake of completciics,s, the references of

Sec. 22. G of

(b)

Hamilton, \V. S., "The Velocity Pattern Arnuml a Ship Model Fixed in Moving Water," Doctorate Diss., IIIIR, Dec 1943. Dcscrilx-s flow measuremi'iils

made on a mmlel

Sun Frnncixco.

of the (icrnian

M.

8.

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.7

TMB

Hamilton (DD 141), destroyer. The U. S. data are unpublished except for one model-ship velocity profile comparison by E. A. Wright S.

(c)

[SNAME, (d)

TMB

(e)

Baker,

1946, Fig. 24, p. 393].

model 3898, representing a proposed twin-skeg Manhattan, described by the present author in SNAME, 1947, pp. 112-125. Unpublished data are on file at the David Taylor Model Basin.

G. S., NECI, 1929-1930, Vol. XLVI, pp. 83-106 and Pis. Ill, IV, and V; also pp. 141-146 (includes tests on models). On page 86 of this reference. Table I gives other sources of test data on models. Baker, G. S., NECI, 1934-1935, Vol. LI, pp. 303-320; also SBSR, 28 Mar 1935, Fig. 5, p. 353. Calvert, G. A., INA, 1893, Vol. XXXIV, pp. 61-77. This reference describes one of the first, if not the

(f)

(g)

measurement of the velocity profile in the boundary layer of a friction plank, 28 ft long. In

99

have been told many times so that they are not summarized or repeated here. A historical summary was given some time ago by K. S. M. Davidson [PNA, 1939, Vol. II, pp. 76-83] and others more recently by F. H. Todd [SBMEB, Jan 1947, pp. 3-7; SNAME, 1951, pp. 315-317].

A

the principal references

list of

is

given in Sec.

45.26 for the benefit of the interested reader.

has been recognized, practically from the

It

beginning of this development, that a friction formulation which correctly expresses the drag of

a thin,

flat

plank or friction plane by no means

applies directly to the prediction of ship friction resistance.

There are a number

of reasons for this:

first

Fig. 9 of PI. Ill Calvert gives three velocity profiles, for speeds of 2, 3,

of 0.44 ft

45.7

and 4

kt, for

from the plank

The Development

a transverse distance

Formulas

lating Ship Friction Resistance.

for Calcu-

Friction resist-

ance was recognized as a sort of separate entity in the ship-resistance picture as far back as the 1790's. Attempts were made then, by Mark Beaufoy and others, to determine its magnitude

[INA, 1925, pp. 109, 115]. It remained, however, for the eminent William Froude to conduct the first systematic friction experiments on flat surfaces

and to establish the

for the

calculation

of

first

friction

systematic basis drag.

Following

extensive towing experiments with thin planks

having

various

he

coatings,

developed

the

expression

R^ =

fSV

(45.i)

where / was his own friction-drag coefficient and the exponent n approximated 1.83 for smooth, varnished surfaces. He found a length effect in addition, but this was not reduced to mathematical terms. R. E. Froude, the son of William Froude, after a re-analysis

of

the observed data,

changed the speed exponent n to

later

1.825.

Following the elder Froude's work the principal

landmarks in the evolution

of a suitable

formula

for calculating ship friction resistance were:

Osborne Reynolds' development in the early UL/v, now named the Reynolds number and expressed (1)

1880's of the_ dimensionless relationship

SLsR„

development of the boundary-layer (2) The theory by Ludwig Prandtl in the early 1900's.

The

highlights

and

details

of

The

drag

surface.

of

(a)

the last three-

quarters of a century of progress on this project

on the plank and on a towing model whose friction calculated from such data, as compared possibility of laminar flow

or plane is

to the fully turbulent flow over practically the entire wetted area of the ship (b) The effects of transverse curvature on the submerged edge or edges of the plank or friction plane as well as of both transverse and longitudinal curvature on a towing model and on the ship (c)

The

effects

especially

the

various

of

longitudinal

pressure

gradients,

gradients,

on

the

curved surfaces of model and ship (d) The variation between the calculated at-rest

wetted surface of a model or ship and the actual wetted surface when it is moving and making waves, as well as changes in flow caused by orbital wave motion and the like (e) The smoothness of the plank or friction-plane surface as compared to the relatively rougher ship surface, especially in

view

of the

need for greater

absolute smoothness on the ship to insure hydro-

dynamic smoothness (f)

Other

in the larger scale

effects of differences in absolute size

or scale.

William Froude, B. J. Tideman, and others, working in the 1860's, the 1870's, and later, recognized that no ship is ever as smooth as a friction plane towed in a model basin. They provided in their friction coefficients a series of positive allowances for what they considered to be unavoidable roughnesses in the ships of their day. They did not know, in those years, that the ships had actually to be smoother, in an absolute sense, to afford the

same degree

of

hydrodynamic

smoothness as obtained on their models. However, the modern friction formulations are all developed for

and apply

strictly

to

fiat,

smooth

plates,

nVDRODVNAMK.S

100 bccaust"

smooth surfaces are icpnxluiiblc and

in that

way can

onlj'

consistent cxperimentul data be

assured.

Despite the extensive studies of recent years there for

is

as yet no comprehensive, accurate formula

bridging

tlie

friction plane or

gap between an experimental model and an actual ship, and

for taking account of the effects

listeil in

the seconil

paragraph preceding. In fact, workers in this field are not even agreed on the form which such an expression should take, or whetiier an attempt should be made to embmly all the bridging

SHIP ni'SICN

l.\

Src. 45.7

result.s. While the.se experiments antedate the year 1932, the line can alwaj's be shifted to accommodate newer and better data. It docs, however, conform to the physical laws for the dependence of friction drag on Reynolds number and it has given satisfactory ship predictions for many years. There is no specific

available experimental

provision in the

.\TTC 1947 procedure

effects,

transverse

effects,

variations

and

longitudinal

for

edge

curvature

wetted surface and flow

in

patterns due to waves, or any other factors.

The

ATTC

1947 (Schoenherr) meanline, de-

by the heavy,

factors, as it were, into a single formulation.

])icted graphically

meantime the naval architect must span the gap somehow, and with assurance that

log-log plot of Fig. 45.E, expresses the relation

the

In

his

predictions

are

reasonably

between CV and

242 "•g^ =

American Towing Tank Conference decided in 1947 that for its work this operation is to be performed by the use of:

The meanline developed by K.

for

expressing the specific friction drag flat,

function of Reynolds

number

(2)

An

additive

specific friction

allowance, resistance

=

of

a

a.s

Cy and

,

sufficient values of

and

the called

form of a

ACV

lated for practical use. in

,

for

SNAMIC

The Schoenherr

meanline, as

was based upon a

its

dated August 1948, for

generic

careful

name

analysis of

50

4.5. c

not readily solved for

Cf and R„

,

The

and

Purr or

Tiiiu;k

TrrKs

oi-

ItocciiiNKHH

model and tabu-

in the

tables arc published

all

who need them. Two to

express

are reproduced in Tables

45. d of Sec. 45.9, covering mniiol

and ship

ranges, respectively.

500

100

Reynolds Number •I.I.FC

(S.xivb)

Technical and Research Bulletin 1-2,

all /?„ values in jtiillions,

Fio.

is

small portions of these tables, modified

ship.

implies,

(o.xiva)

ship ranges, have been calculated

7?„

in

{R„Cf)

4.132 log.o {RJCf)

Since this equation

Cf

the effect of unavoidable roughness on a clean,

new

{C,)-"'

log,o

E. Schocnhcrr

smooth surface

turbulent flow on a

either of the equations

The

correct.

(1)

by

/?„

solid line in the

(

I0"»j-

Ai.uhvanik fou Nll.MII>:lt

^

Siin-s,

1000

(lO"*)

SimwiMi Vauiatiu.vs

wrrii IlKV.Nouns

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.7

Using the ATTC procedure, the friction resistance of the wetted area of a ship is calculated by the general formula given as Eq. (22. iv) in Sec. 22.15, based on specific friction-resistance co-

Methods

Tentative values for the four listed roughness allowances are given in Sees. 45.18 and 45.20.

for fully turbulent flow

on a

SACp

flat,

due to the increment of relative water velocity for longitudinal curvature

1950;

reports

TMB

SNAME,

quoting Rep. 663, 1949;

1951, pp. 327-345]

equivalent resistance of condenser-coohng scoops and discharges and miscellaneous sea chests, as well as the forces involved in driving cooling

-FAzCf due to the increment of drag

for

transverse curvature

+ ApCp for plate or planking roughness + AsCf for structural roughness + AcCf for coating roughness -f-ApCp for fouling roughness]

2ACf)

(45.ii)

where the ram pressure q = 0.5pV^, S wetted area, and V is the ship speed.

TABLE

published

term embraces not only all the roughness allowances listed in Eq. (45.ii) preceding but the

+ AiCp

+

the

this

ship

qS{CF

of

values [Todd, F. H.,

TMB Rep. 729,

smooth plate having the same S as the

=

many

In

efficients:

Rf = qSlCp

101

estimating the curvature allowances are described subsequently in Sec. 45.14. of

45.C—Sample Table of

ff„

is

water through the condensers and in overcoming the effects of forcing water out of and drawing it into certain hull openings.

it

In towed and self-propelled tests of ship models is customary to omit the lips, projections,

openings, and internal ducts belonging to these

Not all ships have them, and in any case they partake of the nature of appendages rather than of structural or other roughnesses. Unfor-

systems.

tunately, no suitable procedures have been

the ship

and Cf for the

worked

out as yet whereby the true additions to ship resistance occasioned by the devices proper and

ATTC

1947

Meanline

in

the

MODEL RANGE

adapted from the upper portion of the table on page 8 of SNAME Technical and Research Bulletin 1-2, pubUshed in Aug 1948. The listings of fl„ in the extreme left-hand column are in terms of (10») or millions. Those in all other columns are Cp(lO'). This table

is

Reynolds Number

IlM)R()l)^ \

102 TAlU.i: l-Vli-SAMIIK This

t«l>le is

published in

I

UlIK OK

A-,

wiKs

AMI Cy

i\ siiir i)isi(,\

Kill TlIK

ATH

'

I'.MT

ndnptoti from ihe upixr portioD of the tiiblo on page 12 of

Aug

104S.

The

other columns arc Cjr(10>).

Reynolds Number in Millions

listings of

R,

in the

Mkasune

Sec. f5.S

IN

THE SHIP

SNAMIC Technical and

extreme left-hand column arc

in

UANGK

Research Bulletin 1-2,

terms of (10*) or millions. Those

in all

Sec. 4

FRICTION-RESISTANCE CALCULATIONS

5.

Cp

(b)

(4)

=

C^^ =

(c)

-

0.0725(log,„ Rn 0.370(log,o

2)-'

application to fresh water

II, p. 82]

Cp = 0.455(log,oi2„)"'-"

C,.

Archiv, 1936, Vol. C,^^ (5)

drag Cip or shearingH. Schhchting gives [Ing.

local specific friction

stress coefficient

=

,

7, p.

=

C.

29]

(2 log.oiJ.

Von Karman, based on

-

0.65)-'-'

the 1/7-power law of

[PNA, 1939, Vol. II, p. 80]; Volume I of the present book:

velocity distribution see Sec. 5.10 of (a)

Cf.

This

is

=

Cr =

(b)

(6)

0.072(E„)~'"

also given as [Rouse, H.,

EH,

Rf =

where

/c2

is

hSV\R„)-''-'''

a rather complicated term defined in

the reference. (b)

[PNA, 1939, Vol.

Cp (7)

1950, p. 106]

0.074(i?„)"°'

Gebers [INA, 1925, pp. 110-111]

(a)

=

II, p. 80]

0.02058(i?„)"°'''

[SNAME,

1951, pp.

373-374]:

/?.)"''''

Prandtl-Schlichting [PNA, 1939, Vol.

For the

103

Rr

['''-

+

(^t)]-'

IIY^Ro^>v\.\^fI^.s i\ snip df.sicx

lot

VS\.

(c)

l'.t;Ui,

\ul.

Tal.lf

11.

ship lengths of 10 through 500 Polliinl, J.,

(ti)

'.1,

Ill,

|).

and DiKlcbout,

A., "Tii(''orif

du

hut with different symbols and metric units, for 120 in, 10. 1 through

ship lengths of 5 through ft.

Taylor, for 20-ft jilanks

(9)

water

in fresh

at

OS

C = 0.03117?:"'" alternative form

(b)

lir

water, and a 20-ft friction plane. (10) Sect.,

I^p and Troost [SNAME, Nortii. 29 Feb 1952; see SNAME Member's

Cidif.

Bull.,

Jun 1953, pp. 18-22]

^

Cfo =

as determined by the .\'1"T'C 1947

(V

argument

smooth

flat,

/?„

plate.

for entering the

complete set of tables

is suflTieient to cover both model and ship regions. The entries in Tables 45. c and 45.d are modificHi so that all /?„ values are in terms of millions [5th ICSTS, Lontlon,

of picking

for

Hy

Cy values by inspection

calculations

is

illustrated

in Sec. 45.22. log.

(It)

O.133(log,off„

+

log.

I

+

C,

bulent Flow.

log.o -4)-'

"FD"

=

the thickness

formula

signifies

+

Rep. 34, 1955,

p. 76,

ICSII,

[7th

Eq.

Cp

is

=

1954,

ness

so that for

/2„

=

nomena.

study of roughwhether the.se are

determine

to

efTects,

laminar sublayer next to

of interest in a

is

viscous

or

primarilj'

pressure

been found [Rouse, IL,

It has

1940, p. 194; Baines,

W.

D.,

"A

phe-

EMF,

Literature Survey

Boundar^'-Layer Development on Smooth and Hout^h Surfaces at Zero Pressure Gradient,"

of

(2)].

Lackenby, and others,

bR~',

of the

5/,

a solid boundary essentially

G. Hughes' "2-diml" 0.014/2;''-"* 1.328«:°'

(12) Telfer,

Laminar Sublayer Thicknesses in TurS<jme quantitative knowledge of

45.10

+ KC"

-

0.724

(11)

+

(5.xiva) or (5.xivb)

]'>|s.

of item (1) of Sec. 45.8, for fully

of the

and using them

friction drag.

C, = a

The range

The meth(xl

where the subscript combination

SSPA

tables give values of the .specific friction resistance

1948, p. 112, item 4, top of page].

= ,..[(f.)v/^]..... =

or

Tables

tables,

developed turbulent flow on a is

the

for

Meanline.

anil 4.j.d are small illustrative sections of

and the formulas

0.00907 .sr' "' for 60 deg F, fresh

=

Coefficients

1Q47

a mentioned in Sec. 45.7, calculate
(Schoenherr) meanline,

(a)

An

ATTC

group of larger

((H'dicient

dog F,

Friction

Specific

Schoenherr or

Nnvirc," 1892, \'ol. Ill, pp. 374-375, using essentially the dimensional formula given previously

31)3.7

45.9

fur-

ft

^'r. 7 1.0

IIIIR, 1951, p. 25] that the thickness «>

Cy = a

,

laminar sublayer

in

5,,

of the

turbulent flow over a rough

surface can be expres.sed by

Here, the lower-case subscript of the Reynolds-

number symbol is not to be confused with the exponent n. A table of the specific friction co"smooth paint surfaces," derived Cf from the I^ackcnby formula Cy = 0.0000 -f0.0791/?:"" for the Froude-Kempf data, is given by G. S. Baker, over a range of /?, from 1 to 75 million (IN A, Apr 1952, p. 02|. efficient

di.

=

(a coeflicient)

4

for

(13) Blasius, for laminar flow on a

flat,

smooth

(a coeincicnt)

where values of the 11.0

5;. '

and

coeflicient [/,

(14) For a completely rough surface of length /> and an equivalent sjind-roughnesa height of Kg as given by L. .\. Haier, ,

"

5,.

r. vary from about

= Vto/p

Using the larger

is

cocfTicient, a

the shear

number

values calculated for a wide range of

Ijlotted in Fig. 45. F. It is to

1.32H/1';"

Cr = [l.89-f l.f.2(log,„^'jJ

12.0,

velocity.

plate,

C, =

to

(r..vi)

li,

of

are

be noted that the

values increase slowly milh Icnyth for a given

speed, hut they decrease rapidly with speed for a

given length.

The

reasons for this are discussed

presently. It

is

interesting to note that the permi.ssible

average ronghne.s.s height

A'

v.

for a livdroilyn.'im-

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.11

105

(45 .v)

Ul

This means that Sl increases very slowly as x

and that it decreases rapidly as U«, For example, if C/„ increases from 10 kt to 20 kt and then to 30 kt, 6x, decreases very nearly to | and then to | of its 10-kt value. If x increases from 5 ft to 15 ft, the increase in 8l occasioned by it is only in the ratio of 1 to (3)°' increases

increases.

or 1.116.

50

1.0

Number

Reynolds Fig. 45.F

ness

ically

500

100

50.0

10.0

in

1000

million5

Variation of Laminar Sublayer ThickWITH X-DlSTANCB (L) AND SPEED

,

Si

smooth

given by the exiDression

surface,

described at greater length in Sec. 45.15 [Goldstein, S.,

ARC, R and M,

1763, Jul 1936, p. 113],

namely

(neglecting the kinematic viscosity).

<

fc.v

5

(45.iii)

Ur

roughnesses should average than half the laminar-sublayer thickness S^ in the ratio of say 5 to 12.6, if they are to produce no roughness effects. Granting that the relationship between the height of the roughness on a solid surface and the laminar-sublayer thickness has an important influence on the roughness effects, it is useful that

indicates

somewhat

the

less ,

to

At the same time, an increase in either U„ or x to three times its original value multiplies the original Reynolds number by three. It can not and be said, therefore, that the change in 5i, hence the change in the effect of a given roughness of a certain absolute size and shape, is a function solely of the Reynolds number of the flow, as determined by the product of the relative velocity [/„ and the distance x from the leading edge

know what

factors influence this thickness 6i

To understand

this,

6i

From Eq.

=

Eq.

(5.vi)

may

.

be written

A given barnacle at the bow of a long ship might project through the thin laminar sublayer there but lie just within this layer at the stern. However, as the ship speed increases, the value of 5i diminishes. A barnacle of the same size at the stern projects more and more through the laminar sublayer and becomes more and more effective as an item of roughness. This is the reason why, in aeronautical circles, it is customary to use a special Revnolds number with the roughness height as a space dimension, instead of the distance x from the nose or leading edge of the

body

or plate. In fact,

mentioned 12.6Kp)°'(r„)-

(45. iv)

the

of Fig.

5

it

To

=

0.059

=

0.059

I

UlRZ

I

Ul

U„x

12.6(0.0295)-°- V"f/;"'(a;)''-'

is

obtained

/ \-0.57-7— 1 t-tO.I 0.1 X V (P)

=

viscosity v

is

~°'

12.6Kp)

the

U„ U„

numerical

assuming

that

(45 .vi)

forms a Reynolds number of this kind, where the space dimension. This relationship is discussed further in Sec. 45. 11

=

Dropping out moment, and

fcAv?7.

45.15.

Combining these two equations, there (^0.059^

>

/cav is

(5.iii)

8l

the Goldstein relationship

manner

5.R or the corresponding equation from the turbulent-flow column in Fig. 45. A, one may also write (S.iii)

if

earlier in this section is rearranged in

values

the

constant for this study,

for

the

kinematic

Friction

Data for Water Flow

in Internal

not the place for an extended discussion of the friction resistance offered by the internal surfaces, both smooth and rough, of water ducts and passages which are separate Passages.

This

is

from those in the maciiinery plant. Some reference data on this subject are given by J. K. SaUsbury [ME, 1944, Vol. II, Fig. 51 on p. 61 and Art. 12 on pp. 62-63], but it must be noted that the weight density

(lb

per

ft^) of

the liquid

is

repre-

HVHROnYNAMICS

\m acuUil

ill

rcfiTi'iiio l>y llu> syii»l>ol p iiisteml

tliat

by the R'STS or I'lTC symbol w. A nitlior comprohonsivo
(Rouse, H., Kditor.

ia")(),

pp. 3S7-1

t.'^j.

Computation of the Wetted Surface

45.12

.\ithough the et)mputation of

Ship,

tiie

of a

wetted

^' of the unilerwater body of a shij) is a problem in solid geometry rather than in hydrodynamics, the flow conditions over dilTcrent

surface

portions of that surface are closed- related to the specific friction resistance coofiicients.

surface

calculations

are

therefore

The wettedmade with

these conditions clearly in mind. Furthermore, a

value of

S

is

required in the earlj' stages of the

preliminary design,

when

as described

in

Sec.

66.9,

may

not yet be sketched and there arc no girths to measure. the lines

W. Taylor solved this problem by the use a wettod-vsurface coefficient, now known as CVs ba.sed upon data from a great number of models and man.v types of lines, not limited to the series bearing his name. When only the di.splacement A(delta; large capital), the maximmnD.

of

,

Ratio of

Bx/Hx

Framed Area

1.0

1.5

2.0

2.5

1.0

1.5

2

2.5

is

3

0.701 Z>.0

IN SHIP DESIGN s«'ctioii ((K'nirient ('x

•l.'i.li

Co.NTOUiUH

l)K ()-l)lMI.

,

the beam-draft ratio B, II,

and the "mean immersed length" L were known, the wettinl siirfaee .S was determine*! by = ChsvAL, where A wa.s in long tons i^ (2,240 lb) of salt water of sp. gr. 1.024, with a volume density of .}.").07.j ft' per long ton. Since the mean immersed length was usually not known until the form was laid out, the waterline length was often substituted for it. Contours of C,rx on a basis of C'.v and B/II were first published by Taylor in the 1910 edition of S and P (Vol. I, p. 47; Vol. II, Fig. 41]. They were repeated in the 1933 edition of S and P, Fig. 20, page 20, and in PNA, 1939, Vol. I, Fig. 33,

page 90. These contours were reworked by of the

TMB

M.

E. Fowler

staff in the early 1940's to include

many additional models of all types. page 22 of the 1943 edition of S and P, embodj'ing the revised contours, thus differs slightly from its predecessors. As C„s is a dimensional (luaiitity, which varies with the system of measurement, 1). W. Taylor's formula is for this book converted to the 0-diml form data from Fig. 20 on

CsVVL

S = Cs Reproduced 3.5

35

Beom-Droft Ratio Km.

Srr. 41.12

to

Lorqe Scole

1

Ficj

45.H

'-^ij.O

4.5

5.0

5.5

4.0

4 5

50

55

Bx/Hx

WK-rTKI>-.S|lKKArB CoKI'riCIICNT (\ Kill

.Sllll'S

(-Jo.vii)

6.0

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.12

where

L

is

now

the waterline length and the

A to F or V is based upon the volume density of salt water previously mentioned. conversion from

Supplementing

this conversion, a further revision

of the contours provides

are

somewhat more

new

values of Cs which

realistic, especially as

every

them carry rudders and other simple appendages. The result ship has to have plating

is

and most

of

a minor increase of about 0.03 over Taylor's

revised values of 1943.

The new

largely on data taken from

plots are based

SNAME RD

sheets

1

through 100, covering modern vessels of many and types and relatively normal form. Fig. 45.G gives the new contours of Cs plotted

sizes

,

on Cx and Bx/Hx

.

As the wetted-surface

coeffi-

cients for the great majority of ships fall in a small

'2.0

2.2

2.4

2.6

107

area bounded by values of

Bx/Hx from

and Cx from 0.9 to 1.05, expanded contours of shown to a consideralily larger scale in Fig. 45.H. A similar plot by M. L. Acevedo [TABLAS, 1943, opp. p. 128] gives values about 4 per cent lower than those in Figs. 45.G and 45.H. The new Cs values have been checked repeatedly 3.5

this area are

since their preparation with all

data,

available

45.H

new

and the agreement has been found to be

within limits of engineering accuracy.

The new

contours are certainly adequate for use in the early stages of a preliminary design.

However, the Cs contours of Figs. 45.G and H are to be used with caution for vessels of abnormal form, such as those of shallow draft, 45.

those

2.8

with

,

broad,

3.0

flat

3.2

sterns,

with excessive

3.4

3.'.

Beam-Draft Ratio B^/Hy Fig.

2.0 to

Enlarged Plot of 0-Diml Wetted-Subfacb Coefficient Cs for Usual Ship Ranges

HYDRODYNAMICS

108

cutaway in tlu' ftuefool or aftfoot, and with chubby luills. For these, a value of C., is

sliort,

with reasonable accuracy, provided the correct value of Cs is available for a prototype vessel whose proportions and coefficients do not

tletormincil

much from

too

differ

surface

the vessel whose wetted

sought. Suppose for example that

is

from Fig.

small by 0.04 for a craft of

is

4.").Ci

Cs

IN SHIP DESIGN

Sec. 45.12

the rules of solid geometry or any convenient

An appendage

method.

when

short

considered small or

is

number

the r-Reynolds

at the trailing

than about 15 milUon at the given speed. As an example, this occurs for a length of edge

less

is

about 7.5 at 30 kt.

ft

at 15 kt, 5.G ft at 20 kt,

If

the appendages are very short, like

and 3.75

ft

the arms of shaft struts, their wetted surfaces are

abnornuil form whose Cs is known. It may be taken as apjiroximately 0.04 small for the same tjT>e of hull, even though the proportions and

neglected,

changed somewhat from those of the "known" vessel. The C'., derived from Fig.

hull plates of cj'cloidal or rotating-blade propellers,

coefficients are

by using the proportions of the given form, augmented by 0.04, may be relied upon for the abnormal type being developed. If it is known,

45.C1

for instance, that the

stem design

wetted surface of a twin-skeg

3.2 per cent greater than that of a

is

and

computed by

their resistances are

the rules of Chap. 55.

The

surfaces of exposed rotating shafts, rotating

and similar areas not subject to translatory motion onlj', require to be handled by mcthotls

No

considered apjjropriate in each case.

logical

and systematic procedures have as yet been worked out for these parts. Friction drag on propeller-hub, fairing-cap, and blade surfaces is

normal-form ship, the latter as given by Fig. 45. G, then this allowance may be applied rather gen-

taken into account in propeller performance.

any twin-skeg stern ship, to the predicted result given by the formula. In any case, because of the present (1955) un-

Sec. 12.3 of

certainty as to the correct roughness allowance for

summation

erally,

for

been practicable, as described in

It has not

Volume

I,

to resolve the tangential

forces on each unit of wetted area into

the direction

to

parallel

components

The

motion.

ship

of

the actual friction forces gives

of

seems not necessary, when making force and power predictions, to calculate the wetted area to a high degree of

therefore a value slightly greater than the

preliminary

of the direction-of-motion

accuracj'.

inequality

any

ship,

it

12. A. Effective

if

not e.xact

mean

achieved by using the

is

sum

components; see Fig. compensation for this

the wetted

girth

calculations of the friction drag on the doubly

without a correction for obliquity, thus giving a wetted-

curved wetted surface of a ship hull assumes that

surface area slightl}' less than the actual area.

flattened into a single thin plate

For those who wish to emploj' the obliquity correction a diagram giving the necessary factors and instructions for their use is published by D. W. Taylor [S and P, 1943, p. 18]. The obliquity

The procedure

the surface

is

currently employed

in

detail

DWL

length equal to that of the which has a ship and a width equal to that of the half girth at each station or frame. Such a plate has the general .shape indicated

by the

0-
curves of

22.A of Volume I. The two sides of the flat plate correspond to the two sides of the ship. This leads to the general rule that the wetted surface of the main hull, without appendages but with large bo.ssings or skcgs, is the product of the waterhne length and the mean wetted girth to the waterline. The mean girth may be computed by Simpson's first rule, using 20 e(iuully spaced stations, or by any convenient e(|uivalent method. The wetted surface of a large appendage, parFig.

ticularly

one which

is

long like a bilge keel,

calculated similarly from to be obtained by

its

mean wetted

girth,

length as projected on the centerplane of the vessel. The wetted surface of small, short appendita

ages, which arc relatively thin

rcsisUincc

is

largely fridional,

correction

amounts

At

and on which the is lalciilalrd by

of interest only for full, fat ship.s. It

and a

B/H

L/H

ratio of 2.2.

the design stage where the girths are taken

the

early

onlj'

the

for

off

is

surface,

to about 0.01 for a ship having an

ratio of 4

usuallj'

wetted-surface

molded

lines

calculations,

are

available,

representing the inside rather than the outside of the plating.

made of

A

small plus allowance can be

for the surface of the ship to the outside

the plating, or the girths can be measureil

deliberately a

little large.

Unless circumstances indicate that the wave

is

any convenient method, and

calculating

for

formation along the side speed for which the

no account

is

A',,

may

taken of the wave

the at^rest wetted surface.

gained is

in

be unusual at the

calculation

is

being made, altering

priilile in

The

wetleil surface

the crests of waves along the ship's side

])riibably

somewhat

less

than that

lost

in

the

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.13

troughs, but this

is

largely

compensated

for

by

the bodily sinkage of the ship while in motion,

The reduction in wetted becomes appreciable, of course, when a fast

described in Sec. 29.2. surface

boat approaches or reaches the

or high-speed

planing range.

Often

109

generous in measuring girths to include the shell plating outside the molded lines. (3) For large appendages, especially those long enough to have an a;-Reynolds number exceeding

15 million, calculate the wetted girth as for

(2)

pre-

ceding and multiply by the length projected on

it is definitely

known that a separation

the centerplane

region exists along some part of the wetted surface,

For small, short appendages, excluding rotat-

(4)

such as that behind a transom stern or inside a sizable rudder recess, or the extent of the zone

ing shafts and the like and the propulsion devices

can be estimated with reasonable certainty. The wetted area next to the separation zone is then

calculate the wetted surface

subtracted from that of the rest of the ship, considering the extent of the zone constant at

all

speeds [Horn, F., 3rd ICSTS, 1937, p. 22; Acevedo,

M.

"Skin

L.,

Friction

Resistance,"

Madrid,

proper,

their resistance

if

primarily frictional,

is

by any convenient

method (5) Make no allowance or correction for actual wetted surface between the at-rest and the wave profile when the ship is in motion except for F„ > 0.6, Tj > 2.0, or for unusual cases

WL

1948, p. 14].

When

a fixed appendage covers a part of the

main ship

such as a roll-resisting keel of V-section, the area so covered is subtracted from hull,

estimates are wanted. Otherwise, neglect them.

the calculated wetted area of the hull.

and appendage wetted areas are frequently lumped together, and although there is some justification for adding an allowance for appendages to the wetted surface S in the early stages of a design, before the appendages Although

all

are laid out,

hull

it

is

preferable to

make

Estimate the wetted surfaces of zones of if it is practically certain that they will exist at the speeds for which resistance and power (6)

separation,

added to the S value

being

of the ship.

Summarizing, the calculation of the wetted surface of a ship, when the shape and size of the hull and the underwater appendages are known, takes the following form: (1) If the lines are not yet drawn, estimate the wetted surface by the use of the wetted-surface coefficient Cg from Fig. 45. H, then combine it with the underwater volume ¥ and the waterline length L in the formula S = Cs 'V'VL. Add a percentage or an area allowance for the contemplated appendages, if it can be estimated at this

stage and

if it is

considered necessary.

(2) With ship lines available, measure the girths from designed waterline to designed waterline at 21 or more equally spaced stations along the waterhne length, including the FP. Compute the mean girth from Simpson's first rule [PNA, 1939, Vol. I, p. 16] or the equivalent, and multiply the mean girth by the waterline length. When measuring the girths, include large bossings or skegs and discontinuities in the sections where the ship plating is carried continuously around them. Be

the areas of

subtract the areas

(6)

(2),

Part

S

The

4.

and

(4),

The

(7).

and

and

Boundary-Layer

Transom-Stem ABC Ship

of

wetted-surface calculation for the

preliminary design of the transom-stern

designed in Part 4 of this volume

is

ABC

ship

made by

S = CsvVL. When

using Eq. (45.vii), namely

the hull lines are available this calculation

(5),

result is the

for the design.

Wetted-Surface

45.13

Calculations for the

of appreciable size (3),

and

value of wetted surface

separate

is

appendages

of fixed

Add

(8)

wetted-surface calculations for the appendages.

This gives the designer an idea of what

Calculate the hull area covered by the attach-

(7)

ments

is

checked by a

embodying the measured

girths at 21

stations, plus those at four half-stations near the

namely 0.5, 1.5, 18.5, and 19.5. At the stage corresponding to the first estimate

ends,

of

wetted surface the pertinent parameters are:

Bx/Hx = The

2.808;

Cx =

0.956;

V =

574,000

ft'.

from an estimated weight 16,400 t and a round-number

latter is derived

displacement of

volume density

of 35

ft''

per ton. Entering the

0-diml wetted-surface coefficient contours of Fig.

H with the first two parameters, the value of Cs by inspection is 2.616. The location of this point is shown on the diagram by the distinctive 45.

double this

circle

volume

with

its

for the

black lower half, used in

ABC

design.

Substituting

these values in Eq. (45.vii),

S =

=

CsVVL = 44,759

ft'.

2.616 \/(574,000)510

no

JIVDRODVN AMK.S

\\ liiri iniiiotl

till-

by

I'xiifl iinili'iwiilor

pliinimetcr,

volume V

!\ Mill'

ditti-

is

Seciyi-f

from girths

the fair lines of the

iisiiiR

DESIGN

Hare-hull surface, plus cutwater,

44,883

foimd to be 575,847 ft'; the correspoiuiiiig wetted surface 5, by Kq. (45.vii), is 44,831 ft'. This is very close to the value determined by the

Hilgc keels (2 of), surface expo.scd to

more

Deduction

ship,

it is

method described

precise

in the

water

next para-

graph.

fixeil

rudiler horn

calculation of wetted surface, using (1) the measure
Simpson and trapezoidal

rules,

and

(3)

hull area covered In-

—10

no

S for the bare hull, incluiling the cutwater shown on Fig. 67.E, of 44,883 ft'. It is found, for this ship, that the wetted surface is about 1.2 per cent higher when using two

half-stations

at

the precision here

much

is

roughness

Cp

,

-

400

=

2,000

ft'.

Using the

at the base,

-

ft,

and a girthwise span

the net area

=

489

2,254

Reynolds number R, 193.5

is

ft=.

for

VL ^ =

calculated

to

Incidentally,

ABC Tronaan-Stem Peamn ,

,,

]

R,-I35III0;; I

a bilge-keel length of

to be found to be 748 ft^. The only separation zone expected around the underwater hull is that abaft the transom. The area of the after side of the transom is therefore not included in the wctted-surface calculation,

Xo

is

ioii

is

tlicrcforo

is

made

in

this calculation,

nor

is any customary, for the change in welted surface due to substitution of the wave profile at designed

speed

for

boundary

The

the

at-rest

watcrlinc

as

an

upper

of the wetted area.

iiull area covered by tlir li\rd luddi r Imrn about 10 ft^ The actual wetted .surfiicc of the tnin.som-stcrn AlU' whip, with all appendages, in ft', is:

i.s

For beyond lis Normol"

2817(10 ')ri^ per set for SoltWller-

Variation ok Boundahy-Layeb Thickness wrrH i-DisTANCE FROM Stem kok .\BC Ship

beyond

its

is

extrapolated

empha-

usual limits. It should be

is

made

is

a flat-plate formula,

that the wetted area on

same as that on one same length, namely The formula employed takes no account

each side of the ship

is

the

side of a thin plank of the

510

ft.

of either longitudinal or transverse curvature in

the ship, or of roughness, so that the thickness values for ship ranges indicated on the plot

may

be altered rather drastically when the ship values are actually known. l']ven then, they could be

considered as only average or

tj'pical,

local boundar3--layer thickness, at

it.

allowance

I

FiG. 45.1

far

and a.ssuming the wetted area

necessary for

a;-

sized further that, since this

deduct

mc

_;

038WBi"

Limits

graph emphasizes that this formula

horn, calculated from the dimensions given in

No

Spi ed Astj inea .s_|05 kt.-o- J'S_6i<tp«r

Thickness is Cokukited b» ine FiotPlole Formula ,„r Turbulent no« 6-

be

surface of the rudder and rudder

using niea.sured girths.

smooth-plate,

=

S

jond b^ ERtropololion

the assumption

Fig. 74. K,

of

the

1.2817(10")

twice the projected area,

.

S

.series of

ft,

522.7 million.

The wetted

flat,

a

of 1.25 ft

(20.5)(l.fl889)(193.5)

V

ship,

0.38(x)(R,y"- of Fig. 5.R and plotted in Fig. 45.1. A note on the formula

turbulent-flow

ft is

R.

ABC

bilge-

keel design of Fig. 73. N, with a length of 193.5

a width of 3.5

the boundary layer for the

when

especially

taken into account. The original estimate of net bilge-keel area of Sec. 6G.9, assuming a keel length of 200 ft, a width of 3 ft, and a girthwisc span at the base of is

2,400

47,875

total, ft',

indication of the absolute thickness

in

greater than for the

friction-resistance coefficient

Net

As an

values are calculated by the

each end

addition to the customary 21 stations. However,

2,743

by

—489

Deduction for rudder horn

correction for obliciuity, gives a value of

1 ft, is

748

for hull area covered

bilge keels

The

of the

2,743

Rudder and

because the

a given

.r-di.s-

tance from the stem, varies with the local radius of curvature, both longitudinal

45.14 ture. coiiicx

and transverse.

Estimating the Allowances for Curva-

For

('--tinialing

transver.se

tlio

;i|)|)i()ximate

ciTcct of

curvature of a body or ship

form, di.scus.sed in Sec.

(>.S

of N'olume

use

I,

is

made of Land Weber's fornnila |TiMli Hep. tiSK, Mar 1919, p. 7] for the increa.se in friction drag of a .semi-subnicrgcd

cylinder n\ rr

(lie

friction

FRICTION-RESISTANCE CALCULATIONS

See. 45.14

drag of a

plate of equal area. This takes the

flat

No

procedure has as yet been worked out for

making allowances

form

This

ture.

1^ =

+

1

^ C,

0.54

(45.viii)

the

111

coves

for concave transverse curva-

seldom

is

of

of great degree, except for

discontinuous-section

the

hulls,

coves along the inside corners of roll-resisting keels, or the coves along the superstructures of

where

Rp

is

the friction drag of the convex surface

some types

Rfo

is

the friction drag of an equal area of flat plate

adjacent convex curvatures on the chines and

Li

is

the length of the convex surface

edges largely neutralize the concave curvatures,

Si

is

the area of the convex surface

so that both

Cf

is

taken for the whole body or ship.

The

sides are vertical at the

For estimating the effect of longitudinal curvature by Horn's method, described in Sec. 22.5 of Volume I, some knowledge or estimate of the sinkage at given speeds, derived from model tests,

other

WL,

hence the girth

WL on one side to the WL on the

angle from the

180 deg.

is

= L and

Taking Li

=

words conL\/Si may be expected to vary from about 10 for a fine form to 4 for a full form. For the ABC ship designed the

sidering

in Part 4

whole

Si

S, in other

form,

ship

may

may

be neglected.

transverse curvature on a

body

ARp =

length

resistance

L

Cp

coefficient

for

the

or for only the bulge length Li

the boundary-layer thickness

is

.

ship

(45. ix)

of

uniform bulge

331

is

109,561 ft^ and Si

=

whence Ll/Si is

14.15

Rf

Rp

whence A^ is

of

ft

is

3 ft

and the length

on each

(3)Tr(331),

35.12.

The

side.

is

is

then

or 3,119.6 ft^

service (sea) speed

for

is a good approximation for normal forms of not extreme proportions and for a range of F„ values from 0.0 to 0.35, T, from 0.0 to 1.18. For the ore carrier previously referenced,

L/B =

is

water from about 1,242 million and Cp from

is

1.491(10"').

Then

=

1

+

0.54(35. 12)(1.491)(10"')

=

1

+

0.0283

of

Eq.

ARp =

9.07,

.25

0.01

l_^

-

B/H =

9.07)'

=

+

5

•(0.35

70/24.885

+

=

(also

'^]

0.881)

1.3

-

2.812 10

0.04326

ABC design, where L/B = 510/73 = B/H = 73/26 = 2.81, and Cp = 0.62,

For the 6.99,

substitution in Eq. (45.ix) gives

25

0.0l[^

ARf

=

Volume I, The value

0.0422(10"').

-

6.99)-

•(0.35

=

(22.iv), in Sec. 22.15 of

0.0283(1. 491) (10'')

=

635/70

and Cp = 0.881, from which ARp numerically equalto AiCp) is found to be

2.812,

fresh

0.0283, or just less than 3 per cent.

A,Cp

Ll

^)

L

whence R„

kt,

Table 45.a Table 45.d

is

-

Cp)(l.3

This

page 102 for the ship as a whole. Taking as an example a modern Great Lakes ore carrier about 635 ft long [MESR, Jul 1952, the bilge radius

+

•(0.35

by the ship length L it seems reasonable to use the same Cp as is picked from Table 45.d on

p. 65],

L/B)-

[

Since

determined largely

-

(11.25 0.01

of

specific

be calcu-

from the L/B, B/H, and Cp values by the formula given by F. Horn [3rd ICSTS, Berlin, 1937, Eq. 2, p. 24], as follows:

or ship, the value

Ll/Si for that region may be considerably higher than the values given; in fact, several times as great. If two I'elatively sharp bulges are involved, each having a girth angle of 90 deg, as where the bottom joins the two sides, the bulges and the angles may be combined to form a smaller, separate body with a girth angle of 180 deg. Eq. (45.viii) may then be used as given. There is a question as to whether to use a value of the

ARp may

be used. Alternatively,

lated

it is 5.8.

Considering only the region of sharp, convex,

In these cases, the

of submarines.

+

+

(0.01)(6.13)(0.97)1.019

2.5

2.81 0.62) 1.3

=

10/

0.0606

For the Lucy Ashton, a ship of quite different form [INA, Oct 1953, p. 350ff], having an L/B

IIM^RODN \

112 ratio of 0.07. a

li

II

ratio of

t.JO,

ami

a

WIIC.S I\ (',.

of

=

0.0i

p^^-^^-^»^)V

2.5]

TMB •(0.8.-,

=

+

0.70o)[l.3

the

like

lAtcij

augment

S.

Hay

^^rr.n.n Technical Paper 428

in Portoti

librarj')-

the .symbols of the present

I'l

volume, and where the factor

is definetl

A"o

solely

as a "roughness parameter," these are:

Aerodynamically rough

(1)

For a paddle steamer in

-^J

0.0320

especially of shallow draft, the

IMSICX

.1.

(unclassified) of 24 June 1954, issued bj'' the Chemical Defense Experimental Ivstablishment of the Ministry of Supply in Great Britain (copy in

0.705:

Ai?,

Sllll'

given by

Ashton,

>

A-„

of velocity

flow.

2..'5

U,

the watcrlinc region arising from the induced

velocity generated ahead of

and abaft the paddles

acts to increase the friction drag. This

amount

Tran.'^itiiina! flow.

(2)

is

determine in figures but theoretically always involves an increase in resistance. Despite the hydrodynamically correct basis for increases in the friction drag due to convex curvature in a ship, both transverse and longitudinal, many cases occur in practice which cast doubt upon the validity of those additions to the friction drag for a smooth, flat plate in turbulent flow. Indeed, there are cases where the entire -(AC^) allowance, for all types of roughness as well as for both types of curvature, is practically zero. There are those who say, and with some reason, that results of this kind lead them to question the smooth, flat-plate, turbulent-flow friction formulation it.sclf, which gives higher C^ values than it should in certain ranges of R„ In any event, the analyses made to date of existing propeller-tiirust data on ships are insufficient to indicate whether the curvature allowances, as estimated by the procedures described, are reasonable or not. All that can be said with certainty is that A,CV and A^Cy are probably no larger than indicated, and that they are both [)ositivc. 45.15 Criterion for a Hydrodynamically Smooth Surface. A.s a crilcrion for liydrudynaiiiic smooth-

2.0

difficult to it

-^

>

>

0.13

Aeroilynamically smooth flow,

(3)

<

ko

To apply

0.13

Goldstein's criterion to the practical

case, it is first neces.sary to sitj'

U,

of shear tq

know

For turbulent

.

_ —

To

^

,

I.F

the local inten-

from Fig. 45. A,

flow,

_ 0.0.')9 — nOi

whence 0.059

ii4{R.y

(5.iii)

.

ness in turbulent n(jw S. CJoldstein has suggested

the exprcs-sion |R and

M

As an example, assume 200

ecjuivalent to 50. G7 fps.

The kinematic

water

ft"

V for salt is

is

IC =

=

60.2.

{to/pT'

From

=

Ef|.

as large as

velocity

V T„/p,

Ah pointed out

tlio

and

in Sec.

v is

1.2817(10"^)

ft^.

45. b li,

Then

2.504 lb per

,^,

<

5

The value is

is

2,507 fps'.

0.059(0.995) (2,507)/G0.2

The shear

[(2.504)/1.9905]"' (45. vi),

U^

about 790 million, whence

u =

ft".

of

viscosity

per sec and p/2

=

velocity

1.1215

assuming that

ft

U,

=

per sec.

[(A-^.f^,)/*']

is

3 ., j(jQ..j

^^^

5,

=

(5,)/f;,

limen,

(/,

is

hills

(5)1.28n(10-')

^

the shear

the left-hand expres-

«ian of the ini'<|uality ha.s the form of a Heynoltis

number, so that it can be rrlatcd to a simple number. Of intcre.st in this connection a .set of crilcri.a i.s

0.08()(10"') ui.

or

the kinematic viscosity.

l.'j.lO,

=

(4.'i.vi)

the average height of the

roughnesses above

is

0.995 slugs per

From Table

whence A\, = fc^,

a destroyer a point

1703, Jul 1930, p. 113]

k,Mr where

for

abaft the stem and a speed of 30 kt,

ft

This

means that the maximum permissible hydrodynamically smooth

rougluie.ss heights, for a

would

i)rol)ably be of the order of onean inch. It amounts practically to a laboratory smoothness, exceedingly expensive and laborious if not practically impo.ssible to achieve on a i.'irge ve.s.sel, even for a .sjiecial trial.

surface,

thousandth

of

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.16

Assume

the 20-ft towing model of this

for

destroyer a point 10

ft

abaft the stem and a

speed of 10 kt, equivalent to 16.89 fps. The kinematic viscosity v for the fresh water of the basin is 1.2285(10"'). The value of p/2 is 0.969 slugs per

To

=

= fcA.

=

viscosity is

density p

is

v

temperature

water

(the

1.42(10"')

ft'

is

per sec and the mass

1.985 slugs per

Then, as a

ft'.

local

value at the stern.

water and Ul is 285.3 fps^. is about 13.75 miUion,

for fresh

ft''

From Table whence E°' =

matic

unknown)

113

To

=

0.059[^^)U^{RS

^

0.059(0.9925)(411)

=

0.485 lb per

R^

45.a,

26.77.

Then

49.63 [0.059(0.969)285.3]/26.77

0.6093 lb per

=

[1.2285(10"')5]/0.6093

10.08(10'')

'-(?r=(^r=°--"--

ft,

whence

Then

=

/cav

ft'.

ft'

1.209(10"') in.

5(1.42)10"

This value for the model, although not for exactly similar conditions, is about twice the

0.494

=

permissible value for the ship.

For the ABC ship, at an a;-distance of 500 ft from the FP, and a speed of 20.5 kt, equivalent to 34.625 ft per sec, i2, for standard salt water is, from Table 45.b, about 1,350(10'). The shear stress To at the ship hull is

To

=

0.059

=

0.059

I

UlR-J-^

(5.iii)

=

1

the procedure

1.051 lb per

U.

ft'.

/

\

is

not

roughness based upon numerous tests of flat and curved surfaces covered with sand grains of different mean diameters. When a rough surface,

whatever configuration, has a

Cp

specific friction

Clf

or local

,

equal

to that of a similar surface completely covered with sand of uniform size, it is said to have an

velocity

=

Although

admittedly empirical, and

based upon good roughness criteria, some practical use has been made of a quantitative measure of

sand

equivalent

Hence the shear

is

resistance, either average

(34.625)'[1,350(10'')]-

1.725(10"') in.

or

ft

Equivalent Sand Roughness.

45.16

of QQfl5 ^^^^

14.37(10"')

is

1.051

roughness

equal

the

to

mean

diameter of the sand grains on the reference surface. This diameter corresponds to the height of

=

0.726

ft

per sec.

the grains as individual protuberances and

1.9905

is

represented by the symbol Ks With grains completely covering the reference plate surface, the sand-grain density is assumed .

whence the laminar-sublayer thickness , h,

_ igr - lofiJl- 12.6 12.6 ^^

=

is

l-2817(10-°)

^^26

The actual mean roughness than the mean grain diameter Ks indicated in diagram 3 of Fig. 5.0. However, this detail is overlooked when establishing equivalent sand roughness as a practical comparator for surfaces whose irregular roughness can not be

to be 100 per cent.

height 22.24(10"')

ft

or

2.67(10"') in,

is

then

less

,

and the permissible average roughness height a hydrodynamically smooth surface is fcA,<

5^ <5i^?||^< 8.83(10-') or

<

for

ft

1.06(10"') in.

For the Lucy Ashton [Conn, J. F. C, Lackenby, and Walker, W. P., INA, Oct 1953, p. 350ff] the waterhne length is 190.5 ft and the speed is 12 kt, or 20.27 fps. The value of U^ or F' is then 410.87 ftVsec'. From Table 45.b, R„ is about 301 million and Rl'' = 49.63. The estimated kineH.,

measured by any available method. M. L. Acevedo at the Madrid Model Basin and W. P. A. van Lammeren at the Netherlands Model Basin in Wageningen have pubUshed tables [TABLAS, Madrid, 1943, pp. 98-117; van Lammeren,

W.

P. A.,

ICSTS, Berhn,

RPSS,

1937,

pp.

1948, pp. 66-69; 3rd

42-47,

100-101]

of

roughness allowances based upon the R. E. Froude formulation and the roughness effects developed by H. M. Weitbrecht from the Prandtl

nvnRODVNA.MK.S

Ill

TABLIC The

lo.e

Sand Roughnkrs Kf OF H. M. Weitbrecht 1'Xiiivaij;\t

Kx

listed vftlues of

inclusive of butts, seams,

rivot heads

.

SHIP DESIGN

IN

ness.

Sec. 5.21 of

known

"now, painted hull plates, ." apply to the

for

and

V'ai,i;i-;s

.

—or

Volume

suspected

I

describes

— aspects

Sec.

n.n

some

of the

viscous

of

flow

over a rough solid surface and the effect of these features on the friction drag generated at the

types of ships indirate
surface. In particular, Sporting and racing craft, torpedoboats and destroyers 0.10

(a)

mm

0.004 in

battleships

Mail

built cargo ships

Carpo ships

(d)

0.15

0.006

new

devised by H. N. Morris [ASCE, Hydraulics Div., Jan 1954, Vol. 80, Separate 390]. Fig. 45..I is a diagram prepared bj' the present

0.20

O.OOS

0.2.5

0.010

carefully

shijxs, fiu
outlines briefly the

conduits,

(b) CrossK-hanncl ships, cruisers,

(c)

it

approach to the viscou.s-flow problems presented by rough surfaces on the inside of pipes and

of less careful work-

manship, tugs

Clear Circumferential

Space Between Rouqhness Elements,

theory. In this

work Weitbrecht used the values

Meosured ot inner Periphery

given in Table 45.e.

Of

In a more recent paper H. Sasajinia and E. Yoshida pointed out rather convincingly that the

roughness embodied

of

t.vpc

coatings

of

most

large

ships

the

in

(not

hull

necessarily

fouling

values of

No.

/?„

[Int.

roughness),

is

Shipbldg. Prog., 1955, Vol.

is

Number

values

friction-resistance

for

of

Roucjhness

l-jpicol

""

in

o

Periphery

Rouohness

^ -^ ^^~^;^-

^h

-^^^^

"-^

^^

IS

I

is

less the

u i.. l. Heiqnt h

'

Elements Shown Are

Radius rg

d/e '

Rouqhness Heiqhl Entirely

Schemotic

2,

In other words, since the

13, pp. 441-450].

derived

n

s

15

Elements

not the t3'pe which produces a constant Cf value at large including

y

Conduit,

Definition Sketch for Roughness PabamETER-s OF H. N. MoRms, Applied to the Inside of

Fig. 45.J

full-scale

A

appear to involve a constant increment of Cf and not a constant total CV the effective roughness is of a t3'pe different from the sand roughness

TlBE

tests

,

of Nikuradse's pipes.

They reason that

the in-

due to a waviness in which there is a degree of pressure and separation drag, ahead of and behind the roughnesses, which adds to the normal viscous drag. This means that the dynamic effects on the ship, varj'ing as V', form only a part of the friction drag of the rough hull surface, and not all of it. crease in friction drag

The effect

feature responsible for this dilTcrcncc in is,

according to the reasoning of Sasajima

and Yoshida, the in

is

effective slope of the roughnesses

the direction of the flow. For example, the

slope of a

wavy

surface

sand-roughened surface.

is

In

less

than that of a according to

fact,

their findings, the slope or the steepness of the

roughness

elenioiit.s is

absohitc height.

It is

more important than

their

interesting in this connection

to c|uote their conclusion "g" on page 450 of the reference:

"The roughness

effect of paint

seems

author as a definition sketch to illustrate the dimensions used by Morris to represent the roughness characteristics mentioned in his paper. The roughness projections shown in this diagram are purely schematic; Morris gives no dimension for

them other than

It

is

their height

termed the roughness index of a surface, more must take account of at least seven factors, repeated here for conIje

or loss regardless of its shape,

venient reference. It

is

possible, in fact probable,

must take account recognized or unknown:

that

it

of others as yet un-

Height of roughness peaks above the limen in terms of mean heights (averaged by some suitable method), maximum heights, and a statistical or significant hciglit (!)) Slopes of the roughnesses, on botli tlie u])stream and the downstream sides of the sloping surfaces with (c) Orientation (a)

or reference surface,

determined by an clement of the smallest height but the steepest Blop(!." They derive curves for various roughness effects which appear to conform, rea.sonably well,

This corresponds to the distance

to the curvf.s derived from

or to the ratio A

to

be

45.17

almost

completely

fuil-H<'ale tests.

Practical Definitions of Surface

Rough-

/i.

pointed out in Sec. 22.14 that what might

respect to the litiuid-flow direction (d) Spacing of roughnes.ses in the flow direction, probably with respect to the roughness heights.

(i)

Type

of

,\

in

l''ig.

15., I,

li.

roughness projections as affecting the

FRICTION RESISTANCE CALCULATIONS

Sec. 45.1R

mind that sand-coated variations of Cp with /?„

115

viscous flow, having in

ness

surfaces give different

roughnesses, the thickness

than surfaces coated with sprayed plastic paints General pattern of roughnesses, as viewed (f) normal to the surface, including spacing, density, shadowing or shielding effects, and the like (g) Finally, it must be possible to ascertain the roughness index easily and quickly in service and to express

it

(or its results) in quantitative terms.

Further development of the shadowgraph procedure described in Sec. 22.14 and illustrated in

an equivalent procedure, should give the heights of the roughness peaks above the limen or above the adjacent surface, in terms of the lengths of the shadows for a given inclination Fig. 22.1, or of

of the light rays with reference to the surface as

a whole. With an inclination of say 15 deg it could be assumed that any region covered by

shadow was

and therefore known, however, that

in a separation zone

— Ap's.

subject to

It is not

this is the proper angle or that the angle

constant.

The

remains

slopes of the upstream sides of the

roughnesses could be determined generally by their relative brightness although it is recognized

down

that the shadowgraph scheme breaks

an upstream face which

lies

at a large angle to

The

the limen, say 80 to 90 deg.

for

orientation of the

sloping surfaces with respect to the direction of

flow

by

is

easily recognized

this

it

is

not so simple to

express this orientation in terms of angles or

numbers, especially as an average or effective

The

spacing, density,

general pattern of the roughnesses,

and

as viewed

normal to the surface, is perhaps easiest of all to visualize on the shadowgraph, although again not so readily put in terms of numbers or scalar quantities. It is

of the

not improbable that some sort of screen may be devised which, when

of the

and the type

of flow exist-

how the shell plates or planks be applied, what sort of workmanship is to be expected, or what the eventual external coating material will be,

will

will be. If trial predictions

only are involved the

and new, but not necessarily smooth and fair. If an average service performance is wanted, fouling allowances must be estimated and added. For an intelligent application of the several sets of roughness allowances which have been dehull will at least be clean

veloped to predict the service performance of a ship, it is necessary to consider the existence of at least six different regimes in the roughness setup.

From the knowledge so far gained (1955) it appears that somewhat different physical laws govern the viscous flow in these regimes and that different sets of practical rules apply.

regimes

may

be described

The

six

as:

I. Zero ACf. where, at sufficiently low values of Rn say up to 4 or 5 million, with a range of Cp above about 3.3(10"''), roughness effects appear to be small or nonexistent, at least for moderate values of speed compared to length. For example, it has long been known that ship models built for routine resistance and self-propulsion tests required no special finish. It appears that small racing sailboats are in the same category, except at extremely low speeds, say less than 1 kt. ,

,

Zero

II.

boat,

surface.

Whatever may be the method (s) ultimately developed for expressing the physical roughness of a surface, the index derived therefrom must be compared with the hydrodynamic parameters of the viscous flow taking place over that particular surface to determine its roughness effect on friction resistance. These may include the downstream distance x from the leading edge of the

the speed

way

characteristics

45.18 Determination of the Allowances for Roughness. It is necessary to estimate the friction resistance and both the effective and the shaft powers early in the design stage. Often it may not be known definitely of what material the shell will be constructed, how smooth the

on a shadowgraph, would give a numerical or other roughness index of any given superposed

ship,

layer,

and

ing in the inner regions of that layer.

or set of screens

relative velocity

boundary

5

from a photograph taken

method although

value for a given area.

of the laminar sublayer in

&[,

body

or

V of the body or ship or the U of the water past it, the thick-

ACf

or

,

at

ship

all

values of

surfaces

i2„

are

where the model, hydrodynamically ,

smooth. Sees. 45.10 and 45.15 explain the circumstances under which the laminar sublayer thicknesses exceed the roughness heights by sufficient margins so that this type of smoothness is achieved. III.

Small ACf

,

at

all

values of K„ throughout

the boat and ship range. In the lower or boat

portion of this range the roughness effects appear to be small, especially at low speeds, despite the existence of normal physical roughnesses. In the

upper or ship part of the range the use of leveling

coatings and

the

existence

of

self-

certain

,

HYDRODYNAMICS

116 as

configurations,

roiighiipss

yet

unknown

in

appear to limit the shij) roughness effects to subnormal values. The nominal roughness heights in this regime definitely exceed the limiting values for hydro<^lynamic smoothness. character,

ACV

IV. Large

relatively uniform with speed in

,

IN SHIP DESIGN

Sec. 45.18

For ship-design purposes in America the American Towing Tank Conference in 1947 adopted an overall tentative roughness allowance ACV of 0.4(10"'). This is a constant addition (not a plus percentage) above the

turbulent flow on a

ATTC

flat,

1947 meaniine for

smooth

plate, regardless

the case of any one ship, in the larger ranges of

of the size or speed of the vessel concerned.

This situation results largely from the use of rougli plastic paints and from fouling. The roughness heights in this regime far exceed those

pictured in Fig.

R,

on page 2 of

1

.

hydrotlynamic smoothness, perhaps hj' several hundred times, yet the total Cp for the ship continues to vary with A', in a generally normal manner. for

V. Very large AC,. total

and other

with practically constant

,

the speed range. For ships

C, throughout

floating

large

this

craft,

condition

probably applies only when the fouling coat is complete and it exceeds 0.4 to 0.5 ft in thickness. In this

ca.sc

the friction resistance

is

in

effect

IC r

in which the various roughand the hull of the ship is kept

The

reasonabl}' clean.

AC,, values, exclusive of

conform to those represented by the C-C or D-D in Fig. 45. E, or to some com-

fouling,

bination of the two.

take care of the effects of normal roughness on a clean, new vessel, involving manj' unknowns, the Froude formulation, listed under item (7) in

used

is still

in

many

parts of the world.

This formulation gives a so-called "Froude Friction Grid," indicated graphically by J. M.

Ferguson and others [6th ICSTS, 1951, Fig. p. 68],

1.5,

according to the length of the ship and

the speed-length constant

(L).

The

latter

is

eciual

Appx. 1. The lines of this grid lie sufficiently above the ATTC 1947 (Schoenherr) meaniine to provide an to 3. .545 times F,

,

as listed at the end of

acceptable roughness allowance for a ship in the "clean,

from 1,000 to 100 ft whereas the former decrease slowly as the ship length dimin-

diminishes

ishes

length

from 1,000 to about 300 ft. Below this the Froude allowances dcircaso rather

There are

definite iiuiications, described in Sec.

that

22.15,

roughness

this

diminish with

/?„

,

allowance

should

at least for low values of speed

V or relative velocity U. For the lower speeds it appears to diminish toward zero in the region of R„ = 3.5 to 5 million, as does the allowance inherent in the Froude formulation. Fig. 45. E of

To

Sec. 45.8,

latter increase progressively as the ship length

,

nesses are normal

lines

and Research Bulletin 1-2 of March 1952, entitled "Uniform Procedure for the Calculation of Frictional Resistance and the Expansion of Model Test Data to Full Size," it is a compromise between the equivalent plus roughness allowances of the Froude formulation and the tentative ATTC roughness allowances adopted in 1942. The

rapidly.

entirely a pressure resistance.

VI. Normal

As

SNAME Technical

ATTC 1947 ATTC constant

Sec. 45.7 embodies, in addition to the

or Schoenherr meaniine

ACp = ance

0.0004

line,

and the

a proposed roughness allow-

C-C proposed by

line

M.

J.

Fergu-son [6th

ICSTS, 1951, pp. 67-69], and a line D-D proposed and used by L. A. Baier for some years past. Baler's line leaves the ATTC line at an R„ of about 3 million and reaches the (ATTC + 0.0004) line at an R„ of about 600 million [SNAME, 1951, Fig. 19, p. 365]. Ferguson's line reaches Baier's line

at an

of

y^„

about 7,380 million, corresponding to

a I,400-ft ship running at 40 kt

Whatever the

line

in salt

water.

or table used to estimate

roughness effects in the early stage of a ship

new" category.

A dimensional and carefully systematized attack

design,

as soon

roughness

— or

as

more

smoothness

is

known about

— to

be expected

the

on

on the problem of predicting the friction resistance of a full-scale ship, including the effects of roughness, is given by W. W. Smith in his discussion of K. E. SchcKMjhcrr's cla.ssic SXAME 193'2 paper on "Uesi.slance of Flat Surfaces Moving Through a Fluid," pages .305 through 308. Smith's proposed methcxJ is too long to be given here, and is likewi.sc

design

wjmewhal

values for the plating, structural, coating, and

ob.solete,

but his

and juHtilies a study of working on the pr<jblcm

line of

attack

is

his jiroposal bj'

logical

anyone

of roughness fridioti.

the hull the tentative value

is

modified, and the

friction resistance is re-calculated.

As.suming that the necessary data are available, the logical

allowance is

method

in

of determining a roughness

the pre-construction stage of a ship

to select

and add together four separate

fouling roughnes-ses, respectively, as describeil in Sees. 22.15

and 45.7 ami as

lislcd in

!']((.

(22. iv)

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.19

Although adequate means do not

(iii)

yet exist for selecting these separate roughness

ing.

and Eq.

(45. ii).

independently

allowances

and

exactly,

it

is

possible to assess reasonable values, within nottoo-close limits, to:

Item

(c)

structural

of fouling roughness

(i)

The roughnesses

(ii)

Those inherent

be assigned tentative individual values as Table 45.f, for values oj R„ greater than

clean

paint, this gives a

in the coating(s) applied after

(10^) Cf.

45.f Tentative Individual Allowances FOR Roughnesses of Three Types

(excluding fouling) having a

Pickled, sandblasted, or galvanized 0.01 to 0.05

(2)

Rusty, pitted, mill scale

Wooden

0.05 to 0.1

planking, ApCfClO^)

molded pl3Tvood, with few seams or the equivalent, very smooth 0.00 Flush seams, planks in the direction of flow, no open seams, and no

(1) Plastic, or

(2)

calking (3)

0.01 to 0.05

rough 0.05 to 0.1

finish

(c)

(2)

(3)

a number of merchant in the range of

and type,

R„ from 150 to 1,800 million, are plotted by R. B. Couch on a plate accompanying Appendix XXVIII of the published Minutes of the 1953 ATTC meeting. The ranges of speed for some individual ships are sufficient to show changes in ACp with R„ it

is

logical to predict

seldom

roughness allowance by adding

all

the Ap

,

As

a ,

and Ac factors. The preservative coating on the bottom may cover up (or even exaggerate) some of the plating (or planking) roughness, just as the

may later

cover up the plating and coating

even

structural

Metal plating, lapped riveted or welded seams, smooth welded butts 0.06 to 0.1 Metal plating, lapped riveted seams and butts 0.08 to 0.15

roughness.

A

Wood

the ship just out of dock, and (2) the ship with x months in service, following the last docking. In any case, a good prediction of bottom roughness, excluding fouling, requires

planking, lapped or clinker

Red

0.00

(3) Self-leveling

paints

Vinyl resin

0.05 to 0.18

Cold

(6)

Hot

plastic plastic

may

the

well predict

more roughness allowances, one other (s) for service conditions.

for trial

The

two or and the

latter should

(1)

rather unusual judgment and a better background of reliable roughness and resistance data than are available at present (1955).

varnish-type bottom 0.02 to 0.12 0.05 to 0.3 or 0.4

(5)

perhaps

designer

correspond to

lead, metallic oxide, zinc

chromate

(4)

for

and

Coating roughness, AcCp(lO') (1) Varnish, yacht-racing enamel, polished metal (2)

2ACp

vessels of varied size

roughness

style, discontinuities in line of flow 0.12 to 0.18 (d)

value of 0.32. For

writing (1955).

fouling

Structural roughness, AsCf(IO^) (1)

Ac)

.

Flush seams, calked, planking not

(4) Soft planks, slash-grained,

+

minimum

approach but usually does not exceed 0.2 [Vincent, S. A., unpub. Itr. to HES, 26 Jun 1953]. These values do not apply to ships coated with plastic bottom paint of the kinds in use at the time of

Manifestly,

0.00 to 0.01

in direction of flow

Ag

a clean, new steel ship with both flush-welded butts and seams, also coated with a self-leveling bottom paint, the value of SACp(lO^) may

Values of plating, ApCj?(10=)

(1)

+

flufsh-

bottom

self-leveling

maximum

with

vessel,

lapped seams, and

SACf (10^) = (Ap

value of 0.09 and a

These correspond to three of the types listed at the end FouHng-roughness predictions are listed in Table 45. g. The present values are intended to apply only to ships of medium and large size, having ship Reynolds numbers at designed speed in e.xcess of about 100 million.

(b)

For a modern

plates, riveted

welded butts, coated with a

built into the ship

of Sec. 45.7.

Metal

discussed in

the plating, structural, and coating allowances

about 100 million.

construction or during docking

(a)

is

undock-

listed in

These serve to subdivide:

TABLE

The matter

in service, after

Sec. 45.20 following.

may

plus fouUng roughness.

(b)

Those accumulated

Using the best information available in 1955,

A

combination of plating and roughness (b) Item (a) plus coating roughness (a)

117

0.1

to 0.3

0.3

to 0.8

45.19

Factors Affecting Fouling Resistance on W. J. M. Rankine, in his 1866

Ship Surfaces.

book on "Shipbuilding: Theoretical and Pracpage 5, says of fouling that "It is very common to find the resistance increased by about tical,"

IlVnROnVNANflCS IN SHIP DESIGN

118

n fourth from

tlii.s

more." I'nfortimatoly,

increaiicd

what

not say

rosistaiuo

W.

or total.

frietioii

entitled

causf; ami iH-rasionally

56,

is

Hankiiie (Iws

whether 1903 hook

involvoil,

is

V. Diiraiul, in

liis

and Propulsion

"Re-sistanee

pages 55 and

it

tabulates

of Ships,"

increases

in

total

on V. S. Naval vessels of the ISDO's as varying from 20 to 200 per cent at speetis of 7 to 11 kt. The.se are understandable in view of the r2-in barnacles reported to have grown on an old ironelad which spent most of its time at anchor [SBSR, 24 Feb 1938, p. 229]. The reader who ma.v question these data has only to look at the photographs in the book "Marine Fouling and Its Prevention," prepared by the Woods Hole Oceanographic Institution rcsistanec

and

due

to fouling

by the

publi.shed

l'.

S.

Naval Institute

in

1952.

The

deposits which form on the surface of any

ship or ship element, immersed in

any type

of

water, are divided roughly into two classes:

may

made up

Sec. 45.19

lake on the a|)|)earance of ha\ing been

mixture of paint and sand.

of a

.Mso mentioned here

is

the deterioration of hot-

due to unfavorable weather conditions, improper application methoils, and similar factors. This deterioration sometimes occurs before the ship is waterborne at the end plastic paint coatings

of the docking period. Runs, supcrpo.sed layers, folds, "icicles,"

and peeling

of the plastic coating

involve roughnesses of the magnitude of those

encountered in fouling. Fouling of the second class is accelerated in salt water, especially with slow relative

warm,

motion

of the ship

and water.

It

is

augmented by

seasonal and other conditions, not too well known,

conducive to the rapid growth of marine

Growth water; much slower when the vegetable and animal. continual motion. It

is

is

life,

both

slower in cold

ship

is

in

almost

practically nonexistent in

fresh water, giving trouble onlj' in exceptional

and then usually along the watcrline. Fouling of both classes maj' be arrested by the on.set of unfavorable conditions for the growing cases

Gelatinous coatings and soft slimes containing no visible solid matter and representing a rela(1)

deposit of apjiroxiniately uniform These are often a factor in the take-off characteristics of seaplanes and Hying bouts. (2) Rough coatings, semi-rigid or rigid, composed of grasses or other marine vegetation, shells, barnacles, and the more-or-less rough and firm growths of all visible types of marine life. thin

tively

paint

organisms, such as moving a ship from

.salt

water

to fresh water. It can not be expected, however,

thickness.

Fouling of the ately

undocking. that

first class

usually begins immedi-

upon immersion, following launching and hour,

It

develops

increasing

its

own

friction

drag from

slowly but progressively

until its effect is overtaken bj' fouling of the second class.

A

ship resting in w-arm, quiet water usually

that this will or that

it will

le.s.sen

the added friction resistance

eliminate the fouling drag altogether.

The

firmly fixed barnacle shells on a ship entering

the

Panama Canal from

not drop

a long sea voyage will

the ship anchors for a few days in the fresh water of Gatun Lake, long enough to kill the barnacles themselves. The effect of hard, rough fouhng is to create a friction drag of the tantjua type, defined in Sec. 5.21 on page 108 of Volume I, varying as the square of the speed. For a ship of medium or off just liecause

large size, this involves a constant

ATTC

AfV allowance

1947 mcanline, or above any

acquires a slime coating rather rapidlj', whereas

above the

one moving continually or resting in cold water may never have more than a thin coating form

friction

on

negligible factor at /?„ values of 2, 3, or 4 milHon,

it.

Although not to be classed as fouling, in the mentioned here a deterioration of the bottom paint which occurs at unexpected places and times. The causes of this action

strict .sense, there is

.seem

t(j

be related to the causes of particular

kinds of fouling

The

in certain

areas at specified times.

to vary by j'ears in the somewhat the same way that extra-warm Hummers or unusuallj' .severe winters are fni'oimtere(l. The action is often extremely rapi
deterioration

.Maine locality,

ajjpi^ar.s

in

I

I

other

modern line.

flat,

smooth-plate, turbulent-flow

Whether

fouling

roughness

is

a

as smaller si^es of roughness appear to be, especially at .slow speeds,

is

not yet known.

What

applies to the latter should, however, also apply to the former.

Numerous

rules

have

time to time to predict the

been

devel()|)c(l

effect of fouling

from on the

resistance, j)ower, and speed of ships. For any one kind of anti-fouling coating these an? based generally upon tlu- time which has elapswl from llic

application of the last anti-fouling coating,

iipiiii IIk-

|ii'ii(Hls,

average speed of the

ami npon the kind and

shi|) iluring ccrt^iin llie IciiipiTMliirc

of

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.19

119

the water in which the ship has been floating.

ship allowance for plating, structural, and coating

Unless an external coating is proof against most types of fouling, an estimate based only on time out of dock is precarious at the best, considering

roughness, described in Sec. 45.18 preceding,

The

the variables involved.

all

effect

of the order of it is

should be one of history, modified in degree

to conform to the anti-fouling properties of the

The

about 0.39(10"') for the

The roughness drag

basis for fouling

is

only 0.25(10"') for the tug whereas liner.

of fouling is

predominantly

a tanqua resistance proportional to V^ and largely independent of /?„

,

is

except possibly at

history embodies a combination of ship location in

low R„ values. It is not a function of the tanvis resistance and should therefore not appear as a

the navigable waters of the globe, ship operation,

percentage of the

coatings on the underwater hull.

outside

The

elapsed time, the seasons during which the ship is

in

latter.

use of a formula with additive specific

exposed, and the portion of the fouling cycle

resistance terms, as in Eq. (45. ii) of Sec. 45.7,

each water area which

this is

requires that the roughness effects of the fouling

the events, and

shape, and distribution of the fouling roughnesses

known. Assuming that the

is

involved,

if

be considered as a primary function of the location,

the time history are fully recorded,

found

it is

that the fouling rates, fouling types, and fouling effects are variable

because of seasonal,

or other factors pertaining to marine

cyclic,

life.

Fur-

thermore, in making predictions of future fouling effects it is possible

only to estimate a probable

any given period. With our present (1955) knowledge, an average result is the best

on the hull

resistance. It has

been the custom in the past to reckon

the effect of fouling as a percentage increase in the friction resistance

Pe

,

or in the shaft

Rf

,

power

va.

F,,

the effective power .

Occasionally

it is

expressed as a percentage of the total resistance

They may be a secondary

function of Reynolds number, at low R„ values,

only because of a laminar sublayer which either persists over fouling .that is not excessively

or which

To

reduce the observed fouling effects to terms

an additive ApCp factor by the older methods is difficult. For most of the cases on record, the propeller thrusts were not measured and the actual ship friction resistances were not known. Furthermore, there is no way to determine how much of these resistances was due to plating, structural, and coating roughnesses, exclusive of fouling. The operation is greatly facilitated by of

or of the friction power Pf but with the disadvantage that, of the five quantities mentioned, only the shaft power is known with any degree of accuracy on ships in operation. Actually, be-

the use of the specific resistances

cause the friction resistance of certain not-too-

plate

Rt

smooth ships present

of

the

—consisted

of

past

—and

some

Cp

-\-

less of

may

indicates that the average

smooth-plate specific friction resistance Cf decreases as the ship size and speed increase. By flat,

for fouling as

well as for other types of roughness decrease

but they increase

rapidly with the designed speed of the ship, as

described in Sec. 45.10. For a tug or ti'awler

Cp

say 2.3(10~^) at an i2„ of 50 million whereas for a fast liner it is only 1.3(10"') at R„ = 4,000 is

million.

Cr remains constant regardThe flat, smoothremains friction resistance Cp

the extent of fouling. specific

to fouling and

up

size (length)

-{

specific

Ct over the clean-bottom value

in

of the total resistance.

somewhat with the

Ct = Cr

assumed that the

residuary resistance

increase due to fouling as a percentage increase

ApCp values

it is

is a change due be represented by ApCp as a This procedure takes no first approximation. account, for example, of a ApCp or a AcCp that

amount of tanqua resistance (varying as V^), was some logic in expressing the resistance

indications, the

if

resistance

there

all

,

constant by derivation. Therefore any increase

of

(varying with the Reynolds number), with a large

Modern knowledge

SACp

the

some

tanvis

rough

increased in effective thickness by

is

some physical action as yet unknown.

history for

that can be expected in the prediction of fouling

surface.

size,

At the same time a "tapering" ACp new-

may

be diminished because heavy fouling covers

original plating or coating roughnesses.

It

may

be presumed that, for a large and a

small ship having exactly the same underwater coating, the

same exposure position with

refer-

ence to the adjacent water bodies and currents, and the same fouling history, the fouling will be exactly the

same on the underwater surface

of

each. In other words, the marine growths will be

same absolute shape and size and will be same manner over each unit of area. If each craft has about the same hull shape and a reasonably large draft, there will be of the

distributed in the

HYDRODYNAMICS

IL'O

no

of

prc-poiuli'raiu'c

along

cfTocIs

foiiliiin

tlic

This boinp the case, the laminar sublayers over the two hulls, at the same absolute speed for each will have only a slightly greater thickness on the large ship than on the small one, indicated in Fig. 45.F of Sec. 45.10. For the higher speed at which it is presumed the larger ship will run, its laminar sublayer will be thinner than on the smaller ship. This means, for example, that a group of barnacles of a given size and ilistrilnition will have a greater roughness effect on the large, fast ship than an identical group of identical barnacles on the small, slow ship. If this physical reasoning is correct, the effect of a

hull,

5t

given amount of fouling in unit surface area of the

with the increase in ship

hull decreases slowly

length but

increases rapidly with the increase

it

magnitude

term

of the speed

U in

the Reynolds

number UL/v. It can not

rate

be

therefore, that a fouling

said,

and a fouling

determined for a

effect

craft will be valid for a large one,

any more than the

Even though same, there

is

size

^'ice

sm-'ll

versa,

roughness

is

and speed.

other conditions remain the

all

almost certainly some non-linearity

of the roughness effects

curve

and

effect of a given

independent of ship

older

of

nith time out of dock. decades ago,

several

An

given in

reference (15) of Sec. 45.21, indicates a moderate ri.se

the

Sec. 45.20

Sllll' l)i;si(;N

placement both

growth

increa.sc perceptibly as the

thickens. Should the ship have to be propelled or

waterlino.

in

IN

immediately after undocking, a rate less than average for the intermediate period, say

from 2 to 4 months, and a rapidly increasing rise at the end of the interval, from about 5 months to months. On the other hand, results of experiments by \V. IMcEntoe, reported in reference (3) of Sec. 45.21, gave rates that were almost exactly the opposite [Taylor, D. W., S and P, 1943, Fig. 43, p. 38]. Later

and possibly more accurate data

indicate that the increa.sc in

A^Cr

for the first

few days and weeks out of dock may be slightly le.s.s than the average while the increase under conditions favorable for marine growth, during a later portion of the

docking period,

may

be greater

moored or at anchor to accumulate ^ marine growths having than the average.

If

the

.ship is left

towed while fouled it is effectively larger than when clean and requires additional power in proportion, over and above that due to the fouling roughness. Ships have been known to pick up from 100 to 300 or more tons of marine growth

when

heavilj'

increa.se in still

fouled.

volume

of

The

equivalent

effective,

water displaced

is

probably

larger.

All additive allowances for fouling effect should

new"

constitute increases in the "clean,

Rr

friction

a ship. This is not ahvays the case when ship data arc reported. In fact, some reports are so ambiguous as not to specify the quantity which increases with the fouling. Stictly speaking, the magnitude of the friction drag is not known for any ship but it can be calculated by the methods described elsewhere in this chapter. It can be estimated as a percentage of the total towrope resistance for the type of ship in question. If corresponding changes in the power and speed are wanted, they may be predicted by the methods described in Chap. 60 for the estimate of power and speed on a new design. In this connection it must be remembered that an increase in roughness due to fouling increases the thickness of the boundary layer at the propulsion-de\ace positions. This in turn almost invariably increases the average-wake fraction drag

of

over the thrust-producing area Aa of the proFurthermore, the additional device.

pulsion

means augmented thrust, higher thrust and undoubtedly a lowered efficiency of propulsion. Estimates of increased shaft power due to fouling are not ahvays accurately predicted, therefore, on a basis of model tests run with an resistance loading,

overload allowance only for a clean,

new

hull

surface.

45.20

Ship

The

Prediction of Fouling Effects on

Resistance.

Simimarizing

the

elTects

of

fouling on shi]) resistance, dist'u.ssed in Sec. 45.19,

the principal factors appear to be: (1)

The type and nature

adheres to the (2)

The

of the fouling

which

.ship hull

history

of

the operation

of

the ship

reaches a

maximum

value by the time the hull

during any one interval between dockings, taking account of the length of time out of dock, and

surface

completehj covered with a growth 0.1

including the kind and temperature of the water

thickncs-ses of inches or

or 0.2

is

ft

thick.

how

It

even

may

feet,

AyCr probably

not become larger no

However, the weight displacement and the volume dis-

matter

dcnst; or thick the growth.

(3)

The

fouling rates, cycles,

and other features These

a.ssociated with the historyfof ojMTation.

rates vary widely in the different parts of tho

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.20

world, from positive heavy fouling to slightly

negative scouring. (4)

The

size

of

operating speed for which the fouling prediction is

sum

to the

the vessel, and especially the

to be applied

of the specific pressure (or residuary)

and the turbulent-flow

resistance

resistance, with or

Considering item first

is

specific friction

without corrections for cur-

vature.

required.

The

121

units of specific resistance which

three items correspond to those which

have been recognized for many years past. The is, in an analysis of fouling effects, believed to be entirely new. One may conclude, from the discussion of Sec. 45.19, that the effect of fouling on ship resistance should be expressed as an additive rather than as a percentage term, as proposed by G. Kempf in 1936 and 1937. This is on the basis that the fouling creates an increment of resistance depending upon its physical characteristics and the flow around it, without regard to the amount of the friction resistance of a clean, new hull to which the fouling is attached, of the separation drag around the hull, or of the resistance due to wavemaking of that hull. A convenient additive form is the use of an increment ApCp expressed in fourth item

,

TABLE

45.g

(1)

at the beginning of this

section, it is explained in Sec. 22.11 that relatively little is

known about the quantitative effect of At the other end of the roughness

surface slime. scale,

a very heavy, thick, and rough deposit

neceSsary viscosity.

the

sum

to

eliminate

entirely

Such a deposit has the

the

effect

effect of

making

of the smooth-plate friction resistance

and the fouling resistance constant, independent of the Reynolds number. For the normal ship situation,

that

AfCf

the viscosity effects are retained, so is

narrow range

roughly constant in the relatively of speed for

any one ship

for

which

fouling effects are to be predicted.

The ultimate solution to this problem, despite demand for simplicity, seems to call for a

the

subdivision of items (2) and (3) of the summary, to take care of conditions which vary widely in

Proposed Form of Tabulation for Determining the Value of ApCp per Day Due to Fouling in an Average Port

FRESH WATER

is

of

IIM)R()l)V\.\Ml(;s 1\ Mill' ni-.SIGN

122 service. Iti'in tion,

(12),

appears to

about nine proups each,

call for

water anil for

for fresh

Table lo.p

is

s^ilt

values

I.

III.

Warm

siilinity of 3.5

water

is

moving

at 2 kt or

1

All

Concerning item beginning of this

that in which the temperature

any, are taken

care of by the variations in water temperature.

Pkoi'oskd

Form ok TAnn.ATioN to

summary

of the

(3)

.section,

the

at the

information

on

and fouling cj'des for specific ports appears limited to that given by G. I). Bengough in reference (22) of Sec. 45.21. These data indicate that certain ports and certain areas appear to be excellent for breeding and attaching marine fouling organisms, and that other ports and areas fouling rates

are relatively free of this nui.sance. Ba.sed on data in the reference quoted.

per cent.

if

reckoned in accordance

fouling efTects

Table

45. h

is

a propo.'^ed

guide for determining the relative fouling rates

of fouling in

193),

relative to the sur-

with the tables are additive.

same. This factor

|i.

"stoppetl"

day

5 deg C. Seasonal variations,

'IS.!!

le.s.s,

l)e

to attach thcm.selvcs.

F or 25 deg C. Cool water has a temperature range of from 77 deg F, or 25 deg C, to 41 deg F, or 5 deg C. Cold water is that in which the temperature is less than 41 deg F or

TABLE

a.s.sumed to

is

rounding water, slow enough for marine growths

than

exceeds 77 deg

The

Sec. -15.20

he table a ship

suffi-

l>e

corresponding

if it is

^'I. is

though contaminated by microorganisms. This water should be sufficiently free of salts to kill or prevent the growth of adhering marine life. II. Salt water is defined as the water found in the oceans and in salt seas, and includes brackish water. It may be expected that the fouling effects in this water will vary approximately in proportion to the salinity or specific gravity, with a specific gravity for average sea water of 1.027, and a

may

lilt

history need be divided into intervals no smaller

to

ciently sweet for drinking purposes, even it

.

study and investigation.

groups,

defined as that which

is

\

V. For the approxiiiiati' mu'IIkxI given, the ship's

these

following notes applj' to this table:

Fresh water

1

be

in

(leterinineil after further

The

water, respectively.

a proposal framework for carrying

numerical

the

involving the history of opera-

or the locality foulinc/ factor in the ports usually

frequented,

assuming the ship at anchor

moving very slowly) and

all

(or

other conditions the

is based upon an average rate an average port, assumed as unity

(1.0).

I'kiimit

Selection ok thk IvOcauty

Fouung Factok

taken from G. D. Bengough, "Hull Corrosion and Fouling" [NIOCI, 1942-1943, Vol. 59, Talilc with the two left-hand groups interchanged.

liBt

of port*

i.s

LocALmr Fouung Factors (Less than 1.0)

5,

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.20

The

daily increments,

when taken from

the

proper "box" of Table 45.g, have to be multiplied by the number of days in each operational condition

and then added to give the ApCp for the and (2) in the summary. The

effects of items (1)

then applied to this sum (by multiplication) to cover the effect of item (3) The upper row of boxes in Table 45. h is left open locality fouling factor is

until such time as data are available to determine

operating in

123

seasons and in

all

waters of the

all

a definite demand for a simple guide which will give the answer in one operation, as it were. Avorld.

Nevertheless, there

is

As an interim measure a set of graphs prepared and published by E. V. Lewis [The Log, May 1948, pp. 50-52] serves as a means of determining by inspection a suitable value of AfCf{10^) for any one of three given operating conditions.

values of the locality factor which are reasonably

Lewis' data are reproduced in Fig. 45.K, supple-

correct,

and until such time as additional ports in the Western Hemisphere can be listed. As for item (4) of the summary, it is perhaps not wise to introduce a set of ship-size and ship-

mented by data derived from the

speed parameters into the fouling roughness pre-

Putnam (DD 287), the U. S. battleship Tennessee (BB 43), and the Japanese destroyer Yudachi. The two former sets of data were used by Lewis; the latter data were

paramproved for roughnesses in general.

diction procedure until the effect of these eters is fully

ships, the

U.

S.

trials of three

destroyer

not. According to information received subsequent

to the date of the reference [unpubl.

B

Itr.

of 15

and when so proved, the variation in A^Cf with Reynolds number R„ will probably resemble the variations in ACp shown by the lines C-C and D-D of Fig. 45.E. Judging from the work done recently on this

Aug

project, it appears hopeless to expect that a single

British Admiralty standard for temperate waters,

and certainly not adequate prediction

with a rate of 0.25 per cent per day increase in

and types.

curvature because of the shape of the curve for

If

rule, table, graph, or reference,

a rule of thumb,

will furnish

data for fouling on ships of

all sizes

1955], curve

was actually based on the

British Admiralty peace-time standard for ships

operating in tropical waters, involving a 0.5 per cent per day increase in friction resistance [INA, 1943, Vol. 85, p.

Rp

,

raised

2].

Curve

A

was based on the

somewhat and given some upward

Line

B

for ships

is

which enter a numbei of ports

where severe

foulincj

encountered

2J Line

A

is

for ships

on overoqe vo^aqes

- n

between tcmperote ports with Qveraqe

rotes of fouling

Line

C

is

unusuall'y

for ships

.

g

having

short stoys

or trodino reoulorlij

in

port

^—

between

ports free from foulino or ports havinq a scourinq action I

6

Fig. 45.K

I

\

L_l

I

L

7

8 9 Months Out of Dr\jdock

Graphs op E. V. Lewis fob Specific Fouling Resistance Allowances, with Curves fob Thbee Ships

MVDRODVNAMICS

124 Tennessee.

the battlciihip

midway between B and

Curve

C

way

the baseline as a rougli

some scattcretl supporting data. Lewis' graphs A and C indicate a progressive increase in SrCr per day for the early months with

fi:uess,

between tioikings while graph

of the perioil

SHIP DESIGN

I.\

what may be

was dniwri

of fouling roughness only, involves a fouling

rate that limits the roughness to a value which,

would be e(|ual to that expected of "commercial" anti-fouling paint in only 'J months. However, the inilial roughness of the hot plastic in 4 years,

li,

for the heaviest fouling, indicat<'s a linear increase

paint

with time. The graphs for the three combatant

a

show a

vessels

Sec.4-y.20

expectetl of hot jjlastic paint in the

slight increase in rate with eliip.sed

extremely high, so that this paint

is

di.^^ad vantage

is

at

compared to the "commercial"

anti-fouling paint until sucii time as

tiie

latter

time for the entire interval, and a rate that

has acquired considerable roughness due to

increases as the next docking time approaches.

increa.sed rate of fouling. It

Fig. 45. L is a duplicate of the three Lewis graphs with the fouling-efTcct predictions for the ABC ship of Part 4, under the conditions set

the average application, and as the ship comes

is

its

estimated that, for

out of dock with a new coat of paint, the of the hot-plastic paint exceeds the

AcCy

ScCf of the

fourth in items (18) and (19) of Table 64. c and

commercial anti-fouling paint by the order of

item (20) of Table 64. d. This ship is expected to have what Lewis terms "average voj'ages"

0.5(10"^). For the purpo.se of this discussion, the

except that at one end of the route the ship

considered in the nature of a fouling roughness.

spends an appreciable time in a fresh-water

To make up

The

fouling rate

below that of The broken

ABC

may

line line

be expected to

lie

river.

somewhat

augmented

with long dashes of Fig. 45. L,

the

for

hot-plastic

paint

is

for this increiused resistance of the

first few months out must have a much smaller fouling allowance ApCy for the remainder of the interval

hot-plastic coating in the of dock,

A.

AcCy

it

ship, involving a fouling rate that

between dockings. Fig. 45. L indicates that the

increases slowly with time, applies to the hull

two predicted ABC ship curves cross each other at 5.4 months out of dock. If the hot-plastic paint is to pay its way, so to speak, the interval lictween dockings must be long enough so that

for the

with a

bottom coating

final

of anti-fouling sclf-

leveUng paint {7wt a plastic type).

The dot-dash

line

of the figure,

representing

10

bne B

is

for ships

which

enter a number of ports -where severe fouhrx] is

encountered

Line

A

is

for ships on

overoqt

vofoqes between temperote ports with overoqe rates of fou 11 no

Line

C

is

for ships hovinq

unusuoll^ short stoys .

ortrodincj

requlorlij

In

port

_a5

between

ports free from fouling or ports,

havino a scourinq action

6

Fm.

4.1.1,

I'liKKirTKn

9^ 7 5 Months out of Drydock

Si-Kcmc T'oiiUNn Ukmistantk Ai.i/iwanck.s

koii

M

10

.MK"

Siiir,

with

Two

Kinhs ok I'mnt

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.21

the time product of the additional A^Cf for the first 5.4 months is less than the time product of

ApCp

the additional

the last 4.8 or more

for

months that would have been involved if the hot-plastic coating had not been used. The respective areas on the plot are indicated by

(10) Taylor,

stracts," (11)

(13)

the reader's attention

called particularly to

is

J. Paul Visscher, numbered and to the book "Marine Fouhng and Its Prevention," prepared by the Woods Hole Oceanographic Institution and published by the U. S. Naval Institute in 1952. Each chapter of this book is terminated by a generous list of references, but unfortunately none of these

(14) Smith,

discusses

the

quantitative

effect

of

W. W.,

and Cost

pp.

1616-1620. Discusses the

Discussion,

SNAME,

1932, p. 305

Bottom Upon Power

of Operation," Nat. Council

bldrs.. Bull. 246,

list,

chapters

1931,

(15) "Effect of Fouling of a Ship's

the pamphlet by Dr. (9) in the

H. F. D., "The Increase in S.H.P. and R.P.M. due to Fouling," ASNE, Feb 1930, pp. 15.5-166 Holm, W. J., "Tactical Horsepower of Submarines,"

,

and pro-

these sources from the literature,

Resistance of Ship Models,"

1929, pp. 45-64

imposed on speed and rpm (hence speed) of submarines driven by Diesel engines due to restrictions on maximum mean effective pressure developed in the engines. Makes out an argument for reducing the pitch of the propellers to suit a condition of partly foul bottom and shows that a pure electric-drive installation would be superior in point of useful horsepower developed for whole period between dockings. Gives curves of Ps rpm, and speed of submarines for various months out of dock (in tropical waters).

lines.

fouling of ships as affecting resistance

1928, pp. 259-269

P., "Frictional

USNI, Dec

References Relating to Fouling as AfThere are listed herefecting Ship Propulsion. under the principal references relating to the

Among

INA,

Voyage Ab-

limitations

is

45.21

pulsion.

125

"Statistical Analysis of

(12) Davis,

needed is an antifouling paint with the smoothness of a selfleveling coating and the anti-fouling effectiveness of hot plastic. The vinyl resin paints show promise along both these

Roop, W.

SNAME,

different angles of hatching.

Needless to say, what

L.,

.1.

23

Aug

Am.

Ship-

1932; also Naut. Gaz.,

MESA, Sep 19.32 and Schlichting, H., "Das Widerstandsgesetz Rauher Flatten (The Law of Resistance for Rough Plates)," WRH, 1 Jan 1934, pp. 1-4 Pitre, A. S., and Thews, J. G., "Fouling of Ships' Bottoms; Effect of Physical Character of Surface," 3 Sep 1932;

(16) Prandtl, L.,

(17)

EMB (18)

fouling on ship resistance.

Kempf,

Rep. 398, Apr 1935

"On

G.,

the Effect of Roughness on the INA, 1937, pp. 109-119,

Resistance of Ships,"

137-158, eap. pp. 117-119 (1)

"The Fouling and Corrosion of Iron Their Causes and Means of Prevention, with

Young, C. F. Ships:

the

Mode

T.,

(20)

XXX,

pp.

McEntee, W., "Variation

of Frictional Resistance of

Ships with Condition of Wetted Surface,"

McEntee,

(5)

Smith,

W. W., "The

Effect of

Model Basin,"

SNAME,

(7)

(24)

Fuel Consumption," ASNE, pp. 357-374. Abstracted 1923, pp. 180-181 and 190-192.

(25)

Gardner, H. A., "Toxic Compositions to Prevent the Fouling of Steel Ships and to Preserve Wood

(26)

May

Effect on

1923, Vol.

XXXV,

SBSR, 16 Aug

G.

S.,

Bottoms," Paint Mfrs. Ass'n. of U. No. 259, Jan 1926, pp. 232-270

Efficiency

and Economy,"

D. W., "The Speed and Power

of Ships,"

"The Corro-

Bengough, G. D., and Shepheard, V. G., sion and Fouling of Ships," INA, 1943, pp. 1-34 "Fouling of Ships' Bottoms: Identification of Marine Growths," Jour. Iron and Steel Inst., Great Britain, 1944

S., Sci. Sect.

"Docking Report Manual: Instructions Regarding the Docking Report and Guide to Fouling Organisms," Bureau of Ships, Navy Dept., Washington, 1944

and Forbes, W. A. D., "Under-Water Paints and the Fouling of Ships," INA, 1946, pp.

E. V., "The Practical Analysis of Merchant Ship Trials and Service Performance," NECI, 1926-1927, Vol. XLII, pp. 63-98 and 125-143

(27) Harris, J. E.,

"Nature and Extent of Fouling of Ship's Bottoms," Bu. Fisheries, Dept. Commerce, Document 1031, 1927, Vol. XLIII, Part II

(28)

(8) Telfer,

(9) Visscher, J. P.,

"Ship

1943, pp. 37-38

1917,

pp. 41-72

in

Frictional

Bengough, G. D., "Hull Corrosion and Fouling," NECI, 1942-1943, Vol. 59, pp. 183-206 and

(23) Taylor,

Williams, H., "Notes on Fouling of Ship's Bottoms

and the

in

D123-D136

Wind and Fouling

Resistances on U.S.S. Neptune,"

(6)

"The Increase

Liverpool, 1942, pp. 1-14 (22)

"Notes from the 1916, pp. 85-90

W.,

SNAME,

(21) Baker,

SNAME,

1915, pp. 37-42 (4)

Jr.,

1942, p. 608

362-389 (3)

A.,

Due to The Action of Water on Bottom Paint," ASNE, Nov 1937, pp. 585-588 Gawn, R. W. L., "Roughened Hull Surface," NECI, 1941-1942, Vol. LVIII, pp. 245-272 and D143D152a; "Roughened Hull Surface," SBSR, 11 Jun

Lewes, V. B., "The Corrosion and Fouling of Steel

and Iron Ships," INA, 1889, Vol.

E.

Resistance

of Application to Existing Ironclads,"

(England), 1867 (2)

(19) Stevens,

240-267

I

Graham, D. P., "Some Factors in the Use Ship-Bottom Paints by the U. S. Navy," 1947, pp. 202-243

of Plastic

SNAME,

IIVDRODYNAMICS

126 (29) W'win.

(30)

v..

"How

v.,

to Dotcrmiiio KfToolji of Ship

Bottom Fouling." TIip I/Jg, May HMK, pp. 50, 52 Bamnby, K. C, "Kronomic Con«cqueniH«« of FoulIN A.

ing,"

1950, p. J 15

"Skin Friction ncnintanoo and tho HouKhnoss," T.MB Hop. 729, Sop 1950. Till- gniph nt the end of thin re|)ort

(31) Toild,

F.

II,,

KfliTtn of

.»
iihows that X-i'y for various c-oatings

is

approxi-

mately roniitaiit over the range of W, roveretl by the normal ship s|)ee
own

Src.4^.22

value, depending

(',•

upon

considerable distance from

number

of

about 40 to 45

lie partlj'

within

the hull boundary layer, they do not generate

own

their

It is

and the average them are lower than the ship speed.

layers exclusively,

velocities over

found acceptable,

anti

it is

customary, to

appendages having appreciable lengths and wetted areas, hence the ii.sual

summation value of

all

wetted surfaces into a

of all

The appendages which

»S'.

are

short enough to give z-Rcyiiolds numbers less

than about 15 million, especially those which are

million.

Kielhorn,

somewhat

the hull,

main, however, ship appendages

single

to a Reynolds

ship

a deep drag pipe on a .self-propelled dredge. Such a one may reijuire this treatment. In the

coatings become practically constant and remain

up

The

.

like

use the ship value of R„ for

so

R,

each appendage. These (V values would be high becau.se of the short lengths and the small HJh. Occasionally there may be a special appendage, exposed to undisturbed flow, which extends for a

bottom

."hip hulls,

its

drag would then be a summation of a bare-hull drag plus a separate friction drag for friction

varying from yellow zinc chromatc to Norfolk hot plastic, would probably of zero. Ix- in the vicinity .\t /f, values of from 25 to 30 million the SfCp values for each of the G coatings for

(.33)

PFSIGN

IN SHIF'

W.

"Military Biological OceanograS<-p 1951, pp. 947-953, esp. pp.

V.,

phy," rSNI, 947-94S and 951 (34) "Marine Fouling and Its Prevention," Report 580 of the WoimIs Hole Oceanographic Institution, published by I'SN'l, Annapolis, 19.52 (35) AmLsberg, II., abstract of a report by Prof. Aertssen on the ext<'nsive full-scale test.s conducted in 1951 and 19.52 on tho Tervaele, formerly the Pomona Victory, including the results of fouling on several voyages, Ilan.sa, 9

May

thick in proportion to their length in the direction of

considered

are

flow,

friction drag.

as described in Chap.

have

no separate

5.5.

For the actual friction-drag calculations ship, a .series of values of

.shii)

speed

for a

.selected,

l' is

extending from the lowest speeii of interest to

beyond the maximum-.speed the plotting of curves of

1953, p. 793.

to

Their pressure drags are predicted

point. This enables

Ry and Py on

V. Using

the selected speeds and the waterline length of 45.22

a Ship.

The The

friction ro.si.stancc of

analysis or design

Eq.

is

is

the

flat,

Ry =

+

A.,

-f-

Af

+

the allowances for

li,

,

ii

2ACV

.ship

of

under

by the general

<3r.S(C,

smooth-piatc

resistance at a given

Ap

calculated

(45.ii) of Sec. A'^.l,

Here CV

Drag

Calculation of the Friction

-|-

^JAfV).

.specific friction is

(A,

-|-

Aj

-}-

and A, and Aj are transverse and loiiKitndinal

Af)Cr

,

the ship, values of R„ are taken from Tables 45. or 45. b for either standard fresh or respectively. /i'„'s

If

the water

is

sixlt

water,

not standard, the

are calculated.

The

values of the

flow coefficient

Cy

flat,

smooth-plate, turliulcnt-

for the

A'FfC 1947 ^Schoen-

herr)

meanline are picked for the given values

of /?„

from Table

45. d. In

Cy

Tables 45. c and 45. are listed in terms of

curvature, respectively.

the numerical values of

Beginning with the ram pres.sure q, ecjual to 0.5pV\ Tables 4l.d and 41.e give values of q in lb per ft" for standard fresh and .salt water, dcg (", over a very respectively, at dcg

convenience llious. The number are given in millions. The tabulated values of Cy are therefore to be

1'',

.">!)

I.")

large range of ship speeds.

Tlur wetted surface

.S

isdctcrinincd as described

4.'>. 12 preceding. If eaih api)endage whiih hud an appreciable wetted area moved through the wuti-r i»y it.self, it would theoretically create it* own boundary layer, independent of the others ttrxl of till! hull proper. It would then have its own Heynolils number, ba.scd upon il.s length in the dirci'tion of inotieui. It wouli! al.su have its

in Kec.

thousands,

called

for

values of Reynolds

multii)lied

by 10"' and

For other l.')..S

the

Cy values

tho.se of /e,

by

lO".

formulations listed

friction

in

Sec.

are calculated for the desired

R„ values or are picked from other tables. Incrca-scs to be made to take care of curvature, either

or

lotigitudiiuil

traiisvcr.se

or

both,

are

applied at this stage. 'J'he total rotighnc.ss

on the

ba.sis

.Sees. 45. IS

of

and

allowance -Af ',•

the general rules laid I."..

JO.

is

.selected

down

in

FRICTION RESISTANCE CALCULATIONS

Sec. 45.23

There follows an example

the procedure

of

described, applicable to the 20.5-kt or trial-speed

ABC

point for the

design of Part

4.

The

basic

data are as follows: (a)

selfrleveling properties,

AcCp

a conservative value of

the highest one listed in Table 45.f, or

is

0.12(10"'). For 12 days out of dock, or 0.4 month,

the fouling allowance

Ship length (wetted length on

510

waterline) (b)

127

be coated with an anti-fouling paint that has

34.62

Adding

about 0.04(10"').

Speed (to be achieved with clean bottom) 20.5 kt equivalent to

ApCp from the

(0.02

per

ft

+

+

0.08

Then {Cp

+

0.12

+

SAC;,)

=

dasshed-line

ABC

curve of Fig. 45. L, applying to the

ft

0.04) (10"')

(1.451

-|-

=

ship, is

SACp

these,

all

is

0.26(10"').

0.26) (10"')

=

1.711(10"'). sec

(c)

Wetted

from Sec. 45.13

ages,

47,875

stage of Sec. 66.9,

ft'

has lapped riveted seams

(d) Plating

and (e)

be noted that, in the preliminary-design ACp (actually SACp) was taken as 0.4(10"'). When instructions were prepared to test the models of the ABC ship, quoted in Sec. 78.6, the corresponding ACp value was taken as 0.3(10"'). These compare with the final estimate It will

append-

surface, with all

Coating

flush butts is

"commercial" anti-

fouling, with self-leveling

of 0.26(10"').

properties (f)

Mass

The ARp value

water in the 20-deg latitude of item (16) of Table 64.c, at 68 deg F, from Table X3.e (involves density

p,

for the salt

no correction

Cf.

Taking account revised {Cp (10"')

for latitude, as

described in Sec. X3.3)

1.9882 slugs

per (g)

Kinematic viscosity for temperature of 68 deg F, from Table X3.h

(i)

(j)

+

wetted length,

line or

LV ^

SAC^) value

=

From Table

45. d the value of

the ship wetted surface as a ship length

Data

=

L

flat,

in turbulent flow,

1,552.6 million

Cp considering smooth plate of ,

1.451(10"').

is

are not available (1955) for determining

the allowances for longitudinal and transverse

curvature in the forms A^Cp and AjCp tively, of

Eq.

in Sec. 45.7.

(45. ii)

Sec. 45.14 the value of

the hull of the

ABC

ARp due

,

respec-

However, in

to curvature in

by

ship has been calculated

method and found to be 0.0606. Considering the plating roughness ApCp

F. Horn's

reasonable

value

for

the

ship,

,

when new,

a is

0.02(10"'), from Table 45.f of Sec. 45.18. Similarly,

a liberal value of the structural roughness

from the same

table, 0.08(10"').

As

(1.711

+

0.104)

(45.ii),

+

ACp)

=

I

V'SiCp

+

ACp)

AsCp

the vessel

is

103,531 lb. of interest

the

{Cp

+

SAC,?)

inspection from Fig. 45. E, using

only the R„ value derived here, are: (1)

1.1372

is

(34.62)'(47,875)(1.815)(10-')

As a matter values taken by

is

(510)(34.62)(10')

V

0.104(10"').

per sec

Taking account

is,

to

new

of the

ATTC

1947 allowance

from curve B-B, 1.85(10"') (2) Considering the roughness allowance proposed by L. A. Baier, from curve D-D, 1.85(10"') (3) Considering the roughness allowance proposed by J. M. Ferguson, from curve C-C, 1.81(10"'). These compare with the value 1.815(10"') derived for clean,

=

=

of this curvature correction, the

1.9882

1.1372(10"')

based on the water-

,

equivalent to a

is

1.815(10"').

Rp = qS{Cp

Time out of dock 12 days Ocean water salt Average sea-water temperature, from item (18) of Table 64.c, 68 deg F.

The Reynolds number E„

Rn

Horn

;',

ft'

(h)

=

Then, by Eq.

ft'

of F.

addition of 0.0606(1.711)(10"')

vessels,

in the foregoing.

45.23 Allowances for Friction Drag on StraightElement and Discontinuous-Section Hulls. The transverse curvature at an unrounded chine is

always sharp. It may be severe if the chine angle (defined in diagram 3 of Fig. 27. A) is of the order of 80 or 90 deg, as on short sailboats and motorboats, especially those which run at low F„ or T, values. The Reynolds number is then low, the Cp high, and the added friction due to convex curvature is also relatively large. Coves or regions of concave transverse curvature are rarely to be

HYDRODYNAMICS

128

found on hulls of

comjiensation for the convcx-furvature

45.25

effects.

Stream.

I^ndweber's transverse curvature correction, described in Soc. 45.14, becomes rather absurdly large for sharp chines, or even for these chines

they are assumed

be rounded

to

to

if

a small

known

SICX

IN SlIII' Dl

no

this kind, so that there is

^.21

Srr.

Drag

Friction

of a Craft

Moored

in a

friction-drag problem ari.ses in con-

.\

mooring of i)()ntoon-bridge and lightships where swift currents prevail and adefpiate ground tackle must with

nection

the

floats, barges, lighters,

be provided. In flood conditions this situation

is

generally associated with chines in pairs, so that

Froude number F^ or Taylor quotient T, is usually small and most of the drag is due to friction. The friction drag due to current may be a maximum when the wind

the increased friction drag caused by the convex

drag

radius. In these cases the increase in 7?^

to be positive, but

On

chine

friction in

coves

forms,

partly or wholly offset

is

to estimate.

it is difficult

discontinuous-section

is

bj'

are

intensified. In these cases the

the concave area. For discontinuous

abnormal shape, such as those E and 76. F, it is acceptable to compute the entire wetted surface and to consider that it bfloiiR.s to a hull of normal form.

is

The

the decreased

zero.

that a vessel

fact

is

andiorcMl

or

stationary in a moving stream, rather than

same

held

])vill('(|

through

sections of not

or pushed at the

illustrated in Figs. 76.

stationary water, has no appreciable effect upon

The

45.24

A

Hull. lift

rises

loses

drag

Friction Resistance of a Planing

planing hull that benefits

bj'

wetted surface by this process. is

dynamic

out of the water as the F„ incrca.ses and

to be taken into account

it is

If friction

then neces-

model or on the craft itself, to determine the length, shape, and position of the wetted portion of the bottom and to compute the actual wetted area. Only those regions over (or under) which the water moves at the same order sary, either on a

its friction resistance. It

calculating

of

relative speed

does not alter the method

the friction drag,

flowing water contains no great scale turbulence. It

is

provided

amount

the

of large-

to be remembered, however,

that a stationary surface vessel near the center of a fast-moving stream,

compared to that

section

of not-too-large cro.ss of

the vessel, has a

which is greater than the average velocity of the stream. This is because the velocities in the boundary layer along the banks and over the stream bed are le.s,s relative velocity in the center

than the average velocity. The same phenomenon is a boundary layer around the inside wall surfaces and the center-

of relative speed as the planing craft are included

occurs in a pipe where there

Those wetted by thin spray sheets moving forward or predominantly

all

sideward are excluded. Furthermore, unless the

H.,

model runs at the same trim as the full-scale craft, either by the action of forces from its own

a shallow river, the relative water velocity under

propulsion devices or equivalent forces applied

the bottom

during the test run, the wetted surfaces are not

current velocity.

as effective wetted areas.

is

often feasible to locate,

or visual observation, on either full-scale

EMF,

the vessel

average velocity [Rouse,

1946, p. 197]. If the bed clearance under small, as for a deep vessel

is

moored

in

probablj- greater than the average

is

Subject to the foregoing, and assuiuing that

comparable. It

line velocity exceeds the

by photographs the model or the

the forward end of the wetted

craft,

surface along the keel. It

is

usually easy to "spot"

the ship axis

lies in

the direction of stream flow,

the computation procedures of Sec. 45.22 suffice for calculating the friction drag. If

the craft

is

moored at both

enils

and does

the corresponding points along the chines. Having

not

these three points fixed reasonably well, the wetted

resistance plays only a small part and the forces on the moorings must be determined by other methods [TMB unclassified Rep. R-332, "Wind Tunnel Tests to Determine Air Load on MultipleShip Moorings for Destroyers of the DD 692 Class," by M. K. Long, Doc 191.-)]. 45.26 Selected Bibliography on Friction Re-

surface

A

is

readily outlined

length

is

necessary to

values of F. and ifl

/?, in

mean

its

fix

area determined. the approximate

the planing condition. This

usually taken as the

the arithmetic

and

mean

wetted length

of the wetted keel

Lws

,

and the

wetted chine lengths.

These matters, including a method

lie

in

of predicting

sistance.

the wettctl length and wett«!d area, an; discus-sed

listed in

53.6 and 77.27, to which the

in detail

in Sees.

reader

referred for specific information on this

is

type of water

craft.

the direction of the stream, friction

For

convenient

reference

this section a incxlerate

there

are

lunuber of the

any nuKlern bibliography on Textbooks are listed in the Introduction of Volume I and arc not imludcd here. multitude of

titles in

friction resistance.

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.26

The

reader's attention

is

and

invited to the fact

of the

Part

not duplicate those hsted in Sec. 45.21, relating to fouling as affecting ship propulsion. There

(7)

is

Zahm [SNAME,

III, pp.

"Uber Flussigkeitsbewegung bei sehr Reibung (On Fluid Motion with Very Small Friction)," Verhandlungen des III Internationalen

Prandtl, L., kleiner

available in the Library of Congress at Washington a long and comprehensive bibUography entitled "Skin Friction and Boundary Flow,"

prepared by Dr. A. F.

Mathematiker-Kongresses, Heidelberg, 1904 (Proceedings

of

the 3rd International Mathematics

Congress, Heidelberg, 1904)," Leipzig, 1905, pp. 484-491; reprinted in "Vier Abhandlungen zur

1932, p.

309].

Hydrodynamik und Aerodynamik," by

The

the present selected bibliography

titles in

Channels,"

Roy. Soc, London, 1883, Vol. 174, 935-982

Phil. Trans.

that the references hsted in this bibliography do

129

Law of Resistance in Parallel

and A. Betz, Gottingen,

L. Prandtl

These

1927.

contain

Prandtl's original statement of the boundary-layer

are divided into three groups, described briefly as:

theory. I.

and historical Development of friction-resistance formula-

Classical

II.

(8)

kleiner

tions

modern

III. References of

Vol. 56, p. Iff

application. (9)

I.

Classical

G. G.,

"On

Turbulent Motion,"

Camb.

Phil.

ance Coefficients)," 435-438

Mem.

divers savants, Sci.

(13)

W., "On Some Difficulties in the Received Rep. for 1869 (publ. in 1870), pp. 211-214. On pages 212-213 Froude gives an amazingly clear and straightforward exposition of the physical phenomena of

was known at that

of his statement applies to the

time.

(14)

(15)

(16)

(17)

physics of fluid friction, as known 85 years later. (3b) Froude, W., "E.xperiments on Surface Friction," British Association Reports, 1872

Froude, W.,

(5)

Tideman, B.

INA,

J.,

and Pis. Ill through XIII "Memoriaal van de Marine II.

(18)

The paper

"Uitkomsten van proeven op den Scheepsmodellen (Results of Resistance Tests with Ship Models)." There appears to be no Enghsh translation of it but a note at the bottom of page 374 of Volume III of PoUard and Dudebout's "Theorie du Navire," 1892, states that Tideman's paper was translated carries the title

Wederstand

van

French) by M. Dislere, Ingenieur de la Marine, in the Memoires du Genie Maritime, 6th Book, 1877. Reynolds, Osborne, "An Experimental Investigation of the Circumstances which Determine whether the Motion of Water Shall be Direct or Sinuous,

(19)

Aug

1923,

pp.

Akad. v. Wetenschappen, Amsterdam, 1924 "Skin Friction Committee's Report," INA, pp. 108-123, esp. pp. 115-116

1925,

Hansen, M., "Velocity Distribution in the Boundary Layer of a Flat Plate," NACA Tech. Memo 585, Oct 1930 Millikan, C. B., "The Boundary Layer and Skin for

a Figure of Revolution,"

ASME,

APM-54-3, 1931, p. 33 "The Prediction of Speed and Power of Ships by Methods in Use at the Experimental Model Basin, Washington," Bu C and R Bull. 7, 1933. Pages

Payne, M. P., "Historical Note on the Derivation of Froude's Skin Friction Constants," INA, 1936, pp. 93-109

Lackenby, H., "Re-Analysis of WiUiam Froude's Experiments on Surface Friction and Their Extension in the Light of Recent Developments," INA, 1937, pp. 120-158. On pp. 136-137 there is a list of 16 references.

(20)

(into

(6)

22

at the Experimental

1874, pp. 36-73

Afdeeling 9e Aflevering," 1876-1880.

WRH,

18-20 describe the modified Gebers formula in use Model Basin, Washington, in the period 1923-1947.

and 1874

"On Experiments with HMS Greyhound,"

(4)

720, 1919-

"Skin Friction Resistance and Law Comparison," INA, 1924; abstracted in SBSR, 17 Apr 1924, pp. 454-455 Burgers, J. M., and van der Hegge Zijnen, B. G.,

Friction

Much

knowledge of the

M

"Preliminary Measurements of the Distribution of

of Fluid Friction," Brit. Assn.

fluid friction, as it

and

the Velocity of a Fluid in the Immediate Neighborhood of a Plane, Smooth Surface," Verh. d. Kon.

(3a) Froude,

View

R

of

Math, et

Phys., Paris, 1865, Vol. 19

ARC,

(12) Shigemitsu, A.,

Soc, 1842

Bazin, H., "R6cherohes hydrauliques (Research in

Hydrauhcs),"

"On

1920, Vol. I, pp. 51-67 (10) Stanton, T. E., "Friction," London, 1923 (11) Bruckhoff, "Reibungskoeffizienten (Friction-Resist-

the Steady Motion of an Incom-

pressible Fluid," Trans. (2)

Stanton, T. E., MarshaU, D., and Bryant, C. N.,

the Conditions at the Boundary of a Fluid in

and Historical

There are hsted in this group a number of the papers which form landmarks, as it were, in the early development of the theory of friction resistance, as applied to bodies and ships moving in both air and water. Included are a number of references which describe the development of the theory, and its practical applications, in much more detail than can be given here. (1) Stokes,

"Grenzschichten in Flussugkeiten mit Reibung (Boundary Layers in Liquids of Small Friction)," Zeit. fiir Math, und Phys., 1908,

Blasius, H.,

(21)

"A Critical Discussion of Turbulent Flows in Channels and Circular Tubes," Proc. Fifth Int. Congr. for Appl. Mech., Sep 1938; published by Wiley, New York, 1939 Davidson, K. S. M., PNA, 1939, Vol. II, pp. 76-82 and Figs. 22-23 Millikan, C. B.,

(22) Taylor,

D. W., S and P, 1943, pp. 31-35

II^l•)ROl1^^•

130 (23) T.kIJ, F.

-Tlio Fuiulam.Mitals of

II.,

IMK,

Uesistaiioe." (2-1)

Rouse.

the

traff-s

xMics i\ ship nrsir.x

p.

150.

friction furmiiliLH, altlioiigh

This

many

ilevclopmoiits of

tccliiiirul

H.,

F.

Rcsistanro;

Metho
M.

.\

from the point of view

"The Dotorminalion of Frictional Review of PremMit Knowledge and

SHMl^H, Jan

1947, pp. 15-19

.•Vcevwio,

111

L.,

and 112 there are a number of references

additional to those given here.

EH,

1950, pp. 75-115 K. E., SNAME, 1932, beginning on 279; MIT Symp., 1951, beginning on p. 101.

(28) Rouse, H.,

(29) Schoenherr, p.

II,

p.

321(T

Dat«man, H., "General Physical Properties of a Viscous Fluid," Chap. Ill of "Hydrodynamics," Bull. 84, Nat. Res. Council, Feb 1932, pp. 89-152. This chapter contains much historical data and an enormous number of references, |>ertaining to all

"Skin Friction Resintance," Spec. I*ubl., Canal do Expcriencias llidrodinflmira.'i, V.\ Pardo, Madrid, 194S. Only the Conclusions of this pa|>er are published in 5th ICSTS, 1940, pp. 93-98. (27) Van Lammercn, \V. P. A., Troost, L., and Koning, J. G., RP^N^, 194S, Ix'ginning on p. 32. On pages (2ti)

(Tlic

Ingenicur-.Vrchiv, 1931, (30)

of bydniuiicd rnlhor th.in naval architecture. (iS) Tjxld,

Sec. -15.26

Turbulent Boundary leaver in Plane Flow at Incrca.sing and Decreasing Pressures),"

stieg

Kri.liormI

I'JU

1:MF, 10U>. iH-RinninK on

II.,

book

Slii|>

phases of this subject.

(37) Schoenhcrr,

K.

F,.,

"Resistance of Flat Surfaces

Moving Through a

On

279-313.

Fluid,"

SXAME,

of 30 references, listing

K.

von Kdrmdn,

Kempf,

T.,

E.,

MPK,

t'.Ott.,

1933

VDI-Forschungsheft, lation available as

anal^'tic

F.,

widerstiind IHjIiticrter

guradlinig

Wiisser

in

Platten (The

Law

summarizes and compares

friction resistance of planes,

/?>•

fiir

Flaehen-

(a

Kempf,

is

G.,

fortbewegter,

of Similitude for the

(Polished)

Plates (43)

friction

constant)

Kempf,

G.,

Frictional

and

and recommends an of the form surface)

F*""/L",

Pis.

Results Obtained in Measuring IXA, 1929, pp. 104-121 tests

made

witli

Friction on Ship Hulls),"

WRH,

7

Mar

(34)

J.

H.,

(47)

Schultz-Grunow, F., "Ermittlung des hydraulischen Heibungswidcrstandes von Platten niit m.ls-sig rauher Oberflaehe (The Determination of the

"meas-

Hj'draulic Friction Resistance of Plates

Rough

Moderately (48) Schlichting,

zum

(49)

"Die turbulcntc RoibungMchicht in I'bcncr Slrrimung Iwi Drurknbfoll und Druckuii-

Untersucliungcn (Experimental Investi-

"E.xperimentelle

II.,

Hauhigkeit.sproblem

1

Kempf, G., "(*biT den Einlluss der Rauhigkeit auf den Widerstjind von SchifTen (On the Induencc of Roughnc.'i.s on the Resistiince of Ships)," RT(^ 1937, Vol. 3S, pp. 159-176; '225-234. In this paper

Kempf

describes and gives the rcsulLs of friction

tests oti long,

imrfaci.fl.

(SS) CinischwiUi, K.,

Having

Schiffahrl-stech-

gation of the Roughness Problem)," Ing.-.\rchiv., 1936, Vol. VIII, Xo.

G.,

Surfaces),"

nische Forschungshefte, Oct 1936, Heft 7

1929, pp.

"Neue Ergebnisse der Widerstandsforechung (New Rcsultfl in Resistance Investigations)," WRH, 7 Jun 1929, pp. 2.34-2.39 and 22 Jun 1929, pp. 247-252. Figs. Oa and Ob on p. 237 «bow mcamired roughness profllca of two typical plate

"On

the Effects of Changes in 'Degree and 'Degree of Turbulence' on Skin Friction ResisUmce and Wake of Models," IN.\,

Lamble,

1936, p. 125fT

91-03

Kempf,

Gott., 1935,

Bakhmeteff, B. A., "The Mechanics of Turbulent Flow," Princeton U. Press, 1936

Hamburg

and in the bottom of long, shallow, pontoons towed in the Hamburg Model Basin. HopiK.', H., "Xeue Messungcn der VVasaerreibung am SchifTskorpcr (New Measurements of Water

z.

(46)

Resistance,"

VI-IX. Describes

Wiss.

of Wetting'

"FlSchenwiderstand (Surface Resist22 Oct 1924, pp. 521-528. This

"Xew

d.

Vol. I

0.125.

uring plates" in the side of the steamer

(33)

stromung," Xach. Gesell.

resistance

(wetted

der kleinen Striingen bei der Platten-

gicbilanz

previous work on

all

paper discusses and gives the results of friction testa on long, towed, floating cyUnders. (32)

Japan), Dec 1934, \'ol. LV II., ".Vmphtudenverteilung und Ener-

(44) Schlichting,

WRH,

ance),"

and Schhchting, H., "Das Widerstands(The Resistance Law for Rough Plates)," WRH, Jan 1934, No. 1; luiglish version in T.MB Traiisl. 258, Sep 1955 ITiraga, Y., "Experimental Investigations on the Frictional Resistance of Planks and Ship Moilels," ZOsen Kiokai (The Society of Xaval .\rchitects of gesetz rauher Platten

(45)

=

where n (31)

for

Nov

and Tietjens, O. G., "Applied Hydroand Aeromechanics," McGraw-Hill, Xew York,

in

expression

1292,

1934

Aehnlichkeitsge.setz

a Straight Line in Water)," Schiffbau, 1921, Vol. XXII, Xos. 29-33, 35, 37-39. A complete translation is found in NAC.\ Tech. Memo 30S of Apr 1925. This paper gives the result-s of extended tests on friction planes at the Vienna model basin. It

NACA Tech. Memo

(42) Prandtl, L.,

"Das

Surface Resistance of Smooth

Moving

rauhen Rohren," English trans-

(41) Prandtl, L.,

and design work.

(30) Gebers,

1933.

361,

1950.

within the last qiiartcr-conturj' for

iisetl

G., Schoenherr,

"Rcibungswiderstand (Frictional Resistance)," IIPSA, 1932, pp. 1-87 Schlichting, H., "Zur Entstehung der Turbulenz l>ei (39) der Plattenstriimung," Nach. Ge.sell. d. Wis. z.

This group comprises references which led to widely

is

of the period 1839-1931. (38) Eisner, F.,

Deiclopmcnl of Fridion-Iicsislance Formulations

the preparation and use of certain formulations

pp.

a list certain published papers

(40) Xikuradso, J., "Striimungsgesetze in

II.

19,32,

page 297 of this paper there

(50)

Kempf,

G.,

towed, lloating pontoons.

"On

the lOfTcct of RoughncsM on

ResiNlAnrc of Ships,"

INA

1937,

pp.

tin-

109 119.

FRICTION-RESISTANCE CALCULATIONS

Sec. 45.26

on

115 gives friction coefficients of ships and of the HSVA pontoon with different roughFig. 3

p.

nesses (see also p.

RPSS,

1948, pp. 48-49). Fig. 5 on

119 gives the effect of density of roughness on

resistance.

(64)

(51) Schultz-Grunow, F., "Der Hydraulisohe Reibungswiderstand von Flatten mit massig rauher Oberflache, insbesondere von Sehiffsoberflachen (The HydrauUc Friction Resistance of Plates with Large Roughnesses, such as Those on Ship Surfaces),"

STG, (52)

(63)

ately

Rough

Zeit.

des Ver. Deutsch. Ing., 1938, Vol. 82, pp. is an English translation of this

(65)

(67)

Surfaces, especially Ship's Surfaces)," (68)

TMB library.

paper in the

(54)

Homann,

F.,

fiir

glatte Flatten

for

Aug

1940, Vol. 17, No.

Smooth

(69)

TMB

(70)

TMB

C71)

Plates)," Luftfahrtforschung, 20 8,

pp. 239-246; English

NACA Tech. Memo 986,

Sep 1941 Sawyer, J. W., "Surface Finish Literature," Machine Design, May and Jun 1955. translation in

(55)

(New Frictional Resistance

Law

tional Resistance and the Expansion of Model Teat Data to Full Size," SNAME Tech. and Res. Bull. 1-2, Aug 1948 Todd, F. H., "The Determination of Frictional Resistance," Rep. 663, revised edition. Mar 1949 Landweber, L., "Effect of Transverse Curvature on Frictional Resistance," Rep. 689, Mar 1949 Schlichting, H., "Lecture Series, 'Boundary-Layer Theory,' Part I— Laminar Flows," NACA Tech. Memo 1217, Apr 1949 Schlichting, H., "Lecture Series, 'Boundary-Layer Theory,' Part II—Turbulent Flows," NACA Tech. Memo 1218, Apr 1949 Landweber, L., "A Review of the Theory of the Frictional Resistance of a Smooth Flat Plate with Turbulent Boundary Layers," Rep. 726, Sep 1950 "Progress Report on Research in Frictional Resistance," Rep. 726, Sep 1950 Todd, F. H., "Skin Friction Resistance and the Effects of Surface Roughness," Rep. 729, Sep 1950 Rotta, J., "Beitrag zur Bereohnung der Turbulenten Grenzschichten (Contributions to the Calculation of Turbulent Boundary Layers)," Max Planck Institut fiir Stromungsforchung, Gottingen, 1 Jul

TMB

"Der tJberganz zwischen den Stromungsgesetzen fiir glatte und rauhe Flatten (The Correlation Between the Laws of Flow for Smooth and Rough Plates)," Zeit. des Ver. Deutsch. Ing., 2 Apr 1938, pp. 405-406 Schultz-Grunow, F., "Neues Reibungswiderstandgesetz

the Calculation of Fric-

TMB

(66)

756-758. There (53)

131 for

TMB

1938, Vol. 39, p. 177ff

Schultz-Grunow, F., "Der Reibungswiderstand massig rauher Oberflachen, insbesondere von Sehiffsoberflachen (The Friction Resistance of Moder-

"Uniform Procedure

1950;

TMB Transl.

242,

Nov

1951.

Assumes that

"the kinematic viscosity and the geometrical conof the wall (wall roughness) only

figuration

III. References of

The

Modern Application

references of this group are

influence the velocity profile near the wall in a is very thin compared with the boundary-layer thickness and that with proper normalization the flow quantities in the remaining zone of the boundary layer appear to be almost independent of viscosity and wall roughness."

layer Sw which

selected to

describe the extensive research and experimentation conducted since about 1940 on the develop-

ment

of the

boundary layer and the characteristics

(56) Prandtl, L.,

"The Mechanics

Aerodynamic Theory, Vol.

of Viscous Fluids,"

Ill,

Durand Reprint-

Comm., Pasadena, 1943 Dryden, H. L., "Some Recent Contributions to the Study of Transition and Turbulent Boundary Layers," Proc. 6th Int. Cong. Appl. Mech.,

(73)

ing

(57)

(74)

Paris, 1946 (58) Carrier,

G. F., "The Boundary Layer in a Corner,"

Quart. Appl. Math. 1947, Vol. 4, p. 367 (59) Dryden, H. L., "Some Recent Contributions to the Study of Transition and Turbulent Boundar}'

Layers," NACA Tech. Note 1168, 1947 Schubauer, G. B., and Skramstad, H. K., "Laminar Boundary-Layer Oscillations and Transition on a Flat Plate," Nat. Bur. Stds. RP 1722, Feb 1947 (61) Schubauer, G. B., and Skramstad, H. K., "Laminar(60)

Boundary-Layer Oscillations and Stability of Laminar Flow," Jour. Aero. Sci., Feb 1947, Vol. 14, or "Laminar Boundarj'-Layer Oscillations and Transition on a Flat Plate," NACA Rep. 909, 1950 (62)

Wieghardt, K., "Increase in Frictional Resistance due to Turbulence Caused by Surface Irregularities," 1948. The English translation is known as A.C.S.I.L. Translation 380 (ACSIL/ADM/ 48/85).

Turbulent Flow in a Two-Dimensional Channel," NACA Tech. Note 2123, Jul 1950 and NACA Rep. 1053, 1951 Todd, F. H., "Skin Friction Resistance and the Effects of Surface Roughness," SNAME, 1951, pp. 315-374 Baines, W. D., "A Literature Survey of Boundary Layer Development on Smooth and Rough Surfaces at Zero Pressure Gradient," Iowa Inst.

(72) Laufer, J., "Investigation of

of viscous flow.

Hydraul. Res.,

St.

Univ. Iowa, 1951

(75)

Schubauer, G. B., and Klebanoff, P. S., "Investigation of Separation of the Turbulent Boundary Layer," NACA Rep. 1030, 1951

(76)

Townsend, A. A., "The Structure of the Turbulent Boundary Layer," Proc. Camb. Phil. Soc, Apr 1951, Vol. 47, Part 2, pp. 375-395

"A Method for the Calculation of the Turbulent Boundary Layer in a Pressure Gradient," Rep. 752, May 1951

(77) Granville, P. S.,

TMB

(78)

Krzywoblocki, M. Z., "On the Foundations of Certain Theories of Turbulence," Jour. Franklin

(79)

Kempf,

Inst., 1951, Vol. 252, p. 409ff

G., and Karhan, K., "Zur Oberflachenreibung des Schiffes (On the Surface Friction of

Ships),"

STG,

(80) Allan, J. F.,

1951, Vol. 45, pp. 228-243

and Cutland, R.

S.,

"Skin Friction

IIYDRODVN AMK.S

132

Hosistancp Derived from Wiiko Mi'iisurriiioiil," Proo, tHTond Int. Conf. Naval Engre., Ostcnd, 1051

Hughes, G., "Kriclional Resistance of Smooth Plane Surfaces in Turbulent Flow New Data and a Sur\ey of KxistinR Data," INA, 10")2, pp. 1-20 K., "Der Kinllus von SandniuhiRkpit auf Karlian. (82) den Hoilmngswiderstand (The Influence of Sand Roughnefw on Friction Resistance)," Scliiff und Hafen, Jan 1952, pp. 8-10 (83) Lap, .\. J. W., and Troost, L., "Frictional Drag of Ship Forms," SNAME, North. Calif. Sect., 29 (81)

—

Feb 1952; 19,S.3,

SNAME

also

Member's

Bull.,

Jun

pp. 18-22

(84) Baker, C. S., "Scale Effect on Ship and Model Resistance and Ita Estimation," L\.V, .\pr 1952,

pp.

41-«3.3

(85) Locke, F.

W.

S.,

"Recommended

bulent

Friction

Bu.Ver

(Navj-

in

Definition of Tur-

Incompressible

Research

Dept.)

Liquids,"

Rep.

Div.

DR-1415, Jun 1952 (86) Laufer, J.,

"The Structure

Developed

(87) Krzywoblocki,

(88)

Flow,"

Pi|H>

M.

Z.,

"On

of

NBS

Turbulonio in Fully Rep. 1974, Sep 1952

the Fundamental.'! of the

Boundary Layer Theory," Jour. Franklin Inst., Apr 19.i3, Vol. 255, p. 2><m Allan, J. F., and Cutland, R. S., "Wake Studies of

Plane Surfaces," NECI, 1952-1953, Vol. 69, pp. 245-266, D6.5-D78 (89) Minutes of the .\merican Towing Tank Conference, MIT, Cambridge, (Ma.ss.), 4-6 May 1953, pp. (90)

9-14 and Appx. XX Landwcber, I.., "The Frictional Resistance of Flat Plates in Zero Presyfure Gradient,"

SX.\ME,

19.53,

On page

20 this paper lists 25 references, of which a number are given here. pp. 5-32.

(91) Morris,

H. N., "A

New Concept

of V\o\\ in

Rough

Conduits," ASCE, Hydraulics Div., Jan 1954, Vol. SO, Separate 390. .\ list of 20 references on friction flow in conduits, pipes, jiiid chimnels is

found on

p.

(92) Gertlcr, M.,

390-123.

"An

Analysis of the Original Test Data

SHIP DESIGN

Sec. 45.26

"Boundary-Layer Characteristics for Smooth and Rough Surfaces," S\.\ME, 1954, pp. 333-35.S. There is a list of 41 references on

(94) llama,

R.,

I'.

pp. 349-.351.

Observed Boundary Layer and Pipe," Jour. Appl. Phys., Feb 1954, \o\. 25, pp. 1S8-196

(95) Sehubauer, G. B., "Turbulent ProccBsee as in

(96) Talen,

H. W., "Collective Research on Paints for

Ships' Hulls," Int. Shipbldg. Prog., 1955, Vol. 2,

No.

401-409

13, pp.

and Voshida,

(97) Sasajima, H.,

E., "Frictional Resist-

Wavy Roughened

ance of

bldg. Prog., 1955, Vol. 2,

Surfaces," Int. Ship-

No.

13, pp.

(98) Ilogner, K., "Influence of lOdges

411-450

on the Boundary

la Mf-canique des Fluides," Tech. Min. Air, Paris, 19.54, pp. 129-134. The paper is in French but there is an English summary in Appl. Mech. Rev., Nov 1955, number 3444, p. 480. This states that "Near the longitudinal edges (of a thin friction plane) the viscous stress is approximately double that in the

LayiT," M<''m()ires sur I'ubl. Sci.

central region."

H., "Boundary Layer Theory," McGraw-Hill, New York, 19.55 (in EngUsh). This is the English-language edition of the German book entitled "Grenzschicht-Theorie," by H. Sehlichting on the same subject, published in 1951. See Appl. Mech. Rev., Jan 1956, p. 33.

(09) Schlichtiiig,

B., and Klebanoff, P. S., "Contrion the Mechanics of Boundary-Layer Transition," N.\CA Tech. Note 3489, Sep 1955

(100) Sehubauer, G.

butions

(101) Allan,

the

J.

F.,

and Cutland, R. S., "Invcstig.ation of an 18-Foot Plank," lESS,

Resistance on

1, pp. 9-56. This paper describes a series of investigations carried out

195.5-1956, Vol. 99, Part

with an

IS-ft

plank

in

smooth

order to determine

its

with a rough surface, and with a surface arranged to represent a ship hull with plate edges, rivets, welds, etc. resistance with a

The

results

finish of the

of

surface,

an examination

of

the

surface

smooth plank and a description

of the

Gov't. Print. Off., Wa.xhington, D. C.

instrument used are given. Tests to obtain an exact mea.sure of the roughness of the rough

Hughes, G., "Friction and Form Resistance in Turbulent P'low, and a Proposed Formulation for Use in Model and Ship Correlation," IX.\, 9 .Vpr

On page .56 there is a bibliography of 11 items. .\ summary of this paper is found in SBSR, 27 Oct

for the Taylor Standar
Mar (93)

IN

1954

19.54,

plank are also described and the results presented.

1955, pp. 541-542.

CHAPTER

46

Reference Data on Separation, Eddying,

and Vortex Motion 46.1 46.2 46.3 46 4

136

46.7 46.8 46 9

Vortex Streets and Related Phenomena Vortex Streets and Vibrating Bodies Practical AppUcations of the Strouhal Num-

139

46.10

References on

General

133

Separation Criteria

133

Detection of Separation; E.xtent of the Zone

.

ber to Singing and Resonant Vibration

Predicting Apparent Flow Deflection Around

.

Separation Zones

Estimate of Separation Drag Around a Ship Separation Phenomena Around Geometric

46 5 46.6

.

.

and Non-Ship Forms

46.1

and 7.19

of

Volume

I, it

Sees.

7.4

appears that the following

Longitudinal surface slope with reference to

the relative direction of motion of water and ship at a distance, in both horizontal and vertical

planes (b) Rising-pressure gradient in

the direction of

motion of the water past the body or ship surface (c) Nature of flow in the boundary layer ahead of the separation zone, whether laminar or turbulent; particularly, the magnitude of the transverse velocity gradient dU/dy just forward of the separation point (d)

Roughness

of the solid surface

ahead

of the

Relative velocity of ship and water, at least

insofar as the size

and shape

zone and the media which both) are concerned

fill

of the separation

(water or air or

region under consideration. It seems that atmos-

pheric pressure can be neglected. (g) Projections, recesses, the ship surface.

Not too much

is

and discontinuities

known

tion

it is

possible to

of

make

.

.

143

Systems, Vortex Trails,

144

Here the medium under body on all sides, and the undisturbed pressure is very nearly the same in all directions and at all points around the body. For a body operating at or near the surface of the water, where the separation phenomena appear to be governed largely by the hydrostatic pressure and the transverse pressure gradient dp/dy, both the pressure and the gradient are nominally zero at the air-water interface and they increase pressure surrounds the

hnearly with depth.

Many

aspects of separation

appear to vary in the same way. Separation Criteria. Despite the numer46.2 ous factors involved, listed in Sec. 46.1, separation appears to be the result, principally, of inadequate lateral pressure, inadequate transverse pressure

and inadequate normal

gradient,

force to accel-

erate the surrounding liquid inward toward the

body which has a local slope greater than a certain amount in any given plane. This critical slope may and usually does vary with the plane or stream surface in or along which the flow occurs. For the transom stern

shown

at

1

in

Fig. 46.A, there is a determining slope for flow

in

quantitatively about

the individual effects of the items listed. However,

by taking the fragments

141

surface of a it

Hydrostatic pressure at the point or in the

(f)

141

.

objects, or bodies in air.

separation zone (e)

.

.

140

Summarizing from

General.

Eddy

.

and Singing

139

factors are involved in a prediction of separation: (a)

.

.

knowledge in combinaestimates of probable

performance in ship scale and to formulate certain rough design rules. Caution is necessary when interpreting or making use of published data on separation which have been derived from tests on models. 133

along the waterline and another for flow under the bottom, the latter generally paralleling the buttocks.

although not certain, that the should be measured along stream or other surfaces of equal ambient or hydrostatic pressure. Knowing the position of these surfaces, It is probable,

critical slopes

and the

critical slopes,

the naval architect might

then predict the locus of the points marking the forward or upstream edges of a separation zone. Around the stern of a ship, for example, at

134

l!^

DRODN

\ WIK.s I\ Mill' 1)1S|(;\

Sec. -16.2

Lookinq Foi^ward

Wave Vyaterline Not Shown

VWave NWalerline Outlines> of

Separ-alion Zone ana Estimated

TypicAL Sktaration-Zone Areas on Ships, as Projected on a Transverse Plane

Tic. 46.A

small

below the air-water interface,

distances

the equal-pressure surfaces would

ma.y be ten or more times that amount. Despite

generally

the gently sloping buttocks, separation of the

parallel to the free-water surface, as at 2 in Fig.

layers close under the wafer surface oc(^urs at

4G.A. This would be true whether the air-water

extremely low speeds. This

interface

lie

essentially flat at low speeds or

is

is

deformed by waves at higher speeds. This is a strong probability that other factors enter into the formation of a .shallow separation

zone abaft the stern. to

be

If so, these factors will

determined and studied

before

have

reliable

easily

\-ortexes, is

when the water

visible

wave profile in way of more accurate to position

the run wliy

rciison

a

that

free

nurfaoc

it inhibit.s

Such a reduction

lence at the surface.

known

is,

affects

flow

vertical turbu-

turbulence

in

to affect flow separation in other cases"

is

(SN.\ME,

1954, p. 396|.

It

might be addcil

llial

presence of the ship

tiie

components turbulence which are normal or nearly normal It

may

be for one or

two

zone

is

usually

bountled

by

having what

butli of

I

he

rcji.sons

is

.sjiiling

line,

fair

form

oul-

iiml

favored with a [icrfcclly normal curve of s<'ction liave

a buttock

hull at the locus of the separation points.

j „-

The

all

(he hull

and the customary appendages abaft the

.S('i)ara-

lie

within them.

On

a moving

water in the vicinity with wocmI separation zone swirl around and follow the .shij) while tho.se outsich^ tli(> zone sjjrinkling the

chips.

Those

in the

arc rapidly carried astern. (

Icncrally, as plotted

indicated in diagram

'1

on a

of

i'"ig.

IjihIv

plan .iml as

•It'>..\,

the width of

only a few

till-

separation zone for a ship with

near the .snrf.uc

niii

is

slopi! i« of

dcgrcca, yet the watcrline slope

fair

streamlines and stream surfaces, leaving the ship

boat or ship the extent of the separation zone on the water surface is readily indicated by

yacht. Such a crall,

considered a

,sei)aration

reasonably

to

upper surface layers under and

Ix-hind the run of u

may

The

these points along the waveline.

tion-point locus

i)rcccding paragraphs that .separa-

tion occur.-^ in the

areiw,

it is

of

the solid surface. lincd in the

known,

is

zone extends far enough astern so that

hull also suppre.sstjs tho.se velocitj'

surface

the surface waterline, on the port and starboard

suggestion that: tlic

further-

For reference purposes a separation zone in the run starts at separation points V.j. and ]•>« along sides, respectively. If the

"Pcrliaps,

is,

almost glassy smooth.

predictions can be made. G. Birkhoff offers the

separation at the stern

.sej^aration

more, marked by a large number of vertical-axis

considerably greater

lii.an

its

,a

pciinted

dcpili

The

DATA ON SEPARATION, EDDYING, AND VORTEXES

Sec. 46.2

zone in

is

deepest at the centerline and

depth toward Ep and Eg

extent of the zone

is

.

it

The

may

135

diminishes

165 deg. This

transverse

blunt entrance, indicated at the right in diagram

rather easily determined by

be either at the after end of a 1

of Fig. 46. B, or at a discontinuity in the run,

attaching tufts to that portion of the model and

pictured at the

watching the behavior of these flexible indicators in the moving water of a circulating-water channel. A considerable amount of non-systematic but reasonably reliable modern data indicates that the slope of a ship waterline at which separation

pointed stern of diagram 2 as a form of transom stern, separation is definitely to be expected at

begins, at the air-water interface,

is

the corners if

diagram

Ep and Eg

Considering the

2.

diagram 3

in

the values of the corner angles

limits of 90

There

of the order

left in

is,

lie

of Fig. 46.

between the

deg and about 165 deg. unfortunately, a serious lack of in-

the relative direction of motion of the ship and

formation upon which to base an estimate of the rate at which the critical slope in a flowplane that

the water and

is

of 13 to 15 deg.

is

This

is

reckoned with respect to

based upon a surface along the more vertical than horizontal.

generally horizontal increases with hydrostatic

ship's side that is

pressure, at levels below the free surface. In the

The

absence of analytic studies or systematic experi-

critical slope given here is somewhat lower than the values of 18 or 20 deg previously quoted in the literature but it has been well checked on ship models. It may be assumed that a separationfree horizontal slope in the run, at the water surface, is in the range of 11 to 12.5 deg, as shown in diagram 1 of Fig. 46. B.

y

No Separation at Surfaoa if

lf^

is

Leas Than 12.5

No Separation at Surface f Cornar Angle is more than 165 deq 1

mental data

it

may

separation-free

be said tentatively that the the

rate

of

on a full-size displacement-type vessel, up to an estimated critical slope of about 36 deg at a depth of 40 ft. The limiting waterUne slope for freedom from eddying abaft a skeg, placed ahead of a single propeller, is given by W. P. A. van Lammeren as 20 deg [RPSS, 1948, p. 94]. The corresponding depth is not stated but it is at least as far below the 0.6 deg per ft submergence,

surface as the tip submergence.

The indications are

that there

is

a corresponding

variation on the model of such a ship, so that the

separation zones and their boundaries are geometrically similar. This

Discontinuity

at

increases

slope

pressure

to be expected of a

is

phenomenon which

when the model

is

is a function of F^, run at corresponding speed.

Fining the trailing edges of sternposts, skegs, 'Separation at Surface if Corner Anqle

Definitel\y

Occurs at Ep

and rudders to conform to these

less than about 160 or 165 deq, provided W/aterline. Slope is

Anqle Does Not Exceed 12.5 deg

horizontal slopes

2

them

separation abaft

In some ships with Waterline/

of Sec. 23.1

known In

of

critical or limiting

not always achieved, hence

is

by no means unusual. the Magunkook

is

full runs, like

Volume

separation has been

I,

to occur abaft the whole underwater hull.

many

of these cases there is not only a greatly

increased drag but a seriously diminished rudder

1^^.^ Transom r"^

Corner Anqle

effect.

3

/

Separation at Surface Definitelvj Occurs at Ep and Es if Tronsom Corner Angle has a Value Between 90 and 165 deg

Fig. 46.B

Sketch Indicating Typical Separation Criteria for Waterlines

On

the stern contour or

zone begins at the point

separation

is

almost certain to occur at any disline, where a sharp knuckle

continuity along that

exists with a horizontal obtuse angle less

than

,

the separation

marked on diagrams

1 and 2 of Fig. 46.C. When the flow is predominantly in the vertical plane, as it is under the run of the wide, flat barge of diagram 1 of that

figure, the

Regardless of the waterline slope with reference to the longitudinal ship axis or direction of motion,

profile,

Ek

maximum

separation-free slope appears

to be of the order of 14 to 15 deg [Dawson, A.

SNAME,

1950, p.

9].

This

is

for a region not

J.,

more

below the waveline on a ship-size is both inward and upward, as under the canoe or whaleboat or "cruiser"

than 2 or 3 craft.

When

ft

the flow

HYDRODVNAMIQS

136

Borge Form with Wide Beom

J_

THy

1^ than 3 ft

The

Sec. 46.3

slope of the flowlines, with reference to

the horizontal, for a considerable distance below

T

Ig

Buttock Slope

—^,__^_

"

I\ SHIP DESIGN (d)

the lower edge of the transom, say at least 1.0

14 de<) or lets

the buttock slopes are nearlj' constant for a

If

I

Hv

and possibly 2.0 times the transom immersion

for ig Limit Given

considerable

portion

of

ahead of the transom,

it

the

length,

may

say 0.3L,

be assumed that

flowline slojie equals the buttock slope.

tlie

this is not the case, as

on the transom-stern

If

ABC

ship hull of Part 4, the actual flowline slopes at

Hy

left&

5

than ft for

"^^

<:r tg Limit Giv»n^^

I

Fio. 46.C

Buttock Slope

^^

Zt6*a

I

the transom edge

Lg or leas

p

may

be appreciably larger than

the buttock slopes.

Further information as to the application of criteria to a transom-stern design are

Typical Separ-^tion Criteria for Buttocks

these Stern of diagram 2 of Fig. 46. C, the separation-free

included in Sec. 67.20.

be as

Notwithstanding the long and extensive use of

great as 25 deg with the liorizontal. However,

tunnel sterns for shallow-water craft, and the

buttock or profile slope near the surface separation

may

niaj'

normally be expected bej'ond the

range of 22 to 25 deg, assuming a full-scale depth

not more than 5 or G

A

special case

below the wavehne.

ft

transom stern described and illustrated in Sec. 25.14 of Volume I, where separation is known to e.xist in

the region abaft the transom.

tative information usually desired

is

(a)

The transom

corner angle,

in Fig. 4G.Ii.

The sharp

(b)

The transom edge

of the tran.som. This

Volume

I

and and

running.

is

angle, at the lower edge

a measure of the dis-

continuity in a buttock line in the vertical plane.

As

illustrated in Fig. 25.1, the

ia

not rounded, and

of the (c)

transom

is

if

of the transom.

less, if

if it

has a

the lower edge

the buttock slope ahead

By

llu of the deepest portion

one

line

of

reasoning this

should be reckoned below the waveline at the outer transom corners, but for wide transoms,

where Bu

=

0.5/i or more, the pressures

conditions are certainly not the

same

acroHS the stern. For design purpo.scs

necessary to

u.se

//„

belrjw the at-rcst \VL.

,

occur

under

and 67.17 describe the design

the

of the

ABC

of the

that, at a

In those tunnel-stern craft having tuiuiel roofs above the at-rest WL, the nominal submergence and the hydrostatic pressure at the top are negative. Only rarely do tunnel-roof slopes exceed 20 deg, at or near the at-rest WL, but it is

doubtful that the

critical slope for

all

and flow the

it is

way

almost

the nmximuin immersion

separation

is

as large as this. So far as known, at the time of

writing (1955), very few craft of this type have been tested in model scale in a circulating-water channel. It is realized that the slopes

mentioned

in

the

preceding paragraphs are not always tiiken along lines

or surfaces of constant pressure,

as

was

out at the beginning of this section.

pointed

However, no better method

not too large.

The submergence

Sees. 67.16

edge angle defines

the lower edge of the separation zone

value of about IGO deg or

would

ship of Part 4, and Fig. 78. F reveals nominal submergence of about 12 ft in the steepest region, there was no separation for a maximum tunnel-roof slope of about 18.5 deg.

corners define the trans-

is

separation

conditions represented by the.se various designs.

the speed at

illustrated

the speed at which the craft

which

at

tunnel roof for the alternative arch-type stern

verse extent of the stern separation zone, regardless of

vessels, there is little systematic quanti-

The quanti-

which the transom will clear in service; in other words, the speed at which the transom surface is entirely free of water contact. This depends upon a number of factors, not yet evaliiated in adequate fashion:

defined in Fig. 25.1 on page 379 of

on large

tative information about the tunnel-roof slopes

presented by the immersed-

is

twin skegs with tunnels between them

fitting of

of defining po.ssible

separation zones ajjpears to be available at this time.

Detection of Separation; Extent of the

46.3

Zone.

In

smooth water and at

close range, such

a punt or skiiT, .separation can be "spotted" with a little practice as abaft

l)y

the square stern

of

noting the vertical-axis vortexes or whirls at

ami near the

surface.

At longer

larger craft, the .scparalion zone

range, is

made

and on clearly

Sec.

DATA ON SEPARATION, EDDYING, AND VORTEXES

463

by larger eddies, by chips, boxes, or blocks of wood thrown into the zone, or by floating refuse caught in it. As mentioned previously, these are whirled around in the eddies or drawn back toward the hull, and dragged along with the ship. visible

The

floating objects outside the separation zone disappear rapidly astern. Special vantage points

are necessary in

many

ships from which to

make

these observations, because the entire waterline or waveline in the run

is

not visible from the

topside.

Under water, where the eddies can not be seen, by the marine

separation zones are often detected

growths which flourish in these areas of low relative velocity. When the separation zone is free of large air bubbles, paint surfaces that little

signs of

regions.

If

wear

may

show

be indicators of stagnant

there are, in an area suspected of

being in a separation zone, any sea connections

which can be shut off from a system and used as pressure orifices, an observed head at or close to the sea connection which is less than the actual hydrostatic head is an indication that a — Ap exists there. Regardless of the exact nature of

Fig. 46.D

Fish-Ete View of a Ship

the water flow outside, this

presence of separation drag

137

— Ap

indicates the

on a portion mentioned here are not to be confused with those which may be developed because of potential flow around certain portions of the ship, described in Chap. 4. By far the most satisfactory method of detectof the hull

which faces

ing separation,

aft.

if it is

The

— Ap's

determining the extent of the

and observing the nature of the flow is to test a model. This can be towed in a basin, using a water box and mirrors for viewing the underzone,

water portion, or it can be run in a circulatingwater channel and viewed through large observation windows. Colored threads, strings, and tufts are attached directly to the model surface or to slender pins driven into the model so as to

lie

at

a distance from that surface. The tufts may be attached to appendages, or mounted ahead of and abaft propellers on wire frames which will not affect the flow appreciably.

which

curl this

point

forward

way and are

Tufts which wave,

which actually unmistakable evidence of that, or

unsteady flow, of approaching separation, or of

Model with Some Partly Reversed Tufts

HYDRODYNAMICS

188 tlic

roviTsed (low uf fully

tk>vi'l<>i)eil

scpaiatioii,

TMH

fish-oye

view of Fin.

It'U, taken in the

eireiilating-water eluiiinel, siiows partially

rcversetl tvifts in a separation

zone at about the

designed waterline (marked by the heavy black and abreast the propeller. The disturbed

stripe)

under surface of the water in this region also indicates tiie presence of eddying flow in the separation zone. Strings or tufts are attached to thin

wands

like

and colored dyes are ejected from moved bj' hand to any position desired around the model. Fig. 46. pictures the trail of india ink flowing from such

left

of

Sec. -16.3

How upward component

axis vortex, giving definite

respectively.

The

IN SHIP DESIGN tiic

alongside the hull a of

velocity

the ink tube and a marked

component

to the right of

it.

The

to

the

downward

flow picture in

4G.F is not clear and complete because the forward ends of some of the tufts shown are attached directly to the model and others are Fig.

fixed to the outer

ends of pins projecting from

its

surface.

High-speed flash (and motion-picture) photoof which Figs. 78. E, 78. F, and those

graphs,

fishing rods,

reproduced

long, thin tubes, both

examples,

in

TMB

Report 810 are further

provide a permanent record of the

steady continuous flow hoped for over

all

parts

and varying-flow separation zones. If minute air

of a ship or of the reversed-

a tube (visible at the extreme right). Part of the

characteristics of

flow from the orifice position passes outboard of

bubbles are injected into the water,

the offset rudder while a small part of

a separation zone formed by a projecting strut-arm pad as small as 0.3 inch wide and projecting only about O.OG inch from the fair surface of a model. Vortexes which are not steady or stationary are detected by dye injected in the vicinity, are

e.xpectedlj-

it

un-

swings inboard of the rudder.

The predominant

characteristic

revealed by the ink in Fig. 40.F

what might be

called

it.s

is its

the

of

flow

slowness and

uncertainty.

The

tufts

reveal the presence of a very large longitudinal-

I'll;.

Iti.l-;

Ki.mi-ICvK

Vikw dk

a Shii'

it is

to detect sw'irling bubbles in

Mohki. With Thau, ok Isiua Ink to ItKVKAr.

I'l.ow

I'm-ikun

possible

DATA ON SEPARATION, EDDYING, AND VORTEXES

Sec. 46.5

Elevation of Ship Model Afterbody in Cikculating-Water Channel with Ink Trail, Tufts on Surface, and Tufts on Pins Projecting from Surface

Fig. 46.F

observed by eye, or are recorded by high-speed

motion photographs. Aggravated air-leakage situations reveal themselves in the channel by air bubbles drawn into the — Ap regions around a model,

The

139

its

propulsion devices, or

appendages.

its

circulating-water channel lends itself to

the simultaneous recording of pressures at

many

small orifices in a model surface, so that pressure

may

contours

and the areas

be plotted for any given conditions of

— Ap may

be definitely traced.

models for which resistance and propulsion data were presented by R. B. Couch and M. St. Denis

[SNAME, hull

1948, pp. 360-379], the flow close to the

and into the propeller

very nearly horizontal,

some

in

regions.

Fig.

if

disc

was

in

many

46. F

cases

downward

not actually

shows exactly

this

type of flow, above the ink "trail." The downward flow was unexpected because the general buttock

was distinctly upward, at an appreciable angle to the horizontal. The slope in these regions

studying the apparent deflection or

phenomenon may be explained, at least in one way, by the presence of separation zones abaft the DWL and the near-surface WL's, and by downward deflection of the water passing under

diversion of flow around separation zones, dis-

the stern. Normally, this water keeps on rising,

46.4

Predicting

Apparent

Around Separation Zones.

Flow

The

Deflection

detection meth-

ods described in the preceding section are most useful

in

cussed in Sec. 7.10 on page 134 of Prediction of this deflection

is,

Volume

I.

in the present state

upon a background of up by watching flow tests,

of the art, based largely

experience,

built

studying and analyzing the photographic records,

and thinking about the problem. Since pressures from external regions are not, as a rule, transmitted through separation zones to the ship hull, there may be little information of direct value to resistance studies in a knowledge of the potential-flow pattern,

with

its

changing

and pressures, outside the separation zones. However, for the prediction of flow into propulsion devices, and for special appendages and attachments to be carried by a ship at some distance from the side, knowledge of these "outside" flow patterns is a must if the special design is to be logical and the service performance velocities

is

to be predicted. For example, in the case

the way to the stern, but with a separation zone extending nearly to the top of the propeller aperture, as in Fig. 46. F, the under-the-bottom all

water and the eddying water obviously can not both occupy the same space. Another explanation of the downward flow is that

it is

due to the presence

ten tanker

a large vortex

the region of the bilge at about the after quarterpoint in the manner outlined by the sketch of Fig. 25.F in Sec. 25.6 of

46.5 Ship.

Volume

I.

Estimate of Separation Drag Around a Sec. 7.8, supplemented by Fig. 7.H on

page 130 of Volume

I,

explains

separation-drag coefficient

by noting the

may

how

the specific

be approximated

sensibly constant specific pressure-

from model tests at low Froude numbers, below the hmit at which resistance coefficient derived

wavemaking of the

of

rotating about a longitudinal axis, streaming off

K.

S.

M.,

resistance manifests itself [Davidson,

PNA,

1939, Vol. II, p. 76;

SNAME,

11M)RI)1)V.\AM1C;S

110

Now York

Sect.,

'Jf.

Apr

1951, p.

lonstaiit specific r»'sistaiirc

is

Fig.

7,

Tliia

1].

n-rkoiuHl iibuvc

ull

nllowniucs for i)oth transverse and longitudinal iur\ature and for plating, stnictural, and coating roughneSv<«\s

which are

applieil to tlie flat,

smooth-

Mill' Dl.SlGN

l.\

Src. 16.6

the u.seful —Ap's. For cxaiiiplc, air drawn to

fill

and

down

the .separation zones behind the arms, legs,

feet

of

high-speed detrimental,

swimmers, as revealed by special photography,

may

be

helpful

or

depending upon whether drag or

propelling forces are involved.

plate, turlnilent-flow friction line.

— Ap's

+Ap's and

caused

B. Perry reports the results of drag measure-

by out wan! deflection of the water at the bow, by speetling up between the forward and after neutral point.*, and by closing in astern, are not of such sign and magnitude as to balance each

ments on surface-piercing bars of rectangular and circular section, and gives excellent photographs of the air-filled holes alongside of and abaft these bars [llydrodyn. Lab., CIT, Rep. E-55.1, Dec 1954]. He reports an effect of surface tension in the formation and behavior of the .spray roots at the water surface. Sometimes these roots form a sort of closure over the separation zone which prevents the admission of air to it. Neglecting the free-surface and lower-end

In the usual case the

when integrated over the transverse maximum-area .'icction. This is especially true if other,

the vesj^el has a bulb of appreciable size at the

bow, or

if

the separation zone at the stern interfere with

enough to

is

large

the closing in of the

potential flow along the run.

Some

of the low-

probably always the result of this action. The remainder,

efi"ects.

and greater

derived

speed

specific

resistance

pressure

part,

is

the stern, especially

is

chargeable to separation at if

the criteria of Sec. 46.2

indicate a sizable zone of

— Ap, when

projected

on a transverse plane. Areas of this kind are illustrated by the hatched portions of diagrams

and 2 of Fig. 46. A. There are insuflicient data from model tests, and practically none from ship trials, to afford an indication of the numerical values of — Ap or of the pressure coefficient — Ap/5 to be found 1

separation zones. Tests in air on geometric forms indicate separation-zone pressures varying in ship

from

—\Aq

behind a 2-diml

behind a 2-diml circular

flat

plate to —1.15(7

cj-linder,

with

its axis

normal to the stream, to — 0.4g or le.ss for a sphere and a circular flat plate, depending upon the /?. of the test. There is little doubt that these

much

values are

too high for separation zones at

it is not yet known whether the — Ap in those zones is a function of q or perhaps of the hj'drostatic pressure -p,,

the stern of a ship. In fact,

.

It is

pointed out in Sec. 7.3 of

aeration,

defined

as

the natural

Volume

I

that

or deliberate

admission of air to a separation zone where the

— Ap's

cause added drag, acts to diminish that

drag. \Vhen di.scussing separation drag, therefore,

most necessary to know the extent to which

it is

atmaspheric air has been admitted to or has found its way into a — A/j region that is under a pressure

than atmo.spheric. In certain regions —Ap's

le.ss

arc

wt up

deliberately, for propulsion purpo.ses,

as on the ijacks of the blades of screw propellers.

important to know to what extent, if any, air has leaked into the.sc regions and diminished

It

iH

Perry reports that

tlie

drag of the

bars per unit depth, at a submergence

\-ertical

may

be from the drag of similar bodies well submerged and trailing water-vapor cavities abaft them. The referenced report gives drag h,

coefficients for bars of circular section, for rec-

tangular bars with one flat edge leading, for wedge-shaped bars with the apex leading (and for various included angles), and for all three kinds when placed at an angle to the flow. 46.6

Separation

Phenomena Around

metric and Non-Ship Forms.

Geo-

It is often useful,

in the design of bo.x-typc or non-ship-shaped

water

and in tlic design and application of appendages, to have information as to the nature of the separation to be expected around them. Some of these data are given in the illustrations on Chap. 7, and references to other data arc furnished in certain sections of Chap. 42. Research on this phenomenon has been underway for many years but the data have not yet been collected and presented in systematic fashion. Over three-quarters of a century ago the following quantitative data were given by W. Froude as the result of towing tests on a cylindrical pitot tube 0.125 ft in diameter and projecting 1.75 ft below the free-water surface. The test was made at a speed of 15 ft per sec, corresponding to about 9 kt. An air-filled hole, called by Froude a "ga.sh," extended for about 3 ft abaft the tube, at which point the ga^sh closed by the gradual meeting of the side streams which craft,

boundeii ".

.

.

there

from ro.sc

which,

ill

it.

lliis

point to alxiut 7 or S feel furlliiT stcrnwarda

vcrlicnlly a rentriil wall of wat
elevation, hail a paraliolic

form

(aa far

DATA ON SEPARATION, EDDYING, AND VORTEXES

Sec. 46.8 as could be estimated

by the

ridge being certainly over 2 feet above the natural waterlevel

.

.

."

[Brit.

Assn.

Rep.,

1874

(dated

1875),

pp.

255-264].

Two of

(5)

I,

are repeated here for the convenience

of the reader. These embody a multitude of photographs taken through the water of a basin, showing the air-filled separation zones abaft towed vertical rods of finite lengths. They were made by A. D. Hay and published in "Flow About SemiSubmerged Cylinders of Finite Length," Bureau of Ships, Navy Department, Contract NObs34006, dated 1 October 1947. Many other photographs of separation zones abaft box-shaped

made by A. D. Hay and

Runyon, are embodied in "Photographs and Resistance Measurements of Semi-Submerged Right Parallelepipedons," Contract NObs-34006, dated I May 1947. forms,

M

references on this subject, listed in Sec. 7.2

Volume

J.

1924

Zahm, A.

(6)

periscopes

or

Similar vortexes

propeller-blade

thick

(8)

NACA Rep. 253, 1927 M., "Die reibungslose Stromung in Aussengebiet zweier Kreise (The Frictionless Flow About Two Circles)," Zeit. fiir Ang. Math, und Mech., Aug 1929 Rosenhead, L., Proc. Roy. Soc, A, 1930, Vol. 129,

(9)

Rosenhead,

p. 115ff

may

be shed abaft faired appendyawed slightly with

respect to the flow.

The

at very low speeds

and those

vortexes in pairs appear in echelon at the

higher speeds. Schematic diagrams of these vortex

groups are given in Figs. 7.M, 14. W, 14.X and 23.E of Volume I, and in Figs. 40.A and 41. D of the present volume. The mechanism by which, at certain combinations of forward speed and appendage diameter or thickness, the alternating circulation associated

with

the

shedding

of

alternating transverse

these

lift

eddies

produces

forces of considerable

magnitude on the moving body,

is

explained in

Sec. 14.22.

For other treatments the reader

is

referred to

the following: (1)

inders in

Roy. Soc, 1930 Biermann, D., and Herrnstein, W. H.,

(10)

Between Struts

Interference binations,"

NACA

(11) Richards, G. J.,

the

R

M

"The

Com-

Rep. 468, 1933

"An Experimental

Wake Behind an

and

Jr.,

Various

in

Elliptic

Investigation of

Cylinder,"

ARC,

pp. 387-392 and Tietjens, O. G., AHA, 1934, text on pp. 130-136, diagram on p. 132, photos in Pis. 24, 25,26 Tietjens, O. G., and Prandtl, L., HAM, 1944, Vol. I, diagram only on p. 225

1590, 1934-1935, Vol.

I,

(12) Prandtl, L.,

(13)

H., HD, 1945, pp. 680-681 Rouse, H., EMF, 1946, pp. 239-241 Wright, E. A., SNAME, 1946, Fig. 3, p. 377 (16) (17) Rouse, H., EH, 1950, pp. 129-130 (18) Rouse, H., and Howe, J. W., BMF, 1953, frontispiece and Fig. Ill on p. 187.

Lamb,

(14) (15)

The

reader

who

wishes to delve more deeply

into the analytic aspects of this matter

to L. Landweber's treatment of this

is

referred

phenomenon

TMB

Report 485, dated July 1942. and Vibrating Bodies. The right-hand diagram of Fig. 46. G, adapted from H. Rouse [EH, 1950, Fig. 93 and pp. 129130], gives quantitative data concerning the vortex trail generated abaft a stationary 2-diml circular cylinder in a uniform stream of velocity U„ It indicates that the whole system of alternate vortexes left behind by a moving body in a on

Vortex Streets

46.8

.

Ahlborn, F., "tjber der Mechanismus des hydrodynamischen Widerstandes (On the Mechanism

(2)

of Hydrodynamic Resistance)," Hamburg, 1902 Benard, H., Comptes Rendus (in French), 1908:2, Vol. 147, pp. 839-842 and 970-972; 1913, Vol. 156,

(3)

Von Kdrmdn,

(4)

Von Kdrm^n,

p.

and Schwabe, M., "An Experimental Flow Behind Circular CylChannels of Different Depths," Proc.

L.,

Investigation of the

sections.

ages such as struts which are

for Simple

Quadrics,"

hbrary. Copies of these reports are in the 46.7 Vortex Streets and Related Phenomena.

Large vortexes, in pairs or in echelon, may be and usually are shed from non-faired appendages or blunt-ended objects, such as submarine

"Flow and Drag Formulas

F.,

(7) Lagally,

P.

TMB

HI

some additional material worked up by T. von KArmdn, is given by G. de Bothezat in NACA Rep. 28, 1918, Note IV, pp. 149-158. Relf, E. F., and Simmons, L. F. G., "The Frequency of the Eddies Generated by the Motion of Circular Cylinders through a Fluid," ARC, R and 917, with

eye), the highest part of the

1225; 1926, Vol. 182, p. 1523; 1926, Vol. 183 T., Nachr. Ges. Wiss., Gottingen (in

German), 1911,

p. 509; 1912, p.

547

with what may be termed a wake For the cylinder shown the value of this velocity is about 0.14 of the body speed, so that the absolute downstream velocity of the system of vortexes is about 0.86 1/» The transverse spacing a between the rows of alternate vortexes, for the case of the cyUnder illustrated, is about 1.3D. The longitudinal spacing h between vortexes in either row is about 4.3D. follows

it

velocity.

.

and Rubach, H., "tJber den Mechanismus des Flussigkeits- und Luftwiderstandes (On the Mechanism of Resistance in Liquids and in Air)," Physikalische Zeitschrift, 15 T.,

Jan 1912. An English translation of

flowing stream, corresponding to this cylinder,

this paper,

U\l)Rt)l)\.\AMlC.,S IN Mlli'

142

Wohe

ULMGN

Velocitv

of Vortex Troil h»-0.66U,

of Vortex Troil - 0.14 U„

eh

Sec. -16.8

Absolute Velocitv

llnstont-' I

I

o

3.0

a -1. 3D

4.0*^

"-

'' I

Dro(j*

1

Outside

Moves 5.0

Some

Direction os 5treor

Eddies

of ^heddint^

Frequency

f-

IQ 4.0

3.0

Vortex

of

in

6.6

Ua,D 5cole of

Lo^iQ

If

iJ

the vortex trail

is

being generated

body instead

l)lunt-ended

2-diml

of a

cylinder normal to the flow,

l)y

a

lireiilar

the dimen^5ion

D

corresponds to the effective diameter or width of the

edge.

trailing

known

there

Unfortiniately,

by which

rule

Relation.'? for Vorte.x-Tb.mi. Probi.e.ms

Giidance Sketch and EDDV-FREqiEsrv

Fig. 46.G

is

diameter

this effective

no

pU^Tr/'2.

2.86(0. 14 i7

may

G

JD/U„

from

culation around the cylinder

must be

.

iSincc the cir-

c<|ual

to

of opposite sign to the net circulation of all

the vortexes, the circulation around

general

i.s,

ciusc.

IIk-

cylinder

— F(;/2.

The approximate magnitude per unit span of the direction,

of

2-4linil

of the

body, acting

lift

force

in either

by I0(|. (44. i), /> = pf ,F for the For this parti
and

{D/U„ ,D v. The

As another example,

diameter D.

effective

assume that a

cylindrical rod having a diameter

of 0.1 ft forms part of

an experimental speed log on the ABC ship of Part 4, projecting 2 ft vertically below the bottom of the ship. A.ssumc also that the average velocity U in the boundary layer in

way

The

f/„

34.02

is

=

=

5.59

Tuf2

maximum

transverse

.9905(32.89) (2.8)

=

lift

.

per sec.

F,/ is

ft'

sec,

about 1.7(t/)D

The

per sec.

2.8 ft' per sec,

circulation

is

ft

At whence

or 0.95(7„

per

ft

32.89

vortex circulation

1.7(32.89)(0.1)

1

is 0.951''

of this rod

0.95(34.02)

U„

The

the left-hand diafz;r:un of Fig.

'

U =

likewise

or

.

about about

terms of the Strouhal number

dzFy

,

Mr J

is

and the applicable Reynolds number f example of Sec. 41.G explains the method of using this graph to predict the eddy frequency for a 2-diml rod of diameter D or for a blunt-ended body

zero.

varies from \- F, /2 to

in

kt,

has reached a steady value of

and

in

20.5

This increase in vortex circulation takes place in such manner that the ulgebraic sum of all the vortex circulation from time zero e(|uals ±r,;/2 after the stream velocity

2.8(4.3/)) (0.

F,/

give values of the relation.ships fO'/v

time, the vortex circula-

tion approaches a steadj' value of

increasing

=

J

The graphs

Horause of the basic theorem of hydrodynamics which requires that the circulation around any clo-scd curve within a fluid must remain constant with time (FIIA, 1934, pp. 192-193], the circulation r(capital gamma) at any instant about the 2-fliml cylinder in Fig. 4().G must be cfjual to, and mu.st be of oppo.site sign to the nd circulation of all the vortexes previously formed [Rouse, H., EH, 1950, p. 129]. At time zero, assume that there is no circulation anywhere in the system and that the uniform-stream velocity is zero. This velocity may then be a.ssumcd to rise from

At the same

aliout 0.8Gt/„

is

1.7C/„D.

46.

.

absolute downstream velocity of

strength of the vortex circulation

he determined for a trailing edge of any shape.

zero to t'„

The

the vortexes as a group

force

183.3 lb per

is

ft

=

cylinder

whence the pUr,i/'2

or

length of span.

TluM/-Rcynolds number is ID or (32.S9)(0.1) about 0.257 million, whence from the left-hand diagram of Fig. 4(t.G the Strouhal number //)'r = about 0.215, from which / = 'i>

(10'')/1.2817 or

(0.215)(32.89) (0.1) .sec.

If

=

71 hertz or 71 cycles per

the virtual nuuss of the rod, including the

ad
vibrates transversely

lus

is

such that

it

a cantilever at a fre«iuency

DATA ON SEPARATION, EDDYING, AND VORTEXES

Sec. 46.9

approximating this figure, resonant vibration will ensue, with a magnification of vibration

edge

amplitude and possible damage to the rod.

1.2817

The use

=

(FB,„d»)(0/''

is

=

of

deflectors

or

longitudinal-vortex

diagram

generators,

to

serve

an auxiliary transfer

number

mechanism

to get fast-moving water from the

as

143

damaged

the effective diameter of the

trailing

(70.86) (0.0625) (10^)/

From

0.3455 million.

the left-hand

46.G the corresponding Strouhal about 0.21. Then since S„ = JD/U^

of Fig. (S„ is

or, in this case, {J){t)/V^u^i«

=

the predicted fre-

,

=

outer portions of the boundary layers into the

quency

inner portions and thus to provide the kinetic

I.

= 238 hertz or 238 cycles per sec. This is well above the low hmit of 10 cycles per sec and well below the upper limit of 700 cycles per sec for

for

audible singing, given in Sec. 70.46. Singing on

energy in the inner portion necessary to defer separation,

is

Volume

discussed in Sec. 36.27 of

However, the necessary quantitative data

the

available at the present time (1955).

of the

Applications

Practical

46.9

the

of

Strouhal

and Resonant Vibration. As the application of the knowledge

to Singing

an illustration of

presently available

to the prediction of

(1955)

possible singing of a propeller blade, take the case of the propeller designed

ABC

the transom-stern

for

ship in Sees. 70.21 through 70.38 of Part 4.

Assume that

this propeller,

originally

manu-

factured with the relatively fine trailing edges

depicted in Fig. 70. 0, has had its edges damaged by curling and nicking so that, as a temporary

measure, the trailing edge from about O.bORu^^ to 0.78/?Ma>t has been chipped

shown by the broken

off as

Fig.

70. P.

thickness ft;

t

It

is

estimated

at this edge

is

away and rounded

line of

that

diagram the

about 0.75 in or 0.0625

see the discussion of this matter in Sec. 70.46.

In other words, the vortex

trail

expected to be

0.21 (70.86) /0.0625

ABC

ship

is

repaired)

is left when the damaged parts are chipped away, as diagrammed in Fig. 70.P. Two illustrative examples of the method of calculating the eddy frequency for 2-diml circularsection rods that may be subject to resonant vibration are worked out in Sees. 41.6 and 46.8, respectively. As an indication of the range of frequencies which may be encountered on highspeed vessels where these hydroelastic interactions are liable to pose troublesome problems, take the case of the very wide strut arms, with a chord length of 3.75 ft, mentioned by P. Mandel

[SNAME,

1953, p. 514].

Assume that the proposed on a large 4.35.

As

ship,

strut section is used with a thickness-chord ratio of

indicated in Fig. 3 on page 408 of the

reference, the effective

t

edge

ft.

2.5 in or 0.21

is

D) along the

(or

Assume

speed of 25

which would be shed by a non-vibrating 2-diml

since at higher speeds the vortex trail

circular-section rod 0.0625 ft in diameter,

moving

The

basic data, for a designed ship speed of

,

The

number

=

0.292.

ft'

then

is

ft''.

VD/v or From number S„

0.6917 million.

Then / = S,y/D =

(42.22)0.292/0.21

In practice the strut problem

=

is

further compli-

may

ft"

Or

lie if

with

its

meanline exactly in the

line of flow.

properly aligned for straight-ahead running,

ft^.

rotational speed of the propeller at the 0.64

halfway between 0.50 and 0.78i2Max

=

(^-Reynolds

cated by the fact that the strut-arm section

per sec

,

is

The blade-

65.15

ft

per sec.

section speed at that radius

is

the combination of

27r(20/2) (0.64) 1.62

in Sec. 46.8, the

is

(42.22)0.21(10')/1.2817

not of salt water, 1.9905 slugs per

per sec,

might be

58.7 hertz or 58.7 cycles per sec.

Speed of rotation of propeller, 1.62 rps Kinematic viscosity of salt water, 1.2817(10"'^)

radius,

As

cavity.

ft

taken as 1.2817(10"'') per sec and the mass density as 1.9905 slugs per

is

Diameter, maximum, of propeller, 20 ft Speed of advance V a 27.87 ft per sec

Mass density

by a vapor

kinematic viscosity

the graph of Fig. 46. G the Strouhal

20.5 kt, are, from Sec. 70.26:

The

replaced

equivalent to 42.22

kt,

trailing

further a ship

shed by the trailing edge corresponds to that

through the water at the same speed and occupying the same position as the trimmed-off trailing edge of the damaged blade.

blade

occur unless a chisel

liable to

edge

1 of

effective

S„(FB,ado)//

damaged (and temporarily

calculating the effect of these generators are not

Number

/

is

the rotational speed and the speed of advance, or

TBiade= [(65.15)' + (27.87)T' = 70.86 ft per sec. The d- or diameter Reynolds number R^ for

even taking account of the twist in the inflow jet which is induced ahead of the propeller position, the strut-arm section may run at an appreciable

yaw

angle

when

probable that,

if

the ship the

yaw

makes a turn. angle becomes

It is

large

enough so that the separation point on that side of the trailing edge which is yawed outward moves aft and becomes essentially fixed at the

HVDRODN

lit trailiiiK imIho, ''"'

riic

vortex street

\ XMK.S

loiiKer I'nnueil.

is riu

IN"

gation

nlloninting ciroiilatioii ecnsos, as docs the

alterHutiiig transvorst^

Further

The

and

research

along these

lift

needed

arc

The

hyilroelastic interactions in the case of the (1)

water for transverse or flatwise vibration of the stmt arm, the damping efTects of the strut .section, when moving laterally, the ukmIc of motion of the

eddy sj'stems abaft the

or

in

trailing

The

somewhat broader by no means complete but it is adequate

References

subject.

(4)

(5)

(0)

These are

section.

and

and 14.22

GieichungPii

den

welclie

Ent.sprochen (On Integrals of I'Aluationa wliirli

I'Jxjire.ss

Jour., IS')H, Vol.

.'»5;

.33 (-Ith

tlic

(7)

(8)

I.

iMiglish Iriinsl. Pliil.

by P.

(

'lolle's

CI.

Mag., ,lan-.)un

8me.s), pp. 4S.5-.51!

"The Problem

1936-19.37,

of the Singing Propeller,"

1937, pp. 205-207; 2

SBSR, 12

Sep 1937, pp. 298-300;

7 Oct 1937, pp. 450-452 Hunter, II., "Singing Propellers," E. and F. N. Spon, London, 1937 Hayes, II. C, and Klein, E., "Methods and Means for

frequencies

of

screw-

Conn, J. F. C, "Marine Propeller Blade Vibration," lESS, 1938-1939, Vol. 82, pp. 225-255, 292-374 Shannon, J. F., and Arnold, R. N., "Statistical and Experimental Investigation of the Singing Propeller Problem," lESS, 1938-1939, Vol. 82, pp. 250-291, 292-374. On pp. 289-291 the authors list

"The

Kerr, W., Shannon, J. F., and Arnold, R. N., Inst.

Mech.

Engrs., London,

Dec

Abstracted on

p.

409 of SBSR, 25 Apr 1940; also

SBMEB, Apr

1940, pp. 180-181.

1940, Vol.

144, pp. 54-90.

in

SBMEB, Apr

105-169.

1940, pp.

after face of a 2-tliml rod of rectangular section are

(11) Baker,G.S., "Vibration Patterns of Propeller Blades,"

in Fig. 22 of the reference. A large separation zone abaft a similar section at higher speed is shown

(12)

Stanton, T. E., and Marshall, D., the

Wake

sional Vol.

I;

"Eddy Systems

of Flat Circular Plates in

Flow," ARC, pp. 202-211

(d) Steinman, D.

B.,

Hydrodynamic

(K)

NECI, D73-DI20

"Singing Propellers,"

.\. W., "Characteristics of Silent Propellers," lESS, 1939-1940, X'ol. 83, pp. 29-102. Abstracted

NECI, 1940-1941,

in Fig. 12.

(f)

11.,

(10) Davis,

shown

(c)

S.S3.

library

Prolilcnis of the Singing Proi)eller,"

(b) Ahlborn,

(c)

TMB

the

35 references. (9)

Tait

F., "Die Wirbelbildung ini \Vid<'r.stand.>!mcchaDismuM des Wassers (Eddies in (lie Mechanism of Ship Ucsi.stance in Water)," ST( I, 1!)05, pp. 07-81. Eddies abaft tlie forward outboard corners and the

Ver.

1937, Vol. 81, pp. SS2

available in

propeller blades.

HydrodynamisWirbGlwogungen Hydrodynamical

Vciitiw Motion),"

London, Edin., and Dublin,

1807, Vol.

Volume

of

Integrale dcr

(a) Hclraholtz, H., "l)l)cr

in

of that

is

the vibrating modes and

in addition to the references

listed in Sees. 7.11

chcn

Table 42.b

in

(The

des

Zeit.

Determining the Natural Modes of Vibration of Mechanical Structures," ASNE, 1938, Vol. .50, pp. 519- .520. The paper is devoted to a study of

patterns involving eddies and vortexes are listed in the text of Sec. 42.2

Hunter,

Aug

an extended study of the to photographs of flow

for the beginning of

,Iul

.3

SchifT.ssehr.iuben

PropolliTs),"

Vol. LIII, pp. 189-222,

list

the present section covers a

field. It is

Ship's

of

an unpublished English translation of this paper, marked T.MB Transl. 123.

of references relating directly to the

edges of bodies of varied type and shape.

1925, Vol. 37, p. 17811

"Das Singcn von

Deutsch. Ing.,

There

(3)

References on Eddy Systems, Vortex There is given in Sec. 4G.7 Trails, and Singing. vortex-trail

Blufl

Richardson, E. G., Proc. Phys. Soc., 1924, Vol. 30,

Singing

46.10

list

Behind

references which follow apply particularly

p. 1.53(T; also

the arms, and the elastic characteristics

of these parts, are not considered here.

a short

M., "E.\ploratory Investi-

Turbulent Wakos Rep. 903, Oct 1955.

TMB

(2) Gut.sche, F.,

hub

including the strut

wliole strut a-ssemhly, all

I.ut/.ky,

to the singing of the blades of screw propellers:

lines.

strut, involving the addc
and

Srr. 46.10

and the

of

Boiiies,"

forces on the section.

experiment

SIIIP DFSir.X

(h) {'oo|HT, R. D.,

II

and

M

"Problems of

.Stability," Proc.

in

Three Dimen-

i:).5.s,

liUl

and

("onf..

Dl-Dr2

Singing Propellers," IIOSS, 1941-1942, Vol. 85, pp. 55-168. On page 130 the author lists 10 refer-

I'.I.12,

.\eri)(iyniimic

Third llydr.

(13)

Vol. 57, pp. 43-66,

Work, C. E., "Review of Marine Propeller Noise and Vibration Studies," U. S. Nav. Ord. Test Sla. Propulsion Memo 74, 7 Sep 1940 Hughes, Ci., "Intlucnco of Shape of Blade Section on

ences. (14)

Hughes, G., "On Singing Propillcrs," INA, 1945,

State Univ. Iowa, Studies in Eng'g., Hull. 31, 1947, pp. 1.30-104. The author lists 10 references on pages

(15) Lewis, F. M.,

I03-lfr».

(16)

Hughes,

(17)

NECI, 1948-1949, pp. 273-.300, D51-D70 Burrill, L. C, "Undenvater Propeller Vibration Tests," NECI, 1948-1949, pp. 301-314, D50-D70

(18)

Work, C.

"Aero
Stcinman, D.

pp. lS.5-210

B.,

Jour. Aero. Sci..

Feb

19,5.5,

pp. 2, 124

132

W.

ME,

Vol. II,

1946, p.

"Propeller

L.,

Blade

E., ".Singing Propellers,"

131

Vibrations,"

.\SNE,

May

1951,

pp. 319-331 (19) Lankest
vestigations

Jun

l'.t.55,

and Wallace, W. D., ".Some In-

into

Singing

pp. 2<)3 318.

Propellers,"

NECI,

7

CHAPTER

The

47

Inception and Effect of Cavitation on

Ships and Propellers 145

47.3 47.4

Scope of This Chapter General Rules for the Occurrence of Cavitation on Ships and Appendages Vapor-Pressure Data for Water Tables of and Nomogram for Cavitation

Numbers The Prediction

147

47.5

47.1 47.2

of Cavitation

Cavitation

47.9 47.10

151

47.1 Scope of This Chapter. The phenomena and mechanism of cavitation in its various forms, and the factors associated with it, are described in Chap. 7, Sees. 7.12 through 7.19, of Volume I. The occurrence of cavitation on ships and pro-

examples

trating the calculation of the cavitation

156

Propeller Performance Under Superoavitation

156

Selected Cavitation Bibliography

157

,

raphy,

and append-

limited to data of a quantitative nature,

and

selected cavitation bibliog-

many

containing

recent papers on the

liu-

pressure p

pressure is

The ambient

say 0.4 psia.

e,

that corresponding to the

70

ft,

full

water

is

of practically all

create useful forces

and negative that the

=

0.4(144)

+

31.13(144)

(0. 9952.5) (f7^

=

com-

is

U')

(C/

(31.13

=

If

F =

sec, so

and the

as low as can be accomplished without

setting

up harmful

cavitation.

Most such

C/„ is

that

U =

of a .surface ship operate within a

Ul

= Ul -

U^

7,013.6

parts

depth of about 37 ft below the free surface. This hydrostatic head, when added to the atmospheric-pressure

C/')

ft'

83.75

-4,446.2

0.4)(144)

ft'

per sec'

30 kt, equivalent to 50.67 2,567.4 ft" per sec", then

ft

per

is

(-4,446.2)

per

-

0.99525

=

to

— Ap's

-

whence

of positive

as high,

salt

,

differential pressures, it is natural

+Ap's should be made

The

factor 144 to transform psi to psf then substitut-

moving ship

by the development

for standard

0.99525 slugs per ft^ Introducing the

bination of water vapor and dissolved air or gas.

appendages, as well as propulsion devices,

pressure p„

absolute head of

or 31.13 psi for standard salt water.

pressure in a particular region in the water drops

As the purpose

mini-

critical

equal to the absolute vapor

is

value of the term 0.5p(rho)

Cavitation

occurs when, for any one of several reasons, the to that of the water vapor, or to that of a

(47.i)

u'-)

For the condition described the

General Rules for the Occurrence of

47.2

+

P-

ing and solving,

subject, concludes the chapter as Sec. 47.13.

Cavitation on Ships and Appendages.

=

P

mum

of general interest to the naval architect

A

155

head of 33 ft, gives an effective head of less than 70 ft before cavitating conditions are reached. To demonstrate this, set down the pressure equation for steady irrotational flow of an ideal liquid, Eq. (7.i) of Sec. 7.12. Transposing p„

number

of cavitation in the present chapter,

as associated with ships, propellers,

marine engineer.

Vor-

illus-

are found in Sees. 41.3, 47.4, and 47.5.

is

Hub

of its practical features,

23.16, of that volume. Practical

ages,

Cavitation and

Prediction of Cavitation Erosion

are discussed in Chap. 23, Sees. 23.9 through

Treatment

Hub

Predicting

47.11 47.12 47.13

for Bodies of Revolution

many

1.53

154

texes or Swirl Cores

and Other Bodies

pellers, as well as

152

Propeller Cavitation Criteria

on Hydrofoils 149

Data

Effect of Cavitation on Screw-Propeller Performance Photographing the Cavitation on Model and FuU-Scale Propellers

146

and Blades 47.6

The

47.7

145

sec', ft

=

2,567.4

+

4,446.2

=

and

per sec.

This means that to keep clear of cavitating conditions the relative velocity of the water

145

H6

HYDRODYNAMICS

moving

past a liwp part of the 30-kl ship,

aft

+

ixpn\sso
AT, can not

cxcccti 83.75 ft

V equals the velocity can not e.\cee
DESIGN

IN SHIP

Concerning the ambient-pre.ssurc not sufficient

to

413

Sec.

consider

the

factor,

it

is

mean depth at

per sec. Since the ship speed

which a hydrofoil section or other movable body

V.

operates, such as the depth to the axis of a screw

the augment

,

=

50.t»7

33.08

W

per sec without the onset of

ft

For the equator of a

cavitation.

augment ACisO.sr^

the

AC is 25.34

;

per sec. This

ft

value of 33.08

if

r„

3-{liml sphere

iso0.t)7 ft per sec,

is less

than the limiting

per sec, so cavitation would

ft

not occur at the equator of the sphere at a depth of 37 ft. For the maximum diameter of a 2-diml

normal to

nxl,

ment

AT

depth

or 50.G7 ft per sec. velocity,

critical

would

cavitation

the

so at

ahead

begin

This given

of

the

It

is

entirely' its

po.ssible

for

a

blade

path, to cavitate through

an arc or region of low hydrostatic pressure and to set up objectionable vibration or other conditions from this cause. At the depth of the .shaft axis, or at the bottom of its path, it might not cavitate at

direction of motion, the aug-

l.OUa.

is

exceeds the

its

propeller.

element, at the top of

In

real,

surface

all.

viscous liquids like water, the over-the-

litiuid velocities

boundary layer are or the velocity

U^

less

at the inner edge of the

than the ship speed

V

relative to the imdisturbed

midsection of the rod.

water.

Aeration of the salt water raises its vapor pressure. This has the effect of diminishing numerically the augment of velocity At/ at which

than they would be o\-er the same body surface in an ideal liquid, becau.se of the displacement

some form

prediction of cavitation

of cavitation takes place.

At shallower

depths on a large ship, or at the shallower drafts and greater speeds customary on high-speed cavitating

vessels,

conditions

are

readily

en-

countered on the hull, the appendages, and the propulsion devices.

Bubble cavitation microscopic

of

vapor or

or

hastened by the presence submicroscopic pockets of is

and gas bubbles, and of cavitaform of impurities, animal or

air or air

tion nuclei in the

vegetable matter, or entities as yet unknown. The water nearest the .surface of the sea carries the mo.st air in solution; this

the surface

if

is

amount

augmented

is

disturbed, as during a storm.

There are more minute impurities carried

in

suspension in waters close to the land but there may be more nuclei of other kinds in waters far the

in

wliicli

citlici-

is

The ambient pressure p„ in The vapor, or the gas-air

to foretell the wor.st that

The

relative

.speed

U„

\'alues of c for fresh water, o\'er a temperature range from freezing to boiling at sea level, are graphed in Fig. -17. A. They are listed in Table

Temperature, deq C

2M

pressure of the iinciislurlKd

or

any

of

it.s

parts

(0 The efTectivc angle of attack «, if the part under conaidcration resembles a hydrofoil.

be expected.

ditions.

the water

of the

may

and propulsion devices which cavitate in the tropics under a given set of conditions may not do so in the polar regions under the same con-

water at the temperature concerned (c)

Fortunately,

Vapor-Pressure Data for Water. The vapor pressure e of water drops rather rapidly with temperature, so much so that appendages

Idihhlc or

water and the brxly or ship (d) The shape and proportions of (he body or .ship (c) The augment of velocity Af/ due to potential and other flow over and around a body, a .ship,

so that accurate

47.3

take account of at least six factors:

(b)

la.ver,

is difficult.

most appendages liable to cavitation are short, with boundary layers of insignificant thickness. In any case a prediction disregarding the boundary layer is usually on the safe side, if the prediction

40

maimer

Hheet cavitation appears to form in the water in which ships operate, a cavitation criterion must

(a)

potential-flow velocities are different

thickness of the boundary

from the land.

From

The

tio

SO

SO

TO

80

90

SHIP

Sec. 47.4

TABLE Degrees

47.a

AND PROPELLER CAVITATION

Vapor Pressure of

FRESH WATER

fob Various Temperatures

147

148

in l)R()M^ \ \Mi(,s i\ Mill' Table 47.b—Cavitation Numbeiis koh a Seiubs or Speeds

Veloc-

1)1

in

s!(;\

STANDARD SALT WATER

Src. 17.4

Sec. 41.5

SHIP

AND PROPELLER CAVITATION TABLE

Velocity, ft

per

sec

47.b— (Continued)

149

n nuonvNANfics

150

"niis

Nomoijroph Represents the E^ootion

Where q

,

V2Q(hthA-hv)

'—^

ship ofsicx liydrufuil

.\iiy

shaped

the Accelerotion Due to Grovity the Depth Below the Water Surface is the Equivalent Head Due to the Atmosphere is the Head of the Water Vapor,

i»

h

tates

may

i(

when

Viy

about 0.57 ft at 59 de<3 F the Speed of the Body

V

is

cr

(siqma)

t-

The

it

excessive angle of attack for a

be either

may

be

i)ositive or negative.

.said

section designed to produce

that for

any

hj-drofoil

the best shape

lift,

of

in feet,

— Ap on

maximum

the back that has the

spread

of the greatest reduced pressure across the chord,

without an excessivelj' low depression.

To Estimotc the Speed

The technical literature contains data derived from a limited number of cavitation tests made on hydrofoils under 2-diml flow conditions. A

of Incipient Covitotion

for a Body. Lou Q Stroiahteaoe on the Given h- and (J-vqIocs. The Resultant Cavitation fifseed is the Intercept

typical result, set

down

graphicall}' in Fig.

on the Speed or V-Scole.

it

is

one which, under the angle of attack to be expected in service, produces a distribution curve

-200

m

well

be for straight-ahead (low, cavi-

may

In general

the Covitatjon Index of the Body

is

incident flow. lifting foil

Sec. 47. f

no matter how

.section,

makes too great an angle with the

it

IS

h/\

Depth h

V

i.\

47.C 20 -o

100

80

90

40

50

60

70

Angles of Attock

a.

30

on

ZO

O'^cl

10

Hvjdrofoil

5i or

9 C^^IO :

^^^^ OZ

-04 -OZ

Nomogram for Relatino Submeroknce Depth, Cavitation Index, and Water Speed for Fjc. 47.B

Since incipient cavitation

<j

"

(po.

—

is

is

From

pressure

witli ffc« to

foil

coeflicient

From Sec. 47.5 and Fig. 47. D, En must diminish numerically

scctioim,

including

and

many

for

an

possible to calculate the ratio of the surface.

From

for all part,s

E, at any point, and hence the absolute pressures all points for any given set of undisturbedvelocity and initial-pressure conditions. Absolute pressures approaching the vapor pressure c of the liquid are in
number and a wide

variety of hydrofoil st;ctions, already made, arc ill

\\fA

|{i|)(.il

H'JI,

W.,

ASME,

Jour. Ai)pl. .Mcrli.,

li)l!),

cavitation occurs simultaneously on both surfaces

VlU^

at

li»l«wj

.1.

Im-

of tluwe u.sed

determine the pressure coeflicient or Euler number

44. .'5.

[Uaily,

infinite span, it is

this ratio it is pos.siblc to

Calculations for a great

Cl

shows that at negative angles of attack cavitation generally occurs on the face and at positive angles of attack on the back. 'riici;c is usually a single angle of attack at which

avoid cavitation.

propeller blade.s,

10

the relation

e)/(0.5pV"), the critical value diminishes as

the water s|K'cd incrca.ws. the

0.8

Cavitation Limits for Lift Coefficient AND Angle of Attack on a Typical Hydrofoil

involved, the cavitation

the critical value.

0.6

Coefficient

Fig. 47. C

Incipient Cavitation

index indicated here

0.4

Lift

nfiTciircd in Sec.

Vol. 71, p. 209],

if

the cavitation index

is

reducetl to a sufficiently

diagram similar to that referenced, (•X(('l)l that it is tierived by an analytic procedure I'm- a whole screw jiropeller, is given bj' J. F. ShaiiniMi and R. N. Arnold |IFS8. 1!):?S li):?9. low nuniljcr.

.\

Vol. 82, Fig. 18, p. 285|.

As

is

the case for the

lift,

drag, and

moment

data on hydrofoils, described and presented in Sec. 11. .5, the cavitation test data are of limited design a|)plication unless aconnpanied by section

drawings or tables of is

possible to

know

coordin.'ites of the foil. If it

also the chcuibvise pressure

SHIP

Sec. 47.6

— Ap

distribution across the

sentative angle of attack, so

AND PROPELLER CAVITATION

side for

much

some

repre-

the better.

Tables

X3.a,

or

41.e

Assuming a value

of

Pa

8(0.4447)

=

3.56

of 14.7 lb per in", a

psi.

vapor

pressure of 0.4 lb per in' and a mass density p of 1.9905 slugs per ft^, the cavitation index works

out as

V^-e _ From

[(3.56

~

q

+

14.7)

-

1.006.

— 2.7

or

at

+4.5

this

to the chord length

liquid

c.

number a

the adjacent

in

smaller numerically than the pressure

is

minimum

coefficient £'„ at the point of

absolute

pressure on the hydrofoil, cavitation occurs there,

hence

at

the

lowest-

point equals numerically

the

critical

the

pressure

cavitation

pressure

coefficient

number acR

As an example of the manner in which the diagrams of Fig. 47. D may be used, consider the situation at the leading edge of a symmetrical streamlined balanced rudder with an all-movable blade.

The rudder lies abaft a

portion of the upper

blade of a screw propeller where the rotational-

the lower diagram of Fig. 47. C

that

Rle

the cavitation

If

0.4]144

0.99525(50.67)'

it is to be parameter the hydrofoil will cavitate on the face or on the back at angles of attack greater numerically than

noted

plotted on a basis of the 0-diml ratio of the nose

radius

Taking a representative case, assume a hydrofoil similar to that diagrammed in Fig. 47. C to be running in salt water at a depth of 8 ft below the surface and at a speed of advance of 30 kt, or 50.67 ft per sec. The hydrostatic pressure is, from

151

cavitation

or tangential-flow

component

is

such as to cause

the water in the inflow jet to meet the leading

edge of the rudder at a given waterline at an Assume a nose radius of 0.25 ft,

angle of 10 deg.

a chord length of 10 ft, a nominal depth of submergence /i of 15 ft, and a ship speed of 18 kt (actually, the local velocity in the outflow jet

deg, respectively.

may

Then from the nomonumber a is about 3.3 if cavitation is to begin at 18 kt. The ratio of nose radius Rle to chord length c is 0.25/10 = 0.025. From the curve for a 10-deg gram

be greater than of Fig. 47.

B

this).

the cavitation

angle of attack in Fig. 47.

D the pressure coefficient where about —3.2. Then

E^ at the point

of lowest absolute pressure,

cavitation will

first

<jcB is 3.2,

and the

to create a gradient

appear,

is

differential pressure available

which

will cause the

follow the rudder section closely

is

water to

represented by

a cavitation number of only 3.3. The "lee" or — Ap side of the rudder section in question is, therefore, just on the verge of cavitation at the given speed.

Contours for pressure minima Ap/q, (2) thickness ratio, and (3)

(1)

for ogival

and

airfoil sections,

given by K. E. Schoenherr "0

0.05 0.06 0.07 0.03 0.04 O.oa 0.01 Ratio of Leadinq-Edae Radius R^e to Chord Lenoth c.

Fig. 47.D

Cavitation, Lift-Coefficient, and

Angle-of-Attack Data for a Stmmetrical Hydrofoil

Fig. 47. D,

by

P.

adapted from a set of graphs given

Mandel [SNAME,

1953, Fig.

7,

gives the average pressure coefficient E„

p. ,

471],

at the

point of

minimum

number

of 2-diml symmetrical hydrofoils at four

different

angles

absolute pressure, for a large

of

attack.

The

£^„-values

are

terms

in lift

of

coefficient,

respectively, are

[SNAME,

1934, Figs.

19-20, pp. 109-112]. These sections are suitable for use on propeller blades.

47.6 Cavitation Data for Bodies of Revolution and Other Bodies. Cavitation may take place on many parts of a ship and its appendages which do not even remotely resemble the hydrofoils discussed in the preceding section.

A

considerable

have the forms of bodies of revolution, or they can be simulated by 3-diml axisymmetric forms, such as certain types of

number

of these parts

bulbs incorporated into the forefoot. Cavitation data are available for

a

great

m DROOYNAMias I\ SHIP DESIGN

152 variety tested

of in

yaw

zero

ends of ivlimlrical bodies, n variable-pressvirc water funnel at londiiiR

angle.

The

princi|)al

source of these data,

and Pressure Distribution: Head Forms at Zero Angle of Yaw," by H. Rouse and "Cavitation

McNown

S.

J.

[State

Univ.

Iowa Studies

in

Eng'g., Bull. 32, 1948], gives the magnitude and

the meridional-distance distribution of pressure coefficient

about a

series of fourteen

head shapes,

covering most practical applications. In addition there are recorded the shapes, axial positions, and

dimensions of the cavities or of the envelopes ("pockets") of tiie regions in which vapor bubbles

were formed around the bodies carrying these heads.

Diagrams

and 3

2,

1,

of Fig.

17.

E

give the

data for a hemispherical head, a 1-caliber ogival head, and an ellipsoidal head having a major-axis to minor-axis ratio of 2, adapted from the referenced report. The several curved lines represent the boundaries of axial cavitation

,

Leng th ond

I

Number

tf •

H

0.20\

-\

037D

Covity Boundaries,. ore Indefinite

Bod\( of

Covitotion

Revolution

Number

tf

•

with

a

Apprommote Shape u-

1

Covitotion 'Fbck e t" or Covit^

Fbsition o f

for Covitotion

I

T

"pocket"

Hemispherical

Head

No Covitotion

for rf

g

of

Rjcket' or Covity '

>0.50

Sec. 47.7

SHIP

Sec. 47.

AND PROPELLER CAVITATION New

the

NECI, (8)

King's

153 College

Tunnel,"

Cavitation

1953-1954, Vol. 70, pp.

121-150,

DISS-

DISS; SBMEB, Apr 1954, Fig. 4, p. 284 "Comparative Propeller Tests," 7th ICSH, SSPA Rep. 34, 1955, Figs. 1-7 on pp. 170-176 and Figs. 11-14 on pp. 180-183.

Although

it is

not yet (1955) standard practice,

the characteristic curves of

-q,

Kt

,

and Kq

of

diagrams similar to that of Fig. 47.F should be accompanied by drawings or sketches showing the location of the cavitating regions on the blades (face or back or both), the type of cavitation encountered

features

visible

(bubble or sheet), and other

a

in

water

variable-pressure

tunnel, for each value of the cavitation index or for each set of test conditions. This is

the 1937

ASME

done for paper of L. P. Smith, referenced

by F. H. Todd Posdunine paper in INA, 1944; Report 6 by H. Edstrand; and for

in Sec. 70.40; for the discussion of the V.

L.

SSPA

for the

the L. C. Burrill and A.

Emerson paper referenced

in the preceding paragraph.

0.4

0.6

0.8

1.0

\.Z

1.4

Advance Coefficient

1.6

J

Fig. 47.F Typical Open-Water Test Data For A Model Propeller, Carried into the Cavitating

Range

47.8 Photographing the Cavitation on Model and Full-Scale Propellers. The visual observation of cavitation on screw propellers when mounted by themselves in variable-pressure water tunnels, initiated by C. A. Parsons in the early 1900's and carried on extensively since the late 1920's, has now reached the stage where excellent instantaneous photographs can be taken

also Vol. 60, pp. 448-452], and by L. C. Burrill and A. Emerson on pages 140-147 of reference (7) following.

The technical hterature contains a considerable number of cavitation characteristic curves for screw propellers, among which may be listed the following: (1) (2) (3)

Schoenherr, K. E.,

PNA,

1939, Vol. II, Fig. 32, p. 182

Taylor, D. W., S and P, 1943, Fig. 143, p. 116 Edstrand, H., "The Effect of the Air Content of Water

on the Cavitation Point and Upon the CharacterSSPA Rep. 6, 1946 Rouse, H., EH, 1950, Fig. 63, p. 930. These are typical curves only, for which no hydrofoil data or test istics of Ships' Propellers,"

(4)

conditions are given. (5)

(6)

"Comparative Cavitation Tests of Propellers," 6th ICSTS, 1951, published by SNAME, 1953, Figs. 16-19 on pp. 78-81; Figs. 23 and 24 on pp. 85-86 Gawn, R. W. L., "Results to Date of Comparative Cavitation Tests of Propellers," SNAME, 1951, pp. 172-213. These give the results of "international" tests of selected

model propellers

in a

number

of variable-pressure water tunnels. (7)

C, and Emerson, A., Some Observations from 16

Burrill, L.

"Propeller Cavitation: in.

Propeller Tests in

and

later

Many

reproduced in the technical literature. photographs are to be found in the

of these

more recent cavitation

references listed in Sec.

47.13 at the end of this chapter.

Fortunately for the marine architect there are techniques and procedures, developed in the early 1950's,

by which

graphs

may

still

also be

and motion-picture photo-

made

of full-scale ship screw

under operating conditions. These photographs are made through a transparent propellers

window

in

the shell near the

propeller.

present availability and use of powerful

The

artificial

lighting dispenses with the former necessity of

running the vessel in the sunshine and in the clear water which is usually found only in the

open

sea.

The motion

pictures are stroboscopic in

nature so that they give the impression of a particular propeller blade standing

still

or

moving

slowly in the ahead or astern direction.

To

facilitate

subsequent analysis and for in-

formation during the observing periods the screwpropeller blades may be marked in advance with suitable identifying letters, numerals,

and

signs.

HVDROUVNAMIC.S

151

Examples puMi.shctl by

photoRraphs of this kind arc \V. Fisher ("Photonraphy at Sea

of J.

of Ship Propeller Cavitation,"

\o\.

(^18,

pp.

m ami

1!)

XKCI, 1951-1952,

5G9-570]. It

is

K.

to be expeetetl that the instrumentation

PXA,

E.,

1939, Vol. II, pp. 175-17G).

In 1932 E. F. Eggert developed a set of rela-

which enabled the propeller user or

tionships

with reasonable accuracj',

designer to predict,

the rate of rotation or the blade-section velocity at which the propeller thrust would begin to o(T

and procetlures for making shipboard cavitation photographs on screw propellers will improve

Sec. 47.9

depth of submergence of advance [Schoenherr,

or the associated speetl

D-1 through D-S). Other

examples are emhotlietl in a paper by A. F. Weeks, entitled "Ship Propeller Cavitation Patterns," presented at the XPL Sympasium on Cavitation in September 1955 [SBSR, 3 Nov 1955, pp.

DESIGN

IN 6H11'

before, not a function of the

from cavitation

SXAME,

fall

efTects ["Propeller Cavitation,"

1932, pp. .58-74].

relationship, embodj'ing

Discussions of this

somewhat

binations of variables, arc found

different

com-

in:

rapidly. This will provide the naval architect with

extremely valuable data which

and analyzed 47.9 sis of

may

be studied

at leisure.

Propeller Cavitation Criteria.

An

propellers,

fast naval

\essels

led to the

establishment of a criterion proposed by S.

Barnaby, involving a

maximum

figure emploj-ed

was 11.25

W.

average unit

loading on the propeller-blade area.

The

original

lb per sq in,

corre-

sponding to a pressure coefficient (based upon atmospheric pressure) of 11.25 divided by 14.7, or approximately 0.765. This unit loading was subsequently raised by Barnaby to 13.0 lb per sq

in,

based

corresponding to a pressure coefficient

on

atmospheric

neither case

the

depth

W.

(3)

Van Lammeren, W.

\V.,

S and

,\.,

UPSS,

II, p.

178

110-117

P, 1043, pp.

P.

1948, pp. 180-182.

Still later W. P. A. van Lammeren worked out a relationship between the two 0-diml ratios

P/D)] and [(t,- (.4 c/.4o) (virtual P/D)] an excellent indicator of the point where the thrust breaks down on a screw propeller [De Groot, D., NSP Rep. 89; Schip en Werf; Gth ICSTS, 1951, published by SXAME, 19.53, Fig. 30 and pp. 93-95]. ^\Tlen plotted in graph form [.//(virtual

which

is

this appears as the simple curve of Fig. 47. d. The graph is based on the tests of many model propellers, all of which give results remarkably close to the line, independent of the tj'pe of blade

0.884.

In for

carrying out cavitation tests on model propellers,

propellers.

the rate of rotation at which thrust breakdown

of

pressure

submergence

of

of

the

by upon

Taylor,

J.

M.

Irish,

and

others, ba.sed

a limiting tip speed for any propeller, independent of-

Taylor, D.

was there any allowance made

Sub.sequently, different criteria were proposed

D.

Schoenherr, K. E., P.\.\, 19;», Vol.

(2)

analj'-

the loss of thrust due to cavitation on ship

when it first occurred on some sixty or more years ago,

(1)

or related to the propeller loading but,

as

section.

will

is

thus possible to predict,

before

take place.

The arc

It

indications given

still

purposes

sufficiently if

by the graph precise

for

the actual or average

of Fig. 47.

engineering

P/D

ratio is

SHIP

Sec. 47.10

used in place

AND PROPELLER CAVITATION

P/D, and

the virtual

of

if

expanded area A e replaces the developed area Ad W. H. Bowers, of the TMB staff, devised a number of formulations whereby a quick approximation could be made by a ship designer of the rate of propeller rotation beyond which the thrust is affected by blade cavitation. One method of rapidly solving the equation given hereunder was a circular slide rule devised by Bowers and L. W. .

Sprinkle in 1947. It

Hub

and

Cavitation

The phenomenon

Vortexes or Swirl Cores.

of

cavitation abaft a rotating screw-propeller hub,

and the production of hub vortexes or swirl cores, are discussed and illustrated in Sec. 23.14 on pages 337-339 of Volume I. This is an important feature

the behavior

of

of

high-speed

vessels

because of the damaging effect of this cavitation

upon appendages which Within

not possible to describe

is

155

Hub

Predicting

47.10

the

the

lie

in its path.

1945-1955

period

been

has

it

and to photograph cavitation

method here but the criterion employed by Bowers took the form, expressed in the symbols

possible to produce

of this book:

circulating-water channels, and model basins. It

the exact

37,500(1

-

Suf'^QiA

+

hn

-

of this

appears from observation of model propellers at atmospheric pressure in the latter two types of facility that the hub vortex is a rather unstable

hy)

affair,

where n are in

To

is

PD

(47.ii)

all

other linear dimensions

rpm and

in

appearing and disappearing with apparently

no change

in test conditions.

believe that

appUcation of this formula,

take the case of the propeller designed for the ABC ship in Chap. 70 of Part 4, and shown in

it is

far

more

There

is

reason to

stable in the full scale.

On it

ft.

illustrate the

type in variable-pressure water tunnels,

the basis of the swirl-core theory of Vi§kovic should eventually be possible to predict the

presence of a swirl core and

approximate

its

diameter behind the taper end of the hub fairing

speed of 20.5 kt and for an assumed typical blade

of a screw propeller. Assuming that it is possible to impart to the water in contact with the outside of the hub, in way of the blade, a tangential

section at 0.8fiMa» are as follows:

velocity equal to that of the

Fig. 78.L.

The necessary

basic data for the trial

hub

surface, the

resulting centrifugal force at a smaller radius

Real-slip ratio, Sr (actually Skt), from Fig.

0.238

78.Nb

Atmospheric-pressure head Ha assumed 33.0 Hydrostatic head at 12 o'clock blade position, hn equal to [26 — 10.5 —

ft

7.5

ft

0.8

ft

,

(0.8)10], for 0.8i2M.x

+

Value of {Ha (33.0

+

7.5

Mean-width

hn

-

—

,

hv)

assumed

39.7

Ph

to the shaft axis,

the wheel.

0.211

The equation

Blade-thickness fraction to/D, from

a vortex 0.049

Fig. 78.L

Pitch P, assumed as 0.982Z) at O.SKm..

Substituting in Eq.

plus the hydrostatic pressure

measured to the actual water (wave) surface over

Cm/D

from Fig. 78.L Diameter D

be taken as somewhere between 0.5 and per sq in. The ambient pressure pa> is the atmospheric pressure Pa existing at the time 1.0 lb

=

0.8)

ratio,

be balanced against the probable vapor and gas pressure in the water. For propeller hubs not deeply submerged in sea water this lower limit

may

,

Vapor-pressure head hr

coil,

of

motion of a water particle in

whirling around a vortex core,

-

1

ap

,

19.64

ft

20.0

ft

pdR

U

where

is

the local velocity and

radius [Eisenberg, P.,

(47.ii)

0.238)'*''''"

there

TMB

R

is

the local

Rep. 712, Jul 1950,

FHA, 1934, pp. 213-214]. From may be derived the relationship

14,399

whereupon n

in

the expected rate of Sec. 70.26.

p at center of vortex core where F (capital gamma)

rpm

above rotation of 97.2 rpm from

is

this

<-')(ii)

(19.64)20

=

is

ft

pp. 4-5;

37,500(1

R

may

119.7. This is well

= p„ — is

(47.iii)

the circulation in the

surrounding the core, p„ is the ambient pressure in the undisturbed liquid at the same vortex

coil,

depth as the center of the

core,

and Rq

is

the

HYDRODYNAMICS

156

outer nulius of the vortex core radius of the vortex

inner

tlio

iiiul

hub cavity or by the root-vortex metliod may be found considerably more difficult. It involves a knowledge or an estimate of the and

"A Review

its size

—

—

and back of a any additional elTect of

difTerences between the face shoulii include

25-27 there are

it

may

of

be

ships that the core persists for at least several

means that it will be the vicinity of any other part of the to be placed abaft the shaft axis and

propeller diameters. This

the propeller.

comes

o(T

the

hub

fairing

with the propeller axis but it Ls often otT.set from the trailing end of a blunt hull. Whatever may be its exact position, it swings rapidly into in line

when this is not The diameter

the line of the aiijacent flow

parallel in direction to the shaft axis.

of the swirl core

is

increased

air gets into

if

it.

The

Prediction of Cavitation Erosion.

47.11

is

in five parts:

Theories of Cavitation lOrosion

II I

Factors AffectingCavitaf ion Erosion Intensity

I

V

Methotis of Testing Erosion Resistances of Various Materials.

Tables VIII and

assumetl from past observations on models and

swirl core usually

56 references in the technical

report

Historical Introduction

I

Although the data on the longitudinal extent

The

of

relative

fresh

IX

list

many

to

cavitation

resistance

type turbines of water-power plants [.\SNE, Nov 1940, pp. 547-549( but this type of construction has been found not too successful on ship append-

attachment and perhaps because of harmful galvanic action between the steel cladding and adjacent bronze propellers. Good design and construction requires the greatest practicable initial smoothness of all ages, perhaps becau.se of inadecjuate

to the ferrous material underneath,

the vapor pressure of water. This

polypha,se alloys.

boundaries

grain

Many

than

corrosion-resisting steels

are austenitic alloys of this type;

among them

the

13Cr-87Fe alloy

in

Cast-steel blades with corrosion-resisting steel

parlance, only a single phase. Single-pha.se alloys

narrower

erosion

cladding have been used with success in propeller-

surfaces

much

alloys in a scale

and sea water, respectively.

and tests to date indicate that the materials which are most resistant to ca\'itation erosion are solidsolution alloys which have, in metallurgical results of metallurgical in\'e.stigations

have

on Cavita-

inter1\'

a swirl core are somewhat meager

listed

The

literature.

I

present in

11

blade.

ference between adjacent blades.

ship likely

of Published Information

-17.

Committee Rep. ACC/2C/54, N151/54, N316/54 (C.M.L. Report RBS)], stamped 8 October 1954. On pages

circulation at the root sections or of the pressure

It

Sec.

tion Erosion," (Admiralty Corrosion

coil.

Prciliction of the existence of a

swirl core

IN SHIP DESIGN

Any

likelj'

to be exposed to cavitation attack.

projecting

irregularity,

waviness of a surface, cavitation

definite

be expected to initiate the pressures in the region approach

if

why

reason

including

may

is

one important

the curved backs of propeller blades

and hydrofoil surfaces .should, if anything, be more regular and more smootii than the faces.

may

is a good example. metal intended to resist erosion by cavitation should have high resistance to lifiuid corrosion,

downstream from a pronounced change in shape of the solid surface. Nicks and turned-over

under the conditions

regions along a leading edge are notorious offenders

A

well

a.s

in

which

it is

to be used, as

high fatigue strength [Boetcher, H. N.,

"Failure of Metals

Due

Cavitation

to

Experimental Conditions," Trans. AS.MI], .'>8-l,

Under II

V!';-

Numerous

tests of a

wide

be expected to occur

well

in this respect.

edge

may

A

sharp, deep nick in the leading

leave a trail of erosion at the radius of

the nick, extending irregularly

all

the

way

acro.ss

the blatlc.

Vol. 58, Jul ID.iO, pp. \]-)-i-m)\.

have indicated a

Erosion of the surface

varictj' of materials

definite superiority in resistance

Pits l)art

and depressions the

of

in

waviness

a surface, not forming a previou.sly

mentioned,

to cavitation erosion on the part of certain alloys.

appear to have much

A

resiKinding projections. However, holes through

brief list of the.se allf)ys, with references to the

pubhshed one series

W.

L.,

test data,

is

givrjii

of tests (Stewart,

in Sec.

W. C, and

70.45.

In

Williams,

"Investigation of Materials for Marine

ASTM, 1910, Vol. 4f), pp. 8:i(3~8l5] the best all-around material was found to be a Propellers,"

0(5.14 nickel-

28.10 co[)per-

There has recently been

-'{.05

silicon alloy.

i.ssued

a paper entitled

less initial effect

than cor-

such as are sometimes drilled for permit jets of water to .squirt through from the face to the back. The discontinuities thus formed in the flow may often be as the

blades,

handling

jiurpo.ses,

damaging 47.12

.'is

a solid jirojection in place of the hole.

Propeller

cavitation.

The

Performance Under Super-

general as])ects of the piTfnrni-

SHIP

Sec. '17.13

AND PROPELLER CAVITATION

L57

ance of screw propellers in the supercavitating

Engineering

range are described in Sec. 70.40 of Part 4. The design comments given there are likewise general

Translated by E. F. Wilaey, Reclamation, Nov 1936. (9)

in nature.

make

to

performance for high-power and high-speed Selected Cavitation Bibliography.

published literature on liquids,

all

its

is

almost

(12)

especially

marine

in the

that relating directly to

field.

down

here.

(14)

(3)

4,

pp. 68-73

and Barnaby, J. W., "Torpedo Boat Destroyers," ICE, Vol. CXXII, Part IV,

Thornycroft,

1894-1895, (4)

1893,

J.

I.,

J.

p. 51ff

Wood, R. MoK., and Harris, R. G., "Some Notes on the Theory of an Airscrew Working in a Wind Channel," ARC, R and 662, 1920 Brodetsky, S., "Discontinuous Fluid Motion Past Circular and Elliptic Cylinders," Proc. Roy. Soc, London, Ser. A, Feb 1923, Vol. 102, No. A718, pp. 542-553

(6)

Mueller,

J.,

Jun (7)

I.,

"The Mean Value

(8)

Van

Iterson, F.

ficielle

Roy.

K.

T., "Cavitation et

Tension Super-

(Cavitation and Surface Tension)," Proc.

Acad.,

Amsterdam,

1936.

Abstracted

in

B.,

M.

Strut

Compared with

Section

the Bureau of Ships Standard Strut

TMB S.,

Rep. 879, Jan 1948

and

Shaffer, P. A.,

Mod.

"Drag

in Cavitat-

Phys., Jan 1948, Vol. 20,

Rouse, H., and

McNown, J. S., "Cavitation and Head Forms at Zero Angle

Pressure Distribution;

(24)

of Yaw," IIHR, Studies in Eng'g., Bull. 32, 1948 Knapp, R. T., and Hollander, A., "Laboratory Investigations of the Mechanism of Cavitation,"

(25)

Gawn, R. W.

Trans.

of the Fluctuations in

pp. 380-384

J.

pp. 228-231

"tlber den gegenwartigen Stand der

Pressure and Pressure Gradient in a Turbulent Fluid," Proc. Camb. Phil. Soc, 1936, Vol. 32,

for

ing Flow," Rev.

1928, Vol. 22, pp. 423-426

Taylor, G.

Water," Jour. Appl. 162-172

and Mason, W. P., High Sound Pressures," Lab. Monograph B-1507, publ. in Jour.

TMB-EPH

Section," (22) Plesset,

(23)

Kavitationsforschung (On the Present Status of Cavitation Research)," Die Naturwissenschaften,

in

"Predicted Cavitation Characteristics for

v.,

the

Those

M

(5)

D., and Whiteley, A. H.,

18, pp.

(21)

Immersion and Speed on the Rupture

ATMA,

Feb 1947, Vol. H. B., Johnson,

ment of Forms Having Specified Critical Cavitation Numbers," TMB Rep. 647, Sep 1947 Macovsky, M. S., Stracke, W. L., and Wehausen,

(19)

in the Propeller Stream),"

1942

(20)

Normand,

Water

Nov

Acoust. Soc. America, Jul 1947, Vol. 19, pp. 664-677 Dieudonne, J., "Resultats Obtenus k la Mer avec des Helices en Regime de Cavitation (Results from Sea Trials with Propellers Operating in the Cavitating Region)," ATMA, 1947, Vol. 46, pp. 253270. The data were taken on various torpedoboats and destroyers at high speed. Walohner, 0., "Contribution to the Design of Ship Propellers without Cavitation," AVA, 1947 Vennard, J. K., "Elementary Fluid Mechanics," 1947, pp. 329-332 Bell, L. G., "Some Model Experiments on the Effect of Blade Area on Propeller Cavitation," INA, 1948, Vol. 90, pp. 79-91. There are some good cavitation photographs opp. pp. 86-87. Eisenberg, P., "A Cavitation Method for the Develop-

(16)

(18)

Vol.

E., McElroy, W. "On Cavity Formation

Bell Tel.

(17)

of Propeller

Rep. 495,

Effect of the Air Content of

"Properties of Liquids at

Reynolds, Osborne, "On the Causes of the Racing of the Engines of Screw Steamers," INA, 1873, pp. 59-60

of

TMB

1946 Harvey,

(15) Briggs,

historical picture:

J.-A., "Note sur I'lnfluence de I'lmmersion de I'Hfelice et de la Vitesse sur la Rupture du Cyjindre d' Eau Actionne (Note on the Influence

"The

H.,

Phys.,

Chaps. 7 and 23 as well as to that in this chapter in Chap. 70 of Part 4. The first three references help to fill out the

(2)

and Observed Speeds About Two- and Three-Dimensional

Water on the Cavitation Point and upon the Characteristics of Ships' Propellers," SSPA, Rep. 6,

and

(1)

of

B., "Calculated

Bodies in Water,"

Some important papers

These apply to material in

Freeman, H.

(13) Edstrand,

not Usted, and some published since 1947 have either been referenced previously in this chapter or are set

Bureau

I.,

of Cavitation

issued, as

work

95ff.

Camb. Phil. Soc, 1938, pp. 534-539 "Rotation Losses at the Rear of TurboMachine Runner Wheels," Escher Wyss News, 1941, Vol. XIV, pp. 14-19

immensity. In December 1947

that time,

S.

p.

Fluid," Proc. (11) Viskovid,

the David Taylor Model Basin prepared and

TMB Report R-81, "An Annotated BibUography of Cavitation." This contains references to most of the material published up to

U.

142,

"The Mean Value of the Fluctuations and Pressure Gradient in a Turbulent

in Pressure

phases of cavitation in

including cavitation erosion,

staggering in

Vol.

W. T., "Flow of Boiling Water Through and Pipes," NECI, 1936-1937, Vol. 53,

(10) Green, A. E.,

craft.

The

1936,

p. 65ff

reliable predictions of supercavitation

47.13

Bottomley, Orifices

While the references of that section contain data relative to the variation in propeller thrust at high rates of rotation, there are no systematic data which permit the ship or propeller designer

(London),

ASME,

NECI, D124 (26) Eisenberg,

L.,

Jul 1948, Vol. 70, pp. 419-435

"Cavitation of Screw Propellers,"

1948-1949, Vol. 65, pp. 339-373, P.,

and Pond, H.

L.,

"Water Tunnel

Investigations of Steady State Cavities,"

Rep. 668, Oct 1948

D105-

TMB

HYDRODYNAMICS

158 (27) IMakp,

V.

Acouiitics

Liquiilii,"

Tech. Hop-

Crump,

'Tlio

Jr.,

('...

I.2,

Onst>t

Hea.

I^^ib.,

Sep 1919

S. F.,

TMB

tion, Cal. Inst. Tech., 19-19

"On

(30) Kiscnbcrg, P.,

the

of the principal references

No.

of Cavitation in a Large-Scale

Tank

SNAME,

IME,

St.

Dec

Jiunes Clayton

its

Lecture,

Vol.

1952,

166,

C, and Emerson, A., "Propeller CavitaSome Observations from 16 in. Propeller Testa

in

the

New

King's College Cavitation Tunnel,"

NECI, 1953-1954,

Vol. 70, Part 2, pp. 121-150,

D185-D188. There are photographs

of

hub vor-

texes or swirl cores abaft model propeller hubs in 17(a) and 17(b) on p. 149; also cavitation photographs of model propellers on pp. 149-150. Tulin, M. P., "Sfe.i
(52)

May

1953

"A Brief Survey of Progress on the Mechanics of Cavitation," Rep. 842, Jun 1953, revised edition; pp. 21-24 contain a list of 44 references Numachi, F., "Cavitation Tests on Hydrofoils in Cascade," ASME, Oct 1953, Vol. 75, pp. 1257-1269 Knapp, R. T., "Present Status of Cavitation Research," Mech. Eng'g., Sep 1954, Vol. 70, pp.

TMB

(55)

Gawn, R. W.

L., "Results to Date of Comparative Cavitation Testa of Propellers," SNAME, 1951, pp. 168-216

Russian) "The Collapse and Rebound of a Gas Bubble," Jour. Appl. Phys., Jan 1952, Vol. 23, pp. 14-17 (in

(40) Trilling, L.,

"The Growth

or Collapse of a a Viscous Compressible Liquid," CIT Ilydr. Lab. Rep. 26-4, 1 Apr 1952 Kcrmeen, R. W,, "Some Observations of Cavitation on Hemispherical Head Models," CIT Hydro. Ijib. Rep. E-35.1, Jun 1952 Wacsclynck, R., "Calcul dc la Pouss6c de rh61ice en rt'gimo Cavitant (Calculation of the Thrust of Cavitating Propellers)," ATMA, 1952, Vol. 51, pp. 365-388. On page 382 there is a list of 10 references, some of them not given here. Garabcdian, P. R., Ix:wy, H., and Schiffer, M., "Axially Symmetric Cavitational Flow," Appl. Math, and Statistics Lab., Tech. Rep. 10, SUnford Univ., 25 Apr 1952 Parkin, U. R., "Scale Effects in Cavitating Flow," CIT Hydro. Ijib. Rep. 21 8, 31 Jul 19.'')2 F.

Spherical

(40) GilliarK,

and

Anthony Falls Hydr. Lab. Project Rep. 42, 1954. There is a bibliography of 16 items on

tion:

75-97

Jour. Theor. Physics, U.S.S.R., 1951, Vol. 21, pp.

(46)

Mechanics

"Cavitation

pp. 31-32.

(54)

"Compara-

(39) Shalncv, K. E., "Cavitation of Surface Roughnesses,"

(44)

T.,

(51) Burrill, L.

Supts., Washington, 1951,

1953, Subject 3,

tive Cavitation Testa of Propellers," pp.

(43)

R.

pp. 150-163 (50) Olson, R. M., "Cavitation Testing in Water Tunnels,"

Numachi Nozzle

770, Jul 1951

published by

(42)

Knapp,

Relation to the Design of Hydraulic Equipment,"

OS Influenced by the Air Content of the Water,"

T.MB Rep.

(37) 6th Int. Conf. Ship

(41) Gihnore,

1,

1

TMB

S. F., "Critical Pressures for the Inception

206-220

Some

(53) Eisenberg, P.,

in 1951)

(38)

for

Jan 1952, Vol.

.\nalvsifl,

1952, revised edition

—

Oump,

Theorems

"E.xi.-itence

M., ".\.n E.\pcrimental Study of Single Bubble Cavitation Noise," Rep. 815, Nov

TMB

(36)

Jr.,

(tS) Harrison,

TMB

on pp. 63-70, a

contains,

B.,

J.

lytlrodynamical Free Boundary Problems," Jour.

Rational Mech. and

of

Rep. 712, Jul 1950. This report, list of about one hundred on the subject. (31) Rouse, H., "Engineering Hydraulica," 1950, pp. 29-31 (32) Birkhoff, G., "Hydrodynamics," Princeton Univ. Press, 1950 (33) Konstantinov, W. A., "Influence of the Reynolds Number on the Separation (Cavitation) Flow," Transl. 233, Nov 1950 (34) Birkhoff, C, Plessct, M., and Simmons, N., "Wall Effects in Cavity Flow I and II," Quart. Jour. Math., Part I, Jul 1950, Vol. VIII, pp. 151-168; Jan 1952, Vol. IX, pp. 413-421 (35) Rattray, M., Jr., "Perturbation Effects in Bubble Dynamics," CIT Doctoral dissertation, issued as a CIT Hydrodyn. Lab. report under ONR Contract N6onr-24420 (NR-062-059), (undated but issued Cavitation,"

1

(49)

Mechanism and Prevention

Sec. 47.13

Flows with Free Boundaries," Jour. Rational Mcch. and Aii;dysi«, .-Vpr 1952, Vol. 1, No. 2 (47) Serrin,

"Determination of Critical Prcssurc.i for thp Inception of Cavitation in Krcsli and Sea Water as Innucnccii by Air Content in the Water," Rep. 575, Oct I'oW (29) Schneider, A. J. R., "Some Compressible EfTects in Cavitation Bubble Dynamics," Doctoral disserta-

(2S)

DESIGN

IN SHIP

CaviUtion in Harvard Univ.,

of

I).,

R.,

Bubble

in

"(Ini>|U('hi-KH

of

Axially

Symmetric

731-734;

ASNE, Feb

On p. 50 a bibliography of

1955, pp. 44-50.

of the latter reference there

is

six items.

(56)

Knapp, R.

T.,

"Recent Investigations

of the

Me-

Damage," NovemberASME paper 54-A-106, presented December 1954 (copy in TMB library). The chanics of Cavitation and Cavitation in

paper describes experiments in a variable-i)ressure water tunnel in which a torpedo-shaped model, run under cavitating conditions, was surrounded by a rather large annular cavity just abaft the forward shoulder. At water speeds above a certain

minimum

this cavity

was

filled

(or partly filled)

with a reversed or reentrant flow rushing forward as a thin sheet next to the model surfuci'. In other words, the cavity accompanying the normal form of sheet c.ivitation was not a periodically

steady-state affair, even in

its

forward and middle

which alternately from the downstream end of the cavity jinil was then swept aw.iy. Cavit.it ion erosion on the aluminum model occurred under tiic region covered by the periodically advancing and retreating reentrant flow. The author Ii.hIs 15 references on p. 12. (57) Kermeen, R. VV., McGraw, J. T., and I'.iikin, H. li., "Meclianism "f Caviljitiim Incepliim ;ind llic- lieportions, because of the water

rushed forward into

it

SHIP

Sec. 47.13

AND PROPELLER CAVITATION

lated Scale-Effects Problem," Trans.

ASME, May

1955, Vol. 77, pp. 533-541; a review of this paper to be found in Appl.

Meoh. Rev., Jan 1956,

p.

is

W., and Johnson, V. E., Jr., "Turbulence and Boundary Layer Effects on the Inception of Cavitation from Gas Nuclei," MIT Hydro. Lab.

Techn. Rep. 21, Jul 1955. On pp. 63-65 there is a bibliography of 38 items; most of those relating directly to cavitation are included in the

list

of

the present section. (59) On 14-17 September 1955 there was held at the National Physical Laboratory, Teddington, England, a

symposium on

cavitation in hydrodj'namics.

The authors and

Scale-effect factors

(4)

Effects on

(5)

Cavitation damage.

29

(58) Daily, J.

159

(3)

hydrodynamic performance

The complete proceedings are to be found in a volume issued by the NPL, Teddington, entitled "Cavitation in Hydrodynamics," H. M. Stationery London, 1956.

Office,

(60) Tulin,

M.

P.,

in

3

"Supercavitating Flow Past Foils and

NPL, Teddington, Symp. on

Struts,"

Cavitation

Hydrodynamics, Sep 1955; abstracted 1955, pp. 570-571

in

SBSR,

Nov

(61) Burrill,

titles of the twenty-one papers presented during this symposium are given in SBSR, 25 Aug 1955, pp. 255-256. The subjects

Vol.

considered were:

some

L.

C, "The Phenomenon

of Cavitation,"

Second Nav. Arch. Congr., Trieste, 14-16 published in

1955; 2,

No.

15, pp.

Int.

Shipbldg.

Prog.,

May 1955,

503-511. This paper contains

excellent photographs of cavitating

(1)

Factors governing cavitation inception

propellers, including

(2)

Experiment techniques

leaving a blade trailing edge.

one

(Fig. 13)

model showing eddies

cnAriKR

18

Data on Theoretical Surface Waves and Ship Waves 48.1 48.2

Purpose of This Chapter ThcoreticAl

Wave

Patterns

160

on

a

Water

Surface

48.3

IGO

Ilognor's Conlribiition to the Krlviii W:ivc

Systom 48.4 48.5 48.6

Summary

161 of the

Elevations and

Troohoidal-Wavc Theory

Sloix-.i

of the Troclioidal

.

Wave

161 1

63

Tabulated Data on Length, Period, Velocity, and Frequency of Deep-Water Trochoidal

Waves

166

Deep-Water

48.

Orbital Velocities for Trochoidal

Waves Data on Steepness Ratios and Wave Heights

166

48.8

169

48.9

Design Purposes Formulas for Sinusoidal Waves for

1

70

•IS.

Spc.

WIND-WAVE AND SHIP-WAVE DATA

^SA

deg for a traveling pressure point, as described in Sec. 10.6 on page 174 of Volume I [Hovgaard, W., INA, 1909, Vol. 51, table facing p. 260 and PL XXIV; Taylor, D. W., S and P, of 19.47

1943, pp. 27-28].

Hogner's Contribution to the Kelvin System. Owing to an apparent misunderstanding of the exact nature of a wave-pattern diagram which was published by Ijord Kelvin in the papers referenced in Sec. 10.5 on page 170 of Volume I, tlie planform illustrated in Fig. 10. of that section has for the past half-century been described in many text and reference books as the exact crest pattern developed by him. E. Hogner brought out, in the 1920's, the fact that the figure given by Kelvin showed only "the envelope curves of the crests of the two-dimensional waves from which he has constructed his three-dimensional waves" ["A Contribution to the Theory of Ship Waves," Arkiv for Matematik, Astronomi och Fysik, Stockholm, 1922-1923, Vol. 17, paper 12, footnote on p. 42]. Kelvin's mathematical formulas actually showed a phase difference at the boundary planes (marked "Line of Crest Intersections" in Fig. 10. B of Volume I) but this was apparently overlooked by most of those 48.3

Wave

who worked

in this field in the 1900's and 1910's, Hogner brought it to fight. Depending upon the assumptions made and

until

the approximations employed,

Kelvin's earlier

theory gives a phase difference, at the boundary planes lying at angles of 19.47 deg to the direction of

motion

of

the traveling pressure point,

of

lf)l

L„,/4 between the crests of the transverse waves

and those

of the divergent waves.

The

crests of

the former system lead the others, just as

if

there

were a first transverse crest formed at a position Lh^/4 ahead of the pressure point. A planform diagram of such a pattern, showing the variations from the Kelvin wave system of Fig. 10. B of this book, is given by Hogner, from which Fig. 48. is adapted [Proc. First Int. Congr. Appl. Mech., Delft, 1924, Fig. 5, p. 149]. In a reworking of the

by Hogner

entire analytic procedure, described

paper listed as the first reference in this section, he shows that the phase difference at the in the

boundary planes is actually Lwfi, indicated in detail by his diagram in Fig. 17 on page 46 of that reference.

These same phase

differences,

although ex-

pressed as 27r/4 and 27r/3, are derived

Lunde [SNAME,

by

J.

K.

1951, p. 71]. In Fig. 6 of that

reference he gives a diagram corresponding to

the solid lines of Fig. 48.A. E. Hogner carries his analytic procedure to the point where he predicts the nature of waves

formed in the area beyond the boundary planes.

He

also substantiates his analytic derivation

by

photographs which reveal the patterns actually formed on the surface of the water. 48.4 Summary of the Trochoidal-Wave Theory. The notes which follow, adapted from G. C.

Manning [PNA, the

Chap.

9.

They

described

are illustrated, as far as practica-

the definition sketch of Fig. 48.B, which

ble, in

the elevation of a

is

summarize and presented in

1939, Vol. II, pp. 6-7],

relationships

wave having a steepness

hw/L^ of 1:7. The principal assumptions

ratio ^Line of Crest Interaections Qs

in Fiq

Broken Lines Depict Full

lO.B

Pattern of

lO.B;

Fio.

Lines Depict Norninol Crest Pattern

Qccordinq to

E.

Hoqn

wave

theory,

satisfying

the

of the trochoidal-

requirements

of

equilibrium, continuity, and uniformity of pressure, are: (a)

The motion

is

2-diml, around circular orbits

in a vertical plane (b)

The

liquid particles revolve in circular orbits

with uniform angular velocity u (omega) (c)

Fig. 48.A

Modification of Kelvin Wave System According to E. Hogneb

The

liquid particles at the crest

move

in the

same direction as the wave is advancing (d) There are equidifferent phase angles d6{theta,) = u dt between successive particles whose orbit centers

lie

at equidifferent distances dL^r along

a given horizontal line

The Kelvin system, corresponding to that in Volume I, is shown in broken lines. The

Fig. lO.B of

modification

(e)

Liquid particles whose orbit centers lie in same vertical line rotate about those centers

according to Hogner, with the transverse waves ahead of

the

the diverging waves,

in the

is

indicated in solid lines.

same phase

UN m^Oin \

162 Direction

Wove

RiM

h

of

Trovol tval

«

-

\\II( s 1\

Wove LcnijtM

Dl'SICN

sllll'

St«epnwa

I

-^

Rotio

of the

Wove Drown a

-IS.-I

Lyv

^.

j

Srr.

"

^

-j-

Wove

Veloclt^^

or Celerity

c

T

Mommurtu-

J^

of Crest

Orbitoi Velocity

"P^b^^

'^Qve Slope

_^ ^ _'t-

..^h^

Cirtulor Orbit Fhth An(]ular Velocitu In Orbit

Depth h

WoveLenqth Lw

"

"T^

V^fave

Celentij c

-^^^

u

Fig. 48.B

T^y -"y

of iiriniipal interest are, based

a wave length L „•

wave period

r«-

,

a

,

a

72.9

gravity g for sea level ft per sec' or 9.80G65

m

=

2-kRrc

,

of of

per sec":

where R,ic

is

the radius of

struction (2)

c

=

V gL

„./2Tr

(6)

= 2.2G3\/L^, =

1

.249

VL

ir

/i„-

,

in

fpswhen L„-

in

mps wlien L »

= IMOVT^-,

in k( wlioii /.„

= 2A27VT^-,

in kt

when

/,„•

is in ft

is

i.s

in

m

f/o,b

m. wiiere

"=

2r^

0.1953c", in

ft

when

c is in fps

ft

when

c is in

=

0.5571c", in

=

0.
i.s

in

=

0.1G97c', in

m when c

is

in kt.

=

ff2l,-/(2,r)

=

5.r217'H-, in

=

1.5(il7';',-.

"

and

=

3.0327',,

in kt

=

1.5G17',,

in

in in

wlicn

Rs =

and

and

=

7r/i„/(0.4419

=

irc(/i„-/L„),

r,,,!, is in

c is in

(8)

5.1217',,. in fps

= 2U,

wlicn

ft

7'„-

is

Y',,-

kt

mps

in .sec

is in

sec.

h„-/2

as derived in See.

4.'^.7,

is

in ft

is in

^

Wave

Till' (irliital vcldrily,

(7)

-

2-KC'/g

/.,..

the rolling circle for the graphic trochoidal con-

*°'e Frequencu- y-

o^

=

upon

and an acceleration at 45 deg latitude

,

"

~C~

=

L„-

(5)

,

32.174

Lir

'

a

wave celerity (velocity) c, a wave height hw b, surface-

particle orbit radius

(1)

*

Definition Dr.\wing for a Trociioidal

(0 The depth of the liciuid body is uiiliinitcd (g) The Uquid is ideal, without viscosity'.

The results

S urfoce- cjRs" u)(-/)- 1Tc(x^j

Orbital Veloci ty at

Wove Period

fps

VZ^) = 7.109/i„-/V^

when

/i

„

and L^ are

in

ft

fjis.

The angular

orbital velocity

(4) preceding, 27r/7'i,.

,

ui

is,

from

(3)

or

2ir

(3)

ini)ersec.

l2wL,r

T„ = \/2rLJg =

0.4419\//y„-, in sec wh en

/vn- is in ft

(9) Tlie

particles

= O.SOOSvLic, insecwlien //„ i IT

—

i.s

in

m.

tt/i"

level.

—

tli(!

(4)

I'rr'(|Ufnry

.?//>„.

=

At

line is

at

of orbit centers of the surface

the

distance

=

con^'spniiding distiineo

is

rn— i

w

2ir

5r(/i„)V(-l^'ii)

=

0.7854(/i„)V/.„. above the still-water any depth h, where the orbit radius is R,

2ye«,

Sec.

R

WIND-WAVE AND SHIP-WAVE DATA

4S3

At a depth h below the

(10)

surface, the radius

depth

of the orbit centers at that

given by

is

163

fortable performance

when steaming

nearly ahead waves having a length Lw

into a regular train of

Then L^ =

of 1.2 times the length of the ship.

=

1.2(L)

By

substituting

Lw = 2vRrc

this

The

becomes

R^e'^'

celerity

VgL^/2T =

=

612

ft;

\/Z^ =

24.75

ft.

of this wave,

reckoned with res pect to the undisturbed water, is equal to

=Rse-'""'"'

72

When h = L^,R =

=

1.2(510)

0.0019i?s

Thus

.

ft

c

2.263

per sec. This

is

a/L^ =

2.263(24.75)

=

56.01

equivalent to 33.16 kt. For an

the orbital motion is virtually zero in water as deep as the wave is long, and for practical purposes the assumed unlimited depth is not necessary; see Table 48.f of Sec. 48.7. (11) The total energy in the wave per unit breadth is approximately 0.125w{hw)^L,r By this formula, a salt-water wave 600 ft long and 30 ft high has about 2,000 ft-tons of energy per ft of

angle of encounter a (alpha) of about 180 deg,

breadth.

wave

representing a head sea, the speed of encountering ship,

water.

The

.

Of the

(12) is

total energy in the

wave, half of

it

potential energy and half kinetic energy.

From

(13)

0.4419

hw

space in

of this

wave

or 0.4419(24.75)

w2-KLwlg = The the number of

is

=

corresponding to

/,

10.94 sec.

which would pass a given point in

crests

1 sec, is

the reciprocal of the period or

0.0914 wave per sec.

The

height

hw

oi the

wave

is

fixed

by the

assumption made in item (24) of Table 64. d, which stated that the height would not exceed 0.55 vL;^ For the wave in question this is

2R.S

^kRrc

2TrR,

T^

period

VLr.

frequency

the relationship

Steepness ratio

is this wave speed plus the speed of the reckoned with respect to the undisturbed

the waves

.

Rrc =

the rolUng-circle radius

/iiF/[27r (steepness

For a limiting steepness ratio depicted in the diagram of Fig. 48.B, ratio)].

Rrc =

The value

(14)

gravity

= \.\Uhw =

/iB^/0.8976

of 1/7, as

2.228Rs.

of the virtual acceleration of

is.

At the crest, {Rrc — Rs)g/RRc At any intermediate point, Rig /Rrc At the trough, {Rrc + Rs)g/RRc For a limiting steepness value of the

first is

1

ratio

is

sin"'

{Rs/Rrc)

or,

in radians,

wave

the

irhw/L^

.

Rg

It is

normal to the radius Ri For the same limiting steepness ratio of 1/7, where Rrc = 2.228fls the sine in question is 1/2.228 = 0.4488, whence the slope angle f (zeta) is about 26.7 deg, as compared to 30 deg for the highest possible Stokes irrotational wave of approximately the same

•

steepness ratio.

As an example

of the use of the

made

data in the

foregoing,

an estimate

teristics of

a trochoidal wave Avithin the range of

size

and proportions

ABC

is

listed for

of the

charac-

the operation of the

ship in item (24) of Table 64.d.

Assume that the

ship

would give

its least

com-

ft.

=

wave surface The ordinates

TABLE

The

steepness ratio

0.0222 or

hw/Lw

1: 45.

in terms of the

wave height

are spaced at equidistant

Ordinates for Construction of a Trochoidal Wave Profile

48.a

The data listed here are from PNA, 1939, Vol. I, p. 207. The stations are spaced equally along the horizontal plane from crest to trough. The base line for ordinates ia at the bottom of the wave trough.

.

,

13.61

The velocity and period of this wave, as taken from the tables of Sec. 48.6, are listed in that section. Its maximum slope and orbital velocity are found in Sees. 48.5 and 48.7, respectively. 48.5 Elevations and Slopes of the Trochoidal Wave. Table 48. a gives the ordinates of a tro-

the

surface

occurs at the point where the orbit radius

=

then 13.61/612

choidal

hw/L^ = 1/7, = 0.55^; of

of the

is

hw

.228^/2.228

last, 3.228£?/2.228 = lA5g. (15) The maximum slope

0.55(24.75)

Statio

IIVHRonVX XMICS

161

I\ SHIP

DESIGN

Sec. 48.5

Expijvnatory Sketch for Surface Slopes of a Trochoidai,

Fig. 4S.C

Wave

intervals along the horizontal plane between the

as indicated at the right on Figs. 48. B and 48. C.

and the trough, in a direction normal the crest and trough lines.

indicated by Eq. (48. i)

crest

The

wave

It is to be noted particularly that the slope

to

that at the position of a

is

is

surface particle lying at the extremity of a radius

based upon the fact that a normal to the wave

which lies at the angular orbit position 6. For a w-ave traveling to the left, as in Figs. 48. and 48. C, this angle is reckoned counter-clockwise from the top center, starting at a crest at the left or advancing end of a wave. The horizontal distance from the crest to the position of tlie

expression for the

surface

any

at

slope j'(zeta)

surface-particle

point

passes

through a point at a distance Rrc above the In diagram 1 of Fig. O.G on page 163 of Volume I, the line P,Ci is normal to the wave surface at P, instantaneous orbit center of the particle.

,

whence the wave slope f equals the angle PiCiOi In the diagram of Fig. 48. C the line Vid is normal to the wave surface at Vt and the wa\e slope ^^ is represented by either the angle VidOi or the .

,

angle

MiPiN*

By

.

u_

particle

is

P4M. J4'>'< _,_

_

Q^^j^

Ki, /l.s

i^^^

The maximum wave

_

Thus

sin a 111 P4 04

^^

for Of

tan f

(48.i)

slope occurs

Fig. 48.

C

normal to the

lies

(c^)

is /»«-/2

=

»-'Ct)

-F

The

-

Rs

sin 0,

with the surface

(l(•^^

Rs

O^M,

cos

fl«

0.86C.«,

Rhc

- ej:im)Lw

O.SGC)/?.,

sin e«

- Rs

Rrc

.

The

+ is

0.5«a

L,r/3 and

latter is

meas-

ured toward the crest, so the particle position

advance

of the

from the crest wave, is

in the direction

and Rhc = Lw/2-k,

To =

9.

/es(-0.5)

=

—

,

value of (360

that of

(3()0

position in

<-->

wave

ha f M..

namely offset

VM* C^O,

desired, reckoned

sin

sin

2ir/3 or 120

Rrc

when the line PaC'a

crest,

by the

J2s(0.8(iC))

of

Since lia

=

=

^^^ g

Hurfacc-parlicle orbit radius P3O3 or lis in the

=

Rs

the orbit, namelj'

where 6 is measured from the top center of the orbit and cos in the lower quadrants is negative.

fii..

from the

0/36O)(Li,), modified

particle Ij'ing at Pi

f^Q^

diagram of whence

therefore the offset distance of the

center

orbit

simple geometry, indicated

in Fig. 48.C,

lan

72s

sin'

it is

2_

M8.iia) /.„

2ir

determine the niaxininn) slope of the t)12-ft of Sec. 48.4, for the .\B(" ship of Part 4, nece.s.sary to

a surfaic particle circle

A';,,-

know

the orbital radius

and the radius of the

Rs

of

rolling

by which the trochoidai surface

is

WIND-WAVE AND SHIP-WAVE DATA

Sec. 48.5

TABLE

48.b

Lengths, Velocities, and Periods of Trochoidal Debp-Water Waves

165

11M)R()1)\.\AMU.S IN Mill' DLSICN

166 T.\HI,I';

This tablo velocities

is iiuluxcxi

IS.c- I'khioii, Lbnctii, l)y iiitof^al

values of

and Vki/icity of

tlip

wave

[H-ritxl

Tro(-hoii>ai. Dkki'-Watkii

7'if in

and the frequencies nith which various waves pass a point

Sec. 48.6

Waves

wo. The table inrludos also the angular orbital

in space.

WIND-WAVE AND SHIP-WAVE DATA

Sec. 48.7

TABLE

48. d

This table

Velocity,

Velocity, Length, and Period of Trochoidal is

167

Dbbp-Water Waves

indexed by integral values of the wave velocity or celerity

c in kt.

iiM)K()n\ \ wjif.s IN

168

siiii>

L'AHLIJ 4i>.d— (Continued)

Velocity,

nrsir.N'

Sec.

-Ift.?

Sec. 4S.S

§50

WIND-WAVE AND SHIP-WAVE DATA

169

IIM)R()in \

170

\\ll( s 1\

MIIF'

'1'aIII.K

nrSIGN

IS.Il

Src. 4S.9

-OlUllNATKS VOR A SiNK-WaVK PhOKILE

Tlio tabic gives 17 ordinut^is for the

hiilf-loiigtii

of a

aitmsoidul nave, distributed at IG equal iutcr\-alB between crest

/«

Ti6b

Ratios ok Wave Height to Wave Length FOR Charactemstic Waves Used in Ship Design

Fig. 4S.E

It has

been the practice for manj''

ship-strength calculations on a

steepness ratio of 1/20. Tliis as a "static"

wave but

following wa\-e that

as the ship, and

is

is

it niaj'

luxs

j^ears to

base

wave having a often referred to

be considered as a

exactly the

not distorted

bj'

same speed the presence

of the ship.

Because this wave is not as steep as tlie storm waves which make trouble for small ships, and is steeper than tho.se which make wavogoing

TABLE

Wave

48.g

length

Niedermaib and Wueelock WaveHeight Design Values

and trough, as projected on a horizontal plane.

Sec. 48.10

plex

WIND-WAVE AND SHIP-WAVE DATA

waves with sinusoidal components, such as

those forming the basis of Figs. 48. G and 48.H of Sec. 48.11, diagrams 2 through 5 of Fig. 48.F give

Equal

° An<jles

171

J

ll^nR()I)^ \ wtK.s in ship

72

WluvKick

the

of

jKJSotl

having a height

A

/iir

=

of

^vll\t^•<

0.")5 V/..H-

Kin.

48.10,

general direction.

wavegoing performanee of ships in lie design stage, adapted from an initial proposal by the author in November 1950. is given in Table IS.i. for the dotorniination of the I

TABLK

Tentativk Sta.nti.^rd W.wk Conditions IS.i KOR DtrrKIUUNATION OK TIIK WaVKOOING PKnf-OR.\lANPE OF iSniPS IN TUB DkSION StAOB

(1)

dksign

This means that

Sec. IS. 11 l>oth trains are

The water depth

is

moving

(WK) ft

.

wave conditions

set of tPiilativp standard

train.

Wind and wind effects on the ship are not considered The waves describc
in

the

same

(KM) fathoms)

or more.

C.\SK III. This is intended to represent the conditionB obtaining in shallow water within a strong wind or storm region, where relatively' large and steep waves are produced by winds of short iluralion. The result is a single, regular train of waves, in wlii<-li the wave velcx-ities may vary from 0.4 to 1.2 or more times the maximum spec
from 0.12.5(I/S) to 0.0025(1/11)) or less. The angle of encounter of the wave Iniin may vary from to ISO <|eg. The depth of water may diminish to 2.5 times (he maximum draft, possibly to 2.0 times that draft.

here.

by some wind

of undefined nature.

Willi the lliicc v;Mi;il)lcs listed in "In

.short,

that

it is

the old rule

holds,

still

and always

the waves of a storm, not

its

will,

winds, that

." IBiRclow, 11. B., and the mariner has to fear: Edmon.«on. W. T., "Wind Waves at Sea; Breakers and .Surf," l'. S. Navy llydroKraphic Ollice publication H. O. (>02, Washington, 1947, p. 401. .

(2)

Table

(

'.V.^E

1

of

namely the ratio Lw'L, the steepne.ss and the angle of eneomiter a, and />i,-

48. i,

ratio /(»

,

.

Unless othenvise stated, the sizes and i)roportions of

the swells and waves are averages or signilicunt values for

the water areas of the world, rather than uncommon ma.\ima of one kind or another. They mux be local averages if the principal conditions are such that the ship can

even with the intervals deliberately made large, the inimber of possible combinations is almost prohibitive, rndoubtedly certain combinations of variables, especially those producing resonant motion, are only

critical.

Study

of those

combinations

ultimately be found sufficient.

The wave

extended to a low range beeau.se

velocities are is

travel only in that area.

may

it

possible for a ship with its forefoot nearly out

of the water, as in the ballast condition, to en(3) The lengths of regular or uniform swells .'ind wmvcs in deep water may in general be taken as a function of their velocities and \'ice versa.

counter short, steep waves who.sc impact coincides with the

natiii:il

l2-n()(l('il

\-iiiration

of the ship

sfriiclurc.

C.\SE

This

I.

is

intended to represent the conditions

48.11

obtaining in the general but not immediate vicinitj- of an area where a wind hiis been blowing for some time in a nearly constant direction. The result is a simjjli', regular train of swells, in

from 0.4 to

1.2 or

which the wave velocities may vary more times the ma.ximum speed of the

ship under consideration. This range large

The

enough to cover the region

is

intended to be

of resonant pitching.

steepness ratios of these swells, expressed as

wave length

wave

may

vary from 0.083(1/12) to 0.04(1/25) or less. The angle of encounter a of the ship with the direction of travel of the wavt; train may vary from (following sea) to 180 deg (head sea). The water depth is (JOO ft (1(X) fathoms) or more. height

CASE

to

All-

I^w

,

T-VBLI;; 48. j

This

is

intended to represent the conditions

storm area and in the immediate vicinity of another. Due to a shift in storm center or other cau.ses, the wind in the latter an-a is blowing in a direction difTcrent from that in which it bli.'W in the former area. The result is one or possibly itclceted

two S4-condary wave trains impo.sed upon a primary train of swells of C.\SE I. When the

wells arc of simple geometric form, this is known as a complex synthelii' two-comi>onent (or tliree-c(mipone.nt) »ea. The secondary wave veliM-itics may vary from 0. to 0.8 nf the maximum H{M-ed of the ship under consideration. In othiT words, they may exceed the primary swell velority. Tin- flireclion of thilie

within

(SO

deg of

wcondary

tin?

(rain (or trains)

direction of the primary

Characteristics ok Tiiukk ComComplex Synthetic Sea

ro.VKNTs OK a

The data II.

obtaining in the general vicinity of one strong wind or

nmy

Delineation of a Synthetic Three-Com-

ponent Complex Sea. As an inilicatiun of the appearance and the characteristics of a synthetic complex sea, a graphic example is workefl out in which three components or trains of regular sinusoidal waves are superpo.sed. The primary train is a.ssumed to travel in the direction of 90 (\v^ true (east), while the secondary trains travel

listed

here apply to the superpositions of

.\l| the wave components are sinuform but their velocities of translation and periods arc ealculateil from the fornuilius for trochoidal waves. For a wave length L\y in ft, these are c " 2.201? v^Z/ic in

Figs. 4S.Ci anil 48.11.

soidal

ft

per

ill

.sec;

'l\y

Direction of

Wove Wave

•

0.4419\//.,ir in sec.

tran.slatioii,

true

00 deg

length, ft

4(1(1

height, ft

s

75 dru 240

i:i5drg

120 I

Steepness ratio

1

/.W

l/IO

!/:«)

Wave

celerity, ft |M>r sec

45.20

:i5.()0

2l.7i)

20.70

20.75

14.(i7

Wave

iwriod, sec

S.840

0.SI7

4.S12

135.7S

105.17

74.373

kt

Distance traveletl by wave in 3 sec, ft

WIND-WAVE AND SHIP-WAVE DATA

Sec.-fS.lI

and 135 deg true. Their wave lengths are 400 ft, 240 ft, and 120 ft, respectively, with rather moderate steepness ratios of 1/50, 1/40, and 1/30, in the order given. The corresponding wave heights hw are 8, 6, and 4 ft. Other characteristics of these waves are given in Table 48. j. All components have sinusoidal wave profiles. Their elevations (or depressions) above the assumed quiet water plane may therefore be added algebraically to produce the elevations at 75 deg

(considered

as

a

(considered as a

+ —

distance)

or

depressions

distance) of the resultant,

173

the desired

step in the graphic superposition

The

positions.

resultant

is built up on a fourth transparent sheet, superposed on the other three, by adding the

pattern

elevations algebraically at a multitude of points

throughout the

field.

To show how much pp.

ATMA,

on top

a starter that to

.

all

of

each other,

for

1949, Vol. 48,

589-608] would be formed by three

crests piled

time

an "ilot" (French

of

[Pommellet, A.,

"islet")

it is

wave

assumed as

three crest lines intersect at the

This intersection

is

the reference point

or origin 0, taken to be fixed in space.

contour patterns, when laid

above or below the reference plane.

The

other in

down

The

three

at the proper

is

angles, are so placed that their crest lines cross the

to draw, to a convenient scale, three transparent

successive

Contours of the composite pattern are 1-ft intervals, with the result shown in Fig. 48. G. Those portions of the composite waves whose surfaces slope downward and to the right have the contours indicated by heavy broken lines, as though in shadow when illuminated by a low sun at about 270 deg true (in the

divisions of the

west).

first

contour patterns for the three sinusoidal waves,

having straight, parallel

lines laid off

normal to

the direction of travel at elevations to represent 1-ft

contours, including the crests

The data

and troughs. between

for positioning the contour lines

wave crests, for various equal subwave height, are given in Fig. 48. F. The three patterns are laid down over each

'

y' J 1

1

\

ON

origin.

then sketched at

The

validity of this

method

N Fig. 48.G

Contour Diageam for Three Superposed Sinusoidal Waves

of superposition

11M)R01)V.\AM1C;S 1\

174 wa-s

"111

puiiitctl

(lorstiier,

his

in

many classic

by

Franz paper of 1802 on the ago

years

trochoidal wave, referenced in Sec. 48.18: "Sine* this llutiry of \vavo« it

is

h.-t.-x"*!

followH that

ii|)on

tho cquality

waves of various sizes to cross in difTerent dirwtions, and ronlinue their motion undisturbed, .\gain genonU c.\|)crienco supplies ample verification. At the e&ma time it explains the numerous elevations which frequently ap|)onr at the surface of tho wat
Univ. of Cal., 1952, par.

Sec. 48.11

ai)ove the undisturbetl level

4

is

+

+

3

'-

=

9

ft.

toward the WSW, is a deep iiole, extending G.4 ft below the undisturbetl water level. Within 14.5 ft of the origin, therefore, one islet,

all

for several

tran.
Dl.SlGN

the origin, tho hcigiit of tho water "i.slct"

Close to this

motions of the »!it»^r which do not cluingc this uniformity of pressure, neither disturb the wave motion. This makes it possible of hydroslntic prp.isurp,

sllll'

.\t

(inds a difference

elevation of 15.4

in

steepness ratio of the

wave near the

ft.

origin

The is

of

the order of 1/18.7, as comjjared to steepness ratios of 1,'30, 1/40,

and l/oO

The maximum wave about 10

for the

near

slope

components.

the

origin

is

(leg.

llOiiKli.^h

On

16, p. 14].

either side- of this group of one high crest two deep troughs, within 300 or 400 ft, the waver level is relatively flat, with crests and .•mil

Assuming

tliat

a ship

is

traveling through

tliis

synthetic complex sea on a course of 70 cleg true, there results the profile in diagram

To emphasize

1

of Fig. 48.1.

the irregularities in surface eleva-

tion, the profile ordinatcs

above and below the

troughs less than 1.5

Following

three-component wave at shifted to the position

undisturbed or quiet water level are magnified

time

6.308 times.

Table

,'//ti

ft in


+

48. j.

magnitude.

composition

the

it

to

,

of

the

synthetic

each wave

is

then

would occupy at the

by the distance indicated in new composite pattern is sketched,

3 sec,

A

\

Fio. 48.H

Contour Diackam m\\ Tiiuee Suruni'OBBo Sinuboidal Wavbh,

3

Seconos Latkr Than

Fto. 48.0

WIND-WAVE AND SHIP-WAVE DATA

Sec. -fS.JZ

175

Composite Wave Elevotion

of

Undisturbed

Water

Level

,15.

4

Profile

ft in

145

ot Zero

Time

tn

ft

Steepness Ratio of Wave ot Origin is about 1/18.7 or 0.0535 Actual Oriqin

Sections

Token

in

Space

in

the Center of

Fiqs

70 deq True

ot

Wove Slope

l/5,66 - ton"'O.I768

iOdeq.obt

46.& ond 48 H

Vertical

Scale

is

6.308

times Honzontol

Profile ot

Fig. 48.1

H

Profiles at 70

Deg True for the Wave Patterns

The

Scale

to+3 seconds

of Figs. 48.G and 48.H

point of origin in space remains at the center of

three-component synthetic may be used as the base and the two secondary trains added to it.

the figure, as before.

However, the three-component sea appears at

indicated in Fig. 48.

A

for a time 3 sec later.

through the origin at a direction of 70 deg true is drawn in diagram 2 of Fig. 48.1, again with the vertical scale multipUed 6.308 times. The "islet" which was in the center has moved toward the ENE, but it is now only 7 ft high. The trough at the origin is slightly deeper than before, 6.5 ft. To the east, the surface is depressed but flatter than before, while to the west a large wave is building up. The area depicted is not large enough to give a reasonable indication of the variations to be expected in resultant wave lengths and wave periods, but within the confines of Figs. 48. and 48.H the lengths vary from 210 to 220 ft in one group, 270 to 280 ft in another group, and over 400 ft in a third. While the horizontal patterns of the waves in these diagrams exhibit some systematic regularities, a close examination of the contours reveals that the surface is almost as irregular as one expects the ocean to be. In fact, C. O'D. Iselin points out that wind waves in nature are not symmetrical, and that their

vertical

section

dominant

characteristic

is

the short length

of the crests of the individual waves,

plots of Figs. 48.

G

and

48.

H

shown by the

["Oceanography and

Naval Architecture," SNAME, New Engl. Sect., Jun 1954]. The plots could be made more irregular, if desired, by adding two more trains to build up a five-component

sea.

Graphically,

only

three

components need be combined at once, since the

this

time (1955) to be sufficiently irregular to

serve for ship-design purposes, as indicating the

kind of waves in which a ship is expected to travel. 48.12 Tabulated Data for Actual Wind Waves.

A table embodying

average relationships between

natural waves in deep water and the wind causing

them is given by Vaughan Cornish in his book "Waves of the Sea and Other Water Waves" [F.

T. Unwin, London, 1910]. Additional data

are given in his Cantor lecture before the Royal

Society of Arts, London, 1914. Cornish's table

is

quoted by E. L. Attwood, H. S. Pengelly, and A. J. Sims on page 202 of their handbook "Theoretical

Naval Architecture," 1953.

It

is

repeated,

with some adaptations, in Table 48. k. It is noted from this table that as the length of

wave

increases

the

steepness

ratio

hw/Lw

According to the figures given, the standard structural-design ratio of li^l^w = 20 stUl used in many quarters can not fairly be decreases.

applied to ships longer than about 470

ft.

More comprehensive and more modern data on the relationships between the winds and waves of nature are given in the tables of U. S. Navy Hydrographic Office publication H.O. 602, 1947, especially Table 4 on page 18 and Table 15 on page 32. The latter embodies a third and necessary variable in this relationship, namely the duration of the wind which is generating the waves. Both these tables appear to take it for granted that the wind is blowing steadily m one

iiVDRonvx

176

TABLE

-IS.k

— AvKR-VGK

XNfK.s i\ Mill'

KKt-ATinvsiiii'

orsicv

Bktwkks N Alt rm. Winhs and

Srr.

\\

tS.n

avks

For the source of those diita, see tho arcompimying text. The Beaufort si-ale numbers and wind velocities do not conform to tho latest U. S. Navy values as given along the top edge of Fig. 48.J. For this tabic it is assumed that the waves travel at the same spocd as the vrind.

Description

Sec. 48.14

„n0

4 8

WIND-WAVE AND SHIP-WAVE DATA

177

!iM)R()n\.\ xMic.s ix siiir

178

30a> »0

-10

£^ •'

c

9

X>

o i

^J?^-

10

^

,-"0 >-20

I

;:v 2: 10

SecticFiG. -l.S.K

i)i:si(;n'

Sec. fS.lf

Ser.4R.I1

Fig. 48.L

WIND WAVE AND SHIP-WAVE DATA

One op a Pair of Stereoscopic

Taken Abeam on the Aircraft Carrier West of Cape Horn

PhoiocjUaiiis

camera horizontal, as was the case with the Oriskany photographs of 1952. As many as three photographs were made simultaneously at times. The reduction was accomplished by the use of a Zeiss stereocomparator. A contour diagram of one pair of

number of sections through the diagrammed wave, are reproduced on page 1980 of the reference. Photographs are to be found on three plates bound in a separate volume of tables accompanying the text. Laas, W., "Die Messung der Meereswellen und ihre Bedeutung fiir den Schiffbau (Measurement of Sea Waves and Its Influence in Naval Architecexposures, together with a considerable

(2)

(3)

179

ture)," STG, 1906, Vol. 7, pp. 391-407 Laas, W., "Die Photographische Messung der Meere-

Oriskany,

Measurement of Ocean Waves)," Institut fiir Meereskunde (Institute of Oceanography), 1921; pubhshed b}' Mitler and Son, Berlin. This report is mentioned in TMB Transl. swellen (The Photographic

204, (4)

Nov

1949, p. 72.

Weinblum,

G., and Block, W., "Stereophotogrammetrische Wellenaufnahmen (Stereophotogrammet-

Wave Photographs)," STG, 1936, Vol. 37, pp. 214-250 and 259-276; Transl. 204, Nov 1949 Schumacher, A., "Ozeanographische Sonderuntersuchungen (Special Oceanographic Examinations)," Erste Lieferung, Stereophotogrammetiische Wellenaufnahmen, Vol. VII, No. 2 of the Scientific Results of the German Atlantic Expedition with the research and experimental ship Meteor, Berlin, 1939 ric

TMB

(5)

HYDRODYNAMICS

180

IN SMIP

DESIGN

Sec. 48.15

Horizontal Reference Plane

Fig.

Nink Wave Phokii.ks Determined krom a Pair of Stereoscopic Photographs Taken from the

4S.M

U.

(6)

(7)

S. S.

Hidaka, K., "Stereophotogrammetric Survey of Waves and Swells in the Ooenn," Memoirs, Marine Observatory, KoIh', Japan, 1941, Vol. 7, pp. 231-30S 'Stereophotogrammetric Apparatus for the Study of Waves Generated by Ship Models," Inter. Shpbldg. Prog., 1955, Vol. 2, No. 15, pp. references. 537-53.S. (Jn page 53S there is a list of

Marusj
A.,

Oriskany

The

iclatioa Ijctween

c^

and

c„

is

shown gra-

\V. Taylor and P, 194:^, Fig. 10, p. 12]. Other relation.ships between shallow-water waves and deep-water waves, taken from W. F. Durand [RPS, 1903, Table \', p. 77], ini' given in Table 48.1.

phically in Fig. 48.x, adapted from

1^.

[8

48.15 Comparison Between Waves in Shallow Water and in Deep Water. Sec. 9.10 describes how, when a decp-wator wave move.s into .shallow water (not necessarily up a sloping beach), its celerity decreases for a given wave length L,p it becomes steeper, and its crests take on a more ,

peaked

Navy

profile.

Table 29 on page 104 of U.

S.

llydrogruphic Office publication H.O. G02

gives the decrease in lengths and velocities of

waves of

advance

different dimensions as they

over a shoaling bottom.

The

stead}' tran.slational speed c* of a

shallow water of constant depth h 9.10 of V^olume

0.

where c„

The

is

= „.{.a„h(g-

the deep-water

may

in

wave

wave

(!).iv)

speed.

velocity in a

ll'Ulll

of

also be expressed as

(IK.iii)

-{fe)'-(!;:f" The

wave

from Sec.

I,

.shallow-water

water h

is,

pericKJ of

a shallow-water wave

fron

Sec. 18.10,

l

L

^rLJe'""-' ffCe"*""

-

+ 1)

1)

]"°

J

Fio. 'IS.N

Graph Showing Ratio Dbtwbrn Wave

\'i;M)crriK8 in SiiAi.utw

and

is Df.ep

Water

Sec. 4R.17

Table

WIND-WAVE AND SHIP-WAVE DATA

Comparison Between Characteristics op Shallow-Water and Deep-Wateh Waves 48.1

18]

182 lO

lUMRODV.NAMICb

l.N

Mill'

DLSICX

Sec. tS.lS 10

WIND-WAVE AND SHIP WAVE DATA

Sec. 48.18 1802. Tiansl.

by R. M. Kay and edited by Oswald

vancement

from an article in German edited by Gilbert, Annalen der Physik, Vol. 32, 1809. Inst. Eng'g. Res., Univ. Gal., Waves Research Lab., Tech. Rep. Ser. 3, Issue 339, TIP U-24940, Sep 1952. The figures from Gilbert's paper of 1809 are reproduced in this translation. Cauchy, A. L., "Memoire sur la Thfiorie des Ondes (Memoir on the Theory of Waves)," 1815. Publ. in M6m. de I'Acad. Roy. des Sciences, 1827; also ," Paris, 1882, Vol. I, in "Oeuvres Completes Sibul,

(2)

.

.

desirable to

.

1st series.

"M6moire sur la Th6orie des Ondes (Memoir on the Theory of Waves)," M6m. de

(3) Poisson, S. D.,

I'Acad. Roy. des Sciences, 1816. (4)

Weber,

Ernst Heinrich, and Weber, Wilhelra, "Wellentheorie auf Experimente gegriindet, oder

iiber

Wellen

die

tropfbarer

Anwendung auf die Sohall- und

or Concerning Non-Viscous Liquids with ApplicaLeipzig, Gerhard Fleischer, 1825. The experiments of the Weber brothers are described briefly and illustrated by H. Rouse and S. Ince in their "History of Hydraulics," Chap. 7, Supplement to "La Houille Blanche," 1955, No. 3, pp. 145-146. In the words of J. Scott Russell [Brit. Assn. Rep. 1844, p. 332], "The work is distinguished by more than the usual characteristics of German industry in the collection of materials, and contains nearly all that has ever been written on waves since the time of Newton, and as a book of reference alone is a valuable history of wave research." Young, Dr. Thomas, "Natural Philosophy," (prior to 1833), Vol. II, p. 64ff. The matter of wave

Waves

(5)

reflection (6)

is

considered in this paper.

and Russell, J. Scott, "Report of the Committee on Waves," British Association Report,

Robison,

J.,

1837. Presented at Liverpool in 1838. (7) Russell, J. Scott,

"Supplementary Report on Waves,"

Russell,

(9)

Russell, J. Scott,

J.

"Results

Scott,

of

Waves

Metropolitana,

LXXVIII,

B.,

"On Tides and Waves,"

London,

1845

(reprinted

in

a

(21)

(22)

Mag., Roy. Soc,

le roulis,

les qualitSs

de Saint-Venant, J.-C. B., "Histoire succinct des recherches sur les ondes (Concise History of Research on Waves)," Annales des Fonts et ChaussSes, 1888, Vol. XV, 6th Serie, 1st semestre, p. 710£f "Expose sommaire de la thSorie (24) Flamant, G., actuelle des ondes liquides periodiques (Summary (23)

Theory of Periodic Waves in a Liquid)," Annales des Fonts et Chaussees, 1888, Vol. XV, 1st semestre

D., "Wave Action in Relation to Engineering Structures," Corps of Engineers, U. S. Army,

(25) Gaillard,

Paper 31, 1904. This paper was reprinted in 1935 by the Engineer School, Fort Belvoir, Virginia.

(26) Cornish, V.,

(27)

441flf

"On the Rolling of Ships," Appendix 2 "On the Dynamical Structure of Oscillating

Froude, W.,

Waves," INA, 1862, pp. 48-62 and PI. Ill Rankine, W. J. M., "On the Exact Form of Waves Near the Surface of Deep Water," Phil. Trans. Roy. Soc, 1863, Vol. 153, pp. 127-138

W. J. M., "On the Action of Waves Upon a Ship's Keel," INA, 1864, pp. 20-34 W. J. M., "On Waves Which Travel Along with Ships," INA, 1868, Vol. IX, pp. 275-281.

(14b) Rankine,

The Report

Phil.

257ff

nautiquos des navires (Waves and RolUng; The Wavegoing Qualities of Ships)," Paris, 1877, p. 37ff WooUey, J., "On the Theory of Deep-Sea or Oscillating Waves," INA, 1878, Vol. 19, pp. 66-79 Gatewood, R., "The Theory of the Deep-Sea Wave," USNI, 1883, Vol. 9, pp. 223-254

of the British Association for the

Ad-

"Waves

of the Sea, and Other Water Unwin, London, 1910 Kriimmel, O., "Handbuch der Ozeanographie (Handbook for Oceanography)," J. Engelhorn, Stuttgart, especially 1911, "Der Bewegungsformen des Meeres (The Motion Forms of the Ocean) in

Waves,"

(14a) Rankine,

(15)

"On Waves,"

5, p.

(20) Bertin, L. E., "Les vagues et

Encycl.

George G., "On the Theory of Oscillatory Waves," Trans. Cambridge Phil. Soc, 1847, Vol.

(13)

p. 676ff

(19) Rayleigh, Lord,

1876, Vol.

Height and Velocity)," Comptes Paris, 9 Mar 1874, Vol.

Sci.,

of the

(11) Stokes, Sir

VIII, p.

Acad.

Prof.

George

entitled

of Variable

Rendus,

separate form)

(12)

of references appear in the

W. J. M., "Waves in Liquids," INA, 1873, Vol. 14, pp. 170-178 L. E., "Nouvelle note sur les vagues de hauteur et de vitesse variables (New Note on

47-57

(10) Airy, Sir

number

(18) Bertin,

on

Investigations

Waves," British Association Report, 1842 "Report of Committee on Waves," British Association Report, 1844, pp. 311-390 and Pis.

Her Majesty's Government

(17) Rankine,

British Association Report, 1841 (8)

to

footnotes of this paper.

of

Sound and Light Waves),"

tion to

make

on these subjects. The findings of this Committee, on page 38, listed as sources of information on waves the references numbered (5) through (12) of this bibliography plus a paper by Cialdi entitled "Sul Moto ondoso del Mare" and some papers in Liouville's Journal of 1866 by Caligny. Bertin, L. E., "Memoir on the Experimental Study of Waves," INA, 1873, Vol. 14, pp. 155-169. A considerable

(Wave

Theory Based upon Experiments, the

(16)

mit

Fliissigkeiten

Licht-wellen

183

embodies the report of a CommitteeconsistingofMr.C. W. Merrificld,F.R.S., Mr. G. P. Bidder, Captain Douglas Galton, F.R.S., Mr. F. Galton, F.R.S., Professor Rankine, P.R.S., and Mr. W. Froude. This Committee was appointed to report on the state of existing knowledge of the Stability, Propulsion, and Sea-going Qualities of Ships, and as to the application which it may be of Science, 1869,

F. T.

Vol. II (28) Cornish, V.,

Cantor

lecture,

Royal Soc. Arts (Lon-

don), 1914 (29)

Zimmermann, E., "Aufsuchung von Mittelwerten fiir die Formen ausgewachsener Meereswellen auf Grund alter und neuer Beobachtungen (Search Average Values for the Form of Fully Developed Ocean Waves, Based on Old and New Observa-

for

tions),"

5

May

Schiffbau,

28 Apr

1920, pp. 663-670

1920,

pp.

633-640;

lIMJ^JDWAMlt..-)

181

E., "A ('oiitril)iilioii to tho Theory of Ship (in Knglish), Arkiv fOr Mntcmatik, Aatronomi och Fysik, Stockholm, 1922-102.S, Vol. 17. Paper 12 (31) Hognor, E., "Notes on Somo New Contributions to the Thi>ory of Ship Waves" (in English), Arkiv fflr Matcnintik, Astronomi och Fysik, Stockholm,

l.\

Wiivce,"

(44)

1924-192"i. Vol. IS, Pai>er 10

"Uebcr die Theorie tier von eincm Srhiff eneuRten Welleii uml ilcs Wellenwidprstnniies (On the Thi-ory of Waves ami Wave Resistance Causo«l l>y a Ship)," Proc. 1st Int. Cong, for Appl.

(32) Hogncr, E.,

15124.

pp.

1

d'aniploiir

"On

the Action of Wind," Pap
the Formation of Water

2.

Wind," Proc. Roy. Soc, Series A, 1925, Vol.

Paper

23, pp. 209-214.

Munk, W.

H., and .\rlhur, R. S., "Forecasting Ocean Waves," Compendium of Meteorology, American

Meteorological Society, Boston, 1951, pp. 10821089. This paper lists 25 references. (47)

Munk, W. H., "Ocean Waves as a Meteorological Tool," Compendium of Meteorology, .American Meteorological Society, Boston, 1951, pp. 10901100. There are 16 references with this paper.

(48)

Mason, M.

A.,

Wave

"Surface Water

Mar

Theories,"

ington, pp. 207-228

ASCE, Hydraulics

"Ocean Waves and ICindred Geophysical Phenomena," Cambridge Univ. Press (England),

Separate 120. .\n excellent, readable, well-illustrated, iion-mathcmatic summary of the subject.

(38) Cornish, V.,

1934 (39) Lavrent'cv,

M.

A.,

"Sur

la

Th6orie E.vact des Ondes

Longucs (On the E.\act Theory of I/Ong Waves)," translation from Recueil des Travau.x dc I'lnstitut Mathematiquc de TAcad^mic des Sciences dc la RSS d'Ukrainc, 1.04G, No, S, pp. l.'Mi9. Also, by the sjime author, "A Contribution to the Theory of Long Waves," translation from C. R. (Doklady) Acad.

Sci.

UR

S.SS

(N.S.),

1943,

Vol.

41,

(49)

Div.,

1952,

Vol.

78,

There is a list of 68 references, of which the first dozen or so give the principal historic papers. Sverdrup, H. U., Johnson, M. W., and Fleming, R. H., "The Oceans: Their Physics, Chemistry,

and General

Biolog.v," Prentice-Hall,

New

York,

XIV, pp. 516-537 Picrson, W. J., Jr., Neumann, G., and James, R. W., "Practical Methods for Observing and Forecasting Ocean Waves by Means of Wave Spectra and 1952, Ch.'ip.

(50)

pp.

Both translations are available in the library of the Bureau of Ships of the Navj' Department, library numbers 50655 and 50656, respec-

Report

under

27.5-277.

Statistics," prepared as Technical

tively.

Contract Nl89s-86743, BuAer Project AROWA, July 1953. On pages 320 and 321 there is a bibhography of 39 items.

Lamb,

Sir Horace,

cations,

New

"Hydrodynamics," Dover Publied., 1945, Chap. IX on

(41) Deacon, G. E. R.,

"Ocean Waves and Swell," The

H.

Waves

B.,

and Edmondson, W.

T.,

"Wind

(52)

(53)

Navy 1947. On

at S«'a; Breakers and .Surf," U. S.

Hydrographic OfTice publ. H.O. 602, page 177 there is a list of 17 selected references, iHjme of which are given here.

"Ocean

Swrfaix'

Waves," Annals N. Y. Acad.

(54) Sci.,

.May 1949, \'ol. 51, pp. 343 .172. This is a collection lifttxin paiNTH by eighte<-n autluirs, reporting on a Oinferencc on (Jcean Surface Waves held by tho Section of Oceanography and Meteorology of tho of

C, "The Generation of Wind Waves on a Water Surface," Jour. Appl. Phys., Dec 1953, Vol. No. 12, pp. 1485-1494. Review by W. H. Munk in Appl. Mech. Rev., Jun 1954, p. 279. Proudman, J., "Dynamical Oceanography," Methuen and Company, London; Wiley, New York, 1953 "Waves, Tides, Currents and Beaches: Glo.ssary of Terms and List of Standard Symbols," 1953, 24,

Occasional Papers of the Challenger Society, 1946 (42) Bigelow,

1

(51) Eckart,

York, 6th

"Surface Waves," pp. 36;}-475. This book contains many references in the footnotes.

(43)

(is

physicist.

(36) Thorade,

(40)

(il

hydraulics but there are a considerable number of general interest to the naval architect and to the (46)

the Sea; Physics of the Earth," 1932. This is Vol. 5 of a work on Oceanography puljlished in Bull. 85 of the National Research Council, Wash-

10, j)p.

Deacon, G. E. U., ".\nalysis of Sea Waves,"

G. H., "Wave Motion," Chap. XI of "Engineering Hydraulics," 1950, pp. 711-7()8. On pp. 76(i-768 the author lists 31 references on waves and wave motion. Some of them appl\' primarily to

107,

H. F., "Probleme der Wasserwellen (Problems of Water Waves)," publisheil in Probleme der Kosmischen Physik, Vols. 13, 14, II. Grand, Hamburg, 19.^1 Patton, R. S., and Marmer, H. A., "The Waves of

interest are:

(45) Kculegan,

Waves by

pp. 1S9-206

(37)

Of particular

of references.

Neumann, C. "On the Complex Nature of Ocean Waves and the Oniwtli of the Sea Under

Deter-

(RigorouB

mination of Permanent Waves of Finite .\mplitude\" Math. Ann., l'.>2.-., Vol. 'Xi, p. 2tiHT (34) Von I>jiri!!ch, Graf, "Sturmsoc und Hrandung (Storm Seas and Breakers or Surf)," Bielefeld und Leipzig, 1925. This book contains many excellent wave photographs. (35) Jeffreys. H.,

list

1.

17-100

(iiiif

375, 401, 441, 4(12, 474, 482, 500, 510, 521, and 54-1. "Gravity Waves: Proceedings of the NBS Semicentennial Symposium on Gravity Waves, 18-20 June 1951," NBS Circular .521, 28 Nov 19.52, Govt. Print. Off., Washington. Contains thirty-three papers by various authors; each paper with its

own

(33) Levi-Civita, T., "DV-lorniination rigniireu.'Je dea ondes p«'rmanente.'!

Scc.-ifi.lS

New York Academy of Sciences on 18-19 March 1948. Separate bibliographies arc to be found at the end of most of the pa|KTs, particularly on pp. 3.50,

CM) HopuT,

Mech., lilft,

Mlir IM.SU.N

Council on Wave Research, Univ. Calif., Berkeley "Gravity Waves: Tables of Council un Wave Research,

Eng'g.

Found'n.,

I'\inctions," luig'g.

1954,

Found'n.,

Univ. Calif., Berkeley (55)

Deacon, G. K. R., "Response of the Sea Surface to Winds," Jour. Inst. Navigation (Unit4.>d Kingdom), Jul 1954, Vol. 7, PI). 252-261

WIND-WAVE AND SHIP-WAVE DATA

Sec. 48.19 (56)

"Ships and Waves," Proc. First Conf. on Ships and Waves, Oct 1954, publ. by Council on Wave

Research and

SNAME,

1955.

Sci. Results, Vol.

V, Part

XV,

Christiania (Oslo), 1906 (6)

Bjerknes, V., Solberg, H., Bjerknes, T., "Physikalische

Bibliography on Subsurface Waves.

For the reader who wishes to pursue the study of surface waves and the Hall Effect beyond the 48.19

185

Pole Exp., 1893-1896,

J.,

and Bergeron,

Hydrodynamik mit Anwendung

auf die dynamische Meteorologie (Physical Hydro-

dynamics as Applied to Dynamic Meteorology)," Springer, Berlin, 1933, and Edwards Bros., Ann Arbor, 1943, pp. 387-391. This reference gives a maximum velocity of subsurface waves,

brief discussion of Sec. 10.20, the following refer-

table of the

ences are available: (1)

H., liD, 1945, pp. 370-375; "On Waves due to a Travelling Disturbance, with an Application to

Lamb,

Waves

in

Superposed

Fluids,"

Phil.

Mag.

(6),

Wave

in a

1916, Vol. 31, p. 3S6ff (2)

(3)

Stokes, G. G., Vol.

(4) (5)

(8)

Froude, W., "Remarks on the Differential

INA, 1863, Vol. Trans. Cambr. Phil.

Stratified Fluid,"

8,

(7)

4,

pp. 216-218

Soc., 1842-1849,

pp. 451-452

"The Mariner's Mirror," Apr 1943, Vol. 29, pp. 73-74 Eckman, V. W., "On Dead- Water," Norweg. North

(9)

depending upon the thickness of the upper (lighterdensity) layer, and its sahnity content. Milne-Thomson, L. M., TH, 1950, Art. 14.42, pp. 367-368, entitled "Waves at an Interface" Ippen, A. T., and Harlemen, D. R. F., "Steady-State Characteristics of Subsurface Flow," NBS Circ. 521,

June 1951 Sverdrup, H. U., Johnson, "The Oceans: Their

M. W., and Fleming, R.

H.,

Chemistry and General Biology," Prentice-Hall, New York, 1952, pp. 585-602, on "Internal Waves." Physics,

CHAPTER

49

Mathematical Methods for Dehiieating Bodies

and Ship Forms ....

180

.

180

Scope of This Chapter; Definitions Ueefulne-'ss of Mathematical Ship Lines E.xisting Mathematical Formulas for Delineating Ship Lines Mathematical and Dimcnsioriless Representation of a Ship Surface Application of the Dimensionlcss Surface Equation to Ship-Shaped Forms Summary of Dimensionlcss General Equations for Ship Forms Limitations of Mathematical Lines Value and Relationship of Fairness and Curvature Notes on Longitudinal Curvature Analysis

49.1 49.2 19.3

The

49.4

49.5

....

49.6

....

49.7 49.8

49.9

.

Scope of This Chapter; Definitions.

49.1

defined

wholij'

or

in

Mathematic Delineation and Fairing Section-.\roa Curve

49.12 49.13

191

Ix)ngitudinal Flowplane Curvature .... Checking and Establishing Fairness of Lines by Mathematical Methods Illustrative Example for Fairing the De-

192

Practical

189

192 193

Selected

195

be

fonnulas and equations which express the coor-

.

.

L'-ilinil

case

it

to divide the intersection or

more

200

204 204

matical Lines for Ships

JOvcn for the

199

203

Forms Relating to Mathe-

Variation of Ship

References

199

for

Faired Principal Lines

.M;itli-

may

19S

Use of Mathematical Formulas

The Geometric

49.16 49.17

196

of a

ABC Ship ....

signed Waterline of the

by mathematical

part

.

49.11 187

omatiiul nicthod.s for doliiR'atiiig the forms of bodies uiid ships are those by which the shape of the outer surface, adjacent to the Uquid,

Graphic Determination of the Dimensionlcss Longitudinal Curvature of any Ship Line

may be convenient outhne into two or

parts, with a separate origin or set of coor-

dinates for each

part,

positioned

to

suit

the

mathematical formulas employed. The term geometric shape defines a body whose represented by some simple

dinates in terms of given reference axes. These

outline or surface

may

mathematical formula. Examples are a cube, a sphere, a circular-.sectioa cylinder, a right circular cone, a symmetrical pj'ramid, a parallelepiped, or an ellipsoid. To achieve simplicitj' it may be necessary to u.sc a particular system of coordinates and to establish limits in one or several dimensions, as for the cube iti cartesian coordinates. For any geometric shape one such simple

be the rectangular

(x,

z)

y,

or Cartesian

coordinates in one, two, or three dimensions, the cylindrical coordinates about an axis, the polar or spherical coordinates about a point, or whatever

may

be convenient for the purpo.se.

With a

selected set of numerical values a.s.signed to the

symbols

of these equations,

surface coordinates or offsets

or part of the

all

may

be calculated. Part of a bodj' surface may be geometric, such as a nose of hemispherical or ellipsoidal shape of a tiixly

revolution,

of

attached

rniddieb(xly or circular section.

to

a cylindrical

Some other part may be highly

of the surface, such as the tail, irregular, impractical for

tion with

any

.set

mathematic representa-

of reference axes.

Instead of covering a whole 8-diml body the mathematical formulas llio.sr>

required

ftatures.

A

int
Hwcli

the

U.S

for

the

typical ca.se

may

delineation is

.'5-
the designed waterline on a

inlerticcting plane.

2-diml

of

the fomiula for the

a plane with the

reference,' axis

.surface,

be limited to

almost invariably

lies

Lines.

is

usually

sufTicieiit.

The Usefulness

49.2

of

Mathematical Ship

Before embarking on a discu.ssion of the

mathematical delineation of the lines or surfaces and ships, it is well to answer the question that arises immediately in the mind of the practical naval architect and shijjbuilder: UTiy bother with mathematical lines when faired lines can be drawn .so quicklj' by experienced jjcrsonnel? It is ca.sy to give two answers to this (jucstion. of bodies

In the

first

place, analysis of the lines of

many

actual ships, in the form available to the naval

surface,

.ship.

expression

is

Hero

in the

archite(!t at

large,

strictly fair

by any

imlicates that

they arc not

criteria, graphical or

mathe-

matical. In the .second place, experienced per.son-

186

MATHEMATICAL

493

Sec.

by no means available in sufficient numbers, especially in a national emergency, to draw all the ship lines that need to be laid down. There are several other good reasons, both practical and scientific. For a ship of a new type, nel are

or of a novel shape,

it is

still

a draw-and-erase

process, even for an experienced hand,

down

to lay

the lines of a 3-diml ship surface that will

have the proportion and shape characteristics selected

by the

When

designer.

these charac-

teristics are achieved, the fairing process remains,

the

or

curvatures

require

to

be

checked,

as

described subsequently in this chapter. Assuming

a perfect drawing,

and

its

dimensions, coordinates,

offsets still require conversion to

numbers, so

that artisans with rules and scales can build the

These numbers have to be "lifted" from the graphic drawing but they are a natural product of the mathematic method.

full-size ship.

The numerical

values of those hull coefficients

and form parameters which are not used to set up the mathematical equations may be calculated before any mathematical lines are laid down on paper.

The

designer

may

likewise calculate the

positions of the various centers of area

volume they

in

which he

fall in

is

and

of

interested, to insure that

the proper places. Actually, the hull

parameters are selected by the hull designer while the subsequent calculations and the drafting work are performed by computing-machine opera-

and di'aftsmen. As an example of what can be done with mathematical lines in an intensely practical case, the shape of the large blisters added to the U. S. battleships of the New Mexico class in the early 1930's was delineated by D. W. Taylor's mathematical method, to be discussed presently. In some respects this was a more difficult job than laying down the lines of the whole ship in the

tors

first place.

Entirely apart from the shipbuilding aspect, mathematic delineation is invaluable when preparing the lines of a series of models in which some parameter is to be varied systematically from model to model. The development of mathematical formulas and methods for representing the principal lines or the surfaces of ships has been somewhat spasmodic and is still far from a logical or practical

A

conclusion.

brief history is given here of the

outstanding events in the development, together

with a (1955).

summary '

of the results achieved to date

LINES FOR SHIPS 49.3

187

Existing Mathematical Formulas for

De-

The use of mathematical formulas for calculating the offsets of ship lines, lineating Ship Lines.

what may be called mathematical ship surfaces, is not necessarily tied to the mathematical calculation of resistance due to wavemaking and other causes, discussed in Chap. 50. To be sure, many of the calculations for pressure resistance due to wavemaking have been carried out for ship forms whose waterlines and transverse sections could be expressed by mathematical equations. These equations may, however, be used for establishing the lines without a subsequent attempt to calculate any element of or better, for delineating

the ship resistance. It appears to earliest

have been

workers in this

in the

field

minds

of the

that the use of

mathematical equations to derive the usual offsets would also serve to achieve the hull proportions and parameters desired by the designer and to tell him whether his volume and area centers would be where he wanted them. who has given an}' down lines was probably naval architect Chapman, who proposed to use a system of lines composed of paraboUc curves adapted to the intended size and proportions of the vessel" [Thurston, R. H., "Forms of Fish and of "The

oldest writer on forms of ships

well-defined system of laj'ing

the distinguished

Ships,"

INA,

(Swedish)

1887, Vol. 28, p. 418].

Chapman's work

in the 1760's or 1770's

followed in the early 1790's by the

first

was

recorded

systematic tests on models, conducted by Mark Beaufoy and others. These models were geometric shapes and could be said to have had geometric or mathematical lines. From the 1830's to the 1870's mathematical curves such as the versedsine curve of diagram A of Fig. 24.G, the cycloid, the trochoid, and the streamlines around a Rankine stream form were proposed and actually worked into the lines of ships of that day by J. Scott Russell, James R. Napier, W. J. M. Rankine, and others. Arcs of circles and possibly of eUipses as well have been worked into ship lines since time immemorial [Narbeth, J. H., INA, 1940, p. 147].

John W. Nystrom, in the 1860's, expanded Chapman's use of the paraboHc trace and developed what he called the "Parabohc Shipbuilding Construction." He utihzed parabolas of varied order, with fractional as well as integral

make up both waterlines and secHis method, described in the Journal of The Franklin Institute [Jul-Dec 1863, Third exponents, to tions.

MYnROnVNAMICS

188 Sorii-.s,

XIA

\ol.

with Pis. fiimpU'to

U

ami

:U-.

PI).

111), i-nablwl

H.V.I

him

for

offsets

of

set

I,

.SSO

aiul

;{•)(>.

to lak-ulatc the

a ship

body plan

represent iiiR an underwater form with a numerical

value of block cocfHcient

He

C/, selectetl in

advanre.

page 358 of the reference:

describes, on

exiTcise of tjisto."

was

DI.SIC.N

Sllll'

for waterlincs

Src. 19.3

and

sections.

The curve

full

The entrance and the bow and stern, respec-

sections are hyperbolas.

run, extending from the

the section

to

maxinnun

of

area,

mathcmatic method, to

use reversetl i)arabolas for hollow waterlincs, to the horizontal and the vertical

calculate both

position of the center of

buoyancy CB, and to volume on a basis

are

because the origins of the mathematical curves are taken at the bow and at treated

separately,

The

the stern.

curves representing

families of

waterlincs and section-area curves are given bj' oth-ilegree polynomials with five arbitrary

able, with this

u.se
familias for

fine sections are 4th-tlegiee parabolas; those for

tively,

"... a vessel coiistrurtcil wholly by the paraluilir nictlicxJ; pvery rrosa soctioti or friiini' is ii paniliolii; tlio friiinu ilruwiiiK or lio
lie

IN

aniplilied prr)cedure, .separate fornnilas are

=

type y

eters, of the

tx

{ ax'

-\-

bx^

-f-

param-

ex*

-\-

dx''.

was apparently' Taylor's intention to give a shape to the waterlinc curves that would inii)art It

amount

a predctemiined

of

or

lateral

normal

draw a curve

of displacement

acceleration to the water flowing aroimd them.

of draft. His

methods are explained in detail in and are illustratetl by examples.

although there

the reference

cite
Xystrom even goes

".

.

.

so far as to

tell,

on

]ian;e

:).")S

how:

of the reference,

Xo parallel body

mentioned in Taylor's paper no difficulty in separating (he hull at the section of maximum area and inserting any desired length of cylindrical prism luuing the maxinunn-section shajje.

to form the displacement so as to present the least

possil>lc

wlien

resistance

forced

water.

throiigli

found theoretically to lie thai the sfiuarc root of the sections (areas) should be ordinates in a parabola, the exponent of which depends on the

diminish in a certain

series,

desired fulness of the displacement (block coefficient)."

The words

in

parent lieses arc those of

I

lie prcscMit

author.

ami shipyard

is

entirely suitable for practical

has been used off drawing model and ship lines at Wa.shiugton for the past 50 years. A number of I'. S. naval vessels have been constructed to the.sc lines. The body plan of a modern design, most of which was delineated by Taylor's metlKul, nil

iiiiij

is

Subsequent papers by Nystrom, all on the same general subject, appear in references (.S) and (4) listed in Sec. A\)M. Shortly after the Wasliinglon Model Ha.sin was put in operation in I'.KK) I). W. Taylor developc^d a mathematic "method of deriving (luickly the

is

of course

Taylor's method

The

immer.sotl area of each frame (station) should increase or

is

in fact, it

u.se;

for

reproduced

in Fig. 4i).C of Sec. 40.7.

l']laboraling

u\wn the quotation

l)aragiaph from

D.

paper, his met hod

W.

makes

Taylor's it

in

a preceding

Um SXAME

|)o.ssible,

by the

u.se

of

eqiiidilTerent or progressive values for the i)aram-

any desired mnnlicr of ship This was of inestimable value in the preparation of lines for large groups of models such as the Taylor Standard Series.

eters,

to develop

forms

in

sysU'malically varying characteristics of models

Using

this

ISXAMI-:, IIKW, pp. 24:3-2C7]. This method covered the delineation of waterlincs, section

.systematic, with the

and section-area curves. A somewhat difTcrent mathematic method of producing waterlines, section-area ciu'ves, and body plans, closely resembling llio.se of actual ships, was proposed by J. N. Warrington .shortly tlicnnrirr |S\A.Mi;,

who had to draw the lines for each model. An excellent sui)i)lementary slalement by (;. P. Weinblmn |TMli Hep. "•*'. ^n) I'-'ot), p. 7),

lines of a nuxlel i)o.sse.ssing certain desired characteristics,

.

.

and

.

.

.

practicable; anil easy

methods

of

."

lines,

l)art

a

series.

method the

not only of

series

became

scientifically

minimum of elTort on the those who planned it but tho.se

from which the following is jjaraphra.sed, .says dial T;i\liir developed mathematical formulas, (he idea that they gave the lines of a

1909, pp. 41I~J52|.

mil

Another decade of development by Taylor, following lii.s original concepts, produced tlu; paper entitled "(Calculations for Ships' Kornis and the I^ight Thrown by Model l']xpeiiments upon Resistance, Propulsion and Uolling of Ships" I'l'rans. Int. lOng'g. ("ong., Nav. Arch, and Miir. Mng., San Francisco, Hll.'i). In this revised and

ship of mininnnn resistance but sim|)ly to obtain

uiili

lines po.s.se.s,sing desired shapes.

This statement

is

important. Contrary to .some attempts to a.scribe

magic

])roperlies to certain analytically delined

curves like trochoids and sine curves, the principle of .systemali/ation llieir .'tdnptiiin.

was the decisive argument

for

MATHEMATICAL LINES EOR

Sec. 49.4

Unfortunately, Taylor's method was described

SHIPS

189

Mathematical and Dimensionless Repre-

49.4

Weinblum

in a publication not conveniently available to the

sentation of a Ship Surface.

average naval architect. There are reprints of this paper but they have been given only limited

references of Sec. 49.3 the problem of the dimen-

circulation. Since the equations of waterlines

and

sections are not linked together into equations of

surfaces in which the hull it

is

treated as a whole,

by those who have

considered preferable

is

studied this problem to develop a broader system ship-hull

of

work

equations than to

of 1915 available to a

make

Taylor's

more extended group

sionless dehneation of a ship hull

710 "Analysis

of

Wave

Resistance,"

written

Blum, Sep 1950. This report is in the category of must reading for anyone studying the subject of mathematical ship lines.

jointly with J.

Wave

758 "The tion,"

May

Resistance of Bodies of Revolu-

1951

840 "Investigations of a Thin

Written Todd. 886 "A

Wave

Effects Produced

by

Body—TMB model 4125," Nov 1952. jointly mth J. J. Kendrick and M. A. Systematic

Evaluation

of

Michell's

Jun 1955, especially those portions having to do with ship lines. Integral,"

Weinblum has developed mathematical sions, to

expres-

be described presently, which:

(a) Are suitable for delineating an entire ship form of given characteristics, based upon an origin amidships. This improves upon the Taylor procedure of treating the forebody and afterbody separately, mth origins at the two ends. (b) Will produce a series of forms -with scientific

systematic variations in these characteristics (c)

Will provide a basis for the systematic investi-

generahzed:

parallel planes at right angles to each other, long

customary

in naval architecture. In other words,

instead of defining the shape

of readers.

reports:

is

by considering the entire underwater boundary as a surface, rather than as a series of intersections of that surface by three sets of First,

lines,

The broader purpose envisaged by Weinblum some fifteen years later, explained in references (8) and (9) of Sec. 49.17, of representing the whole ship surface by single equations, was followed by his more recent work at the David Taylor Model Basin, published in the following TMB

In the

lines,

of bowlines

by

offsets of

and buttocks, and

water-

of section

usually at equidifferent intervals from three

given planes of reference,

normal case by the

it

is

defined for the

from the centerplane or the plane of symmetry for amj point on the hull surface having the coordinates x and z. Second, by expressing the ^/-offsets and the x- and 0-coordinates not as dimensions in well-known length units but as non-dimensional ratios of the respective offsets and coordinates to the length, breadth, and draft dimensions. These 0-diml y-offsets

ratios are given presently.

Third, by placing the origin

of the coordinate

system in the surface waterplane, in the plane of symmetry, and at midlength of the immersed form or underwater hull. The length of this hull is L, the waterline length. While the vertical measurements on an actual ship are usually made upward from the baseplane, in the mathematical system they are made downward because this is the positive direction of the 2-axis of the ship, described in Sec. 1.6 and indicated in Fig. l.K.

In the discussion which follows

it is

assumed

that: (a)

The

ship

is

a simple one which

sidered symmetrical forward of

may

be con-

and abaft the

midlength station (b) The ship is symmetrical with respect to the centerplane, as is customary for real ships. The definition sketch of Fig. 49.A is an isometric diagram of the outline of such a ship, correspond-

gation of wave-resistance characteristics of ships.

This

low

will, it is

if

hoped, lead eventually to forms of

Non-Dirnensional Distances

not least resistance.

(d) Will

provide a basis for the calculation and

prediction of the flow pattern and the pressure distribution around a ship (e)

Will form a more general foundation for

research on other problems of naval architecture

involving maneuvering, wavegoing, and behavior in shallow

water and restricted channels.

Fig. 49.

a

Definition Sketch of a Simple Ship Surface with a Single Origin

HVDROnVNAMICS

190

nisicx

I\ SIIIT

.S>r. -IP.-)

uiulinvator IukIv of a Xortli

somewhat to tlic American Iiuliaii eaiioe. ing

where

general dimensional equation of the hull

The surface

then

is

±l(f.

the

Tj((,

iiull.

The

=

y

±y(x,

(49.i)

z)

f) is

a transverse 0-diml j;-funclion of it is a function of both f and f

In this case

general surface equations serve

as equations of the usual ship lines

the set of coordinates

mmus signs represent

where the plus and

identical

transverse offsets to starboard and port, respec-

and the expression

tively,

y{x,

signifies

z)

(49. iv)

f)

eciuallj' well

when one

the surface waterline, where z or f ef mat ions

of

given a fixed value. For

is

is

zero, the

±T,(f, 0)

(49.v)

become

a

transverse (/-function for the hull. In this case

a function of both x and z. For example, if X were 21"j ft forward of the amidships origin on a certain vessel, and z were 20 ft below the origin it is

=

7/

For the y

=

and

±2/(.r, 0)

whore

niiflscction,

±2/(0,

and

z)

=

,;

r,

=

.r

and

{

are zero, (49.vi)

±»,(0, f)

(the latter in the iilane of the designed waterline),

y would be some value such as ±14.2 ft, measured to starboard and to port, by virtue of the function ifc(/(.r, z). If the j/-function were 1.0 for then the starboard and port

and

«/-ofTsets

When

throughout.

etjual

and z, would be

of absolute values of x

any combination

defined by suitable xwould have the form of a

2-limits the craft

box or parallelepiped.

wall-sidetl

the craft were un.sjnnmetrical fore and aft

If

midlength

would

be

about normally to use two surface equations: the

yy

y^

=

zkyrix,

=

it

z) for

2) for

±2/4 (x,

the forebodj'

necessary

(49.iia)

the afterbody

(49.iib)

For a submarine hull which is not a body of revolution and is not sjTnmetrical above and below any horizontal reference plane, there would be required two sets of surface equations, one for the upper and one for the lower portion. The common origin for the two would lie in some convenient horizontal axis or dividing plane. Again, however, this would break up the vessel as an entity by splitting

it

horizontally.

A

pro-

cedure would have to be devised which would retain a single ship equation for use in analytic studies, say of underwater maneuvering.

Weinblum's general or

ba.sic

procedure for hulls

that are asymmetric with respect to the midlength section is to split up the surface equation into a is symmetric fore and aft and an "asymmetric (skew) deviation" represented by

main part that This procedure has the effect, however, of destroying the ship as an entit}-, with a single conclusion

its logical

two

into

single surface ec|uation. Carried to

and a

origin

di.s.similar

it

would break up the ship one comprising

half-bodies,

the entrance and the other the run, each with

own

set of surface, area, volume,

equations.

its

and moment

To avoid losing the single ship equamay later be introduced into opera-

which

tion,

tions involving

wavemaking, maneuvering, and

wavegoing, Weinblum has developed a special proci'
fore

and

to

the

simple ship,

the next step

aft,

is

KkBi)

this

-

f

,

ij(eta)

2

= |

,

.symmetrical

to convert the x-, y-,

and coordinates to m done they become

z-fifTscta

When

p. 10].

anil for other asymmetric variations, become somewhat involved. One such case is that in which the maxinunn waterline beam does not

lengths,

not discu.ssed here but the reader

study them

Weinblum's

may

consult page 9 and following of

TMB

Report

SS(>,

issued

r(7,eta)

=

fonn.

0-tliml

j^

(lO.iii)

2

form of tiie general (>(|ualion beconiex, adopting W'cinbluin's notation, (l-
(l'.).i)

in

June

l'.)5l{,

pj).

180-215]. liial as more and ami niatiiematical expressions for ship form come into use, whether analytical or general, it becomes necessjiry to use ratios or new symbols for (juantities formerly expressed by abbreviations (SNAME, 19IS, j).

Weinblum has pointed

more mathematical

4l.'i].

The

The procedures involved are who wishes to

occur at midlength.

1955, as well as his earlier paper [STCi,

Ueturning

and

[TMH Kep. SSG, .lun 1955, Procedures and eciuations for the situation where the section of maximum area is not at midlength, with unequal entrance and run

a .secondary e(|uation

A

ca.se in i)oiiil

onl

lines

is

the

u.se of

the ratio IX"H,

with a reference jioint at the FP. Using the ship axes of I''ig. l.K, the distance of (he ( 'H from the

MATHEMATICAL LINES FOR

Sec. 49.5

at midlength

origin

expressed as the linear

is

distance Xb or as the 0-diml ratio Xb/{L/2), plus if

forward and minus

aft.

Application of the Dimensionless Surface

49.5

The 0-diml

Equation to Ship-Shaped Forms.

shape or surface function t]{^, f) of the hull may take a great variety of forms, even for boat- or ship-shaped underwater bodies. The simplest are the binomial forms nik, 0)

=

1

- r

'7(0, f)

=

1

-

(49.vii)

(49.viii)

r"

These produce what are called Chapman parabolas [Weinblum, G. P., TMB Rep. 886, pp. 13-

With different numerical values of the 14]. exponent n other than 1.0, but not necessarily whole numbers, the shape function of Eq. (49.vii) gives parabolic waterlines of varying curvature and fullness, much like those described and discussed by J. W. Nystrom in the 1863 and 1864 Franklin Institute references quoted in Sees. 49.3

and

49.17.

The shape

selected for the designed waterline,

in the simplest case,

determmes the function

of the

0-diml fore-and-aft distance ^ from the origin. The shape selected for the midsection determines the function of 0-diml keelward distance f from the origin. Thus the shape defined by the expression

=

7/

1

—

Eq.

^" of

has an nth-

(49.vii)

That = 1 — f "" has mth-order parabolic by sections and square (plumb) ends. It is possible to shape the waterlines and sections independently by using a surface equation in the form of the binomial product order parabolic waterline and wall sides.

defined

t;

vii, f)

A

=

(1

-

r)(i

-

n

(49.ix)

half-body plan of a hull developed by putting = 2 is published by Weinblum

n = 2 and

[TMB

m

Rep. 886, Fig.

3, p. 20].

Introducing what he

a fining function [TMB Rep. Weinblum produces a 0-diml equation calls

into the first binomial of the product

886, p. 21], of the '!(?,

f)

—

form

=

[1

- r

(a coefficient) (^"

f)f](l

-

n

(49.x)

„

=

SHIPS

-f-

[1

With

191

(0.5757)(f

-

^^)f](l

this surface function

-

f)

(49.xa)

Weinblum produces

the half-body plan of Fig. 49. B, adapted from Fig. 4

on page 21 of

TMB Report 886.

marked resemblance

to

some actual

This has a

ship forms.

\Mu:s

livi)K()i)\.N

192 l>y Ml).

('l'.).iiiV

forimila for this operation

'I'lic

i\ Mill' nisic;\

is

.l(i)

=

Sec. 19.6

2

'

(49.xiii)

„(f, f) f/f

f

Bdr,

Ldt

dx It corrr.spoiiils to

84 of

TMB

(49. xi)

Weinblum's

E(|.

midlength

on

(,2t))

Section-area curve ecjuation with unit ordinate at

|)iigt'

Roport 710.

Somewhat

unfortunately, in Appenilix

1915 paper, D.

W. Taylor gave

the

of

hi.s

name

of

1

Midlength section-area

coefficient

"acceleration" to the second derivative d'lj/dx'. It might well have resulted in some further development in the field of .ship form, in the four decades following that paper, had he comhincd the first and second derivatives to obtain the well-known radius-of-curvature equation, given in Sec. 49.9 as Eq. (49.xxi). Much more might now be known of the hydrodynamic cfTects of surface curvature and the best way of working curvature

^- = l.iiail

7^

= 1'"^"'^)'^^

(^^•-)

wali'rplanc cnclliiMcnt

Prismatic coefficient

into a hull.

49.6 Summary of Dimensionless General Equations for Ship Forms. In Report 88(5,

TMB

in

i.s.sued

down

for

Block coefficient

Weiublum derived and set convenience a number of general 0-diml June

IO.j.j,

equations not mentioned in the foregoing. These are listed hereunder for convenience, as adapted

from pages 8 and 9 of the referenced report, accompanied by some explanatory notes. Weinblum's notation is modified slightly in some places, to bring it more nearly into agreement with the

ATTC

ITTC

and

standards, but this sliould not

inconvenience the reader. are developed from

All etiuations listed

basic hull ecjuation (49.i),

and

namely y

dimensionless. It

all are

is

=

±y(x,

the z),

a.ssumcd that the

maximum

section area occurs at midlcngth. Coordinates and offsets

{(ksi)

= £

,

=

7,(eta)

I

,

f(zeta)

=

J

(19. ill)

2

2

Hull equation r)

=

(49. iv)

±j){k, f)

Waterplane c<|uation V

=

49.7

make

excellent

of cones for the local enlargements around single shafts emerging from the trailing ends of skegs, the elongated barrels of bo.ssings, where the conical axis need not coincide with the shaft axis, and the basic portions of bulb bows, such as the one illustrated in Fig. 07. H. There is a limit, however, where the expenditure of time and labor in this process is not justified by the hydrodynamic improvement in the ship or by other advantages enumerated previously. In general, the field of usefulness of the mathematical line, as it is \nth the accurately faired line to be described presently, centers principally around those traces of the hull which are parallel to the direction of water fiow. Tli(> statements in Chaps. 24, 25, 27, and 28 indicate that neither unfair-

portions

corners and

(I9.vi)

r)

Arca-of-ucction equation

f

=

and

nor fore-and-aft

have too great a

ui)oii resistance. It is

futile as well

unnec-es-

as impo.ssible, to try to

mak(! a hyperliola of the

2()()th

or

the .WOth

a perfectly acceptable midsection composed of a vertical side line, a horizontal bottom order

Centcrplane or profile equation ±7)({, f);

discontinuities,

detrimental effect .•iary

i?=±7;(0,

It

and profitalilc use of geometric shapes and mathematical equations for small "pieces" of ship .surfaces. Examples are to

nes.ses in the transverse sections,

(49.V)

±({. 0)

Midlength section equation

=

Limitations of Mathematical Lines.

is pos.sible

f ({,())

(I9.xii)

line,

lit

and a circular-arc

bilge corner.

nuithematical lines offer an advantage,

Where they

d(j not, furgcl

them.

Where u.se

the

them.

MATHEMATICyXL LINES FOR SHIPS

Sec. 49.R

0.5

Waterline

0.338 0.277 0.215 0.154 Positions are in Fractions

Fig. 49. C

From

Sta. 2

OOSZ. 0.09E 0.154 0.215 0.277 a338 <£ 0.5 of Draft; Buttock Positions are m Fractions of Half-Beam

Body Plan op Ship with Mathematical Lines Following the Taylor Method

through Sta.

The body plan

14,

both inclusive, the

lines of the hull represented here are entirely of

of

Fig. 49. C, illustrating a a multiple-screw vessel of modern (1954) design, is a good illustration of what can be done with D. W. Taylor's system of mathematical lines. From Sta. 2 to Sta. 14, both

form

tentative

for

inclusive, the hull

derivation.

form

is

entirely of mathematical

Beyond those

stations

the reverse

curves and

changes in curvature call for the customary graphic layout and fairing procedure.

For information, the principal 0-diml form coefficients of the hull of Fig. 49.

Cp = 0.560 Cx = 0.976

Cw =

0.684

=

0.547

Cn

LCB =

193

0.5051L

C

are:

L/B =

mathematical derivation.

HVnRODVNAMICS

19}

time inuncrnorial tli:it tlio .'ihip liull should be fair

urulerwatcr surface

of a

in

the direct ion of

water flow along it. This was achioveil by eye in the hewing process or by bending fore-and-aft structural members such as planks into reasonabl}' fair elastic curves. It is entirely possible, indeed probable, that the hewer of old usetl flexible wooden .strips or battens bent around the hull to check his fairing, as does the womlcn-mmlel maker of today. If so, these were the forerunners of the flexible strips or splines later emplo^'ed for drawin};;

to which the shipwrights anil shipwere to work. It is often taken for granted that because a heavj' sphne can not have an abrupt kink put into it without splitting or breaking, it must automatically produce a fair or smooth ship line. Wliether carried to tliis extreme or not it is still lines

fair

fitters

necessary,

in

order

maximum

achieve the

to

degree of what G. P. Weinblum calls "geometrical smoothness of the ship surface," to use the

which can be bent into the desired curve, and to supplement the elastic uniformitj' of the spline bj' sighting along it before drawing

stifTest spline

the

lijie.

In the discussion which follows, adapted largely from the work of Weinblum, his term "smoothness" is eliminated. This makes it sj'nonymous with his term "fairness" and avoids confusion \\\i\i the use of ".smoothness" to describe the condition of a

.solid

How

surface along which viscous

takes

is difficult

to describe or to specify fairness,

in a quantitative sense. Following Weinblum, a curve may be called fair when its

especially

first

axis,

derivative with respect to a selected ship

say dy/dx,

continuous.

is

fairness of such a curve

may

The

order

of

be further defined

OS the order of the highest derivative which

is

continuous. Thus a curve in which there is a continuous .second derivative d'y/dx' and continuous curvature; is fair to the second order

still

[Weinblum,

Geometry

The

(I.

P.,

and Kendrirk,

of the Ship, Part I,"

J.,

"On

mii)iilil.

the

TiMB

and 17 of the referenced report, with "smoothness" replaced by "fairness" and .some minor editing:

rep.).

following

"iSpline curvi.-a

is

drawn

Kplinc.

Since

See. 49.S

draftsman endeavors to avoid

tlie

these concentrated loads in the process of fairing, the order of fairness will generally bo higher than 2."

Weinblum gives .several additional criteria among which may be mentioned:

((uoted from pages

in

the pro|)cr

way

1(>

oliould be at

leant fair to tlio mpcoikI order or have continuoim curvature. This followH inuiieending moment on the Hpline. The Kraph of the tending momi-iit and therefore the curvature remain continuouH oven

Ihougli horizontal conccnlrat4.-d loodii uro cxerU-d

l>y wi-lKlit-t

for

fairness,

(a) A small number of points of inflection in any quadrant between two ship axes normal to each other, preferably only one such point (h) Freedom from flat regions (() M(Mlerate changes in the first and .second derivatives. Weinblum goes on to point out that lie foregoing concepts of fairness, although derived from experience and found u.seful in I

practice,

may

fail

completely to give indications

as to ship resistance, especially that due to wave-

making.

The

uncertainties associated with the fairing

and the lack of fairness found in the shapes of well-known ships were two reasons of ship lines

which led to the study

of longitudinal curvature

Volume I. Others were M. Rankine in the 1860's

described in Chap. 4 of the

comments

of

W.

J.

and 1870's

relative to the curvature of stream forms developed bj' the source-and-sink process, the procedures used to shape airship hulls, and

the findings of aeronautical engineers in the shap-

and similar sections. Rankine chose, for the waterline of a ship, a streamline somewhat removed from the boundary ing of strut

of a source-sink stream

form.

Here, along the

chosen streamline or lissoneoid, as he called

place in a real liquid. It

IX SHIP DESIGN' on the

it,

the curvature was such as to produce only three

changes in differential pressure as litiuid flowetl it, from well ahead to well astern. Around the stream form itself there were five changes in pressure undergone by a particle of liciuid in

along

moving from a great distance ahead to a great astern ("An Investigation on Plane

distance

Water-lines," Brit. A.ssn. Rep., 1803, pp. 180-182, under Mechanical Science; Jour. Franklin Inst.,

Jan-Jun

180-1,

For the

XLVII, Thinl

Vol.

2l-2()]; see Sec. 50.2 no,so or

and

Series,

pp.

Fig. 50. A.

en trainee portions of the hulls

Naval airships Ahron and Moron of which were joined to parallel middle-

of the U. S.

the 1930's, bodies,

an

elli]isoi(l

of

order was employed.

revolution of the third

Based upon a length of

entrance a and a radius of middlebixly

b,

tho

ecjuation of the forebody outline in a longitudinal

plane pa.ssing through the axis was

i'

+

(JO.xix) //

'

MATHEMATICAL LINES FOR

Sec. 49.9

The

where x was the distance of any point on the forebody surface reckoned forward of the forward end of the middlebody, and y was the radius from the airship axis to that point.

When

SHIPS

is

contours in the middlebody had zero curvature,

In Reports and

Memoranda 256

of the (British)

W. L. Cowley, L. F. G. Simmons, and D. Coales report as follows:

(49.xxi)

dx'

the curvature was also zero. Since the straight

Aeronautical Research Committee, dated June

line,

this subject,

d^

which meant that

be called a continuous transition. A 0-diml curvature plot of the outline of a longitudinal axial section would show no break at that point.

any curved

MSI

and

those of the entrance joined them in what might

of

expressed as

the middlebody, the second derivative d^y/dx^ for the outline equaled zero,

Kc

from standard reference works on

x equaled

zero, at the junction point of the entrance

195

radius of curvature

The

absolute curvature

sional because

Re

is

is

l/Rc

',

this

is

dimen-

dimensional. Strictly speak-

an irregular curved line has no definite radius However, at any selected point it has an effective Re equal to that of a circle, called a circle of curvature, which coincides very nearly with the given curved line at the given point. It ing,

of curvature.

1916,

is

J.

ship waterlines on a basis of length along the

P. 167. "Previous reports and preliminary experiments for the present report all

showed that the

air resistance of

a strut was extremely sensitive to slight changes in the form and radius of curvature, especially in the neighborhood of the maximum ordinate. For this reason each strut, of a series in which one proportion only is to be varied, must be made with fair accuracy in those dimensions which are to be kept constant." P. 170. "The results of the investigation appear to show that the air resistance of a strut depends very greatly upon the shape of the fairing in the region in front of the maximum ordinate. In a round-nosed strut the change of curvature and slope in passing from the nose to the fairing piece should not be too rapid, a condition which causes the maximum width to be some distance behind the center of curvature of the nose."

Notes on Longitudinal Curvature AnalyFor determining and analyzing the curvature of any fore-and-aft ship line, such as the 49.9

sis.

designed waterlines discussed in Sees. 4.4, 4.5, 4.7,

and

24.13, there are several

methods besides

the semi-graphic one described in those references.

Assuming an

origin of coordinates at

any con-

venient point along the ship centerplane, with abscissas x parallel to the x-axis

measured transversely line,

and ordinates y

in the plane of the selected

the slope of that line with reference to the

possible to plot the dimensional curvature of

fore-and-aft axis l//?(7. first

by using the

reciprocal values

A. Emerson has done this by employing the

and second

differences of the waterline offsets

each equal to 0.025L [INA, 1937, Fig. 6, p. 178; unpubl. Itr. of 11 Jan 1952 to HES]. Plotting 0-diml longitudinal curvature is described in Sec. 49.10. Any of the foregoing methods involving dy/dx

at

40-station intervals,

or

^y/dx

is

and rates

of

satisfactory only

if

offsets,

slopes,

change of slope are taken for at least 40 equally spaced stations along the length of a ship. No method is satisfactory unless the waterline itself is carefully and accurately drawn. From Eq. (49.xxi) preceding it is apparent by mspection that Re approaches infinity as the second derivative d'y/dx^ approaches zero. This is

equivalent to saying that the absolute curvature

l/Rc approaches zero with the second derivative. Since the curvature of a straight line suitable transition

from a curved ship

is zero,

a

line to

a

straight one, such as the parallel portion of a is marked by a diminution of d^y/dx' toward zero at the junction ^vith the straight line. Proper transition is an acute problem in the laying of tracks for railway cars and trains. If a

waterline,

be measured as a

straight section of track, called in railway parlance

natural tangent or as a function of an angle,

a tangent, were joined directly to a curved section of track having a constant radius, the transverse

X-axis

is

dy/dx. This

where dy/dx

=

tan

may

6.

The rate of change of slope, called by D. W. Taylor the "acceleration" a(alpha) in his 1915 mathematical-lines paper referenced in Sec. 49.3, is

acceleration at the junction

would be torn up. Railway have developed several acceptable methods for making this transition between straight and curved portions of track. One of them rails

[I

dx'

+ tan'

tic

B

or the track

surveyors

(49. xx)

= 5- sec

would be so great on

a high-speed train passing from the straight to the curved section that the train would leave the

involves the use of a second- or third-order parab-

HVDRODVNAMKIS

I9fi

=

ola, x'

aij

=

j-'

or

«'ith its viTtex at

bij,

eiul of the straiRlit soft ion of trai-k. it

involves a similar curve with

its

IN SHIP DKSir.N -Modern

tln'

For a ship,

vertex at the

Sec. I'l.lO

procedure

hull-
equally good transitions be made,

between

the

parts

re(|uires if

fore-and-aft

of

that

practicable,

ship

lines.

parallel portion of the ship

Further, the finished lines should be as fair as

a hotly of

end of the straight or

is

modern technology can make them. This calls for the use of some method for guaranteeing a longitudinal curvature that will eliminate Ap

achievtHl liy joiiiinft a parallel cyliiulrical portion

disturbances along these lines or that will indicate

with half of an ellipsoid of revolution defined by

the presence of localized

the relationship jjiven in Eq.

if

line.

For a

S-tlinil

form,

perfect

revolution,

particularly

transition

of

kind

this

(4!).xL\) of Sec.

49.8

not ea.sy for a

or by the identical relationship

this transition

—+^=

1

I'.l.wii)

1

the c((iuition of the

is

"i-dinil

intersection of

the outer skin with a plane pa.ssing through the

sketched in Fig. 49.D, and not of the

a.\is,

;{-(linil

train,

a

it is

human being to realize how sharp may be along the .side of a ship,

ecrtiiinly not as easily as ill

This

dLsturbances

i)re.s.sure

they can not be avoided. Unfortunately,

around

jiniiifi

would be

it

if

he were

a geoinclrically similar

cUI'X'r. 'I'lir

aerial

\

iew of Fig. 49. E,

nieicliaiit

(ill.")."))

permi.ssioii of the

siiip

taken of a moilern

and reproduced with the

Kockums IMekaniska Aktiebolag,

Sweden,

feature in a almost possible lo discern the Velox waves generated by the Maim<'),

illustrates

this

rather extraordinary manner. It

is

liiiward-shoulder pressure disturbance, where the (31

—

hollow in the entrance waterline shifts rather

»-Axis oi Body^''

h

aorLg

'

to the parallel waterline amidships through a convex transition region of rather sharp

abruptly

curvature. (49*XKi)

^(l7-t^ Whani-O, -r£~0 Qndo-^O

Skktch of Airship Nose Outline of Third-Degree Eluptic Shape

Fig. 49.D

body

The

half-length of the ellipsoid,

is on the two portions; L^ is the and Rh is its maximum

transverse

to

surface.

origin of coordinates

axis at the jvmction of the

parallel

radius,

ec|ual

the radius of the

portion. This corresponds to the

com-

bination of no.se and niiddlebody portions of the hulls of the airships

Akron and Macon, mentioned

in the .section preceding.

drawn on

I'^ig.

49.

D

The

tlu;

the after portion of the entrance or

Upon double Eq.

(49.xxii)

extremely no.sc.

dilTerentialion with respect to

reduces

to

the

value

of

r,

d'y/dx'

indicated on Fig. 49.13 as E(i. 49.xxiii). In this ca.se,

as

d'l/'tlx'

=

shown on the and l/lfc is

figure, *'.

cases where

longitudinal cur\'ature in waterlines,

and diagonals, are given

the 0-diml curvature of a designed

]?riefly,

waterUne

buttocks,

here.

of a ship

is

determined for any selected

point along the length by the ratio

Beam By Length

at the section of

maximum

area

of 1-deg arc of the circle of curvature

longitudinal section

indicates

gradual transition from the parallel niiddlebody t(j

Methods of taking care of this situation,

there is no limitation on the extreme beam and no parallel waterline is necessary, are described in Sees. G7.2 and 67.3. 49.10 Graphic Determination of the Dimensionless Longitudinal Curvature of any Ship Line. Details of the graphic procedure mentioned in Sees. 4.4, 4.5, and 4.7, for determining 0-dind for

I'he

when x = 0, combination of

where both

linear

dimensions are given in the

same luiit of measurement. The value of Bx is taken

directly from the ship

beam on the drawing being analyzed, not that of the .ship it.self. Determining the value of the denominator in the ratio given is facilitated by drawing on lines;

it

is

transparent

the magnitude of the

film,

by photograjjhic reiiroduction

or the equivalent, a

and cylinder described in the foregoing gave most gratifying resistance and propulsi(jn results when used on the large rigid

varied radii, comprising the range of curvature

airships nicntioncd.

analyzeil. ()|)posite eaeh such arc

third-order ellipsoid

to be expected in

.series

of arcs of circles of

any body or

shi]) lines to is

be

marketl, in

MATHEMATICAL LINES FOR

Sec. 49.10

Fig. 49. E

number

beam on

and wdth

the dramng, the length of a 1-deg arc

from the relationLength = 0.017453i?c Three such series of arcs, on two separate sheets of film, have been prepared by the Society of Naval Architects and Marine Engineers, which the transparency, calculated

ship:

•

or location of the station

The

When

covered.

circle of

duced, but

7iot to full size,

of Fig. 49. F.

The

in the

upper

The

is

is

definitely

mean between

fit.

The

solution

obviously too too sharp, and

the two.

1-deg arc length found for each station or

then divided into Bx and the ciuotient is The 0-diml curvatures are plotted on

point

LH

corner

tabulated.

is

length, follomng the

method

of Figs. 4.H, 24. F,

The

prolongations of the ship along the centerplane,

measured

waterline

to be analyzed are there-

in inches.

The transparent sheet is placed over the ship and moved aroimd until some circle of curva-

line

it fits

then which

slack,

circle

the waterline at a selected station,

beams on the drawings

ture on

repeated along

and 67. C. They are reckoned as positive and laid off above the axis for lines convex to the water; negative and below the axis for lines concave to it. The method falls down for sharp corners and discontinuities, as where an entrance (or a run) waterline with finite slope meets the imaginary

these sheets are given in inches. fore also

The

is

curvature makes the best

repro-

lengths of the 1-deg arcs on

process

working from large-scale ship determine just which

determine which

to

is

sheet

all

lines it is often difficult to

select the

first

then tabulated

stations or selected points are

vary from 0.2865 to 28.65 inches on one sheet and from 25 inches to 500 inches on the other small section of the

is

the dimension found opposite that

the length until

is

A

it

circle of curvature.

can furnish film positives for the use of naval architects. The radii of the circles of curvature

sheet.

197

Aerial View of a Ship, Showing Relatively Shabp Transition between Hollow Entrance Waterline and Parallel Waterline Amidships

the same units as are to be used for measuring the

on

SHIPS

indicated in the lower diagram of Fig. 49. F.

1IM)R()|)N\

198

\\ll( s |\ Mill'

1)1

s|(;\

Port of

Sec. 19.1

Dio^rom on Film Overlay Carruinq of Venous Rodii

Circles of Corvotore

Parollel of Line

Portion

Lenqlh in Inches of o l-Deqree Arc on Eoch Circulor Arc \

\

Circle of

Curvoture

.Lenqth of This Rodius \ l-Deqree

Rodiu» of Circle of IS

Somewhat Smoller

\of Curvoture

than the Correct Value. to

Make

^ij

'^"' "<• "^^ »

\

Infinite

''«""*

\

ts

'»

Beam Bi 5.49 in

0.10 in

It Visible

-^0-Diml Curvature!

5.49/0O

0

Fig. 49.F

beyond the bow in this ca-se to

Instruction Plan foh Determining 0-Diml, Curvature ok any Ship Line

(or stern). It

appears advisable

terminate the plot at a point where

the circles of curvature no longer

fit,

say at about

0.02oB.r on each side of the centerline.

A

legible waterlinc

graphic method

sudden changes

in

is

extremely sensitive to

curvature,

and

unfairness,

inaccuracies in the ship line being analyzed.

For determining the 0-diml longitudinal curvature of a

bow

exactly the

line or

same

However, instead traiKWerse Uncar luncc the

buttock the procedure

is

as described for the watcrline. of the

maximum beam Bx

dinicnsi(jn in the

maximum depth from

the

,

the

numerator

DWL

is

to the

lowest point of the buttock measured on the

drawing. This corresponds to the existence of a mirror image of the ship above the DWL, and to

measuring

tht; traiisvcr.sc!

tufire

the

maximum

measured

dimension from the

to

trace from its symmetry. This is

diagonal

the waterline-analysis procedure

both port and starboard diagonal i)lancs are swung upward about the centerplane inter.section if

so as to coincide at the plane of the watcrline at

that intersection.

Mathematic Delineation and Fairing of Those working on tlie analytic phase of wavemaking resistance, developing methods whereby tiiis resistance may be 49.11

a Section-Area Curve.

calculated for certain

.shij)

forms, have endeavored

to determine the effect on ship resistance of the

volume along the length. This shown l)y the ortiiodox sectionarea or /l-curvc, described in Sec. 24.12 and illustrated in Fig. 24. F. Indeed, the optimum distribution

of

distribution

is

form of .l-curve, for minimum resistance, has l)ecn found for a soit of geometric sliij) having rectangular .sections througliout and moving in a non-viscous

combination.

582].

For any diagonal on the ship lines the transverse in thf numerator is taken as

diagonal offset on the drawing,

the

intersection with the plane of

highest to the lowest point.s of the imagc-aiui-ship

linear dimension

along

equivalent

drawing of any scale may be analj'zed, -provided the longitudinal and transverse scales are identical. Although the circles of curvature are fitted by eye to the cur\-e underneath, this

I

licpiid

SupplcniiMitiiig

ISN'.VMi;,

this

wiirk,

lit").!,

P.

(,'.

Kig.

;i.S,

I'icii

ileveloped malliriuatic section-area curves

p.

has

wliicli

MATHEMATICAL IJNES FOR

Sec. 49.13

approximate very closely the A-curves of actual and models [SNAME, 1953, pp. 580-582].

ships

Having the equations

of these curves, a ftirther

development along the lines proposed by R. Taggart, using methods similar to those described in Sees. 49.13 and 49.14, should serve for the mathematic fairing of the curves in question. As a check on the fairing of any section-area curve, whether represented by a mathematical

199

,S?IIP.S

ordinate increments. Drawing the unrolled and

untwisted flowline is followed by a measurement of its 0-diml curvature.

The

process

is

not described in detail or illusit does not take account of

trated here because

the untwisting necessary to get the actual model

flowplane into the single plane of the paper on

which

it

is

laid

down. There can be a large

curvature without twist, in the buttocks of a

curvature

short barge with steeply raked ends, or there can

be determined as described for a waterline in Sec. 49.10. For the A/ Ax curve, the transverse, linear dimension in the numerator of the 0-diml curvature ratio is taken arbitrarily as the height of the maximum ordinate on this curve. It is measured on the plot, and is expressed in the same units of measurement as the lengths of the 1-deg arcs on the circle-of-curvature transpar-

be large twist with small longitudinal curvature, when water flows up and around the bossings on a twin-screw ship. Undoubtedly a graphic method could be developed for taking account of both twist and curvature but this should await more definite knowledge as to the hydrodynamic effects of each

Assuming that the height/length

vention of Sec. 24.12, plots of 0-diml longitudinal curvature of all such curves are comparable

on the underwater hull. 49.13 Checking and Establishing Fairness of Lines by Mathematical Methods. The measurement and plotting of the 0-diml curvature of a

provided the stations on the section-area curve are

selected ship's line, described in Sec. 49.10, serve

equation

or

dimensionless

the

not,

may

encies.

the section-area curve

spaced along

\i

ratio of

1/4, following the con-

length exactly the same as are

its

the ship stations along the ship

curvature plot of the

A/ Ax

ABC

line.

A

0-diml

curve for the tran-

Taylor Standard Series parent form, and for a merchant ship of good design are given in Fig. 67. X. 49.12 Longitudinal Flowplane Curvature. A longitudinal flowplane around a ship hull is defined in Sec. 4.11 and illustrated in Figs. 4.P, 4.Q, and 24.L. This plane is admittedly arbitrary, principally because it is assumed to stand normal to every section line from bow to stern as it som-stern design of the

crosses that hne. It

to represent a

is

likewise

ship, for the

somewhat arbitrary

square stream tube along the

flowline at the hull as twisting so that one side of

the tube, and the same

side, lies

always in the

flowplane.

As the flowplane strict

is

almost never a

geometric sense,

it

flat one, in a has to be untwisted and

straightened into the flat before tudinal curvature

its

0-diml longi-

of these features in creating differential pressures

any hne drawn customary way with a ship's curve, spline, or batten. R. Taggart has devised a mathematical method of checking and establishing fairness, entirely independent of any graphic procedure

as a graphic fairness indicator for in the

[ASNE,

May

1955,

of

form:

y

=

ax

-\-

hx^

+ cx^

-\-

dx*

+ ex^ + fx^

(49.xxiv)

Furthermore, Taggart uses integrated relationships instead of the differential relationships of

Taylor to determine the unknown constants. The constant first term of the Taylor expression is eliminated if an origin be selected along a continuous part of the ship fine where y and x are simultaneously zero. For the customary waterline this calls for:

may

be measured. This operation involves laying out, on paper, what would be the shape taken by the inner edge of a piece of sheet metal if twisted into the flowplane shape,

or run encounters the middlebody

trimmed to fit the side of a model at the flowline, and then untwisted into the flat. It is a somewhat

(3) A slope of zero mum value of x

(1)

Separate origins at the

(2)

A maximum

at the stern

in the ship line at this maxi-

(4)

expanded station lengths as ordinate spacing and the developed lengths of the flowline between stations, measured on the body plan, as

metry in the event the

Offsetting the origin

from the plane

half-siding at the

stern has a finite value.

maximum

bow and

value of x where the entrance

tedious piece of 3-diml geometry, involving the slightly

Instead

337-357].

pp.

D. W. Taylor's fifth-order polynomial y = a -\hx -\- ex' -\- dx^ + ex^ + fx^ he found it necessary to employ a sixth-order expression of the following

of

sym-

bow

or

For convenience the

value of x and the half-beam value of

IIM)R()l)V.\AMI(;s l\ Mill' DlSU.N If

nrv

Ixjtli

plai'oti e<|nal

This

1.0.

tti

pliut-.s

tlu;

data in O^liml fomi. Taggart's intrgnitiHl relationsliips are:

I' r

(l'.).xxv)

are tho.se

xy

j

ilx

listcxl in

-=

/

.VBC ship example

the

0-
tlie

li

iluced as

T.MB

T-yiLr

(ID.xxvii)

B

.r'//f/j

(lO.xxviii)

7.S.,la in

I'"ig.

Table

of

lix

coordinates

SX.VMIO |{D sheet

(he

miMlel

I'.l.wvi)

(

Col.

r,

For

places.

worke
(ransom-s(ern design,

-

',

tlie

shwts the

0-
th

;/

SXAME HD

decimal point. In the de
=

f,

Sfc. -fO.H

are accurate to 4 significant ligures following

Pari

They

I.

for the

repro-

l.jO"),

are

lisle
I9.a.

Jo

T.\HI,E

=

(\

I

l)K.SI(i.Sl-;i>

.MoinKicATioNs OF OrrsFn^ ••on OK .\UC SlUP TO Sl'TP LiMITINf!

W.-.i

\V.\TKKI.INK

CoNDrno.ss kor Mathematical

These may be detennincd

fiDin

iiiiy

curve

l)y

Col.

the

I'aiiu.vg

F lists the 0-diml offsets used in

Pbocess

this calculation.

application of Simpson's rule. Tlie relationship

between the constants and the eocfficients a, b, d, c, and / are given in Taggart's Fig. 3, cor-

c,

responding to Fig. 49.11 of See. 49.14. His explanation of the mathematical procedure Ls detuilwl and complete, hence it is not repeatetl here. His

Col.

Col.

.\

Illustrative

Example

ABC

for Fairing the

Ship.

To

ABC

"prime" from Fig. times stations Hi.G 1/0.990

O.IOS 239 0.3S3

0.120.'>

1217

0.20(i5

2092 430S 5909 7354 8455 9245 9707

0.013 0.121 ().2o2 .

De-

illu.-trate

9 997

999 0.983

DWL

accomplished on that portion of the from the FP back to the position of maxinunn waterline

Fig. 07. A in Part 4 this is at not to be confused with the foreand-aft position of the .section of maximum area,

beam B^x

which

is

.

:m> 0.512 0.079 0.794 0.S82 0.943 9S0

to the steps listed hereunder. Actually, the fairing

Sta. 11. It

F

E

(fi/Bx)o

l.OOS

is

Col. Col.

from

carried out according

is

E

Offsets

Col.

New

RD sheet

.

ship

D

Col.

ship

Taggart's method, a sample calculation for fairing the designetl (2fi.l(l.]-ft) waterline abreast tlie

entrance of the

C -

stations

designwl entrance waterline of the transom-stern ABC ship, described in Part 4 of this volume. 49.14

Col.

li/Bx

worked-out example is supplemented by a second example in Sec. 49.14, covering the fairing of the

signed Waterline of the

B

Ti/By

Original

0.-l2Gri

l)..V29

0.5850

O.GGO

0.72.S0

0.7S1 0.SG9 0.930

0,8370 0.9153 0.9f.lO

S'

n 9(i7

9'

0.9S4 0.990

10'

(I

9S35

9931

9U(K)

(K)00

From

is

at Sta.

10.0.

The

successive steps are

described in .some detail:

II.

O

Locate on Ihe waterline ilrawing the origin of the O-diml waterline

which

is

to be used in

the mathematical analysis. This waterline

Is

to

have a lenglli C()rrcs|)onding to 1 station intervals on the ship, from the FP back to the position of and it is to jiass through the point where ^ii-.v when x = 0. Fig. 07.10 of Part 4 shows that 2/ = the DVVIi offset at the FP is 0.5 ft, wlu'ii continued forward as indicated by the diagonal broken liiu" in the upper right-hand corner of Fig. 19. Ci. However, it is a.ssumed here, t
I.

Draw

Sta.

1 1

the designed waterline from the I'P to

as accuratel}' as po.ssible, considering the

stage of the hull design, or use a waterline drawing already made. It is helpful to continue the waterline for at least two stations abaft (he po.sitiiMi

the

of li„x

,

as

is

done

\)\\'\j in this figure is

Kcule

much

in Fig. 49.(1.

Actually,

drawn with a

vertical

larger than the honzontal .scale, lo

show the various features to better advantage. Drawing thin or any other .ship line to a fairly largo

Hculo

will

necdc-d to take

full

mctluKi. It

is

enough

that

Ht)

i)r(Kluc(!

accurate

olTsets

advantage of the mathematical

preferable to

li/Hx (or actual

the

make

the derive
diviiled

the scale largo

0-
values of

bv the half-beam)

,

the numerical figures coiisisttMit, that the inuldeil ofT.set

a(

(he

FP

on the

shi))

corresponds exactly

on Fig. dimensions on the ship this is = 0.47') ft. A stem of .semilying inside the cutwater shown

(o 0.0i:{ times the half-beam, tabulated 78. .la. In ab.solute

0.0i:{(7:i.08/2)

circular .section, in I'ig. 7.{.B, 0..'i|.")

ft,

would then have a molded radius of large-.scale diagram <>f l'"ig.

from the

MATHEMATICAL

Sec. 49.11

LINES FOR SHIPS

201

^"1,000

13

I

5hip Centerlme-'

FP

The

Half-Sid

O

origin

is

accordingly fixed at the

from the ship centerhne. A line OC, drawn through O parallel to the ship centerline, then forms the basis for measuring the ^/-coordinates of the 0-diml which are to be introduced into the mathematical at a distance of 0.013(B„,x/2)

DWL

formulas. III.

The

length of the 0-diml waterline diagram

is the distance OC in Fig. 49. G, corresponding to the length of 11 station intervals on the ship. This distance is divided into 10 equal lengths and new ordinates are erected, marked on

to be analyzed

Fig. 49.

G

as

1'

through

at the "prime" station

The ship station 11 10'. The distance OC

9'.

then the 0-diml a;-distance of 1.000. IV. The 0-diml value of B/B^ from

from the referenced

The 0-diml value 1.003

-

0.013

=

of

RD

to

E

is

is,

in Col.

VLf

C

of

Table

49.a.

offsets

of the

DWL

Ship

curve at the

10

"prime" stations are then taken off the diagram of Fig. 49.G for the distances marked KL, MN, PQ, and so forth. They are converted into 0-diml values by dividing the half- value of

B^x

into

them, following which they are hsted in Col. E of the table. Since the 0-diml ^/-ordinate at Sta. 11 must equal 1.000 for the mathematical computation, when the 0-diml .T-abscissa also equals 1.000, it is made so by dividing the 0-diml ordinate at station 10'

=

by itself. For this station, 0.9900/0.9900

1.000. All other 0-diml ordinates at the

stations are divided

producing the in Col.

F

VI. If

the

of

final

by the same

prime

factor 0.9900,

0-diml computation ordinates

Table 49.a. 0-diml

B/Bx

values

are

already

available for a given designed waterline, as they

DE -

were for the ABC ship, it is somewhat simpler to plot a diagram like Fig. 49. G, embodying 0-diml B/Bx ordinates on a base of ship length, rather than ordinates of ship beam to some selected scale. The diagram then becomes simply

The

to

DC,

is

values of the 0-diml

FG, HJ, and so on, at the ship stations, by subtracting the constant value 0.013 from the RD sheet values. They are hsted ordinates

are then found

The

ABC

sheet, equal to 1.003.

CE, equal

0.990.

D

is

V.

~^

nq~O.OI3 Byf

Definition Sketch foe Mathematical Faieing op Designed Watehline Entrance of

Fig. 49.G

49.G.

-D

a graphic means of picking

off

the 0-diml ordinates

llVl)R()l)V.\.\MiC;s IN Mill' Dl.SK.N

202 for the

ABC

prime stations.

Tliis is

fiifilitiitttl,

for tlic

ship. t>y iimking the orilinatc Dli equal to

namely 100

100.3 units to a convenient scale,

times

the 0-tiiml

made

e(|Ual

to

The

value.

I..')

units,

99.0 units. In the original

ordinate

DC

is

and C'E then e(tuals drawing for Fig. 41). Ci

one such ordinate unit represented

1

ft

length in

the horizontal scale. \'II.

F

final (Mlinil

coiiiputaliuii

onliiialcs in

of

lation of

Curve

constant terms

Coeilicients in Fig. 49.11, following

f9.N

«, b, c, d,

c,

and

/.

Carrying through

the Check Calculation of Original Curve at the

bottom lative

a series of cumuwhich are the mathematically values of y for the "prime" stations

of Fig. 49.1 produces prtMlucts,

faired O-iliml

r through

10'

on Fig. 49.G. These arc to be com-

liarcd with the unfaired Onliml values for the

Table ID. a are then enleretl as ordinates the second column of Taggart's form for Calcu-

Col. in

The

Sec.

Fig. 49.1, produces the numerical values of the

])rime stations in

Col.

F

of

Table

indication of the modifications that were in the fairing process.

down

The

same

49. a for

faired values are laid

at the prime stations and

the entrance

which the computation outlined in that form is carried through to obtain the numerical values Cj Cj and C, of the coefficients C,

portion of the designed waterlinc in Fig. 49. G

Entering these coefficients in the forni for Calculation of Constant Terms, at the top of

is

,

,

The procedure then

described in steps

worked backward to

2/-ordinates at

tlic

ship .stations,

CALCULATION OF CONSTANT TERMS Multipliers

Constant

is

redrawn through them.

,

For Desianed

an

made

26./63-ft Woterlme of Entrance of

ABC Ship

I.

through \l. the O-diinl

find tlio

B

'By values

MATHEMATICAL LINES FOR

Sec. 49.15

SHIPS

203

CALCULATION OF MOLD" LOFT OFFSETS For Two

Baseline

Maximum

Frame

Frame Positions Alono Desiqned 26.163-ft Wbterline of Entrance of

Intercept ot Station

Ordinate

36.175

ft

Maximum- Ordi note Tanqeno^ Half-Sidinq 0.475 ft

ABC

Ship

at Station

Length of Curve, X^

,

1

1.0

II.

Stations

I1M)R()1)\

204 mntlipmaties, of the liuU

l\v

tlic

i)hvnc of

tlic

ill

.\

\Mlc:s

pmCilc dniwiiig

loiitniir or

symuielry. This in-

volves (usually) a straight kcol, a stem profile of the selccteil tyjjc, and a stern profile to suit the

i.\

DISIGN

Mill'

variation

may

This situation wjus jjointed out by J. L. Kent Lackcnby paper [p. 310]. One may visualize a ship form of low total

cally.

in his discu.s.sion of the

resistance for

propeller anil nulder.

Restrieting the calculations to these four lines

forward for

lished

matic

Fig. •U).K illustrates the location

by the designer.

body

of these four sets of jjoints on a schematic

plan. Calculation of offsets for shii)s of special

may be made,

form tional

line.'?

of coui-se, for as

many

arldi-

The Geometric Variation of Ship Forms. Somewhat related to the use of mathematical 49.16

lines

combination

a

is

of

provement

in

performance. There

better

and other altered features hydrodynamic behavior.

49.17

length remains the same in both is

that in which a

is

made

work

but this ening

is

(1)

(3)

mum-.scction area

Ax

may

may

(4) Jour.

have been the

first

along

II. dc, ".\ Trcati.se

Nystrom scries same volume

of papers; also pp. 2-11-244

Franklin Inst., Jul-Dec 1864, Vol. XLVIII, Scries, pp. 261-261. This paper contains

historical data on Cha|)inan'3 previous work on mathematical lines (principally parabolas) in Sweden. Plate IV of the series, mentioned here, i» bound out of place (opp. p. 236) in the volume

some

not

have a maxigreater than that of the well

consulted.

Geometric variations are almost unavoiduljle when laying out model series in which one parameter is systematically varied, described by D. W. Taylor [S and P, 1943, p. 55) and others. More elaborate procedures arc explained and illustrated in detail by II. Lackenl)y in his paper "On the Systematic Geometrical Variation of Ship Forms" (INA, Jul 19r>0, pp. 280-310].

When a geometric-variation

jjrocedurc

to a given ship form to produce; a

question

witli the

although

Third

original ship.

seriouH

They begin

on Sliip-Builciiiig," by the Rev. James Tnman, Cambridge and London, 1S20 Nystrom, J. W., Jour. Franklin Inst., Jul-Dec 1S63, Third Series, Vol. XLVI, pp. 355-359 and 389-396, with Pis. II and III Jour. Franklin Inst., Jan-Jun 1864, Vol. XLVII, Third Series, pp. 4(>-5I, accompanied by Plate I of the

of uniform section. It

Chapman not

Chapm.iii, F.

in the

speed increase, the new portion inserted

be

(2)

lengthened

by no means mandatory. If tlie lengthaccompanied by a repowering and a

for

translateti into English

ship

is

which

past

the

these lines:

a middlebody. Usually the

of

in

in the ITfiO's,

listed here for convenience.

ca.ses.

.ship is

("ortaiii rcfi'iciices

methods developed

at the maximum-scction-arca position

by the addition cut

The

produce

will

delineating the forms of bodies and ships are

closed

inserted between them.

a.'vsurance,

Selected References Relating to Mathe-

matical Lines for Ships,

may

variation

no

is

modified section-area curve, the modified designed

his elTorts

up and those in the run are opened out, or vice versa. Or, by closing up the sections in both forebody and afterbody, a portion of parallel

to

however, in the present state of the art, that becau.se of the geometric variation alone the

the maximum-area section is shifted along the by holding the .same .sections and

section areas, the stations in the entrance are

way

be an easy

LMA

H. dc

A

may

po.sition achieve what appears to be a better and what should give a slight but definite im-

of F.

is

the entrance and

Stretching

contracting the run

describe

i-axis. Here,

LMA

Fig. GG.L to be too far

speed-length (juotient and pris-

its

coefficient.

mathematics and geometry for effecting a variation of hull parameters and coefficients in a given ship form. Perhaps the simplest procedure of this kind is that in which the fore-and-aft position of

middlcbodj'

by

watcrlinc,

as are desired.

equations for ship

displacement, tiespite an

its

position that appears

is

on the basis that if four sets of points are estabon selectetl frames in accordance with the foregoing, they should be sufficient to insure that the principal dimensions and shape, as laid ilown in any mold loft, will be as contemijlated

Sec. 19.16

not work out so well hydnidynami-

is

new one

whether the water

(5)

ulae," (6)

Warrington,

Forms Derived by Form-

N.,

"System

of

Mathematical Lines

SNAME,

Resistance,

(8)

and

Thrown by Model Experiments upon

the Light

Propulsion

and

Rolling

of

Shi[xs,"

Trans. Int. Eng'g. Cong., lOl."), Naval .\rrhitecturc and Marine Engineering, San Franci.sco, 1915 VVcinblum, G., "Beitriige zur Thcorio dcr Schiffsoberfl.iche

(Contribution to the Theory of the

Ship Boundary),"

is

WRH,

22 Nov

l'.r>9,

pp. 462-

1929, pp. 489-493; 7 Jan 1930, pp. 12-14. This paper illustrates a number of .ship forms whoso

t!ik(;

kindly to the change. In other words, what appoarH to be a good geometric or iiarametric

J.

Ships'

1903, pp. 243-267

1909, pp. Ml-1.')2 (7) Taylor, D. W., "Calculations for Ships' Forms

461); 7

will

"On

SNAME,

for Ships,"

applied there

Taylor, D. W.,

lines

(9)

Dec

were

Woinblum,

d('rive
('•.

mathematically. Wiuwerlinion und Spant-

P., "ICxakt<;

MATHEMATICAL

Sec. 49.17

LINES

flachencurven (Exact Watcrlines and Transverse-

Curves)," Schiffbau, 15 Apr 1934, pp. 120-121; 1 May 1934, pp. 135-142 (10) Benson, F. W., "Mathematical Ship's Lines," INA, 1940, pp. 129-151 Section

(11) Sparks,

W.

J.

C, "A New Method

of

Approximate

Quadrature," INA, 1943, pp. 104-117. This paper gives approximate methods for calculating the following from the values of a few ordinates taken from a ship curve, based upon fitting a 5th-order parabola to that curve: (a)

(b)

Area or fullness Center of area

coefficient

FOR (c)

SHIPS

205

Square moment of area about a longitudinal

axis (d) Square moment of area about a transverse axis. Lackenby, H., "On the Systematic Geometrical Variation of Ship Forms," INA, Jul 1950, pp. 289316 H., "Systematische Entwicklung von (13) Thieme, SchifBinien (Systematic Development of Ship Lines)," Schiff und Hafen, Jul 1952, pp. 241-245. On page 245 there is a list of 31 references, (14) Taggart, R., "Mathematical Fairing of Ships' Lines for Mold Loft Layout," ASNE, May 1955, pp.

(12)

337-357.

CM iMatlicinaticiil

\1'

l-.K

i

Methods of Calculating

the

Pressure Resistance of Ships General Early Efforts to Aimlyze anil Calculate Ship

50.1

50.2

Hosi.stance

Moiiorn Dcvplopmentsi

50.3

Wavcmakinp

.\ii.sumption.':

50.0

Presont-Day Calculations Formulation of the Velocity-Potential

Liniitattonti

Inherent

.

The Calculation Components

Other Features Derived from Analytic Ship-

210

50.10

Wave Relations Ship Forms Suitable for Wave-Resistance

212

50.11

Necessary Improvements Mathematical Methods

214 215

50.12

Practical Benefits of Calculating Ship Per-

50.13

Reference Material on Theoretical Resistance Calculations

The forward-looking ship

architect

and designer, imfamiliar with higher mathematics, has wanted to know about the.sc things but could understand

not

written.

He

has

the

papers

and

felt,

that

justifiably so, that

story relating to the calculation of

could not be

made

made

were

simple,

it

wave

being if

the

resistance

should at least be

Someone should take the understandable to those who

readable to him.

trouble to

make

it

had to spend their dajs fa.shioning and building ships rather than covering sheets of paper with mathematical ctjuations. Beginning in abinit 1950, several workers prominent in the mathenuitical field .set out to do just this. .Anumg their efforts may be men-

[SXAME,

(a)

The

l'j;il,

early paper of T. M. Havelock entitled

Patterns and

Vf.l.

7f;,

pp.

!:«)

Wave

Hesistunrc!"

IIO] which, in the

(IN.\,

The

(c)

220 221

1951, pp. 13-24]

more general (and less bj' G. P. Weinblum "The Practical Use of Theoretical

rather brief but

mathematical) account written

and

entitled

Studies in

Wave

[MESR, Oct

1951,

entitled "Analysis of

Wave

Resistance"

pp. 49-52]

Weinblum's paper

(d)

TMB

Resistance," published as

Report 710

in

September 1950. On page 2 he states that the purpose of the paper: ".

.

.

is

to

show

to

what extent theory has succeeded

how

furnishing valuable practical re.iults and of its applications can

"There

is

lie

e.\t<'nded

common agreement

.

.

\\M known that

it

.

that theory

\\t\s

how

sensitive

be to changes, even small changes,

The most

furnisheti it

is

less

also has given us the proof of consider-

able practical value of

(c)

in

the scope

a valuable description of general phenomena;

wave

in ship

resistjinco

can

form."

interesting accotmt presentetl

by

the mathematician-physicist-naval architect team

.1.

"Wave

219

uf ^^'. C. S. A\'iglcy, describes liie theory "without mathematical complications" (b) The somewhat mathematical but nevertheless xery readable paper presented by Professor Sir Thomas H. Havelock on two occasions in 1950 in the United States, entitled "Wave Resistance Theory and Its Application to Ship Problems"

uf

tioned:

and

in Analytical

formance

21()

217

219

Calculations

50.1 General. 'I'lie iiiriuiiiiig and enterprising marine architect ha.s long felt a need for a story on the theoretical calculation of the wavemaking resistance of a ship. He has known that mathematicians, physicists, and even some naval architects have been engaged on this project for nearly a centurj' but that their work was on a plane "sky-high" compared to his own. He has realized, from looking at some of their simpler graphs, that their results compared rather well with experimental data from model ba.sins, well enough to sustain a keen interest among workers

of their caliber.

210

50.9

Wavemaking

Resistance

and E.xperimental

207

in

of \Yavcni!ikingRcsiiitancc

of the Calculated

of Calculated

Resistances

E.\-

pression

50.6 50.7

Comparison

50.8

in the Calculation of

Pressure Uc-iislancc duo to

50-1

anil

200

of

\. Korvin-Kroukovsky, and "Theory of the Wave Resistance |S\.\MK, liOl, pp. Ships," e.spcci.Mliy Pari (!.

M.

(lii'ir

'.VM\].

The JOG

ill

I

•S.Jil

words

MirkholT,

Kotik

presciil cliiiptcr, piep.'ired

by one

ilelinitely

CALCULATION OF WAVEMAKING RESISTANCE

Sec. 50.2

not in the mathematical part of the field, is an endeavor to present a somewhat different version of the story for the benefit of the practising marine architect. It places emphasis on certain features important in ship design. For the architect and engineer who have progressed this far in a consecutive reading

Volumes

I

and

of

the preceding chapters of

II, it is possible to discuss

the

calculation of the pressure resistance of a ship in

rather

eliminating

terms,

specific

terms

the

207

and to fire the heaviest weight of broadside from war vessels. With some few exceptions, they vessels

nature the composition of the propelling

left to

power

of the sails

and the resistance

of the ship

into a speed through the water that would

meet

the service requirements of those days.

The

designers

who

first

put their minds to a

technical analysis of the ship-propulsion problem

appeared to have an instinctive those

who

feeling, as did

labored at the task until about the

involving viscosity effects as found in the Wein-

period 1850-1870, that there was a ship form of

blum presentation

minimum resistance waiting to be discovered. The fact that speed was a dominating factor in

listed in (c) preceding.

For the period from about 1950 to 1956 the matters discussed here have been under intensive study by the Panel on Analytical Ship-Wave Relations, under Project H-5 of the SNAME Hydrodynamics Committee.

The

present author takes the liberty of quoting

from the

directly

paragraph of Sir Thomas

first

Havelock's 1950 paper, found on page 13 of the SNAME 1951 reference previously cited: "It

work

is

impossible to give any adequate survey of this

and fortunately

here,

it is

not necessary to

make

the

attempt; there are e.xcellent summaries which have been published from time to time, and in particular I would for a comprehensive account with references, to Wigley's recent paper, "L'Etat Actuel des Calculs de Re-

refer,

sistance de

Vagues (The Present Position

Wave

tion of

Resistance),"

ATMA,

of the Calcula-

Paris, 1949, Vol. 48,

most easily propelled ship form seems to have been overlooked, because the range of speeds at that time was still small. However, those seeking this form of least resistance appeared to have a definite thought that, somehow or other, they could calculate or derive its shape by this quest for the

analytic methods. Calculating its resistance

having an appreciable, ship resistance, so

W.

J.

much

if

not a major effect on

so that J. Scott Russell,

M. Rankine, J. R. Napier, and others of made use of certain properties (prin-

their times

cipally the profiles) of trochoidal surface

plotting the profile of a trochoidal

advance:

Russell,

Regardless of what he

their

work

in the past,

the

all

may have

thought of

he should realize that who have been

analysts

engaged on this problem, for the period 1925-1955, have followed up their theoretical work with model experiments, in an effort to prove or to disprove (2)

are

—

—their theories

They have engaged

resistance only.

strived to in

a

make

it

calculation

clear that they of

wavemaking

Other phases of pressure resistance

have been considered, but not included

in their

Early Efforts to Analyze and Calculate

Ship Resistance.

aim the

to

wavy water

use

"the lateral displacements of

to correct the effects of its undulating

." [INA, 1863, p. 226]. be remembered that the developments outlined in this section all took place before the first model basin was commissioned by William Froude in 1872. It is apparent, further, from the

surface,

.

.

It is to

fact that proposals such as those in the preceding

paragraph were made by eminent men of the period, that their reasoning was not equaled by their observation of ship phenomena. It is a sign of real progress that the testing of ship models,

tion of

Until the period 1840-1860 the

the

and builders was to crowd merchant

lem

of ship designers

maximum

panying the afterbody, turning this profile over on its side, and then making the waterline of the ship's run a sort of complement to the wave profile. This was done, in the words of J. Scott

subsequent to this time, has been accompanied by a greatly increased attention to and observa-

predictions.

50.2

in

They

compensation could be achieved by wave accom-

resistance

So far as known, the Wigley paper referenced here has not been translated into English. For the benefit of the naval architect who is giving this matter serious attention for the first time, two features should be pointed out in

practically

waves

laying out the waterlines of their ships.

evidently hoped that a useful degree of wave-

pages 553-587."

(1)

was

a thought and a task for the future. Nevertheless, surface waves were recognized as

of carrying capacity into

hydrodynamic phenomena on

ships, in

full scale.

Rankine, in the early 1860's, tackled the probof the flow of water around a ship from a

iiM)ii()iiv\ \Mi(:s i\

208

purely analytic point of view. a two-dimensional

and then brought

body it

in

an

He

slarled with

unliniitotl

liquid

to the surface, so to speak.

When he did so he realized that surface waves would be formed but of these "principal vertical disturbances" he assumed them "to be so small, compared with the dimensions of the bodj', as not to produce any appreciable error in the consoijuencos

of

the

supposition

of

(licjuid)

motion in plane layers" [Phil. Trans., Hoy. Soc, London, 1S04, pp. 383-384]. Whatever may be said of Rankinc's sense of values and of physical laws in this matter, he did succeed in deriving mathematically an infinite series of 2-diml and 3-dinil shapes for which not only the boundarj' coordinates but the velocity and pressure distribution could be calculated. It seems reasonable to suppose that eventually he hoped to be able to calculate their resistances to motion in a li(|uid. With the assistance of Clerk Maxwell, as related previously in Sec. 2.11, he devised graphic and geometric methods of drawing the outlines of these oval forms, called here Rankinc stream forms, as well as the procedures for constructing the streamlines

around them. Rankine's endeavors [Phil. Trans., Roy. Soc, 18G1 and 1871] constitute, so far as known, the first scientific attempt to take into account the prime factors of velocity and pressure around a ship hull. Tjiis important .scientific

—

siiii'

nisicx

contribution

cinlKRlicii

Sec. 50.2

Kankine's invention

the concept of radial flow, later to be

some

(luartcrs as source-sink

(low,

known

of in

and subse-

quently to be utilized to some extent in practically all

attacks on the wave-resistance problem from

1890 to the present. While

it

G. R. JvirchholT emploj-ed the

is

reporteil that

artifice of sources

hydrodynamics as early as and Ince, S., "History of Hydraulics," La Ilouille Blanche, B/19'}'), Chap. 9, p. 201], Rankine's search for the fundamental velocitj' and pressure relationships in the surrounding flow laid the groundwork for the u.seful

and sinks 1845

in analytic

[Rou.se,

II.,

features of this concept today.

One interesting feature of Rankine's work, seldom brought to mind in these years, is that while he considered the oval shapes resulting from his new procedure to be general forms of waterlines, it was not at all his intention that the blunt-ended "neoids" or stream-form outlines generated

by placing a source-sink pair

in

a

uniform stream be incorporated a.s waterlines in actual ships. lie proposed instead that one of the stream surfaces lying iji the litiuid outboard of the oval form, comprising both hollow regions and convex shoulders, be u.sed as the hull surface at the ship waterline. To this shape of boundary, represented by the trace Ls — Lb in diagram 1 of Fig. 50. A, or by any streamline farther removed from the stream form, he gave the name "lis.sone-

CALCULATION OF WAVEMAKING RESISTANCE

Sec. 50.2

oid," signifying a ship surface over which the water might ghde easily [INA, 18G4, pp. 327-328]. Of these surfaces he said:

"The

which are of

co-efRcients of those Lissoneoids

proportions available for practical use (the length being four times the breadth, and upwards) range from three-

and differ but Uttle in any case from which is also the co-efficient of fineness for a curve of sines" [INA, 1864, p. 327). fifths to two-thirds,

0.637,

The

latter

corresponded to

Scott Russell's

J.

waterline curve of versed sines, reproduced in

A

diagram

of Fig. 24.

G

Volume

in

I.

It

seems

clear that Rankine, as a ship designer of that

and

as well as a mathematician siderable

renown,

use

did

scientist of con-

shapes

resembling

some

lissoneoids for the waterlines of

Rankine points

day

ships.

out, in his 1864 paper, cited

earlier in this section,

that along a lissoneoid,

clear of the stream form,

there

is

a region of

209

by the length L„. of a same speed, with two adjacent crests opposite the bow and stern, and with its trough amidships. Second, he the ship was matched

trochoidal

wave

traveling at the

assumed a hypothetical barge-shaped ship with a given constant beam and a vertically curved bottom, shaped to a nicety so that

it fitted

exactly

wave and

into the trough of the trochoidal

rested

everywhere upon the wave surface, like a sailor relaxing in a hammock. He took for granted, as did everyone else at that time, that the friction resistance along the ship's side varied as the square of the speed. Further, that the friction

resistance along the under side of the bargeshaped ship was balanced by a forward thrust or propelling force which, exerted by the water under

the run, just counteracted the friction effects

upon the whole

barge. This procedure appeared

to be exceedingly clever, because

it

obviated the

+Ap

necessity of estimating or computing those effects.

abreast the leading edge and another abreast the

Rankine then transformed the curved-bottom barge into a ship with a mean girth equal to the

maximum

positive

trailing edge,

pressure

differential

maximum

with only one region of

negative differential pressure

— Ap

abreast the

middle of the body. Around the neoid or stream form proper there are two points, one on each shoulder, where the

Ap drops

maximum

to its

negative numerical value, while at amidships rises

it

somewhat lesser negative numerical This means that, around and along a

to a

value.

barge's beam, and with a run which

was characby a waterline having the shape of a trochoid. Utilizing a few more transformations terized

that

read

a story of alchemy,

like

evolved a formula for the

Rankine

resistance of the

total

ship. Rewritten in the notation of this book, his formula states that the total ship

neoid, the pressure changes the sign of its longi-

tudinal

gradient

and

(rises

falls)

six

times,

Resistance

whereas along a lissoneoid it changes only four times. This situation is shown schematically in diagram 2 of Fig. 50. A. The significance of these changes was appreciated by Rankine, who felt

=

Cf;^- V'L{ ,, Vgirth 2g

I

.

[1

+

4 sin^ in

-F

4 sin' ia

/

+ sin*

in] (50.i)

that the fewer the pressure changes along the side of a ship the better.

With this background, and some previous woi'k on waves [Phil. Trans., Roy. Soc, 1863], Rankine developed two formulas, essentially similar, for calculating the resistance of a ship having a certain shape of waterline. They are described here at some length, not so

much

interesting historic value,

or of their practical

because of their

and physical worth, but because of the lines of reasoning by which they were derived. It is of Uttle present importance that the hydrodynamics was faulty or that they proved inadequate for design purposes but derivation

it

is

important that the of hydro-

was based on considerations

dynamics rather than on the intensely practical nautical knowledge of that day. Rankine considered, first, that the length L of

[1

where Ir

is

the

maximum

waterline in the run and

The

+

sin* in]

slope of the trochoidal

V

is

the ship speed.

third term in the brackets, sin* Ir

,

may

become small enough to be neglected in comparison with the others. Based on the use of English units

of

measurement,

the

friction

coefficient

according to the knowledge of that time, Cp was about 0.0036 for the clean, painted surfaces of iron ships ["On the Computation of the Probable Engme-Power and Speed of Proposed Ships," INA, 1864, pp. 316-333]. The terms to the left of the brackets, combined with the first term within them, namely unity, gave the friction resistance only. The pressure resistance was added by taking account of the ,

IIM)K()1)\ NAMIC.S

LMO second ami third

ti-iins in tlic

luarkrls, hut in such

Mill' 1)1.,SU,.\

l.\

in u.se in

many

Sec.

quarters today, as

may

WJ

be noted

product of the length L, the mean girtli, and the terms within the lirackets "tlie augnientod

from Sec. .'JO.7 of this part of the book aiul from SX.VMI'] Technical and IJe.search Bulletin 1-2, Marcli l'.).J2, page 3. If Rankine did not choo.se to emphasize those factoids which have since become important, he must at least be given credit for outspoken discussion of the subject and profes-

surface."

sional honesty,

a manner that

in

it.

Rankine

hiter.

a t|unntity cakuhitod

way as tlie friction resistance and More is said of tliis uuusiud feature

the same addetl to

it ftiriiuHl

The year

callwl

the conil)iiiation

of

tlie

following the publication of this

first

and after developing his ncoids and Rankine derived from them a similar formula but by a (|uite dilTerent approach, taking formula,

lissoneoids,

"into account not only the direct resistance caused

by the longiludinal component caused

resistance

the

of the friction, but

through

indirectly

the

assuming the vertical disturbance (of the water surface) to be unimportant" (italics and comments in brackets are

Despite his lack of knowledge of the laws of resistance Rankine brought out the

friction

following important points:

The

(a)

thase of the present author) [Phil. Trans., 18()4, p. 384). Rankine's reasoning here is not too clear,

there

is

no douljt that he was thinking intensely

on the subject. The second formula, given "as a probable approximation for lissoneoids" [Phil. Trans., 1864, p. 390], takes the following form when put in the notation of this book:

use of the longitudinal instead of the

tangential components of the friction drag in the direction of motion

especially as to the source of the reduced pressure

at the stern in a region of potential flow, but

highly prized. In the referenced

Resistance."

decrease of pressure at the bow, and diminution of pressure at the stern,

still

on page 390, he headwl the section containing his expression for Eq. (50. ii) with the frank statement "Provisional Formula for Resistance." On page 296 of his later 1871 paper a similar heading reflected his increased confidence in the formula by reading "Probable Law of 18(14 paper,

The use of the velocity with whiili the water moved over the surface of the ship, as

(b)

actually

contrasted to the overall speed of the

.ship.

During the period from 1858 to 1863, and

prcjb-

ably at other times, Rankine (with J. R. Napier) used the formulas of Eqs. (50.i) and (oO.ii) "with

complete success in practice, to calculate before-

hand the engine-power required to propel propo.sed

« = C,|,S'r{l+4(^y]

(.50.ii)

vessels at given speeds" [Phil. Trans.,

1863, p.

136].

where

.S

is

correction

the wetted surface with no obliquity

and AV, measured abreast the

of the bfxly,

miiklle

the increa.se in the "velocity of

is

gliding" over the .speed of the vessel, due to the potential flow around the If the sin* i^

expressions

.ship.

term of Eq.

within

equations become

the

(oO.i) Ls neglected,

brackets in

e.s.sentially

these

the

beam

incrca.scs

both

the

1864; Jour. Franklin Inst., Jan-.Jun

ISiit,

XLVII, Third Series, pp. .308-312]. As with many other things of that

period the

similar in that both

sin"

and (AV/V)'

!«

fact,

resistance. In

the inclusion of the.sc terms to the second

power may not be too distantly conclusions derived

many

later,

to

the

under similar circumstances the calresistance due to wavemaking increiuses

cfTect that culatetl

T. H., IN.\, 1018,

beam

p. Jdll.

Despitr- the inr-on)[)lctc knowli-dge

phenomena upon which they were (.jO.i)

and

(.")().ii)

[Il.uvclnck,

bear a striking


phy.sical

i)a.se
I'](|s.

likeni-.ss to

those

\'ol.

formulas have long since been forgotten, at least in their original form, but their purpose remains as valid as when it was expres.sed .ship-resistance

nearly a

related to the

decades

as a function of tho.sf|uare of the

the friction and the pressure resistance [Phipjis, G. II., Inst. Civ. Engrs., London, 8 and 15 .Mar

two

are indirectly functions of the beam. Increasing

and at the .same time increases the

Other engineers and scientists, working indeon the problem in Great Britain, endeavored to find formulas for calculating both pendently

50.3 of

(•(•ntur\-

ago.

Modem Developments in

Pressure Resistance

The

Due

to

the Calculation

Wavemaking.

early history of the analytit^ allaik on the

problem of ship resistance, sketchetl in Sec. 50.2, shows (irst some groping and spasmodic efforts, then the beginnings of an active campaign that in the period 1920-1955 has become .systematic and has shown increasing promi.se of practical re.sull.s.

CALCULATION OF WAVEMAKING RESLSTANCE

Sec. 50.3

This campaign was initiated by

H. Michell in

J.

Mag., London, 1898, Vol. 45, pp. 106-123] and carried on by T. H. Havelock, W. C. S. Wigley, E. Hogner, G. P. Weinblum, R. S. Guilloton, J. K. Lunde, and others, along somewhat varied and independent lines. It is based generally upon one or more of the following: 1898

[Phil.

(1) Utilization of the slopes of the ship surfaces

with respect to the direction of motion (2) Utilization of source-sink combinations and

fact that it is invariably necessary to establish the velocity potential of the flow around the ship means that there is

concurrently available a powerful tool for deriving of the flow characteristics and hence many

most

useful features of ship performance.

For example, boundary-layer,

propeller-suction, and other should be possible to determine from any one or all of the following:

effects, if it

(3)

Calculation

of

the

(a)

wavemaking

from the velocity potential derived around the ship form.

resistance

for the flow

tions of Rankine's original work on point sources and sinks and the later development of line sources and sinks by D. W. Taylor. The stream-form ship is not only brought to the surface from a region of unlimited liquid all around it, but the surface waves are now so large that the wavemaking effects enter as a major factor in the resistance. A distribution of radial flow from one or more sources and sinks which, in a uniform stream of unlimited extent, produces a given body form,

requires extensive modification to produce the

same form at and near a

do not form a pattern which is symmetrical forward and aft with relation to the ship. Hence, although the schematic ship moves in an ideal liquid, it does possess a pressure drag due to wavemaking. D'Alembert's paradox no longer holds here, where the body is so close to the surface that its motion produces surface waves containing an appreciable amount of energy. calculation of this pressure drag, along

and analytical lines, has been the primary aim of those who have done the recent work on this problem. However, it became evident at a rather early stage that these methods pointed the way to other achievements in calculation and theoretical

prediction

procedures.

Some

them

of

are

direction of flow over the underwater

1948, Vol. 90, pp. 48-63]

The stream

function, which in turn should enable a 3-diml plotting of the stream surfaces in the surrounding field. This takes for granted

the ultimate practicability (not

(c)

The complete

hull

form

(d)

The

pressure distribution over the

points in the field surrounding the hull

where the

local

velocity

The

effect of

An

changes in the ship

somewhat more

of

in

detail,

it

this fact, because it

discussions

of

may is

be well to

often lost sight

theoretical

amd mathe-

types of size,

pro-

example showing the

effect of

changing the

distribution of section area in the forebody

given by

B and

is

Wehausen [SNAME, 1951, Fig. The general subject of wavemaking

V.

J.

p. 26].

resistance as a function of the ship form, pro-

and dimensions is discussed by G. P. in TMB Report 710, dated September

portions,

Weinblum

1950, pages 25-61.

Embodied in this is the disnumber of detail features.

cussion of a considerable

In connection with (e) preceding, it may often be simpler and quicker, especially with modern computing machines, to introduce special conditions into an equation and solve for the answer than it is to endeavor to obtain the answer experimentally.

Regardless of the line of attack employed for

the total resistance,

emphasize

many

and shape.

portions,

on the bulb bow, described in Sec. in

equal to the ship

instrumentation

deriving the

67.6. Before

is

speed, such as are required for

by F. H. Todd [SNAME, 1951, pp. 78-79], among them the analytic work of W. C. S. Wigley proceeding to discuss the modern lines of attack

achieved)

revolution.

de-

scribed

now

stream function for the flow around a 3-diml body which is not a body of of expressing the

(e)

radial flow

The

INA,

free surface. Further-

more, the secondary surface waves set up by the moving pressure disturbances incident to this

The

hull surface at selected points [Guilloton, R. S.,

(b)

This procedure involves considerable modifica-

the expression for the velocity

if

potential can be modified to take account of

distributions to represent the disturbance pro-

duced by a moving ship

211

The

matical methods.

wavemaking

of the three (or

resistance, it forms one more) principal components of

foUomng the W. Froude The others are

subdivision of the early 1870's. friction

of

eddy-making or separation and the interactions listed in Sec. 12.1

resistance,

resistance,

Volume

I, if

they are taken into account.

11M)R()1)^\ AMICS IN Sllir DlSKiX

212

To

ns

l)o suri',

is

cxplninrtl shortly, the ciirroiit

(195o) mathoiimtioal theory Uoos not recognize the fact

the actual sliip

tliat

hqiiid, tliat it

is

moves

in

a real

thickness

varj-ing

more

simple

dcx-s the

beam theory lake account

of the complexities in the ship, yet

stmcturc of a modern

contiiuially

is

it

employed to predict

the stresses and strains in this stmcturc. If corresponding complications do not prevent everyday

use of the simple

beam

theory, the jissumptions

implicit in the i)resenl-day applications of theo-

hydrodynamics to a prediction of ship

retical

behavior should not hinder its use wherever applicable. Continuation of the theoretical and analytical development of the past 50 years for another half-century into the future, corresponding to the lias

been

full

century that the

beam theory

may

use for ship structures,

in

well

bring to the hands of naval architects a flow theory equally simple in application if not in character or exprossion.

Assumptions and Limitations Inherent Present-Day Calculations. The a.s.sumptioiis which must be made to obtain a solution of the theoretical wave resistance of a ship by the most 50.4

in

modern mathematical methods (1955) believed, appear in a ch^arcr

procedure

is first

for

procedure

this

it,

[Lunde,

J.

K.,

and Wave

Apr

(1)

The

first

II.

are principally indebted is

as follows

described

the Theory of

Profile,"

10,

Rep.

"On

the analytic

Wave Resistance

Norwegian Model Basin

1952, p. 2]:

step

is

any wave motion

to calculate

actual assumptions made, as embodied in

The

Lunde 1952

the

reference, are quite definite

and

straightforward: (a)

The

liquid

continuity, and

homogeneous,

is

is

it

it

retains

incompressible; that

is,

its it is

not subjected to ehistic d(?formation

The

(b)

li(|uid

ideal

is

in

that

it

is

without

viscosity (c)

The

action has continued for a sufficiently

long time so that steady motion

is

established

everywhere (d) The wave height is small wave length, with a wave

in compari-son to the

and a wave

slope

steepness that are likewise relatively small (e)

The

velocities

compared (f)

due

wave motion are small

to

to the ship spceil

Outside of the displacement thickness 5*(delta boumlary layer, which is relatively

star) of the

compared to the beam or draft of the ship, motion is irrotational and can be characterized by a velocity potential (/)(phi) thin

the

liquid

which,

when

dilTerentiatcd partially, produces the

body axes:

three comi)oncnt velocities along the

=

M

d(t>

T^

V

ax

=

— ay

dz

These velocities are as.sumed to be so small in comparison with the ship's velocity that their squares and higher powers can be neglected, (g) The liquid motion around the ship can be represented by the combination of a uniformstream flow parallel to the ship axis and a railial flow

to neglect

wave system,

the ship resistance due to wavemaking.

will, it is

explained. Paraplnasiiiff T.

whom we

Ilavelock, to

li^lit if

pressures developed on the ship surface,

th
or from the energ.v in the

surrounded by a boundary layer

and velocity, that it is generally accompanietl by a separation zone at tlie stern, or that it is driven by propellers with velocity and pressure fields of their own. Xo of

From

Src. •in.4

associated

combination

of

with the desired or necessary sources,

sinks,

and

doublets,

produced on the free surface, as if the latter were covered with a sheet of ice which moves aside to pemiit pa.s.sage of the .ship, and to con.sider only the lii|uid motion jjrotluccd by the ship

placed anywhere within or on the hull boundary (h) For rea.sons largely nuithematical, to keep

(2) The second stop is to obtain the wave disturbance produced l)y this motion while ignoring

proportional to the liquid velocity.

the presence of the ship in

its effect

upon these

waves (3)

The

theory,

third step, not yet po.ssible with existing is

to evaluate the influence of the ship

on the waves so calculated (4) Finally, by a stjries of HUcce8.Hive approximations whiili remain to be worked o\it, to determine Ihc actual

wave disturbance

aroinid

the ship.

certain integrals determinate,

the ideal

li(|uid ilocs

it is a.s.sunu>tl

that

exert a small friction force

The damping

thus arbitrarily introduced is dimini.shed to zero in the analysis as soon lus it has .served its purpose. Actually, this procedure insures coeflicieiit

that the surface waves always

trail

the ship,

i)receding,

the

effects of viscosity in the liiiuid are neglecteil

and

(i)

Other than as

listed

in

the boundary layer as such (j)

The

(h)

is

considere
pressure resistance due to wavemaking,

under the foregoing

contlitions,

can be

consiilercti

Sec.

CALCULATION OF VVAVEMAKINC RESISTANCE

50A

equivalent to that encountered

when

viscous flow

influence

each

a first approximation, and be calculated separately. least as

may

1

therefore

(k) The ship form possesses easy waterlines and buttocks (with small slopes), so that separation

The length-beam

ratio

is

large

Condition

'A,

Symmetrical

Direction of

—|lftl^

I

/.

height, the particle velocity in the

K.,

[Lunde,

J.

SNAME,

p.

Motion

'

^

-

•

Modification

^ ^

^ ^

^'

'i

on this Side

•

-I

—

•

I

C Shown

on This Side

Wall Sides and

Porobolic

Z.

WL

0.40

A

Graph 0.35 in

in linear

1951,

J

NPL Model l790B,with

wave, and the slopes of the ship waterhnes and buttocks are limited in magnitude only by the necessity of keeping the general expressions for

form

ti

B Shown

Modification

^

motion do not affect the pressure resistance. This is a simplifying but not a necessary assumption.

and wave resistance

Mid length

1-^3 ft-^

(m) Change of trim and sinkage due to the ship

velocity potential

:

T

with Mode.1 Fore and Aft

1

its boundary and the beam-

draft ratio moderately small

The wave

ft

ft

-4

does not occur in any region around (1)

16.0

1.5

iBoundoru-Layer Displacement Thickness 16 is Greotly Exoqaeroted Here

I

at

other,

Beam,

I

the friction resistance and the resistance due to

wavemaking do not

Lenc^th of Model,

\*

present, as on an actual ship. In other words,

is

213

Model

for a-dimi

Diaqrom

1

Graph B for Conditit

0,

83].

is

Condition A,

OZS

Actually, the ship forms to which the analytic

O.ZO

procedure can be and has been applied are by no

means

excessively thin

and

0.15

fine,

as witness the

forms depicted in SNAME, 1951, Fig. 6 on page 18, Fig. 8 on page 20, Fig. 9 on page 21, Fig. 7 on page 72, and Fig. 3.Q in Sec. 3.13 of Volume I of this book. Change of trim, involving slope drag in addition to hydrodynamic resistance, is not a sizable factor except in vessels intended to run at high speedlength quotients. The pressure resistance due to

wavemaking, in the usual model-testing and shippowering technique, is considered to be independent of the friction resistance, although there are known to be interactions between the two,

°°°

0.16

0.18

0.20

02Z

Froude Number

0.2A

O.Zb

0.28

y-^oL

Fig. 50. B

Calculated Resistance Data for Slender 2-Diml Ship Forms with and without Allowances fob Boundary-Layer Thickness and Separation

is

small in proportion to the ship's transverse

dimensions, indicated at

1 in Fig. 50. B, this is true only from the stem to that region along the

discussed in (d) of Sec. 12.1.

run where the boundary layer thickens perceptibly

This leaves but two limitations of consequence. The fact that the run of the ship must be suffi-

as the ship surface recedes from the water flowing

ciently tapering, both horizontally

to avoid

method

all

as

separation

and

vertically,

means that the analytic

now developed

is

limited definitely to

pressure resistance due to wavemaking. Pressure resistances

due to separation and other factors

have to be calculated separately.

It

is effective,

therefore, in determining only a part of

what

is

generally classed as residuary resistance.

The major

limitation of the analytic procedure

to take account of the effective change in form of the run, especially near and at the stern, caused by the displacement thickness of the boundary layer and by whatever separation zones exist there. While the displacement thickness

is

that

it

fails

past

it.

When it recedes at too rapid

tion occurs in a form such as to

fill

a rate separaout or fair out

the blunt endings.

The

separation-zone effect can be allowed for

by a method developed by T. H. Havelock and illustrated schematically at 2 in Fig. 50. B, adapted from Fig. 1 on page 262 of INA, 1948. Here the ship form is enlarged by the addition of an "appendage" at the stern which is estimated to be of the proper size and shape to produce a potential flow (and a surface-wave system) about the ideahzed ship that is found around the actual ship. Unfortunately, this estimate involves a knowledge of and an abihty to predict separation which is greater than that after a fashion

HYDRODYNAMICS

211 roflotttHi in it is

Clmp.

of this part of tlio hook,

I(>

certainly a step in

Curve

A

tlu- rinht

in iliagrnm 3 of Fig. 50.

=

/•'.

B

gives values

((0.5B)J]''J, on a basis of \'/\/gL, for the eah-iihited

of the expre.'vsion /^h

Frouiie ninnl>er

l>tit

liiicttion.

waveinaking re.sistanec of the 2-din)l model in diagram 1 of the figure, when moving ahead in an iileal li
IN SHIP DI:SIC;N

Sec. 50.5

condition. For this purpo.se a .second 3-diml or

image source B, with a velocity potential of is added at a distance above the free-surface plane equal to the submergence of source A below it. opposite sign,

The

potentials

velocity

sources, taken

Volume

from Eq.

two

the

of

(3.xiii)

3-(linil

of Sec. 3.9 of

are expressed as

I,

'.i

C

The

gives similar data for Modification C.

run

effect of easing the waterline slopes in the

'i>*

They

= JT ^^

*o /<"«

arc added to form the velocity potential of

the source mo\Ting under the

A

flat free surface.

general term

appears to be very large comparofl to the small size of the appendages adiled.

Allowing

boundary-layer

the

for

discussed brieflv

bv

elTect

*.s i.s

K. Lunde [SXAME, 1951,

J.

50.5

Formulation

the

of

Velocity-Potential

Given the a-ssumjitioiis listed in Sec. and accepting the limitations stated there, one analytic procedure may be outlined brief!}' as follows. Granting that the shape of the underwater ship hull, as well as the motion of the water around it, is defined by a given combination of sources and sinks and a superposed uniform flow, the internal sources and sinks, Expression.

.50.4

then added to produce the elTect of all other supplementary sources, whether they are "body" sources below the liquid surface or image sources in the air above it. Hence the velocity potential for a moving source may, to the first approximation, be written is

p. 83).

preceding

= *.+ In

many

.^«

+«.,= -

^-^+

of the references of Sec. 50. K!

2.<

Rs it

will

be

balancing each other in strength, can determine

foiuul

the hull shape but they have no effect upon the

having 47r in the denominator. This is solely because the 3-diml source strength ?h is defined as equal to the quantity rate of flow Q, instead of

external resistance. This

caused solely by the

is

image source(s) used to produce the .surface boundary condition; that is, to keep the free surface sensibly

By

flat.

starting with the force

produced on a typical internal source by the fluid velocity at that point resulting from the image source, it is possible to arrive at an expres-

wave

sion for the surface Expre.s.sed in

more

one

may

with a .3-diml .source placed at some point the

bow

start

in.side

of the schematic ship, below the waterline.

Thi.s source is so placed that, in (Mimbination with

when superpo.sed on produces an entrance

others to be added later, and

a uniform-stream flow,

it

for the ship of the desired size

Moving by

it.self

and

at a steady speed

shai)e. clo.se

under

the free liquid surface, the low source, called for

convenience,

flowing toward

a

surface;

it

not at its

wave above

only

own it.

diverts

level

is

to flatten out the

the

A

liquid

but also produces

Following the procedure

dcHcribed at the beginning of Sec.

bow

.50.4,

step (1)

wav«' above source A,

bringing the free Hurfmc back to

its

The

as Q/47r.

original al-rest

by

latter corresponds to the notation

in this book.

Making use passing

Theorem, ami mathematic complicated and

of the Bernoulli

through a long

transformations,

much

series

too

of

involved to be given here, an expression

resistance.

specific terms,

modilied

that these expressions are

is

derived

which permits almost any finite number of sources and sinks to be used to rejjrcsent the imderwaler form of the ship. 'J'liis velocity potential may, in fact, be expre.ssetl number of dilTerent forms, depeiuling upon ill a the plienomcna which are to be predicted or calculated from it. In any of its forms, however, for the velocity potential

it

must

Second,

first it

conditions

.satisfy

nuist

the continuity conditions. the various boundary

sivtisfy

corresponding to

tlie

.shape

of

the

tmderwater form and the shape of the free surface around the nioviiig shii) (this surface need not nece.ssjirily be fiat in the final form of the velocity pot.<'ntial;

indeed

In thewoi'ds of

it.

is

M.

not

M

fl.-il).

Mmik, when

spe;ikiiig of

CALCULATION OF WAVEMAKING RESISTANCE

Sec. 50.6

vortex theory, one might say that any method

seems not to appeal readily to minds not thoroughly mathematically, and gives rise to confusion among practical men rather than serving to enlighten them" [Proc. First Int. Cong. Appl. Mech., Delft, 1924, .

.

p. 435).

The

50.6

Calculation of

Wavemaking

Resist-

Having achieved a suitable expression for the velocity potential which meets the continuity and boundary conditions, much easier said than done, there are several ways of using it to obtain ance.

the answers desired. In the case of the resistance

due to wavemaking, at

approach

least six lines of

The most

This result

and obvious method, condue to wavemaking is indeed developed as a pressure directly on the ship, is to integrate the longitudinal component direct

of the resultant liquid pressure over the hull.

This is equivalent, as T. H. Havelock says [INA, 1934, p. 439], to obtaining "the combined backward resultant of the fluid pressures taken is

by no means

the simplest method for purposes of calculation." (b)

Introducing

artificial viscosity as

a damping

assumption (h) of Sec. 50.4, or in fact emplo3dng any artificial kind of liquid resistance, means that the energy put into the wave system has to be derived from the rate of dissipation of energy in the liquid around the body. This method, in the words of J. K. Lunde, "... has certain important analytical advantages; effect, listed in

nevertheless, (c)

By

it is

highly artificial ..."

it is

pressure drag due to

possible to calculate the

wavemaking

not given in the later edition]. This force if

when

m

and m' are

of the

same

if

sign,

is

and a

is, if one is a source and one a sink. If we suppose a body to be at rest in a uniform stream, we know that the resultant motion is due to the stream itself together with the given sources

repulsion

of opposite sign, that

and sinks in the region outside the body whilst the effect of the body is equivalent to an internal distribution of sources and sinks. "Now Havelock has shown that the resultant forces and couples on the body may be calculated from the forces on the internal sources and sinks due to attraction and repulsion between external and internal sources and

"The

Vertical

Force on a Cylinder Submerged in a Uniform Stream," Proc. Roy. Soc, Series A, 1928, Vol. 122, p. 387ff].

G. P. Weinblum adds the following comment:

"When

the

velocity

source-sink distribution is

also

is

potential

corresponding

to

a

known, the horizontal velocity

known, and the resistance

X

(the total resistance

can be written down as the integral of the product of the distribution and the horizontal velocity over the region of the distribution" [TMB Rep. 710, Sep 1950, p. 16].

Rt

in standard notation)

By

(e)

the method of G. P. Weinblum, in which

the shape of the hull

is

expressed mathematically,

and 49.5. In general, Weinblum's method differs from the others mentioned here in that the velocity potential is as described in Sees. 49.4

developed on the basis of equations expressing the hull shape in mathematic terms, rather than upon an array of sources and sinks, or upon the slope of the hull surface with respect to the direction of motion.

a direct application of the method of

energy and work,

is

an attraction

sidering that the pressure drag

over the hull of the ship; but this

sinlcs of

iiwpinm.' /r'^

sinks taken in pairs" [Havelock, T. H.,

are open, defined briefly as follows: (a)

215

that the total force between two sources

strengths m and m', respectively, is given where r is the distance between them [Lamb, H., "Hydrodynamics," 5th ed., Art. 144, p. 138.

by

trained

known

is

and two

actually used: ".

"It

the

wave

By

(f)

the method of R. Guilloton, in which the

hull is represented

as a

summation

of simple

geometric bodies, in the form of wedges, and the

used to calculate the

pattern at a great distance to the rear of the ship

IVIichell velocity potential is

known. As the hquid has no viscosity, all the energy put into the wave system remains there, and the wave pattern at that distance is free of all the local disturbances produced by the ship. This is, according to Havelock [INA, 1934, p. 440], the "most natural method" under the

pressure disturbance of an elementary wedge.

circumstances.

Vol.

is

(d)

By utilization of the Lagally Theorem and

forces exerted

Lunde explains this method as Theory of Wave Resistance and Norwegian Model Basin Rep. 10,

follows ["On the Profile,"

of

1952, p. 17]:

sum

potentials, is then expressed

table of offsets [Guilloton, R.,

INA,

1940,

Vol. 82, p. 69ff; 1946, Vol. 88, p. 308ff; 1948, 90,

p.

48ff;

SNAME,

I95I,

Vol.

59,

pp.

86-128; Korvin-Kroukovsky, B. V., and Jacobs,

(g)

strength. J. K.

Apr

by a

W.

sinks)

component

directly as a function of the hull shape as defined

equal

(or

total velocity potential, obtained as the

of the

between the boundaries of bodies

enclosing pairs of sources

Wave

the

The

R.,

ETT

Stevens Rep. 541, Aug 1954, p. 4]. Guilloton has developed a

IMore recently,

new approach

to the calculation of

wavemaking

measurements of wave profiles taken on towing models [Guilloton, R., SNAME, Tech. and Res. Bull. I-I5, Dec 1953; resistance utilizing the

n\i)Rc)i)\N.\Mit;.s IN

216

INA,

1952,

\'ol.

".II,

Kroukovsky, B.

i>.

the

it

is

Tlii.s

in

C,

J.,

Kon'in-

SNAMK,

nictliod has the disad-

difficult to

measure or record

accurately.

positions

profile

appears to shift

model

ami Kotik,

V..

1954, pp. 359-.3961.

vantage that

RirkhofT,

3i;?fr;

any one

The

run, even

profile

when the

moving at nominally constant speed.

is

significance

G. P. Weinblum gives a summary of most of more mathematical terms, in of

TMB

Poport 710, September

It

has been shown

liy

to exactly the

of

The

Lumlr that same result if

all

six

carried

Havelock and Guilloton give identical

derivation of the resistance equations by

methods, as well as the calcu-

lation of the resistance for a range of speed,

exceedingly involved.

No

negative,

benefit from the interferences of all except the

bow and

stern

wave

patterns.

The

general and

physical reasons for this are explained in Sec. 10.14 and other sections of that chapter.

Furthermore, the

three terms contain a

last

and two cosines which vary with K(kappa) = g/V, hence these terms have values which are

attempt

is

The

said to oscillate with speed.

oscillations give

the well-known hum|)s and hollows in the

rise to

liated in diagram

results.

anj- of these six

to

terms of the indicating an everpresent fifth

curves of resistance due to wavemaking.

out correctly. Further, that for a thin ship the

methods

are

series

50.7 is

1!).")(),

pages 89-94.

methods lead

.SVf.

dcscrilunl in the diagram. It

sine

these methods, in

Appendix 2

is

be noted that the fourth and

Further, the difTerences in profile positions for successive speotls are small.

smv design

made

of Fig.

.3

ilhis-

."lO.B.

50.8 Comparison of Calculated and Experimental Resistances. As an indication of the correlation obtainctl between the calculated and experimental values of resistance derived from a model which resembles an actual ship. Fig. 50.D gives the (c)-curves, based on total resistance, for the destroyer model devised by J. K. Lunde and

is

to

it here but those who \\'ish to pursue this matter further may find the work carried out in several ways in the references quoted in Sec. 50.13. One could wi.sh that the ingenuity of the workers in the analytic field had been matched bj' those in the experimental field, and that there were an equal number of methods by which the resistance and other characteristics of a towing model could be determined. Further, that when so determined, the values would all be equal!

give

i(k»ppa) "

of HQvelod<^*~~''

Referente -

o/V

Term

combined gravity-wave system. As an example. Fig. 50.C gives the formula derived by T. H. Havelock for the wavemaking resistance of the essentially 2-diml and symmetrical form shown there, made up of two watcrlines

having

their

vortexes

Y lofasu/

2/ I

(S

f jqure

•

""'sto't* D"E. to the Bow and the Stern Wove Rjtterns. Assumed

^^''

'

"^' Re»i»ton« Due to the Wove

Rjt-

terns from the Two Curved Sides, Indepsndentiv

Existinq

Term

m

15

(-/q^lJ / ^

coi^

9

cos[2«.(0 5L)38ce]de, the

Pesistonce Due to the Interferenc of the Bow ond the Stern

Wove Term

E,

(-)

2 (-fo5|_\ )

e

/ ^ cos

Potterns

sin

[Z *i (05L)sec e] de the ,

Resistance Due to the Inlerferen

Bow or Stem Wavt Fbtterns With Entrance or Run Rittcm

of

Term

"^

•

'

Malpil^

'^"^'^

sin[2»i(a5L)sece]de, the

Resistance Due to Mutual Interference

at

midlenglh |1XA, 1934, Ei|. (28), pp. 441-142|. Thi.H formula consists of a constant factor times a V" term times the sum of five terms whose

this

(l +II*III+Er+Y), where

V^

^ '^Ts io/O.SLW

sion) of the

parabolic

V of

to Exist Indepandenlivy

for shapes

expressions for the surface elevation (or depres-

—""""^ffeferertce -

PRESSURE RESISTANCE DUE TO WAVEMAKING

50.7

which lend themselves to this operation, can sometimes be broken down into four or more parts. These represent the components due to separate wave systems formed at the bow and stem and along the sides, plus the interference efTects between these components. Exactly the same unraveling process may be applied to the

'

I

of thie fioore

rr

Components of the Calculated Wavemaking Resistance. The matiifniatic cxiirc^sions for resistance derived by the processes mentioned,

^Z"-^**^^ °^ Havelock

^'~^C}^^"'^'^''i^ '

g/t*

of the

Wove RrtUirns

fntronce

Fid.

5().{;

of the

and the Run

TAnULATION OK TyI'ICAI, C-OMPONENTS OK Wavemakino Resistance

CALCULATION OF WAVEMAKING RESISTANCE

Sec. 50.9 Resistonces

Total

for Norweqion

Corresponding

-^=10.21

3.418

Cp= 0.653

For Lines of This

Form.

0.526

Form, see

Sec. 3.

Destroyer

c

Form, Coeflicients-

F^°'f Cg-

Cx-0.80?

©I

Representinq

Model 41,

o nd

FVoporti'ons

217

13,

Fig. 3.Q, Volume I

Includinq

—

from 1

i

Re&istanoe,

Friction

Qs Derived

Anolvitic

(

I

J

Treatment of 1

,—

1

Form Generated by Source Distribution C ^Totol

Estimated

Resistance for Ship,

[Lunde,

J.

IImV 1949.

K.,

pp. 'l66-l90].

Includinq Friction Resistance,

QS Derived

0.24 az(,

032 034 Q36

0.30

0.28

from Standard Model

038

0.40

Test

042

0.44

046

048

052 054

Q50

058 060

0.56

062

0.64 0.66

Froude Number f„- V/t/oL

Fig. 50.D

Comparison of Total Resistances for Lunde's Destroyer Model, as Calculated and as Determined FROM Model Tests

depicted in Fig. 3.Q of Sec. 3.13 of

Volume

I

[INA, 1949, Fig. 3, p. 188]. Except for the hump in the curve of calculated resistance at a Froude number F„ of about 0.30, much more pronounced in the calculated data than in the experimental data from a routine towing-model test, the agreement is considered to be remarkably good. The shift in the hump of the ©-curve at an F„ of about 0.48, from its position on the theoretical graph to that on the experimental curve, is considered due to the fact that the displacement thickness of the boundary layer around the towed model gives it a greater effective length than its actual

physical

At

length.

least,

its

naval architect are the features, other than the resistance of a ship in deep water, which the workers in this field have been able to

wavemaking

derive by the use of analytic methods and mathematics.

these

may

be mentioned (with

(1)

Wavemaking

resistance

in

deep water in

accelerated rather than steady motion. This

fundamental

importance

in

the

design

is

of

and

operation of model testing basins and in the

conduct of ship

trials

over measured-mile courses.

"Ship Wave Resistance," Proc. Third Int. Congr. Appl. Mech., Stockholm, 1930, Vol. I, pp. 58-73, esp. Figs. 6-9 on pp. 68-70

Wigley,

effective

length appears to be greater than that of

Among

the source references):

W.

C.

S.,

its

Havelock, T. H., Quart. Jour. Mech. and Appl. Math.,

Other comparisons are given by the following, some of them original and some taken from the

Havelock, T. H., Proc. Roy. Soc, 1950, Series A,

counterpart in the real liquid.

(Oxford), 1949, Vol.

Lunde,

technical literature: (1)

Weinblum, G. on p. 22 and

P.,

TMB

Fig. 7

(2) Shearer, J. R.,

"A

on

Rep. 710, Sep 1950, Fig. 6 24

p.

(2)

an

Preliminary Investigation of the

NECI, 1950-1951, Vol. 67, pp. 43-68 and D2I-D34 Havelock, T. H., "Wave Resistance Theory and Its

(3)

Application," Fig. 7

on

of Hull Forms,"

SNAME,

1951,

Fig.

6 on

p.

and

p. 419ff

J. K.,

SNAME,

1951, pp. 40-44

Wavemaking infinitely

resistance in steady motion in deep canal with veBtical walls.

(3)

Wavemaking

resistance in steady motion in

restricted waters.

18;

p. 19

Korvin-Kroukovsky, B. V., and Kotik, J., SNAME, 1954, Fig. 5 on p. 366. This is the first diagram mentioned in item (3) preceding.

(4) Birkhoil, G.,

Havelock, T. H., Proc. Roy. Soc, 1921, Series A, Vol. 100, p. 499ff

Havelock, T. H., Proc. Roy. Soc, 1928, Series A, Vol. 118, p. 30ff

Weinblum, G.

Other Features Derived from Analytic Ship-Wave Relations. Of great interest to the 50.9

325ff

Sretensky, L. N., Phil. Mag., 1936, Vol. 22, p. 1005ff Lunde, J. K., SNAME, 1951, pp. 44-50.

Discrepancies Between the Calculated and Measured

Wavemaking

2, p.

Vol. 201, p. 297ff.

P., Schiffbau, 1934, Vol. 35, p. 83ff

Sretensky, L. N., Phil. Mag., 1936, Vol. 22, p. 1005fE Weinblum, G. P., STG, 1938, Vol. 39, p. 166ff.

IlVDROnVNAMlCS

L'18

(I)

motion water of uniform depth and unlimited

Wnvt'iiiiikiiiK rcsislaiRo in stciuly

sluillow

in

horizontal extent.

Woinblum, G. KinoshitA,

Weinblum, G.

1950, pp. 94-95

SN.VME,

Sh.illow Sea," Jour. Zoisen Kiokai (Society of

Japan) 1951, Vol. 73. K., Xonvcgian Moilel Ba.'sin Rep.

Naval

J.

Streamlines or lines of flow along the hull

Wavemaking Lumle,

rcsistanee in aci'i'leralcd niotiun

SNAME,

K.,

Diagram

1948, Vol. 90, pp. 4S-63.

adapted from

Fig.

10, .\pr.

2 on

what had been

1

of

.52

p.

of Fig. 50.E,

the reference,

by Guilloton as

achieve<.l

of the dat« of this paper.

(11)

water of uniform J.

motion and quiet

Guilloton, R., "Stream Lines on Fine Hulls," I.\.\,

indicates

in .-^lialUnv

1950,

water.

1952, pp. 4l>-59 ('))

SNAME,

St. Denis, .M.,

surfaces of ships in steady

.\rThitt'ols,

Lunde.

Sec. 50.9

and

P,

pp. 184-248. (,10)

TMB Rep. 710, Sep

P.,

1951, pp. 50-55 M., "Wnvi- llfsisU'ini-e of n Spliore in a

I.umlo, J. K.,

IN SHIP DllSIGN

dcplli.

Lines of etjual

prc,s.surc [f

= ( — r/g)

{d/dx)

corresponding to each waterline] aroiuid the hull

1951, pp. 55-57

(eon.xidiTs

motion

of a ship in steady

in quiet water.

linear acceleration).

Guilloton, R., "Stream Lines on Fine Hulls," IN.\, ((»)

Wavemaking

resistance for steady motion in

1948, Vol. 90, pp. 48-63.

adapted from Fig. 3 on

a sliallow canal of rectangular section.

depicts P., T.MB Rep. 710, Sep 1950, SN.VMK, 1951, pp. 57-59.

Weinblum. G. Lumle, (7)

J. K.,

Wavemaking

p.

95

resistance for accelerated

some

Diagram 2 p.

of Fig. 50.E,

54 of the reference,

on a so-called mathe-

of these lines

matical model.

mo-

tion in a shallow canal of rectangular section.

Lunde,

SX.VME,

K.,

J.

1951, pp. 59-60 (considers

linear acceleration).

Broken Lines

(8)

Wave

moving

and

profiles along the side of

al)aft

Represent

a

Approximate

ship.

Troces of

"Ship Waves," NECI, 19:i0-1931, Vol. 47, pp. 153-196 Havelock, T. H., '"Ship Waves," Proc. Roy. Soc,

W.

Wiglcy,

C.

1932, Series A, Vol. 135, p.

W. C.

Wiglry,

and

S.,

.

Compari.son

".\

Guilloton's

Tontjents

—^

1

also Vol. 136, p. 465fT

E.\porimont

of

Both Bod^ Plons Represent W.C.S. V/iqlev's Model 755, when

and Wuve-Re.fist-

Prop. Roy. Soc, 1934, Series

.,"

.

IfT;

Wavc-Profiirs

Calculate
ance

Some

Streamlines

S.,

.'V,

Run at

Froude Number

of

0.274

Vol. 144,

p. 144ff

W. C. S., "The .Vnalysis of Ship Wave Resistance into Component!! Depending on Features of the Form," Trans. Liverpool Eng'g. Soc, 1940, Vol. LXI, pp. 2-35 (NBS library number TA1.L7) HavelfK-k, T. H., SNAME, 1951, Fig. 8 on p. 20,

Wigley,

from the works of R. Guilloton Lunde, J. K., Norwegian Model 19.52,

Guilloton's

Lines

of

Constont FVessure ^(rel^l

Ba.iiii

Rep.

10,

Apr

wh.re^.-^||WL

pp. 60-84.

Correspondino to Eoch

(9)

Resistancr- of a ship niovinK

l'"i(;.

K., Norwegian MfMlel Ba.sin Rep. 10, Apr pp. 8-1-97. Con.'tiderH first-order cfTects only, neglecting reflection or scattering of waves by the

Lunde,

C.

anioiij;; \va\('s.

J.

.50.

PllK.SSrKK

E .\.s

Sthkami.ink.'a .\Nn T,inks

DkKIVKI)

of Co.v.stant

.VN'.tl.YTICAI.I.V IIY

R. Gfll.lAlTO.N

19.52,

dhip

it-self,

IIavrl<«-k,

and pitching motion. "The Resistance of a Ship .\mong

un well as heaving

T.

IT.,

Waves," Proc. Roy. Soc, 1937, Series A,

\'ol.

|i.

'

Phil.

Drifting

Force on a Ship

Mag., 1942, Vol. 33,

p. 4fl7IT

II

Phil,

Mag.,

II.

INA,

194.5, Vol. 87, p.

S<.rie,M 7,

1910, Vol. 29,

p. 407fT

Ilavclock, T.

In Fig. si'cl

109(T

distribution

.'il

P.,

on

of dis-

T.MB

p.

."iS,

Rep. 710, Sep 1950, pp. 38-50. the author gives some forelxxly

ion-area curves for Mhips of

Ica.tt

re.xlstjince

Froude numbers. In

Pieii, P. C.,

SNAMi:,

l''ig.

32 on

at

60 he reproduces some similar full-length .1-curves from G. Pavlenko. variou.-<

•'>ti5fT

Havel.Kk, T.

longitudinal

of

Weinblum, G.

"The

II.,

Among Waves, and

EITect

161,

p. 299fT

Mavelo
(12)

placement and shajie of the section-area curve.

1953, pp. 5.S0-5S2.

p.

CALCULATION OF WAVEMAKING RESISTANCE

Sec. 50.11

(13) Effect of vertical distribution

of displace-

ment. Weinblum, G.

P.,

TMB Rep. 710, Sep 19.50, pp. 50-56.

Covers influence of the midship-section coefficient, shape of sections, shape of waterlines, section-area curve, bulb bows, and cruiser sterns.

Ship Forms Suitable for Wave-Resist-

50.10

ance Calculations. The simplified ship of J. H. Michell's 1898 paper was little more than a friction form with somewhat convex sides. Many of the forms subsequently used resembled deep canoes more than real ships. This was largely because the slopes of the fore-and-aft lines of these "ships" were small, and because the sourcesink distribution,

when employed, was

for

many

years limited to positions on the centerplane. Possibly

greater

the

part

of

the forms

were

selected because their boundaries could be defined

by mathematical formulas based upon the ship axes. If the expressions were not to become too involved, appreciable limitations were imposed on the shapes represented by them. Body plans and other lines drawings of these forms are illustrated

by: (1)

Wigley, Fig.

W.

C.

1, p.

Fig. 6, p. 18, p. (2)

S.,

and Lunde,

J.

K.,

INA,

1948, Vol. 90,

SNAME, 1951, SNAME, 1954, Fig. 5,

97; also Havelock, T. H.,

and BirkhofT,

G.,

366

Guilloton, R.,

INA,

1948, Vol. 90, Fig.

2, p.

52 and

Fig. 3, p. 54.

While they are not to be classed as ships, the friction forms and thick planes used in friction-resistance tests in model basins lend themselves admirably to the calculation of their wavemaking resistance. No matter how thin they may be constructed they are rarely free of wavemaking at the higher speeds. Of late years, the calculation technique has progressed to the point where combined radial and uniform flow can be utilized to produce hull shapes not unlike those of actual ships. Fig. 3.Q of Sec. 3.13 of Volume I illustrates such a form designed by J. K. Lunde and made the subject of thin

rather extensive studies Figs.

To

and

[INA,

1949,

Vol.

91,

pp. 186-187]. produce a 3-diml ship of this type, simple 1

2,

enough from the naval architect's viewpoint but extremely complex when translated into radialflow and uniform-flow stream functions, may require as many as 30 pairs of sources and 20

The sources of each pair are disposed symmetrically about but offset from the

pairs of sinks.

219

centerplane, as are the sinks, with offset distances

which vary from pair to pair. While the labor involved

in

calculations increases with the

number

flow

points

or

singularities,

it

numerical

the

of radial-

diminished

is

appreciably by the use of certain tables

now

in

be reduced further in the future by the generous use of computing

existence. It can possibly

machines.

A remark made by W. J. M. of his 1866 retical

Rankine on page 83 book entitled "Shipbuilding: Theo-

and Practical" applies

to

many

phases of

predicting ship performance other than the one

discussed in this chapter: ".

.

.

as for misshapen and ill-proportioned vessels, there

does not exist any theory capable of giving their resistance

by previous computation." 50.11 Necessary Improvements in Analytical and Mathematical Methods. All workers in the field of theoretical and analytical wave-resistance calculations

now

(1956)

agree

that

appreciable discrepancies between

there are

the derived

and observed resistance data for most of the forms concerned. While these are hardly first-order and while the wavemaking resistances models can not be measured independently, the variations are large enough to indicate that all the hydrodynamic actions have probably not been taken into account. One of these is the slope drag (or thrust), due to the position of the vessel on the back (or front) of a wave of its own Velox system. This may be the reason for the increased

differences,

of

model of Fig. 50. D at Froude numbers above about 0.48, T, = 1.61. Moreover, it is recognized at the outset that the major viscous effects are neglected, as are all the interactions listed as (d), (e), and (f) in Sec. 12.1. It is entirely possible that the hydrodynamic actions mentioned previously are not recognized in routine analytic and experimental studies of resistance and propulsion, let alone in calculations resistance of the destroyer

of

wavemaking

resistance.

Because of the severe limitations imposed by many analytical methods, such as the necessity for retaining the same type of transverse section from stem to stern of the ship being worked upon, the use of I'adically different procedures studied.

One

of these

is

is

being

the slender-body theory,

widely employed by aerodynamicists but hitherto not applied to surface-ship forms. Without going into details, this tions that:

method is based upon the assump-

iivnuonN \ \Mi(

220 All trniisvcrso

(a)

small in comparist)n with

The

aio

tliiiiciisiinis

assiiin<'
to

!)(>

length

tlie

wave system, caused by the passjige of the slender body through the water, are as*!umed to be eonccntrated along (b)

elevations of the Velox

the j-axis, as if the wa\e system were shifted inward due to a transverse collapse of the body to zero beam.

Xntwithstaniling the modifications to simplify the problem, the mathematical equations are

still

formidable, the procedure has not yet (lOoti) been

have the results received more than preliminary experimental verification. However, the method ha-s the great advantage of lending itself to performance predictions on ship forms with any type or shape of transverse section, and with radical changes in transverse section along tlie length, such as that which occurs at a transom stern. Furthermore, preliminary indications are tliat a great many actual ship forms fail within refined, nor

the "slender-body" category. 50.12 Practical Benefits of Calculating Ship Performance, ^'iewed from that point in the progress cunx' which has been reached to date (195G), the most valuable promise which the analytical and mathematical method now offers

s

i\

is

its

indication of the

relative influence of various shape parameters on

the behavior of ship hulls. Wlien the progress

shape parameters and of particular a.ssumptions and conditions will be made readily apparent and be expressed cjuickly in numerical or engineering terms. This is exactly the function of

the.se

Among be

with

the

the conclusions aiul contributions

may

liste
(a) The combination tlivergcnt- and transversewave pattern due to a moving pressure disturbance, as developed by Lord Kelvin and as worked

on by E. Hogner, T. H. Havclock, and others (b) Extensive knowledge of the phj'sical reasons for

the

oscillatory

\'ariations

the

in

pressure

due to wavemaking, resulting in the well-known humijs and hollows of residuaryresistance and wavemaking-resistancc curves (c) The reduction in pressure resistance due to wavemaking as the displacement volume is taken away from the vicinity of the surface waterline and moved farther down resistance

(d)

A

greater appreciation of the necessity for

fairness in all ship lines, principallj' those parallel-

ing the water flow

The

phy.sical

and

theoretical explanation for

the beneficial action of the bulb tion of pressure resistance (f)

Knowledge as

bow

in the reduc-

due to wavemaking

to separate contributions to

the wavemaking resistance

made by the diverging and the transverse waves of the Velox system. Fig. .50.F, adapted from J. K. Lunde (SNAME, 1951, Fig. 7, p. 72], indicates this feature most vividly for a rather wide range of Froude numbers.

machine which, when it is information and its

of the tide-predicting

supplied

SVr. 10.12

from other sources.

is

such that adequate mathematical expressions can be .set up for ship and liquid motions, the influence

nrsK;\

Whether these c(juld have been achieved by other methods or whether they had already been discovered by observation, deduction, intuition, or experimentation is somewhat beside the point. The fact is that they came out of the analytic "machine" with negligible assistance

(e)

to the practical designer

siiii'

contributions.

basic

wheels arc set going, rolls out the data for tide tables with effortless ease. If

the miKlel-tcsting tcchnifiue

is

advantageous

becau.sc of its relatively low cost, (luick answers,

and

ability

to

lake

all

physical

actions

into

account, the machinc-cahulating method promises a saving in time and labor and a greater degree of

freedom

in .setting

up the basic conditions. The

factors in a mathematical expression can be given

any reasonable

values, they can be given greater

or less weight, as appears to be called

for,

or they

can be omitted entirely.

As

020

(lis

to the indication of the influence of various

shape parameters of a ship ulljick

number

hiia

alremJy to

of importiinl

it.s

and

hull,

cre
the analytic

a considerable conclusions and

— — — — — ?53o Froudt

535

SSS

Number

545

535

SU

Gkaimis Indicating Sei-ar.\te ContriMai>k iiy tick Divkroino and tiik Transverse

Fio. 50.F iii'TiriNM

065

/VsT

Wavks to thk

ToTAr,

Wavbuakino Resistanci3

CALCULATION OF WAVEMAKING RESISTANCE

Sec. 'iO.13

The

knowledge

under certain conditions, which are as yet unfortunately not too well defined, small changes in the longitudinal (g)

definite

that,

(2)

of displacement, indicated by the customary section-area curve, produce relatively large changes in wavemaking resistance. Similarly, that small variations in surface-waterline shape may produce unexpectedly large changes in this

distribution

in "Marine Engineering," 1906 Admiral Fournier of France. His formula is pubUshed in English, with comments, in INA, 1907, page 190. (c) D. W. Taylor, quoted and commented upon briefly in SNAME, 1894, Vol. 2, page 14.3.

Wilda (b)

resistance.

The work done along

these lines during the

period 1945-1955, at least in the United States,

has given a new impetus to the mathematical delineation of ship lines, described in Chap. 49. In particular,

it

of fairing the

—

—

"Experienced

experimenters

are

somewhat

often

bewildered b.y the fact that the wave resistance

may vary

appreciably for different but reasonable types of hnes,

although

(3)

(4)

The

From a

theoretical viewpoint

function of the surface slope in the longitudinal direction,

now why

realize

the solution of the basic

— —

almost hopeless as long as the ship surfaces (or at least their most important features) are not defined in a rigorous way by mathematical expressions. Hence, our first task must be to find equations for the ship surface, continuing the work of D. W. Taylor."

marks

Reference Material on Theoretical ReCalculations. Supplementing the re-

in

Sec.

50.2 concerning early efforts to

analyze and to calculate ship resistance, there are given here a few of the references which contain interesting accounts of this work.

include the

Rankme

They do not

references mentioned in the

text of Sec. 50.2: (1)

An

excellent

done

to predict other aspects of

bibliographies: (5)

(6)

and most readable summary of the work

prior to 1869 relative to the calculation of

ship resistance

by formula

is

to be found in the

report of the Committee of the British Association

headed by C. W. Merrificld and counting among its members Professor W. J. M. Rankine and Mr.

TMB

Weinblum, G.

P., Rep. 710, Sep 1950. Pages 98-102 Ust 116 items, principally by authors. The individual references are extremely sketchy. Wilhamson, R. R., "Bibliography on Theoretical Calculation of Wave Resistance," ETT, Stevens (unpublished and undated). This contains 62

items, listed (7)

model basins mentioned above to estabthe resistance as a function of the form remains of the

50.13

and

amazingly extensive. There are listed here only a few of the references which contain large

on derivatives. On the other hand, the most commonly used (hull) coefficients are integrals, which even when kept constant still admit of very wide variations of the

sistance

modern

their performance, as set forth in this chapter, is

i.e.,

lish

technical literature covering the

resistance of ships

be quite natural, since the wave resistance depends to a first approximation upon a complicated

We

Rothe, "Bemerkungen zur Schiffswiderstandstheorie von H. Lorenz (Note on the Theory of Ship Resistance of H. Lorenz)," Schiffbau, 8 Jan 1909, Vol. 9, pp. 253-354; 2 Jan 1909, pp. 289-290.

(20th century) analytic attempts to calculate the

this appears to

slopes.

Nov

1907, No. 46

the form parameters generally considered

all

as decisive are identical.

problem

Lorenz, H., "Beitrag zur Theorie des Schiffswiderstandes (Contribution to the Theory of Ship Resistance)," Zeit. des Ver. Deutsch. Ing., 16

has initiated studies of the problems Imes of ships, so that this may be

done impersonally automatically, if need be in a manner which mil benefit the overall hydrodynamic performance of the ship. The discussion of this chapter may well be concluded by some comments of G. P. Weinblum, to be found on pages 2 and 3 of TMB Report 710, pubUshed in September 1950:

221

William Froude, Brit. Assn. Rep., 1869, pp. 11-21. Of the work (and workers) which followed that of Rankine, an excellent summary is to be found in a paper by A. W. Johns entitled "Approximate Formulae for Determining the Resistance of Ships" [INA, 1907, pp. 181-197]. In this paper Johns mentions the formulas of: (a) Middendorf, published in 1879 and given by

Lunde,

J.

K.,

by authors.

"On

the Linearized Theory of

Wave

Resistance for Displacement Ships in Steady and Accelerated Motion," SNAME, 1951, pp. 25-85.

Pages 75-76 (8)

list

55 items.

Guilloton, R., "Potential

Theory

of

Wave

Resistance

of Sfiips, with Tables for its Calculation,"

1951, pp. 86-128.

On

SNAME,

pages 120-123 there is a section entitled "Bibhography," listing 91 items in seven different categories. In spite of the completeness of this list it does not give the subjects or titles of the papers. (9) Korvin-Kroukovsky, B. V., and Jacobs, W. R., "Calculation of the Wavemaking Resistance of Ships of Normal Commercial Form by GuUloton's Method and Comparison with Experimental Data," ETT, Stevens, Rep. 541, Aug 1954. Pages 51-53 fist 29 items. (10) Birkhoff, G., Korvin-&oukovsky, B. V., and Kotik, J., "Theory of the Wave Resistance of Ships," SNAME, 1954, pp. 359-396. Pages 384 and 385 list 47 items. This list brings the bibliography on the subject practically up to date (1955), except for the items to follow. (11) Sezawa, K., "Wave Resistance of a Submerged Body in a Shallow Sea," Paper 610, Proceedings, World

HYDRODYNAMICS Knginecring Congroxn. Tokyo, Part

179

pa{pc>D

I.

mathrnuktiral

IVH).

Tliin

1>J'J<.>,

iixIk is

is

Norwegian version there Is a very comprehensive of 1S5 references on this subject.

iippan'iitly

[winiUol to tlie surf:ice

sonu-

iliscus-sioii

of the

list

i\ft)

O.

(17)

Inui,

rosdstaiicc of n moviiiR uiulerwatcr spliere.

"On

(12) Lundo. J. K.,

the Linej»rizo«l Theory of

Wave

Resistanro for a I'ressurc DLstribution MovihR at Constant Speo
(13)

Trondheini, No. 8, Jiin 1951 Unvrentev, V. M.. "The Effect of the Boundary Layer on the Wave-Making Resistance of Ships," Section on Hydromechanics, Doklady of the

Academy

of Sciences,

USSR,

1951, Vol.

"On

and Wave

the Theory of

Wave

thcT.MB Lunde,

Resistance

J.

Profile,"

Ikxlies

1954. In the Bibliography of this report, covering

"Japanese papers on Ship Wave Motion and Kindred Subjects from 1929 to 1953," there are listed 75 additional Japane.se papers. Of this group, 48 have been tran.slated into lOnglish in

library.

K..

"The Linearized Theory

Resistance and

Moving

Its

in

.Application

to

of

Wave

Shi|>-Shaped

Deep Water," Norwegian Ship

Model Basin Re|)ort

2i,

Mar

195:5.

This

is

in

Takao, "Japanese Developments on the Theory Wave-Making and Wave Resistance," 7th ICSM, Oslo, 20 Aug 1954. This paper, with its illustrations and with many additional enclosures, was published as Skipsniodelltiinkens Meddelelse Nr. 34 (Norwegian Model Basin Report 34), /Vpr

of

LXXX,

Xorgcs Tekniske Ilrigskole, Trondheini, Skiixsmotlelltankens Meddelse Xo. 10, Apr 1952. This is the printed version (in English) of Lundc's M. S. Thesis at ICing's College, Newcastle, flnishcd in May 1945. There are copies in (15)

!;. Pavlenko, in his "Soprotivleniye Votiy Dvizheniyu Sudov (The Resistance of Water to the .Movement of Ships)" (Moscow, 1953), devotes Sec. 13 of Chap. IV, pages 1S.3-1S(), to a ".Methoil of Calculating (mathematically) the Resistance of an .\ctual Ship," but he includes no example, and it is doubted whether this method is used in

practice in Russia.

Xo. 6 (14) Lunde, J. K.,

Sec. "iO.n

Norwegian, with an English summary, hut it is IxMiig pul»lislii-
to the exclusion

of a phyiiir.il iliHcussion. Tlio 'iHxIy"

a 2-iliml cylimlcr witli its (ami to till- IkiI). Tlu'n?

I\ SHIP DIISIGX

XXIX.

compriwH n

(mjK-r

liirKoly

trt>:itinoiit,

Vol.

(18)

Japan and anWeinblum, G.

to be published as P.,

"Problems

T.MB in

Eng'g. Res., Univ. of Calif., Series 82, Issue 1, pp. 11-13. Inst.

translations.

Ship 1

Theory,"

Nov

1955,

CHAPTER

51

Proportions and Shape Data for Typical Ships General Comments Parent Form of the Taylor Standard Series. References to Tabulated Data on Principal Dimensions, Proportions, Coefficients, and Performance of Ships References to Tabulated Data on Yachts and Small Craft

51.1 51.2 51.3

51.4

51.1

The

General Comments.

223 223

51 5

51.7 51.8 51.9 51 10

223

228

.

Ships"

ship-design

Designed Waterline Shapes and Coefficients Reference Data for Drawing Section- Area Curves "Standard" Body Plans Single-Screw Body Plans .

.

51.6

Twin-Screw Body Plans Multiple-Screw Sterns

is

procedures of Part 4 are based on the development of each new design as a separate project, to meet

and

the particular requirements set up for

page 92

it,

230 231 234 236 236

out of print. Although the body plan parent form, and the section-

profile of the

area curves for the series are given in Fig. 28 on

rather

than upon copjdng or modifying existing designs, no matter how good the latter may be. Nevertheless, new design requirements often call for a ship hull that resembles one which exists and for which there are proved performance data. It is useful to the designer, therefore, to have proportions and shape data which may be consulted for reference and guidance purposes. The SNAME Resistance Data sheets were developed, prepared, and issued to

228

of

PNA,

1939, Vol. II,

references mentioned,

and

in the

two

the complete data from

the 1943 edition of S and

P

are reproduced here.

Some editing has been done on the drawing but the model and curve shapes and the numerical data remain unchanged. Fig. 51. A embodies the lines of EMB model 632 (modified) and the original group of section-area curves, together with the principal proportions

and form

coefficients.

Table 51.a

lists

the original

who

0-diml offsets for the parent form of Fig. 51. A, in an arrangement somewhat more convenient than

did not have access to the funds of information

those of the references cited in the preceding

and shipbuilding

paragraph, although not as complete as those

fill

part of this

need, especially for architects and engineers available in large ship-design

organizations. Samples of these sheets, filled out

given by Gertler in

with test data for two models of the ABC ship designed in Part 4, are embodied in Figs. 78. Ja, 78.Jb,

78.Ka,

78.Jc,

body plans on

78.Kb,

SNAME RD

are rather small,

and 78.Kc. The

sheets

1

through 100

so that the shape data are

meager with respect to the data on proportions and model performance. Those on RD sheets 101 through 160 are

much

larger.

While limitations on space preclude the reproduction of many large-scale lines drawings in the present chapter, there are given in subsequent sections a considerable

number

of references to

source material embodying such drawings.

Parent Form of the Taylor Standard SerIn view of the recent reworking by M.

51.2 ies.

Taylor Standard Series data, embodied in Report 806 and described in Sec. 56.5, the resistance data from this series are Ukely to be used long after the 1943 edition of D. W. Taylor's book "The Speed and Power of Gertler

of

the

TMB

lists

of

TMB

Report 806. Table 5 Lb

the 0-diml ordinates for the complete series

^4 -curves in

the figure.

References to Tabulated Data on Principal Dimensions, Proportions, Coefficients, and Performance of Ships. From time to time there 51.3

have

been

published

tables

of

dimensions,

and performance data on ships of many types and sizes. Rarely do these data correspond, for any two tables hsting the same ship(s), and often they omit the very information which the inquiring marine architect desires. Taken by themselves, the data are insufficient for design purposes, and perhaps too meager for but taken together they statistical studies, characteristics,

frequently permit analyses of performance that are extremely useful.

For example, many of the ships of the period from 1850 to 1900 and later were extremely narrow by modern standards, having L/B ratios of 10, 11, or more. Their B/H ratios were also

223

224

ll\DRl)l)\.\ A.MICS l\

SI 111'

DISICN

Sec. 51.3

TYPICAL SHIP FORM AND

Sec. 51.3 less

than

is

now customary

(1955).

There

reason to believe that certain of these ships, characteristics vessels.

is

commission or

if

theless, of far

had some wavegoing those of modern Despite the augmented safety standards

not the group as a

class,

superior

to

of the 1950's, it is possible that studies of

a new

and improved hull form could be furthered by data from these old vessels. It is true that many if not most of the ships listed

in

the tables referenced in the present

section are old, even ancient,

TABLE

51. a

and are no longer

SIIAPF,

in

225

in existence.

more than

The data

are,

never-

historical value because

they apply to ships that were actually built, and that gave satisfactory service in eras when it was perhaps more difficult than at present to achieve the performance expected of them. Finally, one

may hope

that listing these tabulated data

may

bring forth corresponding information on modoi'n ships.

In the early 1850's a project was initiated in

Great Britain wliich had as

its

aim the

Non-Dimensional Offsets for Parent Form op Taylor Standard Series,

EMB Model 632

(Modified)

Stations in Forebody Waterlines

DATA

collection

I1M)U()1)\ \ \\ll(

226

S

d

5

5

H

s

1\ sllll' l)lsl(,\

Sec. 5;

J

Sec.

TYPICAL SHIP-FORM AND SHAPE DATA

513

and analysis data for

of characteristics

many

if

not

the steamships then in

all of

operation in the United

and performance

1866 a committee of the British

In

Advancement of Science) was formed to condense and to analyze the numerous data. It was composed of some of the leading engineers and scientists of the country, among them: Association (for the

John Scott

Russell, naval architect

and ship

distinguished

engineer

(2)

Fairbairn,

a a

J.

M. Rankine,

ships, (c)

(published

in

Report

Association 1869),

pages

for

114-139,

1868

recitals of the difficulties

ships studied.

The problems

in this respect, are

found

(3)

and machinery

of

in the folded tables opposite p.

profiles and main deck plans, (e) Outboard midship sections, machinery, shafting, and propeller arrangements of certain of the vessels in these three groups are to be found in the same reference. Pis. 6 through 41. White, Sir W. H., MNA, 1900, tables as follows:

Page 642, 4 warships, 5 entries per ship, W, and P, (f) Page 649, 7 ships, 5 entries per ship, with accent on indicated power Pi (e)

tabula-

tions similar to the foregoing were published, with

accent on the dimensions, proportions, and other

on the

162 of the

centric stability

giving L, B, H,

.

(4)

Durand, W.

F.,

EPS,

1903, pp. 415-425; hull data

for 78 ships, 8 entries for each; propeller

(5)

(6)

vessel's per-

formance. References to a number of these tables

(7)

and

trial

data for 84 ships, 12 entries for each Biles, J. H., "Cross-Channel Steamers," INA, 1903, pp. 243-253. PI. XXXII lists hull and machinery data for 45 vessels of this type, built in the era give arrangement sketches of

mth

characteristics rather than

the

vessel Iris, 6 entries per ship, with emphasis on metacentric stability data (d) Page 138, 10 .ships, all saihng vessels and yachts, 6 entries per ship, with accent on meta-

many

4 driven by paddlewheels and 10 by screw pro-

many

of

dispatch

14 ships of the time,

29 entries for each. In the years foUomng the 1870's,

14

the foregoing three groups are to be

1886-1903, with 24 entries for each. Pis. lists

and

entries

merchant ships, and yachts, 9 entries per ship, with emphasis on inclining-e.xperiment data (c) Page 136, 9 different ships, including the

by no means new.

table

21

Pages 100-101, 23 merchant steamships, 9 on inclining-experiment data 104-105, different warships, 19 (b) Pages

of the present day,

Report for 1869 (published in 1870). This is embodied in a "Supplement to the Second Report of the Committee on the Condensation and Analysis of Tables of Steamship Performance," to be found on pages 330-333 of the refer-

pellers,

vessels

vessels,

(a)

two-page "Revised Table of Analysis, According to Mr. Scott Russell's Method," is given on pages 332-333 of the British Association

The

6

entries per ship, with emphasis

A

ence cited.

special-service

reference, 64 entries per vessel

encountered in obtaining

accurate and correct factual data on the

early

1883-1892,

propellers,

vessels in

entitled

"Second Report of the Committee on the Condensation and Analysis of Tables of Steamship Performance," contains some two dozen pages of tabulated data for a great many steamers driven by paddlewheels and screw propellers. It embodies information on the ships, their machinery, and propulsion devices. What is more, it contains data worked up by Scott Russell and Professor Rankine in an effort to find, by analysis, some formulation which would serve as an indicator of good or superior ship performance. Incidentally, several pages of the British Association Report of 1868 are taken up with

The

per vessel, pp. 1.36-1.37 (d) Additional data on dimensions, form coefficients,

British

pp. 116-1.39.

with 24 entries per ship, on pp. 132-135.

Data on

torpedoboats,

a teacher, scientist, hydro-

dynamicist, and naval architect.

The

I,

(b) Data on early armored vessels of the U. S. Navy, 1874-1893. Similar data are given for 14

James R. Napier, a distinguished engineer

W.

1893, Vol.

dimensions and general information for 2.5 vessels, isting 21 entries per vessel, are found on pp. 128-131.

engineer

civil

SNAME,

data in this paper cover vessels in two categories: (a) Data on early unarmored steel vessels of the U. S. Navy for the period 1883-1893. The principal

versed in structural mechanics

Thomas Hawksley,

John, W., "Atlantic Steamers," INA, 1887, Vol. 28; Table III on p. 164 gives hull data for 17 large ships of that day, 14 entries for each Wilson, T. D., "Steel Ships of the United States

Navy,"

designer

William

who

wish to consult the data:

Kingdom and Western (1)

Europe.

227

are listed hero for the convenience of those

many

XXXIV-L

of these vessels.

Peabody, C. H., NA, 1904, pp. 522-553; 45 ships of 10 types, 13 entries for each Speakman, E. M., "Marine Steam Turbine Development and Design," SNAME, 1905, pp. 247-286. This paper describes vessels driven by steam turbines in the era 1894-1905. It gives, on PL 139, principal dimensions and general information for 50 vessels with 18 entries per vessel.

llU)R()l)\N.\.\ll{:s IN Mill' DI-.SIGN

228 "A

(8) Steveim, E. A., Jr.,

Substiliito for

Formuln." SNAMi:, the text, arid

cspeci.-illy in

gives n considcrnble

I'ls.

amount

;{.">—10,

Adminilty the author

of tabulated data

and merchant

n large numl>or of naval

(9)

tlip

Vol. 21, pp. 40-54. In

IOi:<.

on

ve-tseU,

ranging from the battle-ihijis of that time to fa-ot motor launches and navy launches intended to be CArrie
with 7 entries of hydro
vessel.

These data arc also quoted in The Shipbuilder (now SBMKB), Jan-Jun 1014, Vol. X, pp. 274-275. (10) Owen, W. S., PNA, 19.39, Vol. I, Table 4, p. 53; 13 types of vessels, 22 entries for each (11) PluNinert, N. J., "Modern Tanker Design," SNAME, 1939, pp. 168-lSS: also SBMEB, Apr 1940, pp. 134-137. This paper lists the hull and machinery data for 5 steam-driven and 7 dicscl-tirivcn tankers, of the era 19.30-1939, with 32 entries for each. (12) Bates, J. L., and Wanless, I. J., "Aspects of Large Passenger Liner Design," SNAME, 1946, pp. 317-373. Tables 1, 2, and 3 on pp. 318-319 give the general dimensions, form coefficients, and

machinery

characteristics,

respectively,

of

U.

S.

Maritime

a total of some 25 entries per vessel. On p. 369 are given some additional data on the proposed Ferris superlincr of

1'3-S2-DM

of

1949,

with

1931 and the Queen Mari/. (13) Robinson,

Rocske, J. F., and Thaeler, A. S., 1948, pp. 432-443. This paper contains

H.

SNAME,

F.,

data for thirteen 13,000-t tankers, twelve 16,000-t tankers, and twelve tankers of 18,0(X) t and larger, with about 70 entries for each. tabulated

(14) Lavrent'cv, V. M.,

1949, p. 96.

A

"Marine PropuLsion," Moscow,

translation of this table, with both

metric and English units, appears as Table 51. c. (15)

Todd, F. IL, "Some Further Experiments on SingleScrew Merchant Ship Forms Series 60," SNAME, 1953, Tabic 1, p. 518. Principal dimensions and some hull coefficients are given for the Mariner, the Schuyler Olis Bland, the U. S. Mar. 0)mm. C-Z class, the tanker Pennsylvania, and a Bethlehem 400-ft design, in comparison with TMB Scries 57 models. There arc about 10 entries per ves.scl. Other data on these vessels are given throughout

—

the paper. (10)

De

ocean iron-ore carriers, with about 100 entries while Table 2 gives similar data for 9 Great Lakes iron-ore carriers, with about 92 entries per ves.scl. Table 3 gives data on 1(X) or more features for each of 6 oceangoing general bulk cargo carriers. (18) There is given, in Table 76.d of Sec. 76.4, a presentation of the principal characteristics of 14 Great Ijikes bulk carriers of recent design (19) Table 76.f lists tlie principal dimensions and other ]X!r vessel,

data

by

Stam, Haarlem, Holland, 19,53. On pp. 13-29 and 3.30-3S2 there are given the principal dimcnnions and characteristics, plus the general arrangts mcnt drawings, rif a large number and variety of

The

sinnlliT skf^trhes in the IxKik projHT

arc Huppleniented

by a considerable number

large folded plates in the

of

back of the book.

pp.

"M<«lem Ore CarrierH," SNAME, 19.5.5, 57-1 1. The bibliogriipliy with this piii)er

lijrtii

24 ri'ferenccH. Table

(17) Henry, J. J..

1

1

givis the characteristics

10

icebreakers

of

recent

design

and

51.4 References to Tabulated Data on Yachts and Small Craft. Dixuii Kemp nivo.s a "TaMc of Elements of Steam Yachts" compri.sing 22 vc.s.sels, \vith from 25 to 2G items per vessel ["Yacht Architecture," Cox, London, 1897, 3rd ed., pp. 317-318]. On page 319 of the reference he includes a tabic of "Steam Yacht Performance" for 13 vessels, with 39 items per vessel. On page 52.5 he presents a table listing 29 sailing yachts with their displacement in tons, the total weight of

ballast in tons, the weight of this ballast in the

and the ballast ratio. The amount of ballast compared to the displacement varied from a

keel,

as

maximum

niinimiun of 0.301 to a

of 0.081.

In the appendix of the book cited, on page 532,

Kem]) gives the names and 10 design element.s 35 sailing yachts of that day. AV. P. Stephens, in a paper

eiitilleii

of

"Yacht

Measurcmcnt:Originand Development" [SNAME, 1935, pp. 7-11], includes lines drawings and other design data on American ami Biiiisli yachts of the 1870's to the 1890's.

In his paper "The 'America's'

Cup

Defenders,"

C. P. Burge-ss gave a great deal of design information, including lines drawings of the large J-cla.ss

yachts of that period [SXAME, 1935, pp. 43-87]. No tabulated data are included in the paper. Principal dimensions and fonn coeflicients for 7 fishing ves.sels, 2 small freighters, 3 ferryboat.s, 1 tug, 24 entries per vessel, arc 1 fireboat, and

given by D. S. Simp.son p. 503].

The

first all

(SNAME,

1951, Table

5,

entry gives the actual length of

the others give converted data,

referred to a standard length of 100

II.

ship ty|X'H.

for

construction.

each craft;

Rooij, G., "Practical Shipbuilding," published

5l.i

of 12

si.x

(1930 to 1940), plus the Commission projected design

recent Atlantic liners

Src.

ft.

Designed Waterline Shapes and Coeffi-

51.5

The designed

cients.

waterlines for the |)ad(lle

steamer Mary Powell (afterbody only) and for the Taylor Slandard .Series parent form (EMIi minlel

()32,

G

modified) are shown to small scale in

on page .355 of Volume I. The halfMcKay's dipper .ship watcrline of Dunahl Flying Cloud, described in Sec. 24.13 on pages Fig. 24.

TYPICAL SHIP-FORM AND SHAPE DATA

Sec. 51.5

TABLE

51

229

Russian Tabulation of Ship Data

.0

Translated and adapted from "Marine Propulsion" by V. M. Lavrent'ev, Moscow, 1949, Table Supplementary columns at the right give the length and volume in ft and ft' units, respectively.

Type

of Ship

meters

V,

Speed,

Power,

meters'

kt

horses

Power

S,

page 96.

Adm'ty. Coeff.

(metric)

Fast steamers

Large passenger ships

Small passenger ship

280.0 202.0 190.5

67,700 22,900 21,385

23.2 23.5 22.0

61,800 37,800 27,000

194.0 193.0 170.0 136.5 121.4

22,100 23,200 17,250 13,170 10,340

IS.O 15.0 16.5 13.5 11.5

17,200 9,800 10,600 4,800 2,500

69.5

2,200

10.0

1,050

302 298 327

918.7 662.8 625.03

287 315 305 308 322

636.5 633.2 557.8 447.9 398.3

0.48

190

228.02

77,704

220 211

301.9 275.0

67,638 59,867

1.07 1.65 1.26 ;s

0.40 0.61

0.36 0.24

2,037,964 808,828 755,318

780,572 819,424 609,270 465,164 365,209

92.0 83.8

1,915 1,695

20,0 20.0

5,600 5,400

2.92 3.19

Steam yachts

121.9 116.6

5,710 4,260

15.0 21.5

3,700 9,650

0.65 2.27

307 291

400.0 382.6

201,677 150,463

Large cargo steamers

170.7 152.4 131.1 105.2

24,800 21,115 12,400 7,985

13.5 12.0

5,460 4,000 2,500 1,700

0.22 0.19 0.20 0.21

418 359 316 357

560 500

875,936 745,782

430.1

4.37,968

345.1

282,030

88.1

4,580 3,400 1,760 940 320

10.5

1,225 700 440

307

289.1 261.9 203.8

350 260

0.27 0.21 0.25 0.37 0.81

161,766 120,088 62,163 33,200 11,302

32.0 26.0

130

12.0

12.0

225 220

1.73 3.33

263 172

105

66

85.3

4,592 2,331

Fishing boat

41.0

445

10.9

1.10

194

134.5

15,717

Towboats

40.0 35.0 15.2

390 340 48

11.0

0.90

262 203

9.1

350 520 150

3.13

91

131.2 114.9 49.9

13,775 12,009 1,695

47.2

890

9.5

500

0.56

200

154.9

60.0

481

7.3

205

0.43

156

196.9

62.0 40.5

325 100

9.9

503 250

1.55 2.50

114

11.1

157

203.4 132.9

85

219.9

Canal

(river?) boats

Small cargo steamers

79.8 62.1 47.3 37.8 Small river steamers

Icebreaker

River freight

str.

with prop.

River passenger boats

11.0

n.o

9.0 9.0 8.0 9.0

12.1

1.53

River freight

Paddlewheel drive

Sternwheel drive

Bark (barca)

181

173

155.1 124.0

2.07 1.42

98

164.1

179

131.2

9.0 8.0

1.46

128

1.86

125

153.6 74.9

8.0

2.83

50.0 40.0

300 212

10.3

46.8 22.8

144 43

15.0

23

10.5

620 300

IIVDRODVNAMK.S

280

IN SHII'

'^tton

loK i||Hl9^4co

of flaitmuni

DLSIGN

Sec.

51.6

Biom

ptO<54 Lwi'n 16

17

15

Fig. 51. R

356-357 of ^'()lume

I,

is

L.J_i._L-l ^D

M

12

Desioned

dopiited

II.M.F-W.\TKni.i.sE

in Fi^. 51. B.

The

various

operating at the speed-length or Taylor T, values indicated on

SXAME RD

One past

is

feature of designed waterlines to which

tjTJes.

The

lengths and positions tabu-

of this length, for use in design.

attention has been devoted in the

51.6 Reference Data for Drawing SectionArea Curves. Supplementing the lines, sectionarea curves, and offsets of the Taylor Standard Series models, reproduced in Fig. 51. A and in Tables 51.a and 51.b, there are listed hereunder

the length and position of the parallel

portion of the waterline. This

is not to be confused with the amount and position of the parallel

DWL's on -Porollel

the parallel waterline

of Sec. G6.15 of Part 4

sheet numbers are given for

-

li.sts

optimum. Fig. GG..I shows a range of oi)timum length of parallel waterline while Fig. 66.K gives the optimum fore-and-aft position of the midpoint

the diagram.

middJebody, indicated for three of the

Table ol.d

lated are not necessarily the

four of the waterlines.

insufficient

7

the Ci.H'pkr Ship Flying Cloud

oi--

data for over thirty ships and ship designs of

sL\ vessels typical of those for five different ship

i|Uotieiit

8

Fig. 5 I.e.

In Fig. 51. C there are drawn (he half-DWL'.s of

tJTJes,

L

I

9

10

II

Middlebod"^

i-

Cruiser A

20

19

IS

17

Flo. 51.

16

C

IS

14

13

12

II

Dekio.s'eu Halk-Watkki.ink.s


>i\

\ ks.ski_s

<> Imvk

'I'^

cks oh

Ci.a.s.sem

TYPICAL SHIP FORM AND SHAPE DATA

Sec. 51.7

several references to diagrams

area curves for

new

by which

section-

corresponding to selected form

coefficients

or

M., "A Reanalysis of the Original Test Data for the Taylor Standard Series," Rep. 806, Mar 1954, Gov't. Print. Off., Washington. The data mentioned in the preceding paragraph are found on pp. 2-6 of this report. In addition, on pp. 6-8 there are graphs, tables, and instructions bj' which any section-area curve belonging to the family of the Taylor Standard Series can be reproduced mathe-

Gertler,

TMB

matically.

Encyclopedia,"

(2)

Bates,

(3)

Vincent, S. A., "Merchant Vessel Lines,"

J.

L.,

"Shipbuilding

1920,

Figs. 26, 27

MESA, Mar

1930, p. 138. These have since been improved

(4) (5)

upon

but no published or unpublished revision is available. Schiffbau Kalender, 1935, p. 160 Van Lammeren, W. P. A., Troost, L., and Koning,

TABLE Reference

51.d

SNAME

The which Part

(1)

"Resistance,

231 Propulsion,

and Steering

of

Ships," 1948, pp. 92-93.

ship designs can be drawn,

parameters:

G.,

J.

Resistance Data sheets, one of

is illustrated

4,

in Fig. 78. Ja of Sec. 78.16 of

contain section-area curves, area ratios

and values of dA/dL for the models of some 160 typical ships of many classes. 51.7 "Standard" Body Plans. At various times so-called "standard" body plans have been used for reference and comparison purposes. Some of these were drawn with fixed proportions, in

A/Ax

,

which the maximum (or midsection) waterline beam was always twice the draft. All underwater and abovewater sections were distorted to comply with this proportion. Each half-beam and the whole draft were divided into ten equal spaces. Thus the "standard" offsets or heights for a given position on one ship could be compared with

Reference Data on Amount and Position op Parallel Designed Waterline

o<JO

llM)li()l)^\

wdcs

i\

siiii'

o

1

S Io .

X

g o 3

o

^2

Sec.

^1

i

lO '^

^

S

5

c

nrsicN

fee

"O

I!

•So"

"' r.

_

>

e 1 a

•-

H

—


B--^3 O O

£

a

a*

2 «

g5

o o

8S8 *

8 O

CO

00

S

lO lO

00 00

J! In

go o m

to t^ CO c^ e^ c<

* "

CO 0> 05 c<5 CO ro

N N

O

C<5

O

t^ to 00

ch « O O

to CO CI

si 1.2

M

OS l>. C-1 05 CO u? to to u?

o •O lo

•*

o

C->

C-l

-^

»o

r^ CO -^

OQN'Oio O O -t t^ lO

co-^iO-n^co

00 <0 to 00

^ ^N ^ N to ^ 0> CO

to

•-<

i/>

„a

ocoio

(N to to

cs-^co

00 00

^ « CO oi ^ oi

00 !> CO

lOTt" U5

N coo

S

aw

^1.7

Sec. 51.7

TYPICAL SHIP-FORM AND SHAPE DATA

233

IIVDKODVNAMU.S

231 tliose for tlic

IN

corresponding position on another

ship. Tracings of tlie

"standard" body plans could \vindi)\v or over a light

be superposed against a

compare the section shapes, section-line and other features. However, for hyilrotlynainic analysis, and fur shipniesign purposes as well, tlie.se "13 to 1" body plans do not show the section shapes in their

SI 111'

1)1

SICN

table to

acquired

either because

2 to

4,

not possible to coinparc flow

2 to

1

ratios

may

was (2)

using as a reference the waterline

beam

at the midsection or at the section of maxi-

mum

area.

When

tracings of these

SBSR,

SNAME,

3

may

good

be mentioned:

Aug

EMB model 2933 imd tested at Wiushington.

in

S.\AME UD

Francisco

of

sheet 100.

tlie

1930'8,

on which a German scientific party mado measurements and observations at sea in 1934.

A body shown,

is

plan of this vessel, with no appendages published by G.

Kempf [SN.\ME,

1936,

On

pages 197 through 199 of this paper there are to be found the original observed data

Fig.

(3)

1,

p. 197].

from ship and model tests, including open-water tests of the model propeller. Dimensions and other data of ship and model are given in Table 1 on page 196 of the reference. Passenger and cargo vessel Panama of 1939, designed by George G. Sharp, for which a body plan was published by Marine Engineering and Shipping Age

[May

1939, p. 206).

body plans

are superposed, the waterline offsets for a series of 10, 20, or 40 stations are directly comparable,

as are the drafts and the underwater shapes

when

referred to the beam.

The

staff of

the old

Cramp

delphia prepared and kept on

shipyard at Philafile

a set of three

dozen or more of these "standard-width" body plans. Table .51.e lists these plaii.s, ^nth the names and principal dimensions or characteristics of the proposals, designs, and ships involved. All were drawn on tracing cloth, with a standard waterhne beam of 10 inches. The body plans, both underwater and abovewater, were supplemented (on the same drawing) by tables of principal ship dimensions, non-dimensional coeflicients and parameters, and large-scale layouts of the section-area ratios A/Ax and the half-beams of

the

designed

(or

load)

waterlines.

When

data on model resistances and sliij) elTective powers were added to the sheets. Fortunately, although the Cramp shipyard is no more, the Cramp standard jjody plan tracings are preserved in the files of the De]}artmcnt of available,

Naval Architecture and Marine iMigincering at the Ma.s8achu.setta Institute of Technology in Cambridge, Mass. There they maj' be consulted by all who arc interested in them.

is

1916, Fig. 13, p. 107;

1930, Pi. lOS.

built to these lines

many

bossing termination

angles,

lute width,

these

The d:iUi are available German motorship San Line,

and similar features can not be judged or compared easily on these "2 to 1" body plans. Most of the tip circles would be ellipses if drawn properly, and the slopes of bossings and struts would be the same as their true values only if the B/H ratio of the ship were 2.00. A more rational and useful scheme is to draw all the "standard" body plans to the same abso-

one way or another, and trials have been

owned and operated by the Hamburg-.Vmerican

or more.

Propeller tip clearances,

in

tests

G. S. Baker's modol 56C, of which a body plan also in

vary from

or from G to 10, by ratios that approximate

Among

roproduccil in

patterns by this method since on vessels of the

same type the beam-draft

many

tliem, or beca\ise of outstanding

|)erfonnance. (1)

is

prominence

made on

nor the section-line slopes at their

proper value. It

1I.S

There are

available in the technical literature a few largescale l)ody plans of nuidels and ships which have

slopes, offsets at given stations,

true form

Sec.

Body Plans.

Single-Screw

51.8

Fio. 51.

D

Body Plan for Run or U. S. Maritius CaUOO VB8SEI<

coMMis8ir)N Cl-^f-^ VI Ci .A.S.S OK

TYPICAL SHIP-FORM AND SHAPE DATA

Sec. 51.S

stations

Slopes If

of Desianed

Lenqth

rH

is

ard Other Woterlines for This Form ore Excessive; Seporotion

Limited,

It is Better to

is

Certain to Occur Aboft Them,

Adopt a Different Type of Stern, to Insure Proper Flow of Woter to the Propeller ond Rudder

235

HYDRODYNAMICS

236

V. S. Mnritimc Commission Cl-M-.\Vt rlnss of iho 1940'». The plan of the aflerl)0»ly ami of the wafer-

(\)

as an e.xnmple of a stern that

with

is

definitely too blunt,

slope.i that are exoe.isivo for goo
the

TMB

This chiss was te.'itod as model 3S39, and the complete model results are given in propeller.

RD

SNA.ME U.

sheet 19.

Maritime Commission CS ty|)c cargo vessel, for which a IkkIv plan is to be found in SXAME, 1950, Fig. 77 on p. 5t)3. This class was tested as TMB model 35:J4, but at the time of writing (1955) the complete results had not yet been embodied in an S.

RD

S.\.\MK

(6) To
sheet.

and Forest, F. X.,

Proposed

".\

New

amount of reference data. The Index sheets and Summarj' sheets accom-

Forms and Standard

Scries Lines,"

SNAME,

TMB

Index sheets, and Summarj' sheets, apply to twin-screw vessels as well. Among the ships (or designs) for which body plans arc available in the literature there may be mentioned: (1)

model

scale)

A

(9)

SNAME,

TMB

of

Body

SNAME,

1947. General

profile,

I.

H.

and some

Budd

give a

lines of

characteristics of this

beam, developed by the Sun Shipbuilding and Dry

Dock Company,

(4)

tested

in

small scale as

T.MB

models 3817 and 3821. The lines are shown in Fig. 11 on p. 107 and Fig. 13 on p. 108 of SNAME, 1947. Table 1 on p. 109 gives the general characteristics of the proposed ship. model 3930, representing a twin-sorew liner, 745 ft long on the waterline, with a normal form of

TMB

-stern (Bates, J. L.,

The body plan

is

SNAME,

1947, Fig. 41, p. 137).

accompanied by a table of general

characteristics. (5)

body

"Large Piissenger-Carrying Ships

TMB 745

Typical body plans for (^ivoii in

72.D. Limitations of space of lines drawinns,

body

.sliallow-wiilcr

paddle-

Figs. 72. A, 72. B,

and

model 3917, representing a tunn-screw liner, long on the waterline, with a twin-skeg stern

(Bates,

J.

The body

L.,

plan

SNAME, is

1947,

Fig.

42,

p.

137).

accompanied by a table of general

characteristics.

Multiple-Screw Sterns.

51.10

A

great ?iiMn-

been liuilt in the period 1000-1955, yet the published data on lines, form coefficients, hull parameters, and other ve.s.sels

iiave

hydrodynamic features are surprisingly meager. the roprodiu'tion

In fact, data on the shape of the runs, the jiropeller

plans, or even tabulated

and diameters, hull (tip) clearances, and shape of appendages carrying the jiropeller .'jhafts

i)recliide

data on other interesting and instructive designs. Indeed, in view of the availability (in 19oG) of

SXAME

for

1945,

ft

ber of quadruple-screw

driven vessels are

SNAME,

described in the paper. (6)

pp. 287-301.

L.,

J.

pp. 290-334. Table 1 on page 296 lists the principal dimensions and characteristics of the five designs

plan,

Fig. 7, p. 430]

Bates,

Certain Essential Trade Routes,"

in

flow around the

[SNAME, 1950, many cases lines

plans,

Resistance Data sheots, with

their wealth of quantitative data,

prospect of

plans are shown

116, respectively,

design are given in Table 3 on p. 113 of the reference. (3) Proposed design of a large tanker of extremely wide

is

and in drawings, are published by J. Baader for a great variety of large and small single-screw vessels in his book "Cruceros y Lanchas Veloces (Cruisers and Fast Launches)," published in Buenos Aires in 1951, Figs. 225-239,

some 100

Body

and 24 on pp. 112 and

in Figs. IS

1955, Fig. 9 on p. 449

De Luce and W.

tanker Pennsylvania (11)

Twin-skeg Manhattan design, tested in small scale as model 3898 but never worked up as a ship design or built as a ship.

built

body plan of the Gopher Mariner published by V. L. Russo and R. T. McGoldrick

wave

mo
shijis,

small-scale

(10) II.

TMB

p. 113 of the reference. (2)

all

and open, as

by

.\tlantic liner ^fanhaitan, represented

3041. Fig. 17 on p. HI of SNAME, 1947. General characteristics of the hull are given in Table 3 on

are shown in Figs. 13 and 14, pages 123 and 125, respectively, of the reference.

into the

a

in

SXAME RD

ships, including the notes on the

TMB

closed (as tested in

it

sheets,

sufficient detail to indicate the exact

(8)

add

later)

and present

51.9 Twin-Screw Body Plans. The general comments of Sec. 51.8 relative to single-screw

1951,

the data in forms of the various models, their hull coefficients, and their distribution of section area along the length. It also gives corresponding data for the U. S. Maritime Commission C-2 class of cargo ship, for the ^lariner class, for the modified C-3 vessel Schuyler Olis Bland, for a Bethlehem design of cargo vessel, and for the tanker Pennsylvania. Rus-oo, V. L., and Sullivan, E. K., give a body plan of the Mariner cla.ss, including a wave profile at a speed of 20 kt and a T, of 0.S77 (SNAME, 1953, p. 1 15 and Fig. 12 on p. 122|. This design was tested model 4358\V-3. The stern profiles, both as

through 150 (and

1

slightly difTerent fa.shion.

forms.

1953, pp. 516-5S9. This pajx^r gives

sheets

to the store of information

Series 57

Todd, F. H., "Some Further Experiments on SingleScrew Merchant Ship Forms— Series 60," SN.\ME,

(7)

RD

panying

Basis for the Design of Singli>^orew Merchant >Ship pp. (}42-744. This paper covers the

Sec. 51.9

siderable

nnd run of thin vesBcl lire illuxtrnttHl in Figs, and 51. K, resp«'elivcly. These lines are included

linen ."il.n

(5)

IN SHIP DESIGN

marine architect has ready at hand a very con-

and with the additional sheets year by year, the

positions

are limited largely to stern jihotdgraphs of these ves.sels

on the laimching ways or in dock. l<,l20"s and early HMO's, T. E. Ferris

In the late

made many

studies of a large, high-speed trans-

TYPICAL SHIP-FORM AND SHAPE DATA

Sec. 51.10

atlantic passenger vessel.

He

reported upon these

American Superhners" [SNAME, 1931, pp. 303-350 and Pis. 1-13]. Table 1 on page 318 of this reference gives the ship dimensions and hull coefficients corresponding to three of the fourteen models tested at the studies in the paper "Design of

Model

Washington. All these designs embodied 4 propellers. This paper Experimental

Basin,

was published, practically in full, in Marine Engineering and Shipping Age, December 1931 and January through April 1932. E. P. Trask discussed this design problem further in his paper

[MESA,

Liner" vessel

"A Proposed

Jul

was designed

1932, for

pp.

800-ft Atlantic

268-275].

This

an operating speed

of

28.5 kt.

At the conclusion of World War II, J. L. Bates and I. J. Wanless made an analysis of existing passenger liners and worked up a new design, which they reported upon in their paper "Aspects Large Passenger Liner Design" [SNAME, 1946, pp. 317-373]. This paper tabulates many dimensions and characteristics of the Europa, Manhattan, Conte di Savoia, Rex, Normandie, and a of

projected

U.

P3-S2-DA1

S.

Maritime Commission design

for trans-ocean service.

ships analyzed, the Manhattan, vessel but

all

is

One

of the

a twin-screw

the others are quadruple-screw

237

justification for referring to a paper,

now almost

by G. W. Melville entitled "Notes on the Machinery of the New Vessels of the United

historic,

Navy" [SNAME, 1893, pp. 140-175]. Plate 41 of this paper illustrates the triple-screw States

arrangement

of the U.S.S.

Fig. 51. F is a

Columbia

(old) of 1890.

body plan resembling those

of the

coastwise triple-screw passenger steamers

Yale

and Harvard, designed in the early 1900's, and reported upon by C. H. Peabody, W. S. Leland, and H. A. Everett in a paper "Service Test of the Steamship Harvard" [SNAME, 1908, pp. 167-186]. These vessels gave long and distinguished service on many difficult routes, so much so that their designs would warrant further analysis if accurate and reliable data and drawings could be found. Fig. 51.

G

triple-screw

Northern

is

a body plan of the high-speed, and cargo vessel Great

passenger

(and

sister

vessel

Northern Pacific),

designed in about 1914 and famous for outstanding performance in heavy weather. Unfortunately, it is

not possible to add propeller-disc positions to either of these drawings.

and appendage data

German naval

architects have probably

more experience than

all

had

others combined in the

design of triple-screw vessels. However, as almost all of

these were combatant craft, their lines and

ships.

the design rules pertaining to them appear not

Corresponding information on triple-screw veswith sterns which are the most difficult of any to design, is very scarce. This is partial

to have been published. What might be considered an exception to this is the study for a medium-size fast liner published by E. Foerster [SNAME,

sels,

Fig. 51.F

Body Plan Resembling Those of the Triple-Screw Coastal Passenger Vessels

Yale

and Harvard

ll^^K()n^\ wik.s i\

238

Fig. oi.O

Body Plan of the

Tniri.E-ScRiiw Passenger

1936, pp. 228-287]. TliLs unusual vessel, for wliich section- and hull-shape data are given, was

some

to have

siih' nisir.N

had twin propellers carried by orthodox

bossings, plus a centerline Voith-Schncider pro-

and Cargo Vessel

Srr. 51.10

Great Northern

which was to have been used

for steering

as well as propulsion. Resistance and

power data,

peller

derived from model tests, are given for various

combinations.

One

of the

most modern

of the

German com-

batant vessels, the World War II cruiser Prim Eugcn, was taken over by the United St-ates. Some data on this vessel arc in the files of the U. S. Navy Department. Fig. 51.11 gives the general features of one of

its

transverse sections.

Vessels with five screw propellers have been in the design stage but so far as known no data on those studies iiavc been published (SBSR, 17 Oct 194G, p. 439]. I''urtlier reference data on ves.sels il riven by multiple propellers are given in Sees. 07.14 and

considered

SuiTCii OK Onb SEcnoN or tub Trii'LEScREW Gehman Ciiuihek Print Eugtn

Fio. 61.H

07.15.

CHAPTER Analysis of

52.1 52.2 52.3 52.4

52.5

52.6 52.7

Flow Diagrams and Prediction of Ship Flow Patterns

Scope of Chapter Typical Ship- Wave Profiles Wave Profiles Alongside Models General Rules for Wave Interference Alongside a Ship Estimate of Bow-Wave and Stern- Wave Heights and Positions Prediction of the Surface- Wave Profile Typical Lines-of-Flow Diagrams for Ship .

.

Models 52.8 52.9

52.10 52.11

Analysis of Model Surface-Flow Diagrams

.

Observation and Interpretation of Off-theSurface Flow Data on Models Estimating the Ship Flow Pattern on the Body Plan Prediction of the Ship Flow Pattern at the

From

52.12 52.13

Estimating the Change in Flow Pattern for Light or Ballast Conditions

243

52 14

Predicting Velocity and Pressure Distribu-

the Ship

256

Surface

.

Around Ship Forms Use of Flow Diagrams for Positioning Appendages Estimated Flow at Propulsion-Device Position

244 246

52.15 52.16

248 250 254 255

Supplementing the data on streamline patterns around bodies and the discussion on distribution of velocity and pressure in Chap. 42, there is given here some representative informa52.1

Probable Flow at a Distance

239 239 241

256 257

258

258

tions

52.17

Analysis of the Observed Flow at a ScrewPropeller Position

52.18 52.19 52.20

Flow Abaft a Screw Propeller Persistence of

Wake Behind Wake

....

a Ship

Bibliography on

259 259 261 262

255

Bilges

Scope of Chapter.

potential-flow,

52

ideal-liquid

outstanding feature of the 3-diml flow around a simple ship form, when the latter is brought up from a deeply submerged position 2-diml

bution in the water around ship models. There

and run at the air-water interface. This feature has perhaps more importance for 3-diml forms and actual ships because, at the speeds where surface wavemaking is prominent, the wave

are very few full-scale data on ships, either in the

pattern there influences the flow over a consider-

tion on flow

and on velocity-and-pressure

distri-

technical literature or in form available for publication, with

which to confirm the model data.

Space limitations prevent the inclusion of the amount of model data available in America, mostly at the David Taylor Model Basin, on the flow around ship models, representing many ship types. Indeed, these data comprise sufficient material for an entirely separate study and analyvast

down

to

and

Fortunately,

the

wave

it

is

not too

difficult to

on a ship because

profile

obtain

this region is

available for observation or photographic record-

A

ing.

number

of ships in the past

have had

painted on one side a grid pattern of some sort for the builder's

or the acceptance trials.

By

looking over the side, the intersections of the

sis.

52.2

able extent of the ship's side, often

including the bilge-keel positions.

Typical Ship- Wave Profiles.

An analysis

around a body or ship, at least for a craft running on the surface, begins properly with the surface-wave profile. This is the of the flow patterns

FiG. 52.A

wave profile could be observed and marked on an outboard-profile drawing carrying the same actual

grid.

The two

for the

Observed Wave PROPitEs at

239

Two

U.

full-scale

S. battleship

profiles

Maine

Speeds on a BATiiiESHip

of

Fig.

52.A,

(new), were ob-

nVDROnVNAMIQS

!I0

Wove

FVofile at

12 hi.

Fio.

setAotl in this

1902, p. 49

and

manner PI. 11].

Jy

0371, f„'

OBSF.RVF.n

.'i2.R

[Powoii, J. W.,

Wave

259

Wove

Wave

Fig. 52.B [Peabody, C. H.,

SXAME,

profilos ob.served at

SXAME,

DESIGN

Profile ot 16

M. 1^-

Profiles at

two speeds during tiie trials of the U. S. Coast Guard cutter Manning of the late 1890's are drawn over an outboard profile of the ship in 93;

IN SHIP

(a)

do not show the wave

B =

(b)

is

profile directly (c)

because

sj'stematic

procedures

wave

all,

are

(d)

interesting photograph of this kind

a small battleship of the class at full speed

shows

(e)

German Deulschland

[STG, 1940,

p. 341].

Another,

battle cmisor Moltke of the

qucHtion are rcproductid in the .Inly

79(i to 799.

Xavnl

The

A =

T,

=

A

10,850

this

=

L\(-l

A =

ft,

19.4 kt; T,

475.75

18,400

=

t,

B =

ft,

84.75

Ps = 22,500

ft,

horses,

0.889 at this speed.

photographic wave profile of the U. S. battleship

at the stern [.\SNE,

Aug

photograph appears

in

For a

F„

=

the

wave

The wave is

1897, p. 454).

"Jane's

similar

length at this speed, assumed

waterliiic length of

0.26S2. For a trochoidal Icngtli

A

Fighting Ships,"

thus about half the length of the

Lw

360

ft,

wave

for 17 kt is

thing less than half the ship old

7',

=

0.9005,

deep water, about 1(>2 ft, some-

lengtli.

in

Data

for the

Iowa, corresponding to thase for the French

ships, are:

A = Cx =

= 360 ft, B = 72.0 ft, // - 24.02 ft, Ps = 11,835 horses, Cp - 0.668, S = 31,110 ft', Cr = 0.7:53, .\x - 1,635

/>,r,,

11,363 0.944,

t,

ft«.

(f)

Wave

(g)

The Danish

issue

nuincrical data appenilnl here arc

L = 330 ft, B = 65.5 ft, // = 28.5 t, Ps = 12,000 horses, F = 16 kt;

shows a Velox wave length of about L/2.

ship,

27.5

profiles at two speeds for the Italian crui.'wr Picmontc are publi.shed in INA, 1SS9, Plato XXVII. The ship is 325 ft long, and for the higher s|>ced the wave length is about eijual to the ship length, minus the lag in the bow-wave crest. At 20 kt the value of T, Is 1.11, F. - 0.331; at 21.5 kt, 7', is

1.193 !tnd 19."j4

Institiile Procecdiiig.s, jjages

=

0.881 at this speed.

Voltaire

ship.

crast aimft the

in

ft,

to be 17.087 kt,

World War I pcri(Kl (SchilTbau, 22 May 1912, p. G49|. These indicate in a general way that the first Velox wave is something less than one ship length long, because of the lag of the first wave bow, but otherwise they are useless for analysis by any known method. Some data are listed here relative to excellent photographs of certain French men-of-war of a half-century ago, wlion underway at what appear to Ix; full speed and full power. The i)liotograplis

P.,

t,

to be

1910, p. 192.

German World War I battle cruiser Gocbcn what appears to be full speed [USXI, 1912, Vol. 38, p. 1GG8]. A third sliows wave profiles the

of the U. S.

10,000

Iowa (old), presumably made at or near full s|)oed, shows one crest at the bow, one amidships, and one

at

Gennan

A =

down

H = V =

that appear in the photograph, shows

along.side the

ft,

21 kt (nominal); for 22 kt,

is

For

equally interesting becau.sc of two very large crcstvS

24.5

by the head. The Velox wave length appears

The

profiles along-

side models or ships in advance of tests or trials.

wave

= V =

;/

ft,

about L/2. Here

traveling.

lacking for the prediction of

One

65.33

gives the distinct impression that the ship

state the exact speed at which

Nevertheless, they are better than no data at especially

"Jane's

of

T, = 1.034. French crui.scr Chaleaurcnault of about 1S9S. The photograph reveals a considerable trim by the stern and a Velox wave length of well over L. Here L = 443 ft, B = 56 ft, // = 22.5 ft, A = 8,01S t; Ps = 23,000 horses, V = 23 kt (estimated); for 23 kt, 7', = 1.093. For a speed-length quotient only slightly greater than that of the Condi, the Velox wave length appears to be much greater. French battleship MagctUa of 1890. The photograph

against the ship's side, or

They do not

issues

French cruiser Condi of about 1904, making about 22 kt. The photograph shows that the Velox wave length is about L/2. For this vessel, L = 452.75 ft,

1899, PI.

either:

the ship

contemjiorary

Fighting Ships":

1904, Fig. 20S, p. 513].

(1) The}'

0.i45.

Speeds on a CiiiNnoAT

from

taken

1.161; F„-

20,500 horses,

NA,

There arc in the literature litcrallj' thousands of photographs of ships inidorway, surrounded (on the near side at least) by the waves of the ship's Velox system. Almost never are the.se photographs of more than pictorial value becau-se

(2)

Two

Sec. 52.2

/•„

-

0..3.5.5.

ship Tjaldur

is

shown ninning at IS

kt,

revealing a deep trough at an estirnati'd position of O.l.'iL

from

llic

bow and a

seronil crest (following

FLOW PATTERNS AROUND

Sec. 52.3

T,,-

At-Re5t Woterline ;

Fosi

SHIPS

0.689

F„-

241

0.205

IlVnRODVX AMK.S bulbs,

/, =

0.08, O.OJ,

ami

0.(X), witli

the vortical

scales exftggeratetl about 7 times, are given

E.

M. Bragg

r,

- v/Vl 1.2

in

SNAME,

by

of

/•'.

first bow-wsvo crest abaft FP, on a basis of 20 stations

varying from 0.21 to 0.38, T, of from 0.71

to 1.28.

1938, Vol. 42, pp. 543-5G9]. This plate

approx. 0.0S5/y from FP. Varied

from Sta. 1.6 to Sta. modoLs referenced

1.9 for the three

shows not

only a body plan of the model but a transverse

water surface abreast the model at to 0.05 and 0.95L

profile of the 1.7,

Sec. 52.3

The wave profile for a double-ended model having mathematical lines is given on Plat« 1, page 545 of a paper on wake by C. Igonet [ATM A,

1930, PI. 51:

Station for

About

SHIP DKSIGN

IN

and 19, corresponding from the FP. Stas.

1

E. Ileckscher published a scries of wave pro1.0

About

1.2,

approx. 0.06A from FP. Varied

from Sfa. 1.0 to Stas. three models

1.6 or 1.7 for the

files

alongside a given model, for F„ values of

0.19,

and 0.325, T, of 0.(54, and 1.091, corresponding to hump-and-hollow positions along the curve 0.23,

0.25,

0.295,

0.775, 0.842, 0.991,

0.8

About 0.8, approx. O.OIL from FP. Varied from Sta. 0.7 to Sta. 1.0 for the three models.

five

[WRH,

of resistance with speed

15

Aug

1939,

Fig. 4, p. 2G2].

In the Annual Report of the

Rome Model Basin

X, there are showTi two wave profiles for Rome model C.295, at two speeds. The corresponding T, values are 1.082 and 1.204. These profiles, with the body plan of the model, as published in Table XII of the referfor the year 1941, Vol.

The author

of this paper

comments on the

fact,

amazing similarity of the \va\'e profiles for all three models at a T, of 1.2, the model with the largest bulb had 15 per cent less resistance than the one with no still

unexplained,

that

despite

the

The present author makes the further comment that, at all three T, values, the model

bulb.

enced report, are reproduced here in Fig. 52. E. D. W. Taylor shows the wave profiles for two

models at various speed-length quotients

Wave

[S

and

with the largest bulb had the highest bow-wave

P, 1943, Figs. 21-25, p. 24].

This feature likewise remains unexplained. STG paper on tests of models in shallow and restricted waters, referenced in Sec. 61.3, gives in Figs. 13a and 13b the wave profiles alongside models of a heavy

traced on the body plans of two series of models

crest!

0. Schlichting, in his 1934

cruiser

and a

\videly varying midsection coeflRcients in 26-35 on page 25 of the reference. This set of body plans is reproduced as Fig. 52. Q in Sec. \vith

Figs.

52.7 of the present chapter.

G. do Verdi6rc and

light cruiser, respectively, for values

Wave

V Fia. S2.E

Obbeiivko

Wavk

1'iiorii.Eu

profiles are also

Rrofile for Tq-

I

204,

J.

Gauticr give a series of

F„-0359

Water Surtace at Re^t

^

on Uomk Munr.L Bakin Moiiei,

C.:^05

FLOW PATTERNS AROUND

Sec. 52. 4

wave

determined from tests of four models of ships having waterline lengths L of from 459.3 ft to 448.2 ft [ATMA, 1948, p. 490]. The ordinates are in meters for the full-scale ships and the abscissas in 0-diml length ratios x/L, with Sta. at the AP and Sta. 20 at the FP. The profiles in diagram a of Fig. 8 on page 490 of the reference are plotted with respect to the undisturbed water surface at infinity. Those in diagram b are plotted with respect to the at-rest ship waterplane, so that they differ by the amounts of the sinkage at each station. The T^ values for these plots range from 0.747 for the short ship to 0.756 for the long ship; corresponding F„ values profiles as

mate

Wave

profiles are

shown

for the ten tanker

wave

Six sets of

profiles for

two

self-propelled

models, showing the changes in profile over a

wide range of speed, are given by S. A. Harvald in SSPA Report 13, published in 1949, entitled "Medstr0mskoefficientens Afhaengighed af Rorform, Trim og Haekb0lge (The Dependence of Wake Fraction on Shape of Rudder, Trim, and Stern Wave)." The profiles appear on pages 13, 14, 34, 35, 36, and 40. On the last-named page there is a set of profiles for the model running astern. On pages 56-60 there is a summary in English.

Wave

profiles

at three speeds for seventeen

models of coasters are given by A. 0. Warholm in SSPA Report 24, published in 1953, entitled "Nagra Systematiska Forsok med Modeller av Mindre Kustfartyg (Systematic Tests with Models of Coasters)." The profiles, apparently taken during resistance (and not self-propelled) tests, are printed on pages 85-90. On pages 48-50 there is

a

summary

in English.

wave

of

two

locations.

114, 115,

and

Examples

of these are sheets

144.

Wave

Volume

effects. Fig.

I,

interferences

and

their effects along

Lack

(1)

the

of information as to the variation of

level along the ship of the crests

and trough of

the Bernoulli contour system, described in Sec.

This

10.3.

undoubtedly a function of the^ and it may also be a

is

surface-waterline shape

function of the section-area curve.

Lack

of a precise determination of the effect

of the presence of the ship entrance abaft a point-

pressure disturbance such as a stem

Inadequate knowledge as

(3)

to

the effect of

an

variations in the waterline slopes in such

entrance, discussed briefly in Sec. 10.6 on page

174 of Volume I and in Sec. 48.2

Uncertainty as to the amount of crest lag in the Velox wave systems

(4)

(and trough lag)

generated by pressure disturbances abaft the

bow

Uncertainty as to the factors determining the fore-and-aft position .and shape of a sternwave crest on an actual ship, in the presence of a separation zone, of boundary layers, and of water coming up from under the ship (5)

Lack

(6)

of

knowledge as to the lengths of actual waves for a given celerity, when

(or trochoidal)

occurring abreast a ship instead of in the open,

unobstructed sea. In the absence of these data

down

their

it is difficult

to

wave interferences and a moving ship. If the

specific rules for

effects

individual

alongside

profiles

could

be

positioned longitudinally, there to believe that in effects

General Rules for

profile,

waterline of a ship of normal form are:

set

Provision is made, on SNAME RD sheets having numbers in excess of 100, to depict the wave profiles at designed speed in either or both

wave

resultant

adapted from W. C. S. Wigley, does this for a 2-diml ship having a parallel middlebody and triangular ends. Many barges have nearly square-cornered rectangular waterlines but on most ships the pressure disturbances are regions rather than points. This renders it extremely difficult to predict the shape and foreand-aft position of the wave form generated by each such disturbance. Several further complications in working out lO.F in

(2)

plan of the ship in question.

243 the

taking account of wave-interference

are 0.222 and 0.225.

models reported upon by R. B. Couch and M. St. Denis [SNAME, 1948, Figs. 2(a)-10(a), pp. 360-378]. A single wave profile is reproduced by W. P. A. van Lammeren in RPSS, 1948, Fig, 38, on page 88, for a T, of 0.64, without the body

SHIPS

analytically

determined and is every reason

most cases the interference

could be determined by simple super-

Interference

position of the heights of the transverse waves in

Alongside a Ship. For a ship form having abrupt and localized changes in waterline curvature,

each system at any selected station. K. S. M. Davidson gives a few diagrams [PNA,

52.4

resulting in

what may be considered

pressure disturbances,

it is

as point-

possible to appro.xi-

1939, Vol. II, pp. 66-67] in which this superposition

is

indicated, in addition to the schematic

HYDRODYNAMICS

:n tli:iRrain.s in

10 of

W.

Figs. lO.C;,

10..I,

\olume I. P. A. van I^mmorcn,

uiul 10.

K

of C'liap.

ships,

ami

J.

G.

somewhat difTerent

lines

wave

profile,

in Fig. 52. F.

3.

This extreme variation

32

outlined in Sec. 52. (i, recjuires in

26

an estimate of the heights and bow-wave and stern-wave crests. There is an appreciat>le space lag in the bow-wave crest positions

azo

6r

Prediction of the surface-

particular

models,

tiieir

is

undoubtedly

[RPSS,

Bow-Wave and Stem-Wave

Heights and Positions.

on

profiles ob.servcd

^

40

Estimate of

52.5

Sec.

Eq. (52. i), as indicated

varies from 0.3 to nearly 3.0, indicate*! graphically

1918, pp. 54-')ol.

52.5

DFSICN for the 0-dinil

/>-,r

by the wave L. Troost,

Koniiig discuss the features and effects of wave interference along

IN SHIP

ojso

ZHflST

5 2"

of the

on page ISO of Volume I, especially if the speed is high. This lag is particularly noticeable in Fig. 52.B of Sec. 52.2 and in Figs. 52.1 and 52.J

D«st. Tender

1

MSXA,

18 of

^"-L—n_

Cruiser

18G5,

that the bow-wave crest lags back to a

point abreast midships.

He explains

this feature in

page G3G. A situation reproduced in the familiar photograph of Parsons' Turbinia at full speed Vol.

I

1.0

Graph for

Fig. 52.F

is

(SNAME, HT, 1943, p. 439]. An empirical formula for

estimating

"good

average values" of the height of the bow-wave crest is given by J. L. Kent [NECI, 1949-1950, 435]. This is in the dimensional k{B/LE)V', where h, B, and Lg are in ft, V is in kt, and Jc = 0.083. It resembles a formula given by Laubcuf many years ago [ATMA, 1897,

66,

form h

p.

=

p. 211].

Kent's

/:-value

is

ships," derived from

for

wave

"ordinary jjrofiles

merchant

observed when

towing a number of ship models at the XPL, Teddington. Presumably it appHes to ships without bulb bows. Furtiiermore, it takes no account of angle of entrance at the stem, hollowness or fullness in the entrance wnterlines, flare of sectioiKS,

feature

16

1.4

1.2

Estimati.n'o

20

i.a

Bow-Wave Crest

Height The spot

.ipplying to each vessel

designed speed of

is

for the

ealeulutcti

tiiat vessel

of the reference,

almost exactly similar

Vol.

^

t,-vm: 0.6

Vol. II, Fig. 31, shows a ves.sol being driven so fast

''""feS^^I

08

0.6

Scott Russell, in Plate

*v

DeslroYer

5

of Sec. 52.6. J.

Seoplane lender

\\,

I

position al)aft the stem, described in Sec. 10.15

rake of the stem

which

bow-wave

bow

any other augment the

profile, or of

might reduce or

crest height. Preliminary plots indicate

that the value of

/;

varies rather widelj', from

due to the fact that the ratio Bx/Le does not take adequate account of the WL slopes at and just abaft the stem.

Transformed into a dimensionally consistent equality for any units of measurement, Kent's formula becomes, for the height h of the bowwave creat above the at-rest WL:

projection of the crest on the centerplane farther

forward, toward the stem.

The models on which pressure distributions 2861 and were observed by E. F. Eggert, 3383 [SNAINIE, 1935, pp. 129-150; 1939, pp.

EMH

303-330],

fcjrni

of displacenicnl-lyije

bow-wave

sliow

crests

considerably

higher than those given by either formula, in the

T, range of 0.76 through the

bow-wave

1.2.

crest heights

On

the other hand,

measureil on two

narrow models by W. C. S. Wigley, in the same speed range, are lower than the fonnida values [NECI, 1930-1931, Vol. 47, pp. 153-196; INA, 1935, Fig. 6, PI. XXVI]. It is po.s.sil)le that on

some towed models it is difficult to tell where the wave profile ends and the spray root begins; also that factors additional to those in the formulas affect this

phenomenon. For either or both of these and the Air-curvc of Fig. 52.

regions E(|. (52. i)

arc consiiiercd

lus

preliminary only.

The estimated bow-wave

ABC

crest height for the

ship of Part 4 at 20.5 kt (34.62

ft

per sec),

using a h,r of 1.385 from Fig. 52.F and employing

Eq.

For the range of

large waterline slope not only

behind the stem, but the large slope throws the

tlie

order of 0.015 to 0.13 or more.

A

produces a high value of pressure coefficient close

, ''

-

(52.i), is

,

(l^A ^"

'"\J 2y

=

,

'

oor

73(l,198.r>)

••^^•'(2ii2T5J647rrs

_-

,-f, f' '

'

'

Sec.

FLOW PATTERNS AROUND

52 J

It appears proper that this height be measured from the undisturbed water level rather than of the ship, as might be from the at-rest

WL

painted on

its hull,

bow due

because of the drop (or

rise)

the calculated h the value of this drop for the

0.7, is 17.85

ABC

—2.35

ship,

as

ft,

measured during the

model resistance test, and allowing for the lag in the bow-wave crest, to be determined presently, gives a value of 9.47 ft for the bow-wave crest height, measured above the 26-ft DWL. The full details of this calculation are given in Sec. 66.28.

Based upon observations

of

EMB

model 2861

E. F. Eggert evolved a rule for estimating the

bow-wave

crest lag, defined as the fore-and-aft

distance of that crest abaft the intersection of the

stem and the

at-rest

WL, when

projected on the

[EMB Rep. 392, Nov 1934, The +Ap peak may not always lie exactly centerplane

intersection just mentioned, but

it is

p.

1].

at the

/*"„

For the

.

ABC

ship at

works

out as 0.372(34.62)732.174 = 13.86 ft. From Fig. 52. G the value of the crest lag for a T„ of 0.908

to the

245

number

20.5 kt, or 34.62 ft per sec, this crest lag

combined effects of the Bernoulli contour system and the Velox wave system at the ship speed in question. Adding to of the

SHIPS

T„ and Froude

0.0272L„.z,

is

.

TMB

The value observed on

model 4505 of the ABC ship and indicated on Fig. 66. R, where the crest occurs at about Sta. ftor0.035L;pi

Model data

.

from which the graph of Fig. 52. G was derived, show rather wide variations from the value predicted by Eq. (52. ii) in some cases and exact agreement in others. Thus this equation and the broken-line curve of Fig. 52. G are both to be considered as for a variety of ship forms,

preliminary. S.

"Wake

A. Harvald, in his

Merchant

of

Ships" [Danish Tech. Press, 1950, pp. 81-84], gives a diagram by which the stem-wave height

may

be estimated, as a means of predicting the

amount Fig.

of

52. H,

wave wake

in

any particular

case.

adapted from Harvald's Fig. 41 on

near enough

for all practical purposes. Eggert's formula, in

dimensional form, says that the crest distance x

=

lies

at a

0.033 F^ abaft this intersection,

where the x-distance

is

in ft

and

V

is

0.05

in kt. In

h = Stern-Wave Crest Height Ly/ "= Lenqth of Trochoidal Wave of

0-diml form this becomes, for the distance abaft

WL at rest.

the stem at the

X This equation

is

=

0.372

0.04

7' —

(52.ii)

plotted in Fig. 52.

G

to give

L

= -

^

? s\^ 0.03 o

\\^ \^ \\

\\\

L ^l on a basis of both Taylor quotient ,

—

V

\ \

\\ \

\

W\\\ W \

—

\

values of the crest lag x in fractions of the waterline length

Velocitv^

\\\ s

\

\\

0.02\ \

\>

.\ \ \ \ -n-V^

N^O.14

0.01

L

0.1

-r-

0.5 Fig. 52.H

0.7

\Q.I6

a

z

Crest Lag-

\ \0.20

V

\

0.9

1.3

Graphs for Estimating Stern-Wave Crest Height

page 83 of the reference cited, indicates the parameters employed, B/L, h/Lw and T, Harvald admits that a number of apparently import,

.

ant factors are not taken account of in his diagram but, like the other diagrams of this section, it

something better is developed. ship, or one of its proportions, B = 73 ft and L = 510 ft, whence B/L = 0.143. At a Tj of 0.908, Harvald's diagram gives a value

will serve until 0.6

Fig. 52.

0.8

I.Z

1.0

G Graph

1.4

1.6

1.6

2.0

for Estimating Bow-Wave Crest

Lag Abaft Stem

For the

ABC

UVDKODVNAMK.s

:i6

for

h/L,

Lw

length

of about 0.0195.

From Table

=

If this

water •1.57 ft

O.OI95/.,r

0.0195(231.3)

=

1.57

analysis of systematic dala. This applies not only ft.

to elevations in the wave profile but to the exact speeds corresponding to the profiles, and to the shapes and proportions of the ships making the

reckoned above the undisturbed the height above the 20-ft is

height level,

=

is

DWL

plus the sinkage (about 0.75

ft),

Src. 52.6

There Is a definite lack of accurate, comprehensive, and rcliiible information in Sees. 52.2 and 52.3, and in the literature in general, upon which to develop a wave-profile prediction method by the

48.d the

of a Irochokirtl wiivo having a velocity

equal to Uie ship speotl of 20.5 kt is 231.3 ft. Then, for the estimated height of the stern wave, h

IN Mill' DllSlCN

or 5.32

waves. Nevertheless,

ft.

Although Ilarvald's data arc not intcndcfi to

it

is

possible to sketch

approximation of the surface-wave

an a

profile for

take care of Iraiisoni-slcrn ships, the hciglit of

tlic

ship design by using the empirical data of Sees.

obs»»rved stern-wave crest just forward

the

52.2 and 52.3, plus some additional experimental data relative to the number of wave lengths to be expected between the bow-wave crest and the

of

TMB

transom, as measured from the profiles on model 4505, reproduced in Fig. 66.11, is about 4.1 ft. reckoned above the 2(>-ft DWL. 52.6

stern.

The

Prediction of the Surface-Wave Profile.

19

10

17

Fio. 62.1

16

15

Wavb

14

IS

Profiles for

12

II

10

9

TMB Sbrieb 67,

latter

S

7

data are based preferablj' upon the

6

3

4

J

Modbi, 4200W, at VARioita Spbeds

FLOW PATTERNS AROUND

Sec. 52.6

SHIPS

speed-length or Taylor quotient T„ or the Froude

fall

known that, in general, when wave of the Velox system generated by the bow coincides with the first wave crest of the stern Velox system, there is a

edge of Fig. 66.A.

drop in total resistance. When a trough of the bow system coincides with a crest at the stern, there is a rise in resistance. When these effects are plotted on a base of speed-length quotient T, or F„ the humps and hollows in the curve of total (or wavemaking) resistance are found to

in

number F„

.

It is

the crest of a transverse

247

in the positions indicated along the lower

known,

It is also

normal form,

for ships of

that certain T, values correspond to ship lengths that are multiples of the transverse-wave lengths

whole numbers. Roughly:

(1)

For T,

(2)

For r,

= 0.63, the ship is 4 wave lengths long = 0.72 to 0.73, the ship is 3 wave

lengths long

,

AP

19

16

17

Fig. 52. J

16

Wave

15

14

13

Profiles for

la

TMB

II

For r,

(3)

9

10

Series

57,

8

=

7

0.88, the ship

6

5

4

is

2 wave lengths long

3

2

Model 4202W-1, at Various Speeds

I

FP

lIYDROnVNAMHs

218 (4) Ft>r

length

=

7',

l.l.'>.

sliip

till'

combatant yachts at

By

vessels full

the

resistance

and

about

is

some

loiiR. Tliis is tlic ciusc for

sailing

or designed speed.

same reasoning, the humps curves occur when

the

in

ship

tlic

Icnglli

corresponds approximately to half-lengths of the transverse (5)

wave system. Again roughly:

=

0.1)7,

the ship

is

3J

wave lengths

For T,

=

0.80, the ship

is

L'l

wave lengths

wave

and procedures

rules

along a

profile

shij) of

for

''2.7

predicting

normal form,

in

the usual range of speeds, are described in Sec. 00.28, using the .VHCsiiij) of Part 4 as the example. 52.7 Typical Lines-of-Flow Diagrams for Ship Models. Thanks to the work of D. W. Taylor and his as,sociates at the Experimental Model Basin at Washington in the period 1900-1910

mmiber

These are body plans

of lines-of-flow diagrams.

upon which the projected

long (6)

the

Src.

there appears in the technical literature a

7',

For

SHIP DllSIC.N

Cicneral

\v:i\c

1

large, fast

most tugs ami

for

IN

flowline positions are

long (7)

For T, =

D.'.i'.i

tu

IdJ,

il,(.

ship

is

\\

\v;iv('

length long (8)

For T,

=

1.5 to 1.7, the ship is

about

length long. For most destroyers at

nmning at a T, of about 2.00, the ship what less than half a wave length long. The values given

wave

\

full is

speed,

some-

in the foregoing are drrucii

from preliminary examination of published :uul available wave profiles, without a careful study of the effects of bow-wave crest lag. For this

wave profile shown broadside, for the model or ship length, is much more ii.seful and valuable than a wave profile shown in its projected position on a body plan. When there is a parallel watcrline portion of considerable length, the po.sitions of the crests and troughs abreast it are not readily apparent in an end purpose, a full

view of the

Fig.

52.Ka

Lines of Flow for Old Cruiseu

Wove

Model

Profiles-

hull.

and 52.J show the wave profiles for quotients on each of two models of TMB Series 57, having block coefficients Cfl of O.GO and 0.70, respectively. The body plans and other data for the.se models are given by F. H. Todd and F. X. Forest [SNAME, Figs. 52.1

five

speed-length

1951, pp. 042-G9I].

TABLE Thn

55. Dolt Via. 52.1vb

.'j2.a— Sini'

»hip lonRths and Hpocd.s, except

fr>r

Dwk

No.

Name

or type of vessel

.'J2.Ku

Sun Francixco

(old)

J^WL

,

ft

:iio.o

52.Kb

liaUimore (old)

;i27.5

52. Kc

Penaacola

52.L

Great Lakes ore steamer

570.0 540.0 460.0 04.0 J

62.

M

Collier

.'i2..Nu

Sotoyomo,

.'i2.Nb

Siiloyomo, hIow sfiecd

.VJ.O

Sliidlou'-drafl river Hti-iiiner

62.1'

KiM.-ciiil

full

typo

speed

willi

bulges

more (Old)

Model

fou Mudei.s with Observed Lines ok Flow

the Pensacola, are from D. \V. Taylor

[SNAME,

1907,

planH carrying the lines of flow.

Fig.

I

Lines OK FiAJw Fou Old Cruiser

91. 01

257.0 490.25

peed, kt

j).

\\,

us are

ttie

body

FLOW PATIERNS AROUND

Sec. 52.7

Tq= 1.345

SHIPS

249

HYDRODYNAMICS

250

IN SHIP DESIGN

Sec. 52.8

duction, for ready reference, of one such diagram

previously pubhshed.

The Swedish State Shipbuilding Experimental Tank makes use of the wet-paint technique for depicting flowlines around selected portions of ship models

[SSPA Rep.

Shallow-Draft

Tq=l.ie Fig. 52.0

Lines of

River Steamer

Flow fob Shallow-Draft Steamer

For the

32, 1954, Figs. 18

and

local areas covered

they are excellent. A. F. Lindblad includes photographs of flowlines around the bulb bow of a model made mth this technique [SSPA, Rep. 8, 19, pp. 26-27].

and 17, pp. 18-19]. Published with a model body plan upon which a number

1948, Figs. 15

them

is

of flowlines are indicated.

In 1947 R. Brard and J. Bleuzen published photographs of models in which flowlines were determined during steering tests [ATM A, 1947, Figs. 10, 11, 12, and 13, between pp. 332-335; Transl. 248]. H. F. Nordstrom published similar photographs of the flow near the bowpropeller position on an icebreaker model [SSPA, Rep. 20, 1952].

TMB

Tq

=0.855

Speciol Ship Type

Fig. 52. P

Lines of Flow for Ship with Under-

water Bulges

drawn.

A

considerable

represented

[SNAME,

number

of ship types are

1907, pp. 1-12, Plates 1-7].

Figs. 52.K through 52. Q are adapted from the diagrams in the reference cited, with the proper r, values shown on each. Table 52.a gives the information presently available on the ships represented by seven models of this group. In 1910 Taylor published the hnes-of-flow diagrams for two model series, one apparently for a battleship and the other for a light cruiser of that day, in which the maximum-section coefficient Cx was varied from 0.70 through 1.10 for each group of five [S and P, 1943, Figs. 26-35, p. 25]. Fig. 52. Q is adapted from the Taylor reference by adding the principal hull parameters

and

coefficients, as well as the speed-length ratios. Despite the major differences in form between

the two parent models the flow patterns are remarkably similar. Since 1910 a great many flow tests have been run on ship models at the Experimental Model Basin and the David Taylor Model Basin but unfortunately only a few of the lines-of-flow diagrams have been published in unclassified EMB and TMB reports and the technical hterature. Figs. 52.R and 52. S are copied from two unpublished diagrams. Fig. 52.T is a repro-

In his book "Marine Propulsion Devices," pubhshed at Leningrad and Moscow in 1949, V. M. Lavrent'ev shows body plans on pages 65 and 66 with fines of flow drawn over them. A multitude of photographs have hkewise been made of EMB and TMB models with the flow traces marked on them, but only a few are available for study by marine architects [SNAME, 1947, Fig. 9 on p. 104; Figs. 25, 26, and 27 on pp. 116-117]. Lines-of-flow traces for a few selected locations appear on SNAME RD sheets 114 and 115. It is hoped that, in the future, these can be shown on all such sheets when the

data are available. Fig.

52.U gives a rather comprehensive flow

pattern for the transom-stern

worked out

Chap.

in

ABC

66. Figs. 78.

C and

ship 78.

huU

D are

photographs of the model showing the nature

some of the flow traces. Model Surface-Flow Diagrams. The method of analyzing photographs and diagrams of flow fines and flow patterns taken directly on the surface of a model depends upon the technique employed in tracing the flow. and positions 52.8

of

Analysis of

Wet-paint streaks are usually short but

if

the

paint fines are closely spaced in a fore-and-aft direction they

may

be combined

fike the short

vectors that form path fines, described in Sec. 1.4 of

Volume

I.

The

traces left

ejected from orifices in the hull are

by chemicals

much

longer,

sometimes half the length of the model. They may be assumed to give a better representation

FLOW PATTERNS AROUND

Sec. 52.S

SHIPS

C0QIQI_\3

"

55.8 for

oil

Models Group

of this

/qoiol)^"

1674- for

oil

Models

of this

Group

Cx

Cx 1^0.894.

=

90

Tc[? I.34E,

0.90

Fn= 0.396 for this Group

Fn- 0.266 for this

Group

Cx -^

Fig. 52.Q

=

-

=

1-00

2.9^ and Cp = 0.56 for all Ten Models

Vawation of Flow Pattern with Maximum-Section Coefficient Cx

HYDRODYNAMICS

252

IN SHIP DESIGN linos of flow are

Sec. 52.S

reproduced on pages 6 and 7 of

this report.

Several flowhnes are hkely to come together as they approach the surface, usually between the after quarterpoint and the stern. A case in point that of the flow along hues E arfd F on TMB model 3898, representing the twin-skeg Manhattan is

design,

depicted in Fig. 52.T

[SNAME,

1947,

and Fig. 26 on p. 117]. Here, at Sta. 18.5, the two lines of flow not only join but appear to be about ready to project themselves up through the water surface, just above the junction point. Apparently the two large-size stream tubes along E and F change shape rapidly between Stas. 16, 17, and 18.5, so that opposite the latter point they are both very thin in a girth wise direction and very thick in a direction normal to the hull. The junction point is apparFig. 24 on p. 116

ently close to the separation point at that girth-

wise position, so that abaft Sta. 18.5 the stream

tubes in question have gone

The

following

is

Report 535, referenced "A

off

and

left

the hull.

copied from page 7 of

TMB

earlier in the section:

careful study of the streamlines

on the model

will

afford a fund of information not only as to the direction of

but concerning the nature of the flow. A long, narrow high velocity; a short, wide and smeary line indicates low velocity; a sudden breaking off of the line separation from the surface of the model; and indicates an irregular line or an area with diagonal tails indicates eddying along the model."

flow,

Fig. 52.R

Lines op

Flow for Run op Model op

line indicates

S. S. Clairton

of the surface flow.

The

details of the chemical

methods, some representative

results,

and

in-

The orthodox

structions for interpreting the traces are described

by

May

Hutchinson in

F.

J.

1944, entitled

TMB

Report 535, of

"The Delineation

of Surface

very mdirectly the dii-ection taken by the water aft under a ship model, especially

Wave Profiles at the David when flowing Model Basin." Two body plans showing if the bottom

Lines of Flow and

Taylor TMB

Model 3594

Fig. 52.S

5NAME RD Sheet 98

Lines op

\-0858

F„-0255

Flow for TMB Model

lines-of-flow diagrams, such as

those in Figs. 52.R, 52.T, and 52.U, show only

3594,

is flat.

Bow-Wqve Crest

Fig. 52.

at 5ta. 0.9. -o-

V

is

a fish-eye view,

0.045 L Abotl FP

Representing Minelayer U.

S. S. Terror

FLOW PATTERNS AROUND

Sec. 52.8

Lines of Flow of

Fig. 52.T

TMB

Model

389S,

253

Representing Twin-Skbg Manhattan

'^b c

greatly contracted longitudinally, of the flowlines

SHIPS

tmb

Tronsom-stern Design

Model

4505

Tc^-ogoa

^

under TMB model 3898, representing the twinskeg Manhattan design developed by the U. S. Maritime Commission [SNAME, 1947, pp. 112125].

The

projection

is

made upward on

^^'

the plane

of the designed waterline; all flowlines are

shown

on the same side of the centerplane. Three photographs are available showing the original lines of flow

25 on

The

on the model

[SNAME,

1947, Fig.

116 and Figs. 26 and 27 on p. 118]. transverse spreading of the flow shown by

p.

~^Desi(^ned

on Plane

Fig. 52.U

Parallel

Flow Around Model of

ABC

Ship

Projected Upward

Waterline

to Boseplane '

I

I

Lines of

Transom-Stern

i

I

Lettered Lines of Flow

Are Projected Upward

in

Similar

Fashion

Contracted Lonqitudinallu

7 Fig. 52.V

The

transverse scale here

is

Fish-Eye View of Lines of Flow Under Bottom of

TMB

6

Model

4,57 Times

5

4

3898

4.57 times the longitudinal scale, to permit showing the flowlines to better advantage

HYDRODYNAMICS

254

and C, and by the forward portions of traces L and M, is typical of the flow under models in general. It is possible that it indicates a traces A, B,

down in the next-to-the-huU water layers because of the thickening of the boundary layer under the hull. The increase in x-distance from the stem is one cause of thickening; another is the slowing

increase in width of the flat portion, with its

small (or zero) transverse curvature. 52.9 Observation and Interpretation of Off-

IN SHIP DESIGN

Sec. 52.9

Tufts have the disadvantage of shortness, like the streaks from a transverse line of wet paint. However, there is no Umit to the number of them that can be used over the surface of a ship model.

They

are extremely valuable as nature-of-flow

indicators,

streaming

straight

out

in

a

fast,

and waving gently or lazily in a slow flow that is irregular and uncertain. Off-the-surface vane and rigid-flag indicators regular (or uniform) flow

require

little in

the

way

of interpretation since

the-Surface Flow Data on Models. It is customary in circulating-water channels and wind

they reveal velocity direction only. This is usually sufficient when they are employed to determine a

tunnels to observe the nature and direction of the body or ship surface by watching the

single

behavior of short strings or tufts of yarn. These may be attached not only to the surface directly but to slender pins projecting any required

ends of long, thin tubes, moved to any desired position in the water around the model. Figs. 46.E and 46.F show ink trails along a model. To permit subsequent study at leisure, after completion of the test, flash photographs are made of the tuft positions, like those reproduced in Fig. 52.W, as well as in Figs. 36.F, 36.G, 46.D, 46.E, 46.F, 78.E, and 78.F. Similar still photographs have been made at the Experimental

flow over a

distance from the surface, indicated in Fig. 52. W.

may be used to represent normal distances from the hull. Indeed, the tufts may be attached to the ends of long, thin wands, moved about by hand to the desired Different tuft colors

different

positions.

Fig.

52.W

Une

of flow

such as a bilge-keel trace. may be ejected from the

Colored inks and dyes

Fish-Eye View of Self-Propelied Model in Circulating- Water Channel, Showing Tufts Carried BY Pins and Tufts on Model Surface

FLOW PATTERNS AROUND

Sec. 52.11

Towing Tank, Stevens and published in: (a)

(b)

W.

Institute of Technology,

"Underwater Photographs of Flow Patterns," ETT, Stevens, Note 75, May 1948. This includes some observations made from underneath a model during a turn. Ashton, R., "An Underwater-Photographic Method for Determining Flow Lines of Ship Models," ETT Tech. Memo 101, Feb 1949. Sutherland,

H.,

tests

SHIPS

ABC

on the

(c)

Baier, L. A., "Trouble-Shooting the

(d)

Mar. Eng'g., Sep 1955, p. 54 Baier, L. A., and Ormondroyd,

(e)

Martha E. Allen,"

the forebody, show that the tentative instructions

and study. made by H. C. Sadler, W. Hovgaard, D. W. Taylor, and others, in the discussion and closure of D. W. of Sec. 66.28 require further attention

In this connection the comments

M.

S., and Weaver, A. H., Jr., "Model Flow Around Stern of U. S. Navy Fleet Tug ATF-16S, TMB model 3531," TMB Rep. 810, issued in Jan 1952. This report contains 10 photographs, showing both tuft positions and ink trails.

Harper,

Studies

If

the

flow

contains

eddies,

vortexes,

and

counter-currents, or otherwise varies with time,

motion-picture photographs are taken. However, neither type of photographic record can compare in vividness tion.

and

reality with direct visual observa-

Fortunately, this can include study and

interpretation also

by continuing any given

set

"An Experimental

Investigation of

Stream Lines Around Ship Models" [SNAME, 1907, pp. 1-12], will be found most helpful. 52.11 Prediction of the Ship Flow Pattern at

The

the Bilges.

portion of the hull flow pattern

most immediate and practical

of the

that in

J., "Suppression of Ship Vibration by Flow Control," Proc. Third Midwestern Conf. on Fluid Mech., Univ. of Minn., Jun 1953, pp. 397-411

The

rather large variations between prediction and observations revealed in Fig. 66. R, especially in

Taylor's paper

Other published flow-test photographs showing tufts attached to the model surface and ink or dye injected into the water through small tubes are found in:

255 ship model were made.

way

in Sec. 17.2, in Chap. 33, 59.12.

interest is

of the propulsion devices, discussed

The next

and in

in importance

is

Sees. 52.16

that in

and

way

of

the bilge or roll-resisting keels, especially if these keels extend beyond any parallel middlebody

may be worked into the hull. In some quarters it is considered sufficiently accurate to place the bilge-keel trace, as projected

that

on the body plan, along a

line bisecting the angle

at the bilge between the side and the bottom at the section of maximum area. This neglects the effect of

B/H

quarters

it is

ratio and similar factors. In other assumed that the flow must certainly follow the bilge diagonal, at least close enough for all practical purposes. Both rules of thumb ignore

the effect of the surface-wave pattern as far

down

of test conditions in the circulating-water channel

as the bilge.

may be desired, or until the observer understands what is going on. References to the studies of various experimenters, relating to the off-the-surface flow on models, are Usted in Sec. 52.12 and in Sec. 22.6 on page 311 of Volume I. 52.10 Estimating the Ship Flow Pattern on the

low T, values, the surfacesmall but for fast ships, with medium or high T^ values, the prediction must be based on knowledge of the flow to be expected in this region. There is ample evidence

for as long as

Body

Plan.

It will

some day be considered

as

important, and as necessary, to estimate the flow pattern around a newly shaped hull, in advance of

model

tests, as it is to predict its resistance or

the effective (and shaft) power required to drive

it.

Based upon the physical aspects of flow around a ship form, described in Chap. 4 of Volume I, with emphasis on the flow around surface-ship forms in Sees. 4.10 and 4.11, an attempt is made in Sec. 66.28 to formulate a few preliminary instructions for guidance in predicting the flowline and wave-profile positions. Following these instnictions,

a flow pattern

stern

ABC

in fact, it

is

sketched for the transom-

hull designed in Chaps. 66

was drawn out

and

67;

in ink before the flow

For slow

wave

effect

ships, with

probably

is

that for ships operating at T^ values in excess of

> 0.253 or 0.268, the crests and troughs in the surface-wave system are reproduced to a lesser degree at the bilge-keel level. The bilge0.85 or 0.90, F„

shown by V. L. Russo and E. K. Sullivan [SNAME, 1953, Fig. 18, p. 127], determined by both the chemical method and the vane or flag method, are excellent examples of this situation. Unfortunately, the keel traces of the Mariner class,

wave

profile (Fig. 12 of the reference) does not appear on the same drawing as the bilge-keel traces, so as to make the surface-wave effect

readily apparent.

For ships with a considerable extent

of parallel

side at the waterhne, the surface-wave profile

is

not outhned well enough on a body plan to permit predicting its effect on a bilge-keel trace. The

HYDRODYNAMICS

256

wave

profile in side elevation should

be

IN SHIP DESIGN

prediction of flow in

way

of the bilge keels

(c)

should cover the light-load or ballast condition as well as that for the designed load, using the appropriate speed-length quotients in each case.

Almost certainly the traces wiU be

different,

unless the speeds are low, although the differ-

ences

may be

small.

A decision is

called for in the

design stage to determine which load and speed condition is to be favored in positioning the bUge keels on the ship.

52.12 Probable Flow at a Distance From the Ship Sixrface. At normal or lateral distances from the 3-dunl ship form greater than those

involved in placing the roll-resisting keels, available data for predicting flow conditions become rather rare.

A few

sources giving data on tests of

ship models, which

may

or

may

TMB

In the present state of the art, the prediction of conditions from available reference data only, for an important part of a ship or an important region near the ship, is uncertain at the best. flow

Rehance upon flow

concerned,

Laute, W., "Untersuchungen iiber Druck- und Stromungsverlauf an einem Schiffsmodell (Investigations of Pressure and Flow on a Ship Model),"

STG,

TMB (b)

1933, Vol. 34, pp. 402-460; English version in Transl. 53, Mar 1939. See also Figs. 22.D

and 22.E in Sec. 22.8 of Volume I. Lamble, J. H., "An Experimental Examination of the

Numbers at Sides Indicate ftisitions Wave Profiles and Flow Traces at Those Stotions

a model

is

definitely

Estimating the Change in Flow Pattern Predicting the

52.13

for Light or Ballast Conditions.

flow pattern

when the ballast

—and wave

vessel

is

profile

—for a ship design

assumed to be

hght or

in a

condition requires modifications of the

rules in Sec. 66.28. In the first place, the forefoot

usually well out of water, so that whether

away or is occupied by a lines are by no means vertical cut

are mentioned: (a)

mth

tests

indicated.

is is

Model

number VM298.H11.

not cover the

distances with which a ship designer

Ship's

Placed in a Turbulent Stream," IN A, 1934, pp. 136-143 and Pis. XV, XVI Hamilton, W. S., "The Velocity Pattern Around a Ship Model Fixed in Moving Water," Doctorate Ubrary, Diss., IIHR, Deo 1943. Available in

this purpose.

A

Sec. 52.12

Around a

Distribution of Velocity

used for

it is

bulb, the section in that region. In

by

the second place, the free surface, disturbed

Velox waves, is much closer to the bottom of the ship than at normal draft. The surface-wave pattern may be expected, therefore, to have a considerable influence on the flow pattern, at least as far down as the flat floor under the ship.

Maritime Commission Design

U. S.

of

T2-SE-AI Model 3867

TMB

FULL-LOAD CONDITION Tq = 0.684

Trim, Zero

5 l.i.i

Fig. 52.Xa

Lines of Flow in Full-Load Condition foe U.

S.

I

I

I

I

10 I

I

I

I

1

20

15 I

Maritime Commission Design TS-SE-Al

I

FLOW PATTERNS AROUND

Sec. 52.14

SHIPS

Numbers ot Sides Indicate Positions of Wove Profiles and Flow Traces at

257 U.S.

Maritime Commission Desii

T2-5E-AI

TMB

Model 3867 BALLAST CONDITION

Those Stations

Trim, IZft

Fig. 52. Xb

Lines of Flow in Ballast Condition for U.

With a broad, blunt bulb as a waterline beginbow-wave crest may be

ning, at light draft, the

surprisingly high, although the upper portion of

the crest of a

bow

is

more apparent than

real, in

the form

S.

b\j

theStern

Maritime Commission Design T2-SE-A1

on the basis of empirical data, the fund of informmust be greatly expanded. It now comprises the references listed ation presently available

in Sec. 52.12 plus the following:

feather.

Whether the sections at the forward end of the entrance are sharply flared outward or are of the bulb type, the Bowlines will undoubtedly curve and pass under the ship very close abaft the stem. This means, for one thing, that air entrained in

(1)

Eggert,

E.

SNAME, (2)

Eggert,

E.

ments," (3)

F.,

"Form Resistance Experiments,"

1935, pp. 139-150 F.,

"Further

SNAME,

Form

Resistance Experi-

1939, pp. 303-330

Yokota, S., Yamamoto, T., Shigemitsu, Togino, S. see Sec. 52.3 for the complete ;

the bow-wave crest may be expected to flow along under the bottom at transverse distances rather close to the centerhne.

52.Xa and 52.Xb indicate the differences in wave profile and flow pattern found on two model tests of a tanker. In the light condition the

(4)

than half the full-load displacement, and the trim by the stern is very large. 52.14

is less

Predicting Velocity and Pressure Dis-

tribution Aroiuid Ship Forms.

If

the magnitudes,

and distribution of velocity and pressure by the methods discussed in Chap. 50, this prediction will be for a hull form which has the shape of the physical ship plus the displacement thickness of the boundary layer, as

Vol. 55; English translation available in Research

(5)

Y.,

Fig. 52.Y is a reproduction of one of the afterbody plans of EMB model 3383 from (2) preceding

[SNAME,

are to be calculated

isobars for a multitude of

nearly as the latter can be determined. If the and pressure factors are to be predicted

of Ships, U. S.

"Experimental Investigations on the Resistance of Long Planks and Ships," See. Nav. Arch., Japan, 1934.

Hiraga,

direction,

velocity

and

Izubuchi, T., full-scale experiments on the Japanese destroyer Yudachi, Zosen Kiokai, December 1934,

and Development Division, Bureau Navy Department

Figs.

displacement

A.,

listing

1939, Fig. 30 on p. 314]. It carries the

Ap

values, as indicated

in the diagram.

A comprehensive measurement of pressure around the surface of a ship or model is a prodigious undertaking, yet anything less than comprehensive is not worth the effort, from the

HYDRODYNAMICS

258

IN SHIP DESIGN

Sec. 52.15

the flow directions are desired

is

always of the

and bulk, must be taken into

thin-plate variety. Its position, shape, as affecting the flow,

all

account.

52.16

Estimated Flow at Propulsion-Device

Extended discussion

Positions.

of the flow to the

propulsion-device positions, amounting almost to (it appears in Sec. 17.2, in Chap. 33, and in Sees. 59.12 and 60.7), is considered justified in view of the importance of this feature and the

duplication

insufficient

attention

quarters in the past.

it

many

has received in

However, the extensive

model-basin instrumentation

now available

(1955)

inadequate to give the ship and the propulsion-device designers all the advance informais still

tion they should

have

The huU-surface

in the design stage.

traces of the flow just

of a propeller position, particularly those

ahead on a

centerline skeg in front of a single screw, are

usually good indicators of the type of inflow into

the wheel positions close to the centerplane. For

Pressure Distribution on Afterbody op Model 3383 at a Speed of 3.8 kt, T, = 0.844

Fig. 52.Y

EMB

The numerals on the

isobars indicate differential pressures

same mass density which the model was towed

in inches of water of the

as that in

standpoint either of hydrodynamic research or of ship design.

52.15

Use

of

Flow Diagrams

The comments

Appendages.

for Positioning

of Sec. 52.12 apply

generally to the proper positioning of appendages

such as bossings, shaft struts, small skegs, and rudders, as well as to the outer portions of rollresisting keels.

Special model-basin techniques are available to

determine

the

proper strut-section angles for

shaft struts. Since the variation from straight-

ahead positioning of these parts seldom exceeds 7 or 8 deg, and almost never is greater than 10 deg, a prediction without model-test confirmation would have to be extremely precise, relative to

example, in Fig. 52. R it appears that the flow just ahead of the single propeller, at least into the 11 o'clock to

1

o'clock

and 5

o'clock to 7 o'clock

may

be expected to have only a slight upward component of velocity. For each offset propeller position of Fig. 52.T, it is expected that the flow outboard of the skeg ahead will have a small upward component but that inboard of the skeg it will have a large one. Nevertheless, in the absence of any proved general rules for interpreting them, it can not be said that the surface traces are completely reliable indicators in this respect. Before an acceptable procedure for estimating the flow at propdev positions can be formulated, it will be necessary to make, and to analyze, companion off-the-surface flow traces such as those described and illustrated in Sec. 52.9 and 3-diml wakesurvey diagrams of the type diagrammed in Sec. 60.6. Until that time the surest and most positions,

reliable prediction

method

is

actually to observe

present (1955) standards.

the flow in the vicinity of the propulsion device (s)

When rudders (and diving planes) are of the spade or horn-supported type they are necessarily

on a model of the vessel in a circulating-water channel. If the propdev characteristics are approximately known, a stock model of the device can be added to the ship model and observations made under thrust-producing conditions. In most cases these tests can be made and this study completed at a sufficiently early stage in the design to permit changing the hull or appendages (or both), to correct or to improve the flow.

rather thick to achieve strength and rigidity.

Extended observation of flow around model appendages in the circulating-water channel indicates that their presence affects the flow to

considerable distances on either side. trail in Fig.

not

46.E shows

adequate,

The ink

this feature clearly. It is

therefore,

when making

predictions, to suppose that the object for

flow

which

A

situation

somewhat out

of the ordinary is

FLOW PATTERNS AROUND

Sec. 52.1S

on

encountered

not-too-large

certain

vessels

SHIPS

259

To

determine a systematic wake-fraction variation with radius if one exists, and to embody (3)

where a relatively high power is delivered to a single screw propeller on a vessel having a small

it,

displacement-length

propeller (or selection of such a propeller from

quotient

or

fatness

ratio

V/{0.10LY and a large keel drag. Examples are and bay passenger steamers, tugs, trawlers, and whale catchers. Because of the projection of the propeller below what might be called the main body of the hull it could be expected that the flow would have only a small degree of nonaxiality. However, a considerable dechvity in the shaft, downward and aft, is sometimes necessary to accommodate the machinery position inside river

desired, in the design of a

if

wake-adapted

stock) (4)

To

an early stage

ascertain, at

in the design,

the liabiUty and the magnitude of objectionable variations in thrust and torque, per blade

per wheel, for

all

This latter feature

tion.

and

angular positions in one revoluis

discussed further in

Sec. 59.17. It is

assumed, in the foregoing, that the advance-

velocity vectors for the proposed propeller-disc

the hull.

and are determined by the method described and illustrated in Sees. 11.6 and 11.7 and Figs. ll.E and ll.F of Volume I. This method is, by the instrumentation such as unaffected by the presence of the hull, lying that currently (1955) in use at the David Taylor mostly at an upper level. The present trend (in Model Basin [Janes, C. E., "Instruments and the 1950's) of eliminating the rudder shoe and Methods for Measuring the Flow of Water cutting away the aftfoot on vessels of this typQ, Around Ships and Models," TMB Rep. 487, means that the flow to the lower blades is almost Mar 1948], somewhat artificial. For example, the entirely free of hull influence. Although uniform additional velocity induced by the action of the and regular, it may be expected to have little or propeller when it exerts thrust is not represented, no positive wake velocity unless the vessel on single-screw ships, much of the water moving toward the blades of the propeller, in their lower positions, will be It is to be expected that,

"pulls" a large stern-wave crest above

nor

tabulated,

it is still

necessary to analyze graphic,

and other records from flow-indicating

devices at screw-propeller positions to determine

the principal characteristics of the flow. Simply

making a flow record does not nature of the flow

whether the acceptable or not. In fact,

is

observed

flow

at

a

screw-propeller

position,

suitable instrumentation on

a model, before the model

by

upon the water flowing into the propeller However, a wake determination of this kind is most revealing, and many features of the propeller action can be predicted from a careful

jet acting

position.

study of

it.

Instructions for conducting such a

study, and for determining quantitative values

from

are found in Sees. 60.6, 60.7,

it,

Flow Abaft a Screw

52.18

and

60.8.

Propeller.

The

tell

there are at least four reasons for analyzing the

when determined by

the straightening effect of the propeller

is

it.

52.17 Analysis of the Observed Flow at a Screw-Propeller Position. Although not a part of the estimating or predicting procedure, strictly speaking,

position are 3-diml in nature

is fitted

with or driven

model propeller (s). The record in this case is assumed to be a 3-diml wake-survey diagram similar to Figs. 11. F and 60.D:

water in the outflow jet of a screw propeller producing thrust is known to be contracting at the point where it leaves the propeller disc, illustrated by Fig. 16.E in Sec. 16.6 of Volume I. It is known to be increasing in velocity at that point,

its

and there are rotational or tangential components in it, additional to the component of induced velocity. The brief

velocity axial

discussion of Sec. 17.17 reveals that the screw-

To

determine, by visual inspection, whether there are any longitudinal eddies passing through

propeller outflow

the disc, whether there are obvious differences

jet for

(1)

two or more points near each whether there are obvious large

in flow direction at

and

other,

differences

components (2)

To

wake

in

the

longitudinal

of flow for

or

transverse

two or more such points

estimate the probable magnitude of the

fraction for a screw propeller occupjdng a

disc region of given size (diameter)

and position

unusual among submerged maintains its identity as a propeller diameters astern of the is

liquid jets in that

many

it

disc position.

The first quantitative observations on the nature of the actual flow abaft a screw propeller, in and around an outflow jet, appear to have been made in about 1865 by Arthur Rigg of Chester, England, in connection with his develop-

ment

of

the

first

contra-rudder

[Inst.

Engrs.

HYDRODYNAMICS

260

and Scot. Shipbldrs. Assoc,

Scot,

Vol. IX, pp. 52-64]. of

By

1865-1866,

suspending over the stern

a small sci'ew-propelled vessel a

flat

.ocu5 of

Centers of Lonqfd'l Vortex

m

Propeller

?^^

°

'^"^f'

Sec. 52.18

For

stations.

three

conditions

(1)

The

vessel propelling itself only, at 144 rpm;

35 deg, 2.1 psi (2)

Towdng a

45 deg, (3)

large "flat," with cargo, at 160 rpm;

1.0 psi

WhUe moored

to a post at 136 rpm; 72.5 deg,

0.4 psi.

Other published data on the distinctive features marine propellers have so far not been discovered. Some unpublished data from the tests of two model propellers at the of the outflow jets of

0.61

D A baft

I

Fore-$n d-Aft Position of

\

^"'^ ^°^'^'°"

Disc Position

I

Lonqitudinal

Center of

I

°^ Propelle-

of Propeller

Propeller

|

Equivalent to

0.28 V

H

True Velocity Vector Lies at

an .

-I

"" Fig. 52. Za

0.28 l.00-(-Q29)

Diagrams Indicating Components op Net Augmented Axial and Rotational Velocities in Outflow Jet op Port Propeller on TMB Model 3613'

Transverse Vector Component;

are

Drawn

of V^

to Twice the Scale

and the Wake Vectors

Wake Measurements Available on

Starboard Side Only

Fig. 52.Zb

of

operation he recorded the following data:

swinging

vane with an indicator he measured "the aiigle of the water driven off from the screw" with reference to the centerplane. The vane was raised and lowered to cover a range of positions from 0.285R to 0.8R below the axis. The data given below are for a propeller radius of approximately 0.8R. By turning the vane in a direction normal to the current at its axis and measuring the moment on the vane Rigg was also able to obtain a rough idea of the actual velocity at each of the

Estimated

IN SHIP DESIGN measuring

Diagrams Indicating Axial and Rotational Components op Velocity in the Outflow Jet op EMB Propeller 857, Running in Open Water

Sec. 52.19

FLOW PATIERNS AROUND

David Taylor Model Basin,

partially analyzed,

are presented in Figs. 52.Za and 52.Zb.

marizing these tests

Sum-

briefly:

I. A model of a destroyer, TMB 3613, was towed and a 3-diml wake survey was made at the propeller-disc position. It was then self-propelled by its own model propellers, TMB numbers 2170 and 2171. While self-propelled, at a simulated

ship

speed of 28.6

three additional

kt,

wake

surveys were made, at positions corresponding to 0.607, 2.075, and 3.543 propeller diameters abaft

The net axial and tangential components of velocity (by vectorial subtraction), due to the action of the propeller, as averaged the disc position.

by vectors in the several diagrams of Fig. 52.Za. The thrust-load coefficient Ctl for the conditions given was 0.907. for several radii, are indicated

Other pertinent data applying to this test are added to the diagram. II. A model propeller, EMB 857, of 9 inches diameter, was mounted at the end of the long shaft ahead of the propeller boat [Bu C and R Bulletin 7, 1933, Fig. 5 on p. 24] and the assembly run at a speed of advance of 3.26 kt. Wake surveys were made at 1, 2, and 3 propeller diamabaft

eters

the

disc

position.

The

available

records do not indicate the thrust-load coefficient

was working but it was apparently very high. The axial and tangential components of velocity, due to the action of the at which the propeller

for

several

radii,

are

indicated

by

vectors in the three diagrams of Fig. 52. Zb. III.

A

series

model,

EMB

3424,

was towed and

a wake survey was made at the propeller-disc was then self-propelled by its own

position. It propeller,

EMB

model speed

1884. While self-propelled, at a

of 3.00 kt,

four additional

wake

surveys were made, at positions corresponding

and 24 propeller diameters abaft the disc. These data are available at the David Taylor Model Basin but have not been reproduced to

1, 5,

15,

261

by noting the upward curve in the swirl core or hub vortex trailing a screw propeller on a destroyer model in the circulating-water channel. It is difficult, because of the lack of observations

upper portions

in the

of the propeller outflow jet

abaft the stern of the destroyer model, to estimate the limits and shape of the cone of diffusion between the outflow jet and the surrounding water. With a net augmented axial velocity in the outflow jet which is roughly 20 to 25 per cent greater than the ship speed, the cone of diffusion is

rather thick. Its inner surface, as well as can be

determined,

is

of such slope that the jet core will

persist to a distance of 5 or 6 diameters abaft

the disc.

For the model mounted on the propeller boat, the net augmented axial velocity in the outflow

about 55 per cent greater than the ship

jet is

The cone

speed.

of diffusion

is

indicate that the jet will preserve of its identity to a distance of

enough to some measure

perhaps 15 diam-

eters abaft the disc position.

For

EMB model propeller

1884 on

EMB model

3424, for which no graphic data are given, there are definite signs of augmented axial velocity and rotational velocity in the outflow jet at 15 pro-

There are

peller diameters astern of the disc.

traces of the rotational velocity at 24 diameters astern. 52. IQ is

Persistence of

often useful to

wake

Wake Behind

a Ship.

It

the characteristics of the

the path of a body or ship, mentioned

left in

in Sec.

know

11.11,

even though the ship propulsion

device (s), fike those of the sailboat or the flying boat,

may be entirely

may

involve only the

clear of the water.

mean

The wake

residual velocity

along the ship track, over a section taken across the body or ship path. It

may

involve effects of

another order such as variations from the mean velocity, the scale and intensity of the residual turbulence, the presence of entrained

other characteristics of interest.

here.

relatively thin,

with an inner-surface slope small

propeller in producing thrust in open water, as

averaged

SHIPS

air,

As a

or

some

rule,

the

transverse surface waves of the Velox system are

Abaft the destroyer model, it is obvious that the longitudinal centerline of the outflow jet does not lie along an extension to the propeller shaft axis but rises rather abruptly. This rise begins at

the disc position, increases rapidly, and then coincides more or less with the rise in the water which has flowed under the stern, generally parallel to the

buttock

fines

on the model. This change in vertical

position with distance abaft the disc

is

confirmed

by spreading transversely and by

dissipated,

internal viscous damping, long before the distur-

bances within the water disappear. Quantitative data on the persistence of wake, applying to the mean velocity only, are almost

Perhaps the most extensive and from model-testing techniques, but the vafidity of stepping these data up nonexistent. refiable

are

to ship size

derived

is still

uncertain. It

is

known

that the

HYDRODYNAMICS

262

wake from a

vertical turbulence-stimulating strut

having a diameter of say 0.01 the model beam and a submergence equal to the model draft, when towed a short distance ahead of a small model, causes a measurable change in its resistance. It is often necessary to wait from 10 to 20 minutes between runs in the basin, when towing a large, heavy model, to insure that the residual currents left in its wake have diminished to the order of 0.01 kit or less. On the basis of a 20-ft model running at 4 kt, this means that if the model kept on going it would be 200 lengths away from the finishing point of the run in the course of 10 min. For a 500-ft ship traveling at 20 kt in a channel of

comparable relative

size, this is

the equivalent of

one reason why a ship has to make a long approach run before entering a measured mile [SNAME "Standardization Trials Code," 1949, p. 7; van Lammeren, over 3.3 nautical miles. It

W.

P. A.,

RPSS,

is

1948, p. 352] to insure that

does not meet, as a counter-current,

its

IN SHIP DESIGN

1855), the literature which has accumulated on

the subject since that time

from the preceding run. Model-basin experience indicates that the presence of the walls and bottom, not too far from the model track, damps out the residual currents due to towing and self-propelling. Since the basin depth is of the order of 20 times the model draft and its width the order of 20 times the beam, the corresponding dimensions for a ship like the ABC design of Part 4 would be 520 hardly a restricted ft depth and 1,460 ft width

available data, reliable

elusive,

the 52.20

how

disturbance

toAving-vessel

little

is

on a towed

on Wake. Considering was known or understood about wake

conditions abaft a ship a century ago

(about

and

logical

conditions

problem

beginning

will

at

60.8.

It

appears

have to be studied its

fundamentals.

In view of the inclusion in Harvald's study of

and others which have appeared (1)

Dahlmann, W., Hoppe, H., and

since 1950:

Schafer, O.,

"Messung

der Wassergeschwindigkeiten neben der Schiffswand

(2)

(3)

(4)

(Measurement of Water Speeds near a Ship Hull)," WRH, 7 Sep 1926, pp. 415-419 Baker, G. S., "Ship Wake and the Frictional Belt," NECI, 1929-1930, Vol. XLVI, pp. 83-106 and Pis. 141-146. Describes Ill, IV; discussion on pp. results of tests on planks and ship models, and on the fast channel steamer Snaefell and the singlescrew merchant ship Ashworth. Baker, G. S., "Wake," NECI, 1934-1935, Vol. LI, pp. 303-320 and D137-D146. Describes results of tests on two models, and full-scale observations on the Ashworth and on the Pacific Trader. Igonet, C., "Note on Wake," ATMA, 1938, Vol. 42, pp. 543-569. This paper has apparently not been translated into English.

Sohoenherr, K. E., and Aquino, A. Q., "Interaction Rep. 470, Mar Between Propeller and Hull,"

TMB

(6)

1940 Harvald, S. A., "Wake of Merchant Ships," Danish Tech. Press, Copenhagen, 1950; copy in

TMB

library (7)

practically neghgible.

Bibliography

wake

a practically complete bibliography on wake, there are mentioned here only a few special papers

destroyer, at a T^ of about 1.4 or 1.5, the effect of

of predicting

Fortunately for the profession at large, this work is now (1955) in progress in the United States.

tions, that at

vessel of similar type

and to arrive at a

as indicated in Sec.

analytically,

from not-too-precise observa-

8 to 10 lengths abaft the stern of a high-speed towing vessel of form similar to a

method

certain that the

(5)

It is reported,

short of

Uttle

from a design, but he has found the answer most

—

channel!

is

tremendous. S. A. Harvald has recently (1950) made a valiant endeavor to systematize the

it

own wake

Sec. 52.20

(8)

Harvald, S. A., "Three-Dimensional Potential Flow and Potential Wake," Trans. Danish Acad. Sci., 1954 Korvin-Kroukovsky, B. V., "On the Numerical Calculation of Wake Fraction and Thrust Deduction in

a Propeller and Hull Interaction," Int. Shipbldg.

Prog., 1954, Vol.

1,

No.

4,

pp. 170-178.

CHAPTER

Dynamic

Quantitative Data on Relationship to Other Chapters

53.1

53.6

Wetted Length, Wetted Surface, and Friction

263

53.7

Variation of Total and Residuary Resistances

264 264

53.8

Selected

53

Partial Bibliography on Hydrofoil-Supported

Moments on a Planing

Craft

Determination of Dynamic Lift Typical Pressure Distribution and Magnitude on Planing-Craft Bottoms

53.4 53.5

Relationship to Other Chapters. The phenomenon of planing is described in Chap. 13, and the behavior of planing craft in general is discussed in Chap. 30. Rules and profull-

Chap.

77, with a preliminary design

worked out

for one boat.

The

simple planing surfaces are rather voluminous,

when float field,

the test results on flying-boat and seaplanemodels are included. Several workers in the as related in the sections following, have

....

269

(1)

and Planing Craft

271

Length, breadth, and planform shape of the

contact with the water in any given running condition, with respect to an axis parallel or nearly so to the direction of motion. At running attitude and position, the length dimension becomes the mean wetted length Ljrs and the breadth dimension becomes

mean

chine

beam Be

Wetted area of the planing surface. This is the actual and not the nominal area. (3) Forward speed V with respect to the water underneath the bottom of the planing craft, (2)

neglecting the cosine of the angle of trim

Mass density

succeeded rather well in their efforts to assemble,

(4)

analyze, correlate, and systematize the available

the water

make them directly new designs. It is not

Lift,

planing surface actually in

the

basic data for predicting the behavior of

209

Craft

53.1

planing type of motorboat are to be found in

with Speed Bibliography on Planing Surfaces,

Dynamic .

266

basic

cedures for the hydrodynamic design of a

268

Resistance

Planing Principal Forces and

and Planing

Lift

263

Principal Quantitative Factors Involved in

53.3

53

p(rho)

and weight density w

of

planing-surface data, so as to

(5)

Trim angle

applicable to and useful for

(6)

Rise-of -floor angle /3(beta), for a planing sur-

possible, within the scope of this chapter, to

much more than

do

reference a few of the sources

which contain quantitative data

in

a form to be

readily usable to the designer of planing craft.

face that

condition.

Related to these features are the:

L

(8)

Dynamic

(9)

Total resistance or drag

is

The magnitude

of the

planing surface inclined at a small angle of attack a(alpha), or under a V-bottom boat running at

a trim ^(theta) by the stern, considerable

CP

number

a function of a of factors. Further, the is

of this pressure system, or the point

where the resultant dynamic

lift is

exerted,

and

location with respect to the center of gravity is

any given running

in

dynamic pressure intensity and the dynamic lift under a

CG,

in transverse section

included as Sec. 53.9.

in Planing.

its

V-shaped

Distance of the CP from the after termination, usually a sharp edge of the planing surface,

Principal Quantitative Factors Involved

hydrofoil-supported craft

center

with reference to the horizontal

(7)

In addition to the selected bibhography on planing in Sec. 53.8, a partial bibliography on 53.2

is

d

of

Among

it is

for the design of

these factors

may be

an airplane.

mentioned:

Rt

,

in the direction

motion

(10) Friction resistance

Rf

,

exerted parallel to

the wetted bottom surface (11)

Residuary resistance Rjt

,

as for

any other

surface craft (12)

(13)

Total weight W(ot A) of the craft Buoyancy B, due to partial immersion of

the hull at some speeds (14) Acceleration of gravity g.

There are a number

as important for the proper design of a

planing craft as

lift

craft design:

263

and and planing-

of dimensionless ratios

coefficients utihzed in planing-surface

HYDRODYNAMICS

264

IN SHIP DESIGN

,

(16) Planing

be used

number Rt/W.

if it is

Its reciprocal may-

an advantage to do

so.

Ratio of the distance designated as [CP from trailing edge of planing surface] to the mean (17)

beam Be

chine

the drag of the appendages.

Speed coefficient Cy o r beam-Froude numwhere Cv = V/-vgBc

(18)

ber, (19)

Load

Cw sym= W/{wBc) coefficient, C^l = W/(qBc) =

coefficient,

where Ca or

2iC,n)/C^ (21) Resistance or

drag

is

The

relative-wind

assumed equal to the stUl-air The thrust-deduction force is assumed

in this case

resistance.

,

bolized preferably as Cld, (20) Dynamic-lift

Sec. 53.3

drawn to supplement Fig. 13. C in Sec. 13.3 on page 206 of Volume I. The accompanying figure shows the principal forces acting on a craft during planing. The propulsive force and its component, not shown in Fig. 13. C, are indicated here, as are the buoyancy force (assumed finite and not negligible), the relative-wind forces, and

(15) Ratio of the chine beam Be to the mean wetted length L^s or the aspect ratio

is

probably

and rudder assembly abaft the propeller and on the exposed shaft ahead of it, if not on the strut

=

drag coefficient Cpianins r

as zero, although in practice this

never the case. In the diagram of Fig. 53. A there would be a thrust-deduction force exerted on the

Rr/(wB^).

hull proper.

The marme architect, seeing this first time, is amazed at its length and

list

for the

complexity,

as compared to that for a surface ship of the dis-

placement type. It is perhaps satisfying, but not always comforting for this architect to realize that his amazement is fully justified. The problem of estimating and predicting planing-craft performance is indeed more intricate and involved than that for a normal type of surface ship. 53.3 Principal Forces and Moments on a Planing Craft. As an aid in presenting, in systematic fashion, the quantitative data relating to prediction of planing-craft performance. Fig. 53.

A

There are forces due to the formation of spray and the generation of spray, indicated on the diagrams of Figs. 13. B and 13. D, but their positions and vector directions are not well known. 53.4 Determination of Dynamic Lift. There is no liquid circulation as such about an inclined fiat plate skimming along the water surface, or about any planing craft in the manner described for the hydrofoils of Chap. 14 of Volume I. It is found possible, nevertheless, to estimate the dynamic lift of such a plate reasonably well by calculating the lift due to circulation, as if the roots

is

Lift

Pressure Draq Dpft^ of

Appendoaes

Direction

Woterline Lern^th L^ Croft Qt Rest Force L Wetted Le ngth at 5peed V

of Flow

Under Bottom

—

Weight Thrust-Deduction Force AT is Assumed Zero Buo\;Qnc\j Force B is That Due to Water Displaced b\j Afterbodvj Force

DE

13

Ltane3*(lnduced Droq Di)sece ^ (Slope Draq)sec0

CD is Force Dp;., times sec 9 Force AC is Bottom-Friction Force Dp times sec Force

Fig. 53. a

Force '

NOTE: Not shown here, to avoid confusion, the vertical force (or upward force normal to the shaft axis) exerted by the propeller because of the non-axial flow in which it is operating. This is the force mentioned in the second paragraph of Sec. 53.6 on page 268. It is developed by the action explained in Sees. 17.7 and 33.5 of Volume I, and illustrated in Figs. 17. C, 17. D, and 33.1 on pages 264, 265, and 485, respectively, of that volume. is

W

Definition Diagram op Forces on a Planing Boat

Sec. 53.-1

Fig. 53.B

DATA ON DYNAMIC LIFT AND PLANING

265

Graphs fob Relating the DrNAivac-LiFT Coefficient to Otheb Features of a Planing Form

HYDRODYNAMICS

266

IN SHIP DESIGN

Sec. 53.5

halving this value.

and X (lambda) is the ratio of the mean wetted length L^,^ to the mean chine beam Be

Without going further into the analytic hydrodynamics of planing, set forth in detail in many

floor angle of

were

plate

and

submerged,

completely

then

of the references listed in Sec. 53.8, it is stated simply that the dynamic lift exerted normal to a flat inclined plate of length L and breadth B, in contact with a hquid surface on its under side

only, is expressed

by

(3)

For a V-surface having a constant

{C^l),

=

/3

rise-of-

deg,

-

(C^l)o

0.0065^[(C«^)„]"

(53. iv)

Graphs giving the relationships between these variables, convenient for the use of a planing-craf

drawn in Fig. 53.B, adapted from diagrams previously pubUshed in the references designer, are

=

normal to plate

Li,

of floor

pB'V^a ^ o

(53. i)

listed earlier in this section.

The method

of using the equations listed

and

where a is the angle of attack or trim by the stern and Lz) is not, as customary, measured normal to

the accompanying graphs

the direction of motion.

illustrated for a specific design of planing-type

The dynamic

to be expected from a simple

lift

Murray [SNAME, motorboat

one with straight

53.5

buttocks and keel and a constant rise-of-floor

nitude

planing surface,

defined

as

running at a trim angle

may

be derived

angle

j8,

more

precisely in terms of equations set

d,

up by B. V. Korvin-Kroukovsky, D. Savitsky, and

W.

Lehman [ETT Rep.

360, Aug 1949]. These with their representation in graph form, are used by A. B. Murray in his paper "The Hydrodynamics of Planing Hulls" [SNAME, F.

equations,

1950, Fig. 11, p. 666].

The dynamic 0-diml

is

lift

dynamic-lift

expressed

coefficients

terms of

in

Cdl

,

using

(CdlJo for a planing surface with zero rise of floor

and {Cul)^ for one with a rise-of-floor angle

The equations

/3.

for these coefficients are, strictly

speaking, dimensionless in that

all

composing them have dimensions

of zero.

theless, the fact that the trim angle

the factors

6,

Never-

expressed

is

1950,

described by A. B.

669-670] and

pp.

in Sec. 77.26.

Typical Pressure Distribution and

on

is

Planing-Craft

Bottoms.

Mag-

Diagrams

showing typical transverse and longitudinal pressure distributions on the wetted bottoms of planing forms, similar to those reproduced in Figs. 13.B and 13.D on pages 205 and 207 of

Volume

I,

are rather plentiful in the technical

They

Hterature.

are to be found in

many

of the

and 30 and of Sec. 53.8 of the present chapter. For example, the graphs of longitudinal -|-Ap distribution pubhshed by A. B. Murray [SNAME, 1950, Fig. 19 on p. 675] are taken from data developed by W. Sottorf, in references of Chaps. 13

a paper Usted as reference (21) of Sec. 53.8. Assuming a V-bottom craft, the transverse pressure distribution

is

characterized

by peak

pressures over the regions of origin of the port

and starboard spray

roots,

along the diagonal

At small

as T(tau) in the references, appears to the 1.1

stagnation loci depicted in Fig. 13.D.

power and the term {Cdl)o to the 0.6 power

immersions of the keel, all the pressure is concentrated near the centerplane. At greater immersions the two pressure concentrations move outward toward the chines. Reliable specific data on the distribution of

seems to indicate that other terms as yet unknown should eventually be embodied in the equations. Expressed in standard and ATTC notation these equations are:

(1)

'•^DL

—

W (or A)

—

pressure

Cj^ Z

„2

(53. ii)

and the magnitude of the pressure on the bottoms of planing craft having

intensities

given characteristics, especially to

where Be

the

is

coefficient,

mean

and Cy

chine beam,

Cld

is

the load

For a

flat,

floor angle

/3

Much

of the available information is in a classified

status, so that the naval architect is forced to fall

inclined plate, having a rise-of-

back upon the results of theoretical analysis or upon pubhshed data concerning measurements on the hulls of seaplanes and flying boats.

of zero

and a trim

of d deg,

For the determination (C^l)o

=

e'M0.0120\"'

where {Cdl)o

is

when subjected

relatively meager.

the speed coefficient, pre-

is

viously defined (2)

heavy impact in waves, are

the

lift

+

0.0095X' (53.iii)

ci

coefficient for

a zero

rise

of

CP

positions

in

and graphs set up by B. V. Korvin-Kroukovsky, D. Savitsky, and W. F. Lehman are useful [ETT Rep. 360, Aug specific cases the equations

Sec. 53.5

Fig. 53. C

DATA ON DYNAMIC LIFT AND PLANING

267

Graphs fob Determining the Foke-and-Aft Center-of-Pressure Location Under a Planing Form

HYDRODYNAMICS

268

1949]. Both eciiiatioiis and graphs are reproduced by A. B. Murray [SNAME, 1950, Fig. 10, p. 665]. The distance of the center of pressure CP from the traihng edge of the planing surface, assumed at the after perpendicular AP, is expressed as

The

.r-distance

=

[CP to AP]

K(L„.s)\"

IN SHIP DESIGN

Sec. ^3.6

A. B. Murray illustrates the ETT method of determining wetted chine and keel lengths for a

[SNAME,

towed model

1950, Figs.

14 and 15,

pp. 672-673]. Both wetted length and wetted area may be determined by fish-eye views made

photographically, using a painted grid on the (53.v)

where L^s is the mean wetted length, X is the and is a function of the angle ratio LjTs/Bc of trim 6 and of the rise-of-floor angle /3. This

under surface of the model and a water box, underwater mirror, or other suitable setup [ETT, Stevens, Rep. 378, Sep 1951, pp. 46-47]. The general shape of the wetted area for a V-bottom

relation

craft is the same, illustrated

K

,

is

K = where

/3

and

6 are

+

0.84

30.C, 0.015/3

(53 .vi)

both expressed in degrees. m are derived from

The exponents n and „

+

= -(0.05

m =

0.125

+

O.Olg)

(Sa.vii)

0.0042/3

(53.viii)

where /3 is again expressed in degrees. Graphs giving the relationships between these variables, in convenient form, are 53. C,

drawn

in Fig.

adapted from diagrams pre\'iously published

in the references quoted.

The method

of using the equations listed

and

by A. B.

the accompanjdng graphs

is

Murray [SNAME,

pp. 670-671] and is design of full-planing

1950,

illustrated for a specific

described

motorboat in Sec. 77.26. 53.6 Wetted Length, Wetted Surface, and Diagrams indicating the Friction Resistance. general position and shape of the wetted area under a planing craft when running at or near its designed speed are found in Chaps. 13 and 30. The changes in wetted surface and wetted length at speed are discussed briefly in Sec. 30.8. Since these features are important factors in predicting performance, the method of estimating or determining

them, in a running rather than an at-rest condition, requires further explanation.

The shape and extent of the wetted area of the bottom or dynamic-support surface of a planing craft is rather easily determined by running a model under a given set of conditions. This method is, however, open to the objection that a model which is towed and not self-propelled may not run at the proper trim for the prototype because the vertical forces exerted by the propeller (s) are missing. A change in trim almost always means a change in both wetted length and wetted area, possibly a change in the center-of-pressure position

as well.

30.F,

and

77. P.

by

Figs. 13. D, 30. A,

photographs

Small-size

and diagrams, in the form of fish-eye views .published by A. G. Smith, show the general shapes of the wetted area and of the spray roots under V-bottom planing forms with a 25-deg rise of floor and a 6-deg trim by the stern [5th ICSTS, 1949, pp. 70-73 and Figs. 1-5]. C. W. Spooner, in his unpublished report "Speed and Power of Motorboats up to a Speed-Length Ratio of 3," dated October 1950, gives a table and wetted-

listing the principal characteristics

number of motorboat he includes tentative graphs for estimating the wetted surface of craft of this type, based on a coefficient S/{LB), which increases slowly \vith fatness ratio V/{0.lOLy. For a motorboat mth a single centerline skeg the

surface area of a considerable designs.

In his Fig.

coefficient

13

is:

0.950 at a fatness ratio of 4.0

0.984 at a fatness ratio of 6.0 1.01

at a fatness ratio of 8.0,

where L and B are presumably in ft, and is in ft^. For a bare hull the corresponding coefficient values are 0.860, 0.889, and 0.911, respectively. J. P. Latimer gives the layouts, lines, principal characteristics, and wetted surface for a USCG 40-ft utility boat ["Characteristics of Coast Guard Powered Boats," SNAME, Ches. Sect., 13 Oct 1951]. Contour charts for determining wetted areas »Sr

EMB

of the Series 50 models, applicable as first approximations of the wetted areas of other V-bottom planing craft having speed-length T", values of from 2.0 to 6.0, are described and pubReport lished on pages 6 and 85-94 of

TMB

R-47, revised edition, March 1949. Further data may be found in a paper by

Korvin-Kroukovsky, D. Savitsky, and entitled "Wetted Area and Center of Pressure of Planing Surfaces" [ETT, Stevens, Rep. 360, Aug 1949]. B.

V.

W.

F.

Lehman,

DATA ON DYNAMIC LIFT AND PLANING

Sec. 55.
The method is

computing the friction resistance essentially the same as for any other type of of

surface craft, described in Sec. 45.22.

The mean

wetted length L^s^s used as the length dimension to determine the Reynolds number R„ for the craft in any specified running condition. Throughout the whole speed range the wetted length, Reynolds number, and wetted area all change with speed but at and near the designed speed they are practically constant. Sec. 77.26 embodies an example in which the

wetted area and the friction resistance of a fullplaning type of motorboat ai'e calculated, following the methods described by A. B. Murray in a reference cited earlier in this section. If there is

wetting of the sides as well as the

bottom at full speed it can be taken care of as an augment of the wetted area. Normally, however, consistent wetting of the sides of a full-planing craft is evidence of poor design somewhere. Rather than to calculate the effect, the cause should be

eliminated.

A few words are in

order here relative to rough-

ness of the bottom surface. Although the

mean

wetted length of modern (1955) planing craft is usually low, well under 100 ft or say 30 meters, the rubbing speed of the water is high. By the reasoning of Sec. 45.10, this means a very thin laminar sublayer under the boat and a large increase in drag if the bottom surface is rough.

The

permissible roughness height

though the overall R„ 53.7

may

small,

is

even

likewise be small.

Variation of Total and Residuary Resist-

It is most interesting to note, from the diagrams in Figs. 20 and 21 on pages 676 and 677, respectively, of A. B. Murray's paper

ances with Speed.

[SNAME,

1950],

weight ratios of

that

many

the

total-resistance-to-

planing craft,

when

plotted

on a base of speed-length quotient T, lie remarkably close to a meanline for a rather wide range of speed. The corresponding values for both V-bottom and round-bottom motorboats and sailing craft given by H. M. Barkla exhibit the same characteristic [INA, 1951, Vol. 93, p. 237], as do the data for many types of large vessels plotted in Fig. 56.M of Sec. 56.10. However, the have values that are 2,240 ordinates of Fig. 56. times the ordinate values of the Murray and Barkla graphs. Murray's planing-craft data cover ranges of displacement-length quotient A/(0.010L)^ of from 100 to 180, yet it is only above a T, of about 3.5 to 4.0 that much dispersion is found. These data ,

M

269

by Murray, most useful for preliminary resistance estimates, when the shape and proportions of a new design of hull have not are, as stated

yet been determined.

Considering only residuary resistances

Rr

,

the few available data indicate a greater degree of irregularity

going.

Fig.

40

than that described in the foreD illustrates variations in the

53.

HYDRODYNAMICS

270

"The Longitudinal Stability of Skimmers and Hydro-Aeroplanes," INA, 1913, Part 1, pp. 136-147 and PI. XIII Richardson, H. C, "Hydromechanic Experiments with Flying Boat Hulls," US Navy-Smithsonian Misc. Collections, 20 Apr 1914, Vol. 62 Millar, G. H., "Some Notes on the Design of Floats for Hydro- Aeroplanes," INA, 1914, pp. 313-328 Richardson, H. C, "Aeronautics in Relation to Naval

IN SHIP DESIGN

(5)

(6)

(7)

Architecture," (8)

(9)

SNAME,

Richardson, H. for Aircraft,"

C, "Naval Development

SNAME,

W.

H. C, "The Trend of Flying Boat Development," ASNE, May 1926, Vol. XXXVIII,

(11) Richardson,

pp. 231-253. Contains a great deal of information which still remains of value (1955) in studying and predicting the behavior of planing craft. (12) Richardson,

SNAME,

H. C, "Design

of

a Large Flying Boat,"

(15)

Moment

of Planing Water Craft)," Flugtechnik und Motorluftschiffahrt, 28

(1

6)

Enghsh

Memo

1931

May

619,

Pavlenko, G., of

transl. in

Zeit.

Nov

NACA

fiir

1930,

Tech.

"On the Theory of Gliding; The Motion

a Plank at a Small Angle

of Inclination to the

Water Surface," Proe. Third

Int.

Congr. Appl.

Mech., Stockholm, 1930, Vol. I, pp. 179-183. For a Froude number F„ of 4 and above, Pavlenko gives the resistance formula fi = pV* tan^ a/{'^g), where p is the mass density of the water and a is the trim angle or nominal angle of attack. (17)

Appl.

Mech.,

Stockholm,

1930,

Vol.

I,

pp. 215-219 (18)

(23)

739,

Mar

1934.

W.

G. A., "Porpoising of High Speed Motor Boats," INA, 1933, Vol. 75, pp. 268-296 Wagner, H., "Uber das Gleiten von Wasserfahrzeugen (On the Planing of Watercraft)," STG,

(22) Perring,

205-227; English transl. in 1139, Apr 1948 (24) Wagner, H., "Uber das Gleiten von Korpen auf der Wasseroberflache (Concerning the Gliding of Bodies on the Water Surface)," Proc. Fourth Int. Cong. Appl. Mech., Cambridge (England), 1934, pp. 126-147. On pp. 146-147 there are listed 27 Vol.

1933,

NACA

34,

pp.

Memo

Tech.

Shoemaker, J. M., "Tank Tests of Flat and V-Bottom Planing Surfaces," NACA Tech. Note 509, Nov 1934 (26) Perring, W. G. A., and Johnston, L., "The Hydrodynamic Forces and Moments on Simple Planing

(25)

An Analysis of the Hydrodynamic Forces and Moments on a Flying Boat Hull," and 1934-1935, Vol. II, 1646, pp. ARC, Surfaces and

M

R

553-575 (27) Eshbach, O. W., "Handbook of Engineering Fundamentals," 1st ed., 1936, pp. 6-50, 6-51 (28) Allison, J.

Models

M., and Ward, K. E., "Tank Tests of Having Longitudinal

of Flying-Boat Hulls

NACA Tech. Note 574, May 1936 W., "Gestaltung von Schwimmwerken (The Design of (Planing) Floats)," Luftfahrtforschung, 20 Apr 1937, Vol. 14, pp. 157-167; EngUsh transl. in NACA Tech. Memo 860, Apr 1938 (30) Weinig, F., "Zur Theorie des Unterwassertragflugels Steps,"

(29) Sottorf,

Gleitflache (On the Theory of Hydrofoils and Planing Surfaces)," Luftfahrtforschung, 20 Jun 1937, pp. 314-324; English transl. in NACA Tech. Memo 845, Jan 1938. On pp. 26-27 there

und der

are

1

1

references listed.

W., "Analyse Experimenteller Untersuchungen iiber Gleitvorgang an der Wasseroberflache (Analysis of Experimental Investigation of the Planing Process on the Surface of Water),"

Jahrbuch der Deutschen Luftfahrtforschung, 1937, pp.

Wagner, H., "tlber die Landung von Seeflugzeugen (Landing of Seaplanes)," Zeit. fur Flugtechnik und Motorluftschiffahrt, 14 Jan 1931, Vol. 22, pp. 1-8. English transl. in May 1931.

(19)

Rep. 453, Sep 1932; 1933 reports, pp. 211-213 "Versuche mit Gleitflachen (Experiments with Planing Surfaces)," Part II, WRH, 1 Oct 1932, pp. 286-290; 15 Feb 1933, pp. 43-47; 1 Mar 1933, pp. 61-66. English transl. in NACA Tech.

(21) Sottorf, W.,

(31) Sottorf,

Wagner, H., "Uber den Aufschlag gekielter Flachen auf Wasser (Concerning the Impact of V-Bottom Planing Surfaces on the Water)," Proc. Third Int. Conf.

"The Establishment of Maximum Load W. Capacity of Seaplanes and Flj'ing Boats," NACA S.,

references.

French and the original language and the references extend back to the year 1914. Sottorf, W., "Versuche mit Gleitflachen (Tests with Gliding Surfaces)," Part I, WRH, 7 Nov 1929, pp. 425-432; English transl. in NACA Tech. Memo 661, Mar 1932 Schroder, P., "IJber die Bestimmung von Widerstand und Trimmoment bei gleitenden Wasserfahrzeugen (Determination of Resistance and Trimming

Vol. 21, No. 22;

TMB

library.

1928, pp. 77-88'

(13) In Vol. 32 of the Bulletin d' Association Maritime Technique et A6ronautique (ATMA), Paris, 1928, on pp. 319-324, there appears a long list of references on planing forms. The titles are in both

(14)

informal translation of this paper in the

Memo

variety of airplane fuselages, seaplane and flsdngboat hulls, airship cabins, nacelles, and the like.

Ang. Math. Mech., Aug 1932,

12,

(20) Diehl,

of Floats

S.,

fiir

pp. 193-215. A number of additional references are given in the footnotes. There is an Vol.

1926, pp. 15-28

"Tests on Aeronautical Fuselages and Hulls," NACA Rep. 236, 1926 reports, pp. 131-150. This paper gives drag and moment data on a great

(10) Diehl,

Liquids)," Zeit.

1916, pp. 43-51

Crowley, J. W., and Ronan, K. M., "Characteristics of the Boat Tj-pe Seaplane during Take-Off," NACA Rep. 226; 1925 reports, pp. 393-401

Sec. 53.8

Oberflache von Fliissigkeiten (Concerning Impact and GUding Phenomena near or at the Surface of

(4) Steele, J. E.,

NACA Tech. Memo 622,

Wagner, H., "Uber Stoss- und Gleitvorgange an der

320-339;

Memo

1061,

Enghsh

transl.

Mar 1944 "A Discussion

in

NACA

Tech.

of Certain Problems W. S., Connected wth the Design of Hulls of Flying Boats and the Use of General Test Data," NACA Rep. 625, Nov 1937; 1938 reports, pp. 253-260. Page 260 lists 24 references.

(32) Diehl,

DATA ON DYNAMIC LIFT AND PLANING

Sec. 53.9 (33) Bollay, W.,

"A Contribution

to the

Theory

of Planing

Surfaces," Proc. Fifth Int. Congr. Appl. Mech., 1938, pp. 474-477; published

by Wiley, New York,

1939 (34)

Sambraus, A., "Planing-Surface Tests at Large Froude Numbers Airfoil Comparisons," NACA Tech. Memo 848, Feb 1938. Originally published in Luftfahrtforschung, 20 Jun 1936, Vol. 13, pp.

in

(50)

190-198.

W., "Versuche mit Gleitflachen, Part IV,

WRH,

(Tests with Planing Surfaces, Part IV)," 1

Mar

1938, Vol. 19, pp. 51-56; 15

Mar

65-70 Coombes, L.

P., "Scale Effect in Tank Tests of Seaplane Models," Proc. Fifth Int. Cong. Appl. Mech., 1939, pp. 513-519 (37) Truscott, S., "The Enlarged NACA Tank, and Some of its Work," NACA Tech. Memo 918, 1939 (38) Diehl, W. S., "The Application of Basic Data on Planing Surfaces to the Design of Fljnng-Boat Hulls," NACA Rep. 694, 16 Dec 1939; 1940

(36)

reports, pp. 287-293. (39) Sedov, L.

RTP

"Planing on a Water Surface,"

I.,

Transl. 2506, Brit. Min. Aircraft Prod, (from Tech.

(40)

(51)

1938, pp.

Vosdushnogo Flota, No. 4-5, 1940). Also Durand Reprinting Committee, Calif. Inst. Tech., Pasadena 4, CaUf. Adamson, G., and Van Patten, D., "Motor Torpedo

A

Boats:

Technical

Study,"

USNI,

1940,

Jul

(52)

references on pp. 17-18. Knowler, H., "The Future of the Flying Boat," Fifth Louis Bleriot Lecture, Assn. Frangaise Ing. et Techn. de I'Aeronautique, Paris, 12 Mar 1952; abstracted in ASNE, Aug 1952, pp. 630-638; also in Engineering (London), 14 and 21 Mar 1952 (54) Chambliss, D. B., and Boyd, G. M., Jr., "The Planing Characteristics of Two V-Shaped Prismatic Surfaces Having Angles of Dead Rise of 20

Deg and 40 Deg," (55) Weinstein,

Planing

Dec 1948

W.

S., Jr.,

Murray, A.

B.,

"The Hydrodynamics

Hulls,"

SNAME,

there

a

is

list

(48) Savitsky, D., of

and Kapryan, W.

Characteristics

a

"The High-Speed Rectangular Flat

of

Trim and Wetted

of

J.,

(56)

under the inchned surface, just as oil is drawn into a wedge-shaped gap in a plain bearing. Springston, G. B., Jr., and Sayre, C. L., Jr., "The Planing Characteristics of a V-Shaped Prismatic Rep. Surface with 50 Degrees Dead Rise,"

TMB

920,

Feb 1955

Clement, E. P., "Hull Form of Stepless Planing Boats," SNAME, Ches. Sect., 12 Jan 1955 (58) Kapryan, W. J., and Boyd, G. M., Jr., "Hydrodynamic Pressure Distribution Obtained During a Planing Investigation of Five Related Prismatic Surfaces," NACA Tech. Note 3477, Sep 1955 (59) Pournaras, U. A., and Sherman, P., "Model Test (57)

"An Empirical Study

of

Low

Aspect Ratio Lifting Surfaces with Particular Regard to Planing Craft," Jour. Aero. Sci., Mar. 1949, pp. 184^188. On page 188 of this paper there is a list of 9 references. B. V., Savitsky, D., and (45) Korvin-Kroukovsky, Lehman, W. F., "Wetted Area and Center of Pressure of Planing Surfaces," Sherman M. Fairchild Fund Paper 244, Inst. Aero. Sci., originally pubKshed as ETT, Stevens, Rep. 360, Aug 1949. There is a list of 23 references on pp. 19-20. (46) Bisplinghoff, R. L., and Doherty, C. S., "A TwoDimensional Study of the Impact of Wedges on a Water Surface," Cont. NOa(s)-9921, Dept. Aero. Eng'g., MIT, 20 Mar 1950 (47)

Tech. Not« 2876, Jan

Length," NACA Tech. Note 2981, Jul 1953. Fig. 9(b) on p. 24, also pp. 5-6 of the text, show that there is a depression in the liquid surface just ahead of the pile-up, under the plate, at low trim angles. It is possible that this could be air drawn

DR

Dept.,

I.,

Plate over a Wide Range

and Thieme, H., "Klarende Darstellung

Takeoff of Seaplanes)," Bericht SUO, Hamburg, 5 Jul 1946 (42) Sedov, L. I., "Scale Effect and Optimum Relations for Sea Surface Planing," NACA Tech. Memo 1097, Feb 1947 (43) Locke, F. W. S., Jr., "Tests of a Flat Bottom Planing Surface to Determine the Inception of Planing," NAVAER Rep. 1096, Bur. Aero., Navy

NACA

1953

der Hydrodynamischen Erscheinungen beim Start von Seefiuzeugen (Explanatory Representation of the Hydrodynamic Phenomena Occurring at the

(44) Locke, F.

SNAME

Kapryan, W.

(53)

Vol. 66, pp. 976-996 (41) Schubert, R.,

SNAME,

Ches. Sect., Apr 1951; abstracted Member's Bull., Oct 1951, p. 15 J., and Weinstein, I., "The Planing Characteristics of a Surface Having a Basic Angle of Dead Rise of 20 Deg and Horizontal Chine Flare," NACA Tech. Note 2804, Oct 1952 Blanchard, U. J., "The Planing Characteristics of a Surface Having a Basic Angle of Dead Rise of 40 Deg and Horizontal Chine Flare," NACA Tech. Note 2842, Deo 1952 Perry, B., "The Effect of Aspect Ratio on the Lift of Flat Planing Surfaces," Hydrodynamics Lab., CIT, Rep. E-24.5, Sep 1952. There is a list of 16 Hulls,"

—

(35) Sottorf,

271

Rep. 378, Sep 1951, published by the Inst. Aero. Sci. as S. M. F. Fund Paper FF-6 of the same date. It lists 24 references on pp. 25-27. (49) Clement, E. P., "The Analysis of Stepless Planing

1950,' pp. 658-692.

Planing

of

On

p.

680

of 19 references.

"Wetted Length and Center

Vee-Step Planing Surfaces,"

of Pressure

ETT,

Stevens,

EHP for a Round Bilge 40-Ft Aircraft Rescue Boat Design from Tests of Rep. 1002, Oct 1955. (TMB) Model 4525," Results and Predicted

TMB

53.9

Partial Bibliography

ported Craft.

on Hydrofoil-Sup-

A good, concise list of references on

the development, characteristics, and performance of high-speed craft supported by hydrofoils is

and J. J. embodied in the following partial bibhography which contains additional references of less scientific but

M. Buermann, [SNAME, 1953, p.

given by T.

P. Leehey,

StUwell

264]. It is

more general

interest:

HYDRODYNAMICS

272 Nutting,

(I)

W. W., "The HD-4, a 70-Miler mth Remark-

able Possibilities," reprinted Smithsonian Report for 1919, Publn. 2595, Gov't. Print. Off.,

Wash-

ington, 1921

H. C, "The Trend of Flying Boat Development," ASNE, Ma}' 1926, Vol. XXXVIII, pp. 231-253. Historical data on "hydrovanes," now known as hydrofoils, are found on pp. 245-246. Guidoni, A., "Seaplanes, Fifteen Years of Naval Aviation," Jour. Roy. Aero. Soc., Jan 1928, Vol. 32, No. 205 Keldysch, M. V., and Lavrent'ev, M. A., "On the Motion of an Aerofoil under the Surface of a Heavj' Fluid, i.e., a Liquid," paper to ZAHI, Moscow, 1935; EngUsh Transl. by Science Transl. Serv., Cambridge, Mass., STS-75, Nov 1949 Tietjens, O., "Das Tragflachenboot (The Hydrofoil Boat)," WRH, 1 Apr 1937, pp. 87-90; 10 Apr 1937,

Richardson,

(2)

(3)

(4)

(5)

TMB

library. pp. 106-109. English transl. in (6) Weinig, F., "Zur Theorie des Unterwassertragflugela of Hydrofoils (On the Theory und der Gleitflache

and Planing Surfaces)," Luftfahrtforschung, 20 Jun 1937, pp. 314-324. English transl. in NACA Tech. Memo 845, Jan 1938. On pp. 26-27 there are 11 references listed.

i

i:i!(7) ,vj

,

.

;

(8)

;

jj

!•

Grunberg, V., "La Sustentation hydrodynamique par ailettes immergees: Essais d'un sj'steme sustenteur autostable (Hydrodynamic Support by Immersed Foils: Tests of a Self-Stabilizing Support System)," L'Aerotechnique, Jun 1937, 16th Yr., No. 174 Coombes, L. P., and Davies, E. T. J., "Note on the Possibihty of Fitting Hydrofoils to a Flying Boat Hull," Roy. Aircraft Estab., Farnborough, Rep. B. A. 1440, Nov 1937 Kotchin, N. E., "On the Wave-Making Resistance and Lift of Bodies Submerged in Water," Trans.

.

(9)

of

;..

IN SHIP DESIGN (14) Benson, J.

mental (17)

(18)

(II)

(19)

down from the hull mentions a tj^pe of boat

(12)

"Summary

Jr.,

of

Hydrofoils,"

NACA Vol.

2,

Stivers,

of Airfoil Data,"

Hook, C, "The Hydrofoil Boat

"The

J.,

J.

North.

Abstracted in

NACA

for

Ocean Travel,"

LXIX,

1947-

Possibilities Calif.

SNAME

Sect.,

of

11

Hydrofoils," ftfay

Member's BuU,,

1951.

.Oct 1951,

p. 19.

(23)

"Trag- und Dampfungsflachenboote Motorboats)," Schiff u. Hafen, Apr 1952, pp. 121-122. This article g'ves a very brief resume of the development work carried out on hydrofoil motor boats in Germany during World War II. Tlie boats did not proceed beyond the experimental stage. A boat with an all-up weight

Kaemmerer,

(Hydrofoil

of

100,

t,

,

powered by two 1,600-horse engines,

attained a speed of 41 kt, while a second boat with a weight of 60 t was expected to reach 60 kt; the latter was, however, damaged before trials were run. Knowler, H., "The Future of the Flying Boat," ASNE, Aug 1952, p. 630 (25) Biiller, K. J., "The Hydrofoil Boat," Hansa, 16 Aug

1952, p. lOOOff

"Hydrofoil Boat White Hawk," The Motor Boat and Yachting, London, Sep 1952, p. 361 (27) "Modern Hydrofoil Boat Designed by H. F. Schertel," The Motor Boat and Yachting, London, Oct 1952, p. 414 G., "On the Economy of the Traffic with Hydrofoil Speed Boats," Hansa, 1952, No.

(28) Sachsenberg,

30/31

H. F., "Tragflachenboote (Hydrofoil Supported Boats)," Handbuch der Werften, Band 1952, II, Schiffahrts-Verlag, Hansa, Hamburg,

(29) Schertel,

Plum of the TMB staff. Adamson, G., and Van Patten, D., "Motor Torpedo Boats: A Technical Study," USNI, Jul 1940, pp. J.

976-996, esp. pp. 988-989, describing the Bell-

pp. 43-47. English translation available at the DTMB. For a photograph and description of a

Baldwin HD-4 W., "Experimentale Untersuchungen ziir Frage des Wassertragfliigels (Experimental Examination of the Question of Hydrofoils)," Rep. 1319,

The Motor Boat and Yachting, London, Oct 1952, p. 414. Buller, K. J., "Das Tragfliigelboote (The Hydrofoil

more modern

Ger.

Res.

Develop.,

Est.

for

Aircraft,

Hamburg, Dec 1940

Inst,

for Seaplane

45-ft hydrofoil

boat designed by

Schertel (von Burtenbach) see

(13) Sottorf,

•

Characteristics

SNAME,

steering rudders extend well

evolved by

S.,

(22) Oetling,

(26)

of the craft. This article

of

1948. In Fig. 3 on page 9 of this paper there are shown diagrammatic arrangements of a number of hydrofoil boats, captioned "Italian and German Types," said to have been taken from a patent by H. F. Schertel von Burtenbach, 1938. (20) Rabl, S. S., "Pursuit of More Speed," Chesapeake Skipper, Apr 1950, pp. 12, 31, 32 (21) Hoerner, S. F., "Aerodj'namic Drag," 1951

Moscow, 1937; EngUsh transl., Br. Adm. Document, PG/53280/NID, May 1946 "High Speed Craft: Some Comments on a Patent Specification Recently Filed from Dumbarton,"

May 1940, pp. 440-441. This article shows a proposed design of high-speed motorboat supported by a planing step or a hydrofoil forward and by a second hydrofoil aft, in which there is embodied a screw-propeller drive with a vertical shaft and bevel gears at both top and bottom. The

Investigation of

I.

Trans. Liverpool Eng'g. Soc., Vol.

(24)

SBSR, 2

"An

Rep. 824, 1945

SNAME

311,

S.,

Tank;

Wartime Rep. L-766 Durand, W. F., "Aerodynamic Theory," Durand Reprinting Comm., 1943 Abbott, I. H., von Doenhoff, A. E., and L.

"Approximate Hydrodynamic Calcua Hydrofoil of Finite Span," ZAHI Rep.

lation of

NACA

Effect of DiheSubmersion," NACA Wartime Rep. L-75S, Sep 1942 (15) Land, N. S., "Characteristics of an NACA 66, S-209 Section Hydrofoil at Several Depths," NACA Wartime Rep. L-757 (16) Ward, L. E., and Land, N. S., "Preliminary Testa in the NACA Tank to Investigate the Funda-

and Depth

dral

the Conf. on the Theory of Wave Resist., 1937; English transl. by A. I. (T)

(10) Vladimirov, A.,

M., and Land, N.

Hydrofoils in the

USSR, Moscow,

Air Ministry, R.T.P. 666, Mar 1938; T and R Bull. 1-8, Aug 1951

Sec. 53.9

(30)

Boat),"

STG, 1952, pp. 119-136 "German Contributions

(31) Vertens, F.,

to the Develop-

DATA ON DYNAMIC LIFT AND PLANING Boat," Schiff u. R and M 2836, Sep 1946,

Sec. 53.9

ment (32)

(33)

(34)

of

the Hydrofoil Speed

Hafen, Mar 1953, p. 103 Grupp, G. W., "Speedboats with Wings," Motor Boating, New Yorlv, Aug 1953, pp. 22-23

"Water Wings Add Zip to Navy Craft," All Hands IVtag', Bu. Nav. Pers., Oct 1953, pp. 14-16 Buermann, T. M., Leehey, P., and Stilwell, J. J., "An Appraisal of Hydrofoil-Supported Craft," 1953, pp; 242-279. This paper

is

(37)

TMB

pp. 58-60, 127 K., "New and

(40) Biiller,

Covers

tests

at

zero

yaw

angle,

abstracted in

had

NACA

661-012 sections and one an

Warren, C. H. E., "A Theoretical Approach to the Design of Hydrofoils," Aero. Res. Counc, London,

Jul 1955, Vol.

LXVII, pp.

Messina types, whose characteristics are given, are 59 and 55 horses per ton, respectively.

struts

NACA

664-021 section. (36)

IME,

102-103, with diagram of the PT SO/dJf, a SchertelSachsenberg craft, in its flying position. Brakepower to displacement ratios of the Bremen and

various

Two

Larger Hydrofoil Boats," 4, pp. 5-8;

European Shipbuilding, 1955, Vol.

]

1953.

27 Sep 1954,

F. H., "The Theoretical Dynamic LongiStability of a Constant-Lift Hydrofoil System," Rep. 925, Dec 19.54 (39) Miller, R. T., "Hydrofoil Craft," Yachting, Mar 1955,

Jan 1954 issue of SBSR, pp. 53-54. Coffee, C. W., Jr., and McKann, R. E., "Hydrodynamic Drag of 2- and 21-per cent Thick SurfacePiercing Struts," NACA Tech. Note 3092, Dec depths, and various angles of rake.

Life,

tudinal

in the 14

(35)

"Boats that Fly Atop the Waterj" pp. 56-58, 60

(38) Imlay,

SNAME,

abstracted briefly

273 published 1953

(41)

"World's Fastest (Hydrofoil) Sailing Boat, Monitor," 111. London News, 8 Oct 1955, p. 627; Yachting,

Nov

1955, p. 71

;

SBSR, 17 Nov

1955, p. 637.

CHAPTER Estimating the Air and

54

Wind

Resistance of Ships

....

Scope of This Chapter; Definitions Increase of Wind Velocity with Height Above

274

54.8

Comments Concerning Wind-Friction Re-

54 2

Water Surface Flow Diagrams for Upper- Works Configura-

274

54.3

54.9 54.10

Prediction of

54.1 .

276

tions

54.6

General Formulas for the Wind Drag of Irregular Ship Hulls and Superstructures Notes on Wind-Resistance Models and Testing Techniques Bibliography of Model Wind-Resistance

54.7

Drag

54.4

sistance of

276

.

54.5

278 278

Tests

Abovewater

Coefficients for Typical

Hulls and Upper Works

54.1

The

Scope

general

of

This

an Abovewater Hull

Drag and Resistance with Wind on the Bow

Wind

Resistance for

ABC

.

of Part 4

Magnitude

54.11 54.12 54.13 54.14 54.15

of

Wind

Pressure

Wind Pressure Wind Drag Lateral Wind Moments and Angle of Heel Estimated Drift and Leeway Estimating the Forces on a Moored Ship Surface-Water Currents due to Natural Wind Location of Center of

.

.

.

Lateral

.

54.15 54.17

280 281

Ship

.

282 283 284 285 285 286 287 287

279

Chapter;

phenomena and the

Definitions.

effects of the

flow of air over the abovewater hull and the upper

works of a ship are described in

Sees. 26.15

and

masts.

The

thickness 5 (delta)

may

attain values

greater than a thousand feet [Matveyey, R. T.,

Meteorologiya 20-29;

ASCIL

Gidrologiya, No. 3, 1949, pp. i Transl. 490]. Large wind velocities

Volume I in purely qualitative fashion. The winds of nature, powerful enough to propel

at high airplane altitudes are caused

saihng vessels, produce sizable quantitative effects

boundary-layer

on mechanically driven ships, often of the order of tenths of the power and whole knots or more of speed. Reasonably accurate estimates or predic-

the so-called reference velocity, represented

26.16 of

ments

of

huge

air

,

is

strictly

a

effect.

For the ordinary boundary layer [/„

by move-

masses and are not

in air or

water

by

that at a great distance from the body or

tions of these effects are required, especially

when

ship. Since this velocity is rarely

analyzing ship-trial data [Eggert, E. F.,

EMB

thick and high boundary layer in the atmos-

Rep. 264,

Aug

1930;

SNAME,

1932, pp. 17-44;

1933, pp. 243-295; Taylor, D. W., S

and P, 1943,

phere above a large water surface,

known it is

to use as a reference, for ship-design

for the

customary and ship-

pp. 167-169].

operation purposes, some velocity that

phenomena and effects are given in Sec. 26.15, supplemented by Figs. 26. G and 26. H. It is most important to

measured. In the past, the reference velocity has often been considered to be that observed at a height of 50 ft above the water. However, there is no accepted standard height for measuring the

Definitions applying to these

keep clear the distinction made there between the wind drag D„r which always acts dovmwind from the relative wind direction, and the wind re,

sistance ffwind

•

The

latter is the

and-aft components of both the the wind

lift,

sum

of the fore-

mnd

drag and

acting always along the principal

ship axis, opposite to the direction of motion.

This distinction

is

forces are impressed

necessary because the wind

on the ship separately from

the hydrodynamic forces. 54.2

Increase of

Wind

Velocity with Height

Water Surface. The boundary layer formed by the -wind blo\ving over moderately

is

easily

is assumed to be acting on a boat or a ship as a whole. Nevertheless the mnd

wind velocity which

velocities of interest to

operators

are

greater than

usually

1.0,

of

marine architects and ship e.xpressed

as

multiples,

whatever velocity near the

taken as the reference or the standard. the air velocity over smooth water is zero at the water surface, as for a hquid flonang over a solid surface. Practically, even for model sail boats and sailing yachts having mast surface

is

Theoretically,

Above

heights of

long stretches of water

measurable distances above the water surface are large. Taking all things into consideration, a reference height of 6 ft above the water surface is

is

thick in proportion to

the vertical dimensions of a ship hull, or even of

its

274

1

ft or less,

the actual air velocities at

AIR AND WIND RESISTANCE OF SHIPS

Sec. 54.2

considered logical and

used as the reference in

is

this book.

The

ship designer, naval architect,

and ship

operator then need a curve or table of multiples, to compare the wind velocity at other heights

with that at 6 ft. The necessary data can be and have been derived from (1) theoretical considerations and from (2) observed simultaneous wind velocities at several heights above a reasonably level water surface. Making use of boundary-layer theory possible to develop a simple formula

that the ratio

the wind velocities at two

of

heights

different

is

it

which shows

above a

should vary as the

root of the ratio of the

fifth

heights [Experiment

surface

level

solid,

Tank Comm., Japan, "Ab-

Notes and Data," 6th ICSTS, 1951, pp. Taking hi and h^ as these heights, and TTi and W2 as the wind velocities at these heights.

stract

71-92].

W2 _ Wind velocity Wind velocity Wi

A

discussion

at height h^ (54.i)

at height hi

by D. Brunt,

also based

upon

boundary-layer theory but making use of experimental observations to some extent, is given in

book "Physical and Dynamical Meteorology" [Cambridge (England), University Press, 1944, pp. 247-255]. Brunt is inclined to use a seventhroot velocity variation rather than a fifth-root variation, based upon the distribution in the 1/7-power velocity profile illustrated in the righthand diagram of Fig. 5.K. It is apparent, from his

the discussion presented by Brunt, that the rate of

wind variation with height

ing upon a

number

is

complex, depend-

of variables

not a simple matter to find reliable experimental data known to have been taken over the It is

water. Furthermore, the exact vertical location of

the "Surface" observations used for reference are rarely stated.

man

high as a

Presumably they are at

least as

a small boat.

The low

sitting in

heights

of

several

hundred

interest

to

feet,

micro-heights in the

the

ship

are in

field of

U

designer,

the

say

category of

meteorology.

The only careful, systematic investigations made over the sea appear to be those of J. S. Hay, published in Porton Technical Paper 428 (un-

24 June 1954, issued by the Chemical Experimental Estabhshment of the

lioh -{ h

(54. ii)

C/:.o

where C/1.0 is the velocity at the reference height of 1 meter (3.28 ft), and a and h are numerical values tabulated by Hay for different wind and sea conditions.

The roughness of the sea surface, increasing with the wind velocity at the reference height, changes the type of viscous flow somewhat and with it the numbers a and h. Hay lists 8 references on page 16 of the report. Because of the diminished relative roughness of the average water surface as compared to the average land surface, the speed of the wind for a given atmospheric disturbance

is

greater over

water than over land. Likewise, the reduction in wind speed as the height is diminished, due to the increased wind friction over the land, is greater than over the water [Curry, M., "Yacht Racing," Scribner's, New York, 1948, p. 130]. For this reason, velocity observations made over land should not necessarily be taken as applying over water. However, even though it is known that they do not apply, it has been necessary to make some use of data taken over the land. Based on available sources, Hsted in the next paragraph, the graphs of Fig. 54.A have been prepared. Briefly:

which could be

evaluated only with difficulty in actual practice.

275

above the sea. Hay found that the local velocity U at any height h above the quiet water surface (represented by the symbol z in the paper) varied generally in accordance with the logarithmic formula (1.64 ft to 26.248 ft)

The

I.

solid-line

graph

A

is

based upon a com-

(c) and (e) of which follows II. The short-dash graph B at the left represents values derived from Eq. (54.1), based upon a wind velocity of 1 (unity) at 6 ft above the water

bination of data from references

the

list

appears to represent the probable rate over a reasonably smooth water surface as well, if not better, than most of the experimental data. III. The long-dash graph C at the right of the level. It

of variation

figure represents the

the following

list,

mean

of the data

indicated

from

(b) of

by the small open

circles.

classified) of

Defense Ministry of Supply of Great Britain (copy in library) Unfortunately, however, the observations covered a range of only 0.5 to 8 meters

TMB

.

The (a)

references consulted were:

Schoeneich,

(The

"Der Windwiderstand

Wind

Schiffbau, 22

Resistance

Nov

of

bei

Seeschififen

Oceangoing

Ships),"

1911, Vol. XIII, pp. 121-129.

276

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 54.3

AIR AND WIND RESISTANCE OF SHIPS

Sec. 54.4

where /^wud

is tlie

wind

resistance, exerted

direction of ship motion,

^^

is

m

the (>DCAir)

the abovewater

277

—

tunnels, as well as data formerly expressed in

other units of measurement, called definitely for

non-dimensional wind-drag and wind-resistance formulas. On the basis that substantially all the its upper works is a pressure due to deflection and separation drags, the general equations for the wind drag D,^ with the latter always measured in the same direction as the

drag of a ship hull and effect,

,

relative wind-velocity vector

Dw =

W^

,

are

Here the mass density p(rho) is, from Sec. X3.8 m Appendix 3, taken as 0.002378 slugs per ft^,

for "standard" air conditions at a temperature

of 59

deg F, 15 deg C, and a sea-level pressure of

14.696 lb per in' or 2,116.2 lb per

The area

Ap^^j or

A^

is

ft'.

that of the abovewater

silhouette of the hull or structure in question,

when

projected on a vertical plane normal to the

direction of the relative wind.

wind

The

velocity of that

W^

.For rough calculations it is assumed constant over the whole vertical span of the abovewater structure being blown upon. For more refined estimates the structure should probably be considered as composed of two or more vertical layers, each \vith its own relativewind velocity, dependent upon its average height above the water surface, employing the windis

velocity multiples of Fig. 54. A. In addition, each

Cfl(A,„|4p,„iF«^

layer should be composed of a typical kind of (54. iv)

=

(54 .v)

A^W^

silhouette area of the ship (defined in Sec. 26.15),

as viewed from astern, and Wg is the relative wind velocity, derived from the vectorial addition of the ship speed V and the true-wind velocity WtFor what was supposed to be the worst case, the true mnd was in those years assumed to be always from ahead. The necessity for using data derived from aeronautical studies, many of them in \vind

D,

Cnui.^

7,

A^W^

Fig. 54. B

structure, such as (1) hull, (2)

spars and rigging, so that

upper works, and

if appropriate a separate drag coefficient as well as a separate average relative-wind velocity W^ may be used

(3)

Typical Wind-Resistance Model

HYDRODYNAMICS

278

with each. G.

method

omy"

Baker iUustrates and uses this book "Ship Efficiency and Econ-

S.

in his

[1942, pp. 14-16],

but for a slightly different

purpose.

In

IN SHIP DESIGN

air,

the relative-wind velocity

W^

is

that caused by the motion of the ship itself through the water, so that r = V. The still-air resistance is then

W

UsA —

C/D(Air)o^'l

'

(54 .vi)

(2)

Made double,

symmetrical about the designed

embod3ang two abovewater are then towed submerged

ABC ship designed in Part 4 it is estimated as about 2.6 per cent of the bare-hull water resistance. Although it is not general practice to allow for the

ship-powering

in

resistance

estimates,

always with the ship, so to speak, unless the latter happens to run in a following natural wind having a velocity equal to its own this resistance is

coefficient

Cd( Air)

now

available for the estima-

wind resistance of the hull and upper works of a ship of any size and type are derived almost exclusively from tests of special windtion of the

resistance models,

similar to

that pictured in

These have been run in water and in air, sometimes in both. Despite the limitations in scope of the book imposed in Sec. 1.5 of the Introduction to Volume I, a few notes are given here concerning the rather unusual techniques employed with these models. When making tests with abovewater models to determine wind-drag coefficients, the models Fig. 54. B.

which

circulating-water channel.

When

the

test

is

conducted by procedure

look up from underneath and

watch the position and action of tufts attached to the abovewater hull and the upperworks. This is also possible in a wind tunnel but streamers of dye and ink injected into the slow-moving water of the channel show the flow to much better advantage than jets of gas or smoke injected into the fast-moving air of the wind tunnel. There is little to represent boundary-layer development over the full-scale water surface under these conditions, causing a natural variation with vertical distance, because the

of velocity

mounting board For a relative wind compounded of ship motion and an ahead wind of gale force, the wind resistance can form a large percentage of the water resistance. For the second example of Sec. 54.10, assuming an ABC ship speed of 18.5 kt and a strong breeze of only 23 kt (true velocity), the wind resistance is 10.8 per cent of the barehull hydrodynamic resistance at that speed. 54.5 Notes on Wind-Resistance Models and Testing Techniques. The values of wind-drag

hulls

(3) Mounted on the under surface of a flat platform and suspended, in inverted position, in a

(3) it is possible to

magnitude of this resistance, E. F. As Eggert estimates it as from 2 to 4 per cent of the water resistance [TMB Rep. 264, Aug 1930, p. 1]. The first example of Sec. 54.10 indicates that for for the

model

at any bearing from right ahead to right astern.

waterline,

still

still-air

Sec. 54.5

to represent relative ^vind impinging on the

is

only several times as large as

the planform area of the model. For the model test,

therefore, the water (or wind) velocity is

nearly constant over

all

parts of the model, from

the lower part of the abovewater hull to the

mast

trucks.

B illustrates what is known as a drawingroom model of a destroyer but it shows well the amount of detail which is customarily reproduced on wind-resistance models. The mounting board shown there is greatly enlarged for a windFig. 54.

resistance test in water.

The experimental techniques developed to date do not simulate fully the actual ship conditions. This is not surprising because the full-scale conditions are not yet adequately known. However, the wind drags are usually not-too-large fractions of the total resistance to motion, and the available data appear to serve well for estimating

purposes in the preliminary-design

stage and for analysis and reduction of full-scale trial data.

54.6

Tests.

Bibliography of

There

is

Model Wind-Resistance

given hereunder a partial

list

of

are:

published data relating to model \vind-resistance

(1) Mounted on the under side of a flat board or platform representing the water surface, and then towed inverted in a model basin. The under

tests.

surface of the board

is

with the model upside board, with the model,

held at the water surface,

down

in the water.

The

may be oriented in azimuth

Other data undoubtedly exist but they have not yet been collected. In addition, the list contains references embodying shipboard observations on air drag and wind resistance and other references describing the use of these data in

analyzing ship

trials.

The

list

follows:

AIR

Sec. 5-1.7

AND WIND RESISTANCE OF

"Experiments on the Froude," SNAME, 1911, Vol. 19, pp. 114-115 Schoeneich, "Der Windwiderstand bei Seesohiffen (The Wind Resistance of Oceangoing Ships)," Schiffbau, 22 Nov 1911, pp. 121-129 McEntee, W., "Notes from the Model Basin," SNAME, 1916, Vol. 24, p. 86, and Pis. 70, 71 Smith, W. W., "Effect of Wind and Fouling Resistances on the U. S. S. Neptune," SNAME, 1917, Vol. 25, pp. 41-69 Biles, H. J. R., "Notes on the Effect of Wind on Power and Speed," INA, 1927, Vol. LXIX, pp. 164-173 Kempf, G., and Sottorf, W., "Probefahrtsmessungen (Ship-Trial Measurements)," WRH, 22 Jun 1928, pp. 232-236 Hughes, G., "Model Experiments on the Wind Peabody,

H.,

C.

Aug

Resistance of Ships," Engineering, 8 p.

(22)

Kent,

J. G.,

San Leandro,

Wind on Ship Trials,"

EMB Rep. 264,

Aug 1930

Room Model

"Test of Drawing

of 10,000-Ton Light

Cruisers (Pensacola and Salt Lake City, CL24, 25) in

Water

EMB

to Determine Forces Rep. 276, Dec 1930

"Test of Drawing

Room Model

Due

to

Wind,"

"Sea Trials on a 9,500-ton Deadweight Motor Cargo Liner," joint INA-IME (Institute Marine Engineers) mtg., 5 Apr 1955; abstracted

S.,

"Trial Analysis Methods,"

SNAME,

1932, Vol. 40, pp. 17-44

Baker, G. S., "Ship Design, Resistance, and Screw Propulsion," 1933, Vol. I, pp. 213-221 Hughes, G., "The Effect of Wind on Ship Performance," INA, 1933, Vol. 75, pp. 97-121 and Pis.

VIII-X "Test of Model of U. S. S. Salinas Inverted in Water to Determine Forces Due to Wind," TMB Rep. 345, Jan 1933 Stevens, E. A.,

"Wind

SBMEB,

in

Jul 1955, p. 434.

the adverse effects

that

depended

upon

other words,

in

the

ASNE,

Feb.

SBSR, 2 Apr

1936,

Resistance,"

1936, pp. 19-31; abstracted in

pp. 408-409 Eshbach, O. W., "Handbook of Engineering Fundamentals," 1st ed., 1936, pp. 9-64 through 9-69,

ratio;

craft

was

W. Lap, in a published lecture on ship resistance, quotes extensively from Report 1 of the Japanese Shipbuilding Research Assn., 1954, in a discussion of the air resistances of ships

structures [Int.

and

their super-

Shipbldg. Prog., Sep 1955, Vol.

No. 25, pp. 509-513]

(25) Richter, E., "Strommgsgiinstige

Formen von

Schiffs-

aufbauten (Flow Around the Most Favorable Form of Ship Superstructures)," Schiff und Hafen, Jun 1955, pp. 351-356.

In addition to the tests on the wind-resistance

models

of the ships hsted in the foregoing refer-

ences and on Figs. 54. C, 54. D, and 54.E of Sec. 54.9, it is reported that tests have been made on

models of several large tankers and (1955)

it

Up

54.7

Drag

Coefficients for Typical

resistance; in a 30-kt

head wind as only

0.08 of the total.

Nolan, R. W., "Design of Stacks to Minimize Smoke Nuisance," SNAME, 1946, Vol. 54, pp. 42-82

Abovewater

to the dimensional form,

D^ = kA^W^ When Dw

is

in lb,

^a

is

in

ft^,

(54.vii)

and

Wg

in kt,

the value of k varies from 0.003 to 0.0056, for a relative-wind velocity from directly ahead. A

round value for k, easily remembered, is 0.004. R. Ellis quotes a dimensional coefficient k of 0.0055 for determining the wind drag of a moored, cruising-type sailing yacht, based upon wind

A^

resistance as only 0.02 of the total hydro-

writing

Hulls and Upper Works. Modifying Eq. (54.iii) of Sec. 54.4 by applying it to the wind drag rather than the wind resistance, and adhering

hurricanes.

have reduced the wind resistance only by the ratio of 0.17 to 0.12. Further, they estimate the

of several of

present these data.

sectional area

streamlining on the Lusitania would

to the date

has not been possible to locate and to

velocities in

dynamic

power-displacement

(24) A. J.

"The Transatlantic Liner of the Future," IME, 14 Dec 1937; abstracted in SBSR, 30 Dec 1937, pp. 811-818, esp. pp. 813, 817. The authors estimate that

still-air

The author found wind and weather

upon how hard the

covering wind pressure on structures Malglaive, P. de, and Hardy, A. C.,

maximum

of

being driven.

of U. S.

TMB

A.

Ships,"

of

floating drydocks.

Destroyer Hamilton in Water to Determine Forces due to Wind," Rep. 312, Oct 1931 Schoenherr, K. E., "On the Analysis of Ship Trial Data," SNAME, 1931, Vol. 39, pp. 281-301 Pitre,

Seakindly

of

Vol. 66, Part 8, pp. 417-442

the cargo vessel Pacific

Trader, and the liner Mauretania (old). Effect of

1948, pp. 24-26, 69

"The Design

L.,

and Koning,

(23) Aertssen, G.,

3,

of the tanker

RPSS,

J.

279 P. A., Troost, L.,

NECI, 1949-1950, and D159-D174

184

"The

(20)

Van Lammeren, W.

1930,

Hughes, G., "Model Experiments on Wind Resistance of Ships," INA, 1930, Vol. LXXII, pp. 310-329 and Pis. XXXIII-XXXVI. This paper gives the results of wind-tunnel tests on abovewater models

SHIPS

(21)

beam and

He

reckons the cross-

as the product of the

maximum

the height of the cabin top above

water [Yachting, Jun 1955, p. 60]. However, EUis uses a wind velocity in mph; replacing this with a wind velocity in kt, the dimensional coefficient k should be increased by the factor (1.15)^ or 1.3225. The coefficient k then becomes (0.0055) (1.3225) or 0.00727.

When and

Wr

D^r of Eq.

(54.vii) is in kg,

Aa

is

in

m^

in meters per sec, k is of the order of

HYDRODYNAMICS

280

0.045 to 0.063 for ship superstructures only [van

Lammeren, W. P. RPSS, 1948,

J. G.,

A., Troo.st, L.,

and Koning,

p. 69].

On

the basis of the foregoing, tests with abovewater models towed upside down in basins give

a 0-dinil drag coefficient CccAir) of the order of 0.85 to 1.2 or more; This agrees well with values for short, blunt-ended, 3-diml bodies [S

and P,

IN SHIP DESIGN

Sec. 54.8

the high portions of the ranges listed previously in this section.

Table 54. a presents a number of dimensional wind-drag coefficients, taken from the material referenced there. In every case, so far as known, the coefficients given apply to mnd forces generated by a relative wind of incident velocity Wb blowing from directly ahead, where the ,

1943, pp. 52, 159-160; RPSS, 1948, pp. 25, 69]. When the deck erections and upper works are

relative-wind bearing angle e(theta)

not yet laid out, or are known only sketchily, it is possible to approximate the projected area of the abovewater silho\iette, as seen from directly

account, and

ahead, by E. t. Eggert's formula,

Aa=

(0.5)B1:

.

This assumes an average maximum effective height, above the water, of half the beam Bx For the ABC ship of Part 4, mth its tentative beam of 73 ft, the projected area by this rule works out as (0.5) (73)' = 2,665 ft'. For a passenger-cargo ship it is probably on the small side.

When are

the mass density of the air

dimensional

taken into

measurement and the

consistent units of

the

used,

deg.

is is

formula

coefficients listed in

Table

values for

the 0-diml formula

Cfl(Air) in

Dnr

—

ClXAir)

54. a give

cf

a range of

-^AryR

(54. iv)

which vary from 0.974 to 1.505. These are to be compared with the C^'s for flat plates of various aspect ratios, placed normal to the stream, which

When

The method of using the projected or silhouette area as the basis for the wind-resistance estimate, especially with the relative wind directly ahead,

are fisted in

open to some objection because it takes no account of the fore-and-aft positioii of the parts of this silhouette with respect to each other. A large deckhouse right forward, close to the bow and in the lee of the updrafts from the blunt bow, as on large Great Lakes freighters, probably causes less wind resistance than the same deckhouse farther aft. Further, on a large tanker, the forward house may be so far from the forecastle, and the after house so far from the forward house, that the shielding offered by each on the one astern is negligible, even with a relative Avind from right ahead. Vessels with large fore-and-aft gaps or separations between major transverse

of this section, is converted for use in the 0-diml

is

k

TABLE

54.a

wind, and

Wr

is

in

Group

area Aa [SEE, 1942, pp. 14-16). Non-Dimensional Values of 0^,(^1 r)

fc

beginning

Eq. (54. iv), the value of C^xAir) works out as about 1.18. 54.8 Comments Concerning Wind-Friction Resistance of an Abovewater Hull. In Sec. 54.4 it is

assumed that, because of the irregular shape abovewater portion of a ship, its wind drag

of the

all pressure drag, varying as W^ This is probably true for the general case, where the relative A\dnd may blow from any bearmg relative

is

.

to the ship.

With the

wind nearly ahead, a ship upper works, resembles somewhat a train of streamhned cars behind a relative

hull proper, excluding the

streamlined locomotive. In both cases the sur-

,

S.

fc

listed at the

where fiwind is in lb, Aji is in ft^, projected normal to the tlie formula R^/iad = kA^W^ Unless otherwise stated Wr is directly ahead. 0.004 and Aa if not known, is taken as (Sx)V2 [EMB Rep. 264, Aug 1930, p. 2] 0.004 [S and P, 194.3, pp. 51-52]

Baker, G.

k

employing units as

let.

=

W.

Chapman, C. F. Chapman, C. F.

the coefficient

Approximate Wind-Drag Coefficients for Various Types of Ships

Barnaby, K. C. k

Taylor, D.

k

55.B.

of k.

= = = = =

Eggert, E. F.

Fig.

0.004 of the dimensional wind-drag Eq.

(54.vii),-

areas therefore call for the use of coefficients in

Group I. Dimensional Values The values of k pertain to

=

,

0.00454 for an anchored motorboat [SSBH, 1951] 0.0051 for an anchored sailboat, measuring Aa to top of deckhouse [SSBH, 1951] 0.004 but A^ is determined by adding to the projected area of the superstructure and upper works

a diminished projected area of the hull proper, equal to that projected area times 0.45 (Cb) [BNA,

II.

See the text.

fc

1948, Art. 163, pp. 192-193] 0.0033 for an Atlantic liner and 0.004 for a cargo vessel, combined with a reduction factor which calls for using only about 0.3 of the actual projected hull area when computing the overall projected

AIR AND WIND RESISTANCE OF

Sec. 54.9

faces in contact with the air are large

many and

and

long,

of the contours are reasonably uniform,

friction

drag

no longer

is

StIIPS

281

-Tanker SALINAS -Carcjo Ship CLAIRTON -Passenger Ship 5ANTA

negligible. If the

R05A ^

frontal area of such a ship hull is taken as equal or even to the maximum underwater ai'ea Ax ,

as B{H), with an

L/B

abovewater area

of the

ratio of say 7, the

smooth

= 2{7B)H =

the order of 2L{H)

"wetted"

side portions is of

14B(i7). This

proportion of wetted to frontal area is about the same as for a railway coach. Unfortunately, a

reasonably accurate prediction of the friction

drag for the coach must await more knowledge as to the actual air flow around it [Hoerner, S. F.,

AD,

1951, pp. 169-170]; the

same

is

true of the

ship hull.

54.9 Drag and Resistance with Wind on the Bow. For the reasons explained in Sec. 26.15 and illustrated in Fig. 26.1 of Volume I, the relative wind blowing at an angle on the bow

impinges separately on d-eck erections, stacks, and certain other elements of the upper works

which normally benefit from shadowng when the relative wind is dead ahead or nearly so. Furthermore, a ship hull, lying at an effective angle of attack to the relative wind and acting as a shortspan airfoil, cantilevered above the water surface, is creating an induced drag as well as the lift depicted in diagram C of Fig. 26. H. This induced drag, although not

shown

there, is additional to

measured as part of the wind drag and wind resistance when model tests are made, and is included in the coefficients set the pressure drag. It

is

forth in this chapter.

As a lift

result,

and drag

velocity

the

bow

Wr

the axial component Rwi„d of the forces due to the relative-wind

at a range of relative-wind angles on

usually exceeds the value of the wind

resistance i2wind directly ahead.

when the The ratio 6,

is

from

Then for any measured toward the

pressed for convenience as kg

angle of relative wind

wind

relative

of these forces is ex.

from ahead, /2wind = kgDw when D^r measured at 6 = deg. This is equivalent to right

,

jRwind at angle d

The

rates at

=

fc9(i2wind at

which the

deg)

coefficient kn

is

(54.viii)

vary with

the direction of the relative wind for several ships of different types are illustrated in Figs.

54.C, 54. D, and 54. E.

Two

similar graphs, one

for a cargo vessel with forecastle, centercastle,

and poop, and the other for a passenger ship, are given by W. P. A. van Lammeren, L. Troost, and J. G. Koning [RPSS, 1948, Fig. 8, p. 25].

10

20

Angle Fig. 54. C

30 40

of Relative

Graphs of

50 60 70^-80 90 Wind f rom Aheod, deg kg

for Three Merchant Ships

Anqle of Relative Wind from Aheod, deq O 10 20 50 40 50 60 70 80 96

HYDRODYNAMICS

282

Anqle of Relative Wind from Ahead, deq 10 20 30 40 50 60 10 80 90,

^

*•

-^

1.5

O 1.4

-s

"?

1.3

> Q^

I.Z

o ^^

'•'

"^

1.0

for a Typical

Cruiser PENSACOLA (CLZ4)

0.9 -S

0.8

1

01

az

0.6

8

speed of 20.5

kt.

area

Aa\s

by Eggert's

(0.5)Bx

taken,

With a beam

•

=

0.5(73)'

2,665

transverse abovewater rule of

of 73

ft,

thumb, as becomes

Aa

The dimensional Eq.

ft'.

and k is taken no true or natural wind blomng, W^ is equal to V, and there is no variation of wind velocity with height, due to (54.vii) is

used for a

first

estimate,

as 0.004. Also, since there

boundary-layer

RsA =

effect.

DjfT for this

= kA^Ws = Assuming a the

still-air

The

0.0263.

is

Then

case

0.004(2,665) (20.5)'

=

4,4801b.

hydrodynamic resistance Rt for from Chap. 66, as about 170,000

total

the bare hull, lb,

o 0.5:?

be approximated for the

The

trial


Heavv^

Sec. 54.10

stUl-air resistance is to

.6

iota

IN SHIP DESIGN

resistance ratio

bare-hull

Rr

is

4,480/170,000

value

is

=

used so that

may be added as a percentage, appendage resistance, to predict

the stUl-air drag

Kke the

overall

the probable total trial resistance.

tn

W

0.4 '^

consider

the

relative-Avind

resistance

=

3:

deg (^\'ind ahead), the ship speed at sea is 18.5 kt, and the true wind velocity is 23 kt. The relative-mnd speed is then (18.5 + 23) = 41.5

'S

kt.

-a

0.3 .E 0.2

Next,

when

0.1

Hence

~

i2wiod

= kA^W^ =

0.004(2,665)(41.5)'

a

= 10

20

30 40 50 60 70 60 90 Wind from Ahead, deg

18,360

lb.

This represents a resistance augment, over that trial speed of 20.5 kt, of (100) (18,360/170,000) or 10.8 per cent. It would be a much larger proportion of the total

/'^ngle of Relative

estimated for the bare hull at the Fig. 54. E

Gr.\ph of

kg

for a Heavy Cruiser

Three additional graphs are given by G. Hughes for a tanker, a cargo vessel, and a transatlantic liner [INA, 1930, pp. 321-324 and PL XXXVI]. These graphs are reproduced in SNAME, 1932, Fig. 14, p. 41. Additional graphs for an express cargo hner are given by G. Kempf in Fig. 7 on page 51 of this reference. A graph for the U. S. Maritime Administration Mariner class is published by V. L. Russo and E. K. Sullivan in SNAME, 1953, Fig. 45, page 212. 54.10

ABC

Prediction

Ship of Part

4.

of

Wind

Resistance

As examples

by which the formulas and data sections are

employed

wind resistances Part

4,

of the

for

method

of the preceding

in practice, the probable

of the

ABC

ship, designed in

are calculated for several design stages

and conditions. It is assumed

first,

that at an early stage in the

preliminary design, before the abovewater body is

dra%vn and the upper works are laid out, the

resistance at the 18.5-kt smooth-water ship speed of the

problem given.

As a third approximation it mate the \\dnd resistance of the

is

desired to esti-

ABC ship,

having abovewater hull and upper works of the general form shown in Figs. 66.0, 66. S, and 68. M, when conducting a full-speed run during standardization over the measured mile. Assume that the measured speed is 20.4 kt for a particular run, that the amemometer on top of the after pair of kingposts reads 41.5 kt, and that the Avind direction indicator gives an angle of 22 deg on the port bow. The latter two readings are both for the relative wind, so

it is

ship

is

not really necessary to know how fast the gouig through the water to predict the

wind resistance to be encountered. From the dimensions on Fig. 54. F, corresponding to those on the three dra^vings mentioned, the silhouette area, looking from ahead, is estimated to be about 3,880 ft'. This is nearly half

AIR AND WIND RESISTANCE OF SHIPS

Sec. 54.11

Silhouette from Calculated Lateral Area

of

Fig. 54.F

Abovewater Form, 20,167 sq

Abeam,

Correspondincj

to

Layout

in

Fiq,

68.M

ft

Wind-Resistance and Cbnteb-of-Pressube Layout for the

Aa = (0.5)5i value originTo keep the problem simple it is assumed

ABC

Ship of Part 4

again as large as the

more than its rated maximum power

ally used.

whether the ship could make 20.4 kt on the trial course against a 41.5-kt relative wind on the bow.

that the relative-wind velocity over is

all this

area

the same, eliminating any boundary-layer effect.

The value

of kg is

taken from the Santa Rosa

short-dash curve of Fig. 54. C, for 6 as approximately 1.15. Then, for Wr

Eq.

22 deg, 41.5 kt,

(54.viii) gives

2?wud

= {ke)KAA)Wl =

From

Pe

= =

(1.15)(0.004)(3,880)(41.5)'

=

30,739

Fig. 78. Nc of Part 4, the effective

for the transom-stern design of

predicted from model tests,

For the water speed

is

lb.

power

ABC

ship,

about 9,940 horses.

of 20.4 kt, equivalent to

Rt with appendages, works out as 9,940(550)/34.45 = 158,694 lb. The predicted wind resistance then 34.45 ft per sec, the total resistance

,

54.11

Magnitude

of

Wind

it is

doubtful

Pressure.

It

is

magnitude of the forces exerted by a natural wind on a flat plate or a flat surface normal to the wind direction. A number of authors have given tabulated data of this kind in the past, among them Dixon Kemp ["A Manual of Yacht and Boat Sailing," Cox, London, 3rd ed., 1882, p. 599, on which there is a table of wind-pressure intensity]. His values of normal pressure in lb per ft^, for a range of wind helpful at times to have

velocity of

1

to

an idea

of the

100 kt, corresponding to the

complete range of the Beaufort scale from 1 to 12, were based upon a constant drag coefficient Cd of 1.87. It is now known that this drag coeflacient varies from about 1.16 for a square plate

resistance at 20.4 kt of (100)(30,739)/158,694 or

with free edges to about 1.90 for an infinitely long strip, also with free edges. The figures iia Table 54.b are adapted from a

19.4 per cent. Unless the machinery could develop

table published

represents an increase in

the estimated

total

more recently by K. C. Barnaby

HYDRODYNAMICS

284

TABLE

54. b

IN SHIP DESIGN

Sec. 54.12

Nominal Force, Velocity, and Pressure Due to Natural Winds

The ram pressures are based on a p-value of 0.002378 slugs per ft'. The flat-plate pressures are based on a thin plate mounted in the open, with a separation zone on its leeward side. Column 5 is calculated for a Co of 1.16; column 6 for a Cd of 1.90. The vAnd. velocities correspond exactly to the Beaufort-scale numbers pubUshed in "Instructions for Keeping Ship's Deck Log," NavPers 15876 of July 1955, Bureau of Naval Persoimel, U. S. Navy Department.

1

AIR AND WIND RESISTANCE OE SHIPS

Sec. 54.14

285

wind-resistance load of 22.6 long tons for a large

with multiple derricks. of the dimensional drag coefficient for

collier

The value

a broadside relative wind

0,50

wind or

as for an end-on

very nearly as large having a

is

for a flat plate

0.45

length ecjual to that of the ship and a depth of

0.40

twice the ship height (including the mirror image below the water surface). However, tests on models indicate a somewhat smaller drag co-

0.55

broadside presentation.

efficient for the

For a dimensional expression

0,30

D,

0,25

of the

form

ksA,,W^

(54.viia)

Data Token from

EMB Rep.- 276 EMB Rep. 512 EMB Rep. 334 EMB Rep 345

020

5

-1

0.15

EMB

r

Rep 562

for

FENSACOLA

for

HAMILTON CLAIRTON 5AL1NA5 3ANTA ROSA

for

for for

the dimensional coefficient ks for 6 = 90 deg has values ranging from 0.003 to 0.0042. In their analysis,

Fig. 54.

G

Theoretically,

50 60 30 40 Wind from Centerline

of

Farrell

of 0.004.

make an

estimate of the

I

mnd 10 20 of Relative

Thorpe and

for practice,

It is interesting to

of the Model Tested

Anqle6

and

recommend a kg

Each Report Contains a Photoqroph

0.10

70 80 90 Ship Aheod,decj

m Fig.

54. F

mnd. The

Centee-of-Wind-Pkessure Data fob Five Typical Ships = all graph values should be zero when

ABC

drag exerted on the

when

ship of diagram 3

lying beam-to in a 60-kt storm

silhouette area for 6

=

90 deg and for

the ship at designed draft, estimated from Fig.

68.M and from diagram

3 of Fig. 54.F,

is

20,167

For a /c-value of 0.0042, the maximum quoted by T. Thorpe and K. P. Farrell in Sec. 54.13, the lateral wind drag is ft^

models of the

five ships listed in the

graphs of

and 54. E. Schematic wind-drag force vectors for a few representative relativewind directions are indicated on diagram 2 of Fig. 54. F. G. Hughes gives center-of -pressure data for three aboveAvater models tested m a Avind tunnel [INA, 1930, p. 321 and Fig. 2 on PI. XXXV; Figs. 54. C, 54.D,

INA,

1933,

from 54.13

PL

VIII, Fig.

4],

for values' of

d

Wind Drag.

Ships underway

are often subjected to strong relative \vinds from

abeam, at an angle d of approximately 90 deg, measured from ahead. Vessels anchored and at moorings, lying to the tide or moored at both ends in assigned positions, are subject to cross winds. Moreover, vessels often have to be berthed and unberthed when the true wind is about at right angles to their axes. The wind resistance under these conditions is nearly zero, but the wind drag may be very large. The most extensive and probably the most rehable data as to lateral wind drag appear to be those of T. Thorpe and K. P. Farrell [INA, 1948, pp. 116-117]. These list transverse winddrag loads for a wind velocity of 60 kt as ranging from 37.5 long tons for a large battleship to 7.85 long tons for a frigate or escort vessel.

Smith, in reference

= This

is

304,925

(4)

of Sec. 54.6,

W. W.

mentions a

0.0042(20, 167)(60)'

lb.

almost twice the ahead hydrodynamic

resistance at the designed speed, as predicted

Under

the model test.

to 180 deg.

Lateral

Dw = keA^Wi =

would,

if left

to

itself,

by

this lateral force the ship

heel

and

drift

downward,

as described in subsequent sections.

54.14

Heel.

Lateral It is

Wind Moments and Angle

of

unfortunately possible for certain

craft, especially

when

m

a light or nearly light

wind about abeam, moment which exceeds the righting moment. The craft then capsizes. This can happen in areas of relatively smooth water, if a vessel is struck by a sudden high-velocity squall. In areas where waves already exist, the menace is obviously greater if the ship is perched broadside on a high wave condition, with the relative

to be subjected to a wind-drag

Avith

crest,

a diminished metacentric stability,

at the instant that

it

experiences the

maximum

force of the squall.

to beam winds on about an axis in the waterplane, be estimated by using a 0-diml formula

The

heeling

moment due

full-scale vessels,

may

HYDRODYNAMICS

286

IN SHIP DESIGN

Sec. 54.15

where Ck is the 0-diml heeling moment coefficient due to wind ^A is the abovewater area for 5 = 90 deg, projected on the plane of symmetry, with the

As an indication of the values to be expected under violent beam winds, a model of the World War I Eagle class patrol boats was floated in a shallow pan of water in a wind tunnel, where it was blown upon at various relative-Avind bearings 6 from 30 deg (on the bow) to 150 deg (on the quarter). The scale ratio was 48, the weight of 480 t, and corresponded to the designed ship

vessel upright

the full-scale

developed by the Bureau of Ships of the U, Navy Department. It is

K

hx

=

C;c(0.5p).4^/u(cos=

(54.ix)

the height above the waterplane of the

is

center of the area 0(phi)

Wjt

^)Wl

S.

is

is

A a mth

the relative-^vind velocity, assumed as

value

a

give

of

the

product

Ck(0.5p) of about 0.00147, from which 0.00147/(0.001189) = 1.236. Entering the

Ck = known

assumed values for a given situation, and assuming successive values of heel angle <^, increasing by 10 deg up to as great a range as desired, a curve of heeling moment on a basis of heel angle is plotted for a given wind velocity. Comparing this with the curve of righting or

moments

in stUl water, the intersection gives the

angle to which a ship will heel under the wind effect.

Assuming a given maximum or allowable

angle of heel, the righting

may

X

be set down as

moment

in Eq.

and the

This procedure is in the nature of a rough approximation because, like the example of the preceding section, it assumes a constant wind velocity over the whole lateral abovewater area.

Further,

takes no account of second-order

it

such as the downwind motion of the ship

by the wind, or away from the wind. For a sudden squall, it takes no account of the kinetic rolling energy in the ship when it due to the

lateral force exerted

the fact that the ship

is

heeling

reaches the nominal angle of equilibrium, which

means that the ship would heel beyond the equihbrium angle. However, L. Gagnatto, as the result of a more rigorous analysis [ATM A, 1929, Vol. 33, pp. 53-74], finds that the rigorous method gives a

maximum

angle of heel sensibly less than

that derived from the approximate method. further analysis

was

carried out

and reported a few years

later

A

by Guntzberger

[ATM A,

1934,

Vol. 38, pp. 341-355].

E. A. Wright has published a photograph, with accompanying notes, of a destroyer model undergoing a wind-resistance test (in a wind tunnel)

when

heeled

[SNAME,

At a

simulated in the tests was

This corresponded to (1.012/26.23)5 or

The dimensions and

SNAME RD

full-scale

lines of the vessel

sheet 118.

wind velocity corresponding to

uncommon maximum angle

100 mph, 86.84 kt, by no means

in

hurricanes and typhoons, the

of

heel

was over 37

deg. Surprisingly, this occurred

bow 130 deg away from the wind. The next greatest heel, 35 deg, was encountered with the bow 70 deg from the wind. With the wind abeam, or at bearings of 50 and 110 deg, the heel with the

was

less

deg,

than 33 deg. The smallest

occurred

when the bow was

heels,

150 deg from the relative-wind direction

Rep.

An

20-22

either 30 or

[EMB

15, Jul 1920].

interesting

passage

from

this

report

is

quoted as follows:

for that angle

(54. ix)

corresponding wind velocity be found.

effects

ft.

are found on

the angle of heel

tests

1.012

0.039S.

the vessel upright

directed abeam.

Model

W

GM

1946, Fig. 25, p. 393].

"3. The center of lateral resistance was previously determined by towing a larger but similar model of (an) Eagle boat sidewise and was found to be substantially at the

water surface."

Estimated Drift and Leeway. It is advance, just how fast a ship, mthout power and under given weather conditions, may be expected to drift under the action of wind alone. This is principally because ships vary in their attitudes to the wind when 54.15

difficult to estimate, in

drifting, so the relative position of the ship axis

and the wind direction must generally be assumed. Granted that the ship drifts broadside to the wind, and that it is of normal form, a reasonable value of the 0-diml water-drag coefficient of its underwater body is 1.15. This is derived by

assuming an actual

L/H

ratio

of 20,

but an

low speeds the ship behaves essentially as would its underwater hull, plus a superposed mirror image, drifting downwind in infinitely deep water. At these low speeds the effect of waves resulting from the broadside

effective ratio of 10, since at

motion can be neglected. The drag coefficient Cd of a flat plate of these proportions is, from Fig. 55.B, about 1.5, but the ship has few sharp edges like the thin plate, especially under the

AIR AND WIND RESISTANCE OF SHIPS

Sec. 54.17

287

bottom. In any case, too high a value of Co for the lateral water resistance represents an unsafe

operating propulsion device (s) due to the current flowing by them.

downwind

A ship with a normal proportion of its total bulk volume under water usually rides to the

estimate, since the calculated rate of

then smaller than

drift is

The

resistance to drift

found on the ship. may be expressed by is

current rather than to the wind. This means

may blow at any bearing relative and that the greatest drag due to both current and wind may be expected when the ship is riding head to the current, with the wind about 30 deg on either bow. T. Thorpe and K. P. that the wind

(54.x)

The

force causing drift

the wind drag of the

is

Wr

ship at the relative wind velocity

,

expressed

by

to the ship,

Farrell, in the reference cited,

emphasize the effect because the wind drag varies as the square of the maximum instantaneous of gusts

D^ =

C^(Air>(0.5p^)4^Tf„'

(54.iv)

and

assuming that

velocity,

The

wind force

lateral

equation,

latter

substituted

FDri.t

is

the

for

lateral

Eq. (54.x), and this then solved for the drifting speed

resistance to drift

equation

calculated from the

is

Rorut

of

.

the abovewater lateral projected area A a assumed equal to the underwater lateral area A and Co for wind drag is taken as 1.18, then for equal wind and drift drags If

is

I,

it

blows with this aug-

mented velocity on the whole ship at once. Wind-drag forces on groups of moored ships, lying alongside each other, are given by M. E. Long in TMB Report R-332 of December 1945, entitled "Wind Tunnel Tests to Determine Air Loads on Multiple-Ship Moorings for Destroyers of the

DD692

The naval

Class."

architect will require drag data on

,

moored

vessels only infrequently.

therefore (1.18)

I

(for air) TF^

=

(1.15)

(for water)(7Dri,t)'

|

54.17

FLift

1.18(0.001189)

TFi

1.15(0.99525)

=

be remembered downwind,

It is to

drifting

Wr = 54. 1 6

IFt.u,

that, since the ship is

F:,n,t.

Estimating the Forces on a

A

brief discussion of the forces

is

included in Sec. 12.8. It

Thorpe and K.

is

that a ship lying at a mooring

mentions that

when the

it

pointed out by T. is

1948, p.

116]

subject to forces

tidal current. Sec. 12.8

also subject to slope drag

ship rides at anchor in an appreciable

current, with the

To

is

M

cored Ship. on a moored ship

P. Farrell [INA,

due to wind, waves, and

moored end higher than the

free

the usual resistance forces derived from motion of the ship and the water there added the drag of the non-rotating or non-

end.

relative

attempt

is

Surf ace- Water Currents due to Natural

A

of drift and leeway in wind resistance in general, is not complete without some mention of the surfacewater currents produced by a natural wind blowing over a body of water. Some data are available to relate the magnitude of this current to the wind velocity but without the necessary information as to the height above the water surface at which the velocity is measured.

particular,

0.035

-

No

here to include, with or without

adaptation, any of the tables, graphs, or diagrams

Wind.

Wr

made

given in the references.

whence

is

squalls,

discussion

and

of

E. F. Eggert states that this surface current, presumably more-or-less uniform for the draft of a surface ship of moderate size, has a magnitude of 0.015 times the wind velocity [EMB Rep. 264, Aug 1930, p. 1, based on data furnished by the U. S. Coast and Geodetic Survey]. C. O'D. Iselin states that on the average the surface water moves at about 3 per cent of the wind velocity. This is twice the value just quoted. Further, Iselin

reports

that

the

surface-water

current

moves in a direction about 30 deg to the right the wind in the northern hemisphere (30 deg the

left

of

to

below the equator) ["Oceanography and

Naval Architecture," Jun 1954].

SNAME, New

Engl. Sect.,

CHAPTER

The

Calculation of

55.1

General

55.2 55 3

Scale-Effect Problems

55 4 .

55.5

55.6 55.7

55.1

GeneraL

Appendage Resistance

288 288

Customary Values and Proportions for Overall Ship Appendage Resistance Classification of Appendages by Predominant Type of Drag Lift, Drag, and Other Data for Typical Bodies Representing Appendages .... Allowances for Wake Velocities on Appendage Drag Shadowing AUowanoes for Appendages in

.

Chaps. 36 and 37

list

describe the use and effect of a considerable

Tandem

55 9 55. 10

The Drag of Exposed Rotating Shafts Drag Data for Holes, Slots, and Gaps

55 1 1 55.12

The Resistance

55 13

The Calculation

290

.

.

and

num-

of bare-hull resistance

and form.

The drags listed in (b) are determined separately by towing a model and removing the appendages one by one. This involves some experience and knowledge as to just how much of each type of appendage to reproduce to small

scale.

This

is

comphcated objects such as handrails, antennas, and fittings on submarine models. Screw propellers which are prevented from turning by casualty, or which are locked within

especially true of representations of

the ship for other reasons, constitute a special kind of appendage, at least as far as drag is concerned.

They

of

The Displacement

55.14

submerged geometric

size

.

.

Appendage Resistance

.

295

for

represent a special case of the

295 295

Submerged Vessels

292

appendages (b) Observed drag data for various ship appendages, generally from model tests

Ranges of percentage appendages of normal

294 294

'

"

bodies and shapes approximating those of the

(c)

293 293

... .

291

several sources of information:

for

for

Estimated Resistance of Discontinuities of Large Appendages Considered as Parts of the Ship

.

This

is

of

to determine the

Appendages

.

.

.

.

.

hydrodynamic loads on

the various parts of the appendage, so that these to

of

in

Abreast

288

parts

coefficients

Appendages

Modifications

found on many types of surface vessels of normal form. Within the space available, this chapter endeavors to furnish data by which the resistances of the most common of these appendages are estimated or calculated. This is possible from

Drag

292

Drag

55.8

ber of fixed and movable appendages, respectively,

(a)

55

may

meet

be made sufficiently strong and rigid

all service

requirements.

A great deal has been written in the technical literature about the problems of assessing or determining the Correct resistance of appendages when added to a towed or self-propelled model. An excellent resum^ covering all aspects of this situation in which the 55.2

Scale-Effect Problems.

ship designer

is

interested

Mandel [SNAME,

is

presented by P.

1953, pp. 493-495].

Despite

their efforts to solve the model-prediction problem,

the

techniques

and prediction procedures

various model-testing estabhshments

still

of

vary

rather widely.

The difficulty here is that almost all ship appendages are completely submerged, they do not make gravity waves, and hence dynamic similarity of flow is gauged by the Reynolds rather than by the Froude number. Only in exceptional cases, in model basins, can dynamic similarity on the i2„ basis be achieved while the test of the model as a whole is being conducted on a Froude-number basis. It may be assumed by the marine architect that, until these problems are resolved by the model-testing establishments, each one has good engineering reasons for

its

own

procedure. Its

predictions of appendage resistance

\vill,

in its

situation where the propeller rotates at other

own

than a thrust-producing rate, and as such are discussed in Part 5 of Volume III. There is a second engineering reason for calculating or predicting the resistance of appendages.

necessary, as indicated in the latter part of Sec.

meet the needs of the ship designer, the shipbuilder, and the ship owner. Customary Values and Proportions for 55.3 Overall Ship Appendage Resistance. It is often

288

opinion,

APPENnACE-RESISTANCE CALCULATIONS

Sec. 5y.3

TABLE The

55.a

289

Percentage Increases in Effective Power P^ to be Expected on Trials of Three Types of Ship

source of these data

is

given in the accompanying text.

Ship Type

HYDRODYNAMICS

290

Lammeren,

G. Koning [RPSS, They are reproduced in Table 55.a.

L. Troost,

1948, p. 69].

The graphs

of Fig. 55.

power Pe

effective

and

A

show the

for a large destroyer

individual percentages

An appendage

may

surface

and

Sec. 55.4

considered to add wetted

is

drag only

friction

if:

increases in

when

four types of appendage are added, one by one.

The

IN SHIP DESIGN

J.

be obtained by

the proper subtraction, on the basis that the

dimension

Its greatest

(a)

motion; in other words,

it

the direction of

lies in

has a low aspect ratio

Its surfaces lie in the general direction of flow

(b)

when the

ship motion

is

steady

Its thickness, as a fraction of its length in the

resistance effects of the four appendage types are

(c)

independent of each other.

direction of flow,

A

small or neghgible.

is

is an excellent example Both long and short bossings and large skegs are considered

roll-quenching keel

for all the foregoing. for propeller shafts

essentially as parts of the hull in that their wetted

added to that of the hull. Docking and resting keels are in the same category if their edges and endings are fair and they lie in the lines of flow. The friction drag R,, added by each is surfaces are

then proportional to

its

discussion of Sec. 22.9 of

there

is

wetted area

Volume

<S.

I indicates

The that

as yet no definite rule for assessing the

for these appendages, and for determining the Cf value for each. The appendage is presumed to add pressure drag only when one or more of the following

proper

72^

conditions obtain: 26

30 32 34 Ship Speed, kt

28 Tq

=

I46

36 To

38 =

40

1.98

Graphs Indicating Percentage Increments OF Babe-Hull Resistance for Four Series OF Appendages on a Destroyer

Fig. 55.A

dimension

across the flow,

(1)

Its greatest

and

has an appreciable or a high aspect ratio Its thickness, as a fraction of its length in the

(2)

direction of flow, (3)

lies

it

Its

is

about 0.1 or more

fore-and-aft

length

is

short,

say

not

exceeding 0.02 the length of the ship. If wake

The graphs at

least,

of Fig.

that

the

55.A indicate, for this model percentage additions vary

somewhat with the ship Table 55.b

lists

speed.

the percentage differences of

when a quadruple-screw run at three values of T, = V/ L, with all appendages, and when six series of appendages are removed, one by one. Again the percentage differences are found to vary somewhat with the speed. total bare-hull resistance

cruisei^

model

is

V

P.

Mandel

gives data on appendage resistance

velocities are neglected,

a whole. This

is

the appendage

55.4

Classification

dominant Type

of

Appendages by PreIt is customary to each ship appendage as

of

Drag.

treat the resistance of

predominantly friction or pressure drag. This avoids the complicated extrapolation method customarily used for the ship prediction.

R,, for

Diving planes, short skegs, rudder support horns, strut hubs, exposed shafts, guards, fixed

screw-propeller shrouding, and sound

A

adapted from the reference.

are always

than about 0.02i2„ for the ship. The arm of the strut for an exposed shaft is an example falUng within the limits of (1), (2), and (3).

types of ship, at three speed-length quotients is

;'(nu)

equivalent to saying that

among the appendages

1953, Table 8 on p. 494]. Table 55.c

and

is less

as a percentage of bare-hull resistance for five

[SNAME,

V

the same, for both the appendages and the ship as

domes are

causing pressure drag only.

forming a continuation of the ship may have its wetted area included in that of the main hull, with its drag assumed as entirely frictional. If separate from rudder,

if

hull or of a large skeg,

the hull, like an underhung spade rudder, resistance

is

its

usually reckoned as a pressure drag

W. P. A. van Lammeren, L. Troost, and G. Koning give 0-diml drag coefficients for seven types of rudders of varied section, all only.

J.

APPENDAGE-RESISTANCE CALCULATIONS

Sec. 55.5

having an aspect ratio of 2.5 [RPSS, 1948, Fig.

Form

Dimension

Body

of

291

55.5 Lift, Drag, and Other Data for Typical Bodies Representing Appendages. Appendages are also classified by types or shape of body, on the basis that, if they resemble certain geometric forms, there are 0-diml drag coefficient data available in the Uterature by which their resistances may be approximated. The shapes in this category include symmetrical and asymmetrical

and other parts of airplanes which published drag data are rather extensive. For example, W. S. Diehl gives fuselages,

airfoils,

and

airships, for

Sphere of Diameter J)

p/'

Hemisphere,

ConcQve to Stream

Number

Drag

of Bodvj

Ratio

Number

Coefficient

^•\___U_

Droq Coefficient

10=

0.50

3(10^)

0.20

"jT

>I0^

33

j. _^

"y

Hemisphere,

D

Convex to

Stream

.

JL

V

.

>I0^

,

1^

Ellipsoid,

Major Axis

<50o»)

0.60

>5(I0»)

021

-L to Flow

Ellipsoid,

Dimension Re\(nolds

Form

Reynolds

Rotio

216, p. 326].

XI

Mojor Axis II

i

to Flow

f^ )\<^ ^M.8

Is^.^^ UJ, i_

>2(l0')

Circular Flat Plate,

Normal

^IC^

Stream

=>I0'

l/d-0

>I0'

1

£ 3

A Pfoj'acted

^bRecto ncjular

^-i

>I0^

Normal to Stream

.1

^-0

1-"

K-T: Axis

Ffarallel

to Stream

flow in each case

2

085 087 099 0.63

z

0.68

074

5

I

Axis

Perpend icubr to Stream

10

0.82

20

090

40

98 1.20

L/d-5

>5(l0')

0.35 0.34

2-Diml Strut Section

of

Elliptic

U

moment data on a

on Aeronautical Fuselages and Rep. 236, 1926 reports, pp. 131150]. S. F. Hoerner, in his book "Aerodynamic Drag," 1951, devotes his entire Chapter VIII, on pages 121-155, to the drag of aircraft components. He also gives a vast amount of 0-diml drag data, applicable to appendages in water, in other hulls

["Tests

Hulls,"

NACA

parts of the book. Figs. 55.B and 55.C present the readily available geometric-shape data, with the values necessary

0.06 0.063 Strut

Q094

Fig. 55. B

Drag-Coefficient Values fob a Number OF Well-Known Geometric Shapes

The

velocity vector

flow in each case

U

Cr,^Ar,„,U'

0.20

QIO

2.-Diml StreomlJned

great variety of these

elements, as well as on seaplane and flying-boat

D = c/t.

indicates the direction of uniform

for insertion in the 0-diml drag formula

Abt6(l0*)

_

velocity vector

drag and 1.12

L/D" 1

^

Cylinder,

The

1.90

0.91

7

TCirculor

>\0^

Drag-Coefficient Values for a Group OP 3-DiML Geometric Shapes

1.50

1

4

Circular Cylinder,

Fig. 55.C 1,16

1.20

Plote,

indicates the direction of uniform

Here Ap,„j may be 0.25tD\ 6(/i), L{D), or b(t), as the case requires. These data are adapted from the^foUowing sources: (a)

"The Physics

(b)

Van Lammeren, W. P. A., Troost, L., and Koning, J. G., RPSS, 1948, Fig. 26, p. 52 Rouse, H., EH, 1950, Table 2, p. 126; also Fig. 90 on

(c)

p. 124.

of Aviation," 1942, p. 75

HYDRODYNAMICS

292

As an example

may

one

velocity in the prediction of appendage resistance.

This means that it is necessary to estimate the probable actual velocity past the appendage (or its several parts) from the known or estimated flow pattern around the ship, considering wakes

in

diagram

1

of

D in Sec. 55.7. This is on the basis of no hydrodynamic interference between neck and hull or between neck and head, and the absence of alternating cu'culation effects due to the vortex trail. It may be assumed that the ship speed is 12.3 kt, that the water is salt, at 59 deg F, and that no account is taken of variations in Fig. 55.

velocity across the boundary-layer thickness of

the hull. (1) For the neck, assume a diameter of 1.22 ft and a length below the hull of 3.22 ft. The L/D ratio is about 2.64 and the c?-Reynolds number for 12.3 kt, or 20.77 ft per sec, is Ud/v = (20.77)

(1.22)(10')/1.2817 = 1.98 niilhon. This is greater than the value of 5(10'"') in the lower portion of the box of Fig. 55.B, devoted to the circular cyhnder, with its axis normal to the flow. For

Co =

this situation

(for

neck)

0.35,

hence

= 0.35^^^^

=

[(3.22)(1.22)](20.77)-

590.1 lb.

For the head, assume a diameter

(2)

(10')/1.2817

=

3.419 million. This

is

greater than

the 5(10^) referred to in the foregoing but

than

D

(for

infinity.

head)

much

Hence 1

0.35

=

545.3

and

Volume

I

For instance, in the example concluding Sec. 55.5, if the shape of the ship and the sound-dome position in the ship were given, it could be estimated that for the 3.22-ft length of the neck the local velocity in the boundary layer would average only 0.78 of the ship speed. For the head, it could be predicted that, because in

Chap.

flow

potential

of

52.

outside

boundary-layer

the

head would be 1.04 times the ship speed. The modified drag, not calculated here, might not differ greatly from that derived in Sec. 55.5 but the moment of the drag, taken about the point of support at the hull, would be considerably greater. This is because the drag at various ^/-distances is proportional to the square of the local velocity U, which increases with the' y-distance from the hull. Some appendages Ijdng abaft propulsion devices cloak, the average velocity past the

acted

upon by augmented

velocities,

to

develop thrust-deduction forces. Because of the V^ effect, the percentage increase in drag for a given condition

is

at least twice the percentage

augment of velocity. Those appendages

(or

parts of them)

lying

within separation zones might have drag values

9905

^^^^

=

of all the kinds listed in Sec. 11.2 of

are of 2.11 ft

and a length of 1.72 ft. The L/D ratio is about 1.23 and the Reynolds number is (20.77)(2.11)

less

Sec. 55.6

estimate the drag of the extensible

sound-dome assembly shown

D

IN SHIP DESIGN

of the application of these data,

[(1.72)(2.11)](20.77)'

of the order of zero.

Shadowing Allowances for Appendages Tandem. The shadowing allowance(s) for the downstream unit(s) of a system of similar append55.7

The

in

lb.

total predicted drag

is

then 590.1

+

545.3

=

1,135.4 lb.

A some 55.

C

word may be

said here about the drag of

of the bodies represented

on Figs. 55. B and been reached.

after the cavitating range has

The drag

Cd„ for a cavitation number found to be related in fairly simple fashion to the non-cavitating drag coefficient, as described by P. Eisenberg [TMB Rep. 842, pp. o-(sigma)

19-20],

ages in tandem, like the fins or portions of a

discontinuous roll-resisting keel, diagrammed in

M

on page 553 of Volume I, or for any lying downstream from another, indicated in diagram 2 of Fig. 55. D, depends upon: Fig. 36.

appendage

coefficient

is

who

gives values of the variables for a

few well-known forms. 55.6 Allowances for Wake Velocities on Appendage Drag. With friction drag varying as a power of F in the range of 1.8 to 2.0, and pressure drag excluding that from wavemaking varying as V, it is important that a reasonably correct value be used for the relative water

—

(a) Whether or not the after unit is actually downstream from the leading one, having in mind the local direction of flow rather than the

overall direction of motion.

wake

If

directly in the

upstream unit, th« following one may benefit from positive wake velocities due to viscous flow or separation. If slightly to one side of the

or the other of the

it

may

suffer increased

augmented velocity -\-AU

drag because the water

left in

that passed around the leading unit. (b)

The shape

of the bodies, particularly their

APPENDAGE-RESISTANCE CALCULATIONS

Sec. 55.9

^^^^^H^

293

leading unit and the fore-and-aft distance to the

For well-streamlined sections, it may be the ratio between the section length and the fore-and-aft center-

following

unit.

normal to the

flow,

to-Center spacing.

Whether the traihng unit

(d)

so close to the

is

leading unit as to modify the flow around the it would be by itself change the drag of the leading unit. When placed close enough behind to lie in the separation zone of the leading unit, the follomng one may have negative drag, as discovered by G. Eiffel [Hoerner, S. F., AD, 1951,

latter,

in

kh^i %^

Center-to -Centar DistanC' /struts for Guord-Skeq-

an

over and above what

infinite stream,

and

to

Fig. 7.1, p. 93].

_t____^

!^^

\

Supp ort I^^'II;:^*^—^^—

Quantitative

^^__ _j-

indications

of

what

may

be

when the two appendages or units are the form of struts are given by D. Biermann

expected Offset from (^ '

in

^Length -»^

u_

and W. H. Herrnstein, of

1933,

entitled

Jr., in

"The

NACA

Report 468

Interference

Between

Struts in Various Combinations." Their conclusions,

to be found on page 522, indicate that are to be expected

interference effects

if

the

leading and following units are closer than 5 section lengths to each other, center to center. S. F.

Hoerner also gives a considerable amount

of interference drag data for airfoUs (or hydrofoils), flat discs,

strut sections,

and cyhnders

in

1951, pp. 83-84, 93-94]. A. Borden, D. B. Young, and W. M. Ellsworth, Jr., discuss

tandem [AD,

the drag situation in "Hydrodynamic Induced Vibrations of Cylinders Towed in Various Combinations," FISH-EYE VIEW

TMB

Report C-452, September 1951.

Modifications in Drag for Appendages

55.8

Abreast.

The

general situation relative to ad-

jacent appendages which must, to Fig. 55.

IN

D

Definition Sketches for Appendages

Varying Flow, Appendages in Tandem, and Appendages Abreast

they are long and slender, with their axes roughly parallel. A leading unit of circular section generates a long separation zone

section shape

abaft

it,

in

diminished.

if

which the drag

On

leading unit leaves in its

mented

velocities,

following unit (c)

is

of the follo\ving unit is

the other hand, a streamlined in

wake a

trail of

which the drag velocities

of two 2-diml circular rods and of two 2-diml streamlined strut sections, placed abreast, are

pubUshed by S. F. Hoerner [AD, 1951, Fig. 7.4, p. 95]. These show that, whenever practicable, the

center-to-center

transverse

be at least 4 times the section thickness tx

the

between the centers

spread

maximum

For a spread

should

transverse

of 2tx (or

2D)

of a pair of circular cylinders

drag coefficient Co of each cyhnder is increased from its normal value of 1.2 to about 1.54. 55.9 The Drag of Exposed Rotating Shafts. of infinite length, the

from the leading

unit, positive or negative as the case

largely dissipated

some

design requirement,

aug-

increased.

Whether the wake

may

be, are

by the time the following unit

comes along. This is, as a rule, a function between the thickness and bluntness

ratio

of

fulfill

be placed abreast each other, is depicted in diagram 3 of Fig. 55. D. Graphs indicating the single and combined drag special

of the of the

An

exposed rotating shaft, such as that driving a screw propeller, generates two kinds of friction

HYDRODYNAMICS

294 drag, in addition to a

The

Effect.

The

by the Magnus and discussed in

force

component due

to non-axial flow at the shaft

flow

illustrated in Fig.

shaft also generates a pressure-drag

general flow in the vicinity, at an angle to the

Volume

I

and

be described presently. Rotation of the shaft surface involves tangential friction and an increase in torque to keep it turning. The forward motion of the ship and shaft involves longitudinal friction, much the same as though the shaft were covered by a casing which did not rotate. A pressure drag, due to the oblique flow of water force, to

past the shaft,

is

exerted in the general plane of

flow, at right angles to the shaft.

may

Sec. 55.10

be calculated presently. Neglecting rotation and considering only the

latter is described

Sec. 37.25 of 37. Q.

lift

IN SHIP DESIGN

This drag

position, to

shaft, the axial

normal to the shaft 8.23 ft per sec.

—

is

The Co

The component

[(59.11) sin 8 deg] or

about

of a 2-diml circular cylinder

L/D ratio 40/1.00 = 40 is, from Fig. 55.B, about 0.98. The normal force expected to be exerted on the shaft, neglecting the effect of rotation, is then

may

F = C„^Ap,„,C/=

not have a longitudinal

or divergence

of velocity is [(59.11)

of

component, depending upon the declivity and convergence or

component

cos 8 deg] or 58.53 ft per sec.

of the shaft axis.

0.98(lf«5) [(40)(1)](8.23)='

Taking the last item first, the shaft is considered as a fixed appendage in the form of a 2-diml circular cylinder, placed normal to a flow having an effective velocity equal to that component of

= The drag

lb, for

2,640

the single shaft.

of locked screw propellers

Volume III. Drag Data for Holes,

is

discussed

the actual velocity perpendicular to the shaft axis

in Part 5 of

and in the plane of that axis. In the absence of any better data, the actual streamline velocity

What might be

may be

the form of recesses and holes, are considered here

taken as equal to the speed of the ship, and the direction of flow as parallel to the hull along an appropriate diagonal flowplane, indicated by surface (or preferably off-the-surface) flow markings, described in Chap. 52. This drag

have a vertical or lifting component for most ship installations, possibly having a slight effect on the trim. The exact nature of the axial and tangential components of the viscous flow around an exposed force will

rotating shaft remain

unknown

in the present

is customary, therefore, to both friction-drag components on the

state of the art. It

neglect

shaft, unless the latter is excessively large

and

rotates at high speed, or unless it

it is so long that has to be supported by two or more bearings,

give an idea of the magnitudes involved,

assume two

each 12 inches in diameter, revolving at 400 rpm, and having an exposed length of 40 ft, lying at a mean angle of 8 deg shafts,

to the lines of flow at a speed of 35 kt, equivalent

to 59.11 ft per sec.

The layout

of P.

Mandel

[SNAME, 1953, Fig. 2, p. 466] shows the starboard shaft of a twin-screw arrangement of this The

tangential velocity at the surface of

shaft,

due to rotation only (neglecting cross

kind.

one

is (12/12)x(400/60) = per sec. This is about one-third the forward

flow due to non-axiality),

20.95

ft

speed of the ship and

is

about 2.5 times the cross-

Slots,

and Gaps.

called reversed projections,

in the category of appendages, especially

if

in

they

have physical dimensions corresponding to the appendages usually found on boats and ships. S. F. Hoerner has collected drag-coefficient data for holes and gaps, some based on a reference area equal to that of the opening in the fair surface

and some based on the so-called frontal area of the downstream face [AD, 1951, pp. 55-56].

A

stagnation point

in

diagram

may

be found here, as at Q but if not it may be expected that some -|-Ap's are developed on the

C

of Fig. 7.J,

downstream face. Because of the rather comphcated nature of the drag effects, the marine architect is referred directly to the Hoerner reference for such data as he

external to the hull.

To

55.10

may

The

need.

design of recesses to reduce their drag

is

discussed in Sec. 75.13. 55. 11

The drag

Estimated Resistance of Discontinuities. of

any

large discontinuity, invariably

much

body such as a ship from an appendage projecting well away from the hull, is dependent upon the flow pattern around it. The latter is, in turn, affected by the presence of the boundary layer on the large body, with its variation in local attached to a

larger

hull, as distinguished

velocity across the boundary-layer thickness.

In aerodynamics the resistance of discontinuities under the heading of interference

of this type falls

APPENDAGE-RESISTANCE CALCULATIONS

Sec. 55.14

two essendissimilar forms. Again the marine architect

drag, as developed at the junction of tially

Hoerner's "Aerodynamic Drag," 1951, Chap. VII on pages 93-120, as embodying the essence of most of the known

is

F.

referred directly to S.

Although written for the aeronautical engineer it should be intelhgible to and useful for the marine architect who has read and is data in this

the

55.12 The Resistance of Large Appendages Considered as Parts of the Ship. Large appendages such as deep skegs and long bossings do not resemble bodies for which appUcable and rehable pressure-drag data are available. Further, a skeg or bossing of a given shape may produce different flow, velocity, and pressure patterns, depending upon the form of the hull to which it is applied. There are companion interference effects here, both of the ship on the appendage and the appendage

on the

ship.

It is usually necessary to predict the drags of

these large appendages by: (1)

statistical

percentage data, as in Sec. 55.3 (2) Taking account of the increased wetted area

appendage

when

is,

the external area of the

the bare-hull area covered by

less

applied. This involves

Rp

resistance

and

45.22,

an increased

it

friction

although, as explained in Sees. 22.9,

55.4, there are

no acceptable rules for

estabhshing the correct R^ values for these parts. (3) Determining the drag from model tests, run with and without the appendage(s) in question.

55.13

The

Calculation of

ance for Submerged Vessels.

Appendage ResistThe notes of the

preceding sections of the present chapter apply to the calculation of the resistance of

all

append-

ages on submerged vessels, irrespective of their position relative to the hull.

Those mounted on

top of the hull will, upon occasion, break the water surface. In this case some pressure drag

due to wavemaking, of an amount as yet undetermined, is added to the pressure drag due to forward

may

indeed be more necessary to predict this added drag as a design load on the appendage, rather than as an increment of motion. It

resistance of the vessel as a whole, because this

partly awash

condition

is

not one for which

resistance predictions are made.

The hull

ratio of

resistance

appendage resistance to the bareof

a submersible

is

inherently

resistance

of

the

both the abovewater and

This

is

because

The

(a)

provision of diving planes, and possibly fixed

of

also

of:

stabilizers,

and rope and cable

guards, in addition to steering rudders

The

necessity

carrying

for

one

or

more

periscopes

The high drag

(c)

radio,

of

radar,

and other

antennas, and of the masts or supports for (d)

The

hull discontinuities

embodied

them

in large

main-ballast flood-valve recesses or large flooding

openings for the main-ballast tanks (e) The provisions for normal handling of the vessel as a surface ship

and

for safety of the

crew

when working about the superstructure deck (f) The provision of resting keels (g) The work and expense involved in fairing and streamlining the abovewater portion of a vessel of the submersible type which is to spend only a small portion of

Estimating the pressure drag from

of the ship; that

bare-hull

total

the underwater portions in the surface condition.

(b)

book.

greater

entire vessel, including

field.

familiar with the previous chapters of the present

295

larger than for a surface ship, notwithstanding

its

operating time sub-

merged.

For a craft in the category of (g) preceding, the appendage resistance may well reach 80 or 90 or more per cent of the bare-hull resistance of the craft as a whole. For a true submarine which still requires steering rudder (s) and some kind of deck erection but must also carry diving planes, guards, and other excrescences, the appendageresistance ratio submerged may be as high as 2.0 or 3.0. P. Mandel mentions that, in some cases [SNAME, 1953, p. 466], the appendages added to a submarine may cause the total drag to be 5 times that of the bare hull alone! 55.14 The Displacement of Appendages. The drag of an appendage is of course related to its size,

It

although

may

many

other factors are involved.

be of advantage to the marine architect,

in the early stages of a preliminary design, to

know

the approximate size and volume of the average appendage, for ships of a rather wide variety of tj^jes.

Table

55. d gives

this kind, in the

some

form

available information of of individual weights of

salt water displaced. From the data given, the percentages of the overall displacement can be

calculated. While these data are by no means modern (Jan 1924) they may serve as the beginning of a more comprehensive and up-to-date

compilation.

296

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 55.14

CHAPTER

Observed Resistance Data General

56 1 56.2 .

Comments

Typical Ships Systematic Resistance Data from Model Series; Taylor Standard Series with Contours of fijj/A

.

.

Japanese Fishing- Vessel Standard Series Gertler Reworking of Taylor Standard Series Data of 1954, with Contours of C^ Resistance Data for Very Fat Ships .

.

56 6 .

for

297

56.7

297

56 8 56 9

298 300

56 10

.

.

.

Resistance Data for ParallelMiddlebody Variations Resistance Data for Very Low Ship Speeds Rate of Variation of Model Residuary Resistance with Speed Variation of Total Resistance of Model and Ship with Speed-Length Quotient .... Changes in Resistance with Changes of Trim and Displacement Measured Thrusts and Towing Pulls on Ships

.

....

General Comments.

56.1

.

303

This chapter gives

literature of observed resistance data of

many

on models

types, particularly those tested

as systematic or methodic series to determine the effect of certain variables.

Accompanying notes

where necessary, the location of the of the models or ships. These data are supplemented by information concerning the resistance of unusual ship forms or of more-or-less standard forms run at unusual

indicate, lines or

body plans

speeds.

Means

are described

resistance of ships

when

approximating the

for

their exact shape is not

known, when they have not been tested at model scale at the speed desired, or

ments are

different

when

from the values

for

self-propulsion

test

data

for

which typical

vessels, plus references to other published data,

are to be found in Chap. 60. In almost every case

these give the predicted effective power

Pe

for

the ship (or ship design) represented by the model. 56.2 Resistance Data from Tests of Models of

Attempts have been made from time to time, by interested individuals, to list, collect, and systematize the enormous mass of pubhshed data on the resistance tests of models. With so much time and energy devoted to this particular field, in the model basins of the world Typical Ships.

over the past seventy-five years, it is a pity that only a fraction of the existing test data are in a form usable for analysis and design, and in locations available to the naval architect

.

1 1

56.12

and marine

engineer.

The graphic data published by D. W. Taylor

in

306 306 306

308 312 312

"The Speed and Power of one form or another, the resistance-speed curves of models representing many forms and types of ships, usually as parts the three editions of

Ships"

contain,

in

of small groups or series.

War

The

period since

World

brought a reafization of the necessity for more systematic presentation of data of this kind, as witness the work of the Swedish State Model Basin and of the David Taylor Model Basin in reporting test data on numerous models of vessels of a given class. There is also a wider realization of the fact that, for analysis purposes II has

on the part of a number of workers, the most comprehensive data on models and ships is none too complete.

A

their displace-

data are available.

Some

.

301

information as to the availabihty in the technical

and ships

.

.

56

Models and Ships

Systematic

Resistance Data from Tests of Models of

56.3

56 4 56 5

56

leader in this respect has been the

Model Basin. In the annual

reports

Rome

of

this

estabhshment ["Annali della Vasca Nazionale per le Esperienze di Architettura Navale"], of which Vols. I through XI are in the TMB library, there are included very complete data sheets and graphs giving the results of tests on selected ship models of a rather wide variety of types. As examples, there are included in Vol. X, published in 1941, test results for six models constructed to the

order

of

various Italian

firms.

For these

models there are given: (a)

Tables

sions,

form

one to five each model

the principal dimenand other data for from displacement and trim conditions on

I

and

II, listing

coefficients,

Tables III and IV, giving the observed drag for the six models, at different displacements and trims, with water temperatures (b)

Rt and speed V

and other necessary data

297

HVnROnYNAMICS

298

IN'

SHIP DESIGN

(c) Tables V and VI, self-propulsion data for one model and model propeller (d) Tables VII through XII, body plans, outboard profiles, details of appendages, and sectionarea curves for the six models (e) I'able XIII, drawing of the model propeller

most

tested

per sheet.

XIV through XIX, curves of R^ ,Rb, expanded P e for the six models

Tables

(f)

and

Table

(g)

XX,

curves of self-propulsion data from

them run

of

of the

in

A'^^ A'^^ and A='^''

XXIX,

values of

for all models.

There have been published, to the date of writing

Data test

(1956),

some 160

SNAME

Resistance

These carry complete descriptive and

sheets.

data for the same number of models, repre-

senting a great variety of ship sizes

The observed

and

resistance data are supplemented

by

ships of appropriate standard length, say 100

ft,

400 ft, or 1,000 ft. An example of the latter is the Uner Normandie, RD sheet 39. Two sets of resistance data sheets are included in Sec. 78.16, made up for the model tests of (1) the ABC ship with the centerline skeg and transom stern, TiMB model 4505, and (2) the ABC ship with the archtype stern, model 4505-1. The RD sheets model 4505 were also published in for 7th ICSH, 1954 [SSPA Rep. 34, 1955, pp. 302-

TMB

TMB

304].

There are available, to accompany the whole set of sheets:

Explanatory Notes for Resistance and PropulData Sheets, SNAME Tech. and Res. Bull. 1-13, Jul 1953 II. Index to Model and Expanded Resistance Data Sheets Nos. 1-150, SNAME Tech. and Res. Bull. 1-14, Jul 1953 III. Summary Sheets, 7 in number, containing summarized data for RD sheets 1 through 160, and additional information needed for analysis.

I.

sion

A series of 29 test

data sheets containing the model-

data on that number of fishing-boat

hulls.

SNAME RD

sheets

Copies of this catalog may be on application to the Fishing Boat Section, Technology Branch, Fisheries Division, Food and Agriculture Organization (FAO) of United Nations, Rome, Italy. 56.3 Systematic Resistance Data From Model Series; Taylor Standard Series with Contours of craft.

To make

possible the calculation of the

approximate residuary resistance of ships of widely varied shape and proportions, D. W. Taylor devised his now-famous Standard Series, with the thought that the residuary resistance of a ship could be predicted reasonably well from the measured resistance of a model of the same proportions.

types.

predicted resistance data for geometrically similar

World," reThese

76.12.

There has recently been issued (November 1 of a group of "Fishing Boat Tank Tests," comprising data sheets on 150 models of

i2fl/A.

through

of the

part of Sec.

1955), Part

ship

XXVII

first

described elsewhere but contain less information

obtained

Tables

the

sheets are similar to the

fishing

(k)

at .several displacements, are

book "Fishing Boats

viewed

Table XXI, curves of Ct for the six models Tables XXII through XXIV, curves of Cp (i) and Ct for the six models Tables and XXVI, friction-resistance (j) coefficients / in the dimensional formula Rp = jgyi.s25^ for varied lengths of both model and

XXV

563

published by Jan-Olof Traung on pages 281-310

the one model tested (h)

Sec.

Taylor's primary purpose was supplemented

eventually

by another, equally valuable

if

not

equally important. This was the gradual but wide

acceptance of the Taylor Standard Series residu-

ary resistance as the yardstick for evaluating the worth of a particular shape of hull. This is done

by comparing

residuary resistance to that of

its

the Taylor Standard Series parent form of identical proportions. So outstanding

was the shape

of this

parent form, derived from the hull of the British armored cruiser Leviathan [S and P, 1943, p. 181], it is a definite mark achievement to beat the Taylor Standard Series in that part of the speed range where optimum ship behavior is sought. The parameters varied in the Taylor series, now known as the proportions of the models (and

that even a half-century later of

ships), were:

B/H

(a)

Beam-draft

(b)

Displacement-length quotient, A/(0.010L)^,

ratio,

defined in Appx.

1

(c)

Prismatic coefficient, Cp

(d)

Speed-length quotient, T^

fined in

Appx.

= V/ a/L,

also de-

1.

The parent form used by Taylor is described in The lines and principal features of this

Sec. 51.2.

form, together with eight curves of section areas

OBSERVED SHIP-RESISTANCE DATA

Sec. 56.3

CONTOURS OF RESIDUARY RESISTANCE

IN

POUNDS PER TON OF DISPLACEMENT

Beom-Draft Ratio

Q50

0.55

Q60 Lonqitudinol

0.70 0,65 FVismotlc Coefficient

Cp

299

A

HYDRODYNAMICS

300 for

Cp values

of 0.48 through 0.80, are

shown

in

upon data from the following

Fig. 51. A, based

references:

S and P, 1910, Vol. II, Figs. 79 and 80 S and P, 1933, Figs. 70 and 71, p. 191

(3)

PNA,

(4)

S and P, 1943, Figs. 184, 185, and 186, pp. 182-183.

fatness ratios of from 6 through 15, corresponding to a range of Taylor displacement-length quotient

1939, Vol. II, Fig. 28, p. 92

The end

the form of contours of

in

results,

Rr

pounds per ton of displacement A for the given proportions, were pubhshed in the three editions of "The Speed and Power of Ships," as noted: residuary resistance

in

1910, Vol. II, Figs. 81 through 120, covering a range of r, from 0.60 through 2.00, for two B/H ratios, namely 2.25 and 3.75, and for various ranges of displacement-

length quotient and prismatic coefficient 1933, Figs. 72 through

HI, pages 193 through 271, A/(0.010L)', and Cp as

covering the same range of Tq

,

of 171 through 428. 3.0,

from the

sets of contours

latter reference

are reproduced in Figs. 56. A and 56. B. selected to

To (a)

fit

the

ABC

use these contours, values of

Picked from two sheets for a

2.25,

(1)

They were

ship example of Sec. 57.6.

Rr/A

B/H

are:

ratio of

for a speed-length quotient just

below

that desired and (2) for a speed-length quotient just above it. The contours are entered with the

Cp value along the horizontal

scale

and the

A/(0.010L)' value along the vertical scale. (b) Picked from two sheets for a B/H ratio of 3.75, (1) for speed-length or Taylor quotients just below and (2) just above the desired value. These are the same T, values as for (a) preceding.

The of 2.25

and

3.75,

Rr/A

is then found by between the B/H ratios and then between the two speed-

correct value of

linear interpolation

first,

length quotients.

To

illustrate

worked out

this

transom-stern

ABC

an example is and Table 57. b for the

procedure

in Sec. 57.6

ship having the preliminary

characteristics listed as the fifth approximation in

Table 66.e of Sec. 66.11. 56.4 Japanese Fishing- Vessel Standard Series. Because the Taylor Standard Series extended only to a maximum displacement-length quotient of 250, corresponding to a 0-diml fatness ratio V/iO.lOLf of 250/28.51 or 8.77, it could not be used for predicting the performance of fat, chubby ship forms such as those of tugs, fishing vessels,

B/H values were

2.2

and

to 1.28.

Following their procedure of putting

all

param-

eters in 0-diml form, the Japanese plotted contours of specific residuary resistance

C„

,

where C„

=

The data were published in final form in 1950 by the Fisheries Agency of Japan in a book entitled "Graphical Methods for Power Estimation of Fishing Boats." Z?^/(0.5pV'^'F').

1943, Figs. 189 through 240, pages 189 through 240,

covering a range of Tq of from 0.30 through 2.00, with the

other variables remaining the same.

The

while the Cp values were 0.55, 0.60, 0.65,

0.70, and 0.75. The range of Froude number F„ was 0.16 to 0.38, corresponding to a T^ of 0.537

for the 1910 edition

Two

Sec. 56.4

a standard fishing-vessel series covering 0-diml

(2)

(1)

IN SHIP DESIGN

and icebreakers. During the years 1946-1949 a group of Japanese, Atsushi Takagi, Takao Inui, and Shoichi Nakamura, undertook the testing of

B/T

OBSERVED SHIP-RESISTANCE DATA

Sec. 56.5

more than 2.00 m or 6.56 ft in length; some of them were as short as 1.80 m, or 5.91 ft. There are no data to indicate the water temperatures at which these models were run nor what steps were if any, to insure turbulent flow throughout. Copies of these books, for those who wish to use the data, are to be found in:

taken,

(a)

(b)

SNAME Bureau

Headquarters in

(c)

Bureau

TMB

56.5

of Ships Preliminary

Library, U.

S.

Design Section

Library.

Gertler Reworking of Taylor Standard

transition flow

at low Froude resistance

correcting for the effects of

of

based on the assumption that

is

numbers the

constant,

practically

as

residuary-

specific

=

Cr

coefficient

Rr/(0.5pSV^)

indicated

in

the

is

left

The original data showed that Cr decreased with decreasing speed so long as wavemaking resistance was important. There was then a short range of speed for which Cr remained constant, after which, as the speed was still further reduced, the coefficient again began to

decrease.

This

latter

decrease

was

When

attributed to transition flow, and was ignored.

Towing Tank Conference decided adopt the Schoenherr friction-resist-

The practically constant value of the coefficient Cr is therefore used for all lower Taylor quotients T„ and Froude numbers, down to values of

Series Data of 1954, with Contours of

Cr

.

the American in 1947 to

.

in general

Navy Department (d)

to give the residuary-resistance

Cr The method

coefficient

portion of Fig. 7.H.

New York

of Ships Technical

was subtracted

301

ance formulation

it

was

realized that this pro-

cedure would predict effective powers not directly

=

T,

0.5,

=

F„

0.149.

comparable to those calculated from the original TSS contours mentioned and illustrated in Sec.

number

56.3.

which were towed with and without a turbulence-

The

differences

in

the

calculated

effective

powers result from two causes: (a)

The

differences

between the

PNA,

friction resist-

1939, Vol. II, Table

(a) is reflected as

9, p. 114].

a difference in residuary

and thus requires that a lengthy cormade to D. W. Taylor's Rr/A conrender them comparable to modern data.

resistance

rection to

tours to

Item (b) merely requires a substitution of the Schoenherr formulation with the appropriate roughness allowance to correspond to the Tideman data in the ship-prediction procedure. In view of this situation, plus the fact that water temperatures and turbulence stimulation were not taken into account in the original TSS

was decided at the David Taylor Model Basin to reanalyze the original test data on the Taylor Standard Series models. In the reanalysis,

testing, it

the

methods and procedures employed were same as those currently used at

essentially the

Carderock.

A

of recent tests of

is

not rigorous,

TMB

20-ft

a models

stimulating device indicate that in general tur-

bulence stimulation results in no resistance change models which experience only minor transition

and those from the old EMB 20-ft friction-plank results in the model range (b) The differences between the friction resistances obtained from the Schoenherr formulation in the ship range and from the Tideman data used by D. W. Taylor [Schoenherr, K. E., SNAME,

Item

procedure

this

for

ances obtained from the Schoenherr formulation

1932, p. 285;

Although

total-resistance coefficient for the

model was computed, from which an

ATTC

1947 or Schoenherr friction-resistance coefficient

and those only at the lowest speeds. Good agreement was attained in most of these cases between the residuary-resistance coefficient curves from the unstimulated experiments, faired in the effects

manner tests

described,

with

the

and those

resulting

from the

turbulence-stimulating

device.

This seems to be especially true with forms having the TSS type of bow. Two 20-ft models of the

Taylor parent form, having (longitudinal) prismatic coefficients Cp of 0.613 and 0.746, were tested at the Taylor Model Basin in 1951. In both cases it was found that turbulence stimulation Avas required only at low speeds. The procedure described in the foregoing gave reasonable agreement with the curves in the turbulent range [Todd, F. H., and Forest, F. X.,

SNAME,

1951,

p. 678].

Corrections for restricted-channel effects in the

Washington Basin were made by using the formulas given in TMB Report 460 entitled "Tests of a Model in Restricted Channels," by L. Landweber, dated

May

1939, with the appropriate

model and basin dimensions. This correction was in most cases small; even for the fullest model of the series it amounted to a decrease in resistance of only 2 per cent.

The

results of the re-analysis of the

Taylor

M.

Gertler

Standard Series data, carried out by

HYDRODYNAMICS

502

B/H=3.00 Cp=0.62

Froude Number

11

0.15

IN SHIP DESIGN

0.16

0.17

0.18 1

0.19 1

0.20 1

0.21 1

0.22

Sec.

VgL

0.23

0.24

II

0.25

II

0.26

0.27

0.28

0.29 1

56

OBSERVED SHIP-RESTSTANCE DATA

Sec. 56.6

and other members of the TMB staff, are given in a form which employs a completely 0-diml

"A

presentation [Gertler, M.,

Reanalysis of the

Test Data for the Taylor Standard Series," Rep. 806, Mar 1954, Govt. Print. Off., Washington]. The faired resistance data are given as curves of specific residuary-resistance Original

TMB

Cr on a

coefficient

basis of both Taylor quotient

T, = F/VL and Froude number /^„ = Two of the major proportions used are, the

B/H

and the

ratio

coefficient

Cp

(longitudinal) prismatic

The scope

.

F/V^. as before,

of the series has been

enlarged to include a third

B/H

ratio of 3.00 in

addition to the ratios of 2.25 and 3.75 published

and 1943 editions of D. W. Taylor's "The Speed and Power of Ships." The intermediate values were obtained by interpolain the 1910, 1933,

reworked data for the hitherto unpublished EMB Series 20 which had a B/H tion, using the

ratio of 2.92.

Instead of Taylor's dimensional displacement-

makes use Cv = F/L3

length quotient the Gertler reworking of the 0-diml volumetric coefficient

expressed as a simple

number, without the 10"^

same as the origirial

ATTC

T aylor

10~^.

This

factor, is exactly the

The Cws = replaced by

fatness ratio F/(0.10L)'.

wetted-surface coefficient

S/'VAL, which the 0-diml Cs

,

number times

is di mens ional,

is

= S/VVL.

These and the remaining steps

in the

reworking

process are explained most comprehensively and

meticulously by Gertler in the Preface and intro-

ductory portions of

TMB

Report 806, previously

referenced.

The new

303

By moving

apparent.

and

right

left

across the

page, the original Taylor contours show clearly

the change in

Rr/A

for a

in the range of T, or F„

change in Cp However, where friction resistance .

predominates, say below a T^ of 1.15, F^ of 0.342, the selection of Cp is not made on the basis of a

minimum

value

of

The

Rr/A.

of

effect

A/(0.010L)' or F/(0.10L)' on residuary resistance is shown well by both the Gertler reworking and the original Taylor Standard Series contours. The Gertler data have the advantage that, with three

B/H ratios,

interpolation

accurate. Indeed, for

is

easier

many B/H

and more

values close to

2.25, 3.00, and 3.75, and for a preliminary resistance estimate, interpolation for beam-draft ratio may be omitted entirely.

Although never stated in print in so many words it was felt by many that the Rr/A contours of the 1910, 1933, and 1943 editions of "The Speed and Power of Ships" were rather "heavily" faired, probably because in some regions there were not many spots with which to establish the proper contour positions on the diagrams. Comparisons of Pe for random models with the Pb values of the TSS models of the same proportions,

EHP/Taylor EHP ratios of Expanded Resistance Data sheets, when plotted on F or T^ produced what are known as "angleworm" curves. Although many of these random models represented ships of superior and outstanding performance, their "angleworm" curves showed rapid and often violent plus and corresponding to the the

SNAME

,

minus fluctuations in the values of Taylor EHP], on a basis of variation

[1

— EHP/

in the speed-

presentation differs markedly from the Examining a pair of facing pages, reproduced as the two parts of Fig. 56. D, one sees the

length quotient T^

graphs of C^ for various volumetric coefficients

Nevertheless, variations in the ratio of

Cv = V/L\

reworked TSS Pe values still occur. If not angleworm in shape they are sinuous and irregular, and they are not always consistent with the varia-

original.

or fatness ratios F/(0.10L)', extend-

ing from the lowest speed-length quotient T, of 0.5 to the highest value of 2.0. All the humps and hollows in the complete range of Cr for any ,

volumetric coefficient, are visible at a glance.

The pair of facing pages embodied in Fig. 56.D used with another pair of pages, not reproduced here, to derive a preliminary estimate of the residuary resistance of the ABC ship, by the is

method described in Sec. 57.6 and Table 57.c. The characteristic spot

illustrated in

ship values listed in that table

added to the

is

for the

ABC

1951, all

the

TSS

have the disadvantage that the variation of Cp on Rr/A is not readily

Gertler's data

.

data were reworked in 1948-

"heavy"

fairing

was

carefully avoided.

tions of the original data. Additional

on

P^

to the

comments

found in Sec. 57.6. 56.6 Resistance Data for Very Fat Ships. The lack of resistance data for ship forms of large 0-diml fatness ratio F/(0.10L)', for which the Takagi Series described in Sec. 56.4 fills a partial this feature are

need, led to the analysis of

EMB

and

TMB

data for 44 fat models by R. F. P. Desel and Collins.

The

results are

thesis submitted

figure.

effect of

When

the

TMB

models

embodied

in

an

test

J.

T.

MIT

by them, dated 1952 [copy

in

Ubrary]. Although there were 13 tug

in the group,

and 15 combinations

of the

HYDRODYNAMICS

304 old U.

S.

Shipping Board parallel-middlebody

bows, midship portions, and sterns [EMB Series 53, reported in S and P, 1943, pp. 70-72, 257-271], the models of the whole group forming the basis of this study were only loosely related. Some were

065 Tq-y/VT

IN SHIP DESIGN tested in bare-hull condition,

various combinations of appendages.

|3/^// 10/

/ /

^

'

10//

'////

^^

\',i.'\

"'A^Jl]

7/ ^—J/

^26

/

'//

/ / / /

—r [0.\OLf

/ /

'L ///

/ /

/

// -H-

// /

Fn-V/^ 020

02/

022

Fig. 56.E

Q20

0.21

024

025

026

027

028

0.29

030

C„ Data for Fat Ships, Cp = 0.58

Q22

Fio. 56.F

023

Cfl

aZJ

024

025

Data for Fat

026

027

Ships,

0.26

029 030

Cp = 0.60

B/H

The form coefficients were calculated on a basis of length on the waterline. Residuary resistances were derived by using the ATTC 1947

of 2.0 to 3.0.

/.b

Cp-0.58

The

ratios varied irregularly but lay within the range

1

\5///

Sec. 56.6

and others with

OBSERVED SHIP-RESISTANCE DATA

Sec. 56.6

friction

formulation.

Unfortunately,

the speed

range extended only from Froude numbers of 0.20 to 0.30, corresponding to T, values of 0.672 to 1.007. Takagi's F^ range was from 0.16 to 0.38.

The

thesis data thus derived are in the

form of

contours of fatness ratio F/(0.10L)^ on a basis of

Cr and Cp

Cp

for eight equidifferent values of

plotted on ten sheets for as

many

,

different F„'s.

The cross-contours of fatness ratio, when plotted on Cr and F„ for seven equidifferent values of Cp appear in Figs. 56. E through 56. K. When ,

,

thus presented they resemble those for the Gertler

reworking of the Taylor Standard Series described The Desel-Collins data for Cp = 0.72 are omitted because this is much too large a Cp value for easy driving of a chubby, fat form. Because of the unrelated forms and the rather in Sec. 56.5.

severe

fairing

pattern of data

necessary it

to

was not

of models to indicate the

known

achieve

a

regular

possible in this group

humps and

hollows

and F^ For this and other reasons the contours are shown as broken lines. Although lacking the reliability to be expected from tests of a comprehensive to occur with change of speed

systematic

series,

an indication

14

13

12

.

these data nevertheless furnish

of residual resistance to be expected

305

HYDRODYNAMICS

306

rr-r 1

0.35

IN SHIP DESIGN

0.95

Tq-y//r

/

I6__/.

(2)

(3)

U Ti

Cb-0.70

Sec. 56.7

S and P, 1933, pp. 47, 67, 68, and Appendix D, pp. 299 through 327 S and P, 1943, p. 50 and pp. 70 through 72; also Appendix D, pp. 255 through 271 Brief extracts from these data are given by K. S. M. Davidson in PNA, 1939, Vol. II, pp. 67-69.

(1)

It is to be noted from the body plan of the parent form, given on page 257 of reference (2) above, that the Series 53 models had practically

//

no bulb and were not patterned on the Taylor Standard Series lines. The analysis of these parallel middlebody data, not completed for the 1933 and 1943 editions of "The Speed and Power of Ships," still remains to

-/

be done.

V

/

^

A

^

:/3^ / Z-

/ ^

Speeds.

-7^

dicted from model tests rarely include the range

/

"7'

/

"''

X

Data for Very Low Ship Published data on ship resistance pre-

Resistance

56.8

\/^

(0.101)"

the way down to zero speed, yet it is often convenient to have some idea of the low-speed

all

/

/

^^

resistance, or at least to

know how

it

varies with

speed in this region.

The

tables of

Bull. 1-2 of

F„=V/v5l O.ao

0.2)

022

0.25

Q24

0.25

Q26

Q27

Cp March

SNAME

Tech. and Res. two small portions of which are reproduced as Tables 45. c and 45. d of Sec. 45.9, extend down to an i2„ of 0.1 million,

,^

02a 029

in

1952,

corresponding to a fore-and-aft space dimension Q30

and a speed of 1 kt. The Taylor Standard Series contours [S and P, 1943] stop at a speed-length quotient T^ of 0.30, F„ value of about 0.089. The SNAME RD and ERD sheets carry down to a T^ and an F„ of about the same of about 0.73 ft

Fig. 56.K

Cr Data for Fat Ships, Cp

=

0.70

guide in making resistance and power estimates for ships

having displacement-length quotients in

excess of those of the Taylor Standard Series.

The data given

are based

upon the use

Froude circular-constant system of notation. 56.7 Systematic Resistance Data for ParallelMiddlebody Variations. The first systematic model test data on the effect of varied amounts of parallel middlebody inserted between given entrances and runs were those published by W. Froude [INA, 1877, Vol. XVIII, pp. 77-97]. He plotted

curves of residuary resistance

Rr

for

F

on a basis of length Lp of parallel middlebody, a procedure which has not been improved upon to this day. The low points in the Rr curves for a succession of speeds, or for a given speed, indicate the Lp values for minimum residuary resistance. These are not necessarily the constant speed

values for

minimum

Data from

EMB

total resistance.

tests of the

value.

A

of the

156 combinations of

Series 53, tested in 1931 for the U. S. Shipping Board and plotted on the Froude system, are pubhshed in:

residuary resistance composed entirely of

pressure resistance should vary as F"

all the_way However, plots of i2„/A on V/Vh for low speeds in the Taylor Standard Series show that it is the exception rather than the rule for the exponent of the curve oi RrOhV to approximate 2. This is due partly to the extremely low resistances being measured but there appear to be evidences of viscous and other effects not entirely eliminated in the Froude model-testing procedure.

to

F =

An

0.

approximation to the residuary resistance F = is derived from a plot of Rr/A on

close to

V/'VL on

somewhat

log-log paper,

similar to

vL

= that of Fig. 30. B, for say three values of F/ 0.40, 0.35, and 0.30. Extending the line in a downward gives an Rr on T^ desired. Variation of Model Residuary

generally straight direction

idea of the low value oi 56.9

Rate of

Resistance with Speed. ysis

it is

useful to

For certain

know

lines of anal-

the rate at which the

OBSERVED SHIP-RESISTANCE DATA

Sec. 56.9

307

—

residuary resistance of the hull of a model varies

residuary-resistance formula Rjt

with speed in the equation Rr = fc(0.5p)SF". This matter was investigated many years ago by D. Kemp [INA, 1883, pp. 124-125]. He stated that on the steam yacht Oriental the resistance (total in this case) varied as about V^ in the low-

principal forms of ship hulls, there are plotted in

speed, range, but increased to about

range of 0.82 to 1.04, F„

F"*

Fig. 56.L the values of

RD RD

1948, pp. 368-369]

humps and hollows in the predicted ship-resistance curve, similar to those due to surface-wave interferences in model tests. It is to be expected, therefore, that graphs of pressure drag on a basis of speed will show rather pronounced irregularities.

D. W. Taylor made up graphs of this type for two groups of five models each, representing 400-ft ships. The two groups had Cp values of 0.56 and 0.64, respectively, and five different displacements, with ship values ranging from 1,920 to 11,520 tons. Using the formula Rr = aV" and plotting the velocity exponent n on a basis of ship. speed, he obtained the curves

shown

in

on page 48 of S and P, 1943. For some of the models the residuary resistance varied at a rate exceeding the 11th power of the speed V. This diagram shows definite, rather narrow lanes embracing all the n values over certain speed Fig. 54

1

to 6 variation in displace-

ment-length quotients.

To determine whether

there are systematic or

characteristic patterns in the exponent

n

of the

Design

TX-7

U. S. Mar. Comm. cargo vessel Wilfred Sykes

92 Ore ship 96 Destroyer tender 119 Destroyer

probably of the order of the 1.9 or 1.93 power. Although the absolute values of Cf cover a rather wide range, the rates of change of Cf with

Analytic work on pressure drag due to wavemaking, described in Chap. 50, indicates that what may be termed the V^ component is only one of those acting. There are components of this drag which vary as the 4th, the 6th, the 8th, and higher powers of V. The expressions for these components are periodic in form, and they produce

TCB

74 Tug 79 Cargo ship

as slightly less than the square of the ship speed,

physical entities.

data on

SNAME

Normandie Tanker E [SNAME,

56 Tanker

of 0.244 to 0.310. It is

hitherto been classed as residuary resistance into

test

sheets listed hereunder: sheet 39 Passenger ship

known from measured .ship-thrust data that Rf for hull surfaces of normal roughne.ss varies

ranges, despite the

n from model

nine different vessels, as reported on the

in a T,

V, as indicated by a plot of Cf on R„ (with L and j'(nu) constant), are comparatively small. That portion of the hull drag due to deflection of the water, separation, and similar effects is assumed to vary as V~. Unfortunately, since Rr includes these effects plus the drag due to wavemaking, it is still difficult to break up what has

kV", for the

C-i

U. S. S. Dixie U. S. S. Hamilton U. S. S. Pensacola 121 Heavy ABC ship of Part 4 Transom-stern design. cruiser

residuary resistances for these models were

The

calculated from the formula

Rr =

Cii{0.5p)SV^,

using the values of residuary resistance coefficient sheets for a range of lO^Cjj fisted on the

RD

quotients.

speed-length

These

were,

in

turn,

calculated from the observed model resistance

data and the described

ATTC

1947 friction formulation, as

SNAME Explanatory Notes the RD sheets. Technical and

the

in

accompanying

Research Bulletin 1-13, July 1953. The ship wetted surfaces were obtained from the model wetted surfaces by multiplying by X^(lambda). The Rr values were plotted on log-log paper on a basis of T„ and F„ The velocity exponents n were obtained by measuring the slopes of the Rr curves at even T^ values. This .

work

is

facilitated

by the use

of special log-log

David Taylor Model Basin, which have a supplementary scale

plotting sheets, available at the

of slopes around the margin, to which a slope anywhere on the sheet is transferred by a set of parallel rulers.

A

curve oi

Rr

increasing with

V on

Fig. 56. L is

associated with a finite positive value of n. If the resistance remains constant with increasing V,

= 0, whereas if R decreases as V increases, which it does in certain speed ranges for planing and other craft, as shown on Fig. 53. D, n becomes negative. Large circles on the n-curves indicate then n

the T, for the designed speed along the curve for

each ship.

The new velocity-exponent curves indicate

that:

(a) The curves for various ship types by no means follow the same pattern, nor do they fall in lanes, as do D. W. Taylor's earlier data [S and

P, 1943, p. 48] (b)

The n-value

for the big ore ship reaches 5.75

HYDRODYNAMICS

308

0.2

0.3

a5

0.1

0.6

0.7

O.S

0.9

1,0

IN SHIP DESIGN

1.2

I.I

1.4

1.3

Sec. 56.10

1.5

I

1.7

.6

I.S

at the designed T^ of 0.544. This indicates that

expected that, at T^ values near the

the large volume on a given length, characteristic

n

of this ship,

price in

2.0

1,9

2.1

Variation of Speed Exponent in Rbsiduart-Resistance Formula Rr = kV" FOR Nine Large Ships

Fig. 56.L

carried at an unreasonably high

is

wavemaking

resistance.

The n-value

is

will

maximum,

be negative. This occurs for the

PT

boat

in Fig. 53.D. (f)

There

are

irregularities

n-curves

the

in

only slightly over 3.0 at a T, of 0.4. This reveals

unexplained on the basis of wave interference

an acceptably low wavemaking drag for the lower speeds customary with this type when it was

alone.

first

developed into large sizes in the early 1900's.

For actual ships which are driven hard, values of n exceeding 7.0, 8.0, and over are by no means unusual. High-speed ships may reach the (c)

56.10

Variation of Total Resistance of

and Ship with Speed-Length Quotient.

Model

It is use-

times for the designer to be able to find

ful at

quickly the total resistance of a ship in some

maximum,

everyday terms such as pounds of total resistance

with a greatly diminished n at that speed, as for the heavy cruiser Pensacola and the destroyer Hamilton in Fig. 56.L. The following footnote by

per ton, expressed by flr/A, at say the designed

greatest n-value at a speed less than the

C. Rougeron

quoted from the U.

is

S.

Naval

Institute Proceedings, February 1953, page 190: "Actually, the speed-power ratio increases in a some-

what more complicated manner. In a recent French leader the 'direct' resistance is found to vary in proportion to the square of the speed at low speeds, to the 6th power of the speed in the vicinity of 28 knots; and only flotilla

to the 1.35 of

power

of the speed for speeds in the vicinity

38 knots."

(d)

Some

planing craft show pronounced knuckles

Rr on V, with accompanying sudden drops in the value of n, as in Fig. 30.B. The data from which Fig. 53. D of Sec. 53.7 were plotted show no such sharp discontinuities but they do reveal that at several points the resistance levels out so that it varies with V at some power only slightly greater than 1.0. (e) For high-speed planing craft it may be in the curve of

when only the type of ship and the approximate Taylor quotient T, = F/vL or Froude number F„ are known. For example, the Rt/^ value for a large, modern Great Lakes freighter speed,

at designed speed

Atlantic liner

is

is

about 2

some 10

lb per ton, that of

and that

lb per ton,

an

of a

motorboat is of the order of 600 lb per ton. H. M. Barkla has published a log-log plot showing values of the ratio Rr/W on a base of T^ for eleven sailing-yacht and motorboat hulls, as listed on page 237 of his paper "High-Speed Sailing" [INA, 1951, Vol. 93]. The range of T, is from 0.4 to 10 and of Rr/W from 0.004 to 0.3. fast

Barkla's resistance-weight ratio the ratio

Rt/^, when

is

the latter

pounds resistance per long ton

1/2,240 times

is

expressed as

of weight.

To

provide data for a greater variety of water

craft,

both large and small, there have been

plotted on Fig. 56.

designed

speed,

of

M a

the values of flr/A, at the considerable

number

of

OBSERVED SHIP-RESISTANCE DATA

Hec. 56.10

309

i^kl

4 Fig. 56.

M

5

6 7 8 S

10

Plot of /?r/A on T, for Many Vessels at Their Designed Speeds

many types. The data indicated by the small circles on the figure are derived from calvessels of

are considerably larger than the apparent varia-

respective

tions on the figure. It is possible that a single meanline will not suffice in this region, especially in view of the large variations in characteristics of vessels running at the same T, value. For

Unfortunately, the model

instance, the upper circle at a T, of about 1.93

data on some sheets are for bare hull only; on other sheets they are for the hull plus simple appendages. This variation is considered not too important as the plot is intended for indicating

represents a small patrol boat with a displacementlength quotient of 93.4, while the lower circle at a r, of about 1.985 represents the destroyer Hamilton, with a displacement-length quotient

culated values of the total resistance of the ship,

based upon model

tests, at

general-information

SNAME RD

sheets.

block

the speed listed in the

on

the

approximate values only. It is found that a single tentative meanline passes close to or through most of the designedspeed spots, regardless of the size or type of vessel or of the T, at which it runs. For the higher

plotted in the upper right-hand corner of this

Tj values there

considerable dispersion in the

graph, the final meanline will be considerably

few available spots, especially as the vertical scale is logarithmic and the variations in per cent

high-speed craft of good to e.xcellent performance.

is

of only 40.

The

plot of Fig.

56.M

does, however,

indicate regions of T^ where the data for certain classes of vessels are to be found.

It

is

probable that, as more model data are

lower than the one

now

indicated, especially for

SIO

HYDRODYNAMICS

IN SHIP DESIGN

Src. 56.11

OBSERVED SHIP-RESISTANCE DATA

Sec. 56.12

removed; sec the

series of reports listed

Resistance

subsequently

directly, has

of ships, without their propulsion

been a subject of active discussion architects since about 1850. The

thought that it constituted the only valid method of attack on ship-resistance and propulsion problems was, in fact, put forward in the late 1860's and early 1870's as one of the arguments against the proposals of W. Froude to establish the first model-testing basin. Froude, with his usual wisdom and thoroughness, tackled both the full-scale and the model problems. Under his supervision the hulk of H. propeller,

was towed

M.

Greyhound,

less its

somewhat disappoint-

(7)

571; also

Yarrow, A.

TNA,

Due

to surging of the

—

D =

7.177

21.0 ft (molded)

H

Cb = 0.685 5.0 ft, to bottom

390

S =

Lpp = 190.5

B =

A =

ft

=

t

Data from tests models of the launch are men-

tioned also in Sec. 52.3.

hulk of Japanese destroyer Yudachi, about 1934. Reports published by Hiraga in the two papers "Experimental Investigations on the Y.,

of

append-

Cm =

0.972.

—

1896, Vol. 4, pp. 93-104, esp. pp. 93-94.

Yokota, A., Yaraamoto, T., Shigemitsu, A., and Togino, S., hull of 40-ft steam launch, about 1929. Report embodied in the paper "Pressure Distribution Over the Surface of a Ship and its Effect on Resistance," Proc. World Eng'g. Congr., Tokyo, 1929, Vol. XXIX, Part 1, publ. in Tokyo in 1931. The steel steam launch forming the subject of these tests had an Lpp of 39.37 ft, an extreme beam of 9.79 ft, and a draft of about 3.99 ft. The tests included measuring the thrust at the thrust bearing during self-propelled tests. Further details from this paper and additional general data relative to

Hiraga,

incl.

Conn, J. F. C, Lackenby, H., and Walker, W. P., "B.S.R.A. Resistance Experiments on the Lucy Ashion. Part II The Ship-Model Correlation for the Naked-Hull Conditions," INA, 1953, p. 350ff. The first two parts were published as B.S.R.A. Rep. 107 in 1952. (c) Lackenby, H., "B.S.R.A. Resistance Experiments on the Lucy Ashion. Part III The ShipModel Correlation for the Shaft-Appendage Conditions," INA, Apr 1955, Vol. 97, pp. 109-166 (d) Smith, S. L., "B.S.R.A. Resistance Experiments on the Lucy Ashion. Part IV Miscellaneous Investigations and General Appraisal," INA, 1955.

—

—

(8)

the tests are given in Sec. 42.10.

(5)

4,488 ft^

(b)

Double-ended ferryboat Cincinnati (for New York harbor), 1896. Report published by F. L. DuBosque,

of one-third scale

(molded)

ages

Cp = 0.705

24, pp. 111-117.

(4)

ft

hull proper

torpedoboat, 100 ft

1883. Report published by Yarrow in the paper "Some Experiments to Test the Resistance of a First-Class Torpedo-Boat," INA, 1883, Vol.

SNAME,

vessel,

Scale Measurements,"

long,

(3)

vessel, the

and other to standard and have not as yet (1955) been fully analyzed. British Shipbuilding Research Association, Lucy Ashlon, 1950-1951. This was an ex-paddlewheel steamer driven by abovowater gas-jet engines. The complete set of test reports follows:

1952, p. 449].

F., British first-class

towed

wake from the towing the test data are not up

(a) Denny, Sir M. E., "B. S. R. A. Resistance Experiments on the Lucy Ashion. Part I FuUINA, 1951, Section on Int. Conf. Nav. Arch. Mar. Engrs., p. 40ff. The principal characteristics of the Lucy Ashion are:

Froude, W., H. M. S. Greyhound, about 1874. Report published by Froude in the paper "On the Experi-

ments with H. M. S. Greyhound," INA, 1874, pp. 36-73 and Pis. III-XIII. The towing-test data from the Greyhound experiments have been analyzed by A. M. Robb [INA, 1947, Vol. 89, pp. 6-15; abstracted in SBSR, 5 Jun 1947, pp. 568(2)

S. S. YTB 602; 100-ft, 1,000-horse single-screw harbor tug, early 1950's. This vessel was towed, with its propeller removed, by the U. S. S. LSM 458, the latter fitted with Kirsten rotating-blade

factors,

data have been published, including the Greyhound experiments, are listed hereunder: (1)

XXVI-XXXIII, and

presence of

(by modern standards) of the hull surface. Since that time others have engaged in similar using improved methods and instrumentation. The full-scale towing tests for which

U.

propellers.

partly because of the excessive roughness

projects,

Pis.

that paper. (6)

for resistance in the early

1870's but the results were ing,

S.

and

INA,

Ships,"

"Experimental Investigations on the Frictional Resistance of Planks and Ship Models," Society of Naval Architects of Japan, Dec 1934, Vol. LV. The INA paper described and gave the results of towing tests on the destroyer Yudachi, on a so-called "plank ship," 77 ft long and 0.525 ft wide, as well as on a tug (unnamed), having a length of 114.83 ft and a displacement of 296.93 t. The displacement of the plank ship was 3.356 t; its L/B ratio was 147. Included in the towing test was a 26-ft model of the Hashike and of a 56-ft Vedette boat; see PI. XXVI of the INA paper. Lines and other data of the 300-t twin-screw tug are given on PI. XXXI of

devices, to determine their full-scale resistances

among naval

311 Planks and

TiOng

1934, pp. 284-320

in this section.

The towing

of

(9)

Nordstrom, H. F., hulk of Swedish destroyer Wrangel, about 1952. Report published as "Full-Scale Tests with the Wrangel and Comparative Model Tests," SSPA Rep. 27, 1953 (in English). Large-scale self-propelled model D. C. Endert, Jr., representing a Victory ship; about 1953. Full-scale trials of a Victory ship were conducted by the Dutch in conjunction with tests of five model geosims, plus an independently powered 72-ft

HYDRODYNAMICS

312 model built

One

named the D.

IN SHIP DESIGN

of the first installments of the published

dummy

data

sister ship),

with

hubs substituted. Otherwise the append-

ages on both vessels were the same, comprising

this project

with the mines weeperfSiriits (a

Sec. 56.12

the two propellers of the Aldebaran removed and

C. Enderl, Jr.

was prepared by W. P. A. van Lammeren, J. D. van Manen, and A. J. W. Lap, entitled "Scale-Effect Experiments on Victory Ships and Models. Part I, Analysis of the Resistance and Thrust Measurements on a Model Family and on the Model Boat D. C. Endert, Jr.," INA, Apr 1955, Vol. 97, pp. 167-245. French minesweeper Aldebaran, about 1954. The report of this work was published by R. Retail and S. Bindel in a paper entitled "fitude k la Mer de la Resistance ^ la Marche et de la Propulsion; Rapprochement avec le Module (Sea Trials to Determine Towing Resistance and Propulsion: Correlation with the Model)," ATMA, 1955. These trials 'involved towing the minesweeper Aldebaran on

(10)

of steel,

(11)

roll-resisting keels, twin rudders, exposed twin propeUer shafts, and twin supporting struts. Towline tensions were measured, both on the towing and on the towed vessels. Shaft torques were observed by torsion meter on the towing vessel but no propeller-thrust readings were taken. The vessels were 140.95 ft long on the waterline, with a maximum waterline beam of 27.95 ft and a mean draft of about 7 ft. The displacement with appendages was 380 long tons. Silovi6, S., and Fancev, M., "Measurements on M. V. Rijeka, with their Attempted Practical

Application,"

INA Autumn meeting, SBMEB. Apr

Yugoslavia; abstracted in 264-266.

1955,

in

1956, pp.

CHAPTER

57

Estimate of Total Resistance for Surface and

Submerged Ships 57.1 57.2 57.3 67 4 .

67.5 57.6

67.7

General

Summary of Kinds of Ship Resistance

...

Ratios of Major Resistance Components

Methods

of

.

.

Method

315

57 12

Calculating the Overall Wetted Surface and

310

57 13

Drag

Mathematical Methods

.

Ship Still-Air and Wind Resistance from Chapter 54

Bulk Volume .

316

of

Coefficients

a Submerged Object and Data for Submerged .

.

Pressure Resistance of Submerged Bodies as

57 15

a Function of Depth Resistance Due to Flow of Water Through Free-Flooding Spaces

.

321 321

322

322 322

57. 14

of

Predicting Pressure Resistance

General.

.

.

Bodies

318

Analytical and

57.1

An Approximation of Separation Drag Slope Resistance and Thrust

of Predicting Ship Resist-

ance

57.8

57.9 57.10 57.11

Approximating the Total Resist-

ance of a Ship Ship Friction Resistance Calculation from Chapter 45 Residuary Resistance Prediction from Reference and Standard-Series Data Telfer's

313 313 313

323 323

321

This chapter covers methods

and 12.10

Sees. 12.1

of

Volume

I

and defined

in

and predicting full-scale

Sees. 12.2 through 12.7. This subdivision, based

resistance data for bodies or ships, intended to run

on the Froude theorem that the resistances due to tangential and to normal forces on the ship are for the most part independent and therefore can be segregated, is repeated here in Table 57. for the convenience of the reader. However, the

of estimating, calculating,

on the surface or submerged, based upon available information. It does not discuss the extrapolation of model-test data to full scale for

any

specific

ship design. Descriptions of this procedure, at least as utilized

Towing

Tank

by members Conference,

of the

are

American

published

in

SNAME

Technical and Research Bulletin 1-2, "Uniform Procedure for the Calculation of Frictional Resistance and the Expansion of Model Test Data to Full Size," of March 1952. Details of the testing and extrapolating proceentitled

interactions listed in Sees.

12.1

and 12.10 are

placed under a separate heading.

The following sections describe, in turn, various means of estimating these different kinds of resistance.

57.3

Ratios of Major Resistance Components.

Useful ratios in analysis and design are the per-

dures, corresponding to those in general use in

centages of the friction and residuary resistances,

America, are described in Bureau of Construction

according to the Froude subdivision, making up the total hull resistance. The solid line in Fig.

"The Prediction by Methods in Use at the United States Experimental Model Basin, and Repair Bulletin of Speed and Power

7, entitled

of Ships

57. A, dividing the total Rt into friction R^ and residuary Rr over a T^ range of 0.4 to 2.0, is

Washington," 1933. This chapter also gives some information concerning the resistance of fully submerged bodies resembUng submarines. These data may be found of benefit to the marine architect when he is called upon to approximate the drag of a non-ship form to be towed submerged. 57.2 Summary of Kinds of Ship Resistance.

adapted from V. M. Lavrent'ev ["Marine Pro-

The various

sheets for about twenty ships,

categories into which, in the present

state of the art, the resistance of a ship to steady straight-line

motion

is

divided,

are

listed

in

pulsion Devices,"

Moscow,

The same

diagram

original

1949, Fig. 37, p. 85]. is

published by G. E.

Pavlenko ["Soprotivleniye Vody Dvizheniyu Sudov (The Resistance of Water to the Movement

Moscow, 1953, Fig. 5, p. 16, covering a range of F„ from 0.1 through 0.6]. The broken line is based on data from the SNAME of Ships),"

RD

more

easily driven

than those of the Taylor Standard Series. It includes a roughness allowance (lO')ACp of 0.4.

313

HYDRODYNAMICS

314

TABLE

IN SHIP DESIGN

Classification and Subdivision of THE Resistance op a Ship to Steady, Straight-

Sec. 57.3

57.a

0,20

0.25

0.30

0J5

0.45

O.40|

Ahead Motion I.

Pressure

Drag

or Resistance, due to

Normal Pressure

on the Ship (a)

Deflection drag and closing thrust for the hull proper

(b) Deflection

drag and closing thrust for the hull

appendages

Rg and cavitation drag, appendages (d) Wavemaking drag Rw for the hull proper and for such appendages as may be near enough to the surface to generate waves (e) Drag due to the generation of spray roots and spray. (c)

Separation or eddying drag

for the hull proper

and

for the ,

II. Friction or

Area. This (a)

Tangential Resistance

Rp on

OA

Tanvis resistance, varying as

Z7 or

F

0.6

1.2

1,0

1.1

the Wetted

first

ABC transom-

(b)

The

(c)

stern ship designed in Part 4, for the sustained

Tanqua resistance, varying as U^ or V^ Some unknown combination of (a) and (b), varying an unknown (and probably varying) power of f7 or F

between

A

20

text to the

power

as

I.S

I.

Typical Percentages op Friction and Residuart Resistances for a Range op SpeedLength Quotients The significance of the two graphs is explained in the

considered to be either:

is

0.6

Fig. 57. a

1

and

Both curves are embodying a

subdivision into: (c)

Friction

sea speed and trial speed, respectively.

2.

different classification could be used here,

smooth

circled spots are values for the

on

resistance

such

surfaces, flat or curved, as

may

hydrodynamically be incorporated in

loci of division points for

de-

signed speeds at the various T^ and F„ values given. It

Rf vary

is

to be noted that the ratios of

Rk

to

rather widely over the speed-length range

the ship

indicated. If ships are overdriven the percentage

due to roughness superposed on the hydrodynamically smooth surfaces, flat or curved.

oi Rii

(d) Friction resistance

in III. Interactions

between

and

I.

II.,

as follows:

may

be up to twice as great as that shown

the figure. If underdriven,

it

may

be only

two-thirds as large.

(a) Interaction effect of viscous or friction flow on the pressure resistance due to wavemaking, and the reverse,

symbolized by

Rwf

(b) Interaction effect of separation or

eddying on the pressure resistance due to wavemaking, or the reverse, symbolized by

Rws

Interaction effect of viscous or friction flow on the pressure resistance due to separation or eddying, or the (c)

reverse, symbolized

IV. Air and

by Rsf

•

Wind Drag and

Resistance, embodying:

due to ship motion alone, with a true or natural wind of zero (b) Wind drag D,f, exerted always downwind from the relative-wind direction. This drag has both transverse and axial components, due to aerodynamic lift and drag. (a)

Still-air resistance

Rsa

>

0.6

0.4

08

1.0

1.2

1.4

1.6

1.6

2.0

,

Wind

composed of the net axial by the wind, acting opposite to the direction of ahead motion. The definitions of and distinctions between these terms are explained in Sees. 26.15 and 54.1 and illustrated in Figs. 26.G, 26.H, and 26.1. (c)

resistance iJwind

Percentages of Friction and Residuary Resistances for Three Specific Cases

Fig. 57.B

>

force imposed

57.

Fig.

and

indicates,

for

an

EMB

ABC

research

ship design,

for destroyers as a class, the variation of

friction

V. Gravity Forces Acting on the Ship:

B

model, for the transom-stern

and residuary

resistances throughout the

intermediate and upper speed ranges of those

EMB model 2861 is the subject of the model pressure-distribution tests made by

ships. Slope drag Ds due to the inclination of the buoyancy-force vector to the weight-force vector, with a force component opposing motion (a)

(b)

,

Slope thrust Ts

,

similar to (a) preceding but with

a force component assisting motion.

first

E. F. Eggert [SNAME, 1935, pp. 139-150]. As expected, in the low-speed ranges before appreciable

wavemaking

begins, the total resistance in

TOTAL

Sec. 57.4

each case

is

largely frictional. In the high-speed

and near designed-speed T, values

ranges, at

than O.Sflr

of

only slightly greater

is

.

Methods

57.4

Rp

or more,

1.7,

1.6,

RE.Sl,STy\NCF.

of Approximating the Total

Re-

OF RODY OR SHIP

315

This compares well, as a quick approximation, with the value of 171,830 lb derived in Sec. 66.9 by the use of the Schoenherr mean friction line and the Gertler reworked data of the Taylor

Standard Series described in Sec.

Ct

56.5. Actually,

at 20.5 kt would

sometimes necessary to estimate the total resistance of a ship at a given speed, usually the designed speed, when nothing more is known of it than its principal dimensions

for the destroyer tender, the

and weight displacement. The ship

shape, and form coefficients close to those .selected for the vessel being designed. Reference to the

sistance of a Ship.

It is

in question

ma}' not even be designed or the one making the estimate

may

never have heard of

ship has not been tested in is

no opportunity

estimate

A

model

it

before.

scale

The

and there

of doing so before the resistance

SNAME RD and ERD sheets having proportions,

crude approximation of the total resistance, by the formula

for a speed V, is given directly

(57.i)

where Ct is estimated for the T, or F^ in question by reference to the full-scale values for one or more similar ships of nearly the same size, such

SNAME RD

as those listed in the

The wetted

for the

area

similar ship

or

S is

is

Summary

taken as the value

derived by the Cs

Care is required that the reference ship is of about the same length as the ship for which the total resistance is to be derived, so that for a given T, or F„ the Reynolds number R„ and the specific total friction drag coefiBcient Cp are both nearly the same. For example, in the early stages of the ABC coefficient of Sec. 45.12.

design, described in See. 66.9, the total resistance is

required to furnish a

first

approximation of the

SNAME RD

power. Reference to the Summary Sheets indicates that the destroyer shaft

tender of

RD

sheet 96 closely resembles the ship

being designed.

The

latter sheet indicates that

the appendages are limited to a half -rudder only.

For the tender, at

its

designed speed of 20 kt,

the value of the total specific resistance coefficient

Ct

is

3.023(10^^)

ship

is

and the wetted surface S

The designed speed

46,509 ftl

V

for the

is

ABC

20.5 kt, or 34.625 ft per sec; the numerical

value of

V

is

sheet gives directly

the values of total resistance

per ton of weight or 1000

Rt

,

total resistance

Rt/^, and Pb

for a geosim

1,198.9.

Then, for the

ABC

ft,

as indicated on the sheet.

The

total

resistance of the geosim ship of the length under

design

Rt = Cr(0.5p)SF'

Sheets.

SNAME ERD

appropriate

vessel having a "standard" length of 100, 200, 400,

required.

is

be higher than the figure quoted. One may, of course, pick a vessel from the

is

then determined by correcting for the

difference in friction resistance

due to the

differ-

ences in length and in speed between the reference ship and the "design" ship. This scheme, or a it, has the advantage that curves can be constructed for a range of Tj or F„ considerably greater than will be encoimtered in practice. The full-scale data on the

modification of oi

Rt and Pe

SNAME RD

Summary

Sheets

are

for

the

designed-speed spot only.

Another rapid method

of approximating the

total resistance for the designed-speed spot is to

pick the value of the

meanhne

Kt/A,

of Fig.

at the proper T^

56.M. Multiplying

,

from

this value

by the weight displacement A gives fir at once. For example, the i2j./A value for the ABC ship, at a T, of 0.903, is 10.2 lb. Multiplying by 17,300 tons, the displacement at

an early stage of the

design, gives a total resistance of 176,400 lb. This

compares with the 171,830

lb

quoted

earlier in

the section. It is customary,

if

time

is

available, to estimate

the friction resistance

separately

residuary resistance

Rr hy

Rp and

the

the methods of the

two sections following, using model-test data from a parent form such as the Taylor Standard Series. They are added to give the total resistance Rt This method enables the designer to draw curves of estimated Rp Rt and Pp for a very large range of Taylor quotient T^ or Froude number F„ .

ship,

,

on the assumption of the same Ct and the same S, and for roughly the same speed,

,

.

Rt = Ct{0.5p)SV^

Strictly speaking, the use of standard-series or

from models or ships of different same dimensions and proportions and having exactly the same form reference data

=

3.023(10~')(0.9905)(46,509)(1, 198.9)

shape, even though of the

=

166,960

coefficients, requires the use of a shape-correction

lb.

HYDRODYNAMICS

316

For example, it has to be decided whether the shape contemplated for the design will have less (or more) resistance than the standard-series

factor.

or reference hull of the

same proportions. This is by the EHP/Taylor

after a fashion,

afforded,

EHP or "angleworm-curve" ratios of the SNAME

ERD

However, with many such ratios to formulate anything

sheets.

at hand,

it is still difficult

approaching systematic rules for guidance in this matter. A bulb bow carried by the new if appropriate, will reduce its resistance below the Taylor Standard Series value. This is one reason why the resistance of the ABC tran-

design,

som-stern design, determined by model test, is less than the values calculated earlier in this section.

IN SHIP DESIGN

may have

walking

provide

The

deck.

Sec. 57.5

rather wide flat surfaces on top, to

on

space

the

superstructure

transverse curvature along portions of

the deck edges, even though they are rounded,

is

be more severe than along the bilge corners of a surface vessel. 57.6 Residuary Resistance Prediction from

likely to

Reference and Standard-Series Data. It is possible to approximate the residuary resistance of a surface ship, at a given speed V, or at a series of speeds, by assuming that it is the same as the residuary resistance Ra of a model having the same proportions. Data of this kind can be found in the SNAME RD sheets and similar sources. Continuing the discussion of Sec. 57.4, it is somewhat risky to rely on the proportions Cp B/H, and A/(0.010L)' (or ^/(O.IOL)') as com,

Most books on naval

architecture give several

formulas and methods for predicting the total

and

resistance

power

the

prising

well

as

sole

the

as

preponderant

the

influences on residuary resistance, neglecting the

drawn and certainly before models are built and tested. For example, G. E. Pavlenko describes no less than eleven methods, dating from 1899 to the

shape factors entirely. What appear to be minor differences in shape or proportions often produce appreciable changes in resistance. These will not be explained, and can not be allowed for, until our present (1955) knowledge of ship hydrody-

effective

of ships in

design stage, perhaps before the lines are

present,

.

including

Standard

Taylor's

Series,

Ayre's method, and Doyere's method, for finding the resistance and effective power of merchant

namics

and. naval vessels of different kinds ["Soprotiv-

of speeds

Vody Dvizheniyu Sudov (The Resistance Water to the Movement of Ships)," Moscow,

leniye of

1953, pp. 305-379].

In

all

these cases, however,

it is

most important

or method,

as given in the text.

If

no

limitations are mentioned, they should be sought in other references or directly

from those who

prepared and published them. 57.5 Ship Friction Resistance Calculation from Chapter 45. The methods used and the numbers required for a calculation of the ship friction

is

considerably extended.

Rr/A

calculation of values of

and a given

set

"phantom" ship

it

ship

of

for a range

of proportions,

assuming that these are the same as takes

to note the limitations on each formula, graph, table,

The

exactly

for a

by

TSS

those proportions,

for granted that the shape of the proposed

good as (and no better than) that

of the This does not prevent a designer, however, from estimating that his proposed hull is

TSS

as

ship.

have x per cent

will

less

or

residuary resistance than the

The

hull.

difficulty here, as

y per cent more TSS "phantom"

mentioned previously,

the lack of systematic and reliable data for

is

selecting the x-

and y-values.

The contours

of

Rr/A

for the

Taylor Standard

Two sets of them,

resistance, including all types of roughness, are

Series are described in Sec. 56.3.

set forth in detail in Sees. 45.12

= 0.90, are illustrated in Figs. 56.A These contours are intended to be used for ships having the same proportions Cp B/H and displacement-length quotient A/(0.010L)^. The designer may apply, as x- and y-values, increments or decrements of Rr/A. An illustrative example of the Taylor Rr/A. method, for the fifth approximation of characteristics in the preliminary design of the transom-

The method and

thje

for

through 45.20.

calculating the wetted length

wetted area S for planing hulls

is

dis-

cussed in Sees. 45.24 and 53.6.

The method

of calculating the friction drag of

a submerged submarine

is

essentially the

same

as for a surface ship, except for the inclusion of the entire outer area, surrounding what is described elsewhere as the bulk volume. The transverse curvature of the lower part of the hull of a submarine is, as a rule, relatively less than for the bilge corners

nearly

flat

on a large surface ship with flat or However, a submersible hull

floors.

for

V/Vl

and

56. B.

,

stern

Table

ABC 57. b.

ship described in Part

The

4, is

given in

basic data for this stage of the

design are listed in the right-hand column of

Table

66. e in Sec. 66.11.

The proportions required

TOTAL RESISTANCE OF BODY OR

Sec. 57.6

for this calculation are

and A/(0.010L)' =

Cp = 123.6,

0.62,

B/H =

2.808,

while the value of

r„ at the designed speed selected for this example 0.908.

is

The displacement

The

linear interpolations described in Sec. 56.3

down

in

Table

57. b,

W.

adapted from D.

56.

B

characteristic spots

A/(0.010L)' 2.25

drawn

No

and

values of

=

123.6 for both

(of

The

quotient

of /? a/A of 4.014 lb per ton

A

then multiplied by the displacement

TABLE

57.b

ABC

ship.

made

is

here for the difference

between the salt-water specific gravity of 1.024 for all the TSS data and the specific gravity of 1.027 for the

ABC

The method

ship.

of predicting the residuary resist-

is

ratios

for this speed-length

The derived value

allowance

B/H

were picked from the originals of Figs. 56. A and 56. B, drawn to a scale over three times larger than that of the reproductions. Normally it is not possible to determine the values of Rr/A by inspection to more than three significant figures, indicated in Table 57.b for a T, of 0.95. is

"phantom" TSS ship having the

ance of a given ship from the "phantom" Taylor Standard Series ship having the same proportions

3.75, respectively), at a T, of 0.90.

Rr/^

317

A and Cp = 0.62 and

in Figs. 56.

indicate the coordinates of

the

proportions of the

Taylor's Table VIII-A [S and P, 1943, p. 63].

The

SHIP

to give the predicted total /?« of 65,829

t

for

lb,

assumed here as

is

16,400 tons. are set

16,400

of

rather different

TSS data

when

the Gertler reworked

are employed. These are described in

and a sample calculation is set down in Table 57. c. The ship selected is the fifth approximation of the ABC design, hsted in Table 66.e of Sec. 66.11, but the basic data now involve the wetted surface S and the fatness ratio F/(0.10L)^. These are, from Table 66.e, 44,759 ft' and 4.327, respectively. The mass density p is taken as 1.9905 slugs per ft^ for "standard" salt water. Sec. 56.5

The volumetric

Residuaby-Resistance Prediction for

ABC

Ship

coefficient

F/L^

of the Gertler

From Taylor's Rr/A Contours

The characteristics and proportions listed correspond to those of the fifth approximation in Table 66.e in Sec. 66.11. The method illustrated here is adapted from D. W. Taylor's Table VIII-A in his "The Speed and Power of Ships," 1943, page 63. One particular pair of contours required here is reproduced in Figs. 56. A and 56. B. The calculation is made for one speed only, 20.5 kt (the designed speed), at a T, value of 0.908. Length on waterline, Displacement,

A

A =

L =

510

16,400

Cp = 0.62

123.6

(0.0 lOL)'

B/H 1.50

1

2.25

2.808

-

1.50

2.25

fi

=

73

ft

Draft, ff

=

26

ft

Beam,

ft

t

=

0.372

B =

H

2.

HYDRODYNAMICS

318

TABLE

IN SHIP DESIGN

57.0— Residuary-Resistance Prediction for

ABC

Ship

Sec. 57.7

From Gertler's Cr Contours

The characteristics and proportions listed correspond to those of the fifth approximation in Table 66. e of Sec. 66.11. The Cr contours are given in TMB Report 806, "A Reanalysis of the Original Test Data for the Taylor Standard Series," by M. Gertler, March 1954. One particular pair of contours required here is reproduced in Fig. 56.D. The calculation is made for one speed only, 20.5 kt (the designed speed), at a T, value of 0.908. Length on waterline, L = 510 ft Displacement volume, V = 574,000

Wetted surface, S = 44,759 Beam, S = 73 ft 20.5 kt

1

=0=

34.62

ft

per sec

ft^

Draft, ft'

H

=

V/(0.10Ly

B/H =

26

=

ft

4.327

2.808

= 0.62 0.5p = (0.5) (1.9905) Cp

slugs per

ft'

=

0.9953 slugs per

fts

TOTAL RESISTANCE OF BODY OR

Sec. 57.7

XIV-XVII. These

plates contain several of the

Telfer extrapolation diagrams. (4)

Horn,

"Die Weiterentwicklung des Modellver-

F.,

suchsverfahrens zur Ermittlung des Schiffswiderstandes (The Further Development of Model Test

Methods

(6)

U. (7)

(8)

(9)

on

507 Telfer, E. V., "Frictional Resistance and Ship Resistance Similarity," NECI, 1928-1929, Vol. XLV, pp. 115-184 SNAME, 1932, Fig. 13, p. 89, for three models of the 16

(5)

Nov

to Obtain Ship Resistance)," Schiffbau,

S. S.

1927, pp. 504-510, esp. Fig.

North Carolina

1

p.

(old) series

Van Lammeren, W. P. A., "Propulsion Scale Effect," NECI, 1939-1940, Vol. 51, p. 115ff Van Lammeren, W. P. A., Troost, L., and Koning, J. G., RPSS, 1948, pp. 39-40 and Fig. 13 Telfer extrapolation diagrams have been prepared for

the Lucy Ashton family of models; see the references

hsted under Fig.

20 opp.

INA, Apr

(10)

(11)

(12)

in Sec. 56.12, esp.

(7)

p.

372 and Fig. 23 opp.

INA,

1953,

p. 378; also

and 13 opp. p. 122 Birkhoff, G., Korvin-Kroukovsky, B. V., and Kotik, J., "Theory of the Wave Resistance of Ships," SNAME, 1954, pp. 359-396, esp. Fig. 1 on p. 361 Acevedo, M. L., Comments on Skin Friction and Turbulence Stimulation, 7th ICSH, 1954, SSPA Rep. 34, 1955, pp. 110-117, esp. p. 115 Van Lammeren, W. P. A., van Manen, J. D., and Lap, A. J., "Scale Effect Experiments on Victory Ships and Models. Part I Analysis of the Resistance and Thrust-Measurements on a Model Family and on the Model Boat D. C. Endert, Jr.," INA, Apr 1955, Vol. 97, Figs. 21 and 22 on pp. 184-185 and Fig. 25B on p. 232 1955, Figs. 12

—

(13)

Sund, E.,

"On

the Effects of Different Turbulence-

Exciters on B.S.R.A. 0.75-Block Models

Made

to

Various Scales," Norwegian Model Basin Rep. 11, Aug 1951. Figs. 1 through 11 on pp. 19-22 embody

SHIP

319

G. Birkhoff, B. V. Korvin-Kroukovsky, and J. Kotik [SNAME, 1954, p. 361], it affords a plausible separation

coefficient

excellent

Ct

of the total specific resistance

into components,

representation

visual

ponents. Further,

allowance

and

as well as an

com-

those

of

visualizes the ship roughness

it

illustrates

discrepancies which

still

rather

the

forcibly

exist because of inade-

quate model-testing techniques, lack of complete knowledge of scale effects, and similar factors. The diagram of Fig. 57. C, deliberately drawn in schematic fashion, illustrates most of the features mentioned. The formula for the smooth, flat-plate, turbulent-flow friction line is assumed for simplicity to be an explicit function of Cf and log Rn so the Cf line is straight when plotted on those coordinates. The horizontal gap between the model range and the ship range is deliberately closed to enable the features to be shown to better advantage. It is assumed that the average roughness allowance to be added to the friction line representing hydrodynamic smoothness is practically zero at the point Bi and increases as indicated by the long-dash line B1B2 corresponding to the line CC on Fig. 45.E. The vertical distance between Ci and Ai or between C2 and Bj is a measure of that portion of the total specific resistance Ct which corresponds to the separation drag, at speeds below which there is practically no wavemaking drag. However, as i2„ increases toward the ship range, the hne C1C2 is not extended straight to C3 but beyond C2 becomes parallel to B1B2 occupying the short-dash position C2C4 At small values of R„ in the small-model range, ,

,

,

,

,

on Reynolds number, for four models having scale ratios of 15, 22.5, 30, and 45. Pavlenko, G. E., "Soprotivleniye Vody Dvizheniyu Sudov (The Resistance of Water to the Movement of Ships)," Moscow, 1953, Fig. 154, p. 250. The diagram given is not exactly that of Telfer but the specific total resistance values, plotted

(14)

graphic method

is

the same, including the addition

of a roughness allowance to the friction resistance

for the ship.

,

.

,

the boundary-layer thickness

5 (delta)

increases

rapidly as the absolute model size diminishes.

Even though

stimulating devices on the small models render the flow completely turbulent the boundary-layer thickness is so large in proportion

that the transverse velocity gradient at a given

The graphic procedure has advantages.

First,

it

is

several

definite

easy to visualize the

agreement (or otherwise) of the several spots for model tests at a given T^ or F„ with the inclined extrapolation

The

line

for

made

that speed-length ratio.

easier by plotting R„ on a log scale and Ct on a uniform scale because the extrapolation hues are then all straight (or very nearly so) and parallel, depending upon the

analysis

is

still

formulation used. Indeed, analysis by any method other than a graphic one might be intricate and laborious. Second, as pointed out by

friction

point along the run

is

smaller than

it is

at the

even normal size. This means, by reference to Fig. 7.B on page 124 of Volume I, that the port and starboard separation points on the small model are farther forward than on the large model or on the ship. The separation zone is thus wider and the separation drag is larger. Further, on the small model, there is a curvature effect, transverse in particular, which adds to the specific friction resistance Cp to be expected at that R„ As a third item, listed on Fig. 57. C, the small corresponding point on the

on a model

full-size ship or

of

.

HYDRODYNAMICS

320 Re'ynolds

IN SHIP DESIGN

Number R^

Number Fn

Line of Constant Froude

for Models of All Sizes and for the Ship

at which Wavemokinc^

Sec. 57.7

Resist-

Rbjnolds- Number Abscissa for each

ance Beqins on the Small

Circle

IS

Determined

by

V

as

Absolute Value of

Model

Same

Usinij in

the

Respective Froude Number and L as for the Respecti\

Same

Model orShip^~~^^

Loq

of

Reynolds

Fig. 57.C

its

length,

on

Uniform

Stale

Schematic Representation of the Telfer Extrapolation Diagram to Illustrate Various Resistance Factors

model has a greater to

Number,

effective

volume, in proportion

because of the greater relative

displacement thickness 5(delta) of

its

boundary

D2 and D3 both lie on a line parallel to H2H3H4C4. Almost certainly Di Dj and D^ do not, as may be noted by consulting the many as

,

layer.

Because these three effects increase as the size diminishes they give the impression, apparently not real, that the basic friction line should be steeper in this region. If there are no effects other than those which have been enumerated, and if the wavemaking and other normal-pressure drags vary only as V' in the normal model and ship ranges, it should be possible to extend a hne such as D2D3 by drawing At a ship R„ corresponding it parallel to C2C4 to the F„ value for this line, the point D4 should

diagrams in the references

model

section.

give the total specific resistance coefficient for the

model and on the ship

.

,

listed earlier in this

The accuracy and reliability method therefore rest heavily

of

the

upon

Telfer several

factors, as yet not properly resolved: (a)

Exactly

the

proper

degree

of

turbulence

stimulation on small models to insure that the transition

from laminar to turbulent

onset of separation, relative positions

The

if

flow,

and the

any, occur at the same

along the length as on the large

correct allowance for roughness of the

ship at the given F„ value. Similarly, other lines

(b)

such as E2E3 could be drawn, so that the complete Cr curve HiGiDj for the ship would be predicted.

This is of course equally important, whether or not the Telfer method is

Rarely

is it

found in practice that points such

full-scale ship surface.

employed.

TOTAL RESISTANCE OF BODY OR

57.10

Sec.

Wisdom,

(c)

experience,

and perhaps intuition series of parallel extrap-

know how

to

draw a

olation lines,

in

semi-log or any other

to

known

type of plotting, when the lines joining the corresponding spots for the different geosims are neither straight nor parallel.

Although the

has been most useful for analysis, method manifestly does not lend

in

its

present stage of development,

57.8

must be given in numbers of certain units. Analytical and Mathematical Methods of

Predicting Pressure Resistance.

The use

of pure

analytical or mathematical procedures to calculate

the pressure resistance of a body or ship due to

wavemaking, as of 1955, is described in Chap. 50. This method has not yet progressed to the stage where a quantitative design prediction for a ship of normal form is a practical proposition. Furthermore, the pressure resistance due to eddying or separation can only be approximated, and the resistances due to the interactions listed in III of Table 57. a can not as yet be estimated by any known method.

An

57.9

Approximation of Separation Drag.

It is explained in Sec. 7.9 of

tion

may

Volume

I

that separa-

and cause added drag, abaft Although

occur,

water at the same loading, may be used for the slope angle B, provided account is taken of the change of trim caused by the ship's speed through the water.

estimated with any degree of assurance.

An

The slope

mate delineation

first

an approxi-

of those hull areas

bounding

the separation zone. Several methods for making this prediction are described in Sec. 46.3.

of estimating the drag due to

Means

— Ap's in separation

zones are discussed in Sec. 46.5.

Some

differential pressures

have been observed

at selected points on the transoms of certain square-stern models, but at the time of writing

the data are incomplete and the results inconclusive.

57.10 Slope Resistance and Thrust. It may be assumed for a calculation of slope drag or thrust on a body or ship, described in Sec. 12.7, that the effective-slope angle in the equation sin ^(theta) is that of the conDs (or Ts) = stant-pressure water subsurface passing through

W

the center of buoyancy CB. If this subsurface

not plane is

(flat)

along the ship length,

measured at the

slope

is

CB

not known

it

its

is

slope

position. If the subsurface

may

with a surface

be assumed roughly

is

ft) to the only 2(10~°).

slope drag of a 10,000-ton ship on such a is

about 45

The

lb.

slopes of

many

navigable

rivers are of the order of 5 to 8 ft to the statute sin 6 may vary from 0.001 to W. F., RPS, 1903, p. 119; "New Knowledge on Ship Propul-

mile, in

which case

0.0015

[Durand,

Nowka,

G.,

sion," 1944,

BuShips Transl. 411, pp.

such a river

is

from

1

sufficient to give it

The down

4-5].

slope thrust on a 1,000-ton barge floating

to 1.5 ton, 2,240 to 3,360 lb,

a sizable differential down-

stream speed. This may be 3 or 4 kt over and above the river speed in the middle of the channel, sufficient

to render

it

controllable

by

its

own

rudders.

For convenience, Table

57. d gives values (1) of

the natural sine of the slope angle d and (2) of the

TABLE

Drop

estimate of the separation drag on the

afterbody or run of a ship requires

will flow

statute mile. In this case sin 6

drag unfortunately can not be

this

water

It is reported that

slope as small as 0.125 inch (0.0104

certain discontinuities in the forebody.

explained,

in turn, the latter

to

routine predictions of ship resistance, where the forces

321 If,

can not be determined, the change of trim of the body or ship, reckoned from its attitude in level

it

Telfer

itself,

SHIP

equal to the surface slope.

in

Slope Drag and Thrust Data for 57. d Varying Water-Surface Slopes

HYDRODYNAMICS

322 slope

drag Dg

weight

W of

1

(or thrust

Ts)

a ship

in lb for

long ton, covering a range of water-

IN SHIP DESIGN

Vb

The

.

outer

Snr. 57.11

area (Sb of a

tanks,

from 0.02 to 10.0 ft. These correspond to a range of d from 0.01 deg to 5.7 deg. The values so derived may then be related directly to the values

erections, fairwaters,

Rt

ment A, mentioned

per ton of weight displace-

in the sections preceding.

For

example, the 100-ft version of the 944-t barge on

SNAME RD down a

river

0.12 ft per 100

V of 4.03 kt.

If drifting

having a surface slope of about ft,

the slope thrust

is sufficient

to

overcome the hydrodynamic drag for a 4.03-kt speed through the water. If steered properly the barge would go at least 4 kt downstream through the water. If the current velocity in

barge were say 3.5 kt,

its

way

of the

speed past the banks or

over the bed would be about 7.5 kt. For the ABC ship of Part 4, ascending the river to Port Correo, it

under

certain

may

be assumed that

conditions,

flood

with

a

river

current of 4 kt in that portion of the channel section occupied

by the

drop in surface The corresponding slope

ship, the

level is 0.1 ft per 100 ft.

drag from Table 57. d is 2.24 lb per long ton of weight displacement. Assuming a value of

W

plus

that of the

that

the

of

and

deck appendages except

superstructure, all

those in the "short" category defined in Sec.

The area Sb

45.12.

general

is

of a

submerged object in

the area bounding the portion which

pushes the water aside as the object

is

self-

propelled or dragged along.

The bulk volume V^

sheet 141 has a value of fir/A of

2.414 lb per ton at a speed

is

or of the pressure hull with outer

hull,

level drops per 100 ft horizontal distance varying

of total resistance

submarine

is

the entire volume within

all of that volume buoyant and weight-supporting or not. Any Hquid in free-flooding spaces lying within the overall boundary is considered as solidified or frozen in place, so far as resistance to motion is concerned. For instance, the bulk volume of a whale with a mouth full of water includes the volume of that water because, for this example at least, it moves along with the animal. However, the overall wetted surface does not include that of the inside of its mouth, because there is no friction drag on that surface affecting the body

the wetted boundary, whether is

motion.

The 0-diml bulk

fatness ratio

is

defined as the

volume Vb or Vs to the quantity (O.lOLo^)^, where Lqa is the overall external

ratio of the bulk

length of the hull

when submerged. Values

of bulk

and submarines range from about 3.4

fatness ratio, for submersibles

of

added to the ship's hydrodynamic drag. At the same time the current speed is subtracted from the ship's speed

varied type and service,

to

through the water, say 15 kt, to give a speed of 11 kt made good over the ground. Ship Still-Air and Wind Resistance from 57.11

The overall maximum-section area ^4.y of a submerged body or submarine, as projected on the y-z plane, is measured to the same external boundary as the bulk volume. It is customary to

16,000

t

at this stage of the voyage, the calculated

slope drag

is

35,840

lb.

This

is

to be

Chapter 54. To all the resistances derived or mentioned in Sees. 57.5, 57.6, 57.9, and 57.10, where appropriate, there should be added the stillair or the wind resistance of the abovewater hull, of upper works, and of all projections from both. The ship creates a relative-wind speed Wr equal to its own trial speed V, even though there is no natural wind blowing over the trial course.

The drag,

significance

and wind

of

still-air

resistance

is

resistance,

described in Sec.

26.15 and illustrated in Figs. 26.G and 26.H.

methods

of estimating

wind

The

and calculating them are

5.4,

with values rising to 8.5 for craft intended

for .special .service.

take this area as the

maximum

erections

area

lie

and fairwaters forming a part

in a different transverse plane

maximum

of the

57.13

Drag

fortunately, the validity of

are questionable, because of:

methods,

requires

overall wetted surface

first

a

Sb and

calculation

of

the

of the bulk volume

main hull. and Data for Sub-

merged Bodies. There are many technical papers and reports in existence giving resistances, drag coefficients, and similar data for fully submerged bodies, most of them bodies of revolution intended to serve as basic shapes for airship hulls. Un-

Wetted Surface and Bulk Volume of a Submerged Object. A prediction of the pressure and friction drag of any submerged object, by any one of several Calculating the Overall

of this

than that

section of the

Coefficients

described in Chap. 54. 57.12

transverse pro-

jected area or frontal area, even though the deck

A

many

of these

data

and 1920's of wind tunnels at Reynolds numbers too small to produce flows that were dynamically similar to those expected on the (a)

practice of the 1900's, 1910's,

testing

models in

TOTAL RESISTANCE OF BODY OR SHIP TMB Rep. 758, separation decreases with

Sec. 57.15

323

prototypes [Wuinblum, G. P.,

May

1951, p.

external pressure

1]

is

depth because more

available to create a pressure

(b) Uncertainties as to the interference effects of

gradient which will turn the water to follow the

supporting struts attached to the sides of the

body

bodies, with their axes

normal

(or nearly so) to

Towing models in water at inadequate suband picking up wavemaking drag when the latter was supposed to be absent. (c)

mergence,

F. Hoerner abstracts

most

modern

of the

(1940-1950) drag data for streamlined bodies on

pages 67-72 of his book "Aerodynamic Drag,"

pubhshed

in 1951.

Both Hoerner and W.

S.

Diehl

give extensive drag data on a great variety of fuselage

and

hull shapes

and components

in the

effect

actual

references listed in Sec. 55.5. It is necessary in all these cases to differentiate

much

between published Co values for total and the Co values for pressure drag only, often called "form drag" in the literature. Induced drag becomes a factor when the submerged bodies run at yaw or pitch angles and develop circulation around themdrag, including friction,

selves because of this effective angle of attack.

57.14 Pressure Resistance Bodies as a Function of Depth.

of

Submerged

Sees. 10.16

and

10.18 of Volume I emphasize that pressure resistance due to wavemaking remains a factor in the motion of a submerged body or simple ship, often of considerable importance, until the

submergence

great enough to produce a flow pattern sub-

stantially similar to that at infinite depth. It is

void,

turning

the

effect

nevertheless

remains.

A

clearly

is

this

bodies not

the body axis

S.

slopes in the run. Of the quantitative nature

around streamlined submerged is known, except that at infinite depth there is sufficient pressure to turn the water around any corner, however sharp. This is on the basis that, if the water did not so turn in any region, a cavity or void would be left, in which the pressure would be substantially the vapor pressure of water. The decreasing-pressure gradient toward this cavity would then be very large, and would immediately generate sufficient lateral force to deflect the water and cause it to follow the surface. Although in practice there appears to be no of

third factor enters here, primarily because

water for practically is

it

necessary to rely upon model tests in air or

is

all

pressure-drag data. This

the interference effect of the struts or supports

necessary to hold the model in the wind tunnel, in the

water tunnel or channel, or in the model

basin. If attached to the top, bottom, or sides of

the

body,

the

struts

interfere

with the flow

pattern and change the velocity and pressure fields.

If

attached at the stern, a single longi-

tudinal support or "sting" interferes with

separation zone that

may

any

exist there.

It is unfortunate that many of the published drag data on submerged bodies are to be taken with caution, because in these cases:

not possible to establish an arbitrary limit for this depth of submergence h, reckoned to the

(1)

body

supporting struts are not described or shown in

without taking into account the submergence-Froude number of Sec. 10.17, the ratio

h/Lw ship,

axis,

,

the

L/D

and other

form of the body or A square-bowed body

ratio, the

factors.

obviously needs more depth to eliminate surface wavemaking than one with a tapering bow. A body or ship of normal L/D ratio, reasonably well streamlined and having a transverse section not drastically different

from that

of a circle,

with no

topside appendages or protuberances,

is reasonably free of pressure drag due to wavemaking at a submergence, to its top, of three times its

vertical diameter.

G. P.

Weinblum tackles this problem for stream-

Uned bodies

May

of revolution in

TMB

1951, on an analytical

Report 758, of and mathematical

basis corresponding to that described in Chap. 50. Sec. 7.2 points out that pressure drag

due to

The

type, nature, shape,

and position

of the

the test reports

The depth of submergence of bodies tested water is not known, nor are there any data of record concerning visible or measured wavemaking on the surface. (2)

in

57.15 Resistance Due to Flow of Water Through Free-Flooding Spaces. The flow of

water through the free-flooding spaces of both surface ships and submarines in straight-ahead

motion is discussed in Sec. 20.9 of Volume I. There it is mentioned that free-flooding spaces which extend for a considerable distance forward and aft, so far that openings through the shell at the forward end lie in a. +Ap region while those at the after end are in a — Ap region, may be expected to have longitudinal flow

HYDRODYNAMICS

324

through them. The action

is

much

the

the flow through a heat exchanger with

same

as

its inlet

forward and its discharge aft. The energy required to maintain this flow within the freeflooding spaces

is

necessarily

taken from that

developed by the propulsion device (s). is

method fit (if

of eliminating this

waste of power

is

to

practicable) transverse bulkheads within the

Sec. 57.15

no circulatory any one compartment. Another

free-flooding spaces so that little or

flow occurs in

method

is to so fashion the flooding (and venting) openings that entry and egress, and circulatory

flow, is discouraged.

Eddying, with separation drag,

not possible at present (1955) to calculate this effect in terms of numbers; the designer must resort to large-scale model tests. However, one It

IN SHIP DESIGN

is

liable

to

occur around the edges of shell openings improperly formed. While this drag may be minute for any one opening it can assume sizable proportions for multiple openings, such as often occur by the hundreds in submarines.

CHAPTER

58

Running-Attitude and Ship-Motion Diagrams 58.1 58.2

58.3

Data for Predicting Sinkage and Change of Trim in Open, Deep Water General Conclusions as to Changes of Level and Trim with Speed Data on Sinkage and Change of Trim in

58.1

General.

The diagrams

58.5 325

58.6 325

in this section,

ships

of

various proportions and shapes,

supplement the general discussion in Chap. 29. These data are likewise related to the waveprofile data of Chap. 52, since the trim attitude for displacement-type hulls at sub-planing speeds is

related directly to the

wave

profile.

Data for Predicting Sinkage and Change of Trim in Open, Deep Water. It is beheved that most of the large model-testing establishments have a great amount of data on file relating to the change of level and trim of ship models undergoing test. Unfortunately, most of the 58.2

published data apply to single ships or models, here and there, or to hull forms of unrelated and

unsystematic proportions and shape. Examples of this are the data presented [S

and P,

1943],

where in

Figs.

1.61

ft,

=

0.181 deg.

designed load draft at the FP, reckoned to the

by D. W. Taylor

undisturbed water surface at a distance, increases from its nominal at-rest value of 26.00 ft to

21-25 on page 24

28.35

ft,

an augment of 9 per cent.

by

data for models of high-speed

ships [INA, 1935, Vol. 77, p. 81ff and Pis. XI, XII]. H. Lackenby shows the change of trim, for several different conditions, of the 190.5-ft 16-ft model, for

speeds from 6 to 15 kt [INA, Fig. 15

on

329 331

It is significant that, at the trial speed, the

and no numerical data, and where in Figs. 84-93 on page 73 there are given data on ten more-or-less unrelated models. W. P. A. van Lammeren, L. Troost, and J. G. Koning give change-of-trim data on only one model [RPSS, 1948, Fig. 38, p. 88]. J. L. Kent and R. S. Cutland present some

its

329

corresponding to an angle of (1.61/510)/

0.01745

to the point, the freeboard at the

Ashton and

.

328

For the fifth approximation to the hydrodynamic features of the ABC ship of Part 4, covered in Sec. 66.11 and listed in Table 66.e, the Cp is 0.62 and the fatness ratio F/(0.10L)' is 4.327. To estimate the probable sinkage and trim from Fig. 58.A, at a T, of 0.908, the 0-diml change of level of the bow is found by inspection and interpolation to be —0.46 per cent or — 0.0046L. For the stern it is —0.145 per cent or — 0.00145L. With a waterline L of 510 ft, these work out as — 2.35 ft and —0.74 ft, respectively. The change of trim at 20.5 kt, by the bow, is 2.35 - 0.74 or

of the reference there are only trim indications

change-of-trim

.

.

58.7

representing the in-motion trim attitude of models

and

Shallow and Restricted Waters Changes of Attitude and Trim of Ships with Fat Hulls Variation of Attitude and Position of Planing Craft with Speed and Other Factors References to Published Data

325

General

Lucy

a range of ship

Apr

FP

is

more

decreases

same speed, without any com-

pensating advantages.

Published change-of-trim data on self-propelled models are almost nonexistent, possibly because experimenters thought that there would be little or no difference in level or attitude between the model when towed bare hull and when selfpropelled with appendages. Figs. 58. B and 58. C, embodying the data for TMB models 4505 and 4505-1, representing the transom-stern stern variations of the

ABC

and arch-

ship hull of Part 4,

show that for this design at least the changes in and attitude with speed are significantly

1955, Vol. 97,

p. 124].

level

The published data of D. W. Taylor on the ten models referenced have been incorporated in one set of graphs, embodied in Fig. 58. A. These endeavor to present the information in somewhat systematic fashion, although this

2.35 ft at the

What

is difficult

based on data from only ten models.

when

different.

General Conclusions as to Changes of Despite the handicaps enumerated in Sec. 58.2, it is possible to draw certain rather comprehensive conclusions from the available model-test data on change of 58.3

Level and Trim with Speed.

325

HYDRODYNAMICS

326

Change

of Level

of

IN SHIP DESIGN

Sec. 58.3

Bo

For Cp=0.55 to 0.65

y

-6.98

/ 10.52

NOTE: These Data Apply to De.zp Water Onl\j\

0.2 Fig. 58.A

0.4

0,6

0.6

1.0

Graphs Summarizing the Data of D.

1.2

VV.

\.A

1.6

Taylor for Change op Trim

l.fl

in

2

Deep Water

2,2

RUNNING-ATTITUDE DIAGRAMS

Sec. 5S.3

5

Trim -0.3

0.16

of

Deq

b^

Bow

at

Designed Spaed Solid Line BriDken

Line

is

is

for Model

ABC SHIP

5-0.7

.mI,,J

Towed Bare

Hull

for Model Self-Propelled witli Appendaqes'

TMB

FP Model 4505

Qt Woterllne

Beginning at Bow

T- , V I'^.YTi L

1.2

Fig. 58.B

Non-Dimensional Change-of-Trim Data for

ABC

Fig. 58.C

Ship,

Representing Transom-Stern Self-Pkopelled

TMB

and trim with speed. These are based upon

W.

and P, 1943, pp. 72-74], taking account on many models other than the ten on page 73 of the reference. So many vari[S

4505,

Model

When Towed Bare Hull and When

the conclusions previously formulated by D.

Taylor

Model

When Towed Bare Hull and When

Non-Dimensional Change-of-Trim Data for

ABC level

Srap,

TMB

4505-1, Representing Arch-Stern Sblf-Propblled

veloped by changes in hydrostatic pressure in the surface waterline region predominate over those due to Ap's resulting from hydrodynainic action the displacement type, having the

of test data

(2) Vessels of

listed

waterline area concentrated near amidships, and

ables enter the picture, however, that

it is difficult,

not impossible to extend them over the entire range in which the marine architect is interested.

if

The modified

conclusions, taken with the graphs

of Fig. 58. A, enable reasonably precise predictions

to be

made

for the running attitude of vessels

large

waterline

areas

their

for

bodily about in proportion their waterline endings

and

to

length,

drop

the fineness of

to their displacement-

The drop is with smaller prismatic coefficients Cp because of the rather direct relationship between

length quotient or fatness ratio. greater

supported

Cp and Cw indicated in Fig. 66.H. For vessels having Cp values less than 0.65, with fine waterline endings and the waterline area well con-

primarily by buoyancy, the vertical forces de-

centrated amidships, the bodily settlement and

not too different from the normal forms: (1)

For

displacement-type

vessels,

,

HYDRODYNAMICS

328

bow

the trim by the

increase with the displace-

ment-length quotient or fatness

IN SHIP DESIGN (8)

The

center

Sec. 58.4

gravity

of

planing) vessels rarely rises to or above

ratio.

At low and moderate speeds, below a T, of F„ of 0.3, both bow and stern settle, the bow somewhat more than the stern, for the reasons given in Sec. 29.2 of Volume I (4) Vessels having Cp values higher than 0.65,

(non-

ordinary

of

its original

any practicable speed. Since the

(3)

at-rest level at

1.0,

effect of the

with

water immediately surrounding it, there may be an impression, at very high speeds, that the vessel does rise above its original level. (9) Vessels of special form and planing craft, when driven to their designed high speeds, do rise bodily. Their behavior is described and illustrated in Sec. 29.3, on pages 415-417 of Volume I.

ends, level off at a T, of 1.0 or just below.

full

For T, values

in the

range 1.0 to

1.2,

there

may

be oscillations or perturbations in the trim values.

At

may

greater values of T^ the stern

much more than

to drop

be expected

the bow.

As the speed is increased beyond a T, of 1.0, for vessels with Cp values of 0.65 and below, the bow settles more slowly. It reaches its lowest level (5)

at a Tj of from 1.05 to 1.30 (averaging about 1.15)

and then

rises rapidly.

The bow reaches

level in a T,

range of 1.3 to

continues to

rise.

(6)

The

stern

beyond a T^ settles

by the

At a T,

stern

settlement

of speed.

As a

1.1

or 1.2. Thereafter

is

bow

rises,

it

so

rapidly increasing. 1.7 to

Name

58.a

1.8,

than the bow reaches

the stern

cussed in Sees. 18.7 and 35.7 of sufficient

information

is rising,

speed while doing is

so that

maximum. The much beyond a T^

its

bow always

rises

with increase

result the vessel is rising bodily at

speeds beyond a T^ of about

TABLE

speeds in shallow and restricted waters,

is

Volume

dis-

Only

given here to enable the

2.0.

so.

D

on page 530 of Volume I reproduces some trim data given by D. W. Taylor for a Fig. 35.

scout-cruiser model. Fig. 58.

sinkage of ratios

h/H

bow and

D indicates the 0-diml

stern for three depth-draft

over a wide range of speed-length

number F„ Paulus gives German torpedoboat S119 in

quotient T^ and Froude similar data for the

Characteristics of Prototypes for Which Trim Data are Presented in Figs.

of Vessel

is I.

These are important because of the extremely limited bed clearance with which large vessels transit certain canals, channels, and shoal areas, and the desire to maintain the highest practicable

stern does not change level of 2.0, while the

subject of change of level and trim, at various

more and more rapidly

rapidly than the

of about

settling less rapidly

bodily

58.4 Data on Sinkage and Change of Trim in Shallow and Restricted Waters. The general

marine architect to predict the sinkage and change

that the ship as a whole continues to settle while

(7)

to depress the

it

about

much more

the trim

is

of trim in confined waters in quantitative terms.

settles

of

its at-rest

beyond which

1.5,

passage of the vessel

.

58.

D

and 58.E

RUNNING-ATTITUDE DIAGRAMS

Sec. 58.6

by D. G. Davies

329

in reference (12) of Sec. 58.7 for

Cp values, reveal that at the low speed-length quotients customary

lake freighters having very high

in confined waters the ship trims

means

as in deep water. This keel or

bottom slope

by the bow,

that,

and

is zero,

if

if

just

the initial

the speed

too high, the ship touches the channel bed at forward end.

Changes of Attitude and Trim of Ships

58.5

with Fat Hulls.

and

is

its

forms

full

In former years, excessively fat

and pon-

like large scows, barges,

could rarely be towed or propelled at speeds through the water high enough to change toons,

attitude and

even in shallow and and squat was therefore not much of a problem. With the advent of higher speeds and more powerful tugs and pushboats, the marine architect is left with little or no model their

trim,

restricted areas. Sinkage

OZ

04

0.6

0.8

1.0

I.E

Toylor Quotient

1.4

16

18

20

Tu'V/Vt

Non-Dimensional Change-of-Thim Data FOR High-Speed Scout Cruiser op D. W. Taylor

Fig. 58.D

data or full-scale observations for predicting the changes in normal bed clearance likely to be encountered by these craft in given areas. This situation

towing

by the

aggravated

is

blunt-ended

and

full

possibility

forms

of

through

reference (4) of Sec. 61.22. Other data are listed

regions where the water

in Sec. 58.7.

and where the position of a craft upon a solitary wave will have a large effect upon the actual bed

It is obvious

h/H =

from the short-dash graphs for and

2.38 in Fig. 58.D that the sinkage

change of level are greatly affected by the position of the vessel on the solitary wave which travels through the shallow water at the speed Cc = \gh. This critical speed can change rapidly with depth, as can the normal sinkage due to the Bernoulli contour system and the ship's Velox-wave system, so it must be remembered that a prediction of sinkage and trim for a nominal constant depth is that and no more. For the prediction of the sinkage and change of trim in the cargo-vessel category, W. H. Norley has published rather complete data on the behavior of the models of four vessels in three depths of shallow water as well as in deep water [TMB Rep. 640, Feb 1948]. The graphs of Fig. 58.

E

istics

bow and whose character-

give the 0-diml sinkage of both

stern for the four ship designs

are listed in Table 58. a.

self-propelled

conditions

for

The data

represent

both models and

ships.

An example of the use of these graphs, involving extrapolation to lower h/H values than those given,

is

worked out

for the

ABC

ship of Part 4

in Sec. 72.8.

shoaler than expected,

clearance.

In

ETT,

Stevens, Report 279 of January 1945

there are given on page 15 the change-of -level

data for the two groups of models having displacement-length quotients A/(0.010L)^ of 300

and 400, and Cp values

The

of 0.50, 0.60,

characteristics of these

the referenced report and in

and

models are

0.70.

listed in

SNAME RD

sheets

105-110. 58.6

Variation

of

Attitude

and Position

of

Planing Craft with Speed and Other Factors. The matter of bodily rise of a planing craft above its

position at rest, together with the changes in

trim which occur throughout the whole speed range, 29.4

are

described

and 30.2

of

Volume

and I.

illustrated

in

Sees.

In fact, the sinkage and

trim are related to the whole planing behavior. This, in turn, as brought out in Chap. 77,

most important function

of

is a both weight and

power. Unfortunately, there are no known data by which the trim and vertical position of a planing craft may be estimated or predicted directly,

corresponding to those in Fig. 58.A. Possibly there will never be a simple procedure for deter-

The data derived by Norley and blunt-ended

is

for full-bodied

vessels, as well as those derived

mining these values, because of the considerable of parameters that are intimately

number

HYDRODYNAMICS

330 TQ\^lor 0.1

-0.1

0.2

IN SHIP DESIGN

Quotient Tq-tTt^ 0.3

0.4^

^'- 0.5

0.1

Ta^ylor 0.2

Sec. 5S.6

Quotient To- rn= 0.3

0.4

''^0.5

RUNNING-ATTITUDE DIAGRAMS

Sec. 5S.7

appreciable until the water depth approaches or less than the beam of the planing form. In view of the known performance of displacementtype vessels under similar circumstances it is not surprising that the drag and the trimming moment about the trailing edge of the planing form also increase with diminishing depth of water. Other features accompanying these changes is

are

described

V138.5 = stern

However,

together by no means covers the needs of the marine architect and ship operator of today (1955). (1)

(2)

Some

(4)

placement-length

quotient

Cx was 0.743, and Cw Cp was 0.556. (3)

Gillmor, H. G.,

46.4.

0.659.

Torpedo Boat Morris

(old),"

A.,

ASNE, May

S.

1898,

507 of the reference

it

says of the Morris

wave

with a normal disturbance of the surface of the water." White, Sir W. H., MNA, 1900, pp. 466-467, 475-477. 80-ft torpedoboat

mentioned

in

(5) (6)

Saunders, H. E., and Pitre, A.

(7)

(8)

(9)

(10)

S., "FuU-Scale Trials on a Destroyer," SNAME, 1933. Table 6 on p. 251 gives the trim data for the U. S. destroyer Hamilton (DD 141) for a range of speeds from 20 to 35.6 kt. Davidson, K. S. M., PNA, 1939, Vol. II, pp. 107-108 Havelock, T. H., "Note on the Sinkage of a Ship at Low Speeds," Zeit. fiir Ang. Math. Mech., Aug 1939, pp. 202-205

Taylor, D. W., S and P, 1943, Figs. 21-25, p. 24; Figs. 84-93, p. 73

Van Lammeren, W. J. G.,

(11)

RPSS,

Sund, E.,

"On

P. A., Troost, L., and Koning,

1948, p. 88

the Effects of Different Turbulence-

Exciters on B.S.R.A. 0.75 Block Models

Various Scales,"

these data,

"The U.

The trim by the

T, of 2.07, F„ of 0.616, the trim by the stern was about 2.5 deg. Durand, W. F., RPS, 1903, pp. 121-123

(12)

and Anderson, M.

0.608.

this reference, at a

Cb was 0.413,

From

=

1.72 deg.

For the Yarrow

of the available references follow:

Yarrow, A. F., "Past Torpedo Boats," Cassier's Mag., Jul 1897, Vol. XII, p. 294 Anderson, M. A., and Gillmor, H. G., U. S. torpedoboats Talhot and Gwin (both old), ASNE, May 1898, Vol. X, pp. 493-501. These vessels were 99.5 ft long by 12 ft wide by 3.81 ft mean draft (2.1 ft forward and 5.54 ft aft). The change of trim at speeds of about 21 kt "amounted to about 41 inches (3.41 ft)." This corresponded to a T, of 21/V'9a5 = 2.10, Fn = 0.625, and a trim by the stern of about 1.95 deg. The displacement was 45.75 tons and the dis-

2.04; F„

was about

On page

all of

it

.'502-508.

that "she traveled on the back slope of a

greater part of the pubhshed information appears in the older technical literature.

X, pp.

,

by K. W. Christopher [NACA

Tech. Note 3642, Apr 1956]. As is 58.7 References to Published Data. the case with quantitative experimental or observed resistance data in shallow water, the

331

For this ve.sael, L„l was 138.5 ft, Bx was 15.0 ft, and H (mean) was 4.25 ft (2.75 ft forward and 5.75 ft aft). The trial displacement was 98 tons, with a displacement-length quotient of 36.88. Cb was 0.425, Cx was 0.755, and CwL was 0.687. Cp from the foregoing, was 0.563. At a speed of 24 lit the change of trim was about 5 inch es, or 4.17 ft. At this speed, T, = 24/ Vol.

Norwegian

Made

to

Model Basin 12, 13, and Fig.

Ship

Rep. 11, Aug 1951, esp. pp. 3, 4, 12 on p. 23 Davies, D. G., "Changes in Draft in Shoal Water," SNAME, Great Lakes Sect., Apr 1955; abstracted in SNAME Bull., Jul 1955, Vol. X, No. 2, p. 39.

CHAPTER

59

Predicting the Performance of Propulsion Devices 59.1 59 2 59.3

Relationship to Other Chapters

59.4

Performance Data from Screw-Propeller Design Charts Performance Data on Paddlewheels and

332 332

Estimate of Propulsion-Device Efficiencies Open- Water Test Data for Model Screw

.

.

.

333 59 12 .

335 59 13 .

Sternwheels Bibliography on Paddlewheels Test Results on Rotating-Blade Propellers Available Performance Data on HydraulicJet, Pump-Jet, and Gas-Jet Propulsion Devices Performance Data on Controllable and Re-

59 6 .

59.7 59.8

335 335 337

.

59.9

.

337

59.17

338

Other Chapters.

The

form, use, behavior, and performance of

many

Relationship

to

types of ship-propulsion devices are described in

and 17

Chaps.

15, 16,

and 33

of Part 2.

A

of Part

and

1

rather complete discussion of

The Thrust-Load Factor and Derived Data

drive a single device

to

.

Approximation of Screw-Propeller Thrust from Insufficient Data Relation Between Thrust at the Propeller and at the Thrust Bearing Estimates of Thrust and Torque Variation per Revolution for Screw Propellers .

specifying whether this

.

.

339

340 341

343 345

346 347 348

x horses, without an indicated, brake,

is

is

shaft, or propeller power.

Chaps. 32

in

Performance of Miscellaneous Propulsion Devices Area Ratios, Blade Widths, and Blade-Helix Angles of Screw Propellers Pertinent Data on Flow Into PropulsionDevice Positions Data on Induced Velocities and Differential Pressures

59.14 59.15 59 16

versible Propellers

59.1

.

59. 11

Propellers

59 5

59 10

Estimate of Propulsion-Device Efficien-

59.2

The matters

cies.

and the factors

relating to

the aspects of efficiency of propulsion devices in

governing the efficiency of various kinds of ship-

is found in Chap. 34. The application of data on and values of efficiency in the powering estimates for vessels is covered in Chap. 60.

propulsion devices are discussed at considerable

Notes, rules, and procedures for the design,

tive values of propulsion-device efficiency, there

general

zation,

and adaptation

propulsion device to the

of the

many

many

utili-

forms of

its

effects,

marine engineer who wishes absolute or quantitaare the following:

types of ships are

described in Chaps. 69, 70, and 71 of Part

Cavitation and

length in Chap. 34. For the naval architect and

4.

as applied to screw

(a)

For screw

efficiencies

propellers, the expected

jjoCeta)

open-water

and the probable range

of

propellers in particular, are discussed in Chap. 47.

efficiency for selected characteristics or for charac-

The present chapter endeavors to present, in some of the quantitative information required by the marine architect

teristics

concise but useful form,

who

sets out to design a combination of ship

and

propulsion device. While a great deal of analytic

work has been done along these lines, the designer who is called upon to fashion and proportion the propulsion device (s) for a particular ship large extent forced to

is

to a

work ahead from the known

performances of existing installations. Unfortunately, published data on the behavior of propulsion devices of

is

and

design.

in

the

sense

imreliable

Further,

that

the

it

is

may

state that the

For other types

mechanical propulsion on the water surrounding the ship, there are some published data on systematic series, such as the paddlewheel data referenced in Sec. 59.6, and some comparisons of efficiency to be found here and there in the technical literature. Two examples of these are the (b)

of

devices, acting directly

efficiency curves for (1) screw propellers within a

often

quantitative

data are not completely defined. For example, the source

are found readily from

charts listed in Sec. 70.4

often inadequate for purposes

predictiort

commonly used

the numerous groups of screw-propeller design

power developed 332

fixed shrouding such as a

Schneider

rotating-blade

Kort

nozzle, (2) Voith-

propellers,

and

(3)

paddlewheels in the three sets of graphs of Figs. 34. and 34. N. However, one serious short-

M

coming

of data such as these

is

the lack of ade-

Sec.

PROPULSION-DEVICE PERFORMANCE

593

quate and precise definition for the information presented. Only rarely are the particular forms

propulsion

of

device,

corresponding

to

the

diagrammed or illustrated. The graphs or accompanying text do not always state whether the efficiencies are maxima, averages, or efficiency curves,

service values.

A

rather large array of tabulated data derived

from the self-propulsion vessels with tunnel sterns

tests is

of

shallow-draft

published by A. R.

Mitchell [lESS, 1952-1953, Vol. 96, pp. 125-188]. These data do not, unfortunately, include values of

the screw-propeller efficiencies but they do

embody information on wake and tion fractions

and on propulsive

thrust-deduc-

coefficients.

H. Mueller has presented, for screw propellers of four different

P/D

tions of the current peller,

two

sets of

ratios

and

for three varia-

(1955) rotating-blade pro-

graphs showing variations with

333

334

^0.15

\0.\0

?0.05

0.00

HYDRODYNAMICS

IN SHIP DESIGN

Sec.

593

PROPULSION DEVICE PERFORMANCE

Sec. 59.6 pp. 601-619].

The Cq and Ct

plots in these figures

embody dimensional

data. This paper gives no drawings of any of the model propellers but all

the

TMB

model numbers are included, and the file at the David Taylor Model

met by the

availability of

many

design charts

for the screw-propeller designer.

Bibliography on

59.6

Paddlewheels.

There

drawings are on

appears to be no lengthy

Basin.

pended to any of the better-known published papers and books on paddlewheel propulsion. The list given hereunder is by no means complete but it may serve the reader as a source of background information, as well as a source of experimental data and of information useful in design:

59.4 Performance Data from Screw-Propeller Design Charts. The systematic data derived from the open-water tests of a multitude of series propellers, made in model basins all over the world, are published in the form of charts suitable for use in ship and propeller design. Thirteen

(1)

and

illustrates

later altered to carry feathering wheels of smaller

diameter and higher rate of rotation. On these paddlewheels the blade spacing was only slightly greater than the blade width, the blade faces were flat, and the blades were apparfeathering

ently (2)

designer with the same sort of information from

systematic series as was included on the screw-

(3)

To meet

this

need H. Volpich and

undertook, in the early 1950's, to

on a new

who needs

series of

to

adaptable

to

Pollard,

(5)

Lovell, L. N.,

(7)

Durand, W. F., RPS, 1903, pp. 164-169, 198-203 Paddle steamer C. W. Morse, Marine Engineering, Jun 1904, p. 279 ff

(8)

Kaemmerer, W., "Raddampfer

(6)

ftir

die Anatolische

Eisenbahn-Gesellschaft, erbaut von den HowaldtsI.

werken

in Kiel (Paddlewheel Steamer for the Anatolian Railways, built by the Howaldt Works, Kiel)," Zeit. des Ver. Deutsch. Ing., 12 Nov 1904, pp. 1725-1729. Figs. 9 and 10 on p. 1726 show the

C. Bridge

make systematic

models and to present the his

refers to

J., and Dudebout, A., "Theorie du Navire (Theory of the Ship)," 1894, Vol. IV, pp. 179-193 "American Sound and River Steamboats," Cassier's Magazine, Jul 1897, pp. 459, 482

(4)

designer with tabulated and graphic information readily

Rankine

the preceding paper by J. R. Napier. Riehn, W., "tjber die Wirkungsweise der Schaufelrader und der Schrauben bei Dampfschiffen (On the Operation of Paddlewheels and Propellers in Steamers)," Zeit. des Ver. Deutsch. Ing., 1884, Nos. 18-22

propeller charts of that day. Unfortunately, these

data are not readily applied by one design a modern paddle wheel.

made of wood rather than iron. J. W. M., "Shipbuilding: Theoretical and

Rankine,

Practical," 1866, pp. 248, 251.

59.5

several sets of charts, intended to provide the

and Economy

These vessels originally had radial wheels but were

SNAME

paper, pages 161 and 162. Performance Data on Paddlewheels and Stemwheels. In 1916 E. M. Bragg published a paper on "Feathering Paddle-Wheels" [SNAME, 1916, pp. 175-180, Pis. 90-98] in which he gave

the Effects of Superheated Steam

Oscillating Paddles on the Speed

table on p. 90 gives the principal paddlewheel and blade data for the steamers Concordia and Berlin.

ance predictions from three of these chart types. Other examples illustrating the manner in

The calculation of screw-propeller performance, by a method derived from analytic considerations, is covered by J. G. Hill in Appendix 2 of his 1949

"On

of references ap-

Steamers," Trans. Inst. Engrs. Scot., 18631864, Vol. VII, pp. 86-102, Pis. V and VI. The "oscillating" paddles mentioned in the title of this paper are the feathering paddles of today. The

the procedure to be followed in making perform-

which screw-propeller performance is predicted from published propeller charts are found in Sees. 66.27 and 77.35, and in a paper "Propeller Coefficients and the Powering of Ships," by F. M. Lewis [SNAME, 1951, pp. 612-620].

J. R.,

list

of

comparisons of these charts are to be found in Sec. 70.5, while Sec. 70.6 describes

Napier,

and

kinds of screw-propeller-series charts are listed and described in Sec. 70.4. Comments on and

tests

335

problems.

The

first

installment of these data appeared in the paper

"Paddle Wheels; Part I, Preliminary Model Experiments" [lESS, 1954-1955, Vol. 98, Part V, pp. 327-372], It is understood that at the time of writing (1955) this systematic test program is still underway and that Part II of the report will appear in 1956. The data in this series of papers, taken with those of F. Gebers in reference (31) of Sec. 59.6, should go far toward filhng, for the paddlewheel designer, the need which has been

arrangement of a 4.5-meter (14.75-ft) outside diameter 8-bladed paddlewheel with the eccentric mechanism centered ahead of and slightly helow the wheel center. Hart, M., "Note sur le Changement des Roues des Paquebots Le Nord et la Pas-de-Calais (Note on the Alterations to the Paddlewheels of the Channel Steamers Le Nord and Pas-de-Calais)," ATMA, 1906, Vol. 17, pp. 169-186 and Pis. I through VIII Ward, C, "Shallow-Draught River Steamers," SNAME, 1909, Vol. 17, pp. 87-88 for the feathering

(9)

(10)

(11)

Feathering paddlewheel, Schiffbau, 27 Dec 1911, pp. 210-211

(12) Teubert, O., "Binnensohiffahrt (Inland-Waters Ship

HYDRODYNAMICS

336

Operation)," Leipzig, I, pp. 224-442. A later edition of this book was published in 1932. (13) "Experimental Tovvboats," House (of Representatives), 63rd Congress, 2nd Session, Document 857,

IN SHIP DESIGN

1914, Vol. 27. This report gives the results of

p. 15 of

about (24)

and charts of based upon the work described

this report

were

(26)

"The Bristol Queen: SBSR, 6 Mar 1947,

K.,

(15) Sehaffran,

mit Schaufolrad-

"Modellversuche

Propellern (Model Tests with Paddle Propulsion Devices)," STG, 1918, Vol. 19, pp. 475-520.

Describes tests

made on

a

number

models of

of

feathering wheels, together with correlations with

on several paddle steamers, the Hugo Marcus on the Elbe and the Thommen on the Danube. The efficiencies of the model paddlewheels do not exceed 0.50 in any case. Fig. 7 on p. 486 is a construction drawing of a pair of paddlewheels side by side on a single shaft, each pair with its own feathering mechanism. Sadler, H. C, and Kirby, F. E., "Design of Pa.ssenger Vessels for the Great Lakes," SNAME, 1925, pp. 101-108. PI. 81 shows the design and dimensions trials

(16)

of

the

paddlewheel design.

in the preceding

reference.

paddlewheels

the

K.

EMB Rep. 1)0

and

E.,

176,

characteristic

curves

for

a

(29)

R., "Leistung und Wirtschaftlichkeit von Flusschleppern verschiedener Antriebsart (Power

(18) Zilcher,

556-561

"Notes on the Development of Tug-Boat Machinery During the Past Forty-Six Years," NECI, 1935-1936, Vol. LII, pp. 89-102 and D19-D22. This paper depicts, on pp. 98-99, two

tug paddlewheels of the feathering type, with 6 and 8 blades, respectively. (20) Suberkriib, F., "Der Radschiffsantrieb (Paddlewheel Ship Propulsion)," Schiffbau, 15 Mar 1939, pp. 115-119 (21) Gras,

"Dieselelektrische

V.,

Schaufelrad-Schlepper

Szechenyi (Diesel Electric Paddle

WRH,

15

Aug

15 on p. 250

Tug

Szechenyi),"

1939, pp. 247-256. Figs.

show a

3, 4,

and

direct electric-motor drive to

the paddlewheel shafts. There are double paddles on

each wheel, end to end. R., "Das Diesekadschiff (The Diesel Paddlewheel Ship)," Schiffbau, 15 Sep 1939, pp. 326-327; 15 Oct 1939, pp. 349-357. Fig. 21 on p. 354 gives the lines of the Danube River vessel Stadt Wien, which has a peg-top underwater mid-

(22) Blumerius,

ship section. (23)

Kretzschmar,

Henschke,

W.,

(Shipbuilding

of

(19) Baird, G.,

fiir

mit einem

Schiff

und Hafen, Mar

"Schiffbautechnisches

and

Ship

Design

"Einige Schiffbautechnisclie mit-

(E,x-

1952,

Handbuch

Handbook),"

(32)

Ostend-Dover Paddle Packet Marie Henriette of 1893, SBSR, 15 May 1952, p. 630 Gebers, F., (with a contribution by F. Horn), "Daa Schaufelrad im Modellversuch: Zwei Berichte der Schiffbautechnischen Versuchsanstalt, Wien (The Paddlewheel in Model Test: Two Reports of the Vienna Model Basin)," Vienna, Springer, 1952 (book in German). Krappinger, O., "Schaufelradberechnung (Paddlewheel Calculation)," Schiffstechnik, Aug 1954, pp. 30-36. This paper gives a number of graphs embodj'ing the results of model tests, in a form useful to the designer. No translation known to be available in 1955.

(33) Volpich,

H.,

and Bridge,

I.

C, "Paddle Wheels:

Part I, Preliminary Model Experiments," JESS, 1954-1955, Vol. 98, Part 5, pp. 327-372. A bibliography of 8 items appears on p. 359, several of

which are listed here. The paper gives a brief general history of paddle propulsion and paddle research with a comment on the scarcity of experimental data for wheel design and analj'sis. Important deviations from the laws governing screw-propeller performance are noted and the purpose of the present investigation put forward. The apparatus used in testing two sizes of model wheel is described. The results of experiments with a radial and a feathering 9-float wheel at one immersion are given in detail for both wheel sizes and are discussed, together with methods of presentation.

As the

results

are incomplete for

design purposes, proposed future F.,

speziellen

verkrautete Gewasser

Berlin, 1952, pp. 193-195

onl^r.

and Economy of River Tugboats with Various Kinds of Propulsion)," WRH, 22 Dec 1927, pp.

"Erfahrungen

Water with Weeds),"

of efficiency

number

article gives

pp. 80-81

(31)

variations of radial wheels

The

perience with a Special Paddlewheel for Use in

"Model Tests with Paddlewheels," Sep 1927. Gives curves

R.,

Schaufelradantrieb

vessels of the Greater Detroit class. (17) Schoenherr,

Paddle Steamer,"

pp. 224-227.

138-139. (28) Deetjen,

(30)

for

A Modern

photographs of the model feathering paddlewheels tested and of the self-propelled model of this vessel. (27) Barr, G. E., "The Histor3r and Development of Machinery for Paddle Steamers," lESS, 20 Nov 1951, Vol. 95, Part 3, pp. 101-148. Paddlewheels are discussed on pp. 128-130, with numerous illustrations. There is a list of 7 references on pp.

large

feathering

Switzerland),"

in

pp. 97-134.

analysis of these paddlewheel tests.

of the data

Progress

Helm, K., "tJber den Heutigen Stand der Schaufelradfrage (On the Present Status of the Paddlewheel)," HSVA Rep. 881, 26 Jun 1944 (copy in TMB library). This report contains a treatise on paddlewheel developments and includes curves for

(14) Bragg, E. M., "Feathering Paddle-Wheels," SNAME, 1916, pp. 175-180 and Pis. 90-98. It is believed that

many

(Some Information

Schweiz

der

Shipbuilding

und Werft, 1 Mar 1943, pp. 74-77 Gardner, J. H., "The Development of Steam Navigation on Long Island Sound," SNAME, HT, 1943,

(25)

the report there are listed ten conclusions

drawn from an

Sec. 59.6

Schiff

many

comparative tests run at the Univ. of Michigan, Ann Arbor, on models of radial and feathering paddlewheels, with many parameters varied. On

aus

tcilungen

1012, Vol.

this will

be published

in

work

is

a second paper.

outlined;

PROPULSION DEVICE PERFORMANCE

Sec. 59.8

Part II of this paper was presented to the lESS

on 13 Mar 1956. "Quarter-Wheel Tugs for the Sudan," SBMEB, Deo 1955, pp. 705-700. This reference describes the six tugs of the Tagoog class, 125.5 ft long overall, 32.0 ft beam, and 3.0 ft draft, driven by a pair of radial-blade sternwheels, one on each quarter.

(34)

Test Results on Rotating-Blade ProMany open-water tests of rotating-blade propellers, principally of the Kirsten-Boeing and the Voith-Schneider types, have been made by the old Experimental Model Basin and the David Taylor Model Basin at Washington, by the

A few other embodied in Sees. Kempf,

(3)

(4)

59.7

results of these tests are rare.

The most

useful

although not in the form of the usual characteristic curves, are those presented by data,

Dr.

Hans

Mueller in his paper "Recent Design and Application of

F.

Developments

in the

the Vertical Axis Propeller" pp. 4-30]. Figs. 59.

A

Two and

of his 59.

B

[SNAME, May

1955,

graphs are reproduced as

in this chapter.

Dr. Mueller advises the author [unpubl. to

HES

May

of 4

Itr.

1955] that the pubhcation of

open-water test data on rotating-blade VoithSchneider propellers, corresponding to those mentioned in Sec. 59.3 for screw propellers, were not

made

available in the technical literature for

two reasons. development

of these devices in the I930's

hesitant

release

perfected

to

a

those

First,

the

practical

responsible

data

design

until of

the

for

rotating-blade

which could compete with the best screw propeller. Second, a great deal of the openwater testing with models was done at the Netherlands Model Basin in Wageningen during the German occupation of that country in World War II. The latter data are in existence but have never been published. Dr. Mueller points out that references (1) and (2) which follow may be of help to a designer employing this type of propulsion device. So far as known, these two references have not been propeller

"Der Massstabeinfluss beim Voith-Schneider-Propeller (Scale Effect En-

Mueller, H., and Helm, K.,

countered (2)

with

the

Voith-Schneider

Propeller),"

WRH, 15 Dec 1942, pp. 334-338 Mueller, H., "tjber das Zusammenarbeiten des VoithSchneider-Propellers mit

dem

Schiff

(On the

Ship)," Schiff

37.22, are:

(6)

Propellers (The Steering Force of the VoithSchneider Propeller)," WRH, 1 Jul 1938, pp. 202-204 "Cycloidal Propulsion on Army Vessel {Truman O.

Olson)," Naut. Gaz.,

Mar

1950, p. 25.

Performance Data on Hydraulic-Jet, Pump- Jet, and Gas-jet Propulsion Available

59.8

It is unusual, yet unfortunate, to find

Devices.

that in a search for performance data on hydraulicjet propulsion to supplement the descriptions of Sees. 15.8, 32.5,

and

34.13,

most

pubUshed

of the

data are largely historic. It is known that an English patent was granted to Toogood and Hayes, as far back as 1661 [Schoenherr, K. E.,

PNA,

1939, Vol. II, p. 122]; also that

made

Franklin

Benjamin

a proposal for jet propulsion of

a boat in 1775. K. E. Schoenherr states, in the

was actually by James Rumsey in 1782 to propel an ferryboat between Washington and Alex-

reference cited, that jet propulsion

applied 80-ft

andria, Va.

Most

of the references

on the older forms of

propulsion might almost be termed ancient.

jet

The

newer references are almost equally remote from the modern (1955) marine architect because most of

them

are in a classified status.

Among

the

older references are: (1)

Brin, C. B.,

INA, (2)

White, 1882,

"On

the Efficiency of Jet Propellers,"

1871, Vol. XII, pp. 128-149 W. H., "The Water-Jet Propeller,"

pp.

532-538;

MNA,

MNA,

1900, p. 587ff. These

references mention installations on the: (a)

Waterwilch, 1866

(b)

Swedish torpedo boat, 1878

(c)

British Admiralty torpedo boat, 1881

(d)

German naval

craft

Hydromotor, Fleischer, 1879; Engineering, London, 9 Sep 1881 (f) American jet-propelled boat. "Verso la Soluzione del Problema del la Propulsion Idraulica (Toward a Solution of the Problem of Hydraulic Propulsion)," by Dr. Giacomo Biichi, Engineer, La Marina Italiana, Feb 1935, pp. 45-57. ONI, U. S. Navy, Transl. 76 (copy in TMB Ubrary). (e)

(3)

Inter-

action of the Voith-Schneider Propeller and

und Werft, Jun

and

and Helm, K., "Ergebnisse naturgrosser

Mueller, H. F., "Die Steuerkraefte des Voith-Schneider

translated into English. (1)

G.,

(5)

were

they had

additional to those

15.13, 15.14,

Schleppversuche mit dem Motorschiff 'Augsburg' (Results of FuU-Scale Towing Tests on the Motorship Augsburg)," WRH, 15 Oct 1931, Vol. XII, pp. 347-348 Betz, A., "Grundzatzliches zum Voith-SchneiderPropeller (Fundamentals of the Voith-Schneider Propeller)," HPSA, 1932, pp. 161-170

pellers.

Netherlands Model Basin, and by other testing establishments. Unfortunately, the published

337

references,

the 1944, pp. 113-119.

One of the most systematic accounts is recorded by J. Pollard and A. Dudebout, in their "Theorie

HYDRODYNAMICS

338

du Navire" following

[1894, Vol. IV, p. 201],

translated.

is

from which the

The comments

in paren-

theses are those of the present author:

IN SHIP DESIGN

"As examples

of the application to (ship) propulsion

of the turbine-propulsors of the first

kind

(in

which the

water passes through the turbine radially), we

will give

them in chronological order: "The Enterprise, built in 1853 by John Ruthven; vessel was not successful and was (later) converted a

this

into

be deflected so that they act as rudders. One jet may be reversed so that the boat

same year by Seydell at Stettin, ran successfully on the Oder for ten years "The Seraing II, built about 1860 by Cookerill, at the same time as the identical ship Seraing I, fitted with Albert, built the

articulated (feathering?) paddlewheels

"The Jackdraw, on which, in 1863, the British Admiralty attempted, but without success, an application of hydraulic propulsion "The Nautilus, constructed in 1863 for the British Admiralty, which on trials on the Thames achieved a speed of 10 kt "The English armed gunboat Watenvitch, built in the same

year, successfully

underwent comparative

trials

with

the Viper, of the same type, fitted with twin screws

"The a

Rival, built in 1870

failure,

by the German Navy, proved

due partly to an excess

of draft over the predicted

draft

"Finally,

structed

a rescue or lifeboat recently

by R. and H. Green

(1894?)

of Blackwall

for the National Lifeboat Institution. It

con-

(England),

was

fitted,

by

Thornycroft and Company, with an internal hydraulic propulsor, intended to prevent damage from shocks, beaching, or running foul of another ship." A table on page 203 of this reference gives 20 items of technical data for the: (a) Waterwitch (b) Viper (c) Two Swedish torpedoboats with hydraulic propulsion and with screw propellers (d) Two Thornj'oroft torpedoboats, with hydraulic propulsion and with screw propellers.

by Pollard and Dudebout of the screwbe found on pages 206-210 of the reference

discussion

turbine

is

to

is

when both are reversed the very powerful.

Performance Data on Controllable and Open-water test data and performance characteristics of controllable and reversible propellers, defined and described in Sec. 32.19 of Volume I, are found only rarely 59.9

Reversible Propellers.

Rupp gives openwater characteristic curves derived from tests of a model representing the controllable propeller

and tested on the U.

installed

YTB

[SNAME,

502

cited earher in this section.

1948,

S.

Navy

278-279].

pp.

tug

The

graphs in Fig. 6 on page 279 of this reference

embody

characteristics

settings

of this

shown

five

for

propeller.

different

The

propeller

pitch itself,

in Fig. 4 on page 277 of the reference, has

the following features:

Number

of blades,

Diameter, 9.50

4

ft

Pitch at Q.IR, helix angle 20 deg, ahead position, 7.60 ft

Developed-area

"A torpedo boat with hydraulic propulsion, built in 1878 by the Swedish Government, to be tested comparatively with a ship of the same type fitted with two screws "A torpedoboat of the second class, built by Thornycroft and Company in 1882, for the British Admiralty, and which was run through comparative trials with a similar ship having a single screw propeller

A

axis;

its

stopping action

in the technical literature. L. A.

sailing ship

"The

from

jets issuing

may

the vessel

turns on "379. Principal Examples of Turbine-Propulsors of the First Kind.

Sec. 59.9

The

flow either astern or ahead.

Mean-width

ratio.

Ad/ An

,

0.502

ratio, 0.268

Blade- thickness fraction, variable.

More extensive open-water data are given by W. B. Morgan in reporting the tests of a series of controllable

propellers with

3,

2,

4,

5,

and 6

[TMB

Rep. 932, Nov 1954]. In this case three different hubs were used, to which the proper number of blades were clamped. The report includes a model propeller drawing, with five sets of characteristic curves for normal ahead blades

operation.

Morgan

publishes,

as Fig.

the 4-bladed controllable propeller,

when run

3227,

7 of his

the open-water characteristic curves of

report,

in the astern

TMB

model

direction, xjalled

"back driving." L.

C. Burrill discusses the "Latest Develop-

ments

in Reversible Propellers"

[IME and IN A

joint mtg., 1949, pp. J3-J32] as applying to three

types developed in Europe but unfortunately he includes no open-water test data for models or

One of the few modern references describes a new ferryboat with so-called hydraulic-reaction propulsion, built by the Etablissements Billiez (in

any of these propellers. van Aken and K. Tasseron have published a paper entitled "Comparison Between the Open-Water Efficiency and Thrust

side of the vessel

of the Lips-Schelde Controllable-Pitch Propeller

[Nav. Ports Chant., Jul 1952, Vol. French)].

One pump on each

3, p.

418

takes in water through a converging conduit and discharges

it

through a valve which directs the

full-scale pi'ototypes of

More

and

recently, J. A.

those

of

Troost-Series

Shipbldg. Prog., 1955, Vol.

2,

Propellers"

No.

5,

[Int.

pp. 30-40].

PROPULSION-DEVICE PERFORMANCE

Sec. 59.10

A

by R.

contribution

F.

P.

Desel,

entitled

"Controllable Pitch Propellers in Ship Propulsion,"

appeared in Bureau

of

Ships

Journal,

April 1956, pages 2-6. 59.10

Performance of Miscellaneous PropulWater Intake Through

&rille\

Water Discharge Aft, Forming Propulsive

Jets.

Under Bottom of Boat

Devices.

general

curves for screw propellers.

characteristic

The

may

be mentioned as sources of reference information on the Hotchkiss propeller:

following

Centerline of Ship-""''^

for Single-Unit

339

The

arrangement and method of operation of the Hotchkiss propeller are illustrated schematically in the diagram of Fig. 59. Da. A drawing showing the use of a Gill axial-flow propeller in a hydraulic propulsion device is reproduced in Fig. 59. Db. It has not been possible to find in the technical literature any published systematic performance data on these and other types of miscellaneous propulsion device, corresponding to the orthodox sion

D

(1)

Hotchkiss,

D.

Propeller," (2)

SBMEB, Apr

V.,

The

"The Hotchkiss Internal Cone

Shipbuilder, 1931, p. 180

1937, p. 188. Illustrates "60-in

Drive Cone Propellers for

May

1937, p. 321,

Wood

Worm-

Vessel."

Also

and Jul 1937, pp. 382-384.

(3)

The Motorship, 1937-1938,

(4)

A

lifeboat fitted with

p.

110

Hotchkiss cone propellers

is

and described on pages 45-50 of the 13 January 1938 issue of Shipbuilding and Shipping Record. The following is quoted from pages 45-46: "The Hotchkiss system of propulsion consists of cones constructed of steel and provided with illustrated

Inflow

Inflow from

" Outflow.

Downward and Aft

Fig. 59. Da

Fig. 59. Db

Forward

Explanatory Diagram for the HoTCHKiss Propeller

rotary impellers. One side of the cone is cut away, forming an aperture in contact with the water, which divides into inlet and outlet portions.

As the impeller the water causes

rotates, the centrifugal force of it

to be projected tangentially

from the larger end.

Longitudinal Section Through a Hydraulic Propulsion Device Utilizing a Gill Axial-Flow Propeller

This drawing, reproduced from page 111 of the July 27, 1939 issue of Shipbuilding and Shipping Record, shows a Gill propeller (marked "rotor") with a close-fitting fixed shroud ring. In other installations the ring is attached to the blade tips and rotates with the propeller.

HYDRODYNAMICS

340 "Water

drawn

is

in

through about two-thirds measured from the flows into the cone in the

of the length of the opening,

smaller end.

The water

direction of rotation

and the resultant

spiral flow

causes the water to leave the cone with increased

thereby producing a reactive thrust

velocity,

which takes

effect

upon the

internal surfaces of

the cone."

SBSR, 10 Feb 1938, p. The latter reference

(5)

176; 2 May 1940, pp. 444-445. contains rather detailed draw-

ings of a 25-ft launch equipped with a double-cone

propeller

designed

by Donald V. Hotchkiss

for

operation on the Irrawaddy River where floating debris and weeds are encountered. A grille is pro-

vided to exclude "objects which might damage the impellers if drawn into the intakes." Baader, J., "Cruceros y Lanchas Veloces (Cruisers

(6)

and Fast Launches)," Buenos Aires, 1951; on p. 221 illustrates a Hotchkiss propeller

Fig. 175

IN SHIP DESIGN

Sec. 59.11

propeller-design discussion of Chap.

by the

down

the approximate

in Sec.

67.24,

to

is

no

is much reduced; the cone propeller can pass through weed beds, or over ropes or obstructions without fouling, by reason of other the self-clearing grids provided; installation is a simple matter and the cones can be installed in

craft using it

the most suitable part of the boat.

A

further

important advantage is that the impeller can be employed to pump out the bilges, by providing piping connected to the small end of the cone." Gill propeller, the available information

somewhat more scanty: H. W., "Der Hydraulische Schiffsantrieb fiir besondere Fahrtverhaltnisse (The Hydraulic Ship Propulsion for Special Ship Operating Conditions),"

(a)

Gill, J.

(b) (c)

The The

(d)

MENA,

(e)

SBSR,

Bull. Tech.

du Bureau

Veritas, 1921, p. 199

Shipbuilder, 1921, p. 24

Engineer, 1921, Vol.

of that year, pp. 140, 172

1

1923, p. 345

19

Aug

1926, Vol. 28, pp. 202-204; 1939, Vol.

54, pp. 111-115.

59.11

Area Ratios, Blade Widths, and Blade-

Helix Angles of Screw Propellers. The various blade-area ratios of a screw propeller are defined rather precisely in Sec. 32.8 of the

"Explanatory

Notes

for

Volume

I

and in and

Resistance

Data Sheets," SNAME Technical and Research Bulletin 1-13, July 1953, page 16. Propulsion

The expanded-area

Ae/Aq

ratio

,

also

known

rather indefinitely as the blade-area ratio or the disc-area

ratio,

exclusively

in

is

this

know

rules laid

maximum blade width for a screw propeller having Z blades and a specified (or approximate) expanded-area ratio As/Ag or for a propeller having a given mean-Avidth ratio Cm/D. The maximum width will depend to some extent upon the blade outline and shape but approximate values can be derived for blades of average shape, to permit establishing aperture and edge clearances in the preliminary-design stage. The brokenline graph of Fig. 59. E enables a designer to ,

Expanded Chord

projection outside the hull so that the draft of a

For the

laying out propeller

fitted in

pages 358 and 359 of the September 1952 issue of The Motor Boat and Yachting there is an article, with drawings, about a small cone propeller installation suitable for dinghies. The following is quoted

from page 358: "Advantages of the system are that there

is

when

It is often convenient,

apertures and edge clearances

the side of a vessel

On

(7)

70 of the

present volume.

the

one

book,

employed almost

particularly

in

the

Left-Hand Scole

is

Rotio of

Cf^

^eon Expanded Chord Length

i

PROPULSION-DEVICE PERFORMANCE

Sec. 59.12

propeller design of Chap. 70. It could

and should

be increased when making the revisions to the preliminary design described in Sec. 78.18. In the event the mean-width ratio of a particular screw propeller

is

not known,

it

can be deter-

mined by the formula

m 2Z

1

Table 59.b

lists

341

the blade-helix angles

series of ten 0-diml radii x',

and

<j)

for a

for five pitch-

diameter ratios covering the range normally encountered in ship work. The pitch is assumed constant at all radii for this tabulation. 59. 12 Pertinent Data on Flow Into PropulsionDevice Positions. The flow into the positions occupied by propulsion devices around a ship

(59. i)

hull

is

discussed

in

and covered by various and 69. The

sections in Chaps. 17, 33, 52, 60, 67,

-

duplication and repetition involved are considered

by the great importance of this phase of hydrodynamics as applied to ship design, and by the necessity for devoting increased thought and study to it in the future. The present section

justified

Table 59.a

lists

the blade-helix angles <^(phi) for

ten values of 0-diml ratio x'

= R/Rm„x

for

EMB

model propeller 2294, used as the stock propeller for the self-propulsion tests of the transom-stern

ABC

ship model,

propeller

is

TMB

is

A

59. a

and

lists

material available for reference.

Derivation op Blade-Helix Angles for

ABC

helix angle is given for the tip section,

X'

a few particular features of this a number of sources of published

calls attention to

flow,

TMB

Model Propeller 2294

a drawing of this propeller, used as the stock wheel for the self-propelled test of

senting the transom-stern design of the

The

drawing of this

reproduced in Fig. 78. L.

TABLE Fig. 78. L

4505.

= R/Rua.

ship of Part 4. even though the blade width there

is

zero.

TMB

Model 4505,

repre-

HYDRODYNAMICS

342

One such

feature applies to the element of a

IN SHIP DESIGN screw propellers, the effective velocity

screw-propeller blade on which the instantaneous

the

incident-A'elocity vector impinges in a plane not

normal to the blade

non-axial flow situation described in Sec.

and depicted in diagram again emphasized that for velocity across the blade

17. D.

of Fig.

1

the incident velocity

effective

and the thrust

0.9455, but

dR vary

The

must be remembered any blade element

it

for

as the square of the incident

effective thrust

[1

equal to the stream velocity

times the cosine of the angle of sweepback [Collar,

A. R., "Aeroelastic Problems at High Speed," Jour. Roy. Aero. Soc, Jan 1947, pp. 15-16]. Theoretically, this situation should apply also

2iD abaft the disc position, respectively.

and

to a screw-propeller blade with skew-back,

lift

- (0.9455)'] or about 0.106. Applying also to Fig. 59.G of Sec. 59.13, the graphs of Fig. 59. F indicate the ratios of the inflow-jet and outflow-jet diameters to the diameter of an imaginary actuator-disc propeller, for a range of thrust-load coefficient values up to 6.0. The data given are for positions 3D ahead of and

is

to the blade axis, in a plane generally parallel to is

is

that the

on the tip blade element therefore appears to be reduced by the factor (1 — cos' B), where 5(theta) is the convergence angle. For the case mentioned this is

the component of the speed vector l3'ing normal

the wing. This

of this angle

velocity.

here corresponds to that of the flow over an

lift,

of

of 24, rarely reached in

of thickness

on a plane passing through the base chord of the blade element and the blade axis. The situation

wing with sweep-back. The

G

service, the

times the sine of the angle which that velocity vector makes with the blade axis, as projected

airplane

of Fig. 59.

1

any kind of ship convergence angle of the inflow jet, at the propeller tip, is about 19 deg. The cosine Ctl

17.7 It is

UR

velocity of the air stream, for generating

assumed

is

as the nominal incident velocity.

Sec. 59.13 indicates that for a thrust-load factor

this case the effective

is

same

In the latter case, diagram

corresponding to the

axis,

Sec. 59.12

Only

the case of systematic variations in

in

converging flow of an inlet jet when approaching the propeller disc. In the former

inflow, occurring over

throughout most of the length of the blade, is not normal to the tangent plane of the local incident flow. However, since the effect and the magnitude of sweep-back have not as yet (1955) been incor-

formance. For instance, general prerotation in the inflow jet, in a direction opposite to that of

porated in any of the analysis or design phases for

propeller thrust.

to

the

case,

the local blade-axis direction

2.4

0-7 1=1

0.0

I

I

I

0.4

I

I

I

I

I

0.&

I

I

I

).2

I

I

I

I

1.6

I

I

I

I

2D

I

I

I

I

2.4

increase in efficiency for the generation of a given

I

I

I

Z.8

I

I

M 3.2

C^l A.O

3.£

3.2

2,8

I

I

I

I

I

I

I

3.G

Thrubt-Load Coefficient Fig. 59. F

of the disc area, is it

the propeller, results in a slower rate of rotation, a reduction in power absorbed, and (usually) an

Thrust-Load Coefficient 2.0

most

possible to predict their effect on propeller per-

I

I

I

I

4.0

I

I

I

4.4

I

I

I

I

A.&

I

I

I

I

5.2

11

I

5.G

I

I

07

1^ G.O

Ctl

Graphs Indicating Ratios of Inflow- and Outflow-Jet Diameters to Disc Diameter of an Ideal Screw Propeller

PROPULSION-DEVICE PERFORMANCE

Sec. 59.13

The

following references

may

be found useful

Data on Induced Velocities and Differ-

59.13

by the reader who wishes to pursue further the

ential Pressures.

study of inflow to a screw propeller:

Volume

(1)

M

2,

(2)

Betz, A.,

(3)

Betz,

Propeller," A.,

NACA

of the Inflow

Tech. Note 24,

"The Theory

of

Theory

Nov

of the

1920

Screw Propeller,"

the

(5)

Tech. Note 83, Feb 1922 Munk, M. M., "Notes on Propeller Design-Ill. The Aerodynamical Equations of the Propeller Blade Elements," NACA Tech. Note 95, May 1922 Lock, C. N. H., and Bateman, H., "The Measurement of Airflow Round an Airscrew," ARC, R and 1955, Nov 1924, pp. 385-399

(7)

(8)

(9)

AT,

\z

Fig. 59.G

1

+Ap

of

Volume

I.

— Ap

ahead

of the disc

Here, utilizing the Bernoulli Theo-

3 1

At

+ VCtl + 1 +3VCrL + 1

zero speed of advance, where

nominal value of

4-Ap reaches

IME, Mar

its

infinity,

in

Terms

of

Ctl has a

— Ap

low limit of 0.333 [Troost,

to L.,

1946, Vol. 58, p. 14].

velocity far astern, 0.5 f//

ob

(59. ii)

the ratio of

Numerical values of the ratio

Vol. IV, 1936.

Longitudinal Scale

magnitude of the

and the

rem, the ratio

Weick, F. E., "Propeller Design: Practical Application of the Blade Element Theory-I," NACA Tech. Note 235, May 1926 Weick, F. E., "Aircraft Propeller Design," McGrawHill, New York, 1930 Helmbold, H. B., "Goldstein's Solution of the Problem of the Aircraft Propeller with a Finite Number of Blades," NACA Tech. Memo 652, Dec 1931 Glauert, H., "Airplane Propellers,"

relative

indicated by the graph of Fig. 16. B on page 249

M

(6)

explained in Sec. 16.3 of

abaft the disc for any given Ctl is similarly a function of that thrust-load factor,

NACA

(4)

is

I that the

functions of the thrust-load factor Ctl at which the actuator is assumed to be working. The

pp. 553-576

"Development

It

induced flow and the contraction of the jet passing through the imaginary actuator disc representing a screw propeller are

Wood, R. MoK., "Multiplane Interference Applied to Airscrew Theory," ARC, R and 639, 1919-1920, Vol.

343

,

of half the

induced

to the undisturbed

Hodius R

1

Theoretical Jet Outlines, Axial- Velocity Distribution, and Axial-Pressure Distribution FOR an Ideal Screw Propeller

HYDRODYNAMICS

344

stream velocity

U^

at a distance, are listed in

Table 34. a on page 508 of Volume I for a range of thrust-load factor Ctl of from 0.040 to 360.0. These ratios are indicated graphically in Figs. 34. D and 34. E on page 510 of that volume. In diagram 1 of Fig. 59. G there are plotted, to scale, the longitudinal jet outlines for the liquid

passing through an imaginary actuator disc from 6i2

or 3Z) ahead to

QR

or 3Z) abaft the disc

position, at varied thrust-load factors. If

R

is

the

radius of the actuator. Table 59. c gives the theo-

T.\BLE 59. c Inflow- and Outflow-Jet Diameters AT %R Ahead and Astern of an Imaginary Actuator Disc of Radius

The

ideal liquid

and no external

Thrust-load Ideal factor,

R

values tabulated are entirely theoretical, for an

Ctl

interferences.

efficiency.

vi

Inflow-jet

Outflow-jet

radius

radius

IN SHIP DESIGN

Sec. 59.13

PROPULSION-DEVICE PERFORMANCE

Sec. 59.14

_

.^. ror this model,

^T(for

r

.

,

Lf-i -

-rz 0.5p

_

propellers)

all

~

^ 2 Ao(.for all .

345

/•,

\T727

propellers) V/f(avera()i

M'' --K-

.,--K JfT'

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

1

07

I

I

1 I

I

I

I

I

I

III 0.8

Taylor

I

I

I

I

I

I

I

I

I

I

I

I

I

I

0.9

Quotient, Tc^ •

V/C

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

ITl

3CP3

346 19 18 17

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 59.15

PROPULSION-DEVICE PERFORMANCE

Sec. 59.16

course of a conversion project, to estimate the

(10) 17,000

screw-propeller thrust long before the propeller

lb thrust.

is

=

347

=

170,0001b to (15) 17,000

TD/Q

255,000

value from the Prohaska

Only the proposed ship speed may be known, or at most the power and

logarithmic propeller chart in Fig. 70. B, by the

rate of rotation of the engine.

method diagrammed

A rule-of-thumb

often used involves the dimen-

T = kPs

sional relationship

units

T

is in lb,

Ps

is

in

where in English horses, and k varies from ,

30 on a tug exerting bollard pull at zero speed to a range of 10-15 for normal propulsion. For highspeed racing motorboats it may drop to 3 or less

D.

[Spencer,

Selecting a

designed.

or

selected

Pac.

B.,

N. W.

TD/Q =

and the rate

rpm

It is pointed out in Sec. 34.7 of is

relationship between the thrust

Part 2 and Sec.

a rather definite

T and

signed speed

The torque is

readily

with equal facility by one or the other of the following 0-diml equations, depending upon the

With a

T = From

TMB

the fraction

K^/Kq

TD

0.148

Q

0.0265

T =

from

and other

design,

mate those which

is

probably be used in the

contemplated design. The TD/Q ratio varies only slowly with the real-slip ratio Sg or advance coefficient J. In any case the open-water data

At a

estimated from

and

t

R

T = R/{1 —

t),

where

and the thrust-deduction

are estimated as described in Sees. 60.9,

self-propelled

Using the

respectively,

model

ABC

or are found

from

5.58

817,600

5.58

=

20

228,110

1b.

Sec. 70.6 the predicted propeller thrust,

is

later stage of the

only about

193,500

lb.

Fig. 78.

Nb

ABC The test,

ship

thrust

taken

for the 20.5-kt designed speed,

only 172,170 lb. The range of prediction covered by the preceding examples is rather large, but at

least the estimated values are conservative.

59.16 peller

and

Relation Between Thrust at the Proat the

ship as an example for the

successive stages of this estimate, /c-values of

ceding section,

Thrust Bearing.

For a propeller-

the rule-of-

10 to 15 for

normal propulsion, and for an estimated shaft power of 17,000 horses, gives a range of from

it

is

usually assumed that the

thrust bearing takes the whole propeller thrust. Actually,

the

thrust-bearing

propeller thrust only

when

load

equals

the

the friction effects in

the bearings between the propeller and the forward

end

tests.

thumb method, with

is

thrust estimate of the type described in the pre-

coefficient.

the hull resistance fraction

57.4

real-slip

later stage in a ship design the propeller is

=

derived from the self-propelled model

from

thrust

at a real-slip ratio of about

found to be

From

advance

for the transom-stern,

corresponding to a J-value of 0.735,

0.25,

principal characteristics of the propeller approxi-

ratio or

lb.

2294, presented in Fig. 78.Mc, the value of

worked out at a

any desired

237,104

the open-water test data of the stock

model propeller selected

data.

give appropriate values for

20

V

from open-water model propeller

will

ft-lb.

the thrust

ft,

7 817,600 =

5.

Kc

available plots, provided the pitch ratio

817,600

Hence

a value derived from propeller charts

latter relationship is easily derived

=

6.2832(1.82)

propeller diameter of 20

Thrust-torque factor

The

Sec. 70.6 as 109.2

prediction works out as

information available at the time of the estimate:

TD =

Again

1.00.

found by

the torque

to be exerted by a propelling determined from assumed or known values of the shaft power and the angular rate of rotation n. The thrust may be estimated

—p^

is

17,000(550)

developed by a screw propeller when working imder any given set of relatively steady condiplant

of

ratio

from

of rotation

2im

Q

tions.

P/D

or 1.82 rps, the expected torque at the de-

2 Feb 1951]. 70.5 of Part 4 that there

in Fig. 70. A, gives the ratio

for a

taking the power as 17,000 horses for this example,

SNAME,

Sect.,

5.8

the

and working with and when the shaft

of all elements attached to

shaft

are

neglected,

declivity in the running condition is zero. Otherwise the thrust-bearing load equals the propeller

thrust plus or minus an axial component of the

weight of the propeller, shaft, and

all

engine

HYDRODYNAMICS

348

parts whose longitudinal position

component

axial weight aft.

depending

bearing,

thrust

The

is

is

by the

fixed

upon whether the directed forward or

axial friction effects in the various shaft

and machinery bearings, with the parts rotating at any speed above very slow, may generally be neglected. The axial weight component is usually a secondary factor in the selection or design of a thrust bearing, but it is a factor of importance in the analysis of shipboard thrust measurements,

where

magnitude

its

is

often appreciable, com-

pared to the propeller thrust

[SNAME,

1934,

pp. 151-152].

adapted from Figs. 13 and 14 on 151-152 of SNAME, 1934, illustrates

Fig. 59.L,

pages

diagrammatically several types of machinery, the weights of each to be included in the computation for the axial

component, and the manner

in

which

the various forces are combined at the thrust bearing. As further refinements, not always carried out in practice:

The weight

(1)

of

The

by

water may be reduced by the buoyant forces of the water on those parts (2) Part of the measured thrust is due to the hydrostatic head over the section area of the shaft where it enters the hull stuffing box

Sec. 59.17

-|-Ap's exerted over the projected axial

area of the hub abaft the blades, as well as the

— Ap's

exerted over the forward exposed area

measured in and reckoned in ship trials as part the thrust exerted by the blades.

of the hub, outside the shaft, are

model of

tests

For high-speed vessels such as destroyers, in which the attitude changes materially from the at-rest to the running condition, the actual shaft declivity at any .speed is a combination of that built into the ship (or that imposed by the particular loading condition) and the running trim at that speed. Assuming a change of trim from zero to full speed of 1.5 deg, not

these craft, the axial weight rotating parts of one

uncommon

component

main propelling unit

of the full-speed thrust

[SNAME,

1933, pp. 268,

Estimates of Thrust and Torque Varia-

tion per Revolution for

Screw Propellers.

The

reasons for the generation of thrust and torque variations on the blade of a screw propeller as rotates,

and

for the application of offset forces

Volume

I.

The

equalization of the thrust

and

Restraint

A^T are the Products of the Wcltjhts W, and W2 and the Sines of the Respective ArKjIes of Declivity,

Forces Zi|T and

with Friction Effects

of the of

Rotating

Parts, the

Weiqhl

Weiqhls

the Propeller and of the Shaftino

Sections Surrounded to

be Diminished

of

that Water

b"y

Water are

the Buoyancy

b'^

On Slow-Speed and Medium-Speed Vessels the Chanoe of Trim and of Shaft Declivity the Water

is

Due

to

Usually

Speed Through Neqli(jible.

it

and

bending moments on the shaft, are described in Sees. 17.3 through 17.7, 17.12, and Sec. 33.13 in

Fore- and- Aft

Calculating the Total

is

275, 277].

Jaw Couplinq with No

When

in

of the

changed by the sine of this angle, or some 2.6 per cent. This may amount to 3 per cent or more

59.17

the propeller and of those

portions of the shafting completely surrounded

IN SHIP DESIGN (3)

Nei^lected

PROPULSION-DEVICE PERFORMANCE

?9.17

Sec.

torque for

all

angular positions and the reduction

of the bending

moments

a design problem of

is

long standing. Nevertheless, the advent of higher

on vessels carrying propellers abaft skegs, and the increasing emphasis on freedom from vibration, has made it necessary to devote much more intensive and thorough study to this project than was formerly the case. powers per

A

shaft, especially

Several decades ago R. J. Walker and Cook gave some data on wake and torque

S.

S.

varia-

encountered on the single-screw tankers San Florentino and Sa7i Fernando [Mar. Eng'g., May 1921, p. 395]. They reported variations in tions

maximum

torque ranging from a

of 1.35 times

the mean, at a blade position of about 102 deg,

in

mean

taken as

is

at a position, for the

deg, with angles increasing

a clockwise direction, looking forward, cor-

responding to diagram

symmetry

of

fractions

at

1

the

of Fig. I.E. In the plane

disc

were found

to

position

the

wake

vary from 0.536

at

6 o'clock in the tip circle to 0.627 at 12 o'clock in that

circle.

At

4:30 o'clock the

wake

was

0.255.

0.041; at 10:30 o'clock

Diagrams

Failures"

314-381], have given the

wake-survey diagram of a single-screw ship, together with the calculated variations in propeller thrust, propeller torque,

and other

factors,

lb at the 9 o'clock position to 126,000 lb at 12:20

shafts at sea.

position

pp.

same

motion of the machinery parts and generate vibration in both hull and machinery but to account for actual breakage of the propeller

of about

Shaft

Propeller

of

1952,

143 deg. Here the 12 o'clock

great deal of clever experimentation, carried

blade,

[SNAME,

on a base of angular position of the propeller. These are supplemented by measurements of the axial, torsional, and bending .strains on the protoand 59. N are type propeller shaft. Figs. 59. adapted from Figs. 33 and 34, respectively, of the paper. A list of 20 references is to be found on pages 364-365. Supplementing the foregoing, E. P. Panagopulos and A. M. Nickerson, Jr., made further full-scale tests on a larger vessel. The results of this investigation were published by them in a paper entitled "Propeller-Shaft Stresses under Service Conditions The S.S. Chryssi Investigation" [SNAME, 1954, pp. 199-241]. This paper is concerned largely with the bending stresses in the propeller shaft but Fig. 23 on page 227 is a graph showing the variation in the calculated thrust of- one blade throughout a single complete revolution. The thrust varies from about 15,000

out in the period 1940-1955, has demonstrated that the variable forces and moments can be large enough not only to produce objectionable

to 0.59 times the

Investigation

349

of thrust

it

fraction

M

—

o'clock, to 42,000 lb at 4 o'clock,

and to 123,000

lb at 6:36 o'clock.

A

realistic

definitely

look

at

this

situation

indicates

that an analytic procedure must be

developed whereby the magnitudes, directions, and positions of the variable forces exerted by one

was

and torque variations on a

basis of angular position around the shaft axis, for the single blades of a 3-bladed screw propeller,

and

for the overall propeller, are given in Fig. 218 on page 281 of the Russian book "Korabelnye Dvizhiteli (Marine Propulsion Devices)," written by U. I. Soloviev and D. A. Churmack under the scientific supervision of I. G. Hanovich, Moscow, 1948. These page and figure numbers are the same in the Bureau of Ships (Navy Department) Translation 408 of this book, March 1951. A paper by J. R. Kane and R. T. McGoldrick [SNAME, 1949, pp. 193-252] was devoted to an analysis of the longitudinal vibration of marine propulsion-shafting systems, resulting from variations in the thrust forces with angular position of the screw propeller. On pages 231-232 this paper lists 20 references. More recently, N. H. Jasper and L. A. Rupp, in their paper "An Experimental and Theoretical

x'=R/Rm,

59.M Variation of Thrust-Load Coefficient OF A Screw Propeller with Dimensionless Radius, on a Basis of Dimensionless Radius, At Four Angular Positions

Pig.

350

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 59.17

Sec. 59.17 l.b

PROPULSION-DEVICE PERFORMANCE

351

HYDRODYNAMICS

352 10,000

8,000

^

6,000

n

8.

S4,000

2,000

480

460

420

IN SHIP DESIGN

Sec. 59.11

Sec.

PROPULSION-DEVICE PERFORMANCE

59.n

Qz{(l)

is

F zifi)

is

the torque per blade at the angle Q

Tzid)

=

%.

T{x'

I

e)

,

all

blades at one blade

=

Qivipan

z

For a 4-bladed going becomes

ne) = Tz{6

= Zl "'

/

^z( ^

propeller,

2

1

TT

r^"'

^^^)

1

'^^

"

Setting

'\

-^1

Z =

[F{d)]^.

equal to the total horizontal

transverse force of angle,

where

blades at

4,

the fore-

and

[F{e)],

transverse force of

all

blades at any one blade

equal to the total vertical all

blades at any one blade

angle,

+ 2^p) +

+

+

all

Qi6), then

'"'

designated as T{B), then Ti^)

T{Q) dQ

and

dx'

/

f

Jo

Similarly, letting the total torque for

dx'

any one blade angle be

7,

the total thrust for

= tt ^T

7'M„a„

Hx is

353

is

2,

Then

'^"''

If

thrust

the transverse tangential force per blade

at the angle

angle

The mean

T.(.

Tz{e

+ 2^)

+ ?fl) +

Tz{e

+

f)

[Fie)i

=

t Fz{e + ^f) cos [e + ^f)

[Fie)i

=

t Fz{e + f

) sin

{e

+

f)

CHAPTER

60

Ship-Powering Data for Steady Ahead Motion 60.1 60.2

General Estimation or Calculation of Effective and

60 3

Trim Changes on Power Methods and Factors Involved in Predicting Shaft Power Axial-Component Wake-Fraction Diagrams

Friction

Power

Determination of the Propulsive Coefficient Data from Self-Propulsion Tests of Model

355

60 13 60.14

Merit Factors for Predicting Shaft Power Shaft-Power Estimates by the Ideal-Effi-

Effective

60 4 .

358

60.15

358 360

60 16

Estimating Shaft Power for a Fouled- or Rough-Hull Condition Increasing the Power and Speed of an Existing Ship Powering for Two or More Distinct Operating Conditions Backing Power from Self-Propelled Model Tests

60.5

at Propulsion-Device Positions

Three-Dimensional Wake-Survey Diagrams Interpretation and Analysis of the Three-Dimensional Wake Diagram Estimating the Ship- Wake Fraction .... Prediction of the Thrust-Deduction Fraction Finding the Relative Rotative Efficiency

60.6 60.7

.

.

.

many

.

362 368 370 374

marine engineers for the past century or more has been to find an adequate method of calculating directly the power necessary to drive a given ship

By

direct calculation

is

.

60.17

words, one aim of naval architects and

at a given speed.

meant a

determination of the ship power in the early

60.18

that

may

or reference data

be necessary, but without the building

or testing of a model. is

handbook

The

limited generally to

discussion in this chapter

methods of

direct estimate

or calculation.

total hull resistance

use

several

of

Rt

different

making methods and various

oi ship forms,

sources of test data. Certain of the powers used in

design

ship

Method

are

derived

readily

from

resistance. Others, like the shaft power,

this

those for one kind and size of ship

resistance

is

Many graphs and

can not

method

to

may

it.

either is

the

by estimate,

by-passed, so to

power

for

a given ship form.

methods to give the required

precision required in

known,

in a single step, the probable effective

which of several successive approximations is to be used, depends upon the time available for finding the answer, and the or as

be mis-

speak, by having the marine architect determine,

of the book, that the ship designer needs

selected,

may

Pe = RtV. When

since

not

calculation, or test, its value

in Parts 3

engineering answers. Choice as to the

388

Estimation or Calculation of Effective

60.2

A rule-of-thumb procedure

be most appropriate for one situation yet

highly unsuitable for another.

354

for ships

tables for finding the effective

have been prepared and published

over the years.

several different

388

and Friction Power. The derivation of towrope or effective power for a ship, when its resistance is found by the procedures described in Chaps. 56 and 57, involves only one simple step in

easily.

and 4

387

borderline cases.

power

emphasized here, as elsewhere

385

leading or result in downright inaccuracies for

be calculated directly nor can they be estimated It is

383

hensive as possible. Limiting one's basic data to

multiplication,

Chap. 57 describes methods of estimating the

377 380

.

One caution against all methods of estimating and predicting ship power is that they shall be based on test and other data that are as compre-

stages of the design, directly from the data on

paper, using whatever

.

ciency

Although not always expressed

General.

60.1

.

375

.

Ships and Propellers .

TMB

60.8 60.9 60.10

.

354

Effect of Displacement and

.

in so

60 1 1 60.12

354

It

is

difficult

to

assess

their

validity

and usefulness because

of uncertainty as

what

basic data were used

and how reliable In most cases,

to

these data were in the

first place.

the graphs and tables cover vessels of one type only; possibly even of a small range of size or shape. For example, J. C. Robertson and H. H. in their paper entitled "A Century of Coaster Design and Operation" [lESS, 1953-1954, Vol. 97, pp. 204-256, esp. Fig. 3 on pp. 212-213], give curves of brake power Pb for this type of

Hagan,

SHIP-POWERING DATA

Sec. 60.3

W

ship on a base of displacement_weight for various values of T, = V/'VL, where V is (apparently) the trial speed in kt. H. Volpich, in a discussion of this paper on pages 236-239 of

SBSR, 20 May nomogram (Fig. 12)

the reference [also

19.54,

pp. 634,

355

selected vary as to type they vary only

little in

those proportions affecting hydrodynamic resistance.

A

great

many

additional sets of contours

would be needed to cover the whole ship-design field.

power

Bates' effective-power data are based upon test

approximation of single-screw diesel-driven coasters embodying deadweight carrying capacity, ship length, brake power, and ship speed. It is useful for a quick and ready approximation to the

from the Taylor Standard Series of models and from miscellaneous EMB models. While ship forms have changed somewhat since this analysis was made, the data should still serve for quick estimates of effective power for vessels of the

a

636], gives

power of a small

for the

ship.

Bates has published contours of constant effective power P e for fast yachts having lengths in the range of 100 to 500 ft, speeds in the range J. L.

of 10 to

20

kt,

and the following ranges

of

form

(b)

Prismatic coefficient Cp from 0.62 to 0.66 Displacement-length quotient A/(0.010L)^

from 40 to 45 (c) Maximum-section coefficient Cx from 0.75 to 0.83. These curves are to be found in MESA, September 1921, pages 678-680. Similar contours of constant effective power, for speeds in excess of 22 or 23 kt, are to be found in the 1920 edition of the Shipbuilding Cyclopedia

man,

New

proportions

[Simmons-Board-

York].

is found by a any case, the friction power derived invariably by the formula Pp = RpV.

direct calculation in is

vessels, gunboats,

and

difficulties

determining

in

the

effects

of

roughness, described in Chap. 45, are of course reflected in a determination of the friction power.

Numerical values of friction power are rarely employed in ship design but they are useful in the effects of changing the wetted

illustrating

area and of surface roughness. 60.3 Effect of Displacement and Trim Changes on Effective Power. Knowing the effective power P E for the designed displacement and trim of a given vessel, usually as the result of a model test, it

Contours of constant effective power for vessels of fine underbody, comprising yachts intended primarily for ocean cruising, coastal passenger

listed.

Since friction resistance for a ship

The

coefEcient: (a)

results

is

often required to estimate the

somewhat

Pe

for a

different displacement of that vessel;

and

possibly also for a different trim. Designer's

operator's requirements, besides calling for the

certain seagoing tugs, are

effective-power variations corresponding to the

given by Bates in Figs. 3-5 on pages 681-683 of

usual 10 per cent light and heavy displacement,

the

MESA

reference.

The curves cover a Cp

of

0.56, a range of displacement-length quotient of

from 100 to to 0.93.

150,

and a range

of

Cx

of

from 0.87

Representative vessels in the selected

groups have, according to Bates, the characteristics listed in Table 60. a.

Here again

TABLE The

60. a

references

it

is

noted that while the craft

often extend to the so-called ballast condition, especially

for

displacement

cargo for

a

vessels.

its

Length,

ft

listed in the

Displacement, long tons

Passenger vessel

may

designed draft.

As an

aid in estimating these effective-power

accompanying

Prismatic Coefficient,

Cp

J. L.

Bates, 1920-1921

text.

Longitudinal

Type

design

approach half the designed value, and the trim by the stern of that vessel may be 0.3 or more of

Characteristics of Selected Vessels in the Powering Groups of

from which these data were taken are

Here the weight

cargo-vessel

V

(1^ \100>

VI

HYDRODYNAMICS

356

changes without recourse to additional lengthy calculations or model tests, data have been analyzed from the tests of some two dozen models of ships of various types.

to determine the

is

± gA) Pe for A or Pe for (A ± sA)

Pe

of this analysis

in the relationship

F±

SA

(A

for

The aim

exponent n

b¥

¥

may

It is to

Sec. 60.3

be noted that, because of the arithmetic the exponent n is extremely changes in the power ratio. For

the situation,

of

sensitive

to

example, for a displacement ratio (A of 0.9,

and a power

ratio

— 5A)/A

[{Pe for 0.9A)/(P£

A)] of 0.9, the exponent n = 1.0. For the same displacement ratio and a power ratio of 1.0, the

for

exponent n (60. i)

=

0,

0.81 the value of

=

Avhereas for a

n

=

power

=

2, since 1.0

ratio of

(0.9)°

and

Thus, while the possible selections of n for a given T, from Fig. 60. A vary rather widely, the range of estimated Pe derived from 0.81

f„..A,(^)" It

IN SHIP DESIGN

be expected that these relationships will

vary somewhat with speed-length quotient; possibly also with hydrodynamic ship proportions such as prismatic coefficient and fatness ratio. Fig. 60. A gives a tentative mean line for a variation of n in Eq. (60.i) with T„ or F„ as well

them

is

(0.9)".

rather small.

To avoid

multiplying large numbers by factors

very close to unity, which is the case when sA is small, and to avoid taking powers, the following

formula can be used:

,

as a lane in which the majority of

gA

or

bW

percentages as for small ones.

In general the exponent n -t-5A or -\-bW than for a

- SA

is

or

greater for a

- bW,

especially

when r, > 1.0, F„ > 0.30. The plotting of Fig. 60. A is based only indirectly on physical reasoning. The hulls which are less deeply immersed, more deeply immersed, or inclined with trim by the bow or stern, can only in exceptional cases be geosims of the designed underwater hull. Further, because of the different proportions in each case, the surface waterline changes, the wetted surface varies, and the flow

pattern

[

5 0.8

is different.

^

Pe =

n values may

be expected to lie. They conform reasonably well for SA, bW, or 5¥ values ranging from +0.18 to —0.40, and for large-trim as well as zero-trim changes accompanying the changes in displacement. The lane appears to be as valid for large

cIPe

=

/,:nA""' f/A

A-A"

or

bPe

=

hiA"~'

sA

whence bP,

n(5A)

Pe

and

bPs

= Pf

For small percentage changes

"n(5A)"| (60. ia)

in the

displacement

A, Eq. (60. ia) is more accurate than Eq. (60. i) and easier to evaluate. Take for example the ABC ship of Part 4, at a T^ of 0.9. Assume that the effective power Pe for the designed displacement and trim is 11,902

horses,

equal

to

the

estimated

10,820

horses of Sec. 66.9 plus 10 per cent for appendages

and other factors. Assume also that n is selected from the mean line of Fig. 60.A as 0.72. Then for a partial-load displacement of 16,400 13,975

t,

—

2,425

=

as listed in Table 66.f of Sec. 66.16,

Sec.

SHIP-POWERING DATA

60 J

— sA

representing a reduction

of 14.8 per cent

from the designed value, the corresponding tionships are, from Eq. (60.i),

Pe

for (16,400

Pb

-

2,425) tons

for 16,400 tons "

(16,400

= If

A = for (1

P

P

SA

A

P^

16,400

for

["

"

J

(1.000-0.148) 1°" 1-000

L

= This gives

2,425) 1°

is

000-0.148)A ^ for 1.000

-

taken as l.OOOA, and or 0.1 48 A,

16,400 tons

2,425 tons as

Pb

rela-

0.852A

J

0.8911

=

0.8911 (11,902)

=

10,606 horses.

The reduction in effective power is only 10.9 per cent while the reduction in displacement is 14.8 per cent. This appears disappointing. It must be remembered, however, that if the displacement of the given vessel is increased by 14.8 per cent, a similar calculation indicates that the effective TESTS OF US. MAR. COMM.

357

HYDRODYNAMICS

358

be considered typical for screw vessels as a class.

medium and

Thei-e are in the archives of

many

large single-

ship-model

numerous sets of graphs similar to those of Figs. 60.B and 60. C. In these the effective powers, and sometimes the friction powers and other factors, are given for selected testing establishments

when run at widely different displacements and trims. For cases similar to these, where the light displacements vary by some 30 and 45 per cent, respectively, from the heavy or normal-load displacements, the range is rather

IN SHIP DESIGN

making estimates of effective-power changes by the graphs of Fig. 60.A. 60.4 Methods and Factors Involved in Prefor

dicting Shaft

Power.

The

possible,

however, to analyze this kind of experi-

ence and to set

attempt to do

A

it

it is

down as a design rule. An down in Sec. 60.11.

set

procedure for the preliminary estimate of the

power of merchant ships recently described by V. Minorsky [Int. Shipbldg. Prog., 1955, Vol. 2, No. 9, pp. 226-229] is in reality a dimensional

shaft

version of the Telfer merit factor described in Sec. 34.10. It takes the

form

Powering factor

=

preliminary design of

a ship can not proceed very far until the shajt power Ps needed to drive it at the designed speed is determined in some manner. It is customary to estimate or to predict this power by one or more of a series of methods, involving successive

However,

approximations.

is

difficult,

ship models

large

Sec. 60.4

with experience, to estimate the propulsive coefficient rjp directly, as is done for the first approximation to the shaft power of the ABC ship in Sec. 66.9 of Part 4. It is extremely It

to

better

a

afford

as

compared

V V'Ps

to the 0-diml

Telfer merit factor

M

WV

(34.xxiv)

gLPs

The latter is assumed in Fig. 34.1 on page 518 of Volume I to vary in some manner as Fl with ,

understanding of the procedures underlying some of the early approximations, the later approximations are described first. The discussion here is

further variations for better-than-average or less-

Umited primarily to screw propulsion. The shaft power Ps is obtained directly from the effective power P^ by dividing the propulsive

varies

This is simple but estimating the proper value of tip is not. coefficient T?i.(eta) into the latter.

From

Eqs. (34.xv) and (34.xvi) of Sec. 34.7,

Vp

The value

=

Voiv hJvr

=

Vo^ I

of

770

is

known

— w

for the

working range

a considerable number of screw propellers suitable for driving a wide variety of ships. Published data can be supplemented by informa-

of

obtained from model basins which have tested many propeller models. However, the tion

working range of the advance coefficient J is also rather large, and tjo may vary rather rapidly with J in that range. A J-value may be chosen, for a propeller not too heavily loaded, just under (less

than) the J-value for

maximum

170

.

Estimating the hull efficiency rja involves estimates of both the thrust-deduction fraction t and the wake fraction w. Methods of accomplish-

than-average performance. The expression of V. Minorsky uses only a single average factor, which

somewhat with block coefficient Cb and "F/vL. G. Deparis, in his paper "Etude Comparative des Cargos; Puissance des Moteurs (Comparative Study of Cargo Vessels; Propelling-Plant Power)"

speed-length quotient

[ATMA,

1955, Vol. 54, pp. 499-549], describes

methods whereby "guestimates" may be made of propelling-plant power and speed on a basis of useful load, in an early stage of the preliminary design. The factors given are based upon a study of the characteristics of

undoubtedly the

many

ships,

including

inefficient as well as the efficient

ones. J.

E. Burkhardt discusses several methods of

estimating ship power [ME, 22-28] but

all

of

them

1942, Vol. I, pp. are covered in the present

book, in one form or another. Descriptions of other methods of predicting shaft power are embodied in Sees. 60.13, 60.14, and 60.15. 60.5 Axial-Component Wake-Fraction Diagrams at Propulsion-Device Positions. Characteristics of the

wake

at propulsion-device positions

are discussed in Chap. 11.

Methods

for indicating

ing this, in advance of or without self-propulsion

the situation graphically with respect to

tests of the ship model, are described presently in

velocity

Sees. 60.8

and

60.9.

Estimating the probable value

of the relative rotative efficiency in Sec. 60.10.

jjk is

described

wake

and direction over the whole thrust-

producing area are described there, specifically as applying to a screw propeller.

There

is

a great

amount

of published data

on

SHIP-POWERING DATA

Sec. 60.^

wake, some of it listed subsequently in this section, in which only the fore-and-aft or direction-ofmotion components of the actual wake velocities

der

E.xperiences

and Developments

preponderance of these data might lead a marine

(d) Weitbreclit,

described in Sec.

as

adequate.

is

actual-velocity components do indeed serve as the

(e)

the

propeller

Fig. ll.F

The is concerned. down in Chap. 11 and in The 3-diml representation of

positions

and

of Figs.

60.D through

60. J in Sec.

more

60.6 of the present chapter gives a far

adequate, more accurate, and more useful indica-

(f)

which the propeller

tion of the flow situation in

both magnitude brought out in Sec. 60.7. in

true water veloc-

and

direction,

(g)

irregularity

(h)

(a)

is

(i)

(k)

22 of the

was constructed. A brief of sources embodying wake-survey diagrams with contour and other plots of local fore-and-aft velocity components or wake fractions

it

(1)

G.

"On

A.,

the

Currents," INA, 1893, Vol. Pis. I, II,

early

and

Measurement

of

III. Figs. 3, 4,

pp. 61-67 and and 5 on PL II are

results of

Kempf,

G.,

model

tests.

"Neue Betriebserfahrungen und Ent-

ship

wake 15 Jun

in

WRH,

TMB

Tannenberg.

Contours of by G.

fraction are given

1939, pp. 167-174, especiEnglish version of this paper Transl. 91, Jul 1941, where the

An

found in wake-survey and analysis diagrams appear on pages 10 and 11.

(m) Twin-skeg Manhattan, contours of equal longitudinal components of wake velocity abaft one skeg and for a considerable distance

beyond

;

SNAME,

1947,

Fig. 32, p. 121

"The Effect of Shape of Entrance on Ship Propulsion," INA, 1949, pp. 169-170. Contours are given of equal wake fraction (axial component only)

(n) Troost, L.,

observed wake velocities by combining the wave wake with the viscous wake but a rather large discrepancy remained because he did not take into

account the wake due to potential flow. (b) Kempf, G., "The Wake of a Ship in Relation to that of its Model," SBSR, 14 Feb 1924, pp. 194-196. Describes wake wheels or vane wheels and gives

German twin-screw

is

wake-survey diagrams showing true wake

ship speed. Calvert endeavored to account for the

Yamagata, M., "Wake Measurement by a Working Propeller," 3rd ICSTS, Berlin, 1934, p. 67 Yamagata, M., INA, 1934, pp. 286-396, esp. pp. 387-388 and PI. XXXIX. "Stromungserregte ResonanzschwingMichel, F., ungen (Resonant Vibration Caused by Flow)," WRH, 1 Feb 1939, pp. 29-31

ally pp. 170-171.

Wake

XXXIV,

ponents of velocity and wake fractions, and other features. Fig. 25 on p. 793 of SNAME, 1955, is adapted from one of these diagrams. Baker, G. S., "Wake," NECI, 1934-1935, Vol. LI, pp. 303-320 and D137-D146. Shows wake-survey

Kempf

speeds, in the lines of flow, as percentages of the

(c)

SNAME,

Kempf, G., Mitstrom und Mitstromschrauben (Wake and Wake-Adapted Propellers)," STG, 1931, pp.

equal fore-and-aft

given here for the benefit of the reader:

Calvert,

p. 350,

diagrams for a number of models. (i)

more vividly than

the 3-diml survey diagram of Fig.

from which

and 23(c) on

134-152. This paper contains a considerable number contour diagrams, showing longitudinal com-

TMB

twin-skeg model 3898, published in SNAME, 1947, Fig. 32 on page 121, reveals the general

wake

117-133; also

1931, Vol. 32, pp.

of

TMB

reference,

STG,

1950

are

It is true that the plotting of wake-survey diagrams in terms of contours of longitudinalvelocity components F(l — w) or of wake fraction w reveals certain features not well illustrated by 3-diml wake-vector diagrams of Figs. the ll.F and 60.D through 60.K of Sec. 60.6. For example, the wake-contour diagram for

pattern of

reference quoted. Weitbrecht, H. M., "Uber Mitstrom und Mitstromschrauben (On Wake and Wake-Adapted Pro-

Figs. 23(a), 23(b),

Additional reasons for making use of a 3-diml

ities,

TMB

1930.

Wake-fraction diagrams, indicating the variation in

pellers),"

must work.

wake diagram which shows the

Technique

fraction around a propeller tip circle, for and U-sections, are shown on page 254 of a paper by Dr.-Ing. E. Foerster entitled "Speed and Power of Ships" [MESA, May 1930]. These indicate a minimum wake fraction of about 0.42 for the U-shaped run and of about 0.18 for the V-shaped run. Similar diagrams, showing the variations in wake fractions around a screwpropeller disc behind different forms of bossing, are given at the bottom of pages 256 and 257 of the

reasons for this are set Sec. 60.7 following.

in the

1930, pp. 437-442,

English version in

sterns with V-

work. Nevertheless, it is important to realize that they tell only part of the story so far as flow at

Dec

Nov

1

9.

this

wake fraction in everyday powering estimates and for some analytic

basis for the orthodox

use for

and

(New

H. M., "Mitstrom und Mitstromschrauben (Wake and Wake-Adapted Propellers)," WRH, 15 Dec 1930, pp. 505-507, esp. Figs. 6, 7, and 8

method of wake The fore-and-aft

architect to believe that this

representation

11.4.

WRH,

esp. Figs. 5, 5a, 8,

Transl. 3,

indicated,

Schiffbau-Versuchstechnik

of Ship Trials),"

The

are

359

wicklungen

over the propeller disc of a small coaster, together with graphs showing the circumferential variation of the wake fraction for various radii. (o)

Harvald,

S. A.,

"Wake

of

Merchant Ships," Danish

Technical Press Copenhagen, 1950, esp. p. 80 liner. Two dia(p) Normandie, transatlantic passenger grams of the wake magnitudes abaft the outboard

HYDRODYNAMICS IN SHIP DESIGN

360 bossings,

made

before and after alterations,

are

SNAME, 1949, Figs. 26 and These and other wake diagrams for the Normandie are published by F. Coqueret and P. Romano in SNAME, 1936, Figs. 1-4 on p. 135 and

given by F. H. Todd, 27, p. 234.

9-10 on p. 139. Henschke, W., "Schiffbautechnisehes Handbuch (Shipbuilding and Ship Design Handbook)," 1952, p. 132. Shows wake diagram for twin screws abaft bossings. Figs.

(q)

(r)

Van Manen,

(s)

Kinoshita, M., and Ikada,

No.

8,

J.

D., Int. Shpbldg. Prog., 1955, Vol. 2,

pp. 162-163

1955, Vol. 2, No. 9, Fig.

S.,

Int.

7, p.

237.

Shpbldg. Prog.,

diagram 2 of Fig.

grams.

Three-Dimensional Wake-Survey Diathe wake-velocity vectors are not

If ail

Here, in the 12 o'clock

blade position, the actual inflow-velocity magnitude is U A sec ^(theta) while the effective velocity

with respect to a blade element latter

which

is

increase

considered, in

incident

there or

moving

TABLE All tests were

Model

60.b

made

tested

corresponding to that in

is

the

actually a large

is

and downward moving both for the upward

Taking account

blade.

of the induced

velocities increases these differences.

the

lift

The

fact that

varies as the square of the relative velocity

at which the blade elements

move

still

further

increases the difference.

Typical 3-diml wake-survey diagrams on ship models,

made with

Data Accompanying Wake-Survey Diagrams of

at the

It

effective angle of attack for the

blade and a large decrease in

in the vertical plane,

.

resultant velocity

parallel to each other

nearly constant rate. Non-axial flow then occurs

Ua

motion velocity components. For the special case considered, and for the 12 and 6 o'clock blade positions, the instrument indications are valid. For other blade positions, however, such as those at or near 3 and 9 o'clock in the special

parallel to the direction of

motion but are generally and to one plane which contains the plane of the shaft, there exists what might be called simple non-axial flow. Such a flow might occur at a single-screw position under a wide, flat stern, sloping upward and aft at a

is

measured by a device that records

or indicates only the fore-and-aft or direction-of-

situation

60.6

Sec. 60.6 17. C.

the

TMB

Figs. 60.D

David Taylor Model Basin. The Taylor quotients

13-orifice spherical-

Through 60.H

are based on the ship lengths listed.

SHIP-POWERING DATA

Sec. 60.6

361

ELEVATION OF PORT SIDE LOOKING FORWARD

R' 8.2 Propeller Tip

Circle^-.^^

ft

A-J^i^lZ?--^

IT^S

Values for Circles

Shown

with Broken Lines ore Extrapolated Fig. 60.D

Wake-Survey Diagram for a Twin-Screw Naval Vessel,

head pitot tube, are reproduced in Fig. ll.F of Part 1 and Figs. 60. D througli 60. J of the present section. The diagram of Fig. 60. D is for a wing propeller position on a twin-screw stern of noi'mal form, while those of Figs. 60. E through 60. H are for

single-screw

sterns

with

centerline

skegs,

Diagrams such as those listed in the foregoing, which carry a multitude of survey points, may become cluttered up and confusing if they include the section lines for the portion of .the afterbody or run just forward of the propeller position.

These

section

however,

lines,

wake

features in the

cal data pertaining to these five are listed in Table 60.b. The diagrams of Figs. 60.1 and 60.J, adapted from Figs. 32 and 33 of a paper by H. R. Neifert and J. H. Robinson [SNAME, 1955, pp.

position.

525-526], are for the light and intermediate load

wake-survey diagrams

conditions, respectively, of a

ship Lt. Fig.

model

S.

of the Victory

for comparison,

depicts the

wake

form of a but with two vertical and two horizontal fins ahead of the propeller positions. Fig. 60. of Sec. 60.7 is a wake-survey diagram for the propeller position on the transom-stern ABC ship which is designed and described in Part 4. of revolution

M

show

For a comprehensive analysis they should be available on or with the wake-survey diagram, drawn preferably to the same scale. Appended is a partial list of additional 3-diml of

the

TMB

type,

as

published in the technical literature: (a)

Twin-skeg Manhattan design; wake over propeller disc abaft skeg and for considerable distance beyond;

situation at the tail of a torpedo, in the

body

important

the shape of the ship just ahead of the propeller

James E. Robinson. 60. K,

are

analysis because they

Maritime Administration C4-S-la or Mariner class. Numerirepresenting variations of the U.

U.S.S. Terror

SNAME, (b)

(c)

S.

p.

(d)

1947, Fig. 22, p. 115

Maritime Commission, C-3 cargo vessel, TMB model 3534; SNAME, 1947, Fig. 45, p. 146 U. S. Maritime Commission design for a transatlantic liner, TMB model 3917; SNAME, 1947, Fig. 58, U.

U.

151 S.

Maritime

"closed stern,"

Administration

TMB

Mariner

Model 4358W-1;

design,

SNAME,

HYDRODYNAMICS IN SHIP DESIGN

362

Sec. 60.7

diagram of Fig. ll.E. Since it is most important to an interpretation and analysis of the 3-diml wake-survey diagram that the geodefinition

metric relationships be clearly understood, the definition drawing is repeated here as Fig. 60.L.

The survey diagram is drawn on a sheet representing a transverse plane on the ship or model, passing through the longitudinal center of the propulsion device. For a model running at other than zero trim, and for a screw propeller mounted

on a shaft having both declivity and convergence (or divergence), this plane is very nearly normal to the direction of motion. It is close enough to the plane of the disc, in both position and direction, to serve all engineering purposes.

drawn on projection upon it vectors

The various

this sheet represent

simply the

of the incident velocity vectors

Wake-Survey Diagram for TMB Model 4358W-1, Representing a Variation of the Mariner Class Hull

Fig. 60. E

1953, Fig. 17, p. 176. This diagram

is

the same as in

Fig. 60.E. (e)

(f)

Maritime Administration, Mariner design, "open water" or "clear water" stern, TMB model 4358W-3; SNAME, 1953, Fig. 16, p. 126. This diagram is the same as in Fig. 60. G. Wake-survey data for a model of the T-2 class tankers were published by N. H. Jasper and L. A. Rupp, SNAME, 1952, Fig. 25a, p. 347. Four afterbody sections at and adjacent to the stern are shown on U.

S.

TMB

Model

4358W-2

this diagram.

60.7 Interpretation and Analysis of the TMB Three-Dimensional Wake Diagram. The method of plotting the projections of 3-diml incident-

velocity vectors at propulsion-device positions,

and

of indicating the

of the

wake

and the transverse velocity components, described in Sec. 11.6 and illustrated in the

fractions is

magnitude

Baseline

Fig. 60.F

210 deq

Wake-Survey Diagram for

TMB

Model

4358W-2, Representing a Variation of the Mariner Class Hull

SHIP-POWERING DATA

Sec. 60.7

363

of the water flowing through the disc position.

Using the techniques available as of the date of writing (1955), the propulsion device is not working when the wake measurements are made, so there are no inflow and outflow jets and there is no race contraction. The presence of what might be termed "intersecting" vector projections, of which there are both horizontal and vertical rows in the torpedo wake diagram of Fig. 60. K, means that the flowlines are converging at the base points of the

vectors. fins

The stream tubes meeting abaft

vectors, although there

to

the

obviously can not cross each other, as do the flow

may

irregularities.

be some mixing due

Rows

of

"intersecting"

vectors of this kind are found abaft skeg

and

bossing terminations on ship models, and some-

times abaft shaft struts, sufficiently

if

the measurements are

numerous.

Visual inspection of the wake-fraction numerals,

Fig. 60.H Wake-Survey Diagram for a Model Representing a Variation of the Mariner Class

Hull or

the

sketching

of

contours

of

equal

wake

whether or not these values change in a reasonably uniform manner in all directions across the disc. It is to be expected that the numerical values of the wake fractions will increase progressively toward the adjacent hull, because of the retarded flow due to viscous wake within the boundary layer. Large or sudden changes in a transverse direction across the wakesurvey plane are indications of longitudinal fraction, indicates

discontinuities in the flow; possibly also of partial

separation or incipient eddies.

On

rare

occasions

there

are

indications

of

longitudinal vortexes in a pattern of so-called

"pinwheel" vector projections, appearing to have components about a common center. This center may lie within or without the wakesurvey field. A wake survey for the wall-sided ship of Fig. 25.F of Volume I would show such a rotational

Fig. 60.G

Wakb-Survet Diagram for TMB Model

4358W-3, Representing a Variation op the Mariner Class Hull

HYDRODYNAMICS

364 1.0

OWL

IN SHIP DESIGN

Sec. 60.7

DWL= 28.00

= 28.00 ft

ft

Lenqlh on Woterline,

Desianed

444.0

fl

Droft.for'd.

20.67 ft

Droft.Qft

24.50 ft

Displacement

11,606 1

Speed

^

"^'"^ 240

17.55 kt

for test

Taylor Quotient To

on Lpy^L

,

bosed 0.833

Plane of Surve\j

6.323 ft ford, of

IS

AP

Third numeral Represents of

Tanqentiol

Wahe

06,ll,08~

Moqnitude

Component

of

the

Velocitv

Fig. 60.1

210 1

195

Wake-Survey Diagram for Victory

Ship,

pinwheel provided an adequate number of measurements were made. It would also show a characteristic feature of the presence of a longi-

through the disc position of a screw-propeller. This vortex reveals itself by producing what may be called "opposite" transverse-velocity components, along any one radial line within the disc or at any one blade position. One or more of these components may indicate flow meeting the blade in its normal rotation while others on the same blade may indicate flow which follows the blade. The magnitude of the tangential or rotational incident-velocity components around a circle of radius 72 in a screw-propeller disc, reckoned tudinal-axis

vortex

passing

normal to the blade axis at any blade position, is a rough indication of the amount by which the

[/

ifflo

i65

\l

TMB

Model

at 11,606 Tons Displacement

3801,

meeting or following the flow at that For example, in the diagram of Fig. model 3594, the maximum meeting 60.D, for and following effects for an outward-turning blade

is

position.

TMB

10:30 and at 4:30 o'clock, For the former, at the intermediate

occur at

propeller

respectively. circle

on the diagram, the wake fraction

is

7.2

per cent and the transverse component 15.5 per cent, so that 6

9.5 deg.

The

=

— 7.2) = about meeting the blade. For the

tan"^ 15.5/(100

flow

is

4:30 o'clock position, 6

=

=

tan"' 13.3/(100

about 7.7 deg. The flow

At the circle,

is

-

2.1)

following the blade.

and 7:30 o'clock positions on that meeting and following effects are However, because of the radial com-

1:30

the

negligible.

ponents,

the

element at

1

effective

:30 o'clock

velocity

on that

over

circle,

a

blade

with wake

SHIP-POWERING DATA

Sec. 60.7

DWL=

!.0

28.00

X

\

^.

s

\

=

2Z.40

^

/

^

/

/

/

/

O^^S

\345\

15

/

on Woterlme,

Lentjth

444.0

J)esigned Draft,

\

ft

/

\

\

\

DWL

\

/

/

/

/

s

\

\

/

\

\

\

0.8

365 DWL-28.00ft

ft

13.0

for'd,

ft

ft

20.50

Draft.oft

ft

8,268 t

Displacement

Speed for test

17.92 kt

To^lor Quotient

bosed 0.852

Tt^,

Plane of Survey is

6.3i3 ft

for'd,

of

AP

Third Numerol Represents Moqnitude of the Tonqentiol Component of the

Woke

Velocity

Fig. 60.J

Wake-Survey Diagram for Victory

Ship,

and 14.3 per cent in the vicinity, only about [100 - 0.5(18.2 14.3)] = 83.7 per cent of the ship speed. Here the pitot head automatically takes account of the cosine of the fractions of 18.2

+

is

angularity of flow.

The

effect of the

boundary layer

noticeably on the tip circle at the

where the wake fraction

1

is felt

rather

o'clock posi-

TMB

Model

3801, at 8,268

to take account of them. forces are exerted

Tons Displacement

The

result

is

that periodic

on the blades, which when

transmitted through the propulsion-device bearing usually produce vibration in the ship structure.

The foregoing is what may be termed a qualitaand interpretation of wake-survey

tive inspection

data.

It

lacks a set of specific rules,

not yet

34 per cent.

formulated, to be used by the naval architect or

no model-basin

(1955)

marine engineer to discover flow features which need correction, such as those mentioned previously in this section. In the case of the finer Normandie, these features were revealed only by excessive vibration of the structure, which required withdrawing the vessel from service to

observation methods average them out. Unfor-

rebuild the four bossings. In the case of certain

tunately, the propulsion-device blades do not

large

tion,

Sec.

11.10

points

out

is

that

techniques in current routine use, and no graphic or tabular representations which have so far been

developed, take account of variations in wakevelocity magnitudes If

such

variations

and direction with exist,

the

current

time.

fail

combatant

vessels

of

the

U.

S.

Navy,

HYDRODYNAMICS

366

Vectors

Shown

IN SHIP DESIGN v-20.5 kt

are

Projections of Actual Velocit\(

Sec. 60.7 T„-

Sh ip Side Designed Woterline

0.

5hlp Centerline

Section at Sta.

Rectors on Jronsverse

19.18,

opposite

Propeller

Disc

.330

meter/r\\pione

55.9,18,2^

,,_^ 79.3,6.4| 10.255 '

35.5J8.7

1

ft

tot

I

74.6,4-.6y

7452 ft

Numerals Indicate

Wake

Froctions

Wake-Survey Diagram for a Torpedo WITH Vertical and Horizontal Tail Fins

Fig. 60.K

these features were discovered during the construction period

and corrected by

hull changes

before the vessels were launched.

^

There are a number of methods of quantitative by which magnitudes and variations of

analysis,

wake form.

down

velocity are set

Several

these are

of

wake-velocity

components.

illustrated

in

the

in

Sec.

11.8,

the

analyses take account of either radial or circumferential variations when:

Diagram

of

^

Aciual \"

Velocitvy

"i

9.4

45.3,£

on

(1)

A

series of radii is selected

and the circum-

each radius are averaged, or series of angular positions is selected and

ferential values for (2)

A

Vector on Wake.

Diagror

Slope

of Vector

,Vector and

of Liquid

Numerals on

Woke Diogram

Fore- and- Aft Componenls

, |

-__f

\°t 2nJ Numeral

of Actuol

Velocity

is

Length of

Tronsverse

Component on Percentage

E

Vectors Fig. GO.L

R

Poge

^--Transverse

Veclor

4.4,10.1

60.M Wake-Survht Diagram for TransomStern ABC Ship, TMB Model 4505

L^ertical

Transverse ^°°°**=s==^ Ship Plane

a

4.1

incident-velocity

or

As described

-Plane

-pio.

60.5 for the plots of

references given in Sec.

longitudinal

't

in graphic or tabular

DEriNiTioN Diagram for

TMB 3-Diml Wake-Subvev

Diagrams

Scale

SHIP-POWERING DATA

Sec. 60.7

Plot of Averaoe

',67

Wake

Fraction

w

on Radius

ABC Ship Transom -Stern Desiqn

TMB

4505 EMB Model Propeller 2294 Data Token from Wake Model

JDiQ<^rQm at Propeller

'0

10

30 40 50 60

20

70

80 90

Anc^ular Position, deo, Measured 60.N

Fig.

0.1

Position

100

0.2

03

0.4

0.7

0.8

03

110

120

130 140 150 160

170

180

as 0.6 R/RMqx

O.SO

I?

0.15

i

0.10

a

1.0

Clockwise From Top Center; see Diaqrom

Wake-Analysis Diagram for Transom-Stern Applying to Fig. 60.

ABC

Ship,

M

the radial variations for each position are aver-

development of the future, Brazell

Fig.

60.M

is

a plot of the 3-diml

for the transom-stern

ABC

ship of

at the designed speed. Fig. 60.

N

wake survey Part 4, made is

a graphic

analysis of these data, prepared as a preliminary

step to the design of a wake-adapted propeller for this vessel, described in

fraction

w

Chap.

Values of wake

70.

are plotted in Fig.

60.N

0-diml radii, corresponding to x' 1.00,

0.727,

and

0.453,

for three

= R/Run^

of

on a basis of angular

position around the shaft axis. Averages for the

complete revolution give

R

of 1.00

[SNAME,

1947, pp.

is

given by N.

J.

146-149], but the

present author does not intend that these remarks shall

be construed as an endorsement of

detail steps

all

the

and the calculation methods employed

in that reference.

Finally, the model or ship propeller acts as an averaging or integrating instrument by taking account, degree by degree around a revolution, of the multitudinous variations in

magnitude and

direction of the incident-velocity vectors for the

complete range of radius from hub to

tip.

How-

ever, because of the variations in direction as

well as magnitude, involving changes in effective

w =

0.1923

Rt.

angle of attack, thrust, torque, blade loading, and the

0.727

0.1693

0.453

0.1568

like,

no direct analytic procedure has been wake velocities at a

devised for averaging actual screw-propeller position.

By

finding the speed of advance Vo at

which

A plot of radial variation for wake fractions, when

the

averaged around the entire circumference at each 0-diml radius, is given in the upper right-hand

produces the same torque (or thrust) as when run behind the model or ship, one assumes that the

corner of the figure.

average speed of advance V^ "behind" is the same as the speed Vo in the "open." Then knowing

A

somewhat more comprehensive method of analysis, probably representing more nearly the

same

the speed

propeller,

V

when

of the

tested in open water,

model or

ship,

the

wake

HYDRODYNAMICS

368 fraction

w

is

(F

—

Va)/V. This

quarters as the "analysis"

wake

is

known

fraction.

some That it

in

can be considerably different from the arithmetic mean of the several wake fractions derived from a 3-diml wake-survey diagram, when averaged over a complete revolution of the propeller, is indicated

by the short-dash horizontal

line in the

IN SHIP DESIGN

Sec. 60.S

model self-propulsion tests. Taylor's values are plotted in graphic form in diagram 1 of Fig. 60. 0, together with more recent data from TMB model tests. They suffice for a rough estimate of w for the designed speed at an early stage of a preliminary design, despite the inconsistency of some

both single-screw from S and P, 1943, Table XXV, page 121. Data from selfpropelled tests of the 10 tanker models are from SNAME, 1948, pages 360-379; those for Series 60, the tanker Pennsylvania, and the Schuyler Otis Bland are from SNAME, 1954. J. Lefol in his paper entitled "Les Interactions entre la Carene et le Propulseur (Interactions Between the Hull and the Propeller)" [ATMA, of the values. Taylor's data, for

upper right-hand corner of Fig. 60. N. Here the mean nominal wjake fraction, representing the arithmetic mean of the values of the average wake fraction for the nine 0-diml radii from 0.2 through 1.0, is 0.1735. For comparison, the wake fraction Wt (for thrust identity with the openwater test), for the transom-stern ABC model, when self-propelled at a speed corresponding to 20.5 kt, is 0.190, indicated on Figs. 78. Nb and

and twin-screw

78.Nc.

1947, Vol. 46, pp. 221-251], gives in Part VIII, on pages 235-236, nine formulas for wake fraction, taken from the published literature. Recently, in his discussion of the 1956 SNAME paper by F. H. Todd and P. C. Pien on the TMB Series 60 model tests, A. Q. Aquino proposes for singlescrew vessels a formulation

This single value of the wake fraction, either estimated analytically or derived experimentally, is the value required for the shaft-power predictions of Sees. 60.4

60.8

The

and

Estimating

discussion in

prediction of

wake

60.14.

Ship-Wake

the this

Fraction.

concerning the

section

fractions for ship propulsion,

as well as that in Sec. 60.9 for predicting thrust-

deduction fractions,

is

limited strictly to proce-

dures used in the early stages of a ship design, before any self-propelled model tests are run.

W. the for

J.

first

M. Rankine was among

the

first if

estimating

the

wake

fraction

for

a

not ship

propelled by a single screw. His method, published

book "Shipbuilding: Theoretical and was based on the expanded length of a curved line drawn on the body plan of the ship in question. This curved line began at the center of the propeller and crossed the lines

in his 1866

Practical," page 249,

of successive sections

forward of the propeller at it reached the

right angles to those lines until

maximum-section

line.

The

ratio of the

expanded

length of this curved line to the length of the run

was the approximate wake

Many

fraction desired.

other procedures for predicting the

fraction in advance of

model

tests

wake

have been

devised and used since then, as listed in the partial

bibliography of Sec. 52.20.

dures

is

one of D.

W.

Among

TMB

Wr = (A

constant)

+ -

naval architect to establish a procedure

these proce-

Taylor, published in tabular

form [S and P, 1933, Table XXV, p. 118; 1943, Table XXV, p. 121; PNA, 1939, Vol. II, Table 10 on p. 149]. The data in these tables, as well as the data mentioned subsequently in this section, were taken from special wake measurements on models or from wake-fraction values derived by

ships, are taken

Lxi)'L(6.5

-

5.5CpyA)iS

-

2Cp^)J

k[f(LCB)]

where D is the propeller diameter. A comprehensive summary of existing published data on wake at screw-propeller positions, as well as some not published, has been made by S. A. Harvald ["Wake of Merchant Ships," Danish Tech. Press, Copenhagen, 1950]. This is accompanied by a careful, studied analysis. The paper is replete with graphs and plots but unfortunately it lacks the flow and other diagrams that would have assisted the reader, and that might also have changed some of the author's ideas and conclusions. It is based solely on the

component of the relative and the true-wake velocities, in the form of the customary speed of advance and Taylor wake fraction, and almost exclusively upon wake as affecting one or more stern screw propellers. It is considered most significant that Harvald achieves his only major correlations with practice, and his only really consistent ones, when he uses predictions based on theoretical analyses. In the comparisons with empirical data, employing orthodox form coefficients and parameters, it becomes almost necessary at times to force longitudinal or axial

Sec. 60.8

SHlP-POWERlNG DATA

369

this analysis

somewhat further ["Three-DimenFlow and Potential Wake,"

Potential

sional

Dan. Acad. Tech. Sci., 1954]. Applied Mechanics Reviews, May 1955, page 206, has Trans.

this to say of

it:

"The Rankine bodies generated by various combinations of sources and sinks, situated at isolated points or distributed over lines and surfaces, are computed. The purpose of the work is to compute by this means the velocity field due to the ship's hull in the neighborhood of

the propeller. Since the effect of the ship's boundary layer on the potential flow is neglected, the results should be only roughly applicable for this purpose."

There

is

as yet nothing approaching a formula or

step-by-step

routine

procedure which a naval

architect can use while his ship design

is

progress-

ing.

Despite these intense analytical studies, S. A. in the 1950

Harvald comes to the conclusion,

reference cited earlier in this section, that the

[PNA,

E. Schoenherr

empirical formula of K.

1939, Vol. II, Eq. (110), p. 149]

is,

with slight

known

modifications, the naval architect's best

method

0.05 0.15 QIC OZO Thrust-Oeduction Fraction t

given design,

Graphs fob D. W. Taylor's Predictions OF Wake Fraction and W. J. Luke's Prediction OF Thrust-Deduction Fraction

Fig. 60.O

agreement. At their best, the relationships so established are complicated, confused,

known

hull

fraction for a

shape has been

and the screw-propeller position (s)

delineated

The Schoenherr formula, without

determined.

but with standard symbols, as employed for single-screw vessels of normal or nearly normal design, is modifications

w = of the

when the

wake

and often

conflicting.

The use

of predicting the

boundary most of the

0.10

features of the

layer abaft a flat plate accounts for

and tangential (peripheral) wake variations observed abaft normal forms of single-screw

+

\j

pyiu plJ

1

4.51

(7

-

6Cpv)(2.8

-

l.SCp)

radial

sterns.

The

derivation of the potential-flow

wake

+

1

r^

——

2\_H

fc'

{Rake)

(60. ii)

abaft bodies formed by various combinations of

E

the height of the propeller axis above

sources and sinks in an ideal liquid gives a reason-

where

ably

the baseplane at the disc position, is the propeller diameter,

consistent

picture

of

the

potential-wake

Variations abaft ship forms of varying fullness, proportions, and size. B. V. Korvin-Kroukovsky

Uses this approach in his paper

Calculation

of

Wake

"On

Fraction

the Numerical

and

Thrust

Deduction in a Propeller and Hull Interaction" [Int. Shipbldg. Prog., 1954, Vol. 1, No. 4, pp. 170-178]. However, an understanding of this paper requires a thorough knowledge of sourceand-sink phenomena and stream functions, La-

is

D

{Rake)

is

measured k' is

the rake angle of the propeller blade,

in radians,

and

a coefficient that has values

of:

(1) 0.3 for a normal stern aftfoot cut (2) 0.5 to 0.6 for a stern with

away. This formula,

despite

An example

its

intricacy,

is

non-

of its application, to the

gally's

dimensional.

and ship-shaped forms.

transom-stern single-screw ship designed in Part 4, is worked out presently. K. E. Schoenherr gives a second set of formulas

theorem, friction resistance, and the various kinds of flow around bodies of revolution In a

still

later

paper

S.

A. Harvald carries on

HYDRODYNAMICS

370

[PNA,

1939, Vol. II, Eq. (112), p. 149], for twin-

screw vessels with:

0.190; see Fig. 78.Nb. This

Wo

value of that test,

w =

-

2iC^Yil

Ce) (eO.iii)

-1-0.2cosMy) -

0.02

where jS(beta) is the slope of the bossing termination, measured in degrees (b) Bossings and inward-turning propellers

w =

-

2{Cb)\1

-

0.2 cos' [1(90

+

/?)]

Propeller shafts supported

(c)

,

2(Cb)'(1

0.2

-

For the single-screw

struts

ship of Part

+

0.04

Cs)

ABC

(60.V)

data re-

ship, the

(60.ii)

are,

E D

= = =

L

H

= =

73.08

510 26.163

ft

k'

down

the

Rake Setting

4.51

factors

it is

(based)

loading

we

The comments

w

at

of interest to note,

from

on thrust identity depend on coefficient). The more

(thrust-load

the smaller

ICSTS, 1951 (SNAME,

is

the

wake

1953), p. 143].'

in parentheses are those of the

Prediction of the Thrust-Deduction Fracbeen customary since the 1860's,

60.9 tion.

It has

M. Rankine and W. Froude both

J.

problem [INA, 1865, pp. 13-39], to base predictions of the thrust-deduction frac-

TMB model 4505

tion of screw-propelled vessels

wake

of the

0.6 0.

SchoenheiT equation and

this

fraction

upon the estimate [PNA, 1939, Vol. II, pp.

149-150]. So far as known this procedure has been limited generally to single-screw vessels. In any case, it gave little or no credit to efforts, put forward by D. W. Taylor and others, to decrease the thrust deduction by thinning the

ship sections or "straightening" the surfaces of 1

-

6Cpy){2.8

-

l.SCp)

the hull and

its

appendages ahead of the propeller

area is acted upon by —Ap's ahead of the disc. These efforts were based upon the hope that the thrust-deduction disc, so that less transverse

the

+

the

4.5[2:^??(|f)^3^]

+

-

6(0.822)] [2.8

W.

-

fraction, so as to hold the hull efficiency

J.

Luke was among the

earliest to give

1.8(0.621)]

empirical values of the thrust-deduction fraction

"1

that were of practical use to the ship designer.

r 10.5

_ 20^ _

2 [26.163

73.08

1

would be reduced at a greater rate than

wake

to as high a value as possible.

1

[7

=

fraction

present author.

fraction

0.10

find [6th

worked on

+ =

the self-propulsion

wake

propeller used on

= =

7(7

factor

when W.

CpvCpB\

L

The

the statements of L. Troost, that:

10.5 ft

0.10

+

derived from

the designed speed of only about 0.072.

20.51 ft for the stock

substituting:

w =

4,

curves of Fig. 78.1 indicate a

propeller

from the SNAME RD sheet of Figs. 78.Ja and 78.Jb and the drawings of Chaps. 66 and 67:

Bx

,

0.200.

is

ABC

of the

"Wake

by

quired for the Schoenherr formula

Cpv = 0.822 Cp = 0.621

Wt

For vessels with tunnel sterns, there are little or no published data on the wake fractions to be expected [Harvald, S. A., "Wake of Merchant Ships," 1950, p. 117]. For the arch-stern design

heavily loaded the propeller,

w =

is

derived from torque identity with

In this connection Cs) (60. iv)

+

Sec. 60.9

thrust identity with the open-water test.

Bossings and outward-turning propellers

(a)

IN SHIP DESIGN

^'^^^^j

0.255

This value of 0.255 for the 20.51-ft stock propeller compares with the value of about 0.24

from Fig. 60.O, where Cb is taken, from the fifth approximation in Table 66. e, as 0.593. As a matter of interest, the wake fraction determined from the model self-propulsion test with this propeller, at a speed corresponding to 20.5 kt, is

D. W. Taylor and others quoted these values [S and P, 1933, p. 117; S and P, 1943, p. 120; PNA, 1939, Vol. II, Table 9, p. 148; RPSS, 1948, pp. 177-178]; they are plotted in diagram 2 of Fig. 60.O, together with more recent data from TMB model tests. They, hke the wake-fraction graphs in diagram 1 of that figui'e, suffice for rough estimates in the preliminary-design stage of a ship of normal form. C. H. Peabody, in his 1910 tests of the large.

SHIP-POWERING DATA

Sec. 60.9

powered

independently

model

Froude,

S71

ABC

For the transom-stern, single-screw

wisely

ship

wake and posed somewhat of a

included runs in which the single propeller was

designed in Part

placed farther and farther abaft the sternpost,

thrust-deduction fractions

normal position to about 1.15D astern. Because of missing information it is not possible to analyze Peabody's test data in the

problem, because of the unorthodox stern shape and the lack of empirical data upon which to base

varying from

its

manner presently his

Table

I

to be described. Nevertheless,

[SNAME,

1911, p. 95] indicates that at

reached

the highest speed

thrust- deduction fraction

/

by

this

craft,

the

diminished from 0.35

to 0.077 for the range of propeller positions given.

In a paper "Vom Sog (Thrust Deduction)," H. M. Weitbrecht discussed the physical aspects of thrust deduction but pointed out that it was not then possible to predict the numerical value of the thrust deduction for a given ship form and loading

propeller

[Schiffbau,

Schiffahrt,

Hafenbau, Jun 1938; English version in

und

TMB

Transl. 62 of Sep 1940].

K. E. Schoenherr and A. Q. Aquino, in the period 1930-1940,

made a

careful review of the

existing literature on the ship-propeller interaction

undertook their own analysis, and supplemented it with plotted observations from the results of self-propelled tests on a great many models. Their work is described fully in Report 470, published in March 1940. The problem,

TMB

efficiency r]„ of 1.143

[PNA,

in 1939

Vol. II, pp. 149-150], were developed from

this project: (1)

For the thrust-deduction fraction

of single-

a stock propeller was selected to selfpropel the model, by the procedure described in Sec. 70.6, the wake fraction derived by Eq. (60.ii)

t

=

The thrust-deduction Eq. (60. vi). The value

= kw

= (2)

posed for the supporting horn and the underhung balance portion of the rudder. It seemed reasonable, further, to reduce the calculated value

by

15 per cent, because of the very thin skeg to be

placed ahead of the propeller.

The

predicted

thrust-deduction fraction then worked out as

=

kiw)il

It

was

-

=

0.15)

=

0.5(0.261)(0.85)

0.111

realized at the time that a thin skeg

ahead of a single propeller was Hable also to reduce the wake fraction. For a conservative estimate, without the 15 per cent reduction in i,

(60 .vi)

t

1

0.5 to 0.7 for vessels with streamlined It is

1

-

1

brought out in

rjn

0.131

was

=

1.176

0.261 (2)

and (3) of Sec. 78.17 and wake fractions

0.7 to 0.9 for vessels with double-plate

that the

rudders with internal arms, attached

derived from the model self-propulsion tests are

to square rudder posts

appreciably different from those derived in these

0.9 to 1.05 for vessels with single-plate

two

rudders and external arms

B. V. Korvin-Kroukovsky gives the following equation from H. E. Dickmann for the estimated

For the thrust-deduction fraction of twin-

Ships with propellers and shafts carried

sections.

t

=

by bossings t

(b) Ships

=

by t

=

(w.) I

0.25W

+

0.14

(60.vii)

with propellers and exposed shafts

carried

thrust-deduction

value of the thrust-deduction fraction:

screw ships, specifically: (a)

was derived from was taken

fraction

of k for the latter

as 0.5, because of the contra-rudder shape pro-

or contra-rudders

=

was 0.261, using dimensions and parameters

corresponding to an early stage of the design.

the predicted hull efficiency

screw ships:

where k

seemed reasonable.

When

t

by K. E. Schoenherr

the estimate of the

predictions. With little information for guidance, with a screw propeller of diameter larger than normal, and with a tip clearance smaller than normal, it was guessed in Sec. 66.27 that the wake fraction w would be as high as 0.30 and the thrust deduction as low as 0.20. The corresponding hull

following rules for estimating the thrust-deduction fraction, published

4,

+ Vi +

(60.viii)

{w,)7,i

c,

where w^ is the nominal potential-wake fraction and rji is the ideal efficiency of the propeller. The problem here is to find the value of Wp for which there is no simple solution. ,

struts

O.lOw

+

0.06.

An

entirely

different

prediction

procedure,

HYDRODYNAMICS

372

devised to take direct account of the factors which develop the thrust-deduction force, is based upon

IN SHIP DESIGN The

circles.

jet

Sec. 60.9

area

rather

increases

slowly

are so small at

immediately ahead of the propeller, even for the large thrust-load factors expected in the freerunning operation of a normal ship with a not-tolarge propeller, as indicated in diagram 1 of Fig. 59. G. The values of — Ap are relatively so small, farther forward of the propeller, that the refinement of increasing the disc areas seems not justified by the approximate nature of the overall method. Moreover, the presence of the ship and its appendages, either ahead of or abaft the

2 diameters ahead of the disc position that they

screw-propeller position, distorts the jets out of

can be neglected.

their

the rate of variation of — Ap with fore-and-aft distance ahead of the propeller, and that of -|-Ap abaft it. The assumption is made that these pressures vary with distance in very nearly the for a screw propeller working in open water or an airscrew working in open air, indicated by diagram 3 in Fig. 59.G. It is further assumed that, following D. W. Taylor's patent

same manner as

— Ap's

previously referenced, the

The method

based upon a summation of

is

longitudinal forces exerted

upon

certain selected

transverse sections of the ship, lying within an imaginary cylinder concentric with the propeller

normal axisymmetric shape. Little is known what happens when they are so distorted, of the amount of hull surface covered by the water in them, and the differential pressures in that of

water.

The

"cylinder" procedure assumes

This cyhnder has the propeller diameter D, and extends both forward and aft from the disc

that the rudder always develops a thrust-deduc-

position.

tion force in the

axis.

A

similar imaginary cylinder in this position

foregoing

form

of a drag, acting opposite

to the direction of motion,

and that

it

always

was shown by G. Kempf many years ago [STG, 1927, Vol. 28, p. 180]; also by E. F. Hewins as a method of determining the wake fraction w [Osbourne, A., "Modern Marine Engineer's Man-

contributes to the thrust deduction. However, in

ual," 1943, Vol. II, p. 2311],

on the rudder produces a forward component of lift which exceeds the drag. The rudder then exerts a thrust force on the ship, and helps to push it along. Theoretically, the net thrust force Tr exerted by the helping rudder, mentioned in Sec. 34.8 of Volume I, should be subtracted from the thrust-deduction force exerted on the hull or appendage ahead. This can only be done when the amount of this thrust force is better known. In practice, the "cylinder" procedure involves

For the analysis described here, the transverse and 0.5Z) ahead of the disc position. A fourth section is taken through the maximum-area section of whatever rudder, rudder post, or horn combination lies abaft it. Any other transverse-section positions could be used if desired, and they could extend for more sections are at 2.0Z), l.OD,

than

2D ahead

of the disc position.

assumed that the — Ap values at the three positions ahead have the relative multipliers or weights of 5, 2, and 1, respectively, indicated by the tabulation at the bottom of Fig. 67.V. It

is

The rudder

of 7 because it is

disc

given a multiplier or weight usually closer than 0.5Z) to the

section

is

and the 4-Ap's

in the outflow jet are greater

— Ap's

in the inflow jet for

a screw propeller producing thrust. These multipliers are based upon the relative ordinate

— Ap

transverse

sections

somewhat

arbitrary,

and -|-Ap curves at the

selected.

They

are

and could be varied

still

outflow

I.

On

same applies

is

to

known

that the hydrofoil action

the afterbody lines plan of the ship lay

of the propeller-disc position.

and

A

off

2.0Z) forward

fourth station

is

through the maximum-thickness position of the rudder. Using the coordinates of these special stations, draw the corresponding sections

on the body plan, as

Volume

disc

circles

by amounts

cor-

considered not justified. contraction

of

The

the after disc

in Fig. 33.

V

A

Part

of Part 2 in

a rudder horn is thicker than the rudder, or if any other appendage lies anywhere in the propeller outflow I or in Fig. 67.

draw a

maximum

responding to the enlargement of area of the propeller inflow jet at the three selected forward positions

jet, it is

special stations at O.SZ), l.OZ),

jet,

disc

of

the following steps:

for a

re-analysis.

Expanding the

some forms

streamlined rudder, each lying in a propeller

laid off

numerically than the

magnitudes of the

the case of a contra-rudder, and

of

4. If

section (or sections) representing the

transverse thickness of the horn or

appendage. II.

Draw on

the

body

plan, over the section lines

of the special stations, three circles, each repre-

senting the propeller-disc outline

if

moved

sue-

SHIP-POWERING DATA

Sec. 60.9

cessively 0.5,

1.0,

sum

and 2.0 propeller diameters

along the shaft, forward of the propeller position.

Draw

ship, to obtain a weighted-average area reading.

Divide the weighted area reading by the propeller-

other circles for stations abaft the shaft,

necessary. If the shaft center

if

only one

circle is

disc area reading to obtain the 0-diml area ratio.

nearly or exactly

and the baseplane,

to the centerplane

parallel

is

VI. With this area ratio enter Fig. 60. P and pick off the estimated thrust-deduction fraction for

needed on a body plan showing

the hull.

The two graphs

the ship. III.

Mark

carefully the outlines of the special

These outlines

may

may

be indicated by

The procedure

IV. With a planimeter, or by any other suitable

means, determine the area of the propeller disc covered by the section of the hull and of the rudder (or horn or other appendage) at each of the special stations. In the same manner, determine the area of the propeller disc. this

As only the

—

ratios

analysis the planimeter

of the thrust-deduction fraction in

into absolute area units.

case

V. Multiply the area readings by suitable multiples, as indicated in the tabular portion of Fig. 67.V. Total the products

0.30

is

still

uncertain.

empirical,

largely

The problem

attacked along analytic

and divide by the

been years ago. It

is

is

any given ship and as highly

now

lines, as it

hoped that

(1955)

being

should have

this attack will

Line for Area \"~ Factor ExcludincjV

Line for Area Factor Includino

0.28

Rudder Area \

^ Iwilfred

0.26

0.24

Sijkes^>#

RudderX'

T-5 Victorvj

^0.22

J

—

All the foregoing indicates that determination

readings can be used directly, without converting

f0.20

and

keep the augment of resistance small, is essentially the same as for a screw propeller. Instead of the imaginary cylinder of circular section an imaginary rectangular tube is projected forward of or abaft the basket assembly of blades, for a distance equal to twice the blade length or to the diameter of the bladeaxis circle, whichever is the greater. for designing the hull to

ing, as in Fig. 33. A.

them

for estimating the thrust-deduc-

tion fraction for a rotating-blade propeller,

be marked by different types of hatch-

of areas enter in

still

on the analysis of data from a rather limited number of model tests.

colored lines on the working plan, or the respective

areas

for this figure are

tentative, based as they are

stations lying within their respective projected disc circles.

373

ABC

of the multiples, 15 in the case of the

Ship

Tanker

:v

ABC Ship, Arch Stern

Baker's 56C,

K

0.18

EMB

Victorjj.^^

Ship

Fsef^

AF58^

T-5 • Tanker

Mod&]J§2Z>

Moriner-

:o.i6 ;0.I4

I

TMB

iralamancQ Class J Model 3917, TwjjV Skpqs

UJ

i

.^

j^950 Export Ships,

0.12

0.10

+iTwin-Ske(^

I'O.Oe

DE 1006 1-0.06

0.04

^

Manhattan,

^ABC Ship ^ronsom Stern I

T

TMB

Model 3898

o Area Foctor Includes Rudder • Area Foctor Excludes Rudder Plotted Values of tare from Seif-Propelled Model Tests

0.02

^ 0.02 0.04 Q06 006 0.10 QI2 014 QI6 018 Q20 0.22 024 026 028 0.50 Q52 034 056 058 040 042 044 Q46 0.48 Area Factor -(Averocje Weighted Hull Area Within Disc Cvjlinder)-^ (Propeller Disc Areo) Fig. 60.P

Graphs for Predicting Thrust-Deduction Fraction for Single-Screw Ships by the "Cylinder"

Method

HYDRODYNAMICS

374

continue unceasingly until a logical and reliable prediction procedure

Sec. 60.10

1953, Vol. 95, pp. 446, par. 8(4)].

available.

Finding the Relative Rotative Efficiency.

However, the calculations involved are laborious,

physical and analytical basis for relative

at least with desk-type computers, and the values

60.10

The

is

IN SHIP DESIGN

agree reasonably well with the experimental data" [INA,

rotative or thrust-torque efficiency, as applied to

derived are generally in line with the empirical

a screw propeller working behind a model or ship, is described in Sec. 34.7 of Volume I. Further

values previously used.

comments on

this factor are

embodied

in Sec.

34.16. It

necessary to estimate or predict the prob-

is

able value of the relative rotative efficiency

when

the expression [rio{vH)vR] the propulsive coefficient r/p

is .

riji

used to estimate This prediction,

is much more easily mentioned than made. K. E. Schoenherr gives a few comments concerning this factor. In the absence of any more authoritative information these reliable and comments have acquired the nature of a pre-

however,

diction rule.

He

states that:

Vol. II, p. 150].

recentb^ L. C. Burrill and C. S.

Yang

have calculated the overall thrust and torque, including the K^ and Kq values, for a group of screw propellers operating in certain assumed wake distributions over the propeller disc, corresponding

conditions behind several

the

to

ships

[INA,

Vol.

1953,

the

calculating

95,

pp.

same quantities

hypothetical 437-460]. for

By

the same

propellers working in a uniform flow, simulating

open-water

tests,

they are able to predict the

thrust-torque factors ToD/Qo and TD/Q for the "open-water" and the "behind-ship" conditions, respectively.

Volume

I,

From

T„D

is

then

Q

Ten tanker models;

SNAME,

1948, Fig. 32,

(b)

TIMB

Series 60 parent

models and related

models; SNAME, 1954, Figs. 12(a) and 12(b) on pp. 141-142. The values of rjR range from 1.04

an average

to 1.01, with

of about 1.02.

Todd, F. H., and Pien, P. C, "Series 60— The Effect upon Resistance and Power of Varia(c)

tion in

LCB

through 22 (as all

SNAME,

Position," list

1956. Tables 18

the relative rotative efficiency

e„ in that text) for a wide range of speeds on the models tested.

For the reader who wishes to undertake some own, the value of the relative rotative efficiency tjb is derived from the selfpropelled test of a ship model by the following procedure. The case used as an example is that from the self-propelled test of TMB model 4505-1, of this analysis on his

representing the arch-stern design of the

ABC

ship undertaken in Chap. 67:

and Yang

The

basic data are:

The

propeller diameter D, in this case

ft

The wake

fraction

w,

indicated

manner described

in the

paper

The numerical

[pp.

440-441

values obtained

on

Fig. 78.1 as 0.072 for 20.5 kt

The thrust-deduction

fraction

/,

taken

from the same figure as 0.175

The rate of propeller rotation n, of rpm or 1.502 rps (e) The propulsive coefficient vp of 0.686 (f) The hull efficiency j;„is (1 - /)/(l - if)

(d)

the quantity designated relative-rotative-efiiciency has a real meaning, in terms of the method of analysis usually adopted, and its value can be estimated by calcu.

of the reference cited].

(1)

(c)

result of their analysis Burrill

lation, in the

the pro-

416

(b)

conclude that: .

(a)

24.22

the ship as in open water.

".

make

efficient in

in the following reports of self-propelled models:

(a)

D is the propeller diameter, the same behind

As a

more

pushing the ship than when it is just pulling itself along in open water. Additional information concerning the values of 7?B to be expected on single-screw ships is found peller

the discussion of Sec. 34.7 in

the relative rotative efficiency

TD where

,

ditions are such, therefore, as to

p.

"The average values of the relative rotative efficiencies determined in the tests worked out to be 1.02 for the singlescrew models and 0.985 for the twin-screw models. "It should be emphasized that the foregoing formulas are valid only for merchant ships of normal form operating at speed-length (T,) values below unity" [PNA, 1939,

More

If a condition is assumed in which the torque behind the ship is the same as Qo then a value of 77fi greater than unity indicates that the thrust T exerted by the propeller behind the ship is greater than To in open water. The service con-

Q

90.1

or (1

-

0.175)7(1

-

0.072)

=

0.889.

SHIP-POWERING DATA

Sec. 60.11

The

illustrative calculation is

signed speed only; this

The speed

(2)

V

times

—

(1

cited, this is

(0.928)

=

for the de-

20.5 kt or 34.62 ft per sec.

advance V a is the ship speed w). In numbers, for the example

V^ = ft

-

34.62(1

per sec.

32.127

nD

0.072)

=

34.62

Then

=

1.502(24.22)

TMB

model propeller 1986 used on the test in question, as shown in Fig. 78. H, the value of the real or working efficiency rjo for a J-value of 0.883 is 0.750; this value is indicated by a note and an arrow on Fig. 78.H. From the general expression Vp

=

Voivif)'nR

the relative rotative efficiency

,

the data

all

available to him.

The

was

situation

Bamaby

by K. C. ["The Coefficient of

well described

in the early 1940's

Propulsive Efficiency," INA, 1943, pp. 118-141] and it has not improved materially up to the

time of writing (1955), despite publication of the data to be mentioned presently. In tables published with his 1943 paper,

0.883

Consulting the characteristic curves for

(3)

375

did not trouble to analyze fully

of

32.127

J =

is

made

is

Barnaby gave many values

of

for a

t/p

number

of

types of ships, based primarily on a variation of ?jp with VI or Taylor quotient different

VL

r„

However,

.

in his later

book "Basic Naval

Architecture" [1948, Art. 187, pp. 242-244], he presents these values on a basis of absolute ship

but subdivided for single-screw, twin-

length,

and quadruple-screw propulsion. W. P. A. van Lammeren, L. Troost, and J. G. Koning present values of propulsive coefficient

screw,

0.686 Voivn)

=

1.029.

0.75(0.889)

For the single-screw transom-stern

ABC

ship

the self-propulsion model tests with a stock propeller,

reported in Figs. 78.Na, 78.Nb, and 78.Nc,

gave a propulsive coefficient rjp of 0.761 at the designed speed. For the advance ratio J at which the propeller operated in this test, the value of »7o

from the characteristic curves

was

0.685.

The

hull efficiency rin

thrust

delivered

1.148.

By

by the model

of Fig. ,

78.Mc

based on the

propeller,

was

the relationship between these four

latter presumably all based upon the rate of propeller rotation n [RPSS, 1948, pp. 284-288]. D. W. Taylor gives only general information on

0.761

=

This value is well below the one that would have been predicted by Schoenherr. Since it is less than 1.00, it works to the ship's disadvantage. There is no present explanation for it. 60.11' Determination of the Propulsive Coefficient. A great deal of guessing was involved

and that of little help to the designer ship [S and P, 1943, p. 178]. Since the efficiency of propulsion depends upon

this subject

modern

of a

a combination of the open-water or working propeller efficiency 770 the hull efficiency t//, ,

made

,

relative rotative efficiency

?;«

,

it

should

(a)

Type

rip

in

of

propulsion

whether open

device,

screw propeller, shrouded screw propeller, paddlewheel, rotating-blade propeller, or their equivalents (b)

Relative

device,

the days before model basins

(the

vessels),

respond to variations in those efficiencies with the factors which control them. Among these may be mentioned:

0.968

(0.685)(1.148)

in the estimates of propulsive coefficient

coasters

for

single-screw

and the

sets of 77-values,

„„(„„)

for single-screw ships, for twin-screw ships,

r\p

and

position

ship

of

and propulsion

involving tip and aperture clearances,

shape of hull near the propulsion devices, and

tests of self-

propelled models. Since that time, naval archi-

and marine engineers have rehed heavily upon the results of individual model tests to supply them with needed information as to the shaft power to be installed in the ship built from

other similar factors (c)

tects

a particular design. The result is a dearth of systematic data by which to predict the correct

any given case. One might say that in the days when one had to make this estimate in order to power a ship there was insufficient background information to do it. When the designer no longer had to make it he

Thrust-load factor Ctl which limits the efficiency 57/ and the 0.8-value of that ,

ideal

efficiency, illustrated in Fig. 34. (d)

Wake and

thrust-deduction fractions,

and

the combination of the two (e)

Characteristics of the flow at the propulsion-

device

position (s),

determining

the

relative

propulsive coefficient for

rotative efficiency.

Consideration of

(a)

leads to the conclusion

that entirely separate sets of prediction data are required

for

each

type

of

propulsion

device.

376

34.M and

Figs.

values of

34.

N

give

HYDRODYNAMICS

IN SHIP DESIGN

some not-too-recent 59.A and 59.

vessel because of the characteristically different

for several types; Figs.

tjo

A

(3)

variation

present more recent data on a few different types,

hull shape,

In both series of diagrams the propeller efficiencies are based upon the thrust-load factor Ctl For a given ship resistance to be overcome, or

position,

a given propeller thrust to be produced, with constant wake and thrust-deduction fractions, the

Ctl increases and the

factor

thrust-load

device.

Sec. 60.11

to be expected with type of

is

A

and propulsion-device

relative hull

and nature

of flow at the propulsion

free-running, single-screw tug with a

chubby

hull and a propeller abaft it would be expected to have a different rjp than a long, short,

slender,

with

its

high-speed, propeller

single-screw

more or

less

patrol

under the

vessel hull,

actual propeller efficiency ijReM diminishes with

(4)

decreasing diameter, while the rate of rotation n

propulsion devices and within a single type of

increases. This is because the thrust-load factor

device,

=

T/{Q.5pA^Vl) increases as Ao diminishes, the real or working efficiency tjo decreases as Since Ctl increases, and t/p decreases with tjo the advance coefficient J usually decreases as 78. H, and since r/o decreases, indicated by Fig.

Ctl

.

n = y^/(Ji)), a reduction in the thrust-producing area causes both J and D to diminish, and an appreciable increase

results in

in the rate of

Within a single category as to number of

The reasons

of a screw propeller.

^o

For a good hydrodynamic design of both and screw propeller, based upon data such

(5)

ship

as set forth in this book, the following values of

propulsive coefficient

rip

ate falling

off of

propulsive efficiency with increase

the basis of a clean,

new

much

complex, so

is

exceedingly

no general or

so that

detail

rules have been formulated to predict their effect upon propulsive efficiency. Characteristics of the

propulsion-device

the

at

flow

positions

related to the relative positions of the device

Not enough

the hull.

both

physically

reliable

and

and

is

known

and

of these effects,

analytically,

values of

precise

are

-qp

to

predict

the pre-

in

for this are

explained in a preceding paragraph,

foregoing accounts for the moder-

fractions, singly or in combination,

should be achieved, on hull, at the

Single-screw

(i)

vessels

of

the

merchant and

generally similar types, with speed-length quotients or fatness ratios in or near the design lane

66.A 0.82 to 0.72 Twin-screw vessels of modern (1955) merchant and similar types, having fatness ratios as of Fig. (ii)

in

(i)

preceding

0.73 to 0.65

Triple-screw vessels; no adequate systematic

(iii)

data for vessels having three propellers nearly having larger center wheels

alike, or for vessels

absorbing more power than each of the wing

wheels (iv)

upon the reasoning in the foregoing, upon data derived from the trials of many ships, and upon experience, a few prediction guides are set down:

type

uJu 11 ii (1) For ships driven by screw propellers, the number and consequently the position(s) of the wheels carried by each puts them in different

stern vessels for operation in shallow

r-,\

„

-r^

•„„

ic i categories so far as propulsive coefficients are ,

concerned,

f

1

indicated

Lammeren and by K. latest

publication.

•

both by C.

This

•

W.

Barnaby is

P.

A.

van

in the latter's

elaborated upon in

(5) following.

For equally good hydrodynamic designs there no reason why the propulsive coefficient rip should vary with absolute ship or propeller sizes, (2)

provided the

sizes are

Quadruple-screw

adequate to avoid scale

effect

vessels

of

the

liner

0.65 to 0.60

(v) Single-screw

tunnel

arch-stern

or

vessels

0.68 to 0.55

Double,

(vi)

,

. ,

triple,

,

f'}^''^^'^'^ ^°'' i^"^ nshmg *

^^*;

and quadruple-screw tunneland re^ ^^^. ^ ..

\\i

'^"^^^

..-

propelled

^-^^ to 0.45

'^'^. ^' ^^^^ ^"^ by single screws

iff ^f^^

craft,

j

n79t .', about

averaging

nrc '

0.65.

For speeds other than the designed value, the may vary rather widely [Barnaby, K. C, INA, 1943, pp. 118-141]. Below the designed speed, the value of rip is usually greater than at the designed speed; at higher speeds, it is usually less. For the transompropulsive coefficient

is

designed

speed:

liminary- or contract-design stage. Nevertheless, based

a dimin-

area of the device, corresponding to the disc area

The

rpm, revealed by W. P. A. van Lammeren, L. Troost, and J. G. Koning [RPSS, 1948, Figs, 193 and 194, pp. 285-286]. The effect of the wake and thrust-deduction

j?^

with a decrease in the thrust-producing

ishes

rotation n.

of

T and

assuming a constant thrust

constant wake fraction w, the value of

model

stern

POWERING DATA

SHIP

Sec. 60.12

ABC

of the

Fig. 78. Nc indicates a

ship, as self-propelled,

maximum

r}p

of

about 0.78

at 15 kt for the ship, a value of 0.76 at the de-

377

peller position(s) with respect to the hull and appendages, a model propeller drawing, a set of characteristic open-water test curves of the

signed speed of 20.5 kt, and a diminished value

propeller (s),

of only 0.70 at about 22.4 kt, assuming that there

as well for each propeller position. This

is

enough reserve

of

power to drive the ship that

The

designer

is

pulsive coefficient

means mated

again reminded that the prois

to be regarded solely as a

of predicting a shaft

power from an

esti-

or known effective power. It is not to be taken as a measure of merit in itself. A high value of yjp may be associated not only with a

high value of effective power high shaft power

A may

Ps

Pe

Thus a model

—

the past, there are available in the technical of graphs

which

give model test data in the form used for

many

years by the Experimental Model Basin and the

David Taylor Model Basin [Bu C and

R

Bull. 7,

1933, Fig. 8, p. 31]. Several of these graphs are

reproduced as Figs. 60.Q through 60.T, of which Fig. 60. Q gives data for a U. S. Maritime Commission C-2 design, and Fig. 60.R for a Great Lakes bulk ore carrier, the Philip R. Clarke. Others are listed hereunder, with the type or

name

of ship, or both, and with enough source information to locate them in the Uterature. In many cases, including the figures hsted, the

graphs are not accompanied by the necessary information to understand, to analyze, or to use of them

fully.

tion should include a

the adjacent part of

I. (a)

Pro-

sheets,

Single-Screw Vessels High-speed cruisers of the U.

Ammonoosuc

S. S.

Wampanoag and

classes of 1867. Self-propulsion data

EMB model 2569, with EMB model propeller 685, were published by James Swan

of

.

number

SNAME

Data and Self-Propulsion Data

derived from tests of

test

,

—

one of

samples of which are reproduced in Figs. 78. Ma through 78. Nc.

V

predict for speed

literature a considerable

peller

but also with a

an effective power Pe of 7,200 horses, a shaft power Pg of 9,000 horses, and an vp = Pe/Ps of 0.80. For the same speed V, a test of design B, to meet exactly the same performance specifications, may predict an effective power Pe of 8,100 horses, a shaft power Ps of 10,000 horses, but an 7]p of 0.81. Thus, a ship built to design B, having a greater tj^ would actually require a heavier and more expensive propelling plant, and more fuel to drive it, than a ship built to design A, with a lower r)p This is the reason for stressing the use of a merit factor and an estimating or predicting factor as well which takes account of shaft power directly. 60.12 Data from Self -Propulsion Tests of Model Ships and Propellers. For the designer who is laying out a vessel not unlike many which have been run self-propelled in model scale in design

is

the reasons for the rather comprehensive and elaborate form adopted for the

fast.

make

and perhaps a wake-survey diagram

This pertinent informa-

body plan and enough of the ship to show the pro-

[SNAME, 1927, PL .36]. This plate gives the principal dimensions only. The text of the paper is on pp. 43-54. (b)

ship, U. S. Mar. Comm. Cl-S-Dl design, with a reinforced-concrete hull of straight-element form. 350 ft by 54 ft by 26.25-ft draft; displacement 10,590 tons. Body plan shown in Fig. 76.C. Represented by model 3754M. Prediction data

Cargo

TMB

from self-propulsion

test 2, in ballast condition, at

displacement of 6,200 tons and a trim of 6 the stern, are given in Fig. 60.S.

ft

a

by

378

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 60.12

SHIP-POWERING DATA

Sec. 60.12

TMB

Model 5594 Model Propellers 1975,1976

SNAME RD

5heet 98 SPTest: W= 6,700t 5=28,510 ft^

(j)

TMB

Conditions for This

H- 17,5 ft Trim, Zero

of

6Jun

Test 3,

U.

(k)

The

1947.

general characteristics of the

on

1

p.

109 of

Maritime Administration 622-ft 23-kt design, model 4424, ETT model 1448-1, for which

S.

TMB

Outward

1940, ot

SNAME,

prototype vessel are found in Table the reference.

Rudder Horn, Shafts, Struts D= IZ.67 ft; P- 13.92 ft;Z = 3 Cm/D = 0.252-, to/D = 0.043 Propellers Turnino

379

with normal form of stern. Self-propulsion curves are given by Fig. 15 on p. 110 of SNAME, 1947; general characteristics are in Table 1 on p. 109. Twin-skeg tanker of extreme beam, adapted from (i) preceding. model 3821, for which complete self-propulsion curves are given in Fig. 16 on p. 110

Twin-Screw Mine-Lavjer

complete self-propulsion data arc given in SNAME, 1955, Fig. 4, p. 730. The body plan and characteristics of this vessel are given on pp. 728-729 of the

EMB

reference.

Quadruple-Screw Vessels

III. (a)

Large Atlantic Lafayette);

SPD

liner S. S.

Normandie

SNAME RD

sheets, not yet

(later

sheet 39; also

numbered

U.

S. S.

PD

and

(1955).

The technique results

of predicting, from the test on model ships and propellers, the shaft

power,

the rate of rotation of the propulsive

device (s), and other factors in the full-scale ship

performance has not yet (1955) been perfected that

so

12

II

13

14

15

16

18

17

Ship Speed,

21

22 23

and

S. S. Terror (CM5); EMB model 3594 EMB model propellers 1975 and 1976. SNAME

RD

sheet 98. Fig. 60.T reproduces the self-propul-

Minelayer U.

Medium-size Atlantic

liner

Jun 1940.

America;

SNAME,

1940,

pp. 278-286; the self-propulsion data curves were published on p. 286. The tests were run on

EMB

Medium-size Atlantic

SNAME RD

SPD

sheets not yet

and

(g) Atlantic liner

and

are given for ten different ships [6th

(1)

The model-ship comparisons

and measured shaft power Ps

of

Table

60.

The model

pro-

pulsion tests were run at the ship point of self-

propulsion with

appendages

all

fitted; in

other

model propellers 1803 and

was compensated for by helping the model along. The ship-trial data were corrected to zero relative wind. Where thrustmeters were fitted the comparisons show close agreement on thrust in some

Constitution

sheet 158;

numbered

and Inde-

SNAME PD

(1955).

Manhattan, with normal V-type stern model 3041. by

EMB

bossings, as represented

instances. Uncorrected open-water propeller data

complete set of self-propulsion curves is given in on p. 114 of SNAME, 1947. Table 3 on p. 113 gives complete general characteristics of this

were used throughout. (2)

Fig. 20

is

A

detailed analysis of the values tabulated

not available. It

is

hoped that such an analysis

shed further light on the scale-effect problem. However, certain trends may readily be noted: will

vessel,

TMB

Twin-skeg Manhattan design, model 3898. A complete set of self-propulsion curves is given in Fig. 21 on p. 114 of SNAME, 1947. Table 3 on p. 113 gives complete general characteristics for the hypothetical vessel represented

(i)

ICSTS, 1951,

Table IV, pp. 146-147]. The comments which follow are adapted from those of Couch, as published on page 145 of the reference cited:

A

(h)

eliminated.

words, the theoretical added friction on the model

liners

pendence.

reliably

EMB

1804. (f)

are

are in general based on the identity of predicted

pp. 9-49, esp. Fig. 2 on p. 11. The first portion of this paper was abstracted in SBMEB, Aug 1940,

model 3525 with

effects

the ratios of model prediction to ship performance

Self-Peopelled Model Test Curves FOB A Twin-Screw Naval Vessel

sion data of Test 3, dated 6 (e)

20

\\t

D.T

Fia.

(d)

19

scale

R. B. Couch has published a model-ship comparison, reproduced here in Table 60. c, in which

by

this model,

Twin-screw tanker of extreme beam, Sun Shipbuilding and Dry Dock Company design, TMB model 3817,

(i)

In

for the (ii)

all

cases the rate of propeller rotation

model

is

In nearly

higher than for the ship all

cases the ship

wake

fractions

are higher than those of the models (iii)

On

the assumption

of

thrust-deduction

HYDRODYNAMICS

380

TABLE

60.C

Ship identification

Type

of vessel

IN SHIP DESIGN

Sec. 60.13

Propulsion Factor-s for Ship and Model for Various Types of Naval and Commercial Vessels

Sec. 60.13

SHIP-POWERING DATA TABLE

Ship identification

Type

of vessel

60.C— (Continued)

381

HVnRODYNAMICS

382

TABLE Ship identification

Type

of vessel

IN .SHIP DESIGN

60.C— (Continued)

Sec. 60.13

SHIP

Sec. 60.14

III 0:3

.

05

0.6

POWERING DATA

I

0.6

3.7

0.9

\J0

TB"

I.I

I

T-r.^

T

250 1)

200:

£

Weiqht-Speed- Power Foctorwhere

W

is

lonq tons, V

in

m

6.88

—p

kt, fg in

horses

60 30

'

:e: Loke reiqhters

"0

Corqo Ships,

Tankers

0.02

Corners

Liners,

0.04

0.08

0.06

Destrouers and Destrouer Escorts

O.ia

0.10

0.16

0.14

0.22

0.20

0.18

0.24

±J

026

Froude Number squared - {y/'^aL.) Fig. 60.U

M = 0.61 This line

is

Tentative Mbanline for Selecting the Weight-Speed-Poweb Factor for an Average Vessel (16,573)(20.5)'

12.895

LPs

(510)(13,243)

nearly 36 per cent greater than the mean-

value given by Fig. 34.1, indicating that the

merit-factor

method

of estimation

requires

still

considerable development.

An

alternative merit factor

somewhat simpler O-diml form of

Weight-Speed-Power Factor This

is,

makes use

relationship

of a

in

the

thrust-load condition

=

34.11 of Part

WV

(60.x)

Ps

in fact, the Telfer merit factor

F^

,

as in Fig. 60.U,

indicates a dispersion for normal design as great as

it

that evidenced in Fig. 34.1 for the Telfer merit factor.

Indeed, with a plot having a uniform

instead of a log scale of ordinates, the dispersion in

both would be

much

greater. It

true that the propulsive merit of

vastly superior to that of others.

is

2,

is

Volume

described fully in Sec. I.

An ampUfied

version

of that description is given here for the con-

From the effective power and the propulsive coefficient the shaft power is found. This method also enables the designer venience of the reader.

M divided

by the Froude number squared, indicated as one of the terms in Eq. (34.xxiv) on page 517 of Volume I. When WV/Pg is plotted on a basis of vessels of supposedly

Using the tentative meanline of Fig. 60. U as an indicator for estimating the probable shaft power of an ABC ship design of average merit, the estimated power is worked out in Sec. 66.9. 60.14 Shaft-Power Estimates by the IdealEfficiency Method. A method of deriving the propulsive coefficient jjp from the ideal and real efficiencies of a screw propeller under a given

apparently

some

vessels is

to select a suitable

P/D

ratio for the propeller,

and to approximate its rate of rotation n. Assuming that this procedure is to be used the early stages of a ship design,

it is

in

necessary

to estimate or determine the total ship resistance

Rt and ,

wake and thrustand of the relative

to select values of the

deduction fractions rotative efficiency

w and

tjr

,

t,

which appear reasonable

for the design in question.

The

ship speed

V

is

assumed to be known, as are the number of

HYDRODYNAMICS

384

D

the propeller diameter

If

propellers.

may

tentatively fixed, several solutions

not

is

be worked

out, each for a different diameter.

The necessary formulas

for this calculation are

taken from Sec. 34.11:

=

F.,

-

V{\

Ttq

T =

w)

1

Pe = RtV = 1

\

-

t

IN SHIP DESIGN

using the basic values from the self-propulsion

— w

Rt =

160,120

D =

20.51

ft,

from

Fig.

=

Va =

=

Ctl

in 0-diml form ^2t^3 pD VaVii

(34.xxvii)

When

by

appropriate.

The

= Dl

+

effective

D^ is Dl + Dl + Dl as power P^ is always

Ctl

—

,

calculated 0-diml value of Ctl

160,120(34.62)

position of the

Ctl point along the

G

n

is

found.

D

2.546Pb

2.546(5,543,350) (1.9905)(20.51)'(28.042)'(1.148)

=

0.666

may

It

be simpler and quicker for the user to

calculate the thrust-load factor

C TL

AoVl

by

previously used, the rate of rotation

172,170 (0.99525)(20.51)'(0.7854)(28.042)'

(34.xxviii)

ETT,

= This

is

diagram 3 culated 20.0

0.666

somewhat smaller than the 0.700 of Fig. 59.1 because the latter

for

a

From Table

r],

A

portion of this problem

design of the

ABC

is

worked out

ship

in

sufficient only to derive a value of

what more complete example

is

for

Sec.

Ps

.

A

worked out

0.873 and the 0.8-ideal r/Re„i

is

0.698. This

is

Consulting the open-water curves for the stock

J

for

7,0

=

0.698

is

Mc

the advance coefficient

0.769.

Then J = VA/inD),

28.042

JD

(0.769)(20.51)

somehere,

of

the working efficiency of the propeller at 20.5 kt.

an

66.27,

is

efficiency or real efficiency

whence

early

diameter

34.a, or Fig. 34. B, the correspond-

ing ideal efficiency

tions.

this facilitates

wheel

final-design

of

is cal-

ft.

propeller in Fig. 78.

in

by

T

^

propellers,

A nomogram for solving Eq.

embodied

145;

5,543,350 ft-lb

pD VaVh

Stevens, Technical Note working out a number of solutions for a different combination of assumpis

=

^ ~

0.8-

indicates,

an approximate value of the pitch ratio P/D which may be expected to produce the most efficient propeller under the circumstances. Consulting the open-water characteristic curves of some "stock" propeller which has this pitch-diameter ratio, and entering the open-water efficiency curves with the rjo value from the 0.8-ideal-efficiency curve, give at once the advance ratio / = F^/(nZ>). With the values

Va and

=

(34.xxvii),

reference to the efficiency curves of the three

of

0.070)

is

ideal-efficiency curve of Fig. 34.

Wageningen

-

160,120/(1

the

,

found for the 0.8-ideal efficiency. This is taken to be the actual operating efficiency of the propeller, as yet not designed, and is equal to the open-water efficiency r]„ of some propeller at some advance ratio / = VA/inD).

The

=

t)

Then, from Eq.

curves of Figs. 34.B, 34.C, or 34.E are entered

and a value

per sec

per sec

the total ship figure.

With the

ft

per sec.

(34.xxviii)

dimensional form.

2Z)'

34.62

from Fig. 78.Nb 0.070, from Fig. 78.Nb; vht = 1.148 F(l - w) = 34.62(1 - 0.190) = 28.042 0.190,

several propellers are to be used,

replaced

78.Ma

=

p^ = R^V =

p[Z>=(ft)][Fj(kt)]„„ in

78.Nb

172,170 lb

PcChorses)

290.68

Fig.

self-

trial

for stock propeller actually used,

= Rt/{1 -

T

from

lb,

20.5 kt

ft

^

=

Ctl

transom-stern model, to deter-

mine the agreement (or otherwise) with the propelled model predictions for the 20.5-kt speed. The basic conditions assumed are:

t

t

ABC

test of the

V = Wt =

«'(l^)

Sec. 60.14

=

1.778 rps or 106.7 rpm.

SHIP

Sec. 60.15

POWERING DATA

This compares with the value of 109.7 (or 1.82G rps) derived

from the self-propelled model

test;

indicates that the real or working efficiency of

it

385

a self-leveling (commercial) type of anti-fouling

months out

paint, to be 10

an increase in

and to have due to fouling of

of dock,

specific resistance

Af.CF(10^)

=

ideal efficiency.

predicted

ABC

Taking a Jj-value of 0.748, as determined by thrust identity from Fig. 78. Nb, the real efficiency J/Reai or the open-water efficiency tjo from Fig. 78. Me is only 0.686. Assuming a value 1.02

assumed that for half of the open-sea portion of a voyage under these circumstances, heavy weather has slowed the ship to an average of 17.7 kt. For the remaining half, therefore, in order to meet the sustained speed of 18.7 kt, the ship is called upon to average 19.7 kt. Can the ship do it, when fouled, with 95 per cent of its maximum designed power?

the propeller was

somewhat

than 0.8 of

less

its

for the relative rotative efficiency, riP

=

from

=

ria{vH)riB

Since this

is

0.686(1. 148)(1.02)

in excess of the

Fig. 78. Nc,

-qp

=

=

indicates that the

it

0.803

0.761 derived

relative rotative efficiency is too large.

=

This

is

less

From Table

last

^pCf

5,543,350

AsCf

12,551 horses. (550) (0.803)

than the predicted shaft power of

W.

Taylor,

made

is

tlian

obscured by the deterio-

is

ration

anti-fouling

the

of

it.

coating

assumed as

is

Underestimation

results

slightly larger propeller tiian overestimation"

in

a

[SNAME,

roughness

coating

covering

assumed

is

deterioration

as

the

of

paint

AfCf

overestimate

paint

of the fouling itself

roughness

structural

for

0.1(10"'),

is

from the long-dash taken as 1.25(10^')

is

(0.0

for fouling,

45.L,

better to underestimate relative rotative efficiency to

taken as 0.0 since any

is

roughness here

AcCi? for

several decades

ago, that: "It

is

0.1(10"')

13,243 horses from Fig. 78. Nb. It emphasizes the

statement of D.

It

45.f of Sec. 45.18:

for the plating

and the presence

^= T)P

ship curve of Fig. 45. L.

assumed

The

example of Sec. 60.10 shows that actually tjr was only 0.968. Using an T/p-value of 0.803 would have given a shaft power of P.,

corresponding to the long-dash

1.25,

Then SAC^

-|-

0.1

-|-

0.1

+

line of Fig.

1.25) (10"')

=

1.45(10"').

1923, pp. 69-70].

For the "make-up time" speed j)f^ 19.7 kt or 60.1S

Estimating Shaft Power for a Fouled-

A recommended

or Rough-Hull Condition.

de-

33.27 ft per sec,

=

F„

0.26.

sign procedure for building into a ship a sufficient

resistance

speed margin to enable

0.94(10^').

it

to maintain an estab-

At

T,

this

= T,

19.7/ ,

V510 =

0.872,

the specific residuary

coefficient Cs is, from The Reynolds number R„

Fig.

78. Jc,

for this ship

lished schedule despite the handicaps of winds,

speed, in standard salt water, from Table 45. b of

waves, fouling, and other factors

Sec. 45.4, is 1,324 million, for

and

and

is

described in

Table 64.d, all in Part 4 of this volume. It should be possible eventually to predict the effect of each of these handicaps in quantitative terms, provided the conditions to be met are specified in some detail. Considering the problem of fouling, or of serious deterioration of the paint coating on the underwater hull, the situation is presumably worst just before the end of a dry docking interval. As a check on the speed and power margins incorporated in the design, which are intended to be adequate all through this interval, it should be possible to estimate the propulsion performance in the foul-bottom as well as the cleanSees. 64.3, 65.3,

69.9,

in

bottom condition.

One acceptable method

is

the transom-stern hull of the in Part 4.

The

ship

is

worked out here

ABC

for

friction resistance coefficient is

1.48(10"').

1.48

+

Then Ct

The wetted (69.85) (650.25)

Cp

+

XACp =

=

specific

45.

(0.94

+

3.87(10"').

surface of the ship

78.Ja, 69.85 times

X^(lambda) 45,420

ft'.

for

Then

is,

from Fig.

the ship or for the fouled

ship.

Rr = Cr[~)SV'

=

(3.87)(10~')f— |^V45,420)(33.27)'

=

193,640

lb,

whence

„„ = p = KtV Re

(193,640)(33.27)

ship, designed

assumed to be painted with

=

1.45)(10"')

+

which the

Cp from Table

For the fouled

^/^ 550

n-,,, = 11, /13 horses.

ship, at 19.7 kt, it is

estimated

HYDRODYNAMICS

386 that the

wake

w

fraction

has increased from the

The thickening

0.190 of Fig. 78.Nb to 0.210.

IN SHIP DESIGN the same

of

when the bottom

{<\^\

assumed to have a greater effect on increasing w than the augmented Ctl has on reducing it, as described by L. Troost in Sec. 60.8. It is assumed further that the thrustdeduction fraction t has increased from 0.070 to

is

both clean and

foul,

('?o)Foul('?/r)Foul

the boundary layer, and the increase of viscous-

wake

Sec. 60.15

VoViT

velocity due to fouling are

(0.677)(1.120)

=

0.921

(0.717)(1.148)

W.

R.

L.

Gawn

states,

on page 247 of

his

paper

"Roughened Hull Surface" [NECI, 1941-1942,

0.115, because of the greater thrust-load coefficient

Vol. LVIII, pp. 245-272], that "Relative rotative

Ctl at which the propeller must operate. At this increased Ctl the inflow jet will have a somewhat

efficiency

larger diameter in

— Ap's

way

of the skeg, so that the

on more of the stern area;

will act

another reason for increasing

this is

t.

For the clean ship, at 19.7 kt, tj^ from 78.Nb is 1.148 but for the fouled ship it is ,

^

U^JFoui

_ -

^^

The speed 7[(1

By from

-

_

(1

of

advance

=

w)f„„,]

_ -

Ofou.

_

(1

(^

^^^^^^

Va

_ -

0.115)

Q 210)

Fig.

=

26.28

interpolation from the values of 10~^

is

152,600

lb.

T

-

0.190)

=

11,713

Ps =

=

16,540 horses.

0.708

This is about 3,290 horses more, or about 25 per cent in excess of the 13,250 horses required to propel the clean ship at 20.5 kt, as predicted by the self-propelled model test. It

Then

for a ship carrying

than

Va =

the stock model propeller,

—

VO-

26.95 ft per sec,

w)

=

is

much

not

less

power

margin required to provide the speed differential from the

whole

clean-bottom

18.7 kt (predicted

(predicted

and

rough,

is

Hence

at 19.7 kt, for the

a propeller of 20.51-ft diameter, corresponding to 33.27(1

surface

,"

T

Fig. 78.Nb, the thrust

clean ship,

.

,„„ , ^-^^^

per sec.

ft

.

0.708.

for 19.7 kt, fouled, is

33.27(0.79)

when the

less

is

but he gives no numerical values. = EHP/SHP Interpolating from the r)p values in Fig. 78. Nb, the value of rip for the clean ship at 19.7 kt is 0.769. For the fouled ship at the same speed it is estimated to be 0.769(0.921) = .

Ps

Ps

of 9,320 horses) to 20.5 kt

of about 13,250 horses),

namely

3,930 horses. It corresponds to an average increase

T

power Ps of only about 2.5 per cent per month, or about 0.08 per cent per day, yet when considered as an additional power expenditure it seems large. For the designer who is to recommend a in shaft

A,Vl 152,600

0.639

(0.99525)(20.51)'(0.7854)(26.95)'

For the fouled ship at 19.7

=

193,640/(1

-

0.115)

=

kt,

T = Rr/(l -

218,800

lb.

t)

definite

amount

of shaft-power reserve

owner, the situation definitely

Then

calls for

to the

an investi-

gation of the use of hot plastic anti-fouhng paint Tfou,

instead of the older type of self-leveUng paint.

\S^TLJ-i

From Table

A„[(F^)P„„,]^

I

ApCp 218,800

From a

larger-scale version for a

PjD

of the real efficiency

ijReai

0.717.

a

For a Ctl

P/D ratio

'/Real is

is

0.0, since

any

obscured by the hot-

plastic paint coating

of 0.963

of Fig.

34.

G

and the fouling is assumed to be

0.1(10"'), as before

or

ratio of 1.0, the value

for a Ctl of 0.639 is on the fouled ship, and

of 1.00, the value of the real efficiency

0.677. It is not possible to pick the latter

value from the open-water characteristic curve of Tjo because the J-value and the rate of rotation

n

taking as

A.sCf for structural roughness

0.963

from Fig. 70.B,

is

plating roughness

(0.99525)(20.51)'(0.7854)(26.28)'

=

45.f of Sec. 45.18:

for the plating

in the fouled condition are

not known.

If the relative rotative efficiency t\R is

assumed

AcCp

to cover the initial roughness of the hot-

from the margin of Fig. 45. L ApCp for fouhng only, from the dot-dash fine of plastic paint is taken as 0.5(10"'), left

Fig. 45.L, is 0.11(10"').

Then 2ACf

is (0.0

+

0.1

+

0.5

-1-

0.11)(10"')

=

0.71(10"').

The values

of

Cr and Cp

19.7 kt are 0.94(10"')

and

for the clean ship at

1.48(10"'), respectively.

SHIP-POWERING DATA

Sec. 60.16

Then

as before.

+

C,.

=

SAC;.

(0.94

+

+

1.48

With a wetted

3.13(10"').

+

in Fig. 78.Nb, the value of nr for the clean ship

0.71)(10-')

=

at 19.7 kt

surface of 45,420 ft^

from the preceding example, the of the fouled ship

total resistance

at the 0.739.

=

is

0.769 as before. For the fouled ship

same speed it is taken to be 0.769(0.961) = Hence for the fouled ship with hot-plastic

paint, at 19.7 kt,

is

p JTs

Ct\ £ -sf

i2i

387

C^ = Ck

for the fouled ship

9,474

— Ea — —

This

3.13(10-')(i^^)(45,420)(33.27)'

is

=

12,820 horses.

0.739

r,p

than the 13,250 horses required to

less

drive the clean ship at 20.5 kt.

=

With a

156,610 lb,

shaft

power Ps

of

about 11,200 horses

to drive the clean ship at 19.7 kt, from Fig. 78. Nb,

whence

^^^^«53:^ =

P. =Ze.F =

9,474 horses.

Since the ship with the hot-plastic coating is expected not to be as heavily fouled as with the self-leveling paint in the preceding example, it is estimated that the wake-fraction w is in-

an increase of 16,540 - 11,200 = 5,320 horses is required to overcome 10 months' fouling on the self-leveling paint, whereas an increase of only

-

12,820

11,200

=

1,620 horses suffices to over-

creased only from 0.190 to 0.200, and that the

come both the initial roughness of the hot-plastic paint and 10 months' fouling on that paint. Against this advantage must be placed the additional shaft power that would be required to

thrust-deduction fraction has gone up from 0.070

drive

For the clean ship, at 19.7 kt, 1.148 as before but for the fouled ship it is

to only 0.100. is

ii]h

(1

—

(wFoul

(1

The speed F[(l

=

Ofo

(1

M')f„

(1

-

1.125

advance V a for 19.7 kt, with the on the hot-plastic paint, is

-

i«)f„„i]

=

33.27(0.80)

For the fouled ship at 19.7

156,610/(1

(C

0.100) 0.200)

fouling

lighter

sec.

of

-

-

0.10)

=

174,010

^F°"'

^

kt,

= 26.62 ft per T = Rt/{1 lb.

Then

.

^o[(FJp„„,]^

174,010 (0 .99525) (20 .5 1)'(0 .7854) (26.62)'

= The

is

0.639, the

example. Similarly,

For a Cri

Ctl for the clean-bottom same as for the preceding

TjReai

for this factor is 0.717.

on the fouled ship and a P/D the value of T/u,ai is, from Fig.

of 0.747

ratio of

1.00,

34.G or

Fig.

70.B, 0.703.

Assuming as before

that the relative rotative efficiency

same

for both clean (^?p)i

ship

when

with hot-plastic paint,

and

jjb

is

the

foul bottom,

and

at

all

few months thereafter. This and other powers can be calculated by the method described. 60.16 Increasing the Power and Speed of an Existing Ship. Marine architects are often called

upon

just out of dock

to increase the speed of a

for a

ship

already

by improving its form and retaining its power plant, by changing its power plant and not its form, or by both. In the matter of the power which can be delivered to and absorbed by a single screw propeller or other propulsion device, embodying a question which invariably arises whenever the matter of increased power is considered, it is to be remembered that shaft power is a function of both torque delivered to the propeller and the built, either

rate of rotation of the shaft.

0.747

thrust-load factor

condition

the

speeds,

A

given shaft can

often be run at a higher rate of rotation at the

same torque but only

rarely can the

same screw

propeller be expected to absorb the increased

power and to drive the ship rpm and ship speed.

efficiently at the

increased

It is conceivable that lengthening, fiiiing, or otherwise altering an existing ship, designed for slow speed, may enable the altered ship to be

driven at an increased speed with the same total resistance Rt or effective thrust T{1 — i). The

(^7ci)Foiil('?g)l

may be more than compensated for by the reduced pressure drag due to

increased friction drag (0.703)(1.125)

=

wavemaking and

0.961

(0.717)(1.148)

Interpolating from the

t/p

= EHP/SHP

separation. However, the fact

that the ship speed values

raises

is

increased, automatically

the power by a corresponding amount,

HYDRODYNAMICS even though no additional thrust

is

necessary to

Skeg and stern endings that are too bkint, ahead of a screw propeller, and insufficient clearances, may always be expected to generate vibratory forces and moments. At low speeds these may be of small magnitude and hence not objectionable. At higher speeds, however, a propeller developing increased thrust and absorbing greater power may generate vibratory forces and moments that are by no means acceptable. Air leakage from the surface may be initiated or augmented because of the greater — Ap's in the blade

fields.

Cavitation

may become

of

the

greater

a factor, at

upper blades, because

blade-section

speeds,

possible

and diminished depth the blade sections in the upper

greater propeller diameter, of

submergence of

clutched from ally

it,

Backing

60.18

Model

Tests.

A

Exerting the

towing speeds,

maximum

combined with

from

discussion

of

Self-Propelled reversing

EMB

embodies the results of such a test on model 3594, representing the minelayer U. S. S. Terror. Fig. 60. T contains data for the ahead self-propulsion tests of this model at the same displacement and trim. It is to be noted that the thrust-deduction fraction in the backing condition is very large, as might be expected, and

wake

fraction

is still

is less

positive.

when set for by angling the pitch [SSPA Rep. 2, 1943;

rotation of the 2-bladed propellers

normal ahead running and

is a design problem for any Both economical and efficient pro-

on the surface as well as submerged, is a "must" for every type of submersible, as well as some types of pure submarine. Each of the foregoing is perhaps more of a design than a calculation problem, or perhaps more a problem of operation than of design. The operator and owner usually must decide how much one condition is to be favored over the other. Sec. 67.15 mentions the proposals and actual installations of the past in which designers have attempted to meet the problem of driving a ship with one or two propellers under one operating condition and with two or more under another condition. This still involves running one set of wheels in both ranges, usually at different ship speeds and rates of rotation. It may be done by pulsion,

practically

varying the pitch mechanically or accepting a reduction of efficiency in one or both conditions. Permitting one or more propulsion devices to free-wheel while the others are driving

some added action

of

means

resistance due to the windmilling

the free wheels.

Furthermore, each

pro-

H. F. Nordstrom presents the test results and an analysis of the self-propelled experiments on models of fishing boats, in which astern thrust was achieved (1) by reversing the direction of

speed for shifting quickly from one operating area to the next, is mandatory for any tug worthy of the name. Economical propulsion at cruising speed, combined with efficient propulsion patrol vessel.

The

than 0.40.

developing the greatest practicable free-running

at high or top speed,

and

model-basin establishments equipped to conduct self-propulsion tests can carry out steady-state tests of this kind in the astern direction. Fig. 60.

pulsive coefficient

low

Power

is

that the

at

have to be lubricated continu-

included under maneuvering in Part 5 of Volume III. However, it is stated here that

backing

an old aperture, actually diminishes the clearances, when they should be increased. 60.17 Powering for Two or More Distinct blades, in

thrust

those

all

during such an operation.

blade positions. Fitting a propeller with wider

Operating Conditions.

Sec. 60.17

parts of the machinery which can not be un-

propel the ship at the increased speed.

least in the region of the

IN SHIP DESIGN shaft of a windmilling propeller, plus

blades to give reverse

summary and some Twin

(2)

figure legends in English].

CHAPTER

The

61

Prediction of Ship Behavior in

Confined Waters 61.1 61 2 .

61 3 .

General Typical Shallow-Water Resistance Data The Quantitative Effect of Shallow Water on .

Ship Resistance and Speed

61.4 61.5

critical Range The Square-Draft

to

in the

.

Sub-

Water-Depth Ratio

.

.

394

Procedure

Depth

Practical Cases Involving a Given

61.7

Case la: To Find the Shallow- Water Speed from the Deep-Water Resistance-Speed

61.8

Case lb To Find the Shallow- Water Resistance from the Deep-Water ResistanceSpeed Data Case Ic To Find the Deep-Water Speed and Resistance When the Shallow- Water Speed and Resistance are Measured Limiting Case of 2 Per Cent Speed Reduction in Water of a Given Depth Cases 2a and 2b To Find the Limiting Depth

of

396

Water

Data

.

61 10 .

61.11

390 393

Features Associated with the O. Schlichting

61.6

61 9

389 389

397 :

400

:

:

400 403

61.

HYDRODYNAMICS

390

14

13

15

Fig. 61. a

There

16

17

19 20 Ship Speed, kt

18

are, in the literature, a considerable

number

24

25

26

Water of Varied Depth

water, are only slightly less than the

maximum

running in shallow

give the lines or even the principal dimensions of

for ships

in part

bow and

reproduced in Fig. 35.D. Another set, derived from the trial results of a ship, is adapted from a set of graphs given by the German naval constructor Paulus in Fig. 2 on level at

23

are derived in part from tests on

from ship trials. One set of curves, derived from a model test and illustrating the principal features, including the change of

models and

22

Sec. 61.3

trims by the stern at the lesser (critical or nearcritical) speeds. Unfortunately, Paulus does not

and power with speed

They

21

Resistance and Trim Data fob a Torpedoboat in

of typical graphs giving the variation of resistance

water.

IN SHIP DESIGN

stern, is

page 1872 of reference (4) in Sec. 61.22. The latter data are presented in Fig. 61. A. Others are to be found in the references cited in the list at the end of this section. Paulus' data for the German torpedoboat SI 19 reveal that the maximum trim by the stern occurs at a speed shghtly less than that for which the increase in indicated power Pi (over the deep-

water P,) is a maximum. Also that the trim becomes less than the deep-water trim at a speed very slightly higher than that for which the shallow-water Pi drops below the deep-water P, The trims at the higher speeds, in all depths of .

torpedoboat SI 19 forming the subject of his investigation.

Most

of the model-test data referred to in the paragraph of this section are suspected of giving resistances and powers that are too high, because of the restricting effect of the model-

first

basin walls, added to the effect of the false bottom or other device used to simulate the shallow water.

For example, in reference (34) of Sec. 61.22, where the shallow-water drag tests were intended to simulate behavior in open water of 13 meters depth, the hydraulic radius R,i works out as only about 9.5 m. For unhmited water of 13 m depth, Rh is also 13 m. A more classic example is W. Froude's full-scale towing tests on the Greyhound in the early 1870's, unquestionably made water that was too shallow for the size of the vessel [Robb, A. M., TNA, 1952, p. 449]. 61 .3 The Quantitative Effect of Shallow Water

in

on Ship Resistance and Speed

in the Subcritical

PREDICTED BEHAVIOR IN CONFINED WATERS

613

Sec.

The

Range.

quantitative eiTect of shallow water

of unlimited extent on the resistance of ships

is

and speed

expressed in at least three different

ways, when the basis of comparison is a combination of resistance and speed in unlimited deep water: (1)

The

effect of limited

depth on ship speed at

W.

method has a and partly experimental basis. Some of its assumptions are open to question but it has the merit that it works, as an engineering solution to the shallow- and confined-water problems. It will undoubtedly give way in time to a more rigorous treatment but in the meantime

depth upon resistance for a speed equal to a given deep-water speed (3) Depths of water of unlimited extent beyond which there is no shallow-water effect on either (2)

The

effect of limited

resistance or speed.

The

=

discussion in this section

is

limited to ship

Table 72.a of Sec. 72.3 lists values from 2 through 40 ft. The problem of the wavemaking resistance only in shallow water, and in confined waters as well, has been tackled on a purely analytical or theoretical basis by Sir Thomas H. Havelock, J. K. Lunde, and others. One of Lunde's contri{9h)°-\

of Cc for a range of depths h

butions of

is

Wave

his paper

"On

the Linearized Theory

Resistance for Displacement Ships in

Steady and Accelerated Motion" [SNAME, 1951], in which Part 2, on pages 50 through 60, applies directly to resistance due to wavemaking in shallow water of imlimited extent as well as in a canal. A more recent contribution is that of A. A. Kostyukov entitled "Resistance of Bodies in a Fluid to Motion near a Vertical Wall" (in Russian) [Dokladi Akad. Nauk, SSSR (N.S.) 99, 1954,

pp. 349-352]. This paper

is

abstracted briefly in

Mechanics Reviews, page 534, number 3846.

Applied

None

of the existing

produces results in

The

by

Fig.

reference

The point Ai

cited).

(1955)

December

1955,

is

Rt^

in

V„ achieved with a given power. This be assumed as the customary design point for a normal deep-water ship. Unless otherwise ship speed

may

<» (infinity) in this the subscript chapter applies to the value of a designated

indicated,

quantity in water of infinite depth and width. The total resistance Rt«, is composed of the usual

R^^ and a pressure resistance assumed by Schlichting to be to wavemaking. These components

friction resistance

Rwo,

,

which

due entirely

is

are indicated at the right of the diagram.

The wavemaking

resistance

Rwo

is

associated

with a train of deep-water waves, belonging to the Velox system, whose speed is the same as the ship speed, so that the crests and the troughs

occupy certain fixed positions relative to the ship. The fixed relationship between the wave length L,ra. and the speed c„ of these waves, assuming they are of trochoidal character and form, is given under (2) of Sec. 48.4. Squaring the equality given there,

cl=Vl^

analyses in the

2-K

In shallow water the speed of a trochoidal If of the same length Lwa, is less than V„ .

speed for a water depth h, the ratio between c^ in shallow water and Ca, or F„ in Ca is this

is,

from

Sec.

of Sec. 48.15, expressed

18.10

Seeschiffen auf flachem

Wasser (Resistance

EMB

1940;

also

van

Lammeren,

Fig.

48.N

(61. i)

=

of

Seagoing Vessels in Shallow Water)," STG, 1934, Vol. 35, pp. 127-148; EngUsh version in

and

by

matters was developed some years ago in Germany by Otto Schhchting ["Schiffswiderstand auf beschrankter Wassertiefe; Widerstand von

Jan

represents the

in a

appears to be the most satisfactory of deahng quantitatively with these

56,

is illus-

and the corresponding

unrestricted deep water

deep water

Transl.

method

61.B, adapted from

one of Schlichting's illustrations (Fig. 6 in the

scientific.

method

agreement with observed

basis of 0. Schlichting's

trated graphically

wave

What

fair

model and ship data.

form to be readily useful to the marine architect. There have been a number of much more practical solutions proposed for this problem but many of them do not embody parameters which appear logical or foregoing category

1948, p. 56]. This

relationship between the total resistance

speeds less than the critical speed Cc of a wave of translation in water of the given depth h, where Cc

P. A.,

partly theoretical

it

constant (or at a given) resistance

RPSS,

391

When

<;tanh

(^1^2

the ship passes from deep water into h, it can not make the

shallow water of depth

HYDRODYNAMICS

392 Speed Celerity

Celerity

c^,

Voo of

c„ or

of

IN SHIP DESIGN

Sec. 61.3

Ship in Deep Water of Unlimited Extent Deep-Woter Wave of Speed V^ and Lenqth Lwq

Speed

Vj of

Wove

of

Lenqth L'^qq

J

Resistance

Rwco Due

to

Wovemokinq in Deep Wotsr ot Speed Voo

Resistance

Rpoo -Due to Friction

in

I

I

Deep Water at SpeedVjj,

I

Definition Diagram for the Shallow- Water Speed-Resistance Determination of 0. Schlichting

Fig. 61. B

waves alongside it, of the Velox system, travel any faster than it does. The wave of translation or solitary wave which may go on ahead in a

especially in the limited space between the ship

restricted channel does not enter into this dis-

water which closely surrounds it. In other words, it must overcome a total resistance greater than Rn to maintain the speed c*

cussion. Experience reveals that the crests

and

troughs of the Velox waves remain in essentially the same positions along the length of the ship

down

as in deep water. However, the ship slows

by the

ratio of the wave speeds in shallow and in deep water, given by the ratio c,JV„ of Eq. (61.i). It may be assumed that, despite a change in profile due to increased wave height hw in the

shallow water, and other second-order changes, the pressure resistance jB,^„ at the slower speed

was at the speed V„ in deep water. Here, and in what follows, the subscript the same as

C/,

is

/

applies

V —

Ch

I

.

it

values at an intermediate speed

to

Again

it is

assumed that wavemaking

responsible for

all

The

regarding resistance and ship

is

speed

situation is

now

the pressure resistance.

represented graphically in Fig. 61.B

by the point Bi The pressure resistance Rw^ remains the same as at A, but the friction resistance is diminished from Rf^ to Rfi that is, from its value at the point Ei to its value at .

,

,

the point Fi

Vi

is

.

The

total resistance at the speed

diminished from Rt^ to Rn,

amount

of

this

The

reduction.

,

solely

ship

by the

speed

is

bottom and the water bed, explained

in Sec. 18.2,

the ship in shallow water has to

move

faster

relative to the

or

Vi

.

The

resistance represented

by the point

Bi in the figure is increased to that represented by the point Dj Unfortunately, it is not possible .

to derive a simple expression for predicting or

calculating

this

increase.

Schlichting

therefore

assumes that the resistance Rtu remains the same as at the speed V , but that the ship slows down until its total resistance again drops to Rjh This involves a ship speed over the ground slower than Vi The new reduced speed is V^ represented by the point C, on the shallow-water resistance curve of the diagram of Fig. 61. B. The amount of the first speed reduction Ac or, better, the ratio between the speed c^ and the unlimited deep-water speed V„ is determined solely from theoretical considerations, indicated by Eq. (61. i). The speed C/. or V i is for convenience .

.

,

,

called here the Schlichting intermediate speed or

the shallow-water wave speed.

The

ratio

between

speed and the shallow-water ship speed V^ being sought, or the further speed this intermediate

reduction

AVp due

to potential flow,

is

most

F„ to V i A second effect now enters the picture. Because of the greater augment -\-A.U of stern ward

determine theoretically. It is therefore derived from experiment data on models tested in shallow water. The sum of the constant

velocity due to potential flow in the shallow water.

wavemaking

diminished from

.

difficult to

resistance

R^y^

plus

the

friction

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.4

resistance Rfi at the intermediate speed F/ is applied as the resistance Rrk to the model shallow-

water resistance-speed curve at the point Cj giving the desired shallow-water speed Vh One feature of the diagram of Fig. 61.B

Notched Retjions ore

Moximum

,

Fig. 61. C

Definition Skktch for Term

"Square Draft"

by Rfi

,

described briefly in Sec. 18.11, and dis-

cussed further in Sec. 61.14. Fig.

vessels

61.

C

function

space

the

of

Although a ship

of given

for broad,

indicates that,

under which the bed clearance The Center Scale Gives

the Value

h

of

I

= 20

^

15

shallow

may

often

the Ratio

vhere

Ax is the Mox^ mum-Section Area h IS the Woter

appears logical because the increased potentialflow velocity under the ship, where most of the is

Area Axj

Broken-Line Squares Have Areos Equal to Ax in Each Cose and Sides Equal to (Ax) Known as "Square Droft"

square root of the maximum section area Ax of the ship, divided by the water depth h. This

passage around the hull,

of

is

between the several velocities and speeds are the items of primary interest, the horizontal scale may be laid off in values of what is known as the critical-speed ratio {V„/\/gh), _V„/\/'gL, the ship speed V, or even (VJ-VgL), as may be found most convenient, or in all of them together. The only requirement is that the water depth h and the ship length L remain constant in the problem, and that all the ratios be a function of V. 61.4 The Square-Draft to Water-Depth Ratio. 0. SchUchting found that the ratio V^/Vi is a function of a 0-diml parameter, namely the

its

iSections

,

important. Since the abscissas represent wave velocities and ship speeds, and since the ratios

water flows in

393

Depth,

Same

in

the

10,000

—

8.000 6,000 5,000

—

4,000

Units

a

occupied by the ship.

maximum

section area,

corresponding generally to a ship of given overall size, may have a draft deeper than normal, with

compensated for by the less than normal. In this case more of the water flows around the sides, and less under the bottom. If the beam is very large in proportion to the draft, more water flows under the bottom but with the greater bed

bed clearance,

less

fact that the

this is

beam

clearance there

is

then

then more room for

is

it.

In any case the relationship developed by Schhchting appears to remain reasonably valid

form as well as for all speeds speed of translation of a natural

for ships of varied

below the solitary

what

critical

wave

in shallow water. It

may

be some-

optimistic in predicting slightly too small

a speed reduction for the general case, and it be oversimplified, but it is acceptable until

may

something better

is

of the area of the

dimension, draft. It is

a square

is

worked

The square section,

root

a linear

called for convenience the square

the draft of the equivalent ship having

maximum

section of the given area

with a beam-draft ratio of of

out.

maximum

unlimited

lateral

1.0.

extent

Ax

,

For shallow water the

square

the water depth

draft

For dimension known as the hydraulic radius, symbolized (Ax)"'^

is

related

to

restricted channels it is related to a linear

h.

Nomogram for Determining SquareDraft TO Water-Depth Ratio

Fig. 61.D

—

HYDRODYNAMICS

394

the value of the

be measured only in inches, square draft may actually exceed the water

IN SHIP DESIGN

Sec. 61.5

the shallow water of depth

h, it will

run at the

depth. Fortunately, the relationships previously described continue to be reasonably valid under

speed F„ This does not mean that it overruns the shallow-water Velox-system waves traveling at the speed V, in the depth h but that it runs

these conditions.

in

D

a nomogram, designed and kindly furnished by Professor H. L. Seward, by which the Fig. 61.

is

value of the ratio -\/A^/h is determined by inspection when the values of Ax and h are known. This

nomogram

is

applicable to any system of units

provided h

is

expressed in a length unit and

in the

Ax

same unit squared.

In shallow water of unlimited extent the hydraulic

Rjf

=

radius h.

equals

The nomogram

of 's/'A^/Rh

61.5

Rh

the

depth,

so

that

therefore gives values

under these conditions.

Features Associated with the O. Schlich-

ting Procedure.

Several features of the Schlich-

ting procedure require explanation If sufficient

power

is

and emphasis.

available, corresponding to

the shallow-water resistance at the point Gi in Fig. 61. B, and is applied to drive the vessel in

D.3

.

waves which are the shallow- water counter-

parts of a deep-water Velox-wave system traveling

+

AV„ faster speed V„ important to remember that the Schlichting procedure involves resistances rather than powers. To be sure, the effective power Pe is derived directly from Rr when V is known for any given condition but there is no simple method

at

some

It

of

.

is

the

estimating

shallow-water

shaft

Psh when the deep-water shaft power Ps

The Vi/Va, speed,

is

power known.

relationship Va,/^/~gh controls the ,

ratio

of intermediate speed to deep-water ship

independent of

values of Fo.

,

all

reasonable

absolute

provided the intermediate speeds

remain well below the

critical

Similarly, the relationship

speed Cc

y/Axlh

=

'Vgh.

controls the

of shallow-water speed to interratio Vhiyi mediate speed, independent of the deep-water ,

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.5

The Center Scale Gives the Value of the Rotio Speed of Ship in Unlimited Deep Water Va,

speed F„ again provided that the intermediate speed remains well below the critical. Referring back to Fig. 61. B, the solution in the ,

presented

cases

various

in

Wove

of

By the Intersection

involves

practice

Speed

-y^

of Translation of

o

Stroicjht

Ship Speed V^o

the

Deep Water and a

h of the Shallow

Scole at the Depth Water Under Considerotion

The Value of Q

Token as

Point on the

Ai is known, or in finding the depths of water which G, and H, lie at certain positions relative to Aj This is not as easy as it looks or sounds because, of

for

in

Depth h

in

Line Drov^n

Rioht-Hond Scole at

Between q Point on the

and Hi when the position

finding points such as Gi

395

Left-hand

is

32.174

per sec^

ft

.

first,

is not available, for a typical ship, a curves giving the resistances for a

there

family series

of of

speeds,

waters of

in

many

Vqh-

different

—5

90

—4 —3

10

-5p

depths. Second, the pairs of points such as Ai

and Ci

in Fig. 61.

B

are not directly related to

-2D

each other. Both the speed and the resistance are different for the two spots of a pair. When making calculations of the kind represented graphically

by

this figure it is generally necessary to plot

resistance-speed curves,

_

— JC

?.

two

critical-speed ratio

speeds

F<„),

because

made

A

025 Example:

V„-

Va./'vgh (using a range of it is then easier to determine c^

Vj

or

-p^ot

-300

5

-

^"

close together, is

,

problem. ratio of the intermediate speed

speed ratio, theoretical

F/

to the

ratio

V„/\'gh.

Fig.

61.E shows

of such a curve; the shorter

is

a large-

scale edition of a portion of the longer one, for

easier reading in the lower critical-speed range.

The nomogram

and

of Fig. 61.F, also designed

generously furnished by Professor Seward, gives by inspection the value of the ratio V^/y/gh when the deep-water speed

C

400

V^ and

the water depth h

are known. There is a double scale for F„ by which the right-hand line may be entered either ,

in ft per sec or in kt.

,

3

—

25-

O.0Z5

— O.Oi

-500 % - 600 'S

-^"'

-700 t -800 ^

g.

"

L 1000 Fig. 61. F

Nomogram for Determining

Critical-

Speed Ratio

which the ratio V JV i is plotted on a basis of the square-draft to water-depth ratio \/~Axlh,. The curve determined by Schlichof Fig. 61.G, in

ting [STG, 1934, Jan 1940, Fig. 2,

(1)

EMB Transl. 56, EMB Rep. 460, May 1939,

Fig. 9, p. 135; p. 3;

Fig. 9, p. 11] has

been modified by:

Decreasing slightly the potential-flow ratios

YulV I

for small values of the square-draft

to

This was done to bring the potential-flow ratios in agreement with those

water-depth

ratio.

determined

by

channels

The ratio of the shallow-water speed V^ in a depth h to the intermediate speed F/ called hereafter the -potential-flow ratio, is determined by inspection from experiment curves such as those

-4 —

0.05

— 0.03

called hereafter the wave-

,

is determined by inspection from a curve giving Vj/V:^ on a basis of

critical-speed

two parts

F„

R» 0.563

—

embracing from three to five points, rather adequate if the problem is of limited application. If the water depth h is not known it may be convenient to plot the resistance curves on a basis of ship speed V or of Froude number F„ depending upon the nature of the ratio,

The

Point

6

7

— 0.08 0.07 — 0.06

for the 250

deep-water speed

0.15

10 kt.or 16.89 ft per sec

Depth of Water h-28ft

small range of the critical-speed

.

—^

— O.E

at values of the

the intermediate-speed position

point Bi

0.5

-2

depth h and one for deep water, marking the companion spots Ai and Ci on each. Assuming that the water depth h is known, the conveniently

—

one for shallow water

of the given

plots are

— M_

(2)

[EMB

L.

Landweber

Rep. 400,

May

for

restricted

1939, p. 11].

Increasing the potential-flow ratios

YJYi

rather markedly for the larger values of the squaredraft to water-depth ratio because tests

other

made

in

model basins indicate conclusively that

396 !J~

HYDRODYNAMICS IN SHIP DESIGN

Sec. 61.6

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.7

When

(2)

the depth of shallow water

is

to be

determined:

Case

On

2a.

Resistance Data sheets are available.

Cases 2a. and 2b. are discussed in Sec. 61.11. A Umiting case in the first class involves a determination of the reduction in speed for a specified depth when this reduction does not exceed 1 or 2 per cent at the most. A similar case in the second class involves a determination of the minimum depth at which the effects on speed and resistance shah be minor, say plus

and 2 per

and minus

1

cent, respectively. in practice start

with the deep-water ship performance as a basis. Others require that the deep-water performance be predicted from the shallow-water behavior.

In either case, the relationship between total and with speed in deep water must

friction resistance

be known. These

may

61.7 Case la: To Find the Shallow-Water Speed from the Deep-Water Resistance-Speed Data. The first example, numbered 61.1 for convenience, covers Case la of the preceding section. There, working from predicted deepwater data as to the speed and resistance of a ship, it is desired to

speed, in a depth

be found:

the same total resistance deep water. The region for which shallowwater data are desired is at and just below the

designed speed of the vessel. Example 61.1. The ship selected is the ore carrier covered by SNAME RD sheet 9, represented by TMB model 3818. The ship is 370 ft long by 64 ft beam by with a displacement of 8,850 long tons.

The designed speed is 12.5 kt, for which T, = 0.65, Fn = 0.194. The ship runs from deep water into a shallow estuary 24

deep. If the actual deep-water speed

is 13 than the designed speed, what is the speed in the estuary with the same total resistance? Briefly stated, the procedure is to construct a resistancespeed curve for the given depth of shallow water, and then

ft

kt, slightly greater

to determine,

Rth

the usual effective- and friction-power

determine the shallow-water

h, for

i^r as in

17.5 ft draft,

Some problems encountered

From

from

this curvej the ship speed at

By

calculation from

Cf and Ct values on the ,

i^„

and

full-scale

Cg

in Sec. 61.3, this requires:

SNAME RD Summary

Sheets for vessels that are identical or nearly so (c)

By

calculation from tests on standard series

models or models of similar

To draw resistance

ships.

curves of full-scale deep-water friction

and

Ai

—

on ship and through

of total resistance, based

speed, such as those through Ei

—H

Ji of Fig. 61. B, respectively, requires at

on each, and preferably five. To necessary to work from the F„ and Cr values on the SNAME Expanded Resistance Data sheets rather than from the SNAME Summary Sheets. The tables which least three spots

obtain these,

follow

it is

illustrate

the

principal

steps

in

The

(a) ,

these

calculations, as well as the derived values for each

ATTC 1947 or Schoenherr meanline has been used for calculating the friction resistance Rp at a, standard temperature of 59 deg F, 15 deg C, for standard salt water. The value of ACf is taken as 0.4(10"') in all cases. There follow four practical examples illustratstep. In all tables the

,

ing a suitable procedure for problems falling

which

the same as for deep water. Referring to Fig. 61.B

is

curves derived from tests of ship models (b)

results

having

nearly identical resistance-speed curves.

for a given resistance.

(a)

The

tion of the deep-water resistance, say

tion of the deep-water speed, say 0.99,

SNAME

for other vessels

would be about the same

a given speed Case 2b. On the condition that the shallow-water speed shall not fall below a given frac-

The

class.

resistance shall not exceed a given frac-

1.02, for

still

first

those for which

are

selected

vessels

the condition that the shallow-water

397

under the several cases of the

construction of (Rto,

—

V„) and (Rpa,

curves for deep water, such as those through Ai El -

—

— Ji

V„)

and

H

The determination

(b)

of the positions of the points Bi

and Ci for a series of selected points Ai (c) Drawing an (Rti, — Vh) curve through the Ci spots (d) Picking off the ship speed at Hi for which Rn equals Rt^ In detail, the Vi and V^ values are to be found for a series of Va, values. At each point Ai a line AiBi is to be drawn parallel to EiFi giving the ordinates of Bi and Ci .

.

,

The

and the water are first set up, and the numerical values derived from which the desired data are obtained. From the RD sheet mentioned, the maximum-section coefficient Cx of the ship is 0.9922 and the wetted surface S of the model is 87.82 ft'. The scale ratio X(lambda) of the model is 370/20.274 = basic conditions for the ship

The

ship wetted surface is thus This latter value may also be taken directly from the SNAME RD Summary Sheet listing this vessel. It is assumed that the deep-water and estuary surfaces are at sea level, where g = 32.174 ft per sec', and that both bodies are salt water at 59 deg F, where the mass density p(rho) = 1.9905 lb-sec' per ft*, and the kinematic viscosity v{n\i) = 1.2817(10"') ft' per 18.25, so that X'

is

333.06.

(87.82) (333.06) or 29,249

ft^.

sec.

The 1,111.3

times

area of the ft'.

X',

This

is

maximum

section

is

very close to the

or 3.342(333.06)

=

1,113.0

ft'.

64(17.5)0.9922

Ax

of the

The value

=

model of the

HYDRODYNAMICS

398

STEPS

1

i

Deep Woter

Calculate V;j„//SR Values Cornespondinc^

and Plot Groph af Rjm °" Mao/i^ Calculate CRfo„-V„) Values ond Plot on F?T and Veo /y^h" Scales Fix

4.

5.

6.

0.5a

Sec. 61.7

Colculote or Deten for

2.

IN SHIP DESIGN

Ag

ot Selected

V„/y^

Determine Vi/v,^ from ond Draw Ordinate for

Prow AgB;^

0.54

QSa

0.56

Fiq.

61-E

Vj/y^fi

Porollel to

0.60

Ratio

EgF^

0.6E

0,64

066

Cnticol

Fig. 61 .H

0.70

0.7Z

Ratio

0.74

0.76

0.78

Q84

03Z

0.86

088

Q90

-^-

Diagram Illustrating Construction op a Shallow- Water Resistance-Speed Curve From a Deep-Water Curve

square draft '\/Ax

is

33.34

ft,

whence \/Ax/h

calculation or from Fig. 61. D, 1.389.

clearance of 24

0.68

Wave-Speed

—

17.5

=

6.5

ft,

by-

is,

Even with a bed

the square draft

is

much

The

larger than the actual water depth.

The value of the critical-speed ratio Va,-\/gh for a speed of 13 kt, or 21.96 ft per sec, and a depth of 24 ft, is found from Fig. 61. F, or by calculation, to be 0.790. In this case a range of Vco'\/gk of 0.60 to 0.90 appears to be ample for the abscissas of the points corresponding to Ai and Ei in Fig. 61. B. Instead of using a horizontal scale of ship speed V, as in Fig. 61.B, the abscissas of the

provided the horizontal scales are consistent. The horizontal scale to be used is therefore strictly a matter of convenience, provided it is based on a velocity.

new

diagram for this case, reproduced as Fig 61.H, are plotted on a base of VatyTgh, to facilitate entry into the VjlYa> curves of Fig. 61. E. It is again pointed out that when the water depth h and the ship length L are fixed, as in this case, the Kpco and Rrm curves, whether plotted on a base of Ya, of Vm/y/gh, or of Va>/\/gL, have e.xactly the same shape, ,

first

step in the solution

is

to find the full-scale

Rrm and Rpa, for the range of values of Va>/\/gh from 0.60 through 0.90, so that the deep-water curves may be plotted. This is possible by using the ship values of

values of {IOsjCr for a series of values of F„ for the speed sheet 9 range in question, available on

SNAME ERD

These particular values apply to a geometrically similar ship of any length. The Cfl values for a range of F„ from 0.1637 to 0.2233 are set down as the first line of entries in Table 61.a. A short calculation, as listed in the upper part of that table, indicates that this range of f„ gives a range of criticalspeed ratio Vo,/Vyk of from 0.6425 to 0.8765 for the given estuary depth of 24 ft. The method of working out the friction and the total deep-water resistances Rf^o and for a 400-ft ship.

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.7

Rtoi for these spots is indicated by the successive lines of Table 61. a. Plotting these values gives the curves through

A2-K2 and through E2-F2

The next

step

is

of Fig. 61. H.

to derive the values of Yhlyfgh for

more) selected values of Vm/\/gh. These latter correspond to the five Fn's of the first line of Table

Rth

=

—

Rtcd

+

Rfoi

quicker to draw the line

corresponding segment of the friction-resistance curve (that is, for the same range of Vco/\/gh), and to mark intersection with the vertical line for

five (or

the point B2 at

may

the corresponding Vi/\/gh ratio. the ordinate of C2 and value of

61. a or,

what

is

slightly easier for plotting,

to certain

399

However, it is easier and A2B2 on the graph, parallel to the

Rft

its

The

Rn

ordinate of B2 gives

for the corresponding

principal abscissas on the diagram of Fig. 61.H. In this

point on the shallow-water curve. Through the six points

example the value of Vo:,/\/gh for the 13-kt speed happens to lie at one of these points, namely 0.790. The method of determining the values of Vh\/gh for the selected values of V^l\fg]\ is set down in Table 61. b. The Fz/Fco and Vhiyj ratios give the values of the ab-

such as C21 through C26 the shallow-water Rn-V curve drawn, remembering that the abscissas are really is

scissas Vail\/ gh for the horizontal locations of the points B2 and C2 on Fig. 61. H, corresponding to the points Bi and Ci on Fig. 61.B. Determining the ordinates of a series of points such as B2 and C2 for a series of points such as A2 enables the shallow-water total-resistance curve C21-C25 to be laid down. The value of the total resistance at the point B2 on Fig. 61. H may be derived from that at a selected point Ao

Since s/gh

by picking

off

the value

TABLE

TJ^a,

at A2 and using the formula

A

values of Vai/^/gh.

where Vai/\/gh

Vk

is

is,

(13

Ho

-

,

is

=

13-kt

Vh/\/gh

A2,

ship

of 0.643.

61. a, equal to 27.79 ft per sec,

or 17.87 ft per sec, equivalent to

the answer desired.

10.58) /13

drawn from

representing the

gives the value

from Table

(27.79) (0.643)

10.58 kt. This is

horizontal line

0.790,

is

speed, to the point

The speed reduction

2.42/13 or about 18.6 per cent.

Using the contours published by O. Schliohting [STG, TMB Transl. 56, Fig. 9, p. 11 van Lammeren, W. P. A., RPSS, 1948, Fig. 30, p. 57]_to determine the speed loss, V^/Vgh is 0.790, (V^/VghY is 0.624, and 1934, Fig. 9;

y/ Axlh

is

;

1.389.

Entering with these arguments, the

Calculation op Dbep-Watbr Resistance-Speed Data for Example 61.1, Plotted on P^g. 61.H 61. a Data marked with an asterisk (*) are taken from SNAME RD sheet 9. The value of aCj? is 0.4(10"').

F.

= F./VffL*

HYDRODYNAMICS

400

TABLE

61.b

Selected values of

IN SHIP DESIGN

Sec. 61.8

Derivation op Values op Vnly/gh From Selected Values op Critical-Speed Ratio V„/y/gh

F„/v^

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.9

the

of

friction-resistance

curve in

the

region

between Vi/'\/gh and V^/wgh it is necessary to calculate Rp for a speed somewhat higher than Vi so that the point E3 may be plotted. It is

Rp

well, in fact, to calculate

for a series of ship

401

wave-speed ratio Vi/V„ applied to the tentative deep-water speed F„ gives a ship speed V equal numerically to the intermediate speed previously determined from the potential-flow ratio, then the tentative speed F„ and the ,

,

,

V^/y/gh, are the correct

say the ones corresponding to the F„ values in the speed range under consideration on

ones. Otherwise, the process is repeated until the

SNAME ERD

intermediate speeds and the speed

speeds,

sheet

2.

This

is

done

in

Table 61.c

example set up subsequently in this secand the results are plotted in the long-dash

ratio

critical-speed

ratios

are

for the

numerically the same.

tion,

Having found the proper value of V^/'s/gh and the speed F„ erect this ordinate on Fig. 61.1; it is the one on which A3 is located. Then through B3 draw a line parallel to F3E3 meeting This is one point the V„/\/gh ordinate at A3 on the desired {Rt=, — F„) curve. The remaining points are located in the same way. With the (i^Too — F„) curve as derived in this manner there may be plotted for comparison and

hues of Fig. 61.1. The problem is now to find the speed V„ for which the intermediate speed V i is the correct one for the specified depth. It is known, first, that Foo is definitely greater but probably not also that the value too much larger than Vj ;

V^/'Vgh same

the

is

greater than

of Fig. 61. E with the

value of

Vi/y/gh by

F„ and a

known

ratio of

ratio

V i/V„

at a value of 'V„/'\/~gh

trial

exactly

Entering the theoretical curve

ratio.

numerically than the given 0.55

Vj/'Vgh, a

are selected for

somewhat

F^/V^. 0.56

0.57

larger If

,

,

.

reference the deep-water resistance-speed curve

model

as predicted from

from standard

the

of this case follows.

0.58

0.59

060

tests or as calculated

series or other data.

0.61

0.62

0.63

0.64

An example 0.65

0.6 6

I

STEPS 1.

From Observed Data Plot (Rjh-Vh) Curve

2.

For Q Selected Value ofVh, Calculate Vh/V^

3.

With

Vf^/Vj Ratio

ed from

picl<-

Fig. 61. G, Det-

ermine Vj/-yQh 4.

From Point C3 Draw Horizontol Line to B3

5. For

Voo/y^ Value

Slightly Greoter thon

at Bj, Determine

^l/X» Ratio and Tentative Vooyfj^ from Fio ).

Frorn Tentative ""f

M»/v^

'^i"'^

esponding Volue

Volue Corrof

Vj/Vjo ond Check for

Aoreement with Vi/Ygh Ratio at B3 :

When

Correct Vo<,/VqTi

Known, Draw B3A3 Parallel to F3E3. Determine Aji.etc. in Some Manner and Draw (Rtoq-Voo)' is

Scale for Ship Speed Vh FiG.'^ei.I

in

Depth h Mo'y Be Added Here

CoNSTBUCTioN OF A Deep-Wateb Resistance-Speed Cubve Fbom a

Known Shallow-Watbb Cubve

HYDRODYNAMICS

402

TABLE The data marked with

V/VgZ

or Froude

61.C

asterisks (*) are

number F„*

IN SHIP DESIGN

Calculation of Ship Friction Resistance For Case from

SNAME RD

sheet 2.

Sec. 61.9 l.c

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.10

TABLE

61.d

Calculation of

Selected Vh for ship

Two

Spots on Deep-Water Speed-Resistance Curve from Water Speed-Resistance Curve

403

Known Shallow-

HYDRODYNAMICS

404

IN SHIP DESIGN

Sec. 61.11

0.55 oafl-

0.50

° 040

0.99

-n

8

0.35

0.995 ^

5 025 998

E

Speed Reduction

for

ABC 5hip

175 feet of

in

^ e 0.20

;§

0999 " § 0.15

^ 0.10

To Find ApproKimate Speed

Reduction

Enter Dioqrom with Values

of

and Voo/V^h^

Qfid

Interpolate

^/^/h Between Contours

0.05

Ami 0.4

0.1

Wave-Speed

CrilicQl

V

Ratio

Intermediote- Speed

Ratio

rj^

0995

0,999

0.99

QS

^00

Fig. 61.J

Geaphs for Determining the Limiting Water Depths for Various Small Speed Reductions

reductions of

1.0,

0.5,

and

0.2,

per cent,

0.1

respectively.

While the statement of this example, and of others in this chapter, gives the impression of the principal straining at small quantities, purpose of the example is to illustrate the method. A secondary purpose is to carry the calculations to a limit beyond which they would probably never go in practice. From the 2 per cent curve of Fig. 61. J

At

the

liigher

critical-speed

region

DE, only

both

ratios,

Example 61.11 1.

To show how

ABC

this family of

graphs

ship designed in Part

VH-

is

ft

=

this

F„ = O.iVgh =

speed ft

limiting

42.6/0.393

depth the critical-speed ratio can not represented by the point N. The limiting ship

For

exceed 0.4,

The

0.393.

= \/I^/0.393 =

[32.174(108.4)]''-'^

0.4

=

23.62

equivalent to 13.98 kt. Water deeper than 108.4 must therefore be found in order to run a valid sea

per

trial

sec,

at 20.5 kt.

Assume that a tentatively is

region having a depth h of 175 ft

selected.

then 42.6/175

The

=

square-draft

to

is

water-depth

0.243 and the critical-speed ratio

[(20.5)(1.6889)l/\/32.174(175) = 0.461. Entering Fig. 61. J with these values a point is found (marked by the distinctive circle) at which the predicted speed reduction

is

is

only about 0.3 per cent. This

cent limit.

The

175-ft depth

is

is

well within the 1 per

therefore adequate.

Sec. 61.6, involving a determination of the limiting

The

is

4,

which Ax is 1,815 ft^ depth at which the ship can run slowly, with a reduction of only 1 per cent in speed, is found from the value of for

and

ft.

namely

61. J,

of

effect in diminishing the speed.

used, take the case of the

108.4

on Fig.

both have an

F„/ 'vgh

At greater values

BCD,

therefore h

ratios,

0.1, in the

the critical-speed ratio

in the region

M

is

Cases 2a and 2b: To Find the Limiting 61.11 Depth for a 2 Per Cent Increase in Resistance. Turning to Cases 2a and 2b of the second class of

but at values of \/^A^/h below about affects the speed reduction.

at

depth h

ratio it

appears that at critical-speed ratios V^/'Vgh below 0.4, in the region AB, only the square-draft to water-depth ratio -VAx/h influences the speed reduction.

VAi/h

42.6

ft.

limiting

depth of unrestricted shallow water in which the resistance for a given speed is increased by say 2 per cent, or at which the speed for a given resistance is diminished by say 1 per cent, a simplified and approximate procedure is again justified. Water depths in navigable waters are

PREDICTED BEHAVIOR IN CONFINED WATERS

Snc. 61.11

almost never uniform, so that when a limiting depth is determined, someone must decide whether it is to be looked upon as a mean or as a

minimum

depth.

For slow and intermediate-speed ships of normal or full form, having a relatively large maximum-section area, the limiting depth h is almost certain to be large enough to make the limiting critical-speed ratio V^/'vgh, as well as the ratio \/ Ax/h, rather small, as they are in

HK

the region

of Fig.

61. J.

Indeed, the

first

be so small as to make the wave-speed

may

F;/F„

ratio

practically

unity;

the

see

example following. On the other hand,

first

for a fine,

fast ship running at higher critical-speed ratios,

the depth h

is

so great in proportion to the square

draft '\/~Ax that the value of the potential-flow

Vh/Vi may be

ratio

region

FG

following.

practically 1.00, as in the

of Fig. 61. J; see the second

The

example

V,/V„ then becomes

ratio

the

sole factor in determining the depth.

The approximate method

described here gives

quickly the limiting depth of unrestricted shallow water in which a ship must run to insure that its

shallow-water

resistance

total

Rth

does

not

deep-water total resistance The basis of this method is that the resisti^T-oo ance varies as a certain but undetermined power of the speed in any narrow speed range or exceed 1.02 times

its

.

—

—

at any selected speed.

Critical-Speed f?Qtio

0.538

0.400 0.515

As a rough average

Voo/Vqh, where Voq

Is

it

may

be assumed that

R

=

405

kV^, in which case

dR

=

2kV{dV). For any small range in which k and V may be assumed constant, a 2 per cent increase in resistance is therefore reflected by a 1 per cent increase in speed. This

ment that

is

the basis for the state-

at the limiting depth the shallow-water

speed Fa shall be not less than 0.99 times the deep-water speed F„ for the given deep-water resistance Rto,

.

Since the speed reduction

may

be due to a

decreased Velox-wave speed or to augmented potential flow around the ship both factors

be considered. As the

must

depends upon the critical-speed ratio V„/-vgh and the second upon the square-draft to water-depth ratio 'VAx/h, they can not easily be put upon a conunon basis except to say that for any given conditions the value of h to be determined must first

be the same for both. The speed reduction due to either factor manifestly can not exceed 0.01. From Fig. 61.E the value of the critical-speed ratio V^c/vgh can not exceed 0.658, for which F//F„ = 0.99. From Fig. 61.G the square-draft to water-depth ratio a/aI/Zi can not exceed 0.393, where VJVi = 0.99. Below a critical-speed ratio of 0.40 the intermediate speed Vi is practically equal to the deepwater speed F„ so that this part of the theoretical curve need not be considered. Below a squaredraft to water-depth ratio of 0.1 the shallow-water

Wave Speed m Deep Woter and

CQ_='^fqii

is Critical

5peed

0.642 0.652 0.658 0.586 0.602 0.614 0&Z4 0.634 0577 0.595 0.608 0.619 0.629 0.638 0.647 0655

0.567

0555

0.993 Vj

0.386 0.393

Fig. 61.

K

0378

0.353 0334 Q3I3 0291 0265 0235 0199 0.138 0.323 0.278 0.251 Q2I8 QI75 0.000 0.36Z 0344 0302 Square- Draft to Depth Ratio ''{K^/h, where h is Shallow-Water Depth

0370

Diaqrajh for Determining the Limiting

Water Depth for a Speed Reduction op

1

Per Cent

HYDRODYNAMICS

406

speed

V

practically equal to the intermediate

is

T',,

In the ranges of critical-speed ratio and square-draft to water-depth ratio between those mentioned the sum of the speed reductions due to both causes can not exceed 0.01 for the depth to be determined. This is on the basis that for small values of these differences, not exceeding 0.01, they may be determined accurately either by addition of the differences or by multiphcation of the corresponding speed ratios. For example, speed

I

-

extreme

=

0.9801 while {1.0

0.99)11

Fig. 61.

=

-

[(1.00

-

0.99)

At the 61.K, where Vh/Vt = 0.990, the water-depth ratio s/Ax/h is 0.393,

square-draft

to

whence the Hmiting depth h is 40.00/0.393 = 101.8 ft. Assuming on the other hand that all the speed reduction is due to wave effect, for an intermediate-speed ratio Vi/Va, of 0.990 the critical-speed ratio

F„

=

further developed,

+

The values

of

left

each are taken

from the theoretical and experimental curves of Figs. 61.E and 61. G for a critical-speed ratio of 0.602 (top scale) and a square-draft to waterdepth ratio of 0.323 (bottom scale). The method of using the diagram is explained in the examples which follow. The nomograms of Figs. 61. D and 61. F may be entered for ready determination of the values y/Ax/h and V^/ 'vgh, or these values may be calculated, as in Examples 61. IV, 61.V, and 61.VI. To take care of the situation on low-speed and high-speed ships, where the total resistance may vary at less or more than the square of the speed, additional diagrams of this type may be constructed from the data on Figs. 61. E and 61. G,

Fig. 61. K, the limiting depth

whereas the

common

that value and 20.5 is

or less than 0.99.

Va,/Vgh =

ft.

It

is

=

it

may

be smaller

end of the diagram. For a value

VI

285.27 (0.16)(32.174)

of

=

55.4

ft.

fact that it is not possible, within the limits of the diagram, to achieve a common value for h indicates that

the potential-flow effect

wave-speed 101.8

effect

is

the determining one while the

is

zero.

The

required depth

For the 20-kt speed assume, as a

A

is

therefore

ft.

starter, that the point

represents the operating condition. Here the square-

draft to water-depth ratio

mined from that

ratio

is

is

responding critical-speed ratio derived from

h

=

123.8

ft.

The

cor-

0.602 and the depth

is

(33.78)'

{0.&02yg It is

=

it is

F

=

and the depth deter-

0.323,

40/0.323

=

98.4

ft.

(0.36)(32.174)

obvious that the

first

depth

is

slightly too large

and

that the square-draft to water-depth ratio should therefore

be larger than 0.323. Assume a value of 0.362, at the point B. This gives a depth h of 40/0.362 = 110.5 ft. The corresponding critical-speed ratio of 0.567 gives a depth of (33.78)'

110.3

ft.

(0.567)V of the position of

B was

so that no further computation

is

excellent in this case,

necessary.

For the 30-kt speed, assume the point C where the square-draft to water-depth ratio is 0.199 and the criticalspeed ratio is 0.647. Then h = 40/0.199 = 201.0 ft, and

^^

= ?7r?^ = (0.647) g

Making another

of 10 kt

assume

first

that the

190-6

ft.

calculation for the point D, where the

square-draft to water-depth ratio limiting depth h of 40/0.209

5.672.

For the lowest speed

critical-speed ratio Va:,/\/gh

(O.-ifg

=

h

left

ft,

somewhere between

is

desired to find the limiting

depth of water, at sea level, in which the resistance does not exceed 1.02 times the deep-water resistance at speeds of 10, 20, and 30 let. These speeds are equivalent to 16.89, 33.78, and 50.67 ft per sec, respectively; g = 32.174 ft

^/g

The

the diagram of

0.4,

The estimate

For the sake of simplicity, since only the deep-water speed and the square-draft enter into the problem, it is assumed that the vessel selected for this example has a maximum-section area of 1,600 ft', with a Exainple 61. IV.

value for h

ft.

than the

ratio less

left of

greater than 101.8

is

therefore smaller than 0.658. In fact,

for overall speed ratios correspondingly greater

square draft of 40.00

ft.

lowest value 0.393 at the extreme

The

left-hand scale.

20.5

For any square-draft to water-depth

responding to the right-hand scale, while AH is that due to potential flow, corresponding to the

sec2,

(0.433)(32.174)

=

than 0.400, at the

At and beyond the

Then

T„

until

end of the diagram the speed reduction of 0.01 is assumed to be due entirely to augmented potential flow while at and beyond the right end it is due entirely to reduced wave speed in the shallow water. Between the ends both effects occur, and they are additive, as for EA + AH = EH. Here EA is the speed reduction due to wave speed, corprocedure.

0.658.

(16.889)'

=

h

involves a trial-and-error

it

is

=

0.658 Vfif

(O.QdSyg Unfortunately,

/r \//i .

whence

0.658,

0.9800.

depth.

limiting

Vo,/Vgh

,

K is a diagram for use in calculating the

required

per

Sec. 61.11

of Fig.

left

.

0.99(0.99) (1.00

IN SHIP DESIGN

potential-flow effect limits the depth of water.

=

speed ratio of 0.645, the depth

is

191.4 is

about 0.209, gives a Using the critical-

ft.

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.12

=

/.

^^^=

191.8

h

ft.

The 192

limiting depth required

is

2,921.4

= (0.567)'^

(0.645) g

therefore approximately

407

=

282.4

ft.

(0.3215)(32.174)

These two values of h are close enough so that the two may be assumed as the limiting one. it might be well to set the minimum depth as 290 ft. larger of the

ft.

In this case

To determine

the limiting depth at which the

shallow-water effects become negligible, for practical purposes,

it

may

all

be assumed that this

depth corresponds to a condition where the shallow-water resistance does not exceed 1.005 of the deep-water resistance. As the resistance may again be assumed, for a first approximation, to vary between the square and the cube of the

an increase in resistance of 0.005 corresponds to an increase in speed of the order of about 0.002. Similarly, limiting the resistance in shallow water to that encountered in deep ship's speed,

Example 6 l.V I. At the opposite extreme, assume a motorboat having a maximum section area Ax of 6.25 ft", running at 9.5 kt, or 16.05 ft per sec. What is the limiting depth of unrestricted shallow water in which the speed with a given deep-water resistance does not drop below 0.998Fco ? The value of g is taken as 32.174 ft per sec". As a starter, consider that the overall velocity ratio Fft/Fco

=

arbitrary but with a

rather closely.

VJVi

and the 7//7„

ratios is to exceed 0.998, the values of

both ratios

of the

61.

W

less

Ax/h must be shows that the value of than about 0.218, regardless of the size of

the ship. Furthermore, the percentage of critical velocity

must be

speed. This

is

less

than 0.567, regardless of the

equivalent to shrinking the diagram

K to the point where the vertical limits on both end scales are 0.998 and 1.000. Two values of the limiting depth h are first derived from the two relationships given. If they are not nearly the same the depth h is determined by trial and error as before.

Vh/Vr ratio \/ Axlh

of is

V6.25 =

21.7

ft.

0.115

0.115

For a Vi/Vcc, ratio of 0.9982, the critical-speed ratio Vaily/ gh from Fig. 61. K is 0.563. Again transposing.

hn

I

K

Fig. 61. K, at a

VAx

K

close to 1.000.

VJV

experience they can be estimated

0.115. Hence, transposing.

Assuming that the value speed ratio must exceed 0.998, examination of the corresponding curves of Fig.

must be

little

Then from

0.9997, the square-draft to water-depth ratio

water involves a speed reduction to the order of 0.998 y„ in the shallow water whose depth is to be determined. If the product of the

is made up of the two ratios Vh/Vi = Vj/V^ = 0.9982. These values are admittedly

0.998

0.9997 and

Yl

(16.05)'

fir(0.563)'

(32.174)(0.563)'

=

The

potential-flow effect

is

draft to water-depth ratio

=

25.3

ft.

so small here that the squareis

somewhat indeterminate.

apparent that, because of the greater depth required to produce the assumed wave-speed ratio, the latter factor is also the determining one in this case. The minimum depth is therefore of the order of 25 or 26 ft. Nevertheless,

of Fig. 61.

61.12

D.

it is

W. Taylor's Criterion for

the Limiting

Depth of Water for Ship Trials. A simple formula is given by D. W. Taylor for the minimum depth involving "no increase of resistance" of water [S and P, 1943, p. 79]. This is the dimensional In,

Minimum depth = 10 (draft //) (F/a/L), where the depth h, the draft U, and the length L are in ft, and the speed V is in

expression:

Example 61.V. from

SNAME RD

The data sheet 39;

example are taken model 3796. A liner of

for this

TMB

62,660 tons displacement, 962 ft long

by

117.8 ft

beam

having a Cx of 0.981, is expected to by run at a speed of 32 kt. What is the limiting depth of unrestricted shallow water in which the speed with a given deep-water resistance does not drop below 0.998 Fa> ? No account is taken of other ship-performance factors 34.39

ft draft,

kt.

Taylor gives the following limitations for this

formula: "1.

abnormal form or proportions up Cg of 0.65 For speeds for which V /\/l is not greater than 0.9 The formula may be of use beyond the limits indicated

To

vessels not of

to a block coefficient 2.

such as possible vibration.

3.

The maximum-section area Ax of the ship is 117.8 (34.39)0.981 = 3,974 ft^. The square draft VaI is 63.03 ft. The speed of 32 kt is equivalent to 54.05 ft per sec. The value of g is taken as 32.174 ft per sec^.

above, but in such cases

the potential-flow criterion alone (point F on Fig. 61. K), the ratio y/Ax/h is 0.218 and the limiting depth is 63.03/0.218 = 289.1 ft.

By

By

the critical-speed criterion alone (point B on Fig. V^iy/gh is 0.567 and the limiting

61. K), the value of

depth

is

(it)

needs to be applied with

caution and discretion."

Despite these limits, expressly stated, this formula has been used rather widely for estimating minimum depths of water in which to conduct ship trials.

Taylor's formula as

it

stands

is

not consistent

dimensionally, for the reasons given in Appendix

HYDRODYNAMICS

408 2 of

Volume I. It can be made by substituting 3.367F„

so,

for

there,

quotient

F/VX,

whereupon

/iMin

Applying

=

the Taylor

becomes (61. ii)

33.67(/0Fn

H

is

34.39

ft

and the Froude

at the designed speed of 32 kt

is

54.05/ V32. 174(962) = 0.307, the predicted value of /iMin = 33.67(34.39) (0.307) = 355.5 ft.

This

is

for a

61.11,

compared to a limiting depth

of

290

ft

ARr„ of 0.4 per cent, as derived in Sec. Example 61.V. Taylor's formula is there-

fore conservative or perhaps on the safe side.

Sec. 61.13

the effect of shallow water on ship speed and

somewhat making the

resistance in the subcritical range are tedious,

formula to the liner of Example

this

61.V, where the draft

number F„

it

as explained

IN SHIP DESIGN

and are not well suited

to

on-the-spot estimates often required. Furthermore, they give no indication, not even approximate, as to what may be expected in the supercritical range,

which

may

easily be reached

under

certain conditions in practice.

A

means

of

making predictions

as to relative

speeds and resistances in shallow and deep water by inspection serves a certain purpose in design procedure, although it is admittedly neither adequate, accurate, or reliable. The simplified procedure of Sec. 61.10 and Fig. 61. J could be

Inspection.

extended to cover speed reductions from 2 per cent up to 5 per cent, and possibly up to 10 per

61.5 through 61.11 for determining quantitatively

cent, provided the differences

61.13

Predicted Shallow-Water Resistance by The procedures described in Sees.

between the shallow-

Contours Are Ratios of Indicated Power Indicated Fbwer

Pi in

Shallow Water

F] in

Deep Water

Region of Greatly

Augmented

Power

^. 0.294-

±=(=

/LOO ^'t.O 1

1

;

.1.5^

^'1.25

^^z&^

III Reqion of IReduced Power, Less ,than in Deep

i.oa •'..^•695

IZS,-

^^0.110

Water

—" Pi(5hallow)

Line for Equal

and Equal

^ p^^p^ Ji2

Ship Speed

V

|SolitaryWave Speed Vqh"

03 4.0

0.4

0.5

0.6

PREDICIED BEH/WIOR IN CONFINED WATERS

Sec. 61.14

water and deep-water total resistances at points such as C, and A, on Fig. 61. B could be neglected. For estimates of the change in total resistance

Duct

Closed b

--

same speed, when moving from deep to is considerably more difficult, since the answer depends upon the slopes

/

'^

shallow water, the problem

Rr

on

V

Hydraulic Rodius bh R

"-,

at the

of the graphs of

409

1.

in the region being

Open

Channel

investigated.

Because of the lack of

reliable

methods

for

transforming increased total resistance in shallow

water to terms of increased power, discussed in Sec. 61.16 following, there is some merit in a prediction method by inspection which endeavors

power directly. Even though a ship is rarely pushed in shallow water to speeds which would be considered normal if the water were deep, it is helpful to know approximately how much power would be required under

Shollow Water of Unlimited

Extent

="^

Rh'H

to predict the increased

^\^^^^\W\^^\"^\\^\\\" Sh|p

bh-Ax

W

A graph suitable for such a purpose is the partial diagram at the top of Fig. 61.L, having contours of the ratio (shallow-water power) /(deep-water power) plotted on appropriate arguments. Follow-

Channel with 5emi -Circular Cross 5ection

y^

by 0. Schlichting, these are y/Ax/h and V/y/gh, where F is a given speed, in either deep or shallow water, and "Vgh is the solitary-wave speed in water of

<^^?x.

•

"

Rh =

—^=0.5Rr

0.5rrR(?

h.

The contours

in Fig.

61.L are indicated as

tentative, since they are derived

from isolated

data observed on one series of ship

trials,

the

4-

n\\\\\\\1o:\\\\\\\V

ing the procedure developed

depth

b+2h+G

H

these circumstances.

German torpedoboat

of Sec. 61.22.

in Fig.

61. A.

They

M

Definition Sketches for Hydraulic

Radius

that of

S119', see reference (4)

These data are recorded graphically

diagram of Fig.

Fig. 61.

are reduced, in the lower

Ax has to be estimated, SI 19. Available data from

of these cases the value oi

was done model tests

as

for the

by the method

of

analysis

described, out of line with the ship data

and with

are,

graphs indicating the ratios of indicated power Pj in shallow water to Pj in deep water, for four depths of shallow water,

each other. It seems clear at this stage (1956) that all the pertinent variables in the confined-

on a basis of the ratio V/'S/gh, the same as for the upper diagram in that figure. It is assumed for this reduction that a depth of water h equal

water situation have not been taken into account. 61.14 Calculating and Using the Hydraulic Radius of Channels. As is explained presently,

to

0.951L,

61. L, to

indicated

in

Fig.

61. A,

represents

deep water. It is further assumed that the prismatic coefficient Cp of this vessel is 0.64, from which Ax is calculated to be 45.5 ft^ and is 6.75 ft. The four graphs of the lower diagram

predictions of the effect of the sides of channels

characteristic

and the bed

make use of channel dimension known as

upon ship

resistance

the the

vAx

hydraulic radius, rather than the water depth h

of Fig. 61. L therefore represent indicated-power

used for shallow-water predictions. For a closed duct with no solid body inside it this is the ratio,

ratios at

and

Va^/K

values of 0.110, 0.137, 0.206,

0.294.

Reduction of full-scale ship data in similar fashion, from the references of Sec. 61.22, gives contours which are extremely difficult, if not impossible to reconcile with those of Fig. 61. L, so much so that they are not included here. In most

described in Sec. 18.11, of the transverse duct or flow area to the wetted perimeter of the duct.

where and Rh has the dimensions of a length. An open channel with no ship in it, as in diagram 2, has wetted perimeter on only the bottom and the This situation h, h,

is

depicted at

and Rn are aU drawn

1

in Fig. 61. M,

to the

same

scale,

HYDRODYNAMICS

410

two sides. With the same water area as the duct, its Rh'is, larger. For an open channel with a ship, as at

4,

Rh is the ratio

of (1) the cross-section area

of the water in the channel to (2) the wetted

perimeter of the solid boundaries of both channel ship. In shallow water of infinite width,

and

—*

when 6 and the

CO,

the depth

h,

the ship girth G,

become

ship section area ^4^

negligible

with respect to the water-area and width factors. The hydraulic radius Rh then becomes equal to the depth

is

bed

large

under

clearance

other effects to take account of

b is large

bh b

+

+G

2h

compared to

=

bh -r-

other factors

=

largest

(and

is

them quantita-

tively at the present time.

61.15

Estimating the Effect of Lateral Restric-

Water

Since the speed of a

Rh =

the

towed in it. Since more of the water goes under the bottom of a model with a large B/H ratio than with a small one, the effect of small bed clearance becomes greater as the B/H ratio increases. Unfortunately, not enough is known of these and

tions in Shallow

expressed in symbols as:

Sec. 61.15

widest) flat-bottomed model that

as at 3 in the figure. For a rectangular

h,

canal this

IN SHIP DESIGN

serves as such, apparently because of the very

in the Subcritical

wave

Range.

of translation in a

depends only on the depth of appears plausible to assume that

restricted channel

h

,„,

the channel, ...,

(61.111)

it

O. Schlichting's theoretical assumption concern-

ing the equality of pressure resistance due to

Assuming a waterway with horizontal bottom and vertical sides, not occupied by a ship, the hydraulic radius in the following

Width

Rh

in

6 in

is

related to the water depth h

manner:

wavemaking

at the speed

assumption of SchUchting concerning the speed correction due to the potential flow around the

50

terms of h

0.60

0.33

terms of h

For open

F„ and V, remains The second

valid for these restricted channels.

channels

of

non-rectangular

and

0.909

0.833

0.962

0.990

ship hull requires modification to take account of

irregular sections, with ships in them, the hy-

the width of the channel.

The

by exactly the same procedure, governed by the same rule. Example

oped by L. Landweber

[TMB

draulic radii are determined

61. VII, in the next section, illustrates the

Studies

made

method.

in connection with the prepara-

tion of Fig. 61. L,

combined with analyses under-

taken (in 1956) subsequent to those reported in the remaining sections of this chapter, indicate rather definitely that shallow-water effects cannot be correlated on the basi s of the single "transverse" parameter 'VAx/h, nor can confinedwater effects be correlated solely on a basis of

V Ax/Rh-

This applies particularly to effects

associated with the potential-flow ratio of Sec. 61.5,

between the shallow-water speed Vh and

the Schlichting intermediate speed Vi Analyses of the blocking effect of model basins upon the .

ship models towed in interference

effects

are

them

indicate that the

negligible

even when,

because of the limited width of the basin, the hydraulic radius of its section is not much more

than half of

its

actual depth.

By

this criterion, the

is by no means the equivalent of unlimited deep water of the same depth. Nevertheless, it

basin

200

100

1939,

p.

relationship devel-

Rep. 460,

May

involves, instead of the depth of

10]

water h as before, the hydraulic radius. The necessity for taking full account of the lateral restrictions is emphasized by the following

comments, quoted from a discussion by F. Rayner on page 114 of a paper by A. F. Yarrow fINA, 1903]: one of the greatest difficulties in towing on inland is the friction between the boats and the sides and bottom of the water way. I have myself seen, on some of the narrow canals, steam barges almost stationary when going through what are called, in canal language, "bridge holes," where you get the minimum width, and consequently enormous friction; as soon as the boat gets away from the bridge, she shoots ahead." ".

.

.

waters

The

ratio

-vAx/h,

relating the square draft

water depth, then becomes \/Ax/Rh relating the square draft to the hydrauUc radius. to the

The

fact that

cited,

,

Landweber used,

in the reference

a value twice as large as that defined here

was compensated

for

by

his use of a factor 2 in

the ratio of square draft to hydraulic radius.

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.16

When

the substitution of

A

channels.

for h is

made, the

Vh /Vi for confined waters

potential-flow ratio

becomes a function

Ru

of

y/ Ax/Rh

for the restricted

procedure corresponding exactly to

method described in Sec. 61.5 can then be employed. This means that Fig. 61. serves for making the numerical calculations as the Schlichting

provided the user remembers that the upper scale is a square-draft to hydraulic-radius before,

come into the picture, nor is it necessary to construct any deep-water and restricted-channel resistance curves. Entering the extrapolated broken-line portion of the curve of Fig. 61. G for a square-draft to hydraulic-radius ratio of 1.67, the value of the potential-flow ratio is

0.783. Since

From

the theoretical curves of Fig. 61.E and

F/

=

0.783(13.51)

=

=

Vh

Va> in this case,

Vk/Vi

0.783Fco

10.6 ft per sec or 6.28 kt. This

= the

is

required speed.

It

ratio.

411

potential flow. Since the points corresponding to Ai and Bi of Fig. 61. B coincide, the friction resistance does not

that

is

pointed out in Eq.

(61.iii)

when the channel width

b

of Sec. 61.14

becomes large

in

when a

the experimental curves of Fig. 61. G the speed

proportion to the channel depth

and the

resistance of a ship in a restricted channel can then be computed when its deep-water speed

shallow river Avidens into a shallow estuary, the

known. The procedure to be followed is the same as for computing shallowwater resistance; several examples follow.

radius drops out, leaving simply the quotient

and

resistance are

Take the case of the 370-ft shallowwater ship of Example 61.1 preceding, moving in the channel depicted at 1 in Fig. 61.N. The essential model and ship data are given on SNAME RD sheet 9, covering Exam-pie 61.VII.

TMB

model 3818. What would be the actual ship speed

at a resistance equal to that for 8 kt in deep water? ship has a

maximum

section area

Ax

The

and the

of 1,111.3 ft^

water is at sea level, with a temperature of 80 deg F. The value of the square draft y/Ax is 33.34 ft. The value of g

is

32.174

The

per

ft

sec^.

section area of the water around the ship, using

the values in diagram

=

1

of the figure,

[(250)(35)]

+

+

is

term 2h hh/b,

in

the

expression

h,

as

hydrauhc

the

for

whereupon the hydraulic radius Ru becomes

equal to the depth

h.

The question now

what

arises,

unrestricted shallow water? This

is

constitutes difficult

to

answer explicitly because it depends upon the maximum-section area of the ship being considered with the water and upon the square-draft to hydraulic-radius ratio. Put i n a nother way, '\/

the effect of using the ratio

Ax/Rh

instead

vA^/Zi, where is the restrictedwater depth, depends to some extent upon the of the ratio

In,

position of the ratio point along the graph of

At small values

Fig. 61. G.

toward the

of the ratio

vAxA,

end of the diagram, the potentialflow speed ratio F^/F/ changes very little with change in water depth. In any case, one or two

(35)^

2 35^ 1,111.3

[(.o.e)(f)]

left

calculations involving the hydraulic radius, along

Example 61. VII, should clear up the matter readily. When the channel width becomes from 100 to 200 times the depth, the table in Sec. 61.14 indicates that the restricted channel the lines of

= The wetted

P =

250

9,311.7

perimeter, including that of the ship,

+

467.5

is

has become the practical equivalent of open,

35 cosec (45 deg)

+ =

ft'

35 cosec (30 deg)

+

then 9,311.7/467.5 = 19.92 ft, only a little more than half the channel depth. The ratio is 33.34/19.92 or 1.67. Va^/Rh The equivalent "rectangular" depth Aeq of the channel is

radius

is

the section area without the ship, divided by the surface l,111.3)/(250 35 -|- 60.6) =

width, or (9,311.7

61.16

+

+

10,423/345.6 = 30.16 ft. The value of Vao is 8 kt or 13.51

ft

per

sec.

Then

0.43. •v/32. 174(30. 16) theoretical curve of Fig. 61.E, the correspond-

ing value of the intermediate speed ratio Vj/Va, is 1.00 and Vi = Va, Hence all the speed reduction is due to .

of Reliable

Data on Power and

method has yet been developed

No satisfactory for estimating

the increase in shaft or propeller power,

the

change in rate of propulsion-device rotation, or the variations in other propulsion factors due to shallow and restricted waters. E. A. Wright touches briefly on these matters [SNAME, 1946, Fig.

10,

p.

381].

The present

unsatisfactory

due partly to the limitations imposed by various kinds of propelling machinery on the combinations of rotational speeds, torques, and powers developed by them. The usual shipperformance data are rarely of much help because, situation

13.51

From the

Lack

Propulsion-Device Performance.

ft.

The hydraulic

unlimited shallow water.

is

for example,

the throttle setting

may

be held

HYDRODYNAMICS

412 Width

345.6

Wate

of

Sorfoce

A^-

IHI 3 ft^

^ /%- 33,34

ft

Wetted Girth 98

I

ft

fl (opprox.)

U-eo.eftU—

Shown

Wetted Perimeter

is

Hvdrovilic Radius

Ku"

'

in

Net Area

of

,

—

—

Water Seotion (less Ax) TTT of Ship

—

Sec. 61.17

—

—

Heavy Lines

: o ^, f TT Trzi Perimeter, Includino that Watted .,,

IN SHIP DESIGN

whatever improved performance he can from the ship ui deeper and more open water. When the ship speed is reduced because of the diminished velocity of the Velox-wave system in shallow water, the speed of the ship through the surrounding water in other words, its relative speed is correspondingly reduced because the water stands still, generally speaking, while the wave moves by. This is the reason why the friction resistance is reduced when the ship slows from its deep-water speed to its intermediate speed. The ship resistance Rt is reduced by this decrement in Rp represented by the ordinate MBi in Fig. 61. B, but not by as much as it would be for a corresponding speed reduction in deep water. Thus point Bj in the figure is higher than point L. For the mtermediate speed F/ therefore, the shallow- water power, RrhiVi), is greater than it would be for the same speed in deep water. The rate of rotation drops by a ratio somewhat greater than Vj/V^ assuming the wake fraction w constant, because of the greater resistance that must be overcome and the greater thrust to be developed. Furthermore, as the thrust loading at point Bj is greater than it would be at point L, the propeller efficiency drops slightly, still further increasing the power ,

ForDeterminincj

^^^^ Vj/y^ Vo„/y^,

of Non-Uniform Depth, E
Use the

ond

V^/y^

Etjuivolent

i

Depth hgg

,

to (Water-Section Area)/(WQter Surface Width)'

Offset from Centerlii

,

l^pical

Suez Lonol

Profile of j

R.

About 1950 as Given

Brand, "Moneuverinfj of Ships." 3NAME, with Larqe Ship in Offset Position

1951.

b>y

Fici.lO, p. 241,

at the point L.

As the ship speed diminishes from the intermediate value Vr to the shallow-water value V^ with no change in total resistance, the effective power P E diminishes, as do the thrust T and the unless the augmented speed of advance V a backflow occurs in a region occupied by the propulsion device(s). From here on, the data are ,

,

the Sho

Water Basin at the David Ta-^lor Model Basin, for which the H-ydraulic. Radius Appreciably Less Thon the Water Depth h T^picol Test Condition

in

I

low-

is

Explanatory and Illustrative Sketches FOR Equivalent Depths and Hydraulic Radii op Restricted Channels

Fig. 61.N

constant and

all other

variables allowed to change.

The water depths may

fluctuate

widely with

scanty and the analysis

At a

is

nearly nonexistent.

low value of V^/'s/gJi; the ship speed is reduced solely because of the ratio \/ Ax/h. The speed drops from F„ to V^ but the resistance remains the same. All the water ahead of the ship has to get around astern, it must flow backward in this process, and the backward sufficiently

much

ship location in the shallow area or along the

flow

channel; the resistances and perhaps the speeds

thus has to

is

faster close to the ship.

move

against

The

what amounts

ship to a

fluctuate with them.

contrary current in the channel, so that the lost

Unless a ship is designed for special service in confined waters, only rarely does it have any

of speed

great reserve of power to match the increase in resistance in the shallower channel depths and narrower widths, assuming that it is advisable or permissible to maintain the deep-water speed. If it is so designed, the limiting conditions

become

the basis of the design, and the operator gets

is

equal to the effective velocity of this

counter current. Assuming that the ship moves through the water close around it with the same relative speed, the shaft

power and rate

of rota-

tion of the propulsion device (s) should remain

same as at the speed V„

in

Data on Confined-Water Operation

at

substantially the

deep water. 61.17

PRF.niCTEn BEHAVIOR IN CONFINED

Sec. 61.19

413

some

of

the references of Sec. 61.22.

Dimensions on this Diatjram Are in Meters

All

N

WATERS

Similar data are to be found in

p. 396].

Data on Offset Running Positions and

61.18

Steering in a Channel.

Few

tive data are available

on the

published quantitaoffset

running of a

ship between canal walls, or alongside a single wall, as depicted in Figs.

18.

G

and

18.

H

and

described in the accompanying text of Sees. 18.5

and 18.6 of Volume I; see also Fig. 61.0. The two outstanding sources appear to be:

Yowinq Moment N Acting to 5wi no

Bow Away From Near Bonk

(1)

Garthune, R. S., Rosenberg, B., Cafiero, D., and Olson, C. R., "The Performance of Model Ships in Restricted Channels in Relation to the Design of a Ship Canal," Report 601, August 1948.

TMB

\ Loterol

Force

Section 4 of this report covers the behavior of models in central and offset positions, in varied depths of

NActinq Away From' Near Bonk

channel, both towed and self-propelled,

and with

During many of these tests the ship model was stationary in a current of moving water. Yawing moments, lateral forces, and rudder angles to maintain equilibrium conditions are given in terms of the other variables. different rudder angles.

Offset From

Centerline of

Conal

(2)

Brard, R., "Maneuvering of Ships," SNAME, 1951, pp. 229-257. This paper reports the results of tests

on three ship models in a model channel representing the Suez Canal [SNAME, 1951, pp. 232-242]. Graphs of lift, drag, and yawing moment coefficient, Cy Ci and respectively, are supplemented in Figs. 10 and 11 of the reference by graphs of lateral forces and turning moments for a rather wide range

Centerlina of Conol

,

,

Width

Prism at Bottpml it BottomI

of

^ rv ^1 oee Dioqram 3

^'

1^

r

I

p^

**

of

of Fiq.ei.N

yaw

C

,

angles in three different lateral positions,

on the canal centerline and then offset by 0.15 and 0.30 of the 42-meter bottom width of the fullscale canal section. The ship beam was 25.9 meters or 25.9/42 = 0.617 of that width, and its draft was first

of WQter| Surface.

Diagram op R. Brard's Full-Scale Prototype of Model 111 in Full-Scale Suez-

Fig. 61.0

10.4/13 or 0.8 of the canal depth.

Canal Section Supercritical Speeds.

If supercritical

reached, as they can be on

many

speeds are

fine, fast vessels

where there are no limitations on squat, on the eroding action of waves along the banks, and on interferences with other craft, the shaft power at certain speed-length quotients may fall below the value required in deep, unUmited water. In Sec. 29.7 of Volume I it is explained that a following vessel riding on the front of a transverse wave created by a leading vessel is able to keep station at reduced shaft power and with a reduced rate of rotation

in shallow-water areas

of

its

propulsion

device(s).

In

actual

cases,

have been able to hold position with a 20 per cent reduction in rpm.

following

Data

destroyers

relating

to

the resistance,

speed,

and

change of trim of a heavy cruiser model running at a supercritical speed in a model channel are given by E. A. Wright [SNAME, 1946, Fig. 29,

From Brard's Fig. 10 on page 241 of the reference the lateral force on the ship represented by Paris model 111 was, at the maximum offset, found to be zero at about 1.2 deg yaw angle away from the near bank. From Brard's Fig. 11 on page 242 the value of the turning-moment coefBcient C„ at this yaw angle was about 0.075, acting to swing the bow away from the near bank. A rudder angle apphed toward the bank, to counteract this yawing moment away from it, would set up a lateral force to push the ship away from the bank. Equilibrium would therefore be achieved at a yaw angle less than 1.2 deg. This is the reason why, to get the ship away from the near bank and back into the center of the channel, rudder angle is appUed toward the near bank! 61.19

Locks.

Prediction of Ship Resistance in Canal

The

force required to push

close-fitting ship into or

or pull a out of a lock, discussed

HYDRODYNAMICS

414

in Sec. 35.12, is estimated by methods derived from model tests [EMB Rep. 189, Mar 1928]. It is shown in the references cited that the augmented lock resistance 72i may be related to the open-water resistance Ra by the equation

— where n

Ax

is

1

=

ma.ximum coefficient

section fc

is

some

and the lock boundaries.

foimd by experiment to vary from 6.2 to 20 and over but whose average value may be taken as about 11. Eq. (61.iv), shown graphically in Fig. 6 LP, should predict Rl/Ro within plus and

indication,

ratio of the ship. It

is

recommended that a systematic

investigation with models in shallow water be made, the

only variable being the beam-draft ratio, to obtain further information on sinkage." slight

imevenness in a solid basin

TMB

such as in the

a number which has been

Sec. 61.20

from a study of the sinkage curves, that the sinkage may vary with the beam-draft is

(61. iv)

the ratio of the maximum-section area

The

"There

Very

kn

to the transverse clearance area between the

ship

IN SHIP DESIGN

floor,

shallow-water basin, com-

with bed clearances approaching zero, almost impossible to obtain accurate shallow-water resistance data with models. Bed bined

make

it

irregularities in ship operating areas

similar effects

Unknown

on

full-scale resistance

may have and power.

current magnitudes and directions at

the several depths over an irregular bed influence ship behavior in

may

also

an unpredictable man-

ner.

Until

it

is

known what

experimenters will record

all

to observe,

careful

the data which can

conceivably have any bearing whatever on the result,

when they conduct

ship trials in shallow

and restricted waters. As an indication of some of the unexplained anomalies which now exist, there are fisted hereunder some data given to the author in January 1949 by the then Captain Arleigh A. Burke, USN, based upon his experience as commanding Officer of the light cruiser U. S. S. Huntington

(CL107):

Resistance

Fig. 61. P

Graph for Determining Added ResistWhen Transiting Canal Locks

ance OF Ships

(1) When operating in the shallow waters of the River Plate, with depths varying from 26 to 35 ft, draft of the ship about 25 ft, it was possible to achieve a ship speed of about 15 kt by making

revolutions for about 19 kt in deep water.

minus 25 per cent

for entrance

and

exit speeds

not exceeding 3 kt, as apphed to ships having lengths of 600 ft or more. The model tests covered ranges of n from about 0.2 or less to 2.82. It is perfectly feasible, however, to transit ships with clearances so small that

n

is

approximately 8

to 10.

ever,

tion

when above

How-

increasing the rate of propeller rotathis value, it

was stated that the ship

actually ran more slowly than 15 kt. It

(2)

was found

difficult

to

move

the

ship

sideways in shallow water. This included attempts to

bow and the stern separately as move the ship bodily in crab fashion, motion known as sidling.

move

the

well as to

6L20

Unexplained Anomalies in Shallow and Water Performance. It has been the experience of most analysts and experimenters on ship behavior in confined waters that no sooner have they found a rule which appears to predict performance reasonably well than a case crops up which upsets all their calculations. This indicates definitely one thing: There are certain actions and effects not yet known and taken into account, involving phenomena not now observed. The following extract is from page 6 of Report 640, lebruary 1948, by W. H. Norley: Restricted

TMB

by the (3)

ship

When

passing through the Suez Canal the

would keep

herself

more

or less in the center

without any appreciable steering. If she sheered slowly toward one bank a positive differential pressure would build up on the bank side of the bow and push the bow back toward of the channel

midchannel. Having swung so that the

bow was

headed away from the shore the ship would work herself out from the near bank. 61.21 Summary of Shallow- and Restricted-

Water

Effects.

Summarizino;

the

effects

of

PREDICTED BEHAVIOR IN CONFINED WATERS

Sec. 61.22

shallow and

Depth on the Speed

upon ship perform-

restricted waters

ance, as described and explained in Chaps. 18 and 35 of Volume I and in the preceding sections

the following items appear in

of this chapter,

qualitative terms: (a)

The

(5)

draft below the

surface

still-water

is

increased because of the deeper sinkage of the ship in the intensified Bernoulli contour system (b)

The changes

of trim are

(0)

The

overall sinkage

and trim

INA, 1900, pp. 239-248, giving the results of tests on Italian torpedoboat

and slope

of the ship

of the position

wave

of a solitary

of translation

a function

(7)

on the surface which may be

(8)

is

traveling near the ship (d)

The pressure drag

or resistance

increased

is

because of the constrictions imposed on the ship velocity and pressure fields by the rigid boundaries (e)

The

a function of the slope and the position of the

ship with respect to the solitary

wave

of trans-

lation

The

(f)

slope drag

may

be

sufficient,

when

it

changes sign and becomes a slope thrust, to cause a decrease in total drag with an increase

above the

in speed, at a point just

critical

ary layer, with consequent increase in velocity gradient in the laminar sublayer, when the clearances between the ship and the rigid boundaries

become small (h) The ship vibration is generally and magnified in shallow water.

intensified

and 1900, respectively. "Neuere Versuche fiber Schiffswiderstand in freiem Wasser (New Experiments on Ship Resistance in Open Water)," Proc. Ninth Int.

Schiitte,

J.,

Shipping Congr., Diisseldorf, 1902 F., RPS, 1903, pp. 110-119. Covers the "Increase of Resistance Due to Shallow Water or

(10)

Durand, W.

(11)

Popper, S., INA, 1905, Part L-LIII

(12)

Yarrow, H.; report on the

to the Influence of

speed

(g) The friction drag is increased, partly by the augmented rearward motion of the water past the ship and partly by the thinning of the bound-

models White, Sir William H., MNA, 1900, pp. 469-470 Haack, M., "Nouvelles Recherches sur la Resistance des Carenes et le jFonctionnement des Bateaux (New Investigations on the Resistance of Hulls and the Functioning of Ships)," ATMA, 1900, Vol. 11, pp. 41-48. This is a discussion of shallowwater performance, based upon the published data of Captain Rasmussen and General Rota, in INA for 1899

slope drag or slope thrust encountered (9)

is

Ver. Deutsch. Ing., 10 Dec 1904, pp. 1870-1878. This paper contains records of trials of the German torpcdoboat SI 19, including wave-prolile and change-of-trim diagrams for a series of speeds. Rasmussen, A., "Some Steam Trials of Danish Ships," INA, 1899, pp. 12-26 and PI. V, describing tests on the Danish torpedoboats Makrelen and Sobjornen Rota, G., "On the Influence of Depth of Water on

the Resistance of Ships,"

augmented because

of the intensified Velox-wave system (c)

415

of Torpedoboats)," Zeit. der

Banks and Shoals." I,

pp. 199-201 and Pis. a Yarrow-built

trials of

INA, 1905, Part II, pp. 339-343, 349-358, and Pis. LXXIX-LXXXI Marriner, W. W., INA, 1905, Part II, pp. 344-358 and Pis. LXXXII, LXXXIII Watts, Sir Philip, INA, 1908, pp. 69-70 Watts, Sir PhiUp, INA, 1909, pp. 176-178 and Pis. XV and XVI, reporting on trials of the British destroyer Cossack. The pertinent data for the two measured-mile courses on which this vessel was destroyer,

(13)

(14) (15)

run are:

on the Effects of Confined Waters on Models and Ships. A partial list of references follows on shallow- and restricted-water effects and on the behavior of 61.22

Partial Bibliography

(1)

White, Sir William H., "Notes on Recent Experience with Some of H. M. Ships," INA, 1892, pp. 160-186

(2)

Rasmussen,

"The

Influence

Water upon the Speed

of

London, 7 Sep 1894. This

of

the

Ships,"

Depth

of

Engineering,

article is reprinted in

Laubeuf, M., "Influence de la Profondeur de I'Eau sur la Vitesse des Navires (Influence of the Depth of

Water on the Speed

Vol.

8,

pp. 207-213.

able at the (4)

A

=

Skelmorlie mile, depth h ft

Maplins mile, depth h

=

240

ft,

critical

per sec or about 52 kt

=

45

ft, critical

of Ships),"

ATMA,

partial translation

is

1897, avail-

DTMB.

wave

38.05 ft per sec or about 22.5 kt.

H. C, "The Resistance of Some Merchant

Ship Types in Shallow Water," pp. 83-86

SNAME,

1911,

and Kent, J. L., "Effect of Form and on the Resistance of Ships," INA, 1913, Part II, pp. 37-60 and Pis. Ill, IV. Fig. 5 on PI. IV shows a 2-diml ship-shaped forebody in a

(17) Baker, G. S.,

Size

uniform stream parallel to the longitudinal

(5) following, pp. 18-20. (3)

(b)

speed (16) Sadler,

ships in confined waters:

A.,

(a)

wave speed = 87.8

axis,

and gives streamlines for the flow of the water around this forebody and between two parallel boundaries. The forebody was "shaped" by combining 2-diml line sources and sinks with a uniform stream parallel to the ship

axis.

Einflusses der Wassertiefe auf die Geschwindigkeit

D. W., "Relative Resistances of Some Models with Block Coefficient Constant and Other

der Torpedoboote (Tests of the Effect of Water

Coefficients

Paulus, Naval Constr., "Versuche zur Ermittlung des

(18) Taylor,

Varied,"

SNAME,

1913,

pp.

1-8,

HYDRODYNAMICS

416 2-6 and shallow water esp. pp.

(19)

Pis. 8-11, covering tests

made

Havelock, T. H., "Effect of Shallow Water on Resistance," Proc. Roy. See, London, 1922

(20) Hecksoher, E.,

IN SHIP DESIGN

Wave

(29)

Size

N. H., and Johansen, F. C, "Wind Tunnel ARC, R and

Interference on Streamlined Bodies,"

M 1451, (22) Baker,

G.

1933 S.,

SD,

1933, Vol.

I,

pp. 193-209

den Schiffswiderstand auf Beschranktem Wasser (Concerning Ship Resist-

(23) Kreitner,

J.,

"tjber

ance in Restricted Waters)," WRH, 1934, Vol. XV, pp. 77-82. English transl. in BuShips (U. S. Navy Dept.) Transl. 389, Sep 1950.

H. M., "The Effect of Shallow Water upon the Resistance of Ships," USNI, Vol. 64, May 1938, 709-713. This is a restatement of the data pp.

(24) Heiser,

mentioned by D. W. Taylor in S and P, 1943, pp. 74-81 from W. H. White, INA, 1892, Rasmussen (1899), Rota (1900), and Watts (1908 and 1909). The author gives Taylor's dimensional formula A^in = lOH(y/-\/L); see the comments on this formula in Sec. 61.12. (25) Schmidt, W., and Blank, H., "Geschwindigkeitsanderung von Schiffen auf Flachem Wasser (Speed Changes for Ships in Shallow Water)," Schiffbau, 15 Mar 1938, Vol. 39, pp. 100-103. Part of this paper is an analysis of the shallow-water data given by Rasmussen, Paulus, and Watts, in references (4), (5), and (15), for the S119, Makrelen, Sohjomen, and Cossack.

SNAME,

F.,

Van Lammeren, W.

conditions

"Maneuvering of Ships in Deep Water, in Shallow Water, and in Canals," SNAME, 1951, pp. 229-257, esp. Figs. 4, 5, and 6 on pp. 237-238 (35) Robb, A. M., TNA, 1952, pp. 444-449 (34) Brard, R.,

S., "Investigations of Flow and Drag Conditions of Ships in Motion in Water of Limited

(36) Schuster,

Depth and Width," STG, 1952, Vol. 46, pp. 244288 (in German). The following review of this paper by T. P. Torda is quoted from Appl. Mech. Rev., Apr 1955, Rev. 1239, p. 180:

"An

Oldenbourg, Berlin, 1940, pp. 144-171. A list of 7 references appears on the last page. There is an

of limited of limited

width, are discussed in the light of various theories

and experiments. In particular, the results of model experiments are discussed. The theories of wave form and wave propagation are extended and hydraulic considerations are discussed. In concluding the paper, author notes that the problems of

depth and limited width of water are and cannot be treated by a uniform theory. Author recommends the use of the nomogram developed in the paper for the treatment of actual problems of ship motion in limited waters. Discussions of the paper by F. Horn, G. Weinblum, W. Graff, R. O. Schlichting, H. Dickmann, and Klindwort are given, together with the reply of limited

different

Model Tests,"

509-512 Helm, K., "Tiefen- und Breiteneinfliisse von Kanalen auf den Schiffswiderstand (Influence of Depth and Breadth of Channels on Ship Resistance)," WRH, 1 Sep 1939, pp. 277-278; also HSPA, Part II,

extensive discussion of existing literature

and theories is given. The problems depth, and ship motion is channels

Proc. Fifth Int. Congr. Appl. Mech., 1939, pp.

(28)

1946, Fig. 29 on p. 396.

both subcritical and supercritical speeds. P. A., Troost, L., and Koning, J. G., RPSS, 1948, pp. 17-19, 56-60, 74-76 (33) Lunde, J. K., "On the Linearized Theory of Wave Resistance for Displacement Ships in Steady and Accelerated Motion," SNAME, 1951, pp. 25-85, esp. pp. 50-60 for a discussion of shallow-water (32)

"Contribution to the Question of the

Effect of the Basin Walls on Ship

SNAME,

Describes model tests conducted in a restricted channel at Newport News, with models towed at

W., and Blank, H., "Schiffsgeschwindigkeit in Kanalen (Ship's Speed in Canals))" Zeit. des Ver. Deutsch. Ing., 2 Jul 1938, Vol. 82, pp. 794-796

Tupper, K.

1942, pp. 149-197

D. W., S and P, 1943, pp. 74-81

(31) Wright, E. A.,

(26) Schmidt,

(27)

J. P.,

of

(30) Taylor,

pp. 368-370 (21) Lock, C.

and Hancock, C. H., "The Effect of Towing Tank on Model Resistance,"

Comstock,

"Beziehungen zwischen Antriebskraft

und Geschwindigkeit bei verschiedenen Fahrwassertiefen (Relation Between Propulsion and Speed at Different Water Depths)," WRH, 22 Sep 1929,

Sec. 61.22

English abstract of this paper on pages 224-226 of the referenced HSPA volume.

in

author." (37)

A

list

of

27 references, some of them quoted in the is given by G. S. Baker on pages 124-125 paper "The Effect of Shallow Water on the

foregoing, of his

Movement of a

Ship,"

INA, Apr

1952, pp. 110-125.

CHAPTER Estimating the

62

Added Mass of Water Around

a

Ship in Unsteady Motion General Added-Liquid Masses for Some Geometric Shapes and for Selected Modes of Motion Comparison of a Vibrating Ship with a Vibrating Geometric Shape The Change of Added Mass Near a Large

62.1 62.2

62.4

62,5

419

62.6

Estimating the Added-Mass Coefficients of Vibrating Ships in Confined Waters Estimating the Added-Mass Coefficients for Vibrating Propulsion Devices Added-Mass Data for Water Surrounding Ship Skegs and Appendages Partial Bibliography on Added-Mass and

....

.

62.3

417

Boundary

423

62

432

62.8

.

Damping

In Sec. 3.4 of Volume

General.

62.1 is

there

I

explained the concept of the added mass of

the entrained liquid surrounding a body or ship in

unsteady motion. In a recent paper, K. Wendel

gives a superb exposition of this concept in both

physical and mathematical terms [STG, Vol. 44, pp. 207-255.

EngHsh version

1950,

TMB

in

Transl. 260 of Jul 1956]. Moreover, his discussion is

extended to cover the accelerative-force and

pressure features not treated in Sec. 3.4 or in

433

436 438

439

Effects

For the treatment in Parts 5 and 6 of Volume maneuvering and wavegoing, both of which involve unsteady motions, the added mass of the entrained water almost always enters as a sizable factor. In general, the added masses are of the same order of magnitude as the ships themselves. For the design of a new ship, or for estimating the performance of an existing one, numerical values must be known or III of ship motions in

estimated.

Knowledge

of the quantitative effects

of motion. It should be possible for the reader

water in adding to the mass is also necessary in a study of body and ship

who

vibration in liquids, discussed at

the present

chapter,

with

familiar

is

as

and 3

well

the

as

other

preceding

modes

portions

book to follow Wendel's development intelligently, and to derive great benefit from it, even though some of the details are passed over. His description of the derivation of added liquid masses for ships which are heaving and rolling, with and without bilge keels, apphes to the discussion of wavegoing in Part 6 of of Parts

1, 2,

Volume III. The effect liquid

of this

the added mass of entrained

aroimd a body in unsteady motion,

(2)

Sec. 20.11 of

Volume

I

and

the resulting body accelerations,

called the inertia effect.

in

magnitude added mass is determined normally from a knowledge of the kinetic energy in the velocity field around the body for a given mode of motion. This energy, in turn, is calculated from an exIt is indicated in Sec. 3.4 that the

of the

in a

The added mass

is

often

itself is

field around the body. For practically every case cited throughout the present chapter, where the added-mass coefficient is derived by analytic instead of by empirical methods, the value is calculated on the basis of

the

the following assumptions:

mass moment

in all directions, in

of inertia) coefficients, are often

the inertia

efficients.

some length

subsequent sections

of this chapter.

sometimes called the accession of inertia for the body. In other quarters it is called the hydrodynamic mass. Similarly, the 0-diml coefficients relating the added mass of liquid to the mass of the body, called here the added-mass (or added called

in

pression defining the velocity potential throughout of

relationship of (1) the forces applied to the body,

and

of the entrained

moment

inertia)

co-

These important definitions are

dis-

(or

cussed further in Sec. 62.2.

of

(1) The potential theory is valid for the case in hand. This means that the body is completely surroimded by an ideal liquid of great extent

which only potential flow is without viscosity, therefore no boundary layer exists. takes place.

(2)

417

The

This liquid

flow pattern

and the added mass

of

HYDRODYNAMICS

418

IN SHIP DESIGN

where — Ap's exist because normal ship motions. Further, as R. Brahmig

entrained liquid are constant, independent of the

especially in regions

frequency or

of

tlie

amplitude of unsteady motion

There are no discontinuities

(3)

in

the liquid

surrounding the body or ship, which means that

no separation or cavitation exists (4) There are no damping forces or moments acting on the body or ship, because of the lack For those modes of unsteady motion which

do not involve directly the speed of the body or ship along its major axis, the added mass of the entrained Uquid is independent of this speed (6) For a body floating on water, in a state of equilibrium, the kinetic energy and the addedliquid mass are assumed to be half of the respective values for a fully and deeply submerged "double body" composed of 'the underwater form plus its mirror image above the free surface of the liquid (7)

For some

to determine

of the analytic procedures

developed

the kinetic energy in the Uquid

surrounding the underwater hull of a surface

method

ship, such as the 1929

of F.

M.

Lewis,

described in Sec. 62.3, it is assumed that the ship has vertical or wall sides all around at the

means that there is no the "double body" at the surface-

surface waterline. This

discontinuity in

points out

[TMB

Transl. 118,

Nov

1943, pp. 2-3]:

"Whereas the calculated hydrodynamic (added) mass depends only on shape (of the body), its value may vary with flow conditions in a real, eddying medium. A satisfactory agreement of the calculated result with the mass is therefore possible only when the flow patterns of the two differing phenomena are

increase in the actual flow

of viscosity in the liquid (5)

Sec. 62.1

identical."

There is damping of some sort in practically unsteady motion; certainly in all ship vibration. Assumption (6) requires that the flow pattern around the actual underwater ship form be half of that around the "double body." It neglects the free-surface and gravity effects, whatever they may be, and the dissipation of energy by waves generated around the sides of the ship and moving away from it. Despite all these drawbacks and disadvantages the data derived from potential theory have been most useful. In many cases the simplifying assumptions have only minor influences, and in most cases one can be reasonably certain that the all

not allowed for are definitely

effect of factors

additive or subtractive. It is again

emphasized here,

and

in Sec. 3.4

assumed to be half of those on an elliptic ellipsoid having the same proportions of length, beam, and draft.

That mode must be known

hull of a surface ship are

added mass of the

liquid set in

acceleration or deceleration tion of the

as' is

pointed out

illustrated in Fig. 3.F, that the

water line level. (8) So far as the 3-diml effects of finite length and tapering ends on the added mass of entrained liquid are concerned, the effects on the underwater

mode

of

motion

is

motion during

primarily a func-

of the

body

or ship.

or assumed before

one sets out to estimate or to calculate the addedeffect. For example, in the case of an ellip-

mass

soid of revolution, the field kinetic enei'gies

No

great study

is

practice, with ships

required to reahze that in

and

their parts, practically

assumptions are truly valid. When the ships and appendages are moving through a real liquid Uke water, they are surrounded by boundary layers, but the viscous effects appear to be minor except for very small bodies. There

none

is

of these

increasing

evidence

that

the

added-liquid

masses around a vibrating or oscillating body change with frequency and amphtude of vibration,

especially at the higher frequencies. This

means that the motion

not that of a body in an ideal liquid, surrounded only by potential flow. E. Schadlofsky, in reference (14) of Sec. 62.8, is

went so far as to say that for these reasons it was hopeless to attempt an added-mass determination by analytic methods. At high frequencies and large amplitudes there

may

easily be cavitation.

and

added-liquid masses are by no means the same for

(1)

translational motion in a given

plane

major axis and (2) bending or flexural vibration, with two nodes and three loops, in the same plane. For a 2-diml body of rectangular section they are not the same for translational motion in a plane parallel to the long sides as for that type of motion in a plane parallel to the

parallel to the short sides.

The

latter

difference

is

illustrated

quantita-

tively for the floating box of unit length

rectangular section of Fig.

62.

A

of Sec.

and 62.2,

having a beam 2a and a draft a. The addedliquid mass for up-and-down unsteady motion is 0.76pTra^, while for right-and-left sidling motion the added-liquid mass is 0.25p7ra".

The mass is

of the floating box, for unit length,

2pa'. Therefore the virtual

mass of both box

ESTIMATE OF ADDED LIQUID MASS

Sec. 62.2

and entrained liquid, for unit length and up-and-down unsteady motion, is thb + vii, 2pa'

+

mass

coefficient,

(^

—

VM

=

0.76pTa

(2

+

from Sec.

(2 -V 0.767r)pa"

The

0.767r)pal

=

virtual-

+ mi)lmB or

3.4, is (wib

^ ~

for

It

is

419

equally important that he

know what

is

meant by inertia coefficients, mentioned in Sec. 62.1. In most technical books and papers the inertia coefficients, linear and angular, correspond to the added-mass coefficients described in the

2

2.388

-\-

=

and rotational motion, Sometimes other names, or addinames, are applied to them to indicate the

foregoing, for translational

2.19

2

2pa'

respectively.

The

corresponding

added-mass

coefficient

is

simply mL/niB or i^AM

—

tional

exact .76p7ra '

_

2.388

mode

of motion.

It is customary,

=

1.19

means always

2pa^

although writers are by no

specific in this matter, to base the

on the mass (or mass moment buoyant body which has the same mass as the identical volume of liquid would have. This is always the case for the added-mass

inertia coefficients

This coefficient is always, by the definitions of this book, equal to {Cvm — 1-0). 62.2

Added-Liquid Masses for Some GeoModes of Motion.

metric Shapes and for Selected It is stated in Sees. 3.4

and

3.5 of

Volume

I

that

of inertia) of a

coefficient

defined here. A.

F.

Zahm,

for

one,

puts the matter this way:

the added mass of the entrained liquid around a in unsteady motion, symbolized by m^ determined by the combination of size, volume, shape, and mode of motion of the body and the mass density p of the surrounding liquid. The mass density of the body, symbolized by mg

body

,

is

,

own mass

mass of the volume of liquid that it displaces. In the, general case the added liquid mass m^ has no relation to the body mass me If the body is a 1-ft cube of cork its mass is small; if it is a 1-ft cube of lead, its mass is large. However, for a given mode of motion in each case, in a given liquid, the added mass of entrained liquid for each cube would be exactly the same. There is not much point, therefore, in relating these cork and lead body masses to a given added mass of some liquid surrounding them, for example water, while they execute this is

the ratio of

its

to the

.

unsteady motion. If, however, the submerged 1-ft cube is of heavy wood, so that its weight is exactly equal to that of a 1-ft cube of the adjacent water in other words, if the cube is buoyant then the

—

ratio mi^lniB

It

is

becomes most useful

—

in ship design.

called the added-mass coefficient, symbolized

by Cam The ratio (mt -\- mBiImB for a buoyant body is called in this book the virtual-mass In some quarters coefficient, symbolized by Cvm the latter name is applied to the former ratio, and added-liquid mass is called virtual mass. In other quarters the added mass is called the hydrodynamic mass. It therefore, in any discussion

is

most

important,

of this kind, that the

marine architect know exactly what every case.

is

meant

in

"Each

coefficient therefore is

inertia

body's apparent inertia, due to the inertia of the displaced fluid

Rep. 323, 1929, Part V,

a ratio of the

field fluid, to

moving

as a solid"

the like

[NACA

p. 437].

In this case the last four words are the important ones, because the mass density for the sohd body is then the same as for the liquid displaced by it. This method breaks down for the infinitely thin flat plate which has finite added liquid mass for unsteady motion normal to its plane but zero buoyant or displaced volume. However, it serves very well for

The

all

foregoing

practical purposes. is

a necessary preliminary to a

discussion of the added masses of a variety of

geometric shapes and of ship hulls because of the presence,

on this and proportion involving added mass. These can

in

the

technical

literature

subject, of certain form, shape, coefficients

be confused with the added-mass coefficients and the inertia coefficients for buoyant bodies, in which the displaced-Uquid mass equals the body mass. The text endeavors to make the distinction clear as each of these form coefficients easily

is

encountered.

As a means toward Wendel is followed in

this end, the lead of

K.

stressing the added-hquid

masses themselves instead of the added-mass or coefficients. These added-liquid masses and added-liquid weights are the numerical values required by the marine architect; the coefficients are convenient tools with which to make early estimates, and the necessary tools with which to inertia

conduct analytic investigations. There are a considerable number of geometric shapes or bodies for which velocity potentials

HYDRODYNAMICS

420

Moment

Added

Form

Added Moss

of

Two-Dimensionol

Entrained

Bod\(

of

of Inertia of

Li({uid

Entrained Liquid

Mode

Mode of Motion

of

Motion

Rod of Circular Section

*-

Mode

Mode

of

of

Motion

Motion

Lonq,

K-2a

amount

_JjjJ<2/oira a/b

2.23 1.7

Rod with

power of the mass density p of what the shape of the body or the direction in which it is moving with respect

Fins on

the Corners

i_

first

own

axis.

From

mode

of

motion

is

readily deter-

0.147

JL=k4/)ira^

lated for the motion of

any body for which a and a stream function can be which the kinetic energy in the

%

velocity potential

005

set

up and

for

Dl

Vza^^

flow can be derived.

0.25 '

^

Mode

of

Motion

tTH_"076/)ira

JL=QII7/3ira'*

mi_-Q25/)Tra

62.A contains diagrams of a number of geometric shapes, it indicates one or more modes of motion for each, and it gives the added-mass values in terms of the mass density p of the surrounding liquid and the physical dimensions of the bodies. Most of the data in this figure were derived from those given by K. Wendel Fig.

2-diml

[STG, 1950, Vol. mL"kg/jTra

Floating

Rectonqulor

the kinetic-energy function

mined, as indicated in Sec. 3.4. In general, the added mass of the entrained liquid can be calcu-

0.15

ni_-k3/)1Ta

the

corresponding

015

2L

pos-

the added mass of the entrained liquid for the

0.234

Section

Square-Sectionr

it

the Uquid, no matter to its

94 24

1.98

r~2a~

make

ideal liquid, the total

of kinetic energy involved in the intricate

Ub and

m|_"k|/)ira

Rod of Square or Rectonqulor

an

sible to calculate, for

function involving the square of the body velocity

•^l'qp^'^

>\

2b

a well-known example.

motion around such a body, out to when it moves in one of the given modes of unsteady motion. The result is a

HL'/Jira

Flat Plate

is

velocity-potential expressions

infinity distance,

a^ein^a,)

A]
the top of Fig. 62. A,

particle

/oir(b^cos^a*-

Major

Sec. 62.2

the 2-diml elliptic-section cylinder, depicted near

The

mL"/Otra

—

IN SHIP DESIGN

and stream functions can be set up, applying to simple modes of body motion. Of these bodies

%

\zz

TMB

in

44, pp. 207-255; English version

1956]; those for the

Transl. 260, Jul

general case of the 2-diml elliptic-section cylinder are from L.

M. Milne-Thomson [TH,

Except as indicated

1950, p. 239].

in the diagrams, all the values

submerged at a considerable expanse of liquid, so that at infinite distances from the moving bodies the particle motions are all zero. In a practical sense, therefore, the diagrams apply only to certain listed are for bodies

V///////////////A

depth in an

n|_=

a76/)Tra^

JL-0.059/)Tra*

h-2a^-1 0.61

0.67

m|_- kg/jtra

085

infinite

appendages on a surface ship having a roughly geometric shape, lying well below the surface, and to fully submerged submarine vessels. Fig. 62. B gives corresponding added-Iiquid-mass

data for a series of 3-dinil geometric bodies, and for circular and elliptic discs, derived from data

on standard reference works on hydrodynamics JL=0,055jO-rTa^

Fig. 62. a Added-Liquid-Mass Values for Some Twodlmensional geometric shapes in unsteady motion All values given are for unit lengths normal to the page.

The

respective

modes

double-headed arrows.

of

motion are indicated by the

by

Sir

A

Horace

Lamb and

considerable

L.

number

M. Milne-Thomson.

of references dealing

with the added mass of entrained liquid around bodies of various types is listed on pages 100 and 101 of the book "Hydrodynamics," prepared and published

by the National Research Council,

ESTIMATE OF ADDED LIQUID MASS

Sec. 62.2

Form

Added Moss

of

Three-Dimenaional

of

Added Moment

G. P. Weinblum and

M.

Denis present,

St.

in

of

of Inertia

Body

421

Entrained Liquid

Entrained Liquid

Sphere

graphic form, values of the three linear and the three angular inertia coefficients for the elliptic ellipsoid,

'^/OTrSL^

again for translational motion along, or

motion about the three principal These data cover a range of ratios between the semiaxes a, b, and c corresponding to the proportions of normal ships [SNAME, 1950, Figs. 6-11, pp. 189-190]. For use with added-mass values for the general ellipsoid, the body mass Wb of a buoyant ellipsoid in a liquid of mass for rotational

axes. iL=-3-/)Tra

m\_--j-jova.

cIS Mode

Circular Disc

Movinq Normal

of

Motion

Mode

to Its Plane

of Motion

density p

or Rototinq

About Q Diametei

^L=z|/'a=

As list

Movi nq

m l" ^z^^'"^^")

Broadside

set

is

(4/3)irpa6c.

down

in the

SNAME

paper and in the

to follow, each of these linear (and angular)

inertia coefficients represents the ratio (1)

the added-liquid mass (or mass

between

moment

of

about the complete elliptic ellipsoid to (2) the mass (or the mass moment of inertia) of the complete ellipsoid along or about the axis specified, when it has the same mass density as the displaced liquid. For a half-ellipsoid representing the underwater body of a surface ship, these added-mass (or added mass moment of inertia) values are all halved but the ratios and the coefficients remain the same. inertia)

It

some

interesting to note that, in

is

the mass of half of an elliptic ellipsoid

cases,

re-

is

markably close to the mass of the water displaced by the underwater hull of a ship of the same principal dimensions. For example, in the case of the

ABC

ship designed in Part

4,

a half-

having the same proportions and as the ship has the following dimensions: ellipsoid

Semimajor (longitudinal) = 255 ft, from Table

510/2

Seraiminor Fig. 62.B Added-Liquid-Mass Valtjes for Some Thrbe-Dimensional Geometric Shapes in Unsteady

73/2 = 36.5 Semiminor 26 ft.

(transverse)

a

axis

size

= L/2 =

66.e.

axis

b

= Bx/2 =

H

{not

ft

(vertical) axis c

=

H/2)

=

Motion The

modes

motion are indicated by the

double-headed arrows.

The half-volume of this ellipsoid is (0.5) (4/3) The weight of the buoyant half-ellipsoid is, in lb, the half-volume times p times g. Hence the

Washington, 1932. Formulas giving the inertia

weight displacement of the half-ellipsoid in

respective

coefficients

of

of

Tabc.

a variety of 2-diml and 3-diml

shapes developed from the general or

water at sea level

salt

is

elliptic

having semiaxes a, b, and c, and enabling the added masses (and added mass moments of inertia) of entrained liquid to be calculated for translational motion along, and for rotational motion about the three major axes, are given by A. F. Zahm [NACA Rep. 323, 1929, Part V, Table VIII, p. 445].

l^(long tons)

ellipsoid

1

4\

2

3/

-rrpgiabc)

2,240 3.1416(1.9905)32.174(2.55)36.5(26)

2,240

=

14,490 1.

HYDRODYNAMICS

422

The weight displacement of the The block coefficient Cb of an (or of half

=

7r./6

=

such an elUpsoid) 0.5236.

The block

ship

is

16,400

t.

elUptic ellipsoid

is [(4/3)7ra6c]/(8a?)c)

coefficient

Cb

of the

approximation to the preliminary design of the ABC ship is, from Table 66.e, 0.593. fifth

The mass moment

of inertia

of

the liquid

displaced by the buoyant elliptic ellipsoid

For rotation about the x-x or

^pahcib'^ For rotation about the y-y or

c')

+

c^)

+

b').

z-z or c-axis,

rsT'pabcia

The

+

6-axis,

-x%Trpabc{a'

For rotation about the

is:

a-axis,

British Shipbuilding Research Association

has collected, and

S. L. Smith has published added-mass data for prolate spheroids, for bodies of other shapes, and for surface ships having a rather wide range of or L/V^^^ values [INA, 1955, pp. 525-561, esp. Fig. 12 on p. 542]. The

@

Yo-8

IN SHIP DESIGN

Sec. 62.2

ESTIMATE OF ADDED LIQUID MASS

Sec. 62.3

TABLE

62.a

Body Characteristics and Added Liquid-Mass Coefficients fob a Series of 31 Forms

423

HYDRODYNAMICS

424

general nature of the flow pattern for vertical and lateral unsteady motions, corresponding to

2-noded

vibration in vertical and horizontal planes.

problem

how

is

added mass moment

actual surface-ship hull in

any or

around an unsteady motion in

of inertia,

of its degrees of freedom.

all

The problem

most frequent application, and

of

at least of major interest,

is

that of finding the

added- or virtual-mass coefficients for a ship in vibration. This involves a separate and additional group of degrees of freedom. Many years ago H. W. NichoUs found that, for a rectangularsection model vibrating vertically, the addedmass coefficient was approximated by

—

—

draft of the

model. For the model which he used.

Cam worked

B

where

0.37

was the beam

(62.i)

+

^AM —

623

the corresponding

0.2

=

1.037

-f-

0.2

=

1.237

However, the data from Table 1 of TMB Report 1022, of May 1956, based on the 1929 method of F. M. Lewis and the reduction factor of J. L. Taylor for 2-noded bending of an ellipsoid

[SNAME,

1955,

471],

p.

give a

Cam

of

only

0.978 for 2-noded vertical vibration.

an excellent knowledge concerning the added mass of the entrained water to ship-vibration problems was given by F. H. Supplementing

summary

Todd

I + 0.20 and H the

=

Cj^M

Sec.

mean draft of 24.42 ft, value by this method is

The

to estimate or to derive numerical

values for the added mass of entrained liquid, or for the

IN SHIP DESIGN 473], at a

in

the

foregoing,

of the adaptation of

1947

[SBMEB, May,

Jun, Jul, 1947,

Vol. 54, pp. 307-312, 358-362, 400-403, respectively;

ASNE, Feb

1948, pp. 86-110, esp. pp.

101-104].

out as 0.78. For a triangular-section model he found it to be 0.70 [TMB Rep. 395, Feb 1935,

The use the

B/H

of a straight-line function ratio as a

means

embodying

of determining the

added-liquid mass for vertical vibration,

de.'jpite

unexpected applicability to many types of ship, can at best be considered only a first approximation, to be used in an early stage of the design when the hull form is not yet known. Moreover, it takes no account of the fore-and-aft distribuits

p. 9].

Much later it was stated by F. H. Todd [SNAME, 1947, Vol. 55, p. 160] that, for vertical vibration only: "In calculations on the natural frequency of ship hulls 2-noded vibration), the total virtual mass of the hull and water together varies from 2 to 4 times the ship displacement. The variation is linear with beam-draft ratio, and is given approximately by the line (in

Virtual inertia factor

=

+

tion of the

is perhaps more applicable appendages than to hulls proper. It involves a comparison of the resonant frequency of the appendage structure in air with the resonant frequency of the same structure in water. The structure can be set in motion by a vibration generator, first when the ship is on the building ways or in the building dock, with the appendage surrounded by air. It is again vibrated when the vessel is in the water, with the vibration generator

placed in commission,

1.2

to

The

virtual inertia factor

placement

+

is

defined as the ratio of (dis-

entrained water) to displacement."

Here the virtual

inertia factor corresponds to the

Cvm Cvm — 1.0

The added-mass

virtual-mass coefficient coefficient

Cam

is

where 0.2

is

or

-1-0.2

Ca

(62. ii)

the viscous-resistance or

damping

factor.

For the coefficient

added mass of entrained hquid, other

than to assume that it is the same as on all other ships for which reliable data are available. A somewhat different method, for use after the ship is structurally complete but before it is

ABC ship of Part 4, the added-mass approximated by this method would be

ship

(above the water) imparting its periodic forces through some kind of flexible connection with the appendage.

Then (.An A,

Cam = !(§)

+

0-2

=

0.936

+

0.2

=

1.136

J'

Uin WateJ (62.iii)

For the Gopher Mariner at the heavy displace-

ment [SNAME,

1955, pp. 436-494, esp. pp. 451,

(.A.A,>)^

Sec.

ESTIMATE OP ADDED LIQUID MASS

623

425

Because of the second powers involved, this requires a very careful measurement of

section or hull of the ship

method

calculated

both frequencies. A second method,

geometric form far below the surface. For example,

application,

is

to

much more

of

general

develop procedures whereby

if

2a

is

its

geometric shapes, as outlined in Sec. 62.2 and

draft of a

many

of the

one-half of the value

or

taken equal to 26 in the case of the sub-

merged rod

the added-liquid masses (and mass moments of inertia) can be derived from the known values for as listed on Figs. 62.A and 62.B. For

is

the whole geometric section

for

of rectangular section, in Fig. 62. A,

lower half

is

identical to that of the floating

rectangular box in the same figure, which has a

first

and a beam

For 2a mass m/,

of 2a.

case the added liquid

=

26 of the

for the up-

geometric shapes for which the velocity potentials, kinetic energies of the surrounding flow, and

and-down motion

added-liquid masses are known, the lower halves

transverse sections of the surface ships under

It is rare that any surface ship, except possibly an old canal boat or a special barge, has a constant transverse section, or one that could be termed average for the entire length. Manifestly, the shape of the actual transverse sections, and the

investigation; for 3-diml bodies

applies to the

distribution of this shape along the ship length,

whole underwater hull, as described for the halfellipsoid and the ABC ship of Part 4 in the preceding section. It is then assumed that the added mass of the liquid surrounding the immersed

determine the flow pattern at different stations, the kinetic energy in the surrounding unsteady

resemble roughly the underwater forms of ships having the same size and proportions. For 2-diml bodies, this resemblance applies to the

Unit Lenqth Between

—»^ —»^

Planes Normal to Axis

it

Mode

immersed

Motion

Vertical

Mode

of

Motion

of

flow,

in

for the second case

and the added mass

of the liquid. Further,

the boat, barge, or ship has a finite length, with

of TrbnslQtionol

Periodic

is 1.51p7ra^;

it is 0.767rpa^.

Surroundinq

Sinalc Amplitude

the

Ends

Liouid

to be Ideal and

Plane

is

All

Seqments Are of of Radius

Entirely

is

Assumed

Liquid

Motion

Two-DimensionQl

Circular Section

a^

In Both Cases, Two-Dimensionol

Flow

Assumed to Take Place About Each Seament Independently, Between the is

Ellipsoid of Revolution in

Midposition

-Lenqth of One Seqment

tporollel

Planes

the Midposition

Normal to

Indicated,

Axes

--Midposition

In

Ends Down. Hoc^aina

Dioqratns

Deformation

Fig. 62.E

First Stage in Transformation of Oscillating Cylindrical

Vertical Vibration

Bar to

is

Axis

Z and 3

by Pure Shear

Ship Structure in 2-Nodbd

HYDRODYNAMICS

126 ends; almost invariabl}'

it

ends, so that 3-dinil flow

is

At the time

tapers toward those

number

involved.

of writing (1956), the general pro-

cedure whereby the underwater hull of a surface

more geometric forms added mass of entrained liquid has imdergone about a quarter-centurj^ of development, applying to one particular degree of freedom. This mode of motion, as mentioned ship

is

compared

to one or

to determine the

previously,

is in

addition to the usual six degrees

embodies periodic bending two nodes and three loops or antinodes, such as that encountered in the fundamental resonant vibration of a ship hull in the vertical plane. The processes in this development, which should be understood clearly by the marine architect who undertakes to calculate and to use intelligently the added-mass values for his ship design, are outlined here in a combination of diagrams and of

freedom

in that it

or flexure in a vertical plane, usually with

words.

Diagram

1

in Fig.

section bar of radius

The bar

is oscillating

G2.E illustrates a circulara,

with

its

axis horizontal.

vertically (actually in the

plane of the page) in a pure translational mode,

embodying

rising

and dropping

tances above and below

its

assimied that the rod

is

IN SHIP DESIGN

for equal

ments

made up

623 of a

but adjacent length seg-

separate

of

is

form of thick circular discs, indicated in diagram 2 of Fig. 62.E. The unsteady flow around each of these circular discs is assumed to take place in vertical planes normal to the in the

straight or midposition axis of the rod, so that

each segment the added-liquid mass is irpa' s of the segment. Although the discs near the ends move up and down with a greater amplitude, and a greater velocity, than for

times the length

the discs at the center, the added-liquid mass for each segment is not changed because of this situa-

not for the low frequencies involved However, since there are no imaginary planes beyond the end segments to insure pure tion, at least

here.

2-diml flow there,

it is

obviously not acceptable

mass for each disc by the number of discs and to say that this is the added-liquid mass for the whole flexing or bending bar. One reason is that the bar in diagram 2 is to multiply the added-liquid

deformed

pure shear rather than in pure

in

bending, or in a combination of the two. Another

reason

is

that the flow near the exposed ends

is

certainly 3-diml in character. F.

dis-

normal position. It is buoyant, having the

Sec.

characteristics are concerned,

M.

Lewis,

who developed

this

method

in

1929, utihzed as a solution for the second portion of this

problem a longitudinal reduction

factor.

same mass density as the surrounding liquid, and that at this stage it is deeply submerged in

This repi-esented the ratio between (1) the addedhquid mass around an ellipsoid of revolution in

an ideal, non-viscous liquid. For such a 2-diml body, a section of which is pictured at the top of Fig. 62.A and in diagram 1 of Fig. 62.E, the added-liquid mass -per unit length is irpa^, where p is the mass density of the buoyant rod and of the surroimding hquid. All the unsteady flow

and (2) the added-liquid mass around a circular bar undergoing pure shear deflection, having the same length L as the bar in diagram 2 of the figure but in effect forming part of an infinitely long circular rod. For his solution, embodied in SNAME, 1929, pages 6-11, Lewis assumed that the 3-diml circular-section ellipsoid also deformed in pure shear. This meant that the flow around any section took place between vertical planes normal to the horizontal,

in

this

liquid

takes

place

in

vertical

planes

bounding unit lengths, normal to the horizontal midposition axis of the rod.

The rod

is

next cut

off to

with free or exposed ends. It

a given length L, is then made to

vertical vibration

straight midposition of the ellipsoid, represented

diagram 3

of Fig. 62. E.

He

thus obtained a

vibrate in the vertical plane (that of the page)

in

with two nodes, at its fundamental frequency in the surrounding hquid, taking both the rod mass and the added-hquid mass into account. The problem of predicting the fundamental frequency in advance then resolves itself into one

reduction factor J2-Nodc which he applied to the added-hquid mass around each of the circular

of finding

the numerical value of the added-

mass for this mode of motion. This may be tackled in two ways; they are described separately in the paragraphs which follow. For the first method it is assumed that the rod, liquid

although a single solid entity so far as

its elastic

segments, from one end of the bar to the other.

The reason

for doing this, instead of applying


the whole added Uquid mass, appears

presently.

The reason

for not

summing up the

varied added-hquid masses for the segments of radius

3

is

a, a,

,

Oa

,

fla

•

•

•

of the ellipsoid of

diagram

also explained presently.

To make this elongated and pointed ellipsoid resemble the imderwater hull of a surface ship

ESTIMATE OF ADDED LIQUID MASS

Sec. 62.3

more

closely,

its

numerous length segments,

separated by adjacent vertical planes, could each

be

made

semielliptic in transverse shape.

They

could be given proportions corresponding to the ratio

[(beam)/(section

of

draft)]

the

several

sections along the length of the ship in question.

The

sections forward, for example, could have

major axes vertical; those amidships could have them horizontal. This modification, however, would not assist in the solution being sought since the added-liquid mass around any 2-diml elliptic shape having a unit length and a major axis of length 2a, for unsteady motion normal to their

that axis,

is

irpa",

same as

the

radius a or diameter 2a.

for a circle of

This relationship

is

indicated in the several elliptic sections of Fig. 62.F.

The added mass

of the liquid surrounding

KBeam B-2a-»1

Neqleclino Surface Effects,

the Added-Liquid Mass in

is,

Each Case, m|_- (0.5)Trpa^ '

- (QI25)tt/3E

Fig. 62.F Series op Elliptic Body Sections, All Having the Same Added Liquid Mass Per Unit Length

an

elliptic section in

of one variable only,

an ideal fluid is a function namely the square of the

beam, reckoned at right angles to the directtion of motion. For a section of unit length and

beam Bx

either semicircular or semielliptic in

,

shape, the added mass

0.125p7rB|

mi

is

(0.5)p(7r/4)B| or

would be an advantage, if it could be done, to modify the shape of the horizontal plane through the major axis of the geometric body so that it would have the same beam, at given 0-diml proportions of its length from the nose, It

as

does

However,

the

waterline

designed

waterline

this again is not

of

the

ship.

a satisfactory procedure

beam

B

at

its

appropriate station, at

midlength of the segment. However, instead of using elliptic section shapes, Lewis found that by employing conformal transformation, described briefly in Sec. 41.11,

he could obtain the added-

liquid-mass values for transverse section shapes

which resembled closely those found on ships, including rectangles with square corners and V-shapes with sharp keels. Diagrams showing these shapes were published by Lewis in Plates 2 and 3 of his SNAME, 1929 paper and were reproduced by K. Wendel in Fig. 10 of his STG, 1950 paper; they also appear on pages 21 and 23 of TMB Translation 260, July 1956, and in Figs. 186(a) through 186(g) and Fig. 187, on page 320 of the book "The Design of Merchant Ships," by J. C. A. Schokker, E. M. Neuerburg, and E. J. Vossnack [H. Stam, Haarlem, 1953].

To make

more adaptable

these section shapes

on ships, Lewis employed eight separate proportions for the circumscribing rectangles bounding them.

for comparison with transverse sections

These proportions, symboHzed by H in his paper and represented actually by the ratio [(halfbeam) /(section draft)], for one side only of a symmetrical ship, varied from 0.2 to 2.0. In the referenced paper by Wendel and in TMB Translation

.

427

method, the representative body is composed of a series of constant-section, vertical segments, say about 20 in number, separated by vertical planes representing the equally spaced stations set up when making the lines drawing of the ship for which the added-mass data are desired. Each constant-section segment has the correct designed-

260 the eight circumscribing rectangles

have a half-beam of a and a section draft of 6. It is most important to remember, in this connection, that the section draft corresponds to

the ship draft (vertical distance between

and

baseline)

extends it is

all

the

only

way

if

the section in

to the baseplane; otherwise

the vertical distance from the

because to determine the longitudinal reduction factor for such a body, non-ellipsoidal in shape,

bottom

and usually with fore-and-aft asymmetry, would require a determination of the added mass by a lengthy and laborious procedure corresponding to that employed by L. Landweber and A. Winzer, and described in the latter part of Sec. 62.2. F. M. Lewis worked out a clever alternative scheme whereby the added mass of an underwater ship hull can be approximated by a much simpler and more straightforward procedure. For this

the ship draft.

of the section in question.

DWL

to the

For a transom-

may

stern section, this section draft

The

DWL

question

be only 0.1

referenced pubUcations are

unfortunately not specific on this point but the principal features are

shown

in

diagram 4

of

Fig.'62.G.

Instead of tabulating the added-liquid masses

segments of unit length, Lewis set up a relationship in which they were referred to halj of the added-liquid mass for a segment having a circular section of radius a for these 2-diml section

HYDRODYNAMICS

428

WL

IN SHIP DESIGN

Pure Bendinq Deformation, with

Sec. 62.3

WL

StQiO

,

All Transverse

Sta

Sections

15

Remommq

in

Diaqram 6

Plane

and Normal to Neotrol Axis

Fig. 62.G

Second Stage in Transformation of Oscillating Cylindrical Bar to Ship Structure in 2-Noded Vertical Vibration

and unit length. He used

this

quantity as a

up

reference because, in the process of setting

the relationship, the deeply submerged 2-diml circular-section

segment of

A

brought with a waterHne corFig. 62.

is

to the surface so as to float responding to its horizontal diameter. If the top half of the circular-section segment

the

is

removed,

lower half of semicircular section

buoyant, because

its

mass

is

0.5irpa^

is

still

per unit

length and the mass of the displaced water

is

exactly the same. Lewis' relationship

is

in the

form of a "co-

Added-liquid mass for a ship-shaped of unit length, beam B, and

bottom

of section

Cl„,u = segment

length, radius a or incidentally,

Because C. W. Prohaska also has a relationship supported by different analytical and experimental data, and also designated as C, it appears wise to substitute for the symbols CLewiB and Cprohaska & fc-symbol corresponding to of this kind,

those listed in various places in Figs. 62. A and 62. B.

A

suitable

symbol appears to be

fcgeot

which, for 2-diml flow in a translational mode,

is

same as Cl^wis above. For a rectangu-

lar ship section

beam

having a [(beam) /(section draft)]

by Lewis,

1.512

(given as 1.51 in the referenced

The value

is

of

for rectangles of other

fcgect

proportions are given in a graph by F.

M. Lewis

and K. Wendel [SNAME, 1929,

4 at top;

B/H

2a

although called "the inertia

coefficient for that (ship) section"

is

figures).

PI.

Transl. 260, Jul 1956, Fig. 21 on p.

For a ship section

of unit

B =

/csect

TMB

Half of the added-liquid mass for a circular-section

transformed from

ratio of 2.0, with square corners at the bilges,

segment

section draft to

is

circle.

exactly the

efficient" C, defined as follows:

This,

ship-shaped section of Lewis a

of semicircular shape

ratio of 2.0, ksect

is

3-4].

having a

1.00, since in this case

the added mass of the ship section corresponds to the added mass of the semicircular section

used as the reference.

now

to determine

the added-

not a true inertia coefficient in accordance with modern general usage. It might be distantly

liquid

related to such a coefficient but only because the

responding to one of the shapes depicted by

It

is

possible

mass per unit length

of a ship section cor-

ESTIMA IE OF ADDED LIQUID MASS

Sec. 62.3

Lewis,

429

and having approximately the correct

ratio [(beam) /(section draft)] of the ship section

under consideration. Lrtroducing the shape factor KSoot

I

Added mass

ship-shaped

of

section

of

unit

length

and

/

Added weight

of

added mass

of liquid surround-

ing ship-shaped section of unit length

= where the beam

(62. iv)

h..m->^p{g)B'

B

is

that at midlength of the

constant-section segment in question; in other

words, the local beam. F. H.

Todd made

it

unnecessary to compare

the shape of the given ship sections with the

transformations of F. in

reference

(24)

M. Lewis by

of Sec.

publishing,

a graph which

62.8,

gave the shape factor direct from known values of

and the body plan. C. W. Prohaska modified the diagram somewhat the

ratio

[(beam)/(section draft)]

section coefficient estimated from the

so that the abscissas were values of the ratio

i.

Fig. 62.

of the

196;

[ATMA,

TMB

defining the section coefficient

is

fcgect is

constant for

ratio [(beam) /(section draft)].

all

ships

intricate sections, resembling those

with

the transverse sections of a ship vibrating vertically, calculated is still

by the methods

just described,

valid only for the flow around each 2-diml

segment, where the segment motion and the sur-

drawn

the latter

ratio is 1.0, the ship section is a semicircle

When

more

bossings and other projecting appendages [ATMA, 1947, Figs. 16, 17, 18, pp. 191-192]. These section shapes and shape factors are also derived by conformal transformation. The added mass of the entrained liquid around of

coefficient

values of the

When

for other

semicircle,

in

the value of

Prohaska has supplemented the fcsj„t-values for M. Lewis by values

the ship-shaped sections of F.

rounding flow are confined between two vertical planes at the ends of the segment. This situation is represented by diagrams 1 and 2 in Fig. 62. E,

clearly illustrated

diagram 4 of Fig. 62. G. It is to be noted that for a section of 0.7854, corresponding to that of a

B/H

W. Prohaska's Graphs for Deter-

C.

section

1947, Vol. 46, Fig. 24 on p. Rep. 739, Oct 1953, Fig. 1 on p. 14; SNAME, 1955, Fig. 34 on p. 471]. In all three references cited the ordinates were labeled iS(beta), which is the alternative ITTC symbol for midship-section coefficient. This is misleading because the section coefficient has a value of /3 only at the midship or maximum section. The present author has further modified the Prohaska graphs by substituting the shape factor fcsect for the "coefficient" C. In their new form the graphs are reproduced here as Fig. 62. H; the method of coefficient

H

mining Section-Shape Factors by Inspection

[(beam) /(section draft)] for the section in question

and the ordinates were values

5

Beam- Draft Ratio

and the

for a cylindrical bar

and

an

for

now

of revolution, respectively. It is

ellipsoid

necessary to

apply to the added mass around this segment a longitudinal reduction factor to

compensate for

the [(beam)/

the 3-diml nature of the actual flow, equal or cor-

(section draft)] ratio has values other than 1.0,

responding to Lewis' factor Ja-wode mentioned earher in this section. Because of the use of the standard sysbol J for mass or polar moment of

shape factor

fcseot

is

1.00.

the ship sections having shape factors

fcgect

of

1.00 are all ellipses, because their added-liquid

masses

are,

from

Fig. 62. F, the

same as

for a

inertia, the

3-diml reduction factor

semicircular segment of unit length having the

by R. However, concerning

same beam.

for

an

is

a factor

ellipsoid of revolution

symbolized

R

derived

and applied

to a

HYDRODYNAMICS

430 ship form,

Wendel has

this to

say

[TMB

IN SHIP DESIGN sumably about a transverse and middepth

Transl.

260, pp. 13-14]: "It is true that this kind of approximation must be considered as somewhat rough since it takes into account

body nor the width-depth ratio; nevertheless a better approximation which, no doubt, would also be more complicated, seems to be unnecessary so long as we confine ourselves to

R^ for 2-noded

by shear

neither the specific shape of the displacement

slender bodies."

Plate 4 of Lewis' 1929

SNAME

paper gives

values of the following reduction factors for an elUpsoid

L/Bx

or

of

L/D

revolution, ratio of

covering

from 3 to

a

range

of

724

1947, Fig. 25, p.

where the small diagram indicates

this

type of motion. i?2 for

rotational motion in a vertical plane, pre-

Fig. 62.1

Graphs of Reduction Factors

with deformation occurring

deflection only; this latter feature is

important to remember for 3-noded flexure, with deformation occurring by shear deflection only; this again is important to remember.

Fig. 62.1 is a graph giving numerical values of

these four factors.

For the 2-noded flexure by pure shear, reprediagram 6

197],

flexure,

axis at midlength

sented by diagrams 2 and 3 in Fig. 62.E and by

18:

Ri for heaving motion or pure translation in a vertical plane. This is the same set of values as given by C. W. Prohaska, in his graph

marked "Lamb" [ATMA,

Sec. 62.3

R

in

Fig.

62. G,

the added weight of

entrained liquid for each transverse segment

is

multipHed by the Lewis reduction factor R^ The weights for all the segments are then superposed upon the weights of the masses composing the structure, machinery, cargo, and other parts of the ship, applying the weight ordinates at the proper points or stations along the diagram which

of F. M. Lewis and

.

J.

L.

Taylor for Thkee-Dimensional Flow

ESTIMATE OF ADDED LTOITID MASS

Sec. 62.3

represents the length of the ship; see Fig. 37 on

page 472 of SNAME, 1955. It now becomes necessary to return to a consideration of the second method for determining the added mass of the entrained liquid aroimd the circular rod of diagram 2 in Fig. 62.E, when flexing in 2-noded vertical vibration. F. M. Lewis adopted the schematic method shown in that diagram because he felt that the possible error involved in assuming pure shear deflection, rather than bending deflection, was less than the error involved in shifting from the ellipsoid of revolution (or its lower half) to the actual underwater hull

431

whether he had in mind what has later come to be the difference between Lewis' reduction factor for pure shear and J. L. Taylor's reduction factor for pure bending, or some other effect. In any case, a recent re-analysis of model and ship vibration data indicates that the method of F. M. Lewis, combined with the reduction factor of J. L. Taylor for 3-diml flow, give values of the added weight of the entrained water around a vibrating ship which are still too high, at least for 2- and 3-noded vertical vibration [McGoldrick, R. T., and Russo, V.

L.,

SNAME,

1955, p. 490].

Further study and analysis are required before

of a ship, at least for the proportions correspond-

additional refinements in these prediction methods

ing to those of a ship. However, in 1930 J. Lock-

can be attempted. A comparison of the procedures followed by F. M. Lewis, C. W. Prohaska, K. Wendel, and others in predicting the added mass of the entrained liquid about the underwater hull of a ship, vibrating vertically in its fundamental 2-noded or 3-noded frequency, indicates a number of discrepancies with the assumptions of Sec.

wood Taylor published the values

of a reduction

an elHpsoid of revolution, vibrating an ideal liquid with 2 nodes and 3 by considering pure bending deflection

factor for

vertically in loops,

rather than pure shear deflection. This that, as indicated in

diagram 5 of Fig.

means

62. G, the

transverse planes separating the several segments

remain normal to The segments are and thick on the simple bent beam.

the bent axis of the ellipsoid.

convex side, as they are in a Taylor found reduction-factor values as much as 8 per cent below those of Lewis. A graph of J. L. Taylor's factor for 2-noded pure bending is published by C. W. Prohaska [ATMA, 1947, Fig. 25, p. 197]; also by R. T. McGoldrick and V. L. Russo [SNAME, 1955, Fig. 35, p. 471]; it appears in Report 739, October 1953, Fig. 2 on page 14. It is presented here, along with those of Lewis, in Fig. 62.1, supplemented by Taylor's values for 3-noded bending vibration of an ellipsoid, given on page 170 of his 1930 INA paper, reference (9) of Sec. 62.8. Prohaska's diagram indicates graphically that the reduction factors are for an ellipsoid flexing in 2-noded vibration; those of Report 739 and of the 1955 SNAME reference do not.

TMB

TMB

Since the ship

may

nearly hke a simple

be assumed to bend more

beam when

vibrating ver-

modes of vibration, and possibly 4 nodes, and since the data of J. L. Taylor for an ellipsoid vibrating in this manner are available, it is present practice tically,

with

62.1

which are not discussed there:

thus thin on the concave side

at least in the lower

2, 3,

Although the limiting conditions set up for conformal transformation appear to take account of the free-surface effects, as do the electric analogies set up by J. J. Koch, it is by no (1)

the

means

clear

that

these

cover

adequately the

even in an For example, most of the ship sections developed by Lewis and mentioned in the reference have vertical sides at the waterline although most of those developed by Prohaska do not. There is a question whether full compensation has been situation for ship-shaped sections,

ideal liquid having

made

mass but no

viscosity.

in the analytic process for

the flare or

tumble home to be found on actual ships in this region. K. Wendel comments that in Koch's experiment "••• it is possible to satisfy the boundary condition only approximately; •••"

[TMB (2)

Transl. 260, p. 34].

The

analytic

method described takes

it

for

granted that the ship, built to the shape shown by the lines, has boundaries that remain rigid locally, even though the ship flexes as a whole. It is perfectly possible,

that some

flat

and .indeed quite probable,

or nearly flat areas of hull plating,

(1956) to use Taylor's (smaller) reduction factor

lying generally normal to the direction of vibra-

2-noded vibration rather than that of Lewis. Many years ago E. B. Moullin pointed out that Lewis' added-mass values had to be reduced by 10 per cent [INA, 1930, p. 179]. It is not clear

and forces by magnitude as the hull deformations. Carried to the limit, one would

for

tory motion, "give" or yield or deflect under the external

accelerative

amounts

of the

pressures

same order

of

HYDRODYNAMICS

432

IN SHIP DESIGN

Sec. 62.4

expect a ship with a soft-rubber hull boundary

B)/(section draft)] and selecting by inspection a

amounts of kinetic flow in the surrounding water. The added mass of entrained liquid would then be extremely small. (3) It has been assumed by many analysts and experimenters that the added-liquid mass in vertical vibration for typical ship sections was independent of both frequency and amplitude for the lower modes of vibration, with two and three nodes. Nevertheless, the model experiments

section shape approximating that for the ship.

up only

to set

of H. Sec.

trifling

described in reference

Holstein,

factor

(25)

indicate a large variation in

62.8, ^Tsect

when

of

shape

the frequency and amplitude

The shape

C

[ATMA,

Rather than to work out the problem of premass of entrained water around the hull of the ABC ship of Part 4 in 2-noded vertical vibration as an example of the method described in this section, there is given hereunder a summary of the steps, with brief comments for each step: dicting the added

The

ship

is

divided into 21 length segments,

19 of them having a 25.5

full station

length of 510/20

and the two end segments having a

ft,

=

length of 25.5/2

12.75

ft.

The

=

half-

fore-and-aft

but the two end segments fall on the station locations, 1 through 19. For all the 21 sections, through 20, it is assumed that the section shape on the body plan is representative of the entire segment length pertaining to that centers of

all

station.

the whole waterline beams

B

and the

section drafts (not necessarily the ship draft) for

the 21 stations.

Compute

the 21 ratios [(beam B)/

Estimate the value of the fullness or section each section, by inspection or by some simple method. If there are any concave portions in the section outlines, fill them out by straight tangents before determining the III.

coefficient for

section coefficient.

IV. Using the graphs of Fig. 62. H, determine the shape factor fcseot for each section. These factors may be checked by entering the half-body diagrams of F. M. Lewis fSNAME, 1929, Pis. 2, 3; 1950, Fig. 10;

Fig. 10

on

p. 23]

W. way

1947, Figs. 16, 17, 18 on pp. 191-193; 593].

Prohaska's

as kg^^t

R

of J. L.

Taylor from the indicated graph of Fig.

62.1, for

the

L/Bx

ratio of the ship.

VI. Determine the added-liquid weight per unit of ship length for each station by

mM The shape

=

factor

(62.v)

(fcsect)(i2)(0.125)7rp(fir)B^ fcsect is

usually different for each

station but the reduction factor

R

is

the

same

for

all stations.

Apply the weights thus found to the weight curve for the ship, at the proper stations. J. C. A. Schokker, E. M. Neuerburg, and E. J. Vossnack give a somewhat-too-brief summary of the available methods for estimating or calculating the added mass of the entrained water for the vertical mode of ship vibration on pages 319-321 of their book "The Design of Merchant Ships" [H. Stam, Haarlem, 1953]. On page 340,

in Fig. 222,

they give a nomogram, apparently

published

first

Fig.

1947,

29,

by C. p.

W. Prohaska [ATMA, for

201],

approximating,

vertical vibration, the ratio of (1) the

entrained water to

(2)

mass

in

of the

the mass of the ship,

taking account of the midship-section coefficient

Cm

,

the beam-draft ratio

L/Bx

draft h/H, ratio

is

,

B/H, the length-beam

the ratio of the water depth to

and the block coefficient Cb This found by a rather complicated .

also

formula in Section 131 on page 326. Neither the the equation suffice, however, for determining the longitudinal distribution of the added mass of the entrained water. These authors fist 32 references on pages 341-342 of their book.

nomogram nor

(section draft)].

STG,

of C.

be used in the same

also

V. Select the proper reduction factor

ratio

II. List

then the "coefficient"

VII. Multiply the added-liquid weight per unit length by the length of each of the 21 segments.

Transl. 260, p. 44].

I.

is

SBMEB, Nov 1947, Fig. 11, p. "coefficient" C is also the same

tered on ships. Graphs indicating these variations,

TMB

fcgect

The half-body diagrams

may

Prohaska

are varied, even in a range of frequency encoun-

and the discrepancy with theory for a ship section approximately rectangular, are included in Fig. 32 of the Wendel reference [STG, 1950;

factor

of Lewis.

TMB

Transl. 260, Jul 1956,

with the proper ratio of [(beam

62.4

The Change

of

Added Mass Near a

Large Boundary. All the comments in the foregoing are based upon the motion of a body or ship at a great distance from any rigid or unyielding boundary which would interfere with the flow pattern of an ideal liquid. The air-liquid interface or free surface of a body of water represents a boundary which is, in a practical sense, both flexible and yielding.

ESTIMATE OF ADDED LIQUID MASS

Sec. 62.5 If

a rigid boundary

decelerating ship, as

is

when

introduced under a it

runs suddenly into

shallow water, the kinetic energy in the unsteady flow

around

ship

the

is

increased,

probably

because the particles are no longer free to follow a minimum-energy pattern. Hence, the added of the entrained water begins to increase appreciably by the time the bed clearance under

mass

the ship has diminished to less than its mean draft. This is in accordance with the results

derived analytically by H. Lamb, L.

M. Milne-

Thomson, and others, which indicate that the added mass of entrained liquid increases as a solid boundary of infinite extent is approached. If the decelerating body suddenly approaches a limiting vertical boundary of limited extent but of large proportions compared to itself, such as a small tug which surges up to a large ship at

433

Despite verification of the foregoing

by the ex-

J. J. Koch and C. W. Prohaska, to be mentioned presently, and the full-scale tests by R. T. McGoldrick on the Great Lakes ore

periments of

Kulas [TMB Rep. 762, Jun 1951, on p. 4 and p. 11], F. H. Todd and W. J. Marwood report that, for one ship case at least, the opposite result was found [NECI, carrier E. J.

Table

esp.

1

1947-1948, Vol. 64,

D127].

p.

Assuming an increase

in added-liquid

mass

in

shallow water, the direct result of the increase in total mass is to decrease the natural frequency of

the ship,

so

that resonant vibration in a

frequency range below that of the exciting forces at the operating speed in deep water might occur within that lowered range in shallow water. For example, the blade frequency for the single-screw drive of the ABC transom-stern ship of Part 4

too high a speed, or an exercise torpedo which runs into the side of a hull, the analytic study

at the designed speed in deep water,

that the added mass of the water around the smaller decelerating body should also increase. However, it is reported that in one of the few known cases where this theorem has been applied in practice, the observed data indicated that the added mass of the smaller body was reduced, so that it became easier to

per min.

per min. At the sustained speed of 18.7 kt, this

stop within a given distance or time interval.

propeller

body had the general form of an ellipsoid of revolution and it was approaching the larger body by a sidling motion. It is entirely

blade frequency to 324 cpm.

indicates

The

smaller

possible that other factors were present in the latter case

and were not taken into account.

Estimating the Added-Mass Coefficients The of Vibrating Ships in Confined Waters. effect of shallow water upon a vibrating ship is 62.5

Volume

discussed in Sec. 35.13 of illustrates

schematically

sections of a ship

form

the

flow

I;

Fig. 35.

around the

in vertical vibration. Sec.

35.14 explains that ship vibration, particularly in the vertical direction,

shallow water. This

is

is

greatly magnified in

also discussed

by

F.

M.

Lewis in a paper "Ship Vibration" [Proc. World Eng'g. Cong., Tokyo, 1929, Vol. XXIX, Part 1, publ. in 1931, pp. 203-204]. T.

W. Bunyan

states

Fig. 78.Nb,

The sixth-moded

from physical reasoning and analytic study the added mass of entrained water is greater in shallow water than in deep water.

from

vertical vibration of

still well below the blade frequency at that reduced speed, likewise in deep water. However, when running in the river below Port Correo the

rpm might be reduced to say 81, and the The shallow-water

on the added-liquid mass might be great enough to lower the sixth-moded resonant frequency from 380 to 324 cpm. Not only would this be exactly in the running range but there would be an enormous magnification effect with the nominal bed clearance of only 4 ft under the ship. K. Wendel mentions a case similar to this on page 71 of TMB Translation 260, July 1956. The problem of the naval architect is to determine, and if possible to predict in advance, the magnitude and effect of the changes such as this in added mass, frequency, and ampUtude. effect

The specific information known to be available concerning the effect of shallow water on the added mass vibrating

(1)

Koch,

of the water

vertically,

zur

inertial effect of the

is,

438.8 cycles

is

mental data

Lewis, in the reference cited, states that

=

which for certain reasons might be objectionable, is assumed to occur at 380 cycles

that the various critical vibration frequencies

M.

4(109.7)

the hull,

and amplitudes, in a transverse direction, are also affected by restricted waters such as the Suez Canal [IME, Apr 1955, Vol. LXVII, p. 100]. F.

=

Z(rpm)

J.

is

around a

limited

to

ship,

when

the experi-

of:

J.,

"Eine experimentelle Method

Bestimmung der reduzierten

Masse

des

mitschwingenden Wassers bei Schiffsschwingungen (Experimental Method for Determining the

Virtual

Mass

for

Oscillations

Ing.-Arch., 1933, Vol. IV, Part

2,

of

Ships),"

pp. 103-109;

HYDRODYNAMICS

434 English version in

TMB

Transl. 225,

May

IN SHIP DESIGN

Sec. 62.5

1949

Prohaska, C. W., "Vibration Verticales du Navire (Vertical Vibrations of the Ship)," (2)

ATMA,

1947, Vol. 46, pp. 171-219; abstracted in

EngUsh

in

Nov

SBMEB,

Oct 1947, pp. 542-546 and

1947, pp. 593-599; complete English trans-

lation

(unpubUshed

library.

A

list

in 1956) available in

TMB

of 21 references appears on pp.

214-215 of the original paper. (3) Prohaska, C. W., discussion of paper entitled "Ship Vibration," by F. H. Todd and W. J.

Marwood, NECI, 1947-1948, Vol. 64, pp. D119-D123, plus authors' reply on p. D127 (4) Marwood, W. J., and Johnson, A. J., "Vibration Tests on an

Up

River Colher with Special 3

Reference to the Influence of Depth of Water," NECI, 1953-1954, Vol. 70, pp. 193-216, D103-

DUO. 2-diinl

5

"

S(Bed Clearance)

Added-Liquid-Mass Data of Koch for a Rectangular-Section Surface Ship, Vibrating Vertically in Shallow Water

Fig. 62.J

Koch's data a

4 Beam B

in (1)

electrolytic

were obtained by tests

in

tank, using the methods

described in Sec. 42.13.

The tank

represented a

of the ship

and the bed

of the channel. Fig. 62.

horizontal half of a rectangular-section channel,

gives these data for vertical vibration; Fig. 62.

with half of the underwater body of a rectangular-

for horizontal vibration.

section ship in the center of the channel.

The

half-breadth of the channel was about 7 times

the half-beam of the ship. This was considered by Koch to be the equivalent of a channel of infinite

C

width. Figs. 62.J 1 1

of the

For one who studies the papers of either Koch it is important to remember that the "added mass factor" (phi bar) of Koch's paper (TMB Transl. 225) and the "coefficient" or Prohaska,

and 62.K, adapted from

Koch

Figs. 8

and

reference, give data for determin-

ing the added mass of the entrained liquid around a floating 2-diml body of rectangular section, for a combination of variables involving the beam B, the draft H, and the bed clearance h-H (in the notation of the present book) between the bottom

Fig. 62.K

of Prohaska's paper, although non-dimensional

based upon the masses of two underwater body. This factor and this coefficient are therefore only shape factors for the bodies in question, to be in

both

cases, are

different transverse shapes of

defined presently.

They

are not true added-mass

or inertia coefficients.

The

reference

body

of

Koch

is

a buoyant one

Added-Liquid-Mass Data of Koch for a Rectangular-Section Surface Ship, Vibrating Horizontally in Shallow Water

Sec.

ESTIMATE OF ADDED LIQUID MASS

62

of constant rectangular section having a (26 in his paper)

a unit length. p(5)(B/2)(1.0)

Koch's notation

H of half the beam,

a draft

,

Its

beam

body mass ma

= pBV2 it is 2pb^.

per

and

therefore

is

unit

B

length;

in

Therefore, to obtain

the added mass mi, of entrained liquid for a buoyant rectangular-section body of beam B,

applying to any given combination of the variables listed in the second paragraph preceding, it is necessary to multiply Koch's "added mass factor"

by pB' 12. Then for the given rectangularbody of beam B, the added-liquid mass

section JWi,

=

The

<^pB'/2 per unit length. reference

body

of

Prohaska

is

a buoyant

one of semicircular section having a flat, horizontal top and a curved under side, with a

beam B {2b beam (6 in

in the paper),

body mass m^ length;

in

a draft

H

of half the

the paper), and a unit length. Its is

therefore p(7r/8)-B^ per unit

Prohaska's

notation

it

is

0.5xpt>^.

Hence, to obtain the added mass wii for a floating body having a beam B and any type of constant section within the limits of Prohaska's tests, depicted in his Fig. 19, and for any combination listed by Prohaska (section and depth-draft ratio T/d), it is necessary to multiply his "coefiBcient" C by 0.125xpB^. Thus for the given body of beam B,

of

the

variables

coefficient

/3

435

=

C(0.125)7rpB" per

unit length.

The

body of Prohaska has a semiwhich can be inscribed within the rectangular section of Koch. Therefore, it has a mass vib which is x/4 times that of Koch, from which it follows that Prohaska's C = 4/Tr or Koch's ^ = xC/4. The data of C. W. Prohaska, set down in (2) preceding, were obtained with 2-diml (constantsection) models of limited length and of varied section shape and fullness, moved bodily up and down in a tank of water, with their longitudinal axes parallel to the water surface. The water depth h was varied by altering the position of an adjustable bottom. It was found that V-type transverse sections always gave greater addedmass coefficients than U-type sections, and that the wii-values for hollow sections were approximately the same as for sections which had the hollows filled out by drawing tangents between' reference

circular section

tlie

projecting points.

Fig.

62. L,

adapted from one of the several

shallow-water graphs given by Prohaska, namely Fig. 32 on page 204 of the 1947 ATMA paper, summarizes in diagram 1 the shape-factor or Prohaska "coefficient" C data in terms of (1) the section coefficient, based on the local beam

4

3 F?atio

Via. 62. L

the added liquid mass m/,

of

5 Water Depth h to Draft H

Added-Liquid-Mass Data op C. W. Prohaska for a Surface Ship With Normal Sections, Vibrating Vertically in Shallow Water

HYDRODYNAMICS

436

B

and the

section draft,

and

(2)

the ratio h/H,

relating the depth of water to the ship draft.

Koch's shallow-water shape factors

apply to

them

rectangular sections only, so to use ship one would have to

<^

for a

assume a constant section

IN SHIP DESIGN

section,

made for a ship with somewhat tapering ends by using segments of diminishing section coefficient toward the ends. Applying the data of Koch and Prohaska to the vertical-vibration problem of the ABC ship of Part 4, transiting the 30-ft river between Port Correo and the sea, the basic data are:

=

Draft, i?

26

ft

Depth of water, /i = 30 ft Bed clearance, h — H = A

it

Ratio of draft to half-beam,

2HfBx = 52/73 =

0.71

Maximum-section

coefficient,

Cx = 0.956

Ratio of depth of water to draft,

=

h/H = 30/26

1.15

Ratio of half-beam to bed clearance,

-

Bx/[2{h

=

H)\

73/[2(4)]

=

9.1

Applying these data to Koch's graph with ITTC notation. Fig. 62.J, they fall far beyond the limits of the graph. Applying the equivalent ratios to Koch's original graph. Fig. 8 of reference (1) at the beginning of this section, and extrapolating roughly, ^ appears to have a value of about 5.0 for a ship having a constant rectangular section throughout. Since Koch's^ = mi/(p5.Y/2), the added-liquid mass is of the order of rriL

(0.5)^p5x

=

2.5pBx per tmit length.

From Prohaska's diagram

1

=

=

(0.5)(5.0)pBl-

original data, reproduced in

of Fig. 62. L, his "coefficient"

C

is

about

2.9 for a ship having a constant section coefficient of 0.956.

The

added-liquid mass

is

therefore of

the order of

= C

=

Bl-

=

(2.9)(0.125)7rpB^

1.14pB.v per unit length.

The weight of the added-liquid mass is g{mL) in each case. This is a rather large discrepancy but the comparison is hardly fair to the data of Koch

62.. I

of the present

on page 203 of 1947 paper, Koch's experi-

as well as in Fig. 31

ATMA,

Prohaska's

ments do not cover such a small depth-of-water to draft ratio.

for the entire length. Prohaska's shallow-water

shape factors apply to sections of varying fullness, from 0.99 to 0.37, so that a calculation could be

Sec. 62.6

because, as indicated in Fig.

62.6

Estimating the Added-Mass Coefficients

for Vibrating Propulsion Devices.

added mass

Data on the

of entrained water surrounding the

thrust-producing blades of any type of mechanically driven propulsion device are required

for

predicting

the

the vibration

component parts or

characteristics

of the

entire

of

mechanical

propelling system.

For a propulsion device like a paddlewheel, with blades generally normal to their direction of motion relative to the surrounding water, the added mass of entrained liquid may be approximated by the known tkl for a submerged fiat plate of rectangular outline, in unsteady motion in a direction normal to its surface. For this case, the added mass is given in Fig. 62.A for the rectangular flat plate having dimensions of 2a and 2b. However, the paddlewheel case is by no means simple because all the submerged blades create surface waves, and one or two or more blades are always partly in and partly out of the water. So far as known, no engineering rule has been developed for estimating the added mass niL of paddlewheels or sternwheels.

The

rotating-blade propeller presents a

much

different case because the several blades usually

(except in maneuvering)

lie

at only a small angle

(the attack angle) relative to their direction of

motion through the surrounding water. However, what is wanted in this case is the added mass for a mode of motion which is tangential to the spindle circle at each spindle position. This quantity depends upon the pitch ratio and the exact type of blade motion. Moreover, it changes with the position of a blade on the blade orbit or spindle circle. It can be assumed roughly as one-half the added liquid mass for the blade, reckoned for a mode of motion normal to the projected area of the blade [Mueller, H. F., unpubl. Itr. to HES, 6 Jul 1956]. This Hquid mass, added to the mass of the blade and summed up for all the blades, plus the mass of the supporting and actuating machinery, gives the polar moment of inertia of the whole assembly about the axis of propeller (not blade) rotation.

For the screw propeller the marine architect interested in the added-liquid masses and the corresponding added mass moments of inertia

is

ESTIMATE OF ADDED LIQUID MASS

Sec. 62.6

437

sional-vibration experiments on a group of brass

model propellers, 16 inches in diameter, conducted in both air and water at the U. S. Experimental Model Basin. The P/D values ranged from 0.60 to 2.00. However, these tests produced only the general conclusions that: (a)

For a

amplitude and frequency the

fixed

effect (on the polar

moment

of inertia

directly with the blade-width ratio,

pitch ratio. In other words,

Cm/D and P/D (b)

J

varies

increases as both

increase.

For a given propeller the

moment

./)

and with the

effect (on the polar

of inertia J) increases with frequency

and amplitude In order to determine the per cent increase in moment of inertia in any given case, the amplitude and frequency of the propeller (vibra(c)

(polar)

Remainino Essentially

tion)

Parallel to

must be approximately known.

Mid-

its

Some

Position

Fig.

62.M

Modes op Motion of a Vibrating Screw

for four

modes

of

years later R. Brahmig of

the

made an

torsional-vibration

analytic

problem

of

screw propellers, listed as reference (29) of Sec. 62.8. He considered variations in frequency and

Propeller on a Ship

in Fig.

study

motion illustrated schematically

62.M:

amplitude as affecting the added mass of the entrained liquid, and gave a full statement of the conditions and scale effect involved model experiment technique. Results are

similitude (1)

Torsional or rotational, about the propeller-

shaft axis, as in diagram

1,

assuming that the

latter remains essentially straight (2) Axial, parallel to or

along that axis, indicated

in diagram 2 (3)

Lateral, corresponding to the sidewise

motion

of a propeller shaft in a loose bearing next to the

diagram 3. This also includes a motion due to sidewise bending of the propeller shaft at the propeller, in which the propeller moves only in a direction parallel to the normal disc plane, without diametral rotation. (4) Diametral rotation, as in diagram 4, corresponding to angular motion of the propeller out of the normal plane of its own disc, due to bending or whirling of the propeller shaft about propeller, as in

some

selected diametral axis in the propeller.

There are indications that the depth sion of a screw propeller

is

of

a factor in

modes, because of the "relieving"

immerall

effect of

four

a free

surface close to the vibrating blades.

To determine the value of the added mass moment of inertia for the torsional mode of (1) preceding, a number of tests have been made with model propellers, among them those of R. T.

TMB

McGoldrick, described in Report 307 of July 193L These tests comprised a set of tor-

in the

quoted in his paper for torsional-vibration tests on flat circular discs but none for model screw propellers in the same mode. However, Table 2 of this reference lists rotational-amplitude

and

frequency data for the propellers of three ships. As a rule, the amount of rotation amplitude

and the frequency in water are almost never known with any reasonable certainty for a ship, and the effect of the surrounding water oq the polar

moment

of inertia varies widely as indicated

TMB

Report 307. It was therefore decided, by those working in this field, that the only practical interim answer was to accept a perin

centage increase in the polar

moment

of inertia

mass in air, regardless of the pitch ratio, the mean-width ratio, the ratio of hub diameter to overall diameter, and all other factors. For this mode of vibration, the effect of an abnormally large or small hub is possibly less pronoimced because of the small radii involved. However, the sine of the geometric blade angle of the propeller

is

large at the radii near the hub.

tests, an overall mean of 25 to 30 per cent increase in J, due to the added mass of the entrained water, was used for many years;

Based on these

this is the value given

by

J.

R.

Kane and R. T.

HYDRODYNAMICS

438

McGoldrick on pages 199 and 200

SNAME,

of

1949. Subsequent experience has indicated a single average value of 25 per cent increase in / due to

added-liquid mass for the pure torsional mode of motion [Garibaldi, R. J., "Procedure for Torsional

Analysis

Vibration

Multimass

of

For the

axial

mode

complicated,

usually

lie

and

a major factor.

and

aft,

and the blade width

Kane and McGoldrick

explain

in

be taken as 40 to 60 per cent of the propeller Further experience on their part mass mprop indicates a single value of 60 per cent. In other quarters, a value of 50 per cent "is normally used" [E. F. Noonan, BuShips, Navy Dept., unpubl. •

memo

to

HES

of 15

Jun

Kane and McGoldrick equation

1956].

also give a dimensional

having a semianalytic

basis,

of

the

following form: wii for the axial

=

0.229.

Then

w

mode

ft,

of motion, in lb,

ratio

Z =

4,

Cm/D =

for salt water having a weight density ft^, the added mass m^ for the by substitution in Eq. (62.vii),

of 64.0 lb per

axial

mode

is,

mr.

1

=

0.245(64.0)

'

+

[0.23(1.199)'

1]

•(4)(20.0)'(0.229)'

=

19,790 lb.

The estimated weight

of this propeller in

which

man-

an mi/mprop ratio of only 48.6 per cent. For the lateral mode of vibration, depicted in diagram 3 of Fig. 62.M, no analytic solution or test data appear to be available in published form. A percentage increase of 10 in the propeller mass is recommended by R. T. McGoldrick (Conf. of 7 Jun 1956). For the diametral mode of motion, diagrammed at 4 in Fig. 62. M, McGoldrick recommends a percentage increase of 50 in the mass moment of inertia, in air, of the propeller for the same mode of motion about the same axis, due to the moment of the added mass of the entrained water. 62.7 Added-Mass Data for Water Surrounding Ship Skegs and Appendages. Fins, deep keels, fixed stabilizers, and thin skegs of moderate

ganese

bronze

is

40,750

lb,

gives

to large area are subject to lateral vibration

1

k

when

by mechanical or hydrodynamic forces. The frequency of resonant vibration must be clear of any exciting-force frequency, especially excited

0.23(^

+

at 0.6772Ma«)

•(Z)(0.010D

1

J

in inches)'!

^1

(62.vi)

for a periodic force of large

The graphs

for the axial

mode

of

magnitude,

cation of the resonant vibration

where k has an empirical value of about 9,100. This formula is converted to 0-diml form by inserting the weight density w of the water in which the propeller is working. Incorporating the constant k = 9,100, and eliminating the units of measurement for the diameter D, the 0-diml equation then becomes rrij,

ratio at 0.67/2 m.x is 1.199,

and the mean-width

is

sections

most readable terms on pages 199 and 200 of their paper "Longitudinal Vibration of Marine Propulsion Shafting Systems" [SNAME, 1949]. For axial vibration they recommend that, as an approximate estimate, the added Uquid mass m^ it

20

6].

blade

the

P/D

D =

at rather large angles to each direction

of motion, forward is

Res.

of vibration the situation

since

70.O, the

Sec. 62.7

Systems,"

BuShips, Navy Dept., Unclassified Dev. Rep. 371-V-19, 15 Dec 1953, p. rather

IN SHIP DESIGN

motion

in

EMB

is

if

magnifi-

to be avoided.

Report R-22 of April 1940,

describing full-scale vibration tests of one of the

twin skegs of the battleship Washington (BB55), illustrate the mode of vibration and the resonance variations with frequency for a ship structure of this kind.

When a large, thin, vibrating appendage with moderately sharp edges is surrounded by water, the kinetic energy in the velocity field is high. This means a large added mass of entrained liquid.

=

0.245«;

Indeed, the added-mass coefficient

F^ 0.231^^ at

0.67/?^.,J

+

Ij

reach (62.vii)

iZ){D)f-^

2, 3,

sailing-yacht centerboard, it

may

exceed 6 or

8.

Not only must the magnitude of this mass be known to predict the resonant frequency when but the frequency is often drastically it lies in an undesirable position, within the range of exciting-force frequencies. in water,

For the ABC transom-stern ship of Part 4, having a final design of propdler shown in Fig,

Cam may easily

or 4. For a thin-plate structure like a

lowered, so that

ESTIMATE OF ADDED LIQUID MASS

Sec. 62.S

43'J

but it may be assumed from Fig. 66.Q to have an average depth, normal to the centerline buttock in the vicinity, of about 16.5 ft. This is the semimajor axis of an equivalent semielliptic section. The semiminor axis is estimated from Fig. 66. P as 2.5 ft. Then, for standard salt water hull,

Schematic Flexure f^ttern in Vertical

of

hr

Vibration

/

at 59 deg F, 15 deg C,

the

section,

liquid mass,

moment

For Outer JL,qu,d

Portion

for half of the elliptic

about the point of attachment of

the skeg to the hull,

Jl

and

of inertia of the added-

is

- hy

=

(0.0625)7rp(a'

=

0.0625(3. 1416)I.9905[(16.5)'

=

27,654 slug-ft' per

ft

-

(2.5)']'

length,

= (°0625)TT^(a^-b^)^ per Unit Lenqth

the

latter

reckoned generally parallel

to" the

centerline buttock in the vicinity.

Method of Estimatino the Added Liquid Mass fob a Large, Thin, Cantilever

Fig. 62.N

Structure in Lateral Vibration

on Added-Mass and There are hsted here a number

Partial Bibliography

62.8

Damping

Effects.

of references in the technical literature relating to

the added or entrained masses around bodies, Cantilever structures, comprising a category

which embodies most of the appendages listed, sway with a motion somewhat resembling that of a tree in a gusty wind, illustrated schematically in Fig. 62.N.

The

root of the cantilever

is rela-

most of the motion occurs with the Washington skeg mentioned previously. In the absence of a specific tively rigid, so that

near the

tip, as

analytic solution covering this case, a reasonable

approximation is achieved by assuming that the cantilever has a semielliptic section and that it is hinged to the hull at its midlength, at a point corresponding to the root attachment of the cantilever. This produces a motion, approximately normal to the plane of the thin appendage, which is

greater than that of the cantilever structure

near the root but indicates that

less

at the tip.

Experience

the kinetic energies and added

masses in the two cases are of the same order of magnitude. From the second diagram at the top of Fig. 62.A a 2-diml elUptic-section cylinder in unsteady oscillatory motion about an axis at its center has an added mass moment of inertia J l of (0.125)7rp(a^ — h^Y per unit length, where a is half the semimajor axis and h is half the semiminor

ships,

As an example

of this

method, take the case of

stern of the

ABC ship of Part 4, for which sections

are indicated in Fig. 66.P 66.Q. This skeg

is

and a

profile in Fig.

of variable depth,

below the

of interest to the

marine

men-

tioned throughout the present chapter.

An ment

excellent historical

summary

of the develop-

means for evaluating and taking account of the added mass of entrained water around a vibrating ship is given by R. T. McGoldrick in the introduction and text of TMB Report 395, issued in February 1935. The bibliography on page 30 lists most of the early papers of importance,

INA,

of

beginning with that of Otto Schlick in 1884.

A

bibhography on vibration, containing 73 was collected by the SNAME Hull Structure Committee and pubhshed as part of the work on Project S-7 in SNAME Bulletin, January 1952, pages 14-15. A supplementary list of 30 references was published in SNAME Bulletin, October 1952, page 27. References pertaiiiing to added-hquid mass effects, published subsequent to 1924, include: references,

(1)

NichoUs, H. W., "Vibration of Ships," INA, 1924 pp. 141-163

(2)

Taylor, J.

(3)

1927-1928, Vol. 44, pp. 143-176 Cole, A. P., "The Natural Periods of Vibration of Ships," lESS, 1928-1929, Vol. LXXII, pp. 43-86

(4)

Kempf,

one.

the thin, vertical centerline skeg mider the transom

and typical forms

architect. This list includes the references

L.,

"Ship Vibration Periods,"

NECI,

G., and Helm, K., "Auslaufmeeaungen am und am Modell Dampfer Hamburg (Retardation Measurements on the Ship and on the Model of the Steamer Hamburg)," WRH, 7 Sep 1928, Sehiff

pp. 336-340. These authors found a virtual-mass and straight-ahead for retardation

coefficient

HYDRODYNAMICS

440 motion

from 1.00

of

for small vessels to 1.04 for

IN SHIP DESIGN

"The

Inertia of the

Water Surrounding

Lewis, F. M.,

(6)

a Vibrating Ship," SNAME, 1929, Vol. 37, pp. 1-20 and Pis. 1-5 Lewis, F. M., "Ship Vibration," Proc. World Eng'g.

(20)

Taylor,

Phil.

(11)

pp. 303-309 "Vibration of Ships,"

J. L.,

LXXII, (10)

Inertia Co-

Mag., Jan-Jun 1930, Vol. IX, Series 7, pp. 161-183 Abell, T. B., "A Note on the Direct Measurement of the Virtual Mass of Ship Models," INA, 1930,

LXXII, (9)

"Some Hydrodynamical

Taylor, J. L., efficients,"

(8)

INA,

1930, Vol.

pp. 162-196, esp. pp. 163-164 and Appx.

A, pp. 169-170 Browne, A. D., MouUin, E. B., and Perkins, A. J., "The Added Mass of Prisms Floating in Water," Proc. Camb. Phil. Soc, 1930, Vol. XXVI, pp. 258-272. A brief quotation from p. 263 of this reference is given on p. 299, Sec. 20.11 of Volume I. MouUin, E. B., "Some Vibration Problems in Naval Architecture," Proc. Third Int. Cong. Appl. Mech., Stockholm, 1930, Vol. Ill, pp. 28-30

(12) "Effect of

Entrained Water in the Mass Moment of Rep. 307, Jul

Inertia of Ship Propellers,"

EMB

NECI, 1931-1932,

(14) Schadlofsky, E.,

McGoldrick, R. T., "A Study of Ship Hull Vibration," Rep. 395, Feb 1935. Describes and analyzes staff on the U. S. destroyer tests made by the Hamilton (DD141) and on two structural models. Pages 9-11 discuss the "Correction for Effect of the Surrounding Water." Pages 30-32 of this report carry a list of 29 references. (22) Guntzberger, H., "Effet Amortisseur de l'H61ice sur les Oscillations de Torsion des Lignes d'Arbres (Buffer Effect of the Propeller on the Torsional Vibrations of Line Shafting)," ATMA, 1935, Vol. 39, pp. 251-259. The author finds an augmentation of polar moment of inertia of 60 per cent of the

(21)

EMB

corresponding polar moment of mass of a steel screw propeller. He mentions the fact that an augmentation percentage of 25 is generally used, as listed in Sec. 62.6 of the present book. (23) Lewis, F.

(24)

of Ship Vibra-

(25)

"Uber Rechnung und Messung der

EMB 382 of Jun 1934, also bearing the number EMB Transl. 7. To this report belongs EMB Supplement

"Eine

experimentelle

2,

pp. 103-109; English version in

May

TMB

A.,

tions of Ship Oscillations),"

pp. 295-299

WRH,

1

Oct 1936,

SNAME,

1936,

H.,

"Tragheitsmoment und Dampfung (Damping and Moment Loaded Ship Propellers)," WRH, 15

Aug

1939, Vol. 20, pp. 260-261

"Die Experimentelle Bestimmung des Hydrodynamischen Massenzuwachses bei Schwing-

(29) Briihmig, R.,

korpern

Determination

(Experimental

the

of

Hydrodynamic Increase in Mass in Oscillating Bodies)," Schiffbau, 1 Jun 1940 and 15 Jun 1940; English version in

TMB

This paper carries a (30)

Meas-

urement)," Tekniska Samfundets Handlinger, Goteborg, 1934, No. 4; also "Einige Untersuchungen iiber schiffsschwingungen (Some Investiga-

M., "Propeller Vibration,"

of Inertia of

"Uber Schwingende Korper an der

Vol. 15, pp. 15-19 (18) Lundberg, S., "Vibrationsforeteelser (Vibration

H., "Untersuchungen an einem Tauchschwingungen ausfiihrenden Quader (Investigation of the Heaving Oscillations of a Parallelepiped)," WRH, 1 Dec 1936, pp. 385-389

Holstein,

belasteter Schiffsschrauben

—

Oberflache des Wassers (On Vibrating Bodies on the Surface of the Water)," WRH, 15 Jan 1934,

pp.

liquid surrounding hinged plates.

1932-1933, Vol. 49, p. 259£f

Dimpker,

5,

English)

Baumann,

1949 A Comparison of (16) Todd, F. H., "Ship Vibration Measured with Calculated Frequencies," NECI, Transl. 225,

(in

(28)

for Oscillations of Ships)," Ing.-Arch., 1933, Vol.

IV, Part

Tekniska Sam-

Sezawa, K., and Watanabe, W., "The Vibration Damping of a Ship in her Moving State," Zosen Kiokai (The Society of Naval Architects of Japan), Dec 1938, Vol. LXIII. This reference describes experiments made to determine the added mass of

Method zur

Bestimmung der reduzierten Masse des mitschwingenden Wassers bei Schiffsschwingungen (Experimental Method for Determining the Virtual Mass

in Ships,"

(27)

of the original reference. J.,

1935,

Vol. 44, pp. 501-519

Report 382, containing a translation of the discussion on the Schadlofsky paper, pp. 326-335

(17)

Todd, F. H., "Vibration

(26) Lewis, F.

to

J.

SNAME,

fundets Handlinger, Goteborg, 1935, No.

Vol. 48, p. 65ff

(The Calculation and Measurement of Elastic Natural Frequencies of Ship Hulls)," STG, 1932, Rep. Vol. 33, pp. 280-325. English version in

Koch,

M., "Propeller Vibration,"

Vol. 43, pp. 252-285

Elastichen Eigenschwingungen von Schiffskorpern

(15)

C, "Backing

experiments a virtual-mass coefficient, for straightahead motion, of from 1.16 at the light displacement to 1.20 at the heavy displacement.

125-151

Todd, F. H., "Some Measurements tion,"

of Propellers," lESS, 1934The author states, on found from the Greyhound Froude that W.

J. F.

p. 57,

1931 (13)

of

NECI, 1934-

EMB

209-210. (7)

Conn,

Methods

1935, Vol. 78, pp. 27-83.

Cong., Tokyo, 1929, Vol. XXIX, Shipbldg. and Mar. Eng'g., Part 1 (published in 1931), pp. 193212, esp. the discussion on Water Effects on pp. 203-204. There are 42 references listed on pp.

Vibration: Simple

Estimating Critical Frequencies," 1935, Vol. 51, pp. 259-276

large vessels. (5)

Sec. 62.S

C, "Ship

(19) Burrill, L.

(31)

list

Transl. 118,

Nov

1943.

of 34 references.

Prohaska, C. W., "Lodrette Skibssvingninger med 2 Knuder (Longitudinal Ship Vibration with 2 Nodes)," Thesis, Kobenhavn, 1941

Havelock, T. H., "The Damping of the Heaving and Pitching Motion of a Ship," London, Edinburgh, and Dublin Phil. Mag. and Jour. Sci., 1942, Vol. 33

(32) Lewis, F. M.,

"Dynamic

Effects,"

pp. 139-140. Contains a long

ME,

list

1944, Vol. II,

of references

on

ESTIMATE OF ADDED LIQUID MASS

Sec. 62.S

"Vibnition of Ships," some of which apply to the

(43)

present chapter. (33)

Home,

NECI,

L. R., "Stopping of Ships,"

1944-1945,

Vol. 61, p. 3Uff

"Notes on the Theory of and Pitching," INA, 1945, Vol. 87, pp. esp. pp. 109-110 discussing the added entrained water for ship forms. For Havelock gives a Cam of 0.8 to 1.0; for

(34) Havelock, T. H.,

he gives 0.4 to (35)

Lamb, The

table

of

Heaving

44, pp. 207-255. English version in

109-122,

260, Jul 1956.

mass

on

of

pitching

(44)

circular disc, elliptic cylinder, 85,

of

137

(46)

symmetry, 172.

(36) Prohaska, C. W., "Vibrations Verticales

(Vertical Vibrations of a Ship),"

du Navire

ATMA,

1947,

(47)

Vol. 46, pp. 171-219. Discussion of the added mass of the entrained water is found on pp. 189-205.

On pages 214 and

215 there is a list of 21 references. Abstracted in English in SBMEB, Oct 1947, pp. 542-546 and Nov 1947, pp. 593-599. Complete English translation, as yet unpublished (1956), at the David Taylor Model Basin.

Todd, F. H., "The Fundamentals

SBMEB, May, Jun, Jul,

St. Denis,

SNAME,

M.,

"On

the Motions

1950, pp. 184-248, esp.

McGoldrick, R. T., "Determination of Hull Critical Frequencies on the Ore Carrier S. S. E. J. Kulas by Means of a Vibration Generator," Rep. 762, Jun 1951. In an appendix to this report, pp. 18-19, E. H. Kennard describes a method for

mass of entrained water around a ship for any mode of vertical vibration. Wendel, K., and Boie, C, "Experimentelle Bestimmung der Hydrodynamischen Masse an ganz und Teilweise getauchten Korpern (Experimental Determination of Hydrodynamic Masses on Totally and Partly Immersed Bodies)," Hansa, 8 Dec 1951, Vol. 88, pp. 1788-1790 Weinblum, G., "Uber Hydrodynamische Massen (On Hydrodynamic Masses)," Schiff und Hafen, Dec 1951, pp. 422-427 (in German) Weinblum, G. P., "On Hydrodynamic Masses," TMB Rep. 809, Apr 1952 Havelock, Sir Thomas H., "Ship Vibrations: The Virtual Inertia of a Spheroid in Shallow Water," INA, 1953, Vol. 95, pp. 1-9. On page 7 there is a estimating the added

general, 166

(37)

and

TMB

two spheres, 130 an ellipsoid, 153, 155

in cases of

G.,

Effects (45)

88

of a sphere, 124 of

Weinblum,

pp. 189-192 on Inertia Forces and Free-Surface

"Hydrodynamics," 1945, 6th ed. between

contents and the index,

Inertia coefficients, of a circular cylinder, 77

an

TMB

Transl. bibliography of 27 items appears

252 of the original; pp. 73-74 of the transla-

of Ships at Sea,"

them, list the following pages, among others, for data on added- and virtual-mass coefficients, as well as for data on the body masses themselves:

of

p.

A

tion.

heaving,

0.5.

Sir Horace,

441

Wendel, K., "Hydrodynamische Massen und Hydrodynamische Massentraglieitsmomente (Hydrodynamic Masses and Hydrodynamic Mass Moments of Inertia of Entrained Water)," STG, 1950, Vol.

(48)

(49)

list

of Ship Vibration,"

1947, Vol. 54, pp. 307-312,

(50)

of 7 references.

Marwood, W.

J.,

and Johnson, A.

J.,

"Vibration

Tests of an Up-River Collier with Special Reference

358-362, 400-403, respectively

to the Influence of Depth Water," NECI, 1953-1954, Vol. 70, pp. 193-216 McGoldrick, R. T., Gleyzal, A. N., Hess, R. L., and Hess, G. K., Jr., "Recent Developments in the Theory of Ship Vibration," Rep. 739, Oct 1953, esp. pp. 13-15 of

(38)

Todd, F. H., and Marwood, W.

(39)

NECI, 1947-1948, Vol. 64, pp. 193-210, D113-D128 John, F., "On the Motion of Floating Bodies," Com-

J.,

"Ship Vibration," (51)

munications on Pure and Applied Mathematics,

Mar

1949, Vol. II, No.

(40) Ursell, F.,

"On

Cylinder on the Surface of a Fluid;" Quart. Jour. Mech. and Appl. Math., Jun 1949, Vol. II, Part 2 (41)

Kane,

J. R.,

Vibrations

and McGoldrick, R. T., "Londitudinal of Marine Propulsion-Shafting Sys-

tems," SNAME, 199-200 (42)

May,

TMB

1

the Heaving Motion of a Circular

1949,

pp.

193-252,

esp.

pp.

and Woodhull, J. C, "The Virtual Mass of a Sphere Entering Water Vertically," NOL memo 10636, 3 Mar 1950; ONR project NR-062-024; copy in BuShips, Navy Dept., library. See also A.,

Nat'l. Res. Council, U. S., Bull. 84, 1932, p. 97.

Grim, O., "Calculation of Hydrodynamic Forces Caused by Oscillation of Ship Hulls," STG, 1953, Vol. 47, pp. 277-299 (in German) McGoldrick, R. T., "Comparison Between Theo(53) retically and Experimentally Determined Natural Frequencies and Modes of Vibration of Ships," Rep. 906, Aug 1954, esp. pp. 9, 14 (54) Havelock, Sir Thomas H., "Waves Due to a Floating Sphere Making Periodic Heaving Oscillations," Proc. Roy. Soc, Series A, Jul 1955, Vol. 231, pp. 1-7; see Appl. Mech. Rev., Feb 1956, No. 504, (52)

TMB

pp. 74-75.

PART Hydrodynamics Applied

4

to the

CHAPTER

Design of a Ship

63

Basic Factors in Ship Design 63.1

Definition of Ship Design

63 2 63

Application and Scope of Part 4

63.4

The Fundamental Requirements

.

442 442

General Assumptions as to Propelling Machin-

.

443

ery

63.1

Definition

of

fashions a ship in this

for

Ship Design.

modern age

One who

or cargo over the water from one place to another.

must

meet certain definite requirements; must almost certainly do some things better than any other ship which can be built to meet those requirements. This superiority can be It

indeed,

it

developed in the evolution

of the design, in the

use of the most suitable materials, application of the best

or in the

workmanship throughout.

63

.

Ship Design as a Compromise The Essence of Design The Design Schedule for a Ship The Field for Future Improvements

in

Design

443 444 444 444 444

may be brought out by a process uncovering that which is innate in any architect

tion. Intelligence

of specialization

can not be satisfied simply that it floats, moves through the water, and carries passengers

.

63.7 63.8

Every

itself

63

of

and engineer. Understanding must be learned, and often the hard way. Understanding, in general, means a comprehension of all problems and relationships and phenomena. Specifically, to the one deahng with problems of hydrodynamics, it means comprehension in its fullest sense of the elements and the intricacies of liquid flow, and of the means of dealing with and predicting the characteristics of this flow.

It can

be developed by a combination of all three, but it is in the evolution of the design in general, and the hydrodynamic design in particular, that

63.2 Application and Scope of Part 4. It is hoped that a study as well as a reading of the first three parts of the book has given the ship

we

designer

are concerned here.

Design, for the naval architect and marine engineer,

may

a ship by an

be defined as the art of fashioning intelligent

those features of form,

and size,

logical selection of

proportions,

and

arrangement which are open to his choice, in combination with those features which are imposed upon him by circumstances beyond his control.

Design planning.

largely a matter of thinking and This requires, above all, knowledge,

is

and understanding. One can have any one or two of these quaUties, but without the

intelligence,

third his ship-designing ability lacks that some-

thing

which

successful.

will

make

his

designs

uniformly

Knowledge can be gained from books

and many other sources

of engineering informa-

a generous share of the knowledge, and understanding needed to fashion

intelligence,

the form and features of a complicated modern

As

knowledge increases, so will his and his understanding. He will realize that he can grasp the meaning of those manifestations of nature that may long have remained a mystery to him, and that he can comprehend the whys and wherefores of so many kinds of flow and action phenomena that were formerly bewildering and meaningless. This fourth part of the book therefore undertakes to outhne the procedure whereby the information set down in Parts 1, 2, and 3 may be utihzed in the hydrodynamic aspects of ship design. After taking up various phases of the procedure, in a manner paralleling those followed ship.

his

intelligence

442

Sec. 63

RASTC DESIGN FACTORS

A

the preceding chapters,

in

example

of the design of a

it

gives a practical

modern

ship. It stresses

the specified Umitations and requirements, the free or

open choices available to the designer, and

443

There arc cases also where the type or form of the propelling machinery affects the declivity and the parallelism or divergence of the screwpropeller

shafts,

just

the

as

of

the

determines

the

position

the compromises that are unavoidable in anything

machinery

put together by one man to satisfy the conflicting wishes of other men. No ship design can be carried very far without considering the primary features involving hydrostatics. Among these are displacement and trim,

position of one end of the propeller shaft.

metacentric

and damage

control.

They

are treated extensively

and other references [PNA, and require no further elaboration

may prevent shaping or fining the hull where this procedure would otherwise be

The matter

1939,

really not

here.

that:

propelHng machinery

one for discussion in

this book,

except

are brought in as necessary, without detail

consideration, in the ship-design example which

That phase of ship stability generally known as dynamic stabihty but defined here as dynamic is, however, very definitely a problem involving ship and liquid motion. It is

metacentric stability

location of the machinery aft

may

affect

Volume

accordingly included in Part 6 of

III,

carrying a screw propeller, because of the clear-

ances required inside the vessel

teristics.

The machinery weight

(b)

peller

the most efficient rate of rotation for the selected

type of propulsion device, although too often the is

true.

For propelling the

pulsion device can be driven reciprocating

an

engine,

ship, the pro-

by a

electric

or

turbine, a

hydraulic

motor, or a hand crank, as long as the desired torque is apphed, the requisite rate of rotation is attained, or the necessary

exception to this rule

power is

is

delivered.

,

the case of the ship,

mounting two or more propdevs on opposite which is called upon to make frequent turns and maneuvers at relatively high speeds and powers. Here the port and starboard propdevs operate in liquid streams moving

down under

The matter and

General Assumptions as to Propelling 63.3 Machinery. With a few exceptions which are noted at the proper places, there is no need to consider the type of propelling machinery in any phase of the hydrodynamic design. It is taken for granted here that the machinery is adapted to

assists in trimming the by the stern and pushing the screw pro-

vessel

under the chapters relating to wavegoing charac-

reverse

The

(a)

the shape of the stern and the position of the shaft

follows.

An

desirable.

of locating the

in the stern or in other fore-and-aft positions is

in textbooks

They

On

vessels, the necessary clear-

ances for machinery inside the vessel

Vol.

I],

invariably

some high-powered

subdivision,

floodability,

stability,

almost

water.

of the absolute

speed of the ship, determined by

of its actual size, is usually

economic, military, or other considerations beyond the control of the designer. He must, however, be prepared to predict the results of variations in these factors, and of each upon the other, so that when a final design decision must be reached, it can be based upon sound and accurate premises. 63.4 The Fundamental Requirements for Every Ship. Every ship designer, no matter how logical and realistic he may be, needs to get back to

first

principles every so often in his search for

the best

way

not think

it

to

make nature

serve him.

He

need

in the least beneath his dignity or

intelUgence to write down, in a few lines, as did

the renowned Rankine

many

years ago [STP,

1866], the following simple requirements for every

ship:

sides of the centerplane,

at different velocities with respect to the ship.

The type of propulsion machinery almost certainly affects

the

rates

of

and the powers two sides. Another the ship which must which the maneuver-

maneuver abihty

is

is

the case of

rapidly,

and

in

in direct proportion to the promptness

with which the propelling machinery responds to its

own

controls.

(b)

in (c)

To float on or in water To move itself or to be moved with handiness,

any manner desired

To

transport passengers or cargo, or other

useful load, from one place to another

rotation

delivered and absorbed on the

exception

(a)

(d) (e) (f)

To steer and to turn, in all kinds of waters To be safe, strong, and comfortable in waves To travel or to be towed swiftly and econom-

ically, (g)

under control at

To remain

afloat

severely damaged.

all

times

and upright when not too

HYDRODYNAMICS

444

He

needs, furthermore, courage

and confidence by the

to strike out boldly for the principal goal

shortest

and most direct

route, using first prin-

he has learned and adhering almost religiously to fundamentals. It was this procedure which produced the remarkably successful group ciples

of large

httle or

landing craft in World

no experience to

fall

War

II,

with

back upon and the

Design as a Compromise.

A

designer

must, at least in the early stages, forget about compromises in a really new and pioneering first place, he is by no means compromises must be made. He may be surprised to find that a certain stern shape, odd but seemingly necessary, makes him a gift of improved maneuvering and increased

project.

certain

Sec. 63.5

sarily the largest, strongest, or fastest that

can

be fashioned, regardless of the other features, but the one in which the best combination of elements

produces

most

the

harmonious,

useful,

and

satisfying whole.

63.7 The Design Schedule for a Ship. This book treats only of the hydrodynamic aspects of ship design, and carries some of these aspects

only through the preliminary-design stage. It

fate of nations at stake.

63.5

IN SHIP DESIGN

In the

that

deck space as well as more efficient propulsion. If compromises must later be admitted, it is a comfort to remember that much of ship design and construction is a compromise. This applies equally to roughing out a dugout canoe from the

is

immense

the

visualize

to

therefore,

difficult,

amount

of thought and planning that has to be put into the design of a ship to achieve the best possible results. According to Ambrose Hunter

can be truthfully said that

it takes every a successful modern trawler as to build one ..." ["The Art of Trawler Planning," Ship and Boat Builder and Naval Architect,

".

.

.

it

bit as long to design

London, Feb 1953, p. trawler is true for any 63.8

The

259].

What

is

true for a

vessel, large or small.

Field for Future Improvements in

of a twin-screw ship inside the projected

natural for the naval architect and marine engineer who is blessed with enterprise and ingenuity to strive for improvements in his work. It is human for him to wish to excel and

fine at the stern.

to surpass the

best available tree, or keeping the propeller tips

deck However, if the effects of all the possible variables are known, the designer can choose with wisdom the final size, shape, or form of each of his elements when he makes his compromise. In this way he attains the maximum benefits from the selected combination of all of them. Let the compromises be made \vith profesfessional honesty, sound logic, and good judgment. Let them be known to all and admitted by all. Let them be based upon sturdy reasoning, and let them be tempered by a knowledge and an experienced consideration of all the causes, effects, and consequences. British naval 63.6 The Essence of Design. architects have an old saying, with respect to the shape and form of a ship, that what looks right is right. This invariably brings an immediate rejoinder about who is doing the looking; manifestly not just anybody, but one with an experienced and practical eye. The eye that has deliberately been trained becomes accustomed to look not only for efficiency and utility but for beauty, symmetry, and harmony as really essential features of design. It looks, above all, for simphcity and for the feeling of effortless ease that nature puts into many of her most dynamic moods and manifestations. A good ship, like a good person, is not neces-

Design.

It

is

work

of others.

Remembering that

nothing was ever done so well that

it

could not

be done better, he continually entertains the hope that by his improved understanding of basic

phenomena he can look forward, take form and

life,

as his creations

to greater efficiency

and higher

performance. As certain machines appear to be reaching

their

engineers

or

peak

that nothing in the

be hoped

for,

and

efficiencies

scientists

way

are

of radical

certain

proclaiming

loudly

advances can

other engineers and scientists are

opening up new Unes of attack which often extend the practicable limits by leaps and bounds. This was the case with the piston-type engine and the screw propeller for airplanes

when

the jet-

type engine appeared upon the scene. It is often said that the screw propeller for ship propulsion is about to reach its limit of performance, wherepropellers of increased capacity and improved efficiency under certain working conditions appear in successful service.

upon

It is well in ship design as in

any other work

not to be bound by preconceived ideas of what possible or

by the accomplishments

and others

in the past.

or in fact

is

is

of one's self

A designer who is prepared,

eager to offer novel and improved

new design problems, based upon comprehensive knowledge of fundamental physical laws and the confidence bred of successful solutions to old or

BASIC DESIGN FACTORS

Sec. 63.8

and experience, usually succeeds in finding some ship owner or ship operator who is willing to back his engineering judgment. In this quest for improvement the designer does well to heed the caution expressed by G. Nowka in his "New Knowledge on Ship Propulsion" of 1944 [BuShips Transl. 411, Apr 1951] when he thinking

says

"The

principal guiding rule in shipbuilding

must

read:

Do

not interfere with the laws of hydro-

" dimnmic^ ^

m .

Put tell

another

the water

way

what

it

this

means:

Do

the laws of

has got to do or to make

it

its

behavior.

Another excellent guiding rule for future hydrodynamic ship design, formulated by a ship operator on a basis of economics and experience, says that: "^°°'' hydrodynamic features incorporated into the design of a ship cost nothing originally but afford benefits to the

not try to

445

do something which you desire. It will do what it wants to do, and that only, in accordance*with

owner and operator which

SNAME paper].

last forever" [Lowery, R., Spring Meeting, 1956, in comments on Vincent

CHAPTER

64

Formulation of the Design Specifications Involving Hydrodynamics 64.1 04.2 64.3

General

The

First Task of the Designer Statement of the Principal Design Requirements

64.1

General.

The hydrodynamic design

44G 446

04.4

Absolute Size as a Factor in Maneuvering

64.5

Requirements Tabulation of the Secondary Requirements

pro-

riding on

the

angles.

cities

of

Port Amalo,

Port

Bacine, and Port Correo, leading to the simple project name ABC Design.

Any working example of this kind is but one of a multitude which can be presented to a marine architect. Chap. 76 in this part therefore discusses variations from big-ship rules, applying to the

design of special hull forms and special-purpose craft. It considers

only the problems pecuhar to

the majority of special designs and not treated

adequately or at all in the ABC design. In an effort to cover the hydrodynamic design field for small craft as well as for large ships,

Chap. 77 contains a working example for a motor tender for the ABC ship. 64.2

The

First

Task

is

and aims

quarters that a ship

owner or operator can be relied upon to formulate his own requirements and that these will suffice for the design of the ship. He, however,

is taking only his view of the picture, whereas the designer must look at it from many angles. Furthermore, is

own him to

often so famiUar with his

requirements that it does not occur to pass them on to the designer as pecuUarities.

The

designer

must think

of the

down

here, supple-

more complicated but

equally necessary rules. It covers the development

Com-

only achieved

Once formulated, these aims are kept continually in view and constantly in mind. There is no better way of doing this than to write them on paper, to look at them frequently, and to think about them all the time.

the owner

of a ship specification are set

mented by a few

of fairly complete specifications for the general

of the project.

many

enough to come by it naturally but most have to learn it the hard way, and without any good text or adequate reference works available for study. This chapter is by no means a course in writing specifications but aU the simple rules involved in preparing the hydrodynamic and related features

and the hydrodynamic features of the ABC ship design which is to be prepared as the illustrative

after careful formulation of the purposes

It is considered in

Setting down the ends to be achieved is often not as simple and straightforward a task as appears at first sight. Some designers are fortunate

of a design

of the Designer.

plete success in a design project

452 452

comments, and perhaps find out for himself by and watching the operation of a similar vessel [Simpson, D. S., SNAME, 1951, p. 558]. This is why the designer must in effect prepare his own picture and plan to survey it from all

through this part of the book involves a combination passenger and cargo vessel, because the requirements for such a craft are relatively severe. This vessel is intended to travel between ject carried

hypothetical

.

446

of the right questions to

ask, then ask plenty of them, interpret offhand

446

example.

work up a set of coherent by neglecting or omitting

It is not possible to

design requirements

any considerations whatever of hydrostatics, metacentric

stabiUty,

strength,

engineering,

cargo

handUng, and accommodations such as passenger quarters and crew's berthing and messing. However, only enough of the foregoing features are brought in to make the design specifications hold together, with major accent on those features having to do with hydrodynamics and ship motions.

Statement of the Principal Design ReEven though they may already have been partially or completely drafted by someone 64.3

quirements. else,

it

is

^vise for

the designer to restate the

design requirements in his

own

language.

When

properly worded, these emphasize the limitations

SHIP-DESIGN SPECIFICATIONS

Sec. 64.3

447

—Port Bacine—Port Correo route

Amalo

and conditions imposed by the owner or operator. The latter may have overlooked certain features, seemingly unimportant in appearance but vitally

the Port

essential in design, in his version of the specifica-

The mission a hypothetical vessel of this type, operating in an imaginary part of the world, is rather easily

The

tions.

ship

designer must,

be

moreover,

prepared to present to the ship owner-operator adequate engineering data upon which the latter can make certain design choices within his province.

The data and

facts are to be collected,

developed, and presented by the designer in the

form of clear, concise digests, setting forth the advantages and disadvantages, the premiums and the penalties associated with each choice.

owner-operator can then

The

that he is making from a reasonable

feel

logical,

intelligent selections

number

of design alternatives.

For instance, can the designer build up a case wide bilge or roll-resisting keels forward that project beyond the side at the designed waterline, on the basis of augmented roll- and pitch-quench-

for

ing

Will

characteristics?

was

of

roughed out. The result is given in Table 64.a. This mission, as with the requirements to follow, is intended to emphasize the size, form, power, speed, and other design features having to do primarily with hydrodynamics. It would be amplified considerably

One's views as to what features of the ship are important and controlling often depend upon his position in the overall setup. A limitation on length, for example, may be only an expression of well-hardened opinion on the part of an operator

who

thinks that

it

may

64.a Partial Design Specifications for a Combination Passenger and Cargo Vessel

MISSION The

be,

The guiding

principle in the preparation or

revision of design requirements,

always,

is

forward,

and simple.

plain language

Stress off

the

by

A

and

and short words,

but down, in

specific

setting

just

what the

required to do; just what mission

is

fulfill.

last,

it is

to

ship which ultimately does not carry

is to be reckoned not a no matter how efficiently it may meet one or more secondary requirements. The combination passenger and cargo vessel for

out

its

appointed mission

success,

is

intended

(1)

The

(2)

The

transportation of passengers to and from Port Amalo, Port Bacine, and Port Correo, making the outbound trip from Port Amalo in that order and

the

homeward

trip in reverse order

transportation of liquid bulk cargo from Port

Correo to Port Amalo, and of high-class package cargo back and forth between Port Amalo, Port Bacine, and Port Correo.*

The (3)

service to be rendered requires:

The

safe

and comfortable transportation

of

the

passengers on a rigid, year-round schedule, established well in advance, regardless of local and seasonal

weather conditions (4)

The

(5)

package cargo safe from damage by the elements or from violent and jerky ship motion Performance of the required transportation as

storage

efficiently

and transportation

of the

high-class

and economically as the present

state of

the art permits

and rapid handling and berthing of the vessel under its own power at Ports Bacine and Correo.

(6) Safe

*The "liquid bulk cargo" mentioned in (2) preceding is not composed of heavy oil or its products. However,

necessarily

G. A. Veres has recently (1955) proposed the carrying of passengers on high-speed tankers [SBSR, 23 Jun 1955, p. 797; 7 Jul 1955, p. 5].

to keep the language direct, straight-

informal treatment. Start ship

first,

vessel described in these speciiications

to be used for:

size.

on the other hand, a vital restriction to the designer if he is endeavoring to squeeze out a small margin of speed or power. The salient features of a muddled and verbose specification may need to be brought out so as to keep them alive and vivid before a designing staff. These and other reasons may well justify the extra time spent on highhghting essentials and generally reworking the specifications furnished by someone else. It

considering the ship

TABLE

should be possible to get

everything he wants in a ship of a certain

when

as a whole.

accept a projection of the rudder beyond the extreme stern overhang for the sake of improved flow to the propeller and reduction of vibration?

most

consideration in this part of the book.

owner-operator

the

selected as one hkely to present the

varied and numerous ship-design problems for

The next step is

to write out the principal duties

which the ship is to fulfill, and the principal requirements which must be met. If there are compulsory or mandatory limitations, include them by all means. Do not clutter up these major features of the specifications with details of lesser

importance,

or

with

superlatives

intended

to

emphasize them.

The

first

items to set

down

are those involving

HYDRODYNAMICS

448

size and displacement volume. The ship hull must have enough bulk volume to contain all that is to be put inside it, both below and above water. It must have enough displacement volume

to

float

when

itself

carrying

density cargo which does not these volumes

a

fill

high-weight-

its holds.

List

and weights as a preliminary

to

IN SHIP DESIGN

The outcome

of

Sec. 64.3

this

A

procedure,

for the ship contained in Table 64. b. speed requirement is not yet in the picture.

selected as the example,

Indeed,

is

beginning

before

consideration

of

it

prepared a summary of the meteorologic and oceanographic conditions which the vessel is there

is

to encounter. Table 64. c contains the

summary

estimating and determining the total weight, bulk

for this design problem. If these conditions

volume, and principal dimensions of the ship, but do not attempt to fix the latter features at

during the operating season, as is usually the case, they are carefully analyzed and evaluated.

vary

this stage.

Whatever the custom and procedure may be

TABLE

64. c

Meteorologic and Oceanographic Conditions

elsewhere for determining the overall size of the

assumed

working up a well-proportioned design, that there is no major limitation on size and dimensions except for: ship, it

(a)

is

here, for the sake of

The general requirement

(16) Full account shall be taken, as

conditions in the regions in which the ship

A

specific draft limitation for

passage of a

canal and a river during the voyage.

(17) Tidal

TABLE The

Considerations of Size and Displacement Volume

ship shall be able to:

Carry a liquid-bulk cargo of 4,000 t (of 2,240 lb) from Port Correo to Port Amalo on each trip, for which liquid the weight density will not exceed 42 ft^ per ton of 2,240 lb [Wormald, J., "The Carriage of Edible Oil and Similar Cargoes," LXVIII, pp. 65-91]

IME, Apr

(9)

(10)

1956,

Carry a total weight of package cargo not exceeding 3,000 t back and forth between all ports, requiring a net or usable storage space not less than 300,000 ft' Load and unload package cargo at Port Bacine, both coming and going, without disturbing any through package cargo Carry sufficient fuel to permit bunkering at Port Correo and making the round trip to Port Amalo and return, on the basis of the rigid all-year schedule specified in the foregoing, plus a 15 per cent reserve-

fuel capacity.

exceed 42 (11)

Carry

ft'

The weight

up

density of the fuel will not

per ton.

sufficient fresh

stocking

water and consumable

stores,

Amalo and replenishing upon making the round trip to and from

at Port

return, to permit

Devote a volume

of 400,000 ft' of enclosed space

exclusively to passenger service (13)

(14)

Make

a safe and expeditious passage, under its own power, of the 25-mi ship canal leading to Port Amalo,

which has a minimum depth of 28 ft Negotiate without assistance the 204-mi passage of the fresh-water river from Port Correo to the sea, on the basis of a minimum depth of 30 ft in the navigable area

(15)

The

size

and weight

of the ship shall be a

consistent with these

requirements.

(19)

may

reach 0.5 kt. In the river between

reach 2.75 kt, flowing downstream.

Water temperatures in the fresh-water river at and below Port Correo range from 75 to 80 deg F; those in Ports Amalo and Bacine range from 60 to 75 deg F. It shall be possible to deliver the maximum designed or rated power of the propelling machinery with a sea-water temperature of 75 deg F. Water temperatures in the open sea average about 68 deg F. Fouling is a factor to be reckoned with at all seasons of the year while the vessel

is

at sea. Fouling

stop temporarily while the vessel leading to Port

Amalo and

is

may

in the ship canal

in the fresh-water river

leading to Port Correo but the roughnesses already

accumulated

will

not disappear.

Hurricanes of major proportions

may

be ex-

pected to occur along part of the route during only some three months of the year. However,

unexpected and troublesome storms, with large steep waves, often are encountered for a month

and a

half or

two months before and

after the

hurricane season, overlapping the seasons of heavy

Port Correo (12)

may

the sea and Port Correo the combined tidal and river

current

Vol. (8)

currents in the long ship canal leading to

Port Amalo

64.b

(18) (7)

to

is

the greatest performance from the least ship (b)

is

The average latitude over the whole voyage 20 deg. Surface winds, along the fringes of the hurricane belt between Port Amalo and Port Bacine, may be expected to blow from any direction at velocities up to 90 kt. These are accompanied by ocean waves corresponding to a fetch of at least 500 mi operate.

Table 64.a for

(5) of

important factors in

the design, of the meteorologic and oceanographic

minimum

and subsequent performance

passenger travel. Full account of these adverse conditions therefore

the

design.

plotting

is

taken when laying out

With the rather

modern

careful

and hour-by-hour reporting

of

centers to be expected in the worst areas,

storm it

may

be possible for the ship, with an ample reserve of speed, to save time by running around the storms rather than remaining on course and

down to go through them. Although heavy marine fouling is the

slowing

rule in

SHIP-DESIGN SPECIFICATIONS

Sec. 64.3

certain

warm, salt-water portions

the vessel

is

TABLE

of the route,

traversing the open sea and exposed

(20)

averaging probably not more than 0.6 of that time.

Furthermore, the relatively high speed at which expected to travel prevents this menace from

becoming more than a normal factor in powering. The dock-to-dock schedule which the owneroperator has laid out

is

divided into a canal-and-

ing the allowable navigational speed of 10 kt in

the ship canal in and out of Port

zero natural wind, and at

(22)

reasonably safe speed through the river in and

out of Port Correo. After docking and maneuverall ports is taken into account, the

buoy-to-buoy schedule comes out of the remaining time and distance by simple arithmetic. For this sea schedule the average speed made good in

open water, at either full load or any intermediate displacement and corresponding trim, in fair weather or foul, with smooth or rough bottom, works out as a minimum of 18.7 kt. This is a week-in, week-out performance speed and not a design figure. The ship must be capable of an augmented sea speed to guarantee making the average sustained speed of 18.7 kt under the handicaps of wind, weather, waves, currents,

and

fouling.

The manner

of accomplishing this

and Performance Allowances in Sec. 65.3 and under Powering Allowances in Sec. 69.9. Suffice it to say here that the analysis thus made indicates the necessity explained

is

for

under

Design

the ship to be capable, in smooth water, full

zero natural wind, of

making at

pooped in a following sea, and against carrying away gear on deck are not listed

items

Table

separately because they are implicit in (3)

and

(4)

of the mission,

set forth in

64.a.

all

service dis-

Whatever the augmented sea speed, it shall be attained by the use of not more than 95 per cent of the maximum designed power of the propelling

maximum (24)

The

ship

and machinery shall operate at under conditions (21) and (22) have to slow temporarily in heavy

efficiency

may

weather to 65 per cent of 18.7 kt; this

is

its

average sea speed of

12.16 kt. If so, the schedule must be

met by a corresponding increase in the speed in good weather. The estimated reduction in speed for constant thrust equivalent to a smooth-water speed of 20.5 kt shall not exceed 45 per cent

when running

into a head sea, at an angle of encounter of 180 deg,

through regular waves having lengths Ljp of from 0,8 to 1.5 the ship length L, and heights h^ not exceeding 0.55^/ Lw- (The speed reduction from 20.5 kt to 12.16 kt is 40.7 per cent). Water ballast, preferably fresh water, may be admitted to groups of empty liquid cargo tanks as desired to establish satisfactory propeller submersion and to provide added ship mass on the outward voyage from Port Amalo, when the liquid bulk cargo is not on board. (25) The ship shall be as free of resonant pitching in the waves to be encountered as may be compatible with other requirements (26) A reasonable expenditure of weight or power, or both, to secure to

lurching, against being

any and

machinery

least 20.5 kt.

Other considerations of easy steaming, freedom from wear and tear, long intervals between major machinery overhauls, and general dependability of both materiel and personnel, discussed in Sec. 69.9, require that the 20.5-kt speed be accomplished by the development of only 95 per cent of the maximum designed power. Summarizing this analysis and working in a few related supplementary features produces the speed and wavegoing requirements of Table 64. d. Restrictions against pounding, slamming, and

in

(23) In general, the ship

designed load and in

with clean bottom, at

made good

placement and trim conditions.

Amalo and a

ing time at

or sustained sea speed

with any reasonable amount of bottom roughening and fouling, shall be at least 18.7 kt (21) The augmented sea speed, to achieve the sustained speed, is set tentatively at 20.5 kt. This is to be made in smooth, deep water, with clean bottom, in

and an open-sea schedule by apply-

river schedule

The average

Speed and Wavegoing

each deep-water, open-sea portion of the voyage, in any or all service displacements and under corresponding trim conditions, in any weather, and

to fouling for only a fraction of the voyage time,

it is

449

64.d

the

owner.

diminishing the

effective

roll-quenching

Effective roll

quenching

is

is

acceptable defined

angle to 0.25 (one-quarter) of

as its

natural value.

ments are considered because they may bear some relation to the number and position of propellers to be installed. An analysis of maneuverstatement of the restrictedwater characteristics of various parts of the ing, in turn, calls for a

vessel's route,

somewhat

similar to that of the

meteorologic and oceanographic conditions affect-

The principal features are set down in items (27) through (29) of Table 64.e. The canal bend at Mile 20 is diagrammed in ing wavegoing.

Fig.

64. A,

which contains also the estimated

tracks of large vessels proceeding in both directions,

with their limiting offset positions in the

canal.

The

essentials of the

maneuvering situation

Before going further into the speed and pro-

at Port Bacine are copied from the chart in Fig.

pulsion specifications, the maneuvering require-

64.B, with the estimated ship tracks and positions

HYDRODYNAMICS

ir)0

TABLE

upon leaving its berth at Port Amalo the must make a 180-deg turn in close quarters but tugs are available and will be used

(27) Directly

vessel

ship canal leading from Port

Amalo

to the sea

has a length of 25 mi and a minimum depth of 28 ft. For 16 mi of its length the bottom prism width

and 475 ft. Banks and bed of the hard sand and gravel. At Mile 20 in this restricted portion there is a circularare bend, with short transition sections at the ends, having a total change in direction of 50 deg and an varies between 400

restricted channel are of

inside radius of 3,800 ft; see Fig. 64.A.

when running

at

any practicable

displace-

trim, the ship shall be capable of:

Executing the transient portions of a turn, swinging first away from and then back into a straight course, involving changes of heading of from 25 to 30 deg for each maneuver, and gaining or losing an offset of 400 ft, perpendicular to the approach path, in a curved run of 2,100 ft. This shall be accomplished in a canal prism having a depth of 32 ft and a bottom width of 400 to 500 ft, at speeds of from 6 to 8 kt, and with not more than one-third the maximum rudder angle. (33) Swinging bow to port and stern to starboard, and

(32)

The bottom

width at midlength of this bend is 500 ft and the depth is 32 ft. (29) Port Correo is at the head of ocean navigation on a long, wide, fresh-water river, 204 mi from the sea, with a minimum and fairly constant depth of 30 ft in the dry season and a soft mud bottom. Large trees and other flood debris are often encountered floating (30)

Specifically,

ment and

follows:

The

Src. 61.3

measured from the extreme end of the wooden pier and in line with it, is 1,500 ft. area,

The restricted waters forming part of the route and the required ship operation in them are described as

(28)

IN SHIP DESIGN

64.e— Maneuvering

vice versa,

when operating

the propulsion device (s)

an astern direction, with negligible wind and in water having a depth-draft ratio not exceeding 1.5, or a maximum depth of 40 ft. It shall be possible to execute this maneuver from a standing start or from a straight approach path when moving astern in

at a speed not exceeding 13 kt. (34)

Executing a 180-deg turn within a tactical diameter

in the river.

of 3,000 ft in deep water, with full rudder angle

Adequate steering and maneuvering characteristics

at an approach speed of 19 kt

shall

be provided for traveling in the ship canal

(35)

leading from the sea to Port Amalo, on the basis of

meeting other large ships in this canal. It is not necessary to meet these ships in the bend at Mile 20. Similar requirements are established for the passage of the river leading from the sea to Port Correo. (31) It shall be possible to berth the vessel at Port Bacine, under its own power, in a slip terminated by U-shaped walls of sohd masonry, 100 ft apart in the clear at the head of the slip and extending for a distance of 100 ft therefrom. An open-work wooden pier prolongs one of these walls for a distance of 450 ft, indicated in Fig. 64.B. The vessel must, under its own power, make a 50- or 60-deg turn after backing out of the sKp and prior to proceeding out of the channel to sea.

The

clearance to the opposite side of the navigable

Fio. 64. A

When

and

turning in accordance with (34), the angle of A maximum angle

heel shall be limited to 10 deg. riot

(36)

exceeding 8 deg

At an ahead speed shall

is

preferred.

of 20.5 kt,

on a straight course, it maneuver

be possible to execute a crash-back

and to stop dead

in the

water with a head reach not

exceeding 6 ship lengths (37)

The machinery

shall be capable of developing

an

astern torque of 80 per cent of the rated ahead

and an astern rate of rotation of 50 per cent ahead rate, with the ship stationary in the water, as at the end of a crash-back maneuver If left to itself when running ahead in smooth water, with no perceptible swinging motion and the rudder stationary at zero angle, the ship shall not deviate progressively from its original course. In other torque, of the

(38)

Scale Diagram of 50-Deo Bend in Canal Leading prom Port Amalo to the Sea

SHIP-DESIGN SPECIFICATIONS

Sec. 64.3

Fig. 64. B

Proposed Maneuvering Diageam for

words, the ship shall possess dynamic stability of (39)

(40)

A

ABC

451

Ship in Port Bacine

rudder angle not exceeding 7.5 deg shall suffice

route.

for steady, straight-course running in straightaway

A

reaches of the canal at Port Port Correo, with from 3 to 4

limiting small rudder angle not exceeding 3 deg

shall suffice for

good manual steering In smooth,

deep water and neghgible wind, at all speeds over one-half of the sustained speed, with right or left variations in yaw not to exceed 2.0 deg. This shall include all displacement and trim conditions likely in open-sea running.

Amalo and the ft

river at

channel-bed clearance

under the ship (41)

The

ship shall be controllable when underway in heavy weather at whatever speeds and courses can

be maintained in that weather.

HYDRODYNAMICS

452

IN SHIP DESIGN

Sec. 64.4

added. These are based upon entering the ship head-on, directly from the sea entrance, and upon

far cry

from the same procedure for a self-propelled

model

in a miniature channel,

swinging the ship by a considerable amount, when backing out of the slip, by working on a spring line attached to the outer end of the pier.

possibly five or six times as fast.

Translating the ship maneuvers of Figs. 64.A

B

maneuvering requirements gives the items hsted as (32) and (33) in Table 64.e. Because of lack of authentic information on the astern maneuvering characteristics of ships,

and

64.

into specific

the requirements in (33) are

left

The requirements

in character.

rather general

in (34)

and

(36)

Consider a modern 25-ft pilot model of a large planing boat.

33

The

makes 60 kt at the same T^

craft

covers

its

own

time ratio

required of the vessel on each voyage.

Power

The former

linear scale ratio

(3.24)°'' or 1.8 times as

is

fast for the pilot model.

Other things being equal,

the 25-ft craft turns in a circle over 3 times as

As the absolute

is

With a

latter requires 0.80 sec. of 3.24, the

.

length in 0.45 sec whereas the

tight as the 81-ft one,

restricted-water traveling that

while the 81-ft full-scale

6.6,

maneuvered handily in an emergency. Rather exceptional controllability as regards steering is called for, because of the more than of

model might well run at

pilot

with a T, of

kt,

are intended to insure that the vessel can be

450 miles

with a time rate

and so

on.

on the other

size increases,

hand, the proportion between

(1)

disturbance to manifest

and

itself

the time for a

a

(2)

human

perception or an automatic-control time increases rather rapidly.

On

small craft, often with large powers relative

not a factor in these restricted waters because the speeds are limited by wave wash on the banks, the presence of other vessels close by,

venience or injure personnel and result in damage

and the excessive sinkage at the stern that would

to materiel.

be encountered at the higher speeds. 64.4 Absolute Size as a Factor in Maneuvering Requirements. Maneuvering requirements, in-

cost.

is

to their size, too-rapid

On large ships, demands for improved maneuvering performance can run rapidly at times into increased weight, complication, and

volving steering, turning, stopping, backing, and

64.5

the equivalent, form a sadly neglected part of the

ments.

and sizes of water craft. Increasing emphasis has been placed, and will

been set down, and

specifications for all types

continue to be placed, upon the safety of life of vessels at sea. It has been necessary in

and

past emergencies, and

it will

be more necessary

in future ones, for all types of craft to undertake

turning and other maneuvers which will confuse those

who

air. It

may be

ing

will

selecting definite it

is

(43)

times operate the

account

As long

of

craft, it is

than 0.55

Take

in

necessary to take

these factors. Thinking and giving

piloting orders for a ship transiting a canal

is

a

and discharge water

for heat enchangers at

to anchor with two bower anchors in the river leading from Port Correo to the sea, in

Be prepared up

to 2.3 kt

from whatever such a manner that not form a nuisance to either crew or

(45) Discharge the products of combustion,

source, at such a point

they will passengers (46)

and

in

Be free of spray and high-speed local air currents so that in "outdoors" weather, passengers shall not be inconvenienced in their enjoyment of the sun, sky, and sea

(47) Provide internal heavj'-weather access to all spaces in

as

beings with more-or-less fixed reaction

the ship

the baseplane (44)

large ships, entirely

of its linear ratio to the large craft.

known what

points not below the 1-ft waterline, reckoned from

these can not be based, for small craft as well as

such as the length. a small vessel than on a large one. The rate of motion on a small craft, for geometrically similar maneuvers, increases directly as the square root

is

a square moment of area coefficient of the designed waterline, about the longitudinal axis, not

to be

upon some linear dimension Things happen much faster on

it

(42) Possess

currents

numbers for maneuverremembered that

the principal requirements have

Insofar as practicable, consistent with the principal

definite, will certainly follow.

ing requirements

all

requirements of the design, the ship shall:

appear with increasing

frequency in ship specifications. The insertion of specific numbers, making the requirements more

human

When

less

requirements

When

Tabulation of the Secondary Require-

TABLE 64.f—DESIRABLE FEATURES INVOLVING HYDRODYNAMICS AND FORM

are dropping or firing missiles from the

expected, therefore, that maneuver-

maneuvering can incon-

(48)

which personnel are required during cruising at sea

vulnerable projections outside the main hull first 150 ft of the length, from the keel up to the 35-ft waterline, which might be damaged by the old stone pier at Port Bacine; also have no projections

Have no

within the

below the

fair line of the

bottom

of the

main

hull.

SHIP-DESIGN SPECIFICATIONS

Sec. 64.5

must do, the next step is to put down what the owner or operator would like to have the ship do. This involves listing the secondary or desirable features of the specifications. These afford the designer an idea of the preferences involved, and the relative importance of each. As such, they furnish a valuable guide in working up many elements of the design. It is wise to list all features of this kind, even though at first thought they may seem only remotely related or distinctly unrelated to the hydrodynamics of the problem. A statement prepared along these lines may have the form of that presented in Table 64. f. The

With the

453

desirable features

limitations, restrictions,

it is

of a so-called negative nature.

the

should

specifications

definitely

any and

all

well to include

and other

specifications

In other words,

describe

clearly

and

things that the ship should

do or should not have. The features listed under (49) and (50) of Table 64. g belong in this not

category.

The

specifications in this stage are terminated

by a group of items, not conveniently Three of them appear in Table 64. g.

The problem

classified.

hydrodynamic design becomes apparent as the

working over these requiremutually consistent and are in numerical, coefficient, or other form, ready to apply to the detail design, is taken up in the

design proceeds.

chapter following.

relationship of certain of these features to the

ments

The 64.g— FEATURES

TABLE

NOT OTHERWISE

CLASSIFIED

liquid capacity called for in these specifi-

cations not only permits the ship to carry liquid

cargo on the particular run or in the particular service for

(49)

Freedom from vibration and noise, while not a must, is a most desirable end to be achieved. In any case,

(50)

the estimated frequencies of periodic hydro-

dynamic forces shall be reported to the buOder at least two months before the vessel's first sea trials. It is expected that, by the time the vessel is put into service,

the

harbor regulations will prohibit the

discharge of sanitary drains into the water areas at all

(51)

three ports, the canal,

and the fresh-water

The maximum layover times

river

at the three ports

may

be assumed as follows:

of

until they are

which

it is

designed but enables

carry any other liquid cargo which

may

it

to

be in-

volved in some unexpected service of the future.

In the existing state of world industrialization it appears that for the life of this vessel liquids of

some kind

or other will always be useful

and

profitable cargo. Furthermore, the provision of this

tankage in the after part

of the hull

makes

it

possible to utilize water ballast to insure adequate

Port Amalo, 3 days; Port Bacine, 24 hours; Port

and freedom from slamming and pounding when running in waves at relatively

Correo, 2.83 days (68 hr).

light-load conditions.

propeller submersion

CHAPTER

65

General Problems of the Ship Designer 65

.

Interpretation

of

Ready-Made Design Re-

quirements

65.2

Departures from the Letter of the Specifications

65 3 .

65 4 65 5 .

.

....

Design and Performance Allowances Basis for the Selection of Ship Dimensions Determination of the General Hull Features

65.1

Interpretation

Requirements.

65.6

Limits for Wavegoing Conditions to be Encountered

65.7 65.8 65 9

The Bracketing Design Technique

454

It

is

of

.

.

454 464 457 457

.

.

Ready-Made Design

compromises

whom

possible for the hapless ship

458 458 459

Adherence to Design Details in Construction Guaranteeing the Performance of a New Ship Design

rests

the ship

459

with the owner or operator for being designed. A decision

is

designer to be confronted with a set of pre-

concerning a modification or relaxation of the

posterous requirements and specifications, not of his own formulation. On first reading these may

specifications can only be

the basis of reasonably accurate and

seem to

call for achieving the impossible. After an anxious time the designer may be relieved, but

information concerning the price which the owner or operator

must pay

nevertheless bewildered, to find that he

money

in

is

not

or

performance.

He may, on the contrary, find that they have both claws and teeth, and that he is expected to accomplish what no one before him

structive suggestions,

their severity.

has done. It

most important, requirements and

is

therefore, that

when a set of specifications is handed to him, the designer assess them carefully and that he determine in advance how they are to be interpreted.

However, it is assumed here that the ship requirements are laid down in all sincerity and that they are expected to be observed in the same fashion, both as to their spirit and their letter. If there

is

in

them any semblance

the moon, the reaching

is

of reaching for

clearly indicated

and

good reason for it. A case in point is the and open-sea performance required of the ABC design, which in many respects is a Umited-draft river vessel. If parts of there

is

superlative deep-water

the

requirements

are

intended

primarily

for

and

information

guidance rather than strict compliance, they in turn are clearly so marked. 65.2 Departures from the Letter of the Specifi-

Notwithstanding the most conscientious effort, it is rarely possible to comply with every letter of the complete design requirements and performance specifications for a ship. Some compromises must always be made to produce the cations.

design and

some

be accepted.

relaxation of the specifications

The burden

of

accepting

these

It is

intelligentl}''

on

reliable

for this change, either in

power,

speed,

expected to meet them, but only to be awed by

made

endurance,

a duty of the ship designer to

and

offer con-

propose compromises, or

put forth alternative solutions in all cases of conflict between the original requirements and specifications. This procedure applies as well to conflicts between these requirements and the capabilities of construction materials, machinery, and equipment in the present state of the art. For example, vertical or wall sides are indicated for the in

way

bow

sections of a fast or liigh-speed ship

of the

bow-wave

crest.

To

accomplish this

may

require a rather sharp reentrant curve in the

bow

section lines

above the top of this wave in a way, the gently flaring V-sections which may have been drawn in forward above the water fine for good wavegoing perThis

crest.

formance.

spoils,

The

designer

therefore

prepares

to

estimate the increase in smooth-Avater resistance

and power due to the use

of fair V-sections

to predict the possible adverse effects of

and

somewhat

hollow V-sections when pitching or plowing into

head

seas. Similarly,

he

is

prepared to give figures and power,

relating to the change in resistance

and the modification in roll-quenching characteristics, for

proposed variations in the bilge-keel

length.

65.3

Whether the

454

Design

and Performance

Allowances.

or not they are written specifically into

requirements,

a

ship

designer

must,

by

GENERAL PROBLEMS OF DESTGNER

Sec. r,'i3

interpretation or direct discussion with the owner-

455

It is well at this point to discuss briefly the

operator, arrive at a schedule of allowances or

expression "sustained speed." This term often

performance factors which is to be followed throughout the course of the design. Granting

used but seldom defined, perhaps because to sustain a speed in one area or on one run means something quite different from sustaining it on

that

the

prophet

if

are

estimates

designer's

and

correct

overspeed, and other operating con-

overload,

ditions to be encountered in the If

invariably

he is truly a he can predict the combinations of his calculations precise,

the ship takes these in

for having designed a

of the ship.

life

its stride,

good one.

he

is

praised

If not,

he

is

be blamed because the ship can not take extra once in a while. Indeed, the mark of

liable to

a

little

a superlative designer

may

be as

much

and engineering

intelligence,

he inserts here and there as in the balance which he achieves in the overall design.

intuition,

It is difficult to give rules for these allowances.

The more performance that

is

being squeezed out

the smaller the allowances must

a design,

of

and the greater the knowledge

necessarily be

motorboat,

racing

approach

In an icebreaker they can and

zero.

Emphasis is laid on the primary function of the vessel, and the allowances favor the continued and reliable performance of that function. A ferryboat running on a published timetable, year

and year

schedule,

is

many

out, with

people relying on

its

given a generous power and speed

allowance, provided

A

ship to it

economy

is

make a given

not sacrificed.

tug can always use extra power, to meet the

way

in the

inadequacies

of

or

casualties

to

personnel

(e)

or

Loss of capacity, power, or efficiency because

of deterioration, delayed overhaul,

is

less real

and general

wear and tear (g)

Low quality of fuel Any combination of

the foregoing and any

other adverse influences.

To

average a given sustained speed on a run,

come what may, means that a

ship has to possess

a reserve capacity or ability of some kind. This

not only

to

is

make up

for lost time

but to keep

going regardless of the circumstances, short of hurricanes, typhoons,

allowance

The

of:

Wind, waves, and weather Roughness drag due to deterioration of the paint or other coating and that due to fouling of any and all kinds (c) Improper trim or attitude for the speed range, due to causes beyond control of the ship personnel (d) Temporary slowdowns or stoppages due to

ship,

it.

of

(b)

determined the greater allowance a designer

upon

means that

whatever it takes allowances and margins to average

speed over any run, in spite

this

demands of progress as the vessel puts in more and more years of service. The less accurately some quantity can be

increasing

generally forced to place

sustained speed

has, in self-contained fashion,

(f)

should be large.

in

as a whole. For the general case, the ability of a

materiel

they

example,

for

means both

it

of

the forces and other factors involved. In a high-

speed

ship

parts of the one-way run, as well as the voyage

(a)

in the

margins, allowances, and design factors which, in his knowledge,

ABC

another run. For the

is

and the

like.

No

ship can

be designed to cope with extreme emergencies. The reserve is designed into and built into the

of all

the form

in

allowances.

of

The

design

based upon 100 per cent functioning personnel and materiel. The performance is

proof he has of the validity of some estimate or

allowance takes care of incomplete, functioning,

prediction, or the less confidence he has in

as set forth in (d),

must be

greater

The mission Table

it,

the

his allowance.

of the

ABC

ship requires, from

adherence to a "rigid, year-round schedule, estabhshed well in advance, regardless of local and seasonal weather conditions." The owner-operator is emphatic in pointing out that this

64. a,

means what

it

says.

The study forming the

basis of the speed requirements of Table 64.d

indicates a

minimum

average or sustained speed

of 18.7 kt to achieve the mission.

attained factors?

when

there

are

so

How is

this best

many unknown

(e), and (f) preceding. There are several ways of making these allowances. The most logical and undoubtedly the preferred one is for the designer to modify the owner-operator requirements for his own use and

then to design as closely as practicable to those is thus possible, when the vessel

modifications. It

completed, to check the actual design from the observed performance, and to use the information thus confirmed for future designs. For example,

is

instead of calling for

power,

or

some

15 per cent extra shaft

other

amount picked from

operating data to insure that the sustained speed

HYDRODYNAMICS

456 is

achieved, the designer adds a definite allowance

to that speed. This

may

be, say, one-third of the

power margin, on the basis that the shaft power varies about as V^. The speed allowance is then

+5

per cent.

closely to this

When

He

proceeds to design the ship

augmented speed.

the trials are run

it is

usually as easy,

extra power as the 5 per cent extra speed.

How-

margin that can be reliably predicted, and with a ship fashioned and built for the augmented speed, the designer is in a better position to promise the given sustained speed than if he crowds extra power into a ship built only for that speed. Other reasons for designing-in a speed margin rather than a power margin are set forth in Part 6 of Volume HI under wavegoing. E. V. Lewis points out that with the large powers and high smooth-water speeds of many modern (1956) vessels it becomes increasingly difficult to maintain high average speeds in certain rough-water areas such as the North Atlantic [SBSR, 30 Aug 1956, p. 277]. It may be expected, however, that increased emphasis on wavegoing characteristics and further progress in wavegoing design will increase the rough-water ever, with a speed

when

it is

the

ABC

Sec.

ship, or for

any other design

in

speed rather than a power allowance

653

which a to be

is

incorporated, the selection or determination of

that allowance requires careful study, combined

with intelligence, judgment, and wisdom. There are considerations of sea routes to be followed,

or perhaps easier, to measure the 15 per cent

speeds so that,

IN SHIP DESIGN

sufficiently important,

times of arrival and departure during the day, reliability

in

maintaining the sailing schedule,

economics, and

many

others which need not be

entered into or elaborated upon here.

On

the basis that heavy weather slows the ship

to say 0.7 times

its

sustained speed for a certain

portion of an open-sea run,

simple arithmetic

to

what the augmented sea speed must be bring the average up to the sustained speed.

A

similar procedure can be applied to the speed

indicates

bottom roughening and fouling or to an assumed compulsory slowing of the propelling plant for any given length of time. The contingency in which the delays occur unexpectedly at the very end of a run is met by speeding up for good measure in the early part of the run. This matter is discussed by R. K. Craig, when describing the service performance of a passenger effects of

liner

with engines aft

[SBMEB, Dec

The speed allowance ship,

as

from 18.7 to 20.5

specified

of

1955, p. 693].

1.8 kt for the

kt, or

ABC

roughly 10 per cent,

tentatively in Table 64. d

and as

a high sustained speed can be achieved in any

incorporated in Table 65. a with other design and

service.

performance

For the preliminary hydrodynamic design

TABLE Performance Item

65. a

—ABC

Ship:

of

allowances,

is

intended

to

serve

only as an example of the procedure involved.

Design and Performance Allowances

Src. 65

J

GENERAL PROBLEMS OF DESIGNER

457

surface.

The volume

of the pressure hull, plus the

volume

of all structure, fittings,

However, design to the 20.5-kt requirement means

made

that this can be

the

trial

speed, under ideal

Both the design and the ship

conditions.

trial

can be proved on trial, leaving the owner-operator with the assurance that the ship has an adequate margin of both power and speed. The general method followed here for the ABC ship has been

lying in the water

and equipment

when the submarine

is submerged, determines the displacement or total weight of the vessel for water of the specified

volume displacement

density. This

is

substantially

the same for the vessel under any running con-

because

merchant-type naval for twenty years or more. It has been found eminently successful, for services of varied nature, in most of the oceans

dition, in

of the world.

beam, depth, and draft but the volume, displacement, and weight; possibly even the general shape of the ship. Almost invariably it must be

vary the amount and percentage of reserve buoyancy in a submarine design by varying the shape and volume of the outer hull, since the main-ballast tanks between the two are empty in surface condition and filled with water when submerged. For submerged propulsion all this volume, plus all the water volume in the free-flooding spaces, has to be taken into account, just as if it were frozen into ice and carried along with the ship. This is

decided whether:

the bulk volume of the submarine.

used

the

for

design

auxiliaries for the

At a very

ship, or is

perhaps before that design

is

really begun,

necessary to determine the basis for the

These

selection of the principal ship dimensions.

not only the customary linear length,

include,

(a)

The ship is to be designed on a weight-carrying

basis (b)

The design

is

to be on a volumetric basis, to

provide space (c)

Inflexible

Umits are to be imposed on certain

dimensions, such as for a ship which must inside certain piers at a terminal or which

fit

must

pass through locks in a canal.

The displacement

by the weight

is

as a

of the cargo or load to

be carried plus the weight of hull and machinery, fuel, consumable stores, and margin. The underwater hull must possess sufficient volume to support the total weight in water of the specified density. When ships are to carry bulky but not particularly heavy cargoes such as railway cars, automobiles,

trucks,

and other vehicles

generally possible to carry

much

it

is

of this cargo

Due

volume

above

regard

of course given to metacentric stability

is

the

designed

waterUne.

and other requirements. In designs a large

of this kind,

not the greater part of the useful enclosed volume of the ship is above water, leaving only if

enough volume

in the

specific gravity,

equivalent weight of water, and so on.

however,

It

is

to

Because of available space around and depth under the ship when docking and maneuvering, of limited first cost, of adequate metacentric stability, or of some factor not remotely related to hydrodynamic design it often becomes necessary to impose some definite or arbitrary limits upon the principal hnear dimensions for a given weight or volumetric capacity. This is where the designer's troubles really begin.

of ships carrying cargoes of

high weight densities or specific gravities rule fixed

water of a given

the scale weight of the ship remains substantially the same. If fuel is consumed it is replaced by an possible,

Basis for the Selection of Ship Dimenearly stage in the design of a

65.4 sions.

it

of

U.S. Navy

underwater hull to carry

65.5

Determination

Features.

The

General

the

of

general hull features of a

ship design can be determined in either of

Hull

new two

—

ways. One can start figuratively in the air or with only the operating better, in the water requirements, and fashion the ship out of the blue.

—

Alternatively, one can expand or contract the hull "of a

known

good performance" 1892, p. 211] and approximation to a new vessel vessel of

[EUis, J. J., Froude, R. E.,

thus obtain a

which

first

INA,

will fulfill those requirements.

It is theoretically possible for

an experienced

ship designer, working to a given set of specifications, to select

a type of

hull, to

determine

its

and to make a tentative decision to embody in it some special or unusual feature by working only from general shape, to define

its

proportions,

the total weight.

available reference libraries, including his own.

In the case of submarines it is necessary to crowd within the pressure hull everything which

despite the

can not be entirely or partly surrounded by water when the vessel is submerged or running on the

elements which come into the picture. Indeed, it is often much better to start with a clean sheet,

It has often

been done, and most successfully,

many

indefinite

and unpredictable

HYDRODYNAMICS

458 as

it

were, because then the design problems are

more clearly and they may be solved in the most simple and direct manner. Using an alternative procedure, it is often possible to work up a new hull design as a variant visualized

development of a previous design which has proved itself in the same service and which may be taken as a sort of parent form. This or as a

procedure

is

facilitated

by

reference to the rather

comprehensive data now in existence on the behavior of a multitude of ships and their models, such as the SNAME Resistance Data sheets 1 through 160. The quantitative information required to set up a design and to carry it through the successive steps must necessarily be derived from model and ship performance data which are known to be accurate and reliable. When in doubt, the data are to be used with caution or, if possible, only after a check and double check. The parent-form-copying or development procedure manifestly forms an unsound or at least an uncertain basis for the design of a ship to meet totally new and unexpected requirements. A certain amount of improvement results from successive developments of a given parent design but more real progress is often made by starting

out afresh. Remember that the ship being copied or modified was designed not yesterday but several

years ago.

to admit that

first

Its

designer would

much has been

be the

learned since

then. If starting out today, even he

would not

reproduce the design exactly. 65.6 Limits for Wavegoing Conditions to be

Encountered.

To

develop intelligently a good

ship design for wavegoing requires the establish-

ment,

if

practicable, of

some

sort of limits for the

wavegoing conditions to be encountered, more precise than those of Table 64. d. Will most of the waves be shorter or longer than the ship, or about the same length? Will they be long and regular, or short, steep, and confused? This can be done on the basis of:

IN SHIP DESIGN

Sec. 65.6

and a deliberate acceptance of whatever performance is obtained in other types of seas. sea,

Obviously, the design problem simplified

the ship

if

is

is

materially

to operate on only one

run and to travel only in certain areas, especially if the sea conditions in those areas are reasonably consistent

and predictable.

The Bracketing Design Technique.

65.7

In

a pioneering design, for which the basic physical phenomena are somewhat uncertain and the of past

results

experience are Umited or non-

becomes necessary for a unknown and unHe must commit himself and others

existent, it frequently

designer to reach far into an

trodden

field.

to the acceptance of risks or the expenditure of

funds which under normal circumstances could not be justified as good engineering. In this

predicament he desperately needs any kind of assurance, no matter what its source or reliability. Fortunately, there is one means by which a ship designer can extricate himself from a situation such as this a method which has been found

—

and successful

useful

in

many

other lines

of

endeavor.

The

essence of this

method

is

to determine the

extreme hmits of position in the unknown field, then to fix a position between these limits by any simple convenient method which appears suitable. The region in which the unknown solution is to be found lies somewhere between the two limits and is thus bracketed by them. The position of the region with respect to the limits, in other words the spotting of the region where the solution probably Ues, involves a process of arithmetic averaging or of estimating by a sort of mean proportional of the hmits.

A

design problem of this kind developed with

the shaping of the alternative arch-type or tunnel stern for the It

ABC

ship, described in Sec. 67.16.

was considered most important that the maxi-

mum

fore-and-aft slope of the roof of the tunnel

be as large as possible, yet not so large as to

(a) Existing knowledge of weather and waves along the specified route in the various seasons of

result in irregular flow or separation along the

the year, based on some sort of statistical analysis

that on large ships with twin skegs, tunnel slopes

of extensive data

of 8 to 9 deg were satisfactory, with the roof submerged a moderate amount below the at-rest waterhne. There was evidence on some special models that a centerplane slope of 30 deg, at the same degree of submergence but on a convex body surface and not in a concave tunnel roof, was free from separation. It seemed reasonable to

from the statistical data of the characteristics and pattern of the predominant wave, or the features of the one which is Ukely to prove the most troublesome (b) Selection

(c)

An

give

its

arbitrary declaration that the ship shall

best performance in a specified type of

tunnel roof. There was ample full-scale evidence

GENERAL PROBLEMS OF DESIGNER

Sec. 65.9

halve the 30-deg slope of the special models, giving 15 deg, but at the

same time

it

appeared

risky to double the ship slopes, involving values as high as 16 to 18 deg. Nevertheless, this pro-

cedure narrowed the choice from somewhere in the wide range of 21 deg, between 30 and 9 deg, to the

much

smaller range of 3 deg, between 18

and 15 deg. On the basis that no ship would be built with an arch stern unless a model was first

459

form indicated on the plans

avail unless the

is

reproduced on the ship. Indeed, a projecting welding bead, transverse to the flow in a high-velocity region near the surface, can and has produced cavitation, noise, and vibration faithfully

of plate panels.

Not only

that,

plate metal

has produced and then of the

it

erosion, first of the paint coating itself.

rather important to point out that, no matter

Guaranteeing the Performance of a New Ship Design. Finally, the ship designer must, upon the completion of a design, execute what is in effect a guarantee of its performance. Where the apphcation of hydrodynamics is concerned, as in this book, the guarantee relates to propulsion, maneuvering, wavegoing, and all other normal and special operations taken for granted or specifically mentioned in the original require-

how good

ments.

thoroughly tested, the

maximum

tunnel slope

was set at 18 deg. Subsequent flow tests on the model showed no separation or harmful flow of any kind. 65.8 Adherence to Design Details in Construction.

Although

all

features of ship construction

are outside the scope of this book

the ship design,

it

it is

considered

requires a thorough

65.9

A

who

own

and intensive follow-through, from beginning to end of the building period. Only in this way

embodied

can a designer insure that the continual pressure

specifications need

to cut corners in production does not affect the

conclusion of his work the ship will

service performance

and

reliability of the vessel.

In the event of failure or casualty the blame liable to fall as

much on

is

the designer as on the

has, to his

sufficient allowances to

have

little

is

this follow-through

more necessary

and important than in the shaping, assembly, and finishing of the underwater hull surface and appendages. The most carefully calculated and cavitation-free rudder or strut shape is of no

satisfaction,

meet the various

fear that at the

found lacking in any element of

fail

its

or be

behavior.

Only too often, unfortunately, the designer's hand is forced in that he is required to make disturbing compromises or to

builder.

Nowhere

designer

embody

features

warned by his better judgment or his engineering instinct. Under these circumstances he must go to some pains and often to against which he

is

great lengths to assure himself that his estimates

and predictions are

reliable.

CHAPTER

66

Steps in the Preliminary Design General Considerations

66.1 66.2 66.3 66.4 66.5

Hydrodynamic Requirements Probable Variable- Weight Conditions First Weight Estimate First Approximation to Principal Dimensions; The Waterline Length and Fatness Analj'sis of the

.

.

Ratio

66.6 66.7

The Longitudinal Prismatic Coefficient The Maximum-Section Coefficient; The

66.8 66.9 66.10 66.11

First Estimate of Hull

66^12 66.13 66.14

Selection of Hull Shape

66.15 66.16 66.17

First Sketch of Designed Waterline

.

Draft and First

.

Beam

Volume ...... Approximation to Shaft Power ...

Second Estimate of Principal Weights Second Approximation to Principal Dimen.

.

sions

Layout First

.

and Proportions of

Maximum-Section Contour

Estimate

Relating

to

.

.

.

Maximum-Area Parallel

Curve;

Position

.

Transom-Stern Parameters

.

.

464 467

468 471 471 474

.

486

and

Molding a New Underwater Form Bow and Stern Profiles Analysis of the Wetted Surface Second Approximation to Shaft Power Sketching of Wave Profile and Probable

Small-Scale

of

Profiles

.

.

.

475 476 476

66.31

66.32

Propeller Submersion and

66.33

Maneuverand Shallow- Water Behavior .... Preparation of Alternative Preliminary De-

Trim

66.34

498

of Hulls

Effect of Unrelated Factors

Upon

the

Hydro502

dynamic Design

As a means

preliminary-design

and hydrodynamic

of illustrating the procedures

steps involved in the application of principles

501 501 602

signs

Laying Out Other Types

66.35 66.36

phenomena, paralleling that followed in Parts 1 and 2 of the book. Since knowledge of the hydrodynamic phenomena pertaining to interactions between all portions of the ship is not

496

First Appro.ximation of Steering, ing,

482 483 485 485

496

in Variable-

Load Conditions

The

491 493 493

497

Balance

478 479

486 488

494

Comparison with a Ship Form of Good Performance Abovewater Hull Proportions for Strength and Wavegoing First Longitudinal Weight and Buoyancy

66.30

485

of

66.24 66.25 66 26 66.27 66.28 66.29

flow

the

.

Flowlines

suited to the knowledge, experience, background, and ability of the designer so that each has its particular merits. An example of such an alternative method is given by E. E. Bustard in his paper "Preliminary Calculations in Ship Design" [NECI, 1940-1941, Vol. LVII, pp. 179-206 and D49-D62]. A presentation such as that set down here is of necessity limited to a single method, or at most, to two such methods. These are based logically upon a consideration of

of

.

Center

Preparation

.

of executing the

part

Curve

the

66.23

General Considerations.

complete,

of

Sections

ularly

yet

Section- Area

Position

Buoyancy

There are as hydrodynamic design of a ship, at least in its prehminary stages, as there are ship designers. Each of them is partic66.1

many ways

Longitudinal

.

481

Middlebody

Bulb-Bow Parameters

Shape

The Preliminary

66.21 66 22

Metacentric

Stability

Estimated Draft Variations Sketching the Section- Area

66.18 66.19 66.20

460 460 463 463

and knowledge to ship

design,

the

preliminary layout and a portion of the final design of the

and is

ABC

specifications

vessel, whose requirements were formulated in Chap. 64,

and succeeding chapters. merchant type and is largely

carried through in this

This craft

is

of the

orthodox in character, with elements similar to those found on many past and current designs of ships. A number of unusual features are included, partly to give character to the design and partly to permit application of much of the

hydrodynamic knowledge and many of the procedures previously set down. 66.2 Analysis of the Hydrodynamic Requirements. it is

and

Before beguuiing the preliminary design

well to analyze

requirements

some

of the specifications

formulated

in

Sec.

64.3.

work must be accomplished by empirical methods based upon ship-model tests, ship-trial data, and

Portions of them require conversion into terms

past experience.

resulting in

hydrodynamic design, which can be used as

directly applicable to the

460

quantities

Sec. 66.2

STEPS IN PRELIMINARY DESIGN TABLE

Sector of Voyage

66.a

Resteictbd-Channel and Open-Sea Data

461

HYDRODYNAMICS

462

speed is specified in the river leading out from Port Correo and no safe speed can be predicted until the size

and shape

of the vessel is

known.

Past experience with smaller vessels, however, indicates that this may be hmited to 13 or 14 kt, reckoned as speed through the water rather than speed over the ground. The layover, standby, and maneuvering times are then set down, in hours, as in the upper part

IN SHIP DESIGN rate at the

Sec. 66.2

maximum designed

power. Multiplying

by the hours during which burned at the corresponding rate gives the corresponding hours during which the consumption would be the same if the vessel were steaming these average fractions

fuel is

at

maximum The

designed power.

elapsed times for the underway sectors are

of Table 66. c, starting with the beginning of a voyage at Port Amalo. Opposite these are marked

then calculated, as shown in the lower part of Table 66. c. In the open sea, it is assumed that the fuel consumption for each hour is that corresponding to the designed maximum power,

the estimated average fuel-consumption rates for

despite the fact that the actual speed

the periods given, intended to cover

less,

all

auxiliary

as well as propelling-plant loads. These rates are

slightly more,

expressed as fractions of the fuel-consumption

This extra

TABLE The

66.0

generally

and that the elapsed time

fuel, calculated as

is

longer.

necessary but not

Fuel Consumption Rates fob Voyage Components

expression rated fuel signifies the rate of fuel consumption at

Name

is

averaging 18.7 kt as compared to 20.5 kt or

of Operation

maximum

designed power,

all

services in operation.

STEPS IN PRELIMINARY DESIGN

Sec. 66.4

intended to be burned except in an emergency,

463

by

be noted from Tables 64. b and 66.d that since the bunkering for the whole voyage is done at Port Correo and the replenishment of all

item (10) of Table 64. b remains to be seen as the design progresses. If the ship is slowed by heavy weather it is nevertheless assumed that the fuel-consumption rate remains the same as for maximum designed power and for a speed slightly in excess of 20.5 kt in good weather.

consumable stores at the other end of the line, full load for which storage space must be provided is never on board at any one time. It is estimated that of the 700 1 of fresh water, supplies, stores, and other consumables which can be carried, only 400 t is left on board at Port Correo,

constitutes the reserve fuel supply.

Whether

equals or exceeds the 15 per cent required

The

fuel

it

consumption when traveling in the

shallow and restricted portions of the route

is

estimated only roughly for the present. 66.3 Probable Variable-Weight Conditions. Although the variable weights are not, strictly speaking, a part of the hydrodynamic-design picture, they do affect it in that they govern the displacement and trim and hence the volume and shape of the underwater hull in the several

operating conditions.

They

also,

with the respec-

tive specific gravities of the water, vitally affect

the bed clearances that will obtain in the shallow

and

restricted portions of the route. In

there

are

set

down seven

Table

conditions,

range of displacement that might be encountered.

be carried

is still

when the

full

amounts

of fuel, liquid cargo,

represents the

66.4 in

First

maximum

service load.

Weight Estimate.

the preliminary design

step

Liquid bulk cargo

4,000

t

Package cargo

3,000

t

a rough

Guesses of other major weight items are based on the background experience of the ship designer and such reference data as he may have. These reference to

down

here without

any handbook or other information, to make the example as general as possible. They are:

First Statement of Variable- Weight Conditions,

ABC

All weights are in long tons of 2,240 lb or 2.24 kips of 1,000 lb.

Load Condition

first

(b)

items are deliberately set

66.d

The

to determine the

(a)

are far greater than any possible variation in

TABLE

is

approximate weight of the ship with its cargo, the displacement volume required to support this weight, and the approximate linear dimensions. The following items of the weight estimate, all in tons of 2,240 lb, are known from the requirements of Table 64.b:

guess, but the variations in total displacement

the fuel capacity.

and

package cargo are assumed to be loaded. As indicated in the first line of Table 66.d, this

of

course of a routine voyage, as an indication of the of fuel to

the

66.

out

perhaps a dozen or more to be expected in the

The amount

It is to

Ship

HYDROnYNAMICS

464 (c)

Hull and fittings

6,400 t

(e)

Fuel, including reserve

(f)

Consumable supplies and

stores

types of recent American ships,

are

given in

t

convenient form by Nevitt [ASNE,

May

1950,

2,200

t

pp. 303-324]. However, in

common

with

many

400

t

the reference to indicate the basis on which the

500

t

eter for a ship represented

other graphic aids of this kind, there

in

heaviest condition (g)

Src. ^^.'?

800

machinery

(d) Propelling

IN SHIP DESIGN

is

nothing in

paramby a given spot on a

original designer selected a certain ratio or

Tentative margin, about 3 per cent of the total

Furthermore, one does not know whether the ship represented by that spot was easily driven or otherwise. This latter situation is remedied partly by taking data from the SNAME Resistance Data sheets. These give in most cases the predicted effective power for a ship of standard length with respect to that for a Taylor Standard diagram.

Estimated weight displacement,

(a)

17,300

througii (g)

In kips of 1,000

The corresponding displacement volume, round figure 605,500

ft

35

of

ft'

t

38,752

lb,

at a

per ton of salt water,

is

Series ship of the

.

Another way

arriving

of

the

at

estimated

weight displacement is to base the hull, machinery, and other fixed weights on a percentage of the total. The useful load is, including the fuel: (1)

Liquid bulk cargo

4,000

t

(9)

Package cargo

3 000

t

(3)

Fuel, including reserve'

2^200

t

(4)

Total amount

700

t

9 900

t

'.'.'.'.'.'. of fresh water, supplies,

and consumable storage

is

stores for

which

to be provided on board

.

Total

A

combination passenger and cargo vessel of this type should be able to carry 0.55 of its weight as useful load, leaving 0.45 of the displacement as

Using the

the ship weight.

estimate of 17,300 useful load

the 9,900

and

first

displacement

this ratio of 0.55, the

t,

only slightly smaller than

fisted in

the paragraph preceding,

9,515

is

t

t

Actually, of the latter amount, only 9,600 t

is

on

board in the designed maximum service-load condition, as when loaded at Port Correo. This is because 300 t of item (4) preceding is consumed on the way from Port Amalo. The ship- weight portion of the total, 45 per cent, is 7,785 t, which is somewhat larger than the sum of 6,400 t for hull weight and 800 t for machinery, items (c) and (d) of the previous tabulation. A small-scale graph of the ratio of useful load (actually deadweight) to total design displacement, Atlantic hners,

[SNAME,

,

sions

;

length.

DimenThe Waterline Length and Fatness Ratio,

The next

logical step

to estimate roughly the

is

ABC ship is on the waterline, at correspondmg to the designed maximum s^^'^i'^'' ^""^^ ^t which a speed of 20.5 kt is to be achieved in smooth water. A tentative length "^a^ be taken from plots of empirical data such ^^ ^^^^^ "^ Levitt [ASNE, May 1950, Figs. 7, 8, 9, pp. 308-309], or it may be read by inspection ^^^^^ the analysis summaries of the SNAME RD sheets for combination passenger and cargo ships of about 17,500 tons displacement, and designed speeds of the order of 18.7 to 20.5 kt. The former plots give an Lpp of about 480 to 500 ft for normal ships and 500 to 520 ft for fine ships. This corresponds to an Ldwl range of about 500 to 535 ft. this length for the

^

^"^^^^

The

gives a somewhat less L^wl of the order of 500 ft. A first guess at the minimum length is 500 ft. For this length the Taylor quotient T, = V/ V L is 20.5/ VSOO = 0.917. The Froude number F„ latter

tabulation

definite value for

is

=

T, (0.2978)

0.273,

and the displacement-

length quotient A/(0.010L)'

The 0-diml

138.4.

605,500/(50)'

The eters

=

question

fatness

=

V/(0.10L)^

now

arises,

How

do these param-

the required speed? Is the ship too fat for

speed?

is

plotted

by C. R. Nevitt on a

length

is

4.84.

Is the length too small for the displacement

passenger vessels and

=

17,300/(5)'

ratio

together to insure a ship easily driven?

fit

large

V/ a/L

same

First Approximation to Principal

length of the ship. As pointed out in Sec. 24.2,

for

Considering is

and its

hydrodynamics only, ship

a matter of providing the easy longi-

or Taylor

tudinal curvature necessary to permit an under-

within the range of 0.70 to 1.05

water body of the requisite volume to be driven easily and efficiently at the specified speed. In

basis of speed-length quotient

quotient T,

66.5

1945,

Fig.

plots for selecting this

1,

p.

316].

More

and many other

recent

ratios

and

parameters, based upon data from certain general

selecting

the

length,

hydrodynamic factors

however, enter:

several

other

STEPS IN PRELIMINARY DESIGN

Sec. 66.5 (a)

The proper

hump

so that a

and length

relationship of speed

in the hull-resistance curve is

avoided (b)

A suitable balance between

drag on a too-long

the added friction

with its extra wetted area, and the added pressure drag on a too-short hull,

one, with its sharper longitudinal curvature.

G. S. Baker gives a dimensional formula for determining the length Lpp between perpendiculars,

namely

—

Lipp

where Lpp

is

in

ft,

V

2+

2i'±

V

is

A'

(66.i)

V.

"the speed

(in kt) for

A

is in long average fine weather at sea," and tons [NECI, 1942-1943, Vol. 59, p. 29]. Taking first the sustained speed V of 18.7 kt for the ABC

ship,

17,300

and the estimated t, Eq. (66.i) gives

=

Lpp

18.7

=

(17,300)"'

24'

A

displacement

506.5

of

V =

Lpp

^20.5

~|

definition

indefinite,

and the

upon the type 34.977

=

(17,300)'''

)

515.3

LnrL

V

for

ratio of

of stern.

somewhat L^wl depends

remains

Lpp

Using a

to

specific

V

Lpp

=

trial

speed of 20.5 kt, Eq.

7.33881

2+

volume

¥'

p^

I

of

because the volume of 605,500 specific

volume

is

515.4

ft

ft'

of

expected here

ABC

ship are

ft.

different line of attack

somewhat

on the

empirical and admittedly

still

sources,

among

others:

Bates, J. L., Shipbuilding Encyclopedia, 1920, p. 200 (2) Liddell, E., NECI, 19.34-1935, Vol. 51, pp. D45-D46 (3) Nevitt, C. R., SNAME, 1945, Fig. 2, p. 316 (1)

(4)

Van Lammeren, W.

(5)

Thayer, E.,

(6)

Vincent, S. A., unpubl.

P. A.,

SNAME,

RPSS,

1948, Fig. 39a, p. 89

1948, Fig. 29, p. 409 Itrs.

to

HES, Sep

1947, Oct

1952

SNAME

Resistance Data sheets.

These data, for merchant and combatant vessels orthodox form which have given good performance, cover a wide range of Taylor quotient, fatness ratio or displacement-length quotient, and They have longitudinal prismatic coeflicient Cp been checked and supplemented by comparison with the proportions of models fisted on the SNAME RD sheets which have bettered Taylor Standard Series performance at and near the .

speeds.

The

result

is

two pairs of bound two

empirical curves on Fig. 66. A which

was calculated

design lanes.

35

The upper pair defines the limits of displacement-length quotient A/(0.010L)' and 0-diml fatness ratio F/(0.10L)' on a base of T, and F„

instead of the standard figure of 34.977 If all the

385

of

(66. ii) gives

=

(605,500)'''

sUght discrepancy in length

by assuming a

by the

For a ship length of 515 ft, the ratio Lw/L^l is 385/515 or 0.747. This is rather close for comfort to the low limit of 0.8, but at least it does not he within the range 0.8 of the order of

designed

A

L^. to ship length

Also, a study of available

1.0.

the ocean areas traversed

66.i)

(66. ii)

VJ

20.5^ 7.33881

wave length

ratio of

from 0.8 to

data such as those in H.O. 602, 1947, reveals that the maximum wave lengths to be expected in

(7)

For the

is

is

^iYTvf (34.977)'''

=

when the

taking account of quiet-water performance only, based upon data collected from the following

ft.

becomes

Lpp

A preliminary study of the wavegoing situation, elaborated upon in Part 6 of Vol. Ill, indicates that the greatest speed reduction is to be expected

A

per long ton for salt water, (Eq.

ft'

in the past [Mar. Eng., 7 Jul 1954, pp. 66-67, 81].

length problem,

Baker's formula is put into nearly dimensionless form by substituting V for A, and changing the numerical coefficient accordingly. However, Baker's

30 or more per cent of their original waterline length, is an indication that too long a hull is by no means the handicap that has been anticipated

to 1.0.

the trial speed of 20.5 kt,

24(

hesitant

ft.

20.7

Using for

465

about exceeding that length, even though they do not know what it is. However, the excellent performance of many ships in the past, after a lengthening process which involved an increase of from 11 or less to are

designers

ft'

per ton

ft'

per ton.

governing factors could be known,

The

for

would undoubtedly be found a most efficient length for each such set of conditions. Many

lower pair defines the limits of Cp in the same way.

good

practice

However, the values

and

normal

properly weighed, and taken into account there

for

designs.

good designs may well

Sec. 66.5

STEPS IN PRELIMINARY DESIGN

Sec. 66.6

point plots almost in the middle of the upper lane; the 515-ft length

apparently about right.

is

"natural" values of

PNA,

Sec. 10.14.

sequently in the chapter.

The

At the bottom

66.A there appears a subdivision worked out by D. W. Taylor [S and P, 1943, p. 48] which indicates the position of humps

and hollows

of Fig.

in the curves of residuary resistance

for a large range of T, values. Reference to this

subdivision indicates that the three

TJs

for the

66.6

The Longitudinal Prismatic

prismatic-coefficient

66. A, especially at the

10

20 30 40 50 60

80

|60

4.0

150

ZOO

250

M.,

Coefficient.

lane

Fig.

of

low-speed end, does not

optimum Cp for a given T, or F^ such be obtained from the Taylor Standard Series contours of Rr/^, because in that region ,

the friction resistance

is

generally

the

major

part of the total resistance. For example, the

value of for

Rr/A. for the Taylor Standard and P, 1943, pp. 201, 227] for a T, 0.90 and a A/(0.010L)' range of 138.4

the 500-ft length to

2.5

119.6

for

the 525-ft

V/Vu Z.O

300

Ship Lenqth, Fig. 66.B

S.

may

as

3,0

3.5

design

give the

Quotient Tq or Speed- Lenqth Quotient 4.5

K.

explained in

in

original contours of

5.0

is

English units by which the hollow-hump positions for any ship length and any speed are found by inspection. values

sional

Series [S

6.0

V [Davidson,

ready reference a set of dimen-

p. 48], gives for

in the

Taylor

on

Fig. 66. B, adapted from Taylor's shaded length-speed diagram [S and P, 1943, Fig. 55,

tentative lengths of 500, 515, and 525 ft

all he middle of a hollow, slight but definite, for vessels of normal form. Here Rr is slightly less than it would be for a smooth curve of mean or

Rr

1939, Vol. II, p. 70]. This

least it seems so at this stage. A ship longer than 525 ft on the designed waterline need not be considered until other features are investigated for these three lengths. Although a still greater length involves additional wetted surface there may be other good reasons for using it. The significance of the special spots found on this and succeeding diagrams is explained sub-

At

467

ft

Diagram Illustrating Positions of Humps and Hollows in Residuabt-Resistance Curves, Terms of Ship Length and Speed

in

HYDRODYNAMICS

468

IN SHIP DF.Sir.N

Sec. 66.7

show that the minimum value of Rg/A occurs at a Cp of about 0.52 for a B/H of 2.25, and at a Cp of 0.54 for a B/H of 3.75. These values are considerably less than the average Cp value of 0.62 given by the lower design lane of Fig. 66.A. This is because the longer and more pointed forms, with the lower Cp values of 0.52 to 0.54, have too much wetted area and friction length,

resistance for the specified displacement volume. Similarly, the design lane of Fig. 66. A, in the

higher ranges of

7", ,

gives values of

Cp which

are

lower than those indicated by the regions of lowest residuary resistance per ton ratio, Rr/A, in the TSS contours. This is because the lane is positioned to suit high-speed vessels like destroyers which have to drive easily at cruising speeds that are much lower than the designed speeds. For a vessel designed to run always at high speeds, or for a vessel with sufficient nuclear fuel to elimhiate the

cruising-radius problem, at least so far as fuel

only

is

concerned, the

optimum Cp

for a T, of

Fig. 66.C A Speed-Length Quotient of Nearly Zero and a Prismatic Coefficient Approaching 1.00

A

1916. Photograph

and requirements

depending

upon

the

fatness

ratio,

as

by the TSS contours. and other factors often a Cp somewhat higher than the best

indicated

Restrictions on length require

The middle of the lower lane gives values Cp from about 0.614 for the short 500-ft ship

of

to

about 0.624 for the long 525-ft ship. A good value of Cp at least at this stage, appears to be about ,

number

of

formulas,

most

of

them

for

straight lines, have been developed to approximate

the steep part of the "roller coaster" Fig. 66.

0.50

A

and

Cp

in the restricted region of T, 0.90.

lane of

between

The

the range of values for a vessel of normal form

The Maximum-Section

66.7

Draft and Beam.

There

is

The way of

Coefficient;

little in

the

from a tentative maximum-section any point in the complete range

reliable information, empirical or otherwise,

which to coefficient

select

Cx .

in a range of

for

This

is

equally true, for that matter,

any other parameter

S and P, 1943, Fig.

[Taylor, D. W.,

70, pp. 63-64].

This

may

be,

for the reason stated in Sec. 24.10, that variations

have little effect upon hull However, the branched design lane of Fig. 66.D gives an indication of the general region in which a good Cx is to be found, for approximately the same ranges of T, and F^

Cx

of

in themselves

Beyond the left end of the lower lane, with T, and Fn approaching zero and with wavemaking practically nonexistent, the Cp may approach a very high value as an asymptote, probably of the order of 0.90 to 0.95 or more. This means that craft which are not required to travel fast

can approach a rectangular box shape, as illustrated in Fig. 66. C and as explained under barge design in Part 5 of Volume III. is

again emphasized that the fatness ratio

or prismatic coefficient for every ship need

no means

as in Fig. 66. A.

The

These ignore the need for design

information appl3dng to vessels in other speedlength ranges.

It

for special designs.

resistance.

0.62.

A

author.

that drives easily.

to T^ or F„

figures.

call

by the

lanes are simply to give the designer an idea of

2.00 would be in the range of 0.65 to 0.70 or

more,

horse-propelled cargo carrier on the Erie Canal in

by

within the lanes of Fig. 66. A, or that other parameters need conform to correspondlie

ing graphs to follow in

tliis

chapter. Special cases

T„ of

limiting

optimum value

0.0, as for

of

Cx

is

1.00 at a

a square- or rectangular-section

which rarely has to move. When it does move, hull drag is usually no problem. The ratio Cx may well be made greater than I.O, in hull

fact

up

to

1.1

or more,

if

there are practical

reasons for doing so, such as adding blisters for

underwater-explosion protection. As

V/'vL

in-

widens until at a T, of 1.05, F„ of about 0.31, the value of Cx for good design lies between 1.00 and 0.90. At still higher T, and F„ values, two classes of vessels are creases, the design lane

distinguished: for high speeds, where beam keep down the longitudinal waterline curvature and to reduce resistance due to wavemaking but remains adequate for the service; (1)

is

Those intended

sacrificed to

STEPS IN PRELIMINARY DESIGN

Spc. 66.1

"050

Q60

0.70

080

090

TOO

Taylor Quotient

Fig. 66.D

(lo 130 i40 or Speed-Length Quotient TiO

Tt{

160

[50

WC

50

ITO

200

2

II

Gkaph for Normal Values of Maximum-Section Coefficient Cv

they are indicated by the upper branch of the Cx lane (2) Those designed to travel fast for their length, but for which a relatively large beam is a necessity, to afford stability, internal volume, deck space,

However, these corners have been formed by what may be termed large-scale chamfering, using two chines with about 45-deg angles, as in the straight-element section shape sketched at in Fig. 21. k.

On

vessels built for

1

some European

and small

and on towed steel barges built a halfcentury ago for service on the Erie Canal, the lower hull corners are made by structural angles,

Cx

applied outside the side and bottom plating, with

drop well below the lower limits of the plot of Fig. 66. D, approaching 0.50 or 0.40 [Simpson, D. S., SNAME, 1951, p. 569]. The branch lane for these low values contains no optimum line, because there appears to be little or nothing systematic about the Cx values in this

a bilge radius of practically zero [Nixon, L., SNAME, 1896, p. 20 and PI. 19].

and the

like.

branch of the

They lane.

are indicated

Examples are

by the lower fishing vessels,

ferryboats, tugs, minesweepers, yachts,

freight vessels. In fact, for these types the

values

may

rivers,

Since the

ABC ship is to give good performance

in the shallow

Amalo there

and

restricted waters of the

must be plenty

of

room

for the

pass around the ship, especially under

region.

Port

canal and the river below Port Correo,

water to it. This

means that the maximum-section coefScient Cx If

the ship

is

required to have the largest

volume

or the midsection coefficient

Cm

,

about

0.96,

dimensions, as for cargo vessels which must pass

form.

With a displacement volume

through locks, the midsection is made as full as operating clearances permit. This may give a Cx of 0.995 or more, used on Great Lakes freighters. Since practically all vessels are drydocked or hauled out periodically, certain clearances may be required for these operations. The best structural connection between the bottom and the side along the middle portion of a ship huU calls for a curved plate at the corner.

and a waterline length

practicable

for a given set of principal

on the basis

of

,

should not exceed

a midsection of normal of 605,500 ft^

515 ft, for the middlelength ship of the three mentioned in Sec. 66.5, the maximum-section area Ax for a prismatic coefficient

Cp

Ax =

of

of 0.62 is

605,500

L(Cp)

1,896

ft"

515(0.62)

The minimum depth of channel out Amalo is 28 ft but between one-third and

of Port

one-half

HYDRODYNAMICS

470

IN SHIP DESIGN

have been consumed by then, bringing the ship up in the water by the order of a foot or so. The ship drops to a deeper draft in the fresh water of the river at Port Correo, and ample clearance must be left over the river bed, which has a minimum depth of 30 ft. It appears of the fuel will

The

t

at this time,

Working through the procedure

t

£x = This

is

Ax Cx{Hx)

^ "

1,896

=

75.96

ship 525

ft

Br =

ft.

quite large for a seagoing ship only 515 ft

The length-beam ratio is small, namely 515/75.96 = 6.78. The beam-draft ratio is rather large, equal to 75.96/26 = 2.92. The latter ratio

400

500

described, for a long on the waterline, with a Cp of 0.62,

Ax =

(0.96)26

long.

will undoubtedly give all the area required in the designed

the design.

compared to the

which the ship must carry when fully stocked at Port Amalo. For the 515-ft ship the beam Bx at the maximum-area section is then 700

consumed

Almost certainly it will involve additional pressure resistance from wavemaking, due to the correspondingly large waterline slopes and the pressure disturbances set up around the wide ship. This matter is brought up again, a little later in

Port Correo. From Table 66.d, first hne, and from the first weight estimate, the consumable-store only 400

is

waterplane for transverse metacentric stability. Indeed, it may give too much for easy rolling.

This draft then corresponds to the maximum designed service load being carried when leaving

is

beam moment of

large

square

necessary, at least at this stage of the design, to limit the draft in salt water to a maximum of 26 ft.

weight

Sec. 66.7

not too large but it increases as fuel during the voyage. is

L/Bx =

¥

_

L{Cp)

605,500

1,860

CxiHx)

525

=

74.52

=

1,860

ft'

=

74.52

ft

525(0.62)

(0.96)26

7.05

Bx/Hx =

74.52

=

26

This 525-ft length gives considerably better pro-

600

800

700

Waterline Length, ft 100

125

150

175

200

225

275

300

Waterline Lenalh, meters Fig. 66.E

2.866

Plot of Length-Beam Ratio and Beam on Ship Length

325

350

STEPS IN PRELIMINARY DESIGN

Sec. 66.9

portions for a ship

the speed and service

of

required, although the

beam

voyage. Using the data from Table 64. b and the

is still large.

Supplementing the discussion in Sec. 24.11, Fig. 66. E gives a range of absolute beams on a basis of absolute lengths, based on data from many successful ships, for which a great number of the spots are shown. The meanline indicated is rather an average location for most of the ship values than one drawn through the center of the lane marked by the upper and lower ranges of absolute beam on absolute length. Also indicated is

a curve of 0-diml

L/B

same subdivision as

Some modern

teristic of

many

at

t

42 (b)

Package cargo, 3,000 ft'

(c)

per

168,000

ft'

300,000

ft'

144,000

ft'

300,000

ft'

92,400

ft'

70,000

ft'

t at 100

t

Hull structure, on a basis of 4.5 ft' per t for 6,400 t of hull steel, fittings,

and other construction

materials, -plus 4 times that volcraft built for speed with

among them

ume

manual and

L/B

ratios charac-

(d)

dugout and American Indian canoes

an increasing demand through the years for utility, for inherent stability not always possessed by the canoe with a man (or men) standing up in it, for still more utility with top hamper, and finally for greater all-around safety. This has broadened the beam of boats and small ships gradually, without too much regard for the effect of the small L/B ratio on propulsion. If metacentric stability, maneuvering, and other features are more important than propulsion, the design has to favor them. For the ABC design the beams given in the preceding paragraphs are slightly greater than those shown by the meanline but they are well within the lane. coefficient for the 525-ft vessel

for the waste space

around

it

canoes, sculls,

centuries past. However, there has been

The block

Liquid bulk cargo, 4,000 ft' per t

(a)

ratios corresponding to

racing shells, retain the high

for

in the first weight estimate

of Sec. 66,4:

the meanline.

propulsion only,

471

other items to be carried during any part of the

Estimate for propelling and other machinery (This is very large compared to the figures given by G. G. Sharp [SNAME, 1947, p. 462] but in view of the unorthodox features being considered for an alternative stern, with the propelling machinery aft, it is not reduced at this stage)

(e) (f)

(g)

t at 42 ft' per t Fresh water, lubricating oil, sup-

Fuel, 2,200

plies,

and

stores,

700

.

t

.

other

consumable

at 100

ft'

per

t

.

Accommodations for officers and crew, estimated

(h)

Passenger quarters and service

(i)

Non-usable space

works

.

100,000

ft'

400,000

ft'

100,000

ft'

Total volume 1,674,400

ft'

out as

The Cs

=

605,500

L{Bx)Hx

This checks, as

Cb

=

it

Cp{Cx)

=

0.595-1-

525(74.52)26

0.62(0.96)

=

First Estimate of Hull

Volume.

make a rough

can be accommodated within the is

now

of expansion

hull,

listed is about 2.77 times the underwater displacement volume of 605,500 ft' but it includes practically all deck erections. For a combined passenger and freight vessel, it appears somewhat large but perhaps not too large at this stage of the design. 66.Q First Approximation to Shaft Power. Before making a second weight estimate it is necessary to approximate the propelling power, so as to determine more accurately the machinery

tentative

It is

volu-

metric check of the vessel to insure that everything well as below water. It

volume

The volume

0.595-F

66.11.

66.8

clear, to facilitate access

trunks over the liquid-cargo tanks.

For the three waterline lengths of 500, 515, and 525 ft, and for a constant Cp of 0.62, the proportions and dimensions already worked out and some of those remaining to be derived are indicated for convenience in Table 66. e, in Sec.

advisable at this point to

hatchways

to the cargo, nor for the

should, with

=

foregoing does not include an allowance

for keeping

weights and the fuel capacity.

The

above as

necessary to include

the full weight and volume of consumables and

is

first

rough estimate of shaft power Ps

derived from the assembled data on merit

factors in Sees. 34.10

and

60.13.

The

first of

these.

HYDRODYNAMICS

472

M,

the Telfer merit factor

represented by

is

Fl

is

ABC

small. Since the effect of the 68-deg kinematic

meanUne

gives a tentative merit factor

M

Froude

of Fig. 34.1

about

of

9.5.

Using the dimensional Eq. (34.xxv) of Sec. 34.10,

=

0.61

L{M)

=

(17,300)(20.5)'

0.61 (5 15) (9. 5)

is

viscosity

to diminish the calculated friction

is

resistance, its use

somewhat questionable

is

Entering the large-scale portion of Fig. 45.H

Since the 20.5-kt speed is to be made at 0.95 of maximum designed power, by item (22) of Table

power is 18,582/0.95 = 19,560 horses. Using the alternative weight-speed-power factor WV/Ps of Fig. 60.U, for an Fl of 0.0727, the broken meanhne gives a value of about 125. Then, with the dimensional formula on Fig. 60.U, 64.d, this

17,300(20.5)

=

19,520 horses.

125

The designed maximum power estimate

=

19,520/0.95

a

design.

B/H

with a Cx of 0.96 and a

6.

in

For these reasons, and because the "standard" values of p and v for 59 deg F are easily remembered, the latter are employed throughout Part 4 of the book. preliminary

18,582 horses.

Ps =

latter ratio

or middle

0.0727, the broken

Ps

The

preliminary-design purposes.

all

ship as the example, for which

for a range of

numbers squared. Taking the 515-ft length of

Sec. 66.9

some II per cent less than 1.000, but its effect on Cf at the large ship Reynolds numbers is

WV^/igLPg)

values of

IN SHIP DESIGN

is

then

20,550 horses.

of 2.92 for the 515-ft

ship, the wetted-surface coefficient

The

to be 2.618.

area

then

is

R„

is

CsV^

=

From Table

46,231 ftl

Cs

is

found

approximati on to the wetted

fi rst

2.618 \/605,500(515)

45.b the Reynolds

=

number

about 1391 million for the 515-ft length, for

the 20.5-kt speed of 34.62

kinematic viscosity

ft

per sec, and for a

"standard" salt water of 1.2817(10"') ft' per sec. From Table 45.d the value of Cf is 1.470(10"'). Adding a roughness allowance ACp of 0.4(10"') for a clean, new ship of as-yet-undetermined shape or surface condition, gives

+

Cf

=

ACf.

v in

1.870(10"').

emphasized that, when making estimates from the meanlines, one assumes that a ship of modern design is to perform no better than the average of a number of older ships. Further, since the merit-factor ordinates of both Figs. 34.1 and 60. U are logarithmic, a value picked among the spots for the better ships may easily be from 20 to 40 per cent better than the average. This means estimated powers of from 20 to 40 per cent below

Entering the appropriate graph of the B/H = 3.00 group of the reworked Taylor Standard

those calculated in the preceding paragraphs.

20.5-kt

It is

The

third estimate

is

made by

the use of the

1947 or Schoenherr friction line, the ATTC roughness allowance ACp of 0.4(10"^), and the Taylor Standard Series data as reworked by M. Gertler [TMB Rep. 806, Govt. Print. Off.,

ATTC 1947

Wash.,

At

Mar

Series contours, reproduced in Fig. 56.

speed,

amount

of

wetted surface

is

total drag

Rt

Rt = (p/2)7'S(C« 1.470

+

0.4)10"',

=

1.9905 slugs per

ft' for

is

ft"

0.88726 times the value of

j-

=

1.2817(10"')

per sec for the same standard temperature.

The former

ratio

is

suflSciently close to 1.000 for

and

found to 2.25 group

friction

therefore something

171,830

550

A

round

-I-

underwater hull

(45.ii) of Sec. 45.7,

Cf.

+

ACf)

=

lb,

namely

55(1.246

first

taken as 1.9905 slugs per

RtV Pe =

the standard con-

dition of temperature 59 deg F, wliile the latter

is

where for the

(10"')

from Table X3.h, is 1.1372(10"') The former is 0.99884 times the value

viscosity j'(nu),

=

of Sec.

is

specific

oi the bare

estimated from Eq.

is

per sec.

Cn

D

0.268,

to be watched carefully in the design.

Then Rt =

of p

the

therefore,

water.

ft^

=

is

tion p

this temperature, 68

0.903, F„

considerably more than half of the total resistance, namely 1.870(10"') as compared to (1.870. -I- 1.246)10"' = 3.116(10"'). The

resistance

deg F, the value of

For

=

4.433, the value of

the mass density p(rho) of salt water, from Table X3.e, is 1.9882 slugs per ft'. The kinematic

64. c.

T„

0.62,

be 1.25(10"'). Entering the B/H = with the same values, Cr is 1.21(10"'). Since B/H is actually 2.92, Cr is found by linear interpolation to be approximately 1.246(10"'). At the

The

account of the average temperature of the sea water in which the ship is to run, specified in item (18) of Table

=

F/(O.IOL)'

1954].

this point it is necessary to take

Cp =

56.5, for

-f-

approximaft'

for salt

0.99525(34.62)^(46,231)3.116

whence

171,830(34.62)

550

=

10,816 horses.

figure is 10,820 horses.

As a check method [S and

calculation

by Taylor's

original

P, 1943, pp. 59-60], the friction

resistance per ton of displacement

is

found by

STEPS IN PRELIMINARY DESIGN

Sec. 66.9

taking

first

the dimensional wetted-surface coeffi-

Cws from

20 on page 22 of the reference. With B/Ii = 2.92 and Cx = 0.96, the value of Cws is, as nearly as can be determined, 15.02. cient

Fig.

For a 515-ft ship the length-correction factor Q:(alpha) is 0.997, taken from the diagram at the right of Fig. 188 on page 188 of the reference. Then for a A/(0.010L)'' quotient of 126.7 and a T, of 0.903, the friction resistance per ton of displacement for a ship having a Cws of 15.4,

from the plot of Fig. ship with a

R. =

Cws

188, is 6.1 lb.

of 15.02,

and an a

(15.02) 6.1

=

(0.997)

For the 515-ft of 0.997,

of 0.62,

the displacement-length

B/H

ratio of 2.25,

and the

r„ of 0.90, the value of Rr/^. is, from page 201, 3.55 lb. For a B/H ratio of 2.92, it is, by hnear interpolation between

B/H =

2.25 and

=

3.75, 3.75 lb. Similarly, for T^

0.95,

B/H = Rr/L

is

Again interpolating linearly for T, = 0.903, i2«/A is 3.872 lb for the parameters given.

The

total

wide by 2(200) ft long, or say 400 ft'. The added area for rudder and keels is then 536 2,400 - 400 = 2,536 ft', which is 2,536/ 1 ft

total

+

=

(46,231) area.

On

0.055, or 5.5 per cent of the bare-hull

the basis of additional wetted area

not more than 6 per cent of the which in turn is only about 62 per cent of the total. The increase in total drag is therefore of the order of 4 per cent.

alone, this

is

friction resistance,

it seems wise at this stage to double and allow about 8 per cent of the total resistance for the final appendage drag. Since the requirement of item (26) of Table 64. d states

this effect

quotient of 126.7, the

5.779

and 3 ft wide would have a wetted area of about 2(200)3(2) = 2,400 ft'. The hull area covered up by the bases of roll-resisting keels of triangular section would average about

keels 200 ft long

However,

5.932 lb pert.

(15.4)

For the Cp

473

lb.

bare-hull resistance

Rt

is

that

"A

reasonable expenditure

power, or both, to secure is

effective

acceptable to the owner,

it

of

weight or

roll-quenching"

may

be considered

advisable, at a later stage of the design, to

make

the roll-resisting keels even larger than indicated here.

In the absence of any better information, an is included to cover the drag

then

additional 2 per cent

(1^

+ ^)a = =

(5.932

+

169,610

3.872)17,300

So far as can be determined at

lb. is

The agreement with 171,830 lb as found by the third method is within 1.3 per cent and is good enough at this stage of the design. Another quick method for approximating the total bare-hull resistance

/2j.

of the ship is to use

and the circulating-water making 10 per cent in all.

of the condenser scoop

discharge,

tliis

time there

sufficient allowance for fouling in the

1.8-kt

between the 18.7-kt scheduled speed for the whole voyage and the 20.5-kt trial speed under clean-bottom smooth-water conditions. The tabulated data at the end of Sec. 60.11 difference

give a range of propulsive coefficient of 0.82 to

the graph of Fig. 56. M, comprising values of

0.72 for clean, new, single-screw ships of

iZr/A plotted on T^ over a wide range of relative speeds. It applies to any type of vessel from a lake freighter up to a high-speed patrol craft. Entering Fig. 56.M with a T^ of 0.903, corresponding to the designed speed of 20.5 kt of the ABC ship, the value of flr/A is 10.2 lb per long ton. With an estimated displacement of 17,300 tons, this gives a bare-hull resistance 72?. of 176,400 lb. This is 2.66 per cent higher than the resistance estimated by the third method described, but is at least on the high side for the present. If the vessel is to be driven by a single screw, the ship requirements appear to call for no appendages except a single rudder and a pair of roll-resisting keels. A rudder having an area of 0.02{LH) would have a projected blade area of about 0.02(515)26 = 268 ft^, and a surface area of something over 536 ft^. A pair of roll-resisting

hydrodynamic design. assume that a value of

modern

seems reasonable to iji. as high as 0.74 can be achieved for a single-screw ABC ship, even though the design is not yet worked out. Using an appendage-and-scoop factor of 0.10 for added resistance, and a propulsive coefficient of 0.74, a first approximation to the shaft power is (10,820) (1.10)/0.74

Item

=

(22) of

It

16,084 horses.

Table

64. d states that the sustained

sea speed of 20.5 kt shall be attained by the use of not more than 0.95 of the maximum designed power. The latter is therefore 16,084/0.95 =

16,930 horses. This

is

considerably less than the

and second estimates of 19,560 and 20,550 horses, but aU are within the capabilities of a modern single-shaft plant and a single propeller. Again it is emphasized that all these estimates first

are

for

average

performance,

with

generous

HYDRODYNAMICS

474 such

allowances

appendage

doubling

as

the

IN SHIP DESIGN

estimated

assumed

it is

in all the foregoing that

ABC

the resistance of the final

hull

will

This

on 0.6 lb [Barnaby,

An

estimated allowance

p. J8].

including dehumidification, and for other items

not covered by the hydrodynamic specifications, 0.1 lb per horse per hr, making a total of 0.70

certainly the end to be sought; in fact,

the designer should look forward to bettering the

is

TSS

lb for all purposes.

performance. In this connection the following quoted from a discussion by S. A. Vincent [SNAME, 1948, p. 403], where the comments in

0. Praznik

parentheses are those of the present author:

0.575 lb of

As a check on the first item, W. I. H. Budd and show a fuel rate of slightly under

is

having prismatic coefficients from about few 9.72 to 0.75 are as good as the (Taylor) Standard Series models at designed speeds suitable for the prismatic ".

.

vessels

.

At higher

coefficient (see Fig. 66.A).

or lower speeds for

range of vessels and also for vessels having

this particular

prismatic coefficients beyond this range, the resistance for

below that of the Standard Series, often the designer would do well to considerably below have the Standard Series form in mind when drawing the lines of vessels having prismatic coefficients between

good forms

is

.

.

.

about 0.72 and 0.75." -

^,

,,

i

i.

^

XI.

J.

11

i_

J

1.

J r

1

In the event that the hull shape developed for ^ ,, ,„^ ship should ^, ^c prove more resistful than ABC ,

the ^,

,

.

,

.

„ o/ J J Taylor fetandard ,

ci

-ui

•

-i

•

1

J.

Series, it is possible to apply T i i. XIa contra-guide ending to the single centerline jj ,° mu X ii. skeg, and to use a contra rudder. Ihese together

the

.

1

,

.

,

,

,

,

,

.

IX-

e

^

.

should regain a certain amount of power lost in ,1 „ .X li- Ax xi X -x driving the hull itself. At this stage it appears .

,

.

1

,,,,,,,bow

,.

,

iz-irr

,

might be benehcial. It so, a ,,, ,.,, still greater amount of power could be regained. ^^,« r. jT^xX iiT^i-tT7-t.x 66.10 Second Estimate of Principal Weights. „, .,x-x The most uncertain weight items in the farst . „ „„ ^, XI11 rough estimate of Sec. 66.4 were those of the hull, ,,. ,, xi T the propelhng machinery, and the fuel. In that a bulb

.,

^.

,

•

,

.

,

,

-xLx^x

.

,

.

,

,

,

-Ti

1

.

xi

_„

.

.

.

,

,

design

1

is

,

to be

r

^rv

CI

r,

of Sec. 69.2

xt worked up on the 1

1

1

i-

•

1

accordance with the conclusions

ABC

1-

J-

XL

the r

-

1

basis of a

11

—,,

The

,

•,

,

1

1

•

X xi-

X-

/.

r

X-

best available information, at the time of /,r.rr^

r

I

•

.

1

i

writing (1955), for a complete single-screw steam .',, ^ ,„„„rv X -i-T r,r.r. power plant in the range of 16,000 to 17,000 ..,„.,, ; , mi X X Xx horses is 165 lb per horse, ihe total estimated ,

J.

1

„.

1

.

,

1,

propelling-plant weight

=

,

at

ji

•

this

1

•

X

stage

is

atmosphere control,

for the hotel load, for full

same proportions and weight displacement,

is

lb per horse per hr; certainly

K. C, INA, 1950,

not

exceed that of the Taylor Standard Series hull of the

be

able to produce full power at a fuel rate of 0.58

resistance.

Further,

Sec. 66.10

this size, also at the time of writing, should

per horse per hour for

oil

tSNAME,

1948, Fig.

all purposes This apparently

p. 472].

1,

does not mclude fuel for the hotel services,

Concerning the second item it is probably more determine the fuel rate for services on ^ ^^^^^ ^f ^j^^ ^^^^^ personnel on board per day at tt ^ea or in port. However, as the rates in question are bemg used solely for a design example rather than for an actual ship they need not be more than roughly representative of good practice at ^^e time of writing. The fuel consumption per voyage is then logical to .

,

^j

^.

i

,

,

o To-,

c^t^r^,^^c^n,^\,r^nn\

estimated as 290(16,930) (0.70) = 3,437 kips or . ro^ ^ a j n rm ^ mi_^r/^ ^ 1,534.4 t. A round figure is 1,550 t. This is 650 t ,, ,, ^i „ ,, less than that allowed tor in the nrst weight __„ ^ ^. ^ , ^, ^ estimate, and 200 t more than enough to comi

,

'

j.

,

^^

•

•

-,

j.

r-

.

,

,

'.

..„

^,

t

,,.,.

.

,

pensate tor the 450

„.

,

additional propellmg-

of

machinery weight m the second estimate, ^ ,, ,„ A» further check on proportions of hull-and-

.

,

/.

,

„^^.

•

,

-

,

i

,i

,-

i

,

,

x

i

x

x

.

•

T

i

-,1

.

,

,

, i

r

-

,

on the basis

load,

,

•

^

„

,

i

xi

-i-,

i

,

-i

i

... smgle-screw

^

.

type ,. judicious use special

i

i-

standard tor floodability, the possible use .

i

seams and welded xu x x a three-compartment

i

,

,

,

^

i

useful

all

of riveted

^/ xi. i. n xbutts in the shell plating,

,

i

r

i,

nttings weights to total weight with

of

a

oi

,,, the

,

and

stern,

„ ^ -i of hght alloys for topside weights, ... ^ ^,,,, x .i T n -,i ii indicates that the hull proper with nttings should x or x r xi i mi weigh about 35 per cent of the loaded ship. The .

^

.

,-

i

,

-

.

i

,

i

.

.

i

original hull weight of 6,400 t ,,

.°

,

,

,

- r,^V^

may

mi

.

i

i

•

be reduced at •

-

i

this stage to about 5,960 t. Ihe original margin . ._„ 7 x i o . i ot 500 t, lust uudcr 3 per cent, may safely be ^ ^ oor^ x x u x o x cut to 330 t, just about 2 per cent, •

/•

i

„ A second weight estimate looks about as follows: ,

.1

then

i

,

,•

,

,

,

,

c

,

say 1,250

(a)

Liquid bulk cargo

4,000

t

more than the 800 t of the original estimate, an indication of the surprises that often turn up in operations of

(b)

3,000

t

(d)

Package cargo Hull and fittings Propelling machinery

this kind.

(e)

Fuel, including reserve

(f)

Fresh water, supphes, and the like

(g)

Weight margin

16,930(165) t.

This

is

450

From Table

2,793.5 kips or 1,247.1 t,

t;

or 56.3 per cent

66. c

in Sec.

66.2 the estimated

burned per voyage corresponds to that for approximately 290 hours of steady steaming at maximum designed power. A steam plant of fuel to be

(c)

5,960 t 1,250 t 1,550

t

400

t

330

t

Estimated total weight displacement 16,490

t

.

STEPS IN PRELIMINARY DESIGN

Sec. 66.11

The corresponding displacement volume nominal figure 577,150 It

is

of

35

ft^

at the

per ton of salt water

is

ft'.

again pointed out that the percentages,

unit weights, fuel rates, and other values and relationships in these weight estimates

may

not

agree with those used by some reader-designers

may

they continue to be reasonable figures in the light of technical developments in the next few decades. They are intended only as numbers nor

in

an example and they in no way

affect the

procedures in the hydrodynamic design of the vessel carried through here.

TABLE

66.e

Second Approximation to Principal Di66.11 mensions and Proportions. The second estimate brings the weight displacement down by 810 t from the 17,300 t of the first estimate. On this

made smaller; for one beam can be reduced from the order

basis alone the ship can be thing, the

of 75 ft to a more reasonable figure. It is to be remembered, however, that the volumes to be accommodated within the hull and deck erections remain substantially the same, and that in the first estimate of volume the hull appeared to be

none too

large.

Further, since

it

is

customary to reckon the

Tentative Hydbodynamic Features of Sbvebal Vessels op Different Lengths

For the fourth and fifth approximations, 90 the molded displacement.

Approximation

475

t

has been deducted from the hull weights for the shell plating, to give

HYnROnVNAMICS

476

and to calculate the form molded form, as explained in possible to consider about 90 t

IN SHIP DESTCN

Ser. 66.12

For convenient reference the data derived

principal dimensions

in

coefRcients to the

the foregoing for the tentative lengths of 500,515,

Sec. 66.21, it

525,

is

displacement as helping to support the

of the

weight of the shell plating and appendages. The

volume

of the

frames,

is

3,150

ft'.

molded

or 574,000

by about 90(35)

therefore smaller

Specifically,

the outside of the

hull, to

it is

120.1.

=

90

moment with

ft,

16,400 t

The 0-diml

T„ of 0.903, the

its

fatness ratio

W

of

16,400/136.591 or

is

is

574,000/136,591

just below the middle of the upper

is

The maximum

section area

still

appears

Ax for a Cp of 0.62 is

574,000 515(0.62) ft

1,798

Ax

1,798 74(26)

of 73 ft,

is

a

=

developed through the years, shapes which no if they serve his

designer need hesitate to copy

Ax

1,798 73(26)

side.

Using

L{Cp)

it is

considered far preferable

meet the dethan to make up a new shape by adding a good stern to a good but unrelated bow, or by any process of averaging. These matters

=

0.947

are discussed in greater detail in Sec. 66.24.

and retaining Cp

ft,

=

1,815

=

0.62,

ft'

510(0.62)

Layout of Maximum-Section Contour. Cx as selected from Fig. 66. D determines whether the maximum-section contour is to be rectangular, follomng closely the lines for hmiting beam and draft, whether it is to be well cut away, as in a keel type of saifing yacht, or whether it is to take some intermediate form. 66.13

The

tentative value of

If it is desired, in

Cx =

1,815

displacement-length

ratio is 574,000/132,651

=

fashioning the form, to place

displacement as possible amidships, the

section need not interfere materially with the

which is satisfactory at tliis stage. These new dimensions give an L/B ratio of 510/73 or 6.986 and a B/H ratio of 73/26 or 2.808. The block coefficient Cb is (0.62)0.956 or about 0.593. The Taylor quotient T, is 20.5/22.583 = 123.63,

much

use of a hard bilge and a relatively "square"

0.9563, 73(26)

=

the present state of

to modify a given good shape to

as

the

definitely

to predict the effect of shape changes in a parent

longer than need be. Taking a

574,000

16,400/132.651

and

signer's needs

BxiHx)

little

difficult in

form. Nevertheless,

whence

0.908,

now

the art, especially without benefit of model tests,

0.9345

,

reduced length of 510

Ax =

It is

necessarily adaptable to any vessel designed in subsequent years, especially one with a single screw, it is without question a good shape from the standpoint of easy driving. Other good shapes, excellent ones, have been

found wanting. It is extremely

This is still somewhat low. It is possible that, with some 800 t off the original displacement, the length

and proportions.

existing lines; this has been tried

somewhat on the low

Fig. 66. D, to be

Cx =

principal dimensions

He is cautioned, however, not to attempt "breeding" better ship fines by averaging good

ft'

gives

Bx{Hx)

=

=

This maximum-section coefficient appears, from

beam

to this

purpose.

¥ L{Cp)

Reducing the beam to 74

a

Up

is to take. While it is admitted that the Taylor Standard Series shape, derived from a twin-screw cruiser of the early 1900's, is not

appropriate.

Cx

Selection of Hull Shape.

the middle tenta-

lane of Fig. 66. A, so the 515-ft length

A^ =

66.12

point the preliminary design has involved only

hull

tive length of 515

or 4.202. This

plus a few additional items to be

necessary to think of the shape which the vessel's

3,150

ft' less

displacement-length quotient for a weight

-

ft,

ft',

577,150

ft'.

Considering for the

16,490

=

and 510

derived, are Usted in Table 66. e.

quotient

is

and the 0-diml fatness 4.327. As a convenient

check at this point the graphs of Fig. 66. indicate a mean L/B ratio of about 7.4 for a vessel 510 ft long.

flow except to increase the transverse velocity

gradient and the local friction resistance around the sharp bilge.

In a vessel which

is

to run at not

more than

medium or fast speed in deep water, there is no reason why the bottom can not be perfectly flat over a considerable area. The floor fines at the midsection need

not be raised unless this

is

required for drainage of the tanks and spaces lying just above this bottom, or for practical purpose.

some other

STEPS IN PRELIMINARY DESIGN

Sec. 66.1?

Assuming

Excessive transverse metacentric stability developing ill the course of the design is reheved by narrowing the surface waterline and working tumble home into the midsection or into the

maximum

section of

tance below the

area for a considerable dis-

DWL,

possibly half

way down

volume achieved by working an

to the baseplane. Increased displacement

and carrying capacity is underwater bulge into

this

section

below the

designed waterplane. If the vessel already has

477

for a starter that the floor line

and

the ship's side are both straight, and that the bilge contour is a circular arc, the appropriate

formula

of Fig. 66. F enables the bilge radius

to be readily calculated. For the

comes out as 10.76

ABC

BR

ship this

equal to 0.14745^ for an and a Cx of 0.9563. Taking a half-siding of 1.5 ft, a molded half-beam of 36.5 ft, and a molded draft of 26 ft, one-half of

Ax

value of 1,815

the

maximum

ft,

,

ft'

section

is

laid out as in Fig. 66. G.

adecjuate metacentric stability, this bulge need

not increase the waterline beam. As a check on the tentative value of Cx for the ABC design at this stage a maximum-section contour is drawn. This requires that the rise of floor, if

any, be established. It gives an idea of

the roll-resisting characteristics of the section, leading in turn to an estimate of the bilge-keel

width which

is

required and that which can be

allowed.

To meet it is

There

(a)

the requirements of the

ABC

design

decided tentatively that: to be

is

some

provide

rise of floor, to

and to give more room under the ship in the shallow

for internal tank drainage for

water moving aft

waters to be traversed (b)

The

side of the ship in

waterline

is

Fig. 66.G

way

to be given a shght tumble

home

any case is not to have an outward flare in that region (c) There should be room to fit roll-resisting keels which are at least 3 ft wide amidships, to help counteract the effect of the shallow draft and the wide beam.

A

rise of floor of 1.0 ft is tentatively selected.

and a a floor slope of 0.0286, corresponding to slightly over

half-siding of say 1.5

1.0/35.0 1.6 deg.

1.0/73

=

of 36.5 ft

this gives

ft,

The rise-of-floor to beam

=

ratio

isKF/fi^

FOB

=

heavy bed hue is drawn in at h = 29 ft. The and the slack bilge appear to provide ample room for backflow under and around the ship in the shallow and restricted areas of the river and the canal but of course the large corner radius detracts from the inherent roll-resisting characteristics of the hull. However, there is room enough for roll-resisting keels at least 4 ft wide rise of floor

amidships,

if

desired,

having

without

them

project below the floor line extended or beyond

the extreme beam.

The first conflict between requirements now appears in grapliic form. With the fairly large

0.0137.

6R with

Design

A

B/H To calculate

ABC

if

possible but in

With a half-beam amidships

Half of Maximum-Section Contour

of the designed

no Rise of Floor

ratio of 2.8, the large ratio of

To colculoti

0.1474, 5R-V?.5299(I-C,)Bx-H

R-l/(l-Cx)B«H-0.5Bx-RF

I

Half-Siding

H5

neglected

y^ ^^^

and a value

of

BM

large, there are indications of

that

is

BR/Bx =

certain to be

heavy rolhng ahead,

hence the need for deep roll-resisting keels. The compromise thus indicated between restrictedwater and wavegoing needs may not be the best one but it will be allowed to stand for the time being.

At

least

the restricted waters

must be

traversed twice every voyage while waves that Fig. 66. P

Formulas for Computing Bilge Radius BR

produce deep rolling may or countered on every trip.

may

not be en-

HYDRODYNAMICS

478

First Estimate Relating to Metacentric

66.14

Before the preliminary design proceeds

Stability.

too far

it is

know

well to

the general situation

relating to transverse metacentric stability. this

While

can not be determined accurately until the

waterline shape

Cw and

the waterplane coefficient

is fixed,

other characteristics of the waterline

generally are determined, in turn,

by the meta-

centric-stability requirements.

mated by the use

Cw

coefHcient

Cp and

known

,

Cw was

a ratio between

of

(2)

approxi(1)

the

the waterplane

as the relation coefficient,

symbolized by Cy This ratio was found to be more nearly constant than other ratios among the various form coefficients and was used for

estimating

Cw

[Barnaby, K.

the

before

C, BNA,

were

lines

drawn

1948, p. 24].

Based upon the satisfactory service performance number of merchant vessels, from small

of a large

cargo ships to large

Sec. 66.14

coefficient just described,

and between

(2)

Cw and

the transverse inertia coefficient Cit To use the diagram, start with the value of

say 0.62 for the

ABC

ship,

to the lower diagonal line.

,

The

abscissa of this

intersection gives a good average value of

first

Cw

Cp

then cross horizontally

in this case 0.713.

,

Then go up

to the upper diagonal line,

this ordinate

whereupon the ordinate

of the second intersection gives the value of C, approximately 0.561 for the ABC design. Because j-

In years gone by the value of prismatic coefficient

IN SHIP DESIGN

normal-form ships with there is one diagram for single-screw vessels and another for twin- and multiple-screw vessels. Using the of certain differences in

different

numbers

of

propellers

values picked for the single-screw the square

moment

ABC

of area of the

design,

waterplane

works out as/ = [BUL)C,t]/12 = [73' (510)0.561] /12 = 9,275,150 it\ The metacentric radius BM, equal to I/V, is 9,275,150/574,000 or 16.16 ft.

Long experience demonstrates that a reasonable

with data kindly

value of transverse metacentric height to satisfy

furnished by the U. S. Maritime Administration,

both comfort and safety requirements is about O.OGBx [Niedermair, J. C, SNAME, 1936, pp. 419-420; INA, 1951, p. 144]. For the 73-ft beam

liners,

the diagrams of Fig. 66.

H

have been prepared. They give acceptable relationships between (1) the prismatic coefficient Cp and the waterplane

Cw

coefficient

0,60

0.65

,

corresponding to the relation

0.70

0.75

Fig. 66.H

085

080

Woterplone Coefficient

0.90

of the

4.38

ABC

ship this gives

GM

=

(0.06)73 or

ft.

060

065

Cw

070 Woterplone

080 0.75 Coefficient C-^v

005

0.90

Data for Selecting Waterplane Coefficient and Transverse Moment-of-Arba Coefficient FOR Given Prismatic Coefficients

STEPS IN PRELIMINARY DESIGN

Sec. 66.15

The height

KB

CB

buoyancy

of the center of

determined at this stage by often known as the Morrish formula [Normand, J. -A., "Formules ApproximaConstruction Navale (Approximate tives de

above the basehne the

is

Normand formula,

479

directly a part of the

hydrodynamic design they

are omitted here.

The range of stability and the heeling or righting energy pertaining to dynamic metacentric stability are

approximated, according to Sec. 68.6, hull has been roughed out. First Sketch of Designed Waterline

Naval Architecture)," Paris, Arthus Bertrand, 1870; Pollard, J., and Dudebout, A., "Th^orie du Navire," 1890, Vol. I, p. 113;

when the abovewater

SNAME,

of the vessel is to lay out the designed waterline.

Formulas

for

1893, p. 29]

KB = H

-(- +

66.15

Shape.

The next

The diagrams

—) (66.iii)

step in determining the shape

of Fig. 24.

G

illustrate

some

historic

yet highly instructive waterhne shapes. Fig. 51.C depicts the actual designed-waterline shapes for six typical vessels in several speed-length groups.

The B/Bx For the

ABC

H

design at this stage

26

is

ft,

V

andA^ = 510(73)0.713 = 26,545 ft', whence ¥/A^ = 574,000/26,545 = 21.62. Then KB = 26 - 1/3(13 + 21.62) = 14.46 ft, 574,000

KM

14.46

+

16.16

=

30.62

ft,

KG = KM - GM =

30.62

-

4.38

=

26.24

ft.

= KB

of the fully loaded vessel lies

in the designed

very nearly

It should

easily be below this limit, even with a fairly large abovewater hull and with the sizable upper works required for passenger

waterline.

possible to keep the

CG

quarters. On the other hand, the CG is not so high as to produce undesirable rolling features [Vedeler, G.,

INA,

somewhat lower

1925, p. 166]. It

in proportion

for ocean hners [de Vito, E.,

than

is,

in fact,

customary INA, 1952, Table

VIII; partial abstract in SBSR, 13

is

Nov

1952, pp.

642-643].

The

other waterline shapes

SNAME

Resistance Data

sheets.

expression

Because of the effect of the waterline slopes forward upon surface wavemaking and of the

upon separation, the shape waterplane depends upon the speed-length quotient T^ or F„ at which the vessel is to run. waterline slopes aft of the

Since the relative speed of the

This means that, with the assumptions made,

CG

many

ft',

+ BM =

the

values for

are to be found on the is

KB^ /H s available as a rough BM, where k varies from i

check on the value of

0.08 to 0.10 [Attwood, E. L., and Pengelly, H.

S.,

BM

=

pp. Ill, 476]. For a rectangular box hull,

ABC

ship

is

rather

high, with a T, of 0.908

and an F, of 0.270, a small waterline slope at the stem and an easy waterline in the entrance are indicated, to keep down the pressure resistance Rp due to wavemaking. With the small length-beam ratio of and the Ukelihood of using a bulb bow, a

6.986,

considerable degree of hoUowness in the entrance waterlines

is

a certainty. Taking into account

the speed ratios listed and the Vincent's data of 1930 139;

p.

revised

Cp of 0.62, S. A. [MESA, Mar 1930, Fig. 5,

unofficially

to

1952]

indicate

something between a very hollow and a moderately hollow entrance waterline.

A

study of nominal

WL

entrance slopes is for

easily driven hulls, plus available reference data

on the subject, produced the graphs

of Fig. 66.1.

ABC design, where B is at and H is 26 ft, BM = (say)0.08(73) 26 = 16.40 ft, compared to the value of 16.16 ft determined previously. A complete preUminary design requires, at this or at a slightly later stage, an estimate of the vertical and horizontal CG position as determined by the weights [PNA, 1939, Vol. I, pp. 102-103], including if possible a check from the known values for a somewhat similar ship. It requires also an estimate of the transverse metacentric 0.08357^- For the present 73

stability

ft

for

the light as well as the loaded

condition; possibly also for one or

more

inter-

mediate loading conditions. As these are not

Fig. 66.1

Graph op Design Values for Waterline Slope is at Entrance

HYDRODYNAMICS

480

These exclude the shapes

of

Sec. 66.15

stems made blunt purposes only.

functional

or

construction

for

IN SHIP DESIGN

Past practice, and good performance as well, indicated by the spots in the region of T„ = 0.4 and justified, in a way to 0.75, has embodied the use of large ie values in these low-speed

—

ranges. Further study of the large deflection drag undoubtedly associated with these blunt

plus consideration of the equally large

stems,

wavegoing drag in head in these slopes, in Fig. 66.1

is

if

The

a reduction design lane

therefore lower than one laid out

most

to fence in

seas, calls for

practicable.

of the spots.

Because of the lower

L/B

ratio of short vessels,

explained in Sec. 66.7 and indicated graphically in Fig. 66. E, their is values are necessarily larger. 66.1 contains therefore a branched design

Fig.

lane for vessels of low

The

ratios. rises

L/B

lane for vessels of

but high

L/B =

V/\/L

6.0 to 10.0

sUghtly at high T,'s because of the straight

or slightly convex designed-waterline shapes used

For the ABC waterhne entrance an is value of 7 or 8 deg appears suitable for the present, until the whole waterhne is laid out and its characteristics are checked with various requirements. Hydrodynamically, and for easy driving, any in the forebodies of these craft.

parallel waterlines at

20

10

30

40

50

Lenqth of Parallel Designed Vi/oterline of Ship Lenqth

in

60 70 Percentoqe-

Design Lane for Percentage of Parallel Waterune

Fig. 66.J

and near the surface are

On

the

ABC design the optimum position

to be avoided, for the reasons given in Sees. 4.7

portion.

middlebody is used, parallel waterlines of course come with them. When vessels are built on slips or in docks of limited width, or when they have to pass through canal some parallel waterhne is inevitable, locks, even without parallel middlebody. The lane on Fig. 66.J is an indication of what has been found acceptable in the past on vessels with varying Cp Judging by this the ABC ship could have a up to about 0.22L, parallel portion of the but to keep the longitudinal waterhne curvature more nearly constant a value of O.OL is selected.

appears to be about 0.54L; the exact position is not too important. It will probably depend upon

and 24.13.

If parallel

.

DWL

This

is

The

also within the lane.

fore-and-aft

designed waterhne

position

of

beam Bwx

,

the

maximum may or

which

not be opposite the maximum-area section, determined by the position of the latter to

may is

some

extent. Nevertheless, for easy-driving ships

these positions are well related to the

and hence are shown

logically

on

Cp

value,

different dia-

K

gives a lane of good positions grams. Fig. 66. for a large range of Cp values. When there is any parallel waterhne, the indicated position along

the ship

length

is

for

the midlength of that

DWL

to achieve subsequent adjustment of the nearly constant curvature. Inspection of the many waterhne endings and

run slopes in on the available sheets, for ships of

SNAME RD

normal form and with canoe

or whaleboat sterns, together with those Figs. 23. A, 24.G,

and

shown

51. C, indicates the

in

extreme

shaping such a stern with a slope ig deg or less. Even the TSS parent form, EMB model 632, with a Cw of only 0.66 and an L/B ratio of 6.85, has a run slope at the stern

difficulty of

of 15

as high as 22 deg; see Fig. 24.G.

One

solution,

and the one adopted here for the ABC afterbody, is to use an immersed-transom stern, along the hues described in Sec. 23.2 and illustrated in Fig. 23.A. A conservative preliminary figure for a not-too-wide transom beam B^ on the ABC This may have to be increased ship is 0.3B;r •

later to

keep the run slopes down to the order of

12 or 13 deg.

Despite difficulties encountered with the wavegoing performance of certain full-stern vessels

STEPS IN PRFLTMTNARY nF.STCN

Srr. 66.1 r,

of the past [Thompson, R. C, NECI, 1935-1936, pp. 216-217], no such problems have presented themselves with the multitude of full-stern and

transom-stern vessels of the U.

S.

Navy

able for this preliminary design.

now

It is

possible to sketch a tentative designed

ABC

(j)

(k)

or say 50

ship on the basis of the

Several attempts produce a result that meets sketches are not illustrated here but the final

designed waterline shape appears in Fig. 07. A. A preliminary check of the curvature, by the

graphic method described in Chap. 49, indicates

However, before making another try at the

designed waterline

(a)

Length, 510

(b)

Slope at stem, 7 to 8 deg

(c)

Entrance

ft

from

S.

[MESA,

A. Vincent

=

0.8 to 0.85,

with hollow portion

No

(e)

Slope at stern, 13 deg,

(f)

Beam, maximum, 73

(g)

Position of

(h)

Nearly constant curvature amidships

(i)

Cr =

parallel waterline

0.713;

work

Estimated Draft Variations.

66.16

how

other

out. It

is

useful

underwater body, to have some idea of the

variations in draft to be encountered in the several

maximum

510(73)0.713

The

first statement Table 66.d of Sec. 66.3, requires modification because of the changes in fuel weights. The second variable-weight statement appears in Table 66. f.

variable-weight conditions.

ft

0.54L, or 275.4

Aw =

well to see

is

at this stage, as an aid in developing other features of the

(d)

,

it

parts of the underwater form

1930, Fig. 5, p. 139], for T,

B^x

The preUminary

the requirements fairly closely.

ing.

offsets

O.IOL,

ft.

that the early contours could stand some smooth-

following:

Mar

ft

built

from the middle 1930's to the present. Since the transom stern proposed here is on the small side as transom sterns go, it is considered accept-

waterline for the

'IRl

Transom width Bu = 0.3(Bx) = 21.9 Transom radius in planform, tentative,

of these conditions, given in

ft

=

abaft

26,545

FP ft''

The

tons per foot immersion for the designed-

dimensions tentatively selected are approximately 26,545/35 or 758.4 tons per ft, equivalent to about 63.2 tons per in. This value

0.90

waterline

diminishes as the load decreases and the ship comes up in the water. The change is allowed for in a

rough way by reducing the 758 tons per foot

progressively to a guessed value of 725 tons per at the lighter drafts. On this basis the drafts corresponding to the entries in Table 66. f are about as set down in Table 66.g. These show that ft

when the

vessel

through the canal designed

maximum

Port Amalo

returning to

is it is

some 975

t

fighter

than the

service displacement.

When

Amalo it may be from 2,400 to 3,400 or even more, depending upon the liquid carried. This decreases the mean draft

leaving Port lighter

ballast

by from 3.26 reduce the

to 4.63

maximum

It

ft.

draft,

may be expected to with the stern down

to keep the propeller under water, ft.

OSOM

M

£5 Position

of

Byjx

I

II

I

I

I

60 55 50 40 -4S Maximum Designed Waterline Beam

in

Fig. 66.K

I

Percentaqe of Ship Lenoth from FP

Foee-and-Aft Position of Maximum

Waterline Beam Bffx

The minimum bed

of

the ship in the Port

28

-

(26

-

3.26)

=

by

at least 1.0

clearance under the middle

5.26

Amalo

ft,

which

is then undoubtedly

canal is

more than enough for the limiting speeds of 8 and 10 kt. The designed draft of the vessel might possibly be increased from 26 to 27 ft, but then the bed clearance in the river when leaving Port Correo would be 3 ft minus the fresh-water sinkage

correction,

or

about 2.35

ft.

This

smaller than the 3 ft indicated in Fig.

is

66. G.

HYDRODYNAMICS

482

TABLE

66.f

IN SHIP DESIGN

Second Statement of Variable- Weight Conditions

This table, at the present stage of the design, supersedes Table 66.d.

Load Condition

Sec. 66.17

STEPS IN PRELIMINARY DESIGN

Sec. 66.18

TABLE The

variations from the designed

value for fresh water

is

maximum

reckoned constant, at

Load Condition

483

First Statement op Variable Draft

66.g

service load are taken

its

maximum

value.

from the

last

column

of

Table

66. f.

The sinkage

HYDRODYNAMICS

484

to be determined. Unfortunately, the results of the

parallel-middlebody series of models developed

by D. W. Taylor, reported in the 1943 edition of book "The Speed and Power of Ships," pages 70-72 and 257-271, have not been analyzed and put in suitable design form. It is therefore necessary to use an empirical design curve. Taking his

as a basis Taylor's original 1910 diagram [the

same

as S and P, 1943, Fig. 83, p. 71], his data have been supplemented by parallel-middlebody percentages (Lp/L) for ship models on the SNAME RD sheets whose performance was equal to or better than that of the TSS model of the same proportions. When suitably extended to cover higher and lower values of Cp the new plot of Fig. 66.M reveals that these ship data he in a rather narrow lane running diagonally across the diagram. Since Cp and T„ (or F„) are, for ,

easily driven ships, related

lane of Fig.

66. A,

are therefore plotted in Fig.

The new proper ratio of Lp Cp

only.

D.

by the lower design

the data recently analyzed

66.M on a

to

Lg^Ldiagram

AV. Taylor's original

Fig. 83, p. 71], as well as Fig. (a) is

basis of

design lane gives directly the [S and P, 1943, 66.M, reveal that:

Inserting parallel middlebody of length

Lp

a definite advantage at low T, and F„ values.

For a given Cp it adds displacement amidships and allows finer ends. It also gives rectangular passenger and cargo spaces and may result in reduced building costs.

-

IN SHIP DESIGN

Sec. 66. IS

STEPS IN PRELIMINARY DESIGN

Sec. 66.21

cated in a preceding paragraph, placed with

its

midle ngth at the selected fore-and-aft position

LMA

maximum area. Bulb-Bow Parameters. Considering

of the section of

66.19

next the forward end of the ship,

whether a bulb bow

first

is

it is

determined

largely

by the

ratio of the speed to the length at

the point where

The

maximum

tapers

and

less

off

is

desired.

is

in the region of a T^ of

down

to a T„ of about 0.75 or

greatest saving

1.0; it

performance

diminishes at 1\ values up to 1.5 or

it

From of is

=

is

within the opti-

D

a value

tentatively selected for the designed

range of T, of from 0.828 to 0.908. The detail design of the bulb is worked out in Sec. 67.6.

Transom-Stern

66.20

Parameters.

For

an

estimate of the immersed-transom area and the

value of fn is

in Sec.

lies

the upper diagram of Fig. 67. 0.9

Feb

67.D

0.06

portions of this vessel.

more. Inspection of F. H. Todd's Table 5 [IME, 1945, p. 18], as well as of Fig.

—

mum range, and it affords ample room for the bottom anchor contemplated, although it is somewhat lower than the optimum for the pro-

advisable as a means

of saving pressure resistance. This is governed

485

mediate value of f E

it is

assumed

that the transom

first

definitely to clear at the designed speed

of

67.6, reveals that for the speed-length quotient

20.5 kt. In other words, at this speed the entire

of 0.908, corresponding to the trial speed of the

transom area is to be exposed to the air. On the assumption described in Sec. 67.20 that the corresponding Froude number, using the immersed-transom depth Hu as the length dimension, is hmited to 5.0, this immersed depth works out

ABC

a bulb bow is indicated. It is to be borne in mind that this ship, for probably the greater part of its time at sea, will ship,

run at a speed closer to 18.7 kt than 20.5 kt. In other words, the T, for the majori ty o f service

approximate only 18.7/ VolO = 0.828, F„ = 0.247. At this lower speed the bulb may show up to less advantage. Furthermore, a smaller /^ is called for than at the higher T, of 0.908, in the ratio of about 0.07 to 0.08 or more. The bulb parameters may be worked out by D. W. Taylor's method [S and P, 1943, pp. 65-70, 243-254]. However, it is pointed out in some detail in Sec. 67.6, where this procedure is illustrated, hours

that

as follows:

will

rarely possible to utilize all of the

is

it

optimum

section

interferences with

area in

a bulb,

because

of

bower anchors and possible

under-the-bulb slamnoing.

There

is

one other factor to be considered. In

the lighter-load conditions on the

ABC

ship

it is

F,

_ = ~

6889)1' [ 20.5(1.6: 5.0 L

^t/

=

3^ (6.925)'

,

emerge at less angles of pitch than at full load. If the proposed under-the-bottom anchor

installation described in Sec. 68.11 does not

out, to

may

be necessary at a later design stage bower anchors in the orthodox side locations.

it

fit

work

lay down, in the standard 1:4 box described in Sec. 24.12, a tentative section-area curve for the

ABC

full-load

conditions.

The value

of

representing installations of the past,

enough to make a bulb worth

while.

is

An

hardly inter-

design.

The

typical A-curve on S. A. Vin-

Cp

cent's 1930 data for a

W.

0.02 from the broken hne of Fig. 67.D,

sketching the section-area or A-curve. it will

66.21 The Preliminary Section-Area Curve. With the data thus assembled it is possible to

plot.

=

first

are given in Sec. 67.20.

smaller bulb area Je than that indicated by the full-speed,

ft.

not be larger than this. Further details of immersed-transom design

This consideration alone points to the wisdom of using, for the ABC design, a considerably

Se

1.49

of 1.5 ft, the immersed-transom area at rest would have a maximum value of about 33 ft'. The terminal value Ju is about 33/1,815 = 0.018. A tentative value of f r = 0.02 seems reasonable

Certainly

will

=

Taking the transom width previously agreed upon of (0.3)73 = 21.9 ft and a constant depth

when

submergence. At these varied trims by the stern the bulb at the bow will be nearer the surface and

= V/VgHv,

g{H^) ''^

in the tanks aft will be used to bring the stern

to give the propeller adequate tip

5.0

whence

comtemplated that liquid cargo or water ballast

down and

=

1930, Fig. 4, p. 138]

is

of 0.60

[MESA, Mar

ticked in with dots on the

is checked from the cross curves of van Lammeren [RPSS, Fig. 42, p. 92], from those of F. H. Todd for the TMB Series 60 [SNAME, 1953, pp. 516-589], or from similar

This

P. A.

sources, provided the curves lend themselves to

vessels with bulb bows.

HYDRODYNAMICS

486

is

The position of the section of maximum area marked as 0.515L from the FP. The tentative

value oi fs = 0.06 is laid off at the FP and a tangent to the section-area curve at the FP is

drawn by working backward the formula Sec. 24.12. Since

1.00

-

which

0.06

is

=

fs

intercept

©

as

is

0.9,

gives the

,

FP

A/Ax

abaft the midwidth of the lane in Fig. 66. N.

of

Although the corresponding values are

shghtly different for the final section-area curve.

67.W The value

intercepts mentioned.

illustrates the

of

insufficient

/«

is

laid off as 0.02

but there are

data to indicate a good terminal This preliminary yl-curve is omitted

value of Ir for lack of space but the final curve .

in Fig.

is

depicted

67.W.

Integrating the preliminary curve numerically

an underwater hull volume of 572,050 ft' and a Cp of 0.618. Both values are a little small when compared to the previous figures of 574,000 ft' and 0.62, but before modifying the curve it is well to see what the underwater form looks like gives

when

other requirements are applied.

The

first

y4-curve appears sufficiently fair to permit sweUing it here and there, but it must first be found where these volume changes are of most benefit to the ship. A discontinuity in the ^-curve

or shrinking

to be expected at the stern, where the singleskeg area drops rather suddenly to zero. In this connection it is to be remembered that is

ship

sections,

body

customarily laid

plans,

to the

off

and waterUnes, are molded dimensions

For a metal vessel this is to the outside framing and the inside of the plating.

of a ship. of the

Furthermore,

the

rudder,

roll-resisting

keels,

and other appendages displace considerable quantities of water and thus help to support themselves. The volume occupied by the plating of a steel vessel is assumed equivalent to about 0.0075 times the molded volume if in-and-out strakes are employed. It is about 0.005 times that volume if the plating is flush, as in a welded vessel [Robb, A. M., TNA, 1952, p. 77]. The volumes occupied by the appendages are readily computed when they are roughed propeller, exposed shafting,

out.

For the

ABC

ship

stage that the shell

and nearly

all flush.

it

is

may

be assumed at this

to be rather fully welded

Taking a value

the corresponding volume

is

66.22 Longitudinal Position of the Center of Buoyancy. As an indication of the fore-and-aft position where the CG must He, an integration of the preUmin ary s ection-area curve shows that

LCB is about 0.506 or 0.507L, reckoned abaft the FP. This position is slightly

the midlength ordinate at a value of

Fig.

Sec. 66.22

and the weight is 3,157/35 = 90.2 t; say 90 t. This leaves a molded displacement of 16,400 t or 574,000 ft' as the end point in working up the final ^-curve and the underwater hull form. ft'

intersects

Adding 0.846 to 0.06

0.846.

indicates that the tangent at the

0.906.

by

0.94. Multiplying 0.94

the tentative value of /^

in

@

0.06, the intercept

is

IN SHIP DESIGN 3,157

of 0.0055^,

(0.0055) (574,000)

=

the value of

STEPS IN PRELIMINARY DESIGN

Sec. 66.23

do

this

by sketching freehand on paper with

Hght-blue cross-section hnes, producing the result

waterline to a rounded main-deck planform at

the stern.

depicted in Fig. 66.0. Small profiles, sections, and

The

deck plans, plus a midship section, bow and stern profiles, and a stern elevation to larger scale, suffice for this purpose. The first such sketches for the ABC design were drawn to a scale of 80 f t = 1 in. For a complete preliminary design these sketches would be supplemented by an inboard profile and several additional deck

calls for

plans,

drawn to a considerably

larger scale.

The maximum-section contour

of Fig.

66.

G

and the preliminary designed waterline form the bases of these sketches.

A

tentative freeboard

487

wide,

somewhat shallow underwater form

rather drastic narrowing aft

if

proper

flow to both top and bottom blades of a single

A pronounced cutting might give a reasonably good performance with twin screws; a twin-skeg form of stern almost certainly would. However, the use of two separate propelling plants for an output of the order of 16,000-20,000 horses propeller

up

is

to be achieved.

of the stern

involves increases in space, cost, weight, operating personnel,

upon

and so

in Sec. 69.2,

on. it

For the reasons elaborated appears not

justifiable.

and then checked as described in Sec. 66.30. A sheer line is drawn in, more or less by eye, with the low point of the deck well aft of amidships and with a sheer

The efficient, economic transportation required by item (5) of the mission, in Table 64. a, calls for high propeller and propulsive efficiency. One method of gaining the former is to use a screw

forward that looks right, to be checked later as

propeller of the largest practicable disc area

outlined in Sec. 68.4.

diameter.

amidships of 23

A

ft is selected

curved raking stem and a bulb that projects

and

below the

For the current style (1955) in single-screw merchant vessels having canoe or whaleboat (cruiser) sterns, a good rule for the propeller diameter D is to keep it less than O.IH at the

designed waterline and a stern profile raking

designed-load condition. This insures reasonable

The square

submergence at drafts not too much smaller than the maximum, and as good submergence as can

slightly

scale

forward of the

bow

profile.

transom depth sUghtly forward

transom

is

of

is

FP

At the

complete the smallstern the immersed-

1.5 ft is laid

added above

off

it.

indicated as fading out above the

25 5-ft Station Spacmq

Fig. 66.0

Sketches of Outboard Profile, Main Deck and Waterline, and Sections

HYDRODYNAMICS

'IfiS

H

IN SMTP DESIGN

Sec. 66.21

be expected in wavegoiiig. With a draft of 26 ft, this gives a hmiting diameter of 18.2 ft.

Molding a Within the framework

New

For better-than-average

portions, coefficients,

and parameters, plus the

efficiency the propeller

should be considerably larger, with a diameter of the order of 20

ABC

the

It is

ft.

The

latter size is selected for

ship, as the basis for further sketching.

soon found that, even by working reverse

curvature into the buttocks ahead of the transom, to make room for such a large on the centerline. The situation is eased somewhat by eliminating the rudder shoe, carrying a semi-balanced rudder on a fixed horn, and dropping the propeller disc almost down to the baseplane. However, when enough fore-andaft room is left for the rudder, the horn, and the propeller aperture abaft the upper blades, the it

is

difficult

propeller

propeller-disc

position

rather

is

far

forward,

where the buttocks are definitely curving downward. Flattening the under side of the main hull to fair into the transom leaves a sort of shelf of considerable extent just above the wheel. The latter is thus shielded exceptionally well from air leakage but it is difficult to provide a large tip clearance at the top center.

An

66.24

now required to fashion a good underwater form. So far as propulsion is concerned, it should have the smallest practicable shaft power which will drive it at the designed maximum sections, it is

meet

and

speed

requirements. It

vicinity of the centerline

the lower apex of the V-sections in the skeg ending, the rudder shoe, and other obstructions to

be

accommodated

abreast the propeller on the centerline

Moving the

propeller farther aft, where more vertical clearance between the baseplane and the buttocks, by shortening the fore-and-aft length of the rudders. There would be twin rudders behind the two skegs instead of (b)

there

is

a single rudder. (c)

The

creation of such a shape, as the best final

most complex flow and resistance problem in hydrodynamics, is probably as much a matter of unconscious understanding and of inspiration as of the straightforward use of all

hydrodynamic knowledge. The selection good underwater form as a guide is contingent upon the availability of a store of information on available of a

ship forms, contained in the designer's

hterature,

Providing room for a propeller of greatly in-

much

smaller tip

clearance needed inside the tunnel.

Further developments of this alternative stern, an arch form, are described in Sec. 67.16.

called It

becomes apparent, as the small-scale afterbody it

own

files

in the

may

require different

widths and shapes of the designed waterline in the run than the transom stern.

SNAME RD is

among

sheets,

and

in

equally contingent upon the

those data, of a form re-

sembling the one wanted, and on a certain amount

knowledge and good judgment, mixed with when working over that form. Many good shapes have been developed through a long process of intelligent refinement, as witness the Taylor Standard Series. For the ABC design being carried through here the Taylor Standard Series form has too low a maximum-section coefficient, 0.923 as compared to a range of 0.955 to 0.96, it has too low a waterplane coefficient, 0.66 as compared to at least 0.71, and it does not have a bulb bow. Further, of

experience,

as the

form,

it

TSS

parent is essentially a twin-screw appears not suitable for the single-screw

project in hand, even though the

B/H

ratio of

ABC

beam-draft ratio of 2.808. The Series 60, block 0.60 parent form, having a Cp of 0.614, has too full a maximum section {Cx = 0.977) for the easy shallow-water driving required of the ABC ship, too small a B/H ratio (2.50), too much parallel waterUne (15 per cent), and no bulb bow. Rather than to follow some other well-developed form of good 2.92

creased diameter because of the

sketches proceed, that

specification

not have a low

solution of a

availability,

have

may

hull resistance, but it must embody a machinery plant that represents the minimum in first cost and in operating expenses consistent with durability and refiabihty.

skegs offers advantages which appear to warrant the development of a preliminary-design variation along these fines. This arrangement eliminates man.y of the usual difficulties in singlescrew sterns by: the

normally

or

total

similar sources. It

which

remaining

the

may

or in those available to him, in the technical

adaptation of the twin-skeg stern with a mounted in the tunnel between

Removing from the

Form.

of the selected ratios, pro-

general shape tentatively selected in the preceding

single propeller

(a)

Underwater

is

close to the

TMB

performance, or to use

body plan

for the

clean sheet,

both

new

it

as a guide, a large-scale

ship

literally

is

roughed out on a figuratively, on

and

STEPS IN PRELIMINARY DESIGN

Sec. 66.24

the basis of present hydrodynamic knowledge.

The guiding

principles in this procedure are

based upon an understanding of the water flow around a ship-shaped form, and the effects of this flow.

One such

principle

is

based upon the

fact that, for the underwater hull of a surface vessel

which varies not too widely from the normal,

the upper layers of water

met by the

ship pass

around the sides of the entrance while the lower layers pass under the bottom. This feature is

by Figs. 4.0, 22.E, 24.L, 25.G, 66.R, and a number of diagrams in Chap. 52. In the run, the water which has passed around the sides rises rather rapidly toward the surface, so that toward the stern the water flowing over the hull is largely that which has come up from under the bottom. The shortest paths from the bow to the stern are, in general, those which cross the section lines at right angles, indicated by the position of flowlines when projected on the midsection and shown in a body plan. However, it is illustrated

not always possible for the water to flow in this fashion under a more-or-less flat free surface and

around a hull which must meet requirements other than those of minimum resistance. Since neither the section shapes nor the flowline positions for

an entirely new hull are known at

the outset, this means that both have to be

worked

in simultaneously,

(streamlines)

as for the flowlines

and the equipotential

lines

of

a

Compliance with

this shortest-path rule, con-

formity to the general flow pattern described in the references listed, and consideration of curvature changes along the flowlines, calls for V-shaped

and the run. Consideration of pressure resistance due to wavemaking, and of the height of the bow-wave crest sections in both the entrance

in

particular,

sections in

way

vertical-sided

calls

for

of the

bow-wave

crest.

entrance

A bulb bow

does not work well into V-shaped bow sections, nor is it easy to fashion a deep forefoot from them,

where the bulb must be. These considerations, coupled with the division of flow described in (1)

of

the following paragraph,

indicate

that

U-shaped bow sections are to be preferred to V-shaped sections, for this ship at least. Specifically, a few more detailed rules may be formulated for guidance in shaping the hull of the ABC design, with its B/H ratio of about 2.8 and its T„ of about 0.9. These should be part of a

comprehensive set for a large range of values, hull shapes,

this set is

yet completed.

The present

B/H

and speed-length quotients

a formidable task not additional rules are:

Along the region of the designed waterline, extending below that line for the order of 0.20 to 0.25H at the bow, 0.9H amidships, and O.IOH at the stern, the water flows primarily around the sides. The position of the dividing line at the stem between the side and the bottom water depends also upon the height of the wave crest at the bow and the change of level at the bow when underway. (2) To minimize surface wavemaking the changes (1)

in longitudinal curvature along the flowlines in this belt, as well as the curvature itself, should

be a minimum. This embraces the number of curvature changes between bow and stern; the

number

lowest possible (3)

Changes

in

is

two.

curvature

region indicated in

the

in

side-water

at successively deeper

(1),

depths below the designed waterline, should if practicable be offset longitudinally, and should not occur at any one transverse station. The reason for this is explained in Sec. 4.8 and the

accompanying

Fig. 4.1

In the region at the stem below about 0.20 to 0.25H, measured downward from the designed waterline, the water flows outward but then (4)

swings downward rather rapidly, to pass under the bottom inside the turn of the bilge, below

about 0.9 to l.OH (5)

flow net, described in Sec. 2.20.

489

but making up

The

twisting of the stream tubes accompany-

ing this turning of the flow, depicted in Fig. 4.P,

should be accomphshed as easily and as gradually as practicable. Some remarks by D. W. Taylor,

made many are

still

years ago

[SNAME,

pertinent at this point;

1907,

p.

comments

11],

in

parentheses are those of the present author: "... this work shows the importance of an easy bilge, that is to say, at about one-

tolerably well forward,

quarter the length of the ship from the bow. The water is trying hard to get under the bottom, and if you have

a shape such that

it is difficult

to get

around the

sections,

you have a ship that is harder to drive. Some of our analyses of model trials appear to indicate that at about the point where the water wants to go under the ship, you ought not to have (a) full section not over eighty-five

—

per cent coefficient of fullness (section coefficient) at the outside."

(6)

If

the ship has a deep centerline skeg under

the stern the stream tubes passing out from under

the

bottom must twist back again through

nearly 90 deg as they approach the skeg ending. Assuming a single propeller carried by the centerline

skeg the flow should,

somehow

or

HYDRODYNAMICS

•-190

other,

axis as

be brought nearly parallel to the shaft it passes into the propeller disc.

IN SHIP DESIGN

Sec. 66.24

outline at the

AP

rules

67.20.

of Sec.

next sketched, following the

is

Since the afterbody

is

to

as for the side-water paths, the

terminate in nearly horizontal shelf-like sections

changes in curvature along the bottom-water paths should be a minimum, both in number and magnitude. This means easy and gradual longitudinal slopes in the actual flowplanes,

approximating the form of the immersed portion of the transom it is evident that any centerhne

with small magnitudes of curvature.

to be added under the

The same

(7)

skeg must of necessity be relatively thin. This

is

So much

mind

as sketching of the sections progresses.

The

maximum-area

la3'out of the

from Fig. 66.G, forms the basis

The

be kept in

for the general rules, to

station

offsets

of

the

section,

for the

tentative

plan.

designed

laid off along the 26-ft designed

waterUne are

waterline trace on this plan and are

numbered

accordingly. Short vertical hnes are sketched in

through these points in the entrance, to serve as zero-flare references for the section lines where they cross the designed waterline.

The bulb-bow

FP

section at the

the rules of Sec.

following

is

67.6.

drawn

A

first,

tentative

then sketched in at the forward is taken from a curve of section coefficient based on ship length, section at Sta. 5

is

quarterpoint. Its section coefficient

similar to Fig. 67.1 of Sec. 67.10.

The

section

tangent to the floor hne at the bottom and to the vertical reference hne at the DWL; a large radius or easy sweep is used below about

outhne

is

0.3H. This

does care

is

is

the region where the bottom water

and where particular required to insure easy flowlines. Except greatest twisting

its

for the designed-waterline region

it is

probably

the most important part of the hull, at least in the entrance, and the part that has the greatest influence

upon pressure

resistance. Before easing

the section at Sta. 5 too much, the area is measured and checked with the forward-quarter ordinate at Sta. 5 on the preliminary section-area curve. Section 5

is

reshaped as necessary to give

the proper area and section coefficient; see Sec. 67.10. This may involve a possible widening of

the

DWL. By

the use of the bilge diagonal for

fairing, or several waterlines, or both, it is fairly

simple

sketch in the remaining entrance meeting the designed waterline along

to

sections,

the short vertical reference

lines,

including inside

them the areas given by the preliminary sectionarea curve, and conforming to the section-coefficient

curve.

The abovewater

portions

of

will, in fact,

stern profile, the centerline or half-siding buttock,

the one meeting the bottom of the transom and

taken

body

form a sort of major appendage main hull. The next step therefore to sketch in, on a separate large-scale

skeg

the

section lines in the entrance are reserved for the

time being.

Turning to the afterbody a tentative transom

representing roughly the top of the skeg. There

must be room

at about the after quarterpoint,

from the

or possibly at one-fifth of the length stern, for

main

a large-diameter motor or gear on the

shaft,

low down

in the vessel.

must

The

half-

no farther aft than the after quarterpoint and must rise rather rapidly to meet the bottom of the transom. Indeed, if reverse curvature (concave downward) is to be worked into the after end of this buttock, as is desirable, the latter must rise at a rather siding buttock therefore

angle

steep

forward

One must be prepared

of

the

start

concave

to bring

it

portion.

upward

at a

slope approaching closely the critical angle for

separation at a submergence of about Q.7H. It

known

is

that the owners will require one or more

model tests as a check on the performance of the underwater hull. It appears, therefore, that a centerline or half-siding buttock slope as steep

as 17 or 18 deg design. scale

may

Laying

on what

this

will

be risked at this stage of the buttock down to a large

eventually be the stern profile

gives a series of heights for the termination at

the centerhne of

all

main-hull sections in the run.

Taking the after quarterpoint at Sta. 15 as a sort of midpoint in the run, an easy curve is swept in between the designed-waterline intercept and the half siding at the baseline. The lower or inboard portion of this section is made somewhat flat and the upper portion is given a slight outward flare at the DWL. The area at Sta. 15 is then measured and checked with the A-curve, whereupon the section is readjusted as necessary. Sections between Stas. 10 and 15 are rather easily drawn, following the general procedure for

the sections between Stas. 5 and 10. as

if

A

section

meet the centerhne buttock, there were to be no skeg; see the broken

line is

drawn

first

to

hnes at Stas. 16 through 18.5 in Fig. 66.P. The skeg is then drawn in separately. However, the stations abaft 15 include the skeg as a part of the main hull, so some little sketching and re-

STEPS IN PRELIMINARY DESIGN

Sec. 66.25

491

A All

Wolerhne Heights and BuUock Dislancts ore

in

1^ lO-deg Flare

feel

Parallel

Deck L

TT

Line' of Floor

22 1.5

I

36.70 ft to

Maximum

Wolerline

Beom

A rea Section at

ABC

Body Plan of

Fig. 66.P

ft-^

ot Sto.ll

Ship with Single-Skeg Transom Stern

adjustment is necessary to bring their areas into conformity with the tentative 4-curve. As the skeg area diminishes to zero at the forward end of the propeller aperture, leaving only the

hull

main

a discontinuity in the

abaft that point,

^-curve appears there. Holding the waterline (level-line) slopes in the upper part of the skeg termination to a value not exceeding 15 deg involves a considerable amount of drawing and erasing. It requires the use of with rather small radii where the upper end of the skeg ending merges into the hull. transverse

fillets

However, these small disadvantage generally

parallel

and does not

fillets

The body plan stern

is

The

fillets

provided

the

to

cross for

reproduced in

offer

the

no particular

resulting

fore-and-aft

flow

is

line

of

it.

the single-skeg transom

its final

form

5ta. 10.3 _

in Fig. 66.P.

question of "clubbing" the lower part of

the centerline skeg Since the aftfoot

is

is

discussed in Sec. 67.23.

to be cut

away on the

ABC

design, working a club into the remainder of the skeg, just

above the

keel,

would leave it rather be effective.

far forward of the propeller to

66.25

Bow and Stem

Profiles.

To

finish

roughing in the centerline skeg the position and shape of its termination are added to a large-scale is done by starting at the transom termination the location of the AP and working forward. With a single skeg and a single screw, a single rudder is indicated. It should have some mechanical clearance ahead of the transom; 2 ft appears adequate at this stage. To meet the maneuvering conditions in Port Bacine the rudder needs to have ample area. By the first approximation of Sec. 74.6 this area is say 0.02iL)H = 0.02(510)26 = 265.2 ft'. Assuming for the moment that the rudder height is

stern profile. This

—

—

492

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 66.25

STEPS IN PRELIMINARY DESIGN

Sec. 66.27

about

0.7//, or 18.2

roughly 14.5 or 15

fore-and-aft length

its

ft, ft.

With a clearance

between the leading edge

is

of 2 ft

and the end

of the rudder

after edges of the propeller blades, the after

hub is of the order of 19 ft forward AP. Estimating the propeller hub as about 4 ft long, the plane of the propeller disc is about 21 ft forward of the AP. of the propeller of the

At

this disc position the height of the tentative

half-siding buttock, already laid

down,

is

about

above the baseline. When the aftfoot is cut away to save wetted surface and improve maneuvering, the propeller should have at least 0.5 ft clearance above the baseplane. With a tip clearance at the hull of about 2.4 ft, a rather small figure for a large wheel with a shelf-type stern 23

ft

above

the relative tip or hull clearance for a

it,

works out as 0.12Z). It is doubtful whether a larger screw could be accommodated under this type of stern, on a draft of 26 ft. The propeller tip circle is now drawn in on the 20-ft propeller

and a rough outline of the propeller side projection added to the stern profile. Making the aperture clearance ahead of the upper blades at least 0.2D or 4 ft, rather larger than customary [ME, 1942, Vol. I, p. 275], terminates the upper aperture some 26.5 or 27 ft forward of the AP. This is the position into which the upper part of

body

plan,

the skeg

is

to be faired. After the rudder

is in-

creased in area, and other small changes are made,

the resulting stern profile

is

as

The worked-out example

Fig. 66.Q.

delineated in in Sec. 59.11,

combined with the design rules for propeller apertures in Sec. 67.24, and with the characteristics of the screw propellers found suitable for this design, indicate that the aperture

the upper blades

is still

Details affecting the Sees. 67.4

it

and

somewhat

bow

forward of

small.

profile are

20

ft.

These are done in the sections follow-

For a given volume or weight displacement

very nearly as L"'^. At this stage the 510-ft length of the

Analysis of the Wetted Surface.

The

wetted surface, by the estimate of Sec. 66.9, is to involve an expenditure of well over half the maximum designed power in overcoming friction.

As a check

it is

useful to consider D.

W.

Taylor's

broad conclusions on this subject [S and P, 1943, pp. 22-23]. They are adapted here to an analysis

ABC

appears that

it

ship

is

not too

great in relation to other dimensions or with respect to the ship's mission. (b) For a given displacement and length the wetted surface varies little within the permissible hmits of beam and draft in service. With a B/FI

and a Cx value

ratio of 2.808

ABC

hull, reference to Fig. 45.

of 0.956 for the

H

the wetted-surface coefficient Cs

minimum

indicates that is

in a region

normal vessels. (c) For a given displacement and dimensions, the wetted surface is affected very little by minor close to the

for

variations of hull shape.

The

ABC

sections are

neither the extremely full ones which, according

somewhat

to Taylor, are

prejudicial to low S,

nor are they the extremely fine ones which are

markedly (d)

prejudicial.

After length, the most powerful controllable

factors affecting wetted surface are the forefoot,

the aftfoot or deadwood, and the appendages.

The

have large surfaces For the ABC design the presence of the bulb bow should more than repay its extra wetted surface. It is proposed to cut the aftfoot away by an undetermined amount. The rudder, with its large surface in parts listed in

compared to

(d)

their volumes.

proportion to its volume, is necessary. The fixed horn to support it, if given a twisted or contraform to recover energy in the propeller outflow jet, should likewise pay its way. The roll-resisting

not a part of the main

considered

hull, are

in Sec. 73.18. is

some added surface under the transom ABC ship. It is hoped that the extra

stern of the friction

drag of this surface

may

be overcompen-

sated by the energy recovered in straightening (leveling) the flowlines of the water leaving the stern.

66.27

Second Approximation

Making use

ing.

66.26

(a)

the wetted surface varies mainly with length,

There

68.7.

Before proceeding any further with the lines is well (1) to insure that the wetted surface is

not becoming too large in proportion to the size of the ship, and (2) to make a second check of the probable shaft power for a propeller Dma^ of

of the ABC design but they apply to any usual type and form of ship:

keels,

covered in

493

to Shaft

of the thrust-load factor

Power.

method

for

powering described in Sec. 60.14, the results for the

ABC

ship are as follows.

the resistance

R

From

for the bare hull

is

Sec.

66.9

estimated, in

round figures, as 172,000 lb. An increase of 10 per cent for appendages gives an estimated final hull drag of 189,200 lb. The corresponding propeller thrust

T

for

an estimated thrust-deduction

HYDRODYNAMICS

194 fraction

-

of 0.20 is 189,000/(1

/

=

0.20)

236,500

IN SHIP DESIGN the

if

the Velox system waves

disc area A^ of the 20-ft propeller is 314.16 For an estimated wake fraction w of 0.30, the speed of advance V a is 20.5(1 — 0.3) = 14.35

kt or 24.24

ft

the disc area

per sec. is

coefficient

Ctl

= is

T/qA„

The corresponding

1.287.

236,500/183,725 = taken as

To of 0.5, F„ of about 0.15; at this low limit a small or a large waterline slope in the entrance

=

from Fig. 34.B, is 0.636. This working condition of the propeller.

-

hull efficiency r;„

0.2)/(l

-

0.3)

=

=

=

Voivif)vR

—

(1

is

0.8/0.7

a relative rotative efficiency value of vp 0.7415. This

=

0.9953

real efficiency,

0.877,

The

load over

qAo

The

lb.

=

??«

=

=

is

770

for the

t)/{l

1.143.

—

w)

of 1.02, the derived

0.636(1.143)1.02

=

remarkably close to the value of 0.74 assumed in Sec. 66.9.

is known about the and its probable performance, the latest derived power and machinery-weight figures from Sees. 66.9 and 66.10 are allowed to stand, namely 16,930 horses and 1,250 tons.

hull shape

Sketching of

66.28

The

Wave

Profile

appears not to have too great an

Using the procedure described

=

Assuming

is

able Flowlines.

the height of the

effect,

one way

or the other.

Until something further

new

that

thrust-load

The ram-pressure

183,725

52..J

bow-wave crest is a function of the Froude number F„ or the speed-length quotient T^ and of the waterline slope z'e in the entrance. The bow-wave crest height (not necessarily the spray of the boAV roll) becomes noticeable at a

then (0.5)pAoFi

(314. 16) (24.24)'

observed from Figs. 52.1 and

It is

The

ft'.

r]p

to the bilge

are relatively deep.

lb.

(1

way

Sec. 66.28

and Prob-

Standard-Series procedure

developed by Taylor was an effort to predict, in advance of or without a model test, the probable effective power required to drive the bare hull of a ship of given proportions. This procedure omitted any means of judging the effects of changes in shape for fixed proportions. One method of accomplishing this is an analysis of the flow diagrams around a model of the selected

However, to employ this method for predictions, in advance of model tests, it must be possible to draw a lines-of-flow diagram from a rough set of lines, such as those of the ABC shape.

design at this stage.

bow-wave

height

crest

Unfortunately, neither the method of analysis

in Sec. 52.5, the

the

ABC

ship

is

measured from the plane of the undisturbed water level at a great distance from the ship. To find how far this crest may climb up the side of the ship there must be added the predicted sinkage or change of level of the bow. The graphs of Fig. 58.A give this change of level as -0.0046L or -0.0046(510) = — 2.35 ft. At the stern the change is about -0.00145L, corresponding to -0.00145(510) or about -0.74 ft. calculated as 7.17

This

ft.

is

The predicted lag of the bow-wave crest, worked out in Sec. 52.5, is 13.86 ft. This is at about 0.027L abaft the FP, where the sinkage of the bow, by linear interpolation between —2.35 ft and —0.74 ft, is about 0.05 ft less than at the bow. The bow-wave crest may then be expected to rise up the side by (7.17 -|- 2.35 - 0.05) ft or 9.47

indicated in Fig. 66.R.

ft,

It is

almost certain that the effect of the bulb

bow on no

ABC

the

predicted

ship

data

quantitative

lowering

is

to lower the crest height

by the referenced formulas. However, is

are

available,

so

this

not taken into account. Since a small

waterline-entrance slope and a bulb

go hand in hand,

or the techniques of drawing the lines of flow in

for

bow

generally

probable that a substantial

it is

reduction in height occurs on vessels having these features.

advance have been worked out. Nevertheless, the latter is attempted here, on the basis of the principles set forth in the sections preceding, and with the background of the diagrams in Chap. 52. If it is possible only to tell whether or not a form

profile

has objectionable features the prediction pro-

the ship and as observed on the model are intended

worth while. In any case the

to be independent of any thin spray roots extend-

cedure

is

well

experience gained will go far toward working out

unknown methods and techniques. The first step is to start with the wave

the

it.

This

effect

there

profile

extends

all

is

any

lying inside a rises

would have

flare

whatever in the section

bow-wave

crest,

the

wave

higher on the ship's side than if

it

the section lines had been vertical.

The bow-wave

crest heights as predicted for

ing above the crest

The graphs

because the surface contour along the side affects the flow pattern below

When lines

line.

H

52. and the procedure produce a predicted sternwave height for the ABC design of 5.32 ft. This is for a normal form of stern, probably of the canoe

of Fig.

illustrated in Sec. 52.5

6

14

Fig. 66.

R

4

known data

to

what the stern-wave height would be

for a transom-stern hull. Since the water closes

much

in at a

slower rate along the small waterline

slopes ahead of the transom, one

i£

4

G

1

8

\h

\h

Wave Profiles and Flowlines for Bow and

Predicted and Observed

or whaleboat type; there are no

indicate

4%

STEPS TN PRELIMINARY DESIGN

Sec. r,6.2S

might estimate

Single-Skeg Transom Stern

coincides with a hump, there may be a wave hollow at the stern, or a crest of greatly diminished height.

The

shape of the accompanying wave a function of the shape of the

exact

profile is manifestly

and

some

a wave height above the surface of the undisturbed water at a distance of something less than 2/3 the predicted amount for a normal stern,

hull

say 3.55

sharp as those of the parallel-sided, wedge-ended form of Fig. 10. F, secondary wave systems are

ft.

The stern-wave

crest

may

be

expected

to

climb up the side of the ship at the outboard corner of the transom by this amount plus the stern sinkage of 0.74

The data

or about 4.29

ft,

ft.

listed in Sec. 52.6 indicate that a ship

corresponding to the

ABC

design, running in a

range of T, values from 0.828 to 0.908 (from 18.7 to 20.5 kt), F„ of 0.247 to 0.270, is accompanied by transverse waves of the Velox system about half as long as the ship.

At

20.5 kt there

is

a

first

of

certain

distinctive

known and some unknown. has

pronounced shoulders,

features,

a ship waterline

If

not

necessarily

as

generated. Their transverse Velox waves combine

with those of other systems to form a rather complex pattern. A predicted wave profile for the

ABC

hull with a single-skeg

transom stern

is

sketched in light lines in Fig. 66. R, before any test runs are

To

made on

a model.

predict the flowline positions

it is

estimated

that the dividing point on the stem, between the water passing around the side and that under

because of the

crest

the bottom,

trochoidal

and the expected drop of the bow of about 2.4 ft. A figure of O.SH or 7.8 ft below the DWL appears about right; this is at

about 0.027L abaft the FP, a second crest at about amidships, and a third crest at or near the stern. As a matter of interest, the length of a ship

is,

wave

at the 20.5-kt speed of the

from Table

formulas, 234.3

ft;

ABC

48. d

and the accompanying

This

is

roughly 0.46L. The

general pattern for these and other speed ranges,

on cargo-ship models, and 52. J. Furthermore,

it

is

is

shown

known

that

in

Figs.

52.1

when the T,

large

B/H

the 18.2-ft

relatively high,

is

ratio

WL. The

It is to be expected that the wave profile, representing a constant-pressure upper boundary, will influence the shape of the flowlines passing

value coincides with the position of one of the

around the

hollows along the lower edges of Fig. 66. A there

waterline or below.

is

a prominent wave crest at the stern.

When

it

flowlines sketched in the

forebody resemble those of diagram 3 in Fig. 4.0, and of the many illustrated in Chap. 52.

The

side,

flowlines

perhaps down to the

under the nearly

flat

10-ft

bottom, not

HYDRODYNAMICS

496

shown

maj^ be expected to diverge

in Fig. 66. R,

move

slightly with distance as they

a run that

is

roughly

the flowlines

lie

flat,

aft.

Under

or of a shallow V-shape,

generally along the buttocks,

parallel to the centerplane of the vessel.

When

IN SHIP DESIGN

6629

Sec.

volumes for accommodating the passengers and crew and for carrying the machinery and cargo. The ratio of total hull and superstructure volume to underwater hull volume of 2.77, derived previously in Sec. 66.8,

is

somewhat

therefore

the buttocks terminate at a knuckle under water,

large.

as at Stas. 18 to 20 in Fig. 66. R, the flowlines

stand rather high out of the water.

somewhat parallel to the buttocks may be expected to leave the ship surface at the knuckle.

with a short forecastle to give added freeboard

lying

The

predicted flowlines are indicated in light

broken Hues on the body plan of Fig. 66.R. The actual flowlines, determined from a test of a 20-ft model, using chemicals on the model surface, are shown in heavy

wave

profile

full lines in

marked along the

indicated also by a heavy

is

the figure.

side of the

It

is still

model

possible,

of

Good

with a given set

of principal proportions and form coefficients, to vary the underwater shape within rather wide limits, and to obtain perhaps wider variations in Existing forms, the resistance for a given F„ often several of them, are therefore wisely used as guidance or as a means of keeping one from getting too far afield. Certainly a well-tried parent form or a ship form which has a high merit coefficient and which has proved itself in service can be employed as: .

(1)

(2)

A A

starter for laying sort of running

down a

comparison as the hull

for judging the performance of the

new

(or

bad)

is

to be

performance.

The

will

flush-deck

and

hull depth at the stem, and with so-called tonnage openings below the main deck near the stern.

Taking 23

ft at

for a starter a

minimum

freeboard of

the lowest point of the deck at the side,

the hull depth Z)

=

26 -f 23

is

49

By

ft.

May

R. Nevitt [ASNE,

the

1950, pp.

318-319] and others,

it appears that the 49-ft depth and the L/D ratio of 10.4 he within a good design range for a length L of 510 ft and a draft of 26 ft. The ratio of draft to depth D is 26/49 = 0.531. The depth from the keel to the

R

R

top of the highest superstructure, to the beam,

=

76/73

Based upon Atlantic-liner practice

INA,

when

related

approximately

is

[26 -1-23-1- 3(9)]/73

=

1.041.

[de Vito, E.,

SBSR,

1952; partial abstract in

13

Nov

1952, pp. 642-643] this ratio could be as high as

any

case, it is

assumed that the

necessary preliminary strength calculations, not

gone into here, show the assumed hull depth of 49 ft to be adequate for a static wave whose height

is 1.1

form.

made, however, past or existing forms should not be too slavishly copied unless one knows rather accurately just what features are responsible for their good future progress

A

indicated, as in Fig. 66.0, possibly

is

1.16 or 1.20. In

A reference, after model tests have been made,

If

abovewater hull

set of lines

shaping proceeds (3)

type of ship

criteria of C.

full line.

Comparison with a Ship Form

66.29

Performance.

The

It appears that the

designers of these

mair,

J.

VL,

or 1.1

V510 =

p. 14]. Fig. 48.

E

in Sec. 48.7

of these heights for various

The

24.84

ft

[Nieder-

C, "Ship Motions," ASNE, Feb

1952,

embodies a graph

wave

lengths.

ship appears to have adequate freeboard

throughout, of the order of 0.045L or more, the abovewater hull

is

made

large

enough

when

for the

forms would be the first to admit that they could unquestionably be improved with further thought

volumetric capacity and for the required depth

and

hull,

effort.

Following a series of model

comparisons powers of a new design with the effective powers of the TSS ship of the same proportions. This comparison for the ABC hull, comprising the transom stern designed in this chapter and an alternative arch stern described in Sec. 67.16, is to be found in Sec. 78.16 and Figs. 78. J and 78.K. 66.30 Abovewater Hull Proportions for Strength and Wavegoing. The ABC ship requires, as do many others, rather large internal

may

be

made

of the effective

tests,

of ship girder.

taking

A detailed

all

study of the abovewater

necessary factors into considera-

Chap. 68. A further study of its wavegoing service requirements is deferred to Part 6 in Volume III. However, it is possible at this stage to make the first estimate of its natural rolling period. For this estimate the added mass of the surrounding water is not taken into account, partly because it is not known, and partly because the actual period is then longer than the estimated one. As tion, is given in

ability to

a result,

meet

all

the ship should

comfortable than predicted.

be somewhat more

STEPS IN PRELIMINARY DESIGN

Sec. 66.31

The volumes

497

Using the standard formula [PNA, 1939, Vol. II, p. 11, Eq. (22)] and assuming different values for the gyr adius k and the transverse metacentric

spaces, can be contained within the total

height GM.

of the hull

For a

GM

(2)

When

For a

(a)

(b)

k

of O.OQBj, or 4.38

GM

of

0.045x or 2.92

ft,

0.25Bx or 18.25 ft, T = 11.82 sec O.SOBx or 21.9 ft, T = 14.19 sec.

is

GM

66.31

First Longitudinal

Weight and Buoyancy

Before completing this

Balance.

preliminary design

it

is

first

stage of the

necessary to determine

approximately whether, for the designed maxi-

mum (a)

service-load condition:

The

with the as the

in nearly the

same transverse plane

CB

The

(d)

hull

volume

is

hull

so large as to be objection-

strong wind.

A

body plan on a much

larger scale than the

small sketches of Fig. 66.0

is

now

available in

Fig. 66. P for

an adequate estimate of the areas, volumes, and moments to be used in this operation. Further, it is assumed that the abovewater hull has already been roughed out, as in the upper part of Fig. 66. P, and that a rough outline has been made of the upper works (superstructure). is

now

possible

to sketch in the principal

subdivisions between passenger and crew accom-

modations,

package-cargo

space,

liquid-cargo

machinery spaces. These are indicated by the hatched areas on the tanks,

fuel-oil

tanks,

and

profile of Fig. 66.S.

A

rough integration of these volumes, allowing

5 per cent for ship structure in the dry spaces,

comparison there are volumes of Sec. 66.8.

listed

It is next necessary to

TABLE Item

room within the

sufficient

is

gives the tentative volumes of Table 66. h. For

ship has reasonable longitudinal balance,

CG

There

able from the standpoint of ship handling in a

It

apparent that, with the large beam, the lowest permissible will produce the most comfortable ship. It

and superstructure. This requires a

gears or motors on the propeller shaft

ft,

=

When k = When k =

and cargo volume

structure for certain large items such as reduction

0.25Bx or 18.25 ft, T = 9.65 sec, for a complete roll. This is somewhat too small for the comfort of passengers and the safety of package cargo. (b) When k = O.SOBx or 21.9 ft, T = 11.58 sec. This is still rather short for comfort, on a rolling ship, but not too short as to be disturbing at this (a)

as well as of the passenger quarters

(c)

v:gGM (1)

of the various parts of the ship,

re-check of the hull volume estimate of Sec. 66.8.

2irk

T =

(b)

66.h

Second Estimate op Volumes for

ABC Design

also

the required

determine whether the

HYDRODYNAMICS

498

13

IN SHIP DESIGN

"9 5 7 6 S Inner Bottom Spaces not complete

12

Cofferdom Spaces not shown

Tentative Distribution op Principal Volu.mes in the

Fig. 66. S

Sec. 66.32

ship trims properly with the principal weights in

after developing

ABC

what

is

Design considered to be an

longitudinal weight balance comes out as indi-

CG is found to be from the CB of that shape, do not change the shape to bring the CB to the CG position.

cated at the bottom of Table

Rather, rearrange the internal spaces, volumes,

the locations indicated. centers

Selecting

approximate

gravity for each of the items the

of

66.i.

This tentative balance for the designed-load condition

is

necessarily crude.

The volume and

location of the package-cargo spaces, the tankage,

easily driven hull shape, the offset

and weights to bring the

CG

to the

CB

position

of the low-resistance hull.

Propeller

66.32

Submersion and Trim in Havi ng fou nd reasonthe LCG and LCB values for

the machinery spaces, and other items on Fig. 66.S are still only approximate. Since these

Variable-Load Conditions.

matters involve static problems only, not directly related to the hydrodynamic design, they are

the weight balance in the designed-load condition,

followed only to the point of checking the trim in two of the variable-weight conditions, de-

consider the situation when:

However, an important hydrodynamic-design rule,

for these as well as for the later stages is

well kept in mind:

TABLE Moment arms

Item

at the 26-ft draft in salt water, there remains to

(1)

scribed in Sec. 66.32.

described in Chap. 67,

able agreement in

66.1

If,

The

leaving

vessel

condition (2)

is

only partly loaded, as

when

Port Amalo in the hurricane season,

When

Hi

of

Table

66.f of Sec. 66.16

arriving at the river

mouth below Port

First Longitudinal Weight Balance

are in terms of station spacing, 25.5

ft.

Moments

are taken about the midlength at the

DWL,

Sta. 10.

STEPS IN PRELIMINARY DESIGN

Sec. 66.32

Two

Selected Inclined Waterlines for the

Fig. 66.T

499

Principal Variable- Weight Conditions

Correo. Table 66.g indicates that the estimated drafts under these two conditions are

the centers of gravity in the two loading conditions

mean

coincide with the CB's for the displacements

and 20.01 ft, respectively. For round numbers assume that these are 22.75 ft and 20.00

stern drafts selected.

22.74

ft,

mean

involving reductions in the 26.0-ft

of 3.25 ft

and 6.00

draft

a bulb

bow

check

have an idea of the changes in trim for a given internal arrangement of the principal weights. It

is

necessary at some stage

and

made

then

to

used, as in the present

if

case, it will

not be too close to the water surface

is

The

is

made

24.25

transom at the

ft,

AP

stern draft for the

-

heavier condition, 16,400 t It is useful to

is

insure that,

for open-sea running.

ft.

A

2,425 t

=

13,975

t,

bottom of the a few inches under water in

to place the

the at-rest condition.

The

stern draft for the

-

=

on the transverse metacentric stability for these two loading conditions. However, the most important hydrodynamic feature is to keep the propellers well under water, with a reasonable tip submergence and as good shielding from air leakage as can be

which gives a tip submergence at the propeller disc of just under 2.5 ft. Fig. 66.T illustrates these features. While this submergence is admittedly small, both absolutely and relatively,

obtained.

thrust-load

of the preliminary design to check

The procedure

followed in the

two drafts

to establish

first

aft,

ABC

design

is

corresponding to

the two variable-weight conditions, which will insure air-free flow to the propeller. Following

lighter condition, 16,400 t is

the propeller

TABLE

66.J

is

4,400

at

this

light

should be sufficient to

Mean

fill

all

the volume between

Projecting the traces of the two waterlines

Two

Variable- Weight Conditions of the

22.75

Corresponding weight, at 35.977 ft' per ton, less than designed weight, actual

t

Tons

LCB,

in fraction of

L from FP

Coefficient of square

Calculated

BM,

moment

of area C, ^ of

WL about i-axis

ft

Inclined waterplane area, ft^

KB,

KM,

estimated, from derived, ft

KG,

estimated, ft

GM,

probable, ft

Normand

formula, Sec. 66.14,

ft

displacement.

hull just forward of the transom.

Weight, Buoyancy, and Stability Data for

draft, ft

t,

the at-rest waterplane and the under side of the

figures given

Tons less than designed weight, from Table 66. Weight displacement, nominal, t Trim by the stern, selected, ft Volume displacement, from molded lines, ft'

12,000

running at a considerably smaller

factor

apply to the molded shape and dimensions of the transom-stern underwater weight displacement, molded, in standard salt water is 16,400 tons.

The

t

ft,

Furthermore, the stern- wave crest at 20.5 kt

the internal weights are so arranged that

this,

selected as 23.0

ABC

hull, for

Ship

which the

HYDRODYNAMICS

500

TABLE From Table

66.k

66.]',

LCB

IN SHIP DESIGN

Longitudinal Weight Balance for 20-ft is

0.513

L from

the FP. This corresponds to a

With a weight displacement of 12,090 tons, from Table tons times station lengths, is -0.26 (12,090) = -3,143.4. abaft Sta. 10.

Item

Mean

CG

66.],

Sec. 66.32

Draft, 6-ft Trim by the Stern

location at Sta. 10.26, or 0.26 station-length

the corresponding after

moment,

in

terms of

Sec.

STEPS IN PRELIMINARY DESIGN

6634 In

propeller.

the

design

stage,

consideration

501

at least in the river below Port Correo, as

make

many

siiould be given to increasing the capacity of the

cargo vessels

after ballast tanks of cargo vessels to permit fully

traveling

submerged propeller operation."

rapid response of the ship for an equal degree of

First Approximation of Steering,

66.33

Maneu-

and

Shallow-Water Behavior. It is difficult to obtain an idea of the steering, maneuvering, and shallow-water characteristics of the hull as roughed out at this early stage of the design. Nevertheless, something should be known vering,

of

them before the preliminary design proceeds

much further. Good steerability, Volume

III,

excessive

dynamic

matter of avoiding and providing sufficient swinging moment through the use of the rudder. The former is largely a function largely

movable

fin

a

instability of route

amount and

the

of

is

position of the fixed

rudder, horn, skeg, and the like. It

may depend

somewhat on the shape and proportions In the

hull.

and

area at the stern, comprising the

ABC

design there

and skeg

latitude in the rudder

is

of the

considerable

areas, especially

away by a "suitable" amount. The swinging moment is a function because the aftfoot of the

first,

is

to be cut

shape and area of the rudder, and

second, the magnitude of the lateral forces which

may

be expected on a rudder horn,

on the adjacent portions

amount

of the swinging

—or

on the ease is

swung

inward

The

of the

moment,

difficulty

—with

fitted,

and

hull.

The

if

main

depends which the ship

in turn,

to a drift angle that generates sufficient

lift

to balance the centrifugal force.

ABC

ship

must traverse rather

consider-

able distances with relatively small clearances

under the bottom. Time lost in these inland waters means just as many hours to make up as the same time lost in the open sea. Furthermore, the

maximum

speed in the long,

fresh-water

on the downstream trip with the ship heavily loaded, may be limited as much by the ability to steer the ship and to turn it around bends in the river as by the action of the shallow and restricted waters in augmenting the resistance or causing unfavorable changes in its running river, especially

attitude.

turns in the river leading from Port Correo and in the canal leading to Port Amalo are known to be of sufficiently large radius to enable the average cargo vessel to negotiate them without difficulty.

However, the

ABC

design

is

expected

to average nearly as high a speed in these waters,

sea.

Furthermore,

means more

Considering the single-screw, centerline-skeg design of stern depicted in Figs. 66.P, 66. Q, and 67. R, the single rudder is directly behind the

where it works in the outflow jet. It is enough abaft the propeller to take advantage some augmented outflow-jet velocity abaft

propeller,

far of

the disc. It

as close as possible to the stern so

is

arm

of its swinging

moment

is

large.

There is good opportunity to tailor the movable and the fixed areas to suit all the steering requirements. Adequate and possibly superior steering

may

therefore be predicted at this stage, leaving

the detailed design until later.

Considering

next

the

maneuvering require-

ments. Fig. 64.B indicates that when backing out of the slip at Port Bacine the ship must turn with

a minimum radius of about 1,090 ft. When going ahead, out of the harbor, the minimum radius is

about 1,490

ft.

The

latter represents a steady-

turning diameter of 2 (1, 490) /5 10, or a

little over This must be accomplished at a relatively slow speed since the ship is at a stand-

5.8

lengths.

still

at the inner end of the

When

backing,

the

"Y"

in the harbor.

steady-turning

radius

is

equivalent to about 2(1,090)/510, or some 4.27 lengths, likewise at a relatively slow speed. It is

manifest without making any calculations

that the ship's propeller will have to supplement the normal rudder forces to create the necessary

moments

swinging

for

making

these

turns.

possible that both the

ahead and the astern turns must be effected more by swinging the ship on its vertical axis than by changing its heading through fore-and-aft motion. Normally, this situation would point up the need of twin screws. However, as the turns are to be made in a counter-clockwise direction, bow to port and stern to starboard, in which a vessel with a single right-handed propeller normally swings, it is possible that the necessary augmentation can be obtained with a single propeller. Indeed,

66.34

The

open

higher speeds

safety.

that the as pointed out in Part 5 of

in the

these

at

it

is

Preparation of Alternative Preliminary

Designs.

Often the ship for which the design is prepared is a large or important one. Possibly a number of vessels are to be built to being

the same design, or major decisions may depend upon the performance of one ship. Wisdom then dictates that several studies be

made

in the pre-

HYDRODYNAMICS

502

IN SHIP DESIGN

Sec. 66.35

liminary-design stage or that alternative designs

cusses these variations for a rather wide variety

be carried along far enough to indicate their

of hull forms.

relative merit in meeting the established require-

ments and

specifications. In a sense, this is only

a part of good planning, which pays handsome dividends in any kind of endeavor. The phenomenal

success

of

the

transatlantic

Cunarders

Upon The requirements

Effect of Unrelated Factors

66.36

Hydrodynamic Design. the

ABC

the for

design in Chap. 64 were deliberately

set up, as should be the case for every boat or ship, to give the designer as

much freedom

as

permits an excellent degree of bracketing for the

and proportion the hull. This applies to the parts both above and below water, in an effort to produce the maximum of performance so far as all phases of water flow and ship motion are concerned. At the least, he should have latitude in establishing the one feature which may be found most critical when developing

by extending these studies deliberately beyond those contemplated for the

are imposed on the layout of a high-speed ship

Lusitania and Mauretania (old), designed in the early 1900's,

was due

amount

study and preparation carried out

along

of

many

directly to the extraordinary

different

lines

before

plans

their

were completed.

The preparation final design

of

multiple

design

studies

into regions

actual ship. Rather surprising results, exceeding

those possible

by following conventional

lines,

are often unearthed or revealed in this manner.

There are facilities available in practically all maritime countries for exhaustive testing of ship models under a wide range of conditions, at a cost that

There

is

small in proportion to the ship cost.

is little

excuse for embarking on a major

possible to shape

the design.

If,

for example, rather severe limits

in everything except the length, the designer

still

can do a great deal by adjusting the length and by fixing the shape and proportions of his vessel to meet the exacting requirements imposed upon him.

More forced

often than not, however, the designer to

employ

his

strongest

is

arguments to

obtain the latitude he needs in such a principal

shipbuilding project without comparative tests,

feature. All too frequently

on model scale, of several different hull forms. For the proposed 4-day American superliner of the early 1930's, T. E. Ferris built 22 models and tested no less than 14 of them [SNAME, 1931, pp. 314-315]. For the transatlantic liner America of

make

he

is

stymied and must

the best of a situation which he realizes

Newport News shipyard alone

from the beginning is crowding him against the wall. Faced with a reluctance on the part of the ship owner or operator to make the ship longer than a set figure, confronted with the forces of nature in shortening the roll of a ship which is

tested approximately 50 models, although these

too wide, or recognizing the limitations of channels

were small ones and some of them involved changes in the principal dimensions [SNAME,

which the ship must traverse, he is driven to fuller forms than he would otherwise select or to the incorporation of features which his better judgment tells him to avoid. Often, too, through no fault of anyone in particular, factors not even distantly related to hydrodynamic features are given priority over them. Whether the water flow is of paramount importance or not it is still governed by certain physical laws. The designer must get this knowledge, then use it to minimize the harmful effects of unrelated factors, and to assess these effects when they can be minimized no further.

the late 1930's, the

1940, p. 10].

66.35

Laying Out Other Types of Hulls.

It

is intended that the discussion and the design dia-

grams in the preceding sections of this chapter cover the preliminary hydrodynamic design of ships within a rather wide range of proportions. This range extends as far as the limits of the coefficients and parameters of the various graphs. Since most of the plots are based upon 0-diml variables, the range of size extends all the

way

from boats to liners. The design of the roundbottom motor tender for the ABC ship, carried through in Chap. 77, reveals much the same procedure as for the larger vessel.

For special-service vessels, certain proportions and functions are exaggerated at the expense of resistance, propulsion, and other characteristics normally considered important. Chap. 76 dis-

It goes

without saying that

many considerations

other than the ones discussed in this chapter enter into a determination of the weight and volume displacements, the principal dimensions, the proportions, the shape, and the general arrangement which mark the end of a preliminary ship design. One of these, and a most important

STEPS IN PRELIMINARY DESIGN

Sec. 66.36

one for merchant

vessels,

is

cargo

handling,

especially of the package rather than the bulk

type. It

by

is

most ably and

interestingly discussed

F. G. Ebel in "Notes on

Cargo Handling"

503

vessels with box-shaped holds, discussed in Sec. 76.5.

In practice, a dozen or perhaps two dozen

combinations

may

be worked up as indicated in most promising of them

[SNAME Member's

this chapter before the

Another one

are carried along further in greater detail.

is

Bull, Feb 1954, pp. 19-27]. cargo stowage, particularly for

CHAPTER

67

Detail Design of the Underwater Hull General

67.1 67.2 67.3 67.4 67.5 67.6 67.7 67.8 67.9

Design of a Bulb Bow Laying Out the Bulb for the ABC Ship ... Check on Bulb Cavitation Selection of Section Shapes in Entrance and

67.10

Variation of Section Coefficient Along the

Shape

of Vessel

Near Designed Waterplane.

Waterline Curvature Plots Underwater Hull Profile

Stem Shape

at Various Waterlines

....

Run Length Hull Shape Along the Bilge Diagonal

67.11 67.12 67.13

...

Side Blisters or Bulges

General Arrangement of Single-Screw Stern

.

Vessels

67 18 67.19 .

67.21 67.22

The Design

67.23

515

67.24

517 517 517 518

67.25 67.26 67.27 67.28

Shaping the Hull Adjacent to PropulsionDevice Positions; Hull, Skeg, and Bossing Endings Aperture and Tip Clearances for Propulsion Devices Baseplane and Propeller-Disc Clearances Adequate Propeller-Tip Submergence Design for Minimum Thrust Deduction The Final Section-Area Curve Modification of Normal Design Procedure for a Hull with Keel Drag Underwater Exhaust for Propelling Machin-

Notes on Three- and Five-Screw Installations The Arch Type of Single-Screw Stern ... Flow Analysis for the Arch Type of Stern Design of Hull and Appendage Combinations Comments on Design of an Unsymmetrioal

67.1

.

General.

.

528

Single-Screw Stern

67.20

Proportions and Characteristics of an Im-

mersed-Transom Stern

529

of a Multiple-Skeg Stern

....

531

Design Notes for the Contra-Guide Skeg

Ending

Stern Forms for Twin- and Quadruple-Screw

67. 14

67.15 67.16 67.17

504 504 506 506 508 508 510 514

67.29 520 521 521 525 526

67.30 67.31

Based upon the preliminary

532

.

.

.

.

.

.

.

which

may

537 540 541 541 542 543 545

ery General Notes on Water Flow as Applied to Hull Design

of the interactions

536

545

be expected, em-

ship layout described in Chap. 66, the hydro-

ploying the best available thought and knowledge

dynamic design proceeds with the fashioning of the individual parts, making decisions as to certain secondary form characteristics, such as the more definite determination of the waterlines, section lines, and diagonals, and the shaping of the hull ahead of and adjacent to the positions

on the subject. 67.2 Shape of Vessel Near Designed Water-

The

plane.

shape

of

Sec.

66.15,

together

The factors considered here are those which govern smooth-water performance. Whether they may be expected also to result in good behavior during maneuvering and wavegoing, and possibly also during operations in shallow and restricted

DWL parameters.

and

is

considered in Parts 5 and 6 of

in

Chap.

particular features which have to

a

the

given

Some

consideration

with

a

making a is

presentation selection of

required

of

of

good

possible

modifications to the nominal at-rest designed-

waterplane shape due to the ship's own waves. If the changes in surface level due to wavemaking

Volume

72, respectively, together

for

speed-length quotient T, or F„ are discussed in empirical methods for

III

governing

waterline

designed

of the propulsion devices.

waters,

features

principal

the

and if the have sloping sides,

at the selected T, are appreciable,

with

sections near the waterplane

do primarily

the shape of the waterplane ai the actual wave

with those special operations. The matter of smoothness of the hull and minor fairings is covered in Chap. 75; only the

change enough to alter the expected full canoe or whaleboat stern, well tapered in way of the at-rest waterplane but flaring to a wide deck above, may possess a considerably greater slope than the designer intended along the raised surface of the stern-wave crest, with consequent undesirable separation. A heavy flare above the

major features are discussed here. In this attack on the design problem the size and shape of each part is selected on the basis of its anticipated action in one or more of the fundamental types of flow around it. The whole design is then modified or adjusted on the basis

profile

may

performance. For example, a rather

entrance waterline, by humping up the bow-wave

504

UNDERWATER-HULL DESIGN

Sec. 67.2

may

crest,

neutralize

much

505

of the benefit gained

in careful shaping of the at-rest waterline at the

•

designed draft. It is mentioned previously, but the caution is worth repeating, that too much hoUowness abaft the bow, resulting from an effort to fine the bow waterlines to an extreme, may involve an excessive and undesirable slope in front of the forward

shoulder.

For the transom-stern ABC ship laid out in Chap. 66 the first sketches of the designed waterline are modified to suit the development of the underwater hull described in detail in this chapter. The final waterline shape, with its parameters and 0-diml offsets, is drawn in the lower diagram of 67.A.

Fig.

That

of

the arch-stern alternative

design, described in Sec. 67.16,

is

drawn

in the

upper diagram of the figure. For a stern shape which is wide and essentially flat on its under side, like that of a scow, the horizontal waterUnes at the stern close in toward the centerplane at steep slopes with that plane. For a truly flat stern with no rise of floor in the sections this waterline slope Ir reaches 90 deg. However, in cases of this kind, the flow upward and aft under the stern is primarily along the buttocks, or at least more upward than inward. the waterline slopes lose their significance.

If so,

Fig. 67. B reveals very steep slopes for the near-

surface waterlines at the stern of the

waterlines.

ABC

ship,

the centerline-skeg

faired rather abruptly into

However, inspection

of Fig. 66. Q

shows

easy buttock slopes in this region; Fig. 66.R indicates that the actual flow under the stern is

more or less along these buttocks. The surface waterplane has a definite

function,

not only in minimizing a surface-wave disturbance, but in providing sufficient square moment of area to insure the necessary transverse metacentric

stability.

As a

rule,

way

the best

to

change the metacentric height is to change the maximum beam, assuming that this can be done. Certainly, it is to be preferred to pulling the designed waterline in and out, here and there.

This nibbling and padding usually changes the moment of area only shghtly but it may have

major adverse teristics of

hand, so

effects

upon the propulsion charac-

the underwater form.

much

hydrodynamic features that

its

On

the other

attention can be devoted to the of the designed

waterHne

stabihty features are overlooked.

Exactly this happened in the course of the

preUminary design

of

the

ABC

ship.

It

was

^-

HYDRODYNAMICS

506

considered that, by reason of the wide waterplane

way

shown in the lower diagram of Fig. 67.A, enough square moment of area would be gained there to more than compenof the transom,

narrowing of the whole hull in the entrance. A check of the designedwaterline It value, which shoidd have been made sate

the

for

Sec. 67.3

After Portions of Afterbody Waterlines for the Transom-Stern

Fig. 67.B

aft, in

IN SHIP DESIGN

rather

drastic

ABC

Ship

how suddenly

this 0-diml curvature can change, a straight line tangent to a circle of diameter Bwx involves a sudden change of 0-diml curvature

from

of

(b)

to 114.6.

No

great

extremes of concave or convex

curvature at any point along the length (c)

A

curvature plot with the

minimum

of longi-

was made after the lines had been sent to the model basin. It revealed a. C,t oi only

tudinal waviness. Generally such waviness indi-

sUghtly over 0.52 whereas the preferred value

waterline.

was 0.561 and the required value, from item (42) of Table 64.f, was 0.55. A proposal to remedy

of constant or nearly constant curvature, as for

this situation is discussed in Sec. 78.18.

the

before, actually

Waterline Curvature Plots.

67.3

A

designed

watei'line is to be checked for uniformity of cur-

before

vatiu'e

before

it

is

it

is

considered acceptable and

used as a basis for shaping the

re-

of the hull. Sees. 49.10

operation.

The

0-diml curvature plots for the designed

waterlines of the

ABC

transom-stern, single-skeg

ship, as well as for the alternative arch-type stern

described in Sec. 67.16, are given in the lower

diagram

plots

Series parent form,

and

for a

The upper diagram

of Fig. 67. C.

corresponding

for

EMB

merchant ship

three indicate

certain

of

the

Taylor

gives

Standard

model 632 (modified), good performance. All

correct

features,

(d)

A

curvature plot with rather long portions

TSS

waterline, provided there are no abrupt

changes at the ends of these portions.

Underwater Hull Profile. The bow prounder water is determined from the desired section and waterline shapes at the bow, extending from the baseline up to the designed waterline, rather than from an effort to achieve a particular profile that supposedly has merit. In other words, the bow profile is determined in a sort of automatic fashion, just as if one whittled a wooden model to the desired section shapes forward and then cut away the model on each side until the waterlines met the centerplane. Developed in this way a ship bow with wall-sided sections all the way to the stem terminates in a plumb stem. One with pure triangular V-sections terminates in a straight raked profile passing through the 67.4

file

through 49.14 describe approximate and precise methods, both graphical and mathematical, of accomplishing this

mainder

cates poor fairing or inaccurate dra\ving of the

so far

as they are known, for a good designed-waterline

lower vertexes of these sections.

For

many

which operate in shallow

ships

waters, temporary grounding forward (a)

Not-too-violent changes in curvature with

^---distance

along the length. As an indication of

unusual occurrence. craft to cut

It

up the

may

is

a not

be advisable on these

forefoot

and thus remove

UNDERWATER-HULL DESIGN

Sec. 67.1

Fig. 67.C

Non-Dimensional Curvature Plots op Designed Waterlines for Three Ships

that part of the ship which

is

most vulnerable to

damage when taking the ground. Also, as described in Sec. 25.5, a small amount of friction and pressure resistance often

ming up the

507

may

be saved by trim-

forefoot slightly,

in

addition to

illustrated in Fig. 67.E.

Sec. 73.3

The

and

The

latter is described in

illustrated in Fig. 73.B.

stern profile below water

is

influenced

by the number and type of stern propuldevices selected and their tentative positions,

largely

sion

a single propdev on or near

saving some wetted surface.

especially

There may be merit in shifting progressively aft the forward waterline beginnings with depth below the surface, as explained in Sec. 4.8 and

the centerplane. For a screw propeller, the comthe type,

illustrated in Fig. 4.1. This is especially true

rudder(s) leaves

waterline entrances are blunt. This

bow

if

the

if

there

is

bination of proper hydrodynamic position with shape,

and position little of

of

the steering

the stern profile to be

shape,

delineated to suit the engineering sense of the

embodying a heavily raked underwater profile resembling the Maier bow, saves some wetted surface and may result in a slight reduction of

individual designer. Furthermore, that portion of

pressure drag. There

is

reason to believe, however,

that better performance

some T, carrying

is

achieved, at least at

values, by fining all the them nearly to the FP.

The bow

profile of the

ABC

waterlines and

design

is

the result

combining a bulb bow of slightly ram form, extending forward of the FP, with a sharp cutwater. The former is described in Sec. 67.6 and of

the stern profile just below the

DWL

must be

considered in conjunction with a larger portion lying above the

DWL.

usually so dependent

In

fact,

the stern profile

is

upon other considerations

having to do with skeg endings, propeller clearances and apertures, transom forms, and similar features that it seems wise to discuss these features in detail in those parts of the

devoted particularly to them. The is

no exception

in this respect.

ABC

book design

HVDRODYNy\MIC.S IN SHIP DESIGN

508

Stem Shape

67.5

minimum

at Various Waterlines.

For

pressure resistance and reduction in

bow-wave crest, and for the elimination and feather, the horizontal sections at the stem of a vessel, just above and just below

erosion,

of spray

and panting

surface

waterline,

made

are

possible. Theoretically, they are

sharp

as

as

formed by con-

tinuations of the entrance and bow waterlines, with whatever hoUowness the latter may have, when carried forward to their normal intersections in the plane of

The

symmetry

hull structure of a

of the vessel.

wooden

or metal vessel

inside the extremely thin, tapering

stem dictated by these hydrodynamic considerations is difficult and expensive to fabricate. A simple solution is to cut the structure back and terminate the stem in a blunt or large-radius section,

radius of

1 ft

sometimes with a

or more, producing the circular-arc

beginnings depicted in Fig. 25. A.

bow

A

feather

is

The

resulting

then accepted. leading edge,

joins the nearly straight side of the entrance,

susceptible

On

to both

certain to tear or

causing noise,

is

separation and cavitation.

a high-speed vessel, therefore, the planforms

pound

off

and inducing vibration has in fact occurred on high-speed

of the plating

abaft projecting welding beads

where flush

vessels

shell plates

a rabbeted stem casting. radius, fair or not,

and

is liable

Any

were attached to measurable stem

to cause separation at

farther down, if pushed to speeds of the order of 40 or 50 kt. 67.6 Design of a Bulb Bow. The purpose of the bulb bow, explained in Sec. 25.3, is to reduce the height of the bow-wave crest and the magni-

the

surface

cavitation

tude of the pressure resistance caused by

it.

This does not mean that the blunt surface waterlines producing the high crest are to be retained just because there

is

to be a bulb to cut

down

the

By moving some

high waves caused by them.

displacement volume from the region of

of the

the surface to well below

because of the sharp change in curvature at the point where it circular-arc

is

the paint coating. Harmful cavitation, setting up

size of the

the

Sec. 67.5

the shell plating. It

into the bulb,

it,

possible to fine the surface waterlines.

it is

Both the

finer lines and the presence of the bulb act to improve the hydrodynamic performance of the

ship. It

may

be

said, therefore, that in general

the design of a proper bulb

bow

involves also a

and near-surface

at various levels of the stem, especially near the

definite

surface

waterline, are made elliptical, with a gradual change in curvature and an easy tran-

regions in the entrance.

sition into the side.

bulb form, good design procedure based on hydro-

Blunt stems build up relatively high dynamic below the waterline, which adds

resistance

directly to the pressure resistance of the ship.

The blunt nose

of a

submerged bow bulb, and the

bluntness in the horizontal sections of the stem

some distance above it, are accepted for the sake of the benefit they afford in other respects. They also enable the ship length to be kept to a

for

minimum. Both the hydrodynamic and the

in the

form

of

a sharp, narrow cutwater. That

73.3

and is

ship

is

described in Sec.

illustrated in Fig. 73.B.

With modern there

ABC

fabrication

no excuse

and erection methods

for lapping the shell plating

on the outside of the stem to form a discontinuity, D in Fig. 7.J. Indeed, there is a definite disadvantage to this construction on a high-speed vessel because of the cavitation that

diagrammed at

takes place abaft the discontinuity in the regions of low hydrostatic pressure, near the surface. This may be accompanied by possible erosion of

a normal form of

bow

is

converted to a

dynamics requires that the displacement volume in the bulb be removed from a surface-waterline region immediately abaft the stem, say from the FP back to about 0.15 or 0.20 of the waterline length. This reduces the angle of entrance and the amount that the surface water is pushed sideward in the vicinity of the first bow-wave crest. Normally it need not and should not be

removed structural

problems described in the foregoing, at least on a metal vessel, are solved by adding an appendage designed for the

When

fining of the surface

from

the

surface

and

near-surface

waterlines in the vicinity of the forward shoulder.

When

a relatively large bulb

ment volume

is

outer corners of

is fitted,

displace-

removed from the lower the sections at and ahead of the also

forward quarter point, for a region extending from about 0.15L to 0.40 or 0.45L, depending

upon the shape of the original hull and the amount of volume to be shifted. The manner in which both these changes are made is well described and illustrated by E. S. Dillon and E. V. Lewis in Figs. 7 through 11 of their paper "Ships with Bulbous Bows in Smooth Water and in Waves" [SNAME, 1955, pp. 726-766].

The

following

is

quoted from page 731 of the

UNDERWATER HULL DESIGN

Sec. 67.6

An

referenced paper, with additions in pai'entheses

by the present author:

attempt to reconcile the model-te.st data M. Bragg, and A. F. Lind-

of E. F. Eggert, E.

and to evolve systematic values

blad, displacement gained in the larger bulbs was removed in the region of the design(ed) waterline so as to progressively fine the angle of entrance ".

.

.

Some displacement also was transfrom the shoulder near the turn of the bilge into the larger bulbs while at the same time the design(ed) waterline was filled out almost imperceptibly at the as bulb size increased. ferred

shoulder

(forward)

to

which had been

recover

ance bettered or equaled that of the Taylor Standard Series have been plotted therefore on a basis of speed-length quotient.

waterplane

transverse

This latter step, while perhaps not best from pure resistance point of view, was nevertheless essential in maintaining stability characteristics constant for the design

When it

is

first

is

lor's analysis [S

for a

new

0.238.

The bulb appears

=

=

to be

0.14

'

die

'1 0.^0

r

oM

S

<

i-

limit of T,

around

1.9 or 2.0.

The proper value of /g appears to depend upon Cp and the displacement-length quotient A/(0.010L)' or the fatness ratio ^/(O.IOL)', but the various model-test data show conflicting trends. It is probable that the best value of /^ increases with both Cp and the fatness ratio.

0.80,

most useful

Quotient Tq 0.15

'

(Jk

'lab Froude

E-

10.12

o.^^

I'

i.ko

'

' I

o.iz

o.^^

I'

'

ci.^,

Number f„- V/VqL -iO.I4

Optimum and Minimurn fg Values for o Ronqe To Give Minimum

Pressure

of Speed-Length

Quotient_^

;J0I2

Resistance

•^

g oioi-

"1 0.10 of f£ Volues.

^ 0.081.g

=

(b)

To>^lor

o.y

some upper

zero at

LO.

0.I6E-

limit of L50, F„

(a) The fs values do not increase indefinitely with T„ beyond the range of T, = 1.5 shown in the diagram. They almost certainly diminish to

a

p. 69] indicates

indicate a low limit of the order of T,

=

and a high

were

following shortcomings:

the question for a ship section-area curve. E. M. Bragg's tests and analysis, in the same reference,

in the vicinity of T,

0.208,

D

a low limit of

,

better rules are developed should recognize the

design

low Umit of the order of T, = 0.7, F„ = 0.208, but at this low speed the optimum terminal value Ie is close to zero, which is almost out of

F„

indicate, for T,

0.447.

W. Tay-

D.

its use.

and P, 1943,

these plots 67.

Those who use them as interim guides until

bow

appropriate to

=

F,

0.70,

necessary to determine whether the

speed range

They

derived.

sizes."

considering a bulb

From

the tentative design lanes of Fig.

lost b5f fining the angle of entrance.

throughout the range of bulb

of the design

parameters f e and Ie from them, has so far proved unsuccessful. The design values actually used on a considerable number of vessels whose perform-

from the parent form

inertia

509

-|0.08

I"

S 0.06^

-=0.06

0.04

Lower f?Qnqe of f^ for Existing Vessels (1955) with Orthodox '

I

I

I

I

I

I

TQ\jlor

Fig. 67.

D

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

Quotient To

Design Data for Bulb Bows

Bower-Anchor Instoliatio I

I

I

I

I

I

I

I

I

I

I

I

I

HYDROnVNAMICS

510

The upper and lower limits of Cp and ratio for which bulb bows give beneficial (c)

fatness results

value

(d) It is possible that the best

factors other than T, but

qUe depends

so no definite

if

trends are yet apparent. Selecting the proper

value oi

If.

appears, however, to be less important

than using the proper value of /e

A

rather surprising feature of the lower or

optimum

value, although in one case

it

approaches and in another case it exceeds the optimum. These low values are traceable partly to conservatism, partly to lack of precise knowledge of the behavior of bow bulbs at sea, but

mostly to possible damage from bower anchors, dropped from the orthodox stowage positions high in the vessel and close to the stem.

The

design rules laid

summary

in the

down by W.

of his classic

They are set down here, with the present author's comments in parentheses, and with only minor changes to comply ^ath the nomenclature in this book:

The is

useful speed range of a (ship with a)

generally from T,

(somewhat (2)

The worse

itself is,

bulb, (3)

different

=

V/VL

from that is

of 0.8 to 1.9

of Fig. 67. D)

wavemaking

the

the more gain

the

of

hull

to be expected with the

the

lines

(forward)

are

extremely

hollow the best position of the bulb

is

with

its

(longitudinal) center at the bow, that

is,

with

its

The bulb should extend

as low as possible

consistent with fairness in the lines of the hull (5)

The bulb should be

and as wide

as short longitudinally

laterally as possible, again

having

regard to the fairness of the lines

The top

approach too near to the water surface. As a working rule it is suggested that the submergence of the highest part of the bulb should be not less than its own total thickness (measured transversely). (6)

Moving duced

of the bulb should not

the bulb well forward of the

excellent

results

on

pre-World

ABC

of the construction

FP by the length

to provide a nearly

water, as virtue

plumb

cutwater

of a

possible

it

external profile below

drawn in Fig. 67. E. There is no particular this plumb profile as such, except

in

possibly as a matter of appearance.

there

Ship.

design, projecting the bulb forward

such as mentioned in Sec. 67.5 makes

is

none in the ram-bow

Likewise

profile that

accompany a bulb bow forward

of

would FP,

the

relative to the waterline.

Extending the bulb below the baseplane

FP proWar I

is

generally out of the question in practice, although

might be done on vessels designed to meet it might be extended below the baseplane as a special appendage. Taking the ABC ship as an example of the design procedure, the fitting of a bulb bow on this vessel was settled, at least tentatively, in Sec. 66.19. It was decided to use, pending a further check, a section-area intercept f e of 0.06 and a terminal value of Ie = 0.9 at the FP. These values are indicated by special spots on Fig. 67. D. It remains to be seen whether a value of t it

particular requirements, or

fit

the final section-area curve.

Assuming for the moment that the bulb can be worked physically into the ship, a brief calculation is

made

to determine

how much

pressure resist-

be saved by it. Taking values of iJ/j/A in lb per ton from Figs. 241 through 244 of D. W. Taylor's S and P, 1943, a curve of residuary resistance in pounds per ton of displacement is ance

nose projecting forward of the hull (4)

ABC

For the

as small as 0.9 will

and vice versa

Unless

1939, pp. 303-330].

Laying Out the Bulb for the

67.7

paper "The Theory

Bulbous Bow and Its Practical Application" [NECI, 1935-1936, Vol. LII, p. 65], can hardly be improved upon today, twenty years later.

(1)

[SNAME,

except to get the bulb into that forward position,

C. S. Wigley

of the

bulb

1910 to the Arizona class of about 1915. even greater forward projection is embodied in the recent French liners Flandre and Antilles [SBSR, 24 Jul 1952, pp. 115-117]. A bulb of extremely large f e ratio, very low, very wide, and very flat on the bottom, was the "platypus" forefoot of model 3383, developed and tested by E. F. Eggert in the late 1930's class of

EMB

.

f E diagram of Fig. 67. D is that, for a large number of existing vessels of good propulsion performance, the bow bulb-area ratio f b is rarely more than half the

Sec. 67.7

Navy, from the Delaware

An

are not yet determined

upon

IN SHIP DESIGN battleships of the U.S.

likely to

is

plotted in Fig. 67. F for the fine ship of series A.

This has a Cp of 0.60, a displacement-length quotient A/(0.010L)' of 60, and a B/H of 3.35.

Four

Ru/L

1.006,

and

reasonably

T„

=

values,

for

T^'s

of

0.559,

0.783,

1.118, enable this curve to be located well,

especially

for

the

region

of

0.8 to 0.9. Reference to Figs. 248 through

252 of S and P, 1943 edition, enables a second curve of residuary resistance in pounds per ton displacement to be plotted for the fat ship of

UNDERWATER-HULL DESIGN

Sec. 67.7

Stations

).5

Fig. 67.E

series B, for

which Cp

length quotient

The next

is

two

Peofilb,

.qj

Bulb Bow, and Cutwater for

0.65, the displacement-

and the

B/H

is

set

bow

to the

ABC

where T, = 0.828. J. M. Ferguson has very recently (August 1955) prepared an analysis of D. W. Taylor's test data by which it is possible to determine by inspection

in tabular form.

The

four

A

the saving in

total

(not residuary) resistance

by

using the best values of the terminal value

t

ships without

and the FP area ratio /, or other combinations of t and /, without making the special calculations

0.9, are indicated

just described. Ferguson's data are unpublished

The Rg/A values bulb bows to the two ships

but they are on file in the Ubrary. The ABC bulb bow is to extend forward of the FP, hence the area corresponding to /e is measured at that station. If the bulb were rounded into the FP, the area would be that at the plane of the forward perpendicular lying within the bulb

points corresponding to the Rr/A. values calcu-

and

bulbs, at T, values of 0.8

series

and

B

as such on the plot of Fig. 67. F.

by fitting are indicated by the vertical to be saved

justify fitting a bulb

to determine the residuary

vessels without bulbs, having

down

lated for the series

Ship

design, even for the sustained speed of 18.7 kt,

parent forms identical with those of the Taylor Standard Series, and proportions as given in the preceding paragraph. In Table 67.a this derivation

enough to

ABC

ratio is 3.20.

is 150,

step

resistances of

is

Bow

511

intercepts between

the four points just mentioned and the curves for the corresponding ships with bulbs.

Reducing these intercepts to percentages of Rr/A. of the parent-form ships without bulbs, as in Table 67. b, the savings to be expected are of the order of 11 to 18 per cent at a T, of 0.8

and 14 to 18 per cent at a T,

of 0.9. This is certainly

TMB

surfaces

when extended

to that station, disregard-

ing the rounding.

Since the bulb volume should be as far below the designed waterline as possible the bottoms of

HYDRODYNAMICS

)12

IN SHIP DESIGN

Sec. 67.7

may, for a ship to run in the open sea, range from 20 to 45 deg, depending upon the contemplated width of the bulb proper. The aim angle. This

to prevent objectionable pounding

is

and slam-

ming under the bulb. bulb section were made triangular, with apex at the and with a zero rise of floor, width at the bottom would be that of the

If the its its

DWL

divided by half the draft.

section area at Sta.

Two

diagonal lines are drawn, one of which

marked DC in the two sides which

is

Fig. 67. G,

diagram

is

representing

1,

With a diameter

of this triangle.

of the order of one-eighth greater

than

the total bottom width of the triangle, draw a construction circle tangent to the baseline. Using the half-beam at the

Comparison of Residuabt-ResistancePer-Ton Values for Normal and Bulb Bows

Fig. 67.F

the floor

lines,

DWL,

the keel half-siding,

the straight-sided triangle, and the

construction circle as guide lines, sketch in a

the bulb sections intersect the baseline. good shape for the bulb section, extending all

way up

A all

DWL,

decanter shape, as

67.G

for the

ABC

is

done

ship.

in

diagram

1

The fs value here

of Fig. is

0.06.

and lying in or projected upon the transverse plane of the FP, is that of a

found that, in general, the bulb section passes close to the upper intersection of the

decanter.

As a starter in laying out this section, draw two short vertical lines at the DWL, at the half-beams selected for the stem, and then

triangle

first

maximum beam

the

to the

lay off the keel half-siding on each side of the baseline.

From

two short

the outer edges of the keel draw

floor

hues at a suitable

TABLE

67.a

The data presented here derived values of

FINE SHIP, Cp = 0.60

Rr/A

Series

A

rise-of-floor

Derivation of

Rr/A Values

are taken from the

TSS

are plotted on Fig. 67.F.

It

is

and the construction circle, and that its is about that of the circle. Adhering strictly to Wigley's criterion (6), quoted earlier in this section, that the submergence of the

top of the bulb be not less than

breadth, fob

its

maximum

the construction circle for any bulb

Two TSS

Ships

contours of 7?k/A given

Without Bulb Bows

by D. W. Taylor

in

S and P, 1943. The

UNDERWATER-HULL DESIGN

Sec. r,7.7

513

should have a diameter not much greater than half the draft. If this design rule is followed, the area ratio /e of a bulb laid out in accordance with these rules is limited to a maximum of

about

0.10, indicated in

diagram 2 of Fig. the upper part

If larger ratios are desired

67. G. of the

bulb must approach the surface closer or the lower part must assume more of a triangular or platypus form, with a diminished rise of floor.

A

=

bulb with an area ratio /b

0.135, on a where B/H = Dillon and E. V. Lewis

vessel of relatively shallow draft, 3.07, is

shown by E.

[SNAME,

1955, Fig.

circle for this

S.

9, p. 735].

how

Q.SH, depending upon

To

The

construction

bulb has a diameter of from 0.7 to it is

used.

simplify construction, with the rather heavy

plating called for in this region, the sides of the

bulb are

if

Sections

made developable surfaces, The lower part of the

possible

u If c J- .' HQlf-S,d,ng|

described in Sec. 27.1.

may

be the surface of a cone, not necessarily a circular one, whose vertex lies well ahead of the FP. The following is copied from D. W. Taylor bulb

[S

and P, 1943,

p. 69]: architect will have

"The ingenious naval

in devising bulbous forms where

the structural plating

is

TABLE The value

of

little

no

difficulty

or no furnacing of

necessary."

67.b

T, for the

ship at 18.7 kt

is

Fig. 67.

G

Layout Diagram for a Bulb-Bow Section

Sketching in a section similar to that of the FP, 1 or 2, corresponding in area to either or both of those intercepts on the sectionarea curve and fairing generally with the bulb at about Sta.

18.7/ VSIO

flij/A

At r„ =

6.96 ftl-

Predicted Improvement in Residuary Resistance

ABC

0.

Fine ship, without bulb

Shown

^^^^pp

=

Due to Bulb Bow

0.828.

Saving in Residuary Resistance with Bulb

HYDRODYNAMICS

514

IN SHIP DESIGN

Sec.

^Axis EquoM\j

Fig. 67.H

5poced

an approximation

of the

DWL,

FP. If some variation from a developable conical shape is acceptable, the waterlines through the

still

apex forward

of the

maximum transverse thickness of the bulb may approximate the shape of a single-ended Rankine ovoid generated by a single 3-diml source placed in a uniform stream. Fig. 67. H illustrates the method

graphic

of

construction,

described

in

Chap. 43, and shows the shape of an axial section through one-half of such a form. The proportions are varied by changing the source strength relative to that of the uniform stream. The lower profile of an ovoid bulb could be delineated in the

requirement of a

same way except for the flat keel

for docking support.

practical

extending well forward

Having

this in

mind

it is

convenient to terminate the lower profile in a radius tangent to the base plane, say of the order of O.lOff [SNAME, 1930, PI. 41], or it may be about equal to the mean radius of the extreme nose of the Rankine form. For the ABC design the dimension adopted is 3. .5 ft; this means that the straight keel for docking extends forward to the FP. The matter of shaping the bottom of the bulb to avoid pounding and slamming during wavegoing is discussed further in Part 6 of Volume III. If the bulb remains normally well submerged in service, as it might in inland waters, where pounding or slamming is rarely if ever encountered, the bulb sections may be made rather definitely triangular, with a fairly flat bottom

[Eggert,

Lindblad,

E.

A.

F.,

SNAME,

F.,

Bows," SSPA Rep.

1939,

pp.

303-330;

"Experiments with Bulbous 3, 1944, p. 7]. This puts the

Bow

centroid of the bulb area even farther below the

slenderness of the bulb cone and the position of its

Ovoid

Ordinotes or Radii

Construction of a 3-Diml, Single-Ended Rankinb Ovoid foe a Bulb

sections at the FP, gives

of

r,7.fi

with

accompanying advantages. It is work developable surfaces into the

its

possible to

bottom and the sides of this triangular bulb. 67.8 Check on Bulb Cavitation. In the past there has been no definite low limit of draft, in smooth water at least, at which it is not advisable to fit a bulb at the bow. Even for high-speed light-draft vessels intended to run in large waves,

bulb bows have been used to advantage. An example is the pre-World War II Itahan cruiser Pola, having a standard displacement of 10,000 t, a length of approximately 600 ft, a beam of 67.7 ft, a draft of 19.5 ft, and a B/H ratio of 3.47.

At a speed about

of 33.9 kt, T<, for this vessel is 1.38;

A

F„

is

is

published in Schiffbau

0.41.

close-up

bow view

Mar

[1

of the

Pola

1933, p. 89].

Other examples are the heavy cruisers U.S.S. Pensacola and U.S.S. Salt Lake City, described on SNAME RD sheet 121, with /b values of 0.083; see also Fig. 52.Kc.

For the first time, so far as known, cavitation was recently (1954) observed on each side of the bulb

another

of

light-draft

high-speed

vessel

somewhat resembling the Pola. In smooth water the two cavities were plainly visible from the forecastle head.

This

new development

elliptic or

definitely

calls

for

pointed rather than circular beginnings

of the waterlines well

below the

DWL. The

shape

and possibly also the shape of some other characteristic line, must therefore be one for wliich cavitation will not of the waterline at each draft,

occur at the cavitation

number

o-(sigma) actually

encountered on the ship at designed draft in smooth water. This check was not made for the bulb design of the

ABC ship since the observations

UNDERWATER-HULL DESIGN

Sec. 67.9

paragraph were reported long after the completion of the underwater hull design and the construction and tests described

of the

ABC

When the ship the

preceding

the

in

number

calculating the cavitation

for

and to omit head above the

well to be conservative

it is

increased

for

bow. The transient cavitation which occurs along the sides of the bulb during wavegoing, when the bulb rises toward the surface, may be accepted. Incidentally, it is not possible to observe either the separation or the cavitation on a routine model test because the Reynolds number R^ or jSj at the stem is too low to produce a flow dynamically similar to that on the ship, and because, with full atmospheric pressure above the basin crest or to sinkage at the

the model cavitation

higher than in the

Assuming

quarter-length are necessarily of U-form.

number

is

much

for the

ABC

aft into a more or less straight be vertical or flared outward.

work

may

Following this of the

ship that at

some

light-

ABC

rule, the sections in the

of the entrance lying inside the

sensibly vertical so

above the with a consequent increase in pressure

crest with outward-sloping section lines

DWL,

drag due to wavemaking. An easy path for the curved and twisting flowlines around the lower portion of the entrance is

achieved by working as large radii as possible

into the lower "corners"

for the

ABC

in Fig. 51. A. It has hull resistance

hy)

=

-

(13.5 -h 33

also that the speed

is

0.5)

=

18.63

This value cavitation

is

ft.

46.0

—

Assuming

ft.

20.5 kt, or 34.62 ft per sec,

=

the velocity head hu (64.348)

=

Ha

Then

o-

Vy2g = (34.62)7 = 46.0/18.63 = 2.47.

far in excess, numerically, of the

number

o-

=

0.50 at which cavitation

occurs on the hemispherical head of a body of revolution, from diagram

1 of Fig. 47. E.

Indeed,

the U-sections in is

in the

TSS body

been possible to reduce bare-

lower outer corners of the sections abaft the bulb

and relocating the displacement volume upward by filling out the waterlines of the same sections. At the suggestion of S. A. Vincent, this was done with the first set of forebody fines of the ABC ship. Following the model tests of the hull shown in Fig. 66. P it is believed that the form would benefit by a further change of the same kind. If

deep or shallow V-sections are to be used in

the entrance, the section shapes follow a fairly regular pattern from the stem to the

Studies in Eng'g., Bull. 32, 1948, pp. 54, 65]. No cavitation in smooth-water running need be

sections are well illustrated

bow of the ABC ship. number corresponding to

expected around the bulb

The

cavitation

cr,

conditions on this or any other ship,

quickly by the use of the

by entering

it

monogram

is

found

of Fig. 47.B,

with the total head in

ft

and the

ship speed in kt. 67.9

Selection of Section Shapes in Entrance

and Run.

The

first

decision

with

respect

to

and the run is predominantly U- or

section shapes in the entrance

whether they shall be of V-shape. If the vessel

is

to give its best perform-

is

plan

by the order of 8 per cent in a bulb-bow model solely by cutting away the

in excess of that at which cavitation occurs on a blunt head [Rouse, H., and McNown, J. S., "Cavitation and Pressure Distribution: Head Forms at Zero Angle of Yaw," State Univ. Iowa, it is

illustrated

design in Figs. 66.P and 66.R. It

to the axis or Avidest part of the bulb, reckoned

-\-

of

of the forward quarter. This

from the at-rest WL, is only 13.5 ft, that the head hJ^ corresponding to the atmospheric pressure is 33 ft, and that the head due to the vapor pressure of water, hv ,is 0.5 ft, the total static head represented by {h

made

is

as not to accentuate the

shown more prominently

is

which

forebody

estimated position of the bow-wave crest

load displacement and trim the depth of water h

at the axis of the bulb

side,

ship are of predominantly U-form.

That portion

way

full scale.

hour-glass shape at the bulb,

considering the abovewater sections as well, and

bow-wave

various parts of the bulb due to the

water,

fifth- or

They begin with an

model.

allowances

515

ance under conditions which make a bulb bow of advantage, the entrance sections in the forward

of the hull

outer corners well rounded. differences

main body

forward of amidships, with their lower

between

The

relatively small

and U-shaped by G. Vedeler, in a

V-shaped

diagram embodying alternative hull designs for a given set of specifications [6th ICSTS, 1951, pp. 169-170].

The design of cutaway dory-type bows with pronounced V-sections, as in the Maierform, in icebreakers, and in vessels like the old pilot boat New York, is discussed under these special forms in Chap. 76. The shape of sections in the run is determined largely by the tentative shape selected for the designed waterline and by the positions selected for the propulsion devices. The latter is a major

HYDRODYNAMICS

516 factor,

Sec. 67.9

struction," submitted in partial fulfillment of a

Near the

B.Sc. degree at the Stevens Institute of Tech-

the nature of the flow to these devices.

rudder position (s).

may

be the tentative For normal-form sterns the

stern a secondary factor

twin or multiple screws calls for sections predominantly V-shape. For single screws a V-shape merging into a U-shape helps to provide fitting of

of

a

IN SHIP DESIGN

because the section shapes largely govern

greater

degree

of

equality

in

the

vertical

wake velocity, and possibly also a higher average wake fraction than a V-shape. With the latter it is almost impossible to obtain distribution of

anything but blunt endings in the upper part of

nology, Hoboken, N.

J.,

in 1884:

"This eddy resistance, produced by an 'unfairness' in the run, is a fault common to many boats otherwise well designed. The run is the most important part of the sJiip,

as well as the most difficult to design,

therefore, receive very attentive study. If

and should,

it is

not given

a shape, capable of letting the water close in naturally and smoothly under the stern, the negative pressure of the water against that part of the ship, will be lessened, or, what amounts to the same thing, the direct head resistance will be increased, thus producing a decided loss in

a centerline skeg. It is to be recalled, when sketching in the run sections, that most of the water passing the run

efficiency."

comes up from under the bottom. Put in another way, the water coming up from underneath the

the

ship covers a greater surface area of the run, as

resembles more nearly the orthodox twin-screw

on the body plan, than the water coming around the sides. The importance of good shaping in the run was appreciated many decades ago and its need could well be brought to the attention of naval architects every few years. The following extract is taken from pages 16 and 17 of a thesis by Mr. H. de B. Parsons entitled "Ship Design and a Systematic Method of Con-

rather than the single-screw hull. This shape of

projected

TABLE

Name

or

67.C

Number

Data on Section Coefficients

of Ship

With the

ABC

relatively large

ship,

section lines in

B/H

ratio of 2.80 in

and a transom at the stern, the the run fall into a pattern which

run does not lend

itself

to deep U-sections in the

portion leading to the propeller. For this reason,

and to hold the thrust-deduction forces to a minimum, the centerline skeg was made as thin as practicable, having due regard to accessibility and lateral stiffness. It was then added to the main hull as a sort of appendage, indicated by

in the

Entrance for Typical Merchant Ships

UNDERWA lER HULL DESIGN

Sec. 67.12

the broken section lines

the afterbody of Fig. 6G.P.

line in

To

and the skeg tangent

preserve a nearly constant waterline slope

at the stern, in the actual

wave

profile at trial

speed, the waterlines just above the 26-ft

DWL

terminate in a vertical knuckle at the outer lower corner of the transom. With a sharp horizontal

knuckle at Sta. 20 it seems preferable to carry the latter knuckle forward until it fades out

between Stas. 16 and

17.

Variation of Section Coefficient Along

67.10

the Length. One means of knowing whether the lower corners of the sections ahead of and at the

forward quarterpoint are cut away sufficiently is to plot the section coefficients on a base of ship length. It is indicated in Fig. 24.1 that a normal

form

curve passes through the given value maximum-area section, diminishes

of this

Cx

of

at the

slowly toward the FP, and rapidly toward the AP.

Because of the parallel middlebody worked into

some ships

it

is

also necessary to consider the

shape of the forward portion of the sectioncoefficient curve with respect to the entrance length

Le

Many

rather than the ship length L.

years ago D.

W. Taylor emphasized

the

importance of easy curvature in the section lines at about the forward quarterpoint. He stated then and it appears to be true by present knowledge that "at about the point where the water wants to go under the ship, you ought not to have a full section not over 85 per cent

—

—

—

coefficient of fullness at the outside"

[SNAME,

1907, p. 11]. While a section coefficient of 0.85

at the forward quarterpoint (0.25L abaft the FP), represents a good design for easily driven vessels, it

can and does rise and fall with the value of Cx perhaps better to say that the lowest value

It is

of the section coefficient in the entrance should

within the range of 0.25 to 0.45Lb from the FP. Within this interval of length it should have a value of the order of 0.80 to 0.90 of the Cx value. These ranges are taken from the data of Table 67. c, for the position and value of the minimum

fall

section coefficient in the entrance of a

number

of

merchant ships and designs, and from unpublished data on a rather wide variety of combatant vessels.

Fig. 67.1

the

ABC

stern

is

a plot of the section coefficient for

ship with both the single-skeg transom

and the twin-skeg arch

the curve this ship,

is

stern.

The shape

typical for a vessel of this type.

with a Cx of 0.956, the

minimum

of the section coefficient is 0.873.

0.165L, or 0.320Lj;

,

abaft the FP.

of

For

value

It occurs at

The

ratio of

-

517

HYDRODYNAMICS IN SHIP DESIGN

518

Sec. 67.13

blisters or bulges

on a ship. Sec. 76.9 discusses the design of ship hulls with discontinuous sections and includes a number of design rules. Certain of

however, are these small enough to avoid separation at the DWL.

these are applicable also to ships with blisters and

hull

bulges.

flow to the wheel, and the

augment

due to the reduced-pressure

field in

Manifestly, the addition of a blister to the

main

hull or the swelling of a bulge on the

boundthe volume

it comprises an integral part of which must be pushed through the water. The form coefficients and parameters of the ship carrying them apply therefore to its outside dimensions, shape, and surface. A ship already built, to which a bulge or blister of large size is appUed, becomes in fact a new ship, with new

ary of

proportions,

new parameters, new hull

coefficients,

and a different shape. Assuming that the transverse section contours of a bulged form are fair, the discussions of Sees. 24.10 and 25.8 show that neither the maximumsection shape nor its fullness coefficient Cx have an appreciable effect on the ship resistance. This means that the bulge can be shaped and positioned to suit other requirements. If it comes at the designed waterUne, of course,

changes the

Bx/H

ratio,

slope in the entrance coefficient

Cw

it

the angles of waterline

considerable latitude in these values for a good

General Arrangement of Single-Screw or fantail type of stern, with its relatively thin and deep centerhne skeg, its rather long fore-and-aft abovewater overhang, and its wide upper decks, came down through the sailing ships of the Middle and Modern Ages. It persisted as the normal form of stern for mechanically driven vessels until the 1930's and beyond. In the two decades preceding the time of 67.13

The counter

(1955)

it

not only for propulsion but for propeller maintenance, is that the single

wheel be kept well submerged in

With the

conditions.

all

large powers

put into single screws,

operating

now

being

of the order of 20,000

horses or more, and the likelihood of

still

greater

single-shaft powers in the future, as ship speeds increase,

ahead

it is

imperative that the waterUne slopes

of the propeller aperture

tively to avoid

At the level

any

be such as posi-

liability of separation.

of the 0.7 to 0.9 radius

on a propeller

blade in the 12 o'clock position, the skeg waterline slopes just

ahead

of

the aperture should not

exceed 15 deg for near-surface

deg for face in

20 below the sursmooth-water running. This slope is to levels, or 18 to

levels that are always well

be carried

aft,

as close as practicable to the aper-

ture, eliminating blunt endings

stern

weldments,

or

forgings,

on sternposts or

The

castings.

to prevent corrosion on thin sections, say 0.1 ft

of area

design.

writing

jet.

What is equally important,

moment

,

DWL

Stem.

of resistance

the inflow

terminal radii should be no greater than necessary

and other parameters. If it C,t comes below the it changes only the fatness ratios A/(0.010L)' and ¥/(0.10L)\ There is coefficient

is really important is the underwater shape forward of the propeller, as it effects

and run, the waterplane

the transverse

,

almost certainly

What

has,

for

reasons

still

rather

or less on large vessels.

The aftfoot may be cut up in profile to meet maneuvering requirements, to form what is sometimes called a clear-water stern, provided dynamic stability of route is assured, and the necessary

docking support remains along the

centerline keel. If

and upward

it is

known

that the flow

is

aft

in

cutaway region the level lines the skeg termination may be rather blunt. It

is

the hull slope along the actual flowline that

in the

counts, below as well as above the shaft axis.

In some tugs the aftfoot clear-water stern, ability

is

to afford

cut away, as in a

greater maneuver-

but the keel bar and the sternpost are

extended

aft

and downward,

respectively,

to

largely

carry a rudder shoe and to act as a guard for

difficult to build,

both propeller and rudder ["Kort Nozzle Tug Maamal," SBSR, 20 Nov 1952, p. 676]. Freedom from objectionable stern vibration in service is often a requirement that ranks in

been replaced as the normal single-screw stern by the whaleboat or canoe (cruiser) type. The latter has the practical advantage that it is probably less costly and less obscure,

to the rudder

projections

and

that

and

it

affords better protection

in

smaller

importance \vith efficient propulsion. Meeting this demand means, in addition to a fine skeg ending ahead of the propeller, an adequate aperture clearance ahead of the sweep lines of the propeller blades. This must be enough to keep down to acceptable limits the periodic lateral forces on

the stern.

Rarely,

the skeg as each blade, with

and

propeller,

that,

lacking

not likely to give trouble in a following sea. Hydrodynamically, it

discontinuities,

it is

usually offers better shielding of the propeller

against air leakage and, because of the greater waterline surface

length,

it

should

waterliue slopes at

result

its

circulation pattern

UNDERWATER-HULL DESIGN

Sec. 67.13

and pressure

field,

passes through the aperture.

An

hull.

519

The arrangement then resembles

that of

adequate and proper aperture clearance, although undoubtedly a function of the pressure distribution around the adjacent blade elements,

each side skeg in a twin-skeg design, discussed

can not be defined within close limits on the basis of present knowledge. This matter is discussed

as easy as might be expected, with this arrange-

further in Sees. 67.23 and 67.24.

levels of the skeg

A

modern form

of whaleboat or canoe stern merchant vessels of normal design is represented by the sterns of the five TMB Series GO parent forms for block coefficients from 0.60 through 0.80. The typical stern profile is illustrated in a diagram published by F. H.

for

single-screw

in

and

67.21

Sec.

[SNAME,

the technical literature

in

1947, pp. 97-169]. However,

it is

not

ment, to obtain the requisite fining of the upper ending while giving the skeg

an ample degree of lateral stiffness. The profile drawing of Fig. 66. Q is an elevation of the aftermost quarter-length, drawn in orthodox fashion. The centerline buttock is included as a sort of construction line, indicating the profile

adaptation to a particular propeller is dehneated by J. B. Hadler, G. R. Stuntz, Jr., and P. C. Pien

shape of the after main-hull sections on the basis that the thin centerline skeg is treated as an appendage. The transom-stern body plan. Fig. 66. P, indicates this feature in the form of broken-

[SNAME,

hne continuations

Todd [SNAME,

1953,

Fig.

28,

p.

562].

The

1954, Fig. 2, p. 123].

In a modification of the normal single-screw stern, such as that laid out for the ABC design in Figs. 66. P and 66. Q, the transom leads forward to a sort of shelf,

worked at about the

level of

the top of the propeller aperture and the top of the rudder.

One purpose

of this shelf is to protect

the propeller from air leakage as long as the shelf is

submerged. Another

is

to permit fining of

the upper portion of the skeg ending ahead of the upper propeller blades by making the skeg

more

of

an appendage than a part

Fig. 67.J

of the

main

of

the sections at Stas.

16

through to the centerline without taking account of the skeg. The aperture clearance forward of the upper through

18.5, carried

blades

made

is

exceptionally large

of the skeg is cut

away

and the

and to improve maneuvering.

It is to

that whereas the centerline buttock for

about 11

ft

aftfoot

to save wetted surface

forward of the AP,

be noted

is

horizontal

it

was found

not possible to level out the lateral buttocks in the same

way without

decreasing the slopes of

the lower transom edges or losing displacement

Port Quarter View op Transom-Stern Model for

ABC

Ship

HYDRODYNAMICS

520

Fig. 67.

K

Profile View of Transom-Stern

volume by hollowing the main portion of the hull at and forward of the propeller position. The upper after corner of the rudder is rounded off to provide a moderate gap below the free-water surface and to avoid breakdown of the rudder at large angles.

of

These features are pictured in photographs TMB model 4505, representing the transom-

stern

ABC

ship,

reproduced here as Figs. 67.

and 67.K.

A

IN SHIP DESIGN

Sec. 67.14

Model for ABC

Ship

screws, could be designed for the

ABC

stern hull, with the shafts supported

further modification of this shelf or transom

ship, as

an additional example of hydrodynamic design procedure. However, a twin-screw stern (excluding bossings) usually poses fewer shaping problems and interferences, and it may be expected to have less bare-hull resistance than an equally good single-screw stern. Save for the cases where quadruple screws are carried underneath a flat-bottomed or transom-

by

struts, or

propeller bearing

where two of the four quadruple screws are carried by deep skegs, the design of a normal form of quadruple-screw stern follows that of the normal twin-screw stern rather closely. The inboard propellers are placed in about the same positions as for twin screws. The outboard propellers are mounted farther forward and farther from the centerline, usually far enough so

strut,

that their discs are clear of the inboard propeller

design, particularly for a high-speed craft, limits

the single centerline skeg to a sort of vertical bossing which terminates just below the shaft.

Carrying this design one step further cuts the bossing back to a short length of fairing where the shaft emerges from the hull and supports the

by a single-arm or double-arm with intermediate struts as may be neces-

sary.

discs

Stern Forms for Twin- and Quadruple-

67.14

Screw Vessels. stern,

The Taylor Standard

Series

delineated in Fig. 51.A [S and P, 1943,

185 and 186, pp. 182-183], was adapted from the British twin-screw armored cruisers of Figs.

it still represents an excelform for twin-screw hulls of today. It is adaptable to several types and shapes of single centerline rudder, including the spade or underhung rudder, as well as to rather wide variations in profile. It may be used with open struts to support the twin shafts or twin bossings may be superposed on it.

the 1895-1905 era but lent basic

Lack in

for the cases

of space precludes the insertion of sections

which a second alternative

stern,

with twin

of

when both

the

sets are projected

maximum

propellers

project

far

sides of the hull, as

Omaha

on the plane

Whether the four beyond the above water

section.

on the

light cruisers of the

whether they below the hull as on a wide transomstern design, is more a matter of the general hull shape than of the underwater hull design. Rarely, if ever, is the hull shape modified for the outboard propellers, except as may be necessary to accommodate machinery parts inside. The four shafts are carried in bossings, in open struts, or in any desired combination of the two. The positioning of screw propellers relative to the hull, especially the matter of tip clearances, is discussed further in Sees. 67.24 and 69.3. (U.S.)

lie

entirely

class of the 1920's, or

UNDERWATER-HULL DESIGN

Sec. 67.16

Notes on Three- and Five-Screw InstalAlthough triple screws are, at the time

67.15 lations.

of writing (1955), not favored for

many

early turbine-driven vessels of the

1900's, the passenger vessels Great Northern

Northern Pacific of 1914, and the

many

and

cruisers

and large German capital ships of the World War I and World War II periods. An excellent photograph of the Cunard liner Carmania, fitted with triple 3-bladed propellers, is shown on Plate 161, SNAME, 1905. A photograph of the Columbia in dock, showing the three 3-bladed built-up

propellers,

published

is

Magazine [Feb 1896,

p.

325].

The

economically and efficiently speed and at full speed.

at

both

cruising

modern ship

have been many successful installations in the past. Notable among these were the U. S. cruisers Columbia and Minneapolis of the designs, there

1890's,

521

in

Cassier's

triple-screw

While attractive from the point of reducing number of propelling plants and propulsion devices on a high-power ship, triple screws may have to be associated with something rather new and different in the way of ship sterns to the

realize their full possibilities.

It is not beyond the bounds of probability that with further increases in ship power it may be found advisable to fit five screw propellers on a ship. A stern design for such a vessel appears to

involve

many problems

of

both the triple-screw

and the quadruple-screw stern. Because of this and other reasons it has not, so far as known, been attempted on more than model scale.

The Arch Type

arrangements on the Argentine battleships Moreno

67.16

and Rivadavia are illustrated in Schiffbau [11 Oct 1911, p. 19]. There was a proposed triplescrew World War II German destroyer of the

With the

of Single-Screw Stern.

increased reUabiUty, decreased weight

[ASNE, Feb

with internal-combustion engine drive 1948, pi. opp. p. 30]. There were four

and space, and reduced fuel consumption of the larger sizes of modern ship propeUing plants it becomes increasingly desirable to take advantage of the inherent simpUcity and lower first cost of

engines of 10,000 horses each coupled to the

single-screw propelling machinery, to say nothing

Z-51

class,

center shaft and one each of 10,000 horses to the

two wing course vessel

The

shafts.

much was

center propeller was of

larger than the

two

others.

The

to carry a large centerline spade rudder

and smaller

offset

twin rudders.

of

its

higher

with propelling machinery and propeller design. The hull shape in way of the center skeg or center portion ahead of a middle screw difficulties

Propeller

coefficient.

much

higher than those dehvered to single wheels

in the past can be absorbed at reasonably

rotational

The triple-screw stern, despite its use on many medium and large vessels in the past, presents

propulsive

design has progressed to the point where powers

sufficiently

speeds.

If

increased,

the if

rate

of

low

rotation

the propeller

is

is

made

and if it is kept adequately submerged, the shaft power of 50,000 horses mentioned elsewhere may be achieved in the not

large enough,

distant future.

and the wing

Much higher propulsive coefficients can be and have been obtained with single-screw than with twin- or multiple-screw propulsion but these are predicated upon advantageous flow conditions at the propeller disc. Good flow is obtained with relatively long and thin vertical skegs ahead of

necessary,

the propeller, giving reasonably high hull

vastly different from the shape ahead of the

is

wing screws, even when the bossings.

The

latter are carried

by

friction wakes, the angularity of

the flows, and the uniformity of water speeds

over the discs will not be the same for the center propellers. Although not strictly almost never possible to make the center propeller absorb the same power at the same rate of rotation as the wing propellers.

Many

it is

designers

have been disillusioned by

attractive proposals to use the center propeller solely for intermediate-speed

ciencies [riH

(1

—

0/(1

—

"')]

effi-

at the propeUer

position without excessive circumferential variation

and without objectionable separation or

eddying.

As the

and cruising pur-

poses, only to find in service that:

=

size of vessels in this category increases,

so does the beam-draft ratio, because the draft

(1)

There were practical difficulties in uncoupling the wing shafts and permitting their propellers to

more severely Hmited by depths in the waterways of the world than the beam is limited by berthing and docking facihties. The progressive

free-wheel while cruising

increase in beam, over the years, due largely to

There were many problems in designing a center propelling plant which would operate

damage-control

is

(2)

requirements,

has

meant

in-

creased difficulty in fining the waterUnes forward

HYDRODYNy\MICS IN SHIP DESIGN

522 to keep

down

making.

It is

pressure resistance due to wave-

perhaps even harder to draw in the

lines aft so they merge into a long and relatively narrow skeg ahead of the single propeller. Unless the stern is deliberately made wide and flat, incorporating a feature not well adapted to vessels which must operate with a great variation in draft aft, the demand for fine lines at both ends of a medium-speed or fast vessel cuts

severely into the waterplane area necessary for

transverse metacentric stability. All things considered, it is difficult to fine the designed waterline

ending in a single-screw ship of normal form without encountering separation and accepting the drag which comes with

To avoid

it.

surface

separation completely means limiting the waterline slopes to a value

not exceeding about 12 or

With beams continuing

13 deg.

situation

is

to increase, this

slowly becoming worse. Something

needs to be done about

The termination and

it.

the slopes of waterlines

forward of a single-screw propeller aperture have on many occasions in the past been relatively blunt and heavy, with no consistently objectionable effects. This was principally because the

powers absorbed by individual propeller blades were small and the transient forces and moments produced when these blades swung through regions of highly variable wake were also small. With higher and higher blade loadings the periodic forces and moments likewise increase, so that turning out a design with greater power than a previous design, or re-engining a ship to accomplish the same purpose, is by no means as simple as making the propeller shaft a little larger and mounting a new propeller to absorb the In the orthodox single-screw stern the propeller in the

same

vertical plane as the:

(c)

Arch structure over the aperture Rudder Rudder horn, if fitted

(d)

Sternpost

(e)

Rudder post

(f)

Shoe projecting from the heel of the ship to

(a)

(b)

Any attempt

tip clearance, or to leave

vertical clearance in the aperture, runs

into the situation that also be

ones,

and hanging each

skeg,

much more room

on the it is

the space

accommodated

By shifting the fixed

many

needs,

it

centerline.

far easier to

of

them behind an

is left

offset

for a single propeller

Furthermore, in a wide ship

work gentle

slopes into the sides

upper portions than into a single

of twin skegs, especially in their

where they join the

hull,

centerline skeg. If a single propeller

mounted

is

between the offset skegs with an arch-shaped roof overhead it can have a diameter 20 to 25 per cent larger than would otherwise be possible. The fact that the tip clearance in this tunnel can be made sensibly constant for more than half-way around the propeller disc means that this clearance can be very small. It can indeed be vastly smaller than is thought necessary on an orthodox single-screw installation to keep vibration down within reasonable limits. This leaves still more room to swing a larger wheel. For the ABC design, a propeller-disc diameter of 24 ft was selected as one which would always remain submerged; that is, as one for which the wheel could be kept submerged during the several in a sort of tunnel

variable-load conditions

by the use

of liquid cargo

or salt-water ballast in the after peak tanks,

coupled with the inflow

jet.

The

filling of

the tunnel by a solid

tip clearance of

to be a reasonable value,

1 ft

was estimated

considering

that

it

would be constant over at least half the circumference. It was not too small to bring the blade-tip fields too close to the hull and not too large to lose the benefit of whatever boundary layer existed on the inside of the arch. This reasoning was based upon satisfactory ft for

propellers

of one-third the diameter

on tunnel-stern pushboats. In fact, since only mechanical clearance is required, the tip clearance on a 24-ft wheel might be reduced to less than 0.5 ft, assuming flush with

to increase the propeller diameter,

more

all

dividing the one large rudder into two smaller

hull plating abreast the propeller, truly concentric

carry the lower rudder pintle.

to provide

planes where each has

clearances of the order of 0.25

increased power.

is

Sec. 67.16

more

head on

other parts must

in the centerplane.

parts into different vertical

its axis.

For a 20 per cent increase in propeller diameter over that for the transom-stern design, from 20 to 24 ft, the disc area is increased 44 per cent. The thrust-load coefficient is reduced 30.5 per cent (1.00/1.44 = 69.5) by this change alone. A comparison of the propulsive efficiencies of the 20-ft

and

propeller with

the single centerline skeg

of the 24-ft propeller with the arch stern is

given in Sec. 78.15.

The afterbody plan

of Fig. 67. L

shows how the

UNDERWATER-HULL DESIGN

Sec. 67.16

tunnel between the side skegs

is

widened

slightly

p. 116]

52S

indicated a definite thinning of the bound-

way

with distance forward of the propeller in an endeavor to allow for the increased area of the inflow jet with that distance. The tunnel is neces-

ary layer in

deep in that portion of the length normally occupied by a single centerline skeg because of the need for providing docking support in that

hull surface. This

region.

alternative

sarily

At the time

the

first

modern twin-skeg

sterns

were developed, an easy slope of the tunnel roof was considered an important feature, so much so that the 9 deg. It

maximum value was limited now known that separation

is

to 8 or

does not

occur at these small slopes, even at the freewater surface. Well below the surface, where

much more gradient

is

the slopes can be considerably greater than the 12- or 13-deg surface hmit. it

fairly

was believed

For the

ABC

safe to increase the

high transverse velocity gradients at the is

an additional guard against

the tunnel. Incorporating these features into an

ABC

arch-type stern for the

ship

produced the body plan of Fig. 67.L and the stern profile of Fig. 67.M. The resulting stern arrangement is not unlike one proposed in 1874 by Robert Griffiths [INA, 1874, pp. 165-178 and PI. XXIV, Fig. Sa). He, too,

was concerned about adequate flow

of

water

to the screw propeller.

The

profile

drawing in Fig.

67.

M

shows the

starboard skeg, looking from outboard, with the starboard

rudder.

The

centerline

buttock

re-

design,

sembles in shape that of the transom stern,

maximum

depicted in Fig. 66. Q, except that in this case the

slope to about 18 deg, provided the tunnel areas

ahead of the propeller were kept large enough. In fact, unpublished model test data on the twin-skeg Manhattan hull form [SNAME, 1947,

Fig. 67.L

bottom con-

separation farther aft along the sloping roof of

hydrostatic pressure and pressure

available to change the water direction,

of the longitudinal

vexity at the forward end of the tunnel, with

transom immersion at it

this

buttock

is

only 0.5

ft,

extends horizontally up to the propeller position,

and

it

does not

fair into

The maximum buttock

Afterbody Plan of Arch-Type Stern for

ABC

the keel until Sta. 14.5.

slope, at

Ship

about Sta. 17.35,

524

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 67.16

UNDERWATER HULL DESIGN

Sec. 67.17 is

18 deg. This

is

maximum

about twice the

recommended

slope

[SNAME,

1947,

increase the positive

for

Rule

wake

9,

back to

130]

67.17

p.

aftfoot

525

as that of the transom-stern design

Sta. 11, corresponding to 0.55L.

Flow Analysis for the Arch Type of Although it may involve some duplication

Stem.

of material in the preceding section, there

is

given

velocity at the pro-

here a brief analysis of flow conditions under the

cut away, not so

indication of the study that should be given to a

arch type of stern. This analysis serves also as an

peller position.

The

same

tunnels

between but it is made deliberately steeper in an attempt to slow up the water passing through the tunnel and previously

skegs

the

on each skeg

is

deeply as in the transom-stern design but extending farther forward.

To

eliminate unnecessary

novel design of this kind in the preliminarydesign stage.

wetted surface, to improve maneuvering characteristics, and to insure a better flow of water into the forward end of the tunnel between the skegs, the lower edge of each is cut up for a considerable

What is termed here the arch stern for deepwater vessels is distinguished from the tunnel stern found on craft intended to operate in

distance to a height of 2.33 ft (28 in), above the

fact that, in the former, the tunnel roof never

two docking 2 ft wide and

extends above the designed waterline. Design rules for tunnel sterns with roofs elevated above

baseplane, equal to the depth of blocks. This horizontal skeg foot

extends from about Sta.

Between

Stas.

is

16.25

15 and 16 there

Sta.

to is

another

18.3. flat

shallow water, described in Sec. 25.19, by the

the water surface are contained in Sec. 72.13.

There has been no

difficulty in

keeping the

horizontal region at the bottom of each skeg,

centerline tunnel full of water on ships with twin

a distance above the baseplane corresponding to the rise of floor at about the 16-ft buttock. The fish-eye view in the lower part of

skegs

lying at

Fig.

67.

M

indicates the

manner

which the

in

skegs converge slightly with distance, from their

forward to their after ends. Transverse sections at the stations in the vicinity of the propeller position are

diagram

shown to

large scale in the right-hand

of Fig. 67. L.

The twin

when proportioned

[SNAME,

this is

tunnel or arch type of single-screw stern, the and proportioning of the tunnel area,

starting

from

curved-blade, tilted-stock twin rudders of the Thornycroft destroyers of a half-century ago [INA, 1908, PI. IV, Fig. 6]. The tops of the rudders

in area as

ft

Perhaps

case the propeller disc occupies nearly all of the tunnel area at the propeller position. In a single-

great care.

are depressed 4

as outlined previously

130-131].

selection

rudders, lying close to the projected

on either

pp.

because in a twin-skeg design, with propellers carried by each skeg, only a part of the tunnel area is occupied by propeller discs. In the present

resemble somewhat the

tip circle

1947,

side,

below the

DWL

to guard

tically

fills

its

forward end, therefore needs

The propeller inflow jet, contracting it moves toward the propeller, practhe tunnel. Too small a tunnel could

be highly detrimental to propulsion. In fact, there were indications when an alternative arch

ABC

was being planned, that

against air leakage and possible rudder breakdown

stern for the

on turns, with the ship heeling and diminishing the submergence of the top of the rudder on the

towboats and pushboats suffered from excessive thrust-deduction forces, apparently as a result of constrictions in the tunnels ahead

high

side.

To

avoid awkward fairing in the vicinity of the rudder head the transom contour is dropped at the sides to 3.5 ft below the DWL, on the basis that some separation drag due to non-clearing of this deep portion is preferable to irregular eddying

above the top

of the rudder.

Outboard

of the skegs

the section lines

fall naturally into a V-pattern corresponding to that of a narrow ship with

centerline skegs such as would be obtained by removing the center portion between the 14-ft buttocks and bringing the two outboard sides

together.

The forebody

of the arch-stern design

is

exactly

ship

tunnel-stern

of the propellers.

It

was

possibly be avoided in the

felt

ABC

that this could ship

by keeping

the tunnel roof well up in the region just ahead of the wheel.

To diminish the tunnel-roof slopes on the ABC design to values smaller than those indicated in

M

would involve loss of valuable disFig. 67. placement volume, shifting part of the propelling machinery farther ahead, a longer exposed propeller shaft, and a further widening of the forward or entrance portion of the tunnel. Any net increase in resistance, such as that caused by thrust deduction, is of course only justified if the

HYDRODYNAMICS

526

gain in power from the expected high average

wake drops the

propeller or shaft

power below

the value to be expected with an orthodox type of stern. It is recalled in this connection that,

model tests of normal-form sterns and twin-skeg sterns, on a comparative basis, showed higher effective powers but lower propeller or shaft powers for the twinpractically without exception, the

skeg form.

By

retaining the high tunnel slopes, at values

which would just avoid separation or — Ap's along the roof of the arch, it was hoped to create artificially a forward wake current over most of the tunnel area. This is exactly what is accomplished by a bulb at the bottom of a skeg ending,

IN SHIP DESIGN

it.

the propeller disc in the

ABC

like the

tunnels of the late 1930's and the early 1940's

squats and

1947,

pp.

These

97-169].

velocities

the water passing

all

However, as the tunnel does not cover ABC design, it was expected that below the shaft axis the wake velocities would be appreciably lower than those above the axis. In relatively slow-speed tunnel-stern pushboats and towboats built to operate in shallow waters there appears to be no great difficulty in getting water through a narrow bed clearance under the vessel, into the tunnel (s), and thence aft to the propeller(s). However, this does not necessarily assure the designer that this flow is adequate in a deep-water vessel with the same type of stern, which has to traverse shallow waters occasionally, through

all

sketched in Fig. 25. L. It appeared, furthermore, that the wake velocities within the arch should be higher than they were in the original twin-skeg

[SNAME,

Sec. 67.1S

forward wake velocities in

ship.

What

saves the situation here

the necessity for the

is

down

slow

Finally,

is

small, else

it

stern drags on the channel bed.

its it

deep-water vessel to

the bed clearance

if

is

realized that the increased disc

should also be considerably more uniform across

area and improved flow pattern expected with

the tunnel area because of

this arch type of single-screw stern, pictured in

its

circular section,

without the inside corners of the earlier tunnels on twin-skeg ships. Furthermore, by having the propeller disc

fill

nearly

all of

the tunnel area

it

should be possible to take advantage of the

Fig. 67. N, are offset to effect of the

some extent by the adverse

items listed hereunder, based on a

comparison with a single-screw stern of normal form: (a)

Increased wetted surface of the side skegs.

This has been reduced somewhat by cutting up the skegs 2.33 ft, the height of two docking blocks. (b)

Necessity for a shaft strut within the arch

to support the propeller bearing (c)

Drag

of the

exposed propeller shaft and of a

short fairing or bossing at (d)

its

forward end

Necessity for two rudders, neither of which

lies in

the propeller outflow jet

Probable necessity for placing, farther forward than in a normal single-skeg stern, that part of the propelling machinery directly attached to the shaft, because of the reduced rate of rotation associated with the larger propeller and (e)

the larger main gear.

Despite these

initial

disadvantages, the

ABC

type of arch stern was considered by several experienced naval architects who examined it to

have

sufficient

promise to justify the building and

testing of a model. In the present state of the art, this is the best that

can be done with any new

design.

Design of Hull and Appendage ComVery frequentlj' the final design of that portion of a ship hull adjacent to a fixed or movable appendage is only possible after the 67.18

binations.

View from Aft of Arch-Stern Assembly on ABC Ship Model

Fig. 67.N

UNDERWATER HULL DESIGN

Sec. 67.18

appendage

detail design of the

This

particularly true at the stern of a vessel,

is

in the vicinity of a screw propeller

A

completed.

itself is

and a rudder.

suitable procedure to be followed here

illustrated

by the

stern for the

is

well

design of the arch-type

first

ABC ship. It involved a closely spaced

pair of skegs and rudders, a large screw propeller with exceptionally small tip clearance, an exposed propeller shaft, a propeller-bearing housing abaft

the propeller, supported

and a contra-propeller

by multiple

effect in

strut arms,

the strut arms.

527

take advantage of the augmented outflow velocity, described in Sec. 33.21.

obvious reason,

However, there

is

no

except perhaps an instinctive

one, for maintaining this fore-and-aft distance,

expecially as the rudders do not

outflow

lie

within the

jet.

Moving

the propeller bearing with

its

sup-

porting struts abaft the propeller clears the tunnel

and makes

of this obstruction

it

possible to use

the strut arms as vanes for taking out the rotation

and developing an additional

in the outflow jet

manner

After this arch-type stern was completely designed

thrust, in the

was found that an installation very similar to it had been embodied in the Dravo pushboat Pioneer nearly two decades before, even including the twist in the strut arms [SBSR, 14 Mar 1935,

more, by using three and possibly four arms, curved to straighten the flow in the outflow jet,

it

pp. 291-293].

The

general arrangement of these

appendages, as built into and tested on the propelled model of the

ABC

of a contra-rudder. Further-

these arms can have long, thin sections while at the

same time they provide adequate support One or two arms, gen-

for the bearing housing.

self-

erally vertical, take the weight of the propeller

vessel, is illustrated

and the after half of the exposed shaft while the two side arms steady the bearing laterally. The arms are so spaced as to encounter the bladepressure fields at random or in succession rather

and 74.L in Chaps. 73 and 74 on fixed and movable appendages, respectively. Supporting a propeller bearing within the centerline tunnel requires either a V-strut of the usual type ahead of the propeller or a strut of special type abaft it. Since the tunnel is partly obstructed by a short bossing where the shaft comes out of the hull and a length of exposed rotating shafting, sketched in Fig. 67.0, a V-strut ahead of the propeller would only add to the obstructing effect. Standard strut arms, because in Figs. 73.F, 73.H,

than

simultaneously,

The arms

indicated

in

Fig.

67. P.

and of relatively large chord, to give good hydrodynamic performance. The multiple-strut and bearing-housing combination can possibly be assembled in place and welded into the ship, if considered advisable, as an are thin

integral part of the structure.

To remove

the propeller in such a setup

it is

and short fore-and-aft

necessary either to split the propeller-bearing

lengths, are not suitable as deflectors to impart

housing and drop the lower half or to provide a separate section of exposed shafting. Removal of

of their isolated positions

reversed rotation to the flow in the inflow see Sec.

the

discussion

36.9.

The

moving the

the

of

jet;

contra-propeller

in

arch-stern arrangement permits

propeller

well

aft,

into

a nearly

such a section enables the propeller to be pulled forward a short distance, far enough to get the shaft extension out of the after bearing.

scheme

horizontal portion of the tunnel, but at the expense

the

of getting the rudders too near the propeller to

the standard

Transom Immersion at

first

t

Transom Immersion

O'^^r

method

of propeller

with attachment of

ELEVATION, LOOKING TO, PORT, WITH NEAR SKEG REMOVED

Ruddei

'

~f

Fig. 67.0

i9

Normally

objectionable because

is

Stations

TT

'

Arch Stern Underwater Profile of

18

ABC

Ship,

with Near-Side Skeg Removed

HYDRODYNAMICS

528 DWU

IN SIITP DESIGN

^-*— 5htp

Corner of Transom

Centerlinb

Rudders Toe Out

Bottom of Skeq Cut Up

b\j

to Suit Conver-

Heiqht of

Two DocNina

of Tunnel

Blocks!

ond Flow Outside of SUeos

STERN ELEVATION, LOOKING FORWARD Fig. 67.P

ABC

Abch-Ttpe Stern Arrangement, Elevation from Aft

taper, keys, and nut, the shaft extension must have a diameter smaller than the root of the

threads for the nut.

To

obtain sufficient area in

becomes so enough to remain

the propeller bearing the journal

long that straight.

it is

This

no longer is

stiff

aggravated by the additional

length required for the propeller nut.

The load

solution

(a)

axis.

Provide a permanently

The purpose

fair surface

of

outboard

of the propeller tips, so as to hold the small tip

clearance

constant throughout the

life

of

the

vessel is

then far from uniform on the propeller-bearing material, with unequal and excessive wear.

The obvious

about the propeller-shaft this heavy plating is to:

(b)

Maintain a

fair surface

the rotating pressure

fields at

under the action the blade

of

With

tips.

correspondingly heavy transverse framing inside,

is to:

local forces are distributed over the

whole stern deform

Attach the after end of the exposed propeller shaft directly to the forward end of the propeller

structure, instead of being permitted to

with a pair of bolted flanges sufficiently substantial to take the bending and torsion loads and to

thickness of this belt, at least double that of the

(1)

withstand the torsional vibrations in the rotating system. These flanges are indicated in broken lines in Fig.

67.0 and in

full lines in Fig.

74.L.

Fashion the propeller journal integral with it. The journal can then be made any size and shape desired.

the structure in their immediate vicinity.

adjacent shell plating, combined with verse

curvature,

renders

it

free

its

The

trans-

from panting

without excessive local stiffening. (c) Serve as a strong connection for the hull

(2)

ends of the four strut arms. These ends, approxi-

the propeller hub ahead of

mately straight fore and aft, are intended to be passed through slots in the heavy belt plate and welded to the internal framing as well as to the belt plate. Fig. 73.F of Sec. 73.8 gives typical longitudinal and transverse sections through the belt plate, showing its attachment to the two upper strut arms.

Structural plans for this type of stern should call for

a wide transverse belt of double-extra-

heavy plating abreast the 24-ft propeller and the 4-armed strut, extending approximately from the bottom of the port skeg to the bottom of the starboard skeg. Except for the forward end near the top, this belt

is

cylindrical in shape, concentric

67.19

Comments on Design of an UnsymThe function of a

metrical Single-Screw Stern.

UNDERWATER-HULL DESIGN

Sec. 67.20

contra-guide stern or skeg ending, described in

and discussed

Sec. 25.16 67.22,

is

in greater detail in Sec.

to change the direction of the water

flowing past the skeg ending so as to meet the

cases the

and the 6 o'clock positions. The skeg is deliberately twisted away from the centerplane of the ship, for a half-propeller diameter or more ahead of its termination, to cause the water to contrary

flow to the propeller in the desired

unsymmetrical construction more than pays for its added resistance by the resulting increase of incident velocity on the blade eledirection. This

ments, the increased effective angle of attack,

and the higher

The normal is

efficiency of propulsion.

flow of water on a ship with a more-or-less stern, carrying

generally

a right-handed propeller,

upward and

under the

aft

stern. It

meets the downward-swinging blades in the

and 4

o'clock

flowing aft and

positions.

2,

3

However, the water

upward on the port

side of the

than meets the blades and 10 o'clock positions. The problem confronting the marine architect is to

deflection occurred on both

sides of the skeg so the propeller did not benefit

from

it

any more than

upward

rotating propeller blades in the vicinity of the 12 o'clock

529

downward

it

benefits

from the normal

flow on both sides.

It should

not be necessary deliberately to create

a separation zone on the port side of the .ship to deflect the flow downward on that side. Bulging the stern out to fill the space which would be

occupied by such a zone means that, on a ship of limited length, there

would be another separaadded drag.

tion zone abaft the bulge, with its It

is

not yet known

downward

how

to accomplish

this

deflection of water

on the port side without using up all or more of the energy to be gained by the change but there is undoubtedly some way of doing it. Any asymmetry in the stern in a scheme of this kind has no appreciable effect upon maintaining the upright position of the ship. Likewise it

should have no effect in steering or turning;

indeed, such a change might improve the steering

single skeg follows rather

characteristics because of the present need

in the 8, 9,

carrying 2 or 3 deg of right rudder on a single-

now

screw ship with a right-handed propeller. 67.20 Proportions and Characteristics of an

increase the propulsive efficiency of a single-screw vessel

still

further, possibly as

much

as 3 or 4

per cent, by changing the direction of the water

on the port side so that it flows downward and meets the upward-swinging blades. If this full change can not be made, because of prohibitive drag and other reasons, it may at least be possible to diminish the upward angle of flow on the port side.

There is no structural, machinery, or hydrodynamic reason why the stern of a single-screw with a single symmetrical if there is gained by making it much more so than vessel

stern. Indeed, there is is

to benefit

centerline

be

decidedly unsymmetrical,

the present contra-guide

no reason why,

by the change, the

propeller need

skeg need

a distinct advantage to be

if

the ship

axis of the single

be in the centerplane or even

exactly parallel to

it.

There are cases on record which the flow near the end carrying a single propeller

of tanker

is

of

models

in

it

Stern.

There

is little

reason,

at least as far as resistance, speed,

and power are concerned, for the use of an immersed-transom stern unless, at some speed below the designed value, the water clears the transom and leaves its exposed to atmospheric knowledge indicates that this speed depends mostly on the immersed depth of the transom at its lowest point, and partly upon the buttock slopes just ahead of the lower edge entire

after

surface

pressure. Present

of the transom.

As described

"transom"

in Sec.

25.14,

a

submergence Froude number F,, may be set up, having as its length dimension the greatest immersed draft Hu of the transom below the at-rest waterline. For so-called

reasonably

flat

or

buttock slopes at the stern, indi-

cated as Ib in Fig. 25.1,

F,,

may

be as small as

5,

Table 67.d gives a set of

possibly as small as

4.

immersed-transom

drafts

and

corresponding

a centerline skeg

speeds, for a g value of 32.174 ft per sec^, at which

downward

number F„ equals 5.0. In general, the immersed-transom draft H[/ is selected upon the basis of the lowest speed at which economical operation is desired, partic-

directed

meets the propeller. This may be due to deflection from the under side of a separation zone below the water surface and above the propeller, or to downward flow on the insides of two large longitudinal-axis vortexes coming off the bilges, somewhat larger than the one diagrammed in Fig. 25. F. Unfortunately in these as

Immersed-Transom

for

the Froude

ularly when this speed lies below that at which the underwater portion of the transom is completely exposed to the air. The lower this speed, the

shallower should be the immersed portion of the

HYDRODYNAMICS

530

TABLE

67.d

Here V/\/gHu

Speed V,

IN SHIP DESIGN

Sec. 67.20

Immersed-Transom Drafts Hu and Corresponding Speeds for a Transom-Submergence Froude NUi\rBBR Fh of 5.0

=

5.0.

The

draft

Hy is measured in the at-rest condition. The value of g is taken as 32.174 ft

per sec^

UNDERWATER-HULL DESIGN

6121

Sec.

corners

probably

is

than

objectionable

less

I'oiinding the lower edges.

The transom bottom transverse plane,

such

is

is

measured in a slamming and as

slope is

related to

discussed in Part 6 of

,

Volume

III.

ABC

was completed, in the course of preparing the body plan of Fig. 66. P, the transom depth was increased from the original 1.5 ft to 2.0 ft. This gave more slope to the lower transom section lines and decreased the probability of pounding or slamming under the stern. The planform of the ABC transom stern at the

DWL

is

ship

made

is

one to be given consideration. A square, vertical transom should apparently be avoided for this reason, yet large vessels with a stern termination of this type have reported no difficulties in service.

Taken by and

Before the shaping of the transom stern of the single-skeg

531

the matter of throwing spray or meeting waves

large, the

German World War class,

transom stern

II destroyers of the

portrayed in Fig. 67. R,

is

of the

Narvik

commended

as

slightly convex, with a radius

of O.IOL, partly to facilitate angling the vessel

much greater than its and partly for the sake of appearance. The transom width at the DWL, projected to the plane of the AP, is 0.33BaThe transom of the ABC arch-type stern, sections of which appear in Figs. 67. L and 67. P, into a short berth, not length,

•

deliberately made deeper at the outer corners than the depth which will clear at 20.5 kt in order to avoid the most troublesome problem of

Transon Stern on Model of German Destroyers of Narvik Class

Fig. 67.R

is

fairing the

upper parts

under the

hull.

Some

of the

two skeg endings,

separation

is

certain to

exist in either case. It is considered far preferable

to fair the hull directly into the upper portions of the

two rudders, and to accept eddying abaft

the deep sides of the transom, than to permit

separation farther forward, nearer the propeller

and possibly

interfering with rudder action.

The transom planform shghtly convex,

of this vessel is

with a radius of 0.15L.

made The

transom width at the DWL, projected to the is 0.4455^ In profile, the shape of the transom is generally determined as a matter of appearance and construction. In all vessels which may upon occasion be required to run astern at considerable speeds, plane of the AP,

.

embodying all desirable hydrodynamic features and offering a pleasing and ship-shape appearance without expensive or complicated construction. 67.21 The Design of a Multiple-Skeg Stem. Design rules for multiple-skeg sterns are available in rather

complete form in the technical literature

[SNAME,

1947,

pp.

130-132].

The

historical

examples in that reference are supplemented by a quadruple-screw design for English channel service by John Dudgeon [INA, 1873, pp. 88-95 and PL VIII]. The hull form illustrated in the

two skegs, with two screws inboard and two screws outboard of them. latter reference comprises

The tunnel between was ever

the

way

craft of this

type

the skegs extends

to the bow. So far as

known, no

all

built.

For the design

of multiple skegs

on a modern

craft the rules in the

SNAME

considered adequate,

when supplemented by the

1947 reference are

following: (1)

Consider the use of twin skegs or multiple

skegs only on afterbody forms which lend them-

which beneficial includes wide ratios, where it is

selves to this arrangement, or on

Probable Direction of Flow Leaving a ^ Sharp- Edc^ed Transom Terminotina ot the Knuckle Fig. 67.Q

Diagram of Probable Flow Under Rounded Transom Edge

results

may

ships, or ones

be

expected.

with large

difficult to close

This

B/H

the waterlines in to the center-

plane without large slopes. In general, the after-

body should have a prismatic 0.60 or larger.

coefficient

Cp

of

HYDROnVNAMTCS

532 Incorporate

(2)

forebody

a

employed Math a normal form

Do

(3)

would

which

be

IN SHIP DESIGN ahead

of a

termination

of stern

not hesitate to use twin or multiple

Sec. 67.22

screw propeller. The unsymmetrical usually extends both above and

below the propeller

axis,

but this

is

not necessary.

skegs under a transom or shelf-type stern

The plane

concerned about asymmetry (4) Do not be between the inboard and outboard sides of skegs carrying screw propellers if the water flow or propeller performance is improved thereby

lies close

Give serious consideration to the use of twin or multiple rudders. If maneuvering qualities

jet of the propeller. Before proceeding

(5)

twin rudders are placed abaft

important,

are

Work

arrangement whereby the and shafting can be disassembled or removed with the least interference between themselves or from other parts (6)

to leave as

an

out

For rudders mounted in propeller races, keep far enough from the propellers to permit removing the propellers without disturbing the rudders other than turning them to a convenient (7)

them

angle (8)

If the full,

of the

as explained in Sec. 25.16,

is,

as possible of the rotational or

little

component

tangential

of velocity in the outflow

design of a contra-guide skeg ending,

known whether

a contra-rudder

is

it

with the should be

to be fitted

purpose.

The

propellers,

and

The purpose

to the shaft axis.

contra-guide feature

abaft the propeller to accomplish part of this

twin propellers.

rudders,

of the termination passes through, or

afterbody of the ship

and the ship

is

is

especially wide

to have three or four

design problem consists

of:

Determination of the true deflection angle 9s is a general problem involving the flow about the trailing edge of any body when circulation is not (a)

abaft any unsymmetrical skeg ending. This

present, discussed in Sec. 36.3.

Subdivision into a series of subproblems, one

(b)

each for a series of horizontal planes passing through the termination of selected radii on the propeller.

It

customary

is

R

to

subdivide

the

propellers, consider spreading the skegs far apart,

propeller

and carrying the outboard or wing

indicated on the propeller drawing of Fig. 70.O.

The

the skegs.

inner propeller(s)

propellers in

may

be placed

radius

tenths

into

or

twentieths,

the exact or final propeller diameter

If

D

is

may

not

between the skegs, with the shaft (s) for the inner propeller(s) carried by double-arm

known

struts of the erect V-type.

the waterlines used for delineating the remainder

in the tunnel

Study

of flow

phenomena

since the publication

of the 1947 reference indicates that the

limiting slopes for the tunnel roof

may

former

be approxi-

mately doubled, making them 16 to 18 deg, but probably with an accompanying increase in thrust-deduction

The flow pattern however, by taking the usual

be

by horizontal planes passing through

intersected

of the hull. (c)

Selection of the actual angle ds to which the

flow into various radii of the propeller shall be deflected. This flow

the propeller blades

is

directed always to 7neet

when

rotating in the ahead

direction.

fraction.

should be checked, flowlines around the skegs and inside the tunnel in a

the skeg ending

at the time,

model basin, and by observation

a circulating-water channel.

(d) Selection

the

of

offsets

of

the

deflector

terminations from the ship centerplane or from the construction plane of the skeg, to give the

of tufts in

The thrust-deduction

values require checking by a self-propelled model

angles selected in

(c)

Avoidance of separation on those sides of the deflectors having the steeper waterhne slopes. (e)

test.

If tests

tufts

on a model with chemical indicators or

show

irregular flow within the tunnel or

water crossing underneath the skeg in the design as completed, the skegs may be shifted sideways until a satisfactory flow pattern

twin skegs of

full

is

obtained. If

depth interfere with maneuvering

may be cut away in profile in the manner of a clear-water single-skeg stern. 67.22 Design Notes for the Contra-Guide they

Skeg Ending.

These

design

notes

apply

to

coutra-guide features in a vertical skeg termination

Reference books on the design of hydraulic

machinery,

including

appear to give

little

propeller-type

pumps,

or no specific information on

the actual design of guide vanes ahead of impellers.

One

of the early patents

1,500,073,

by Hans Haas,

that

deflector

the

specially suitable"

shape

on

this device [U. S.

July 1924], states "has proved to be 1

when the product

of (1) the

component imparted to the water opposite any propeller radius and (2) that propeller radius formed (3) a constant quantity rotational velocity

UNDERWATER-HULL DESIGN

Snc. 67.22

the entire radial extent of the deflectors. This means roughly that the natural sine of the deflection angle ds imparted to the water abaft the skeg termination at any selected point, times for

R

the propeller radius

at that point,

is

constant,

or that the natural sine of the deflection angle varies inversely as the radius.

A. Betz of Gottingen in his paper "Zur Theorie der Leitapparate

Propeller" ["The Theory of

fiir

Guide Vanes Apphed to the Propeller," NACA Memo 909, Sep 1939], makes the basic assumption that the tangential velocity component in the outflow jet, due to induced velocity, varies inversely as the radius from the propeller axis. This corresponds to the variation mentioned Tech.

the Haas patent. Unfortunately, the Betz paper does not tell how to design the vanes. The outline of a proposed method follows. Consider first the determination of the correct or effective deflection angle for any given unin

symmetrical skeg ending. Obviously, from ence to Fig. 67.S, there

is

no

Direction

of

refer-

single flow in the

533

would be rather moderate. on the other hand, what is desired is to lessen the angle of flow by which water in the inflow propeller inflow jet If,

jet follows the blades,

described in Sec. 33.12,

then even small slopes on the concave or pressure side of a skeg ending or bossing termination can be most effective. For design purposes

assume

sufficiently precise to

it is

that, as indicated in Fig. 67.S, the direc-

tion of flow at a small distance abaft the traihng edge of a skeg corresponds to the direction of a tangent to or extension of the median line of the

skeg ending at that edge.

A

"small" distance

is

assumed to be from 0.5 to 0.9 times the width of a blade on the propeller. If the aperture clearance is greater than 0.9 times a blade width, the direction of flow expressed

by the

speed-of-

advance vector Ua is assumed to be more nearly a prolongation of the +Ap or concave side of the unsymmetrical skeg ending. Actually, the amount of prerotation to be imparted ahead of the disc by the design being worked out depends upon:

Motu (1) The tangential component of induced velocity which is to be imparted by the blade element at any radius. This in turn is a function of the effective or hydrodynamic angle of attack aj of

Streomlines

that element, the strength of the circulation there,

and the magnitude Maximum

Waterline

(2)

region

Method of Laying Out Skeg Waterline FROM Median Line

abaft

the

ending where

works but a confluence

of

two

flows.

There

the rotation in that region.

effective flow abaft

moves more nearly

some contra-guide

is

the traihng edge of a hydrofoil surrounded by circulation

or whether

feature, such as a contra-rudder, is to be fitted

propeller

side,

ample evidence that the

to be put in

abaft the propeller, to take out the remainder of

the

having the greatest slope to the longitudinal axis, is the predominant one. There is

is

of the disc to give zero resultant rotation

abaft the disc,

It is often necessary to design the

httle reason to believe that the flow over the

convex

induced velocity Ur

Whether enough rotation

ahead Fig. 67. S

of the

far astern.

5lope^^

in the direction

However, the around the whole ship hull in a horizontal plane, due to the sUght asymmetry in question, is surely very small. Whereas the flow abaft a thick airfoil or hydrofoil producing hft is predominantly in the direction of that passing

appendages,

model test, before the propeller design is worked out, so that the values in item (1) may have to be estimated or taken from data on some other design. It is a difficult design problem to achieve the first step listed in item (2). at least for a

may

be said, therefore, that in the present

of the concave or straight side.

It

circulation

state of the art a skeg ending should not be

along the face or indicated by this is

many

+Ap

side of the

foil,

as

is

published flow photographs,

unhkely to be the case here.

If it were,

the prerotation which could be given to a screw-

called

upon

to compensate for lack of a contra-

guide device abaft the propeller. It is not possible without more

extended knowledge of the intricate flow which takes place between a skeg ending and a screw propeher to state definitely the parameters and the relationships which should govern the variation of medianline slope ds with radial distance from the pro-

HYDRODYNAMICS

534 peller axis.

Were

these relationships available

it

be necessary to substitute in them some data assumed for the propeller proposed but not finally selected. It appears sufficient, therefore, to state that the skeg ending slope ds should vary with propeller I'adius at some rate of the less than the geometric blade angle proposed propeller. Table 59. b lists these angles for tenths of blade radii and a rather wide range of P/D ratios. A good working rule, admittedly an engineering compromise without theoretical foundation until the analytic and experimental development is carried further, is to vary the offset termination with propeller radius as The 6s is then left to adjust itself by sin" proper fairing of the skeg ending into the offset

would

still

<j)

(t>.

termination.

and

sin"

A

table listing the variation of

with R, for a

P/D



ratio of 0.98, is

given in Fig. 67. T, described later in this section. Practical considerations, both structural

and

hydrodynamic, usually limit the maximum offset of the trailing edge to somewhat less than the half-diameter of the propeller-bearing boss.

not wise to work too large a hunk of metal into a cast stern frame where the deflected portion inside

of the

Too small a reentrant angle on

the

deflected portion of the skeg or

stern frame encircling the propeller shaft bearing is

not conducive to good flow.

The geometric blade

angle

has an appre-

small

propeller;

it is

about

ratio of 0.6. Similarly, the

velocit}^ kiUr generated at the tip has a but appreciable axial component. Even

when the

sin^ relationship is used, the skegending slope ds is a little more than zero opposite the blade tips. The reason for using the sin^ <^

function



to avoid offsets which are too large

is

opposite the tips; this

brought out more clearly a

is

in Sec. 74.16, in connection with the design of

contra-rudder.

Further,

the propeller blades

if

are already heavily loaded at the tips,

wise to load them further.

On

it is

not

the other hand,

makes the point ["Zur Theorie der fiir Propeller (The Theory of Contra-Vanes Applied to the Propeller)," Ing.

A.

Betz

Leitapparate Archiv,

p.

1938, in

transl.

Vol.

NACA

435-452;

pp.

9,

Memo

Tech.

English

Sep 1939,

909,

is gained by carrying the beyond the propeller radius.

that efficiency

13]

twist to distances far

This means that a skeg ending need not terminate top and bottom with symmetrical waterlines. It is found, in

median

most

cases,

that

when a

fair

and skeg side by the

line is laid out, as in Fig. 67. T,

section lines are

drawn on

either

equal-radii construction shown, there

is

a shght

hollow on the side of the skeg having the smaller curvature. This is arbitrarily filled in to produce fair surface.

By

Stations Fio. 67.T

any

induced

a still

Sec. 67.22

P/D

10.8 deg for a

It

is

joins the boss.

IN SHIP DESIGN ciable value at the tip of

the requirements of Table 64. a, item

ia.75

19

Design of Contra-Guide Skeg Ending for

ABC

Transom-Stern Ship

18.5

(5),

UNDERWATER-HULL DESIGN

Sec. 67.22

the propulsion of the

ABC

vessel

to be effected

is

as economically as the present state of the art

A

permits.

bearing boss to a 1.1

is

therefore indicated for the single-

skeg transom stern. The skeg waterlines above the

and would be easy to work a considerable degree deflection into that structure. However, above

way

occur in

of the inside of the skeg deflector,

another practical limit to which the

shaft are fined to reduce the thrust deduction

there

trailing portion

the shaft axis the aperture clearance

made

is

deliberately

be derived from doubtful. Further, the lower part

large, so that the benefit to

prerotation

is

below the shaft

of the skeg,

any

cut

axis, is

away

so

factors

all

decided

is

ending, assuming this waterline to be genei'ally

especially at the shallow drafts. This

into

consideration,

provide

to

a

therefore,

contra-guide

it

is

skeg

maximum median-line slope at the WL, at about x' = 0.16, to some 8.8 deg, a maximum slope on the convex side of 18

to hold the

deg at the same

is

laid out for the

upper half only of the single skeg of the ABC ship, producing the form shown in Fig. 67. T. This embodies a more nearly vertical profile above the shaft, with less aperture clearance than for the symmetrical skeg ending.

shown body plan of the transom-stern The maximum offset value, at a

radius of the propeller bearing boss

in Fig. 66. P, the

L75

ft.

starting level of x'

—

is

boss radius, or 0.85(L75

ft)

P/D

the blade angle

4>

0.90682. This

R = O.l^Max above taken as 0.85 times the

0.1 or

the propeller-shaft axis,

is

=

1.4875

ft.

Assuming

ratio of 0.98 for the propeller, is 72.225 deg and sin^ a sort of reference value cor-

at O.IK is



responding to the x' = 0.1 offset of 1.4875 ft. For example, at x' = 0.7, <^ is 24.019 deg and sin^

(^

is

0.16569.

Then

(0.16569/0.90682)1.4875 in the table is

admittedly

and checking from actual ship designs known to be successful. Values which are definitely out of bounds can be determined from vessels where separation, vibi'ation, and air leakage are known to exist. For the ABC ship, Fig. 67. T, it is possible

with

a constant

is

a rather indefinite rule which requires amplifying

not

is

under normal circum-

stances not exceed 18 deg or, at the most, 20 deg,

herein, a contra-guide ending

design,

be bent. The slope of any

in the plane of flow, should

ending for the transom-stern afterbody. Nevertheless, as an example of the rules given

The

may

waterline through the offset portion of the skeg

deflection effect

would be lost on the propeller. A contra-shape is to be worked into the fixed rudder horn, above the shaft axis, and there appears to be room for enough shaping of the horn to remove much of the jet rotation. Taking far that

smaller value at 1.0 or

especially in front of the upper propeller blades,

it

of

much

times the propeller radius.

Since no separation, or semblance thereof, must

twisting of the skeg ending to give

a contra effect

535

on

the offset at x' ft

Fig. 67. T.

17.325 deg, sin'



is

(0.08868/0.90682)1.4875

= At

0.2718 x'

=

ft,

1.0,

=

0.7

=

0.1455

The use

level.

contra-guide skeg ending is approached with caution when the waterlines (or flowlines) leading up to the forward edge of the propeller aperture in a skeg have a slope already approaching the limit beyond which separation may be expected at that level, indicated in Sec. 46.2. Superposing the deflector shape upon a symmetrical skeg ending diminishes the waterline slope on one side but greatly increases it on the opposite side. The augmented slope on the outer or convex side, away from the deflection, may easily become greater than the critical slope for separation. of

a

Since the blunter waterlines are generally to be

found above the shaft

axis, it is wise,

the skeg to the region below the shaft boss, the

upper portion symmetrical,

leaving

where

equal waterline slopes on each side.



The slope of the median line bisecting the angle between the terminal portions of the level waterlines on each side of the skeg ending is limited to the order of 0.175. This corresponds to just under 10 deg, as reckoned from the ship centerplane or the construction plane of the skeg. These limits are admittedly rather arbitrary, to comply with the requirements of the paragraph following. The median-line slope varies from this maximum value just beyond the radius of the propeller-

with

In view of the limited pressure, and the low

is

ft.

under these

circumstances, to limit the deflecting portion of

as Hsted

0.08868 and the offset ft

is

12-ft

pressure gradient available on the convex side of a twisted skeg or stern, the

water on that side

not easily changed in direction. This means that a relatively long time, coupled with a

is

relatively long distance, of the order of 0.5 to 1.0

times the propeller diameter, may be required to it any appreciable transverse component

impart to

of velocity

without risking separation.

To

take

care of this situation, the asymmetrical slopes of

the contra-ending are to merge gradually into the symmetrical waterline slopes ahead of them.

HYDRODYNAMICS

536

Generally no part of the median line is straight until it merges into the centerplane or the skeg

may have

construction plane. It

other suitable shape. If

it is

a parabolic or

expected that the

IN SHIP DESIGN

Sec. 67.23

selected propulsion device

that the inflow jet

is

contracts in lateral dimensions and area as

it

approaches the device, normal to the flow direction.

Further, this contraction continues in the

service conditions, run with a

outflow jet for an appreciable distance down-

portion of the contra-guide skeg ending exposed to the air, the terminal median-line slope at the

stream from the device. These axial distances are of the order of at least one diameter in the case of a screw propeUer; of the blade length,

will, in

ship

some

about 3 deg. In

free surface should not exceed

any

case, it is wise to

work gentle

slopes into

any

twisted skeg ending, consistent with achieving the desired prerotation of the inflow jet. If the

measured transversely, in the case of a paddlewheel; and of the "basket" diameter in the case of

a rotating-blade propeller. The contraction pointed out in Sec. 16.3, is a function of

owner and builder are to go to the trouble and expense of twisting such a skeg ending, the twisting can at least be done properly. For twin-skeg endings, assuming outward-

ratio, as

turning propellers, the twisting involves deflection of the lower portions of the skegs in an outward

the outhnes of the inflow and outflow jets for

direction.

This

markedly

expanding

is

inadvisable

tunnel

produces

it

if

sides,

On

specifically

the thrust-load factor Ctl

.

Since the thrust, the

propeUer-disc area, and the speed of advance are

known reasonably

well at this stage of the design

be

can

operation

open-water

by

visualized

reference to Fig. 59. G.

A

second guiding principle

is

that the hull

the other

should produce, in the region selected for the

hand, one way to increase the efficiency of twinthe skeg propulsion is to slow down the water lower after portion of the tunnel. Good design

propulsion device, a flow of water which results

cautioned against in Sec. 67.21.

m

much

expansion in tunnel thought to be consistent with regular flow, to be confirmed by thorough tests in a circulating-water channel with the therefore indicates as

area in this region as

propellers driving.

is

Any

adverse or detrimental

flow conditions pertaining to the twisted skeg

endings will certainly show up

when the

flow

This is specially recommended if the skeg endings have full lines, with large waterUne slopes, and if contra-guide features are incorporated in them. pattern in this region

determined.

is

Indeed, a necessary step in the design of any contra-guide skeg ending, as

it is

for a deflection-

type bossing and a contra-rudder,

is

a flow test

in the

most

efficient

and most uniform loading

of

the blades. For example, the swept volume of a

rotating-blade propeller and a paddlewheel includes the whole thickness of the boundary layer

next to the hull, as portrayed in diagrams

1

and 2

of Fig. 11. C, plus a region of potential flow outside

the blades. This

is

not particularly objectionable,

however, where the mechanism is able to take it. Furthermore, the sum of the overloading forces for all the

immersed blades, as created within the

boundary

layer, remains nearly constant through-

out each revolution of the device. A third principle, really a corollary of the second,

is

that unavoidable local loading of the

blades, one at a time, with the resulting unequal

loading of the whole device,

is

to be reduced to a

when

in a circulating-water channel, using tufts, dye,

minimum. This occurs

or the equivalent, to check freedom from separa-

or the outer portion of a single screw-propeller

tion,

irregular

or

cross

flow,

and any other

Design rules for deflection- type bossings, usually vertical, are

given

blade passes through the region of high wake boundary layer or behind a

zone of separation. progress of the last two

The commendable

decades, in which screw-propeller blade shapes

in Sec. 73.10.

Some

the tip

velocity in a ship

questionable features.

more nearly horizontal than

particularly

notes applying to the incorporation of

have been brought into

close conformity with the

and contra-rudders in auxiliary saiUng yachts and propeller-driven small boats are presented by F. A. Fenger [Rudder, Jan 1954, pp. 76-79].

drawings,

Shaping the Hull Adjacent to Propulsion-Device Positions; Hull, Skeg, and Bossing Endings. One guiding principle in shaping a hull form to produce efficient operation of a

that individual propeller shaft struts had to be

contra-guide

67.23

features

is

at the time of writing (1955) be-

ginning to be matched by general refinements in sternpost, skeg, and bossing terminations at the

forward edges of propeller apertures. The fact as thin as possible specify

made

it

relatively easy to

and to obtain sharp terminations at

traihng edges.

Since

the

advent of

their

cast-steel

UNDERWATER HULL DESIGN

Sec. 67.24

537

German "schncUboote"

sternposts and bossing or spectacle frames the

shafts of the

square and blunt endings of forged-steel stern

speed S-boats of World

frames have largely disappeared. However, the slopes are too steep and the trailing edges of sternpost castings are in general

still

much

too

blunt to eliminate objectionable separation and

eddying behind them. Also there is no more excuse to lap shell plating on the outside of a sternpost than to lap it on the outside of a stem. The effect is different but it is an objectionable discontinuity just the same. The projecting portions of Thermit welds used to join several cast or forged sections of a sternpost— or a stem need not be left for reinforcement. They can and should be trimmed off to conform to the shape of the adjacent parts. Likewise, butt welds can and should have the external reinforcements removed. The slope angles on the trailing edges of skegs and other major parts should be 15 deg or less, reckoned from the known or the predicted direction of water flow. Drawings of these trailing edges should call for smoothnesses and tolerances of the same order as those required on shaft struts. Despite all that is said here and elsewhere about the fining of skeg endings ahead of a screw

—

propeller, experience indicates that

some

delib-

erate thickening of the skeg ending ahead of

its

termination increases the wake fraction at the disc position. It

is

particularly beneficial below

War

affect

aperture clearances,

discussed at length

67.24

Aperture and Tip Clearances for Pro-

pulsion Devices.

the

blades

The

lift

load per unit area on

any moderately loaded

of

unit of wing area on an airplane, rather narrow limits, say 8 to of heaviest loading, say

ment has been

in use for

many

years on motor-

boats and larger vessels, such as on the center

within in".

from 0.5 to

0.95i2, are

quite similar for both narrow and wide blades of

a modern screw propeller. lation patterns

On

this basis the circu-

and the pressure

fields

around

all

screw-propeller blade elements in the given radius

range may be taken as roughly similar, using the expanded-chord length as a reference dimension. Based on these assumptions, the pattern of corresponding streamlines and isobars

is

roughly

proportional in size to the chord length or blade

width. Very approximately, therefore, at least for a not-too-wide

range of thrust loading, a

point in space one blade width from a blade pressure as a point in the

expose the propeller shaft, and support the propeller bearing by a V-strut just ahead of the wheel. This arrange-

lies

13 lb per

Furthermore, the section shapes within the region

element on one propeller

shorten the skeg drastically,

screw

propeller, corresponding to the weight loading per

where the average wake fraction is usually much smaller than above the axis. The greatest thickening can be applied at the bottom, just above the keel, where the upward and aft flow of the water eliminates most of the boundarylayer wake. For this reason the thickening of such a skeg ending is called clubbing. However, the design of a club ending or bulbous skeg, illustrated in Fig. 25.L, is a ticklish procedure. If the thickening is carried too far, it may do more harm in producing vibration than help in improving propulsion [Williams, E. B., Thornton, K. C, Douglas, W. R., and MiedUch, P., SNAME, 1950, p. 78]. No design rules have as yet been formulated for this feature. As a means of reducing the interference from a skeg ahead of a screw propeller the designer

may

Its

in the section following.

the shaft axis in a ijormal form of single-screw stern,

or high-

use undoubtedly diminishes the wake fraction at the propeller but it may diminish the thrust-deduction fraction by a greater amount, and it may reduce the periodic vibratory forces from the propeller. As a rule, the profiles of major hull and skeg endings are not too important except as they II.

is

same same corresponding

subject to the

one blade width distant from a blade element on another propeller. This is an absolute rather than a relative value because, ahead of the position,

propeller at least, the reduced pressure can not

drop below the vapor pressure of water. The foregoing argument may be a reason for specifying propeller-aperture clearances, defined

and indicated in Fig. 33. D as "upper "upper forward," and so on, in the form of absolute dimensions for a certain range of pro-

in Sec. 33.3 aft,"

[ME, 1942, Vol. I, van Lammeren, W. P. A., RPSS,

peller diameters or ship sizes

Table

1, p.

275;

1948, Fig. 73, pp. 127, 278]. It may be a reason even for specifying these edge clearances as functions of the propeller diameter [Ayre, Sir

Amos

L.,

INA,

1951, pp. 145-148]. It appears,

however, that the propeller-aperture clearances are logically a function of the maximum blade

width of the propeller. In general, the aperture clearance ahead of the propeller, at the Q.IR, should be equal to, qv

HYDRODYNAMICS

538

IN SHIP DESIGN

Sec. 67.24

greater than the e.rpanded chord length of the widest

Taking the 4-bladed Wageningen B.4.40

pointed out in Sec. 33.3, and diagrammed in Fig. 33. E, that the clearance abaft the wheel, at the 0.772, may be less than

for example, the note in small print at the right

element or section. It

is

However, it should not be small enough to interfere with the circulation flow around the blade elements, or to bring the trailing edge of the blade through a region of large +Ap ahead of a blunt rudder post or equivalent. A good rule is to make the after edge clearances, both upper and lower, as marked on Fig. 33. D, not less than the maximimi thickness of whatever hull element or fixed or movable appendage may that ahead.

lie

It is well to note that the application of the

knowledge of the the propeller which it

rules given here require prior

maximum

blade width of

to run in the aperture being designed. Also that

most

of the propeller charts

employed to work

out the preliminary design of a wheel, following Sec. 70.6, do not give the ship designer the

blade-width

Table 8 on page 204 of the Dutch book "RePropulsion, and Steering of Ships" [RPSS, 1948] states that the (expanded maximum)

of

sistance,

blade-element length at 0.6/2m«. is 0.2187Z). For the after aperture clearance, specified as not less

than the thickness of the fixed or movable appendage lying abaft

data for

the

optimum

propeller.

He is then required to use the maximum expandedchord width for that series propeller which best meets the needs for the preliminary design.

it,

the designer

rough out these parts;

this

is,

is

required to

in fact, part of the

preliminary stern design.

A

general guide at this point as to the loading

on the individual blades and the aperture ances necessary

abaft the propeller.

series,

Ctl on the

factor

clear-

the value of the thrust-load

is

propeller. If of the order of

1,

may

be somewhat on the low side. If 2 or greater, the clearances must be larger to the clearances

avoid vibration. Fig. 67.

U

is

a diagram which indicates, by the

small circles and the rules set down, aperture clearances which are in general acceptable, for a

screw

propeller

not too

heavily

loaded.

The

contours give the actual clearances worked into the preliminary transom-stern design for the

ABC ship. Rules similar to those for single-screw propeller-

WQterline~-|^

Designed

aperture clearances govern for the edge clearances

Clearance to Nearest Point 'of Hull

Arch

|T,p Submerqence

at the termination of bossings, multiple skegs,

and the

like,

indicated in Fig. 33.B of Sec. 33.3,

with the proviso that this clearance, at any propeller radius, should be not less than the O.ZT) or

C0.7R,

length at 0.7 radius, whichever is qreater

chord

expanded chord length is

difficult,

entirely independent,

weep Line s, Aft and Ford.

for\

0.05 to 0.10 ft

Small Croft

Boseline^ Small Circles

0.E5 to 0.5

Indicate

a

Than Rudder Post Thickness Aboft Propeller

- Not Less

NOTE 2-

If

NOTE 3-

Edge

Leodinq

Rudder Profile

Stern

is

Fine

Shown

ABC

for

Lorqe Vessels

Minimum Normol Clearances

NOTE

ft

or

Rudder

of Rudder Post or and Well-Shaped

is

That

of

Transom-

Hull

Fig. 67.U Elevation of Rudder Horn, Propeller Aperture, and Skeg Ending for ABC Transom Stern

of the blade at that radius.

with present knowledge, to formulate a rule for determining the hull tip clearance of a screw propeller, illustrated in Figs. 33. B and 33. C. In fact, probably no one rule or group of rules could cover all cases to be encountered in ship design. Two features, not It

are involved here.

First,

the propeller blade tip should not be subjected to brief passage through a region of high wake velocity where the

lift

and drag forces on

its

elements are suddenly increased. Second, assuming uniform, non-axial flow, a blade tip should not swing close enough to the hull to cause a sudden large force on the shell plating or an adjacent

appendage due to the pressure field around the blade or beyond the tip. Keeping the blade tips clear of high-wake regions (a)

is

a matter

of:

Boundary-layer thickness, a function prin-

cipally

of

absolute ship speed, of fore-and-aft

UNDERWATER-HULL DESIGN

Sec. 67.24

539

the V-shaped portion of the hull, sometimes

or .T-distance from the stem, of transverse hull

is

curvature, and of hull roughness

rather narrow, lying above the arch of the propeller

(b)

Boundary-layer velocity

profile,

which

is

a

function of hull roughness, transverse curvature,

and other factors. For example, a tip clearance which may be greater than the boundary-layer thickness

5 (delta)

when the

The shape

of hull endings, of

skeg and bossing

terminations, and of objects ahead of the propeller

may

which

(cruiser) type. The volume is small and the obstruction occupies only a small part of the circumference around the tip circle.

whaleboat

An

ship has a clean

bottom, freshly painted, may be much less than 5 when the bottom has been severely roughened by barnacles and other marine growth. (c)

aperture in a single-screw stern of the canoe or

adjacent structure of considerable area,

lying generally in a longitudinal plane passing

through or close to the propeller axis, calls for greater tip clearance even though it is thin. A larger area is exposed to the pressure fields

beyond the

tips as the blades pass by.

The

tip

clearance for such a structure could possibly be

produce near-separation.

as small as O.IZ) or less for a lightly loaded pro-

Keeping the

most intense part beyond the tip involves

hull clear of the

of the blade-pressure field

much more knowledge

of this field

than exists at

present. For a given thrust loading

it

roughly

is

similar

for

all

screw

propellers leads to one of the rules in present use,

which gives the hull

tip clearance as

a function

Ctl of the order of 1.0, yet as large as more for a heavily loaded one, with a

0.2Z) or

Ctl

of the order of 3.0.

An

appears,

however, to be a direct function of the circulation distribution at the tip. The assumption that this distribution

peller,

flat in

adjacent expanse of hull plating, generally shape and more or less normal to the plane

of the propeller disc, calls for

an ample

of the preceding paragraphs.

A

tip clear.33.3 and and com-

ance, following the reasoning of Sec. logical

prehensive rule has not yet been developed for

minimum

of the propeller diameter. Since the thrust loading

calculating a

among

under these conditions. Incidentally, this clearance is measured transversely, in the early stages of a design, between the propeller disc or tip

different

types

of

ships

varies

rather

widely, however, this latter factor can no longer

be neglected.

Furthermore,

the

increased and the pressure field sified

when

is

circulation

is

greatly inten-

the tip swings through a high-wake

portion of the boundary layer. Both the factors mentioned therefore require careful thought and study when establishing hull tip clearances. The shape of the ship sections opposite a screw-propeller position, whether concave and generally concentric with the propeller axis or convex to that axis, is an important feature, although it is not yet known how this effect is related to or combined with that of tip clearance. The volume of the adjacent hull or appendage is at times a controlling factor. Blade tips often pass an appendage or a part of the hull which occupies only a small area and

a small radial distance in the plane of the disc. Examples are the shoe at the bottom of a sternpost to carry a lower rudder bearing or a rope and cable guard on a submarine.

clearance

is

Only mechanical

then necessary, say 0.10 to 0.50

ft,

depending upon the size of the vessel. If the appendage is liable to be bent toward the propeller axis in service, as for the cable guard of the submarine, this clearance may be increased by say twice the dimension of the appendage, measured radially from the propeller axis. Another example

circle

and the

When

it is

or a desirable tip clearance

hull section directly abreast

it.

known whether or not the propeller is to be raked, and when the slope of the adjacent hull surface can be determined, the minimum clearance is measured from the tip circle of the swept volume normal to the hull, as in diagrams 1 and 3 of Fig. 33.B.

The recommended method

for selecting screw-

propeller tip clearance abreast a generally flat

fore-and-aft structure Fig.

45.C

or

is

to determine

from Eq.

(5.viii),

from nominal

first,

the

thickness of the turbulent boundary layer at the a;-distance

position.

from the bow selected

The

sustained speed

is

for the propeller

the one used for

this estimate because it gives the greatest value 5. The boundary-layer thickness thus derived only a rough approximation for large values of X, but it is at least an approximation. It is also estimated, from the turbulent-flow

of

is

velocity profiles of Fig. 5.K, that the friction-wake velocities in the outer half-thickness of the

bound-

than about 0.1 the ship velocity V. At the same time it is known that the boundarylayer thickness is increased by fouhng of the hull surface, as in Fig. 22.H. It seems wise, therefore, ary layer are

to

fix

less

the hull tip clearance at a value at least as

HYDRODYNAMICS

540

IN SHIP DESIGN

thickness

draft

5 (delta).

ABC

For the

transom-stern

estimated x-distance of 489

and 0.75

Fig. 45.1,

1.96

is

ft.

ft,

design,

2.8 ft

5 is

From

Fig. 66.Q the

tip clearance at the top of the wheel,

at indirectly,

2.62

is

ft.

an from

at

arrived

This should take care of

a certain amount of thickening of the boundary layer under the stern due to fouling, for which there are no rules at present (1955). Since so

little is

known concerning

the effect of

Sec. 67.25

For certain vessels whose

great as 0.7 times the noininal boundary-layer

is

maximum

or extreme

appreciably less than the channel or

river depths

where they are to operate, the base-

plane clearance

may

be negative. The propeller

then extends below the baseplane for a distance limited only by the height of the blocks when the vessel is drydocked or hauled out. disc

Only rarely should is

a

this exceed 4

ft;

probably 5

ft

maximum.

When

propellers

mounted abreast each

are

other or nearly so their disc clearances may,

if

hull shape

necessary, be reduced to mechanical values only,

ness 5, at the proposed propeller position (s), extending from a point inboard as close to the hull as may

say O.OoD, regardless of the direction of their relative rotation. Indeed, the large 19.5-ft twin

be experimentally practicable, to a region outboard, at least O.IR beyond the far side of the

Majestic, built in 1889,

propeller disc(s).

Ferry,"

and curvature on this nominal thickwake measurements are made on a model

The nominal boundary-layer the short model

is

thickness

S

on

greater in proportion to the

screws of the old Atlantic liners Teutonic and

ance of 5.5

propellers," 1900, pp. 64-65]. disc

6.8 and illustrated in compensated for by the inevitable thickening of the ship boundary layer when the hull surface is roughened by fouhng. The propeller tip circle should, if practicable, be kept outside the boundary-layer region on the model where the wake fraction is 0.25 or more, reckoned

disc

described in Sec.

ship,

Fig. 6.E. This

preferably

is

by

the

pitot-tube

survey

method

and edge clearances are both involved, as for the wing propeller of a twin-screw vessel with long bossings, and where vibration is to be minimized, the combination of theory, model

Where

tip

negative disc clearJ.,

"The

Atlantic

The port

propeller

was placed 6.25 ft ahead of the starboard and the tips of each wheel swung beyond the

centerplane, to the opposite side of the vessel,

through a large aperture in the centerHne skeg. Contemporaneous accounts of the behavior of these passenger liners, at that time the largest on the Atlantic, make no mention of vibration or other disturbances caused by these overlapping propellers, possibly because of their large diameter

and

illustrated in Sec. 60.6.

had a

[Maginnis, A.

London, 1892, pp. 186-187; Cassier's Mag., Jan 1897, p. 231; Barnaby, S. W., "Marine

than the nominal thickness on the

scale ratio

ft

relatively light thrust loading.

When

adjacent propellers are offset by appre-

ciable fore-and-aft distances,

as on quadruple-

screw vessels of normal form, great care in establisliing the disc

is

required

clearance between the

indicate that fore-and-aft

outboard and inboard wheels, reckoned by the

edge clearance is more important than transverse tip clearance. In other words, it is better to move the propeller aft and to cut away the bossing

projection of their discs on a transverse plane.

tests,

and experience

all

termination as far as possible, than to move the away from the hull [Tomalin,

propeller outward,

P. G.,

SNAME,

Propeller-Disc

Clear-

clearance for a screw determined by the service operating conditions, by considerations of drydocking, and possibly by the fact that the ship may rest on

ances.

The baseplane

propeller

is

the bottom at certain wharves out, as in the

Thames

general direction of flow in

it is necessary to sketch in the probable boundaries of the inflow and outflow jets of each propeller, doing this on a plane passing approximately through the propeller shaft axes and

when

the tide

is

at London. For a propeller

normal to the hull plating in the

is

and inflow by angular between the flow direction and the

not

modified

appreciably

to follow the general ship flow.

p. 279].

Lammeren, W.

P. A.,

RPSS,

ft

on

1948,

On

direction of flow through the outflow jets

mum

on small vessels to 0.5 or 0.7

vicinity.

the principle that, at designed speed, the general

differences

large ones [van

of these

preferably in a circulating-water channel. Follow-

unprotected by a shoe, say on a twin-screw craft, the baseplane clearance may vary from a miniof 0.2 ft

way

approximated by analytic methods or determined by flow tests on a model, offset propellers is first

ing this,

1953, p. 592].

Baseplane and

67.25

The

shaft axes, the propeller jets should be resketched

They do not, in AVhen so modified the forward propeUer theoret-

general, follow the shaft axes.

the outflow jet of

UNDERWATER-HULL DESIGN

Sec. 67.27

be clear of the disc of the after

ically should

propeller.

This means that

the general ship

if

flow runs parallel to the ship centerline there can

be nominal overlap small

of the propeller discs,

negative disc

with a

because of the

clearance,

contraction in the outflow jet of the forward propeller. In the

Omaha

cla,ss

of quadruple-screw

cruisers of the U. S. Navy, designed in about 1919, there was negative disc clearance of this kind but the vessels ran successfully for many years without vibration troubles. Similar difficulties reported on other quadruple-screw vessels with offset wing propellers having positive disc clearances are beUeved due to excessive light

elasticity of the thrust-bearing foundations within

the ship.

541

Numerical values or

ratios are not available

minimum

for estimating the proper or

mergence as functions

and

of (a)

tip sub-

(b). It is

known

only that the greater the thrust loading, the greater the advance ratio, and the greater the circulation near the blade tips, the greater

the

is

— Ap on the back of the blade tips and the thicker must be the superposed water layer to prevent Regions of high wake velocity air leakage. close to the water surface augment (a), (b), and (c) locally and call for good shielding. If

the hull shape

is

such as effectively to shield

the propeller from air leakage, say in the form of

a wide transom stern over a single wheel, the nominal tip submergence can be small, approaching zero. In fact, under the tunnel stern on a

When a vessel with offset propellers turns with a drift angle, the propeller outflow jets change shape, rather drastically if the turn is a tight one.

shallow-draft

Undoubtedly in these cases the outflow jet forward or wing propeller on the outside

of the

low- and medium-powered ships having propellers

of the

of adequate diameter, the increase in water depth due to the wave crest which forms at the stern when running at designed speed is usually

turn passes through the disc propeller.

Two

propellers on the

the inboard

of

same

side of the

the

vessel

For the thrust loadings and advance

ship can almost never be given sufficient disc

sufficient to shield the wheel.

clearances to avoid this interference.

ditions, the

Adequate Propeller-Tip Submergence. As a general rule the greater the tip submergence

be small.

67.26

the better, until

it

reaches a value equal approxi-

mately to the propeller radius R. This is the minimum tip submergence used for open-water propeller tests in model basins. There

standard or is

no need

eliminate

increasing

of

reduce

or

it

further unless to or

cavitation,

to

insure

adequate submergence when the ship is pitching heavily during wavegoing. The tip submergence required for any load or operating 33. C,

condition,

and 33.D,

is

indicated

in

Figs.

33. B,

a function of the:

(a) Thrust-load factor at which the propeller is intended to work. The greater the value of Ctl the greater the submergence needs to be. ,

(b)

Advance

(c)

Radial distribution of circulation along the

ratio or slip ratio, related to (a)

propeller blade, particularly near the tip. Large

— Ap

values near the tip

call for

a water layer of

appreciable thickness over the propeller. (d)

Amount

of shielding

from

air leakage

which

When

nominal

tip

upper blade ing

by the

tips

become extremely

decreased)

the propeller position.

nominal

tip

sub-

crest (or trough) over

may

also

large. Shield-

only effective

preventive against air leakage.

The degree

of

submergence

expected during wavegoing sequently in Part 6 of

—or

is

Volume

emergence

considered sub-

III, together

with

on propeller performance. 67.27 Design for Minimum Thrust Deduction. The manner in which a thrust-deduction force is exerted on a hull, either inside the limits of the inflow jet ahead of the propeller or inside those its effect

of the outflow jet astern of

it,

leads to the con-

clusion that the transverse projected areas within

these jet limits should be a

minimum. This

is

accomplished for a skeg carrying a screw propeller

by keeping the skeg

as thin as possible for at

ahead of the wheel, within the limits of an imaginary cyUndrical surface projected from the screw disc along the propeller axis, described previously in Sec. 33.2 and least 2 diameters

a wing propeller

(or

on

Under these con-

submergence

hull, as in tugs, is the

illustrated in Fig. 33.A.

Increased

ratios

maneuvering rapidly, such as during

attitude of the ship (e)

is

crash-backs, the pressure differentials around the

can be expected from the hull at the running

mergence due to a wave

submergence

tip

definitely negative.

is

A

large bossing carrying

likewise as thin as possible

consistent with stiffness as a shaft support.

For

a tunnel within which a screw propeller is mounted the roof of the tunnel is not to drop too sharply

HYDRODYNAMICS

542 in the

2-diameter regions just ahead of and just

abaft the disc. Fig. GT.RI indicates that this condition

A

is

not met in the

ABC

arch-stern design.

single-screw stern having an exceptionally

thin skeg, with the after part cut entirely away,

leaving the propeller supported by a projecting is illustrated and described by H. Waas [STG, 1952, Fig. 9, p. 209, and Fig. 18, p. 214]. If found practicable in any particular case this is one way to reduce thrust-deduction and lateral

stern tube,

IN SHIP DESIGN deduction

fraction

Sec. 67.28 is

negative.

however, to rely upon this unless

by a model

It

unwise,

is

it is

confirmed

test.

The reduced-pressure

field ahead of a sternwheel extends forward of the point of immersion of the foremost blade for a distance estimated as twice the maximum depth of blade immersion,

or dip, as

it is called.

For

this

and other reasons,

set forth in Sec. 72.11, the buttock endings of a

sternwheel vessel are given an easy slope, and

vibratory forces at the same time. If the after

possibly reverse curvature, below the level of the

end of the stern tube needs support, it can be provided by a V-shaped strut assembly. Paddlewheels mounted abreast parallel water-

wave profile at designed speed. The first approximation of the resistance augment to be expected at the designed speed is found by the transverse-area method, described in Sec. 60.9. The method of performing this

lines or in

way

of the

maximum

waterline

beam

are admirably placed for eliminating practically all

resistance-augment forces. In

fact, it is quite

with a pair of paddlewheels amidships, for the —Ap field to extend forward into the possible,

entrance and the

The

+Ap

field

differential pressures

forces

in

Station

back into the run.

then generate thrust

the ahead direction and the thrust-

operation for the transom-stern

ABC

design

is

illustrated in Fig. G7.V.

67.28 all

The

When

Final Section-Area Curve.

principal parts of the underwater hull, ex-

cluding the appendages, are worked out ciently

to indicate the distribution of

suffi-

volume

UNDERWATER-HULL DESIGN

Sec. 67.29

throughout the ship length, a revised section-area curve is drawn. The areas are determined for at least 20 sections, the A /Ax values calculated, and a fair curve passed through the 21 ordinates. A bulb bow calls for fairing to a designated /c value at the FP; a transom stern to an /« value at the AP.

A discontinuity of sorts is to be expected

opposite a skeg ending, especially at the forward

end

of a propeller aperture.

for the

are

ABC

drawn

ship, covering

The final ^-curves both types of stern,

in Fig. 67. W.

Except for the regions known to be discontinuous the eye should detect no unevenness in the curve, nor should it appear when using a batten. However, the eye is often deceived by the presence of other lines in the vicinity, even those in

Hence the 0-diml and preferably 40 stations along its length is determined by one or more of the methods described in Chap. 49 and is plotted to the same base as the section-area the

coordinate

network.

curvature for at least 20

X shows a 0-diml curvature plot A-curve of Fig. 67.W for the ABC design with the transom type of stern, as well as similar plots for the Taylor Standard Series model, EMB 632 (modified), and for a merchant ship of good performance. Integrating the section-area curve, by whatever procedure may be appropriate [PNA, 1939, Vol. I, curve. Fig. 67. of the

pp. 13-27], gives: (a)

By

its fullness coefficient,

prismatic coefficient

Cp

.

should be within 0.01 or

the corresponding

For the

less of

ABC

ship this

the selected value

of 0.62. (b) The molded underwater volume, without appendages, up to the designed waterfine. This

ABC ship displacement weight of 16,400 t for standard salt water (c) An accurate determination of LCB, with respect to the FP, for reference and comparison should correspond to the

.

purposes.

This revised A-curve

may

final if the analysis brings

features or irregularities in

and and

V

be considered as

out no objectionable it, if

the values of Cp

are reasonably close to those selected,

if final

indicates

fairing of the lines to a large scale

no appreciable changes

in the

amount

or distribution of volume.

67.29 Modification of Normal Design Procedure for a Hull with Keel Drag. It often

becomes necessary, coefficient, rotative

for reasons of propulsive speed of the propelling plant,

o

543

5444

UNDERWATER-HULL DESIGN

Sec. 61.3]

propeller, or other causes.

On

the other hand

it

may

be worse because of increased drag due to separation behind fuller waterlines at the stern. the keel drag

If

may

easily

is

limited to small

become more

amounts

it

of a nuisance in laying

out or building the ship than a help in performance.

its

service

true

if

the gas-producing portion of the propelling

machinery can be placed if

the draft aft

On

is

close to the stern,

reasonably constant.

is

provided in the form of a

slender stack, to care for lighting

off,

tall

port opera-

may

be assumed that the duct area required for underwater exhaust need be no greater than that for vertical exhaust at full it

20

sides

is

forward on either

ft

depth of 2

— Ap

ample to provide the necessary outlet

may

pressure

high velocity of the combustion gases in the ducts leading to the underwater stern outlet. insure that the gases are discharged into

the separation zone deliberately formed abaft the stern, within the variations in draft which will

occur there, a high-level as well as a low-level is

required.

Both may be connected

to the gas discharge lines which should enter the high-level outlet box from the top, to prevent

entry of sea water back into the gas

line. Escape from the high-level outlet when running at the shallower draft at the stern is prevented by a combined gravity- and buoyancy-operated flap valve which closes when it is above the waterline but opens when it is submerged. On the basis of limiting slopes of 15 deg for separation at the light- and deep-draft waterlines of a vessel of about the size of the ABC ship but having a canoe stern, the separation zone is

of gas

area.

of the order of

be slightly negative, due to the

experiments

full-scale

are

model and

necessary

to

verify

this point.

When underway in smooth water the stern-wave may rise above the at-rest designed water-

crest

Une by an amount estimated as from 2.5 ft to 4.0 ft, depending upon the stern shape and other

may

circumstances. It

be necessary to provide

several levels in the outlet boxes so that one

may

condition.

When

the ship

pitching in waves so that the

is

mean

selected underwater gas outlet for the

alternately

is

submerged and exposed,

it

draft

may

be

necessary to lock the flap valves closed in the outlet boxes

and to

resort to vertical stack-gas

discharge.

67.31

condensation of steam in the exhaust gases or the use of stack-gas coohng as a margin against too

gas outlet

is

in the separation zone. Further

power. This takes no account of the possible

To

side.

ft for

The estimated back

post or

low-speed running, maneuvering, and emer-

gencies,

to points at

Assuming a each outlet screen, one-third of the length of the separation zone on the two least

be selected which best suits any given operating

the basis that an alternative vertical gas

outlet

tion,

and

AP

estimated to extend from the

zero, or it

Underwater Exhaust for Propelling Machinery. A passenger-carrying vessel having propelling machinery that produces gaseous products of combustion and that is intended to run at all times with the propeller(s) fully submerged offers a favorable opportunity for installation of underwater gas exhaust. This is especially 67.30

545

General

Notes

Applied to Hull Design.

on Water Flow as At the risk of boring

the reader with duplication

it

can not be too

recommended that the flow pattern and the wake diagram at the positions proposed for any type of propulsion device be adequately investigated and recorded on a model by chemical or physical means, by strings or tufts, and by strongly

spherical-ended pitot tube. These data should be

when

finally fixing the form appendages adjacent to the propeller positions and when establishing the

given great weight of the ship

and

its

propeller clearances. It

may

be taken as an axiom, in the detail

design of the underwater hulls of ships and their

appendages, that separation and cavitation and all

other

forms of discontinuity in a liquid,

whenever and wherever occurring, are detrimental to good performance. As such they are to be carefully and systematically minimized or avoided altogether.

CHAPTER

68

Layout of the Abovewater Form 68

1

General Design Features, Exclusive of Wavegoing

68.2 68 3 68 4 68.5

Reserve-Buoyancy Requirements Freeboard and Sheer for Protected Waters Freeboard and Sheer for General Service Design of Abovewater Section Shapes;

68.6

Tumble Home; Compound Flare .... Check of Range of StabiUty and Dynamic

.

.

.

.

.

Metacentric Stability

68.7 68 8 68.9 68.10 68.11

Abovewater Selection of

.

Profile and Deck Deck Camber

Bulwarks and Breakwaters Design of Anchor Recesses Proposed Under-the-Bottom

Details

.

Anchor

.

.

stallation for Ships with Bulb Bows Knuckles and Other Longitudinal Discon.

.

.

546 546 547 547

68.12

68 14

Transverse Discontinuities Shaping and Positioning of Superstructure

551

68.15

Design of

68 16

and Gas Discharge Reducing the Wind Drag and Rigging

68.17

Consideration of Increased Draft Through

68.18

Preparation of Hull Lines for Model Tests

tinuities

68 13 .

.

and Upper Works

553 553 553 554 556

.

558 560 561 561

Abovewater Smoke

Facilities for

563 of the Masts, Spars,

566

the Years .

566 566

In-

68.1 General Design Features, Exclusive of Wavegoing. Were it not for wavegoing requirements the abovewater portions of a ship down to the ship-wave profile at designed speed could be given a strictly utilitarian shape. This shape might even be found adequate to meet damagecontrol and floodability requirements. Actually it is done with many ferryboats, day-service pas-

is

senger vessels for inland waters, river and harbor

distance above the heeled waterplane. This takes

craft, and canal boats. Since the abovewater shape of the average seagoing vessel is so intimately related to wavegoing, a considerable part

accompanying a

of the discussion pertaining to it is found in Part 6 of Volume III. The design rules in this chapter therefore apply principally to ships of

when trimmed,

aU types operating

by the general

to

plus a rise of the forward and aft in the form of

For the heeling and change-of-trim conditions be expected in service, assuming that the

situations represented static,

by them

are essentially

a certain margin of buoyancy or freeboard

necessary, particularly in the form of a limiting

care,

among

other things, of the overshoot action

incidental waves.

relatively

sudden

list,

The margin may take

of a corresponding distance

or

of

the form

above the waterplane

to give protection against the

water in the crests of waves made by the ship's own motion or by passing vessels. Certain types of craft acquire temporary and unexpected lists,

service

Kke the heel

Reserve-Buoyancy Requirements. Reserve buoyancy in the form of intact or waterti^it volume of the main hull above the designed waterplane, a rather important feature of submersible and submarine vessels, is rarely set 68.2

is

of a tug

when a heavy

towline tension

exerted transversely or the heel of a small

day-service passenger vessel

when a

passengers crowd suddenly to one All craft

rail

great

many

or the other.

may at times be subject to unsymmetrical may have to run at the corresponding

loading and

down

as a design item for a surface ship. It is not to be found in the requirements of Chap. 64

ABC

mentioned,

line

sheer.

every vessel.

for the

just

weather-deck

in protected waters, as well

as to those features covered of

freeboard,

lists

or trims for uncomfortably long periods.

The reserve-buoyancy volume

could well be

appears partly as the customary specification for minimum freeboard to

reckoned, not from the designed waterplane with

some

profile

ship. It

specified deck,

when the

designed to remain afloat with one, two, or three compartship

ments flooded. It also appears as a requirement for an adequate range of transverse metacentric although rarely stated in so many words. Wavegoing requirements are not forgotten but they generally take the form of a minimum stabiUty,

the vessel at rest,

is

when the

but from the actual wave is running at its designed

ship

volume and the reserve-buoyancy volume of a small, fast tug have an appreciably different shape in speed. For example, both the buoyant

way

of the surface when the tug is running free than when it is pulling and standing almost still. It can be argued that a vessel will never be

546

ABOVEWATER-FORM LAYOUT

Sec. 68.4

running at its

designed speed

its

reserve buoyancy.

when

The answer

it

needs

to this

is

all

that

regardless of that

one never knows what a ship may have to do during its lifetime, nor what kind of rough handling and severe treatment it may receive

ancy requirements.

when

position

trying to do

A

its best.

and practical

logical

mentng that

specification,

supple-

and range

of trans-

verse metacentric stability, calls for a

minimum

of floodability

reserve-buoyancy volume, expressed as a percentage of the displacement volume below the designed waterplane. A minimum of 25 per cent for a

a reasonable and not particularly exacting requirement. Reserve-buoyancy ratios for a number of submarines, of the vintage of

new

vessel

is

by E. Dodero [Ann. Rep., Rome Model Basin, 1941, Vol. X, pp. 95-107]. These vary from 0.112 through through

1901

are given

1918,

The watertight closures by no means as secure as

0.467, averaging 0.252. of a surface ship are

are those of a submarine, so these values represent

some

sort of

vessel.

more

minimum

For the

is

latter,

maximum

of 0.35

or

not too much. This, with freeboard and

other requirements, should insure that hatches

and other vulnerable

hull openings are reasonably

out of reach of the destructive action of solid, green water [Goodall, F. C, "Whaleback Steamers," INA, 1892, pp. 192-193]. Even though the hull may be extended farther

upward than reserve-buoyancy requirements demand, such as the deck of a ferryboat which must match the top of a landing platform at various stages of the tide,

it

may

not be necessary

to build an intact or watertight hull

One item taken

all

the

way up.

care of in floodability calcula-

on small vessels for which these calculations are not made is the matter of the fore-and-aft position of the reserve buoyancy. If a craft is bilged and flooded aft it does little good to have a great volume of reserve buoyancy forward. On many fishing vessels, especially tuna clippers, the freeboard aft is deliberately low to facilitate getting fish in over the side. It has to tions but often overlooked

be recognized that the safety of these craft is equally jeopardized by the absence of adequate reserve buoyancy there [Hanson, H. C, "The Tuna Clipper of the Pacific," SNAME, Spring Meet'g., 1954, p. 68.3

Waters.

6].

Freeboard

Any

craft

and Sheer for Protected which produces bow and

wave crests of appreciable height when underway in protected waters, such as a freestern

its lifetime

the

bow

embodied

to operate

called

upon during heavily by

when trimmed

or the stern

and shape

in the reserve-buoy-

may be

If it

it

needs

still

of the sheer line

to the designed waterline

by the

more.

The

with reference

then controlled largely

is

and reserve-buoyancy

wave-profile, trim,

requirements.

The

craft

may have

a curved sheer line, as may have a straight

for a seagoing vessel, or it

weather-deck line exceeds optical

if

the freeboard everywhere

minimum. However, there illusion involved in looking at any the

with a straight deck line throughout which makes it appear that the hull slightly. is

When

appearance

desirable to incorporate

is

is

an

vessel

its

length

is

hogged

a consideration,

some curvature

it

in the

deck or hull line at the side, with the bow normally higher than the stern and the stern higher than some position near or slightly abaft amidships.

for the average surface

a

547

running tug, needs a certain amount of freeboard

reasons for straight deck throughout a considerable part of the length, possible to retain the sheered appearance by

If there are practical

lines it is

adding sheer only at the bow, or in the forebody. By the clever and artistic use of curved bulwark

combined with the slight depression in the deck edge at the side due to camber, or even of curved painted lines on the hull, it is possible to avoid entirely the appearance of hogging while holding a perfectly straight deck line at the

lines,

centerplane.

was generally found best for appearance' sake to the lowest point of the freeboard about one-fifth to one-seventh of the ship's length abaft amidships; and to "It

fLx

give rather quicker curvature aft so as to prevent the tangent to the sheer line falling below the horizontal when the ship had the maximum trim by the stern" [Narbeth, J.

H.,

INA,

1942, pp. 144-145].

68.4 Freeboard and Sheer for General Service. Concerning freeboard requirements for general service, it may be well at this point to review the object of freeboard, and its functions. These were well expressed some seventy years ago in

the following terms: "Perhaps the most important of these are: to limit the ship's load; to provide a reserve of buoyancy, both as a margin against leakage and as lifting power in a sea way; to assist in securing a sufficient range of stabiUty; and to

to provide a suitable height of working platform,

protect the vessel from deck

INA,

1883, Vol. 24, p. 205].

damage" [West, H. H.,

HYDRODYNAMICS

548 It

is

buoyancy

minimum

in Sec. 68.2, that a certain

IN SHIP DESIGN

Sec. 6S.4

Volume III, is the bow rather

design for wavegoing in Part 6 of

mentioned, in the discussion of reserve

therefore usually measured at

centric stability, floodability

than amidships, although the freeboard for good wavegoing is sometimes reckoned at 0.3 the length from the FP, or at 0.1 that length. The latter procedure is based upon the reasoning that the most objectionable water comes over the side at

rolling

those positions.

freeboard of the intact hull amidships, the lowest point of the sheer

line, is

or at

more often

than not regulated by law. This takes into account considerations of the range of transverse meta-

and damage control, and righting energy, classification and insurance rules, and the like, which need not be gone into here. All these and other features are discussed by H. F. Norton in Chapter II and by J. F. Macmillan and J. P. Comstock in Chapter V of PNA, 1939, Vol. I. Normally the minimum freeboard based upon the considerations set forth therein is sufficient to meet the wavegoing requirements for the service of any particular ship. However, the freeboard may be and often is determined by the difference between the hullgirder depth D necessary for strength and rigidity, and the draft H. This is the basis for selection of the freeboard of the

ABC

Fig.

To

dimensional,

and generally

wave length

if

position

T1

n^rr

I

I

In other words, short

decreases.

is

tentative. In general, the ships

still

those below the line are definitely lacking in

the

freeboard forward.

The minimum

freeboard forward (and aft)

is

by a combination of minimum freeboard amidships and a sheer height forward also determined

board for wavegoing, discussed more fully under

50

is

average

with ratios above the line have proved to be good-to-excellent sea boats in service. Many of

is

l"iT'1\

the

craft like a fishing boat the ratio of freeboard forward to length must be large while for a large liner this ratio can be diminished considerably. The heavy curved line of the figure is intended to indicate this relationship. It is broken because its

not to be inundated when pitching at sea. As a rule, the lower the minimum freeboard the higher must be the sheer forward. The freevessel

that

waves are steeper than long waves. For a short

ship amidships, ex-

also at the stern,

the reason

for

steepness ratio of natural waves increases as the

must be added sheer

this freeboard there

a diagram for selecting a value of

is

preliminary-design stage. Its scale of abscissas

plained in Sec. 66.30. at the bow,

68.A

the freeboard at the forward perpendicular in the

III

I

I

II

l|

I

I

I I

250

200

150

III

I

I

II

300 meters I

I

Waterlme

Leriolh,

0.09-

Spot for

ABC Ship 0.08-

\

\\

o

0.07-

-^. '0.06

0.06-

T'

0.05-

-0.05

004-^

004

llllllll

100

2^00

300

400

500

600

Woterline Fig. CS.A

700

Length

Tentative Freeboard Ratio

j'or

in

600

SCO

1000

feet

Ships Traversing the

Open Sea

1100

1200

ABOVEWATER-FORM LAYOUT

Sec. 6S.4

TABLE

68.a

Sheer Heights

Source and Reference

in Fractions op

Wateblinb Length

549

HYDRODYNAMICS

550 Fig. 68. C,

apply to types of vessels in the following

are in the

services: (1)

Low- and intermediate-speed merchant

types,

low point of sheer at or close to amidships, 0.50L from FP, sheer at stern about 0.5 of sheer at bow. In average heavy- weather areas the wave speeds are greater than the speeds of these slow vessels. For a considerable part of their running time they are being overtaken by seas, hence the need for rather large sheer at the stern. (2)

Medium-speed passenger and cargo ships and

intermediate

low point

liners,

of sheer at

about

0.575 to 0.625L, sheer at stern about 0.33 of sheer at bow. These vessels, running at speeds

higher than those in their

(1)

preceding, spend less of

time being overtaken by following seas.

Furthermore, they often have more than the

minimum

freeboard in order to have internal

space for accommodations. However, at the higher speeds, they pitch

With

IN SHIP DESIGN

more than the slower

same category

Most

of the tankers

as the intermediate-

speed merchant cargo types, running for a large percentage of the time in overtaking seas. However, at these speeds they require

more sheer

aft

than the cargo vessels because their average is less. The trawlers and fishing vessels heave to or creep along at slow speeds on all courses and in all weathers so that they are overtaken by waves to about the same degree as other ships encounter them. (5) Tug and similar types, lowest point of deck profile at about 0.65 to 0.8L, sheer at stern about 0.4 of sheer at bow. Ocean-going tugs may require from 1.5 to 2.0 times as much sheer forward as harbor tugs. To prevent the excessive heels mentioned in Sec. 68.2 it is necessary that the towing bitts of tugs be kept close to the water. This means that the low point of the profile is well aft, in the vicinity of the bitts, and that the

freeboard

vessels.

their finer entrances the pitching axis

Sec. 68.4

ships, parallel to the baseline.

sheer aft

is

is

of safety

the

minimum

permissible

which have been proved

by standards in

everyday

farther aft. (3) Large medium- and high-speed liners, low point of sheer at about 0.65 to 0.75Z/, sheer at stern about 0.2 of sheer at bow. To obtain internal volume and superior wavegoing performance the freeboard is usually exceptionally high. This means that the pitching depth at the stem and at the stern are adequate without using great sheer. The latter may, in fact, be governed more by appearance than by wavegoing, or by the necessity for rapid shedding of the water that may come

aboard. (4)

Tankers, trawlers, fishing vessels, and other

low-freeboard craft, low point of sheer at from 0.5 to 0.65L, sheer at stern

bow.

An

about 0.7

of sheer at

alternative straight-element profile for

is indicated in broken lines. There are incUned straight lines at the bow and stern and about half a ship length of straight sheer amid-

tankers

Fig. 68. B

service.

For

sailing yachts the

line is usually

much

low point

of the sheer

farther aft than for

any other

type. It can be as far aft as 0.75 times the overall

length from the bow. All the sheer curves in Fig. 68. C are arcs of

second-order parabolas, x^ directed keelward for

-|-

=

—az, where

z

is

values. Their axes are

and their vertexes are at the low points by circles. The forward and after arcs belong to different parabolas but they can belong to the same one if the low-point position and the forward and after sheers correspond. New sheer lines are easily drawn by taking constant percentages of the ordinates shown in the figure, as

vertical

indicated

illustrated for the sheer fine of the If

ABC

design.

construction costs are a factor, any part or

of the sheer line

Typical O-Duil Freeboard Ratios for a

may

all

be straight, as shown in

Whale Catcher

Sec. 68.5

HYDRODYNAMICS Oranje of 1939 [Prius, H. N., and

liner

Ijssel-

muiden, A. H., De Ingenieur, The Hague, Holland, 23 Jun 1939, p. 50; 30 Jun 1939, p. 74; WRH, 15 Oct 1939, pp. 316-323; Transl. 128, Nov 1939]. The tumble home amidships is 8.75 ft in a height of about four decks above the DWL, for a waterline beam of 83.5 ft. This is so extreme that the lifeboats can not be launched clear of the

TMB

ship's side.

Tumble home

not called for by the particular

is

ABC

requirements of the

ship. It

is

incorporated,

however, in the body plans of Figs. 66. P and 67. L, in an effort to provide parallel sides and constant

beam

in that portion of the ship set aside for

passenger accommodations. Laying out, building, and equipping staterooms and similar rooms is greatly simpUfied

if

the region has parallel straight

and no deck camber, corresponding to a building on shore [Watsuji, H., SBSR, 2 Aug 1934, p. 118].

sides, practically zero sheer,

Tumble home confined

abovewater

the

to

usually, but not necessarily

is

extended below the reduction in C/r

,

DWL

list

may

be

in order to achieve a

some respect, or when the vessel is

[SNAME,

It

to modify the rolUng charac-

teristics in

sHght

hull.

to take care of a in light condition

1905, PI. 119].

It is often desired,

for wavegoing,

to incor-

porate flare in the abovewater sections forward for a considerable distance above the DWL. To

avoid the excessive top weights and volumes involved by carrying that flare all the way to the weather deck, a compound-flare section of the type sketched at E in Fig. 26. B is useful.

Compound

flare built into

the bows of British

cruisers for the past forty years has proved its worth in service. More recently it has been worked into the cargo vessels of the British Windsor class, both forward and aft [MESR,

Jul 1952, pp. 89-90]. It is often of advantage, with no appreciable impairment of wavegoing behavior, to widen the deck below the weather deck so as to get more useful room there. This is because internal space lying above a ship's side with excessive flare is difficult to utihze.

The flare

following

method

IN SHIP DESIGN

way, in

working a compound is adapted

from that employed by the Naval Construction Department of the British Admiralty and is pubhshed with the kind permission of the Director of Naval Construction, Sir Victor G. Shepheard:

The shape and

at the side

is

position of the weather deck

determined from operational and

three planes.

The

in the

6S.5

usual

section lines forward

though there were to be no compound flare. (b) A fair knuckle Une is then drawn on the outboard profile (sheer drawing) in the position desired for the lower edge of the diminished-flare region. Its vertical position, shape, and curvature depend upon the position of the internal decks below the weather deck, the anchor-stowage positions selected, and other factors. The line of the knuckle runs more-or-less parallel to the weather deck, or at a slope to it, either up aft or down aft, depending partly on appearance and the aesthetic sense of the designer. (c) At two selected stations, about 1/3 and 2/3 the length of the knuckle from the bow, two

level lines are

drawn on the body

plan, represent-

ing the height of the knuckle line at those stations, as taken from the outboard profile

Two

(d)

partial-section lines are projected

down

on the body plan from the weather deck edge, at the stations in question, to the knuckle level lines at those stations, giving the knuckle halfbreadths. A suitable flare slope above the knuckle is about 80 deg (with reference to the horizontal). It is not necessary that the flare slope be constant for all stations; appearance and room inside the ship may determine this. (e) Laying out the knuckle half-breadths at the two selected stations, and the fore-and-aft position

of the

knuckle line at the stem, a

drawn on the half-breadth breadths of the knuckle at

fair line is

plan, giving the halfall

stations along its

length (f) Level lines for the remaining stations are then added to the body plan, whereupon the knuckle half-breadths for these stations are laid

off

on them

(g)

With the

points thus determined the knuckle

completed on the body plan, and the straight section-line segments above the knuckle are drawn in between the weather deck and the knuckle line projection is

are

The now

original section lines

below the knuckle meet the

flared out in easy curves to

knuckle intersections at the respective stations, which the section-line segments above and below the knuckle, and the knuckle itself, are after

check-faired

Adjustments may be necessary if the resulting below the knuckle is too great to avoid objectionable pounding or slamming (i)

(a)

all

faired

is

are faired into this deck edge and completed as

(h)

of

into the abovewater entrance

Sec.

other requirements and

flare

Sec.

ABOVEWATER-FORM LAYOUT

^.?.,'?

For structural reasons the knuckle should be (j) well clear of all deck edges along the shell.

The knuckle and

forebody sections of the Fig. 66. P, are laid out

The knuckle

compound

the

at Sta.

ABC

flare in

the

ship, delineated in

by the procedure described. —0.5 lies shghtly above the

knuckle line because of discontinuities in way of the single centerline bower-anchor position.

For vessels carrying wing screw propellers it may upon occasion seem wise to afford lateral protection

by widening the above them, rather than by

abovewater hull fitting abovewater propeller guards. 68.6 Check of Range of Stability and Dynamic Metacentric Stability. At this stage in the preliminary design, if not before, a check is made to insure that: (1)

sections of the fast sailing ships of the 1840's were

what is now known 1 and 2 in Fig. 26. D. It is regular shipyard practice to camber a straight stem to compensate for the optical illusion of concavity inherent in a perfectly straight stem carried forward to produce

as the clipper bow, pictured at

bar [Baier, L. A., unpubl. Itr. to HES, 4 Aug 1950]. Profiles and planforms for transom sterns are discussed and illustrated in Sec. 67.20.

For the

the propellers

to

The range

of positive metacentric stability,

in a transverse plane

and

653

the flaring, slightly concave abovewater entrance

made

is

ABC ship the planform of the main deck the stern, solely as a matter

elliptical at

Some

additional abovewater volume and deck space are achieved by carrying the transom all the way up to the main deck, as has been done on many U. S. warships, but at the expense of some additional weight and an unquestionably heavy, clumsy appearance at the

appearance.

of

stern.

adequate for the service expected of the vessel. This operation is particularly important for a vessel of special shape, such as sketched subsequently in diagram 1 of Fig. 68. K in Sec. 68.12.

The forebody portions of the ABC transom and arch sterns, above the DWL, are exactly alike back to Sta. 11. However, the afterbody portion of the ABC arch-type stern above the DWL is slightly different from that of the tran-

The method

som-stern ship because of the greater waterline

for the static case only,

is

many

of accomplishing this is set forth in

and reference books on naval architecture [PNA, 1939, Vol. I, p. 135]. (b) The vessel possesses adequate dynamic metatext

beam

it

has sufficient stored-up righting energy

more than absorb the dynamic

to

[Vincent, S. A.,

This matter

1939, Vol.

I,

rolling

energy

pp. 135-136].

discussed further under wavegoing

is

in Part 6 of

PNA,

Volume

AP. The main deck planform and

same way, except

centric stability in a transverse plane; in other

words,

at the

the uppermost level lines are rounded in the to a larger radius.

Selection of

68.8

weather deck, with a

desire to achieve a certain appearance. Centerline

rise at

normal

the centerline amount-

of the ship (0.25 inch per foot of

to 0.02085x),

Abovewater Profile and Deck Details. The abovewater profiles of a ship, like the section shapes, are governed partly by the necessity of meeting certain wavegoing requirements and partly by utilitarian needs. They may result from fairing the sections into the ends, or from a

A

ing to say 0.020 or 0.025Bx for the widest part

III.

68.7

Deck Camber.

degree of circular-arc or parabolic camber in a

some help

is

beam corresponds

in

shedding water

during wavegoing but it is hardly to be classed as a quick-unloading device for a boarding sea

an emergency. Constructions

in

parabolic arcs are illustrated at

by G. de Rooij

68. D; also

and and 2 in Fig.

for circular 1

in "Practical Ship-

building" [1953, Figs. 329a and 329b, p. 133].

No

one camber shape among a number that

anchor stowages at the bow and stern, propeller-

are available has

aperture clearances for single-screw vessels, and

superiority or significance.

other features usually play a part more important than hydrodynamics [Coqueret, F., and Romano,

appropriate, therefore, to the drafting as well as

P.,

SNAME,

to the shipfitting

any particular hydrodynamic The camber may be

and fabricating procedures. For camber curve may be used for

this reason a fixed

1936, pp. 131-132].

In the main, however, the abovewater profile

all

widths of deck along the length. The curvature

should, like the underwater profile described in

or slope need be sufficient only to insure that,

Sec. 67.4, be a sort of automatic result of first determining the ship form desired, in transverse

within the

planes,

and

forward and

then

carrying

aft, in fair

at the centerplane. This

the

hull

surfaces

shapes, until they is

meet

what happened when

-pressions

life

in

of the ship, there will be

no de-

the deck at any small heel angle

because of ill-formed or buckled plates or minor service

damage.

Flat, straight decks are admittedly economical

riYDRODYNy\MICS IN SHIP DESIGN

554 All

Comber Heiqhts (About

ore

10

Exocjtjerated

times

in

Dioqroms

I,

2,

two

and 3)

Sec. 6S.9

straight elements, lying at a constant angle

to each other.

The

ridge surfaces are then develop-

able cyhnders of very large radius.

In fact,

if

a circular or parabolic arc of constant

employed for the deck-beam lines on a cambered deck, and if the intersections of the deck-beam Unes with the centerplane lie on a straight line fore and aft, as at 4 in Fig. 68.D, the shape

is

whole deck is a developable cylindrical surface. the deck line at the center or at the side follows a curved sheer, corresponding to 5 in the figure, the departure from true cylindrical form, for any one plate, is usually insignificant. If

A

ridge-type deck, having the

centerline,

possesses

same rise at the more slope

considerably

amidships and less slope at the sides of the vessel than a camber with a circular arc or even with

paraboUc arc. Whether this represents an advantage for the straight-element deck in shedding water is debatable, especially as at one angle of list the high side has no slope at all. 68.9 Bulwarks and Breakwaters. Bulwarks, either partial or full, are appropriate for both a

Ridqe Line Mq\j Be Held Fixed in Position ond Shape (straight in this Cose) ond Sheer Line at Side Allowed to Take Its Shape "Automaticallu" Construction

b\j

the Geometric

~

large (a)

and small

vessels

when

it is

desired to:

Afford some protection along a deck edge

Sheer Line at Side Held Fixed in Position and Shope and Ridcje Line at Centerplanc Allowed to TaUe Its

against wind and spray blowing across the deck

Shape

slopping over onto the deck

(b)

Automoticalli^,

Constant Ridqe Slope Assumed FiQ. 68.D

in

Dioorams 4,5

and fabricating stages

welding. Generally there are

more plating buckles

there are upward. Here

where the greater

stifi'ness of

plate of equal or slightly less

is

a case

an aluminum deck weight might be a

advantage. Ridge-type decks, hke the low ridge roof of a

di,stinct

house, illustrated at 3 in Fig. 68. D, are composed of

two

the

flat surfaces

horizontal,

each lying at a small angle to

enough to insure and joined in a low knuckle

only

large

drainage in service, at the centerUne. This knuckle is a straight line if the ridge surfaces are flat [Dawson, A. J.,

SNAME,

1950,

Fig,

10,

p.

13].

However, the

knuckle can be curved, with a sheer incorporated in

it,

from

(c) Retain on board loose gear, small items of deck cargo, fish dumped from nets, and the like.

but no ship deck, certainly not one of metal, ever finishes fiat nor does it remain flat. It always bends downward under its own weight, if not under compression loads due to riveting and

downward than

crests

"^

Straight and Curved Deck Camber Lines

in the drafting, shipfitting,

Prevent marginal waves and

leaving the deck-beam lines composed of

If the owner desires or permits, bulwarks may be added solely for the sake of appearance, as when carrying a graceful sheer line along a straight deck edge. While bulwarks can hold back some marginal water from coming over a deck edge they can and do keep on deck large menacing weights of water which need to be unloaded quickly, before the next sea comes aboard. Freeing slots along the lower edge of the bulwarks, or hinged-cover freeing ports in the bulwarks, are provided for this purpose but the average head to make water run through them rapidly is rather low. Furthermore, the port edges are usually sharp and the orifice coefficient is also low.

customary to provide a port opening of bulwark area and to hmit the bulwark height to 5 ft [Lovett, W. J., "Applied Naval Architecture," 1920, p. 174]. This rule takes no account of the width of the vessel and the volume of water trapped between bulwarks of a given height, apparently on the theory that for a given It is

0.1 the

ABOVEWATER FORM LAYOUT

Sec. 6S.9

555

angle of heel, the greater part of the water on a

two breakwaters

wide ship

appreciable fore-and-aft distance,

To

spills

over the top of the bulwarks.

require that a deckload of water,

top of the bulwarks, should run

off

up

to the

completely

within the interval of one pitching cycle would taking

away

bulwarks

practically

require

altogether.

It is therefore necessary to

that some

the

assume

water

in

tandem, separated by an so

that

the

one is trapped by the second. A set of tandem breakwaters of concave section is fitted on the French battleship Jean Bart [The 111. London News, 9 Apr 1955, p. 661]. A breakwater of any type requires adequate spilling over

angle or pitch angle, or both, will

bracing against the hydrodynamic forces. These

unload most of the water over the bulwark rail. To get rid of the rest of the water in one pitching or rolling period it appears that the freeing-port area should be more nearly 0.2 the bulwark area. Furthermore, this freeing-port area should be provided abreast the volume which needs to be emptied if the vessel ships a deckload of solid

known but magnitude may be estimated by assuming a dynamic load imposed by solid water striking the breakwater at a certain velocity. For a head sea, or an angle of encounter Q:(alpha) of

roll

water.

Bulwarks at the extreme bow can serve as an effective

increase in

freeboard in that region,

over and above that provided by the intact hull. If not extended too far aft, say to not farther

than the point where the local beam exceeds 0.55x it should be possible to leave them solid, without freeing ports or slots. Breakwaters require positioning and shaping so that the maximum water is deflected for the minimum of splash or spray over the top. This calls for a deflecting surface which is never or rarely ever normal to the onrushing water and which does not form an objectionable spraythrower for water in quantities greater than the breakwater is designed to handle. The water deflected from the forward side should have no upward component, and as great an outward component as possible, to throw it toward the gunwale and get it off the deck. Fig. 68.E illus,

are not accurately or even roughly their order of

180 deg, this

is

compounded

of (1) the speed

Not Less Than

J-enqth

—

of

1.25 3l"ont

Breakwoter on One Side

and 4, two alternative methods of accomphshing this. The function of the horizontal lip along the top of the barrier is to throw moderate quantities of water back forward but to permit large quantities to pass over the breakwater without too violent obstruction. The breakwater on a forecastle is usually of V-shape in plan, with its vertex forward and with diagonal sides extending practically to the deck edges. The planform angles may vary from 45 to 60 deg with the centerline, indicated at 1 and 2 on Fig. 68.E. The height at the center, where the water can not run off the deck freely, should be higher than at the sides. A breakwater having an elliptic or parabolic planform, with the sharp curvature forward, is shown for an early German trates, at 3

"schnellboote" (high-speed boat) in Schiffbau [26 Oct-2 Nov 1921, Fig. 4, p. 114]. There may be

V

which it is estimated the ship can make in heavy weather and (2) the orbital velocity Uorb of the crest of a wave which breaks over the forecastle and strikes the breakwater. While, strictly speaking, the dynamic pressure is that due to the component of (7 + (7 Orb) normal to the breakwater, there is little assurance that the deck load of water sliding aft on the forecastle will strike the breakwater from ahead. The blow may just as well come from the side, striking against one face for

Fig. 68.E

Design Sketches fob Forecastle Brbakwateks

*1 |

i

HYDRODYNAMICS

556

whole length. Only one such impact is necessary is not sufficiently strong or sturdy. It appears unwise, therefore, to use for the design any striking velocity less than the sustained speed V plus the orbital velocity

IN SHIP DESIGN Design of Anchor Recesses.

68.10

its

Sec. 6S.10

Protrud-

to tear loose a breakwater that

ing stockless anchors are unsightly and they are

f/o.b.

abominable spray-throwers. They represent definite collision hazards in that such an anchor can tear open the whole side of another ship, when the bumping or sliding damage might otherwise

The

force on the breakwater, exerted parallel

to the deck,

may

be taken as that developed by

a uniformly distributed

(F

+

pressure q

=

0.5p

Uorh)' acting over the whole area of the

When an

face.

ram

obstruction of this kind deflects

onrushing water back upon

itself

a doubling of the impact load. This

there is

is

usually

compensated

by the fact that a stream of water only half as high as the breakwater can be reversed in direction by the action of the deflectors shown in Fig. 68. E. A deeper layer of water is only deflected upward, with a ram pressure corresponding to (F f/orb) and a force on the breakwater that is not doubled. for in the present instance

be

slight.

on the German World Bismarck and Tirpitz the anchors were hauled, not into orthodox external hawsepipes or anchor recesses but up onto the main deck. There they lay flat, suitably secured. When it was desired to anchor, they were apparently pushed over the side by mechanical gear. This left the sides of the bow entirely clear of any major projections or recesses, and eliminated the throwing of spray from that cause. It

is

War

reported

II

On

the

that

battleships

German World War

II cruiser Prinz

+

Fitting the breakwater at an angle of from 45 to 60 deg to the ship centerline, indicated in the

outward

water

deflects

figure,

and

helps

to

reduce the impact load on the structure for seas

coming from directly ahead. For the ABC design, it may be assumed that the ship can maintain 18.7 kt in a sea made up of regular waves 800 ft long with an angle of encounter a of 180 deg. If these waves have a steepness ratio as great as 1/20 the orbital velocity in the crests

is,

10 ft per sec.

then 31.6 10

ft

from Table

approximately

striking velocity

is

per sec (equivalent to 18.7 kt) plus

per sec or say 42

ft

48. e,

The nominal ft

per sec. Taking a round

value of 1.00 for 0.5p in salt water, the

ram

pres-

approximately 1.00(42)" or 1,764 lb perft^. This is just over 12 lb per in'. The ultimate-load factor for an installation of this kind, where it is sure

is

particularly important that

it

not be torn loose or

that leaks should not be started in the forecastle deck, should be at least 5 times the calculated load. If

it

amount

is

of

to expend

desired

only a moderate

weight on a breakwater, the generation

of excessive

ram and dynamic

pressures on

it is

prevented by cutting holes in it. These are of moderate size, at about midheight. The holes permit the breakwater to catch and shed small amounts of water but relieve the load on it when large

quantities

of

solid

water come rushing

against the breakwater structure 1954, p. 43], In this respect

it

[SBMEB, Jan

resembles the dive

brakes of certain airplanes, in the form of flaps rather well perforated with holes.

Fig. 68.F

Anchor Recess as Used on Great Lakes Freighters

ABOVEWATER FORM LAYOUT

Sec. 68.10

557

Eugen the spare anchor was stowed in a centerhne hawsepipe well up in the clipper bow but there were no hawsepipes as such for the port and starboard bower anchors. They were drawn up, practically on top of the weather deck, onto shelves built into the side and the deck at the gunwale, where the anchors lay nearly horizontal. arch piece over the stock held the anchor in

An

position

and kept the chain from jumping out

of

the shelf. However, because of the acute angle between the stock and the deck line a projecting

was necessary. These bolsters and the still throw some spray. Similar stowages have been provided on certain classes of small combatant vessels of the U. S. Navy during the 1940's and 1950's. Recesses of varied types have been worked bolster

anchors could

Fig 68.G

Anchor Housed in Recess, Great Lakes Freighter

Photograph by courtesy of the Great Lakes Engineering

Works

into ships in the past to house stockless anchors,

many

of

which are

still

unsightly and are objec-

tionable spray-throwers.

A

proper anchor recess

respective

the

of

side

Crossed

centerplane.

recessed anchors were used successfully on the

U.

Navy submarines

Argonaut,

should really house the anchor, not only within

3,000-ton

the fair line of the side but, so far as practicable,

and may have been used elsewhere. Wherever an anchor chain under load changes direction on a ship, at least three consecutive links should bear on some fixed bolster or structure. Since the chain can lead in a great range

within the hull plating

itself,

leaving only enough

opening to pass the anchor when the flukes are the stock. Recesses for stockless

in line with

anchors

may

properly be fitted on vessels as

small as 100-ft harbor tugs [AM,

Apr

1953, p. 21].

Anchor recessing is accomplished on the Great Lakes by the general arrangement shown in Figs. 68.F and 68. G, in successful use there for the past four or five decades. The "backroom" required for this scheme is made available in lake freighters by the extremely blunt waterlines in the vicinity of the recess and the hawsepipe, with

Nautilus,

S.

and Narwhal

in the

1920's,

or directions in service this poses a problem,

whether the chain comes out of a hawsepipe recessed in a pocket or whether it runs over an external bolster.

that there

is

The

little

designer

must also remember by pulling the

to be gained

anchor up into a recess and then adding, outside

horizontal slopes of the order of 40 or 45 deg.

the fair plating surface, a tripping plate or bolster that will throw nearly as much spray as the anchor

On

itself.

the British battleship Vanguard, completed

in the late 1940's, the external surfaces of the

anchors form a remarkably

fair

continuation of

18 [111. London News, Sep 1954, p. 473]. On some British passenger liners of the same era, among them the Himalaya, the anchor recess opening is not much larger than the crown and tripping lugs of the anchor, corresponding to the small openings on the Great Lakes freighters.

the adjacent ship's side

On bows

of relatively fine form,

completely

It is also

a problem to provide an external

bolster large enough, let alone the lower corner

a bower anchor which must drop clear of a sizable bulb of a recess within the hull plating, for

at the forefoot.

Considering specifically the

ABC

design, with

an abovewater bow shape shown on

beam

Fig. 67. E, at the level of either the

there

is sufficient

main

or the forecastle deck to permit full recessing

of stockless anchors in the usual

way. This would the

by offsetting the port and starboard anchors in some convenient fashion, and by bringing the chain for each bower anchor up on the opposite side of

involve

the vessel. This arrangement gives space for each

appears to be no objection to protecting the anchor windlass from the weather by mounting it on the main deck under cover.

recessed stockless anchors can be fitted

anchor recess about equivalent to the full width of the bow instead of limiting it to a space on its

crossed

chains,

however,

leading

starboard anchor chain to the port wildcat and vice versa. As the vessel is not to be required to

moor with two anchors and a normal

service, there

single

chain in

HYDRODYNAMICS

558

However, the

IN SHIP DESIGN

Sec. 6S.ll

abovewater body at the hawsepipes is so narrow, as compared to the width of the bulb bow under them, that a dropping anchor is sure to strike the shell plating at the

wrapped around it accidentally. Under-the-bottom anchors were installed on the famous ironclad Monitor and on

bulb.

have frequently been proposed through the years for ships that could not house them conveniently above the water; one such was the "great mushroom anchor" to be hung under the semi-globular

It

is

widlli of the

therefore proposed that the

ABC

ground

tackle consist of: (a) One heavy under-the-bottom anchor, housed and handled as outlined in Sec. 68.11 (b) One abovewater bower anchor housed in a

to clear turns of chain which are

several British-built vessels of the 1860's.

naval battery Cerberus

[SNAME,

They

1904, Pis.

7,

A

centerline hawsepipe in the stem, with its flukes

combination of underwater mushroom anchor and abovewater stockless anchor was in

drawn up

use for

tightly against the projecting bow, above the crown and forward of the hawsepipe. 68.11 Proposed Under-the-Bottom Anchor Installation for Ships with Bulb Bows. Since an anchor is always used under water it seems absurd to hoist and carry it above water, unless possibly

Fig. 68.H

I85].

many

years on U. S. submarines in the

early part of this century [Nimitz, C. W.,

Dec

1912, pi. facing p. 1200]. G. de Rooij

an under-the-bottom anchor

for

USNI, shows

modern sub-

marines ["Practical Shipbuilding," 1953, Fig. 611, p. 264].

Proposed Housing for Mushroom Anchor in a

Bow Bulb

ABOVE WATER-FORM LAYOIH^

Sec. 6S.11

Anchorinq Dioqrom Showinq Both Choins Tonqent to Bed Surface at Respective Anchor Positions

Hull

ABC

The

One

(a)

Proposed Under-the-Bottom Mushroom Anchor for

proposal involves:

13,000-lb centeiiine

Navy

water, of the U. S. as an

LWT

bower anchor above

lightweight type,

anchor, housed in the

known

manner shown

67.E (b) One extra-heavy centerline mushroom anchor, below water, housed within and dropping out of the bulb at the keel, indicated in Fig. 68. H. Fig.

The mushroom anchor more

is

proposed because

it is

by the chain than any other type, and because it houses reliably and firmly, out of sight, in a hawsepipe of simple shape and sturdy construction. Above the mushroom anchor and to a point just under the wildcat, at the main deck level. Fig. 68. H shows a length of chain free of fouling

several

sizes

chain. This in

pp

Openinq Fig. 68.1

by

,559

is

heavier than the regular anchor to insure that no breakage occurs

not easily accessible when The heavier chain next to the

a section which

the ship

is

afloat.

is

ABC

Ship

prevent the chain from rattling and banging in the chainpipe with the ship underway. Indidentally, this arrangement provides a full half-

turn

chain

of

possibly

1

or 2

around a horizontal wildcat, hnks more than is customary on

bow-anchor windlasses of the orthodox type. One great advantage of anchoring through a keel-line hawsepipe is that a much flatter "lie" of the anchor and chain is obtained, with a much shorter scope of chain, illustrated by the box diagram of Fig. 68.1, than if the chain is led from a hawsepipe many feet above the surface. This is especially true in the shallow water of rivers, estuaries, and harbors, where the ship occupies a much smaller mooring circle. On the ABC ship the difference in level of the hawsepipe openings is

some 50

ft,

or well over 8 fathoms, indicated in

The heavy mushroom anchor,

the small-scale diagram of Fig. 68.1.

chain pendant next to the

some 46

ft or

over 6.5 fathoms long,

is

of great

anchor also increases its holding power. Both chains going over the wildcats are of the standard

assistance here. These factors combined might

size for this vessel.

anchor, which must be normally at least 2.5 times

An

alternative arrangement for housing the

bottom anchor farther If the it is

anchor windlass

necessary to

aft is is

move

shown

in Fig. 68.1.

heavy as a stockless anchor for the same holding power in firm ground. It is, furthermore, far

to be kept well forward,

easier to obtain a three- link bearing for the chain

leading out of the morning-glory-shaped bottom

at about 0.05L, in

anchor recess than out of any known shape of abovewater hawsepipe and bolster. Lastly, the anchor and hawsepipe are mounted much lower in the vessel than is customary, helping to lower

1,

order to house the anchor completely above the baseplane and to provide a slope of 15 deg in the

hawsepipe leading from the anchor recess to the

A

as

the hawsepipe as far aft

as the vicinity of Station

wildcat.

permit reducing the weight of the mushroom

slope of this order

is

necessary to

the

CG.

HYDRODYNAMICS

560

It is recognized that the under-the-bottom anchor scheme for the ABC ship has several disadvantages of major proportions: (1)

Greater weight of mushroom anchor,

servatively estimated as 64,000

lb,

IN SHIP DESIGN

Sec. riR.12

Bulqed Fender Stroke of Constant Rodius Forms Port of the Shelf Plotinq

con-

compared to

22,500 lb for a stockless anchor, or 13,000 lb for

an

LWT

anchor. Slightly greater weight of

due to the extra-heavy 6.5-fathom shot just above the anchor. chain,

(2)

Greater power required in the anchor windlass

to hoist the heavier anchor and adjacent shot of

heavy chain. Inasmuch as the holding power calculated for the ABC ship is 160,000 lb, a standard windlass might be adequate for the purpose if not required to hoist both anchors

Bulged Fender Strake for a Small Vessel

Fig. 68.J

simultaneously. (3)

Greater hawsepipe and chainpipe weights

(4) Lost buoyancy due to water around anchor and chain in hawsepipe and lower part of chain-

amounting to about 5 tons in the ABC design. Sufficient volume is left above the cup of the anchor to clear stones, clay, and mud caught pipe,

in the cup, as well as to permit the

anchor to drop clear in the river below Port Correo, where there may be less than 4 ft bed clearance above the

mud.

(5)

Difficulty of buoying the

external knuckle of the compound-flare tj'pe of section proves quite acceptable.

The

projecting edges of thick fenders or fender

strakes rec[uire chamfering in a transverse plane to prevent their hanging

up on

along docks, especially

when the

and

similar projections tide level rises

This chamfering should also be sufficient to prevent the fender from throwing objectionable falls.

spray, although the offending surfaces need to be

nearly vertical to eliminate

all

spray.

A

bottom anchor when

dropped

neat solution to the problem of the abovewater fender is offered by the heavy, bulged fender strake of Fig. 68. J, forming a part of the

(6)

Impossibihty, except in clear tropical waters in dayfight, of noting the direction in which the

main hull. In addition to dynamic requirements

anchor chain leads from the hawsepipe. However, with a bottom anchor and a short scope, this information is not really necessary.

great inherent stiffness as a fender because of

Although the proposed under-the-bottom anchor by no means proved itself sufficiently to warrant working it into the design of a

installation has

ship to be built,

is carried through here as preliminary design because it permits the use of a moderate bulb and a fore-

part of the

shape and

it

satisfying all the hydro-

construction

this

requires no care

and preservation

other than that afforded

service,

The

proper.

ship designer

is

to

in

cautioned, however,

not to place a bulge of this kind where the water can climb up around its convex surfaces in normal running.

it

ABC

Reentrant discontinuities or coves, near the waterline, are to be avoided where

designed

wide and blunt. Knuckles and Other Longitudinal Dis-

continuities.

its

the hull

castle that is not too

68.12

has

Flaring sides, projections, recesses,

and other discontinuities of considerable fore-andaft extent often have to be worked into the abovewater form to meet service or utilitarian needs. For smooth-water conditions, with relatively small waves, these discontinuities have little or no adverse effect provided they are kept clear of the ship-wave profile along the free surface under any conditions of load, trim, heel, and speed fikely to be encountered. Even for wavegoing, the

Internal Coves

and External Chines Need

Not

ie Filleted or Rounded if

The-y Lie Generollij

Porallel

Fig.

to

The Lines

68.K

of

Flow

Projecting Blisters and Sponsons

ABOVEWATER-FORM LAYOUT

Sec. 68.14

practicable but not necessarily shunned. Reen-

trant angles in these coves, typified

by the long

purpose.

561

Even wind

screens and shelters have to

be provided for passengers, especially on highspeed ships [Currie, Sir William, SBMEB, Jul

cove at the bottom of the set-back trunk of diagram 1 in Fig. 68. K, and by the long junctions of hull and sponsons in the ferryboat section at 2 in Fig. 68.K, and in SNAME RD sheet 84, can approach 90 deg provided this small angle is necessary for other reasons. Little extra drag is encountered if these coves are under water in

involve some air drag and produce some wind

some load condition provided the corners follow

resistance.

the temporary flowlines reasonably well.

be provided or exerted, or speed must be sacrificed.

Keeping abovewater discontinuities out reach of waves at sea

is

The

change in direction as the water strikes the discontinuities the less spray they throw and the smaller are the hydrodynamic forces exerted on them. 68.13 Transverse Discontinuities. Any longitudinal discontinuity which runs for a considersmaller the

discontinuity.

The

latter

is

is

also a transverse

distinguished here

—

as one which involves a projection or a recess from the fair section lines in the vicinity which is large compared with its fore-and-aft length. A good example is an old-fashioned gun sponson on a combatant vessel, protruding from the ship's side like a bay window to obtain a line of fire

along the side. Projections or recesses of this

kept clear of the ship-wave

profile, need from a hydrodynamic standpoint for ships which travel in relatively smooth water, surrounded only by their own

type,

no

if

special consideration

waves.

The use

of isolated transverse braces or sup-

ports for overhanging portions of the abovewater hull or upper works, even of the

wave

profile,

is

when nominally

clear

not encouraged. Under

some unusual and unlooked-for circumstances these transverse members are liable to become fouled by floating debris, ice, or breasting floats (camels).

Abovewater projections may be fitted, as on whaling factory ships [SBSR, 5 Dec 1946, pp. 625-635], to increase the deck space locally, to serve as large-area fenders for protection of the

underwater hull when other vessels lie alongside in the open sea, and for other purposes. 68.14 Shaping and Positioning of Superstructure and Upper Works. Several major considerations enter into the design of that portion

any ship lying above the main hull. Every deck erection, every spar or post, every protuberance of whatever kind has a utilitarian of

these upper works on weight, cost, and transverse

metacentric

stability,

practically

To overcome

this,

of

all

extra power

them must

of the

Avell-nigh impossible.

able distance along the ship

1955, p. 435]. Some of these purposes are served only in port, some only at sea, and some are used almost all the time. Aside from the effect of

"The model

Mauretania required an into drive the structure added to represent deck houses" [Barry, R. E., Mar. Eng'g., Sep 1921, p. 690]. of the (old)

crease of 20 per cent in

power

Regardless of the type of vessel or the service it, any owner and operator may be expected to affirm that convenience of access,

expected of

availability of outside light

and

comfort of

air,

the passengers, and the needs of the crew are to take precedence over the reduction of

resistance of the upper works.

way, he

will

Put

wind

in another

unquestionably be found reluctant

to sacrifice utility, passenger comfort,

and other

having to do with the handling and operation of the vessel for the sake solely of reducing its wind resistance. Nor will he generally find it a paying proposition to spend a great deal of money and effort to diminish the wind resistance, at no sacrifice in other features, unless some outstanding improvement is to be gained. Tests at the Case School of Applied Science, on 33-in wind-tunnel models of the Atlantic liner Manhattan, showed that by completely streamlining the whole ship in other words, by treating both hull and upper works as a unit the wind resistance with the relative wind ahead was reduced approximately 84 per cent, compared to the Manhattan as built. This was for a ship speed of 20 kt, a true wind speed of 23.2 kt, and a relative wind speed of 43.2 kt. The modification involved an entirely different concept of a passenger ship, with everyone completely housed at all times, but it indicates what can be done if all factors

—

—

other considerations are disregarded.

This

effort

shows how easy

it is

to lose sight of

the fact that so-called streamlining of individual

deckhouses and other erections above the hull by no means insures that it will be easier for the crew to make their way about the upper works under storm conditions. Structures of fair form,

when blown upon

in a direction

approximating

HYDRODYNAMICS

562

that for which they were shaped, rarely have sizable regions of reduced velocity or separation

around them. They create few eddies

in

which a

person can stand, as is possible in the lee of a square corner on a deckhouse, and fewer calm areas in which a passenger can

"The wind excessively

velocity

streamlined

sit

in comfort.

over the open decks superstructure),

even

(with an in

quite

mild conditions, can be such as to render intolerable any attempts to walk or sit out!" [Hind, J. A., SBSR 14 Jul 1955,

To

p. 37].

IN SHIP DESIGN

Sec. 68.14

equal distance back of the side of the ship. This is because of the separation zones behind the

sharp corners at the deck edges and the reduced velocities in way of the miscellaneous small obstructions on the deck. Unit air pressures on

the exposed sides of deck erections increase with

above the main hull and Ukewise with the absolute size of the areas subjected to ram pressure from the wind. For a wind velocity their height

of 60 kt, or 101.33 ft per sec, with

pass around a streamlined structure in a

wind of ferocious velocity; becomes a struggle if one is heavily clothed. Nevertheless, certain things can be done to reduce the air drag without sacrificing any functional features of the upper works. First, it is possible, even in rather small vessels, to provide complete internal access from hving quarters to operating stations for all officers and crew. Indeed, this is now general practice on large vessels and may be taken for granted in any modern new design. If the same provision is made for unusual operating conditions and for manning emergency stations it is possible to eliminate the necessity for crew members to move around outside the upper works in bad weather. The diagram for composition of air velocities around a ship, indicated at C in Fig. 26.H, shows that the ratio between the true-wind velocity Wt and the ship velocity V has an appreciable effect upon the bearing angle of the relative-wind velocity r at the ship. For winds normally encountered in good weather at sea, with velocities not exceeding 20 kt, this relative-wind angle increases, for a wind nominally on the beam, from 45 deg abaft the bow at 20 kt to about 59 deg abaft the bow for 12 kt. For winds of stronggale force, say 60 kt, the difference between the relative-wind angles for a nominal beam wind is still appreciable, of the order of 71.5 to 80.5 deg abaft the bow for 20 and 12 kt, respectively. Streamlining a deckhouse which can not swivel into the wind like a weathervane but which is shaped to give minimum air drag with the true and relative winds both dead ahead appears

in a stagnation area

an

ram pressure

ture of 59 deg F, the

is (0.5)

air

tempera-

q due to

wind

(0.00238) (101.33)' or

gale requires bucking a

12.22 lb per

this

a 60-kt wind, developing a relative velocity of 90 kt, or 152.00 ft per sec, the corresponding ram

W

somewhat absurd.

A

deckhouse not extending

all

the

way

sides or to the ends of a surface ship hull

to the

and not

having any overhanging deck at its top level, may be considered as relatively sheltered from the wind if it has a height not exceeding 0.12 or 0.15 times the beam of the ship and if it hes an

pressure

is

ft'.

For a 30-kt ship steaming into

27.49 lb per

ft'.

Shaping the deck erections for least wind drag is based upon a relative-wind direction of about 30 deg on either bow, because it is at about this angle that the wind blows separately on the several structures spread along the length of the

This is also the angle, indicated by the diagrams of Sec. 54.9, at which the fore-and-aft wind resistance i2wind becomes a maximum. The beneficial effects of housing uptakes, ventilators, mast and instrument foundations, and the hke, within deck erections necessary for some other purpose, are not to be overlooked. Objects which vessel.

can not be so enclosed often objects

(inside

the

lie

in the lee of larger

separation

and

eddying

region behind them), at the 30-deg relative-wind angle,

and so do not require any streamlining

themselves. It

is

for

not to be forgotten, however,

that swirling backflows into these regions, where

— Ap's and

exist,

may

them smoke, soot, from poorly placed

take with

foul gases discharged

openings.

what may be expected in about a great variety of deck erections and upward projections from the hull and superstructure, for a relative wind from ahead, Fig. 68. L shows the velocity vectors in both elevation and plan view around the hull and upper works of a large ship. Diagrams 1 and 2 of this drawing were adapted from a series of five detailed diagrams pubUshed by H. N. Prins, in an article describing the hull features of the Dutch passenger liner Oranje [De Ingenieur, The Hague, Holland, 23 Jun 1939, PI. II and p.W. 56]. The comprehensive data were taken from windtunnel tests, made on a specially constructed model of the vessel, complete to the last detail. Unfortunately, they cover only the wind-ahead

As an way

the

indication of

of air flow

ABOVEWATER-FORM LAYOUT

Sec. 6S.15

563 Uniform

More or Less Undi sturbed

Troce of Surface Above Which the Flow

.

Air

From

and Reversed Flow Occurs Aboft Almost

Edd\(inq

Fig. 68.L

All

and Exposed Objects ond Aboft tht Abrupt

Projections

Air-Flow Pattern Over a Passenger

condition but they illustrate vividly the back

and the extreme irregularity

the eddies,

flow,

of the air flow in general.

For the many smaller

The Motor

736;

Ship,

ships,

and some

large

SBSR, 2 Dec 1954, London, Dec 1954, pp.

374-375], on which the deckhouses and other deck erections (except possibly for a raised forecastle)

are

the

all

way

aft,

there

is

a possible major shift and upper

of the center of pressure of the hull

works which may affect maneuverabiUty in a high wind. Apparently this offers no real problem in operation, aside from learning initially how the ship behaves and controlling it accordingly. It

is

customary, for

many

ship designs,

to

build a simple, inexpensive model, usually called

a

drafting-room

model,

embodying the

hull

DWL

and all the principal deck erecabove the tions and exposed parts in their proper shapes, sizes, and locations. Fig. 54. B shows such a model. It is an easy task, for which techniques are well developed [Nolan, R. W., SNAME, 1946, pp. 46-60], to mount this model in a large wind tunnel at various angles to the relative wind and to determine the nature of the flow over and around it. A hght thread or tuft, carried by a thin wand which is manipulated by hand and placed at selected points, indicates instantly the

type of flow to be expected there. Multiple tufts of contrasting color, attached to the model at

many

photographed for record, such a model may be tested in the open provided a platform or deck is available, over which a uniform wind is

at

points, are readily

any

thread or far

ones [Swedish tanker Oceanus, p.

blowing.

test condition. Indeed,

Ship,

A

Endincjs

I"

low

Ahead

Deckhouses

of

from a Model Test

long fish pole, carrying the roving

tuft,

enables the experimenter to stand

enough from the model so that

not interfere with the uniform

his

body does

air flow

near the

model.

Shepheard describes the results made at the NPL, Teddington, upon such a model of the British Royal Yacht Britannia [INA, 7 Apr 1954, pp. 11-13]. In this case white smoke filaments were used, which were found to photograph satisfactorily. It is possible to make exactly the same type of flow test on an upside-down model of the upper works attached to a large horizontal surface board and suspended in the water of a circulatingwater channel. Jets of water from a suitable pump are caused to issue from the stacks at a velocity having the proper ratio to that of the overall stream, corresponding to the relative- wind velocity. Colored dye injected into the water streams from the stacks gives a true and vivid indication of the paths of the exhaust gases on the full-scale ship, complete with swirls, eddies, Sir Victor G.

of wind-tunnel tests

and the like. Methods for calculating the

air

drag and wind

resistance of ship hulls, upper works,

and deck

erections are given in Chap. 54.

Abovewater World War II, a considerable amount of research and development on methods of keeping combustion and objectionable exhaust gases and soot clear of passenger and operating spaces on ships has 68.15

Design

of

Facilities

Smoke and Gas Discharge.

revealed that:

for

Since

HYDRODYNAMICS

564

These gases must be discharged into regions smooth and regular flow, rather than into flow containing large-scale eddies. The discharge must be above and outside of separation (a)

relatively

of

zones,

else

scattered

are

the gases

widely in

drawn back and downward by the reversed flow and the eddies. (b) Stacks of large diameter, width, and horizontal area create their own separation zones, regions of low velocity or are

into which the escaping gases are drawn, thence

to find their

way

to the decks below

Raising the stack top to a great height,

(c)

projecting far above the top of the turbulent region, will not of itself prove satisfactory because

and dirt that falls upon the ship at wind velocities approaching zero [Smith,

of the soot

relative

W. W., SNAME, 1946, pp. 76-77] (d) To insure that gases issuing from

a stack top open are projected far enough into the regular flow to prevent their mixing with the turbulent flow behind the stack or over the ship in the

it

is

necessary that the stack-gas velocity

S,

IN SHIP DESIGN

Sec. 68.15

may

be larger than the opening,

structure that

chimneyshaped stacks are not acceptable, combustion and exhaust gases may be discharged from the after upper corner of a stack casing, as on the liners Constitution and Independence (1950-1951). Supplementing (a) preceding, wind-tunnel tests on ship models reveal that set-backs or steps in the forward surface of a multi-deck superstructure give the equivalent of a streamlined forward face if the set-back slope through the upper edges of the various vertical surfaces is not more than 30 deg with the horizontal. If the slope is as great as 60 deg, the turbulent separation region above the uppermost deck is about as high and as large as if the superstructure face were a solid vertical wall, with a 90-deg slope. Furthermore, performance on the ship is found to be somewhat better than the model tests predict [Acker, H. G., SNAME, New Engl. Sect., Oct 1951, p. 5]. For the reader who wishes to pursue the subject (g)

If,

for reasons of appearance, tall

further the following references are quoted:

approximately vertical, be at least as great as the relative-wind velocity

S may have

velocity

volume

Wr

in the open.

to be 1.5 or 2.QiW r

of stack gas is not large.

general service conditions the

if

The the

(1)

p.

For the worst

maximum

should exceed 65 turbulent

ft

areas.

per sec

For

ships the actual relative

fine,

if

(3)

there are adjacent fast,

high-powered

vortex of a long, thin stack shaped like a symmet-

is

properly placed

at the

(5)

forward edge of the gas

opening, and not at the forward edge of a stack

stack

lie

Squire,

M

(6)

Nuisance," (7)

SNAME,

1946, pp. 42-82

Sharp, G. G., "Design of

Modern

Ships,"

SNAME,

1947, pp. 462-466 (8)

Valensi,

J.,

and Guillonde, L., "Sur les

Formes de

Carenage de Chemin^es de Navires Propres k Eviter le Rabattement des Fumfees (On the Shaping of Stacks of Ships Intended to Prevent the Settling of

Smoke over the Decks)," ATMA,

1948,

Vol. 47, p. 173

stack-gas

turbulent region. This shield or elbow, however,

Ingenieur, 7 Jul 1939, p. 79. In Figs. 27, 28,

above and abaft the stack. H. B., and Troucer, J., "Round Jets in a General Stream," ARC, R and 1974, 1944 Nolan, R. W., "Design of Stacks to Minimize Smoke to

rical airfoil. If

velocity in an effort to keep the gases clear of the

1941

this page, there are given three diagrams arrangements tested, apparently in a wind tunnel. For each of the diagrams there is sketched the type of flow found to issue from and

of

to project the objectionable gases into the tip

of

Mar

A. H., "Machine- en electrische van het m.s. 'Oranje' (Machinery and Electrical Installation of the Motorship Oranje),"

De

upward component

of

installatie

and 29 on

the

de fumee (maquettes (Method of Smoke FilaAirplanes and Airplane Tech. du Ministere de

fillets

Ijsselmuiden,

works should still be smoke- and gas-free. (e) It may under some circumstances be possible

of

Julius Springer, 1936, Vol. Ill,

Mich. Res. Bull. 29, (4)

60 or 65 kt, corresponding to 100 or 110 ft per under conditions when the decks and upper

some

AT,

Wings)," Publ. Sci. et I'Air, 1938, No. 128, pp. 11-16 Sherlock, R. H., and Stalker, E. A., "A Study of Flow Phenomena in the Wake of Smokestacks," Univ.

sec,

caught in such a vortex the gases remain there reasonably well, at least until they are downwind far enough to be clear of the ship. (f) For fast ships in which the relative wind is generally in the forward quadrant a shield around the forward side of the stack opening or a partial elbow directing the combustion gases aft as well as upward, long used on French men-of-war and built into the German cruiser Prim Eugen and other naval vessels, is a simple means of retaining

F.,

"Methode des

ments using Models

relative-

wind velocity may reach

W.

165

d'avions, ailes d'avions)

W

wind velocity r may be taken as 40 kt, so that for no contamination the stack-gas velocity

Dui-and,

(2) Valensi, J.,

(9)

Eustaze,

S.,

"Le Rabattement des Fum6es sur

les

Fonts d'un Navire; Essais sur Modeles et Dispositions Pratiques (The Settling of Smoke over the Decks of a Ship; Tests on Models and Practical Arrangements)," ATMA, 1951, pp. 285-307

ABOVEWATER-FORM LAYOUT

Sec. 68.15 (10)

(11)

(12)

and Burge, C. H., "Funnel Design and Smoke Abatement," INA, 1950, Vol. 92, pp. J19-J37; also ASNE, Aug 1951, p. 704. Seven references are listed on p. 730 of this latter article. Acker, H. G., "Stack Design to Avoid Smoke Nuisance," SNAME, New England Sect., Oct 1951 Valensi, J., "Sur un Moyen Propre h Eviter le Ower,

E.,

Rabatteraent des Fumfees sur les Fonts des Navires (On a Good Method of Getting Rid of the Smoke Settling on the Decks of Ships)," Bull. Tech. du Veritas, (13)

(14)

Mar

1952

Thieme, H., "A Contribution to Funnel Aerodynamics," Schiff und Hafen, Nov 1952, p. 453 Richter, E., "Neuzeitliche Schornsteinformen (New

Forms

of Stacks)," Schiffstechnik,

Aug

1954, pp.

36-44 "Passenger Liner with Engines Aft," IME, Deo 1955, Vol. LXVII, Figs. 21 and 22, pp. 446-447; abstracted in SBMEB, Dec 1955, pp. 689-693.

(15) Craig, R. K.,

circular outlet not

more than

for a gas velocity

S

of placing the pro-

machinery as far aft as practicable in the ABC design are augmented by moving the exhaust fan or smoke discharge aft with it, where the gas may be projected upward through one or two tall,

slender stacks.

The

G.,

SNAME,

1952,

of each stack casing could

then have a width of say 3.5 or 4.0 ft with a ft. This leaves room for a safety-valve escape pipe and for a damper and fore-and-aft length of 5

mechanism

its

to keep

the stack-gas velocity

high at reduced powers, as when running in the

Port Amalo canal and the river below Port Correo.

To

give the structure rigidity without the use of

heavy scantlings or of the order of 5

some 8

to

ft

ft.

stays, the

The bottom

bottom width length

is

is

increased

to give the profile the appearance of

The aft edge is raked downward and aft transom profile. The streamlined casing,

sturdiness.

in the

form

of a round-cornered rectangle at the

converts to a square-cornered rectangular

top,

shape just above the rigid

fidley. This is to provide a foundation where the ends and sides of the

stack casing attach to the transverse

beams and

fore-and-aft carlines directly below them.

superstructure for housing the passengers

and the public spaces clear the forward

The top

ft

1946, p. 68;

1947, p. 465; SuUivan,

W.

E. K., and Scarborough, pp. 488-490].

55 to 75

C, SNAME,

SNAME,

Sharp, G. G.,

3.0 ft in diameter

of the order of

per sec [MacMillan, D.

like the

The obvious advantages pelling

565

is

a unit placed well aft to

deck for the handling of package

cargo and to be close to the pitching axis.

The

derrick posts forward are to be in pairs, so

it

appears logical and architecturally consistent to carry this scheme aft by mounting two tall

If it

were considered that an underwater smoke

discharge, into the

— Ap

region of the separation

zone, along the lower edge of the transom, could

be worked out in the course of the design of the

steam generators well admirably to this arrange-

vessel, the position of the

aft

would lend

itself

ment.

inlet-and-exhaust-air shafts over the superstruc-

ture and placing two steeple-type

smoke stacks

one over each steam generator. An estimate of the extent of the turbulent region well

aft,

M

over the ship is sketched in Fig. 68. with a moderate true wind of 25 kt from ahead, on the basis of H. G. Acker's estimate that the thickness of the turbulent zone over the top of the super-

structure

is

of the order of 0.8 the height of

a

stepped-front superstructure above the main hull.

Combined with a wind velocity

The

is

ship speed of 20 kt, the relative-

45

kt, or

stack gases from

about 76 fps. each of two modern

8,500-horse steam generators should require a ,.

-

Combustion

—

;j.^ ..'-'^"*%.

GQsesp

Estimated

Upper Limit

of Turbulent and

-

Exhaust -^'r]

Fig.

68.M

/ ^^

EsTI^LA.TED

Eddv/inq

"Necessity, if not reason, has provided another flourish. Large steamships now e.xpel their waste gases through giant chimneys surmounted by all manner of strange devices. To prevent these unpleasant vapours obstinately returning to spotless decks below, invention has run riot in providing amusing, if not always elegant or effective, headgear for funnels. Angels' wings, admirals' caps, upturned pudding bowls, skeleton triplanes all of these and other fancies now proudly sail the oceans in the cause

—

of science and clean decks. What shall we see tomorrow? Perhaps someone may get rid of those obnoxious fumes somewhere else? Why not through the stern?" [SBSR, 1 Apr 1954, p. 401].

Some

excellent

comments

relative to the dis-

posal of the products of combustion, Flo

Not Less Than 0.8

hg

"Tf ^IL

Air-Flow Pattern Over the

ABC

Ship

made by

HYDRODYNAMICS

566

John Johnson two decades ago, are

still

worthy

IN SHIP DESIGN neath.

A

Sec. 6R.16

transom stern

may have

its

immersed

designer

draft increased to the point where the transom

[Thomas Lowe Gray lecture, IME, 10 Jan 1936; SBSR, 16 Jan 1936, p. 74]. 68.16 Reducing the Wind Drag of the Masts,

does not clear at the designed speed. Finally, a

consideration

serious

of

and Rigging.

Spars,

self-propelled

vessel

ship

raked masts on

Tall,

a

undoubtedly reUcs of

are

They

saiUng-ship days.

the

b}^

serve well for the flying

propeller designed for the original displacement

may

be heavily overloaded at a later one, when

the average draft has increased.

Model

Preparation of Hull Lines for

68.18

It is recalled that the design rules for

Tests.

apertures

and

clearances

the working of long derrick booms. Nevertheless,

bodied in Sec. 67.24 are in

many

cases based

with their attendant rigging they are subject to heavy loads when rolling and they represent

propeller-blade widths,

of flags,

the carrying of navigation lights, and

wind resistance out

A

usefulness.

attached

to

of

the

ship

outside and, in the proper places, for the propelhng

and without

machinery within the ship, it is necessary to run through a prehminary design of these devices, in the manner outlined in Chaps. 67, 69, 70, and 71. Before attempting to delineate the whole ship hull on a single drawing, the fixed and movable appendages need to be roughed out and checked for position, shape, and dimensions. This procedure is described in Chaps. 73 and 74. Furthermore, the hull-and-appendage combination requires design attention and checking to insure that shallow-water maneuvering, wavegoing, and other requirements are met. These matters are covered in Chap. 72 and in Parts 5 and 6 of

structure

serve as an air intake or exhaust,

all

at the

same

time. It can not easily be streamlined for flow

bearings in which high relative winds are

wind drag

encountered but

its

by the number

of functions

is

at least justified

which

performs

it

simultaneously.

Masts intended to be used as ventilators appeared as far back as 1860 on the steamer Ly-ee-Moon [SBSR, 9 Nov 1939, p. 507]. It is possible that these in turn were rehcs of the early smoke stacks which were extremely tall in order to obtain good natural draft.

stays eliminated to reduce wind drag, inter-

ference,

and expense, are coming rather rapidly

into use [SBSR, 8 Oct 1953, pp. 484-485;

Dec

On

1953, p. 53;

SBSR, 24 Jun

MENA,

1954, pp. 800-801].

the Uner Orsova the running rigging for the

derricks

is

[SBSR, 20 68.17

carried

May

entirely

inside

the

posts

1954, p. 645].

Consideration

of

Increased

Draft

Through the Years. Before leaving the prehminary design of the abovewater body as finished it is to be remembered that, as the result of a continual series of modifications and changes in the course of its life, most of which act to increase the weight, the ship sinks slowly but steadily deeper in the water. This is specially true for a

combatant vessel or

for a

merchant vessel which

likely to be converted to a naval auxiliary in time of emergency. A heavy or pronounced flare or a sharp knuckle may in this way be brought too close to the designed waterline. A flat counter may be lowered to the point where it is subject

is

to frequent sea slap

Volume

and slamming from under-

Simultaneously

III.

working

needs

design

volumes,

Self-supporting masts and derrick posts, with all

of

proportion to their

can mount a radar antenna, hold up one end of a radio antenna, support a crow's nest, carry a range or masthead light, and

all

upon the thicknesses

pole or post, properly

benefit of stays,

on

emupon

rudder posts, and so on. To determine whether there is room for the propulsion devices on the

all

tall vertical

screw-propeller

over

the for

strength,

capacities,

preliminary

arrangement,

metacentric sta-

damage control, and other non-hydrodynamic requirements. With this work accomplished, and with the bihty,

shape and principal features of the underwater and abovewater hulls, propulsion devices, and

appendages worked out, a set of lines for the hull as a whole is drawn. This is in no sense a set of lines to which the ship is to be built. For the hydrodynamic design, its principal function is to guide the building of a model or models for towing, self-propulsion, maneuvering, shallow- water, wavegoing, and other tests.

The preparation

of lines

to

embody

all

the

features developed in the foregoing sections largely a matter of drafting, except as

is

mathe-

processes such as those discussed in Chap. 49 may be used to calculate the offsets for drawing (and fairing) these lines.

matical

A

high degree of precision at this stage

called for.

large

The

scale,

fines

is

not

should be to a sufficiently

not only for construction

of

the

model, but for a fairly detailed design of all the appendages which are eventually to be added to it.

CHAPTER

The General Design Introductory

69.1 69 2

of the Propulsion Devices

Comment

Type and Number

.

of Propulsion

Devices

.

and Limiting Dimensions .... Effect of Type and Design of Propelling Machinery Number and Position of the Engines Use of Systematic Wake Variations .... Rate and Direction of Rotation of Propul-

69 3 69.4

Positions

.

69 5 69 6 69.7

69 9 .

69.10

69.1

Comment.

Introductory

ances and Reserves 69.

are

common

Discussions propellers, lers,

of

specific

like,

69 14

573 574

69.15

There are con-

down

Rudders .

.

The

these (1)

69.2 Type and Number of Propulsion Devices. Only rarely can lines be sketched for the form of a new ship without first making a tentative decision as to the type, number, and position of the pro-

the propelling machinery

is

The

to drive these devices

and powers which result in the highest efficiency and the greatest economy for both. Generally speaking, therefore, the type, number, and position of the propulsion devices are determined directly from the ship requirements. The corresponding features of the machinery are at rates

So many considerations, most

of

them con-

enter into the selection of the propulsion-

device characteristics that

it

is

difficult

to set

on the basis

(2)

Maximum

(3)

Best general position in the

of:

including limiting

re-

vessel, considering

of wavegoing anticipated, with (4) Amount consequent change of position of the instantaneous water surface with reference to the region in

which thrust

being produced, such as the disc

is

of a screw propeller (5)

Type

This boils

of propelling plant available or desired.

down

generally to the rate of rotation

output shaft on the last machinery unit, just ahead of the propulsion device. In the past, slow-speed engines drove screw propellers through multiplying gears, and in the present, high-speed of the

engines

drive

paddlewheels through reduction need be few Umitations in

gears. Therefore there this respect. (6)

Facihties available for repair or replacement

of the propulsion devices

selected to suit the devices.

flicting,

first,

the latter's type, functions, and duty

are

function of

selected

is

and available depth of water ship speed and total power quired to be absorbed by the device (s)

type of propulsion device are worked out or

are installed to drive the ship.

type

Operating requirements,

draft of vessel

selected in actual practice.

these features

The

serve until something

well in a region of poor flow.

order in which the characteristics for any one

often

580

better is developed, remembering first, last, and always that no propulsion device, whatever its type and position, can be expected to perform

two chapters

determined by the types, sizes, and powers of the propelhng units available; admittedly this procedure is inescapable at times. It is proper to remember, however, that the propulsion devices

may

579

580

the procedure in systematic form.

outline given here

on the water. devices such as screw

of

578

579

Vibration Frequencies

act

are found in the

Too

....

572

The systematic treatment

devices.

Re-

Disadvantages of Unbalanced PropulsionDevice Torque Propulsion-Device Design to Meet Maneuvering Requirements Relation of Propulsion-Device and Hull-

.

design features does not necessarily follow the

pulsion

Adjustable,

69 13

.

paddlewheels, rotating-blade propel-

and the

following.

which

576

Feathering,

of

Propulsion Devices to be Used with ContraVanes, Contra-Guide Sterns, and Contra-

to the design of all mechanical ship-

devices

Selection

versible, or Controllable Features

sidered in this chapter only those features which

propulsion

H

69. 12

sion Devices Design to Equalize or to Apportion the Powers of Multiple Propellers Powering Allowances Graphic Representation of Powering Allow-

69.8

567 567 568

570 570 572

.

.

.

69

areas where the ship ship's force or (7)

567

by

is

and

their parts in the

to operate, either

by the

repair crews

Frequency with which the propulsion devices

HYDRODYNAMICS

568

IN SHIP DESIGN

Sec.

are to be used, such as those on a self-propelled

the design demand, and no more than the

floating crane.

for

Concerning the Jiumbcr of propulsion devices, the following considerations govern:

69.3

number

which good working positions can be found.

Positions and Limiting Dimensions. The matter of how far to keep the thrust-producing 69.3

away from the hull and its boundary layer, how close to bring them to the hull, is discussed

areas

Available depth of water in operating areas,

(a)

limiting extreme draft, probable draft of hull of vessel,

and approximate beam-draft

ratio of hull.

This item involves factors such as adequate tip submergence to prevent air leakage to submerged

adequate hydrostatic head to prevent

devices,

most

cavitation,

efficient

missible extension, It

may

fit

a larger

if

blade lengths, and per-

through 67.25 and other devices in Chap.

for screw propellers in Sees. 67.23

and

for paddlewheels

71.

The

selection of the particular position of the

propulsion

device(s)

in

any ship

takes

into

account:

any, below the baseplane.

be necessary, for some of these reasons, to

number

or

of small-diameter or small-size

propulsion devices, or a fewer

number

of large-

(1)

The nature

of

the flow into the possible

positions, considering

wake

fraction, uniformity

of inflow velocity, non-axiahty,

and absence

of

contra-flow

or

excessive turbulence

diameter ones. (b) Special operating

requirements such as those

maneuvering in restricted waters and emergency stops. Wing propellers provide appreciable swinging moments by going ahead on one and backing on the other. (c) Probability of large exciting forces and excessive hull vibration if large powers are concentrated in too few propulsion devices. As of 1955, the largest power applied to the propeller of a singlescrew vessel, the tanker W. Alton Jones, is about

for

22,000 horses [Mar. Eng'g.,

However, powers

Nov

1955, p.

119].

of the order of 50,000 horses

by the individual propellers and these may eventually be reached by the propellers of fast,

are being developed

of quadruple-screw installations,

single-screw ships. K. E. Schoenherr pointed out

some years ago that

it

was then "possible

(2)

The

possibility

of

fitting

contra-guide devices adjacent to the propulsion device (s) (3)

Freedom from entrained

air

coming along

the hull from forward, leakage air coming from the free surface, and eddies in or trailing abaft

separation zones (4) The tip submergence considered necessary in view of the specified loading and anticipated wavegoing conditions (5)

Permissible

depression

of

blade

the

tips

below the baseplane. Usually this can not exceed about 4 or 5 ft, the height of the keel blocks in the average drydock.' (6)

Available

propelling-machinery

positions

within the hull.

Each design

to

case

is

on

considered

its

own

design propellers to transmit 50,000 horsepower

merits, taking account of all the items listed in

on one shaft and to obtain propulsion efficiency of as high as 80 per cent on single-screw ships" [SNAME, Phila. Sect., 21 Feb 1947].

down

(d)

Interference likely to be caused with internal

arrangements in the vessel by the presence of one, two, or more shafts, including their shaft alleys or tunnels (e)

Efficiency of propulsion.

device,

if

there

is

room

for it

One and

large propulsion if

indicated, almost invariably proves

good inflow

more

is

efficient

than two or more small ones, reckoning efficiency here on the basis of the least propeller or shaft power for a given weight displacement and length of the ship. (f)

Reliability

and safety aspects

of the entire

engine-shaft-propulsion-device combination

A

good general rule is to use no more propulsion devices than the special requirements of (g)

and in Sec. 69.2. It is difficult to set which apply even in the majority of especially when the relative importance of

this section

cases,

rules

the several controlling items often

is

not known

N. J. Brazell has given some good ideas in a paper entitled "The Positioning of Propellers and Shafts" [ASNE, Feb 1948, pp. 32-48]. On the motor vessels Brunshausen and Brunsbiittel the single propeller is mounted about 9 ft abaft a clear-water stern post, in an effort to improve propulsive efficiency and to reduce vibration [SBSR, 12 Jan 1956, p. 38; MENA, Jan 1956, p. 28; both references embody photographs of the stern]. The result of an analysis by H. Dickmann in advance.

[Ingenieur-Archiv, 1938, p. 452], set

down

by K. E. Schoenherr [PNA, 1939, Vol. is

that:

briefly

II, p. 145],

GENER/VL DESIGN OF PROPULSION DEVICES

Sec. 69.3

for best efficiency of propulsion the screw propeller should be located in a high friction wake, a negative or ".

.

.

low positive streamline (potential-flow) wake and in the crest of a wave."

propelling machinery.

condition that the propeller work in a

negative or low positive potential or streamline wake is that which obtains generally in a normal

form

of ship

if

the hull

is

assumed

to be

expanded

to include the displacement thickness 6* (delta of the boundary layer. With run lines of easy slope, such an expanded form has only a moderate positive streamline wake fraction due star)

to potential flow.

To

achieve the highest practicable negative wake fraction, propellers could be

streamline

mounted on

outriggers abreast

the section of

about the same Here the speed of advance becomes greater than the ship speed. Because there is no ship forward of the side propellers, the thrust-deduction fraction becomes practically zero. High negative-wake fractions are actually to be found inside Kort nozzles and

maximum position

area,

as

occupying

paddlewheels.

other types of fixed propeller shrouding. When some form of hydraulic jet propulsion

been faced and always that

employed, requiring large volumes of water to be taken within the hull boundaries and discharged from internal ducts, the positions and shapes of the inflow and the outflow openings become almost a part of the main hull design. These features, of which relatively little is known, are indeed

worthy

of

more attention than

is

will

be faced with the

and

shipping

these devices are too small. Never-

theless, larger facilities

the past and

have always been

built in

they will continue to be

made

no reason why the propulsion-device designer should be bound by existing facilities if he can produce a better or more efficient ship. Since most propulsion devices rotate, there are problems of gearing and transmission, which may govern the rate of rotation and through it available in the future. There

may

is

influence the size of the propulsion device,

the thrust-load coefficient, and the hydrodynamic

Furthermore, the necessity for me-

efficiency.

protection

chanical

of

damage by

against shielding

the

propulsion

external

against air leakage, as

it

device

and for done for a

objects, is

screw propeller by the main hull of a single-screw tug, may call for a diameter smaller than would otherwise be used. required thrust-producing area Aa of any

type of propulsion device being considered is readily calculated from the ship resistance Rt and the speed V. After estimating or assuming

wake and thrust-deduction

values of the

w and which

t

and

T =

Ctl

a good value of the real efficiency

will give

(0.8?;/),

fractions

selecting a thrust-load factor

the values are substituted in the formula

normally

devoted to the position of a screw propeller and the shape of the hull in its vicinity. Following the practice on jet-propelled aircraft, the ram action of the water flowing toward the hull is utilized to force water into the inlet and to keep it moving

probable that the

fabrication

existing

facilities for

The is

is

designer of ship-propulsion devices always has

fact

The

It

569

C,

i2j

Cr

AoVl

Ao[F(l

-

w)f

whence

A„ =

against the friction and pressure resistance en-

2Crz.(l

pRrlVil

- W)f t)

the internal ducts. This is where practicable, by an inlet opening facing directly forward or forward and

for determining quickly the diameter of a screw

outward.

propeller in the course of a preliminary design

countered

within

accomplished,

As

for the limiting dimensions of propulsion

devices,

it

is

obvious that there are practical

by good all-around engineering, good mechanical design, and economic operation of the vessel which are in conflict with hydrodynamic requirements for the ultimate in prolimits dictated

pulsion-device efficiency.

To

E. Burtner gives a simple dimensional formula

[ASNE, Aug

1953, pp. 545-548]. This formula

appears to give reasonable values for both 3- and 4-bladed wheels and for a rather wide range of

expanded-area

D

ratio. It is

[Ps (in horses)]" (in

ft)

(69.i)

(rpm)°"

increase the latter

means increasing the thrust-producing area and lowering the thrust-load coefficient Ctl but at the expense of increased volume occupied by and increased weight of the propulsion device and the

On page

547 of the reference Burtner includes nomogram for finding any one of

a small-scale

the three values quickly

when the other two

known. For example, assuming

for the

ABC

are ship

HYDRODYNAMICS

570

Ps is 16,000 horses and D is 20 ft, the estimated rpm are about 118. The rates of rotation derived by the use of several propeller charts in that

from about 104 to about 110 rpm. 69.4 Effect of Type and Design of Propelling Machinery. The general design of propulsion devices is never dissociated entii'ely from the type and design of propelling machinery because these units or systems are, always figuratively Sec. 70.6 vary

and generally literally, at opposite ends of the same shaft. Nevertheless it may not be amiss to point out in this book that the greatest freedom of choice for the design, construction, and position in the ship for both the propulsion-device and the propelling-plant systems is afforded by a suitable combination of the following elements:

IN SHIP DESIGN

An

(1)

Sec. 69.4

generating plant,

electric

driven by a

steam, internal-combustion, or gas-turbine engine,

some type unknown at present but be found feasible in the future. This plant is to be in units of sizes and powers which lend themselves readily to manufacture, to mstallation in the most advantageous position (s) in the ship, to economical and efficient operation, and to progressive maintenance. or a plant of

which

An

(2)

may

electric transmission system,

DC, with

or

either

AC

the necessary safety and control

devices

A

(3)

high-speed

reasonably

rugged

electric

motor or motors, suitably cooled and protected from dirt, moisture, spray, and liquid. The modern railway traction motor fulfills all these requirements.

A

plant

which

need not be located in the ship in some

specific

(a)

type

of

power-generating

gearing

Speed-changing

(4)

double-reduction

of

epicycUc

or

the

single-

type,

or

utilizing

region, dictated by the position of the propulsion device (s), but which can be placed where it best satisfies ship operating conditions. It should not

wherever practicable the so-called flexible construction which provides uniform load distribution along the gear faces and consequent maximum

be forced into a certain and not always deposition because the propulsion-device sirable design requires compliance with a completely different set of conditions, nor should it be such

loading on the teeth.

—

—

that

into only one position in the ship.

it will fit

completely flexible power-transmission (b) A system by which a power-generating plant or driving member can be connected to a driven member on the propulsion-device shaft with

freedom

of

direction

of

rotation,

direction

shaft axes, relative position in the vessel,

distance between the two. is

afforded

by

Freedom

of

and

of this type

electric-wiring or piping systems.

(c) A propulsion-drive unit which is small, light, compact, and adaptable as to location, requiring a minimum of maintenance

speed changer which (d) A propulsion-drive permits use of the optimum speeds for both the propulsion-drive unit and the propulsion device.

At the time of writing (1955) these requirements met for a wide range of powers by the following units grouped in one machinery plant. The important matters of space, weight, and cost are not are

disregarded but are for the

moment

considered

although

powers only,

are

It

is

who

[Lisle, 'T. O.,

p. 36],

often

is

keenly interested in the hydrodynamics

of his propulsion device (s), that active develop-

ment along 69.5

these lines will continue.

Number and

Position of the Engines.

comment in items (a) through (g) on the number of propulsion devices,

ParalleUng the of Sec. 69.2, it

may

be said that:

(a) A single machinery unit is lighter, more compact in total volume occupied, more cheaply and easily installed and maintained, and cheaper to run than several units of the same total power. Aside from only one engine there is only one

thrust bearing, one line shaft, one propeller or

stern-tube shaft, and one set of shaft bearings

and

(b)

The space and weight be devoted to other useful

hull stuffing boxes.

of the fuel

saved

for crew's stores.

flexibility.

installation

available

to be hoped, for the sake of the ship designer

to fulfill the requirements of the preceding paragraph. Such an installation comprises:

an

of

where weight and space are at a great premium.

items.

of

some

themselves in severe service afloat Motorship, New York, Mar 1953,

The specific mention here resembUng an electric-drive plant is intended solely as an example and not as indicating the best or the ultimate achievement

secondary to

by the them in limited and have proved

Practically all the elements required foregoing,

A

may

single unit requires fewer operating per-

and weight devoted to crew accommodations and required

sonnel. This in turn reduces the space

(c)

Modern machinery may not yet be sufficiently

GENERAL DESIGN OF PROPULSION DEVICES

Sec. 69.5

never to require any reserve pro-

reliable so as

home

pelling unit(s) to bring the vessel

in the

event of casualty. It is, however, vastly more than was the machinery of a former age, which saw a shift to twin-screw machinery reliable

largely to provide this measure of safety.

The

position of the propelling machinery in

the vessel

the

(d) Affects

the hydrodynamic

of interest in

is

design principally because

it:

and

declivity

the

horizontal

angle (s) of the propeller shaft(s), as well as the

shape and positions of the shaft struts or bossings

main hull the size and shape

(e)

Affects

of

large

motors,

of the hull in

condensers,

gears,

way

other

or

machinery parts which need certain clearances from the hull structure Concerns the readiness with which the screw (f) submerged in

kepi

are

propellers

all

operating

conditions. This item is considered most important

[Rupp, L. A., and Jasper, N. H.,

SNAME,

1952,

pp. 352, 354]. (g) Affects

the disposition of the products of

combustion and the air resistance of stacks, standpipes, or other deck erections (h)

Controls the possibilities and the methods of

underwater gas exhaust.

Assuming that the

ABC

ship

is

to be driven

by

screw propellers at the stern, the following hne of reasoning was employed when determining the proper number. With the tentative beam-draft proportions of the 66.e

of

Sec.

combinations of Table varying from 78.25:26 to

first

66.11,

74:26, it appears easy to

twin screws. However,

fit

the propellers are there to drive the ship, not necessarily to

make

it

easy to design or construct.

On

the basis of requirement (5) of Table 64.a, for "Performance of the required transportation as

efficiently

and economically as the present

of the art permits,"

indicated.

The

corresponding

a single screw

resultant increase

in

San Francisco (old) and Maui of the and middle 1910's, running between San Francisco and Honolulu. Two later Matson hners, designed primarily for carrying cargo, and having the single-screw machinery installed way aft, were the Manulani and the Manukai [MESA, Sep 1921, pp. 707-708]. This arrangement, incidentally, was adopted as far back as the period 1843-1845 in the American auxiliary sailing ships Commodore Preble and Bangor [Bradlee, F. B. C, "Steam Navigation in New England," Salem, 1920] and in the Edith and the vessels

early

Massachusetts, built for R. B. Forbes [American

Neptune, Jan 1941,

external to the

saving other

is

in

fuel

useful

should be of the order of 3 per cent. It

state

definitely

is

and items

agreed,

571

version

is

Pis.

2,

A much

5].

later

the Shaw-Savill finer Southern Cross,

a pure passenger ship, with a single mast and single stack, far aft

1953, p. 1020;

[111.

London News, 19 Dec 1953, p. 569; SBSR,

MENA, Dec

Int. Des. and Equip. No., 1954, pp. 3-4]. In Europe an after machinery position was first used on the EngUsh coastal colher John Bowes in 1852 [Bowen, F. C, SBSR, 30 Sep 1937, pp. 421-422]. It is no longer necessary, as on the latter vessel, to put the machinery and the smoke

stack "right aft," out of the

way

of the fore-and-

on three masts. Nevertheless, the other reasons for placing the machinery in the stern are as valid today as they were in 1845, 1852, and again in 1892, when the steamer Turret was built in this fashion. These reasons, stated at the time by F. C. Goodall [INA, 1892, pp. 194-195] and later by G. C. V. Holmes ["Ancient and Modern Ships," 1906, Part II, p. 120] are summarized here from those authors: aft sails

(1)

When

to trim

the ship

by the

without cargo

is

stern,

it

helps her

and thus gives good immer-

sion to the propeller (2)

Water

or fuel tanks

may

be

fitted in

the after

part of the vessel, to help submerge the propeller,

shown on Plate XXIII

as

of 1892. This vessels, (3)

and

is

is

The main

of the Goodall paper

now standard on

all

incorporated in the shaft

is

shorter

Great Lakes

ABC

and

design.

lighter,

with

fewer bearings to watch and lubricate

The hold space occupied by the

shaft tunnel

however, between the designer and the future

(4)

owner and operator, that a prehminary design with twin screws is to be worked up if time and

is

opportunity permit.

rectangular section amidships, greatly facilitates

The layout

selected for the

ABC

design calls

machinery units to be placed as far aft as practicable, following in some measure the designs of the combination passenger and cargo

for the

saved

(5)

Using the most valuable part

the stowage of cargo (6)

[SBMEB, Jan

Less useful volume

ery components, part of the vessel.

if

of the hull, the

is lost,

1953, p. 4]

around the machin-

they are placed in the after

HYDRODYNAMICS

572

A subsequent commentary is equally applicable: bow and moving through many feet and the amidships movement only angular, and this space occupied by the ." [Lord engine, and the engine was never seasick "... of the ship in a big swell pitching, the

stern

.

Brabazon, SBSR, 23 Oct 1952,

.

p. 555].

Comments on machinery-aft positions were made by G. Gravier, concerning the performance of the passenger steamer El Djezdir [SBSR, 23 Sep 1954, p. 397], and by A. C. Hardy [SBSR, 7 Oct

Were

recently E. C. B. Corlett has

made

Sec. 69.6

necessary to equalize the blade

it

loads per unit length for any reason this could be

done by narrowing the blade at its inner end and widening it at its outer end. For practical and mechanical reasons, it is advantageous to have the greatest blade load nearest to the point where the torque is delivered to the wheel.

end

The

increased loading at the inner

paddlewheel blade, or at the hull end of a Kirsten- Boeing rotating-propeller blade, is accordof a

ingly accepted.

1954, p. 465].

More

IN SHIP DESIGN the ship.

The

rotating blades of a Voith-

further study of the advantages and disadvan-

Schneider propeller develop thrust on opposite sides during any one revolution. It is possible to

tages of installing machinery aft,

take advantage of the velocity variation in and

modern

He

conditions.

a

based upon

also discusses the question

of placing the navigating bridge

and

all

the crew

accommodation aft [The Motor Ship, London, Feb 1955, pp. 483-485; IME, Jun 1955, Vol. LXVII, pp. 84-85]. 69.6 Use of Systematic Wake Variations. It has been said [author unknown] that "The more uniform the wake, the simpler does it become to design an efficient propeller." Fortunately, because of the practicability of changing the

size,

form, and attitude of the blade sections along a it is only needful that this maintained for the complete travel path of any given blade section. For a screw propeller this calls for circumferential

length or a radius,

uniformity

be

beyond the boundary layer by

local changes in the width but not in the section of a blade. 69.7 Rate and Direction of Rotation of Propulsion Devices. Rather extensive comment concerning the rate of rotation of screw propellers is given by J. E. Burkhardt [ME, 1942, Vol. I, pp. 28-35]. These remarks, coupled with the discussion of Sec. 70.10 on the rate of rotation of screw propellers as an element in design, is sufficiently general so that no further comment is needed here about other propulsion devices. The matter of selecting a rate of rotation that will not cause vibration of the ship structure or of its major parts in resonance with the shaft or blade

frequencies

The

uniformity in the wake fraction at any radius.

When

examining wake diagrams such as those

is

discussed briefly in Sec. 69.15.

selection of the direction of rotation of

new ship

upon the

relative

variations which permit the propulsion device to

design usually depends importance of the propulsive efficiency to be achieved and the maneuvering

be adapted locally to them. The next step

and other

qualities desired. For small depend upon the availability

in Chap. 60 the procedure

is

to look for systematic

is

to

determine the correct or proper average wake characteristics in the regions

from

where the variations

contemplating the design of a paddlewheel, for instance, it is known that, apart from a of

ship-wave

effects,

may

also

craft it of pro-

pelling plants developing the necessary individual

and which rotate in the directions For the smaller where one may have to use available

shaft powers

this average are the smallest.

When

consideration

these devices for a

the

wake

velocities near the ship hull are positive because

boundary layer alongFarther from the ship, outside the boundary

desired, left-hand or right-hand. vessels,

stock machinery, rotation in a desired direction

may

be too expensive because of necessary modifi-

may

involve the carrying of too many w^th engines

of the viscous flow in the

cations or

side.

spare parts on a craft equipped

layer, these velocities are negative because of the

rotating to both hands. In large vessels practically

accelerated regions of potential flow abreast the

all

diagram C of Fig. 6.B. Theoretically, the paddle blade elements away from the ship should travel faster than those next to the ship. However, this is not feasible in a shipboard installation and it might not be advantageous hydrodynamically for other

can be

ship, indicated in the velocity profiles of

reasons.

ship

is

The blade

load per unit area next to the

therefore larger than at a distance from

propelhng plants, at least in the design stage,

The gears

made

to operate in either direction.

interposition of reduction or multiplying

may

or

may

not change an engine direction

to the desired propeller direction. Nevertheless, it is

generally possible, even in the construction

stage, to obtain a desired direction of rotation of

the propulsion-device shaft

if

there are sufficient

advantages to be gained thereby.

GENERAL DESIGN OF PROPULSION DEVICES

Sec. 69.8

Assuming that the

latter is the case, a syste-

matic variation in the flow at the position of the propulsion device is looked for, one which will give a superior efficiency or perhaps a larger thrust

absolute

a

for

rotation. This matter

and

particular

is

direction

of

discussed in Sees. 33.4

upward component

on the outboard side of a twin skeg is larger than on the inboard side, outward-turning screw 33.6. If the

of flow

propellers are indicated so that the outer blades

moving downward may "meet" the water flowing upward to them. If for some special reason the reverse

is

the case, as with the outside water

flowing horizontally and the inside water

upward

through a tunnel, inward-turning propellers are found more efficient. If circumstances limit the design of long deflection-type bossings or asymmetrical skegs to a particular diversion of the

surrounding water the screw-propeller rotation to take advantage of

is

provided of course that other design requirements are met. Considering hydrodynamics only there are

selected

very few reasons single-

rotate

the

in

why any

multiple-unit

or

direction

it,

propulsion device of a

may

installation

which best

the desired performance of that unit

This

is

on the basis that the outflow

not produces

by

itself.

from

jet

any one device does not pass through the

disc

or thrust-producing area of another device,

and

that the resulting unbalanced torque applied by

the propelling plants to the hull, discussed in

It is

customary for large

vessels,

but by no

for all vessels, that screw pro-

pellers be rotated in the following directions:

573

As soon

of Multiple Propellers.

as

Twin

screws, in opposite directions, especially

proper proportioning of the powers, regardless of the number of propulsion devices, to the designed powers of the propelling units which are to

them.

drive

The

quadruple-screw

large

ocean service but for around-the-world cruising the outboard screws were to be removed entirely,

by the inboard These were capable of absorbing two-thirds of the total power and were the only ones which could be reversed. Proper design procedure involves consideration leaving the ship to be driven propellers only.

and,

if

possible, control of the following items at

each propulsion-device position:

for

Boundary-layer thickness and velocity profile, both clean- and foul-bottom conditions

(b)

Retardation or possible reversal of flow behind

(a)

blunt bossing or skeg endings, involving wake fractions

with

exceeding

LO

large

positive

values,

possibly

General and local direction of flow through

(c)

propeller discs or other thrust-producing areas,

plus wake-survey

flow (d)

is

of

data.

This

is

a case where

only the axial component of

definitely not adequate.

Non-axiality of flow, due not only to the

shape of the adjacent hull but to the necessity

(b)

much

of the time with part or all of their

out of water, if

must rotate in opposite

the large lateral forces pro-

duced by them are to be balanced (c) Triple screws embody wing propellers rotating in

opposite

directions.

most

The

center

propeller

and convenient direction, especially if under some conditions the vessel is to be propelled entirely by the center propeller, with the wing propellers free-wheeling. (d) Quadruple screws rotate, in pairs, in opposite directions on opposite sides of the ship. rotates

69.8

in

the

Design

suitable

to Equalize or to

an outflow

Apportion the

its

jet

way

from a propulsion

into the inflow jet

of one abaft it

upper (f)

blades

directions in pairs

Possibility of

device ahead finding

Surface propellers or those which run for

and

the propulsion devices outside (e)

hands, symmetrical with the centerplane

liner

Empress of Britain of the early 1930's was propelled by two large inboard screws plus two smaller outboard ones. All four were to be used in trans-

the flow patterns are decidedly of opposite

if

is

about the problem of equahzing the powers absorbed by all of them. This corresponds to the

for placing shafts to suit the engines inside (a)

it

decided to use multiple propulsion devices, two or more in number, the designer begins to think

consideration

Sec. 69.13, lies within acceptable limits.

means necessary

Powers

Rate

The

of rotation of the various propulsion

when absorbing

devices

propeller torque

the

designed

powers.

may

be so large that the engine delivers rated torque at less than the designed rate of rotation, preventing the develop-

ment

of full rated power.

speed of advance

may

reaches

rpm

its

rated

On

the other hand, the

be so high that the engine when developing less than

the rated torque. (g)

Necessity for accurate correlation of torque

and rate

of rotation to achieve full rated

powers

for internal-combustion engines driving (single or)

multiple propellers.

HYDRODYNAMICS

574

The

available data relating to power equalizaand proportioning and to correlation of torque and rate of rotation on existing merchant ships or on self-propelled models of them are by no means extensive. J. M. Labberton in a paper entitled "A Method for Determining Proper Pitch for the Inboard and Outboard Propellers on a Four-Screw Ship" [ASNE, Nov 1937, pp. 576-584], discusses this question and tion

gives the following data for the old Mauretania,

taken during the

Rate

Shaft power, horses

AH

ft.

however, propelled

still

it

tests,

practiced

in

20,650

20,650

18,600 ft

and

velocities

and

both at

positions,

to

estimate distribu-

it

is

possible

An

thrust-deduction

estimate of

fractions

Before a model

for hull features not

or

method,

17,350

wake magnitude and

One

alternative

188.6

is

is,

self-

should be possible to determine what

of the designer.

The

1S8.6

variations in propeller design are necessary to

compensate

This means that the ship hull is shaped to be driven efficiently at a speed greater than the sustained speed when developing its maximum

186.6

the propeller

difficult.

advantages to be gained by designing a speed margin rather than a power margin into the ship.

187.3

use of existing model-testing techniques

individual

repeated subsequently in the

concentrated on the outstanding

sustained speed and then to add a large power

tion at each propeller position.

the

being

Outer

In this case the rates of rotation

these data

are

The emphasis

Inner

the hull and appendage surfaces and at distances from them. It is possible, for example, to make a wake survey at an after propeller position with a model propeller working in a position ahead. Facilities have been developed but are not yet in general use in model basins, whereby a wake survey is made just ahead of a working propeller.

From

is

characteristics in Sec. 65.3.

Inner

which indicate and record the flow

rather closely the

that section,

present one,

down

some

The designer may find that he has only limited freedom in shaping the hull and placing the propulsion devices. After he has done what he can in positioning these devices properly and working out the adjacent appendages he is able

at

set

Star.

pellers.

directions

in

is

Star.

were as uniform as could be hoped for in such a new ship but the inner propellers were absorbing some 53.5 per cent of the total power, or about 15 per cent more than the outer pro-

make

formulated,

Port

large

to

whose principal

ship

Port Outer

four propellers had a diameter of 17

a pitch of 15.75

Sec. 69.9

applying to the hydrodynamic features of a new

power.

trials of 1907:

rpm

of rotation,

IN SHIP DESIGN

under the control

more series

of self-propelled

possibly with a change in propeller design in

quarters,

is

to design the ship hull for the

allowance. This might be acceptable if the problem were only one of overcoming increased resistances due to heavy weather and to fouling. However, it results in overdriving and poor performance at the augmented speeds necessary for a ship which, running on a definite schedule, has to make up time after a spell of bad weather. Good design of the propelUng plant of any water craft calls for a reserve of power (1) to meet emergeircies, (2) to enable the plant to keep running and to deliver a sort of average power with minor casualties, and (3) to permit it to run much of the time at less than maximum rating. With pressures, loads, and other factors reduced, wear and tear is usually diminished and the periods between overhauls is increased. Almost every plant is capable of developing an emergency overload power for a few minutes, perhaps for a few hours, if it becomes a matter of saving life or the ship. Since this

may

result

but permanent damage to the machinery, it is not considered in the customary powering calculation. The maximum designed shaft power therefore that "for which the propulsion is machinery is designed to operate continuously" [SNAME, Stand'n. Trials Code, 1949, p. 11]. For powering a boat or ship, the machinery reserve is reckoned below this level. In general, the reserve of power is a function of the length of time that operation at maximum designed power is required. For a racing motorboat which may run at full throttle only a few hours between engine overhauls, but which must then in slight

do the

its

utmost, the reserve

game

is

is

practically zero. If

considered worth the candle, so to

between, should insure reasonably close equaliza-

speak, the emergency power

tion or apportioning of the full-scale shaft powers,

which case the reserve is negative. The other extreme is a boat or sliip wliich operates under a wide range of conditions and which stops for repairs only when it will no longer run. The

and correlation of the torque-rpm values. 69.9 Powering Allowances. A doctrine involving design and performance allowances.

is

called upon, in

GENERAL DESIGN OF PROPULSION DEVICES

Sec. 69.9

may then be as much as maximum designed power.

reserve of the

maximum power

able to develop

its

continuously, a full measure of

everyday operation, over most

reUable life, is

is

of

its

maximum designed developed by say 0.95 of

assured by limiting the

speed to that which

is

maximum designed power [Burkhardt, J. E., ME, 1942, Vol. I, p. 28]. It is usually assumed the

that this speed

is

to be achieved at the full-load

or other specified draft, in smooth, deep water of

the given specific gravity, in fair weather

(little

no wind), and with a clean bottom. In other

or

words,

it

maximum

represents a trial speed at 0.95 of the

designed

machinery reserve

power,

with

propeller, (in horses)

word "designed"

Notwithstanding that the implies that the machinery

0.3, 0.4, or 0.5

a

so-called

of 5 per cent.

Actually, a ship design starts with the designed

turn

it

bearing,

575

not in terms of the power absorbed but in terms of the torque required to

and the thrust achieved at the thrust all

at a specified rate of rotation [Smith,

E. H., lESS,

1954-1955, Vol. 98, Part 3, pp. encountered in transmission between the thrust bearing and the propulsion 127-128].

The

losses

device are then to be estimated or predicted by the propeller designer in cooperation with the

machinery designer. As has often been done in the past, the designer may wish to add a reserve of power over and above that necessary for the sustained speed to be achieved under trial conditions in good weather, following the method of

may

wish to base his reserve on an analysis of

the particular situation involved.

schedule which the ship

and sometimes

to maintain, or from

preceding.

average percentage to this power, using a figure taken from good practice, or he

sea speed or service speed, determined from the is

(c)

He may add an

six or

more

At

least four,

factors enter into the

a study of economic and other reasons. For the

percentage increase applied to the power pre-

ABC

dicted for sustained speed in good weather and

design this operation was completed

by

the owner and operator before the design require-

ments were formulated. To compensate for slowing down in heavy weather a reserve of speed above the designed

sea

speed

is

necessary.

This

with clean bottom. These factors, customary percentages, are: (1)

is

achieved either by one or by a combination of the following: (a)

Specifying

it

as

an

increment

of

resulting in the 1.8-kt differential of the

speed,

(b) CaUing for a 'percentage increase in speed over the designed sea speed, varying from about 8 to 15 per cent

(3)

Increase with age of structural

and

and of some vessels)

dis-

placement

(in

(5)

Machinery reserve, to care for minor casualties, inefficient handling, fuel under standard quality, normal wear and tear, and slow deterioration in performance with length of service Still-air and normal wind resist-

(6)

Scale effect between model and

(7)

ship (may be plus or minus) Cavitation loss in high-powered

(4)

from 20 to 30 per cent or more. taking account of small percentages the

machinery is to be delivered; also as to the kind of power represented by it, whether indicated, brake, shaft, or propeller power. There are different means employed to measure power, and there is still some uncertainty as to just where along the hne, from the heat-to-work conversion point to the propeller, the power is to be measured. It is most important, therefore, that the hull and propeller designers know exactly where this point is, and what is transmitted there. In fact, there are many good reasons for rating the

6 to 20 or

propeller roughness

Requiring a percentage increase in power

question arises as to the point in the ship at which the maximum designed power of the

8 to 15

other roughness

over that necessary to drive the ship at the designed sea speed under trial conditions, usually

When

Weather, involving an increase in power to maintain speed against head winds and seas or to make up time lost by slowing in waves Fouling by marine organisms or

ABC

design (the difference between 20.5 and 18.7 kt)

(c)

(2)

with their

2 to 5

4 to 6

ance of ship

2 to 4

1

to 3 or 4 to 10

or more.

vessels

All these factors,

more

if

taken into account,

may

from 23 to 54 per cent or more, depending upon their individual signs and values. It is customary to omit some and to emphasize others, total

particularly the increase for fouUng.

The

total

increase in power, over that required to maintain

the sustained sea speed under

trial conditions, is

HYDRODYNAMICS

576

then of the order of 20 to 30 per cent [ME, 1942, Vol.

I, p.

28; Troost, L.,

It is to be noted that

SNAME, item

1953, p. 576].

(6) of

the tabula-

IN SHIP DESIGN power increase

formulation of requirements or in the preliminary

into

design,

know

to

or

the speed-power relationships

all of

these increases in resistance

and power are in effect. For example, when the bottom is dirty the wake fraction becomes greater and the thrust loading of the propeller is increased. It must also be decided at what power the propelling plant is to operate at maxi-

mum

efficiency.

At a

later stage the detail pro-

an estimate of the propulsion factors at what might be termed the propellerpeller design calls for

design point, to be explained presently.

p.

running

permit

32]

model under conditions propellers

in

a

Bull.

7,

self-propelled

which the model

develop thrust under or over that

necessary to push the model through the water.

The auxiliary towing

or retarding force

is

adjusted

to provide the equivalent of underwater resistance, additional drag

body

due to roughness

of

may

be

the hull surface, and any overload that

expected on the ship due to fouling, adverse weather, and the

like.

This procedure admittedly

does not change the velocity

profile,

and other features

boundary layer

of the

the thickness, cor-

responding to the effects of the roughnesses which

produce the additional drag but

it

the model propeller thrust loading.

does increase

Any

desired

thrust overload can be applied to the model or

runs can be

made

predictions for

given speed.

many

\vith

varying overload to give

any estimated power increase at a

One method

speed but with a cent

acting on the ship and a 25 per cent

forces

increase to be expected toward the end of the

docking interval, \vith some adverse weather and other overloads thrown

Data derived from

in.

this

procedure are definitely

to be preferred, for predicting service performance

and

for design of the ship propellers,

to data

derived from driving a smooth model faster than the sustained speed by the use of the maximum

power that

it is

It is pointed

proposed to put in the ship. out in Sec. 65.3, and

it is

again

emphasized in a discussion of speed reduction in wavegoing in Part 6 of Volume III, that a ship is

much

in

the

it

better position to maintain a high if it

has a speed margin designed

rather than a power margin designed into

machinery alone. The speed be a percentage above the sustained may be a speed increment, as men-

propelling

margin

may

speed or

it

(a) and (b) preceding. It may be determined by a graphic method such as that

tioned

in

described in Sec. 69.10. Whatever the

method

employed to determine the speed margin, the designer has more assurance of achieving the extra speed required to make up for lost time if the ship

fashioned to

is

make

that extra speed

easily.

R

Model-testing techniques [C and 1933,

12.5

of

trial conditions.

sustained speed

when some

trial

per

above that This 12.5 per cent increase is a sort of selected average between clean-bottom trial conditions with no adverse required for

above does not include a sort of average is customary in some quarters. This is taken care of by the modeltesting establishment, on the basis of the kind, number, shape, size, and location of the appendages, relative to the hull and to each other. When estimating and applying the power percentages to the predictions derived from model tests it is most important to insure that an allowance corresponding to one or more of the foregoing factors has not already been worked into the model-basin predictions. In America it is customary to omit all the allowances listed except the S(ACi?) for plating, structural, and coating roughnesses to be expected on a clean, new vessel under trial conditions; see Sec. 45.18. It is generally necessary, at some stage in the tion

allowance for appendages, as

Sec. 69.10

conditions at the designed

successfully used for

years predicts ship and propeller operating

Graphic

69.10

Representation

Allowances and Reserves.

of Powering Assuming a no-over-

load condition for the ship, involving only the plating, structural, and coating roughnesses to be expected in the clean, new

unavoidable condition,

a typical speed-power

indicated by

AGB

curve

as

is

in Fig. 69. A. If the clean,

new

maximum designed power under perfect trial conditions, the speedpower point would be at B and the speed would be Fmsx If the power were limited to 0.95 of the maximum designed value, the speed-power point would be at G and the speed would be Firiai Running the vessel at the power Pmsi with A;, per cent of increased resistance due to adverse ship were run at the

f Mas

,

•

•

elJects,

along the curve

AGE OVERLOAD"

DGjC marked "AVER-

on the

figure,

gives

the

speed-power point C for a speed somewhat less The ship can now than the trial speed Ft rial run at this speed with maximum designed power •

Pmox

or

it

can run at a reduced speed Vt with

GENERAL DESIGN OF PROPULSION DEVICES

Sec. 69.10

0.95 of

Moximum Designed 5hoft Power

No Covilotion Allowances

Shown Here

Curve of Shaft Power on

Speed

FULL OVERLOAD

=

Pfv^q,,

577

Mochirier>)

less

for

Conditions, Involvinc) Storrrnj

Unexpected

Weather, Heavu Foulinc),and

Adverse

Effects~^

Curve of Shaft Power on Spaed for^ AVERA&E OVERLOAD, with Averoe^e

5 peed Vy Power Pg5 Under Perfect

Adverse Wind and Sea and Averaoe Bottom. Points on This Curve.

Trial

ot

Foul

ore Often Selected for

Trial Conditions

Propeller-Desiqn Points, Represent(nq Averaqe Conditions ^-r

'^^

>

Lower

^^^Curve

_^

^^

Ends of

Curves

All

^,

;.

^^^wer on

Speed with

NO OVERLOAD

but Includinej

Resistance and Normal

Still-Air

Not Shown

,

of Shaft

Rouqhness Allowance for o Clean, New Correspondinq to Model Basin Prediction for These Conditions

Vessel,

Curves Are for Desicjned Displacement and

Ship Speed, kt Fig. 69. a

"^Sustained

95 per cent of maximum power. Under what might be termed "FULL OVERLOAD" conditions,

^Triol

Explanatory Diagram for Powering Allowances in a Large Vessel sustained

corresponding to the curve FGaE, and

utilizing only 95 per cent of the designed

maximum

speed

and

of

up with

keeping

its

schedule.

Unfortunately in practice the designer rarely if

ever knows the precise location of the average-

is able to maintain a sustained speed Fsu.t at the speed-power point Gj If the ship is really to sustain this speed for

overload or the full-overload speed-power curves on his plot, despite the availability of procedures such as those in Sees. 45.22 and 60. 15. He is reason-

must be capable of running faster of the time. Assuming full-over-

ably certain in the design stage of the no-overload,

power, the ship

.

,

long periods

it

than Fsust part load conditions

by

Fig. 69.

A

all

the time this

unless the

power

is

is

not possible

increased above

P95 (and above Pm^i as well). Rather than to

do

assumed, and logically

this it is

sustained speed

is

so,

that the

to be achieved under average-

overload conditions, along the curve

DG2C

in the

This means that with a sort of average power, represented by the ordinate of the point H, figure.

the ship has a reserve of power represented the ordinate

HG2 With .

to P95 at the point Gi

,

this reserve, it is

by extending up

capable of achieving

This speed is somewhat less than but as long as the speed margin (F, — Fsu.t) is greater than the possible speed reduction (F3 — F4) to be anticipated over any lengthy period, the ship is assured of maintaining the the speed Fa FTriai

,

•

speed-power Fjuns

and

curve

FTrioi

•

AGB, with its values of He knows, furthermore, that

the speed-power values along the curve

AGB

be checked by carefully conducted ship

He also knows may therefore

the required sustained speed. select a

can

trials.

He

speed Fi such that the

speed margin (Fi — Fsust) is sufficient in his opinion, and in the judgment of the owner and operator,

From

to

make good

the sustained

speed.

the no-overload ctu've of the figure, this

speed Fi then corresponds to the point A, also easily determined in advance with reasonable

accuracy and subject to confirmation on trial. The corresponding power is PNom, which with an average overload should give a speed F3 ,

,

slightly in excess of the sustained speed or at least

not

less

than that speed. For most ship

IIYDROnYNAMICS IN SHIP DESIGN

578

about 1.25 or 1.30 times PNorm Pm.i One means of making this procedure more precise is to have the self-propelled model run with an estimated average overload, say 1.25 designs,

is

times the no-overload ship resistance, as mentioned

DGiC

preceding

the

in

as well as curve

Then curve

section.

AGB

is

obtained and the

speeds Fj and V^ are predicted reasonably well.

The next problem,

equally as important as the

establishment of these speed-power-overload relationships,

is

propeller

is

selecting the condition for

to be designed.

First,

it

which the must be

capable of absorbing the power Pm.i at some rate of rotation n which can be acliieved by the engine

when

that power.

delivering

Second,

it

must

operate efficiently at either P95 or PNorm whichever the owner and operator thinks most im,

higher speed

This

is

its best.

power

sarily the

This

for

usually but not neces-

is

which the propelling plant

is

designed to run most efficiently and economically.

At the power,

ship speed,

and overload condition and

selected the rate of rotation of the propeller

the propelhng plant must also correspond.

In general, the propeller-design point

taken as Gi

in Fig. 69.A. If so,

a check

is

may

insure that the propeller efficiency does not off

appreciably at the points

D

be

made

and H. This

one reason

why some

reluctant to

work a propeller near the peak

its

efficiency curve,

designers

propeller

to

fall

of

for fear that at the lower

loadings and real-slip values the so-called working

point

If

pass

will

hump and

slide

over

down

the

maximum-efficiency

utilized the

maximum power Pmsi

is

can be devel-

oped only at the exact rpm for which the engine designed. This rate of rotation must in turn correspond to a certain ship speed for that power.

is

If

maximum

efficiency at a sustained speed cor-

of these points,

what was done in Table 64. ABC design, when the trial kt was required at a power expendi,

corresponding to the point

G

on Fig. 69. A. To prevent the problem from becoming too complicated, especially as overload values are not accurately known, the ABC propeller is also designed in Chap. 70 for the speed-power point G. The data from the model self-propulsion test, without overload, correspond to that point. The additional shaft power from P95 to Pjnax is taken care of by the macliinery designer.

Under other circumstances the

propeller could

be designed equally well for the points Gi or G2 depending upon advance knowledge as to over,

machinery to be installed, the judgment of the designer, and the wishes of the owner and operator. loads, the type of

Feathering,

Adjustable,

Reversible, or Controllable Features.

Feathering

the steep side of the r/-curve.

internal-combustion propelling machinery

designed

Sec. 66.9 for the

ture of 0.95PMai

is

ai'e

maximum

essentially

speed of 20.5

ship to do

at

embody one

therefore logical to

the selected power and to an overload condition operator wishes the

for,

say G, as one of the design requirements and to call for a check of it as a sliip-contract stipulation.

and

the owner and

Sec. 69.11

aimed

power corresponding to an average overload at the point C, the speed-power and the propellerdesign points are then represented by that point. It is again emphasized that speed-power points such as G2 or C are only achieved accidentally on a ship, when the overload from all causes happens to be either the average or the full value assumed by the designer. It is therefore not possible to check these points on an actual ship by full-scale tests. On the other hand, the speedpower points B, G, and A are easily reached and checked under planned trial conditions. It is

portant, and at a ship speed corresponding to at which

is

69.11

Selection

of

features on paddlewheels form an integral part of

the design of these devices.

are discussed in Sees. 71.6

and

As such they

71,7.

Feathering and folding propellers are fitted

almost exclusively on sailing yachts with auxiliary

desired, the speed-

power, as a means of reducing the drag of the

power point G2 should be the propeller-design point. Although F is also a point on the full-

stationary propeller. Notes relative to their use

responding to

full

overload

overload speed-power curve the power developed

is

it

may

not represent

by the internal-combustion

are found in Sec. 71.13.

Adjustable sci'ew propellers, described briefly in Sec. 32.19, carry blades

whose position

relative

the engine-

hub can be changed only when the adjusting mechanism is out of water. They permit

propeller combination can drive the ship at full

pitch changes in the event that the ship resistance

engine at a rate of propeller rotation corresponding to the speed V^

overload

at

the

.

However,

speed

if

corresponding

to

the

almost certainly can, with some lesser power, maintain the slower speed at F. If a point G2

it

to the

in service is

found not to agree with that predicted

in the design stage.

manner

is

Altering the pitch in this

one means of insuring that internal-

GENERAL DESIGN OF PROPULSION DEVICES

Sec. 69.13

combustion engines can run at the proper rate of rotation to develop their

maximum

power. It

may

found in service that fouling rates, with consequent increased friction powers, are higher than those contemplated during the design. also be

The

foregoing advantages, including the very-

practical one of replacing a

damaged

blade, are

balanced against the slightly diminished efficiency resulting from the larger hub and from unfairness

around the blade attachments. This matter

is

propellers,

which

in

the

blades

swivel and the shaft continues to rotate in the

same

eliminate

direction,

reversing

mechanism

in the

and

gears

reverse

propelhng plant. This

only done at the expense of mechanical com-

is

pUcation in the shaft and the propeller, increased

diameter and bulk of the propeller hub, and

hydrodynamic disadvantages described in However, if reversibihty of thrust is the primary object, the latter are not too importcertain

Sec. 32.19.

ant.

The problems

are then primarily ones of

engineering rather than hydrodynamics.

So many extraneous problems enter into a no attempt is made to give them here. The designer decision to use controllable propellers that

may

with benefit study the references Usted in

and repeated here

Sec. 32.19 (a)

McEntee, W., 43-47

SNAME,

Gutsche,

(c)

Ackeret,

(d)

Fea, L., Ann. Rep.

F., Zeit. d. Ver.

1927, pp. 87-91,

and

Pis.

Deutsch. Ing., 15 Sep 1934,

Escher-Wyss

Bull.,

May-Jun

Rome Model Basin,

1935, p. 63

1938, Vol. VII,

pp. 74-89

Rupp,

(e)

SNAME, Burrill,

(f)

A.,

L.

L.

"Controllable-Pitch

Propellers,"

C, "Latest Developments in Reversible IME, 1949, Vol. LXI, pp. 1-11; INA,

1949, Vol. 91, pp. J3-J32

Nichols,

H.

J.,

"An

Propeller System,"

Hydraulically Controlled

Motorship,

New

York,

C-P

May

1949, pp. 22-23, 44-46 (h)

(i)

(i)

J., "Cruceros y Lanchas Veloces (Cruisers and Fast Launches)," Buenos Aires, 1951, p. 209 Doell, H. A., "What is the Controllable-Pitch Propeller?" Mar. Eng'g., Aug 1953, pp. 71-76 Van Aken, J. A., and Tasseron, K., "Comparison Between the Open- Water Efficiency and Thrust of the Lips-Schelde Controllable-Pitch Propeller and

Baader,

those of Troost-Series Propellers," Int. Shipbldg. Prog., 1955, Vol. 2, No. 5, pp. 30-40.

A

Do not expect be found worth while to install a controllable propeller solely to enable the propeller to run at the proper pitch for any given loading that

word

it will

of caution is included:

is

made

much

service installations are in

to present

better positions

to design controllable propellers than

the ship

is

designer.

The fairing caps of the hubs of many controllable shifting

mechanism and are as long

than the propeller hub proper.

It

if

not longer

may be necessary

an allmovable rudder blade to clear the hub cap [Mar. Eng'g., Feb 1953, p. 1; Jan 1955, p. 104]. 69.12 Propulsion Devices to be Used with Contra-Vanes, Centra-Guide Sterns, and ContraRudders. In general, as described in Sees. 33.12, 36.8, 36.9, and 37.16, it is immaterial whether to cut a notch in the leading edge of

rotation

is

introduced in the inflow jet of a screw

and taken out by that propeller or whether the rotation produced by the propeller is taken out by a contra-rudder or equivalent device placed in the outflow jet. However, for a given propeller

average resultant water velocity at the blade elements, the angular speed of the propeller if

some rotation

the inflow jet ahead of

it.

is

is

imparted to

Actually, as far as the

concerned, it may be proceeded with on the basis of no prerotation, following which an adjustment may be made to determine the probable angular speed for a given is

torque and thrust.

Good

propulsion-device design, and good ship

design as well, calls for a thrust-producing device

1948, pp. 272-358

Propellers,"

(g)

and so any of them in this chapter. It may be assumed that organizations which have produced successful complex that no attempt

usually sUghtly less

for convenience:

1073 J.,

in the detailed design

of controllable propellers are so speciaUzed

design of the propeller

(b)

p.

The problems involved

1948, p. 273].

propellers contain essential parts of the blade-

discussed at length in Sec. 70.43.

Reversible

579

SNAME,

condition [Rupp, L. A.,

which inherently leaves as turbance as possible in requires the least

amount

rotation in the inflow

little

its

systematic dis-

wake,

and which

of predeflection or pre-

jet.

Disadvantages of Unbalanced Propulsion-Device Torque. On semi-planing and planing craft carrying multiple propellers below the hull in such position that the flow to both the port and starboard sides of each propeller is sub69.13

stantially the same, there are

numerous

practical

reasons for selecting and installing main engines

and propellers which rotate in the same direction. However, this arrangement has the disadvantage that,

because of the rotation in the propeller

outflow jets or races abaft the propellers, there

may

be a resultant asymmetrical lateral force It may be difficult to find

from the rudder (s).

HYDRODYNAMICS

580

may

the neutral angle for each and this angle

IN SHIP DESIGN

Sec. 69.14

are usually too small to be of

any considerable Indeed, if any

change with speed. An effect of this kind is more pronounced when the rudders lie within the propeller outflow jets. Furthermore, there is a cumulative torque reaction from all the engines which results in an appreciable listing or heeling moment and an ever-present heel at moderate to high speeds. This heeling moment due to torque should be counteracted, not by a fixed moment, as of ballast or rnachinery asymmetry, but by a torque which

benefit

varies generally as the engine torque, increasing

during which any ship

gradually with speed and power. This

operation, the requirements for developing astern

best

is

in

maneuvering.

rapid

is to be made in a vessel's turning path it is necessary to reverse the wing propeller(s) on the inside of the turn. It is doubtful if any vessel carrying screw propellers can have its turning characteristics materially improved by any practicable positioning of the wing screws or wing shafts at a large distance from the center-

drastic change

plane.

Despite the overwhelming percentage of time

employed

is

in

may and

ahead

accomplished by applying a hydrodynamic torque

thrust and for maneuvering

which automatically increases with speed. For right-hand engines and propellers, a positive heeling moment is required, acting to produce a starboard heel. On some V-bottom planing craft [Bureau of Ships Bull, of Inform. 32, 1 Oct 1948]

influence the design of the propulsion device (s).

the chine spray strip

furthermore, enter and leave the water vertically,

is

modified to slope

edge downward and outward, giving

it

its

lower

a negative

dihedral angle with the bottom of the boat.

The

water moving out transversely from under the boat is deflected sharply downward, and an upward force results from this change of direction.

often do

For example, on a paddle tug with independent frequently employed in backing and

wheels,

turning, the paddle blades are properly straight

if

without too

this is feasible

An

They

than curved in section.

rather

which

icebreaker

thrusts to

fulfill its

much

needs

mission

complication.

powerful

may

have screw propellers with blade sections nearly completely

or

symmetrical,

as

for

the

propellers of the double-ended ferryboat.

an

starting, stopping,

as to develop a

lift

the propeller outflow

jet,

so

force forming a torque opposite

to that of the propeller. Fig. 73. P illustrates

and

By and

large

propulsion devices with large thrust-producing areas.

The

larger these areas the better, since

the form of a cross, placed in the outflow jet of a

upon the thrust-load

single screw propeller to accomplish this purpose.

the disc area.

and size of the propulsion devices when maneuvering is a major consideration. For stopping and running astern, some design comments and pertinent references are given by J. E. Burkposition,

hardt [ME, 1942, Vol.

I,

pp. 35-38]. Fortunately

69.15

V a the thrust depends

advance

for a given speed of

sented here a few features relative to the type,

screw

any special requirements for and turning are fulfilled by

Sec. 73.21 describes a pair of twisted hydrofoils in

69.14 Propulsion-Device Design to Meet Maneuvering Requirements. The design of ship hulls to meet maneuvering requirements is discussed in Part 5 of Volume III. There are pre-

astern

advantageously

The hydrodynamic compensating torque is also produced by a well-cambered hydrofoil placed in offset position in

should,

factor

and ultimately upon

Relation of Propulsion-Device and Hull-

Vibration Frequencies.

A

discussion of machin-

ery and hull vibration as such

is

definitely outside

the scope of this book. Nevertheless,

it is

pointed

out here that the rate of rotation of the propulsion devices, whatever their type, should not be fixed until a study has

been made of the probable

vibration characteristics of the hull and propelling

machinery

under

ME,

[Lewis, F. M.,

various

loading

conditions

1944, Vol. II, pp. 130-137;

and McGoldrick, R.

SNAME,

there are available sufficient data from tests of

Kane,

model propellers running

1949, pp. 193-252]. This insures that the propul-

references of Part

5,

astern,

listed

in

the

to enable the designer to

J.

R.,

sion-device

rpm

T.,

or the blade frequencies n{Z)

do

check the ability of a propeller to produce a

not coincide with a 2-noded or 3-noded hull

There are

frequency in vertical or horizontal flexure, so that a slight mechanical or hydrodynamic unbalance

specified thrust for astern operation.

also available in Sec. 60.18 the results of backing

on one self-propelled model. While it is true that ships can be and have been steered by changing the rates of rotation of wing propellers carried by them, the turning moments tests

is

magnified over the whole ship. Strictly speaking,

the

torsional

hull

frequencies

should

also

be

estimated and compared with the proposed shaft

rpm.

GENER/VL DESIGN OF PROPULSION DEVICES

Sec. 69.15

It is usually easy to design or to alter local

581

Probable torsional and longitudinal resonant

structures or small parts of the ship to keep their

fre(]uencies

resonant frctiucncies out of the range of propdev

turbine (or motor) system are likewise estimated,

rpm

or blade frequencies at speeds where the

exciting

forces

are

high.

However,

to

make

material changes in these characteristics of the hull proper, or of large parts of

nigh impossible.

it,

is

often well-

of

the propulsion-device-shaft-gear-

to insure that they

shaft

or

do not

fall

within the range of

blade frequencies at

or

near service

power or maximum desigued power [Sullivan, E. K., and Scarborough, W. G., SNAME, New Engl. Sect.,

Apr

1952].

CHAPTER

70

Screw-Propeller Design 70.1 70 2 70.3 .

70.4

70.5 70.6 70.7 70.8

General Considerations Design Requirements for a Screw Propeller Comments on Available Design Methods and Procedures Requirements for, Availability of, and Listing of Propeller-Series Charts Comments on and Comparison of PropellerSeries Charts Prehminary-Design Procedure, Employing Series Charts Modification of Series-Chart Procedure for Other Design Problems Preliminary Comments on Propeller-Design .

Features

70 9 70.10 70.11 .

Determining the Rate

of

Rotation Ratio;

70.16 70.17

Choice of

583

70.27

584

70.28 589 592

596

598 599 600

Number of Blades

Use of Raked Blades

Hub Fairing ...

601

Determination of Expanded- Area Ratio; Choice of Blade Profile Selecting and Applying Skew-Back Design Considerations Governing Blade

602 603

Propeller-Hub Diameter;

....

Width

605

70.18 70.19 70.20

605 606

Partial

Type of Blade Section Blade Edges and Root Fillets Bibhography on Screw-Propeller

Design Design of a Wake- Adapted Propeller by the

606

70.21 70 22

ABC Ship Propeller Designed by Lerbs'

70.23

Choice of the Number of Blades for the ABC Design Determination of Rake for the ABC PropeUer

Selection of

Shaping

of

Circulation .

.

.

Theory

609 1954

Method

70.24

.

Pitch

Variation with Radius

70.12 70.13 70.14 70.15

70.25 70 26

596 597 597

Selection of Propeller Diameter

The Proper Pitch-Diameter

583

582

611

612 612

70.46

SCREW-PROPELLER DESIGN

Sec. 70.3

Must not

avoids major duplication and appreciable overlaps

"(III)

with published material in books, papers, and

vibration

reports, especially those readily available to the

"(IV)

The major

average marine architect. is

method

ABC

ship, the hull of

which

is

laid

out in Chaps. GG, 67, and 68. This description, inciis believed to be among the first based

dentally,

on

theory by which

this

all

the elements in the

by a continuous, straightforward procedure. This makes it suitable for a design are derived

mth

no background or experiknowledge of flow and circulation and its apphcation to the ship and screw-propeller combination, to be found in Chaps. 14-17 and 32-34 of Volume I of this book. The symbols, terms, and definitions employed in this chapter conform to those listed in Appendix 1 of this volume. They are described in SNAME Technical and Research Bulletin 1-13, containing "Explanatory Notes for Resistance and Propulsion Data Sheets," July, 1953, and illustrated in Figs. 32.F, 32.G, and 32.H of Sees. 32.8 and designer

Uttle or

ence, save the

"(V)

Must be

manship

must be better

erode, or at least

in this

and first-class workfrom trouble.

of sufficient strength

to ensure a long

life

free

"The information given in the papers gave no guidance in these directions. It might be the case that these 'purchaser's' requirements can be

met

but it is surely a serious on ordinary practice to suggest that propellers as now fitted are, on the average, 10 per cent less efficient than they might be." 70.3 Comments on Available Design Methods and Procedures. It is expected, when many minds work on a problem in the atmosphere of a democratic way of fife, there will be many fines of attack and many partial or complete answers. This is as it should be, because different kinds of answers are required for different situations. Furthermore, the problem screw-propeller design in particular is so complex that no single line of attack can do more than make a rather narrow path through the entire region to be in exceptional cases,

reflection

covered.

The procedures now architects

itself.

McAlister,

when

discussing

the

among naval

use

heavily theoretical to the intensely practical, but situation.

For example, as long ago as 1938 a propeller

in

and marine engineers vary from the

fortunately

the practical needs of the ship

—

—

Design Requirements for a Screw Propeller. It is possible that one reason for the shortcomings in the numerous design methods and procedures, including those discussed in Sec. 70.3, is a partial lack of appreciation of the basic requirements to be met and of the practical needs of the ship owner and operator. Perhaps even more basic are what might be termed 70.2

F.

be due to the existing propeller

Must not

32.9.

designer,

must eliminate whatever

of Dr.

along for a propeller to be used with the transomstern design of

or

respect than the existing propeller

portion of

devoted to a description of the H. W. E. Lerbs for the design of a screw propeller, based on the circulation theory. Accompanying a step-by-step description of this method, a sample calculation is carried the chapter

short

may

583 vibrate

each

An

is

useful

engineer

may

in

some particular a propeller

select

diameter and pitch by some simple formula or

nomogram and

order a propeller out of a catalog, he and his assistants may toil for several months, calculating a propeller design for which no ready rules or precedents are available. The day is past, or nearly so, when the marine engineer sketched his propeller freehand in the foundryman's notebook, penciling in the few principal or

dimensions. It is well to recognize, therefore, that

a group

symposium on marine propellers [NECI, 1937-1938, Vol. LIV, pp. D141-D142], declared that, as reported in SBSR, 6 October 1938, page 415, "none of the papers in the symposium tabulated the qualities required (the italics

scheme of things, even in a so-called advanced age. For example, in the design of the underwater hull of the ABC ship, begun in Chap. 66, one of the principal aims is to swing as large a propeller

are those of the present author)

as possible.

results

of

a

for full-sized

of several of these

methods has

its

place in the

Since the limit of ideal efficiency

He

described in Sec. 34.2 increases as the thrust

suggested that from the purchaser's point of view these requirements were:

loading decreases, and the latter decreases as

propellers for ships under service conditions.

"(I)

That the (new)

possible efficiency

"(II)

—

propeller

must be

of the highest

say 10 per cent (or more) than the average existing propeller

efficiency

Must not

sing or be unduly noisy

higher

the propeller diameter increases,

it

works out

that the larger the propeUer, the greater the propeller efficiency, aU other things being favorable.

The

draft, is

tentative diameter of 20 ft, on a 26-ft based on a propeUer somewhat larger

HYDRODYNAMICS

584

than that given by the rule of thiunb, equal in this case to 0.7(26) or 18.2

When,

D <

IN SHIP DESIGN The

0.7//,

that

ft.

at a later stage of the design, after the

first

Sec. 70.4

group labors under the disadvantage

applies only to propellers with the

it

number

of blades,

same

blade shape, section shape,

had been estimated, together with the wake and thrust-deduction fractions, it

and so

was possible to calculate the thrust-load factor and to know that it was low, as desired. When the shaft power was estimated, it was found from

concerning the nature of the physical water flow

resistance of the hull

charts

propeller-design

several

propeller

would absorb

that

a

when running

it

20-ft

at a

when

was necessary to pick a suitable stock propeller for the model self-propulsion test, the P/D ratio and other still

later stage,

knowledge

deficient in that factual

is

around a propeller and the applicable hydrodynamic theories, as well as the necessary confirmations of the latter, lag rather far behind the necessity for knowledge to give the practical answers.

reasonable rate of rotation.

At a

on, as the propellers of the series tested.

The second

The

it

principal characteristics were determined approxi-

chart

method

only what happens to moments on a propeller

tells

the overall forces and

which someone has already fashioned, whether it

be well fashioned or not. The analytic method

mately by several established methods, called chart methods, mentioned presently and de-

ing of the physics of the problem, which governs

scribed in Sec. 70.5.

the forces and moments, and hence to an indica-

For the of the

latter part of the preliminary design

ABC

ship, a final design of screw propeller

for a second series of

was

carried through

model tests (not conducted) by the Lerbs short method,

based upon the circulation theory, described in Sees. 70.21 through 70.38.

lations required at different stages of a ship

Some

design

call

call

for

tion

just

of

how a screw

propeller should be

fashioned to give the desired results.

Requirements

70.4

Availability of,

for,

Listing of Propeller-Series Charts.

and

should be

It

recognized at the outset that any chart or analytic

procedure may, and probably will take a different

These several methods are mentioned to show that the approximations, estimates, and calcupropeller

leads gradually but surely to a better understand-

different

these 5-sec, 5-min,

procedures, depending upon

5-hr,

how soon

and

procedures.

and 5-day the answer

wanted. The precision of each is of the same Others call them the 1st, 2nd, 3rd, and 4th approximations. The important fact is to realize that the first approximation is based upon the application of one single rule of thumb; the last one upon all is

order as the time required.

the scientific and engineering information avail-

them have their logical functions in the design of any one propeller. In general, neglecting the thumb rules, the various procedures fall into two groups: able. All of

Those based upon systematic experimental model propellers in methodical series, with uniformly varying parameters and characteristics. The data, when checked and analyzed, are put in the form of graphs, diagrams, or charts, whence the name chart design. (2) Those based upon the application of hydrodynamic theories and knowledge of flow, embodying such gap-fillers and correction factors (derived usually from experimental data) as are required to compensate for lack of accurate and adequate knowledge here and there.

form, depending upon the characteristics that are given or fixed

and those which are to be

derived. For the pvn-pose of this book, one pro-

cedure only of each kind

freedom

characteristic

ance,

embodying

described,

is

of choice for the designer in that

which should,

him

permit

the

primary

for the best perform-

leeway.

greatest

For

example, in the hull design of the ABC ship, roughed out in Chap. 66, the weights to be carried

by the

ship are specified, as

the speed,

is

leaving the length free for selection of the

optimum

dimension.

For the propeller designs to be worked out as examples in this chapter, the power to be absorbed is governed by that required for driving the hull at the designed speed. It

is

anticipated

that the best screw propeller will be that having

(1)

the greatest practicable diameter, so the hull in

data, derived from tests of

the vicinity of the propeller position

is

designed

with this in view. Strictly speaking, this means that the propeller diameter is fixed at the beginning of its design, but at a figure which should

produce a most tion, the

efficient wheel.

The

rate of rota-

pitch-diameter ratio, and other factors

remain to be selected so as to give high propulsive efficiency in service. In other circumstances the

propeller

power and rate

of rotation

might be

with the best diameter to be found. Regardless of the primary characteristics given

fixed,

SCREW-PROPELLER DESIGN

Srr. 70.4

and to be derived, a good screw-propeller dala sheet or design chart meets the following require-

ments, listed in the order of their importance:

Possibility

(6)

by auxiliary

585

and

There should be

(k)

effect of cavitation,

perhaps

charts. sufficient charts in a

to permit a propeller designer to enter

group

them with

As for any graph of its kind, it should ". show at a glance the variation of the most import-

given values of any of the primary variables

ant dependent variables with the independent

Future chart groups should embody the (1) approved symbols adopted by the International

(a)

.

variable" [Schoenherr, K. E.,

SNAME,

.

1951, p.

629]

The range

of the sheet or chart should cover

Towing Tank Conference.

reasonably be

expected

Propeller-series charts must necessarily be adaptable to the several variations of the design problem actually encountered. These depend upon

(c) The most important variable to be derived from each sheet should appear in the formulas applicable to that sheet in its first power and should occupy the principal position in the formula

which factors are known or given and which are unknown. K. E. Schoenherr has set down this situation in systematic fashion, from which the following is adapted [PNA, 1939, Vol. II, p. 159]:

(b) all

propulsion conditions that

may

or chart (d) The primary numerical design values to be taken from the chart should require little or no interpolation between curves to give the precise engineering answer (e)

The primary

variable on at least one sheet of

a group should be the pitch/diameter ratio (f) The chart should be readily entered and the desired values found without effort, confusion, or misunderstanding. It

charts than to

embody

is

better to have separate

too

many

features on one

chart. In other words, a propeller design chart

"should possess graphical simplicity, permitting ease of I'eading and interpolating" [Kane, J. R.,

SNAME, (g)

All chart parameters should be dimensionless,

derived by simple substitution and calculation

The

chart should be no larger than necessary

for the precision required in ship

and propeller

design but large enough for easy visual selection of the data desired (i)

practicable, for determining the values of chart parameters and certain physical quantities (j)

With

at least three variables given, the chart

the data for the preliminary

all

design of a screw propeller, specifically: (1)

Diameter, pitch, and pitch-diameter ratio

(2)

Number

of

,

,

the best efficiency.

Second, Final Design. Given the curve of effective

P E as a function of ship speed V, the prodiameter D, the rate of rotation n (in rpm) and the engine output in horses, at the designed rpm, as delivered to the propeller shaft. Required power

to

find

the

efficiency

570

propeller ,

blades

(considering propeller

A

considerable

propeller

obtainable

41-44; Gawn, R.

(5)

Maximum

(I)

SD, 1933, Vol. II, Fig. 14 and pp. W. L., INA, 1937, pp. 159-187; van Lammeren, W. P. A., RPSS, 1948, pp. 251Baker, G.

or actual open-water efficiency

number

Charts of R. E. Froude; also known as the R. W. L. Gawn [Froude, R. E., INA, 1892, pp. 292-294; INA, 1908, pp. 185-204;

Hub-diameter ratio

expanded-area

shape

or both

V

available, in one

(4)

(3)

the

of chart groups are form or another, to the propeller designer. These are fisted hereunder, as an adaptation of a listing and a description by F. M. Lewis [SNAME, 1951, pp. 612-613]:

now

series charts of

ratio,

P,

under the given conditions. Third, Analysis. Given the propeller dimensions, the ship speed V, the shaft power Ps the propeller thrust T, and the rate of rotation n, in rpm. Required to find the fractions Sr for real slip, w for wake, and t for thrust deduction.

ratio, mean- width and blade-thickness fraction Blade shape (outline) and blade-section

efficiency only),

pitch

and the ship speed

,

Nomograms should be embodied, wherever

should yield

Preliminary Design.

Given the designed ship speed V, the corresponding effective power Pjs or total resistance Rt and the propeller diameter D. Required to find the propeller pitch P and the rate of rotation n (in rpm) for the best propeller efficiency. (ii) Given the designed ship speed V, the corresponding effective power Pe and the rate of rotation n of the propeller shaft. Required to find the propeller pitch P and diameter D for (i)

peller

1951, p. 626].

with dimensions in any system of units to be (h)

First,

256].

S.,

HYDRODYNAMICS

586

The

coefficients are, in

Baker's notation:

X =—

Slip constant

IN SHIP DESIGN

dimendo not produce ship-design data for

sional they

—

where

,

Sec. 70.4

in fresh water. Since the coefficients are

is

A''

in

water unless a correction

salt

made

is

for the

mass density [Kane, J. R., SNAME, 1951, pp. 625-626]. D. W. Taylor's statement that "... marine propellers work in water of ." [S and P, 1943, practically constant density differences in

rpm, D in ft, and Fi (= Va) advance in kt Diameter constant

is

the speed of

.

where

H

speed of advance in is

from

kt,

P

and

D

are in

ft,

and

B

a thrust factor for the blade type, actually an

arbitrary function of blade-area ratio.

The

latter

presumably the ratio Ad/Ao Cross curves of the diameter constant Y and the revolution constant X^Y are plotted on a grid of X, Y, and is

.

77(eta).

The

Gawn's

series

The method charts

is

developed-area

A^/Ao

ratio

up

propellers extended

W.

1.10.

R. E. Froude-Gawn

of using the

explained by

to

of

van Lammeren

P. A.

in

detail in the reference cited. (II)

Charts of D.

W. Taylor

99-102, 109-112, 275-292].

in

Nov

Va

is

Berlin, 1916. Later published in English in

was virtually a

,

where

P

Vol.

sequently in

WRH,

see

also

pp.

15

W.

Nov P.

of

blades

is

generally

coefficient,

_nD

= nD

(or

such

where

IJ is

is

is

is

the

the diameter, and

the speed of advance,

Revolutions-torque

where ,

V a)

where n

~Va

Ve

in con-

all

sistent units

.

v\

van Lammeren,

coefficients are:

Slip constant C,

VE

1934, Vol. 15, pp.

A.

1948, pp. 191-196.

the

the propeller power

added as a subscript to the basic as 5p3

Bu =

XL,

254-320 and Pis. II-XII. Some of these data were published sub1923-1924,

324-327;

is

NECI,

Propulsive Efficiency of Merchant Ships,"

the speed of advance in kt

VI horses. The number

what

on the subject, entitled "The Influence of Propeller Revolutions Upon the treatise

rate of rotation in rps, Z)

NP°

in

Charts of K. Schaffran. First published in in "Systematische Propellerversuche (Systematic Propeller Experiments)," Strauss,

basic coefficients

is

Va

given by L. P. Smith [ASNE,

German

and P, 1943, pp.

in rpm, d

is

1935, p. 562].

[S

is

ships operate in

water that varies

(Ill)

The

A''

in

fully fresh to fully salt.

kt from 5 to 50,

A

y

diameter in ft, and

B,

where

,

and others

table of values of Va^, for a range of

RPSS, The

Nd = -:^

8 (delta)

A

.

Many

too sweeping.

is

fresh water only,

the thrust power in horses, Vj the

is

100]

p.

p/D _fl_ r ifi) D'Vl 1{P/D) + 21J\bJ'

M

is

constant

=

C„„

Uy

'71'

the torque

the thrust power in

Diameter-torque constant

d^ =

horses.

Cross curves of

P/D

and

6

efficiency e are plotted

of

abscissas.

Other chart forms are used with the

as ordinate

Diameter-thrust constant

and Bp or B^ as

on a grid

is

d

=

where &

DVj,

the thrust

coefficients:

,

"^

p/d,

U

Revolution-thrust constant C„

U

Cv = a

where a

is

the pitch ratio

diameter, and p .

lOOOaU

— yA

,2x^3

a

,

,

^,

,

,

where the symbols are as de-

scribed previously for the Taylor charts.

These

coefficients

and

charts, as given in the

reference quoted, are for model propellers tested

VI

d and C, on C„

.

W. Schmidt ["Zusammenfassende

Darstellung von Schraubenversuchen (Summarized Description of Propeller Experiments);" this

a pamphlet published by

Zeit. des Ver. Deutsch copy in TMB Ubrary. See also a paper entitled "Vorausberechnung der Giinstigis

Av =

basic grids are C. on

(IV) Charts of

UOOO/

the thrust power in horses, d is the is the pitch, both the latter in ft

is

The

=

Ing., in 1926;

sten Schiffsschraube

(Calculation

of

the

Most

Favorable Ship Propeller)," by H. Volker; abstracted by W. Hinterthan in WRH, 1 Dec 1939,

SCREW-PROPELLER DESIGN

Sec. 70.4

pp. 368-370]. Schmidt's presentation was based upon the model-test data of K. Schaffran.

The

J (= F^/nZ) by standard

coefficients are

= NP" 'Vr2.5

B„

587

P

where

,

the propeller power

is

vl

ses in English horses

notation) and:

lOOOl^lP

©

PHP

©

PHPw"

PHP

®

,3

where

pD'Ve

PHP

is

Ve = Va is the speed of advance in kt, and D is the propeller diameter in ft. There is another set of coefficients in which the propeller power is replaced by the thrust power. Cross curves of P/D ratio and e ( = tjo in standard notation) are plotted on a logarithmic grid of coefficient

coefficients are

=

a

=

Bu

=

— — ^:rrj73

— D

© of the preceding

The

list.

J

other

determined by inclined logarithmic

[PNA,

(V) Charts of K. E. Schoenherr

1939, Vol.

the pitch in ft

is

IP

'

„2.6

,

U

where

the thrust power

is

m

English horses

^ (— V

=

V,

K„

coefficient,

A (lambda) rjj,

scales.

where Ho

,

D •(my Viooo/

the propeller power

in horses,

and

A„

where K, the

the 0-diml thrust

is

0-diml

torque

the advance coefficient

coefficient,

Vs/nD, and

the propeller efficiency.

The contours are 8 and tj, on a grid of Ho/D A^ on a grid of the same kind, Cp ratio and Bj, on the same kind, and £„ on the same kind. (VII) Charts of L. Troost ["Open Water Test Series with Modern Propeller Forms, Part 3, Two-Bladed and Five-Bladed Propellers," NECI, ,

II,

pp. 158-168].

The

principal coefficients,

Thrust

coefficient

K,

all

dimensionless, are:

= prv'd*

1950-1951, Vol. 67, Part

Torque

coefficient

K^ correspond d

is

K. = —^,i

pna

to the standard

,

Kt

where K, and

and Kq

,

and

This

known

3, pp.

89-130].

a later system developed by Troost,

as the continental or "/i(mu)-o-(sigma)"

system.

The

principal relationships are:

the propeller diameter

H Efficiency

The

is

e

=

values of K,

^{^ ,K^ and ,

= V efficiency e are plotted

to a base of J.

(VI) Charts of L. Troost and

Lammeren [RPSS,

W.

P.

A. van

These pp. are based upon a so-called A-series of model propellers, copied from G. S. Baker, in which rather narrow blades and airfoil sections give good performance but are suitable only for lightly 196-223].

1948,

loaded propellers, outside the cavitating range; and a so-called B-series, in which wider blades are able to carry greater thrust loadings, the

e{-qn), and (^(phi) are and
Cross curves of P/D,

plotted on a grid of

J.

Kane [SNAME,

R.

The

coefficients are '550

B

from cavitation are small, and the propellers are generally free from singing.

PHP

/

,

where A^

is

the rate of rotation in

the propeller diameter in F„ (=. Va) is the speed of advance in kt

1951, pp. 626-627; also

limited,

550

where

J and: to be used

pVl

basic coefficients are:

ND 8 = -r-^ rpm, D is

ju

p. 629].

losses

The

= n

PHP PHP

to is

when n is

limited

be used when

D

is

the propeller power in

English horses. ft,

and

Cross curves of e

(=

efficiency

P/D

r/o),

and

are plotted on grids of J,

B

or

A (delta).

HYDRODYNAMICS

588

W. Keith

(IX) Charts of H. H.

IN SHIP DESIGN

(formerly pro-

Loading

MIT). These were carefully drawn to about 7.25 in by 7.25 in, but were never pubUshed. They involve two coeffifessor of naval architecture at

coefficient

Efficiency e(=

jjo)

Sec. 70.4

Ku =

=

jf^'^'

cients:

Cn

= NU°

(this

is

with D.

identical

W.

Taylor's B^j) tto.s

Cr,

DV\

PD'V}

These charts give contours of the 0-diml coefficients Kt Kq Ku and e (= efficiency r?o), as listed in the foregoing, on a basis of J and P/D, using data from the Wageningen B.3 and B.4 series of model propellers. A number of examples in the reference cited show how these ,

,

,

charts are used.

where

A''

the rate of rotation in rpm,

is

D

thrust power in English horses,

diameter in

ft,

and Va

is

is

U

is

the

the propeller

the speed of advance

inkt.

values of the advance coefficient are extremely

The values

of

(= efficiency rjo) are Co and P/D. The latter scale

Cn and

plotted on a grid of

e

uniform and exceptionally

is

(XIII) Charts of W. E. Fermann, formerly of the General Motors Corporation, developed specifcally for towing and similar situations where the

of these charts are in the

(X) Charts of 631-633].

The

J.

large.

Photostats

TMB library.

G. Hill

[SNAME,

1951,

pp.

_ —

P

These charts are

in four groups:

Design coefficient So = VA[p
peller

principal coefficients are;

(_

low.

J =

ep

and advance coefficient and a reference line of

101. 3dV a/ {Npd),

with So constant Design coefficient S^

2TrQn

ei>(Maj)

vD'V

abscissas

= V a[p/{PsNp)]^''^ ratio a = p/d

as

and pitch-diameter

as

ordinates (uniform scale), with contours of ep and

J = 101.33V a/ (Npd), and (Sjv

where

V is the speed of advance {V^ in ITTC nota-

tion)

and

all

The shown by

other symbols are standard.

propeller efficiency

ijo

(not so marked)

is

contours on the two sets of diagrams. To render them more compact they are plotted as the square roots of Cp and Cs on a base of J in each case.

(XI) Charts of C.

W.

Prohaska. These are log-

arithmic-type diagrams based upon the earlier charts of G. Eiffel and W. Schmidt. They embody both the dimensional coefficients of D. W. Taylor and a group of corresponding 0-diml coefficients, with double inclined logarithmic scales. Examples of these charts are given in Figs.

to follow,

and

and they are described

in Sees. 70.5

70.6.

cients are:

Thrust

Torque

1951, coeffi-

line of e^jMaj,

with

Design coefficient Eo = VA[pd^/PuY^^ as aband pitch-diameter ratio a = p/d as ordinates (uniform scale), with contours of Cp and J = 101.33V a/ (Npd) and a line of ep(Mai) with Ej) constant Design coefficient E.y = Va[p/{PuNp)Y^^ as abscissas and pitch-diameter ratio a = p/d as ordinates (uniform scale), with contours of ep and J = 101.33V a/ (Npd) and a line of epfu^x) with scissas

Etf constant.

Here Va

is

the speed of advance in kt,

the shaft power (per shaft) in horses,

Np

Ps is

is

the

propeller rpm, d the propeller diameter in ft, p the propeller pitch in ft, and p the mass density of the water.

As mentioned

M. Lewis [SNAME, 612-615 and 618-620]. The principal

(XII) Charts of F. pp.

70.A and 70.B

a

constant

previously, Fcrmann's charts are

particularly valuable for the design of propellers for tugs

and

for

towing purposes which operate

at low speeds of advance and high thrust-load coefficient

coefficient

Kt =

T pn'D*

For many of these problems the range of D. W. Taylor's charts is entirely inadequate. The Fermann charts have not been published factors.

or circulated but a set

Kq = p7l'D

library.

is

available in the

TMB

Sec. 70.

SCREW-PROPELLER DESIGN

•)

known, the design methods and charts developed by C. W. Dyson ["Screw Propellers," Simmons-Boardman, New York, 1924] are no longer used by propeller designers. 70.5 Comments on and Comparison of Pro-

So

as

far

Some

peller-Series Charts.

charts listed

peller-series

or

in

all

Sec.

certain disadvantages, rendering

of the pro-

70.4 possess

them

than

less

convenient for the use of the propeller designer:

Schmidt

The parent teristics known

series of

designs.

models possesses charac-

"Nouvelles R6cherches sur la R&istance de (New Research on Air Resist-

(1)

I'Air et I'Aviation

ance and Aviation)," Paris, 1914 Ex^cutfe Pendant la Guerre, (2) "Travaux 1915-1918 (Projects Completed During the War, 1915-1918)," Paris, 1919

"L'Etude sur

have

they

of the chart

and so on. This is makers but a feature in-

herent in their age. necessary to interpolate between irreg-

(b) It is

ularly curved lines to find the proper

The

D. W. Taylor admirable in

[S

and

this

P/D

Bp and Bu

basic series diagrams or

ratio.

charts of

P, 1943, pp. 275-292] are

tion

scales of pitch-diameter ratio, closely subdivided. (c)

It is necessary to

make preliminary

tions or tabulations, to

draw an

on the chart, and to locate curves

chart

certain

its

before

intersections with

determining

the

The

charts as reproduced in the literature

are too small

and too crowded with

everyday work. This situation

some

in

cases

by procuring

may

lines for

be remedied

large-scale prints of

They

advance

coefficient ,

The Fermann

many

J

or large values of the real

as for problems involving towing.

charts are in effect inversions of

paramlow advance coeffi-

of the standard charts, in that the

eter values corresponding to cients

and

the group based upon tests of single propellers.

One such diagram diagram

This

useful

in

7j„

,

all

cient

the

preliminary

logarithmic

a rather concentrated serving of technical all on one piece of paper.

information,

logarithmic method of presentation, as

Eiffel in

,

ordinates are a series of simple

ranging from 0.006 to

1.0,

for

the

vertical scales are logarith-

There are 4 diagonal scales on the diagram, and 1 single. The upper scales of each

of

the

three

was originated by Gustav

France and later developed by Wilhelm

pairs

represent

values of the factors A,

Ba

,

Taylor's notation, respectively.

dimensional

the

and Bp

of

D. W.

The mathematical

expressions for each of these, in English units of feet,

column

in

horses,

and knots, are

the upper left-hand

The lower

0-diml factors

6,.

in

listed

corner

of

a

the

scales of each pair represent

the 0-diml thrust-load factor Ctl

The

The

Kg

,

3 double

type of propeller chart has much to recommend it. This is on the basis that the designer does not object

far as can be learned,

Kt

Both horizontal and

fraction

so-called

propeller

0-diml coefficients and for the efficiency fractions.

The

to

The

S.

numbers,

and operations other than propulsion must be the

usual

the

two separate scales, are 0-diml values of the advance coefficient ./ and dimensional values (in English units) of the Taylor advance coeffi-

design of a ship, where backing, maneuvering, considered,

presented in Fig. 70. A.

and open-water efficiency non-dimensional. The abscissas, embodying

diagram.

Considering the rather varied amovuit of proinformation

is

contains

characteristic curves of torque coefficient

tons,

extra-large real-slip ratios are at the

working ends.

peller

data from the Wageningen series of propellers developed by L. Troost but there are others in

are not usable for small values of the

slip ratio Sr,

in Copenhagen. diagrams are based upon test

of these

mic.

the charts from the originators. (e)

Prohaska, of the Institute

Denmark,

of

thrust coefficient

value of the parameter desired (d)

Many

calcula-

auxiliary curve

W.

that of C.

is

Technology

of

with their uniform

respect,

of

the most useful, as well most comprehensive logarithmic presenta-

as the

root sections that are too thin,

no fault

(A Study

The most modern and

root

ogival

sections, blade outlines without skew-back, blade

I'H^lice Aeri6nne

the Airscrew)," Paris, 1920.

to be inferior to those of later

Specifically,

589

Germany, indicated by the following

references to Eiffel's work:

(3) (a)

in

and bg

,

and the basic

of Prohaska, respectively.

fourth single scale gives values of the 0-diml

TD/Q.

Prohaska charts, such as those 70. A and 70.B are adapted, carry additional scales showing the values of Kt and tjo for / = 0, and the values of / 7vo for Kq = and Kt = 0. These hmit scales are omitted from the reproductions to avoid excessive original

from which

,

Figs.

,

complication.

The

values on the three curves of

Kq Kt and ,

,

HYDRODYNAMICS

590

Sec. 70.5

IN SHIP DESIGN

PROPELLER FOR DOUBLE-ENDED TERRYBOAT

H.EN0RD5TROMJ947 Number

Z" 3

Blodes

of

Exponded-Areo Ratio

0.42

°

Me on- Width Ratio (Width Qt 0.9R)/(MeonWidtl^ Pitch Ratio P/D--

0.960

Blode-Thickness Fraction^ 0.045

Hub-Diometer Ratio d/D'0.16 Ro><e Angle

Sl<ew-

Bock

=

:

Zero None

Blode Sections Symmetricol

Wash Back:

LOGARITHMIC /j= 1.99

^

Kt

Ib-sec^/ft^

n

is

m

rps

Ka

N

is in

rpm

,-

PROPELLER DIAGRAM

Diameter

of

Model Propeller

Units for Mixed Form are

jo6''"'af>' 'yid

Fig. 70.A

in:

ton s, feet, Horses, knots '

Screw Propeller Logarithmic Chart of C. W. Prohaska for a Single

'7o"

SCREW-PROPELLER DESIGN

Sec. 70.5 7/0

of Fig. 70.

A

by a them

are related to each other

vertical ordinate intersecting all three of

at the particular advance coefficient

J

(or

8)

Such an on the figure through the points C, E, and F. Corresponding values on the three double and one single inclined scales are determined by dropping perpendiculars on them from the three intersecting points C, E, and F, indicated in the diagram. A single perpendicular is dropped from the r/o-curve interat which the propeller

ordinate

is

drawn

in

is

operating.

broken

lines

CM

section to the scale of

TD/Q. Two perpendiculars

E on the Kr curve, one to the double scale of first basic coefficient and the other, EG, to the double scale of thrustload coefficient. A single perpendicular is dropped from the point F at the Kg-curve intersection to the point H on the double scale for the second are dropped from the point

By

first

591

basic coefficient br at the intersection near E.

By and

large, the use of

any particular

series

chart for the preliminary design of a screw pro-

same kind of answer. on the basis that the test data for the model propellers from which the charts were constructed did not suffer from scale or surface effects, that the observed data are accurate and peller gives essentially the

This

is

carefully plotted,

and that the use

of dimensional

expressions does not omit important factors or

unknown errors. For example, since model propellers are almost invariably tested in

introduce

fresh water, the derived data are also for fresh

A

water.

omitted

mass-density factor p(rho) for

convenience

which

simplification,

or

was done by D. W. Taylor, may make a 2

is

as

or 3

per cent difference in ship-propeller data calcu-

SNAME, 1951, SNAME, 1951, p. 628].

lated for salt water [Kane, J. R.,

having the two scales of each pair opposite each other at the feet of the perpendiculars EG, FH, and the second short perpendicular from E, it is convenient to pick off either dimensional or non-dimensional values,

p. 626;

or to enter the diagram with these values.

characteristics worked out from the charts was rather more than would now be acceptable. It must be remembered, however, that the parent propellers all had rather different characteristics, especially with regard to mean-

basic coefficient.

Assume that a symmetrical-section

CEF

is

propeller

erected through the point

comparison of

ago by H. F. 8-24].

The

discrepancies between the five sets of

E

width ratio and blade-thickness fraction. Unfortunately, a more modern comparison is not

worked out in the same detail. Some comments are to be found in the discussion of a recent paper by F. M. Lewis available,

and the 0-diml J value is read from either the top or the bottom scale as 0.596. If the speed of advance Va and the propeller diameter D are known, the rate of rotation is obtained directly from the relationship n = Va/(.JD). The actual working efficiency at the point C on the ijo curve is read off from the side scale as 0.6L

rather general

type of

initial

The 0-diml value of the second basic coefficient bg is determined by dropping a perpendicular

desired

by

F

whereupon the 0-diml value of bg is read off as 0.313. With the values of mass density p, speed of advance Va and rate of rotation n all known, the torque Q is determined from the bg formula given on the diagram. The power Pp which will be absorbed by the propeller is calculated from the derived values of n and Q. If the rate of rotation n is given and the power Pp is known, corresponding to the situation in Sec. 59.15, the torque Q is derived by direct from

to the inclined scale at H,

,

calculation.

value of

The

TD/Q

T is

found eitheiifrom the at the intersection M, or from the thrust

kinds of propeller-series

five

was made some two decades D. Davis [ASNE, Feb 1932, pp.

charts then in use

preliminary-design

such as that depicted on Fig. 70. A is to be used and that the 0-diml thrust-load factor Ctl is L065. The scale of Ctl is entered at the point G and a line GE is drawn perpendicular to that scale until it intersects the Kr-curve at E. The ordinate

A

Schoenherr, K. E.,

[SNAME,

1951, pp. 621-641].

For a beginner in the find so

many

bewildering to

field, it is

kinds of charts,

all

ostensibly for

the same purpose, but actually varied to suit the

data and the nature of the answer

several groups of people, experienced

in these procedures. It

is

likewise

most confusing

to find different symbols on each kind of chart,

with some expressions dimensional and others non-dimensional. After trying them that are available, he

decide which meets his

all,

or all

in better position to

is

own

particular needs,

either for analysis or for practical design. It is characteristic of

any and

all

propeller-

procedures that the numerical values required for the full-scale ship are obtained only by estimating the wake fraction w and the series chart-design

thrust-deduction fraction

t.

The Vq of the openVa on the ship,

water test corresponds only to

whence

V =

Fx/(1

—

w),

and the thrust T

HYDRODYNAATICS IN SHIP DESIGN

592 required of the ship projieller

Srr. 70.6

greater than the

derived in Chaps. 66 and 67.

predicted total ship resistance i?r by the ratio 1/(1 0- Further, the propeller efficiency t/b

speed, for wliich the propeller

behind the ship is greater (or less) than the openwater efficiency ijo by the relative rotative effi-

this speed

is

Pb

is

is

—

These three unknown factors may be trial data on similar ships [Davis, H. F. D., ASNE, Aug 1932, pp. 332-352; Schoenherr, K. E., PNA, 1939, Vol. II, Chap. Ill] or, as is usually the case, they may be determined from tests of a self-propelled model. ciency

Tjfi

.

estimated from analyses of

Preliminary-Design Procedure, Employ-

70.6

ing

Series

For the screw-propellerin this book several

Charts.

design procedure set

down

of the series charts are utilized in the preliminary-

design stage,

particularly

characteristics

and

determining the

for

for selecting a suitable stock

propeller to be used in the first self-propulsion tests of the

ABC

ship models. This

not to be

is

taken as an indication that series charts are suitable for making only first approximations in the early stages of a ship design. In fact, by far

number

the greater

of

propellers

practice and manufactured for up from these charts, insofar

designed in

worked

ships are

as the propeller

features can be determined from them.

The

is 20.5 kt. The ship resistance at estimated in Sec. 66.9 as 171,830 lb, or say 172,000 lb. The corresponding effective

performance,

power

10,827 horses.

estimated from Eq.

is

The wake

(60. ii)

in

fraction

Sec.

w

60.8 as

from the 0.255 example in that section because it is calculated at an early stage of the design, using preliminary dimensions and parameters instead of the final ABC values inThis figure

0.261.

is

worked out as the

different

illustrative

serted in the illustrative example.

The thrust-deduction fraction by the method described in Sec.

•

/

estimated

is

applying a 15 per cent reduction to the value derived from Eq. (60. vi) because of the very thin skeg con60.9,

templated ahead of the propeller. This gives a predicted value for ^ of 0.111.

To keep the

propeller loading as low as possible,

consistent with good performance, four (4) blades

are to be used. This means that the blade width and blade thickness can be small, with a resulting rather high efficiency. The mean-width ratio

Cm/D to

references of Sec. 70.4 in which the various

The designed ship is to give optimum

taken tentatively in the range of 0.20

is

The

0.25.

assumed to be

blade-thickness

fraction

t^/D

is

describe in considerable detail the procedure to be followed .for the particular problem at hand.

These values are typical for 4-bladed propellers [PNA, 1939, Vol. II, p. 157] and are considered reasonable for the first approximation. Since adequate

In many cases they also contain examples worked out to illustrate these procedures.

aperture on the transom-stern

charts

propeller-series

As examples series

of the

there

charts

are

methods are

published

usually

of using propeller-

given

here

employed and the calculations made

the

steps

for the pre-

liminary design of a propeller for the transomstern

ABC

ship,

leading to the selection of a

stock propeller for self-propulsion tests of the first model.

The (1)

of

clearance

EMB

of

down

in

ahead

tests

PNA,

should not be unduly large. There appears to be therefore, of raking the blades, especially

as they

would then have to be thicker to with-

stand the offset centrifugal forces. preliminary-design procedure

described and illustrated

and

SNAME, That

F.

M.

Lewis, based

upon

tests of

B-series propellers, as described in

W.

five

ratio,

three

20

ft,

-qo

graphs, one each for a given

Fig. 70.A. In addition there are three

(i)

P/D

plus the four sets of diagonal scales of

.1 is

all

somewhat more intricate

70. B, adapted from one of these charts, contains five sets of Kq graphs, five Kt graphs,

Certain data were taken as basic for methods, using a propeller diameter D

of

is

used in a somewhat different manner.

efficiency

of C.

is

Prohaska's pro-

Fig.

and

1951, Vol. 59, pp. 618-620

is

Prohaska, based upon logarithmic charts embodying the test data of the Wageningen B series of model propellers. (3)

first.

peller-design chart, as contrasted to the propeller-

data chart of Fig. 70. A,

(2) That of Wageningen

and

no need,

design charts

through 4

ship,

the inclination of the streamlines in the

thin,

1939, Vol. II, pp. 158-168, including propeller1

ABC

of the propeller is relatively

inflow jet with reference to the propeller axis

The Prohaska

K. E. Schoenherr, based upon

series propellers, as set

allowed in the design of the propeller

since the skeg

following three methods were used:

That

is

of the order of 0.04 to 0.05.

maximum-

graphs for use when:

The tbrust-load known

coefficient

Ctl

or the factor

Sec. 70.6

Fig. 70.B

SCREW-PROPELLER DESIGN

Logarithmic Chaet of C. W. Prohaska for Five Propellers, Wageningen B.4.40 Series

593

HYDRODYNAMICS

594

The basic factors br or Bu are known The basic factors bg or Bp are known.

(ii) (iii)

For the study on the diagram for the B.4.40

number

series

is

its

This

selected.

expanded-area ratio

The mean-width

0.40.

ratio

only

is

from the information block in the upper right corner, but this group of propellers appears to correspond most nearly to that desired.

The first step is to find the thrust-load coefficient Ctl using the expression Ctl — T/{Q.5pAqVI). The thrust T is obtained by dividing the total resistance Rt oi 172,000 lb by (1 - ^ = 0.889; it is found to be 193,476 lb. The speed of advance ,

is

the ship speed, 20.5 kt, times

0.739], or 15.15 kt.

The

[(1

—

=

w)

thrust-load coefficient then

becomes 193,476

—

Ltl

(0.5)(1.9905)(0.7854)(20)'[(1.6889)15.15]'

=

0.945.

Prohaska's chart. Fig. 70.B, is entered on the lower of the pair of upper right-hand diagonals,

marked Ctl

Draw

a perpendicular to this line

Ctl =

0.945, marked on the diagram by an arrowhead. Where this perpendicular crosses the graph marked "tjmsx for Ctl ,"

at the value of

P/D from the Kt curves for various P/D ratios. The optimum P/D value corresponding to the interpolate for the correct value of series of five

crossing

marked with an "x" on the diagram

is

1.02.

From of

draw a vertical line to the Where this line cuts the series

this crossing

top of the diagram.

efficiency curves, at a point corresponding

r/o

P/D

of 1.02, marked by a small solid circle, read the corresponding efficiency value ?jo From the scales at the right or left the open-water

to a

•

efficiency is 0.68.

Continuing up the vertical

fine to the

lower

horizontal scale at the top, the value of the ad-

vance

J is read off as J = Vo/inD) or the rpm as follows:

coefficient

relationship calculate Vo_

JD

_

Vj_

JD

_

0.703. ra

1.6889(15.15)60

= =

From

the

Vo/{JD),

109.2 rpm.

(0.703)20

If this rate of rotation

appears to be not suit-

some reason or other, it may be necessary to sacrifice some propeller efficiency for a desired rate which is faster or slower. The amount so sacrificed is determined by following the procedure able, for

and

values for the crossing of the Ctl perpendicular and the graph of "r/Max for Ctl or A," they are picked for the crossings of that perpendicular

with the several values.

open

The

circles.

The

P/D

Table

70.a.

in

TABLE

Kt

Thrust-

P/D

marked by small

values derived for the complete

available on the chart are listed

Variation op Epficienct with Rate OF Rotation and P/D Ratio

70.a

The data listed here are propellers

graphs for a range of

latter crossings are

range of

0.189,

VA

r/o

J

ship, the propeller

series is

Sec. 70.6

described, except that instead of picking

indicates that the propeller has

four (4) blades and that

Ab/Ao

ABC

IN SHIP DESIGN

for the

Wageningen B.4.40

from Prohaska's logarithmic

series

chart, Fig. 70.B.

SCREW-PROPELLER DESIGN

Sec. 70.6

Then Schoenherr's

K, =

K„i{J)~. For a range of

values of the advance coefficient 0.80,

J from

O.GO to

the calculated values of K, are listed in

Table

70. b.

TABLE From

The parabola corresponding

Data for Plotting Auxiliary Curve on Schoenhbrr Chart 70.b

the text, K,^

Advance

to these

Coefficient

=

0.371245

=

0.371.

A',

=

K,,J^

0.1336 0.1569 0.1819 0.208S 0.2376

values

At the

is

then drawn lightly in pencil on Chart

L

intersection of this pencil parabola with

the heavy broken line marked "eMax (or rjuax) for Ktd Const." the following optimum values are picked off:

595

HYDROnVNAMICS

596

gave graphs and rules for finding the developedarea ratio of a screw propeller in the preliminary-

Data

["Recent

stage

design

on

pp. 39-47].

1,

ABC

to the

The

Sec. 70.:

[RPSS, 1948, pp. 259-260], based upon the following references:

Cavitation

Criteria," Inter. Shipbldg. Progr., 1954, Vol.

No.

IN SHIP DESIGN

following values pertaining

transom-stern design were used to Ad/Ao by the procedure on

HSPA, 1940, Vol. II, p. 46 C, lESS, 1934-1935, Vol. 78,

(a)

Kempf,

(b)

Conn,

(c)

Gebers, F., Schiffbau, 1933, p. 235

(d)

Robertson,

1,

G.,

J. F.

C, MESA,

J.

p.

27

1929, p. 102.

calculate the ratio

The only comprehensive data

page 45 of the reference:

Thrust to be delivered by the propeller

in salt

water, 193,476 lb

Rate

n (assumed), 109 rpm

rotation

of

or

advance Va or

of

Ve

15.15 kt or 25.59

,

per sec

ft

Number

of blades Z, 4

Submergence

propeller axis below at-rest

of

waterline, 15.5 ft

Assumed height at-rest

WL,

of

stern-wave

Value of pressure head

(p„,

—

e,

peller

ft

,

=

0.532.

one of the alternative calculation methods Manen the value of Ao/Aa (his

given by van

0.546.

chart

series

The developed-area

ratio

is

expanded-area ratio, at least for not-too-wide blades, so that no distinction need be made between them. The diameter is thus slightly smaller than that sufficiently close to the

Comments

is

intended

for

at least

some indication

of

the effect of these

changes upon the predicted performance of the

new

A

design.

few

of the principal propeller features

to be decided

have

upon before the preliminary design

begun; they are the given quantities, so to

the final design computations for the ABC propeller, at the end of Sec. 70.31, give a r&t\o A e/A^

of the blade profile or the rake.

indicating reasonable agreement with

any proand

analysis

valid only for other propellers

is

of 0.478,

Propeller-

having the same geometric shape and physical characteristics. For example, systematic data based on tests of model propellers having small solid hubs do not represent the expected performance of full-scale propellers with larger built-up hubs. In the case of almost every new design it is necessary to depart from the parent propeller in some physical respect. The designer must have

in the calculations preceding, and the pitch-diameter ratio is some 5 or 6 per cent less, but the area ratio is considerably larger. However,

assumed

on

speaking,

Strictly

ft.

pitch-diameter ratio P/D, 0.952

is

Preliminary

Design Features. 48.5

design purposes

Developed-area ratio Au/Ao

FJF)

F.

70.8 e)/iv,

Cavitation number ao at a value of R/Bm^^ 0.8, in the 12 o'clock position, 4.01

By

what might

Nordstrom in "Screw Propeller Charac[SSPA Rep. 9, 1948]. In this report Nordstrom presents the results of tests on nine 4-bladed model propellers, with P/D ratios varying from to 1.6, over a range of advance coefficient J from -|-2.0 to —2.0. The problem of designing screw propellers intended to run normally in the partly immersed condition is discussed under surface propellers in

by H.

1 ft

ft

values were:

Diameter D, 19.75

for

backing conditions are those given

Sec. 71.10.

Atmospheric-pressure head, 33

Mean

above

1 ft

Assumed vapor-pressure head

The derived

crest

full

teristics"

1.817 rps

Speed

be termed

available on the

model propellers

characteristics of

speak. Others can be determined after the principal

known, such as the exact shape

characteristics are

An

alternative

method

is

preliminary designs with

to

work up a

series of

the given quantities

the foregoing.

varied systematically, and then to select the best

Modification of Series-Chart Procedure For preliminary for Other Design Problems. designs in which the propeller is required to have

development toward a done by K. E. Schoenherr for four different propellers, to determine the effect of varying D and n [PNA, 1939, Vol. II, Table 18,

70.7

good backing performance, as for tugs and ferryboats, there are few propeller-series charts available. The stopping and backing situation is discussed rather fully in Part 5 of Volume III of this book. Suitable propeller-design features are well set forth

by W.

P. A.

van Lammeren

of the series for further final design.

This

is

p. 172]. If series charts are used, the

for each design

is

time involved

so small that this should almost

be considered as routine procedure. Rather than to burden the description of the series-chart

method

in Sees. 70.5

and 70.6 or the

SCREW-PROPELLER DESIGN

Sec. 70.10

Lerbs short method in Sees. 70.21 through 70.38 with paragraphs involving considerations of engineering instead of analysis for hydrodynamics, there are given here

some

comments on the

brief

selection of certain physical features as governed

by the problem

in hand.

Selection of Propeller Diameter. 70.9 In both the series-chart and the Lerbs short-cut exaritiples worked out in this chapter the propeller diameter is selected in advance. If there are operational or other limitations on diameter, the designer has Httle or no freedom of choice. He must do the best that is possible under the circumstances, but with a clear understanding on the part of everyone concerned that it is not the best that could be done if he were free of these

propeller

was

597

to keep the thrust-load coefficient

low and to obtain a wheel that would work in a region of the highest possible ideal and real efficiencies, the latter represented by a value of about O.Sjjj Another reason was that pointed out by E. K. Sullivan and W. G. Scarborough in their paper on "Machinery Design of the Schuyler Otis Bland" [SNAME, 1952, pp. 467-503]. There (on page 474) they stated that, as a result of .

their studies, "the largest propeller that could be

accommodated would have the

Objections against large casting and shipping

and weights can be overcome by developments in detachable blades and welded assemblies described in Sec. 70.43. It is assumed in the sizes

limitations.

foregoing that the

he has freedom of choice as to diameter, he proceeds on the basis that the propeller is the most important unit in its part of the ship, and that it can have whatever diameter best fits it for the task to be performed. If propulsive efficiency is not a primary requirement then almost any available propeller can be used and only

propeller shaft can be

If

the sketchiest of design procedures Sec. 34.2 describes

why

and

is

illustrates the reasons

and the lowest thrust loading may be expected to work at the highest real efficiency. Some years ago K. E. Schoenherr said ". in general, that propeller

is

optimum diameter.

D

quantity and

is

rate

rotation

of

and

n

the

of

adjusted to suit the

is

If not, n becomes a given one of those to be found by

the design procedure.

Means

of

determining the proper diameter,

and comments on optimum screw-propeller diameters, are

given by:

necessary.

screw propellers with the largest diameter

.

annual

least total

operating cost."

(1)

PNA,

Schoenherr, K. E.,

1939, Vol. II, pp. 159, 165,

170, 172 (2)

Van Lammeren, W.

(3)

Lewis, F. M.,

RPSS, 1948, pp. 232-233 1951, pp. 619-620

P. A.,

SNAME,

(4)

Van Manen,

(5)

Edstrand, H., "Model Teats on the

J.

and Troost,

D.,

SNAME,

L.,

1952,

pp. 446-448

.

the best choice which has the largest

eter for Propellers,"

SSPA Rep.

Optimum Diam-

22, 1953 (in

EngUsh).

diameter admissible in the propeller aperture"

[PNA,

1939, Vol. II, p. 166]. F.

M. Lewis removed

the latter restriction by saying that "In nearly cases of

all

will

modern

be the largest that

1951,

p.

619].

way

is

practical,

the ship hull

If

accommodate the other

optimum diameter

ships the

propeller,

.

.

is

."

[SNAME,

designed to

rather

than

the

around, the latter will be properly

guarded against

air

leakage from the surface,

against racing at sea, against rotating through a region of excessively high wake, and against

other

ills

to which a large propeller

is

all

supposed

to be subject.

The

aim in the prehminary design of was to swing the largest possible single propeller. This was the reason for developing the arch type of stern, which permitted a propeller diameter D of 24 ft on a draft of only the

26

principal

ABC

ft.

from

The arch air

effective

ship

hull

is

recess afforded effective shielding

leakage and

was hoped) equally protection against racing when the

pitching.

(it

The reason

for using the large

If

the propeller power and the ship speed are

low, the friction

becomes large

and pressure drag

of the blades

in proportion to the thrust.

Some

by reducing the propeller optimum given by the

efficiency 7nay be gained

diameter

below the orthodox design procedures. However, the designer is cautioned against any reduction of this kind for higher powers and higher speeds, where it

may result in an actual loss arguments against this are

The by H.

of efficiency.

set

forth

Edstrand, in reference (5) preceding, especially pages 24-27 and Figs. 13 and 14. His diagrams illustrate

in

clearly the reasons for decreasing

one case and holding

Determining

70.10

Closely

related

diameter

is

to

it

the

the

D

in another.

Rate

selection

of of

Rotation. propeller

a determination of the proper rate

of rotation. On the basis that the propeller designer has the same freedom of choice as for propeller diameter, and that optimum propulsive perform-

ance

is

desired, the rate of rotation

n should be

HYDRODYNAMICS

598

maximum

that which gives the

under the

Tjo

propeller efficiency

or designed-load

trial

conditions

DESIGN

IN SHIP

the selected

P/D

Sec. 70.11

ratio (interpolated

gives the working efficiency

When

specified.

propulsion

is

by a piston-type

internal-

which the mean

effective

pressure in the cylinders

solution, several practical requirements are to be

value,

met before this value can be approved, as it were. The first involves the ability of the selected or

Sec. 69.8, to

probable type of propelling machinery to deliver the required torque and power at the specified

maximum

rate of rotation. This situation

is

discussed at

some length by J. E. Burkhardt [ME, 1942, Vol. I, pp. 28-33]. It is assumed here that no problems are presented because of the type of engine and the reduction gear or transmission system

of

employed.

K. E. Schoenherr illustrates a procedure whereby the effect on propeller efficiency tjo of varying n, P/D, and certain other variables is readily determined [PNA, 1939, Vol. II, p. 172 and Tables 19, 20]. the vibration

Finally,

characteristics

the

of

and the machinery

ship, the engine, the shafting,

foundations must be considered

when

the rate of rotation. However, this

selecting

primarily

is

a matter of the number of blades, and as such

is

torque very carefully in order to achieve the full

neglecting transmission losses.

It

most im-

is

portant, therefore, that after the engine

is

selected

both the pitch and the diameter of the propeller be correct for the shaft power and rate of rotation available.

Experience through the past several decades that inaccurate predictions almost always err on the side of designing a propeller which absorbs too much power at the specified rate of rotation. If slowed down to match the indicates

power less

of the engine, the rate of rotation is usually

than for

remedy

maximum engine power. The common

to cut off the blade tips; this enables

is

Assuming that the rate

propeller.

Variation with Radius.

of rotation for the designed is fixed,

or rated brake power. In other words,

power of the engine is to be utilized, deUvered at a certain rate of rotation and at none other, the power absorbed by the propeller connected to it has to be exactly the same, the

if

but often

power

maximum

limited to a

becomes necessary, as pointed out in match the rate of rotation and the

it

The Proper Pitch-Diameter Ratio Pitch ;

specified

is

the engine to run up to rated speed (and power)

discussed in Sec. 70.12. 70. 11

necessary),

in

While the design procedures described by examples in this chapter give n as a part of the

combustion engine

if

to be expected.

r;

maximum

or that

it is

certain limits, the pitch of the propeller

next factor which logically evolves, zero real shp the effective pitch

is

There

or other

to he within

a great deal of discussion in the litera-

wisdom

the necessity of attempting to match the

the

or

since

for

pitch

speed of advance divided by the rate of rotation.

is

shape of a useful part of the

ture on screw propellers concerning the

is

the average

spoils the

each radius with the average wake is under-

at

velocity at that radius. This matching

taken on the basis that the blade element at each work at an effective angle of attack

and ship-design purposes the pitch-diameter ratio is found to be a preferable

radius should

parameter.

elements should not be underloaded while others

However,

for analysis

In Sec. 34.15 the of too high

and

illustrated.

all propeller-series

blade tips involves excessive tip-vortex losses.

possible to pick a

maximum

lodnnx)

P/D

ratio

propeller efficiency

working conditions. In Fig. is noted that there is a

it

curve of optimum efficiency

A

of

In practically

it is

for a given set of

jjodua:;)

for thrust-load

normal to the inclined double A cuts the heavy line for at the best J-value. Interpolation between

Ctl

by any reasonable method

reckoning. Furthermore, overloading the extreme

70.B, for example,

scale for

overloaded,

are

some

for that radius. Obviously,

ratio are described

which gives the

factor

on propeller efficiency

is efficient

P/D

and too low a

design charts

rjo

effects

that

line

Ctl and

Kt for the various pitch-diameter along the normal line mentioned, gives the optimum P/D values. A point vertically above

Three situations are to be considered here, in which there may be: (I)

An

appreciable variation of

wake

like

torpedoes,

tion,

ratios,

coincides with the

on the curves

of efficiency

tj

for

velocity

fraction) with radius

the values of

this intersection,

wake

from the propeller axis, combined with a reasonably uniform wake velocity around the circumference at any radius. This situation occurs abaft most bodies of revolu(or

(II)

Some

when

body

the

propeller

axis

axis.

consistent variation of

with radius from the propeller

wake

axis,

but

velocity in

which

SCREW-PROPELLER DESIGN

Sec. 70.12

the magnitude of

wake

velocity around the cir-

cumference at any radius

is

highly irregular. This

the case in the disc position of a single screw

carried abaft a centerline skeg

on a ship

of

normal

form. (Ill)

tlie

ideal or

hydrodynamic

by the adoption of these procedures is very is overshadowed by the effects of blade-efficiency (i.e., section-drag losses, etc.) introduced by the changes in angles of incidence where the wake concentration is high efficiency

small,

is

599

gain which might be achieved in

and

On the other hand, the above results suggest that no from the adoption moderate pitch variations which are favourable from the point of view of cavitation or flow breakdown, and this leaves the designer considerable freedom in the "(3)

A

possibility or probability of cavitation, or

special loss in efficiency is to be expected

of

perhaps a certainty of

it if

the effective angles of

attack of the blade elements at each radius are

not kept within certain limiting values. Although cavitation is not normally to be expected in the

upper blade positions of the propeller of a singlescrew ship, it can and probably does occur if the vessel is fast and if it is driven hard in a loading condition where the at-rest tip submergence is small, approaching zero.

Good

propeller design to

meet situation

matter of adopting such alternative pitch-variation lines from root to tip of the blades as might be considered desirable from this point of view "(4) It appears that the

quantity designated relative-

rotative-efficiency has a real

methods

meaning, in terms of the and its value can be

of analysis usually adopted,

estimated by calculation, in the manner described in the paper. The numerical values obtained agree reasonably well with the experimental data."

(I)

a radial variation in

In the example of propeller design by the circu-

pitch corresponding generally to the radial varia-

lation theory carried through in detail in Sees.

unquestionably tion in

wake

for

calls

velocity, so that a given distribution

of thrust with radius fraction is achieved. It

been the aim of

many inventors and

has

ship designers

to incorporate a stern bulb around a single-screw propeller axis which

wake

would produce a high average was reasonably

velocity as well as one which

uniform around a circumference at each radius. However, because of the predominantly upward component of flow under the sterns of most ships, this desirable end has so far not been attained. L. C. Burrill and C. S. Yang made a comprehensive theoretical

study of

many

situations,

involving both uniform and non-uniform

wake

velocities over the propeller disc, for a series of

screw propellers having a great

many

types of

variation of pitch with radius [INA, 1953, pp. 437-460]. In fact, they cover analytically most of the situations that

would be encountered

in a

wide variety of ship designs. They arrived at certain

pitch

phases

a ship

Items quoted

general

and Yang "(1)

conclusions

concerning

radial

which appear to cover most of situations (II) and (III) preceding that designer might be likely to encounter. through (4), listed hereunder, are (1) verbatim from page 446 of the Burrill

variation

From

reference:

70.21 through 70.38 of this chapter a propeller

worked up by the Lerbs short method single-screw transom-stern design of the It

may

ABC ship.

be argued that, by the Burrill-Yang

criteria, the variations in wake velocity and wake fraction for this case, indicated by Figs. 60.M and 60. N, are not sufficient to justify the

design of a wake-adapted propeller. Furthermore, cavitation is not expected to be a problem in the

propulsion of this vessel. Nevertheless, the Lerbs 1954 design procedure is carried through on the basis

that

both

of

these

features

do require

special attention. This renders the design solution

more general

in

character and

makes

fully

it

as described, for a situation where wake variation and the possibiUty of

applicable, radial

cavitation should definitely be taken into account. If large ship propellers could be and were purchased from stock, there might be some reason for omitting a propeller-design calculation that

requires

more than one

or

two man-days. For a

large ship, expensive to run as well as to build,

requiring a custom wheel, so to speak, there is every reason why a propeller-design procedure should take account of all the possibiUties and should take advantage of all the latest develop-

ments

in the art.

the point of view of overall efficiency, and apart

from any consideration of cavitation or flow breakdown, there appears to be no material advantage to be gained from the adoption of a radial variation of pitch, both in a uniform stream and in a variable wake-stream "(2) In particular, it seems that there is no special advantage to be gained from the application of the various alternative methods of design, based on the principle of minimum-energy loss, which have been examined, as any

is

for the

70.12

Choice

choice of the decisions to

of

Number

of

The

Blades.

number of blades is one be made in the design

of the first of a

screw

two more preliminary designs may be worked up as a sort of series, each with a different number of blades. The final selection is usually based on a propeller.

or

As an

aid in reaching this decision,

HYDRODYNAMICS

600

IN SHIP DESIGN

consideration of the natural frequencies of vibra-

machinery foundations, the and the propulsion system

tion of the hull, the

propelling

[Kane,

plant,

J. R.,

and McGoldrick, R.

T.,

SNAME,

1949, Vol. 57, pp. 193-252]. The number of blades which best avoids these frequencies or their major harmonics in the operating speed range is

chosen [Brehme, H., Schiff und Hafen,

Nov

It

is

Sec. 70.13

interesting to note that screw-propeller

designers, even in the earliest days of develop-

ment of this some latitude exercised

number

of blades

it.

Use

70.13

had and usually

device, considered that they in the

of

Due

Raked Blades.

to

the

contraction of the inflow jet ahead of the propeller,

high power requirements, indicate the use of 5 or even 6 blades. Also this number of blades may be

the water enters the propeller disc at a slight inward angle, depicted in Fig. 32. M. A slight rake aft places the blades normal to the flow, with a gain in efficiency. On the other hand, rake causes an increase in the bending stresses in the blade due to the fact that the centrifugal force is offset from the blade root. In heavily loaded or

necessary to keep resonant frequencies outside of

high-speed propellers this latter factor

the operating speed range. Two-bladed propellers are used on sailing ships with auxiliary power, as

the controlling one in limiting rake. Rakes of

abstracted in English in

MENA, Aug

1954;

1955, pp.

318-321].

In some cases restrictions on propeller diameter, or the need for large blade area, coupled with

they

offer

the least resistance

when housed abaft

the skeg in the saiUng condition.

For twin- or multiple-screw ships, a 4-bladed propeller can be of smaller diameter than a 3-bladed propeller for the same power. This means that smaller bossings and struts can be used to maintain the same hull tip clearance. Usually, the reduction in appendage resistance more than compensates for the small loss in propeller efficiency

when using

four blades.

As

in single-

ships, propeller efficiency is usually a secondary consideration in the choice of the

screw

number

of blades. First, there is little variation

between 3- and 4-bladed and second, vibration considerations in efficiency

propellers will again

be the controlling factor, especially for ships of

moderate to high power. In many cases other factors,

inders,

number

such as type of engine, number of cyl-

and the

like,

enter into the choice of the

Further discussions of the proper number of blades to be used for a screw propeller are given by: G. S. Baker, SD, 1933, Vol. II, pp. 49-50 (b) R. H. Tingey, ME, 1942, Vol. I, pp. 277-278 (c) D. W. Taylor, S and P, 1943, pp. 143-144 (d) W. P. A. van Lammeren, RPSS, 1948, pp. 225-226. (a)

Although

it

appears absurd from the point of

balancing and of reduction of bending

over 15 deg are seldom used in any ship or propeller design.

Forward rakes are rarely seen. Sir Charles Parsons at one time advocated a forward rake of 1 in 10 for very thin propeller blades on the high-speed experimental vessel Turbinia. His idea

was that an axial component of the centrifugal them would act in an after direction and

force on

help balance the thrust forces acting forward [Burrill, L.

moments

on the propeller shaft, there are some appi'eciable advantages in the use of a single-bladed propeller. These are discussed by S. Sassi [Ann. Rep. Rome Model Basin, 1938, Vol. VII, pp. 95-99]. There is reported the case of a sliip which normally traveled at 10.5 kt at 70 rpm but which, with all blades except one broken off, made 7 kt at about 85 rpm [SBSR, 6 Mar 1924, p. 289].

C, IME,

1951, Vol. LXIII, p. 15].

In some ship designs, where the maximum volume must be crowded into a given length, the hull profile

is

not only carried well aft toward

the propeller position (s) but the waterlines have large slopes in this region. Blades

may

then be

raked aft to augment the fore-and-aft clearances between the propeller sweep line and the forward

edge of the aperture opening, if the vessel has a single screw, or between the sweep line and the hull, bossings, skegs, or struts if it has multiple

W.

screws.

of blades.

usually

is

P. A.

optimum (a)

van Lammeren [RPSS, 1948,

the following limits (not design or

p. 229] gives

values) for rake:

With moderately loaded screws

vessels, 6 to 10

deg for single-screw

for

merchant and 8

ships,

to 12 deg for twin-screw ships (b)

With heavily

loaded, fast-running screws for

warships generally no rake

When

is

used.

running under load a propeller blade

actually bends forward. This

may

be as

much

as

at the tip of a destroyer propeller.

0.10 or 0.12

ft

Thus

desired to run at the designed speed

if it is

with no rake peller

it

with a

would be wise to design the prolittle

rake aft to allow for this

bending effect. If proper attention

is

given to the details of

SCREW-PROPJiLLER DESIGN

Sec. 70.

the stem arrangement in the design stage, allowing ample clearances in

rake

all directions, little

required. There

is

or

no

usually no excuse to

is

be forced to excessive angles of rake in order to obtain proper aperture clearances. 70.14 Propeller-Hub Diameter; Hub Fairing. Some general comments on hub-diameter ratios

d/D

More

are given here.

detailed

comments

are

but

is

601

attached to the fixed part

the rudder horn, or the rudder in Sec. 74.15

and

the rudder,

t)f

itself,

as described

illustrated in Figs. 66.

Q

and

74.K. It is customary and convenient, as well as good design, to shape the propeller hub and its

cap as a

fair,

tapering continuation of the barrel

or boss just forward of the propeller which houses

means that the end

to be found in Sec. 70.43, under a discussion of

the propeller bearing. This

the mechanical construction of screw propellers.

the propeller hub next to the bearing has a

hydrodynamics hub shape and diameter

diameter about equal to that of the bearing barrel. The end away from that barrel has a

one at the

reduced diameter, as small as is consistent with the necessary mechanical strength and rigidity

It is rarely possible to consider

alone in a discussion of

for a screw propeller, especially for

stern of a hull. Obviously the blades

must be

attached to some sort of hub or enlargement on the shaft, which can not have too small a diameter.

for the type of

Further, the geometric pitch angle 0(phi) becomes

able or demountable blades

very large as the radius

R

zero; too large, in fact, to effective

there

is

producing

in

is

diminished toward

make any

useful

thrust.

blade

lift

Finally,

no point in making the hub much smaller

than the diameter

of the

housing for the propeller

shaft bearing just ahead of

it.

There have been recurring proposals, over the past century or more, for propeller hubs having diameters of one-third or more of the propeller

Some

diameters.

early

ship

propellers

were

way. While it is true that the root sections of a normal screw propeller do relatively little work as a rule, at least they permit the water to pass through, which a large solid hub

attachment

of the

hub

of

to the shaft.

In the case of built-up propellers with adjust-

make

to

it is

rarely possible

the hub diameter as small as the bearing

barrel so that the fair surface of revolution between

the latter and the end of the hub cap has a bulge in

it

in the vicinity of the disc plane.

In a speed range where the smaller, pointed end of a propeller fairing cap is covered with a

hub vortex

sometimes having a

or swirl core,

diameter half as great as that of the cap at its larger end, the portion of the cap within the core obviously serving no useful purpose.

is

some

in

It

is

to eliminate the swirl

built in this

possible,

would not do.

square at about two-thirds or three-quarters of its length from the after end. The separation drag which occurs abaft this blunt end is almost

From

considerations of strength and mechanical

core or

cases,

hub vortex

entirely

magnitude than the drag from the presence of vapor pressure

certain to be less in

attachment, both of the hub to the shaft and the blades to the hub, the diameter of the propeller

resulting

hub depends partly upon the diameter of the shaft and partly upon the widths of the blade sections at

diameter. If the pressure

the root, where they join the hub. It usually varies

persist,

between 0.16D and 0.20D for

solid propellers.

For

controllable or built-up propellers the diameter of

the

hub may be

maximum

of

are

favorable,

the

swirl

core

may

even abaft a blunt or square ending ["All Hands," Bu. Nav. Pers., U. S. Navy Dept.,

Feb 1953, pp.

18-19].

on a fast or high-speed any reasonable slope at the pointed

It appears unlikely, ship, that

end or of

of

a fairing cap

will eliminate the swirl core

hub vortex entirely. Certainly the small slopes 8 and 10 up to 20 deg (with reference to the

shaft axis), previously used on the fairing caps of the fastest vessels,

German

avoid separation and cavitation abaft the

hub, a fairing cap

is

usually fitted at the after

end. This cap also covers the propeller nut. In

many

conditions

such as the World

War

II

cruiser Prinz Eugen, are inadequate for

this purpose.

0.670.

To

only inside a swirl core of somewhat smaller is low enough and other

as large as 0.28 or 0.30Z), with

0.25D for a propeller having blades that are demountable but not adjustable [ME, 1942, Vol. I, Fig. 2, p. 269]. It is pointed out in Sec. 70.43 that a loss of efficiency of from 1 to 1.5 points may be expected if a built-up rather than an integral hub is used; for example, a drop in tj from 0.685 to 0.675 or a possible

by cutting the cap

off

cases the

hub

fairing cap does not rotate

Swirl cores abaft the fairing caps of model

and photographed model basins, variable-pressure Avater tunnels, and circulating-water channels. However, because propellers have been observed in

HYDRODYNAMICS

602

IN SHIP DESIGN

Sec. 70.15

of the

known and unknown scale effects, it is not make full-scale predictions from a model experiment. Swirl cores and hub vortexes

the area ratio of the parent model (s)

yet safe to

expected to give the performance indicated by the chart. Variations from the parent values

have been and can be observed on ships through

have in the past usually been left to the experience and judgment of the designer, with little to rely upon if he does not have that kind of experience. Only recently there have appeared a new series of graphs and a procedure based upon cavitation characteristics of the models of certain propeller series, devised by J. D. van Manen, whereby values of the proper developed-area

special glass viewing ports installed

in proper

locations in the shell. 70. 1 5

Determination of Expanded-Area Ratio Profile. For design purposes in ;

Choice of Blade this

book the blade area

of a propeller corresponds

to the expanded area of

all

the blades. This

is

usually expressed as the ratio of the expanded

area

Asto the disc area .4o As a means of arriving is made of the .

at the blade outUne or profile, use

mean-width

ratio,

represented by the ratio of

ratio

this

the average expanded chord length c^f of one

blade to the propeller diameter D.

low limits for these

The high and

ratios, in recent

and current

propeller design, are given by K. E. Schoenherr and W. P. A. van Lammeren [PNA, 1939, Vol. II, p. 157; RPSS, 1948, p. 227]:

Propellers for

may

1954, Vol.

be determined 1,

method

No.

1,

may

be

[Inter. Shipbldg. Progr.,

pp. 39-47].

Data derived by

are presented at the end of Sec. 70.6.

In the example of the Lerbs' method of designing a wake-adapted propeller

by the

circulation

theory, described in Sees. 70.21 through 70.38, in

which cavitation

is

definitely to

be avoided,

the chord widths of the sections at the outer radii are selected to give

—Ap

values which will

SCREW-PROPELLER DESIGN

Sec. 70.16 (a)

Van Lammeren, W. K.

(b) Schoenherr,

On page

E.,

P. A.,

PNA,

RPSS,

1948, pp. 226-227

given a formula (119) which produces a practical form of expanded blade outline that is generally elliptical in shape. Although

not stated there, this

is

of

1939, Vol. II, pp. 157, 162.

157, 1st col., there

is

for

a propeller not subject

First

Tronsporent 5heet ot 2

R

*\/

concerning proper blade widths are

and

Selecting

70.16

Skew-Back.

Applying

reasons for applying skew-

back to screw-propeller blades are explained in Repeated briefly, skew-back is used to prevent certain corresponding points on the blade sections at every radius, or at a group of adjacent radii, from passing simultaneously through a region of high wake velocity directly abaft a skeg ending, a bossing termination, or a large strut. The necessity for skew-back in the design of a surface propeller is perhaps somewhat easier to understand. Here it is not desirable Sec. 32.15.

that the entire length of the leading edge of a

an appreciable portion of that edge, should swing downward and strike the water blade, or

surface at the

The

same

instant.

actual application of skew-back

capped, however, because

what part

it

is

is

handi-

known

not yet

a blade element requires to be time or in angular position, from the high-wake region. This part is probably not the leading edge, nor the trailing edge, nor

just

of

offset successively, in

the locus of the midlengths of the expanded elements. It

is

possibly the locus of the centers of

pressure of the elements, possibly the locus of the points of

maximum

thickness, or better

still

the

locus of points opposite a certain part of the pres-

sure field of each element, as yet not known.

Lacking of

this information, the locus of the positions

maximum

blade-element thickness

is

probably

the best but, as explained presently, the use of this line is neither convenient nor practical. Little is yet

known about

the rate at which

the backward offset of the selected skew-back line

should change with blade radius

what should be

words,

its

or,

shape,

in

other

defined

in

Sec. 32.15. Manifestly, the basic reference line

or plane for estabUshing skew-back of the region of

near

its

maximum wake

is

the position

velocity, at or

intersection with the plane of the pro-

peller disc.

For a

vertical, symmetrical, center-

this is the vertical plane through the propeller axis. For a contra-guide skeg ending the locus of the maximum-wake positions in the plane of the disc is not known

plane

skeg ending

|g

25^''( \

/\ J>^^\.

X .^ x V=^/\

^iieq Ending-,

given in Sec. 70.17.

The hydrodynamic

Rotation

Position of

to cavitation.

Comments

603 40

Arc for Meosurinq Ancjles

Intersection

45

50

HYDRODYNAMICS

604

Straight in the disc plane, not coinciding with

(e)

Curved, usually with a sweep-back toward

(f)

is

opposite to the direction of rotation.

Whatever the shape which

of the locus

on the propeller

not to pass simultaneously across the

is

basic reference trace abaft the hull ending, the

drawn on a sheet of thin transparent same scale as the reference trace. In Fig. 70. C the transparent material is shown as rectangular in outline and the selected-skewback locus is drawn in its proper position with former

is

material to the

reference to a straight radial line tangent to the

hub radius. To the transparent sheet added concentric circles at 0.2/?, 0.3i2,

locus at the

there are

and so

on.

A

pin

inserted through both the

is

transparent overlay and the under sheet upon which the skeg ending is drawn, at the propellershaft axis, so that the overlay

may

be rotated to

An

simulate the rotation of the propeller.

added on the under

is

circle in

by which the overlay

arc

sheet, just outside the tip

the figure, to indicate the angular is

amount

rotated from an assumed

zero position.

The

overlay

is

turned in the direction of proon it crosses the

peller rotation until the locus

basic reference trace at

maximum

the

it

is

selected fraction of

The angular

radius, say at 0.2/2.

By

0.3/2.

on

construction

sections

line

in

forebodies of the blade sections at the various

then adjusted in shape until the leading edge resulting from this construction gives the desired equidifferent angular intersections. This radii, is

determined by the method diagrammed in

is

Fig. 70. C, substituting the leading edge for the

schematic

purely

At

or near the tip

differences

rotating it is

shown

there.

because of the large-

increase

will

locus

expected that the angular

radius curves used to form the tip profile.

The

midlength locus is preferred over the locus of the chordwise positions of the maximum thickness of each section because the former is usually

made tangent

to the pitch reference line at the

hub and

less

it

has

Until more locus, it

is

curvature at the outer

known concerning

appears wise,

if

radii.

the controlling

possible, to give definite

the midlength-of-chord locus and to the position-

position

is

again noted.

taking the angles between successive angular Fig.

is the most suitable which to introduce the skew-back. This midlength locus, to which are applied the half-chord expanded lengths of the

expanded blade

turned until the locus crosses the

The angular

positions, set

high-wake region. It is not feasible, however, by any method as yet known, to fashion a suitable projected-blade outline, with fair root-to-tip characteristics, by working from the leading edge. Experience indicates that the locus of the midlengths of the

angular separation at the successive radii to both

is

reference trace at the next selected radius fraction,

say

the one whose radial segments

then noted, following

position of the overlay

which

some

-projected outline as

Sec. 70.16

should swing successively and uniformly into the

a radius, from the hub radius to the tip radius the tip that

IN SHIP DESIGN

down

70.C,

as

first

differences in the table

possible to determine at a

of-maximum-section locus. In addition, both fair from root to tip of the blade, as should the leading and trailing edges. Good values for the skew-back at the tip, should be

glance whether the successive differences between

measured as indicated in Fig. 70. of Sec. 70.36 and by Fig. 78. L, lie between 20 to 25 per cent

a group of adjacent angles are small or appreciable,

of the

it

is

A

or whether they are equal or unequal. of

equal and

group

appreciable differences indicates

successive crossings of the locus and the reference trace at equidifferent angular

A

and time

intervals.

group of zero differences indicates a simul-

taneous crossing over the corresponding portion of the blade radius. This simultaneous crossing is

almost invariably to be avoided.

A

limited study of propellers with swept-back

blades

that

have

performed

well

in

service

indicates that successive crossings of the leading edge are spaced at

more nearly uniform angular any other known

intervals than the crossings of

locus. Therefore, until a better locus

is

found

it

appears acceptable to take the leading edge of the

The

maximum designer

is

chord length Cmsi of the blade. cautioned, on a moderately or

heavily loaded propeller at least, never to apply

an appreciable amount

of

skew to a screw-

propeller blade in a forward or ahead direction, for the reasons given in Sec. 70.44.

For a given

maximum

thickness tx at each

a blade with large sweep-back has a smaller thickness ratio tx/c because the lengths of the sections are usually greater in the circumsection,

ferential direction of flow across the blade

than

they would be in a blade with no sweep-back. This thinness is generally a help in deferring cavitation.

Theoretically the dynamic ram pressure built up on the extreme leading edge of a fast-running

SCREW-PROPELLER DESIGN

Sec. 70.] S

propeller

and

large,

is

its

harmful

reduced by skew-back, but the angle

p,Af:

3,058(125.66)

made by

pn^d"

1.9905(1.8333)'(20)'

the leading edge with the radius has to be large to

make much

384,268

difference here.

Design Considerations Governing Blade Width. The matter of proper blade width for a screw propeller, usually expressed as the meanwidth ratio Cm/D, follows rather closely after of

For a speed

G.

some

includes

Hill

[SNAME,

instructions

brief

advance

= Zl = nd "

7

70.15. If the designer has

J.

of

of 15.15 kt or 25.59 ft per

sec,

expanded-area ratio in Sec.

no preconceived ideas regarding the blade width he usually encounters difficulty in this phase of the problem. A partial solution is to adopt the blade width, or approximately that value, of the series model propeller which appears to give the best performance from the chart-design procedure. For example, W. P. A. van Lammeren gives [RPSS, 1948, pp. 204, 214] the chord length of the widest section for one series in terms of the propeller diameter D.

0.359

1,070,410

70.17

the discussion

605

can be

effect

For a p/d

25.59

=

0.698.

(1.8333)(20)

ratio of 1.0 this point falls well within

the region of no cavitation.

Lammeren

(2) Cavitation check by the van method, employing his symbols:

Po

—

"

p.

=

Po

-

p,

=

=

ft'^,

from

preceding

(1)

3,058

3,058

0.99525(25.59)'

651.7

P.

0.5pF;

Factor

3,058 lb per

=


=

=

4.69(0.4) (1.0)

4.69

1.87

1949, p. 152].

Assuming that the blade width and selected, the next step is a

J/p

outline are

check to determine sufficient to avoid

whether the blade area is cavitation, using one of the available cavitation

Using these

=

'-ff

=

0.698

the plot

factors,

Fig.

of

47.

indicates that they are in the region of no cavitation.

RPSS, Wageningen Model

L. C. Bunill,

(a)

(b)

p.

One

1948, Fig. 123a, p. 186

RPSS,

Basin,

1948,

Fig.

123a,

concerning blade width, rarely disis

that of

its effect

upon

the periodic vibratory forces excited in or on the

186

(e)

D. van Manen and L. Troost, SNAME, 1952, Fig. 455 D. van Manen, Int. Shipbldg. Prog., 19.54, Vol. 1, No. 1, pp. 39-47 H. W. E. Lerbs' data in PNA, Vol. II, Figs. 30 and 31,

(f)

pp. 179, 181 W. p. A, van Lammeren's chart in 6th

J.

(c)

featui'e

cussed in the literature,

14, p.

adjacent ship structure. Assuming the same shape of

(d) J.

Fig. 30, p. 94, reproduced with of detail in Fig.

47.G

(and -)-Ap) chordwise pressure-distribu-

is

and narrow blades deliver-

mean — Ap

ing equal thrust, the

the wide blade

ICSTS, 1951, some modifications

of the present

— Ap

tion curve on both wide

are less pronounced. It follows that, for a given rate of rotation, the periodic forces exerted .

volume.

on

(or -|-Ap)

smaller and the pressure peaks

by

the wide-blade pressure fields should be smaller

Two

examples

illustrate

how

for the 20-ft propeller of the

this is done,

ABC

both

transom-stern

ship: (1)

in

magnitude

and

longer

in

duration.

ing the vibratory forces on the ship carrying

Cavitation check with Lerbs' data, using the

in Figs. 30 and 31 of the reference, with a rate of rotation of 110 rpm and a depth

symbols given

to the shaft axis of 15.5

Ae/Ao =

0.40,

Ae =

=

0.40(Ao)

n = 110 rpm Pst.tic

p.

ft.

=

-

=

p.

=

14.7(144)

=

2,116

Po

-I-

0.40Tr(10)'

=

125.66

ft'

or 1.8333 rps

p.

+ 994

15.5(62.43)(1.027)

-

52

=

-

3,058 lb per

52 ft'

Both

features favor the wide-blade propeller in lessen-

70.18

The

Selection

of

Type

of

Blade

it.

Section.

and proportions These may be different for the inner, the intermediate, and the outer radii. What is more important, perhaps, is that the type, shape, and proportions of the blade sections be suited to the work to be performed. Of the blade-section types illustrated in Fig. 32. K, the single-ended and double-ended symmetrical sections are employed primarily on propellers intended to give good stopping and backing performance, and to run astern for long periods, as on a double-ended ferryboat. selection of the proper type

of the blade sections is important.

HYDRODYNAMICS

606

what

Airfoil sections with

known

is

as lifted

leading and trailing edges, set back from a base

chord passing through the main portion of the way of the roots and the

face, are necessary in

inner

to

radii

good flow through the

obtain

regions where the blades are close together; see

the blade-spacing diagrams at the lower left-hand corners of Figs. 70.O and 78. L. If the leading

edges are not

lifted sufficiently,

cavitation and

erosion are liable to occur on the faces, close abaft

IN SHIP DESIGN

Sec. 70.19

Both leading and enough to:

must be

trailing edges

thin

Eliminate excessive dynamic pressures along

(d)

the leading edge because of the relatively large velocity with which the blade passes through

the

This

water.

particularly

is

true

for

the

sections at the outer radii. Although screw propellers are rarely designed for partial immersion,

there are large

dynamic pressures due

when the exposed blade

to impact

portions strike the water

those edges. surface.

There are many types

of airfoil section suitable

Some

most satisfactory forms are those developed by the National Advisory Committee for Aeronautics, based upon for screw propellers.

of the

the principle of superposing the ordinates of a

symmetrical hydrofoil upon a curved or cambered meanline, with or without minor modifications

and there. The merits of these NACA sections and the advantages of using them are described in detail by I. H. Abbott, A. E. von Doenhoff, and L. S. Stivers, Jr., in NACA Report 824, issued in 1945, and entitled "Summary of Airfoil Data." The manner in which these sections here

are developed for a particular case

is

described

singing.

For the leading-edge shape, a circular arc is and satisfactory. This is achieved as indicated in the axial view of Fig. 70.O by bringing the face and back section outlines in to tangent points on a small circle. For the trailing simple

Shaping of Blade Edges and Root Fillets. In former years many propeller drawings did not specify the detailed shapes for the blade edges but this procedure is no longer compatible with good design. One method of doing this, for

and setback shown by W. P. A. van Lammeren

sections with circular noses

[RPSS, 1948, Fig. 126,

The enough

much

edges

smaller circular arcs are used.

and

tails

p. 190].

leading edge of a blade

must be thick

by

It is possible that

Fig. 70.P in Sec. 70.46.

some

edge at the blade tip

Withstand the impact of small objects without nicking or deforming the blade edge permanently (b) Avoid local cavitation, either on the face or back, when the angle of attack changes from its predicted value; that

is,

when the

direction of

the incident velocity shifts with respect to the blade.

This change can occur throughout one

revolution because of local circumferential variations in the wake velocity or it can occur for the whole propeller because of changes in displacement, in ship resistance, and in thrust loading

over the disc area. (c)

Render the blade section reasonably invul-

rounded form

be found which

of

will

increasing the diameter of the vortex cores.

In the working drawing of a

final

propeller

the exact shapes of the leading and trailing edges of the tip edge are to be shown by an adequate number of large-scale details, such as those given by R. H. Tingey [ME, 1942, Vol. I, Fig. 6, p. 280,

and

W. Henschke

thickness) of 0.0015Z) (a)

full or

may

diminish the intensity of the tip vortexes by

Detail "A"].

to:

If,

however, the blade sections are rather thick at the extremity of the run, they are given a chisel

70.19

is

Prevent the formation and shedding of eddies lateral vibration which causes noise and

(f)

and the

shape, illustrated

in Sec. 70.31.

as well,

Eliminate losses due to separation drag at

(e)

the trailing edge

of

0.008c

gives a tip radius (in

and a

trailing

["Schiffbau Technisches

edge radius

Handbuch,"

1952, p. 145].

The

days shape diagrammed by R. H. Tingey in Fig. 16 on page 292 of "Marine Engineering" [Vol. I, 1942]. This produces a form resembling that given by nature to the bottom of a tree, where the trunk joins the roots and where large bending moments are to be resisted. 70.20 Partial Bibliography on Screw-Propeller Design. Although they are not all quoted in this and other chapters relating to screw propellers, root

fillets,

gone by, are

now

also lacking details in

of the constant-stress

nerable to changes in the angle of attack, due to

there

variations in the local speed of advance, in the

principal references on the design of screw pro-

direction of flow,

and other

factors.

is

given here a partial bibliography of the

pellers for ships,

most

of

them dating from about

SCREW-PROPELLER DESIGN

Sec. 70.20

A

1939.

few applicable references covering

air-

Hydrodynamik und Aerodynamik (Four Treatises on Hydrodynamics and Aerodynamics)," Gottin-

screw design are included. A very complete bibliography containing 227 items, listing references in the literature for

50 or 60 years prior to 1939, Schoenherr [PNA, 1939, Vol.

some

II,

pp.

of

them duplicating the

PNA

extending only to the year 1942,

W.

P. A.

van Lammeren [RPSS,

The

references in

is

given by

1948, pp. 295-

the appended

chronological

(13)

Goldstein,

order,

p. 151

list appear without any

attempt at grouping or classification. They do not duplicate the references in Sec. 70.4, listing the literature concerning propeller-series charts

Weick, F. E., "Aircraft Propeller Design," McGrawHill, New York, 1930 (15) Lerbs, H. W. E., "Kurventafeln zur Berechnung Starkbelasteter Freifahrtschrauben nach der Tragfltlgel theorie (Graphs for Calculation of Heavily Loaded Open- Water Screw Propellers According to Airfoil Theory)," HSVA Rep. 101; WRH, 1 Feb 1933, pp. 29-31 (16) Gutsohe,

(2)

A.,

"Schraubenpropeller

luftschiffahrt, (3)

(17)

1924, pp. 150 and 170 Kdrmdn, Th., "Zur Theorie der Luftschrauben (On the Theory of the Airscrew),"

(18)

(5)

1926, pp. 565-569; 22 Dec 1926, pp. 588-595. Transl. 15, Feb 1936. English version in

WRH, (19)

Horn,

F.,

(Tests

STG, (8)

(9)

(10)

Slocum,

"Versuche mit Tragflugel-Schiffsschrauben with Airfoil-Section Ship Propellers),"

1927, Vol. 28, pp. S.

E.,

"Practical AppUcation of

Modern

Hydrodynamics to Marine Propulsion," ASNE, Feb 1927, pp. 1-38 Helmbold, H. B., "Nachstromschrauben (WakeAdapted PropeUers)," WRH, 7 Dec 1927, pp. 528-531 Hehnbold, H. B., and Lerbs, H., "Modellversuche zur Nachpriifung der Treibschrauben-Wirbel theorie (Model Tests to Verify the Vortex Theory for a Propeller Producing Thrust)," WRH, 7 Sep 1927, pp. 347-350

Nov

15

C,

Chartier,

breitfiiigeliger

(Schiffsschrauben)

1933, pp. 319-324

"Sur

le

Champ Hydrodynaniique

dynamic Field Around a Screw Propeller with Three Blades)," CR, Acad. Sci., Paris, 1933, Vol. 196, p. 1642 (20) Gutsche, F., "Verstellpropeller (Variable-Pitch Pro-

Deutsch. Ingr., 1934, Vol. mentioned in NECI, 1937-1938, Vol. LIV, p. D212. In the latter reference Gutsche tells about a series of propeller charts giving T, Q, and and going down to zero speed or 100 peller)," Zeit. des Ver.

78, p. 1073;

t]

per cent

slip.

K.

(21) Schoenherr,

E.,

peller Design,"

"Recent Developments in Pro1934, Vol. 42, pp. 90-127

SNAME,

"Quick Approximation for Preliminary PropeUer Design," ASNE, Nov 1935, pp. 557-568

(22) Smith, L. P.,

(23)

Durand, W. Division

342^46

Wirkungsweise

autour d'une Helice k Trois Pales (On the Hydro-

Dec

EMB

(7)

"Uber den Einfluss der Strahlkondie

(On the Race Contraction and its Effect on Broad-Bladed Screw Propellers (Ship Screws)),"

Motorluftsohiffahrt, 1925, p. 209

Helmbold, H. B., "Die Betz-Prandtlsche Wirbeltheorie der Treibschraube und ihre Ausgestaltung zum Teohnischen Berechnungsverfahreu (The Betz-Prandtl Vortex Theory and its Development into a Technical Calculation Method)," WRH,

B.,

auf

Influence of the

Zeit. des Ver.

Luftschraube bei Berucksichtigung des Profilwiderstandes (The Most Favorable Thrust Distribution for the Airscrew)," Zeitschrift fiir Flugtechnik und

1933, pp. 286-289;

in English.

Helmbold, H.

Schraubenpropeller

Motorluftsohiffahrt,

Deutsch. Ing., 1924, p. 1237; Vol. 68, Nos. 48, 51; Vol. 69, No. 25 Bienen, Th., "Die gunstigste Schubverteilung fiir die

Aug

of papers relating to ship propellers, with

summaries traktion

Bienen, Th., and von

9

1933, pp. 267-270; 15

Sep 1933, pp. 303-306 Kempf, G., and Foerster, E., "Hydromechanische Probleme des Schiffsantriebs (Hydrodynamic Problems of Ship Propulsion)," Teil II, Oldenbourg, Munich and Berlin, 1940. This book contains a

number

1920

(4)

(6)

Aug

1

Helmbold, H. B., "Zur Aerodynamik der Treibschraube (On the Aerodynamics of the Screw Developing Thrust)," Zeitschrift fiir Flugtechnik

und

"Versuche an Propellerblattschnitten

F.,

(Tests on Propeller Blade Sections)," Schiffbau,

mit geringstem Energieverlust (Screw Propeller with Minimum Loss of EnergjO," with an Appendix by L. Prandtl, Nachr. der Kon. Gesellschaft der Wissenschaften zu Gottingen, Math-Phys., 1919, p. 193 Betz, A., "Eine Erweiterung der SchraubenstrahlTheorie (An Expansion of the Screw-Race Theory)," Zeitschrift fiir Flugteohnik und MotorBetz,

Vortex Theory of Screw Soc, London, Series A,

(14)

1

(1)

the

1929, Vol. 123, pp. 440-465

and design purposes.

for analysis

"On

S.,

Propellers," Proc. Roy.

items but

301].

generally in

Helmbold, H. B., "tJber den Vortriebswirkungsgrad (On Propulsive EfHciency)," WRH, 22 Apr 1928,

187-194].

Another extensive bibliography with 191 items,

many

gen, 1927 (12)

given by K. E.

is

607

(11) Prandtl, L., and Betz, A., "Vier Abhlandlungen zur

F.,

L,

"Aerodynamic Theory," Vol. IV, by H. Glauert, Springer,

written

Berlin, 1936

C, "Champ Hydrodynamique autour d'une Helice Marine Triple Propulsive (HydrodjTiamic Field Around a 3-Bladed Screw Propeller)," CR, Acad. Sci., Paris, 1936, Vol. 203, p. 1232

(24) Chartier,

"Die Entwicklung der Schiffsschraube in Neuzeitlichen Stromungslehre (The Development of the Ship Propeller in the Light of Modern Flow Theory)," Zeit. des Ver. Deutsch. Ing., 26 Jun 1937, pp. 745-753. A partial translation

(25) Gutsche, F.,

Licht

der

HYDRODYNAMICS

608 of this paper

is

given in

ETT

IN SHIP DESIGN

Stevens Note 202 of

12 Oct 1952. (26) Losch,

"Uber

F.,

die

Wirkungsgrades

Berechnung des induzierten

stark

belasteter

Luftschrauben

(33)

unendlicher Blattzahl (On the Calculation of the

Induced Efficiency of Heavib' Loaded Airscrews of Infinite Blade

Number)," Luftfahrtforschung,

7. English version in NACA Tech. Memo 884, Jan 1939. (27) .\t the session of the North-East Coast Institution of Engineers and Shipbuilders for 1937-1938 there was held a "Symposium on Propellers," at which the following ten papers were presented. These papers are published in NECI, 1937-1938, Vol. LIV, pp. 237-414, with the discussions on pp.

(34)

Jul 1938, Vol. 15, No.

D133-D222. The paper

"The

titles

(a)

Baker, G.

(b)

Behind a Ship" Horn, P., "Measurement of

S.,

and authors

are:

Qualities of a Propeller Alone

(36)

and (37)

Wake" Screw Propellers"

(c)

Allan, J. P., "Aerofoil Sections in

(d)

Duncan, W.

(e)

Gawn, R.

(f)

Performance" Troost, L., "Open- Water Test Series with Modern

J.,

"Torsion and Torsional Oscillation

of Blades"

W>

L., "Effect of

Shaft Brackets on Pro-

peller

Propeller (g)

Kent,

(h)

Kempf,

J. L.,

Forms" "Propeller Performance in

Rough Water"

Model Tests on Immersion of Wake and Viscosity" Benson, F. W., "Propellers for Tugs and Trawlers" Yamagata, M., "Model E.xperiments on the Optimum Diameter of the Propellers of a Single-Screw G., "Further

Propellers, Effect of

(i)

(j)

Ship." (28) Troost, L., "Open- Water Test Series with

Modern

Propeller Forms," NECI, 1937-1938, Vol. LIV, pp. 321-326 and D185-D192. This paper covers the tests of the 4-bladed narrow-tip A. 4.40 Wageseries, the B.4.40, and the B.4.55 series. These had 15-deg rake and airfoil sections at all

ningen radii.

(29) Troost, L.,

"Open- Water Test Series with Modern

Propeller Forms, Part 2, Three-Bladed Propellers,"

NECI,

(30)

(31)

1939-1940, Vol. LVI, pp. 91-95 and D41-D48. This second paper by Troost covers the tests of 3-bladed propellers of the B.3.35 and B.3.50 Wageningen series, also having 15-deg rake and airfoil sections at all radii. Troost, L., "Open-Water Test Series with Modern Propeller Forms, Part 3, Two-Bladed and Five-

Bladed Propellers, Extension of the Three- and Four-Bladed B Series," NECI, 1950-1951, Vol. 67, Part 3, pp. 89-130; discussion in Part 5, pp. D45-D50; author's closure in Part 6, pp. D51-D54 Kramer, K. N., "Induzierte Wirkungsgrade von Besf^Luftschrauben endlicher Blattzahl (Induced Efficiencies of Optimum Airscrews with a Finite

Number

of

Luftfahrtforschung,

Jul

An

English translation of this paper appears in NACA Tech. Memo 884, Jan 1939. Gutsehe, F., "Einfluss der Gitterstellung auf die Eigenschaften der im Schiffsschrauben Entwurf 1938, Vol. 15.

;(32)

Blades),"

(35)

bexiuteten Blattschnitfe^ (Influence of the Stagger

Sec. 70.20

on the Functioning of the Blade Sections Used in Ship-Screw Design)," STG, 1938, Vol. 39, pp. 125-175 Schoenherr, K. E., "Propulsion and Propellers," PNA, 1939, Vol. II, Chap. III. This chapter, on pp. 187-194, lists 227 items of reference. Flugel, G., "Die giinstigste Sohubverteilung bei Propellern (The Optimum Thrust Distribution in Propellers)," Schiffbau, Schiffahrt und Hafenbau, 15 Apr 1940, pp. 108-112; 15 Sep 1940, pp. 250253; 15 Oct 1940, p. 272 Gutsehe, F., "Versuche an umlaufenden Fliigelschnitten mit abgerissener Stromung (Experiments on Rotating Airfoils in the Stalling Condition)," STG, 1940, Vol. 41, pp. 188-226 Tingey, R. H., "Propellers and Shafting," ME, 1942, Vol. I, pp. 267-304 Lerbs, H. W. E., "Der Stand der Forschung iiber den Schiffspropeller im Hinblick auf die Technische Berechnung (The Present Status of Theoretical Research on Ship Propellers with Respect to its Technical Application)," WRH, 15 Feb 1942, pp. 57-62; Transl. 243, Jan 1952

TMB

C, "Developments in Propeller Design and Manufacture for Merchant Ships," IME,

(38) Burrill, L.

Aug 1943, pp. 148-169. This is a comprehensive but concise paper of general interest, covering many phases on the subject. On pp. 13-14 the author gives a list of 24 recommended references. (39) Burrill, L. C, "Calculation of Marine Propeller Performance Characteristics," NECI, 1943-1944, Vol. 60, pp. 269-294 and Pis. 8-11. Design is normally based upon the model-test data of D. W. Taylor. The circulation or vortex theory is utilized to develop improvements not incorporated in existing series. A mean camber line is selected and the blade sections are superposed on it. (40) Baker, G. S., "Fundamentals of the Screw Propeller," IME, Jan 1944 (41) Ludwieg, H., and Ginzel, I., "Zur Theorie der Breitblattschraube (On the Theory of the BroadBladed Screw Propeller)," Aerodynamische Versuchsanstalt, Gottingen, Rep 44/A/08, 3097, 1944 Guilloton, R., "Considerations sur les Helices (A (42) Discussion of Screw Propellers)," Publications Scientifiques et Techniques de la Direction des

UM

Industries Aeronautiques, Paris, 1944 (43) Abbott,

L.

S.,

Rep

H.,

I.

von Doenhoff, A.

"Summary

Jr.,

and Data,"

E.,

of Airfoil

Stivers,

NACA

824, 1945

(44) Strassel, H.,

MAP

"Camber Corrections for Screw

Volkenrode,

K.

(45) Schoenherr,

Feb

Sect., 21

E.,

MAP-VG

1947. There

paper on pages 17 and 18 of Bulletin for

May

Profiles,"

90-T, 1946

"Propellers,"

SNAME,

Phila.

an abstract of this the SNAME Member's is

1947.

"The

Lift Distribution of Swept-Back Wings," Zentrale fiir Wissenschaftliches Berichtswesen, 1942, No. 1553. There is an English translation of this paper in NACA Tech. Memo 1120,

(46) Weissinger, J.,

Mar

1947.

(47) Burrill, L,

C, "On

Propeller Theory," lESS,

Mar

SCREW-PROPELLER DESIGN

Src. 70.21

1947, Vol. 90, pp. 449-488; ,Iun 1947, pp. 489-501.

On pp. 475-476 there is a bibliography of 27 items. Van Lammeren, W. P. A., Troost, L., and Koning,

(48)

J.

"Resistance,

G.,

data are plotted

Propulsion and Steering of

(65)

Theory," Cambridge, England, 2nd

ed.,

Aerodynamics

of the Airscrew)," Berlin,

L. K., Jr., "Theoretical

(50) Loftin,

Data

for

a

Number

of

6A-Series Airfoil

(67)

NACA

forenings Forlag, 1949. (In English)

"The Design

J. R.,

Vibrations

SNAME,

and McGoldrick, R. T., "Longitudinal of Marine Propulsion-Shafting Sys-

SNAME,

tems,"

Guilloton, R.,

INA,

1949, pp. 193-252

"The Calculation

of Ship Screws,"

1949, Vol. 91, pp. 1-26

H. W. E., "An Approximate Theory of Heavily Loaded Free-Running Propellers in the Optimum

(56) Lerbs,

Condition,"

SNAME,

INA,

of

an Unequal 1952, pp. 442-468

S.,

"The

for

Effect of Radial

1953, pp. 437-460

Hannan, T. E., "Principles and Design of the Marine Screw Propeller," Ship and Boat Builder, Part 1, Jan 1953, pp. 221-227; Part 2, Feb 1953, pp. 263-270; Part

Apr (68) Lerbs,

862,

Mar

3,

1953, pp. 306-311; Part 4,

1953, pp. 347-353

H. W.

"The Loss of Energy of a Propeller Varying Wake Field," Rep.

E.,

TMB

in a Locally

Nov

1953

(69) Edstrand, H.,

"Model Tests on the Optimum Diam-

SSPA Rep. 22, 1953 R. E., and Graham, D. J., "Effects of Leading Edge Radius and Maximum Thickness Chords; Ratio on the Variation with Mach Number of the Aerodynaniic Characteristics of Several Thin NACA Airfoil Sections," NACA Tech. Note 3172, 14 Apr 1954 (71) Lerbs, H. W. E., "Propeller Pitch Correction Arising From Lifting Surface Effect," Rep. 942, Feb 1955

1950, Vol. 58, pp. 137-183

(70) Berggren,

TMB

(72) Silverleaf, A.,

and O'Brien, T.

P.,

"Some

Effects of

M., "Propeller Coefficients and the Powering of Ships," SNAME, 1951, pp. 612-641

Blade-Section Shape on Model Screw Perform-

H. W. E., "On the Effects of Scale and Roughness on Free-Running Propellers," ASNE, Feb 1951, pp. 58-94. On pp. 93-94 the author gives a

1955, pp. 172, 174.

(57) Lewis, F.

ance,"

(58) Lerbs,

list of

(59) Ginzel,

15 references.

I.,

"Influence of Blade Shape and of Circula-

on the Camber Correction Admiralty Research Lab., ACSIL/ ADM/52/46, Oct 1951 (60) Burrill, L. C, "Sir Charles Parsons and Cavitation," Parsons Memorial Lecture, IME, 1951, Vol. LXIII, pp. 1-19 tion

Distribution

Factor,"

(61) Okeil,

M.

E.,

Propeller,"

"The Optimum Loading of a Marine INA, Jul 1952, pp. 162-178. This

represents a study under the supervision of L. C.

based upon the circulation or vortex theory of the screw propeller. Most of the references Burrill,

on pages 177 and 178 are included

in this bib-

liography. (62) Ginzel, L,

(63)

C.

"The Design

eter for Propellers,"

of Propellers,"

1949, pp. 143-192

Kane,

SNAME,

C, and Yang,

Propeller,"

AEW

(53) Hill, J. G.,

Optimum Diameter

1952, pp.

Pitch Variation on the Performance of a Marine

and E.xperimental

NACA

Burrill, L.

SNAME,

D., and Troost, L.,

J.

Velocity Field," (66)

1940

Rep. 903, 1948 (51) Lerbs, H. W. E., "The Applied Theory of FreeRunning Ship Propellers," Rep. 42/48, Nov 1948 (52) Burrill, L. C, "Propeller Design and Propeller Theory," read on 11 May 1948 before the Shipbuilding Group of Dansk Ingeniorforening; published by Teknisk Forlag A/S Dansk IngenioSections,"

Van Manen,

Ship Screws of

1948

(49b) Weinig, F., "Aerodj'namik der Luftschraube (The

I

Number

73-123

and Airscrew

The

"Moderately Loaded Propellers of Blades and an Arbitrary

E.,

with a Finite

has a huge bibliography of 191 items on propellers of Aerofoil

0.2 to 1.1.

chart form.

in

Distribution of Circulation,"

and propulsion. "The Elements

(55)

W.

(64) Lerbs, H.

A^/Ao from

Ships," 1948, Chap. II, Propulsion. This chapter

(49a) Glauert, H.,

(54)

r,oo

developed-area ratio

"Theory

(73)

Van Manen,

Broad-Bladed Propeller,"

Admiralty Research Lab., Jun 1952 Gawn, R. W. L., "Effect of Pitch and Blade Width on Propeller Performance," INA, 29 Sep 1952, Vol. 94, pp. 316-317; SBSR, 16 Oct 1952, p. 496 and pp. 509-511. Describes open-water tests of 37 model propellers in a systematic series. All the propellers are 20 inches in diameter, are 3-bladed, and have ogival blade sections with elliptic blade outlines and no skew-back or rake. The series covers a range of P/D ratio from 0.4 to 2.0 and of

1955. Abstracted in

D., and van

J.

SBSR, 10 Feb

Lammeren, W.

P. A.,

"The Design of Wake- Adapted Screws and their Behavior Behind the Ship," lESS, 1955, Vol. 98, Part 6 (74) Burrill, L. C, "Considerations sur le Diametre Optimum des Helices (Considerations Governing the Optimum Diameter of Ship Propellers)," ATMA, 1955, Vol. 54, pp. 231-261 (75) Burrill, L. C, "The Optimum Diameter of Marine Propellers: A New Design Approach," NECI, Nov 1955, Vol. 72, Part 2, pp. 57-82; abstracted in SBMEB, Apr 1956, pp. 267-271 (76) "Propeller Design and Performance Calculations,"

SBSR, 5 Jan

1956, pp. 9-10.

For the reader's additional

of the

NECI,

subject,

benefit,

references,

given by

J.

there are

closely

G.

Hill

related

some 17 to

[SNAME,

this

1949,

p. 170].

70.21

Design of a Wake-Adapted Propeller by Propeller design by the

the Circulation Theory.

chart method is analogous to the design of a hull by working from a series such as the TMB Series 60, or by virtually copying a previous design having the proportions desired, combined with a

good performance. However, there comes a time

HYDRODYNAMICS

610

when

the design requirements are so unusual, or

the situation

is

no existing waters must be

so special, that there

design from which to work.

New

is

traversed, so to speak, which are not only un-

but for wliich there are few reliable One such situation occurs when cavitation is to be expected and avoided. Another occurs when wake surveys show an unusual distribution of velocity at the propeller familiar

sailing directions.

—

position, or

when

it is

desired to take full advan-

tage of a more-or-less normal third

might

arise

possibility

all

requiring the

if it

tip-vortex

of

wake

variation.

A

were desired to eliminate cavitation

cores,

(2)

(3)

(4)

Schoenherr, K. E., "Propeller Design

by the Betz-

Prandtl-Helmbold Circulation Theory," PNA, 1939, Vol. II, Chap. Ill, Sec. 10, Art. 3, pp. 168-170 Van Lammeren, W. P. A., "Design of a Wake- Adapted Screw by Means of the Circulation Theory," RPSS, 1948, Chap. II, Sees. 138-140, pp. 248-250 HiU, J. G., "The Design of Propellers," SNAME, 1949, pp. 143-192 Van Manen, J. D., and Troost, L., "The Design of Ship Screws of Optimum Diameter for an Unequal Velocity Field,"

SNAME,

1952, Vol. 60, pp.

442^68

(5)

Van Manen,

(6)

Vol. 98, pp. 463-482 Eckhardt, M. K., and Morgan, W. B., "A Propeller Design Method," SNAME, 1955, pp. 325-374.

and van Lammeren, W. P. A., "The Design of Wake-Adapted Screws and their Bahaviour Behind the Ship," lESS, 1954-1955, J.

For the design

D.,

what

Sec. 70.21

adapted propellers by the circulation theory, there are gaps and omissions which make it practically impossible for anyone except an expert in the field to carry through a design by the methods described. The sections to follow in this chapter give a complete and continuous story

new method, recently (1954) developed by Dr. H. W. E. Lerbs of the David Taylor Model Basin staff. It is a short-cut method based on the theory he described completely in his paper for a

"Moderately Loaded Propellers with a Finite of Blades and an Arbitrary Distribution

Number

of Circulation"

No

blades to be almost completely

unloaded at their tips. For problems of this kind, and for developments of the future leading to appreciable improvements in propeller performance, it is necessary to fall back upon an analytic method. This in turn must be based on the fundamental hydrodynamics of the problem, in this case the theory of circulation as applied to a screw propeller. There are to be found in the literature at least six papers dealing with this subject and making use of the successive developments of the theory up to the time each paper was prepared and published. These are: (1)

IN SHIP DESIGN

attempt

[SNAME,

is

made

1952, pp. 73-123].

to give here a theoretical

explanation of the principles involved. There are quoted only the formulas actually employed,

accompanied by a written and tabular explanation of their use.

Lerbs' short-cut

method was chosen

for several

reasons: (i)

It has not

and thus (ii)

been published before in this form a new approach to the problem

offers

produces the answer rather directly and

It

a minimum of reliance on intuition, background, and previous propeller-design ex-

involves perience (iii)

It gives

method

promise of becoming an excellent wide variety of

of rational design for a

screw propellers (iv)

and

It

is

backed up by Lerbs' theoretical papers

based on sound hydrodynamic principles

is

(v) Design calculations using this short method were checked by parallel calculations with Lerbs' rigorous method, described in his referenced paper. The results gave satisfactory agreement.

theory for moderately loaded, wake-

Lerbs'

adapted propellers that

the

is

based on the assumption

induced-velocity

components

of

the

second and higher degree can be neglected. In the

mental hydrodynamic concepts of circulation set forth in Chap. 14. At the present stage of the art

development of the short-cut method two additional assumptions are made; first, that the induced velocity is always perpendicular to the resultant relative velocity and second, that the

necessary to call upon certain semi-analytic and experimental sources for information which

Goldstein function may be applied, relating the behavior of a propeller with a finite number of

will enable a propeller designer to start

blades to that of one with an infinite

of

is

called a wake-adapted

propeller, the procedure is to

employ the funda-

it is

with his

and end with a screw-propeller design. To do this, the designer need have only the knowledge that is set down in Volumes I and II of this book. In most discussions of the design of wakerequirements

number

of

blades.

The

propeller

chapter

fisted are defined

proceeds:

design

is

carried

along the following

lines.

out in this

The terms

and described as the discussion

SCREW-PROPELLER DESIGN

Sec. 70.22

Determine the number

(a)

hub diameter, the

peller diameter, the

rake,

Ludwieg-Ginzel

k

By

(d)

Sc

based upon the notation of D. W. Taylor [S and P, 1943, p. 137] Non-viscous thrust, as in a perfect hquid Ratio of local radius R to tip radius

successive approximations, calculate the

Ti

to develop the required thrust

x'

Determine the

lift-coefficient product,

apply

the lifting-surface correction to the hydrodynamic

iSi-

pitch angle, and calculate the hydrodynamic pitch

Wj'

^Max of propeller Average local wake fraction Average local wake fraction, corrected to

distribution

From

(f)

strength considerations determine the

(3/

Choose the type of meanline and thickness form to be used for the blade sections Using cavitation

(h)

mum

camber

of

criteria,

determine the maxi-

the meanline and the chord

lengths of the blade sections from appropriate

Tjff(eta)

ratios,

and

lift

co-

Apply the curvature

(j)

correction to the

camber

ship speed

advance

(k)

the final pitch distribution. (1)

Determine the amount

(m)

Draw

of skew-back,

if

any

the propeller

(n) Calculate the final propeller efficiency corresponding to the design conditions.

Owing

to the intricacy of

all

existing design

screw propellers, based upon the vortex or circulation theory, it is necessary to employ a number of special symbols. For the

methods

for

Lerbs method described and illustrated in the sections following, all

the special symbols, addi-

tional to the standard

symbols

1,

are defined

less,

when they

are

listed in

first

Appendix

used. Neverthe-

these special symbols are listed here in one

place, with brief titles for each:

{Ctl)s

Thrust-load coefficient based upon the ship speed V instead of upon the usual speed of advance

i

Tangent

Va

one half the angle of rake of a screw-propeller blade, based upon of

jet

equal to

V

coefficient,

based

instead of speed of

Va

Viscous-flow correction

ju(mu)

Cavitation number based upon ship

(sigma)

speed

V

instead of the resultant inci-

dent velocity

of attack at the various blade sections. Calculate

coefficient,

advance

Absolute

Xs

ratio

Correct for viscous flow by adding an angle

with

yx/(7mD)

(Ts

efficients

efficiency,

Absolute advance

X

(lambda)

upon

chord lengths, camber

ideal

rotation

Fair the blade outline and determine the

(i)

wake

section

Kramer's

charts

final

effective

Drag-lift ratio of an airfoil or blade

e

(epsilon)

(g)

match the

Corrected hydrodynamic pitch angle

c (beta)

blade-thickness fraction and the maximum-bladethickness distribution

curvature correction,

Maximum section camber, corrected Allowable stress in a propeller blade,

m.Yo jet rota-

hydrodynamic pitch angle and the thrust distribution over the blade which allows the propeller (e)

and P,

applied to the camber ratio

Calculate the required thrust-load coefficients

and advance coefficients (c) Determine the ideal efficiency with tion from Kramer's charts

[S

1943, p. 134]

if

any, and the rate of rotation (b)

611

W. Taylor

the notation of D.

the pro-

of blades,

70.22

ABC

F^ on

a blade section.

Ship Propeller Designed by Lerbs'

As a help in understanding Lerbs' method, and as a practical illustration of its use, a screw propeller is designed here for the transomstern ABC ship. The design is based upon the wake survey diagrammed in Fig. 60. M. Although cavitation is not expected on this ship, and the wake-velocity distribution is in no way unusual, the design procedure is carried through as though these two features presented 1954 Method.

real problems.

When

selecting the

in the self-propulsion

stern

ABC

model propeller to be used model tests of the transom-

ship designed in this part of the book,

an estimated propeller thrust of 193,476 lb was used. This led to the conclusion presented in Sees. 70.6 and 78.4 that the stock model propeller should have a P/D ratio of 1.02, four blades of moderate width, and airfoil sections along the inner radii. The calculated rate of rotation was 109.2 rpm at the designed ship speed of 20.5 kt. The corresponding advance coefficient J was 0.703,

and an open-water

efficiency of 68.0 per

HYDRODYNAMICS

612

That this estimate was fairly accurate is shown by the recorded rpm of 109.7 at 20.5 kt in the model self-propulsion test. However, cent was expected.

using the resistance of the ship with appendages,

obtained from the resistance test of

TMB

model

4505, and a thrust-deduction fraction of 0.07 at 20.5 kt, obtained from the self-propulsion test

with is

TMB

model propeller 2294, a revised thrust

20.5 kt;

Pe =

10,078 horses, from model-

resistance test; thrust-deduction fraction

550Pb

Rq

550(10,078)

=

t

=

0.07

160,098 lb

1.6889(20.5)

Sec. 70.23

skeg ending and cuts through the boundary layer

beneath the transom. Cutting back the lower portion of the skeg should have reduced the magnitude of the wake velocities in the lower half of the propeller circle. Nevertheless a localized

region

moderate

of

positive

wake

With such a wake

configuration,

advisable to use a propeller with an even

1

-

160,098

=

172,148

0.93

t

than the combination used in selecting the model stock propeller, based on the higher

efficiency

thrust.

Consulting Prohaska's logarithmic charts for Series B.4.40 and B.4.55 model pro-

Wageningen

one of which

is

reproduced as Fig. 70. B,

and entering with the thrust-load coefficient Ctl of 0.709, based on the lower thrust value and an effective wake fraction of 0.195 from the selfpropulsion test, the following optimum characteristics are

J =

P/D =1.2 n = 1.620

rps or 97.2

ships, unless a

4-bladed

subsequent analysis indicates that is needed to place the blade

a 6-bladed propeller

frequency (n times Z) in a certain range.

Ample edge

clearance

aperture of the

ABC

allowed in the propeller

is

transom-stern design, be-

tween the end of the skeg and the propeller sweep line, to keep vibratory forces to a minimum. 70.24 Determination of Rake for the ABC Propeller. The propeller aperture and stern arrangement of the transom-stern ABC ship are designed so that no rake is required. There is

some contraction in the inflow jet, to be sure, as for any screw propeller, but this is not augmented greatly at the disc position because the lines of

the skeg ending ahead

determined:

The open-water

A

the logical choice, as has been found

is

from long experience with single-skeg single-screw

The predicted thrust required to drive the ship is much less than the estimated thrust. This means that a new combination of P/D ratio and rate of rotation n might give a higher propeller

pellers,

is

minimize the unbalance in thrust between the blades in the 12 o'clock and 6 o'clock positions and to reduce the periodic bending of propeller

lb.

it

number

of blades, to

the propeller shaft in a vertical plane.

R,

T =

velocities

remains in the neighborhood of the 6 o'clock position.

calculated.

V =

IN SHIP DESIGN

propeller circle, where the propeller passes the

ipm

made

0.86 r?o

=

fine.

of

The rake angle

is

it

are

set at

design carried through here but 0.72

it

deliberately

deg for the could have

been set at any angle up to about 5 deg

propeller efficiency obtained from

if

the

designer wished to take advantage of the inflow

the self-propulsion test with the stock propeller at the designed speed was roughly 68 per cent.

contraction.

a possible gain of about 4 per cent in propeller efficiency, with a cor-

The transom stern of the ABC ship was designed to accommodate the largest practicable propeller diameter on the given draft of 26 ft. This was

This means that there

is

responding increase in the propulsive coefficient. new propeller design for the ABC ship is thus

A

Propeller-Disc

70.25

and

Hub

Diameters.

design are embodied in Sec. 70.12. Those in this

done to obtain the greatest possible propulsive coefficient, on the basis that the machinery could be designed to produce the required shaft power at whatever rate of rotation appeared best for the propeller. The maximum propeller-disc diameter resulting from this procedure was 20 ft.

section are limited to the final design of propeller

The diameter

definitely indicated.

Choice of the Number of Blades for the General comments concerning the number of blades to be used in a screw-propeller 70.23

ABC

Design.

for the transom-stern

ABC

This vessel, with the afterbody profile of Fig. 66. Q, supplemented by Fig. 67.U, is designed with what is known as a clear-water stern. As might be expected, and as

is

revealed in Fig. 60.M, there

of the propeller is thus considered

fixed at the outset of the design.

ship.

is

a high-wake-velocity region near the top of the

rotation

n

in

chosen to give the

The rate of now to be

P/D

ratio are

maximum

propeller

rpm and

the

and pro-

pulsive efficiency.

For a design situation where the diameter not

fixed, it is

necessary to determine the

is

optimum

SCREW-PROPELLER DESIGN

Sec. 70.26

value of

D

by the use

of existing propcllcr-design

comments given earlier in by model experiment. On the ABC ship, no shaft calculations were made for the transom-stern design, so the hub diameter was assumed as 0.18Z), the same as for the stock model propeller. The hub is faired into the rudder horn as shown in Figs. 66. Q, 67.U, and 74.K. charts, subject to the

Sec. 70.9, or

70.26

Calculating

and the Advance

Thrust-Load

the

Factors

With some

Coefficients.

of the

primary characteristics fixed it is possible to start the design of the wake-adapted propeller by Lerbs' short method. For the ABC propellerdesign problem only the thrust T, the ship speed V, and the maximum propeller diameter D are fixed. The rate of rotation n is to be chosen to give

maximum

In

efficiency.

restrictions

on the

size of

many

rpm

design cases

due to reduction gears or by a

there will be limitations on

as well,

requirement for a given rate of rotation at a given power with a direct-drive diesel engine. In these cases, the designer accepts the limitations

and attempts

to attain the

efficiency possible,

optimum. For the

maximum

maximum

even though

it is less

propeller

than the

Pe =

61-

10,078 horses, from model resistance test

Thrust T = 172,148 lb Thrust-deduction fraction I = 0.07; 1 — / = 0.93; from model self-propulsion test for 20.5 kt

wake fraction w) =

Effective

Number

ship a rate of rotation to give

propeller

efficiency

was chosen

in

on the basis of the Wageningen Series propeller data as laid down on Prohaska's logarithmic charts. These indicated an t/o of 0.72 for an n of L620 rps or 97.2 rpm. For Lerbs' short method it is best to work on a thrust basis. Because of the assumptions involved in this method, described in Sec. 70.21, corresponding formulas on a power basis do not yield equally good results. When using the rigorous method described by Lerbs in his referenced paper on moderately loaded propellers, either a thrust basis or a power basis can be employed. Thus if the designer is limited to a given power plant, he must convert the shaft power to effective power Pe and this Pe to thrust. In the design of the ABC ship, there is no maximum limitation on shaft power, so the design is started by using the thrust obtained from the model resistance test

I

—w=

0.805;

of blades

Z =

4

Average local wake fraction at the various radii, w^. from the wake survey on TMB model 4505, derived by the method described subsequently ,

in this section

p

=

1.9905 slugs per

=

0.5p

for salt water at 59 deg

ft^

0.99525 slugs per

The next

step

is

F

ft'.

to calculate the thrust-load

and advance

coefficients

coefficients.

The

initial

based on non-viscous flow. therefore necessary to convert the thrust

calculations are It is

all

calculated from the model test to a non-viscous thrust.

A

good approximation

for this is given

by the following relationship, which was determined by considering the viscous forces on a blade element:

=

Tj

ABC

0.195;

from model self-propulsion test for 20.5 kt Rate of rotation n = 1.620 rps or 97.2 rpm; from Sec. 70.22

1.03T

where T is the customary thrust in viscous flow and Ti is the thrust in non-viscous flow.

Sec. 70.22,

Speed

=

Ao

=

=

20

7ri?Ma.

Designed ship speed

Radius Rm..

ft

V =

=

314.16

20.5 kt

=

ft

34.622

advance Fa ft

=

= F(l -

177,312 lb

w)

=

34.622(0.805)

per sec

C TL

—

Tr

Tr

i0.5p)AoVl

(0.5p)7r(fiMa.)'Fl

177,312

=

0.99525(3 14. 16) (27. 871)'

The ('•

^7

thrust-load coefficient based on ship speed TLjS

—

ft

per

is

{0.5p)AoV177,312

=

0.4731

0.99525(314. 16)(34.622)

The

absolute advance coefficient J^b, or

The

= V, wnD

27.871

=

0.2738

(3. 14) (1.620) (20)

absolute advance coefficient based on ship

speed

ft'

=

1.03(172,148)

Thrust-load coefficient

X 10

of

27.871

with appendages, calculated in Sec. 70.22. The following data are known:

Diameter, D^a.

=

Ti

V

34.622

wnD

(3.14)(1.620)(20)

0.3401

HYDRODYNAMICS

611

.001

0,002

0.004

0.02

5.01

0,04

0.1

IN SHIP DESIGN

0.2

0,4

Absolute Advance Coefficient Fig. 70.

D

=

=

0.730 and

by and

0.2738, enter Fig. 70.D, a chart prepared

Kramer

1,5

I

Z

3

4

56

irnD

Khamee's Contours of Ideal Efficiency

Using the calculated values of Ctl X

=

A

Sec. 70.26

t/a-

with Jet Rotation

rem, considers only the axial component of the

induced velocity.

To

determine the ideal efficiency with jet rotation tik This ideal efficiency tja- differs from the t// de-

get a good value it is best to plot a curve of Enter Fig. 70.D with X on a basis of C'tl along the bottom scale, in this case 0.2738, follow

scribed in Sec. 34.2 in that

the diagonal line

reference (31) in Sec. 70.20],

[see

it

considers the effect

both the axial and rotational components of the induced velocity. The better-known ideal efficiency ?;/ derived from the momentum theoof

,

riK

then in

Ctl

move

the

=

up

to the

number

of blades Z,

vertically to the several curves oi rj^

vicinity

of

the

0.730 previously

thrust-load calculated.

coefficient

The

final

SCREW-PROPELLER DESIGN

Sec. 70.27

The

6L5

average local

wake

fraction w,-

at each

0-diml radius, obtained from the wake survey, 0.85

shown in Fig. 60.N. It is found that the average wake fraction over the propeller-disc position obtained by pitot-tube measurements with the

is

model propeller not mounted, called the nominal wake fraction, rarely agrees with the wake fraction obtained from the model self-propulsion test at the same speed, known as the effective wake fraction. This is a common occurrence in model testing. It indicates that the action of the pro-

and the presence of the rudder have a on the wake velocities. For the ABC ship, the nominal wake fraction over the propeller disc, obtained from the wake survey and shown in Fig. 60.N, is 0.1735 at 20.5 kt, as compared to the effective wake fraction of 0.195 from the model self-propulsion test. To compenpeller

definite influence

06

05

°-™a4 Fig. 70. E

09^

OB

077

Thrust-Load

Coefficient

Cj|_

Vaeiation of Ideal Efficiency Thrust-Load Coefficient

determination of Fig. 70.E.

Thus

for the exact

tjk r,K

=

Ctl

0.783 for C'tl

is

=

with

yik

shown

in

Approximation of the Hydrodynamic Pitch Angle and the Radial Thrust Distribution. The next step is to calculate the 70.27

First

hydrodynamic pitch angle /3/ using the following formula, which represents Lerbs' approximate optimum condition for a wake-adapted propeller: ,

tan

Here

x' is

/3j

=

-7

•

—

(70. i)

-;

the ratio of the local radius

tip radius i?Ma:i of the propeller,

^/Bmsi

,

and

Wx-

is

R

the corrected average

at each radius, to be explained presently.

TABLE Col.

A

to the

namely

70.d

x'

wake

sate for this difference, the local

0.730.

each radius

is

multiplied

by the

fraction at

ratio of (1) the

wake from the self-propulsion test to wake from the pitot-tube survey. The method thus makes use of the wake-fraction distribution found by the wake study, with the effective (2)

the nominal

numerical values modified so that its average over the propeller is the same as that derived

from the self-propulsion test. In the ABC propeller design, the local nominal wake fraction at each radius is increased by the factor

=

wake

0.195

0.1735

=

1.1239 OTW,.

Calculation of Hydrodynamic Pitch Angle

=

1.1239

iZi,-

HYDRODYNAMICS

filfi

The in

calculation of

ffi

from

Eci. (70.i) is

shown

Table 70.d.

The next ship's

step

d{CTL)s

efficient

is

to calculate a thrust-load co-

,

at each radius, based on the

using the formulas to be given These values, when integrated over

speed,

presently.

the whole radius, should give a thrust-load coefficient which is close to the desired coefficient,

{Ctl)s

,

calculated earlier in Sec. 70.26. If the

values are not close, within it is

make

necessary to

or 2 per cent, then

1

additional approximations

by modifying the hydrodynamic pitch angle

Pi

until the required accuracy is obtained.

The formulas necessary

for executing this step

are:

tan ^

UiT

= _ ~

^=^ 2 sin

)3,

sin

-

(1

(70.ii)

w,.)

{I3j

(70.iii)

sin^

Va

^ = ^(1-h;..)

(70.iv)

(70 .va) (7

(70. vb)

where 13 is the advance angle UiT is the tangential component

of the

induced

velocity

K (kappa;

capital) represents

what

is

known

as

the Goldstein factor.

Most

of

the

relationships

in

the preceding

paragraphs and several which appear in subPropeller-Shaft

N/

of

Aheod Thrust

IN SHIP DESIGN

Ser. 7n.2S

Sec. 70.29 l.b

SCREW-PROPELLER DESIGN

617

HYDRODYNAMICS

618

IN SHIP DESIGN

Sec. 70.29

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3W S3^

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a

e;^!^^

£h6uS

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!;;_

-f.

c366o6c366o6

Sec. 70.29

^1.0

SCREW-PROPELLER DESIGN

619

HYDRODYNAMICS

620

distribution than the fraction 1/2

The

and the Table

shown

there.

calculations for the lift-coefficient product lifting-surface

correction are given in

70.g.

Having applied the lifting-surface correction hydrodynamic pitch angle, it is possible to calculate the initial hydrodynamic P/D ratio for each 0-diml radius by the formula factor to the

(P/D)^.

where 0(phi) /3/c is

=

irx'

tan

(70.ix)

4,

the pitch angle and

is

is

equal to

at this stage of the design. This calculation

also

shown

ratios is given

in

The upper curve 134

Table

70. g.

A

plot of the

by the lower curve

P/D

of Fig. 70.1.

in this figure is explained later.

IN SHIP DESIGN

Sec. 70.30

SCREW-PROPELLER DESIGN

70 Jl

Sec.

Substituting in Eq. (70.x) (908) (3 ,3 12 .5)

+

(4.123)(97.2)(20)'(/o/^)

paragraph, give

= whence ta/D =

The

621

NACA

64A, and 65A thickness forms. These, in combination with one of the meanlines recommended in the following obtained with the

+

6,000

(20)\97.2)'

0.053.

maximum

radial distribution of the

ness of the blade elements

is

which have low uniform distribution of pressure along the chord length. For the latter reason they have favorable cavitation charac-

thick-

obtained from the

by J. D. van Manen ["The Design of Ship Screws,"

teristics.

airfoil sections

and

ratios

drag-lift

12,788

16, 66,

The

four

recommended thickness forms

are listed in the order of preference, although

following equation, given

there

and

66 form has zero thickness at the trailing edge;

L. Troost

SNAME,

1952, Fig. 11, p. 453]:

D^ where tx/D

is

+

/I

must be modified

'tjp

D

D

a;'

and t-nJD

is

(70.xi)

]

J

maximum

section thickness to the diameter at

radius

blade-

any 0-diml

assumed as 0.003, a typical

at that edge.

Values of / for the various radii are:

= R/Rm„

0.2 0.788

/

on marine screw propellers

The other

it

thickness distributions can

NACA

16 thickness form has performance characteristics similar to those of the

TMB EPH

section.

The

combination of an ellipse at the nose, two parabolas along the two sides, and a hyperbola at the

0.4 0.551

0.3 0.665

0.5 0.443

tail;

derives

it

letters of these

0.7 0.251

0.8 0.162

0.9 0.079

1.00

is

no

EPH

The

calculations for tx/D values are

made

in

(70. xi) and the values are Table 70.h. strength calculation may be phase, as long as the required tx/D

accordance with Eq.

down in Col. B Any method of

set

used in this

of

ratio at each radius

is

obtained.

A

designer

is

no means restricted to using the formula shown section.

The strength

of

the propeller

related definitely to the design problem, but

by in is is

independent of the fundamental propeller theory. 70.31 Blade-Section Shaping by Cavitation Criteria.

It

criteria, to

is

now

possible,

by using cavitation mx of the mean-

determine the camber

the chord length c, and the lift coefficient of each blade element. This is done by the use of line,

K

one

of

use these charts

it

charts; Fig. 70.

is

them. is

first

decide on the blade-section shape.

necessary to

Modern

airfoil

shapes are found as satisfactory as any. They are obtained by superposing a given set of thickness ordinates on a given meanline. in effect,

is

What happens,

that a selected airfoil sectipn, with a

base chord through its midwidth, is bent until this base chord becomes the selected curved meanline. In this way, all cambered airfoil straight

sections are transformed

from symmetrical

sec-

tions.

The same shape is used for all blade sections from the root to the tip. Good blade sections are

its

name from

the

first

an form but unfortunately there

three types of curve. It

is

design chart available, corresponding

to those for the

To

NACA

slightly to give finite thickness

be used directly without modification. The

efficient thickness

0.6 0.344

this

among them. The

latter is a

value.

x'

difference

therefore, for use

(h

the ratio of the

is little

NACA

designer should use

eddying abaft

it

sections.

A

propeller

with caution because the

its trailing

edge might cause the

blade to flutter or to sing. Additional comments

on thickness forms are made in Sec. 70.34. Meanlines commonly used with the thickness forms listed are the circular-arc and the so-called a = 1.0, a = 0.8, and a = 0.8 (modified) meanline. The "a" meanlines have uniform chordwise pressure distribution from the leading edge to the point designated by a = x/c, where a; is a distance from the leading edge. From this point to the trailing edge the load decreases linearly. The a = 0.8 (modified) meanline has slight curvature in

the

decreasing portion

of

the load

curve.

Because of this pressure distribution the "a" meanlines have good cavitation characteristics. Also when combined with a given thickness form they give blade sections with less hollow on the face than if the same thickness form were used with the circular-arc meanline. The a = 0.8 (modified) meanline is usually associated with the NACA 6A-series airfoils. Complete data for the NACA 16 and 66 thickness forms and the a = 1.0 and a = 0.8 meanlines are given in NACA Report 824, 1945. The data for the NACA 64A and 65A thickness forms and the a = 0.8 (modified) meanline are given in NACA Report 903, 1948. The exact process for combining a meanline and a thickness distribution to obtain an airfoil section

HYDRODYNAMICS

622

.

o o o o o o

lOOOOOOOOi 6

6

^

„

d o o oO O

1

0,00,0

rH

o

ft

.-I

O O O O O

<

o

o o o o o o o

o o o o o

ooooooooo H

3

O O O O

'

CO.

O to.

O

'OOOOOOOO

O O O O O O O

OOOOOOOO'H

IN SHIP DESIGN

Sec. 70.31

Srr. is

SCREW-PROPELLER DE.STGN

7031

explained iu detail in

NACA

Report 824, 1945,

pages 3-4.

The

chart in Fig. 70.

K

was constructed

for

Karman-Trefftz blade sections. This type of section, obtained by a conformal transformation from a circle, has a circular-arc face, a circular-arc back, and a circular-arc meanline. Fig. 70. K can be used, with only a .slight sacrifice in accuracy, for a circular-arc meanline in combination with various thickness forms, such as the NACA 16 or the 60-69 series. It can not be used, however, for

any other meanlines. In the design for the

ABC

of the propeller

ship the circular-arc meanline

adopted because, at the time 1955), the chart

shown

is

of writing (early

in Fig. 70.

K was

the only

one available. Similar charts for the following combinations of thickness forms and meanlines are under construction at the David Taylor

Model Basin: Thickness

Form

62.^

HYDRODYNAMICS

624

where

T'^ is the resultant velocity

approaching

the blade element (Ts

number

at each

blade

element, with the blade in the upper vertical or 12 o'clock position, based on the ship speed V

a

the

is

cavitation

resultant velocity Poo is

number,

on

based

=

14.7(144)

Po,

-

e

ft'

x'{Rm^x)w is a term to correct the cavitation number to each blade element, with the blade in the upper vertical or 12 o'clock position

w is the specific weight 64.043 lb per x' is the

of

standard

water

salt

=

ft'

0-diml ratio R/Rm^x

For the ABC ship the shaft centerline is 15.5 ft below the designed waterline. The wave crest or hollow due to the wave profile at the designed speed

ignored in these calculations.

is

ship,

the positive

=

The

wave height

In the resulting

+

15.5(64.043)

-

52

3,110

remaining

=

=

calculations

the

for

3,110 lb per

3,058 lb per

ft'

ft'

cavitation

for

maximum-camber

ratio

chord length c, and the lift coefficients of the blade elements at the various radii are shown in Table 70.h. rux/c, the

When

the vapor pressure of salt water at an average

service temperature, taken here as 0.36 psi or

ABC

p.

numbers and

the static pressure at the shaft axis, or the

52 lb per

70J]

from the crest at the stern adds a shght margin

the

Vn

atmospheric pressure plus the hydrostatic pressure with the ship at rest e is

Sfc.

of safety against cavitation.

the cavitation

is

IN SHIP DESIGN

rrix/c

entering Fig. 70.K to pick the ratios

and

ix/c, the

value of

per cent, as shown in Col.

customary to do


is

reduced by 15

M of Table 70.h.

this for all

It is

merchant ships as a

safety factor to guard against intermittent cavi-

may

tation which of the

wake

arise

from the non-uniformity For ships

in a peripheral direction.

which there are highly concentrated wakes, such as those behind a bossing or a large strut, the reduction should be as much as 20 per cent. For high-speed, high-powered vessels with fast-runin

ning propellers, where

it is

almost impossible to

avoid cavitation, no reduction in a

is made. There are additional limiting factors in the propeller design which must be considered at

this time. First, the blade-thickness ratio tx/c at

the l.0f? =

Rr

hub

section or at the 0.2/2 section should not

exceed values of 0.16 for destroyer-type propellers,

and 0.18

Above

to 0.20 for merchant-ship propellers.

these

limiting

values,

the

drag-to-lift

ratio of a blade section begins to rise rapidly.

Second, section

Expanded Blade Outline From CoYitotion Criteria

the

Rodiol Disc Line /

Faired Outline

OA H

0.3 R

O.Z R^.^

I

-Expanded Width at 0.2R Petermined lyy Strength and Riqidity

Considerotions

Expanded Blade Outlines with Minimum Widths for Cavitation Prevention

Fio. 70. L

exceed

Cl

for

about

any blade 0.6.

Values

ping and backing characteristics and increase the

/

II

not

greater than this give propellers with poor stop-

leakage from the surface. Using the values of 0.85(7 and C tic/tx), calculated in Tables 70.h and Fig. 70.K, the bladethickness ratios tx/c and camber ratios mx/c are found only for the 0.5 to 0.95 radii. The inner radii are off the chart, which means that cavitation is of little or no concern at these blade sections. In this case, a limiting value of tx/c of 0.20, mentioned in the preceding paragraph, is assumed at the Q.2R section. The Q.2R chord length is then calculated. This length, together with those determined from Fig. 70. K, are laid down on a sketch and a smooth expanded blade outline is drawn. The result is illustrated in Fig. 70.L. The expanded blade lengths are, for the time being, laid out symmetrical to the radial disc line. The method of introducing skew-back is described liability of air

.

lift-coefficient

should

later.

Sec. 70.33

SCREW-PROPELLER DESIGN

625

626

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 70.33

Sec.

SCREW-PROPELLER DESIGN

7035

the hub. A wake-adapted screw for the latter type of wake variation has a pitch distribution with the P/D ratio increasing toward the tip. Just the opposite is obtained in the ABC design.

70.34

ABC

Blade-Section

Final

Shapes for

the

ABC

ship

Design by Lerbs' Method.

The

propeller, designed here, has hollow blade faces

and a mussel shape

in the outer sections

outer

radii, similar to

World War

many German

in the

designs of

Hollow-face sections are unusual for merchant-ship propellers at the time of writing (1955) but if they improve the cavitation II.

performance of a propeller they are worth while. of modern production methods, hollow sections are only slightly if any more

Taking advantage difficult to

a

=

manufacture.

By

use of the a

=

1.0 or

0.8 meanlines, the hollow in this case could

probably be reduced or eliminated. Since the charts used in this design, shown in Figs. 70. and 70.M, were not available for the a = 1.0

=

and a

meanUnes

combination with suitable thickness forms, the circular-arc meanline was employed and the hollow sections accepted. The design procedure is the same regardless of what meanline or design chart is used.

The

0.8

propeller designer

in

is

cautioned, however,

that screw propellers with hollow-face sections do

not perform well when backing; some do not even meet normal needs for routine ship maneuvering.

Whether they would is

in the case of the

ABC

ship

not determined here. For this and other reasons

some

propeller

sections

at

sections

with

designers

the

inner

straight

prefer

radii

faces

to

use

airfoil

and circular-back (orthodox

ogival

k

the curvature correction

is

[A(?nxo/c)]

The loss in lift due to reduction in camber is then compensated for by the addition of an angle of attack aj The pitch angle 4> becomes /3/c -f «] -f ofj The added angle of attack needed to compensate the lift for any reduction in camber ratio depends on the meanline. For a circular-arc meanline, the correction is given by Eq. (70.xviii). This formula, when used with a = 1.0 or a = 0.8 meanhnes,

the reduction in camber ratio.

was considered unacceptable. trial-and-error method,

an angle

i.e.,

of attack added,

It is moi'e or less a

the camber

is

reduced,

and the pitch

distri-

These three items are then

checked.

bution adjusted

until

obtained.

Since the

satisfactory

ABC

relationships

ship propeller

are

is

an

unusual case, the hollow-face sections are accepted rather than to adopt flat sections with an unfair pitch distribution. In the normal merchant ship, hollow sections can be avoided, if desired, by using one of the other recommended meanlines,

and by adjustment of the angle camber ratio as necessary.

and

of attack

Hollow-face sections, as obtained in this design,

have satisfactory cavitation when these sections have thin leading edges, as they would with the undoubtedly

will

performance. However,

NACA

16 thickness forms, they are sensitive to changes in angle of attack, which occur in any wake field due to non-uniformity of flow into the

A

blunter leading edge reduces this For this reason, the NACA 65A thickness form [NACA Rep. 903, 1948, pp. 6-7] is used for the ABC ship propeller. It gives the desired leading-edge thickness with only a sUght propeller.

sensitivity.

loss in the

cavitation characteristics along the

rest of the chord length. If the blade sections

no hollow then the

NACA

have

16 thickness forms are

better.

NACA

The

ness ratio.

is

This procedure was tried for the ABC design, but it resulted in an unfair pitch distribution and

shapes) for the outer radii.

In many cases the hollow can be removed by reducing the camber ratio mxo/c until it is no more than Q.5tx/c, where tx/c is the blade-thick-

G27

65A

thickness

form

with

the

circular-arc meanline gives airfoil sections

which are curved near the trailing edge. The back or — Ap side is convex to the flow, and there is a concavity on the face or +Ap side. Again this can be avoided by using the a = 0.8 (modified) meanline, in which case the trailing-edge surfaces

.

are straight lines.

.

introduces only a small error.

^2

=

2(57. 3)/c

[4^)]

(70.xviii)

Undoubtedly more desirable blade be obtained with the Fig.

the

ABC project was underway

is

the added angle of attack in deg

70. K,

in

course

sections will

design charts, similar

to

of

preparation [Eckhardt,

when

M.

K.,

and Morgan, W. B., "A Propeller Design Method," SNAME, 1955, pp. 334-338]. However, the main purpose of this chapter is to outline a method of propeller design. Availability of the

new

charts will not change the method.

70.35

where a^

new

Blade

Introducing

Profile.

Sec.

Skew-Back 70.16 states

the

ABC

that a

good

in

628

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 70.35

SCREW-PROPELLER DESIGN

Sec. 70.37

range of values of the skew-back at the tip 0.20 to 0.25cMax

skew-back

is

.

ABC

For the

is

from

propeller, the tip

taken as 0.245cMax or L25

ft.

An

easy curve, representing the locus of the midlengths of the blade-section chords, is then drawn

skew-back line, starting at the extreme-tip section and approaching the pitch reference line as a tangent at the hub. The expanded outline is laid out, half a chord length on each side of the skew-back line. From this the projected outline is drawn, explained in Sees. 32.9 and 32.10 and for the

illustrated in Fig. 32. L

sketched

With the

projected outline

the angular variation of the leading

in,

edge as each blade section passes the vertical plane through the 12 o'clock propeller position

The

checked.

is

the

ABC

interval

ship propeller,

Sec. 70.36,

is

between sections for in Fig. 70.O of

drawn

as follows:

629

except that

has constant rather than variable pitch, is illustrated in a photograph published by The Marine Engineer and Naval Architect [Aug 1954, p. 300]. teristics,

it

One point needs

The

explanation.

blade-thickness fraction to/D

is

required

0.053 as calculated

from the strength considerations. The bladethickness fraction shown on Fig. 70.O is only 0.049.

The axis thickness to on Fig. 70.O has been determined graphically by conventional practice [SNAME, Tech. and Res. Bull. 1-13, Jul 1953, As can be seen from Fig. 70.O, this conp. 22]. vention gives a blade-thickness fraction that is not truly representative of the thickness at the hub. Thus the actual tx equal to AB in Fig. 70.O, is greater than CD, indicated by the construction lines for determining to The propeller ,

.

actually has the correct thickness required

0.2ft1.5

0.053 0.3ft-

2.1

the face and back lines were straight.

if

However,

deg

ventional

for the sake of uniformity, the con-

method

for finding

0.4ft-

Calculating the Expected Propeller

70.37 0.5ft-

deg

2.7

deg

graphically should

to

always be followed.

2.4 deg

2.8

by

strength considerations, and to/D would equal

deg

The

ciency.

final step in

short method,

E&-

by Lerbs'

to calculate the expected pro-

is

0.6ftpeller efficiency.

the design,

This

given by the following

is

relationship: 0.7ft1

2.7 deg

-

2X,e (70.xix)

0.8ft-

[-(i)d

4.4 deg 0.9ft-

where

This shows a fairly regular interval and

is

con-

may

be necessary at times to draw several skew-back lines before a satisfactory angular interval is obtained. sidered

satisfactory.

It

Several schemes were tried to achieve this. It

was

rjo

the propeller efficiency

is

the ideal efficiency with jet rotation and

r]K is

e(epsilon) is the drag-lift ratio of a blade section

or airfoil.

A

close

approximation of

finally concluded, as related in Sec. 70.16,

that the locus of the midlengths of the expanded

blade sections represents the most convenient construction line. It is almost impossible to start

with an arbitrary projected outline and finish with fair contours in the expanded outline.

Cl Xj

0.008

Ci, at 0.7ft

0.3064

to

delineate

the

propeller.

The

x'

tan

/3,

c

0.0261

at 0.7ft, where tan

from Col. G, Table

7/0

=

1

-

70.i.

c is

obtained

=

0.3711

2(0.3711)(0.0261)'

0.783 1

no

/J/

70.g.

0.7(0.5302)

final

drawing of the ABC design, following the arrangement and details laid down in Fig. 32. F of Volume I or on the SNAME PD sheet of Fig. 78.L, is shown in Fig. 70.O. A large propeller having the same general blade shape and the same charac-

given by:

obtained from Col. D, Table

is

=

e is

0.008

70.36 Drawing the Propeller. All unknowns have been calculated or determined so it is now possible

is

equal to 0.783, from Fig. 70.E

0.026l \ + 2Y 3A0.371I/

=

(0.783)(0.9367)

=

73.3 per cent.

=

0.733

J

HYDRODYNAMICS

630

By way

of comparison,

Wageningen propeller

P/D

as discussed in Sec.

chart

logarithmic

Prohaska's

70.22,

series

for

70.B,

Fig.

B.4.40,

the

and a propeller efficiency t/o of 0.72. The same parameters as calculated by Lerbs' short method are P/D = 1.193 at the 0.7 radius and t/o = 0.733. This shows satisfactory agreement with a good standindicates a

ard propeller

ratio

of

IN SHIP DESIGN

(14) Calculate the final propeller efficiency; use

Eq.

1.2

series.

Summary of Design Steps for Lerbs' Short Method Schoenherr's Combination. Sum70.38

Draw

(13)

Sec. 70.38

the propeller

(70.xbc).

The Lerbs 1954 method,

described here,

is

con-

sidered neither too long nor too intricate for the

design of a screw propeller to go on an important or costly ship, especially as it gives the designer more flexibility in taking account of unusual conditions than a method based solely final

marizing the procedure of Sees. 70.21 through

on empirical or experimental data. The calculations proper can be made by anyone who knows arithmetic, algebra, logarithms, and elementary

70.37:

trigonometry.

;

rake, (1) Determine the number of blades Z, the the propeller diameter D, the hub diameter d, and the rate of rotation n (2)

Ctl Calculate the thrust-load and the absolute advance coefficient

the coefficient {Ctl)s

,

The

correction

several

factors

involved in this procedure, some of them semiempirical, will disappear with increasing knowl-

The

edge.

analytic framework of this

method

should serve well for the insertion of results of future research and the presentation of additional

,

and Xs (3) Determine the ideal tion riK from Fig. 70.

useful data for the propeller designer, especially

coefficients X

efficiency

with jet rota-

when more

is

known

of the flow in

and around

the propeller position.

(4) With successive approximations, determine the hydrodynamic pitch angle ^i and the thrust distribution over the blades which will allow the propeller to develop the required thrust; use ,

(70.i) through (70.vi) and Fig. 70.G product hft-coefficient the (5) Determine Cl{c/D), apply the lifting-surface correction, and calculate the hydrodynamic pitch-diameter ratio

K. E. Schoenherr has recently [SNAME, 1955, a logical, workable combination of the propeller-design chart and analytic method embodying the following steps, adapted from the

p. 366] outlined

reference:

Eqs.

P/D

for each blade section; use Eqs.

through

(70.vii)

(70.bc)

is first solved by the use of and the methods described in PNA, Vol. II, Chap. Ill (b) The method of Th. Theodorsen in his book "Theory of Propellers" [McGraw-Hill,

The problem

(a)

design

charts

calculate the (6) From strength considerations, blade-thickness fraction to/D, and the maximumblade-thickness distribution ratio tx/c; use Eqs.

New

and (70.xi) and Fig. 70.J (7) Choose the type of meanline and thickness form to be used for the blade sections (8) Using cavitation criteria, determine the maximum camber of the meanhne nix the chord lengths c of the blade sections, and the Uft co-

thickness distribution are

(70.x)

,

efficients

Cl

of the

sections; use Eqs.

(70.xii)

(c)

the

lift coefficients;

use Fig.

70.M

if

Apply the curvature correction to the camber ratio; use Eq. (70.xvi) and Fig. 70.N (11) Apply the viscous-flow correction and calthe

final

pitch

distribution;

and (70.ix) (12) Determine the amount lay out the skew-back fine

use

The blade

area, blade width,

and blade-

chosen to keep the

calculated,

if

not already available, by the method

of L. C. Burrill, explained in reference (39) of

Sec. 70.20 is read from the liftand the final pitch distribution obtained by smoothing out the calculated

The angle

of attack

coefficient curves is

results

necessary

(10)

culate

then applied to obtain the

out of cavitation, to meet strength requirements, and to give good thickness ratios (d) Lift-coefficient curves for the sections are

(e)

Draw and fair the blade outline and determine final chord lengths, maximum cambers, and

is

propeller

through (70.xiv) and Fig. 70.K (9)

York, 1948]

lift-grading curve

Eqs.

(f)

The

effective pitch obtained

from the fore-

going calculations is compared with the pitch obtained from the design chart as a check on the

accuracy of the solution.

According to Schoenherr, "... variable wake

(70.xvii)

of

skew-back and

can be introduced procedure.

readilj'"

into

this

design

SCREW-PROPELLER DESIGN

Sec. 70.40

Avoiding Air Leakage with Inadequate Submersion. For a designed-speed and a designed-load condition, assuming no severe limits 70.39

imposed by the projected service of the vessel, a tip submergence so inadequate as to permit drawing air is a matter of ship rather than pro-

This of

G3I

shown by

is

ship

L. P.

Smith

where,

propellers,

for several

after

models low

reaching

points in the thrust curves due to cavitation, the thrust begins to rise steadily as the rate of rotation

is

[ASME,

increased

Jul 1937, Vol. 59, pp.

imposed, and ships do have to propel themselves

409-431, esp. pp. 415-419 and Figs. 6, 7, and 11]. It is also shown by R. W. L. Gawn for a pair of motor torpedoboat propellers [NECI, 1948-1949,

with

Vol. 65, Fig.

peller design. Nevertheless, limitations are often

reasonable

submergences)

The

at drafts (and tip than the designed amounts.

efficiency

less

operation of propellers under these con-

7L10 and is well summarized by W. P. A. van Lammeren ditions

described in the references of Sec.

is

[RPSS, 1948, pp. 262-263]. From this reference it ". appears that screws having blades with wide tips and circular-back sections are more likely to be free from air-drawing." 70.40 Design Comments on Propellers for the Supercavitating Range. If the cavitation noise, erosion, and vibration are not serious, a certain amount of either bubble or sheet cavitation, or both, may be tolerated on heavily loaded screw .

.

provided this loading represents the

propellers,

maximum

may

be encountered under any condition of service. This is somewhat analogous that

to loading a boat to the gunwales if

that the boat

When

is

it

known

is

to encounter no waves.

pushing screw propellers to their limit of performance, involving large — Ap's,

ultimate

large real-slip ratios,

and high velocities over the it becomes necessary, at

backs of the blades,

coefficient

cavitation at that. This

is

Under the conditions described, not only is the pressure over the whole suction side of the blade then reduced nearly to zero absolute, representing the limit for service conditions, but the friction resistance on the back of the blade

because

craft,

par-

ticularly racing motorboats.

It

is

described previously, in Sec. 23.12, that

the practical limit of intensity of the

—Ap

on

the suction side of the blade, from which most of the Uft and thrust are derived, occurs at the vapor pressure of water. As the cavitation number is lowered, sheet cavitation covers more and more of the back of each blade. The thrust falls off rapidly and the rate of rotation increases, so that the propeller serves no longer as a suitable or efficient driving mechanism for the ship which

carries

The

cavitating range.

resembles

that

of

it.

flow over the blade then

the

right-hand

diagram in

Fig. 23.1.

There has been some theoretical work done in Russia on the supercavitating propeller but, so far as known, the only published references translated into English at the date of writing (1955) are: "On the Working of Supercavitating Screw Propellers," INA, 1944, pp. 138-149

(1)

Posdunine, V. L.,

(2)

Posdunine, V. L., "Problems in Ship-Propeller Design," Soviet Science, Feb 1941; English transl. in SBMEB, Feb 1946, pp. 69-70

(3)

Epshteyn, L. A., "On the Action of the Ideal Supercavitating Propeller," Inzhenerniy Sbornik, 1951, Vol. IX. This paper lists five previous Russian references, published in the period 1943-1945. Posdunine, in his 1944 paper, speaks of experimental proof for his claim to reasonably high thrust and efficiency in the supercavitating range. Despite his assurance that these data would be forthcoming they appear never to have been published in English. In the discussion of Posdunine's 1944 paper by F. H. Todd, on p. 144, there are given the results of variable-pressure water-tunnel tests at the NPL, Teddington, on a screw propeller, when extended into the supercavitating range.

if

the propelling machinery

is

able

One

feature of the design problem,

unexpected situation develops. When finally the whole back area is uncovered and exposed to vapor pressure in the

much more remains

cavity a further increase in the rate of rotation

affecting the pressure

usually

eliminated,

it.

However, to turn

is

moving water no longer touches

Under these conditions the propeller is fully cavitating, and is said to be running in the super-

the case with high-

speed and ultra-high-speed planing

p. 370], where at an advance about 0.62 to 0.67, the values of

14,

of

Kt begin to increase after reaching their minimum values. In fact, for one propeller, the Kt value at J = 0.6 is as high as at / = 0.75 and at J = 0.83, with a mimmum value at J = 0.67.

least in the present state of the art, to accept

sheet cavitation in the running range, and heavy

/

it

fast enough, a rather

results

in

a slowly increasing thrust.

to be done,

is

upon which that of pre-

when altered by the sheet cavity over the back of one blade, from adversely

venting the flow,

blade. This

is

on the face done by:

of the following

HYDRODYNAMICS

632

(a) Reducing the number of blades and the blade overlap (when viewed generally normal to the

blade surface) to a

minimum

Sec. 70.41

the "antiUft." This force exceeds the dynamic

upward

by the lower blades

created

lift

propeller rides too high but

(b) Keeping the slip ratio low, with a reasonably low angle of attack on each blade

Increasing the pitch-diameter ratio, to in-

(c)

IN SHIP DESIGN

upward

is

less

the

if

than the

the propeller rides too low.

lift if

of incorporating this feature in

Means

a propeller design

are described in considerable detail by E. C. B.

Motor Boat and Yachting, Sep

Corlett [The

crease the gap between blades.

it

1954,

pp. 387-388].

The

down by

can only be held

slip ratio

area,

but

is

Free-Riuining.

Bow Propellers, Coupled and Bow propellers are either driven

best accomplished in the case of the

by independent

engines, at a speed suitable to

by reducing the ship and the propeller thrust to the lowest possible values. At the high speeds in question, this is only possible with planing craft in which the resistance varies as some power of the speed

Design of

70.41

loading

the propeller lightly. This may be achieved by increasing the disc area or the expanded blade

the needs of the moment, or they are, in the case

many

double-ended ferryboats, coupled to the

supercavitating propeller

of

resistance

engine and the stern propeller by a straight-

Two-bladed pro-

through shaft. Icebreakers with bow propellers are in the first category, along with the larger ferryboats, where fuel economy is important. Icebreakers and other vessels with bow propellers are usually required to back hard upon occasion, or to run in the opposite direction. The bow propeller then becomes the stern one. Under these conditions symmetrical sections are employed, with straight meanlines. Actually, since

pellers are preferred. Pitch-diameter ratios should

the propellers rotate in opposite directions at

than the square, possibly even less than the power; see Fig. 53. D. Not more than three blades, and not too wide blades at that, should be used on a propeller

less

first

working

most part

for the

in the heavily cavitat-

ing or supercavitating range.

probably exceed or more. If it is

1.4,

known

and may run as high as 2.0

that a propeller will cavitate

throughout the running range, its blade sections may be of triangular shape, with blunt or square trailing edges. The blade speed is so extremely high, and the static pressure usually so low that the water can not possibly close in

behind even a fair blade section. Wedge-shaped propeller blade sections for supercavitating propellers are discussed by G. Rabbeno [Ann. Rep.

Rome Model stiffness

—and

The

Basin, 1938, Vol. VII, p. 91].

strength

— of

the

blade

may

be

concentrated in the metal near the trailing edge, enabling the leading edge and the blade section to be considerably finer than normal.

on supercavitating flow past

foils

Comments and

struts,

applicable to the propeller-design problem, are

given by

M. P. TuUn NPL, Oct

dynamics," 3

Nov

["Cavitation in Hydro1955,

paper 16; SBSR,

1955, pp. 570-571].

For the ultra-high-speed screw propeller which provides the dynamic

lift

for holding

up the

stern

No

Tests.

its proper level. One solution is to set up a compensating downward vertical force known as

existing propeller-design procedure

is

comprehensive and reliable to give an accurate prediction of the open-water performance of a screw propeller built to a particular design, sufficiently

either

on model or

peller design

is

full scale.

When

new

the

pro-

only slightly different from that

of a propeller which has already been tested it would appear that the designer could be reason-

ably

certain

of

predicting

its

performance.

minor changes which seem insignificant often produce appreciable differences

Nevertheless,

in performance.

One never knows when

this will

happen. It seems wise, therefore, in the case of a new propeller design, to build a

open water,

was not

at

or

running in the open, give identical performance when rotating one way or the other. 70.42 Open- Water and Self-Propelled Model

stabiUzing influence to hold the stern of the boat

craft,

elliptical

this kind,

tunnel,

very fast planing

are

midchord position, similar to those of Fig. 70. [S and P, 1943, Fig. 153, p. 132, Type 3]. What might be termed double-symmetrical blades of

with the propeller shaft, the struts, and the propeller hub normally out of water, it is important that there be a of a

sections

symmetrical on each side of the

lens-shaped,

fully

the

times,

different

(1) in

and

(3) in

ship for which

it

(2) in

model and

to test

it,

a variable-pressure water

a self-propelled model of the is

designed. Unfortunately,

it

wake-adapted propeller designed in Sees. 70.21 through 70.37, nor to include the test data in Chap. 78. possible to do this for the

SCREW-PROPELLER DESIGN

Sec. 70.43

Mechanical Construction Type of Hub 70.43 Shaping and Finish of Blades. The mechanical design and the details of construction of screw propellers, of both the solid and the built-up types, have become rather well standardized in the past century. They are described and illustrated by R. H. Tingey [ME, 1942, Vol. I, pp. ;

267-293, esp. pp. 291-293] and by the authors of up-to-date handbooks on marine engineering.

The

choice of whether a particular design of

propeller

to be of the solid or built-up type

is

made by

usually

is

the owner and operator, often

based upon considerations far removed from hydrodynamics. The marine architect is called

upon only ciency

to state

involved

is

how much

if

reduction in

the wheel

depends upon the ultimate

and shape

size

effi-

built up. This

is

of the

hub, including the flanges at the roots of the blades, the fairing of the bolts and nuts for these

in

the fairing of the whole hub into the and other features. The probable reduction efficiency on the ship, mentioned in Sec. 70.14,

is

of the order of 2 or 3 per cent. If a solid pro-

flanges, hull,

has an efficiency

peller

built-up propeller

=

0.679. In

(70

-

numerals,

67.9)

=

of (0.70) (0.97)

ijo

what are known as

by marine engineers percentage

of 0.70 the equivalent

tjo

may have an

points, often

indicate

to

this

a

is

used

a change in reduction

of

2.1 points.

633

distant future there will be developed a strong,

not-too-expensive, ferrous

alloy

corrosion-resisting,

propeller

for

weldable

which

blades

will

permit the separate blades of a screw propeller to be cast individually with specially shaped root

palms and welded to a steel hub, or to an enlargement on a short stub shaft. An arrangement diagram of the latter scheme, for the arch-stern

ABC (3)

ship, is sketched in Fig. 74.L.

The

availability of a strong,

alloy will,

among

rigid,

ferrous

other things:

Enable the larger propellers, whose shipexpensive and inconvenient, to have their hubs and blades assembled by welding at the yard where the ship is built. Annealing of the welds is possible by induction heating. (b) Eliminate the trouble, expense, and vulnerability of tapered fits, keyways, keys, screw threads, and nuts necessary to attach the present (a)

ment

is

propellers

much (c)

to

their

shafts.

Bolted

flanges

are

simpler and more reliable.

Eliminate

need

the

galvanic-action

for

protectors in the neighborhood of bronze propellers,

with their never-ending added drag and

continual expense (d)

By

the use of plated

chromium

or

some

other material, such as on the stub shaft project-

ing abaft the

ABC

ship propeller in Fig. 74. L,

eliminate the need for bronze bearing sleeves on

of reducing this loss and retaining demountable-blade advantage, there are several possibilities which call for comment:

As a means

steel shafts.

the

(1)

The

many blade

without

propeller

built-up

decades, the base or bolting flange of each is circular.

geometric pitch

is

over a blade, and of plus and minus 1/2 per cent in local pitch variation, are now being approached

constant

or exceeded. Blade thicknesses in important posi-

means equivalent

is

bolted firmly

if

the blade

must be a This

is

by no

to a constant change in linear

pitch P, or even to a constant percentage change in P, because

P =

2tR changes with

2:rfl

tan

radius.

and the distance

<^

The

great

number

of

a small need for the adjustable feature and for changing pitch in service. By eliminating the adjustment in angle, solid propellers in use indicates

and with

it

the need for the circular base flange on

each blade, detachable

it

is

possible to

or demountable

make

the blades

without greatly in-

It appears

almost certain that

tions are being specified

excellent as far as

it

mean

face pitch

and measured. This

goes, but

it still

is

leaves as un-

back or —Ap is a growing appreciation of the importance of back shape among owners and operators as well as among propeller designers. Lack of suitable equipment to make measurements on large propellers, both during manufacture and inspection, is delaying specified the shape of the entire

surface of the blade. However, there

progress along this

Edge shapes

line.

of propeller blades are important.

These require delineation on the drawings by

creasing the size of the hub. (2)

propellers

plus or minus 1/4 per cent in

for all blade sections.

d(j>

is,

conforming more nearly to the design drawings, has produced valuable results. Tolerances of

This permits some adjustment in

on the hub. However,

in place

the past two or three decades, that

when the blade

shifted in this process, the shift

angle

adjustable

In the orthodox design, followed for

features.

Constant pressure and attention applied to the manufacture of more accurate propellers for

in

the not-

large-scale details or

by geometric dimensions.

HYDRODYNAMICS

634 described in Sec. 70.19.

checked

b.v

They

are rather easily

small full-scale templates.

Considering that the surfaces of a screw-problade almost always travel through the water faster than the ship, and the surfaces of peller

the outer portions often several times as

fast,

the blade surfaces should be as smooth as modern tools and techniques can make them. Indeed, in keeping with the necessity for smaller roughness

tolerances on a large ship than on its model, to

make

IN SHIP DESIGN

(a)

Schoenherr, K. E.,

SNAME,

(b)

Schoenherr, K. E.,

PNA,

"6.

re-emphasizes Decision 2 of the 1948

Conference on this subject, which stated that 'It is necessary that the model propellers should be made to a. high degree of precision and in all published work the measured tolerances "

and the quality

of the surface finish should be

stated.'

How to keep this ship-propeller surface smooth, even on the "stainless" metals which are essentially resistant to corrosion

and

erosion, is

(e)

Van Lammeren, W.

(f)

Hecking,

marine engineers. 70.44 Blade Strength and Deformation. On many if not most screw propellers it is necessary to shape the root sections, and possibly also

some

others, to give the necessary strength

rigidity to the blades. ships,

structural

those

of

On

icebreakers and ice-

considerations

hydrodynamics.

and

may

However,

outweigh it

is

not

book to devote space to this feature, other than has already been done in Sees. 70.19 and 70.30. possible in

this

P. A., RPSS, 1948, pp. 269-273 J., "Strength of Propellers: Analysis Made in Connection with Classification Rules at the American Bureau of Shipping," MESA, Oct 1921, pp. 762-767.

It may very well be that elastic deformation under heavy load of the blades of a nearly perfect "static" design will modify rather appreciably the shape and the performance contemplated by the designer. This is a manifestation of hydroelasticity, described in Sec. 21.5 and mentioned in Sec. 70.13. Furthermore, this deformation may take place periodically and in varying amounts as a blade rotates through a complete revolution, leading to blade vibration and other

objectionable results. It is interesting to note in this connection the

comments made by Dixon

Kemp

in

the late

1890's in his treatise on yacht design

["Yacht

Architecture," Cox, London, 1897, 3rd ed., p. 284]: "There would seem to be some advantage if the blades and bend whilst revolving, especially in the case of small vessels; and Messrs. Yarrow have recorded a case within their e.xperience of torpedo boat propulsion

are elastic,

where, by submitting a thin elastic blade for a perfectly rigid one, the speed

was

from

altered

It is unfortunate that

n\ knots to

19 knots."

no record has yet been

found of the shape and materials of these thin, elastic blades, nor an explanation of their superior performance. To return to a consideration of modern wheels, the propeller designer so-called deformation

still

a problem, but one for metallurgists rather than

1.57

Taylor, D. W., S and P, 1943, Chap. 29.3, pp. 127-141 (d) Tingey, R. H., ME, 1942, Vol. I, pp. 281-291

the two surfaces hydrodynamically smooth,

The Conference

1934, pp. 113-114

1939, Vol. 11, p.

(c)

the full-scale propeller surface should actually

be smoother than that of its model. In particular, no lifting holes should be drilled through the blades, contrary to the design shown by R. H. Tingey [ME, 1942, Vol. I, Fig. 1, p. 268], nor should nicks and bent-over portions of the edges be permitted to remain after the first opportunity to repair them. It often happens that, if the dock trials are run with the ship's own propellers in place, pieces of wire rope and other debris which have been dropped overboard at a fitting-out dock may be picked up by the propellers, with damaging effects. If a ship's propellers have been so menaced, it is wise to have all blade edges examined by a diver after the vessel is in clear water, before it is permitted to undertake standardization and acceptance trials. In this connection the following is quoted from the Conclusions of the Sixth International Conference of Ship Tank Superintendents, 1951, page 10:

Sec. 70.44

Rather complete procedures for determining blade thicknesses adequate for strength and rigidity, and for calculating stresses in the blade material, are found in the following references:

in

is

advised to sketch a

diagram

of his propeller,

which the estimated deformations under thrust

load are greatly exaggerated for emphasis.

aim

is

The

to delineate the shape of the propeller

blade under load and to determine changes in pitch at various radii. Procedures for constructing these diagrams are as yet not well formulated but a few hints may be helpful for guidance: (a)

The

thrust forces are exerted roughly normal

to the line joining the nose

The drag

force

generally in line (b)

At the

and

tail of

each section.

may

be neglected because it acts with the chord of each section.

effective angles of attack

normally

SCREW-PROPELLER DESIGN

Sec. 70.45

encountered, and with hydrofoil or

airfoil section

may

increases the

G35

lift

on the outer elements, and

in-

be expected to act at a point between 0.25c and 0.40c abaft the nose of

of attack «;

greater.

A

each section

vicious cycle continues until the vessel speeds

up

shapes, the

Tlie

(c)

force

lift

bending forward

(in

the direction of

thrust) of cantilevered screw-propeller blades

to thrust load

is

due

usually not diminished as the

designed thrust-load factor decreases because the blades are

made

thinner in an effort to increase

creases the twist deformation.

down because

of

effective angle

still

thrust, the engine slows

the increased torque, or the

blade takes a permanent set in twist. A sequence of events of this kind is encountered when a heavily loaded propeller with swept-back blades has

the efficiency

thereupon becomes

match the increased

to

The

direction of rotation reversed, as

its

taking deformation into account, the radii of

during a crash-back maneuver. The greatly disturbed condition of the water around it probably saves the propeller but at least one case is on

the sections involved, and the rate of rotation

record where blades have been bent in a sudden

The

(d)

centrifugal forces acting on raked blades

amount

are functions only of the

CO

of actual rake,

high-power reversal.

(omega).

70.45

The deformation

of heavily loaded screw-pro-

peller blades is best counteracted,

not by thicken-

ing the blades but by using materials of the highest practicable

modulus

of

elasticity.

The

nickel-

copper alloys and the corrosion-resisting chromium-iron alloys are considerably superior to the

materials

ment

obtain.

point

Screw-propeller blades which have long, thin

overhangs such as those of the weedproof type shown in diagram 12 of Fig. 32. L and those fitted on the liner Normandie in the early 1940's, almost certainly suffer some bending of the overhang in an ahead direction. This reduces the geometric pitch angle 4>, straightens out the meanline,

and diminishes the blade camber

region. local

The net

effect is to

but the overall

lift

in that

reduce not only the

of the blade sections at

A slight additional camber of the overhung portions may well be introduced to overcome this deformation and to make all the those radii.

blade area work effectively.

On

a propeller which

is

loaded moderately or

One now known

of the

and Coatings to most satisfactory

for use in screw propellers

which must resist corrosion, erosion, and impact from sand, ice, and the Uke is an alloy composed of approximately 14 per cent chromium and 86 per cent iron. This alloy is capable of heat treat-

best bronzes in this respect, although accurate data as to elastic moduluses are often difficult to

trailing

Propeller Materials

Resist Erosion.

to give yield points of the order of 70,000

As

lb per in^.

for other iron alloys,

is fairly definite;

bronzes and brasses containing large quantities of copper.

The proper kinds

and

irons

ability

must work

A

of corrosion-resisting

have proved in practice their to withstand severe usage on vessels which steels

in the ice.

corrosion-resistant alloy of austenitic charac-

teristics

was employed by the Germans some

years ago for the propellers of destroyers and similar naval vessels. This

22 per cent chromium and

most

of the

propellers

of

is

11

an alloy containing per cent nickel, with

remainder composed of this

speci^-l cutting tools, and tedious machining procedures but once fabricated they

stand up well in service. Examples are the two

outer elements, lying near the forward quarter-

at Annapolis, Maryland.

or third-points of these elements, of

would be much

the torsion axis in the root

sections of the blade than they are abaft that axis in a blade

swept or skewed normally

aft.

This would mean a greater twisting moment forward, and a greater increase in the geometric pitch angle than the reduction in that angle when the blades are swept back. This increment

A0

increases the effective angle of attack «/

,

Screw casting

techniques,

corrosion-resisting steel propellers

farther ahead

iron.

alloy require special

skewed to an appreciable extent in the forward or ahead direction. Were this done, the centers of pressure on the heavily, the blades are never

the yield

this is not the case for the

German

the

destroyer

removed from Z37 and now (1954) on

exhibition at the Engineering Experiment Station

Some comments on means

of preventing

it

cavitation erosion and on marine propellers and

appendages are given by S. F. Dorey Inst. Metals, Great Britain, Jul 1954; ASNE, Feb 1955, pp. 94-96]. On page 95 of the other

[Jour.

latter reference appears the following,

modified

slightly for emphasis:

"A

reasonable assessment of the erosion-resistance of an

alloy

is

given by the product of

(1)

the suifaoe Brinell

HYDRODYNAMICS

636 hardness number and

(2)

the erosion-fatigue resistance

expressed in tons per in- for 50 million cyeles of reverse

bending.

The more

excess of SOO,

and

in

highly resistant alloys have values in

descending order of merit they include

IN SHIP DESIGN

Sec. 70.46

Application and curing of a durable plastic all the external surfaces except those

(4)

coating to

which have to be

in metal-to-metal contact with

the propeller shaft. (a)

Austenitic stainless steels

(b)

Aluminum bronzes, with or without nickel additions Low-nickel stainless steels

(h)

Manganese bronzes

(i)

Silicon bronzes

beheved that the blistering and other with plastic and similar propeller coatings in the past have arisen from the presence of moisture and gases within the metal proper, underneath the coating. The procedure outlined in the foregoing is similar to that which was found necessary and which has been employed successfully for many years in vacuum-impregnating the wound coils of electric motors and other electric

(j)

Phosphor bronzes

devices.

(c)

(e)

monel Monel metal

(f)

High-tensile bronze

(g)

Turbadium bronze.

(d) Silicon

"Below 800 are placed the normal:

(k) (1)

It

Gun metals Cast irons Aluminum

(m)

is

difficulties

Prevention of Singing and Vibration.

70.46 It

alloj's.

is

assumed

in Sec. 23.7 that the singing of

is due to the alternating circulacomponent around a blade section, and the periodic variation in lift, accompanying the shed-

propeller blades

"This does not imply that the manganese bronzes which have given such good servide have poor resistance, but they are used purely as a basis of comparison."

Designs and techniques have been evolved, and are in use on the blades of propeller-type turbines in hydroelectric plants

[ASNE, Nov

547-549; Maritime Reporter,

whereby a thin is

1

form

of

pp.

1955, p. 17],

corrosion-resisting steel cladding

applied to a cast-steel blade

in the

Mar

1946,

by welding,

either

a multitude of welding beads from

corrosion-resistant rod or a thin sheet of rolled corrosion-resisting metal.

ding of alternate vortexes in a vortex street or trail.

It is possible

lateral

steel surfaces of

the

to relate the frequency of

vibration with

Strouhal number S„

the

blade velocity,

the

and the Reynolds number

,

Rn provided the diameter or transverse dimension of the vibrating (and eddy-creating) body is known. This transverse dimension corresponds

generally Anqle at

with

the

t

in

Tanqent at

Fig.

70. P,

E,

Point

E

deq or More,

18

thickness

Separation

E,

Should Be

some form of plastic coating may be evolved which will protect a blade from minor mechanical damage. This coating might resist the action of sand and mud, prevent corrosion, resist erosion by cavitation, and serve as an insulating layer over a copper alloy so that no galvanic-action protectors would It is entirely possible that

be needed on the adjacent

tion

With Respect to Ton

NOTE!

Points Ei.Eg, ond Ej Must 8e Shorp to be Effective

Estimated General Direction of Flow in

Edqe

Vicinity of Trailinq

and the appendages. To make such a coating reliable and successful, however, will undoubtedly

hull

call for

a special application procedure, involving

the following operations: (1)

Heating the entire propeller in an oven for a

considerable period, to drive out in the interstices

all

the moisture

between the metallic crystals

(2) Subjecting the heated propeller to an almost complete vacuum, to pull out not only all the moisture but all the gases to be found within the

metallic structure (3)

Application of a sealing

propeller fill

up

all

Not Less Than 165 Fig. 70.P

heated and under a vacuum, to the internal crevices and pockets where

is still

gases or moisture might otherwise collect

Sketch of Chisel Type of Trailing Edge

To eUminate

singing effectively

it is

most important that

the corners at Ei E2 and E3 be sharp, to create definite, fixed separation points there. ,

,

average position of the on one or both sides of the blade. If the trailing edge of the section were approximately semi-circular it would be easy to estimate the value of /, but difficult to confirm it. roughly

compound while the

d

abreast

separation points

the

E

SCREW-PROPELLER DESIGN

Sec. 70.46

For a complex shape

of trailing edge, as in the

figure, the eftective thickness is

tentative prediction

Kokai, Japan,

May

Notes and Data

both

difficult to

A

means of making a given by F. Kito [Zosen

estimate and to confirm. is

Eq. lies

S„

possible.

is

worked out If singing is

Sec. 2.22 the Strouhal

= =^

Here /

is

,

or /

=

,S„(|)

=

S„

number

^

occurring,

is

10 per sec and below 10,000 or 12,000 per sec. Practically, the highest audible frequency of a

The

velocity

is

about 700 to 1,200 cycles per

U

is

the blade velocity Feude

,

obtained by combining vectorially the rotational velocity 2-KnR with the advance velocity

V a The

blade velocity varies with radius R, with rate of propeller rotation n,

The maximum combination of limit

it

and with ship speed V.

occurs at or near the tip at

minimum

at

should be satisfactory to use

R =

0.4/?Ma:c

n = 0.5nMai and V = O.ST^Max The blade-section Reynolds numbers R„

no large slope well ahead of the trailing where separation might begin, the two corners thus formed comprise two definite and fixed separation points at the upstream end of a narrow separation zone between them. The eddy pattern in this zone remains sensibly steady, to the extent that any eddy pattern can do so. At least, the circulation around the blade does not vary periodically, with a frequency in the audible range, nor does it fluctuate in magnitude at any such frequency. Other methods of providing fixed separation

calculated for these

are

two extremes, and from the

left in Fig. 46.

G

the corresponding

is

edge

points along the trailing edges of propeller blades, to prevent singing, are

shown by

[European Shipbldg., 1955, Vol.

•

,

graph at the

full

some smaller the three variables. As a low

designed speed; the

thought probable, or if it is actually almost invariably prevented or

is

sketched in heavy Unes in Fig. 70. P. Provided there

the vibration frequency, lying within the

singing propeller

it

illustrating this procedure

in Sec. 46.9.

eliminated by the use of the so-called chisel edge, (70.XX)

audible range to produce singing, generally above

sec.

An example

is

1951, pp. 41-42

ICSTS,

(in English)].

From

(70. xx) the frequency / is calculated. If / within the audible range, objectionable singing

1948, No. 277; also Abstract

for 6th

637

Hmiting values of S„ are found. The value of t for the limiting radii is then estimated and from

F.

J.

A. van

Aken

4, Fig. 3, p. 31].

The singing propeller is discussed briefly by M. Lewis [ME, 1944, Vol. II, p. 131]. A partial

list

of references relating to singing propellers is

given in Sec. 46.10.

CHAPTER

The Design 71

.

of Miscellaneous Propulsion Devices .

638 038

.

038

General Considerations Design Features of Paddletrack Propulsion Notes on the Hydrodjoiamies of Paddlewheel Design Calculating the Blade and Wheel Proportions and Dimensions Alternative IMethods of Determining Paddlewheel Blade Area Relation of Paddlewheel Diameter and Propulsion to Ship Hull Design Design Notes on Paddlewheel Details and

1

71.2 71 3 .

•.

71.4 71 5 .

71 6 .

71.7

Mechanism Normal Paddlewheel Design Design Notes for Hydraulic-Jet and PumpVariations from

71.8 71.9

Jet Propulsion

The Design

71.11 71.12 71.13

Auxiliary Propulsion for Sailing Yachts

641

71 14

Vertical Drive for Screw Propellers; Under-

642

71 15

643

71.16

645

71.17

the-Bottom Propellers Design of Devices to Produce Transverse and Vertical Thrust Design Features of Tandem and ContraRotating Propellers Design Notes Relative to Rotating-Blade

71.18

Airscrew Propulsion

.

.

.

General Considerations. The screw pronow so widely employed for propulsion in water that ahnost any other type of device is unusual by comparison. Likewise, in a program of research, experiment, and development that is in keeping with the total number of propulsion devices employed, a very large proportion has been devoted to screw propellers. types has suffered

rather severely. In fact, in most books of this

kind the discussions of other propulsion devices aire hmited to brief mentions only. Design notes

and

rules

these

for

miscellaneous devices are

notable by their absence. This situation

not

hence the notes and

easily nor quickly remedied,

comments for by no means

is

these devices, in this chapter, are

comprehensive,

as

and

definite,

helpful as they should be.

Although the

title

does not so indicate

it,

chapter treats also of certain design aspects

this

when

screw propellers and other propulsion devices are

tandem

The

are under-the-bottom screw propellers,

and contra-rotating

propellers,

propellers.

order of subjects in this chapter follows

in general those of Chaps. 15

Data

for predicting the

pulsion devices of

all

and 32

in

Volume

I.

performance of pro-

types, or references to those

data in the literature, are given in Chap. 59. 71.2 Design Features of Paddletrack Propul-

I

sion.

Paddletrack

briefly in Sec.

propulsion

is

mentioned and

15.4, described in Sec. 32.2,

illustrated in Fig. 32. A.

051

.... .

651 652

.

053 654

655 656 658

Propellers

Very

little

analytic

work has been done on

paddletracks and there has been only a moderate

amount and

of systematic experimentation

full scale.

Correlation of the large

on model

number

of

on both self-propelled models and full-scale craft, made in the United States during the period 1940-1955, is difficult and time specific tests,

consuming, so much so that it may not be undertaken or completed for an indefinite period. The hydrodynamic design requirements for reasonably efficient paddletrack propulsion in the water have been pushed rather far in the back-

ground by the need for closely spaced cleats which will insure adequate traction and support on the ground. It so happens that almost any kind of deep cleat gives some measure of propulsion in the water (or in liquid mud) but only certain cleat designs provide substantial support and withstand severe usage over any type of ground, including submerged rocks, reefs, and concrete roads.

intended to work in unusual positions. Examples of this

of Surface Propellers

Asymmetric Propulsion Feathering and Folding Propellers

648

71.1

result, the design of other

648 050

71 10

peller is

As a

71

For the reasons given, no attempt

is

made

here

to furnish design notes or criteria for paddletrack

propulsion. 71.3 Notes on the Hydrodynamics of Paddlewheel Design. It is reported that S. W. Barnabj', in his treatise on propeller design of 1885, stated that "As a propelling instrument the paddle is not inferior to the screw and some of the best recorded performances have been obtained with it." Screw-propeller performances have improved since then but so have those of the paddlewheel, especially of the feathering type.

638

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 71.3

There are many

rivers in the so-called navigable

areas of the world in which the depth of water of the order of 2 or 3 ft only, logs,

and

all

manner

of debris,

and

is

which trees, floating and waterin

logged, are constantly encountered.

Under these

conditions paddlewheel or sternwheel propulsion is

almost a necessity [Hobson, C. A., "Sternwheel Work," Ship and Boat Builder

Vessels for River

and Naval Architect, London,

May

1953,

pp.

The

geometry of the feathering paddlewheel, a type which is almost universally used when the propulsive efficiency

Paddlewheels are

still

to

be considered for

and

are described in Sec. 32.3 32. B.

The

text

of the various

terms.

is

important,

illustrated in Fig.

and drawings include definitions hydrodynamical and .mechanical

Diagram 2

of Fig. 15.

G

indicates that the

effective thrust-producing area of

a pair of side

paddlewheels, equivalent to the disc area Aq oi

a

371-377].

639

action and

screw propeller,

equal

is

to

the

combined

(transverse) length 2s of the blades of both wheels

pleasure steamers, tugs, and other craft plying

times the

on the smooth, shallow waters of lakes, estuaries, and rivers, where draft restrictions prevent the use of screw propellers large enough to give high or even moderate efficiencies. If the paddles are separately driven, as on many European tugs, the maneuverability can not be approached by any

edges,

maximum immersion

known

as the dip.

The

of their lower

dip ratio

is

the dip,

measured to the at-rest WL, divided by the blade width or height h. Based upon the principle that the most efficient '

propulsion takes place

when

the least -|-A?7 value

other type of propulsion except multiple rotating-

imparted to the greatest mass of hquid, the blades of an efficient paddlewheel should have

blade propellers diagrammed in Fig. 37. P.

the greatest area (transverse length times radial

The low

n of paddlewheels does not match the high n of most modern propulsive machinery, but the current and future developments in reduction gearing and flexible couplings give promise of adequate means for utilizing

rate of rotation

both,

while retaining their individual

advantages.

Although the paddlewheel does not retain the prominence it once enjoyed, it is still reckoned as one of the standard ship-propulsion devices, for which design data should be available. For this reason, and because the paddlewheel data in the Uterature are rather scanty and widely scattered, some space is devoted here to a moreor-less systematic presentation of them. Judged on the basis of the rotating-blade propeller and the screw propeller with a Kort nozzle, both reasonably acceptable as shallowwater propulsion devices, the efficiency curves of Figs. 34. and 34.N reveal the paddlewheel as a rather poor third. If, however, corresponding curves were added for screw propellers working under tunnel sterns, as alternatives for shallowwater propulsion, it would be found that they too had low efficiencies. In fact, it is believed that the latter will average about 0.4 at reasonable thrust-load values, and that these efficiencies will rarely approach or exceed 0.5 in actual service.

M

Provided, therefore, that the thrust-load factor

paddlewheel design can be kept between and 0.5 or below, it need not suffer from the handicap of low propulsive efficiency for its of a 1.0

particular applications.

is

width or height)

consistent

with a balanced

wheel-and-ship design. Plunging the blade into the water and lifting it out again constitutes unwanted and undesirable motion and involves

wasted energy in the water. The blades are therefore as long, parallel to the water surface, as their positions and as operating requirements permit. In other words, blade area is achieved preferably with blade length measured transversely, rather than with radial width or height. Theoretically, since the ships on which

modern

paddlewheels are fitted encounter waves only on rare occasions, there are apparently

the

transverse

length

of

blade

no Umits to

except

those

imposed by mechanical and structural considerations. When the blade length becomes excessive, with undue twisting of the blade on a feathering wheel, two separate paddlewheels, side by side, are mounted on each side of the vessel and keyed to the port and starboard ends of a single shaft, with a separate feathering mechanism for each of the four assemblies. However, if the blades are too large and the thrust loading is too small, too great a proportion of the work is expended in blade friction through vertical motion, and there is too much churning through plunging each blade into the water and Ufting it out again. Like a screw propeller, the paddlewheel can have too much blade area for its own good. The volume swept through by an immersed blade is partly boundary layer, with an average U less than the ship speed V, and partly a potential-flow region where the average U is almost

HYDRODYNAMICS

640

IN SHIP DESIGN

Sec. 71.3

than V. Since so little is known of these velocities for the paddlewheel positions on ships, especially as the wheels extend outward from one-third to one-half the beam, it is cus-

larity of feathering blades as they

tomary to assume that the speed of advance V a and the ship speed V are the same. There has been in the past some difference of opinion among commentators and designers with regard to the radius at which the tangential

careful analysis of the path of the paddles at

certainl}' greater

the

and the presence

circle

of

swing around external

rings

serving as guards and as ties between the arms.

"The

actual slips can only be determined

by

given speeds of boat and wheels" [Taylor,

SNAME, SNAME,

1908,

E.

Stevens,

245;

p.

A.,

S., Jr.,

velocity of a paddlewheel blade

1908, p. 246]. It appears customary, however, to measure the tangential blade velocity at the midheights of the blades for a radial

for the

wheel, and at these positions or at the trunnion

is to be measured, purpose of determining the slip ratios.

By some

measured at a radius corresponding to the distance from the wheel center to the bottom of a blade in its lowest position. Twice this radius is roughly the overall wheel diameter, leaving out of account the anguthis velocity is

centers for a feathering wheel

The

p. 187].

Fig. 32.

B

difference usually

the hlade

circle.

The

Normal

to

is

in this

book

represented by the symbol V° (vee

of Fig. 71.

A

indicates

called

tangential velocity of this

The vector diagram Blade Lent^th

1926,

not appreciable.

indicates that the circle corresponding

to these trunnion positions

circle is

FeQtherino

[SNAME,

is

in the all

circle).

lower right corner

the velocities

known

to

Link and Blade

is

Paae

Foul

be acting in the case of a paddlewheel drive, with

Here

their

correct ahead or astern directions.

Their

diagram are, however, purely schematic. The}^ will remain so until more data magnitudes

are

made

in this

available, covering the flow across the

entire width of a paddlewheel (length of a blade), its inboard to its outboard end. When the curved paths of the blades and the waves on the

from

surface

the adjacent water are taken into

of

account, the velocities are not

all

horizontal, nor

do they remain the same in various parts of the field swept by the blades. In the past, as previously described, this situation has been simplified at one stroke by assuming that V = V. The apparenta.

then

slip ratio is

V

of blade circle

V _ V

of

blade circle

V

Positive Wave- Wake

Blade Dip-

WG

Speed


I

Woke

Biometer of Trunnion

Shtp Speed V-

Cirde-A|C°2AC

u.auii

r*—'<j^Speed V plus Induced UActual

Sli|

Velocity

sj^

H-n-n(AC)

Fig. 71. a

0.5

— F

of ship

_ V° — V

of blade circle

["Binnenschiffahrt

to

Feathering Paddlewheels

Operation),"

midheights of the blades.

Va

v°

For radial wheels the ratio Sa ranges from 0.2 to 0.3. For feathering wheels on ships of relatively fine form it varies from 0.1 to 0.2, averaging about 0.15. E. M. Bragg gives values of Sa for nine passenger ships, ranging from 0.146 to 0.223, when reckoned on a basis of the tangential speed of the midheight of the (feathering) blades [SNAME, 1916, PL 90]. For paddlewheel tugs O. Teubert gives a range of s^ values from 0.3

Definition and Design Sketch for

For the wheel shown here, the trunnions are placed at

—

of blade circle

1912,

p.

(Inland-Waters Ship

445].

For operation

in

shallow and restricted waters, Teubert adds 0.1 to

all

the apparent-slip ratios mentioned.

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 71.4

7L4

portions and Dimensions.

may

Wheel Pro-

Calculating the Blade and

Each

Rq 2p7°(7°

=

{s)h

side paddlewheel

-

641

7)

be assumed to act on a quantity of water 176,400

moving within the bounds of a horizontal stream tube of rectangular cross section, corresponding and the height h

to the length s

The water speed

may

tube

of one blade.

in the outflow portion of the

be assumed equal to the tangential

blade-circle speed

The volume

V°.

acted upon per unit time

water so

of

is

=

163.4

ft'

2(1.9905)(41.2)(6.58)

For a check, consider the Long Island Sound passenger steamer Commonwealth, for which

trial

data are given by E. M. Bragg [SNAME, 1916, PI. 90]. This vessel is selected from among the nine listed in the table because

has the greatest

it

engine power and a speed of 20 kt, close to the

Q =

=

sih){V of blade circle)

The mass

sih)V°

(71. i)

water passing through the p(rho) times the quantity The increased velocity imparted

of the

tube in unit time rate in Eq. (71. i).

is

(F of blade circle — F of ship) or (F° V). Assuming that all the blades encountering water on each side can be replaced by one effective blade on that side, the thrust to

by the blade

it

is

—

exerted

is

then

=

r(per effective blade)

When 0.0,

p{s)hV°{V°

-

T

exerted

(71. ii)

Rt =

Er

The

effective area of a blade

length s and height

89,876

in

fraction

is 0.0,

ft,

ran 29.8

rpm

circle, is

of

(7°

6.81 ft per sec.

40.59

=

-

The

7)

meanhne

lb,

and 66

-

V)

is

7 =

to be driven

(F°

-

20.5 kt or 34.62 ft per

7°

V)

is

=

6.81/

0.16,

=

0.167° and V°

=

41.2

ft

to obtain the effec-

= 2p7°(7°

-

7)

by two

derived in Sec. 66.9 from the

= V° - V =

(71.iii)

89,876

The

1.191

F

per sec.

81.67

ft'

blades on this vessel were actually 14.5 ft

long by 5.0

ft

wide, with an area of 72.5

ft'

per

blade. This gives a reasonable correlation with

the calculated value, considering the assumptions

that had to be made and the simplifications involved in the formulas used, to be explained presently.

=

=

3.981(40.59)(6.81)

The

thrust per unit area of each blade

works out at 89,876/[(2)72.5]

whence

33.78

rr (s)7i

ABC

56.M. Assume also that the apparent-shp ratio Sa is 0.16, and that the thrustdeduction fraction t is 0.0, so that Rt = T. Then s^

-

apparent-slip ratio s^

tive area of a blade

Fig.

of

then 40.59

as

per sec.

ft

(71.iii)

assume that the

practical example,

176,400

is

moment

40.59

0.1677, which agrees closely with Bragg's

paddlewheels instead of by a single screw propeller. Also that the total hull resistance Rt for is

=

x(26)0.497

h, is

2pV°{V°

sec

At full power the wheel The tangential velocity

ft.

or 0.497 rps.

Substituting in Eq.

a given condition at

T is also 89,876 lb.

so that the thrust

the diameter measured to the midheights

The value on each wheel, of

Rt is unknown

third

The diameter over the blades of the Commonwealth wheel is 31.0 ft. With a blade width of

the blade

Rq

ship of Chaps. 64

A

lb.

at tne midheight circle, taken for the

V)

At 20 kt

tabulated value of 0.167.

{s)h

As a

also assumed,

by assuming that the thrust-deduction

is filled

of the blades is 26.0

-

2pis)hV°iV°

=

5.0

2[r(per effective blade)]

=

5,520(550)/33.78

effective

Then

0.5,

5,520 horses.

is

or 33.78 ft per sec the total resistance

taken as

of the ship.

of

r)p

Pe

the effective power

is

blades of the two side paddlewheels equals the total resistance

propulsive coefficient

by the two

the thrust-deduction fraction

the thrust

V)

ABC ship. With an indicated power P, of 12,000 horses for the 20-kt speed, and an assumed overall mechanical efficiency of 0.92, the shaft power Ps is 11,040 horses. With a 20.5-kt speed of the

To

=

619.8 lb per

ft'.

continue with the design example for the

proposed paddlewheels to drive the ABC ship, necessary to decide whether the calculated effective area per blade of 163.4 ft' is to be it is first

The ft

so-called slip velocity

per sec.

Then

is

(F°

—

7)

=

6.58

reduced by some factor which brings the simplified

IIYDROnYNAMICS IN SHIP DESIGN

642 calculation of Eq.

into agreement with

(Tl.iii)

corresponding values calculated from observed ship data. There are several difficulties here.

The

published data available to the analyst lack one

more

important values necessary for a The simple formula of Eq. (71.iii) takes no account of velocities induced by adjacent blades, spillover around the edges of the or

of the

calculation.

logical

motion worked out

loop-shaped path

blades,

of the blades in a

as

in the early years of

paddlewheel

propulsion [S and P, 1943, Figs. 168 and 169, p. 149],

m

and changes

of the. water surface in

the elevation and shape

way

of the blades.

Further-

assumes that not several but only one blade at a time, on each paddlewheel, is acting more,

it

upon the water. The rectangular area stream tube in which to the water,

when

the

of

momentum is being imparted so derived,

is

larger than the rectangular area of

undoubtedly one blade. It

may

be more nearly the area of the thrustproducing segment indicated by the hatched rectangles on each side of diagram 2 of Fig. 15.G. Purely as a means of working out a numerical example it is assumed here that a reduction factor may be applied to the calculated blade area, because of the conditions described in the preceding paragraph. This factor is established arbitrarily for the

moment

area per blade on the

=

only 163.4(0.9) factor

tugs

may

it is

effective

paddlewheel

147.06 ft^

be taken when

The necessary

as 0.90.

ABC

A

it is

better reduction

no reduction area should be made.

The next

step

is

then

found. For paddle

possible that

the blades.

is

in calculated

shallower they are,

The average 32.

B and

pitch

and paddlewheel length and overall beam The deeper and shorter the blades, the less can be the wheel width and the overall

beam but at

the expense of greater wheel diameter

and a slower rate

of rotation.

of rotation the larger

The slower the

and heavier

is

rate

the propelling

machinery.

The average value

of length-height ratio s/h a blade in Bragg's referenced table is slightly in excess of 3.0, with a maximum blade width

-of

for the nine vessels hsted of 5.0

blade width of 6.5

ft for

the

ABC

ft.

Taking 10 blades as a

ABC

of the

trunnion

diameter

its

is

and the length-height This length

is

ratio is just

under

3.5.

within the limit given by D.

W.

illustrated

in

Fig.

=

9.75

ft.

starter, the circumference

=

circle is 9.75(10)

97.5/7r

=

31.03

97.5

ft;

ft.

The outside diameter of the paddlewheel, assuming no circumferential rings external to the blades, is approximately 31.03 -{ 6.5 = 37.53 ft,

=

giving a blade-height ratio of 6.5/37.53

This

somewhat

is

0.1733.

larger than the largest value of

0.168 (for the Tashnwo) in Bragg's table. It could

be reduced by using 11 blades instead of 10 but with the selected pitch ratio of 1.5, this would increase the overall wheel diameter to about 40.7

X

The blades could be narrowed

ft.

a blade-circle diameter of

giving

=

-I-

=

6.0)

0.16.

However,

increase the blade length to 147.06/0.6 still

ft,

would

this

=

24.5

of the order of one-third of the

of 73 ft for the of

to 6.0

[11(6.0)1.5]/

31.5 ft and a blade- height ratio of only

6.0/(31.5

each blade

ABC is

ft.

beam

ship, the length-height ratio

4.09,

which

is

considerably too

by one feathering crank

Methods

at

Determining methods of calculating the effective area per blade, such as that described by D. W. Taylor [S and P, 1943, p. 150], are based upon the same combination of the engine power (possibly determined previously by the owner or operator), the ship speed, the slip ratio, the wheel diameter, and the rate of rotation. Taking the formula given by Taylor Alternative

71.5

Paddlewheel Blade Area.

A =

Assuming a

twice the power of the fastest vessel tabulated there, the blade length is about 22.6 ft

ratio,

ship, developing

nearly

states that

the midheights of the blades, of 1.5(6.5)

one end.

of the vessel.

who

between adjacent trunnions of a feathering paddlewheel divided by the blade height, is of the order of 1.5 for the most modern designs in the Bragg table. This gives a circumferential spacing on the trunnion circle, assumed for the moment as equal in diameter to the circle passing through

higher shaft

150],

defined as the circumferential distance

large for actuation

rate of rotation, but at the expense of

p.

good practice requii'es the blades for a seagoing no longer than one-third the beam. A blade length of O.iB is a good figure for any type of smooth- water ship; a maximum value for any design, except paddlewheel tugs, is 0.5B.

the smaller can be the wheel diameter and the its

Sec. 71.5

and P, 1943,

[S

vessel to be

While

to select the proportions of

The narrower and

Taylor

where

A

is

K

of

Other

V

the area of two blades, in

(71. iv)

ft",

one on

each side of the ship

K the

is

a coefficient depending primarily upon

apparent-slip

ratio

and secondarily upon

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 71.6

many

other

For

factors.

K=

ranging from 0.10 to 0.30,

P is the shaft

apparent-slip

-

[212.5

375(s^)]

Ct.

Q.bpAoV

or indicated power; unfortunately

89,876

a rather loose definition

V

Assuming for the bare-hull ABC ship an power of 10,816 horses, from Sec. 66.9, and a propulsive coefficient rjp of as high as 0.55 for a modern design, the value of P for Eq. (71.iv) is about 19,660 horses. That of K, for an assumed effective

apparent-slip ratio of 0.16,

=

A = Kyz =

152.5

-

[212.5

is

Eq.

152.5. Substituting in

=

0.3599, say 0.36

0.9953(219.82)1,141.1

the ship speed in kt.

is

643

T

ratios

Assuming the same value

=

Ctl

using the value of 72r

= T =

for the

ft

ABC

per sec, and

176,400 lb mentioned

earlier,

Equivalent area

375(0.16)]

(71. iv)

^^^

of

ship at a speed of 20.5 kt or 34.62

^0 =

T C'rL(0.5p)F-

347.9 ii\

176,400

=

410.8

ft'

0.36(0.9953)1,198.5

The

on each side of the vessel is half of this value or 173.9 ft^. This is a somewhat larger area per blade than the value of 163.4 ft^ calculated by Eq. (71.iii) but the discrepancy is perhaps not too large, considering the assumptions made. The additional formulas given by W. F. Durand [RPS, 1903, pp. 198-201] and by 0. Teubert effective blade area

["Binnenschiffahrt," 1912, p. 446] are dimensional, as

the formula given by D.

is

require in

W.

Taylor.

addition an estimate of the wheel

Another method if

of

approximating a suitable

complete and reliable reference data

were available,

make

to

is

use of the thrust-load

and to work backward to find the equivalent thrust-producing area Ao by the following formulas, assuming as before that coefficient

=

Vj,

area of 147.06

derived previously in this section

factor of 0.9.

The

usefulness of the

Ctl method obviously

depends upon knowledge as to proper thrust-load coefficients for design purposes. For instance, the value of Ctl for the Tashmoo from Bragg's table, using a mechanical efficiency of 0.9 and a propulsive efficiency of 0.55, is only 0.26 as compared to the 0.36 of the Commonwealth. For a paddle tug, pulling heavy loads at slow speeds of advance, the thrust-load coefficient might reach or exceed 10 times these values.

V:

71.6

T

Cr

ft',

by using the momentum method, with a reduction

They

diameter and the rate of rotation, or both. blade area,

This is the estimated thrust-producing area on both sides of the vessel; on one side it is 205.4 ft'. With a tentative dip ratio of 1.35, the estimated area of one blade is 205.4/1.35 = 152.1 ft'. This value is only slightly larger than the estimated

Q.bpAaVl

Equivalent area ^o

0.5p(equivalent ylo)F' for

,

both

Relation of Paddlewheel Diameter and

Position to Ship Hull Design.

Taking account

of general design considerations, the selection of

paddlewheel diameter

is

one rather closely related

sides,

to the overall ship design, because

it

concerns the:

Space which can be allowed for the wheel boxes or recesses (b) Overall beam of the vessel, measured to the guards outside of the wheels (a)

CrL(0.5p)F'

For example, taking the total resistance Rt

oi

the Commonwealth, derived earlier in this section as 89,876

lb,

and assuming that

(c) it

equals the

T of both paddlewheels, with a thrustdeduction fraction t of 0.0, it is possible to derive thrust

the thrust-load factor

speed

is

20

Ctl

33.78

kt, or

ft

for this vessel.

per sec.

The apparent

dip of the blades, so called by Bragg because

measured to the

at-rest

length of each blade 14.5

=

219.82

ft'.

is

WL,

14.5

Then

ft,

is

The

7.58 ft

so that

Ao

it is

and the

=

2(7.58)

(d) (e) (f)

Type

of engine, and of reduction gear if fitted Rate of rotation n of the paddlewheel drive Speed of the vessel Probable values of wake fraction w and real-

slip ratio Sr

.

In general, the greater the wheel diameter the

more

efficient

is

its

propulsive action.

larger diameter the blades enter

With a

and leave the

water more nearlv tangential to the resultant-

HYDRODYNAMICS

644 Blodes, Trunnions,

Links

in

Drown

Crank Arms, and

IN SHIP DESIGN

Sec. 71.6

Line Normal to Blode Face

Approximote /*"

Solid Lines ore^

C'

Sweep

for Trunnion'

Flonqes Stiffen

at Lower Cerrter

Lines

Ends

of

Blodes I

of Blodes

Reduce

and

Water Spillover at These Points I

Center of Poddiewheei Shaft-

Broken Lines -Show Speciol

Blode Actuated

DK

el

ft

875

ft

3+5 fj

Trunnion Axis for Blade

Fig. 71. B

velocity vector, indicated in the left-hand diagram of Fig. 32. 71. B, for

B and

in the layout elevation of Fig.

a greater part of their width. There are

more blades acting simultaneously, with a lighter loading on each and smaller losses from induced effects. Furthermore, the submerged blades move more nearly parallel to the straightalso

aft direction in

which the water

is

to be accelerated

by them.

The

correct fore-and-aft

position

important for efficiency if profile has marked crests and troughs,

paddle-

of

the is

wave

governed

by the position of the wave crests along the ship when running at the speed for which the best propulsion performance

is

much more important

desired. This feature

for a vessel running in

water than in deep water. To take advantage of the wave wake the wave crest should be approximately under the wheel center. This position can sometimes be estimated for a shallow

new

design,

and

it

may

be predicted by com-

parison with an existing design

the same shape.

Wave

if

the hulls have

some paddle steamers are shown in Sec. 52.2; references are given there for other published profiles. The wave profile is quickly and reliably determined, however, from a model test.

From

Ship

Fig. 78. Ja, it appears that the best fore-and-aft

position for a pair of paddlewheels on that vessel

at about Sta. 11. This happens to coincide very nearly with the position of maximum wateris

line

beam.

The next problem position

of

is

to determine the vertical

the paddlewheel shaft center with

respect to the designed waterline.

The selection how far the

of the dip ratio, or the decision as to

wheels,

is

ABC

Layout Accompanying Example of a Feathering Paddlewheel Design for the

the

wave

profiles for

profile of the

stern ship, given on the

ABC

SNAME RD

transomsheet in

bottom

of the deepest blade is to

at-rest

waterline

at

the

drop below the

designed

draft,

may

on practical rather than hydrodynamic reasons. It depends upon the wheel diameter, how many blades are to be in the water at any one time, whether feathering is employed or not, and hinge

the

maximum

variation in anticipated draft for

which propulsion is to be reasonably efficient. For a shallow-water vessel, the greatest submergence depth of the bottom of a blade should be slightly less than the draft. Consideration of these and other factors, for vessels of various types, results in blade immersions varying from only some 0.7 of the height to immersions of 1.4, 1.5, or more of the blade height. D. W. Taylor points

may reach 2.0 for a very narrow blade on a large wheel, without loss of efficiency [S and P, 1943, p. 150]. Another relationship between the wheel diameter and the blade dip involves the angular out that the dip ratio

long,

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 7 J.

length of arc of the blade

circle,

the blade trunnions, which

is

passing through

immersed

the

in

designed-draft condition. For a paddlewheel to run at a medium rate of rotation, or perhaps

above average, say not more than n

=

35

rpm

or 0.58 rps, this arc should extend for about 50

deg forward and aft of the lower center position, or a total of 100 deg. For a fast-running paddlewheel of less than average diameter, with normal dip, the arc on either side of lower center may be 55 deg or more, corresponding to a total of 110 deg.

For use in selecting a

ABC

the

in

ship,

final

dip ratio for the condition

designed-load

at

645

mechanism is to be outside the wheel, with the eccentric pin carried by a fore-and-aft guard forming the lower edge of the paddlewheel

feathering

is an outer shaft bearing carried by guard the feathering links must be pinned to an eccentric strap around the shaft, and possibly also around the bearing. The mechanism then resembles that sketched in Figs. 32.B and 71.A. Although the dip appears large when drawn in the elevation from aft of Fig. 71. B, the markers

box. If there this

WL

showing the

elevations at Sta.

two variable-load conditions Fig.

66.T indicate that the dip

is

for the

11

66.32 and

of Sec.

actually too

which the paddlewheels are to give their best performance, Bragg's table has values of apparent

small for those lighter displacements.

measured to the at-rest waterline, varying from 1.27 to 1.52. The ABC value of 1.35, selected tentatively in Sec. 71.5, combined

the radial width or height and the radial position

dip

ratio,

with a blade height of 6.5 With a diameter of 37.53 ft,

the wheel center

lies

ft,

gives a dip of 8.76

ft

and a radius

18.77

-

8.76

=

ft.

water surface at an angle ahead

therefore

of the lower center of cos"'(10.01/15.52)

deg. This

may be

is

acceptable,

and the dip

is to change more-orpermanently during the life of the vessel. It would be very much better, of course, if the vertical position of the paddlewheel axis could

less

-

ft,

A

the draft at the wheel axis

strikes the at-rest

15.52

may be changed without too much and expense after the ship is built. certain measure of adjustment is desirable if

of the blades

difSculty

10.01 ft

radius of 18.77

=

are designed so that both

of 18.77

above the at-rest water level. The circle passing through the midheights of the blades, with a 3.25

Some paddlewheels

=

49.8

ratio of 1.35

considered as fixed.

be changed as well. 71.7 Design Notes on Paddlewheel Details and Mechanism. The next phase of the design involves an analysis of the dimensions, ratios, proportions, and other features to insure that

With an apparent-slip ratio of 0.16 the value V° = 41.2 ft per sec, from Sec. 71.4. Dividing this value by the blade-circle circumference of 97.5 ft gives a rate of rotation n of 0.4225 rps or

those tentatively established in Sec.

of

produce a good overall mechanical and hydrodynamic design. This involves a more careful

25.35 rpm.

arbitrarily in Sees. 71.5

It is

now

possible to sketch a layout of the

paddlewheel alongside the transomstern ABC ship, about as indicated in Fig. 7 LB. Rounding out the dimensions to get rid of the small decimal fractions, the paddlewheel center proposed

is

placed 10.0

WL. The

ft

DWL,

above the

or at the 36-ft

external wheel diameter

is

nominally

but for a wheel of the feathering type the volume swept through by the outer edges of the blades is not a true cyhnder. Nominally, the outside wheel diameter is twice the distance from

37.5

ft,

the wheel axis to the bottom of the blade at the lower center or 6 o'clock position, corresponding to twice the distance

The maximum

AG

in Fig. 71.B.

waterline

beam

lies

very close

and a mechanical clearance of 0.4 ft between the hull and the inner ends of the blades to Sta. 11,

appears to be adequate. With blades 22.6 ft long, their outer ends lie 23 ft from the widest portion of the ship's side (including the shell plating).

The

consideration

of

the

features

and

71.6

selected

will

rather

71.6.

Clearance between inboard paddle ends and the fixed hull

is

generally limited to the

minimum

permissible mechanical value, say from 0.2

ft

on

on large ones. The value of 0.4 ft indicated in Fig. 71.B is rather small but not too small. Every fraction of a foot added here adds to the overhang of the shaft. small vessels to 0.5

The

ft

blade-spacing or pitch ratio, defined as

the circular-arc distance

FG

CJ over

the blade width

in Fig. 71. A, should preferably be

times

the

blade

depth,

to

avoid

about 2.0

interference

between blades. However, this calls for very large wheel diameters. Practical limitations on weight and space are usually such as to reduce this ratio to as low as 1.6 or 1.5. If the dip ratio WG/FG of that figure is made about 1.2 to 1.5 the combination of pitch ratio with dip ratio and a reasonable blade-circle diameter gives a total immersed-blade area of from 2.0 to 2.5 times the area of one blade, irrespective of the angular

HYDRODYNAMICS

646 position of the wheel.

The

blade spacing of 9.75 the

ABC

pitch ratio of 1.5 and

previously adopted for

wheel appear not too small.

The average

CP

ft

on each moving blade, in the course of is somewhat below

travel through the water,

have to position

H

somewhat

in Fig. 71. A. This

PiQ on

However, on the

XjYi

XY

Furthermore,

if

trunnion to the

its

comply with

to

from tangent

The blade would

.

about

shift angularly

the forward

after side, the

far

is

or parallel to the vector QiPj

its

only 0.4 times the blade width from the bottom. It is customary to

below the midheight point

to the resultant-velocity vector side of the wheel.

its

possibly

place the blade trunnion at a point

Sec. 71.7

leaving edge of the blade

position of the center of pressure

geometric center,

IN SHIP DESIGN

one wishes to

hensive analysis, the position of

condition.

this

make a comprethe wave profile,

the direction of flow within the wave, and the

known component

71.A

Fig.

of

velocities

all

means that the blade-circle or trunnion-circle diameter is somewhat greater than twice the

require to be taken into account.

radius to the midheights of the lowest blade, at

edge of an entering blade meet the water surface

the 6 o'clock position. For the nine vessels listed

with the blade tangent to the resultant velocity

in Bragg's table, reference (14) of Sec. 59.6, this

Curving the blade radially, with its concave and +Ap side aft, helps to accomphsh this. However, this very curvature can be said to impart a greater upward component of velocity when the blade leaves the water than would be the case if its surface were flat. The major source

diameter ratio varies from 1.00 to 1.04. The ratio of the height of trunnion above the lower edge of the blade in the 6 o'clock position to the blade height varies from 0.40 to 0.50. For the

ABC

ship of Fig. 71.B

Thus

it is

taken as 3.0/6.5

=

from starboard, at the left of Fig. 71. B, GH is 3.0 ft and HF is 3.5 ft. The trunnion circle passing through has a diameter of 2 (AH) = 2 (AG - GH) = 0.462.

in the elevation

H

-

2(18.75

3.0)

=

31.5

CJ in Fig. 71.B, to the nearest whole number. There is no particular advantage in using an odd or even number of blades but the minimum practical number is about 6, preferably not less than 7, although paddlewheels have been spacing,

for the

ABC

The number

ship in Sec. 71.4,

is

10, selected

a good average

value from the Bragg table.

There

undoubtedly an advantage in mounting the port and starboard paddlewheels on their shafts at an offset or phase angle corresponding to half the angular distance between adjacent blade trunnions, so as to have the water entry of the port blades taking place midway between those of the starboard blades. This would depend, however, on the torsional-vibration characteristics of the paddlewheel shaft. Even with feathering blades, it is almost never possible to use a wheel diameter (or trunnioncircle diameter) large enough to cause the blade edges to enter and leave the water in a direction is

parallel to the resultant-velocity vectors at those

points.

For instance,

of the entering blade

LA the lower edge almost exactly tangent

in Fig. 7

TS

is

practical solution

make the lower

to

is

vector.

of noise

and vibratory forces

a paddlewheel

in

drive appears to be the periodic impact of the entering blades. This involves a sufficiently

blow,

for

example,

audible before

ft.

Having determined the trunnion-circle diameter, the blade width, and the blade spacing, the number of blades becomes approximately ir times the trunnion-circle diameter divided by the blade

built with only 5 blades.

The

it

to render

heavy

a paddle vessel

appears around a bend in a river.

It is important, therefore, to favor this condition

and to provide as nearly shock-free entrance as possible at this point. It

is

the excessive lifting

water as the blade leaves the surface which raises the high crest abaft most paddlewheels, pictured in Fig. 73.J, and which makes it possible to use a fixed contra-vane abaft the wheel to of the

such good advantage.

There

is

no fixed value, nor are there very

definite limits, for the radius of curvature of the

blade faces. This

may

blade-circle radius,

be as large as 1.5 times the

AC

in Fig. 7 LA, or as small

as 1.0 times that radius.

The

in the layout of Fig. 71. B,

15.5

used taken as

latter ratio is

where

it is

ft.

feathering wheels are fitted to a doubleended ferryboat or other craft which must run If

equally well in either direction the blades are

made

flat

rather than curved.

The

feathering

mechanism can be so designed that they enter and leave the water at about the same angles

when going

astern as

when going ahead.

To provide plenty of leverage for the unbalanced on the entering and leaving blades made from 0.5 to 0.7 times the blade width. This length is 4.0 ft, or 0.615 times the blade width of 6.5 ft, for forces acting

the lengths of the crank arms are

the layout of Fig. 71. B.

>

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 71.7

Whereas most elementary diagrams of paddlewheels show the crank arms at right angles to the base chord of the concave blades [S and P, 1943, Fig. 170, p. 150], these arms are sometimes set as much as 15 deg or more, up or down, from the normal positions. Using an up angle, as in the ABC ship layout and as indicated at D, in between the

Fig. 71. A, results in a larger angle

feathering link and the crank

when the lower

edge of the entering blade touches the water. There is one fixed arm on the orthodox feathering hub or eccentric which serves to turn it as the wheel rotates. The drag links connecting

hub

this

uniformly around

what

arms

or eccentric to the crank

blades are attached to the

known

is

its

of the

hub by pins spaced

periphery.

as the pin circle.

These

The

lie

on

result is

GF

base chord

top of the blade circle. Actually, for the wheel shown, the base chord for the blade section at J the base chord ST, when passes through Ci That through extended, passes through Bi X,Yi passes through still another point, and these points would all change position for new blades in corresponding positions if the wheel ;

.

rotated one blade space. If

the pin-circle radius were zero, such as would

be the case if all the inner ends of the feathering hnks were pivoted at the eccentric or hub center B, the locus of the outer ends of these links, cor-

this simplified special case, the

the proper position for that

when" each successive blade trunnion passes through the lower center (the position C in Fig. 7 LA). In other words, if the wheel of Fig. 7 LA

have the proper

rotated by one blade space, the angular positions

than shown there. This is because the eccentric strap does not move by an angular amount of [360/ (number of bla,des)] deg about its own center when the wheel of the several blades will be different

proper rotates through this distance, due to the

arm on

angularity of the fixed

and the blade crank to which

the eccentric strap it is

pinned. Thus,

M

D

in Fig. 7 LA, and responding to the points circle with its center at B. For

would be a true

different angular positions of the several blades

is

647

of the lowest blade intersects the

the

selected

of finding

A) such

attitude

the

for

conditions

not easy, because of the curvature

is still

of the blades.

problem

(relative to

and leaving blades would

entering

When

many

there are as

B

the pin-circle radius

is finite,

solutions as there are

number

depending upon the position around

of blades,

the circle of the fixed

arm

KD

actuating the

feathering mechanism.

The problem is partly simplified by using the arm to position the entering and leaving

fixed

blades,

7 LB.

as

is

Even

done in the left diagram the problem remains one

so,

of Fig. of trial

and leaves the water at slightly different angles from all the other blades. The smaller the pin circle on the hub or eccentric, as shown in Fig. 7 LB, the

and error because the designer does not know and the tangential-velocity the radius APi

one of the reasons

other parameters involved. Having arrived at a reasonable solution for the entering blade, the position of the leaving blade is then sketched.

as the wheel rotates, each blade enters

smaller

the variation. It

is

is

mounting the feathering mechanism on the outside of a paddlewheel which does not have an

for

[ATMA,

outboard bearing

V

and

tricity

B

VI].

E

The

1906,

other reason

and the

is

vertical offset

Vol.

17,

Pis.

that the eccen-

Z

is

built

itself

In it is

sketched in for a

be far out of proper position, farther than

A new

solution

is

worked

out, perhaps taking

enced table reveals that good designers by no means arrive at the same answers, but it may very well be that they are trying to achieve a

to shifting

many

is

for given values of the

the blade angles with

shift

A

large

strap, rotating on a fixed eccentric around the inboard shaft bearing of the paddlewheel, involves more lubrication problems and does not

lend

may

and

indicated at the extreme left of Fig. 7 LB.

of the center

the at-rest water surface.

to

It

B

account this time of the wave profile in the vicinity, omitted from Fig. 71.B. Bragg's refer-

found desirable to respect

given position of

hub can be shifted readily after and placed in service, in case it is

of the rotating

the ship

,

vector PiR, until the linkage

its

position at a later date.

elementary treatises on paddlewheels

stated that the use of a feathering

mechanism

wheel diameter. In other move as though they were part of a radial wheel having a center at or near the point Ai in Fig. 7 LA, where the

effectively doubles the

words, the blades are supposed to

slightly different result each time.

There

is

undoubtedly a best geometric

relation-

ship between the eccentricity i? of a feathering

paddlewheel, of

Fig.

the

trunnion-circle

diameter

AC

CD. by M.

7 LB, and the blade-crank length

For the French paddlewheels illustrated Hart [ATMA, 1906, PL V], E is 0.5 meter, D is 5.660 meters and the blade-crank length is 0.8 meter. For the Anatolian paddler of reference (8)

CM

HYDRODYNAMICS E is 0.24

of Sec. 59.6,

meter,

L(blade-crank length) tricity ratio is 0.5/0.8

and 6.24/0.36

=

D

=

0.625 in the

more recent

tricity ratios of the

paddlewheel in Fig. 71.B It

by

possible,

is

above the

3.56 meters and

is

first

The

0.667 in the second.

table vary from 0.584 to 0.69.

B

i.s

0.36 meter. Tlie eccen-

is

case

eccen-

vessels of Bragg's

That

ABC

of the

2.625/4.0

=

0.656.

raising the eccentric center

level of the

wheel axis A,

to:

Help bring the leaving blade more nearly tangent to the resultant-velocity vector on the (1)

after side (2) Avoid or reduce the mechanical interference between a blade and the feathering link which operates it, on the forward side of the wheel. In diagram 1 of Fig. 32.B, the nearly horizontal feathering link on the forward side just clears the upper edge of its blade. The same is true in

Fig.

71.

A

but,

the ne.xt blade above,

for

A

the

is

met

of

rec-

similar situation in practice

by making the feathering tangular section and bending them either

to

clear

the

1906, Vol. 17, Pis.

With the usual

V

so as to clear

hnks [Hart, M., and VI].

ATM A,

feathering mechanism, having

an eccentric center forward

water

of the shaft center,

They impart

[Teubert,

useless

upward

motion to the

of

"Binnenschiffahrt,"

0.,

1912,

S and P, 1943, Figs. 168, 169, p. 149] and they leave a great deal of energy in a series of short, steep waves trailing astern. Wheels with fiat, smooth blades geared to a shaft so as always to stand with their heights truly vertical, and with annular support rings always above the waterline, as devised by Georg Fricke of Lembruch, Germany, have proved excellent for propulsion in calm waters, grown thick with grasses and weeds. The blades press the weeds down vertically and do not become Figs. 305, 306, p. 441;

foul [Deetjen, R., Schiff

German

pp. 80-81; this

May

SBSR, 8

A

partial

on

und Hafen, Mar

1952,

article is abstracted in

1952, p. 579].

list

model and

of

references in the technical

paddlewheels,

full-scale devices,

both

to

relating is

to be found in

Sec. 59.6. It

links

the blades [Teubert, 0., "Binnenschiffahrt," 1912, p. 444], or by notching the inner edges of the blades

ticularly efficient.

See. 71.S

and downward components

literature

feathering link actually fouls the inner edge of

the blade.

IN SHIP DESIGN

should be clear from the foregoing that, its place in the scheme of things pro-

whatever

pulsive, the analysis

represents

and design

marvelous

a

of a

exercise

paddlewheel practical

in

hydrodynamics and practical machine design. Not only does the paddlewheel need an extension of the motion analysis published by M. Hart [ATMA, 1906, Vol. 17, Pis. II and III] but the experience gained in such an analysis would be

when analyzing

the feathering links are in compression, especially

invaluable

when the blades are The links can not,

entering or leaving the water.

propulsion devices and in preparing systematic

therefore, be too slender for

rules for their design.

their length without risk of buckling.

J.

Scott

Design Notes

71.9

Russell proposed a variation of the usual geometric arrangement whereby the eccentric center

Pump- Jet

(B in Fig. 71.A) Hes abaft the wheel axis. The blade cranks are thus on the after or +Ap sides of the blades, and the feathering Unks are, when loaded heavily, always in tension. 71.8 Variations from Normal Paddlewheel Design. Where damaging debris is frequently encountered and repairs to blades must be made on the spot or locally, often by the ship's force,

described in Sec.

radial blades are used, bolted to the wheel arms.

The

blades can be shifted in or out, radially, to

suit a more-or-less

trim.

permanent change

They can be

radially, to

in draft or

varied in width, or shifted

permit the wheel torque and speed

to be varied so as to obtain the

maximum

engine

power with the greatest ship speed or towline tension. The radial blades are simple and cheap and they produce thrust but they are not par-

what

Propulsion.

the action of other

for

Hydraulic-Jet and of achieving

Methods

often termed hydraulic propulsion are

is

Sec. 32.5.

The

15.8

and elaborated upon

efficiencies of the principal

are discussed in Sec. 34.13. In Sec. 59.8 there

given a

list

of the principal references

on

and

Some

subject, both historical

them

is

this

of

are valuable in design as indicating the

pitfalls to

It

technical.

in

systems

is

be avoided.

pointed out in Sec. 15.8, and

it is

again

emphasized here that the air, gas, or water jet employed for propulsion may, hke that from the airscrew, be discharged into the atmosphere above the water. An example of this is the Russian shallow-draft river launch propelled by twin water jets and pictured in The Illustrated London

News

[11

Dec

1954, p. 1070].

Hydraulic-jet propulsion lends special duty,

where the outside

itself

to craft for

of the hull

must

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 71.9

be kept clear of protuberances or where some similar characteristic is more important than the

downright

efficiency

lifeboat installations (those operating

saving stations ashore)

protrude beyond the siderable

accepted.

If,

as

may

most

from hfe-

the jet ducts can not

fair hull hne,

in

sacrifice

In

propulsion.

of

propulsive

both the

inlet

649

and the outlet water, so that the

minimum

hydraulic losses will be a

Estimating or calculating the rating of the

(4)

pump drive

and the power necessary to

or impeller it.

and a conefficiency

be expected for these

is

craft,

good backing qualities are required, the pump must be of the axial-flow or propeller type unless flap valves in the ducts are employed. ManeuverabiUty and steering as well as propulsion are achieved with a pivoted jet, arranged to discharge water in any relative direction desired. As with a steering propeller, however, it is mandatory to incorporate a low-friction thrust bearing in the swiveUng head, because all the propulsive thrust is exerted through this swiveling connection between the jet elbow and the boat, indicated in Fig. 71.C. If the friction

is

large

There have been many recent successful developments of guide-vane assembUes by which the flow of water can be changed in direction abruptly yet

efficiently.

Relatively sharp turns can

worked into the ducts

now be

of the hydraulic propulsion

setup without excessive hydraulic losses. This gives the designer considerable latitude in leading a stream of water around inside a vessel. Prac-

modern

tically all

circulating-water channels

of

model propellers under cavitating conditions

embody

corner guide vanes of this type. Up-todate design rules and criteria have been worked out by the St. Anthony Falls Hydraulic Labora-

tory in Minneapolis, Minnesota. In fact, possible sSwivelina

Mechanism

Stern

Bottom

of

Water.from Pump

Boat

by employing a

the rated

output.

Swivelinq-Nozz-le Assembly in

Solid Black

[FMTM,

Fig. 71. C

Schematic Arrangement of Reversible Jet-Propulsion Device for a Small Boat

in this large-diameter bearing, often incorporating

a watertight stuffing box as well, the craft can not even be steered.

When working up the design of one of these systems the procedure divides itself naturally into

The

and the amount to be imparted to this mass

of increased velocity of

water to produce

the thrust required

pump

the

The

method

whereby this and led to the to impart the augment

to be taken in is

and velocity to

it

fashioning of the ducts and passages, for

built craft

hull of a craft designed for reasonably

propulsion

special forming in

discharges,

bow

with

way

fixed

ducts

requires

of the jet intakes

and

whether these openings are at the

or stern or along the hull.

The

installation of importance should

or impeller which

of pressure (3)

out

1950,

through the water. This is also used to help force the required quantity of water through the duct toward the pump, against the friction resistance

efficient

of the jet(s),

EH,

making use of the ram or dynamic pressure up at the duct inlet by the motion of the

Determination of the quantity-rate or amount of water per unit time to be handled, the area(s) (1)

is

axial-flow

1947].

of the walls.

Working

or

fixed blades should

Supercharging of the pump, to increase the ambient pressure and to delay or prevent cavitation of the blades, may be accomplished by

several steps:

(2)

Propeller-type

pumps with

least as well [Rouse, H.,

Jet

quantity-rate

is

do at Chap. XIII]. Design and performance data on hydraulic pumps of various kinds are given by J. W. Daily in the reference cited and by G. F. WisUcenus

Propelling

Shown

it

large rotary valve with

vanes to "switch" the water from one duct to another or to reverse its direction. Centrifugal pumps of good design show efficiencies of well over 0.80 and reaching 0.90 at impeller

Is

and

variable-pressure water tunnels for the testing

design of any

be checked at

by flow tests on a small model and preferably by performance tests and pressure measurements on a larger model. The curved-vane diffusers and the various other means adopted by hydraulic engineers to least

HYDRODYNAMICS

650

raise the operating efficiencies of propeller-type

pumps can

be applied to the propulsion of

all

IN SHIP DESIGN

Sec. 71.10

developed by hydraulic engineers for the design of ducts and pump impellers rather than by

itself

those worked up by marine engineers for pro-

to the building in of the necessary ducts or jet

working in the open. Unfordata on hydraulic-jet propulsion apparatus are relatively meager, particularly because there has been little in the way of logical, progressive, modern development except on classified projects for combatant vessels and new weapons. It should be kept in mind always, however, that efficient hydraulic- jet propulsion requires the largest practicable diameter of jet and the smallest relative velocity of jet water, reckoned with respect to the surround-

a ship,

the hull has a shape which lends

if

hardly to be expected that a underwater hull which, over many

boundaries. It

form

of

is

decades, has evolved into one suited to the screw propeller

be found readily adaptable for

will

the efficient use of fixed propeller shrouding, propeller-type pump-jets, or hydraulic jets. Experi-

ence with the Kort nozzle, described in Sec. 36.19, indicates that

it is

not easily fitted to a vessel of

normal form.

The same

basic

hydrodynamic laws and

rela-

tionships are used for the design of axial-flow

impeller

pumps with The

quite different.

the

design

ing undisturbed water. It is

proposed in Sec. 34.13, and repeated here,

is

that the whole jet-propulsion system be designed

available engineering data

on an energy or work basis, rather than on a pressure and force basis, as is customary for

are in such form as to apply only to the design of

tunately,

casings as for open-stream

ship propellers but the attack on the problem

devices

pulsion

each class of devices by

itself.

For this disand propellers,

screw propellers.

inside the solid casing boundaries of cross-section

71.10 The Design of Surface Propellers. There are no systematic data, so far as known, for the design of surface screw propellers. These are deliberately intended to run with only

A must remain the same from inlet to outlet,

partial immersion, either because of draft limita-

known

cussion they are

as impellers

respectively.

The quantity area

rate of flow

Q =

¥t

= AUt,

,

hence

it is

pump

used as a basic quantity in the impeller-

design. If Af7

is

the increase in velocity

imparted by the impeller from the casing to the casing outlet, the impeller thrust

from Newton's second law

inlet

T

is,

tions or because of the

obtained from them,

[ p{AU) Jq

few references pertaining to design phase are:

of

is

the same as Eq.

Eq. (34.xxix)

dQ = pQ(AU)

(71 .v)

(71.ii)

of Sec. 71.4

and (c)

of Sec. 34.13.

Assuming that the inlet velocity is the difference between the ship speed V and the wake speed V w at the inlet 'position, reckoned here the same as the speed of advance V a at a propeller position,

then Finiet

this

33.11.

particular

of motion,

(b)

This

force that is to be

A

(a)

T =

lift

described in Sec.

= Fx = V— Vw The

in velocity AC/ through the casing

increase

(d)

(e)

and impeller

taken as a fraction of the inlet velocity Va Also Q = T/{pAU). The pressure or pumping

Smith-Keary, E. M., "The Effect of Immersion on Propellers," NECI, 1931-1932, Vol. XLVIII, pp. 26-44 and D1-D17 Kempf, G., "Immersion of Propellers," NECI, 19331934, Vol. L, pp. 225-248 and D123-D138 Kempf, G., "The Influence of Viscosity on Thrust and Torque of a Propeller Working Near the Surface," INA, 1934, pp. 321-326 and PL XXXIV De Santis, R., "The Effect of Inclination, Immersion, and Scale on Propellers in Open Water," INA, 1934, pp. 380-385 and Pis. XXXVI-XXXVIII Baker, G. S., "The Qualities of a Propeller Alone and Behind a Ship," NECI, 1937-1938, Vol. LIV, pp. 239-250 and D135-D146.

is

head hp then required

of the impeller is equal to

General comments and design data on "ParImmersed Propellers" are given by W. P. A.

tially

the increase in kinetic energy of the water passing

van Lammeren,

through the pump, or

[RPSS, 1948, pp. 262-263].

hp

=

KVa

+ Avy -

Some VI]

L.

Troost,

and

J.

G. Koning

practical pointers for the design of surface

propellers on high-speed racing motorboats are

published by E. C. B. Corlett in "Trends in Very High Speed Craft" [The Motor Boat and Yachting, Sep 1954, pp. 386-388].

From

here

The

on the design problem becomes

lengthy and complicated, to be solved by methods

is

thrust-load factor for a surface propeller

of course

based upon the fractional disc area

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 71.12

which

is

propeller

expected to be immersed when the

by diagram

operating, indicated

is

7

of Fig. 15.G.

The unbalanced blade-disc forces from the immersed and working blades, depicted in diagram 1 of Fig. 33. K, are usually balanced by introducing equal and opposite forces from a second propeller rotating in the opposite direction. If these forces are desired or needed to give the craft angular acceleration

when

and

turning,

if

always in the same direction, as in a motorboat which always makes left-hand turns during a race, they are balanced by a lateral force produced by a constant rudder angle when straight running is desired. Since there are certain to be air holes instead of cavitation pockets on the forward or reducedthe turning

is

pressure sides of the partly immersed blades, the available thrust peller

is

low, as

the

is

maximum

Conservative design

efficiency.

calls

profor

the use of an efficiency not greater than half or two-thirds that of the same propeller working fully

to be expected in

and running condition service, the hub of a surface draft

propeller should be just clear of or just touching its

angle.

As the mechanical propulsion is an auxiliary the helm handicap can be

drive at the best,

accepted for larger benefits which

when

A

rather

comprehensive

article

is

under

side.

This

may

eliminate

asymmetric

This

114].

drives

and

article reveals that

auxiliary

latter discussed in Sec. 71.13,

same

serious

vicinity as

much

is

hub is

surface.

almost a necessity over the partly for

of a surface propeller,

and partly to keep down the showers of spray and geysers of water which would otherwise be thrown up at the stern. 71.11 Asymmetric Propulsion. It is often safety

convenient to offset the propulsion device from the centerplane of a vessel, especially in auxiliary yachts where an aperture for a centerline pro-

adds to the sailing resistance and detracts from the efficiency of the steering rudder [Baader, J., "Cruceros y Lanchas Veloces (Cruisers and Fast Launches)," Buenos Aires, 1951, Fig. 203, p. 255 and Fig. 205, p. 256. The situation is similar peller

to that of a crippled multiple-screw ship driven

by one wing

propeller, with all other propellers

missing.

Moment

calculations,

experience with if

drives,

damaged

the rudder area

is

supported vessels,

by

sufficiently large

offset of the thrust line

from the center

does not exceed 15 per cent of the

beam, the asymmetric moment

service

indicate that

and

if

the

of gravity

maximum

of thrust is only

the

both require the

consideration of flow in their given to the propeller position on a

larger vessel.

71.12

and

Feathering

Folding

Propellers.

The proper design of all vessels with two or more means of propulsion, such as the sailing yacht with auxiliary power, requires that the propulsion devices of one system be not a hindrance when

The

problem of the effect of screw-propeller resistance on the sailing speed of a yacht is discussed by K. S. M. Davidson and D. S. Connelly ["If We Hadn't Been Dragging That Propeller," Yachting, device to free-wheel or to coast,

cover or guard

"A

pubhshed by M. E. Williams [Yachting, Feb

1955, pp. 54-55,

May

upper blades

entitled

trations of asymmetric drives for sailing yachts,

shaft. It will certainly free the propeller of friction

A

be derived

Propeller for the Auxiliary," with several illus-

the necessity of a watertight stuffing box for the resistance on the

may

sailing.

those of the other system are being used.

submerged.

At the average

the water on

651

secondary importance in steering and possibly also in turning. For a saiHng yacht, this may require carrying some small compensating rudder of

1940,

p.

68].

Permitting one propulsion if it will, is one

answer but not always the best one. In the early days of steam as an auxiliary power in saiUng ships this problem was usually solved by fitting a 2-bladed propeller and placing its blade axes vertical when it was stopped. The sternposts on those ships were so wide that the

two blades, if not the hub, could lie neatly "shadow" of the post, within the eddies

in the of the

separation zone directly abaft the post. Other solutions of this problem are to feather the pro-

done on modern aircraft, to them, or to house the propeller in some suitable manner. J. Scott Russell mentioned feathering propeller blades nearly a century ago peller blades, as is

fold

[MSNA,

A

1865, p. 474].

is defined as one whose thrust-producing blades can be turned on their own axes so that the blade sections are generally

feathering propeller

parallel to the direction of motion.

the-bottom

rotating-blade

feathered, for example,

propeller

An

under-

would

be

by rotating each blade

on its spindle axis so that all the leading edges would face directly forward. A folding propeller is one in which the thrust-

HYDRODYNAMICS

652

IN SHIP DESIGN

Sec. 71.13

the direction of motion. In a 2-bladed folding

put a permanent propeller, to serve as auxiliary propulsion on a sailing craft? There is no good place. In almost any position the propeller is a

screw propeller each blade folds aft so that its blade axis is sensibly parallel to the shaft axis,

To

with a frontal area considerably smaller than

able place. All locations have disadvantages, from

that of a feathered propeller. Both feathering and

the point of view of both saiUng and propulsive

producing blades are hinged so that their axes

swung

are

into positions generally parallel

by

to

Baader on page 210 of his book "Cruceros y Lanchas Veloces (Cruisers and Fast Launches)" [Buenos folding propellers are illustrated

J.

nuisance for sailing and a misfit for propulsion. is

not even a least objection-

Even the temporary outboard prohung over the stern or the side, has its

efficiency. peller,

drawbacks.

The usual position and arrangement, embodying

Aires, 1951].

A

be honest, there

2-bIaded screw propeller with folding blades,

a centerline propeller working in an aperture cut

for sailing vessels with auxiliary power, arranged

partly from the sternpost or the after end of the

and form a continuation of the propeller hub, was proposed and illustrated by Henry Claughton in the early 1870's [INA, 1873, pp. 52-55 and PI. IV]. The folding was accomplished by a rod which slid lenghwise within the hollow propeller shaft. The inventor claimed,

and partly from the rudder, is depicted in diagram 2 of Fig. 71.D. To be sure, the propeller outflow jet impinges on the rudder but a sailing craft has a rudder adequate for controllability at low speeds, regardless of the method of propulsion. The propeller aperture, small compared to

and

the boat profile,

to swing aft

rightly so,

that the folding propeller was

keel

almost necessarily has thick

wood, the edges

superior to the feathering one because the blades

boundaries. If the craft

always have some objectionable twist, no matter what the angle at which they are feathered. At the time of writing (1955) folding screw propellers are available in diameters

the opening are liable to be very thick compared

of

the

latter

of the order of

or 2

1

have a drag only

when

it is

and Naval

An

0.1

ft.

They

is

to the propeller diameter. FISH-EYE

of

As much

fairing

of

as

VIEW

are reported to

that of a solid propeller

not rotating [Ship and Boat Builder Architect, London,

May

1953, p. 378].

adaptation of the "shadowing" 2-bladed

propeller,

lying

sternpost,

is

in

the eddies

what may be

behind a wide the housing

called

Schematic Lowut

and held snugly against the hull, was proposed a half-century ago for large vessels [Hamilton, J., INA, 1903, pp. 233-235 and Pis. XXX, XXXI; De Eusett, E. W., INA, 1903, p. 237]. In the 2-bladed form, and with the feather-

As-ymmetnc Screw Propeller with

of

Propeller

propeller. This device, pulled in axially with its

ond

All

Appendoqes on One Side

shaft

ing feature developed in recent years,

possible

aft.

They

can then, when the propeller and shaft are pulled inward, be drawn into a relatively narrow groove left for this purpose in the end of a skeg supporting the shaft. Provided the mechanical problems can be worked out, this affords one solution for a 2-bladed bow propeller on an icebreaker, mentioned later in Sec. 76.26. Here the propeller is either very useful if it can be run or it is a nuisance if left extended, depending 71.13

There

upon the

ice conditions.

Auxiliary Propulsion for Sailing Yachts.

is only one answer to the question often asked by yachtsmen: Where is a good place to

Woterline

^^--Jesioned

Shoft Line

Propeller

Rudder Stock

it is

to swing the blades nearly fore and

entirely

Rudder Stock

Leodinij Edi^e of

Moment

Rudder

nto Keel, so that

is

Gap

Recessed is

Smoll

Tronsmilted

9

Through Here to

Deep

Lower Portion

Keel

'-

Rudder Stock ..^^Jesiqned

Propeller is

[/*

S\\c^ht\^/\

Offset so

\s

Rudder\\

\

ond Tube are

D

Hinge Gop

i

s Smoll for

Its

Entire Lenoth

^^

^^~^---__3^

Clear of Rudder Stock

Fig. 71.

,

\\

\^

that Shaft

Woterline

^^

Auxiliart Propulsion Arrangements FOB Yachts

3

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 71.14

practicable on the forward and after edges

is

behind the forward side of the aperture, to keep the wake velocities from being irregular, and to minimize indicated,

prevent

to

separation

the augmentation of resistance on the after side

A 2-bladed propeller lies generally

of the aperture.

when mechanical propulsion

within the aperture is

not required, 'provided there

is

a blade-position

marking inside the vessel, and there is some way to place and hold the shaft in the proper angular position. The aperture detracts from the steering and maneuvering characteristics of the vessel but as the rudder is generally large enough for control at speeds much less than that at which the propeller drives the craft, it remains adequate for the purpose.

249-256

(in Spanish)].

In this chapter he gives

three design graphs for the auxiliary powering of these yachts.

71.14 Vertical Drive for Screw Propellers; Under-the-Bottom Propellers. The combination of a screw propeller mounted on a short horizontal shaft and driven by bevel gears from a vertical shaft is knowri everywhere in the form of the familiar outboard-motor propulsion unit. However, design features which can be accepted for units in which the power in horses rarely exceeds one or two hundred are not always workable in larger units, such as are hkely to be utilized in the future.

On

all

the

modern portable

there

is

drive shaft from working

May

be' considerably larger

offset slightly

The

propeller shaft

from the centerline to

must be clear the

installa-

a horizontal barrier or "anticavitation" plate to prevent air in the separation tions

A propeller may be mounted above the top of the rudder with a short exposed drive shaft and a short single-arm strut [Rudder, Mar 1954, p. 37; 1954, p. 78].

653

zone abaft the casing which carries the vertical down the after edge of

the casing into the propeller disc. This plate must aft

and must extend farther

when a more powerful

propeller

used.

is

rudder stock.

Indeed, the vertical casing sections will them-

A somewhat more ship-shape installation, based on both the mechanical and the hydrodynamic features involved, is to drop the upper end of the rudder and leave, in its stead, a fixed portion of the after end of the fin keel under the hull. The propeller shaft passes through this fixed portion and the propeller is mounted abaft it. The arrangement permits a reasonably sharp fin-keel ending ahead of the propeller, with fillets between keel and hull which taper to zero at the extreme after end, about as indicated at 3 in Fig. 71. [Yachting, May 1951, p. 62; Rudder, Apr 1954, p. 37]. Again, however, the propeller and its shaft must be offset slightly from the centerline, to permit the shaft tube and the rudder-stock casing to clear each other. The propeller bossing in the fixed fin above the top of the rudder then has an offset termination similar to those of certain bossings and multiple skegs in large ships but with the disadvantage that in the smaller

selves require lengthening

craft the flow

may

cross the swelling for the

A is

yacht in which the mechanical propulsion same order of importance as the sail

of the

that

known

as the

motor

sailer.

A

most

useful

discussion of the propulsion and design problems

J.

and

water-excluding

fining.

and

devices and systems are called for

Efficient

lubrication

if

the vertical

drives are to transmit powers in thousands of

horses instead of hundreds, and

if

they are to

run continually for days on end. Besides being retractable by hinging or swingcustomary outboard-motor assembly,

ing, as in the

vertical- drive propeller

systems lend themselves

to packaging in self-contained units. These

may

be installed in vertical recesses or wells and removed when desired, similar to the Sea Otter installations of

World War

II.

The

the lower ends of the assemblies

below the baseplane, or below a

propellers at

may

project

flat,

cut-up

portion of the vessel at the stern, similar to that for

the usual type of rotating-blade propeller

Large-diameter 2-bladed propellers be passed through small-diameter wells or small openings by keeping the blades vertical. In

installation.

may

the early days of steam

it

was

possible to

lift

well in the hull at the stern.

A modern installation,

proposed for an oceanographic research is

shown

A

vessel,

in Fig. 33. J.

partly sectioned isometric view of a

modern

given by D. Phillips-Birt [Rudder, 1955, pp. 12-15, 46-55].

outboard-propulsion unit in package form, de-

Baader devotes a whole chapter to the

ical

of this class

May

reliable

the 2-bladed propeller up on deck through a

shaft at a slightly greater angle.

is

and

is

upward by mechanshomi by A. C. Hardy ["Modern

signed to swing the propeller

means,

is

auxiliary propulsion of the sailing yacht ["Cruceros

Marine Engineering," London, 1955, Vol.

y Lanchas Veloces", Buenos

p. 154].

Aires,

1951,

pp.

II,

HYDRODYNAMICS

654

Flow to under-the-bottom propellers, working below vertical wells which house retractable or removable units, is practically axial but it may suffer from non-uniformity because of the presence of the boundary layer. If the propellers are actually below the baseplane, and in a region where the ship bottom is sensibly flat, parallel to the direction of motion, there should be little augment of resistance due to the pressure fields created by the propellers. Although thrustdeduction forces were observed on the Sea Otter model, this is believed due to the fact that the closures at the bottoms of the vertical wells in the models were not watertight. The — Ap and -f-Ap fields set up by each propeller extended up into the lower portion of each well, where small forces acting aft,

and

opposite to the direction of

were developed on both the forward

motion,

after walls of the well.

Design of Devices to Produce TransFor docking, mooring, and shifting berth, in areas where the port facilities are not adequate, it frequently becomes necessary for a ship to sidle or to change its heading. This usually happens when it is not possible to shift an appreciable distance either ahead or astern, certainly not far enough to create the offset or make the change in heading by the ordinary operations of maneuvering. This offset or change in heading requires the application of a more-or-less static force at one or both ends of the vessel, in a direction approximately perpendicular to its centerplane and in line with 71.15

verse and Vertical Thrust.

the shift in position desired.

IN SHIP DESIGN

Sec. 71.15

bevel-gear mechanism

if a different type of drive employed. The problem here is keeping the gears small enough so that the area occupied by

is

gear

the

casing

in

the

except

water

the

is

straight-

type

of this general

Canadian ferry Princess that

A

not excessive.

is

through installation

moved

is

found

Vancouver,

of

transversely

through a duct of rectangular section by a Voith-Schneider propeller [111. London News, 19

Mar

1955, p. 516;

If sufficient

MENA, Mar

beam

is

1955, p. 112].

available at the position

selected for the transverse propeller or thrust-

producing device vertical-shaft

it

may

propeller

be advisable to use a a Z-shaped passage

in

having offset openings to port and to starboard. Fig. 71.F is a schematic arrangement for such an installation. It removes from the water passage the bevel-gear box which would be required for a straight-through transverse duct, with a drive shaft entering at right angles to

axis.

its

The

vanes are placed in the two elliptical intersections of the circular ducts, where the increased area compensates for the flow restrictions imposed by the multiple vanes.

two

sets of corner

The figure,

propeller

may

shaft,

shown

vertical

in

the

lead in any desired direction to the

drive motor, permitting the latter to be placed in the

most convenient and protected position

in the ship.

The Z-shaped duct remains

transverse

plane through the

this plane

may

drive

in the

shaft

but

be either vertical or horizontal

may lie at any convenient angle. To prevent separation of the inflowing water at points such as E, and Ea in Fig. 71. F the or

Normally these forces are applied by tugs pushing and pulling or by ropes between fixed objects and the ship, connected to capstans or winches.

When

Alternative

Bevel-Gear Drive

neither the tugs nor the fixed

objects are available,

and when the

and

offsets

changes of heading are required to be performed frequently as a routine part of a vessel's operation, this may be accomplished by fitting separate auxiliary

propellers

apply

which

transverse direction [SBSR,

20

thrust

Nov

in

1952,

a

pp.

659-660].

The

simplest installation of this kind

is

the

straight-through type illustrated schematically in Fig. 7 I.E.

A

substantial shroud ring encircles the

propeller to carry the gear teeth. in diameter

The

increase

—and area—at the propeller position

enables a larger and more efficient wheel to be used, and partly compensates for the area

occupied by the shaft and

its

bearings, or

by a

Not Shown Here Are

Method of Attaohin* Means of Preventino Thrust Beorinas, Stuffing Boxes, and the

Fig. 71. E

like

Schematic Arrangement of .Auxiliary Propeller for Exerting Transverse Thrust

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Sec. 11.16

may

655

be short. They are well removed from the so the

center of gravity of the ship,

moments

Any

turning

are large.

large transverse opening,

such as for a

transverse propeller, cut through the thin skeg of its

a ship just ahead of an unbalanced rudder at after end, may or may not be detrimental to

turning. built

The opening permits leakage

up by the rudder on the

of

+Ap

inside of a turn.

If the vessel is turning at a large drift angle,

there

Propeller

may

be cross flow through the duct from

I

Shaft

I

the outside to the inside of the turn. Further-

is

Shown

more,

Vertical

It

Con Be

/Placed

if

the propeller

is

not locked by nonit may wind-

overhauling drive gears or a brake,

Here But

under these conditions. Design Features of Tandem and ContraRotating Propellers. Normally, it is not good design to place propulsion devices of any kind mill

71.16

in

/Any Desired Position

Generally /Porollel to the

enterplane

tandem, even when they are as far away as bow and stern propellers of a double-ended ferryboat. If, under unusual circumstances, it becomes necessary or desirable to absorb a

in

the

Fig. 71. F Schematic Arrangement of VerticalDrive Screw Propeller for Exerting Transverse Thrust

relatively large

amount

of

power by a propulsion-

entrances are rounded, say to a radius of 0.1 or

device combination occupying a limited disc or thrust-producing area, it is possible to achieve

more of the duct diameter. There should be enough hydrostatic head above the uppermost

devices separately. This enables each to run at a

duct to prevent drawing air from the surface. The efficiency of a propeller-type device to produce transverse thrust is measured, not by the usual ratio of output to input but by whether

upon the

or not the device works. This depends

thrust

lateral

developed.

The

thrust

in

turn

depends first upon the diameter of the propeller and the rate at which momentum is imparted to the water in a transverse direction. It depends also upon the length and shape of the transverse duct, because of the friction and pumpingpressure losses in the water being forced through it.

two openings of the transverse duct lie where there is much slope to the waterthere is liable to be some slight but definite

If the

in regions

reasonable efficiency by driving the propulsion

proper advance coefficient

J = V a.I(iiiU),

de-

pending upon the speed of advance at its own position. Still better is a type of drive which adjusts its rate of rotation so propulsion device absorbs a pre-deter-

automatically that

its

mined power. For tandem screw propellers, described Sec. 32.20, a device which has possibilities certain applications

interposed

in for

a sort of contra-propeller

is

between the leading and following

units of a pair of

tandem

WRH,

propellers [Schmier-

Sep 1939, pp. 278-279; HSPA, Vol. II, 1940, pp. 79-102, with English summary on pp. 217-218]. This star-shaped set of guide vanes, with or without a fixed shrouding schalski,

H.,

I

not possible to close the

around the outside, is intended to recover the rotational energy in the outflow jet of the leading propeller and to impart enough pre-rotation to

when they are not in use so that when the vessel yaws or turns there may be some

the inflow jet of the following propeller so that the rotational energy in the final outflow jet is

lines,

effect of these discontinuities

underway.

It is generally

when

the vessel

is

openings

transverse

This

flow

may

unless

it is

The

of

cause

water

through

the

duct.

windmilling of the propeller

locked.

best

positions

for

propellers

producing

transverse thrust are in the forefoot and in the aftfoot.

These are usually

thin,

so

the ducts

very

nearly

zero.

The mechanical problems

involved in placing a fixed appendage of this kind between two tandem screw propellers on the shaft have not, so far as known, been tackled except on model scale. It is customary, although not necessary, to

same

HYDRODYNAMICS

fifiG

the

place

discs

contra-rotating

of

propellers

them along the

close to each other, spacing

axis at only a small fraction

shaft

the propeller

of

diameter, just sufficient for the hubs and the

The

blades to clear each other. peller

is

made

following pro-

slightly smaller in diameter

than

the leading propeller because of the contraction

from the latter. both propellers of a pair rotate oppositely at the same rate, the pitch of the after wheel is made slightly greater to produce generally the same thrust, torque, and power as the forward one. There is no reason, however, why both in the outflow jet If

propellers need rotate at the

same

rate

if

IN SHIP DESIGN

tangential components of the induced velocities

are large. Normally, large

References to test results on propellers of this

type are given in Sec. 59.7. Additional references in the technical literature are:

im Stromungsa Flo wing- Water Channel)," Schiffbau, Sohiffahrt, und Hafenbau, 1936, Vol. 37, pp. 168-173, 206 Mueller, H., "Einfluss des Hohlsogs auf das Arbeiten des Voith-Schneider-Propellers (Influence of Cavitation on the Working of the Voith-Schneider Propeller)," Zeit. des Ver. Deutsch. Ing., 1938, Vol. 82, pp. 566-568 Fuller, W. E., "A Radical Departure in the Conventional Tugboat Design, and a New Use for Cycloidal Propulsion," ASNE, Aug 1953, pp. 639-645 "German Craft with Voith-Schneider Propellers," SBSR, 23 Sep 1954, pp. 409-413 Mueller, H., "Schiffsmodellversuche gerinne

(2)

(3)

design of contra-rotating propellers poses

a problem discussed in Sec. 67.22 for the contra(4)

is

to find the exact direction

of the flow in the outflow jet

from the leading

Rotating-

functioning of the rotat-

is described and illustrated in and Figs. 15.1, 15.J, and 15.K. Its use for steering and maneuvering as well as propulsion is discussed in Sec. 37.22 and illustrated by the diagrams of Figs. 33.H, 37.0, and 37.P.

it

guide skeg ending. It

to

accompany

ing-blade propeller

mounted on

The

ratios

Sec. 15.13

other

approaches the leading propeller, both propellers of the group can be raked aft to advantage, provided centrifugal-force and other factors are properly taken care of.

The

Blade Propellers.

(1)

shaft axis as

P/D

small thrust-load factors Ctl 71.17 Design Notes Relative

rates or ratios are preferable.

For contra-rotating propellers such as those the afterbody of a torpedo, where the flow is definitely converging toward the

Ser. 71.17

(Ship

Model Tests

in

"Voith-Schneider Propulsion;" booklet of 23 pages prepared and published by the J. M. Voith Com-

(5)

meets the leading edges of the blades of the following propeller. This is a matter partly of determining the direction at which the flow leaves the trailing edges of the forward wheel and partly of the amount of induced velocity imparted to it by that wheel, at a distance astern represented by the forward sweep

can be employed to produce thrust in any direction within any selected plane of rotation, whether horizontal, vertical, or

line of the after wheel.

inclined.

propeller as

it

There are two published design procedures available: Lerbs, H. W., "Contra-Rotating Optimum Propellers Operating in a Radially Non-Uniform Wake," Rep. 941, May 1955. On page 22 there is a list of 6 references. In general, this method takes account of the effects arising from the difference of the wakes at the propeller discs and from the contraction of the race between them. Tlie design procedure is outlined by steps but no example is

(1)

pany in

(2)

and Sentid, A., "Contra-Rotating INA, Apr 1956; SBSR, 3 May 1956,

J. D.,

Propellers,"

pp. 302-303; SBMEB, Jul 1956, pp. 462-463; Int. Shipbldg. Prog., Sep 1956, Vol. 3, No. 25, pp. 459-473. Eight references are given and a numerical example is included.

H. pairs

P/D

W. Lerbs

observes

of propellers are ratios,

that

efficient

say more than

1.2;

contra-rotating

only for large

that

is,

when

the

(in English).

Copy

Ubrary.

It is desired again to

emphasize that this type

Diagram 2

of

Fig.

33.

H

illustrates

schematically a rotating-blade propeller fitted to

a submarine with its axis horizontal, or nearly so, and its plane of rotation generally vertical and parallel to the plane of

A

suitable

rotating-blade

T/{0.5pAoVa), to

Ac which

the

is

maximum

known

Van Manen,

Heidenheim, Germany

of propulsion device

TMB

given.

of

TMB

symmetry.

thrust-load propeller, is

factor

expressed

Ctl for by Ctl

a

=

based upon an area equivalent

rectangular in shape. It represents transverse section through

as the basket or barrel formed

what is by the

blades, having a height equal to the blade length

and a width equal to the diameter

of the pitch

This corresponds to the hatched area of diagram 6 of Fig. 15. G. In practice, the proporcircle.

tions of this rectangle remain sensibly constant, having a ratio of pitch-circle diameter to blade length of about 1.5 to 1.75. W. Henschke gives a sketch and a table of principal dimensions of Voith-Schneider propellers, taken from "Schiff-

DESIGN OF MISCELLANEOUS PROPULSION DEVICES

Ser. 71.17

baukalender," 1935 ["Schifl'bautechnisches Iland-

buch (Ship Design and Shipbuilding Handbook)," Berlin, 1952, p. 192]. For this series of sizes the (basket

of

ratio

or

barrel

diameter) /(blade

nominal

thrust-producing

but the —Ap's are usually of smaller intensity. It is probable that, with a stern cut away sufficiently to provide easy flow to an under-thebottom propeller, in a direction generally normal to the blade axes, the thrust-deduction fraction

length) has a constant value of 1.67.

The

057

area

a

of

rotating-blade propeller may, and generally does

occupy more area normal to the direction of motion than a screw propeller; sometimes more than twice as much. The thrust-load factor is

be lower than for a normal-form stern with a screw propeller. will

An

efficient design

blade propeller

and

calls for

installation of a rotating-

blades that are sufficiently

graphs of Fig. 34.N show that, below a Ctl value of about 2.2, the efficiency of a VoithSchneider propeller may be expected to exceed

narrow to eliminate interference between them sufficiently long to provide adequate area for the thrust to be delivered. There must be sufficient submersion of the whole assembly to avoid harmful cavitation in way of the upper ends of the blades. While the presence of the large flat under surface of the hull above the

the 0.8-ideal-efEciency value of a screw propeller.

propeller

therefore, less

like

that of the paddlewheel,

than for a screw propeller to do essentially

the same work.

Diagram 2

of Fig. 34.

The thrust-producing area its

much

M

and the

adjoins the hull at

upper or inner end, without the tip clearance with a screw propeller. The wake

associated fraction

at

the propeller position

is

therefore

—

almost certain to be higher and more variable than for a screw propeller in the same position. There are no published formulas or as well

—

and

regions,

minimizes it

is

leakage

air

difficult

The arrangement shown electric

reference data.

The area

orthodox

or

is

of the propeller inflow

jet is larger, because of the larger equivalent

Fig. 71. G

not

routine

A„

,

Fig.

71.G

is

in

motorship Helgoland of 1939, at that

pp. 644-645]. This vessel

determined from

in

time "the largest seagoing vessel yet fitted with Voith-Schneider propulsion" [SBSR, 21 Dec 1939, perpendiculars of 328

Similarly, the thrust-deduction fraction

—Ap

general similar to that of the stern of the turbo-

wake

readily

the

cavitation at high blade loadings.

systematic data available for a prediction of the fraction.

to

prevent detrimental

to

and a speed

of 17 kt.

ft,

The

a

had a length between beam of about 43.5 ft,

rotating-blade propellers

were each designed to absorb a shaft power of 2,000 horses, with electric driving motors mounted directly on the propeller casings.

Areangbment of Twin Rotating-Bladb Propellers at the Stern

HYDRODYNAMICS

658

The

rot.ating-l)lade propeller lends itself par-

which must hold position and other forces

ticularly well to craft

wind,

against

when

tidal-current,

stationary

nearly so.

or

[SBSR, 12 Mar 1953, p. 342], "German Small Craft," that:

It

reported

is

an

in

article

on

"The Voith-Schneider propeller has proved of particular value in applications where large athwartships thrusts are required. It has therefore been fitted for buoy lifting and laying

which have to be operated

vessels

difficult

waters."

The

article

sloping,

accompanied by the outboard

one well out on each

axes

with

set

upward and inward. The

pointing

blade tips are well above the baseplane. However, the tops of the blades

come rather

close,

perhaps

The

large diameter of the rotating assembly of

a propeller of this type lends itself equally to a high gear reduction from a high-speed engine or

motor or to a low-speed motor speed of the propeller

drive.

The angular

usually not a major

is

and Fast Launches)," Buenos

the other hand, the rotating-blade propeller,

Propulsion by airscrew (s)

Weeds,

is

The

out of the question

and the engine are so high above the water surface, as in a, hydrofoil-supported craft, (b)

that

hull

it is

undesirable or inconvenient to transmit

the power to a propeller under water (c)

It

is

necessary to eliminate the noise and other

made under water by mechanical

propulsion devices. This

complication and

a

internal mechanical gear.

more blades

Aoilnerability

With

of

the

half a dozen or

selected when:

grasses,

certain fishing operations.

relative

is

and other marine growths are so profuse and thick that hydrodynamic propulsion by weedproof screw propellers, or by sculling propellers, paddlewheels, and similar (a)

whatever type, has been plagued from the beginning of its development by the unavoidable of

Aires,

1951, pp. 222-224].

disturbance

design problem.

clearly indicated, since

design instructions and data for the powering of this type of craft ["Cruceros y Lanchas Veloces

devices

too close, to the water surface.

is

types of high-speed boats driven by airscrews are shown by J. Baader, in a chapter in which he gives

with a long,

side,

Sec. 71. IS

air-rescue task

the wide, flat-bottomed craft was capable of a speed of 50 miles per hour. A later type is shown by D. Nicolson [NECI, 1937-1938, Vol. LIV, Fig. 5, p. 117]. Sea sleds or inverted V-bottom craft driven by airscrews are illustrated in Motor Boating [New York, Jan 1946, p. 112]. Two

cut-up stern and two Voith-Schneider

propellers,

On

An

(Cruisers is

profile of a small lighthouse tender

their

in particularly

IN SHIP DESIGN 538].

(d)

It is desired to free

craft,

of

may

be mandatory for

measure the hull resistance of hydrodynamic propulsion

all

efTects.

To compensate

to position, not only for straight-

for the down-pitch

moment

of

ahead steady running but for changing the pitch and changing the direction of the resultant thrust, the mechanical-design problem is difficult at the best [Mueller, H. F., "Recent Developments in the Design and Application of the

above the line of action of the water-resistance forces, any small boat carrjdng an airscrew must have a large hydrodynamic moment resisting the

SNAME, 1955, pp. 4-30].

sled-type craft of rectangular cross section, re-

Vertical Axis Propeller,"

Simplifications have been effected to

make

parts more sturdy, but these changes have, often than not, involved

hydrodynamic

efficiency.

some reduction

By

dint

of

the

more

of the

excellent

engineering the rotating-blade propeller continues is possible that some of the developments which have brought a greatly increased measure

to run. It

of rehability to the controllable propeller

do the same

for the

may

most useful rotating-blade

device.

71.18

Airscrew Propulsion.

An

early type of

"skimming boat" with airscrew propulsion, apparently intended for work in extremely shallow water, was designed and built by Yarrow of Glasgow about 1921 [Mar. Eng'g., Jul 1921, p.

the airscrew thrust, at a large relative height

thrust

moment. This

is

one reason for the use of

sembling the floats of early seaplanes. Airscrew propulsion is exceedingly inefficient indeed,

it

is

almost ineffective

—when

the speed

advance is low, as it would be for even a small swamp boat plowing through a heavy growth of weeds. Air flow through the propeller then resembles that depicted in Figs. 16. K and 16. L, when momentum is imparted to only a small mass of "new" air in any given interval of time or given distance of forward travel. The propulsive efficiency mounts rapidly as the speed of advance of

increases in proportion to the velocity of the

outflow jet of the propeller. For this type of drive, therefore, the resistance of the craft to be

driven should be low and the resulting speed high.

CHAPTER

72

Design Features Applicable

Shallow and

to

Restricted Waters 72.1 72.2

General

72.5

Economical and Practical Speeds in Shallow and Restricted Waters Design for Reduction of Confined- Water Drag, Sinkage, and Squat Transverse Dimensions and Section Shapes

72.6 72 7

Length, Longitudinal Curvature, and Wetted

72 8

Modifications to

72.3

72.4

for Shallow- Water

Running

General.

72.1

660

Normal Forms

The

to Shallow- Water Vessels

Slope and Curvature of Buttocks

.

of

the

for

predicting

or

.

72.16 72 17 .

flow

estimating

666 667 668

Shaping

Adequate Flow of Water to the Propulsion Devices

72.13 72.14 72 15

The Design

Tunnel Stern Hull Surfaces Abreast Screw Propellers Powering of Tunnel-Stern Craft Handling of the Vibration Problem in Shallow Water Partial Bibliography on Tunnel-Stem Vessels

than the

less

of a

.

average depth

about a body or ship in shallow and restricted waters are discussed in Chap. 18; the behavior of actual ships under the same conditions is described in Chap. 35. Formulas, graphs, and procedures

Bow

72.11 72 12

661

for Shallow-

elements

666

Design

of Straight-Element

72 10 .

660

665

Surface .

The Adaptation

72.9

662 663

Typical Shallow- Water Vessels

.

Water Operation

659

Reference Data on River, Canal, and Channel Slopes and Currents

h.

.

668 669 672 672 673 673

The speed V^ may always be

critical

speed Cc for the shallowest

These craft usually carry passengers and moderate amounts of freight. (2) Self-propelled, full-bodied craft of moderate speed, where V^ does not exceed about 0.7c ^ part

the

of

the

route.

,

behavior of ships in confined waters are set

Chap.

in

The

down

maximum amount

the carrying of the

for

of

cargo on a given set of limiting dimensions

61.

design comments, suggestions, and rules

(3)

Non-self-propelled barges, lighters, and scows

given here apply primarily and rather exclusively

(4)

Self-propelled pushboats

to craft which operate in water that

is

more

shallow with reference to the

linear dimensions of the vessel.

One

rule of

depth is one which is less than the beam of the vessel. Perhaps a better one is that a shallow depth is less than twice the draft. Another rule, for the is that the depth is less than the so-called square draft; in other words, less than the square root of the maximum-section area, or VAx. To be sure, many such shallowwater vessels are required to traverse deep spots now and then but at some sacrifice in performance, if need be, to insure the best shallow-water

subcritical range only,

may

critical

speed Cc

.

Design notes and rules

for the latter

Volume

group, carrying capacity

is

III.

two groups

For the second

usually of far greater

importance

than efficiency of propulsion or hydrodynamic performance. Bottoms are flat and of large area,

Waterlines are so,

lying at the limiting-draft level. full

and

except perhaps in

sides are vertical or nearly

way

of the inflow jets to

screw propellers. The hydrodynamic design features in this chapter are therefore limited generally

to vessels in the

first

category preceding.

Design notes previously published for particular

For design and operational purposes,

craft

intended to run in shallow and restricted waters

types and for shallow-water vessels as a class

may

are divided into four categories:

(a)

Self-propelled, fine-lined craft having a shal-

low-water speed V^ that

than the

exceed the

are given in Part 5 of

behavior.

less

for

thumb

for all speed ranges is that a shallow

(1)

and towboats,

which the free-running shallow-water speed V^

or less continually

critical

but always speed Cc for the nominal or is

close to

659

be found in the following references:

Ward,

C,

SNAME, (b)

"Shallow-Draught

River

Steamers,"

1909, Vol. 17, pp. 79-108

R. C, "Construction and Operation Western River Steamers," SNAME, 1913, Vol. 59-65 pp.

Wilson,

of 21,

HYDRODYNAMICS

fifiO

"Ship Design, Resistance and Screw Propulsion," 1933, Vol. I, pp. 209-212; Vol. II, Chap. XXVI, pp. 136-142

Baker, G.

(c)

S.,

(d)

MitcheU, A. R., "Shallow Draught Ships," INA, Jul 1952, pp. 145-153

(e)

Mitchell, A. R.,

"Tunnel Tj-pe Vessels," lESS, 1952-

1953, Vol. 96, pp. 125-188.

Reference Data on River, Canal, and Channel Slopes and Currents. The free surfaces of all flowing ri\'ers, tidal estuaries,

open channels,

and canals in which horizontal currents flow, have some slope with reference to the horizontal. Data on the surface slopes of all the principal rivers in the United States, subdivided into river regions where the slopes change rapidly or where there are reliable data, are given in both tabular and graphic form in a paper by H. Gannett entitled "Water-Supply and Irrigation Papers of the U. S. Geological Survey, No. 44, Profiles of Rivers in the United States," U. S. Geological Survey, Washington, 1901. Nothing in this paper indicates the slopes which might occur during flood conditions, or those which might obtain in short reaches of the 1

dams

many

in

The

mile in length.

construction of

of the rivers since

1901 has of

changed the situation materially. The slopes cover a rather wide range, as indicated course

Drop

Location

per

in ft

geographical

mile

of

6,280 ft

Sacramento River Missouri River Platte River Colorado River

3.0,

maximum

1.0 average; varies

from

0.7 to 1.3

Two

steepest slopes are 22.0

and

31.2, corresponding to natural tangents of 0.00417 and 0.00591;

Nowka

European

S.O.

gives the surface slopes of

rivers as

about

in 1000

1

some ["New Knowl-

edge on Ship Propulsion," 1944, BuShips Transl. 411].

Here the slope thrust

is

sufficient to

produce

a speed which gives steerageway to a non-selfpropelled barge when drifting downstream. This equivalent to a 5.28-ft drop per geographical mile or a 6.08-ft drop per nautical mile. is

The

steepest reaches in

any large navigable Yangtze in China,

river of the world are in the

where the river rises some 600 ft in the 1000 miles between its mouth and the city of Chungking. Certain sections when in flood have free surfaces so steep that the currents in the navigable channels reach velocities of 12 to 14 kt.

The method

body

of calculating the

drag and thrust

is

floating

is

upon which a

described in Sec. 57.10.

72.3 Economical and Practical Speeds in Shallow and Restricted Waters. Decisions as to

the designed speeds for shallow-water vessels are

made

b)y the prospective

operators, on a basis of

many

owners and

factors other than

hydrodynamics. However, the designer may be called upon to give information and advice on this matter. He is therefore required to have some knowledge of the factors involved and some quantitative data for reference. The first things to know about the shallowwater and restricted-water regions in which the ship is to run are the depth, bottom contours, channel dimensions, water-section outlines, current

current

directions,

velocities,

and

local

may

be greatly complicated by variations in these factors due to flood and tidal conditions. These in turn depend upon the weather as well as the seasons and the current irregularities. This

rotation of the earth. It is not adequate to

values

of

depend upon average

the water factors previously hsted,

either as averages of distance or of time. It

necessary to assume extremes as well,

if

is

ship

is to be maintained on schedule. Further, may, and usually does lurk around the

operation

corner of the one operating situation that has not been investigated properly and for which preparations have not been made.

a reasonably uniform depth h

is

deter-

for a certain section of the route,

under

First,

mined

Averages 5.0 or 6.0

remainder are 6.0 to

G.

ship or

disaster

hereunder:

Sec. 72.2

to the declivity of the surface

properly

72.2

order of

IN SHIP DESIGN due

The next the solitary wave

given conditions.

speed of

step

is

to find the

in that depth,

so

a given shallow- water ship speed Fj to the critical wave speed Cc may be known. As an aid in relating contemplated ship speeds to the solitary-wave speed for any depth. Table 72. a gives the latter speed for a considerable range of depths to be encountered in practice. that the

ratio

of

The values given in this table are for stillwater conditions, with no current. When the water in an estuary, river, or channel is flowing in one direction or the other, the solitary wave speed of Table 72. a is still valid when reckoned with reference to a point fixed in the water. When a ship is overtaking a solitary wave, therefore, it makes no essential difference whether the ship is moving with the current or against it. The important factors are the wave speed and the ship speed, both reckoned through the water. It is emphasized, however, that the critical

Sec.

DESIGN FOR CONFINED WATERS

12A

speed of the solitary wave or wave of translation can and does change rapidly with the depth of

water and the configuration of the bed. Since the wave itself is short, a change in depth that is relatively short in the direction of motion changes the speed of advance of the wave rather suddenly. For instance, in passing over a narrow rock ledge its speed is changed in proportion to the clear depth over the ledge. It may be more than disconcerting to the pilot of a ship moving at just below the critical speed in the deeper water to find the sohtary wave suddenly dropping back and raising the bow of his vessel. of Fig. 61. L indicate the regions

The contours

both the critical-speed ratio V J -sfgh and the square-draft to depth ratio a/Aj/Zi, where the total shallow- water resistance Rn is only slightly greater than the total deep-water resistance Rt as well as the regions where the ratio of these of

,

two values mounts to depth ratio

rapidly. If the square-draft

's/A^/h

is

low, the point where

the resistance begins to increase rapidly

about 0.8 Vgh or 0.8cc This corresponds to a speed, in

ft

is

at

per sec, of

TABLE

Solitary-Wave Speeds for a Range 72. a OF Uniform Shallow- Water Depths

The g

wave or wave of translation by the formula c = y/gh, where is taken gravity. In Enghsh units

celerity c of the soUtary

related to the depth h

is

is

as

the acceleration of

32J74 ft per

Water depth

sec*.

h,

For

<;

this table,

1

kt

is

1.6889 ft per sec.

661

HYDRODYNAMICS

662

IN SHIP DESIGN

Sec. 72.5

diagonal bulges of the maximum section is one means of reducing the effect of the second factor.

water

A

of the flow passes

3.0.

raising the floors or

corresponding to displacement-length quotients A/(0.010L)' of from 40 to 43. If the overall

better one, because

most

the ship under the bottom,

is

decreasing the draft. This gives more flow area between the ship and the stream bed.

Fortunately, these are equally good solutions to the handicap imposed by lateral boundaries close aboard. It is seldom that the beam or the waterline width of the sections can be appreciably reduced because of the need for deck space, for

large metacentric stability, or for lateral room within the hull. In any case, the possible reductions in waterline

usually

they

may

beam

or overall hull width are

inconsequential

of

affect the

amount,

except as

behavior of the ship in a

tight-fitting lock.

known method and squat found trouble-

best and, in fact, the only

The

of reducing the sinkage

ratio,

is

a factor,

is

one having a low fatness

F/(0.10L)^, of the order of not more than

Sometimes

this ratio is as

low as 1.4 or

1.5,

if power is cheap, and if useful crowded on, the designer may have to fill the waterway section with all the ship that can be pushed through it, regardless of the square-draft to depth ratio vX^/Zi. One way to reduce the maximum-section area Ax is to reduce the draft, but practical considerations may set a minimum limit. There must be enough displacement volume to carry the weight of the vessel and its useful load. There must also be enough hull depth to give it structural strength and rigidity. Too large a beam-draft ratio is not

size is limited,

load

is

advantageous for propulsion because

bow and

the waterline slopes at the

it

increases

stern for a

at high speeds is to increase the backflow area and the bed clearance. On the basis that a given restricted channel can not be made wider

given displacement volume. However, if propulsive efficiency is not a major factor, there is no

and deeper the solution is to make the vessel shallower and the maximum-area section smaller. There are no formulas or systematic data available for predicting the sinkage and squat under confined-water conditions but Sec. 58.4 contains some sinkage and change-of-trim values for a

intended for restricted-channel operation. Obviously, it must be necessary for two such craft

few vessels in shallow water. Sec. 58.7 lists references in which other data of this kind, derived from model tests, may be found. The importance of this feature is emphasized

displaced water,

from a letter of F. A. Munroe, Jr., Marine Director, Panama Canal Company (of unknown date), published on page 74 of "Marine Engineering" for January 1955:

has

some

in the extract

"A minimum

of 5 feet of

water under the keel

is

con-

sidered essential to guard against the squatting effect of a large body moving in a restricted channel and the seiche in the

Cut created by the drawing

Miguel Locks end

of the

of

water at the Pedro

Cut."

Transverse Dimensions and Section Shapes for Shallow-Water Riuining. The combination of water depth h and speed V^ to be 72.5

achieved

is

almost invariably fixed before the

design of a shallow-water ship is undertaken. This leaves the designer, if he has some freedom

with the length, the choice of the area Ax and the shape of the maximum section and the in relation to the water depth h. overall draft

H

Within reasonable

limits,

the hull most easily

driven at the relatively high speeds often required of these vessels, where wavemaking in shallow

hydrodynamic hmit to the beam

meet or pass each other

to

in the

a

of

craft

same channel,

or for a single vessel to pass through a lock. If

the craft

is

sufficiently shallow to afford

a sizable

clearance under the bottom for the passage of it

may

well be that a vessel with

a large beam-draft ratio and a small draft is actually easier to handle and less liable to run foul of the banks or of other craft than one which less beam but also The most efficient

less

bed clearance.

solution,

considering

all

phases of the water flow around the hull, is to embody a large rise of floor in the midship or the

maximum-area section, together with a large bilge radius. The use of floor slopes as high as 10, 15, or

20 deg in the transverse sections acts is more of a nominal

to increase the draft but this

than an actual increase because of the limited width of the deep-keel portion. If the waterway bed is soft or yielding, occasional encounter of this deep-keel portion with that bed does nothing

more than rub off the paint. The maximum draft may be limited severely by some especially shallow part of the operating area. The necessary displacement volume is then achieved only by using a nearly flat floor and a relatively large maximum-section coefficient

Cx

,

may

possibly 0.9 or more.

When

this occurs, it

be necessary to hold to the relatively flat floor lines for only a limited length amidships.

DESIGN FOR CONFINED WATERS

Sec. 72.6

Bx' 37.6

ft

Hx-8.l4n

G63

of The Franklin Institute, July 1879, Vol. 78, pages 18-27. A model of this vessel, 530, was made and tested at the old Experimental Model Basin at Washington. The results were reported upon most favorably by D. W. Taylor.


EMB

Detroit River excursion steamer

(b)

the body plan of which

[SNAME, Rise of Floor/Bx - 0.0246

Bilqe

Podlus/Bx" 0.232, obout

1901,

is

Tashmoo, reproduced in Fig. 72.A

1-12;

pp.

complete lines of both the

PI.

3

contains the

Tashmoo and the

SNAME, HT, 1943, pp. 383-386] Erie steamer City of Erie, the body plan of which is given in Fig. 72. B. It was, City of Erie; also

Fig. 72. a

Body Plan of Detroit River Steamer Tashmoo

Along the greater part of the ship length, there is adequate room to pass the displaced water underneath the bottom. This was done in the design of the Hudson River paddlewheei steamer Mary Powell, with a rather flat floor [Int. Mar. Eng'g., May 1920, pp. 406-407], and in the design of the large Lake Erie paddlewheei steamer Greater Detroit, to be described presently. 72.6 Typical Shallow-Water Vessels. It is helpful here to examine the forms and other data still

some

or

hulls,

Tashmoo, designed by Frank E. Kirby, and river steamers. Its famous race with that vessel in 1901, in the like the

who

specialized in lake

relatively shallow waters of

remembered [SNAME, (d)

Lake

Hudson River steamer New

plan of which

is

Erie,

is

still

1901, pp. 1-12].

York, the

reproduced in Fig. 72. C

body

[SNAME,

fast shallow-water vessels with slender

—vessels which have given many decades of

splendid and even superior performance.

some

The

fact

were designed and built nearly a century ago is supplemented by the amazing realization that their performance is still good by the standards of today (1955). Many of them, therefore, appear to be perfectly valid bases for a modern, systematic analysis of that

The Lake

(c)

of these craft

Bili5ef?adius/Bx=

Fig. 72. B

Body Plan of Lake Erie Steamer City of Erie

design for a fast, shallow-water vessel.

Among

these vessels are mentioned:

and 15]. A model of was made and tested at the old Experimental Model Basin at Washington. This and the two vessels preceding are listed in the table of E. M. Bragg [SNAME, 1916, PL 90]. 1906, pp. 31-40

The famous Hudson River steamer Mary Powell, designed and built in 1861, when naval (a)

in the United States was only emerging from the practical stage. The designed waterline of the run of this vessel is illustrated in diagram B of Fig. 24. G. The complete lines are to be found in "International Marine Engineering" for May 1920, pages 406 and 407; see also a paper by B. F. Isherwood in the Journal

architecture

Afterbody

Rise of Floor/ Bx'0. 0224 !

0.121

this vessel,

(e)

and

EMB

Pis. 14

529,

Hudson River steamer Hendrik Hudson, deby J. W. Millard and Brothers, New York

signed

J., MESA, Feb 1930, pp. 100, 104] Lake Erie steamer Greater Detroit (sister vessel Greater Buffalo), designed by Frank E.

[Mason, C. (f)

Fore body

/Mom

Hull

Extends Above This

Lin.

Frame Number

Frome Numbers

Fig. 72. C

Body Plan of Hudson River Steamer New York

HYDRODYNAMICS

664 Topmost

Porlion

Hull

,ol

Not Shown

24( WL

IN SHIP DESIGN resembhng Detroit

the

Sec. 72.6

general

[SNAME, HT,

design

of

the

Greater

1943, pp. 97-134].

How-

were of relatively shallow draft, these vessels appear not to have been designed to run in particularly shallow water. They are not further described here as having ever, although they

design features useful for shallow-water craft.

The Fig. 72.D

Body Plan of Lake Erie Steamer Greater Detroit

Kirby

in conjunction with

H. C. Sadler

design of shallow-water vessels for inland

waterways in Europe is discussed by G. Lauterbach in "Schiffbautechnisches Handbuch (Shipbuilding and Ship Design Handbook)," Berlin,

[SNAME,

1952, pages 613-635.

a

Possibly because high-speed vessels built for

adapted from the reference. Earlier vessels of this general type are

service in confined waters have been considered

1925, pp. 101-108

body plan

and

Pis. 64-83]. Fig.

72.D

is

of this vessel,

described and illustrated elsewhere

[SNAME, HT,

1943, pp. 377-378, 382].

Some dimensions and form data on vessels, unfortunately

these

not complete and not too

rehable because of conflicting published figures, are given in Table 72. b. Additional data on

some

of these vessels, pertaining principally to their

feathering paddlewheels,

[SNAME,

1916,

PL

is

given by E.

M. Bragg in the

period from 1850 to 1910, resulted in the developof fast vessels driven

TABLE

72.b

by

side paddlewheels,

of Ship

least,

pages printed nearly a century ago contain information than those of recent outstanding article in the latter

much more years. One

category treats largely of the machinery and speaks only briefly of the hull [SNAME, HT, 1943, pp. 97-134]. Most of the published data essential information

huU coefficients, or the by which these data can

be calculated. If the length is given the displacement may not be, and vice versa.

Dimensions and Form Data for American River Steamers of the Period 1870-1940

All the vessels in this table were driven

Name

these and other ships are rather hard to find in the technical hterature. For large vessels at

are lacking the customary

90].

Steam navigation on Long Island Sound,

ment

as specialized craft, factual data on the hulls of

by

side paddlewheels.

DESIGN FOR CONFINED WATERS

Sec. 72.7

TABLE

72.C

Dimensions, Ratios, and Proportions for American River Steamers

The dimensions marked by ratios

and

L*, ft

6f)5

asterisks (*) are tliose listed

coefRcients are derived

by J. Scott Russell [MSNA,

from the published dimensions.

oi''

the Period 1850-1870

1865, Vol.

I,

p. 666]. Tlie

remaining

HYDRODYNAMICS

666

which acts to increase the friction resistance, especiall}'- with a high backfiow velocity. However, the gain from a small square-draft to water-depth ratio yTAxlh is likely to be greater than the loss from the increased wetted area. A ratio of \/X^//i less than 1.05, as shown by the curve of Fig. 61. G, produces a speed loss from augmented potential flow of less than 10 per cent, while a ratio below 0.375 is responsible for a speed loss of only 1 per cent. If the length is limited, increase the beam but hold a small draft. The additional bed clearance provided for normal flow under the bottom

should more than compensate for the greater waterUne slopes associated with the wide beam. It is comforting to know that, in general, a form of hull suitable for confined waters is found to give good performance in water of any extent and depth, especially for low values of Cp and of fatness ratio F/(0.10L)l Thus a vessel designed to do well in the shallow portion of a route of varying depth is by no means at a disadvantage when operating in the deep portion of the route.

72.8

Modifications

to

Shallow-Water Operation.

Normal

Forms

for

For the vessel which

IN SHIP DESIGN

ABC

For the 10-kt

Amalo

canal, T,

Sec. 72.8

is

26

ft,

26

=

1.08.

From

as a basis, the estimated sinkage

the

bow and 0.004L

2.04

respectively.

ft,

It

and

necessary to extra-

is

polate the graphs to obtain these values.

For the 14-kt speed (through the wate r) in the below Port Correo, T, is 14/^/510 = 0.62;

river

at a draft of 26.5

ft in

the fresh water, the value

hlU = 30/26.5 = 1.13. The estimated sinkage at the bow is 0.0068L or 3.47 ft; at the stern it is 0.0062L, or 3.16 ft. A much greater extrapolation of

is

required here, in Fig. 58. E, than for the Port

Amalo canal estimate. The Cp value of the T-S tanker is 0.74 compared

ABC ship, and the fatness ratio compared to 4.327. Despite the greater

to 0.62 for the is

5.76

beam

ABC

appears that the be reduced to about 0.8 of the values given. Even so, the nominal 2-ft bed clearance in the Port Amalo canal is of

the

ship,

estimated sinkages could

it

all

reduced to only 2.0 — 1.75 = 0.25 ft; in the river below Port Correo it is only 3.5 - 2.78 = 0.72 ft. These are small but probably representative of

sign

of the latter the critical speed is 18.40 kt.

is

E

= 28/ T-2 tanker 0.0043L at

at the stern; or 2.19 ft

depend upon the relative importance of ship performance in one and in the other. A good example of this situation is the ABC ship, for which the design requirements are set forth in Chap. 64.

depth

0.443; at a draft

Fig. 58.E, using the

modern medium-speed

Port Correo, it is noted from Table 72. a that for the 28-ft depth of the former the speed of the wave of translation is 17.77 kt. For the 30-ft

=

the value of depth /i/draft

of

runs mostly in deep water but also has to perform well in shallow and confined waters the concessions to the shallow-water requirements

Considering the features of this vessel as regards its operation in the canal leading from Port Amalo to the sea, and in the river below

speed in the Port

s hip

10/\/510

operations

shallow-

in

water areas.

The Adaptation

72.9

of Straight-Element

Shallow-Water Vessels.

to

A

vessel

Dere-

quired to operate in confined waters, with restric-

imposed by channel bed and bound-

tions to flow aries,

should logically receive more than the usual

amount

of careful hull shaping. It needs every-

thing that can be done to improve the flow around the hull. Nevertheless, the bed and side clearances for

most

of these vessels

in

some

many

parts

approach zero

part of their operating areas; often in of those areas.

The

practical impossibility of shaping the hull

to compensate for

more than a

fraction of these

Both

are well over the speeds contemplated in those portions of the route, hence the ship will

handicaps makes it good design, as well as good engineering, to take this opportunity of incor-

be running in the subcritical range in both cases. The matter of providing room for the backflow under and around the ship is handled in Sec. 66.13, when laying out the contour of the maxi-

porating straight-element features in the under-

mum-area

the Hillman

A

section.

power is almost always available to overcome the augmented resistance in confined waters, because the deep-water speed at any draft and trim is in excess of that permitted by local reserve of

regulations

when

traversing confined-water areas.

water form.

A

judicious use of chines, coves, and

developable surfaces affords a surprising degree of flexibility to the designer, as is evidenced by shallow-water pushboat.

A

body

plan of a craft of this type, 115 ft long by 27 ft beam, is reproduced in Fig. 72. E. Its outboard this vessel

drawn in Fig. was designed primarily

for pushing, the general

shape should serve well

profile,

72. F.

less

While

numerous

details, is

DESIGN FOR CONFINED WATERS

Sec. 72.10

20 at Extreme After End

Station

-^

Ratio

=

any other type

running

reentrant angles in the forebody sections of the

flare

its

from becom-

bow wave. At

same time they provide support with

for a

the

wide deck

pushing pads (or for passenger accommo-

dations or cargo). Forward of and abaft Sta. 2.5

the section

lines

lie

Hul

.J-S

deq

Body Plan of Hillman Pushboat with Sthaight-Element Frame Sections

of shallow-water vessel

way

of

Rise of Floor ^

forward of Sta. 2.5 prevent the ing excessive in

End

about

at moderate speed.

The

at Forward

Station

of

0.0432

Fig. 72. E

for

667

approximately normal to

decks in a vessel which must carry most of its useful load above the main hull, produces the large flares in the entrance

shown on the body

plans of Figs. 72.A through 72.E. If

the length

is

not restricted, the designed

waterline slopes in the entrance and run can be

made acceptably

small, despite a large

maximum

beam. This helps greatly to counteract the effect of heavy flare in the entrance sections. The

DWL

Mary

the lines of flow as the water from ahead passes

entrance slope of the

under the

was only about 6.5 deg; that of the New York about 5 deg. The maximum run slopes were 13.8 deg and 15.5 deg, respectively. A scow, sled, or spoon bow lets most of the water flow easily under the bottom but when

vessel.

In the afterbody, the extension

of the nearly vertical side

down

to a long hori-

zontal knuckle, lying at an appreciable distance

below the

DWL,

prevents leakage of air to the

propeller region, well inboard from the side. craft depicted

in

Figs.

72.

E

and

The

72. F

addition fitted with two Kort nozzles,

was shown

in

the bed clearance

in

the

bow must

sides. Further,

of a vertical skeg

channel,

it

appears that the water flow along the

afterbody would likewise

move

easily

under the

Bow

with this type of entrance to provide a stabilizing or fulcrum effect for assistance in steering

turning. This

is

Shaping the bow and the entrance is a much more difficult operation on a shallow-water craft with a B/H ratio of from 4 or 5 to 10 than on a deep-water vessel, with a ratio of 2.5 to 3.5. The large beam-draft ratio, coupled with the usual requirements for wide Shaping.

Fig. 72. F

and

the reason for the V-shaped fore-

foot of the Hillman design of Fig. 72.E. A. R.

Mitchell recommends that on full-bodied

section lines shown.

72.10

reduced nearly to nothing, it flow easily around the

something approaching the shape is required forward on a vessel

outline only in the latter figure, which served as

was not possible to arrange for a flow test of a model of this vessel in the TMB circulating-water

Powell

also let

additional shields against air leakage. Although

it

is

for the

of this type the slope of the less

ci'aft

DWL forward be not

than 28 deg, because at a lesser angle more

of the

water flows around the sides and not under

the bottom [INA, Jul 1952, p. 148].

He further recommends that to facilitate this under- the-bottom flow "... stem in profile should

Outboard Profile of Hillman Pushboat

Both Figs. 72.E and 72.F are adapted from drawings kindly furnished by the Hillman Barge and Construction Company of Pittsburgh

HYDRODYNAMICS

fifiS

IN SHIP DESIGN

Sec. 72.11

be swept aft as gently as possible below the load

efficient propulsion.

waterline; the buttocks forward should be very

this feature are included in Sec. 71.6.

easy and the bilges rounded" [INA, Jul 1952, p. 148]. This is done in the Hillman pushboat

When hmitations on overall beam prevent the use of side wheels, the paddlewheels can always be placed at the stern. Here they may be either in

previously referenced, as depicted in the profile of Fig. 72. F.

The

forefoot

Mary

fashion on the

is

cut

away

Powell and the

in similar

New

York,

Further comments concerning

the form of a pair, one on each quarter with the

mechanism

drive

may

in between, or there

be

indicated by the lines drawings in the references

only a single wheel, extending

cited for those vessels.

the ship. In either case it is by no means easy to provide the necessary displacement volume at the stern and at the same time to embody the

Slope and Curvature of Buttocks.

72.11

In

the slow- and moderate-speed ranges, on a wide, shallow craft, most if not very nearly all of the

The buttock demand the same

all

the

way

across

reverse curvature in the buttocks under the run

flow passes under the bottom.

slopes

which

and curvatures therefore

atten-

wheels in a direction that

will project the inflow to the stern is

paddleroughly horizontal.

tion as the waterlines near the surface in a deepwater ship design. This calls for easy transitions where the forward buttocks or forelmes curve

against which the outflow

downward and

are going astern, can be reflected aft from the hull.

and under the bottom. Examples of these are found m the keel profile and the chine line at the bow of the Hillman design ofFig.72.F. For drafts of the order of 8 to 6 ft or less, it is well to hold the buttock slopes under the run to a maximimi of 15 deg with the horizontal; a aft

maximum

of 12 or 13 deg is better. Apparently to save time and labor and to facilitate fabrication and erection, the buttocks under the run of small shallow-draft vessels often have a sharp knuckle where they leave the baseplane. Abaft this knuckle they are straight, with constant slope. If they are given reverse curvature, so as to slope downward and aft behind the propeller position, there is a second sharp knuckle where this change is made. It is pointed out 1 and 2 of Volume I that sudden change in direction,

repeatedly in Parts

water

resists

often

with

this

objectionable

consequences.

It

is

found, furthermore, that with some planning and some alteration of the structural usually plans,

it is

just as easy to provide a

for the M'ater flow as to

Adequate Flow

make

good path

a poor one.

Water to the Propulsion Devices. The provision of means whereby water may have free and easy entry to the propulsion devices is much more important in a shallow-water than in a deep-water design. The 72.12

of

use of side paddlewheels eliminates the necessity of shaping the hull locally to suit some particular

kind of device, especially to msure good flow to it. In fact, this problem almost solves itself, except for the proper fore-and-aft position of the wheels along the hull to bring them in the crest of a transverse

Velox wave for the speed of most

The

after termination of the hull, just

ahead

of the stern wheel (s), should not present a surface

an appreciable part

If

when

jet,

of it is so reflected,

engine order for astern rotation followed

the wheels

by an ahead motion

is liable

an

to be

of the ship!

If rotating-blade propellers

with vertical axes

are fitted at the stern, or at both

bow and

stern,

one or both ends are cut up toward a flat bottom region in the vicinity of each propeller. This prevents the blade tips from extending below the keel. The blades are approximately vertical and the water coming from under the ship meets

them

in a nearly horizontal direction.

be found advisable to

fit

It

may

several of these propellers

abreast because the draft limitations are certain to restrict the lengths of the blades.

A

shallow-water craft of normal form, to be

driven by screw propeUers, generally requires at least two screws if the draft is limited and the

speed

is

high enough to

powers. not manda-

call for large

In addition, twin screws are useful

if

overcome the sluggish maneuvering any vessel under which the bed clearance is small. To prevent any undue reduction in propeller diameter and disc area, with its loss of efficiency and maneuvering power, designers of years gone by resorted to arrangements which are still used to advantage if the situation demands: tory

to

quahties

(a)

of

Make

the tip submergence slightly negative,

with the tips normally out of water, on the basis that they will have adequate submergence in the stern-wave

This

only feasible

there

is

to be such a crest at the propefler position and

if

crest.

is

if

the propellers are to be lightly loaded. (b)

Place the propellers under a wide torpedoboat

DESIGN FOR CONFINED WATERS

Scr. 72.13

with its lower surface lying very slightly below the DWL, and with a small tip clearance under this surface. N. G. Herreshoff and others stern,

built

many

designer and builder of tliose craft, A. F.

Yarrow

["The Screw as a Means

Shallow

of Propulsion for

Draught Vessels," INA, 1903,

p.

107]:

successful craft to this design.

Use surface propellers

for extremely small This scheme, of course, does not increase the thrust-producing area in proportion to the (c)

669

draftSi

"There motion

be an increased resistance to the forward due to the action of the screw in reducing the pressure of water at the inclined part of the tunnel forward of the propeller, and this increased will

of the vessel,

is common, more or less, to all screw ships, probably proportionately greater in this class of vessel than in those where the propeller in in the usual

resistance

increase in diameter. (d)

Employ a

tip

submergences ranging from a small positive

tunnel-stern design, with at-rest

to a large negative value.

but

it

is

There is also a loss of efficiency due to the resistance of the inclined surface of the tunnel aft of the proposition.

peller."

The Design

72.13

Tunnel Stern.

of a

The

tops or roofs of the tunnels described in Sec. 25.20

and diagrammed designed

in Fig. 25.

waterline

M may

extend

or

below the

lie

above

it.

The

design rules given here apply generally to a tunnel

whose roof extends above the

DWL.

how much

region of

DWL, Good

of the propeller disc

and the

maximum is

slope, at

about half

usually not far below the

where the hydrostatic pressure design

maximum

When laying out a tunnel stern, whether for one or for multiple screw propellers, it is first decided

The

height of the tunnel,

to

prevent

separation

is

calls

small. for

a

roof slope, in a vertical plane through

the shaft, not exceeding 14 or 15 deg. A. R. Mitchell recommends a limit of 12 deg in fast

and 15 deg

in slow ones [INA, Jul 1952, on the basis of a negligible change of trim when underway. However, limiting the roof slope to avoid separation is only part of the story, on the basis

vessels

This

upper blades can be out of water. It is believed that a tunnel system can be designed to function properly even if the shaft axis has above the DWL, as for a surface propeller. This extreme may be considered necessary to permit removing a propeller through an access hatch above, provided the vessel can not be trimmed by the bow for this purpose. However, it is preferable to place the axis at least O.IOD below the DWL, where D is the propeller diameter. This keeps the propeller bearing always lubricated (if this is a practical item), keeps the tunnel entirely full of water,

p. 148].

and prevents cutting too much out of the for the tunnel slopes forward and aft.

be of the order of 6 to 10 deg, instead of 12 or 15 to 18 deg. The Hillman design of Figs. 72.E and 72. F achieves this and more. Moving the

The

hull

tip

clearances need

hull

be only large

enough to insure against mechanical rubbing under all conceivable circumstances and to pass any foreign material that may be in the water without jamming it between the propeller tips and the hull. A tip clearance of 0.04 times the propeller diameter appears to be ample, both mechanically and hydrodynamically. The small tip clearances necessary to insure that the highest

part of the tunnel runs full of water partial

insurance

losses, particularly

The next major

mum

against

when step

is

excessive

the shp ratio

may

be a

tip-vortex is

large.

to determine the maxi-

permissible fore-and-aft slope of the tunnel

Although described in Sec. 25.20, it is well to emphasize here the effect on propulsion of the roof slopes, both forward of and abaft the wheel. In the words of a renowned

top, forward of the wheel.

is

that propulsive efficiency sufficient

is

a design factor of

importance so that

regarded completely.

A

it can not be disvalue of i7p(eta) superior

to those achieved in the past, even though it is not comparable to that of a large deep-water vessel, is possible only by rather drastic levehng of the tunnel-roof slopes,

both forward of and may have to

abaft the propeller position. These

tunnel boundaries farther forward of and abaft the propeller position reduces the displacement

volume aft so that the stern portion of the hull becomes not much more than a cover over the propeller inflow and outflow jets. There are major structural problems involved in stiffening and supporting a long stern overhang with a buoyancy that is small compared with its size and weight. One solution is to raise the deck aft and increase the girder depth, as was done by the Dravo Corporation for the 200-ft pushboats A. D. Haynes II and Valley Transporter [Maritime Reporter, 15 Dec 1955, p. 11]. Another important reason for small fore-and-aft slopes in the roof of a tunnel oyer a screw propeller is to provide as great

possible with a given shaft

an astern thrust as power and a given

HYDRODYNAMICS

670 This

Portion Transverse and

Main Decki^..

1

/

q

|ii,e

Vertical,

Ironsom

IN SHIP DESIGN the

ship

Sec. 72.13

centerline.

The

may,

tunnels

with

propeller shaft axes, even diverge slightly with

distance

aft.

often

It

on the other extremely small,

happens,

hand, that the bed clearance

is

so small in fact that the propellers can not be fed

adequately

One

solution

is

with to

draw

water from underneath. it in from the sides, from

the open regions abreast the hull, using oblique,

G

Afterbody Plan of Twin-Screw Vessel with Oblique Tunnels

Fig. 72.

overall disc area of the propeller (s). All shallowdraft self-propelled vessels are required to do a

great deal of maneuvering.

Furthermore, they

maneuver under the handicap

of sluggish response

because of the limited bed clearance and the obstructions to under-the-bottom flow within that clearance. A configuration of the bottom of

converging recesses that are tunnels in

G

and 72. H, adapted from model fines by A. R. Mitchell ["Tunnel Type

Figs. 72.

published

Vessels," lESS, 1952-1953, Vol. 96, Fig. 9, p. 141], illustrate

screw

one form of oblique tunnel for a twinThis proved its vessel.

shallow-draft

superiority in self-propelled

configuration providing good flow from ahead.

water. Fig.

The

slope of the roof abaft the wheel

to be reduced to the order of 5 deg,

if

may have

the backing

model

tests over a

when run in shallow 24 on page 165 of the lESS reference

vessel with parallel tunnels,

is

a photograph of half the afterbody of a model

built

to this design.

The same photograph

characteristics are sufficiently important.

reproduced in INA, July 1952, Fig.

Contraction of the inflow jet to the propeller allowed for by flaring the sides and widening the tunnel from aft forward, in much the same

page

is

the tunnel between twin skegs is widened. The same effect is achieved by progressively increasing the radius of the tunnel

manner

as

only.

able to their use.

the hull and the tunnel roof which facilitates is therefore almost as important as a

flow from aft

name

These oblique tunnels were developed at least as early as 1938 and were said to have performed well in service, when the conditions were favor-

Results

148.

of

rather fully on pages

the

tests

10,

are

is

facing

described

143 through 150 of the

Mitchell reference.

For

a

tunnel-stern

towboat,

built

without

oblique tunnels, on which the flow to the propellers

was inadequate because

of limited

bed

from aft forward. customary to drop the elevated tunnel

clearance under the hull in shallow water, L. A.

the propeller position until at the extreme stern it meets or falls just below the at-rest water level. This prevents air from being

building a large-diameter duct through the hull

roof, also

It is

roof abaft

drawn astern.

into the tunnel

when the

It also keeps debris

the tunnel from aft

when

rise to

length required

an easy slope abaft the propeller positions may be as much as 0.15 or 0.18L; that for a 14-deg maximum slope forward as much as 0.23

for

to 0.25L.

For vessels having two or more screw propellers, customary to provide a separate tunnel for each propeller. If the vessels are to run in regions where there is enough bed clearance to permit a

it is

water to the propellers fro7n under appears best for the tunnel recesses ahead of the propeller positions to be parallel to of

the bottom, it

by

Fluid Mech., Univ. of Minn., Jun 1953, pp. 406,

is

an added thrust-deduction force which detracts from the propelling power, described in Sec. 25.20 and

good flow

effected a solution

at rest.

Unfortunately, this shape also gives

The

Ormondroyd

floating into

the vessel

earlier in the present section.

J.

for each propeller. This duct took in water forward, above the baseplane, and discharged it downward and aft through the tunnel roof ahead of the propeller [Third Midwestern Conf. on

propeller rotates

from

Baier and

411].

Waas shows

H. river

craft

a twin-screw shallow-draft with propellers far outboard, each

housed in a tunnel that fits the tip circles closely but is of limited circumferential extent. A partly underhung, balanced rudder is fitted abaft the skeg endings just outboard of the wheels. The propellers are carried by struts forward of them [STG, 1952, Figs. 16, 17, p. 213]. If the exposed positions of the blade tips of the propellers can be accepted, there is no reason why the tunnel in which they work can not extend abaft the propeller in a direction nearly horizontal.

The

elevated portion of the outflow

acted upon by gravity forces,

falls

jet,

at a certain

Line of Top of Roof or

Crown

of

Bottom Outboard

Line, of

Tunnel

The Afterbody Plon

of

of

OUTBOARD

Hull

PROFILE

Tunnel

of

This Vessel

is

Shown on

72.&

Fio.

FISH-EYE VIEW, STARBOARD SIDE

L<£, 10.5

II

Fig. 72.H

10

9.5

9

Stations

Outboard Profile and Fish-Eye View of Vessel with an Oblique Tunnel

The top downward shghtly to

rate; in addition, the jet contracts aft.

when the

of the tunnel can be bent

the flap levels out;

take care of these two propeller,

when

effects. It is

easy for the

rotating ahead and accelerating

propeller

the waterline.

A

is

starting.

its after

good tunnel

seal

is

The

conditions of loading.

in all

When underway

end usually

rises above maintained

resistance

is

the vessel in that direction, to sweep the air out

lowered because of the reduced inclination of the

and to fill it completely with water. However, keeping debris out of the propeller and

automatic

keeping air out of the disc when going astern, as

is

of the tunnel

mentioned previously, require a closure for the if the after end is not closed in some way the craft may not go astern at all. Making this closure by dropping the tunnel roof is not always the best solution, especially when there are large changes of draft aft. This difficulty is overcome by a simple yet effective hinged flap, after end. Indeed,

tunnel roof abaft the propeller. Going astern, the flap is forced

down onto

a

sill,

set at the lowest point of flap travel.

which This

maintains the seal in the tunnel and the propeller continues to work in solid water [Mitchell, A. R., lESS, 1952-1953, Vol. 96, p. 183].

When

the change in draft aft

small,

is

for

various service conditions, tunnel endings with

5tern

of

Vessel

introduced by A. F. Yarrow in the early 1900's, which may be lowered to close the after end of the tunnel. Fig. 72.1 shows schematically the arrangement of a device of this kind. The flap forms the upper part of the tunnel

-Flop

in

when Underway

Roise^-^Position, as

-Ap proximate

Lme

Woterline

of Hull,

ending, either close abaft the propeller or at a it. The raising and lowering be done mechanically or automatically; in

short distance from

may

Flop 03

in

is

L

Ootboard of Tunnel

\

Lowered Position

when Stortinq or Backinq

Vertical Curtoin Plates

on Each Side of Tunnel,

by the outflow the proper angle. The flap

the latter case the force exerted jet holds the flap at

I

I

Between

which the Flop F,ts Neatly

i

Propeller

'

^—

sealed along

of a foot

its sides. Its lower edge is a fraction below the at-rest waterline, with the

vessel in the light condition, so as to exclude air

Arrangement Sketch op a Hinged Flap Closing the After End of a Propeller Tunnel

Fig. 72.1

HYDRODYNAMICS

672 small

down

slope give satisfactory performance

and avoid the added complications

IN SHIP DESIGN an example

Sec. 72.14

what not

of

The

do.

to

hoisting

ago, that the design of a tunnel-stern craft should

can be of the recessed type, similar to those illustrated in Fig. 75.F. The doublers can be converted to thick, single-layer shell plate

be such as to enable the vessel to pivot longi-

and the strut-arm connections can be

tudinally about the fore-and-aft position of the

within the hull.

matic

flap.

Ward

C. E.

propeller(s)

as

of the auto-

pointed out,

many

the loading changes

years

[SNAME,

1909, p. 100]. In other words, the draft at the

propeller

position should

constant

with

volume and the

remain more or less in the displacement

changes trim.

If,

instead, the draft at the

stern can be kept nearly constant, the tunnel

remains closed at

its after

fittings

end to the same degree

and a tunnel flap is not necessary. One problem in twin- or multiple-screw tunnel sterns, where a propeller is mounted so close to

The is

entirely

strake or ring of plating abreast the wheel

preferably

made

heavier than

the rest,

ship in Figs. 67.0 and 73.F. It

is

as

ABC

illustrated for the arch type of stern of the

to be held in

by substantial internal framing. of any access hatch over the pro-

position securely

Careful fitting

peller is necessary to insure a flush surface in

the roof. Bolts, nuts, and other securing devices

the ship or tunnel side does not

hatch are to be kept clear of the tunnel The curved under surfaces of all tunnels, both ahead of and abaft the propeller positions, are to be fair, with sufficient stiffness to remain so and to avoid panting and vibration. The Germans have proposed for small tunnel-

project far enough below the actual waterline to

stern craft that the portion of the tunnel roof

form an adequate pressure barrier, air is sucked under and into the propeller. Large chunks of air striking the propeller produce objectionable noise and vibration. L. A. Baier and J. Ormondroyd report that "vicious stern vibration" on a twinscrew towboat, resulting from air leakage of this kind, was corrected by adding vertical streamlined fins outboard of the propellers [Third Midwestern Conf. on Fluid Mech., Univ. of Minn., Jun 1953, p. 406].

directly

the side that the hull plating forms virtually one side of the tunnel,

is

that air

is

be drawn

liable to

into the inflow jet because of the reduced pressure there.

When

The necessary thrust-producing easily

area

ilo is

not

limited

is

by a shallow

draft.

Tunnel-stern craft are, therefore, usually designed to be driven is,

by two,

three, or four screw propellers.

however, the case of the tunnel-stern

tugs built for six

Yukon River

service in 1898, with

screw propellers, each 3.33

beam ASNE, Aug a total C. E.,

diameter, on

ft in

Jun 1898; 1898, Vol. X, pp. 740-745; Ward,

of only 32 ft [Mar. Eng'g.,

SNAME,

72.14

The

1909, pp. 105-106].

Hull Surfaces Abreast Screw Propellers.

hull surface in

way

of the small tip clearance

provided under the roof of a tunnel should be flush, free of

without

seam

laps

projecting

and

rivet

rubber rather than 7,

by A.

[STG, 1952, Figs. 6 and a structural advantage,

steel

pp. 207-208]. There

is

and possibly a lessening of the vibratory forces the hull boundary in way of the propeller tips

if

yields with the pressure variations in the blade

The

fields.

effect of a yielding

boundary on the

continuity and other characteristics of the water is not known well enough to justify the use of a resiUent boundary as more than an experiment.

flow

Powering of Tunnel-Stem

72.15

self-propelled

propellers

shallow-draft

must

vessel

R.

Mitchell

finished

screw

any appreciable sector

state of the art, enclosing

of the tip circle within a tunnel recess reduces

both the propulsive coefficient propeller thrust T{\

—

t)

-qp

and the

effective

at low speed. This

is

undoubtedly because of excessive thrust-deduction forces on the tunnel roof(s) for relatively long distances ahead of and abaft the disc positions. In any case, available published data, principally those of A. R. Mitchell [lESS, 1952-1953, Vol.

employ a value

of

-qp

if

for speed

ever

is it

and power

predictions greater than 0.50. Indeed, Mitchell

goes so far as to state that:

[lESS,

1952-1953, Vol. 96, Fig. 15 on p. 155; INA, Jul 1952, Fig. 6 opp. p. 147], with its protruding strut-arm pads, doublers, and hoisting eyes, is

with

face the fact that, in the present

safe to

The

The

Craft.

naval architect and marine engineer designing a

96, pp. 125-188], reveal that rarely

it.

of

In other words,

points

good workmanship can make illustrated

and preferably and welding and smooth as

made

over the screw propeller be

resilient instead of stiff material.

butts,

heads; in other words, as fair

tunnel

surface.

obtained with a single screw propeller

whose diameter

There

for this

it is most unmse to guarantee speed when the depth of water under the keel than the draught of the vessel" [INA, Jul 1952,

"Generally speaking,

a

specific

is less

p. 152].

DESIGN FOR CONFINED WATERS

See. 72.17

In this connection

Twin screws

to be noted from Figs.

it is

72.E and 72.F that whereas the Hillman boat depicted there carries a pair of screw propellers having a diameter large in proportion to the draft, there is only a vestige of a tunnel in the afterbody plan. Further, the down slope abaft the propeller position is rather small. This craft reported to perform excellently in all respects, and the principal reason given is the free flow of water to the wheels [E. W. Easter, unpubl. Itr. of 2 Feb 1951 to HES]. 72.16 Handling of the Vibration Problem in Shallow Water. Sees. 35.13 and 35.14 describe the manner in which vibration of the ship hull and its many smaller elements is manifested in motion of the water and is magnified in a shallowwater region. The only known method of avoiding

tunnel recesses. (4)

these objectionable effects

The

by the blades

forces generated

pulsion

reduced,

are

devices

periodic

(5)

(6)

explained

means be provided whereby

from another

This

direction.

it

(8)

(9)

man-made

attractive they

72.17 Vessels.

may

paths,

(11) "Mississippi- Warrior

There

is

shallow-water

sterns but unfortunately

and

descriptive.

section lists

and most

The

some

of the

craft

much

of

tunnels, with a tip emergence at rest of

0.37D.

(12)

tunnel

superficial

partial bibliography of this

ones, omitting

many

Thomycroft, Rivers,"

(2)

(3)

Sir

"Steamers for Shallow Magazine, Marine Number,

Cassier's

Jul-Aug 1897, Vol. XII The twin-screw river gunboat H.M.S. Sheikh is described briefly in ASNE, Feb 1898, Vol. X, p. 230 Notes concerning the "Ught^draught gunboats" Heron and Jackdaw, built for the British Navy, are to be found in ASNE, Feb 1898, Vol. X, pp. 227-228 and May 1898, pp. 556-559. These vessels are 100 ft long by 20 ft wide by 2 ft draft.

Each

9.33 ft

propeller

has

P =

ft.

and

8.5

four

blades,

about with

"Experimental Towboats," House (of Representatives), 63rd Congress, 2nd Session, Document 857, 1914, Vol. 27. This is the full report of a most comprehensive investigation, both in America and abroad, to determine the best type of shallow-water

towboat and towed barges

for inland waters. It

and screw-propeUer comparative tests on models of radial

vessel forms for paddlewheel

of

John,

ft

gives the results of a multitude of model tests on

drive

those containing general descriptions only: (1)

and

200

long by 40 ft beam by 10 ft depth, with a draft of 6.5 to 7 ft. There are two propellers operating in

of the older technical references

modern

article describes

illustrates the vessels of the Natchez class,

D =

with

it is

I,

different

River Towboats," Mar. Eng'g.,

Jun 1921, pp. 432-437. This

appear to the eye.

on Tunnel-Stem a vast technical literature on

much

R. C, "Construction and Operation of Western River Steamers," SNAME, 1913, pp. 59-66

no matter how

Partial Bibliography

self-propelled

Teubert, O., "Die Biuuenschiffahrt (Ship Operation

(10) -Wilson

geometrically similar boundaries, that the water follow

1903,

Yarrow, A. F., "The Screw as a Means of Propulsion for Shallow Draught Vessels," INA, 1903, pp. 106-117 Ward, C. E., "Shallow-Draught River Steamers," SNAME, 1909, pp. 79-106 and Pis. 23-86; especially pp. 96-101

pp. 476-481. A second edition, not from the first, appeared in 1932.

behind the oblique tunnels described in Sec. 72.13. However, it can not always be assumed, without the confirmation of flow tests with will

Navigation

and Inspec-

ATMA,

on Inland Waterways)," Leipzig, 1912, Vol.

can come in

the reasoning

is

la

h.

ships. (7)

such as those of high wake. When water can not flow freely to a propulsiondevice position from one direction, because of confined-water limitations, good design dictates

also

Vol. 14, pp. 298-300. This paper contains drawings of eight types of tunnel sterns for shallow-draft

in certain regions,

that

or 9.13 kt.

Int^rieure (Note on the Construction tion of Ships for Inland Waters),"

in

by reducing the thrust loading, using larger thrust-producing areas and lower slip ratios; then by cutting down the high loading Sec. 33.15, first

mph

Ward, C. E., "Speed and Power Trials of a LightDraught Steam Launch," ASNE, Feb 1898, Vol. X, pp. 183-192. This was a tunnel-stern, single-screw craft, 60.5 ft by 10.5 ft by 4 ft depth, with a draft of 1.83 to 2.0 ft and a weight of 12.03 tons. The propeller had a diameter of 2.5 ft. The art of designing these craft would have advanced much more rapidly than it did if all trial results had been published in as complete a form as given here. De Berlhe, B., "Note sur la Construction et I'fichantillonnage des Navires Destines

of various pro-

as

10.5

is

ASNE, May 1898, Vol. X, pp. 509-510; ASNE, Aug 1898, Vol. X, pp. 783-785

eliminate the

to

is

The speed

Brief notes on "light-draught steamers," specifically

the Melik and the Sullan, are to be found in

is

vibratory forces at their source.

ri73

3.41 ft in diameter are fitted in twin

and

of

and feathering paddlewheels. (13)

"Experimental Towboats," House (of Representatives) 67th Congress, 1st Session, Document 108, 1922, Vol. 9. This report, of 194 pages, describes the full-scale trials made as a result of the recom-

mendations in House Document 857. Since so many different experiments were tried by modifying at least three different existing craft, the results were inconclusive, as could

have been expected before

they were begun. (14)

McEntee,

W.,

"Model

Experiments

with

River

HYDRODYNAMICS

674

—Stern-Wheel

and

"Der Dreischrauben-

carrying 4 flanking rudders, 2 steering rudders, a

schlepper Direktor Schiiiter (The Triple-Screw Tug Direclor Schluler)," WRH, 22 Feb 1929, pp. 59-61.

and a single propeller inside a Kort nozzle. Dawson, A. J., "The Development and Economic Potential of Inland Waterways Transportation," First Pan-Amer. Eng. Conf., Rio de Janeiro, 15-24

Towboats Pis.

and

SNAME,

Tunnel

Propeller

1925, pp. 63-66

(21)

44 through 60; also pp. 83-90

Foerster, E.,

and

Shows a tug

Stapcl, G.,

for inland waters with three screws

single-tunnel stern,

(22)

abreast in three tunnels. (16) Hinz, M.,

and Lang, H., "Der Dreischrauben-Motor-

schlepper Amsterdam (The Triple-Screw Motor Tug Amslerdam)," WRH, 7 Feb 1930, pp. 43-48. Shows

body plan and stern lines of a shallow-water tug having three screws abreast in three tunnels. (17) Brodie, J. S., "Modern River Towboats," SNAME, 1936, pp. 350-388 (18) Dawson, A. J., "Power of Shallow-Draft River Towboats," SNAME, 1937, pp. 145-159 (19) Tunnel-stern

towboat

1939, p. 172.

A

St.

Louis Socony,

profile of this craft

MESR, Apr

shows a 10-deg

slope to the tunnel roof forward of the propeller

(20)

Sec. 72.17

"Standardized River Towboats," AM, Oct 1948, pp. 36-39. This article shows stern and bow photographs and an outboard profile on a vessel

Tj^pes Compared,"

(15)

IN SHIP DESIGN

and an I1.2-deg slope in the after portion. The tunnel roof embodies sharp transverse knuckles with no rounding. Edwards, V. B., and Cole, F. C, "Water Transportation on Inland Rivers," SNAME, HT, 1943, pp. 400-422, esp. p. 412

(23)

Jul 1949, esp. pp. 5-21 Alaskan river boat. Rudder, Aug 1951, p. 41. This vessel has a length of 64.5 ft, a beam of 17.33 ft, and a draft of only 1.0 ft, with a tunnel stern. With a brake power of 165 horses it is designed to

make

11 kt.

(24) Mitchell,

A. R.,

"Shallow Draught Ships," INA,

Jul 1952, pp. 142-153 (25) Mitchell, A. R., "Tunnel Type Vessels," lESS, 1952-1953, Vol. 96, pp. 125-188. This is a compre-

and informative paper, well and ship-test data and generously illustrated with drawings and photohensive, instructive,

supplied

with

model-

"Ein Neuer Schiffstyp mit Grossraum(A New Ship Type with an Enlarged Tunnel)," STG, 1954, Vol. 48, pp. 154-164.

(26) Jastram, H.,

tunnel

CHAPTER

The Design 73.1

of the Fixed Appendages

General Rules for Design of Fixed Objects

a Stream The Design of Leading and Trailing Edges in

73.2 73.3 73.4 73.5 73.6

.

The Stem Cutwater Selection of Struts or Bossings

Strut Design for E.\-posed Rotating Shafts Strut- Arm

.

Speeds

Appendages for the Arch-Stern ABC Design Layout of Contra-Struts Abaft Propellers The Design of Bossings Around Propeller

73 10

Design Rules for Defiection-Type or ContraGuide Bossings Vertical Bossings as Docking Keels .... Design Notes on Fixed Screw-Propeller Shrouding; The Kort Nozzle Shaping and Positioning of Contra- Vanes Abaft Paddlewheels Design Features of Supporting Horns for Rudders; Partial Skegs

.

Shafts

73.11

73 12 .

73 13 .

73.14

73.15 675 675 676 677 678

Section Shapes for Ultra-High

73.7 73.8 73.9

.

73

680 681 682 682

686 686 687 688

690

73

HYDRODYNyVMICS IN SHIP DESIGN

676 is

it

so constant in service that cavitation or

separation does not occur on one side or the

other of the nose (b)

Lengthening the long nose or entrance inand the friction drag Thinning the entrance or nose renders it

creases the wetted area (c)

vulnerable to

There the (d)

damage and the

also

is

susceptible to corrosion.

cavitation

of

possibility

if

body runs at an appreciable yaw angle. A Umber entrance is easily set in vibration by

periodic external disturbances.

At a

free-water surface, a leading edge can

rarely be too thin to reduce resistance, spray, feather,

provided

random

side loads

it

is

and

strong enough to resist

and has enough

lateral stiffness

to hold itself firm against lateral vibration.

A thin

leading edge projecting through the surface

vulnerable to

damage by

is

floating debris.

As the depth below the

free surface increases,

the leading edge can be thickened,

if

there are

advantages to be gained thereby. However, this is to be done with caution, having in mind the following: (1)

There

is

ample

pressure available to

hydrostatic

make

or

pumping

the liquid close in

around the body abaft the nose (2)

A

Section

semi-circular leading edge joined to the

Proposed by

NACA Symmetricol

P Mandel,

Ip Abscissa

ID'S fi

5NAME,

Section, t/c-l/e

EM^^^NovySt'd. Strut Section

/

in

per cent

/

5

ip >!

1953

/

of

o

TMB

EPH

/Section

o "^ip

W^

,^'V__ Nose Radius 0.015

Chord c

c.

Sec. 73.3

FIXED-APPENDAGE DESIGN

Sec. 73.4

Waterline slope at the stem nearly to zero

677

and I

smooths out

local discontinuities at the

same time.

Ur

In fact, shell plating may be applied to the outside of a stem without a rabbet if faired by such a

The

device.

4;o

Q545->]]-

FP

Saction

Plan

at 26 Designed

Waterline

slope of a cutwater, in a horizontal

plane, need rarely average less than 5 deg, or

about about

in 12. Usually, a slope of 6 or 7 deg, or

1

in 10 or

1

1

in 8,

is

small enough.

may

radius at the extreme leading end or

The

less.

nose

A

is elliptic

rather than circular. itself to

modern

methods, and adaptable to a bulb bow,

ABC

ft

waterline section at the extreme

design lending

for the

The

be 0.04

ship in Fig. 73. B.

the false stem or cutwater

fabricating is

sketched

The space

is filled

inside

with a light-

weight, water-excluding, and rust-resisting material such as a foamed-in-place resin. This prevents

the nearly flat sides from panting under the pressure variations they are likely to encounter at high speed

an

and takes care

of

maintenance for

The sharp, "soft" cutwater is obviously not adaptable to a vessel which must, during a turn-around, have its nose pushed up against a pier or quay. For a ship with bower anchors in the cutwater

enough to withstand the the bow.

The wetted

is

made sturdy

pull of a chain crossing

surface of a stem cutwater

73. a

is

is

a

there-

Design of Cutwater fob the

added to the taken

account

Since

leading edge,

where the

resistance coefficient

the

it

ABC

Ship

an appendage and

latter as

into

friction drag.

when

its

calculating

directly behind the

lies

local

Clf has

specific

its

be

cutwater surface should

friction

highest value, exceptionally

smooth. 73.4

designer

continuation of that of the main hull. It

TABLE

fore

surface

indefinite period.

side hawsepipes,

Fig. 73. B

Selection of Struts or

may

find useful a

Bossings.

summary

The

of the ad-

vantages and disadvantages of both struts and bossings, so that all phases of the selection problem

Comparison of Design, Construction, and Operation Features of SuArr Struts and Bossings

ADVANTAGES Bossings

Struts

Access to more shafting and shaft bearings without docking Protection of shafting and bearings (except propeller

Lighter overall weight

Less volume and weight displacement More precise alignment with flow

bearing) from foreign matter, wear, corrosion, incidental

Smaller shadowing effect of appendages projecting from hull

Less overall first cost Less liability of vibration due to periodic forces exerted

on hull by propeller

damage, and major damage from striking piles, buoys, and chains Some degree of pitch damping and steadying effect in a following sea Appreciable reduction in shaft power due to deflection or contra-guide features, if employed Greater average wake fraction at propeller positions

DISADVANTAGES Struts

Inadequate protection of exposed shafting from corrosion or from damage to corrosion-resisting coating or Less protection of shaft and propeller bearings from foreign matter, wear, and striking large objects such as buoys and their mooring chains Greater liability of cavitation ahead of propeller, with

and corrosion

Probably greater overall

first

cost

Greater hability of irregular flow abaft bossing termi-

covering

erosion

Greater overall weight

of strut

arms

nations Greater periodic vibratory

forces

exerted

on hull by

propeller

Reduction of maneuverabihty and turning characteristics

HYDRODYNAMICS

G78

may

may

be studied and the merits of each

new

assessed for every

design as

Whatever the advantages

to be closed

is

up

The workmen who

completely from the outside.

have to get inside

any

of these bossings for fabrication,

erection, riveting, or welding are of more-or-less

who must take

fixed size, as are those

and maintenance

repairs

care of

for the life of the vessel.

For these reasons bossings are

little

used on small

vessels.

Table 73. a summarizes the advantages and disadvantages inherent in the great majority of

and bossing

strut

The comments

installations.

apply to single-screw and triple-screw ships as well as to the arrangements customary on twin-

and quadruple-screw It

to

is difficult

vessels.

make any

general statements

power to be achieved by the use of either shaft struts or bossings in any particular case, assuming that concerning

reductions

in

shaft

alternative designs benefit from the

to

other

causes,

indicate

the wisdom

of

the limit given.

a low limit to a

is

bossing size unless the latter

and

Sec. 73.5

avoiding them unless the arms are shorter than

it arises.

of bossings for

particular application, there

be

IN SHIP DESIGN

The proper

or

best shape of the strut-arm

section has been the subject of long

study, based

upon structural as

dynamic considerations. The between the various shapes

and careful

well as hydro-

differences in drag of long-established

usage are small, even in proportion to the total appendage resistance. It is probably more

important that the strut arm as installed conform closely to some specified shape, worked out by a long development process, than that the shape be of a particular kind or have special characteristics. The section delineated by D. W. Taylor, used in U. S. Naval vessels for many decades past, could have been shorter for the same thickness, with a c/tx ratio of 6.0 instead of 7.5. This would have involved cutting off only the tail; in fact, this portion often disappeared anyway as a result of erosion, pitting, or rusting in service.

Excellent replacements are the:

same amount

native strut and bossing designs through to the

(a) EPH or Ellipse-Parabola-Hyperbola section developed by the David Taylor Model Basin during World War II. This has a trailing edge sufficiently blunt to get rid of the previous difficulties with fabrication and corrosion of the slim Navy Standard strut. It is not so blunt as

model stage at

to

[Mandel,

and

experimentation,

study,

of

SNAME,

P.,

development

1953, pp. 466-468].

The

designer of a large or important vessel, or one

which

to serve as the lead ship for quantity

is

production,

is

least.

Design

Strut

73.5

Shafts.

If

weight

the

bulky bossings left

believed justified in carrying alter-

is

for

Exposed

Rotating

displacement

of

large

undesirable, propeller shafts are

exposed, carried by water-lubricated bearings

supported from the hull by double arms set in the form of a Vee. For certain applications, single

arms have been employed, especially when they are short and can be given adequate rigidity. Parsons used a number of them successfully on the three shafts of the Turbinia in the 1890's

[SNAME, modern shaft

1947, Fig. 10, p. 105].

However, more

experience, \vith larger sizes and higher

powers,

indicates

that

when

the

single

arms are longer than the maximum strut-hub diameter they suffer from:

Lack

(b)

PossibiUty of resonant lateral vibration as a

flow

Excessive lateral loading by

when

separation

Magnus

lift

Effect

due to cross

turning, or both. Fractures of

modern

single-arm struts in service, due to transverse

lift

produced by cross flow when turning, to vibration,

eddy

and

sizes (b)

normally used for shaft

Section proposed

by

P.

struts.

Mandel [SNAME,

1953, pp. 468-469], with a c/tx ratio of 4.3.

The comparative proportions and shapes

of the

NACA

symshown graphically in Fig. 73. C. The abscissas and ordinates for constructing the section outlines accurately are tabulated by Mandel [SNAME, 1953, Fig. 3, p. 468]. Many other characteristics are described by him, three sections mentioned, plus an

metrical section, are

with design considerations involving both structural and hydrodynamic features. Of far more importance than the shape of the together

is

the placing of this sectiori in

the local direction of flow so that in service

of lateral stiffness

cantilever weighted at the outboard end (c)

objectionable

strut-arm section

(a)

on the shaft, or hydrodynamic

cause

buffeting of the trailing portion in the absolute

yaw

it

runs

is

true

that the local direction of flow changes with

yaw

with no

angle or angle of attack. It

during steering, with rate of swing during turning, and with ship position during wavegoing. It may

change with displacement, draft, and trim. it probably remains constant within a degree or so at all normal operating speeds in also

Nevertheless,

FIXED-APPENDAGE DESIGN

Sec. 73 "15

5cQ e l

of

Ordin ates

Chord C

x-Distonce from Leodinq

Fig. 73.C

Edqe

straight-ahead motion on a given course. seems reasonable to assume that the ship running in this fashion for about 98 per cent of

It is

its

operating time.

The proper

angle can be estimated after a

around the stern as Nevertheless, good design requires an experimental determination on a model with special apparatus. It is preferred, because of the influence of induced velocity in the water passing into a propeller disc, that the strut-arm section angles be determined while the adjacent propeller is delivering normal thrust. This can be done, along the lengths of the two struts of a pair, by apparatus described and illustrated by H. F. Nordstrom [SSPA Rep. 32, 1954, Figs. 22 and 23, pp. 30-31]. Twisting the strut arms to suit the angle of flow is usually an inconvenience when the struts are built, but failure to align the strut sections with the flow, especially ahead of a propeller disc, only invites trouble by setting up disturbfashion, using data for flow

given in various chapters.

ances in the inflow

Whether a

jet.

two or more arms lies ahead of or abaft a screw propeller, it is well to avoid a strut-vee angle (see Fig. 36. B) which is nearly or exactly the same as the angle between two blades which may be passing the arms simultaneously. A convenient example in this respect is

strut with

the four-arm strut abaft the 4-bladed propeller

of the arch-stern

ABC

ship, described in Sees.

73.7 and 73.8 and illustrated in Fig. Sec. 73.8.

When

73.F of

looking forward on this vessel,

consider the radial position of the lower port strut arm as zero angle. With spacings and 75 deg between the three pairs

of 75, 60,

of arms, reckoned in a clockwise direction, the angular

positions are tabulated as follows: Lit

Arms

in

Per

Cent of Chord c

Half-Sections of Five Strut Shapes

679

HYDRODYNAMICS

680

IN SHIP DESIGN

A Circle Tbni^ent to the

Both Dioqrams are

Inner Sides of Both Strut Arms and to the. Strut Hub Should Hove a Radius Not Less Than That of the Outside of the Hub

Projected Forward on

Transverse Plane

hole in the water

Sec. 73.6 is

certain to form at the free

surface abaft the strut, because of the low hydro-

pressure there.

static

separation abaft the

The minutest degree the section

tail of

is

of

almost

certain to provide a reduced-pressure passage for

extending from the hole at the surface all to the propeller hub. Here the air

air,

way down

the

the manner by Fig. 2.3. D, reduces the thrust, and creates noise and vibration. If it ever becomes necessary to carry or to rig a strut section which must come to the surface, passes into the propeller disc in illustrated

a

subsurface plate resembling those in Figs.

flat

7.E and 36.0

is

attached to

it

just below the

surface and in the line of flow. This plate prevents air Strut VeeAn(5le Should Be

Greater Than 50 dea

Good

Flow and

for

from leaking down through the bottom

of the

An

extra-

hole in the water, just abaft the strut.

long fairing strut

Fig. 73.

D

Hydrodynamic Requirements for Strut-

these go through into the hull, no fairing if

When

is

neces-

they stand normal to the shell or nearly so. the transverse reentrant angle at the shell

becomes 70 deg or less, a fillet some convenient method. The

introduced by

is

fillet

radius in-

becomes smaller. bend the strut arm and have it enter the hull nearly normal to the shell. Struts are attached to the hull by external palms only when no other method can be used. The palm endings are sloped and faired so that a creases as the reentrant angle It is often possible to

section through them, in the direction of flow,

approximates that of one side of a standard (or acceptable) strut section.

Normally

it is

not necessary, for hydrodynamic

reasons only, to mcrease the length or the fineness of a strut-arm section

strut

hub

where

attaches to the

it

or to the shell. If fairing

is

required on

the sides of the section, for structural or other

a longer termination

reasons,

necessary

if

is

the section fineness

the surface or to throw inordinate amounts of

that surface

is

It

may

is,

square to the baseplane. tilt them out

often be better to rake or

if they can be shortened thereby, can be placed more nearly normal to the direction of water flow, or if better attachments can be made to the hull structure. The angle of rake or sweep-back can be as large as 30 deg

of these planes if

their axes

If piercing

with the transverse plane.

the free

unavoidable it is best to rake the strut down and forward. This creates less separation than when raked down and aft, as explained in surface

Sec.

is

36.17 and illustrated at 5 in Fig.

36.0.

Strut-Arm Section Shapes for UltraHigh Speeds. For planing craft which operate 73.6

at high speeds

and

for ultra-high-speed racing

motorboats the exposed propeller shafts are invariably carried by single-arm or V-type struts. The submergence of these struts is small because hence the cavitation At the high speeds impossible to make a

of the relatively small draft,

index

is

correspondingly low.

at which they travel

it is

strut section sufficiently long to be free of cavita-

tion over its after portion.

It

is

the practice

to be main-

these sections, making the entrances fine and narrow, and terminating them in square or boattail endings in the manner illustrated in Fig. 73. E.

is

propulsion performance at a displace-

ment and trim corresponding

customary to place the strut-arm axes in

transverse planes, that

therefore to utilize only the forward portions of

Under no circumstances should an upper strut arm join the hull at a point above the free-water if

the

automatically

tained.

surface

if

not to create excessively large waves at

is

It is

with the strut hub are lengthened with largeradius fillets forward and aft, principally to give stability of position to the strut hub. At the hull ends of the strut arms, provided sary

necessary above this plate

spray.

Hub

AjiM Positions at the Strut

is

Ricjidit'y

to the position of

considered of major importance.

They then resemble

the transom stern on a fast

motorboat. Single struts having blunt ends may be placed forward of the propeller provided there is an exposed sloping shaft ahead of the strut.

FIXEID-APPENDAGE DESIGN

Sec. 1^.1

681

built-up propeller

Direction of Motion

Not More Thon About

more simple and sturdy, with

a smaller hub diameter.

As an

(e)

alternative

to

(c)

or

separate

(d),

blades of alloy or corrosion-resisting

steel.

These

be solid or, as in an Italian proposal, may be of hollow cellular construction, with welded

may Fig.

73.

E

Boat-Tail Strut-Arm Section for High Speed

ditch made by the shaft may be large enough so that the water clears the strut arm

The open

altogether. It

often possible to place a fixed single-arm

is

strut abaft the propeller

and to use

it

as the

forward or fixed portion of a compound rudder. The forward edge of the rudder blade is close behind or is mounted inside the after edge of the strut arm.

Appendages

73.7

Design.

for

the

Arch-Stem

67.16 describes the

Sec.

general

ABC con-

siderations governing the design of appendages at

the after end of the

ABC

ship with the arch-type

some of the details. A few addinotes are added here to cover certain

stern, as well as

tional

features illustrated subsequently in the following

parts of steel plate [SBSR,

or the blades

p. 459].

may

be welded to short stubs, made

ruple-arm strut hub in Fig. 73. F.

A

(f)

propeller-bearing sleeve which

is

mounted

in its housing at an angle approximating that of

the slope of the propeller journal

when

all

parts

are in place

A propeller-bearing sleeve which is

(g)

aft

from

its

withdrawn

housing, to afford ample clearance for

the propeller journal

when

installing the propeller

from the ship (h) A propeller journal surface of heavy chrome plating with a ground finish, thus eliminating a bronze sleeve which might cause corrosion of the propeller journal and the hub assembly or removing

(i)

Contra-struts abaft propellers, Fig. 73. F of

Oct 1953,

integral with the hub, illustrated for the quad-

drawings: (1)

1

Each blade may have its own root palm or flange, welded to the steel hub and to the adjacent palms,

it

A strut hub of cast steel with the usual internal

circumferential

lands

bearing sleeve.

To

for

the

carrying

shaft-

the outside of this hub are

(3)

cast four short arms, curved in contra-fashion to permit the inner or shaft ends of the strut arms, fabricated from heavy rolled plate, to be buttwelded to them. The fillets at the forward and

flange connections to shaft,

after ends of the strut-arm connections at the

Sec. 73.8 (2)

Short bossings for propeller shafts. Fig. 73.

of Sec. 73.9

Large propeller, built up by welding, with and twin rudders abaft twin skegs. Fig. 74.L of Sec. 74.15.

The arrangement developed

for the first pre-

nuts,

all

and the

An

taper

fits,

keys, threads, propeller

after shaft or propeller journal

and nuts

in the orthodox fashion for a

As an

alternative to

attached by bolted flanges to the hub at its after end and to the

flanged stern-tube shaft at (k)

A

(c),

its

forward end

rotating shell forward of the propeller to

cover the bolted flange and to serve as a fairing

(1)

A fixed

hub

conical cap of suitable shape

and pro-

portions abaft the propeller-bearing housing or strut hub, forming the after

end

of the stream-

lined assembly comprising the rotating shell, the

propeller hub, the strut hub,

(m)

A

suitable

means

and the

tail fairing

of inducing adequate

water

flow through the propeller bearing for lubrication flared rope guard at the forward and cooling.

A

built-up adjustable propeller (d)

readily removable exposed rotating pro-

into the propeller

like

(c) Separate propeller blades, bolted to the shafthub-journal combination with circular flanges,

studs,

A

flanged propeller

which is short and of large diameter, with adequate stiffness to prevent bending and to insure reasonably uniform loading of the bearing surface (b)

(j)

peller shaft,

and 74.L embodies:

(a) An integral forward bolting flange, propeller hub, and after shaft or propeller journal of steel,

eliminating

entirely in the short arms,

cast integral with the hub.

liminary design and indicated schematically in Figs. 73. F

hub are incorporated

separate propeller

blades which are removable but not adjustable.

Eliminating the pitch-changing feature and the necessity for circular blade flanges

may make

the

end

of the strut-bearing

hub and a

large hole in

the after end of the fixed fairing cap, opening into what would be a separation zone or a swirl core

abaft the hole, should be sufficient for this purpose,

HYDRODYNAMICS

682

Layout

73.8

are both

Abaft

Contra-Struts

of

If the propeller

pellers.

Pro-

bearing and the barrel

mounted abaft the

carrying

it

as in the

ABC arch-stern design,

propeller,

the procedure for

laying out contra-struts to hold the bearing barrel or strut

hub

follows in general that described in

Sec. 74.16 for a contra-rudder.

a

much

struts

as

There

is,

however,

smaller background of experience for to

acceptable limits for median-line

angles, twist offsets,

and the

In the design of the

was evident at an

ABC ft,

it

a reference value of

large, in that the median-line slopes

at the leading edges of the struts Falling back

upon the

must often be done, basic offset ft,

is

became excessive.

designer's judgment, as

this ratio

was halved. The

therefore (0.85/2) 2.25 ft or 0.9562

listed at the

bottom

Arch Section at Midlength

Rodlol

of

of the table Strut Arms,

S'.'ib

73. F.

the median-line slope of the leading

mined by using the

relationship described

sin'

in Sec. 07.22. Details of the resulting design of

contra-strut and

hub assembly, with a heavy belt and strut

plate in the shell abreast the propeller

arms, are drawn in Fig. 73. F. considerable

number

of references relating to

contra-propellers and guide vanes, both forward

and abaft a screw propeller, are listed by P. A. van Lammeren [RPSS, 1948, References 136 and 137 on pp. 299-300]. 73.9 The Design of Bossings Around Pro-

of

W.

peller Shafts.

The

first

step in the design of

any bossing, whether long

or short, or of the

straight (fairing) or deflection type,

is

to position

the screw propellers to be carried by

matter

is

it.

covered in Sees. 67.23 and 69.3.

/^boft Propeller Ceni

PositI

Double Extra-Heavy Shell Plateond in WQv of strut Arms Pr opeller

on Fig.

so,

Sec. 7B.S

edge at 0.2Ru„^ is 32.5 deg, although this could be reduced somewhat by changing the shape of the median line. The remaining offsets are deter-

A

arch-stern struts,

0.85 times this radius at O.liZMai of the propeller

was much too

Even

like.

early stage that, because of the

large barrel radius, 2.25

IN SHIP DESIGN

tOR

This

When

FIXED-APPENDAGE DESIGN

Sec. 73.9

the rate of propeller rotation propeller

power

is

known and

is

the

within rather narrow

fixed

and other by the bossings

limits, the size of shafting, bearings,

naechanical parts to be housed

are determined within equally close limits. In

combination with the room needed for internal these features

access,

minimum

the

fix

size

of

certain parts.

The second

step

is

to settle

upon the exact

nature and function of the bossing. Is the short or the long type? Is

and

it

it

to be of

solely for fau'ing

for protection of the shafting

and bearings?

Is it to be of the deflection type, possibly

mth

an auxihary support strut for the propeller bearing, as in diagram 3 of Fig. 36. H? It may be that, under a broad, flat stern, the bossing is to be called upon to serve as a docking keel as well as a bossing.

The at

third step

is

to find the direction of flow

and near the hull surface

occupied by the bossing. bossing

is

in reahty

tight hull. It

is

can be modified

in the region to

be

the long type, the

If of

an extension of the water-

not an external appendage which

and when

later, if

desired.

Because of the length and the appreciable volume of a long-type bossing, the flow around it when in place may be significantly different than that indicated around the bare model when the initial flow tests are made. For instance, suppose that the principal plane of the bossing has been placed over the trace of a flowline observed on the model hull without the bossing. The water which formerly flowed easily along the hull surface is now displaced by the bossing volume. It has to flow somewhere else, and in so doing it may take a route that is not conducive to good flow or good propulsion. A second flow check on the model is therefore indicated, to be followed

by

wake

observations

in

the

propeller-disc

position abaft the bossing, including records of

the directions of the velocity vectors.

A

further

683

have even revealed an extensive uncovering upper surface of the bossing, exposing parts of the upper blades of a propeller carried by it. That portion of a bossing of any type which encloses a propeller shaft is fixed at its after end by the position of the propeller bearing. At its forward end some latitude in position with respect to the emerging shaft is permissible. This depends upon the size of the bossing at that end, the position of the propelling machinery, and other tions

of the

internal arrangements. If the bossing

is

for fairing

and shaft protection only the bossing termination slope /3(beta) and the traces of the bossing body along the hull are established in such manner that flow takes place around it with the least possible interference. It

is

hull.

often difficult to estimate the

and traces

of this flow along the Lines of flow taken on a model, especially

local directions

with a temporary rod in place to represent the bare propeller shaft, are most helpful at this stage. Better

still

are flow directions, indicated

by

flags

or vanes at a distance from the hull equal to the

mean

projection of the bossing at each station.

customary first to sketch the bossing shape on the body plan by stations, sections, or frames. These are supplemented by the traces of bossing flowplanes, flat or slightly curved, passed through the bossing at varying distances from the adjacent It is

main

The

hull.

traces correspond generally to

bound-

intersections of the stream surfaces in the

ary and adjacent layers, diagrammed in Figs. 36.

D and 36. H.

The

transverse slope of a bossing,

only, is approximately normal to the slopes of the section lines in the vicinity. This reduces the wetted area to a minimum and avoids reentrant angles less than 90 deg. Proposals have been made in the past, requiring

intended

for

fairing

such rigid adherence to this rule that the bossing plane is curved in transversely, so as to remain

normal to the section

lines as the latter

become

on the uniformity of flow as it leaves the upper and lower surfaces of the bossing. If a long bossing is not properly shaped and positioned, the flow around it may contain large corkscrew vortexes. It may develop a combination of longitudinal and transverse eddies which

steeper with distance aft, toward the propeller

cause the flow at a given point abaft the bossing

from vibration

check

is

called for

to fluctuate with time.

An

unsteady flow of this detected on a model only with instruments

kind is which are sensitive to these variations. On high-speed vessels, especially those of light draft, where the head of water over the bossmg is necessarily small,

model

tests of

proposed installa-

[Volker,

to

WRH,

1

Jun 1934, pp. 131-132].

When

selecting the transverse slope it

make

sure that no part of the bossing

to the free surface of the water in

condition,

efficient

if

is

propulsion

is

well

lies close

any operating and freedom

desired.

Section shapes for the bossings of twin-screw vessels are to be (a) Sadler,

found in the following:

H. C, "The Effect

of Bossing

Upon Re-

sistance," lESS, 1908-1909, Vol. LII, pp. 147-159

and

PI.

IX. Discusses

termination angle

/3.

effect

of large

and small

HYDRODYNAMICS

684

Simpson, G., "The Naval Constructor," New York and London, 4th ed., 1919, p. 59 (c) Baker, G. S., SD, 1933, Vol. I, Fig. 7, p. 14 (d) Hughes, G., "Model Experiments on Twin-Screw Propulsion, Part I", INA, 1936, pp. 145-158 and Pis. XVI-XX. Four bossings with very small termination angles are shown on PI. XVII. (b)

Eggert, E. F.,

(e)

SNAME,

the bossing sections of

model 3383, stern

S-Sj

(g)

bossing symmetrical about the bossing plane, with

a termination slope angle of 21 deg. (h)

De

Rooij,

G.,

and satisfactory

1953,

p. 241; Figs.

Fig.

562 and

large apertures, small slopes in the bossing flow-

planes,

and sharp

with strength,

The

trailing edges are

and ease

rigidity,

cantilever

rigidity

be

adequate.

blunt

dynamic

the

crowded out the hydro-

designer

must decide whether the

cylin-

which houses the shaft and

the propeller bearing should attach to the bossing tangentially or radially. It structural, mechanical,

rigidity of the bossing structure.

is

is

possible to favor

and other considerations

provided the flow over the entire bossing surface free

from

termination

much

Figs.

crossovers,

eddies,

changes. For example,

portion around the propeller bearing, deserves as attention with respect to fining as the

in

design.

be afforded ahead of it, consistent with proper support of the propeller bearing and adequate actual termination, inboard of the barrel

have

ships

terminations

past which spoke only too eloquently of a struc-

propeller deserves all the edge clearance which can

The

the heavy frame

some

Nevertheless,

excessively

carried

The

shaping the bossing termination, the

of

compatible

of fabrication.

carrying the propeller shaft bearing must certainly

drical or conical barrel

When

two decades of successful adequate proof that

service. It is

tural design that almost

"Practical Shipbuilding,"

252b on p. 105; Fig. 561 on 563 on p. 242.

Sec. 73.9

are fitted have given over

1939, Fig. 52, p. 329, shows

EMB

Van Lammeren, W. P. A., Troost, L., and Koning, J. G., RPSS, 1948, Fig. 54, p. 99 Baker, G. S., INA, 1952, Fig. 13, p. 109. This shows a

(f)

IN SHIP DESIGN

surprising that the vessels to which these bossings

is

36.D and

offset

if

and

abrupt

the plane of the bossing

from the shaft

axis,

as in

73. G, the reentrant angle at the

much more,

bearing hub should be not less than 90 deg.

incidentally, than has often been accorded it in

sections through the bossing term-

Further, the bossing surface on the "full" side need not project much beyond the bearing hub.

by the Newport Dry Dock Company for

long, straight bossings at the stern apply also to

termination of a shaft strut. This the past.

The

is

ination in Fig. 73. G, developed

News

Shipbuilding and

S. Talamanca and class, indicate what can and should be done in this respect. They afford

the S.

the propeller full opportunity for doing

its

in the water trailing abaft the bossing. It

Shell

is

best

not

The

design rules set

down

in the foregoing for

those which might be fitted for twin

PiQt

Fig. 73, G

bow

pro-

on an icebreaker, or for bow and stern propellers on a ferryboat. Short bossings are used primarily to fair an pellers

Twjn-Sorew Bossing Tisbmination Casting fob

S.

S,

Talaimnca and CijAss

FIXED-APPENDAGE DESIGN

Sec. 73.9

Shape of Short Bossing for

73.H

Fig.

exposed propeller shaft where

it

the hull, described in Sec. 75.10. are essentially the

same

emerges from

The

design rules

as for long bossings,

ABC

685

Arch-Stern Ship

not necessarily parallel to those marked by flow indicators directly on the hull. This modification

adds shghtly to the

except that deflection or contra-guide endings are

effect is small.

never incorporated in them because the endings are too far from the propellers. A short bossing is

somewhat

An

example

stabilizing-fin area

but the

appendage producing

of a fixed

coupling or flange which connects the section

a bar of pointed or arch shape, mounted in an inclined position under the exposed rotating shaft of a high-speed motor-

an exposed propeller shaft to the stern-tube

boat. It creates an air- or vapor-filled separation

Were

zone in the form of an inclined ditch, within which the propeller shaft revolves with negligible liquid friction [H. B. Greening patent apphcation]. On most short bossings the flow crosses the bossing barrel around the shaft bearing at a

often required

of

provide a fairing around a

to

shaft just ahead of

it.

it

not for

this,

the

be limited to a projection from the main hull on the inboard side only, filling in the space where eddies would otherwise form and leaving only mechanical clearance next to the fairing could well

shaft.

On

similar effects

considerable angle. either long or short bossings

some pressure

drag can be saved, for an insignificant increase in wetted surface, by "pointing" the outer or upstream surface of the bossing upon which the flow impinges.

To

the customary circular trans-

A

is

fining of the trailing ends

of the bossing flowplane traces is achieved

continuing

the

bossing

termination

by

along the

leeward or downstream side of the barrel. This modification,

along with the pointed arch,

incorporated in the short bossing of the

is

ABC arch

verse shape or section of the outer barrel of such

stern,

added a triangular or Gothicarch portion, about as shown in the two end

To

propeller shafts are sometimes run through the

views of Fig. 73. H, depicting the short-bossing

shell plating

a bossing there

is

design for the arch-stern

amount

ABC

of pointing results in

A

moderate

marked

fining of

ship.

drawn

in Fig. 73. H.

save weight

and displacement, exposed

simply by cutting a clearance opening The stern-tube bearing and the

in the plating.

fittings pertaining to it are

then installed entirely

the leading ends of the traces of the bossing

within the fair lines of the hull.

flowplanes lying generally parallel to the hull in that vicinity, indicated by Sections B-B, C-C,

presented,

and

D-D

of the figure.

The

locus of the "points"

added triangle or arch, when projected on the body plan, lies parallel to the flowlines in that region. At a distance from the hull these lines are of the

filled

as

partly inert water, ference to the flow.

it is

The

recess thus

with the shaft and with

presents no sensible inter-

A

small fairing

may

be

fitted

and astern of the protruding shaft, mentioned in a preceding paragraph of this section and illustrated in Fig. 75.1 of Sec. 75.10. Separainboard

HYDRODYNAMICS

686

IN SHIP DESIGN side

expense of an insignificant increase in volume displacement, weight, and wetted surface. 73.10 Design Rules for Deflection-Type or Contra-Guide Bossings. Ship designers have

sufficient potential

been reluctant to use deflection-type or contraguide bossings on vessels with wing propellers

Sec. 73.10

some kinetic energy into energy and pressure, with an

by the conversion

tion and eddying at this point are avoided at the

of

adequate pressure gradient, to accelerate it inward toward the bossing surface, at right angles to the latter.

In the present state of knowledge,

it is

perhaps

well to hmit the angle between the convex side

because of the uncertainty as to just how much twist can be used and just how it can be worked into them. They fear that this twist may cause

of a deflection-type bossing

eddying, introduce vibration, and do more ultimate harm than good to the propulsion charac-

well to limit the reentrant angle at the after

teristics

and behavior of the vessel as a whole. a deflection-type bossing, even though designed only to reduce the unfavorable component of flow as it enters the propeller disc, requires

60 or 65 deg, reckoned from the adjacent hull

True,

surface.

much

so developed

greater care in shaping than the fairing type

of long bossing. Further,

it calls

for

more thorough

checking by model tests. Separation of flow may occur with careless or improper design, leading to ensuing vibration and other troubles. well

As wdth a contra-guide skeg ending the

twist

and the corresponding same ship design

side of a fairing bossing for the

to a

maximum

of

about 8 or 10 deg.

of a deflection-type bossing to a

he

It is also

minimum

of

end some

When the designer has done his best on paper may try his hand in modeling clay. The bossing is

added to the model and run for may be in a model basin but,

flow directions. This if

at

the flow should be observed in a

all possible,

circulating-water channel.

A flow

test

and a wake

survey, including measurements of velocity

mag-

nitude and direction in the propeller disc, are

is

imparted in a direction contrary to the rotation when running ahead. If the wing propellers are definitely to turn outward, and the stern is of normal form, the bossing termination lies at a small slope fi with the horizontal. With inward-turning propellers the slope is larger than for a bossing of the fairing type. Indeed, the termination may approach a vertical position, with a slope of 70 or 80 deg or

much more

of the propeller blades

than for one of the fairing type.

more.

power at

The

necessary for a deflection-type bossing

designer

who

is

looking

—and hoping—for

a real reduction in shaft power, of the order of 5 or 10 per cent, such as that achieved on the U.S.S. Warden, should not be discouraged when a

first

attempt at laying out a deflection-type

bossing produces erratic flow around the propeller

may

illustrates

produce no reduction in shaft the design knowledge relating to this type of bossing is still so limited that only by accident could a designer expect to arrive at the proper shape and proportions on the first trial. Modified bossings are rather easily applied to a model and more easily checked for

these features as applied successfully to the U. S.

flow in a tuft test in a circulating-water channel.

The amount of twist which can be imparted is a function of the fore-and-aft length of the bossing and of the smallness of the reentrant angle against the shell, on the reduced-pressure side of the bossing, convex to the flow. Fig. 36.

destroyer Warden

(DD

352),

where the reentrant

angle on top of the bossing was

than normal.

H

much

smaller

It is true that separation generally

occurs alongside a surface

when

the slope of that

surface with the direction of motion exceeds a limiting angle. However, a twist imparted to the

water by a long bossing with easy curves

may

possibly act to diminish this critical slope

changing the general direction of flow at

by

its after

designing a contra-guide bossing

it

is

kept constantly in mind that the water is being forcibly deflected on the straight or concave side and must follow the bossing-flowplane curvature there. It is only constrained to follow the convex

all.

Indeed,

In fact, it can be stated as an inflexible rule that no contra-guide bossing should be incorporated in a ship design and in the construction drawings without the most complete flow investigation on a model, both with and without the propeller working. This involves measuring on the model, if

it

is

practicable, the transient variations in

torque and thrust as each propeller blade passes through a complete revolution. At some time in the future

end.

When

position. It

it

should involve measurements of the

periodic pressure fluctuations

on the bossing and adjacent

and force variations hull.

Vertical Bossings as Docking Keels. 73.11 For vessels which are wide aft in proportion to their immersed depth, with rather flat stern

FIXED-APPENnACE DESIGN

Sec. 7).12

sections and cut-up

profiles,

the angle

/?

bossing termination often works out as close to

90 deg. In other words, the bossing stands nearly vertical. It is usually difficult to provide adequate docking support for the sterns of these vessels. A logical procedure is to use the vertical bossing as a support keel, since a high degree of strength and rigidity is required in it to support the shaft

and

propeller. Fig. 36.

little

E of Sec.

36.7 indicates that

or nothing need be sacrificed in the

way

(5)

(6)

(7)

(8)

of

form to provide the necessary flat surface on the bottom of such an appendage. A bossing designed to act also as a docking keel should have a slope

(9)

such that the line of action of the support force from the docking blocks, at midwidth of the flat

under surface bossing until

The

remains

of the bossing, it

enters the

main

ivithin the (10)

hull.

fact that the propeller blades project

below

the docking support surface and that the blocks

under the bossing (s) have to be built up higher than the remainder may be taken care of by modern (1955) drydocking procedures. 73.12 Design Notes on Fixed Screw-Propeller Shrouding; The Kort Nozzle. Certain screwpropeller installations involving fixed shrouding are described in Sec. 32.5 and illustrated in Figs.

(11)

it

can not be described adequately in the

a

number

of recent references

which contain the

An

summary of these two papers is given German) and a most workable design procedure, with examples, is found in "Handbuch der Werften (Construction Handbook)," published by Hansa in Hamburg, 1952, pp. 67-88. On page 88 excellent

a bibliography of 14 items. 4415 section is recommended for a Kort F. Horn and H. Amtsberg; it is shown by W. Henschke, in "Schiffbau Technisches Handbuch (Shipbuilding and Ship Design Handthere

(12)

D and 32. E. Propeller nozzles in general and Kort nozzles in particular are described in Sec. 36.19 and diagrammed in Fig. 36. P. The detail design of Kort and other fixed nozzles is intricate and specialized, so much so space available here. Instead, there are given

Importance of Shrouded Ship Propellers)," STG, 1939, pp. 150-167 Dickraann, H. E., "Grundlagen zur Theorie Ringformiger Tragfliigel (Fundamentals of the Theory of Ring-Shaped Airfoils)," Ing.-Archiv, 1940, p. 36 Riddell, A. M., "The Theory and Practice of the Kort Nozzle System of Propulsion," INA, 1942, pp. 87-114 Some design notes given by W. P. A. van Lammeren, RPSS, 1948, p. 267 Amtsberg, H., "Entwurfs- und Berechnungsverfahren fiir Kortdusen (Design and Calculation Methods for Kort Nozzles)," Arbeitsblatt 5/1950/01 der KdT, Berlin, 1950 Horn, F., "Teil A (Part A)," "Thooretische Grundlagen und grundsatzlicher Aufbau des Entwurfsverfahrens (Basic Theory and Design Fundamentals)," STG, 1950, Vol. 44, pp. 141-169, with a list of 8 references on p. 169 (in German) Amtsberg, H., "Teil B (Part B)," "Praktisches Auswahlverfahren fiir Optimale Diisensysteme Selection Method to Determine (Practical Optimum Nozzle Systems)," STG, 1950, Vol. 44, pp. 170-206 (in German) Scientific

(in

is

An NACA nozzle

32.

that

687

(Economic and

of the

by

book)," 1952, pp. 165-166. The nozzle section and the sketch of Fig. 73.1 is adapted from Fig. 44 on p. 167 of the Henschke reference. (13)

"Triple-Screw Ohio River Tugboat John J. Rowe,"

SBSR,

17

Nov

1955, p. 641.

The

three propellers of

this craft, 7.67 ft in diameter, are in

Kort

each enclosed each

nozzles, with a steering rudder abaft

best description of this procedure available in

the Hterature: (1)

Gutsche, F., "Fortschritte in der Entwicklung des Binnensohiffs mit

Development Waters),"

Eigenem Antrieb (Progress

in the

Inland Deutsch. Ing., 1935, p.

of Self-Propelled Ships for

Zeit. des Ver.

1155 (2)

BiJohi,

G., "Possibility di

Reoupero Delia Scia ed

Esperienze sul Mantello d'Elica Exploiting Propeller

(Possibility

of

Wake and Experiments with Shrouding)," Ann. Rep. Rome Model the

TMB

(3)

Basin (in library), 1936, Vol. VI, pp. 91-98 Gutsche, F., "Einflusz der Gitterstellung auf die Eigenschaften der in Schiffsschraubenentwurf benutzten Blattsohnitte (Influence of the Cascade Position

on

the

Characteristics

the

Blade Direction of Inflow

Mitteilungen der Preuzisohen Versuchsanstalt

When

Wasserbau und Schiffbau, see also (4)

of

Sections Used in the Design of Ship Screws),"

STG,

Berlin, 1938,

Bedeutung

unmantelter

Goinqj

Ahead

No. 34;

1938, p. 125

Roscher, E. K., "WirtachaftUche liche

fiir

Plane of Propeller Disc

und

wissenschaft-

Schiffaschrauben

Fig. 73.1

Definition-Design Sketch for Kort Nozzle

HYDRODYNAMICS

688 propeller.

The

reference embodies a stern view of

the vessel on the ways, showing the propellers, nozzles,

and rudders. There are

si.x

a

of

44

ft,

The

craft

a depth of

I,

p.

84

tural anchorage

ff;

of rigid struc-

available at or near the top

is

Although a distance equal to

of the shrouding.

the fore-and-aft length of the shrouding

is

able for this attachment, the real need

ft,

Shipbuilding, 1955, Vol.

(15)

beam

and a draft of 6.5 ft. Roscher, E. K., "Kort Nozzle Propulsion 10

(14)

ft,

Sec. 73.13

Here a reasonable amount

sterns.

flanking rudders

in addition to the three steering rudders.

has a length of 164

IN SHIP DESIGN

of Ships,"

abstracted in

IME, Apr 1956, Vol. LXVIII, pp. 105-106 Van Manen, J. D., "Recent Research on Propellers in Nozzles," SNAME, New York Sect., 30 Oct 1956.

the bottom of a large ship skeg carrying a nozzle-

not mandatory,

is

greatly

it is

to be preferred. It can not be very deep, otherwise it it

would extend below the baseplane. Likewise, it would interfere with

can not be very wide or

the contraction of the inflow jet to the lower part

the advisability of using fixed shroudings with

of the propeller disc. Nevertheless,

screw propellers will require reference to the paper "Open-Water Test Series with Propellers

relatively rigid portion of the ship structure

D. van Manen [Inter. Shipbldg. Prog., 1954, Vol. 1, No. 2, pp. 83-108]. D. S. Simpson has the following to say concerning this type of installation: in Nozzles,"

"The Kort

by

J.

nozzle,

now almost

universally used on the

river towboats, has (made) a definite contribution to all vessels used principally for little

change

in

route

free

indicate that the hull

it shows Experiments

towing, although

performance.

must be designed

for it as nozzles

added to existing (hull) designs have not given the expected improvement in towing power" [SNAME, 1951, p.

for

width of anchorage, to hold the shrouding concentric with the propeller-tip circle. While a horizontal strut connection or tie to enclosed propeller

For design purposes the Horn and Amtsberg references of 1950 are the most useful and valuable. Although it does not contain design rules as such the marine architect who sets out to study

availis

it is

a

tie to

a

and

should be utilized to the utmost. Shaping and Positioning of ContraVanes Abaft Paddlewheels. The action of contra-vanes forward of and abaft paddlewheels as such

it

73.13

and sternwheels

is

described in Sec. 32.4 and

These vanes are fixed improve the efficiency

illustrated in Fig.

32. C.

appendages applied

solely to

of propulsion.

So far as known, the only model experiments on and full-scale trials of either leading or trailing contra-vanes were those made under the supervision of F. Siiberkriib ["Vergleichende Modell-

560].

versuche mit Siiberkriib Leitflachen an einem

A

very real problem associated with the provision of fixed shrouding is building the necessary rigidity into it

and attaching

it

firmly to the hull.

This appUes equally to the design of shrouding intended for mechanical protection only and to that installed for improving the efficiency of propulsion. The shape of the shrouding is so foreign to that of a normal ship that when added as an appendage

freifahrenden Schaufelrad, Teil II (Comparative

Model Experiments with Siiberkrub Guide Plates

On

Free-Running Paddlewheel, Part 2)," Rep. 321, 3 Mar 1936 (in German), copy library; "Neue Verbesserungen in der in Hydromechanik des Radantriebs (New Improvements in the Hydromechanics of Paddlewheel a

HSVA

TMB

WRH,

Propulsion),"

15 Sep 1941, pp. 269-271].

never appears to belong to the ship. To obtain an integrated design it may eventually be necessary to design a whole new

The notes

type of afterbody. If the shrouding or nozzle is part of the initial design, a stern with a shallow transverse arch and gently sloping buttocks over the propeller is indicated. The under side of the arch then forms the top of the nozzle opening. The nozzle proper benefits by two hull attachments, each as long as the nozzle, and spread laterally by the width of the arch.

first the forward or leading vane, pointed out in Sec. 71.6 that a side paddlewheel is best positioned so that a wave crest lies

it

The application of a nozzle-shaped fixed shrouding or enclosing duct to an existing ship best limited to propeller positions abaft large skegs or to those underneath wide, rather flat

is

in this section are based partly

on

these data and partly on the general hydrodynamic

knowledge

set forth elsewhere in the book.

Considering

it is

about opposite the point where the blades enter the water on the forward side of the wheel. If the leading contra-vane is placed under this crest, the water flows to it in a direction nearly horizontal. As a hydrofoil, cambered to deflect the water sUghtly downward, its lift is exerted in a direction close to the vertical. There is very little or no thrust lift is

component

of this

otherwise not useful

minimum. The entrance

it

lift

force; as the

should be kept to a

of the

contra-vane

is

FIXED-APPENDAGE DESIGN

Sec. 73.13

therefore placed so that the is

meanhne

at the nose

parallel to the streamlines of the incident flow.

For a leading contra-vane ahead as in diagram 2 of Fig. 32. C,

of a stern wheel,

it is

necessary to

determine the flow direction at the nose position by some kind of ship or model test. M. Hart has published two diagrams which

show the

resultant-velocity vectors, with reference

mentioned

689

earlier in the section.

The contra-vane

best placed where the flow vector at the subsurface level of the vane has its steepest slope. is

In the layout of the figure

it is

possible to keep

the vane above the at-rest waterline, although a position under other wave-slope conditions might be as low as the lowest trunnion level of the blades. The lower surface of the run portion of the trailing

to a stream of undisturbed water flowing past

contra-vane,

the side of the ship, of the upper and lower edges

should conform generally to the flow within the wave crest at that position and level.

of the blades in a series of

[ATMA,

immersion positions and Pis. II, III].

1906, Vol. 17, p. 179

These do not take account of the velocities induced by the blades, for which no comprehensive, reliable data can be found. It is considered, therefore, that the run or after portion of the leading vane can best be shaped with its upper surface parallel to a tangent to the sweep circle of the outer blade edges at that point. There should be enough clearance between this upper surface and the outer blade edges to pass any floating debris that may be drawn down below the surface.

The

lie

edge of the forward contra-vane

at about the level of the blade trunnions,

perhaps slightly below the midwidths of the blades in their lowest positions.

and

As

for chord length fore

can be of the order of 1.5 to 2.0 times the blade width on the paddlewheel or aft,

this

sternwheel, for both leading and trailing vanes.

For the after or trailing vane, the predominant flow is that which forms the high, steep wave just abaft the wheel. This is indicated in Fig. 73. J, adapted from the Siiberkriib reference

Outline

of Section

lift

ahead of the

of the after

of

Cbntro-Vone,

Entire Lanqth of Paddle

Incident- Velocity site

edge,

vane has a forward

thrust component, this curved-section hydrofoil lift and a low drag. The meanboth leading and trailing vanes will have a rather large camber for their chord lengths.

should have a high lines of

The contra-vanes may be made reasonably

thin

supported at say two intermediate transverse points as well as at the ends. Their curved section shape gives them inherent stiffness, as for a blade

if

of the wheel itself.

Were a

vessel fitted with contra-vanes to run waves these devices would be subject to impact or slamming. They would have to be designed to withstand an impact load much larger than the lift load. The equivalent static load would prob-

ably be of the order of 2,000 lb per sq ft or more. This is about 4 times the uniform propelling load applied to the blades of a paddlewheel.

Side paddlewheels are in themselves effective roll-quenching devices.

are

much more

may

Lyinq Abaft

or

Vector is Generolly Porollel to the Wave Surface Bock Of the HydrodynatrKc Center of the Foil

Fig. 73.J

Proposed Contra-Vanb Aerangement of

F.

Suberkbub

but even

require support for

vertical forces far greater than those

Blade

rather

The contra-vanes

effective for this purpose,

without impact they

The Ahead Thrust Force Exerted by the Contra-Vane Under the Conditions Pictured is T

The

trailing

in

trailing

should

Since the

just

imposed

690

HYDRODYNAMICS

upon them when acting ouly

to change the direc-

pressure

hydrostatic

surfaces of the guide vanes separation, tion

and

on the upper

makes

cavitation,

a problem. The situabecause the considerable

air leakage

aggravated

is

transverse length of the contra-vanes requires for their support a series of vertical plates

up

project

Despite

all

through that

may

the

free-water

which

surface.

be said to their advantage,

contra-vanes are in the category of the short vanes of the contra-propeller described in Sec. 36.9,

with most of the disadvantages enumerated

there.

the friction drag of both sets of contra-vanes

If is

considered too

much

a handicap, the forward

set can be omitted, since

it is

probably the least

effective of the two.

The

these bearings

Sec. 73.14

become

Such a

excessively large.

distorted design requires, as a rule, long (high)

tion of flow.

Limited

IN SHIP DESIGN

smaller the wheel diameter, the greater

the dip, the greater the immersion arc of the trunnion circle, and the greater the angle (with

bearings, having length/diameter ratios so large

that

it

is

almost impossible to obtain uniform

pressure over the whole bearing length because

bending or deformation of the parts. As a the bearings wear unevenly and excessively, leaving the rudder free to vibrate. Since the rudder is already in a region of disturbed flow the resulting slackness may cause pounding, with more wear and still more vibration. Partial skegs intended as restoring-moment stabilizers benefit from large aspect ratios and relatively narrow tips. Those intended as dampingmoment stabilizers have a moderate to large area in combination with the attached movable rudder. Skegs intended to be self-clearing when encountering ropes, cables, and nets, such as those on submarines, require their leading edges to be set at of

consequence,

rather small angles to the direction of ship motion.

the horizontal) which the blades enter and leave

These are not necessarily small with respect to the direction of local water flow. The outer or

the waves, the more useful should be the contra-

lower ends of horns or partial skegs, especially

vane

if

installation.

Design Features of Supporting Horns Rudders of the for Rudders; Partial Skegs. balanced, partly underhung, compound or flap type require a fixed support in the form of a horn or partial skeg ahead of the hinge or stock axis. This support may take a great variety of shapes, depending upon the single or multiple functions for which it is designed. It may be a structural support only, it may be intended to 73.14

exert large lateral forces

from a movable

tail,

vertical stabilizing

features built

by pressures induced

may have to serve as a and it may have contra-

it

fin,

in. Profiles of

representative shapes

are sketched or illustrated in Figs. 21. B, 24. C,

26.E, 28.A, 33.B, 37.A, 37.D and 37.J of

Volume

I,

they are long in a fore-and-aft direction, should generally parallel to the adjacent flow except

lie

appendages of this nature as are utilized docking or resting purposes.

for such for

Structural skegs intended only for docking or resting can be integral parts of the hull or addi-

on the bottom. If the latter, it is simpler to omit the fairings along the edges where the skeg

tions

sides join the hull; this

is

acceptable

if

the con-

mentioned in Sec. 75.5 are satisfied. It is generally the case for a partial centerline skeg. ditions

If the skegs are built as integral parts of the hull it is

simpler and better to fair

them

easily into

the hull surfaces and to provide generous means of

access

from the

inside.

Incidentally,

it

is

by no means necessary that

desirable although

and 75. E of this volume. horn or partial skeg is determined by the structural support it is intended to give, the location of internal members to which it can be anchored, and the amount of vertical projected area desired in it. Few rules can be given for laying out these profiles. It can only be pointed out that structural skegs or horns usually require a long base on the hull or a long extension

However, to save displacement, wetted surface, and vertical fin area in the lateral plane, they can be cut up from the keel plane by the heights of

into the hull.

or projecting skeg

and

in Figs. 74.K, 74. N,

The

profile of a

skegs

which

have

docking

functions

should

terminate with their lower surfaces on the baseplane or at the level of the bottom of the keel.

one, two, or three tiers of docking blocks, generally 14, 28,

The

and 42

inches, respectively.

Hydrodynamic considerations should never be permitted to squeeze the upper and the lower bearings of any rudder-and-horn assembly so

on any horn determined by the range of du'ections from which the local flow may impinge upon it under normal operating conditions. In other words, the horizontal section has sufficient

on

thickness abaft the leading edge so that separation

close together vertically that the lateral forces

fineness of the leading edge is

FIXED-APPENDAGE DESIGN

Sec. 13.15

and cavitation are not

liable to occur alongside

stern runs normally at angles of attack varying

is,

axis. If

the

forward edge of the movable tail of the rudder is finished to form a surface concentric with the axis, the mechanical clearance between this sur-

and the fixed manner in which

from zero to a few degrees on either side. However, when the stern swings around and skids over the water in a turn, the angle of attack on this fixed appendage may rise initially to 15 or 20 deg. The angle of attack

forward of the stock

recess, directly

except for short periods. For example, the horn supporting the rudder under a ship with a broad, it

fiat

691

face

lug this

may may

be quite small. The be accomplished

is

illustrated in Fig. 73. K.

Selecting

73.15

Number

as explained in Sec. 36.10,

the

Position,

Type,

The

of the Roll-Resisting Keels.

and first

applied in the wrong direction to facilitate the

step in the design of roll-resisting keels

turn.

mine whether or not they are actually needed. If required, what are the operating conditions, and what are the keels called upon to do? It is pointed

Separation

is

almost certain to occur on the may occur as well,

inside of the turn. Cavitation if

the top of the horn

is

sufficiently close to the

water surface. By making the leading edge of the horn reasonably blunt this separation or cavitation is at least confined to a limited region. It would otherwise, on a thin section with a sharp entrance, extend all the way forward to the leading edge. The skeg section is usually combined with the rudder section to make a streamlined whole. Section shapes found satisfactory on high-speed vessels

are

grammed

similar

in

Fig.

given by P. Mandel

to 73. C.

the

strut

sections

dia-

Their coordinates are

[SNAME,

•

is

to deter-

out in Sec. 36.13 that the discontinuous or multiadvantageous only when the

fin t3Tpe of keel is

vessel

is

moving through the water.

or sohd type

is

indicated

teristics are required at

when

if

A

continuous

roll-quenching charac-

low or creeping speeds or

at anchor.

Assuming that the continuous type selected, the next step is to

determine

of keel its

is

general

and location on the hull. some extent governed by the damping expected or demanded and

proportions, dimensions,

The

total area is to

degree of

roll

3, p. 468].

the inherent roll-quenching characteristics of the

and forming

portions, for the reasons stated in Sec. 37.3. It

underwater form. A hull shape approaching a circular form, as on some submarines, requires a high degree of quenching from the keels, compared to the rolling moments apphed by surface waves. A hull with nearly square sections in the middlebody calls for a smaller degree of quenching

and simply achieved by providing one fixed lugs on the inside of the rudder

moment. Practically all roll-resisting keels involve some increase in appendage resistance.

Horns supporting rudder

1953, Fig. tails

compound or flap-type combinations require special shapmg and recessing for the tail. This is to give the minimum clearance and pressureleakage

is

easily

or

more

area

between the fixed and movable

The

best transverse location for the keels

is

on the corners of the bulge between side and bottom or at positions having the greatest radius from the rolling axis. The position must insure practically if not definitely continuous submergence under all operating conditions. If the rolling axis is not known from model or full-scale tests,

may be assumed at the intersection of the centerplane and the waterplane, or at a parallel line through the center of gravity CG for the particular it

weight distribution assumed. A. Caldwell ["Steam Tug Design," 1946, p. 42] states that "the bilge keels will answer their purpose most effectively if placed at that point on the shell which is farthest from the metacenter." He does not explain his reasoning in

Rudder Post or Fixed

Portion of

2.

Compound Rudder Fig.

73.K

Hrr^GE-GAP Closures fob two Types

Rudder

of

this matter.

A first approximation to the midsection position obtained by drawing on the body plan a diagonal from the rolling axis to the point where the is

HYDRODYNAMICS

692

diagonal offset on the midsection

There should

is

a

maximum.

make an

80 dog. The angle that counts the shell, not with the horizontal. least

is

is

at

forms in

effect

a

diagonal stream surface, parallel to the lines of flow at the ship hull

and

for the entire

clearance

away from the

especially

influence

of

the surface-wave profile.

A

that the flow corner

bilge

diagonal

it

may

the

for

ofl^set is

region

0.9 or

more

of the

bilge-diagonal intercept amidships. It

excrescences that can be applied to

it,

motor

roll-resisting

lifeboat, it is possible to

fit

two

made

at least 6 times the

each keel to insure

bilge-

its

proper functioning.

was

vastly

row of such was added below the main row [WRH, 15

keels

Jan 1939,

Occasionally it happens that when laying out a trace from the optimum position amidships,

the keel leads up too close to the free-water surface or down too close to the floor line or the baseplane.

One portion of the keel may then be terminated when it moves out of optimum position and another portion started in an offset position, reckoned girthwise, where it may be placed to better advantage for performing its function. The

Be- of

radius

1.5

is

less

increased.

Having determined the girthwise position the roll-resisting keel, a point

is

to 2,0

Times

the Bilge-Keel

Width Near the Gap

I

k^After Section Offset Upward Here;

^^^ It Can Be Offset I

Jownword Fig. 73. L

Bilge-Keel Arrangements With Gap and Offset Amidships

of

selected on the

exterior portion of the diagonal, indicated at

in fact, overlap

the Order of

The

transverse spacing was, with than that prescribed in the foregoing for solid bUge keels abreast. 73.16 Bilge-Keel Extent, Area, and Other Features. Because of its greater lever arm, and possibly also because of its width with reference to the thickness of the boundary layer, a keel on a sharp bulge, designed to give a certain degree of roll-quenching, may be relatively narrow. It must be wider, however, as the bulge p. 21].

justification,

the hull.

"Offset Should

On

built with discontinuous bilge keels of the

with surface lines of flow on a model. It is still better to double-check the position with tufts or flags mounted on pins and extending for at least 0.9 the maximum width of the bilge keel from

x^A\^^

is

of

the Dutch liner Oranje of the late 1930's, which picket-fence type, a second partial

may,

such as a

maximum width

preferable, however, to check a proposed trace

keel endings at this offset

upper

layout the spread between the adjacent keels

maximum is

illustrated in the

keels abreast on each side of the hull. In such a

be assumed

where the

is

midsection,

approximately parallel to the

is

of the

For a vessel with a large but exceptionally slack and a limit to the width of the

is

speed or the highest speed at which the ship is to run for the greater part of its time in service. For slow-speed vessels with nearly square sections in the middlebody,

way

profile of Fig. 73. L.

generally the service

is

not available for keels in

is

adequate. Such a design

trace

conforming to the flow at one particular speed therefore selected. This

on each

preferred,

midship bulge, the roll-resisting keel may be omitted there. Separate shorter keels are then laid out, forward and aft, where the clearance is

width of

hull. These lines of flow, on a fast or a high-speed ship, change position and shape with speed because of the

the keel

is

between them. In general, the girthwise offset should be at least 1.5 times and preferably 2 times the full width of each keel near the gap, shown by the middle diagram of Fig. 73. L. For ships of such full sections that working

the one at

For negligible pressure resistance and minimum It

of the taper

shown in the lower profile of Fig. 73. L. There may, of course, be a fore-and-aft gap of any desired length

friction resistance, the keel should lie along the lines of flow in its region.

Sec. 73.16

by the length

keel but no overlap

angle with, the tangent to the

at the diagonal intersection which

shell

longitudinally

a further condition that the diagonal

is

IN SHIP DESIGN

K

FIXED-APPENDAGE DESIGN

Sec. 73.16

on Fig.

73. M,

where the included angle between

the two adjacent tangents to the hull

The

120 degrees.

100 to

is

distance between the point

/Assumed

Position of Rolling Axis

K

and the hull gives an acceptable hydrodynamic as For a persquare-cornered

bilge

should, a width of zero.

this

gives,

as

The maximum width

for a semi-circular midsection,

where

it is

is

0.302

120-deg angle. length of the keel

is

^\

it

(B/2) for a 100-deg angle and 0.154(5/2) for a

The

Between Rodiol Line OB^ and Tanqent to Shell Qt Inner Edge of Bilge Keel Should Lie ^^ "^X\\ \Betwean 80 ond IOO^eg\

An(^le

well as practical width for the keel. fectly

cm

determined partly by

Distance KE Should Be Such That the Angle Between the Vertical MNE and the Tangent KN, f> More Than 3 dea

the area required, assuming that the average

width has already been determined, and partly by the length of that portion of the ship for which an adequate lever arm for the keel can be obtained. When the transverse sections have narrowed or contracted so that the lever arm, i^^ as measured by the distance OB on Fig. 73. M, becomes less than a certain fraction of the lever

-Lines

Through K Tangent to5hell-

,

arm

at the

keel

is

maximum

>

a

Diagram at

downward

bilge-block

0.90,

toward the centerline of the dock. In some cases it may be necessary to provide this clearance above the floor line rather than above the baseplane. In fact, this requirement may be expected for all vessels which are to have bilge blocks hauled under them when drydocking. To obtain

may

shave

,

0.90, this fraction

For vessels

may

this point (0.8)^ full

=

midsection, say

be kept larger than

of slack section,

minimum value of The midplane of

where Cx

<

0.75 might be justified.

the roll-resisting keel

efficiftnt

keel

is

obtained by making

it

as

wide as possible amidships and keeping it of approximately constant width. This is because the additional width amidships has a much greater lever arm than at the ends of the keel. All too frequently the maximum width or the amidships width of a roll-resisting keel is limited by working clearances around the keel edges. This prevents damage when lying alongside quay walls and when entering graving docks. The clearances are expressed generally as (1) a distance inboard of the point of extreme beam at any section and (2) a clearance above the baseplane throughout the length. The latter is desirable

when hauling

bilge blocks, especially

bearers

slope

the required clearance

change angle with the horizontal, at a gradual and moderate rate from amidships to either end, as may seem appropriate when considering the flow of water in its vicinity, at a distance from the shell. Use of the "tangent rule" set down at the beginning of this section produces a narrow keel alongside the sharp-bulged sections of a form and a very wide keel alongside the narrow or slack sections. For the same total area, however, a

more

Bilge-Keel Design Midsection

Rk there is little to be by making the minimum Rk less than

about 0.8 the maximum. At For vessels of rather

Cx

M

bilge-diagonal offset, the

0.512.

0.85.

73.

terminated. Since the effectiveness of the

keel varies about as

gained

FiG.

when the

off

it

slightly

is

often necessary to

the bilge-keel width amidships.

The forward and

after ends of the keels are

tapered gradually to practically zero width.

A

gradual taper occupies a length at least 3 times the keel width, with a

maximum

slope of about

40 deg. For any leading edge lying forward of about 0.5L from the FP, the taper should occupy

maximum

at least 5 times the keel width, with a slope of 20 deg for medium-speed

and 10 deg

for

high-speed ships. This taper avoids fouling or catching ropes and cables on the ends and ehminates sharp structural discontinuities where the keels terminate. It is possible that ships with sections projecting

beyond the

Cx

>

A flat,

1-0,

limits

of

waterline

where

beam,

hardly need roll-resisting keels at

all'

shallow raft with a deep fixed keel, having

a Cx approaching 0.0, likewise needs no additional appendage because of the powerful roll-damping effect of the keel. Yachts, with deep fixed keels,

no bilge keels, and values of Cx behave much like the raft, except

less

than 0.5

for the addi-

tional steadying effect of their sails.

Of

all

the

intermediate forms, the craft which needs the

maximum

roll

damping

is

one having a

B/H

HYDRODYNAMICS

694 ratio of 2.0,

a Cx of

7r/4 or 0.785,

waterplane,

maximum

a semi-circular at

the

and a

center

rolling axis in the

the

of

circular-arc

design curve or lane to give suitable values

of the roll-resisting keel area

some other a

The

Sec. 73.17

roll-resisting keels are in effect principal

longitudinal

sembhng

members of the ship structure, reAs such they must diminish

stringers.

gradually in section so that the shell connection

section.

A

IN SHIP DESIGN

section,

Ak

with relation to

have about 0.785, cor-

suitable term should therefore

maximum

at a

Cx value

of

any point may carry the increment

at

keel

and the

together.

The

must

hull

stretch

to the shell should project well

minimums

1.0

of the keel proper,

Mandel has given such a design lane Cx from 0.7 to 1.0 [SNAME, 1953, 492], based upon the ratio 10A^:/(LH),

7.3.N of Sec. 73.18.

and

Cx approximating

0.0. P.

for the range of

Fig. 25, p.

and compress

securing angles attaching the keel

responding to a semi-circular midsection, and two at values of

of shear

load appUed at that point. In other words, the

beyond the end about as diagrammed in Fig.

If the roll-resisting keels

extend forward to the

vicinity of the quarter point,

and

if

they

rise to

where

Ak

the bilge-keel area on one side of the

points above the baseline greater than about 0.3

vessel.

The graph should in fact diminish toward Cx values of 0.4 or less, corresponding to

the draft in any operating condition, the forward

zero at

is

73.17

The pubhshed

related to

literature

Some

of bilge-keel design.

of these are closely

hydrodynamics and are accordingly

discussed briefly here.

I

The

Structural Considerations in Bilge-Keel

and reference books on the structural design and construction of ships overlook many of the important features

Design.

ends require strengthening against wave slap

and water impact.

those of deep-keel yachts.

Roll- Resisting

!

U-:

is

Coniinuous

transverse shape of a roll-resisting keel

should remain relatively sharp and pointed at its

outer edge. If

it

needs lateral stiffening, such

by a half-round bar, this is by an outer-edge flange such as that on an I-beam with the outer flange trimmed down. This construction gives increased damping as

is

often afforded

best provided

Keel in

[-e

This Interval |

End of Toper Cul at Toes of Shell Angles

o'2_5^

,

hl.'O^J

Terminal Plate Forward Riveted to Shell Plating

—

^-^^

U-r I

f

0.75

Rivets as Close to Heel of Anqle

QS Practicable

Fio. 73.

Section B-B

N

Structural Layout for Roll-Resisting Keels for the

ABC

Ship

Section A-A

FIXED-APPENDAGE DESIGN

Sec. 73.19

some

with

in

increase

resistance.

friction

It

(i'J5

keel width of 3.5

ft,

or about 0.0477i?.v

still

,

requires a rather careful preliminary flow study-

leaves a clearance of about a foot above the floor

on a model, to insure that not only the keel proper but the outer flange lie in the streamlines. A flange on the free edge should not carry around the tapered portion at the ends but should itself

line

be tapered to zero where the width-tapering of

as

the keel begins.

A

triangular keel section affords immeasurably

greater structural rigidity than a thick flat section. It

and displacement

preferred where weight

is

considerations permit.

The

section can take the

form of an acute-angled triangle with a peak 15 deg, without any

angle of not more than sacrifice of

damping quahties. On

expected to

roll

heavily the base of the triangular

section of a roll-resisting keel 0.4 or

more

large vessels

may

be as great as

of the keel width.

Bilge keels are heavily loaded in an alternating

The extreme forward end

is partly unsupbrought to a rather long, sharp point. All in all, the normal bilge keel requires a special structural attachment to render it secure for long periods of hard service. Indeed, the forward sections of roll-resisting keels on fast and high-speed vessels could well be built of heavier scantlings than the rest. The attachment of the base of the keel to the hull should be stronger than that of the sides or projecting portions of the keel to the base. This insures that if the keel is overloaded in any way, the shell connections will remain intact. 73.18 Design of Roll-Resisting Keels for the

cycle.

ported unless

ABC

Ship.

ABC

ship,

it is

The

roll-resisting keel traces for the

shown on

Fig. 66.P,

were determined

by flow tests on the model, using pivoted flags which projected from the hull for a distance corresponding to some 3 ft on the ship. From the straightness of the traces as projected on the midsection plane it might appear that they were simply drawn as diagonals on the body plan. It so happens that the flow on either side of the bilgekeel positions straightens

as

itself,

it

were, in

these regions. This does not always occur, as

evidenced by the class,

wavy

keel traces on the Mariner

reported by V. L. Russo and E. K. Sullivan

[SNAME,

1953, Fig. 18, p. 127].

Were the

crests

of the Velox waves more pronounced along the side of the ABC ship, the bilge-keel trace might well be affected by them.

and troughs

The

slack bilge of this ship

was

laid

out to

permit the attachment of wide roll-resisting keels, for the reasons given in Sec. 66.13.

The maximum

and a foot

The

inside the side of the ship.

bilge-keel area

was governed

in this case

only by the rules in the sections preceding and

by the endeavor

to obtain as

much

bilge-keel area

without sacrificing other features. The keels were carried forward and aft, as shown in Fig. 66. P, to points where they were considered as no longer paying their way. The possible

effective

length

is

some 7

stations (Sta. 7 to Sta.

14); this is equivalent to 178.5 ft or 0.35 times the

waterline length.

The

taper at the forward ends was

18 ft long,

shown

made about

in Fig. 73. N, or over 5 times

the depth, exclusive of the structural terminal plate

and

fairing bar.

That at the

after

end was

made some 10 ft long, or about 3 times the depth. The width of the triangular keel at the base is 1.5 ft, or 0.43 times its maximum depth. The hydrodynamic loads imposed

in

quenching

roll

are transferred to the hull as a combination of

The

shear loads and normal loads.

and out on the

shell in line

the triangular structure. this structure,

riveted

latter pull in

with the side plates of

Any

offset

members

in

such as side plates of the keel

to shell angles,

are almost certain to

develop high bending moments and eventually to become loose. It is for this reason that the shell

angle should be very heavy.

which hold

The

rivets

this angle to the shell are placed as

close as possible to the force-application lines in

the side plates. This means as close as they can

be driven to the bosom of the bar. 73.19 Design of Docking, Drift-Resisting, and Resting Keels. The best design procedure

heavy ship where is mandatory, is to make them unnecessary by working the desired flat supporting surface into the bottom of the ship itself. In regions where direct support is required and the normal faired lines lie somewhat above the blocking level at the baseplane, the bottom of the ship is brought down deliberately for docking keels,

on a

large,

considerable off-center support

to the level of the tops of the docking blocks. Figs.

67. L

and 67.M

for

the arch-stern

ABC

design indicate, in the regions near the baseplane at Stas. 14 and 15, how this is done. Although in this ship the hull terminates at the after quarter-

point in a

flat

surface coinciding with the floor

the shape would be essentially the same if brought down to the baseplane. In many ships line,

this

modification

involves

only a surprisingly

HYDRODYNAMICS

696 small change in form, even

support

is

from

offset

when

the

the docking

centerplane.

The

resulting discontinuities are moderate, distorting

the flow only slightly and involving

little or no added drag. Obviously, at the ends of a ship with the usual deep forefoot and aftfoot the major support area is under the centerline keel. Such

a keel

kept down to baseplane level for as

is

a proportion of the length as possible,

great

consistent with good flow

and drag and with the

required maneuvering characteristics. In a normal

design the

keel should

flat

in the baseplane

lie

for at least 0.8 of the waterline length, although in special cases this ratio 0.6,

or less

[Clark,

may

diminish to

ATMA,

L.,

ABC

For the transom-stern

1900,

hull

this

p.

0.7,

361].

ratio

is

66.Q and 66.T, even though the aftfoot is cut away. For the archstern ABC design, centerline support is provided for 0.75 times the length plus two rows of side support, under the skegs, each for about 0.15L,rL If the hull proper can not be brought down to the level of the baseplane for docking support, the next best procedure is to raise part of the docking-keel level above the flat-keel level. In any one area this can be done by adding standard layers of material, say 4 in or 14 in thick, to the tops of the regular docking blocks. A ship of moderate draft usually has ample clearance over the raised blocking in a dock, even when some 0.925, indicated in Figs.

IN SHIP DESIGN

Sec. 73.19

circular pressure hull through their

upper flanges

and a heavy horizontal closing plate was bolted to their lower flanges. The bosoms of the two channels, on the outside, were

filled

with blocks of

lead bolted in place as more-or-less permanent ballast. These centerline box keels were rugged enough to serve as resting keels when the ship lay on the bottom or as support keels when it was docked. There is no practicable limit to the depth of a

drift-resisting

keel

provided

it

sufficiently

is

sturdy to take its share of the load when docking. The keel is designed to be of watertight construction, with one

bottom plate and two

If

the keel

is

long relative to the vessel

becomes members.

it

in effect one of the longitudinal strength

As such the side plates are attached to the hull in a manner to prevent transverse cracking of both the side plates and the adjacent shell plates. A flanged plate or a channel is used for the bottom

member

so as to bring the fore-and-aft welds

above the lower outboard corners and

relieve

them of concentrated loads during docking. Not only the knuckles or lower corners of the keel but the upper corners should be as sharp as practicable, with reentrant angles not less than

90 or 100 deg. The junction of the drift-resisting and the hull should not be filleted as is the

keel

The

case of the keep keel on a sailing yacht.

compartments are damaged and flooded. The designer may cut out the unwanted or undesirable

ately introduced to offer the

portion of a deep keel or skeg without sacrificing

resistance on the advancing side of the keel

blocking support by raising the bottom or support

the

by a multiple of the block67. and 67.0 show that

surface parallel to itself

ing thickness. Figs.

under the two

offset skegs of the

design, the level

by

M

is

keel and skegs

ABC

raised 28 in, or 2.33 is

arch-stern ft.

Support

thus provided over 0.913 of

Blocking-support areas in a small ship should preferably be at least 6 in wide. In a large ship ft is

An

the

minimum, but

3 or 4 ft

is

preferred.

excellent drift-resisting keel for metal-hulled

vessels

is

a centerline box keel placed underneath

the main hull.

An appendage

fitted to the single-hull

outside and inside corners mentioned are deliber-

maximum

tion

maximum

of pressure resistance

on the retreating side

of

of

dynamic and

due to separa-

when

the keel

drifting or sidling.

The

inside of the keel

may

be

filled

with

of this kind

was

type of submarines built

(3)

an inert

The

gas.

deep sections of some fishing vessels, resembling those of a deep-keel yacht, have fine,

excellent inherent drift-resisting as well as roll-

damping characteristics. Body plans and lines shown in an article reporting NPL tests with

are

models,

entitled

"Experiments

with

Herring

Boat Company during the period 1900-1925. This keel was used as a duct for

Drifters" [SBSR, 28 Jul 1938, pp. 103-106].

pumping out water tanks along the length of the hull, as well as a means of holding fixed ballast. It was made of two heavy channels with their flanges facing outward. They were riveted to the

provides sufficient

by the

(1)

some lightweight water-excluding material blown into place, with (2) some inert ballast which will not accelerate corrosion of the metal, or with

the waterline length.

2

side

plates, the latter attached to the flat keel plate.

Electric

Whether any

centerline

drift-resisting

keel

quenching to permit elimination of the roll-resisting keels is open toquestion. This depends upon the shape of the transverse section

roll

and the length

of the lever

arm

of the

FIXED-APPENDAGE DESIGN

Sec. 73.20

centerline keel from the rolling axis. It appears well established, however,

downward beam-

that any

projection on the centerplane, for a normal

draft ratio, has a beneficial effect in quenching

roll.

For vessels of nearly rectangular section and two drift-

697

to take vessels of large horizontal area which

have these of

floor

keels.

A

may have

may

ship with a rather large rise

well-curved

flowlines;

the

docking or resting keels preferably follow them. The direction of flow toward and away from

known

large beam-draft ratio, say 4 or more,

docking and resting keels

resisting keels fitted at the lower corners of the

and remains fixed for all steady-state straight-line travel. For this reason the ends are invariably fined on both sides of the keel. The bottom surface is carried out to a

and as docking

hull serve also as roll-resisting

In this case, the lateral spread is made large, at least 8 times the keel depth, to avoid interference and to make both keels fully effective

keels.

when subjected

Resting keels on a submarine

may

or

may

not

upon the design

They need not even be

requirements.

flat

on the

an advantage in a special shape. and resting keels flare outward above the support surface, and they meet the hull so that the reentrant angle is greater than 90 deg. This feature is illustrated in Figs. 36.N and 73.0. Docking and resting keels offer the minimum of resistance when they follow the flowlines under the bottom. This means that under a flat-bottomed ship they should diverge slightly from forward aft,

bottom,

The

there

if

point,

then

to transverse flow.

project below the keel, depending

rately from

is

sides of docking

by the directions of the under-thebottom flowlines of Fig. 52.V. This divergence is of no particular consequence in a dock equipped

indicated

One

(or Two)

tMo'y Be

<^

Vertical on Outsid;

give the

to

may

Keel to

rather accu-

maximum

support surface,

be cut up rather sharply, as .shown at 6

Notches, deep and wide enough to permit making their boundaries securely watertight, may be worked into the upper portions of deep keels. These help in the venting of air bubbles which find their way under and inside the keels and which might work their way up into injection openings. The venting openings are necessary in submarines which have main-ballast flood valves or flooding openings below them. Excess air from the blowing of these tanks can not be trapped

below the 73.20 or Fins.

keels.

The Design of Fixed Stabilizing Skegs The design of fixed skegs or fins intended

primarily to act as stabilizing surfaces, excluding in this case stabilization against roll,

The damping

forces

is

based upon:

and moments required to

be exerted by them in the angular motions of pitch and yaw. Damping of the translatory motions of heaving, surging, and sidling is seldom necessary and (2)

Shallow Dockintj

is

tests

in Fig. 73.0.

(1) l>=Heiqht of

model

is

excluded here.

The hydrodynamic

lift

exerted

by these

and the corresponding restoring moments developed by them, when the ship axis departs from the normal straight-ahead motion axis and

Reduce

surfaces,

Resistance

I

Alternative

Method

of

and Docking Keel Altogether

Knucklina Hull

Eliminating

the surfaces run at a finite angle of attack. This be an angle of either yaw or pitch. Good

may Upper Levels of Dock.ing in Blocks locks

Omitted

m

Cutup Equal to the Total Height of a Whole Number of Docking- Block Heights, such as 14, 28, or42 inches, to be Cribbed^ Up in This Region

,

LL

Wq>1 of WqvJ ,

NormaT^Level

of

Tops of Blocks

4

design requires that the fins or skegs be placed in a region of relatively smooth flow, as distinguished

from a region of eddying in a separation zone. In general, the lift force developed by them should be zero for the normal attitude and normal operating condition of the vessel.

In airplanes the disposable weights usually are Side Elevotion o^ a Docking or Resting Keel, Showing Notch or Passage.

Large- Scale Section

Venting

Bilge Keel

Hull

Vent^

May Be Similar

Fig. 73.0

Design Sketches for Docking Keels

too small to permit achieving equilibrium by moving them forward and aft. Stabihzer surfaces

with adjustable angle of attack are often provided in the tail to produce compensating moments for maintaining trim balance. In submarines provision

is

made

in the liquid

trimming system for

HYDRODYNAMICS

698

changing quickly the longitudinal compensating moments. It is not feasible in these vessels to proAdde hydrodynamic moment compensation because of the increased drag, weight, and mechanical complication of an adjustable stabilizer. There is the further important fact that the submarine

may

be running slowly or be

stopped when trim compensation is required. The trailing end of a ship hull, together with such rudders or planes as may be attached to it, possesses

a

definite

property. Actually,

unknown

but

damping

stabilizing

and yaw

in pitch

both ends of the hull about the corresponding axis, but restoring moments are expected only from the after part. results

from the swinging

of

For angular damping the area of all movable rudders, planes, and fins mounted normal to the direction of local motion is added to the area of the fixed portions. For the most effective dynamic damping from these surfaces they are mounted as close as possible to the hull, to prevent unnecessary leakage from the +Ap to the

— Ap sides. Just surface

how much fixed and movable stabilizing is demanded for stability of route is not

a matter for ready calculation or reUable prediction, especially if the hull under design is of

from that of a hull which has been satisfactorily stabilized in the past. This matter is discussed further under Maneuvering in Part 5 of Volume III. To insure zero restoring force or moment on fixed stabilizers when none is desired, they must be placed exactly in the lines of flow. For a surface essentially different shape

vessel these fines are only

by accident

or coinci-

dence parallel to the axis of the ship or its direction of motion. For a stabilizing fin or skeg placed in the outflow jet of a screw propeller, the water

when the

IN SHIP DESIGN

Sec. 73.20

pattern does not change materially for small variations from the normal running attitude.

Considering only the restoring forces and moments produced by hydrofoil lift at an angle of attack, stabilizing fins and skegs act more efficiently as their aspect ratio is increased. However, there are practical limits to the distances which these appendages may project beyond the hull or to which they may approach certain other

boundaries such as the baseplane or the planes defining extreme half-beams. A reduction in the aspect ratio must be accepted area

is

large.

This

is

if

the stabilizer

not a disadvantage because

a surface short in the direction of motion and long in a direction normal to it has low dynamic damping. Taking all factors into account, the best fore-and-aft length for such a skeg or fin

appears to be approximately equal to its extension hull. If the hull is relatively large in area at the point of attachment, compared to the size

from the

of the stabilizer, the effective aspect ratio

is

of

the order of 2.0, for the reasons given in Sec. 14.11. It is difficult to formulate design rules for the

but common form of stabilizing or "fulcrum fin" required on any flat-bottomed boat to provide a pivot point for the rudder moment. On a small centerboard sailboat, the board is raised or lowered to give the required area. For

different

the balsa rafts of the Incas, exemplified by the of T. Heyerdahl, thin planks pushed

Kon-Tiki

down

vertically

between the fore-and-aft logs

at selected positions served as multiple stabilizers.

This gave the "rafters" a great freedom for adjust-

ment and

relieved the builder of the burden of

—

—

and proper set of positions was put together. On a high-speed motorboat carrying a fulcrum

selecting a fixed

when the fin,

raft

a trial-and-error process of positioning

is

is

indicated, at gradually increasing speeds, or else

rather than the direction of the

propeller axis. If the stabilizers are near the surface

a miniature centerboard may be used, mechanically operated from the driver's seat. J. Baader

the flow directions almost certainly change with

shows the shape, relative

speed because of the change in profile of the Velox wave system. This calls for the selection of a

this

follows the hull-flow pattern self-propelled

vessel

given speed at which the lines of flow are to be

which must perform well on the surface as well as below it this procedure is further complicated by the paralleled. In the case of submersibles

possible existence of different lines of flow for

the surface and submerged conditions. Usually,

which fixed stabilizers are required occur during submerged running. When well below the surface the flow

however, the

critical conditions for

size,

and position

of

forward or fulcrum fin for a number of successful motorboats ["Cruceros y Lanchas Veloces (Cruisers and Fast Launches)," Buenos Aires, 1951, pp. 115, 119, 322-325, 341]. Fixed stabilizers and skegs, especially on submarines, may often be called upon for complementary functions such as propeller guards and docking supports for the stern. In this case their outer edges may be reinforced with shallow flanges simflar to those described for the rollresisting keels in Sec. 73.17.

These flanges must

FIXED-APPENDAGE DESIGN

Sec. 73.22

699

be placed in the lines of flow, but the proper

as

determined from a tuft test. Design of Torque-Compensating Fins. 73.21 So far as known, there are no finished designs or working shipboard installations of devices in-

resultant velocity at

increasing propeller torque throughout the ship

tended to counteract the effect of the unsym-

speed range.

position

metrical

is

easily

propelling-plant

torque,

described

in

Sec. 33.19.

The approximate heel angle resulting from unbalanced propeller torque is readily determined by entering the righting-moment curve of the ship with the propeller torque Q. In this case it is assumed that the righting moments are not altered due to forward motion of the vessel. Any such effect is usually of the second order of mag-

the propeller

torque

is

a function of the

an average blade element.

The counterbalancing torque thus ship speed

and rate

increases with

of rotation, to

match the

To provide the necessary compensating torque from one diametral fin, the contra-effect could be somewhat larger than is customary for a contrarudder. Methods of developing the twisted shape for the latter are described in Sec. 74.16.

A

set of torque-compensating fins, each

that this be accomplished by fitting abaft the

having symmetrical with respect to the shaft axis, could be used if convenient in place of the single fin with two arms. The problem here, as with the two-arm assembly, is to support the contra-fins in their proper positions without increasing the appendage resist-

screw propeller a fixed fin traversing some convenient diameter of the outflow jet. This fin,

ance by a disproportionate amount. Fig. 73. P is a sketch of such a device, with a vertical fin worked

well-known contra-rudder described in is twisted on opposite sides of the shaft axis to develop thrust while extracting rotational energy from the outflow jet. It thus combines a torque-compensating device with a means of improving the propulsive efficiency. The counterbalancing torque produced by this device is a function of the velocity of flow over it, just

compoimd-type contra-rudder assembly. is supported at the center by the rudder post and at its outer ends by two vertical struts. An upward component of flow abaft the single propeller might require a tilting of the horizontal arm, downward and forward. Sec. 69.13 describes a method of using imsymmetric spray strips on a high-speed planing craft to achieve a measure of dynamic reaction to

nitude.

As the

first

stage in such a study

it is

proposed

like the

Sec. 37.16,

Heelini^

Moment Due

to Engine.

Lateral

Forces

Exerted on Contra- Fins In

three

or

more

radial

arms,

into a

A

horizontal fin

unbalanced engine torque. 73.22 Fixed Guards and Fenders. Projections from the fair surface of the hull in the form of fixed guards or fenders are of two types, those primarily vertical and those which lie generally parallel to the direction of motion. Of the first type are guards for external scupper

Rotating

Water

of

Propeller

-Outflow Jet

and drainage leads or, occasionally, for operating gear which must be external to the shell. Of the second type are fenders and projecting fender strakes, extending over considerable portions of

the length but covering limited portions of a transverse section.

PLAN VIEW FROM ABOVE

The vertical projections are an abomination from every point of view and are to be avoided wherever practicable. They throw spray at all except the lowest speeds and they cause pressure resistance and separation drag, with holes in the water behind them. They cover up shell surfaces hable to heavy corrosion and they are vulnerable to damage from other craft or heavy objects lying alongside.

Fig. 73. P

Proposed Scheme for Counteracting Unsymmetric Engine Torque

Longitudinal fenders, section or construction,

regardless

of

type

of

must often be placed at

HYDRODYNAMICS

700

maximum waterline or extreme positions may vary vertically, or

IN SHIP DESIGN

73.23

Sec.

the positions of

1946, Fig. 14, p. 332].

beam. Tiiese girthwise, from station to station on a ship, so the fenders can seldom be led along the Unes of flow to insure minimum drag. Perhaps this is just as well, because most of them lie near the freewater surface. Here the lines of flow under the waves of the Velox system change with speed and with position along the length. Moderate amounts of roUing and pitching also change the direction

schematic sketch of a similar fender strake.

of the resultant flow accordingly. first-cost,

and maintenance factors, as well as hydrodynamics, nothing can equal or surpass the heavy fender strake which forms an integral part of the shell plating.

It involves practically all

no

discontinuities

A

its

grammed

at

1

in Fig. 73. Q. It

is

dia-

adequate, never-

it,

in

[(now

bow rudder

close-fitting guard, designed for a cross-

SBMEB)

Another one

is

is

published in

The Shipbuilder

Jan-Jun 1914, Vol. X, p. 36]. given by G. de Rooij ["Practical

Shipbuilding," 1953, Fig. 495, p. 203]. Twin weed skegs outboard of the twin propellers of a 63-ft

motorboat are shown

in

(American) Motorship,

April 1948, page 34.

in

stiffness,

necessary

profile aft, plus the

rather large-scale drawing of a

and

some transverse

for

a

throw spray.

parts of the

curvature

it is

is

the deepest draft-aft condition, to insure that these guards remain out of water and do not

form of the hull except the strake care of all problems of leaky connections, unseen corrosion, spray throwing, and the like. It serves best when acting as the outer boundary of an irregular hull section, with It takes

wave

73.Q

the usual disturbed-surface layer covering

in the fair

edges.

of Fig.

placing propeller guards

to take account of the

channel steamer,

Considering structural, fabrication,

increase in drag. It eliminates

When

Diagram 2

Design

73.23 ages.

Means

to

Avoid Vibration of Append-

predicting

of

and avoiding the

singing of screw propellers are outlined in Sees. 23.7

and

70.46. It

is

equally important that those

main ship

and those appendages

hull

the vicinity of the propulsion device (s)

be designed to have certain natural periods of vibration in water.

These

.should

be different from the

exciting frequency of the blades or other principal

parts

the

of

propulsion

device (s).

There are

techniques available, similar to those described

TMB

in

Report R-22 of April 1940, whereby the

natural frequencies of the parts of appendages in Sinole- Thickness

may be determined on existing ships, or on new ships -prior to the first sea trial. This involves the local attachment of small vibration generators question

Fender Stroke

Transverse Curvature Gives This Plate

Inherent Stiffness

in watertight casings,

appendages

or the excitation of the

in their natural

modes, also in water,

by connecting the generators and the appendages ^

Fender 5tral<e

with long struts.

Long, slender, and well-streamlined appendages Uke strut arms nevertheless require checking for their susceptibility to resonant vibration. Under

Structure is Schematic and ExQoaeroted for Emphasis

operating conditions they Fig. 73.Q

Forms of Heavy Fender Steakes

vortex street or

trail.

may

be followed by a

Existing data (1955) are far

from adequate as to the eddymaking charactheless,

with possibly some slight increase in

teristics of

weight, for vertical ship sides against vertical

yawed

walls, sketched at 2 in the figure.

wavegoing.

A

heavy fender strake

made an

of this type

is

always

outside strake. If the seams are riveted

A

elongated sections, especially in the

attitudes to be found during turning

few general rules

may

be laid

(1)

fender strake of this kind, standing vertical at

any

section,

are

opposite separation points,

the

maximum beam J.

L. Bates

of an underwater bulge, is and I. J. Wanless [SNAME,

as a

help to the designer in this respect:

or if they are welded a strake is easily removed from the outside for repair or replacement. A

shown by

down

and

A

vortex street or

yawed

trail

may

be shed from

or otherwise, on which there

these separation points

may

shift

and on which forward or aft

FIXED-APPENDAGE DESIGN

Sec. 73.24

along the section outline without encountering abrupt discontinuities. One such section is a thin ellipse; another

is

a strut section with an

The probable

angle of non-axial flow for any

may

appendage section

The nominal

(a)

be estimated from:

The The

(c)

non-axiality of the flow, con-

flow-obstructing or flow-straightening

For example, an appendage far removed from the estimated position of the pivoting point in a tight turn has a nominal degree of non-axial flow

than the average drift angle measured at the CG. On the other hand, if the appendage is in a tunnel, or directly abaft a long skeg, it is protected, in a way, from is

far greater

of the ship,

this cross flow.

An example

of the

method

of estimating the

vibratory characteristics of a typical streamlined

appendage

in the

form of a long strut arm

is

given in Sec. 46.9. 73.24 Design of Water Inlet and Discharge Openings Through the Shell. This section treats only of the design of inlet and discharge openings for circulating water to the main propelling machinery or to pumping plants large in comparison to that machinery, such as in a fireboat. The design of secondary openings for taking water into and discharging it from the hull of a ship represents no particular problem that does not occur with the major openings. The comments and illustrations of Sees. 8.6, 8.7, and 36.20 apply to all these openings in a general way. For the discussion of the present section to

assume axes

it is

convenient

of reference fixed in the ship.

surrounding Avater

is

The

then considered as a stream

flowing past a stationary opening in the hull.

The

kinetic energy in the

main injection narrow limits by the position of the internal heat exchangers. There is some

The

longitudinal position of the

fixed within rather

latitude

position of the appendage on the ship

features in the vicinity.

that

mining figure appears not to be the speed-length quotient or the Froude number but the absolute

is

sidering the type of ship motion (b)

exceeds 20 kt in service. In this case the deter-

speed of the ship.

elliptic trailing edge. (2)

701

boundary layer may

be utilized for forcing water through internal piping and heat exchangers of one kind or another whenever there is sufficient velocity head for conversion into the requisite pressure head. In this case the available velocity head is that corresponding to flow in the boundary layer along the shell. This may be taken as 0.5 the nominal ship speed for prehminary estimates, less the head corresponding to the desired velocity through the internal system. In practice, it is found that there is no particular advantage in using the scoop type of injection unless the speed of the ship equals or

in

transverse position to suit service

conditions, with the proviso that the injection

must always remain submerged under the most severe kinds of wavegoing. For an icebreaker the logical position for the injection is under the bottom, clear of as much ice as possible. For a vessel to operate in shallow water it should not be too near the bottom, otherwise it may be in the mud. For vessels which may be required to operate in waves in a relatively light condition, especially at light or shallow draft forward, there

problems other than that of picking up water with the scoop. Air bubbles are entrained by wave action or impacts under the forefoot, but it is probable that they follow fairly definite paths under the bottom. Water injections are to be kept clear of these paths, using model tests to determine the airare

bubble routes. Particularly, injections should not be instaUed close below roll-resisting keels, docking and resting keels, or other longitudinal appendages beneath which air is liable to be trapped.

When

considering the use of a condenser-scoop

installation, or

when

selecting the type, the price

—and

to be paid in resistance

effective

power

always involves a combination of the scoop inlet and the discharge. Since it is the discharge which often creates the hydraulic (suction) head necessary to draw water through the condensers, this is the element of the pair which may be expected to develop the greater resistance.

Regardless of the merits of any one hydrodyof inlet scoop or discharge outlet

namic design there

is

always the problem of finding room for

these fittings in the bottom or the lower corners

under or alongside the machinery is assigned there is the matter of cutting into main structural members. Finally, the large piping has to be led to and from the condenser(s), and space must be made available of the ship

spaces.

When room

for a stand-by power-driven circulating

pump

for

maneuvering. In Sir Charles Parsons' Turbinia of 1897 there were two condensers with circulating water fed to them in series from two scoops, one on each

HYDRODYNAMICS

702

Each scoop was fitted with a one could act as a discharge while the other was acting as an inlet. By thromng over both flaps, the water direction was reversed and side of the vessel. flap so that

any

was drawn

foreign matter choking the tubes

overboard.

At a

later stage in the life of the vessel

an overboard discharge was fitted in the crossover between the after ends of the condensers so that both scoops could take in water simultaneously and pass it through the condensers in parallel [INA, 1897, p. 233; ASNE, May 1897, p. 376]. In the flush-lip inlets of the Schmidt type, in which there is no scoop or external projection as such, it is no small matter to guard against the entrance of large fish and foreign objects into the heat exchangers. Longitudinal bars must be fitted across the scoop entrance, spaced perhaps 0.3 ft apart. They need rigidity to serve as guards and to prevent lateral vibration. They must have bolted end connections for ready removal.

flow must be maintained around desired quantity.

The bars and

them

their

The

must make so Uttle disturbance that air is not pulled out of solution in the water and passed along to the heat exchanger. For all types of inlet it seems best to mount the guard bars or in a single, integral streamlined assembly which can be held in place by recessed bolts and removed as a unit. There is great merit in a type of inlet and discharge, hydrodynamically efficient, which can lead into and out of the machinery spaces in a transverse plane, making a rather sharp angle

guide vanes

shell,

oped in

Italy,

up

to 90 deg.

Such a design, devel-

employs a generally rectangular

Partial Afterbody; Plan

of

Tronsom- Stern

ABC

blocks of ice, and other foreign objects. Besides having an efficiency and a resistance

fish,

apparently comparable to scoops of the Schmidt design, the Italian arrangement of Lattanzi and Bellante [Italian patent 404,551 of 18 Jun 1943;

Bureau

of Ships,

Vol.

especially

Fig. 73.11

is

Basin, 1940,

superior

of

flow,

the absence of vortexes within the

Although it has not, so far as known, been tested as a discharge outlet there is no reason inlet diffuser.

why

it

should not work equally well in either and discharges

direction, as did the similar scoops

in

destroyers and other vessels of the

War

World

I period.

Despite the scoops there

is

known workability of flush inlet much to be said for a scoop

also

—which project

and a discharge

sufficiently

from

the ship's side to take advantage of the greater the boundary layer at a small distance velocity

m

from the shell. The right-hand upper diagram of Fig. 73.R is an attempt to sketch a device which may produce the desired result. In an orthodox form of flush scoop the slowly moving water entering on the forward side, combined with the faster moving water entering on the after side, often creates an eddy with backflow just abaft the forward surface of the diffuser.

The guide-vane

arrangement should be such as to pick up an appreciable "belt" of water at the inside of the

Ship, from

Outlet

Dept., Transl. 529. Also

Rep Rome Model

X] has the advantage

Fig. 66.

The Purpose

of the

to Obtain the in

I

Navy

Orlando, M., Ann.

is

^-'^^j

Sec. 73.24

opening with a moderately projecting Hp. A set of sharply curved guide vanes, as used ui aU modern water tunnels and channels, changes the direction of the water. The guide vanes serve also as strainer bars to prevent the entry of large

in the

end connec-

tions

with the

IN SHIP DESIGN

Unequal Guide-Vane SpQcint]

Moximum Uniform

the Diffuser

on Starboard Side

Main-Injection and Discharge Layout for Transom-Stern

ABC

Ship

Velocity

FIXED-APPENDAGE DESIGN

Sec. 73.25

boundary layer and accelerate

The

it

inside the scoop.

vanes should pick up a smaller quantity of water in the more rapidly moving after guide

intermediate layers and slow

it

down

pended

diffuser the

is

(4)

speed craft as well, the roll-resisting keels along the bilge corners act to collect the air bubbles passing under the ship and to shoot them out

two streams from the after inboard sides of phenomenon is particularly

the bilge keels. This

when

air

with the water. The regions in the vicinity of the flowlines emanating from the trailing edges of the bilge keels should therefore be kept clear of injection or inlet openings through the shell, to prevent accumulations of air in the water sides or cooling jackets of heat-exchanger systems. The position shown in the left diagram of bubbles

Fig.

are

73.R

main condenser

of the

ABC

this air-collecting region

ship

is

on the port

if

fitted,

the

(5)

and involves too

large a

Bibliography

on

of

the

flow

into

inlet

F.,

"Some Notes on E.H.P. Characteristics,"

Calculations

ASNE, Nov

1933,

XLV,

dicted (6)

by

tests of a self-propelled model.

Schade, H. A., Calculations,"

534-535. This

"Discussion of Notes on E.H.P.

ASNE, Nov is

1933, Vol.

XLV,

pp.

a discussion of the preceding

reference (5).

(8)

(9)

Schmidt, H. F., "Further Discussions on Notes on EHP Calculations," ASNE, Feb 1934, Vol. XL VI, pp. 107-109. This is in turn a reply to reference (6). Schade, H. A., "Discussion of Mr. Schmidt's Reply," ASNE, Feb 1934, Vol. XL VI, pp. 110-111 Schmidt, H. F., "Reply to Discussion by Lt. H. A.

Schade," ASNE, May 1934, Vol. XL VI, pp. 251253. This article contains a photograph showing flowlines into an inclined inlet without lip. (10) Schmidt, H. F., "A Criterion for Scoop Cavitation," ASNE, Aug 1934, Vol. XLVI, pp. 352-356. Facing p. 353 of this reference there is a photograph

Condenser

Ap-

the six

in

densers through inlet scoops, utilizing the forward motion of the ship. The author points out that this increment has to be added to the power pre-

Scoops.

rapidly for the past half-century or more.

191-213. Discusses dis-

drive the ship, of taking in cooling water for con-

(11)

Research on inlets of the scoop type, for taking water into condensers and other large heat exchangers, has continued steadily if not

14 inches out

pp. 528-533. This brief paper discusses the influence, on the effective power required to

corresponding to those in the referenced Partial

features

Schmidt, H. Vol.

(7)

sketches.

73.25

practical

and Propeller

hole in the shell, fairing pieces can always be

first

scoops for internal heat exchangers:

it,

sidered too elaborate,

1939, Vol. 51, pp.

the

The arguments and explanations

structural, mechanical, or space considera-

demand

7), for

references which follow afford a useful insight into

side.

water can be discharged into the boundary layer at any angle up to 90 deg with the flow, diagrammed in Figs. 8.G and 8.H. Rarely, however, is there not sufficient room to provide a short elbow with multiple turning vanes for changing the flow direction mechanically instead of producing a hydrodynamic disturbance in the boundary layer. If the elbow is contions

May

(CL

charge as well as inlet performance.

well clear of

Openings in the hull for the discharge of water from internal machinery may be located with relative freedom to suit the internal arrangements. In fact, they need not even be below the water surface under all conditions of operation. It is logical to lead water out through the hull in the same manner as it was brought in, by inverting the scoop section and directing it into the boundary layer at a small angle to the flow there. To be sure,

Schmidt,

U.S.S. Raleigh

circulating

for the circulating-water inlet to the

partial

from the shell, in way of the inlet-scoop position. Weske, J. R., "Investigation of the Action of Condenser Scoops Based upon Model Tests," ASNE,

by the (2)

noticeable in a circulating-water channel

giving

wishes to pursue

(3)

water shall be moving regularly at

On high-speed vessels, and probably on medium-

in

who

H. F., "Theoretical and Experimental Study of Condenser Scoops," ASNE, Feb. 1930, Vol. XLII, pp. 1-38. Comprises a basic treatment, beginning with hydrodynamic fundamentals. Hanzlik, H. J., "Condenser Scoops in Marine Installations," ASNE, May 1931, pp. 250-264 Schmidt, H. F., and Cox, O. L., "Test on a OneQuarter Scale Model Scoop on the U.S.S. Welborn C. Wood and Preparatory Laboratory Experiments," ASNE, Aug 1931, Vol. XLIII, pp. 435-466. Fig. 5 opposite p. 437 shows the inlet flow in the plane of the shell. Fig. 13 on p. 445 gives variations in pressure and velocity, as measured on the

that at the entrance to the

four velocity vectors of Fig. 73. R.

of

this subject further:

inside the

more-or-less uniform velocity, indicated

is

references

coverage for the reader

(1)

The aim

scoop.

703

a Hst

(12)

showing the lines of flow into the model of a lipless inlet scoop of the Schmidt type. "Comparative Tests of Condenser Scoops," EMB Rep. 384, Jul 1934. Describes tests run on EMB model 3293, representing the DD 364-379 class of destroyers of the U.S. Navy. Rabbeno, G., "Appunti Prelimineari sulle Variazioni per Reciprooa Influenza nelle Potenze Assorbita dalla Circolazione Refrigerante e dalla Propulsione

HYDRODYNAMICS

70-1

Turbonavi Veloci (Preliminary Notes on Variations, due to Reciprocal Influence, in the Power Absorbed by the Cooling (Condensing) Water and by the Propulsion Plant in High-Speed Turbine-Driven Ships), Ann. Rep. Rome Model Basin (in TMB library), 1936, Vol. VI, pp. 67-76 velle

"La

(13) Orlando, M.,

Circolazione ai Condensatori nel

(The Circulation

Naviglio Veloce

in

the

densers of High-Speed Ships)," Ann. Rep.

Model Basin

(in

TMB

library),

IN SHIP DESIGN

Sec. 73.26

a measure of design and construccomparable to that devoted to the bossing, strut, and propeller design. The use of

should

call for

tion effort

partly

recessed

zinc

socket-head

plates,

cap

and similar devices is one step toward improvement, indicated in Fig. 73. S. bolts, shoulder nuts,

Con-

Rome

1936, Vol. VI,

pp. 76-90

and Hewins, E. F., "Condenser Scoop Design," SNAME, 1940, pp. 277-293; 301-304. This is an excellent, comprehensive, detailed dis-

(14) Reilly, J. R.,

cussion of the problem of designing inlet and dis-

charge scoops, with a great deal of e.\perimental and design data and an example worked out for a

and outlet scoops. The text is supplemented by numerous flow diagrams. TMB Report R-43 of September 1941 entitled "The Effect of the Flow of Water Through Condenser Scoops on the Resistance of a Destroyer Model."

Limit Line for Wastage Before (?eplacement

pair of inlet

(15)

(16)

A

Chamfer Outside Edaes

All

Around Reaordlcss of Flow Direction

Elastic

Stop Nut

y'inch Stud Nf45dei]

theoretical discussion of the water flow into scoops

of various shapes, in which flow nets have been prepared by conformal and Schwartz-Christoffel transformations, is given by C. Igonet in ATMA, 1945, Vol. 44, pp. 447-466. So far as known no translation (17)

is

MQ>y

available.

Be End-Welded Studs With

BuShips Translation 529, of article entitled "Esperienze Aerodinamiche su Modelli di Booohe di Presa per I'Acqua di Raffreddamento dei Condensatori Marini (Aerodynamic Tests on Models of Intake Scoops for Cooling Water of Marine Condensers)," by Dr. B. Lattanzi and Dr. E. Bellante, Aerodynamic Laboratory of Guidonia,

^45 (^q

All

Arc-Initiating

Material

Dimensions ore

in

2

Inches

26 Jul 1941 C. W., Davis, W. F., Randall, L. M., and Mossman, E. A., "Experimental Investigation of NACA Submerged Duct Entrances," NACA Rep.

(18) Frick,

ACR

Fig.

73. S

Proposed Fairing and Attachment Galvanic-Action Protectors

of

A5I20, Oct 1945

and Ellsworth, W. M., Jr., "Progress Report: Research on Main Injection Scoops and Overboard Discharges," Rep. 793, Sep 1951 (20) Spannhake, W., "Comments and Calculations on the Problem of the Condenser Scoop," Rep 790,

(19) Breshn, J. P.,

TMB

TMB

Certainly there appears

which prides ments,

for

itself

the

protectors on

proportion of

Oct 1951.

on

little

its

addition

excuse, in

an age

technologic achieveof

fully

protruding

any ship which spends a reasonable its life

underway.

In areas of the waters of the world where Pertinent design notes on discharge openings are given

by E.

P. Worthen, with a drawing of the

device used on the

[SNAME,

Manner

class of the 1950's

1953, Fig. 43, p. 201].

Design and Installation of GalvanicAction Protectors. It can not be expected that carefully shaped bossing and skeg terminations, strut arms and hubs, rudder posts, and other fixed appendages will give creditable hydrodynamic performance if cluttered up with excrescences in the form of galvanic-action protectors, studs, nuts, and what not. It appears probable that these protectors will have to be fitted for some time to come. Their installation 73.26

corrosion of the steel hull plating

is

exceptionally

severe, this corrosion is often reduced to small

proportions by bolting rows of plates or blocks of

anodic materials directly to the shell plating [Kurr, G. W., "Check Costly Hull Corrosion," Mar. Eng'g., Nov 1954, pp. 57-60, also p. 12]. The added drag of these excrescences is undoubtedly large. However, it might well be less than the added friction drag of the loose bottom paint and the severely pitted plating surfaces which would be encountered without the anodic protectors.

Other methods involving external devices

in

the form of appendages, temporary or permanent,

FIXED-APPENDAGE DESIGN

Sec. 73.27

are described

Streever

by H.

[SNAME,

F.

Harvey

Jr.,

and 0.

1953, pp. 431-403]; also

J.

by

D. P. Graham, F. E. Cook, and H. S. Preiser in paper "Cathodic Protection in the U. S. Navy; Research-Development-Design" [SNAME, their

Nov

Design Notes for Locating Echo-Ranging and Sound Gear on Merchant Vessels. A good underwater sound installation for transmitting and receiving, whether of the fixed or retractable type, involves a neat combination of acoustic and mechanical engineering, hydrodynamics, and naval architecture. Aside from the purely acoustic features involved, the most important single factor in an efficient design is to shape the sound head or sound dome so that it is free from cavitation and separation. It must also be placed under the ship in a position where it is clear of air entrained in the streams which 73.27

A

it.

sound head

lined

body

form

of a

of

may

be in the form of a streamresembling the hull

revolution,

stubby true submarine vessel or an carried by a post or strut, it forms an assembly which is usually retractable. Such a form is reasonably free from flow noises but it does not lend itself to swinging bodily in azimuth for horizontal search. Furthermore, when yawed slightly it is no longer a streamlined body. A airship.

with the

sound head rotating inside it, can rarely be made long enough to be entirely free of separation, air bubbles, and possible cavitation along its after or trailing portion.

A

1956].

flow past

705

vertical, streamlined 2-diml enclosure,

When

fore-and-aft location of the sound gear at a distance abaft the stem of about 0.15F^, where V is

in kt

and the

.r-distance is in

as satisfactory as any.

ft,

appears to be

More important, however,

than both shape and fore-and-aft position may be the sound-head distance below the hull. A deep projection keeps the sound head always under water when the vessel is pitching. Further, it is below the boundary layer and beneath the streams of air bubbles entrained at the bow, near the free surface, and flowing aft under the hull. This usually requires that the head be extensible

and retractable. For the ABC ship at say 20 kt, the distance abaft the stem would be 0.15(20)^ or 60 ft, corresponding to about Sta. 2.35. At a distance of 4 ft below the keel the head should be well below the most disturbed portion of the boundary layer. For a fishing trawler traveling at say 10 kt, the head could be at a distance of 0.15(10)'^ or 15 ft from the bow. If also placed 4 ft below the keel it should be in a good listening position and should remain submerged unless the vessel is pitching deeply.

CHAPTER

The Design

74

of the Movable Appendages and

Control Surfaces 74.1 74.2 74 3 74.4 .

General

706 706 708

Positioning Rudders and Planes Single or Multiple Rudders?

74.7

the Rudder and the Adjacent Portion of the Ship Design Procedure for Conflicting Steering Requirements First Approximation to Control-Surface Area Determining the Proper Areas of Various

74.8

Positioning the Stock Axis Relative to the

74.9

Selection

74.5 74.6

Shaping

Control Surfaces

Structural fected

74.11 74.12

713

720 of

Chordwise

Sections

74.10

713

715

Blade; Degree of Balance

and Proportioning

709

722 Control-Surface Design as Af-

by Hydrodynamics

.......

Design Notes for Motorboat Rudders Design of Close-Coupled and Compound Rudders .

723

.

724

.

726

74

MOVABLE-APPENDAGE DESIGN

Sec. 74.2 Twin

Rudders

I

down

707

to the lower corner, air

may "jump"

to the

reduced-pressure side of the rudder. This occurs when the gap between the transom corner and

rudder

is

small enough or the pressure differential

large enough.

The

resulting air leakage greatly

For the

reduces the rudder force on a turn. V

Schemotic Inflow"

rudders described in Sec. 37.18, air leakage of this kind is necessary to the success of the arrangement, but for a ship not carrying "lifting"

Jet Diometer Less Thon

'

D But

Velocity Greater

Relotiv

Velocity

Fig. 74. a

VftOt

Disc Position

Thon VX

them,

Diagram Illusteating Augment op

OtJTPLOW-jET Velocity at a

air finding its

way

to a rudder

detrimental. Testing techniques are

Rudder Position

definitely

is

now

available

matically an installation of this kind. This rule

model basins whereby this air leakage can be photographed and detected on a free-running model during a turn. The air leakage

a two

could be prevented in a transom-stern design by extending the bottom beyond the transom plane

in

also applies to the fore-and-aft positioning of single rudder

between the outflow

jets of

screw propellers, provided the jets are close enough so that they impinge upon it at reasonable rudder angles, say 20 deg or more. Indeed, for single-screw ships, where rudder effect alone considered,

it is

is

well to keep the leading edge of

the rudder well abaft the propeller

if

this can

conveniently be done.

Some

useful information relative to flow at the

the larger

as a thin horizontal

introduce

lip.

However,

when backing

difficulties

running in an overtaking

this

might

or

when

sea.

Rudders and planes hung wholly or partly on fins, and keels are most effective as lateral-force-producing devices when coupled closely to those fixed members. This the after ends of horns, skegs,

mean that they give rapid when angled quickly, as discussed in

does not necessarily

on a model, as affected by the boundary layer, by the outflow jets from adjacent screw propellers, and by the lateral motion of the stern during a turn, is given by W. G. Surber, Jr. ["An Investigation of the Flow in the Region of the Rudder of a Free-Turning Model of a Multiple-Screw Ship," TMB Rep. 998, Oct 1955]. It has not been possible to unearth corresponding data from tests of single- and

response

twin-screw models.

This usually forms abaft the hub or fairing cap of a screw propeller on a fast or high-speed ship but there are evidences that it may appear at a

centerline rudder position

On

where maneuverability and rudder an important requirement, the movable blades of rudders are placed well below the surface or their upper portions are protected in some other effective way from partial breakdown due to leakage of air from the surface. The blade lengths at the top, near the surface, may be made shorter than at the bottom. The upper after corner of a rudder may be cut back, as was done for the vessels

effect is

transom-stern

ABC

ship; see Fig. 74.

K

of Sec.

Sec.

74.18.

Special devices to prevent leakage

pressure through the hinge are

of differential

very

much worth

some of them are deand 74.14 and illustrated

while;

scribed in Sees. 73.14 in Fig. 73.K.

A rudder or plane should definitely be kept clear of a swirl core or hub-vortex cavity, described in

and

Sec. 23.14

illustrated in Figs.

23.K and 23.L.

moderate speed. The cavity is likely to be so large that the portion of a rudder against which it

strikes is totally ineffective.

The rudder

struc-

subject to pitting, erosion, and hammering, which may result in fracture of the parts and tearing off of the portion under attack. ture in its

A

wake

is

rudder on a fast but not high-speed ship,

subject to

damage

of

this kind,

is

shown by

change of trim, and other factors which obtain during turning are not to be lost sight of in checking for

V. L. Russo and E. K. Sullivan [SNAME, 1953, pp. 124-125]. Another such rudder, on a slower

possible air leakage to the reduced-pressure side

York, October 1954, page 44. It is known that in some cases, such as following a sharp turn, the swirl core or hub vortex shifts around on the fairing cap. In other words, it does not always trail

74.15.

of the

The

effects of heel,

wave

action,

rudder during that maneuver.

The

trailing edge of a steering rudder should not be placed too near the lower corner of an immersed transom. When the speed is high enough

to expose the whole after surface of the transom,

ship, is illustrated in

Marine Engineering,

New

from the exact point or tail of the cap. A good rule, therefore, is to keep clear of a possible swirl core

HYDRODYNAMICS

708

having a diameter as large as that

of the hub,

and

following the direction of the streamlines for the ship flow in the \'icinity.

Wherever practicable, it should be possible to remove propellers, dismantle propeller shafts, and examine propeller bearings without disturbing or removing rudders or diving planes mounted near them. It is not necessary that the axes of offset rudders be exactly vertical or that those of multiple rudders be parallel, if their hydrodynamic performance can be improved thereby. Mechanical

simplicity in the steering gear need not be a

determining factor in cases of this kind. With regard to the placing of rudders in regions

Projected Rudder Area at

Full

Sec. 74.3

good flow, where they can do what is e.xpected of them, the design rule embodied by W. J. M. Rankine on page 95 of his 1866 treatise on "Shipbuilding: Theoretical and Practical" is as applicable today as the day it was written: "It is also necessary that the rudder should be immersed, not in a mass of eddies dragging behind the ship, but amongst particles of water whose motion, relatively to the ship, consists in a steady flow astern. Hence the

same

and fineness of the water-lines and buttockafterbody which are essential to speed and

fairness

lines of the

economy

of

power are

good steering also."

essential to

Single or Multiple Rudders? 74.3 In a normal form of twin-screw stern a single rudder hung between two propellers usually angles far enough so that a considerable portion of the trailing area of its blade swings into the projected

DWL

Anole

IN SHIP DESIGN of

disc area of one or the other of the propellers. On a Stern of Normal Form the Flow

is

Aft, Upward,

ond Inward. The Propeller Outflow

Marked b'y Broken Lines, Follow Jets,

Propeller- Disc Positions

\ Propeller Outflow- Jet Section

Opposite the

Tail

of

This Flow

is true even though account customary inward and upward

This

twin-screw propeller outflow

taken of the

is

shifts

the

general

and

to the contraction in those jets.

direction

of

of

the

conforming to

jets,

the vicinity,

flow in

Diagram

1

of Fig. 74. B illustrates schematically the situa-

tion described.

the Rudder

A

single rudder

is

sometimes placed between

two screw propellers which

lie

so far apart trans-

versely that the rudder blade does not swing

appreciably into the outflow jet of either at

Broken Lines Represent SchemoticQlly the Sec-

tions of the Propeller Outflow Jets

Opposite the

Rudder Positions Rudders May Be Positive Cleorance from

Hub

'as

5hown

Desiroble But Not Necessary

Inboard or Outboard of the

o

Shafts

Schematic Outlines of_-— Propeller Jets,

Neqiectinq

For on Original Installation of this kind,

Presence of Ship

It is possible that the single rudder,

-

lying in

The same rudder, Ij'ing in a "weak" flow, with a large positive wake velocity and a small speed of advance, is inadequate to maneuver the ship. Smaller twin rudders, lying desired lateral force.

close to or within the outflow jets, are indicated for situations of this kind.

Separated b^ Greater

if

a "strong" flow having a small positive or a slight negative wake velocity, produces the

Propeller and Rudder

.Should

its

extreme range of angle. Although not always lacking in steering and turning action, such a rudder is liable not to function adequately, no matter what its area.

by diagram 2 whatever

Here again, depicted

of Fig. 74. B,

lateral

or

account

is

taken of

displacement,

vertical

or

both, results from the fact that the propeller

outflow jot contracts and that

it

follows

the

direction of flow under the hull.

Rudder Ancjle

Efforts to achieve the

same

biplane or triplane rudders, is

found

inadequate,

may

with so-called

efi^ect

when a be

single blade

disappointing.

Multi-blade rudders, operated by a single stock FiG.|^74.B

of Multiple Rudders Respect to Outflow Jets

Positions

'

with

and steering

gear, are usually used.

These repre-

sent a simpler alteration than fitting twin rudders

Sec. 74

MOVABLE-APPENDAGE DESIGN

A

abaft the propellers. In the event multiple blades are used, the wmg or offset blades should lie abaft the stock axis of the main blade, so that

when swung farther

from the centerplane, indicated

away from the outflow

they are supposed to

utilize.

merchant or combatant,

jets

one-quarter of the beam, should have a rudder

behind it. Every propulsion device on a submarine should have a diving plane in its outflow jet. A multiple-skeg stern logically embodies a rudder behind every skeg carrying a screw propeller, whether a high degree of maneuverability specifically called for or not.

ABC

arch stern of the

On

the alternative

ship, Avith its single large

two skegs, it is logical to hang a rudder on the after end of each skeg. Fig. 74. of Sec. 74.15 shows how this is done. When shifting from a single rudder to twin rudders in a design, without other major changes in the hull, it is good practice to give each twin rudder a blade area of about 0.6 to 0.7 the area of the single rudder. This is justified by the propeller between

increase in turning effort achieved with the larger total area. It is realized that the total weight of twin rudders, supports, and steering gear, based on only 0.5 the area of a single rudder, is almost certainly greater than for a single rudder. In other words, if the increased weight of double is accepted, it is good design to make it worth while by increasing the rudder effect at the same time. However, this should not be

rudders really

carried so far that the turns

made by the

vessel

are excessively sharp and the ship speed in the

turn

is

so greatly reduced that its

maneuvering

characteristics are impaired.

The minimum

transverse distance between the

stock axes of the blades of multiple rudders practicable,

maximum fore

and

made

is, if

equal to or greater than the

blade length of each rudder, measured

aft, so

that the pressure field of one will

not interfere too

much with

when_^they are fully angled.

requires multiple

traveling in swift, turbulent currents, the craft requires multiple rudders for itself alone, to say

nothing of the need for maneuvering when other craft are being pushed.

may

be required to dodge aboveAvater and underwater missiles in a future emergency. For a ship requiring a high degree of maneuverability every offset screw propeller whose axis lies within a reasonable distance of the centerline, say not more than

is

itself,

and turning moments. For maneuvering in extremely shallow water, when the bed clearance is measured in inches rather than in feet, and when

the wing blades back ships,

the entire puish as well as

in dia-

elements are swung to achieve large angles of they move toward the centerline by (1 — cos 8) times their offset distance. In effect,

modern

depth, and with need for steering and maneuvering

rudders to achieve the necessary lateral forces

attack

All

709

shallow-draft pushboat, with limited rudder

move

at an angle the wing blades

3 of Fig. 74. B. Otherwise, as the Aving rudder

gram

A

that of the other,

In

many

by sternwheels,

river craft propelled

the rudders are placed ahead of rather than abaft the propulsion devices. Here they do not

an outflow

in

jet of

augmented

the equivalent effect

work

velocity, so that

achieved only by fitting

is

multiple rudders of larger total area.

The

limited

Sometimes the multiplication of rudder area ahead of the sternwheels on these vessels is not sufficient. To make up for it, one or two "monkey rudders" are hung on a frame abaft the wheels, to take advantage of the draft

is

also a factor here.

increased velocity in the outflow

jet.

Shaping the Rudder and the Adjacent

74.4

Portion of the Ship.

Fortunately, the designer

often has considerable freedom in shaping the

and

stern profile of a ship,

in the contour

position of the rudder(s). Further, he

is

and

often

permitted to work up alternative stern arrangements; in these he can forget tradition and strive for maximum performance. For example, in a

somewhat from the normal form it may be found possible to work in a sort of flat or shallow-V shelf, well submerged at load draft, over the top of a spade-type rudder. single-screw stern departing

If so,

the vessel benefits from:

(a)

An

increase in the rudder aspect ratio

the

lift

coefficient for

and

a limited range of rudder

fit and the negligible between the hull and the top of the rudder. To keep the horizontal gap small, at the top of the rudder, bolted palms for connecting the blade to the stock may be placed somewhat below the extreme top of the rudder. The recesses for assembling the bolts may be

angle. This

is

due to the

close

differential-pressure leakage

closed

by cover

plates.

Providing the equivalent of a surface plate to prevent undue air leakage from the surface and breakdown of the rudder action when the — Ap's (b)

are large (c)

Providing an excellent internal support for

the thrust bearing,

tiller,

and steering

gear.

HYDRODYNAMICS

710 111

case the V-shape of the stern

ately shallow,

and the

sides rise at

angle from the edges of the there

is

flat

is only moderan appreciable

over the rudder,

an opportunity to derive some lateral swingmg moment directly

pressure on and some

from

the hull itself.

This

because the hull

is

is

near the top of the rudder and because of the close fit there. At the designed speed, the crest of the stern

wave

is

expected to cover a sizable

IN SHIP DESIGN

Sec. 74.4

are thus decreased. Nevertheless, such a

gear,

is logical only when the vessel is intended almost exclusively for ahead operation, as in saihng craft. It is an advantage if backing is only incidental and if there are no specific requirements about handling the rudder during backing

design

or

when moving astern. The horn or compound-type

at 5 in Fig. 37.D,

area of the hull above the rudder, as projected

Actually,

on the centerplane, in addition to that which lies below the at-rest waterline. This increases the area over which Ap's are exerted. A spade rudder may be tapered (reduced in fore-and-aft length) toward the bottom to:

rather small.

its

is

rudder, illustrated

not in the foregoing category.

effective

aspect

ratio

is

usually

For an isolated rudder, not attached to a deep skeg or keel, or to a horn, too high an aspect ratio is to be avoided because of the breakdown in hydrofoil flow

—and in

lift

—which occurs at

rela-

Lammeren, W. P. A., RPSS, 1948, p. 323]. High nominal aspect ratios in single rudders, say up to 3.5 or 4.0, can be tively small rudder angles [van

(1)

Increase the aspect ratio

(2) Reduce the strength of the tip vortex at the bottom when exertmg heavy lifts and lateral forces (3) Thin the lower part and reduce its drag (4) Diminish the bending moment at the head

of the rudder.

accepted

rudder

is

velocity

Sometimes the

possibility of air leakage to the

top of a spade rudder can not be prevented. It is then wise to reduce rudder area at the top, shortening the rudder and moving

its

contour line

farther from the adjacent water surface.

The area

if

the rudder

as any. This

A

change

two decades ago

like this

in

was found

successful

the design of the U.S.S.

Farragut, a destroyer of the

DD348

produces

when

it

the

greatest

lateral

forces

follows as closely as possible the contour

of the stern.

There should be the minimum leakage

area between the rudder and the adjacent portions

upon which the rudder pressure fields act. The lower the horizontal joint between hull and rudder, the greater the hull areas above it, projected upon the centerplane, which are acted upon by these pressure fields. Whether this enables the use of a smaller rudder depends upon of the ship

many

A

in

combination

use rudder angles

(rather than for steering only) a control surface

point lift

approximately square is as serviceable is because the breakdown or stalling

is

is

deferred to larger angles.

A

greater total

or lateral force can be achieved, greater maxi-

control-sui'face angles can be used, and the bending and torque moments in the stock are

more nearly balanced. Wherever practicable, a rudder deUberately placed in an outflow jet to take advaiitage of the induced velocity should span the whole jet close to a diameter. Excessive underhang in spade rudders, clearances to withdraw propeller shafts,

and the presence

of swirl-core

cavitation

may

In this case spanning a portion of the of course much better than missing it

interfere. jet

is

altogether.

When

other factors.

rudder hung from a skeg along

ratios, to

mum

class.

A centerline rudder on a twin- or multiple-screw stern

fact that the

beyond the stalhng value of 20 or 25 deg. Long experience with spade and horn-type rudders and horizontal diving planes, on bodies as well as on ships, indicates that for maneuvering

making the rudder longer the top.

The

augmented outflow

may make it unnecessary,

with these high aspect

which

bottom than at

partly or wholly within

benefiting from the

thus removed from the top of the blade is shifted to the bottom, well below the surface, possibly at the

lies

the outflow jet of a propeller.

one or more operative conditions

of

a

entire

vessel involve large changes in draft in the vicinity

and preferably fitting the huU advantage that it is developing the maximum turning moment on the hull. While it is completely unbalanced it can

of the rudder, the actual immersed rudder area must be proved satisfactory for all conditions. As a rule, both hull and rudder come out of the water simultaneously so that the smaller immersed area of the rudder suffices to control what is left of the hull in the water. However, adequate performance in such a situation can by no means

leading

its

edge,

closely along its top, has the

be made smaller (shorter or narrower) than a rudder not so closely fitted. The torques upon its stock,

and those to be exerted by the steering

MOVABLE-APPENDAGE DESIGN

Sec. 74.4

be taken for granted.

model

test

is

A

separate calculation or

called for to cover

tliis

condition.

An

L-shaped or J-shaped rudder hung behind a thin hull or skeg should not have an excessively long forward balance portion, indicated in diagrams 1 and 2 of Fig. 74. Ca. When such a rudder is swung hard-over, say to the right, the forward end of the balance portion savings to the left or to port.

The

region of 4-Ap on the ahead or

starboard side of the balance then

lies

under the

port side of the skeg. In normal circumstances a large

— Ap

is

being developed here to augment

the transverse force to port. Although, so far as

known, no

specific studies

have been made on

this point it appears that the presence of the

-|-Ap

and

— Ap

regions so near each other

is

detrimental to maneuvering.

R. E. Barry reports a situation similar to this on a French cruiser, as indicating a rudder shape and position to be avoided in practice ["Random Notes by an Old Seaman," Mar. Eng.'g., Feb 1921, p. 137 and Figs. 8, 9]. This vessel had a Negative Differential

Pressure

-6p\

+Ap an Rudder,

on This 5idc of Leodino Edqe of

Balance Portion

in

This Region, Especially

When 6alonce

Portion

Excessively Elevation of Toil of

When Swung j^\.o Near Side Blade,

Situotio

+Ap

is

Lono

Field on For Side of Skcq, Opposing the Desired Turn

711

HYDRODYNAMICS IN SHIP DESIGN

712

mL

rudders

_pwL/^"|gr~ Aperture

Wide Hinqe Slot

flow

Abreast Propeller

Permits Excessive

all

Blode Tips Permits

^p Leakage

Ap Leokoqe From One Side of Skeg to the

from

One Side of Rudder

Other

Sec. 74.4

by no means a

necessity, provided fair

reasonably certain around the rudder at all operating condi-

is

rudder angles and under

tions.

For practical reasons, such as to provide bottom

to

the Other

is

clearance Avhen docking,

it is often necessary to terminate the bottom of a rudder in a horizontal plane parallel to and just above the baseplane. When such a rudder is mounted under the stern of a ship, it may Lie in a region of flow having an

appreciable

upward component of velocity, indiThe after ends of the lower

cated in Fig. 25.K.

Large Aperture Forward

of

o Stern Ruddei

•of Adequate Area Provides Room For o Short Horiiontal Circulation

Path and

ffesponse

Rapid

Insures

to Angling

Rudder

rudder sections then project into the flow lines, as does the af tfoot in that figure. If a reduction of area

bottom can be made up by an increase elsewhere on the blade, the after lower edge of the rudder may be cut up or the bottom of it may at the

be sloped to conform to the flow hues in this These changes should save some pressure drag during the greater portion of the time, when the rudder is serviiig only to steer the vessel. It is good design to shape a close-coupled rudder (at either bow or stern) as a continuation of the adjacent hull surface. Nevertheless, this procedure can become detrimental if the adjacent hull is full and the thickness ratio of the rudder becomes large or if the sides of the rudder have much slope [Denny, M. E., lESS, 1934-1935, Vol. 78, p. 411]. In any case, the free or swinging edge of the rudder, the one that is do^vnstream when the rudder is steering, should generally be tapered to a reasonable thickness and not terminated region.

Gap Length

Fore-and-Aft

Should 0.3

ond

Be at Least Preferobly

0.4 of Greatest Fore-

bluntly.

Wherever and whenever practicable the leading edge of a rudder

is recessed into a groove in the edge of the horn, the skeg, or the keel supporting it. This is partly for fairing but mostly

trailing

Apertures and Gaps Ahead op Ship Rudders

Fig. 74.D

for

closing the hinge

gap against detrimental

leakage. Further steps to close the gap are de-

good circulation path for the water. It is too large as a leakage gap. It probably does more harm in steering than the benefit it affords in reducing

scribed in Sec. 74.14

propeller vibration.

baseline for the foot of the rudder

Diagram rather

1

of Fig. 74.

common

in years

D

illustrates

a design,

gone by, in which the

provision of working clearances for removal of the pintles and their bearings, and for lifting out the whole rudder, was apparently more important than ease of steering. The large leakage gap detracts from the usefulness of the rudder and

diminishes the lateral force built up on the adjacent hull by the angled rudder.

Rounding the

outline

or

profile

corners

of

and

illustrated in Fig. 73.

of Sec. 73.14.

The

fact

that positive clearance above the is

often

man-

datory should never deter the naval architect from extending it below the baseluie if the needs of the situation require it. The rudders of many Chinese junks slide along a diagonal axis, parallel to that of the stock, so that they extend well below the baseplane when at sea. The portable rudders of small sailboats almost invariably project below the baseplane when they are shipped. The successful use of fixed rudders projecting below the baseplane on many vessels,

MOVABLE-APPENDAGE DESIGN

Rec. It. 6

adjacent

damage, as might be supposed. Furthermore, provided these operations are planned in advance,

as

they do not represent serious inconveniences when drydocking or hauhng out. A variety of types and shapes of rudder, hull, and aperture are shown by K. E. Schoenherr

[PNA, 1939,

Vol.

II,

pp.

224-226].

and W. P. A. van Lammeren show a

larger

and shape [RPSS, 1948, pp. 331338]. G. de Verdiere and V. Audren describe the results of model tests on still other rudder shapes and arrangements [ATM A, 1951, Vol. 50, pp. Design Procedure for Conflicting Steering Requirements. It is as necessary to know the range of speeds for which optimum steering 74.5

required as

it is

to

know

the speed for

optimum

performance of the hull or the propulsion device(s) In this respect the saihng craft poses the most design problem. It must steer and maneuver well throughout the entire range, from the greatest speed of which it is capable down to difficult

practically zero speed. It is interesting to note the

manner

this is achieved, especially for vessels

in

which

with flap-

type rudders hung directly on the main hull. If the vessel is relatively small, say less than 100 ft in waterhne length, the underwater hull is cut away sharply at both ends and the remaining portion

is

the vessel. it is

short

The

compared to the

overall size of

horizontal circulation path around

short, so that the response to rudder angle is

good at any speed. The rudder is hung directly on the skeg or deep keel, so that steering is adequate and reliable even at slow speeds. For the large sailing ship the slow-speed steering is equally good, but the underwater hull is much longer in comparison, and the response slower. In this case, however, the response should be more dehberate. It gives the crew the

is

extra time necessary to trim the sails and perform

other duties connected with the sailing evolutions. It

would be dangerous,

in

many

cases, to

permit

the vessel to swing too rapidly.

The mechanically propelled vessel poses a The shape and position of a

different problem.

rudder,

the vessel

and

its

relation

with respect to the

is

called

upon

often included, and understandably tion in such a case appears to

to steer well,

the solu-

so,

embody two sepa-

rate features: (1)

A

large tail section of the rudder blade lying

directly abaft a sizable portion of the hull, or

abaft a horn or skeg of appreciable area compared to that of the

tail,

with the smallest practicable

hinge gap (2)

A sizable foil portion having ample clearances

and abaft it, to provide room for the up of the circulation needed to produce immediate steering response. ahead

of

rapid setting

The designs

491-514].

is

when

it is

variety, including the screw-propeller position(s) for each type

hull, is

with the propulsion device rotating very slowly or actually stopped. Since both requirements are

Of these,

however, the single-plate rudder of his Fig. 15 is practically obsolete, except for inexpensive installations on small vessels. L. Troost, J. G. Konmg,

7J3

not necessarily the same when quick response at moderate power is required

operating in shallow as well as deep waters, proves that they do not suffer frequent or serious

stern

of the rudders for

and arch-stern

both the transomABC ship were

hulls of the

carried out with these features in mind.

A

better

probably to use one or more spade rudders of generous area, provided these can be accommodated in the design. 74.6 First Approximation to Control-Surface all-around solution

The

Area.

is

discussion in this section

mounted

to rudders

in

is

limited

the vertical plane,

or

Diving planes of submarines and other control surfaces are omitted because of the widely varying requirements for different types of service. Although the rudders of mechanically driven vessels have developed through the years in the almost complete absence of specific steering or maneuvering requirements, the resulting rudder nearly

so.

parameters and hull-rudder proportions lie within not too wide a range. Based solely upon the ratio of the rudder area

Ar

to the lateral area

product of the length relative

size

gradually

of

^l of the ship, or to L and the draft B.,

the the

steering rudders has increased

but steadily during the past halfmany ships built in the 1900's

century. In fact

had to have their rudders increased in by as much as 20 or 30 per cent, indicated by the listing in Table 74. a. A rudder of or 1910's

area,

often

given area, working in a propeller-outflow

jet,

gives greater lateral forces as the propeller power is increased, and may even provide better man-

euverability at a higher speed.

The

shift to pro-

portionately larger rudders appears to be a sign of unconscious but actual stepping-up of maneu-

verabUity requirements. It

may

be expected that and that

this intensifying process will continue,

HYDRODYNAMICS

714

TABLE

74. a

All the vessels listed

IN SHIP DESIGN

Original and Increased Rudder-Area Data on U. THE 1900-1920 Period

had

single rudders.

So

far as

S.

Sec. 74.6

Naval Auxiliaries of

known, the areas apply to the movable rudder blades only.

MOVABLE-APPENDAGE DESIGN

Sec. 74.7

somewhat shielded from

715

flow by the ship ahead of them, those on the

on "Steam Tug Design" [London, Jul still used by aeronautical engineers

outside of the turn are exposed to a greater degree

tioning the rudders of dirigibles.

of the turn are

One may say that,

of cross flow.

cross

for a first approxi-

mation, an average of these effects forms a good estimate.

The

total absence

rudder

and the

files,

of

diagrams showing the

the ship or large-appendage pro-

profiles,

movable

relative positions of the

uJ 11 rudder blades and the adjacent ship render all irujjj. f published data of the kind shown -iu the references ,

,

,

,

1

,.

,,

,

J.

fiuiju

.,

xu-

•

m

ii-something less ,, f T f i than useml. In tact, it appears j-u that only by taking n P .1 account ot these features, which govern the ,. J.U r ii, proportion otc fi\ (1) the transverse force on the jj i ^o\ xu i X r xi_ J rudder to (2) the total transverse torce on the end ,, ,, r X, ot the ship, can the major inconsistencies of the ,

1

i-

1

cited previously in this section as 1

-J.

J.

,

1

J.

.

,

,

,

1

1

•

,

J.

i.

,

J.

t-T

.

.

u

J X ui

1,

1

•

.

,

J

1

published tables be cleared up. .

m •

,

,.,,

...

J.

.1111

,,

architecture, ot proportionmg the movable-blade r XIjj X xi. -J Xf xi area ot the rudder to the midsection area of the ,. -^ Xr -vTr T HT Ti -innr^

ship.

J.

m

•

M. Rankine 1

Quotmg from W.

1866

ran^Tii u- u -u xi_ x A,r [SIP: itrru Thatx eminentx shipbuilder, the late Mr. T u ITT J J XTu jxi. xi 11 John Wood, made the breadth of the rudder , /oxu X r XI. I.ji mi.X xi -ii l/8th otr xithat ot the ship. 1 his meant that, with •

i

J?

J

J

JJ

r

xi.

X

I.

X

1

XI

i-j

^

J^

a depth ot rudder about equal to the draft, the ,1 ,, u X r. inr Xxi_ -i rudder length was about 0.125 times the mid,m, xu J f Xxi section beam, i lus method of selecting the proper J, rudder area is given by A. Caldwell his book ,

.

,

..

1

iA/~.iJii-i-ii m

TABLE

74.b-RATios of Rudder-Blade Area Aj, to Length-Draft Product (LH) for Merchant-Type Vessels

~

Liners, large, fast and high-speed Passenger and cargo ships, large, medium-speed Tankers, large, fast and medium-speed ... Passenger and cargo ships, small, slow-speed .

s

formulated for use in the preliminary design stage of a ship:

w ,

A

,

,

.

r

,

^

r,

n

>

i

,

.

,.

,

is

must

,

,.

tree of greatly , n

m

,•

•

lie a reduced

and reversed flow

velocity, eddies, ,,

r^

^,

rudder, to be fully effective,

.

region of flow which

„ „ JNo mechanically propelled vessel, regardless

s

t,t

(b)

,,

•

,

,

,

^ , . ,, ,. ,,, should have a ratio ot rudder area Ar to , ^.^rs „ V rectangular underwater area L(H) smaller than -, ,.,„ ,^ l.D per cent. A minimum of 1.7 per cent might ^ -r. ,; ,, ,„^„ ,, better; be the 1953 table of r. Mandel shows a , „ minimum ot 1.9 per cent, /,

'

,

01 type,

,

,

,

,»..

,

,

.

,

,

s

,

,

.

,

,

,.

rr,,

,.

i

,

,

,

,

(c) I he percentage ot rudder-blade area over,„ , f ,, ,, lapping the propeller outflow let at the ruader .

,

.,

,

;

,

•

,

,

,

,,

,-

,

rr^,

•

.

,^ is •„, especially true tor vessels operating at a i value „ ,„ ,,, ,,. ii,-, less than 1.0 and lor flows past the rudder which position should be as large as practicable. I his ,

,•

,

„

,

,.

r,

,

,

•

are suspectcd ot being ,

.,.

,

wake

velocities ,,

,i

,

Weak,

„

„

,

,,

^

With large positive ^ ,i ot rudder ad^

...

and small speeds .,

.

,

,

,

vance. It is possible, as stated previously in -,. „ „.„,,, ,, „ n strong Sec. 74.3, that a flow, with a large , , i , „ , spced ot ruddcr advancB aud a Small overlap, has ,.

,

^

,

.

r^

.

,

,,

r

,

,

,

more benencial effect than large overlap of the « ,, n same rudder m a weak flow, ,s rr^, ,, (d) ihe percentage ot cutaway area and the ^^^^^ ^f cutaway length to ship length he within rather narrow limits for the average vessel. If .

.

.

,

,

,,

,.

,

,

cutaways are adequate,

the

appear not to be major factors in

exact its

ratios

maneuver-

ability. fp^jj-^

rudders.

a g

Based upon the data in the references listed and upon the ratios given in Tables 74. a and 74. b, a few general rules are

the

The rudder area is considered to be that of the movable blade only. The proportions given are for ships with single

is

in propor-

earlier in this section

/

Ml XI, X r xv, 1 XX 1 1 11 It is possible that further analytic study should 1 ,, J ,.,,, J be given to a method, little-used modern naval1 Tx

,

1946]. It

ps,

as

/

River steamers, fast Cargo ships, normal, medium-speed

1

Cross-channel ships, required to maneuver in harbors Sailing ships, large

w'^kh°^t''^^

....

11

Inland waterways

2.0-2.2 2.0-2.5 2.5-4.0 4.

craft, for

.

" 7-2 .0

1.7-2.5 1.9-2.4 „ „ „ o 2.0-2.3

Auxiliary vessels for national defense /. ^ „ coasters ^ Cargo ships, small;

Ferryboats for harbors, fishing vessels

1.6-1.8 1.6-2.0 1.7-2.1 1.7-2.3

confined waters

'.

'.

r\\ n

4^0-8.0

—

^^-j rudfjgj-g fgr large ships may have a combined blade area as great as 0.03L{H). A baseplane clearance of 0.5 ft appears to be adequate for any deep-water vessel, regardless of size. (f ) When adequate draft is available and multiple

rudders are used, the aspect ratio jarge,

is

made

rather

to give the greatest coverage across an

outflow jet or the

maximum

pressure abaft a skeg.

74.7

Determining the Proper Areas of Various j o _i; t^u xixuSurfaces. There is outhned m this section a new procedure for determimng, as a second or third approximation, the required area of the movable blade of a control surface. The method as described here apphes to a steermg rudder in a vertical plane but it is essentially the ^^me for a control surface mounted on a surface ship or submarine in any other plane. /^

x

i

Control .

..... •

•

HYDRODYNAMICS

716

A

IN SHIP DESIGN

Sec. 74.7

and adequate rudder-design method

course in the shortest possible time and distance

should produce, to meet a given set of steering and maneuvering requirements, the proper type

than for guiding it precisely around a steady turn with a large change of course. The situation is

of rudder, the rudder-blade area, the proportions

somewhat

suitable

and shape angle.

of the blade,

and the maximum rudder

To meet unusual

operating conditions

it

Table

similar to that specified in item (32) of

64. e where, to

make

a canal turn properly,

must accomphsh an

the vessel

offset of

400

ft

from

should also produce the rate of angUng or laying the rudder and other design features. Looking

the approach path extended in a curved arc of

at the rudder-design problem in

is

its

larger aspects,

should also be coordinated with what might be termed the maneuvering design of the hull as a

it

whole.

Because the project

is

description which follows

incomplete,

still

the

simply a statement

is

some comments on each. The project has not been carried through to the point where a numerical answer, acceptable by engineering standards, can be obtained by it for a given situation. Presenting an outline only is considered justified because of the need for thought and study on this design problem along new and logical lines. of the various steps involved, \\ith

The

a careful analysis of the steering and maneuvering requirements of the starting point

is

vessel for which the rudder

are

preferably

somewhat more

specific

ship in Table

64. e,

to be designed.

is

expressed

in

numerical

than those for the (27) through

upon

his

own

to

amount very

full

its

rapidly and a certain

maximum swmging moment

A'',

to be discussed

must be applied by it to the ship. The sheering maneuver at the beginning

presently,

which to guide the rudder design because:

by the designer

experience in the

other gear required for maneu-

dition. It is usually the case, although it may not be taken for granted, that the lesser requirements are then satisfied as a matter of course.

Just what constitutes the most severe maneu-

—the one calling for

opthnum or specified can by no means be determined by

the largest rudder area at the

—

steady speed on a straight approach path when is ordered, the rudder must be angled

a sharp turn

Avith

(41),

and the propelling machinery necessary for propulsion, must as a rule be designed to meet the most severe operatmg con-

rudder angle

and to follow a tortuous path, but there is reason to believe that the initial sheering maneuver is the most demanding and the most important. This means that, vnth the vessel proceeding at

ABC

vering, like the hull

vering requirement for a ship

tance from the dive or "execute" point. To be sure, every ship must be able to change its course at will, to reverse its direction of swing,

is

operation of similar types and sizes of ships.

The rudder and

at a specified speed

turn

especially items (28), (30) to (32), and (34). If requirements for maneuvering have not been laid down by the owner or operator they are pre-

himself, based

ft,

exactly the

These terms

items

scribed for the ship under study

and rudder angle. It same as that faced by a diving submarine. In an emergency, the submarine must get under the water surface and point its nose downward in the shortest possible time and dis2,100

a

The

and moments exerted on a ship few seconds of this transient stage largely determine how rapidly, and in what ahead distance, the vessel can clear its approach path extended, change its heading, and sheer off to one side or the other (a)

forces

in the first

(b)

For an analytic solution, the velocity mag-

nitude and direction of the water flowing toward

when beginning a turn may be assumed same as it was a few before, when the ship was proceeding

the rudder

to be substantially the instants

along the approach path with zero rudder angle, in a steady-state condition. tion,

With

this simplifica-

only the effect of the angled rudder need

be evaluated just after the

initial

point of the

turn. (c)

Once the

ship

is

m the turn, the determination

moment produced by the rudder moment produced by the ship itself,

inspection of the oAvner's and operator's specifica-

of the swinging

For the average vessel, however, it is more important to change direction quickly and decisively in an emergency maneuver, to avoid colhsion with obstructions or with another ship, than it is to make a subsequent turn at a given radius or speed. In other words, the rudder is

and the

more valuable for sheering the vessel off its origmal

many model

tions.

of

a logical as well as a practical assumption

acting as a hydrofoil -with an angle of attack,

becomes exceedingly complex. This

is

true for an

experimental as well as an analytical attack on the design problem. (d)

As an

incidental argument,

it is

possible in

basins to measure the transverse

MOVABLE APPENDAGE DESIGN

Sec. 7-f.7

model

force exerted on a ship

position

when

the rudder

move

constrained to

is

rudder angled and the model

is

what amounts

in

to a

straight continuation of the approach path. This

serves as

some

sort of check for a particular pre-

liminary design of rudder rather than as an aid in the course of the design.

The sheermg maneuver must be terms

specific

vering specifications of a ship or as the

controlling

defined in

maneu-

to form part of the

if it is

factor

in

if it is

to serve

a rudder design.

These terms should include the rate of change of heading followmg an order to turn and the shift of position of the CG laterally from the approach path, in the positive or negative direction of the 2/o-motion axis. All these should be on a basis

time and of advance in the

of

The complete involves too

many

answers to render

itself is

designer then determines, by estimate from

by

ISiter

calculation,

the proportion of this lateral force F^ which he may reasonably expect to be exerted on the hull

and the

fixed appendages. This portion

is

indicated

Fu in the figure. The remainder of the transverse

as

force

that to be exerted on the movable rudder fully angled. This is normal to the

is

blade

when

F^

ship axis, mdicated as

maximum

With an assumed an effective angle the rudder equal to it, an assumed

rudder angle

of attack of

5

.

(delta),

aspect ratio, and an average value of

lift

for hydrofoils suitable as rudders, the

coefficient

problem

is

worked backward and the hydrofoil or blade area is

approximated. The calculation

as

many different

is

listed

may

repeated for

many different

ship speeds, or as

assumptions, as

Of the data

first

be desired.

under

(1)

determination

through

(5)

pre-

maximum

ceding,

the

work-

swinging

neces-

problem.

moment N poses by far the most difficult The method of finding it for any

sentence of the second paragraph of this section able with present techniques (1955). It

717

empirical data and possibly

initial

.ro-direction.

outlined in the

solution

The

aljreast a

sary at this stage to assume reasonable, tentative values or conditions for some of the answers,

namely:

of

the

is not yet worked out but the following factors require consideration:

particular design situation

The maneuvering

(i)

characteristics of the hull

and shape of the its maneuvering

without the rudder (s). Carried to the limit with respect to rapid change of heading, a ship in the form of a circular tub would require

(2) The fore-and-aft position of the rudder and rudder stock along the hull axis. The assumed swinging axis of the vessel may be taken at its CG.

only enough tangential force at its surface to overcome the polar inertia and the friction

The

(1)

general dimensions,

size,

ship hull, as well as certain of characteristics

The

distance from the

position force,

the

is

CG

moment arm

to the rudder-stock of the lateral

rudder

although, strictly speaking, this distance

should be measured to the instantaneous center of pressure (3)

CP

of the rudder blade.

The type

(or types) of

may

rudder to be worked

be required for alternative rudder

types (and shapes). (4)

and

Some

hull or the (5)

with respect to the adjacent

nearby fixed appendages

The maximum swinging moment

A'^

to be

applied to the hull under the most severe

change in position, a long slender craft

requires rather extreme measures in the

applied forces and offset

The

situation

is

as

sketched in Fig.

moment

A'^

the ship at

of

(ii)

the

The

polar

vertical

moment

of inertia of the ship

swinging axis

for

the

about

particular

loading condition specified

The added

inertia of the entrained water for

swmging mode of motion, when the ship starts to turn (iv) The steady speed of the ship along the apthe superposition of the

proach path

manLever

Arm

for Reauired

Rudder Moment on 5hip

' ]

74. E.

by the moment

arm a of the rudder gives the transverse Fl required to be exerted on both the rudder and

way

to accomplish the

from the extended approach path which

euvering requirement. This is a major feature, which should be derived rather than assumed, by a process to be discussed shortly.

Dividing the swinging

moments

required for a sheering maneuver,

(iii)

idea of the shape of the rudder blade

of its position

resistance. Carried to the opposite limit for rapid lateral

is

into the design problem. Alternative preliminary

designs

proper,

and near the rudder-stock

force blade

position.

Fig. 74. E

Diagram of Rudder and Ship Forces and

Moments

HYDRODYNAMICS

718 (v)

The

water,

if

possible effect of shallow or restricted

operation in confined areas

involved.

is

The

may

process of deriving the swinging moment be largely empirical untU the method is

further developed. Eventually it should be determined by a relation analytically derived.

On

the basis that the sheering maneuver de-

scribed previously in this section calls for the

swmgmg moment and

greatest

rudder

effect,

the analytic method appears to involve: 1.

Laying out a

series of successive positions, at

IN SHIP DESIGN

Sec. 74.7

If a dynamometer is available to carry a model rudder and to measure the lateral force on its stock, the rudder-force fraction F r/F ^ may be determined during the test of a constrained ship model, run straight ahead with angled rudder under a towing carriage in a model basin. The

model can and should be

self-propelled during

this test.

Following a determination or an estimate of F g, on the rudder, the designer proceeds to apply the laws of the the transverse force component hydrofoil and to calculate

how much area 4i/ is equal to this force. As

equidifferent time intervals, with respect to the

required to produce a

point where the emergency turn order is given, known as the "execute" point, and the approach path extended. There is a considerable backlog of this information, pubhshed and unpublished, with which to approximate or to bracket the

previously mentioned, the problem

required data for a 2.

Finding

the

number

positions while

angular

initial

a(alpha) required to

make

By

it is

possible that the

moment

swuiging motion, including the added inertia of the water, the required swinging moment is given by

N

The value

of

N may

Jscc

(74.i)

well be found to vary with

approach speed so that the designer

upon range

to

work out a

5.

However,

it is still

necessary to

know

especially as this speed enters the lift-force formula to the second power. The potential-,

the initial

in

of the ship for

=

angle

responding to the rudder's speed of advance,

may

N

the effective angle of attack «/ of the rudder as a hydrofoil is equal to the mechanical rudder

acceleration

calculating or estimating the polar

Js

simplified

is

by assuming that

the relative water speed past the rudder, cor-

be obtained on board ship from simultaneous course and rudder-angle measurements, made by recorders now available.

of inertia

for the case being described

the ship occupy these

moving forward

portion of a turn. In fact,

necessary data

of ship types.

lift

series of solutions

if

is

called

the speed

is large.

On

the basis that the total lateral force Fl of Fig. 74. E is determined, and that the sheering

maneuver occupies the predominant

role, the next step is to determine, in terms of numbers, the fractional part of this force that is exerted on

the hull. In the present state of the art the fraction Fh/Fl alluded to previously and called here the

friction-,

taken

and wave-wake

velocities

account,

the

into

velocity due to the

-plus

must all be negative-wake

augmented velocity

in the

outflow jet of any propulsion device lying ahead of the rudder.

A two-part rudder composed of a tail and an underhung foil is illustrated for the general case in diagram 5 of Fig. 37. D and for the transom stern of the ABC ship in Fig. 74.K of Sec. 74.15. For such a rudder it is undoubtedly not valid to assume that each part (tail and foil) generates its own lift independently, by its own set of rules or by its physical action alone. Nevertheless, this approximate procedure must be used until something better is developed. In addition to the assumed kinds and nominal aspect ratios of the various hydrofoil elements of

the rudder blade, the effective angle of attack,

and the speed

of advance,

the section, the designer

mentioned

now knows

earlier in

or has esti-

can at best only be estimated. A correct estimate must be based upon knowledge of the pressure field exerted by the angled rudder

mated the total lift force F r required of the rudder. Assuming a sort of standard type of hydrofoil or flap section for each part, it is possible for him to estimate the lift coefficients and to determine with

in its vicinity. Available data

reasonable accuracy the area necessary to exert

,

hull-force fraction,

on

this feature are

they are neither analyzed nor published. It might be more realistic, therefore, to say that rare;

for the present the hull-force fraction

guessed. It

may be of the order of

is

only

1/4, 1/3, or 1/2,

leaving 3/4, 2/3, or 1/2 of the total lateral force

Fl

to be developed

by the rudder

blade.

the required hft force on each part. Graphs giving

some

of the necessary data are found in Figs. 44.A through 44.D. Other data are to be found in the references listed in Sees. 44.3, 44.4, and 44.5.

The sum

of the areas thus derived

may

be equal

MOVABLE-APPENDAGE DESIGN

Sec. 74.7

from the total movable area tentatively assumed when the blade was first sketched. Adjustments are made to the area or shape or aspect ratio, one or all, and a second hydrofoil calculation is made, similar to the first. For the case of the compound or flap-type but

to,

rudder the exact value of the ratio of the movableblade lateral force F^ to the hull lateral force F,f

and the exact value

of the lift coefficients

calculate the movable-blade force,

used to

depend upon

the tightness assumed for the hinge closure. Unfortunately the effect of actual hinge gaps and

hinge leakage

is

not yet assessed in the

full scale.

Data from aeronautical tests require some analysis before they are applicable to the ship problem. Similar

comment

applies to the assessment of

the effects of horizontal gaps between parts of the

rudder and the hull, and a determination of the proper effective aspect ratio for each part of the rudder. Certain useful data derived from tests of low-aspect-ratio hydrofoils are included in Sec. 44.3.

In the event that the maximum turning

719

The model was run with

will usually differ

post of rectangular section ahead of the rudder, then with four fixed fins of uniform thickness

added abaft the post (and ahead representing full-scale lengths of

and 6.25

ft.

The combined

of the rudder), 0,

2.08,

full-scale

4.16,

fin-and-

rudder area was always 144 ft^ indicated in Fig. 1 of the reference. The area of a fairing of varied width added ahead of the rudder post, as well as the area of the post itself, was not included in the

nominal fin-and-rudder area.

On

the basis of these test data Bottomley then calculated the fore-and-aft length of four hy-

when placed behind the four fins mentioned, would give the same initial ship-turning moment at small rudder angles pothetical rudders which,

(5 deg) as the original rudder (called R4) when mounted abaft the rectangular-section rudder post. If four rudders of these lengths had been mounted abaft the four fins mentioned, horizontal

sections through the assemblies would have appeared as sketched in Fig. 74. F. Assuming that

moment

required in a steady turn, to meet certain

is

the usual fixed rudd('r

R

^^ ^ \rn

operational needs, the physical action on both

Behind Rudder Post Only

rudder and ship is no longer simple or well known. The design procedure is not yet outlined and may not be for some time to come.

As an indication of the absolute magnitude of moments required to maneuver a ship there

the

are available the results of model tests in which

the rudder was angled by various amounts while the model was constrained to travel in steady, straight-ahead motion. This corresponds, as pre-

moments after a given but before a ship has time

viously described, to the few signal to turn

is

Fig. 74.F

to change direction from its straight approach

Among

path.

these tests are

some conducted by

H. Bottomley at the NPL, Teddington ["Maneuvering of Single-Screw Ships: The Effect of Rudder Proportions on Maneuvering and Propulsive Efficiency," Inst. Civ. Engrs., London, 1935, No. 175]. The model represented a ship having the following characteristics: G.

By

Ruddeb-Fin Assemblies of G. H. Bottomley

calculation, all five of these assemblies give the

initial

ship-turning

moment

of the order of 5 deg.

Bottomley's calculations were correct, and that the scale effects in the model tests were insignificant, each of the five assemblies appearing in the figure would give an initial turning

Lpp

400

,

B, 52

ft

,

0.70

t

V, 14 kt

Pe

,

2,200 horses

Ps

,

3,160 horses

assumed at midlength between perpendiculars CG to rudder stock, about 200 ft Area A « of standard rudder, 144

ft^

An/[L{H)]

moment

on the ship used as the basis of the tests, reckoned about the CG. The values of this moment at rudder angles of 15 and 35 deg are given in Table 74. c, copied from the Bottomley reference, together with the torques that would have been required to hold the rudders in those positions. Considered as a design referof 2,400 ft-tons

CG

ft

H, 23 ft A, 9,400

Cp

same

for small rudder angles

=

0.016.

ence,

the tabulated ship-turning

moments

are

HYDRODYNAMICS

720

TABLE

74.C,

IN SHIP DESIGN

Sec. 74.8

Ship-Turning Moments and Rudder Torques for a 400-ft Ship

Adapted from G. H. Bottomley, "Maneuvering of Single-Screw Ships," ICE, London, 1935, No. 175, Appx. fins listed in the two left-hand columns are illustrated diagrammatically in Fig. 74.F.

The rudders and

I,

p. 19.

MOVABLE-APPENDAGE DESIGN

Sec. 7-f.S

non-overhauling the effort or the time required to take

may

rudder angle in an emergency

off

too great to justify letting the

be ahead the rudder

CP move

721

Designed to run for long periods with small rudder angle, with a premium on steering effort and power, and wear and tear on the steering (a)

of the stock axis under any condition. If torque becomes excessively large, the fore-and-aft length of the blade and the actuathig moment required to turn it must be decreased and the

mechanism (b) Where a reduced rudder-angle

aspect ratio increased, as was done on the large

in the event of a casualty to the

hand-steered sailing ships. This can, of course, also be done on ships which are mechanically

gear which leaves the rudder free to swing.

— —

With

certain types of hydraulic steering gears

possible for an overbalanced rudder to take

it is

charge in an emergency and swing rapidly to its hard-over position, causing the ship to circle out of control as long as it

The

is

moving ahead.

Which may have

(c)

(3)

steered.

rate

may

be

accepted for astern operation

The rudder may be

to maintain speed ahead

power steering

slightly overbalanced at

small angles for ahead operation at service speed:

When

(a)

the friction in the mechanical or

emergency gear is enough to prevent the rudder from taking charge if power is lost and from swinging to the hard-over position.

necessity for going astern on mechanically

and for much backing and maneuvering on special-service vessels, often calls

(4) The rudder may be overbalanced for angles not more than one-third of the maximum and

for the least practicable steering rudder torque,

appreciably overbalanced for the small angles used

propelled vessels,

whether the

craft are steered

by power

or

by hand.

This generally requires that the center of pressure CP when going ahead be forward of the stock axis so that the CP when going astern mil not

be too far from that axis. Shifting the stock axis on the blade takes care of this situation but involves the additional disadvantage of possible rudder instability and chatter at zero angle, especially with slackness in the gear, and a aft

tiresome job of steering

hauling type.

The

Lf

the gear

is

of the over-

relative position of the

for steering: (a) On special-service vessels called upon for much backing and maneuvering, or for hard-over rudder shifts at the maximum rate, when it is an

advantage to have the ahead and astern rudder torques equahzed as far as practicable, with neither of them very large

On

(b)

ing gears.

two Non-uniform flow over the control-surface whose general effects are described in Sec.

therefore

CP's and the axis, for all service conditions, is determined by the most important

blade,

service operating requirements.

37.7,

The

vessels provided with reasonably reli-

able power-operated auxiliary or emergency steer-

following design rules govern the degree of

balance on rudders for steering and turning. They upon reasonably uniform flow over

may

influence the balance situation; at least

the possibility or probability of this flow requires consideration in the design stage.

may

The nature

of

control the distribution of balance

are predicated

the flow

the whole rudder blade:

area along the stock axis, generally normal to the adjacent hull, and the position of this area

(1)

The rudder

on any (a)

definitely should trail at all angles

craft:

Designed

relative to the retarded water

m boundary layers

or to the accelerated water in propeller-outflow for

hand

steering,

and

for pleasure

jets.

For example, a spade rudder blade

only

Designed for hand steering, and where, for efficiency and safety, the rudder effort must be "felt." Examples are racing sailboats and motor(b)

boats. (c)

Steered by one

man who must

also attend

to other duties, such as a lone fisherman.

made

is

often

shorter (in the direction of flow) at the

bottom, well below the hull, than close to the hull, in order to reduce the stock bending moment. This means that the balance portion is longer (fore and aft) near the hull than below it. In fact, the length of the balance portion compared to the blade length, defined as the length-balance

(2)

The rudder

is

best

made

slightly

under-

balanced at small angles for ahead operation at service speed on

any

vessel:

may be greater near the hull than the area-balance ratio. At the bottom of the rudder it may be less. With the long portion of ratio in Sec. 37.2,

HYDRODYNAMICS

722

the blade working in the boundary layer and the short portion in a propeller outflow jet, the balance ratios mthin the jet largely determine the actual rudder balance and are the ones to be given primary consideration in the design.

a partly underhung rudder is laid out with a balance portion so long that, at or near the hard-over position, the forward end of this portion swings into a propeller-outflow jet, the

IN SHIP DESIGN (e)

TMB

Additional design data are given in Part 5 of

Volume

If

negative torque thus created appreciably affects the balance situation as determined on a uniformflow basis.

In some cases a balance portion hes only in of a scrcAV-propeller outflow jet, or mostly in that jet. It is then acted upon by water one-half

having a tangential component of velocity due to rotation imparted by the propeller, primarily in one direction. A balance performance predicted for

uniform or for axial flow

may

require appre-

Sec. 74.9

Hagen, G. R., "Effects of Variations in ThicknessChord Ratio of Rudders in a Slipstream," Rep. C-487, Jan 1952.

III.

Selection and Proportion of Chordwise

74.9

development unpredictable for which

Considering solely

Sections.

the

of lift or lateral force, there are situations

fortunately not yet fully

—

—

a thick, flat-plate blade attached at the ship or hull end to a cylindrical stock is the best rudder section to use. Certainly nothing much more elaborate than such a plate, rounded at the leading

edge and fined at the trailing edge, is justified for many small boats. A rudder on a large ship, however, gets a free ride, as it were, for

the ship

a good part of the time that

in operation, since steering rarely in-

is

ciable modification because of this tangential or

volves a contmuous rudder motion. In this case high lift is only one of several factors; easy flow

rotary flow, quite apart from any consideration of the neutral angle of the rudder. Special studies

and low resistance carry considerable weight when a rudder-blade section is chosen. As a

model

or

design.

tests

are required

to insure proper

The same may apply

to the design of

rudders encountering inward-and-aft flow

offset

at the stern.

consequence, the overall advantages of fitting rudders are so outstanding that

streamlined then- use

is

taken for granted wherever this type

of construction

Numerical balance ratios, either of area or of length, have meaning only when apphed to control surfaces of given section and shape in a given type of flow. They can be distinctly misleading when comparisons are made between dissimilar rudders. It is the position of the CP with respect to the axis for each condition which counts. In other words, the degree of balance is determined by the actual rudder torque and not by the balance ratio. determination

The CP position requires careful when the torques are large or when

definite over- or underbalance

is

being sought.

foregoing general design procedure apphes also to the positioning of the stock axes for diving planes, active fins, and other control surfaces.

The

Data for estimating control-surface torques for a degree of balance and for a blade shape tentatively selected are given by:

is

at

all feasible.

The exact

section

not too important provided certain basic principles are borne in mind:

shape

(a)

is

The

leading edge

is

to be neither too sharp,

produces discontinuous flow when the angle of attack is large, nor too blunt, so as to develop excessively high dynamic pressures at the nose (b) The section at the leading edge is made so that

it

elliptical

in

shape,

not

semicircular,

for

the

reasons given in Sees. 36.3 and 67.5. If cavitation

not expected at zero or neutral angle, it should be deferred, at least for the small angles encountered when steering. (c) The curvature in the entrance or leading portion is easy, diminishing gradually from the nose to the region of maximum thickness, complying with instructions in the last paragraph of Sec.

is

49.8 R. C, "Hydrodynamic Characteristics of Rep. 341, Twelve Symmetrical Hydrofoils," Nov 1932

(a) Darnell,

EMB

(b)

Schoenherr, K. E., PNA, 1939, Vol. II, pp. 204-210. Chap. 44 of the present volume gives adaptations of

(c)

(d)

some

of Schoenherr's diagrams.

Van Lammeren, W.

P. A.,

RPSS,

(d)

Hagen, G. R., "Rudder Design Data from Tests on Five Model Rudders," C-125, Jun 1948 .

.

.

Obtained

TMB^Rep.

section

creases

is fair,

outhne or contour along any without jogs, buckles, welding

and upset Unes, or other discontinuities

across the streamlines trailing portion is no thicker need be for structural purposes. It is well tapered, terminating in an edge that is only thick enough to withstand nicking and corrosion. (e)

1948, pp. 319-332

The

streamline

The extreme

than

it

MOVABLE-APPENDAGE DESIGN

Sec. 74.10

For a ship on which the rudder is required to produce good steering and maneuvering but behmd which the rudder region is filled with slowly moving water, the usual symmetrical hydrofoil section, tapering in the run, is not adequate to give prompt rudder response. The rudder section may then be carried aft from the stock axis at full thickness, with a square ending, or the sides may even be splayed outward toward the trailing edge. This section shape gives the necessary lift forces at small rudder angles for adequate steering in the manner described in Sec. 37.17

and

There appear to be no design rules, or even thumb, to use for guidance in the selection delineation

splayed

of

or

fish-tail

rudder

most cases these sections are employed to compensate for extreme eddying or backflow.

sections. In

As the poor first

flow conditions should not exist in the

place there

is

little

point in conducting

systematic research to find out

how

to correct

them by using unusual rudder sections rather than by reshaping the run of the hull. Whatever the shape of the trailing edge of a rudder (or diving plane) section, whether inside a propulsion-device outflow jet or not, it should be such that there is never any doubt in the mind of the water as to just where it is going to separate from the section. If the trailing edge can not be fine, narrow enough so that the eddies abaft it are insignificant, it should be cut off square, or even splayed like the split tail of a weathervane. It is never to be rounded enough to permit the separation points on either side to shift backward and forward, with consequent eddy buffeting, rattling, vibration, and perhaps even more serious

one reason for not using a rounded section at edge. This section can, if desired, be

consequences. This

TMB EPH the trailing

is

section, vnth. its

terminated in a double-chisel shape, depicted in

diagram 2 It

is

of Fig. 70. P.

doubtful whether any rudder section

suitable for practical use can be kept free of

separation effective

A nose shape is selected for which the lift coefficient CL

is still

increasing at this attack angle.

The maximum

thickness of a rudder section,

occurring almost invariably abreast the stock

and the variation depth of the rudder, axis,

of this thickness along the

generally a matter of

is

As such

structural design.

it is

not covered here.

When

the blades of rudders and planes are made removable from the stock it may be necessary to increase the thickness ratio tx/c at the support

ends of spade rudders and cantilevered diving planes to a

maximum

and cavitation at extremely

large

angles of attack, of the order of 30 to

35 deg. These are always encountered when a rudder is swung rapidly to a hard-over position

However,

of 0.25.

large thickness should not be

illustrated in Fig. 37.L.

rules of

or

723

carried

this

too far

along the blade. Normally, the thickness ratio tx/c does not exceed 0.20 or 0.167 at the stock

Toward the free, unsupported a cantilevered rudder or plane, where the required section modulus is diminishing rapidly, end end

of the rudder. of

the thickness ratio can be reduced considerably.

The value

of tx/c is usually only

about 1/6 of

that at the stock end. The sections of a close-coupled simple rudder, or of the close-coupled portion of a

compound

rudder, form a continuation of the hull, skeg, or fin to which it is attached. There should be no enlargement and no more discontinuity at the hinged joint than is required to give the rudder clearance to swing from one side to the other. Tests of various rudder sections at the David Taylor Model Basin indicate that a simple section shape composed of a semi-circular nose and per-

fectly straight sides, tapering to zero thickness at

the

edge,

trailing

possesses

superior to those of the for rudders.

and is

less.

The

NACA

hit-drag

ratios

sections suitable

thickness ratios tx/c were 0.15

Further, the breakdown or stalling point

delayed to a greater angle and the maximum is increased. So far as known, no confirmation

hft

of these features in full scale is available at the

time of writing (1955). It is possible that the use of a short elliptic nose to prevent cavitation there would not detract from the advantages of the section.

The

straight-sided shape of these sections, or of

sections smiilar to them,

may

be found valuable

dynamic stabihty of route, disdetail in Part 5 of Volume III. The

in a study of

cussed in

straight course or

convex side of a rudder, exposed to the angled

perhaps is swinging in the opposite direction. The probable maximum effective angle of attack after the ship has started swinging, at a rate approximately half of that in a steady turn, has

flow on the "outside" of a ship in a yaw, may set up undesirable — Ap's acting to increase the yaw.

while the ship

is

moving on a

to be estimated, using the best

known

procedure.

Straight rudder sides of the proper shape would develop +Ap's, acting to reduce the yaw angle. 74.10 Structural Control-Surface Design as

HYDRODYNAMICS

724

IN SHIP DESIGN illustrated

effect,

Sec. 74.11

schematically

the

in

lowest

diagram of Fig. 74. G. The boundary plates of a rudder or a diving plane should be attached primarily to internal structural members which run fore and aft, parallel to the streamlines of the liquid flowing over it, as in the topmost diagram This

of Fig. 74. G.

surface

is

especially true

if

the conti'ol

within the outflow jet of a screw

lies

propeller or other propulsion device. If

practicable,

anywhere

Transverse Members Should

Not Be

^°^^ Wrapper Plate '^'l

Welded to Side Plotinq

I

'"

°"^

^'^^^

should

there

welding beads, or the

like,

no

be

joints,

transverse to the

floAV,

in the entrance of the control surface.

This is achieved by wrapping a single plate around the nose and both sides of the entrance, and attaching it to the frame only by fastenings parallel to the flow. These fastenings are spaced as closely as practicable, normal to the flow, so as to make the plating relatively rigid, with little likelihood of panting or bending between supports and of failure through fatigue. Design Notes for Motorboat Rudders. 74.11

The general principles for the design of

the rudders

TABLE

74.d Ratio op Rudder Area to LateralPlane Abba for Motorboats and Similar Craft

Rudder Structure with One System of Welds Parallel to the Flow

Fig. 74.G

Affected by Hydrodynamics.

Any

control sur-

on a high-speed vessel, requires a structural design and a fabrication procedure which Avill insure that the selected control-surface section, along the Ime of flow, is achieved m the building of the ship and is maintained in service. The finished boundary plating on a structure that is hollow, as are most control surfaces, must be fair and smooth, Avithout wrmkles or bulges. Further, it must be so stiffened that it maintains its fairness and shape while subjected to many face, especially

different kinds of loading,

—steady, intermittent,

The data listed here are translated from the book of J. Baader entitled "Cruoeros y Lanchas Veloces (Cruisers and Fast Launches)," Buenos Aires, 1951, pages 333 and 335. The percentages of Group III include, for each case, the total projected area of the two rudders. On pages 334 and 337 of the reference Baader gives profiles of thirteen launches, motorboats, and motor yachts, showing the relative positions and comparative sizes of screw propellers and rudders for these craft. I.

Normal

II.

is

completed. Internal stiffening members

weld metal when cooling. If the internal stiffeners are placed generally normal to the flow, welding gives the boundary plates a washboard of the

.

2

and

steering

2.5

Ideal surface for steering and

man-

euvering Best surface for going astern

...

3

Maximum surface for special cases Boats with Two Screw Propellers and

4 to 5 10

One Rudder (between them)

Minimum Normal

surface for steering

surface

for

...

2,5

and

steering

maneuvering

3

Best surface for maneuvering con-

Indeed, the process of welding a rudder assembly

attached to the boundary plates by inside welds produce ridges in those plates because of shrinkage

surface

for

.

direction of flow.

the ship

surface for good steering

maneuvering

is

may introduce discontinuities in the surface before

{W')Ar/L{H)

One Rudder

Minimum

one reason why the thin coverings of airplane wings and control surfaces are attached to ribs or stiffeners which lie in the

and alternating. This

Boats with One Screw Propeller and

4 to 5

ditions III.

Two

Screw Propellers and Rudders

Boats with

Two Minimum Minimum

surface for steering

...

surface for steering

2

and 2.5

maneuvering Advisable surface for steering and

maneuvering Best surface for going astern

3

....

4 to 5

MOVABLE-APPENDAGE DESIGN

Sec. 74.11

of

mechanically powered small boats

725

embody

those of Sec. 74.8 relative to balance and trailing, plus the increased relative rudder area indicated for small craft in Tables 74. b

many

and

74. d.

Whereas

were operated by hand, some of them now have power gear, and a few of them automatic steering. For craft which run at speed-length or Taylor quotients T^ of 3 or more, F„ > 0.89, the rudder formerly

of these rudders

and moments are large compared to other and moments. This applies to heeling as well as swinging moments, so that whether or not a boat banks properly (inward) on a turn may depend as much on the rudder as on the hull. As the Tj and the absolute speeds reach higher forces forces

it is increasmgly important that the rudder be of the proper size and shape.

values

Moximuir Rudder

Fig.

Blunt-Ended Parallel-Sided Motorboat

74.1

Rudder The numerals may

represent any units of measurement

or serve as relative proportions.

or tail portion

and a wide, square

trailing edge.

It is cut

away

at the after upper corner because:

The

+Ap

built

(a)

upper after corner

up on the ahead side of the an angled rudder with a

of

horizontal top, indicated in Fig. 74. H, exerts a lift

and depresses the bow. an advantage in straight-away

force under the stern

While

this

is

running, it is liable to cause the bow to trip in a turn [Grenfell, T., "Some Notes on Steering of High Speed Planing Hulls," SNAME, Pac.

Northwest

27 Sep 1952; abstracted in Jan 1953, p. 35]. (b) The portion removed permits a more-or-less solid stream of water to pass over the angled rudder, close under the hull. This acts as a shield

SNAME

Fig.

74.H

Motoeboat Rudder with

Streamlined

Sections

Sect.,

Bull.,

to prevent air leakage to the astern or of the rudder.

Fig.

74.H indicates the outline and prmcipal

dimensions

of

a

type

of

streamlined

rudder

developed by Elliott Gardner for a 45.5-ft air boat, based upon systematic full-scale

rescue

and experience extending back to 1925. It is reported to be suitable for all speeds from 5 to 50 mph, or 4.3 to 43.4 kt. Fig. 74.1 is a more modern rudder of somewhat similar design, intended for use on a 52-ft air rescue boat, but having parallel sides in the run tests

Whether cut away or

— Ap

side

not, it is

preferable to place the rudder so that

it

lies

completely under the hull at any angle, to obtain the

maximum

shielding effect from air leakage.

The nominal

aspect ratio of the horizontal-top

rudder of Fig. 74.H

is

1.247 whereas that of the

more modern design in Fig. 74.1 is 1.224. The design of rudders for high-speed motorboats of the planing type, especially those which travel at values of the Taylor quotient T, in excess of 5, is

= V/'vL

based largely upon experiment

HYDRODYNAMICS

726

and experience.

A

made

to

available

generous portion of both is the profession in a paper

"Some Notes on Steeling on High-Speed Planing Hulls," by T. Grenfell, previously referenced in this section. Grenfell recommends entitled

that the aspect ratio of rudders for these ultrahigh-speed craft be of the order of 2, making them twice as deep as they are long.

IN SHIP DESIGN

Sec. 74.12

s\vinging or steering propellers can not be used,

one or more tubular or box rudders or swinging Kort nozzles may be employed, arranged so as to

change the direction of the whole propeller-outflow Fig. 74. J illu.strates an experimental rudder

jet.

of this type.

Design of Close-Coupled and Comsimple close-coupled Rudders. Any rudder is in reality a compound rudder, but its effect is not easy to predict because the greater 74.12

pound

part of the quantitative data in existence are for flap-type hydrofoils of rather different proportions. However, sufficient information has been obtained

from special model tests [Abell, T. B., INA, 1936, pp. 137-144 and PI. XV; van Lammeren, W. P. A.,

RPSS,

1948,

pp.

327-328] to enable a fairly be made of the part of the

reliable estunate to

total transverse force exerted

by the movable

rudder and the part exerted on the fixed or ship structure adjacent to the rudder. Part 5 of Volume III contains a series of diagrams from which these fractional parts can be estimated for any probable rudder arrangement. From that point on the design follows the procedure described in the Fig.

sections preceding.

The

indications from a series of rudder

and corresponding graphs of ship P. A. van Lammeren [RPSS, 1948, Fig. 221, p. 331] are that none of the fixed fins or posts shown there contribute much additional force to that exerted by the movable rudder blade. When designing a compound-type control surface, or one with a movable blade carrying a flap, it is well to limit the angle of the movable stern profiles

turning

moment given by W.

portion, or the flap, to the order of 20 deg either

way, especially if the length of the movable portion or flap is less than 0.4 of the chord length of the whole section [NACA Rep. WRL-419, Jan 1944]. This eliminates any possibility of stall. However, if the whole control surface is of low aspect ratio, or if the movable portion is very large compared to the whole, it is possible that the movable portion or flap may remain effective up to angles of 35 deg either way. 74.13 Conditions Calling for Tubular Rudders.

When

steering in shallow,

prompt rudder action at

may mean and

or

moment

the difTerence between a safe passage

disaster.

blade

flowing rivers,

fast

just the right

For

this type of service

multi-blade

rudder

is

no

A

74.J

Pair op Tubular, Swiveling Rudders

and

single-

adequate.

If

For proper mechanical clearance the stock axis close to or through the plane of the propeller disc. Even then a constant small tip clearance is not possible unless the tubular rudder has a shape abreast the propeller that is approximately spherical. Against the efficacy of a proper design of tubular rudder must be balanced the liability of bending the tube on rocks or debris in the stream bed and jamming the propeller inside it. 74.14 Closures for Rudder Hinge Gaps. Sec. 37.3 and diagram 9 of Fig. 37. D illustrate the manner in which differential-pressure leakage can take place between the +Ap and — Ap sides of a rudder-and-support assembly, even when the

must pass

clearances are reasonably small. ships

it

as easy

was customary

movement

On

old sailing

to keep this gap as small

of the

wooden parts would

permit. Clearance spaces left for lifting the rudders

enough to get the pintles out of the gudgeons were covered by filhng plates [Barry, R. E., Mar. Eng'g., Sep 1921, p. 689]. In general, plates or other closures should be fitted on the fixed portion of the post-and-blade assembly. This is the reason for the fixed lugs on the sternpost shown by Fig. far

73.

K

of Sec. 73.14.

MOVABLE-APPENDAGE DESIGN

Sec. 74.15

For an excellent discussion of the hydrodynamic and other problems associated with the closing (or narrowing) of vertical and horizontal gaps the reader p.

referred to P.

is

Break"].

S.

Mandel [SNAME,

1953,

—

"Rudders Gap and Horizontal F. Hoerner gives useful information

489, under

concerning the relative drag of various across-theflow gap configurations between a symmetrical-

and

section airfoil

trailing-edge flap, together

its

with notes on the effect of the airfoil thickness and flap thickness at the hinge [AD, 1951, pp. 57-58]. These data apply directly, for straightahead running, to ship rudders hung abaft thin skegs or rudder horns. 74.15 of

ABC

Rudder Designs for Alternative Stems The estimates of area for the

Ship.

rudder designs of the ABC ship, described in this section, are based only on the first approximation of Sec. 74.6, and not upon the more logical procedure outlined in Sec. 74.7. Furthermore, the designs of the rudders themselves are carried

only far enough in this section to produce control devices which would have about the same resistance (certainly

no

less)

than could be expected

of the final refined rudder designs for the

alternative

When

ABC

two

ship sterns.

roughing in the stern profile of the ABC first part of

727

transom submergence clearance of 0.5

ft for

of 2 ft

and a baseplane

the foot of the rudder, the

portion of the blade abaft the stock axis could

be at least 22

ft

high by 10

ft long,

with a pro-

Adding say 25 per cent for the balance portion of the foil ahead of the stock gave a tentative total area of 220 -|- 55 = 275 ft', which appeared ample. With the balance portion extending from 0.5 ft above the baseplane to about 1.5 ft below the shaft axis (at the 10.5-ft WL), its height was 8.5 ft, giving a tentative jected area of about 220

ft'.

fore-and-aft length of 55/8.5

=

6.5

ft.

The length

balance was then 6.5/(10 -|- 6.5) = 0.394. This value seemed rather large but not too large for a rudder which must be angled without requiring

an excessive torque when going astern. With a clear-water skeg ending and a baseplane clearance of 0.5

the propeller, the baseplane

ft for

the rudder appeared someowner and operator. It was therefore increased to 1.0 ft. The upper after corner of the tail of the blade was also cut away to provide a greater gap and more protection against air leakage below the edge of the transom. The three lower corners were left square. The shape and dimensions of the blade when sketched at clearance of 0.5

what small

ft for

to the

the conclusion of the preliminary design of the

Sec. 66.25, a first approximation for the area of

transom-stern huU appear in Fig. 74.K. It has a total area of 273 ft', or 0.0206 of the product

the movable blade of a single centerline rudder was

L{H)

ship with transom, described in the

0.02(L)F, or 265.2

ft'.

From Table

74.b this

is

a

The

=

510(26) at the designed draft. horn as sketched

lateral area of the fixed

about 89

or roughly 24 per

high-hmit value for large, medium-speed passenger ships. The selection of the maximum

in the figure

and cargo

cent of the combined area of blade and horn.

value in the table was based upon the need for excellent steering and turning qualities in the

Because

Port Amalo canal and when maneuvering out of the harbor at Port Bacine, indicated in Figs. 64.A and 64.B. Based upon the use of a clear-water aftfoot and no rudder shoe, the rudder had to be partly or completely underhung. To avoid placing the

horn wUl add materially to the

single rudder in the paths of the hub vortexes from the single propeller ahead, it was decided to embody a partly underhung rudder and to carry it by a horn which extended far enough below the hull to include a fixed fairing abaft the propeller hub. A foil of generous area placed below the horn, with a short circulation path and plenty of clearance for the circulatory flow, would

is

ft',

of its closeness to the blade it

appears

that the differential pressures set up on the fixed exerted by the blade

For the arch-stern

when the

ABC

lateral

force

latter is angled.

hull described in Sec.

67.16 and illustrated in Figs. 67.L and 67.M, there was little in the way of design data for guidance, by which to select a ratio of rudderblade area to the product of the waterhne length draft. The stern was laid out so that, at a reasonably small rudder angle, either the port or the starboard blade would swing into the

and

projection of the propeller disc. Fig. 67. P indicates

that the traihng edges of both rudders, at zero angle, lie close to this projection. The contraction in the outflow jet is

assumed small because the

only about 0.33D abaft the disc

provide the quick response necessary for steering the ship in the Port Amalo canal and in the river

stock axes

below Port Correo.

It was estimated that an increase of at least 25 per cent over the blade area of a rudder lying

Small-scale

sketches indicated

that,

with a

lie

position.

HYDRODYNAMICS -ae.'O

Fbrward Edqe of Horn, c u/ ij Forging or Weldment

2:0Centerline

Fig. 74.K

Bultock-

characteristics as the alternative transom-stern

The adverse

effect of the increased lateral

area of the twin skegs would,

by the increased

it

was

believed, be

which the twin rudders would, acting as flaps, generate on the portions of the fixed skegs just ahead of them. Further, the addition of an underhung foil on each rudder would provide the quick steering and turnmg response needed for running in the confined waters at each end of the ship route.

When

Sec. 74.15

a

,,'

^

'

5.5 Trp 1

"^

oubmerqence = ,

Details of Aftfoot, Propeller Aperture, Rudder Support, and Rudder for Transom-Stern Ship

give the arch-stern ship as good maneuvering

offset

if

».

abaft a single propeller would be required to

ship.

IN SHIP DESIGN

Designed Woterhne

lateral force

finally sketched, as in Fig. 74. L, the total

movable-blade area of both rudders was 346.74 ft^. This was 346.74/13,260 or 0.0261 of the product L{H), an increase of 26 per cent over the same

ABC

of the inside skeg waterUnes close to the anticipated flowlines in the tunnel. The convergence of the outside waterUnes is such as to terminate the skegs and rudders in trailing edges that he as

close as possible to the outflow jet of the propeller.

The

and unsymmetrical sections some uncertainty as to the hydrodynamic behavior of the hinged tail portions, when acting as flaps hinged to the main skegs. In view of the lack of information about them, a series of maneuvering tests with a model is definitely indicated before the arch-stern design is carried beyond this resulting thick

leave

preUminary stage.

The

selection of the proper thickness ratios

and

ratio for the single, centerline-rudder design of

shapes for the single, streamhned rudder of the transom-stern ship involves no .such hmitations as those just de-

the transom-stern ship.

scribed for the arch-stern design.

These twin rudders are in effect only the trailing edges of the two arch-stern skegs. Each is arranged to swing about a vertical axis 8 ft fonvard of what would be the skeg ending and each carries an underhung foil extending below the bottom of the skeg termination. The rather

thickness ratio for the single rudder

unusual horizontal sections of the

tail

portions of

these rudders arise from a deliberate continuation

the

horizontal

section

To be is

sure, the

to

some

extent governed by the thickness of the fixed

horn

which

is

necessary

to

afford

rigidity to the lower rudder bearing.

adequate This is a

matter of structural analysis and calculation and it is outside the scope of the book. The thicknesses indicated on Fig. 74. N of Sec. 74.17

as such

are estimates only, based

upon

similar installa-

MOVABLE APPENDAGE DESIGN

Sec. 74.16 26'

Fig. 74.L

Designed

Vertical Centerplane Section Through Shaft, Propeller, and Strut-Bearing Support of ABC Arch-Stern Design

tions with fixed horns of

somewhat

less relative

depth.

Before the tinie came to sketch the streamlined rudder for the transom-stern ABC ship it was decided to use a form of contra-rudder. A fairform rudder with a flat meanline plane, even when designed as a unit with the fixed horn, involves design problems which are adequately covered

by P. Mandel [SNAME, 1953, pp. 474-490] and by others listed at the end of Sec. 74.8. They are not further discussed here. The layouts of the contra-rudder and the contra-guide horn, as applying to the

ABC

transom-stern design, are

described in Sees. 74.16 and 74.17 which follow.

Centra-Rudder. Strictly speaking, the contra-flow feature on a rudder is not a functional part of the rudder as a 74.16

729

Woterlii

thrust-producmg device. In fact, it need not be movable, as is the rudder. Typical horizontal sections for a compound rudder with contrafeatures in the fixed portion only, and in both the fixed and movable portions, are shown by W. P. A. van Lammeren [RPSS, 1948, Fig. 55, diagrams e and f respectively, p. 100]. However, as a rudder ,

required with normal screw propulsion, the friction drag of a separate fixed surface is elimin-

is

ated by incorporating the contra-flow feature in the rudder. For the design of this feature, the

rudder

is

considered to remain at

its

zero or

neutral angle.

The

design problem consists

of:

Design Notes for a

control surface but

is

an energy-recovering and a

(a)

Establishing

a

series

of

above and below the propeller

horizontal axis,

planes

described for

the contra-guide skeg ending in Sec. 67.22, for

HYDRODYNAMICS

730 1<2U[

IN SHIP DESIGN

Sec. 74.16

0060

AUi-»^h-

^ t Q n"' r'<2UiSini;(-UASin9s1 Ec^.(74.l)

Fig. 74.

M

Vector Diagram for Design of Contra-Rudder

which separate velocity diagrams and rudder sections are to be drawn (b) Estimating the magnitude of the mduced velocity Uj at each propeller radius, as well as k^ and fcj in Fig. 74.M. These the factors fci data are required to determine the resultant velocity vector Urs for the given radius at the ,

fore-and-aft

,

location

selected

for

the

leading

edge of the contra-rudder. The latter position is usually determined by the aperture clearance provided abaft the wheel. (c) Drawing velocity diagrams smiUar to those

74.M, assuming that a contra-guide skeg ending, if one is to be used, is already designed (d) Estimating the magnitude of the induced velocity to be set up by the contra-rudder hydrofoil section itself, of which half may be expected to develop ahead of the leading edge of the contrarudder. It is of interest to note that the flow due to cii'culation through the aperture between a in Fig.

and a contra-rudder blade is in the same direction for both, namely forward in the direction of motion of the propeller blade. In many cases the velocities induced by the rudder are small and may be neglected in the design. propeller blade

(e)

Selecting a curve for the leading edges of the

transverse plane.

then laid

off

in detail in a (f)

The

edges are

offsets of these

at each level. This matter

is

discussed

paragraph following.

Calculating

(or

a

estimating)

minimum

thickness for the contra-rudder. This involves the calculated diameter of the stock or

main

vertical

member

necessary to carry the side loads expected. These in turn have to be estimated rather roughly until more of the rudder is laid out. structural

If

is to be of the compound with a fixed forward portion, a certain

the contra-rudder

type,

stiffness is required for this latter (g)

member.

Selecting a hydrofoil section thick enough to

meet the needs

of

combmed with proper maximum thickness tx

(f),

fore-and-aft position of the

(h) Calculating the lift on the selected section at the nominal angle of attack indicated by the velocity diagram for the propeller radius in

question.

From these data a second approximation

to the loading curve on the stock

is

found, by

which the stock scantlmgs are checked. Although the lateral thrust loads are

m

opposite directions

above and below the shaft axis the bending moments and shear loads are heavy in the vicinity of that axis. (i)

Adjusting the several hydrofoil shapes and body based upon them

hydrofoil sections of the rudder blade at the

positions so that a S-dunl

various levels or propeller radii, as projected on a

is

fair

with respect to

its

traces in a series of

MOVABLE-APPENDAGE DESIGN

Sec. 74.16

vertical transverse planes

and the

trailing edges of the rudder.

steps listed in the foregoing require

through

some

given here in the same order as (i).

The velocity diagrams of Fig. 37. K, for a contrarudder installation only, are supplemented by those of Fig. 74. M, for an installation of both contra-guide skeg ending and contra-rudder. In

the latter diagrams the incident flows on the pro-

shown

two adjacent blade sections, unrolled into the flat. This is an aid in visualizing the flow leaving the skeg endmg, represented by the vector U a and that forming one of the components of incident flow on a blade section at the same level. It is customary to show the flow meeting a peller are

for

,

moving-blade element with reference to axes in The vector Ua is therefore combined with the rotational vector 2irrii2 and with the induced-velocity vector fcj Uj to give the incidentthat element.

velocity vector Uri

.

When

moving blade along Ur2 to axes fixed in the ship

it is

is

it

with the

equivalent to combining the inflow vector

?7jj3

cidence with respect to the ship

centerplane,

smooth flow around the rudder with a reasonable lift force and forward-thrust component. What is wanted first is the value of the angle Br which the vector U r^ makes with will insure

the ship axis. Second, the

amount

of offset of the

leading edge of the contra-rudder section determined. If the fraction

fej

is

is

to be

estimated (or determined in

some manner)

it is possible to derive Br by a graphic construction such as that in diagram 2

The

by the hydroshown as /cjC// in the

velocity induced

section of the rudder,

corner of the figure.

For a contra-guide skeg ending designed as in Sec. 67.22, the angle ds is known for any blade radius or level. If the skeg ending

is

symmetrical,

as in Fig. 37. K, the expression for Br reduces to that of Eq. (74. ii), alongside the large-scale

diagram 3 of Fig. 74.M. The value of Ui is always small with respect to U a and /cj is always less than 1.00, because the full value of Ui is developed only far astern. Eq. (74.ii) therefore reduces to Br = tan~^ (C sin 0). Here C, representing kiUi/U A is a small fraction, say 0.15. For any normal propeller the geometric blade angle 4> seldom exceeds 65 deg at the hub surface, hence C sin has a maxunum value of about 0.135. The angle 9r then has a maximum value of about 8 deg, where Br = sin Br = tan Br approximately. ,

,

,

Actually,

it is

possible to derive the average

Ua

only from model tests

or very special ship tests. Further,

the same for at

It is now required to select a section shape for the contra-rudder, and a nominal angle of in-

of Fig. 74. M.

RH

U a is almost never constant along the upper or the lower blade radii, either in magnitude or direction, nor does the mean upper value of U a equal the mean lower one. As a consequence, and because of the varying circulation at different blade radii, the maximum induced velocity Uj is almost never

by combining

.

foil

The

nominal value of the obliquity 6r of the velocity vector U R3 incident on the rudder section, may be calculated by Eq. (74.i), set down in the upper

value and direction of

edge of the blade element, the latter equal to k^Uj The flow meeting the hydrofoil section of the rudder is then represented nominally by the

which

the diagram.

again referred back

U A with the induced-velocity vector at the trailing

vector

in

the flow leaves the

rotational vector 2imR, but in a reverse direction.

This

731

marked

blade angles

,

The

explanation, (a)

between the leading

/ci

all radii,

nor

is it

known

precisely

any radius. To cap all the foregoing, the factors and ^2 are not well known. While values reason-

ably close to the actual ones could undoubtedly

be substituted in the expressions for Br in Fig. 74. M, there are practical factors which require a more realistic approach to this design problem. It is recalled that for the design of a contraguide skeg ending discussed in Sec. 67.22 the value of Br derived analytically for points opposite the outer propeller radii are small but they are still

too large for practical use. Employed here,

they would produce a rudder which had no straight or symmetrical sections whatever. Whether this much of a departure from the orthodox stream-

Imed rudder would be the best device for steering a straight course for long periods could only be determined by successive full-scale installations on the same vessel. The doubt expressed in the

small-scale diagram 1 of the figure, is omitted from the large-scale diagram 1 to avoid confusion. It is also assumed, for the sake of simplicity but without appreciable error, that the induced-

rarely possible to use hydrofoil sections

fci Ui and fca Uj he normal to the base chord of the blade section, at the geometric

at zero angle.

velocity vectors

foregoing

is

heightened by the fact that

deliver the water directly astern

The

large

mth

it is

also

which

the rudder

camber necessary to

HYDRODYNAMICS

732

accomplish this imposes the thickness ratio and

loads which increase

lift

make

it

more

difficult to

lay out hydrofoil sections of suitable shape. solution employing a leading-edge offset on the -v'aryiug as sin^

<^,

utUized previously for

the design of the contra-guide skeg ending discussed in Sec. 67.22, is employed here for the

The offset taken as a be based, as before, on a value of about 0.85 times the propeller hub radius d/2 opposite the 0.1 propeller radius. A graph for contra-rudder as well.

reference

may

selecting the angle

which the median

luie at the

a fixed contra-propeUer blade is to make with the fore-and-aft plane is given by R. Wagner [STG, 1929, Fig. 44, p. 224]. This

leadmg edge

of

graph could be used as well for the leading edge of a contra-rudder, whether this edge were the fixed portion of a compound rudder or the leading edge of a balanced rudder. It calls for an angle of 45 deg at O.lSfi (of the propeller), 19 deg at

and 9 deg at O.SOi?. Whatever rule is used, some asymmetry in the form of leading-edge angle does and should 0.48fi,

remain abaft the propeller-blade tips, as for the contra-guide skeg endmg, at vertical distances above and below the shaft axis equal to the propeller radius R^^^ A transition is necessary from the maximum twist toward the trailing edge of the propeller .

blades at the 12 o'clock position to the maximum twist in the opposite direction (but also toward

may

mean plane

of the

rudder blade. All

require that, not only

must the leading

edge be directed and offset one way from this plane, but the trailing edge must be offset the other way. The transition takes the form of a crossover from one side to the other, abaft the propeller hub, in both the leading and trailing edges, but in opposite directions.

rudder as

tinuities in the

offset

structure abaft the of this

method

is

to

this

means

the rudder

hub are avoided. A variation work a bulb into the rudder

at the transition pomt, extending well aft on the

rudder [Maritime Reporter, If all

the rotation

propeller-outflow

jet,

is

1

Feb

1954, p. 23].

to be taken out of the

the median lines of the

In one of the earliest descriptions of the contrapropeller, for installation abaft a screw, R.

blades eccentrically to the hub center" [transl. of Schiifbau, 14

Feb

1912, pp. 365-366].

statement.

The diagram accompanying the

may

possibly be better

refer-

this

offset

somewhat more

gives the designer

freedom in shaping the vane or blade which is to convert some of the rotational energy into thrust, and places the base chord at a greater angle to the ship axis. If other conditions are right, a

somewhat greater forward-thrust component derived from a given lift force. For the single rudder

of the

ABC

is

transom-

decided not to incorporate any offset in that part of the blade lying abaft the it

is

its

trailing edge.

When,

as

described in Sec. 74.17, a contra-shape is incorporated in the fixed horn ahead of the rudder stock,

there will be an

appreciable

lift

force

acting to starboard on the unsymmetrical hydro-

assembly composed of this horn and the tail Combined with the Hovgaard Effect, described in Sec. 33.17, there wA\ be a continual lateral force acting to push the stern to starboard when the ship is going ahead. This foil

of

the rudder.

swinging effect can be counteracted only by giving

a hydrofoil

zero or neutral position. It

does

ence has the trailing-edge offset marked by a symbol, not mentioned in the text. Incorporating

be parallel to the mean plane

its

He

not, unfortunately, give specific reasons for this

a contra-shape to the underhung

rudder in

Wagner

mentions that: "A particularly good result is obtained by shaping the trailing edges of the

trailing edges of the contra-rudder sections should of the

are

called for

rudder stock or in

m

an easy transition

well,

when the trailing edges from the mean plane of the blade.

also

is

the "shadow" of the propeller hub. In fact, one good way to make it is to use a cylindrical propeller hub and to Avork a large hub fairmg into

By

of

the water must flow, and of structural discon-

stern ship

the contra-rudder in this region.

As a means

avoiding sharp corners and coves along which

the trailing edges) at the 6 o'clock position. This should be made gradually, not abruptly, across

abrupt and harmful discontinuities

Sec. 74.16

rudder sections at an appreciable

of each of the

angle to the this

With these considerations m mind a compromise rudder

IN SHIP DESIGN

lift

force to port.

of force to starboard

may

still

more than the usual amount

foil

and exerting

The preponderance require carrying

lateral force

rudder to maintain a straight course. This is another reason for not working a contra-guide ending into the upper portion only of the centerline skeg ending.

thrust,

It too

to

make

the face, on the -|-Ap side of the trailing

edge, parallel to this

appreciable forward

it is

mean

plane.

component

of

Also,

the

if

an

lift

or

on the rudder is to be realized as advantageous to place the base chord

would exert a

of right

lateral force to starboard

and

MOVABLE-APPENDy\GE DESIGN

Sec. 74.11

augment the right rudder

to be carried to inaintaiii

a straight course.

The

design of the contra-shaped movable

733

speed ship in bending the leading edge of a rudder, contra-fashion, instead of using a simple stream-

foil

lined affair, with the base chords of all sections

follows the design of the contra-shaped fixed horn

parallel to each other. In the rotary cross flow

or skeg above

it,

described in Sec. 74.17. Normally,

the thickness ratio of the

foil

sections in a partly

underhung rudder diminish rather rapidly from the lower bearing to the bottom of the rudder, until at the lower edge this ratio

order of 0.03.

The high value

the section at the 2-ft

74.N

Fig. (1)

The

WL

of Sec. 7-4.17 is

of

may be of the about 0.115 for

for the foil

due

is

in

because

foil,

extended below the propeller

shaft axis (2)

The uncertainty involved

in drastic thinning

of a contra-section, expecially in a rudder of this

type.

Thinning the lower-edge sections represents no problems, provided it is determined that the contra-performance can be maintamed. If the lower sections are left thick, a flow test might indicate the advisability of sloping the lower edge of the foil down and forward, with a baseplane clearance of say 0.5 ft at the forward end and

The compensating

by the

force exerted to port

is

at a greater effective angle of attack

m

the out-

water which, below the shaft axis, is directed aft and to port behind a right-hand wheel. Rather than to offset only the trailing edge of the tail, above the shaft axis, and to introduce a discontinuity in the rudder structure, the entire flow-jet

portion of the blade abaft the stock axis

is

made

symmetrical.

when

is designed, and a checked in a circulatingwater channel with tufts attached to various

Finally,

model

is built,

the rudder

the flow

buffeting,

and noise. An example- of a severely pitted Mariner class rudder, not so shaped, is given by W. G. Allen and E. K. Sullivan [SNAME,

W. Bunyan

1954, Fig. 25, p. 541]. T.

illustrates

the pitting which occurred on a combination of abaft

it,

and a rudder hung directly

lying in the outflow jet of a single,

centerline propeller. Both were streamlined but were entirely symmetrical about the vertical plane through the propeller axis [IME, Apr 1955, Vol. LXVII, No. 4, p. 105]. 74.17 Design of a Contra-Horn for the ABC Transom-Stem Ship. For the transom-stern ABC ship whose stern profile is shown in Fig. 74. K, the rudder horn or small skeg abaft the propeller extends below the shaft axis so that a fixed

dummy

fairing for the propeller

hub may

be carried by it. For ease in removing the shaft nut and the propeller on the actual ship, this fairing is

made removable.

In view of the appreciable fore-and-aft length

probably augmented by holding the trailmg edge of the foil on the centerplane; that is, by not offsetting it to port, as is customary in contra-rudders. The foil then works foil

shape acts to

erosion,

pitting,

vibration,

1.5 ft at the after end.

contra-shaped

cavitation,

thin rudder post

to:

short vertical height of the

the fixed horn

shown

of the outflow jet the contra-flow

reduce

is

parts of the rudder. One test should be made with the propeller working, and another with the rudder at an angle. Unfortunately, it was not possible to do this with the model of the transom-stern ABC design. Entirely aside from the increase in propulsive coefficient which may be achieved by a contrarudder on any ship, which should be from 4 to 6 per cent under average conditions, there is a decided advantage on a high-powered, moderate-

of the fixed

rudder horn

incorporate

all

of the

contra-guide device in propeller axis.

found possible to and camber of a the portion above the it

is

twist

As explained

in Sec. 74.16, this

leaves the tail sections of the movable blade entirely symmetrical. all

Below the propeller

the twist and camber

is

axis,

incorporated in the

balance portion of the rudder

foil,

forward of the

rudder-stock axis, also described in that section.

In the original layout of the propeller-hub end of the rudder horn it appeared that the diameter of this fairing at its juncture with the horn would be 3.0 ft, with a radius of 1.5 ft. As a basis for calculating the fairing at the lower

offsets for the twist at the leading

edge of this

horn, the offset at O.lflMas above the propeller axis was taken as 0.85 times 1.5 ft or 1.275 ft.

The remaming

offsets,

rule described in Sec.

calculated 67.22,

by the

sin^

<^

are tabulated on

The offsets below the shaft axis, to be embodied in the leading edge of the foil, are the same as those above that axis, for the same radii. When TMB model propeller 2294 was selected from stock to drive the transom-stern model, it was necessary to reduce the hub-fairing diameter at its junction with the horn from 3.0 ft to 2.67 Fig. 74. N.

HYDRODYNAMICS

734

Elevotion, Looking £6'

:.N

Aft

20

However, the leading-edge offsets of the horn above the shaft axis and the balance portion of the rudder foil below it were left unchanged. This necessitated a short length of reverse curvature

(inward) just above the hub fairing, shown in the end elevation at the left of Fig. 74. N. The maximum median-lme slope at the leading edge of the contra-fairing on the horn, just above the hub fairing, is 22.5 deg. This is considered acceptable because of the large angle djt Avith which the water leaves the propeller-blade elements in this region. Separation is not a problem here provided the mcident flow from the blade elements at the root strikes the leading edge of the horn at about this angle. The fixed horn and the tail of the rudder (when at zero angle) are considered as a smgle assembly

by

laying

The

(1)

out the section outlines for the

thickness ratio at each level

is

governed

the profiles of the rudder and horn, which

establish the

chord length

necessary

thickness

for

structural

stiffness.

The

c,

and

(2)

by the

the horn, to give it latter determines the

No section designations or sets of value of tx coordinates are specified or recommended here .

19.33

19.5

Arrangement and Details of a Contha-Hokn and Rudder for

ft.

horn.

Sec. 74.17

DWb^

Stations

when

IN SHIP DESIGN

ABC

Transom-Stern Ship

because there are a considerable number of good ones from which the designer may choose [Mandel, P.,

SNAME,

1953, pp. 486-488].

An

important feature of section outlines for compound rudders, similar to the one shown in Fig. 74.N, is the shape of the extreme nose. This statement holds even though contra-guide sections are worked into the forward or fixed portion.

A

shape too nearly circular leads to cavitation or

separation along the sides of the section, a

abaft the nose, especially

A

nose that

is

too pointed

if

the radius

may

is

little

large.

also be subject to

cavitation or separation on the "lee" side,

when

no contra-shape and when the angled flow from a propeller ahead strikes the leading

there

is

edge of the rudder at a large angle with the meanline plane through the rudder. A practical example of this is described in the last paragraph of Sec. 74.16.

M. Kinoshita and S. Okada show the results of measurements on models made by M. Yamagata, in which the flow just below the propeller hub makes an angle of over 50 deg with the meanline plane of the rudder Vol.

2,

No.

[Int.

Shipbldg. Prog., 1955,

9, Fig. 8, p. 238]. It is

clear that, as

MOVABLE-APPENDAGE DESIGN

Sec. 74.20

these Japanese authors

pomt

out,

much more

needed concernmg the details of flow abaft an actual screw propeller before the designer is able to shape properly the leading edge of a rudder horn or a balanced rudder. 74.18 Design for Rapid Response to Rudder Action. The development of a given lift or normal force when angled is only one of the things which a rudder or other control surface is called upon to do. It must also do this rapidly, so as to provide quick response on the part of the ship. An excellent example is the control surface in the form of an active roll-resisting fin. This has only 10 sec at the most in which to shift its position from hard over one way to hard over the other and to produce a useful force and rolUng moment before it has to shift position back again. Another example is the rudder of a ship traversing a canal, for which rapid response is much more important than the simple ability to steer or to turn one way or the other. The shorter the circulation path around a rudder the smaller is the mass of water to be set in motion and the sooner are the circulation and lift estabhshed. A hydrofoil which is called upon to exert a normal force rapidly should be short in the direction of motion and have reasonably large clearances or apertures both ahead and astern. A short, high spade rudder is the best answer to this design problem. A balanced rudder hung on a small horn, short in the fore-and-aft direction,

knowledge

is

is

the next best.

driven by side paddlewheels), the clearance for circulation in a horizontal plane

around the rudder

provided by an aperture forward of the rudder. This resembles the aperture in which a propeller would be fitted if the ship had only a single screw. is

Two

such apertures are sketched in diagrams 3 of Fig. 74. D. An equivalent aperture of large area hes ahead of the underhung foil portion of the rudder in diagram 5 of Fig. 37. D. 74.19 Utilization of Automatic Flap-Type Rudders and Diving Planes. There appears to be a definite application in the field of control surfaces for the hinged hydrofoil with automatic flap, depicted in diagram 2 of Fig. 14. U. This device is called here, for want of a better name, the automatic flap-type rudder or divmg plane.

and 4

is

incorporated in

or equivalent

angle as the main control surface is angled. Both the control-surface angle and the flap or tab angle are in the same direction, whether the

rudder

right or

or the plane is at rise or always increases the lift of, and the lateral force on the control surface. This device has been utihzed successfully for a number of years on the active fins of the Dennyis

The

dive.

left,

flap action

Brown roll-stabilization gear, referenced in Sec. The linkage for applying flap angle auto-

37.9.

matically

outside the watertight hull of the

is

vessel but in view of its extreme simplicity

it

it

some simple leverage

mechanism to apply

positive flap

has

operated well in service.

Although no designs have been prepared, or made, so far as known, it should be

installations

possible to substitute this device for almost

any

rudder or diving-plane installation which fits closely against a fixed portion of the hull. The simple Denny-Brown linkage or its equivalent

may

be used for operating the flap. For a control surface subject to severe pounding or slamming when in waves, the flap may have to be restricted to only a portion of the rudder height

the

or

diving-plane

width.

The

total

impact forces on the flap may then be small enough to be withstood by the automatic angling mechanism. 74.20 Design Notes for Bow Rudders; Rudders for Maneuvering Astern. It is pointed out in Sec. 37.11, supplemented by Fig. 37. G, that a bow rudder produces decidedly inferior steering action with the ship going ahead.

For a simple, balanced rudder or a flap-type, unbalanced rudder at the stern of a twin- or multiple-screw ship (or at the stern of a ship

There

735

rudders are

required to back for appreciable distances. these conditions, the

Bow

primarily on vessels

fitted, therefore,

Under

bow rudder becomes a

stern

steermg rudder, in the normal sense of the term. If it were suflBciently important to pay for the

and the added steersman, on a long, fast, slender craft, operating m shallow and restricted waters. With such a rudder it might be possible additional complication

a

to

bow rudder might

move

wmd

justify itself

the ship sideways, or to hold

and other

it

against

would act in this case much as the bow planes on a submarine; in other words, not as a turning mechanism but as a effects. It

transverse-force-producing device.

The bow velocity to

rudder, as a rule, has no induced

augment

its effect,

from a reduced speed friction wake.

suffer

of

The that

fitting of

is

There

rather

is little

a

but neither does it advance because

of

bow rudder

requires a forefoot

and thin in section. to be gamed by mounting the stock full in profile

HYDRODYNAMICS

736

the forwaid portion of the rudder. Usually

in

there

is

not adequate room for the stock and

bearings

if

this

is

The

done.

the after end of the aperture that

its

is

so thick at

it is

not possible

hull

to take advantage of a balance portion abaft the stock,

where the flow would be

The customary

solution

is

to

ver}' disturbed.

mount the

stock at

IN SHIP DESIGN

Sec. 14.21

requirement could be imposed on rudder mstallations in Avhich any part of the rudder rises above the water surface during wavegoing. 74.22

Centra-Features

Whether placed

for

Diving

Planes.

in the outflow jets of propellers

or not the diving planes of submarines rarely

work

in flows that are

symmetrical about the

the extreme after end, with or without a pintle

mean plane

and bearing at the keel level. A rudder of this type is sho^\^l by G. de Rooij ["Practical Ship-

vertical plane

building," 1953, Fig. 495, p. 203].

to locate the diving planes in symmetrical posi-

74.21

Bow and

General Design Rules for

Stem Diving

Planes.

Bow and

stern

diving

of the blades. First, the flow in

any

rarely symmetrical ^\dth respect

is

to the submarine axis. Second,

it is

The

rarely possible

any plane component of The neutral plane angle must be ad-

tions relative to that axis.

position usually has

some

flow at

vertical

planes on submarines suffer from certain design

velocity.

limitations which should be but are not yet over-

justed accordingly or the leading edge of the plane must be bent or twisted to point into the

come: (a)

The bow

planes, almost invariably required

to rig in or house within the fair hull lines, are not easily supported

when given

great span and a

large aspect ratio. Furthermore, their inner ends

can rarely

lie

mth

close against the hull,

gap throughout the complete range

the leading edge of a contra-rudder, prevents the center of pressure from lying too far forward of the plane axis.

A pair of diving planes,

a small

and

of rise

position

The port and starboard

stern planes, placed

Recover rotational energy

(1)

across the propeller-outflow jet(s),

can almost never he with their inner ends close against the hull, or close to each other, principally because of the triangular gap necessary to s\ving the steering rudder between them.

withm (c)

It,

too,

must

To produce

the

maximum

compromise to meet all these conditions calls for an aspect ratio of approximately 1.0, with no cantilever or image effect. In other words, the diving planes are made effective

roughly square in planform. It is assumed that they do not benefit in lift by being close to the

some

diving planes of a submarine

are so near the surface,

when the

vessel

Setting Neutral Control-Surface Angles. rudders are offset from the vertical plane

When of

symmetry, either as parts

is

not

or submerged, that in a

never flows past them in a direction parallel to that plane, with the ship moving straight ahead

To achieve equal turnmg effects, with equal amounts of right and

at a steady speed. right left

and

left,

rudder angle, each rudder must be placed

carefully at zero angle in its neutral position.

This adjustment

is

made

for the condition

The

when other

determined with relative by any one of several methods. However, if there is a possibility either of laminar flow or of separation on the rudder, due to its form or to the shape of the hull the vicinity, there may be some scale effect, because of unexpected shifts in the transition or neutral position

separation points. If

entire horizontal area.

are uncertain

similar but possibly less drastic

all

conditions are assumed to be normal.

heavy sea they are subject to severe impact in the form of wave slap. This applies to both bow and stern planes. A good design requirement, admittedly formulated on a not-too-scientific basis, is that these planes shall withstand as a working load an impact pressure of 1,000 lb per ft" over their

A somewhat

of single-rudder or

multiple-rudder installations, the water almost

the propulsion de\'ices are working;

large vertical surface.

The non-housing

to useful thrust

Compensate partly for the unbalanced reaction exerted by the submarine propelling plant, in the manner described by Sec. 73.21. (2)

74.23

possible vertical

breakdo"wn range of a symmetrical hydrofoil.

hull or to

it

to:

in the outflow jet

lie

and size of installation the planes are often worked far beyond the normal

awash

and convert

or close to the outflow jet(s).

forces for a given weight

An

placed in a symmetrical

abaft the propeller of a single-screw

submarine and twisted, contra-fashion, serves

dive angles. (b)

direction of flow. This bending, similar to that at

is

ease in a self-propelled model test

m

so,

the model predictions

when applied

It is diflScult

if

to the ship.

not impossible to determine

MOVy\BLE-APPENDAGE DESIGN

Sec. 74.24

neutral rudder positions on a full-scale vessel.

The

and rudder proportion to the hydrodynamic

friction forces in the steering gear

stock are large in

737

when

the propeller

steering

or

turning

not

is

desired.

combined with the swing-

Efficient propulsion,

torque on the stock at small rudder angles. The torques due to friction may even exceed those

ing motion of the horizontal shaft and the pro-

due to water flow around the rudder. Furthermore,

angled propeller does not encounter undue interference from parts of the hull ahead of it. Unless

unless

it is

known

definitely that the rudder

-will

one is reluctant to disconnect the tiller or bypass the steering gear with the vessel traveling at the speed for which the correct trail if left to itself,

neutral position

is

required.

happens that a neutral position which gives zero torque on the stock of an offset rudder is not the one which results in minimum resistance It oftens

or shaft power. Either the ship designer or the

owner and operator must then decide whether the neutral setting

to be for

is

minimum rudder

torque or minimum overall resistance. For multiple rudders operated by a single steering gear, with tillers connected by drag hnks,

sometimes possible to fit a temporary link for the early sea trials and to replace it by a permanent link having the proper length. 74.24 Selection of Swinging Propellers for Swinging propellers, Steering and Maneuvering. described in Sec. 37.22, form perhaps the simplest and most efficient of steering and maneuvering it is

devices. In fact,

any

driven through the

propeller, large or small,

medium

approximately vertical, to this thrust,

means

lends

itself

is

admirably

The complete

propeller

somewhat modified by a large non-axial flow when the propeller is

albeit

degree of first

of steermg.

of a shaft that

swung to a

an oblique

force.

large angle, remains available as

A large

force

component normal

peller, reciuire that

the inflow jet of water to the

the speed of advance jet follows the

small the axis of the inflow

is

predominant flow

in the vicinity

instead of the angled propeller axis. If the vertical drive shaft and its housing do not project from underneath a portion of the

stern which

is

continually submerged, a horizontal

subsurface plate

is

required on the housing at

some point below the water surface to prevent leakage of air from the atmosphere to the propeller.

A

so-called "anti-cavitation" plate of this

kind, although usually

much

is

em-

all

out-

below the

keel,

too small,

bodied in the vertical-shaft housings of

board-motor If

installations.

the propeller disc

lies entirely

a steering propeller lends propeller at the bow. It

itself to

may

operate either singly

or in combination with one or propellers at the stern.

however,

wake

is

use as a tractor

more other

A bow

steering

steering propeller,

rarely able to take advantage of

any

velocity due either to viscous or potential

and upward, like an outboard motor installation when shallow water is suddenly encountered, it must usually swing outward and upward. For auxiliary propulsion as well as steering flow. Instead of swinging aft

available the so-called "active" or is Pleuger rudder developed in the early 1950's in

there

Germany

[Hansa, 16 Jul 1952, Vol. 89,

to the ship axis serves as the equivalent of the

also p. 921]. This device, comprising a

transverse force which would otherwise be exerted

sible electric

p.

918;

submer-

mechanism high-powered installation must be

motor driving an auxiliary propeller and swinging about a vertical axis like a rudder, is described at some length in Sec. 37.22. At the

from the vertical shaft takes charge and swings

time of writing (1955) it is available in limited powers only, not exceeding several hundred horses.

by a rudder. The mechanical

steering

for a large or non-overhauling, otherwise the torque reaction

CHAPTER

The Problem

of Hull Smoothness arid Fairing

General Considerations; Definitions

75.1 75. 2 75.3

....

The Importance Specific

of Smoothness and Fairing Smoothness Problems on the Shell .

The

Utilization

of

Inside

.

The

The

75

The Termination

.

742 742 742

.

743

Comers Requiring

Negligible Fillets

Fairing of Appendages in General

.

.

.

75.1 General Considerations; Definitions. Smoothness as related to hydrodynamics is a physical characteristic of the underwater surfaces

.

and Bossings Precautions Against Air Entrainment Design Notes for Shallow Recesses .... Practical Problems in Achieving Underwater Smoothness and Fairness on a Ship of Skegs

.

due to excess effect in

friction

resistance.

reducing underwater noise

.

.

.

.

746 747 747 748 749

Its

possible

is

not dis-

fillers,

almost every case the occurrence of high Ap's,

appendages, hence

is

properly considered as a

general item applicable to elements. Fairing,

fillets,

all

consider

them here

the external ship

transition pieces,

external ship elements, hence

it is

appropriate to

as a class.

absence of small irregularities of the kind associated with rough or fiaked paint coatings, rust, pits, rivet points,

and welding beads.

It indicates

also that a surface has the proper curvature it is

cussed here, although that

in fishing

separation,

or cavitation increases the drag of

the appendage. It

Smoothness, as used in this chapter, denotes the

that

75.12 75.13 75 14

745

Fairing of Exposed Shafts at Emergence Points

their equivalents likewise apply to all the

or location of those surfaces. It applies to the hull,

the propulsion devices, the control surfaces, and

and

11

.

of

may become a factor and other operations of the future. Fairings, fillets, and fillers are applied primarily to avoid high dynamic pressures, cavitation, or separation. In some cases these discontinuities in the flow create undesirable disturbances ahead of propulsion devices and control surfaces. In

of a vessel, regardless of the size, configuration,

all

.

744

Hubs in Front Compound Rudders

Fairing of Propeller

Simple or

Casting or Welding

Recessed Lifting and Mooring Fittings Fairing the Enlargements Around Exposed

.

Propeller Shafts

The

75.9 75 10

Fillets

75 5 75.6 75.7 75 8

738 738 739

Plating

75.4

75

and

free of waviness such as is often en-

is

pointed out elsewhere that

added drag at each appendage may be insignificant compared to the total drag of the ship. Nevertheless, the cumulative effect may be considerable, sufficient to neutraUze the improvement gained from some special design of hull or the

propulsion device.

countered at and between internal frames or

The

structural discontinuities inherent in the use of

as

dynamic pressure, and separation are pressure effects and such vary as the square of the relative velocity

lapped seams and butts, raised strakes, doublers, and other irregularities involved in applying the

of

water flow. The

and

shell plating in relatively small pieces. Fairing,

speed of the vessel.

aside from its frequent use as a general term,

negUgible increment of pressure drag on a slow

applies principally to portions of generous radius,

medium-speed cargo vessel for the sake of of construction becomes a matter of inefficient propulsion on a high-speed finer, where an increment of first cost is easily justified by a saving in fuel over many years of operation. 75.2 The Importance of Smoothness and Fairing. Nature goes to considerable pains to work fairings into many of her creatures. Man can hardly do less if he is far-sighted and looking for improvements. A close study of many natural

stiffening

members.

It

takes

for

granted

the

expressed in multiples of the shell-plating thickness,

worked into or apphed to various parts to

insure easy water fiow around them. Fillets are

defined as the roundings worked into coves or internal corners or castings, weldments, and other

members, as well as the transition added to bridge gaps and discontinuities in the hull and its appendages. In general, smoothness is sought and required in an effort to avoid unnecessary power losses structural pieces

increased drags due to

cavitation,

effects of

inadequate fairing

filleting therefore increase

rapidly with the

What may be

accepted as a

or

economy

structures reveals the hitherto little-recognized

738

HULL SMOOTHNESS AND FAIRING

Sec. 75.3

fact that

many fairings are indeed not excrescences

but parts at that.

of the structure

A tree is so shaped

and important parts above its point of

just

attachment to the ground that the stresses in the wood of its trunk are very nearly constant with height when the tree bends with the wind as a cantilever beam. This is almost identical with the most modern type of fairing at the roots of screw-propeller blades, employing a constantstress transition shape where the blades join the hub. The fairing of the afterbody of a whale or a porpoise into its horizontal flukes is an admirable combination of hydrodynamic streamlining, rapid and effective change of cross-section area and shape, arrangement of muscles for manipulating the flukes as propulsion devices, and muscular

739

the relative liquid velocities in the inner portions of the

boundary layers

will

be high. This applies

to a belt about 2 or 3 times the inlet width

perhaps 10 times

The

(3)

its

afterbody, say from about 0.6 to 0.7L to

the extreme stern. Fig.

7.5.

A

an adaptation of

is

Rouqhness Consisted of V- Grooves Runninq Tronsverselij Around Model

cr-

of Model, from FP to Fore-ond-Aft Position Indicated, in Per Cent of Totol Wetted Surfoce

Rouqhened Surfoce

•^

I "

and

length.

90 80 70 60 50 40 30 20

a)

fe

_

10

IZO^

flexing of the flukes as control surfaces.

Plates bounding the ship hull are intended to

be

flat

or gently curved, as the case

when they

may

are incorporated in the design

delineated on the drawings. Only rarely unfairness

allowed

for

when

is

calculating

strength or the rigidity of a ship structure.

be,

20

and any

18

^

FP

AP

Variation of Friction Drag Due to Roughness Along the Ship Length

Fig. 75. a

the

Why,

then, does the ship not deserve equally honest

treatment when

it is

built?

realize instinctively that the

vessel

must be

Even

the uninitiated

underwater hull of a

fair to insure efficient propulsion.

Why then should the vessel be penalized

through-

because of unfairness resulting from a few days of improper work during its construction? Increases in friction resistance due to roughout

its life

ness, of the order of 30, 40, 50,

and up to 100

are being per cent of the smooth, flat-plate Rp encountered on large, fast, modern vessels. This fact should be adequate proof that something drastic needs to be done. Fairness and smooth,

ness are essential parts of a ship.

the part of

An

attitude on

concerned which recognizes that

all

these are not something to be applied, like a

coat of paint, just prior to launching will go far

toward solving 75.3

problem for the designer. Smoothness Problems on the

this

Specific

Shell Plating.

In the matter of the

greatest

practicable smoothness of the shell in the finished ship, at least four areas deserve attention:

model-test data pubhshed by G.

Kempf [HSPA,

1932, Fig. 7, p. 81], indicating the variation of friction-resistance augment, up to 140 per cent

when a model was roughened by cutting V-grooves around it for of the smooth, flat-plate total,

various percentages of (4)

The

its

length.

region immediately ahead (within

diameters) of a propulsion device,

1

or 2

when the water

leaving this surface flows directly into the device (5)

The examples

of Sec. 45.15 indicate that the

greater the absolute speed of the ship, the smaller

the permissible roughness to achieve a hydrodynamically smooth surface.

is

The

foregoing states, in effect, that the only

part of the hull which need not be smooth is that around amidships. However, if any favoring is

know where smoothing is most worth while. These comments apply equally, if not primarily, to structural roughnesses, many of which can be prevented or eliminated in the design and drafting possible, or practicable, it is well to

attention

to

stage. (1)

The extreme bow, and a

belt abaft

say 0.2 or 0.31/ from the FP. This

it,

up to

because the local specific friction resistance Clf is very high for the small ^-distance and the low R^, in this region, indicated (2)

The

by

is

Fig. 45.E.

region directly in front of inlet scoops for

condensers and other heat exchangers, so that

The rounded

or peaked points of countersunk

rivets should project of the shell

from the

by not more than

cated in diagrams

1

and 2

fair

of Fig. 75.B. This

sufficient to insure tight rivets

reasonable

corrosion

of

the

Welding beads, regardless

outer surface

the amounts indi-

of

and to allow

point their

in

is

for

service.

orientation

HYDRODYNAMICS

740

CASE 1. WORKING LIMITS ON STRUCTURAL ROUGHNESS FOR FLOW IN ANY DIRECTION PARALLEL TO THE SURFACE, FOR CRAFT TRAVELING AT Tq
In d JlO

If riveted butts

lapped,

Sec. 75.3

normal to the flow are to be

exposed

plate edges should face forward on slow-speed ships. Here the separation

the

or le»s

to

drag abaft plate edges facing aft

.'^J

n

DESIGN

IN SHIP

greater than

is

the dynamic-pressure drag against edges facing Lorqe

Rivets/ I

I

forward.

Mediom

I

(«-U*(

When

faced forward the exposed plate

i

edges are to be chamfered as indicated at

Rivets |<-|dH

in

1

Fig. 75.C.

Be Rounded, and

InGenerol, Finished Rivet Points Are To

Not Pointed

CASE

WORKING

2.

LIMITS

ON STRUCTURAL ROUGHNESS NORMAL TO THE

APPLYING TO EDGES GENERALLY DIRECTION OF FLOW, FOR SHIP SPEED

« Direction

-*

^

'i Inch Mox. for Plate

5

4

Thicknesst=|-lnch or More

Q

of

RANGES OF

Tq
Water Flow

•»

^"'^*'

This Slope Preferred in

Reqion

TrQilino-Edqe Lap

of

Designed Waterline I

Maximum Abrupt Joo '*

'

To

When

.Up to -^ But Not More Than

^

^

tj)>t2^,

^-

jg-

*

Flow

'

Minimum

Transition Slope

^1

Direction of Water

Inch in

is

I

in

4

Any Cose

—T'^// /V

.

Wooden^

z:j:pian>i^Nll|vlMT[ -(Outer

LQ<^er)\

Diacjrams and Are to Apply I

rZWhen

Edges

Are Within,

Working Limits on Structural Roughness, Flow Parallel to the Surface, Case 1

Fig. 75.B

with respect to the prevailing flow, should not project from the fair surface limits indicated in

diagrams

by more than the 4, and 5 of Fig.

3,

75.B.

When

Fig. 75. C

Working Limits on Structural Roughness, Case 2

prefabricated

sections

of

a

ship

are

welded together, they are found sometimes not to fit properly. The alignment at the shell, considering smoothness only and not structural continuity, should conform to the limits indicated in diagram 7 of the figure. When the abutting plates are of unequal thickness, and the excess is on the outside, the length of the transition taper is to be not less than 4 and preferably 6 times the difference in thickness; see diagram 6 of Fig. 75. B. Corresponding smoothness and offset hmits for the adjacent planks and the calking of wooden boats are depicted in diagrams 8 and 9.

For ships

of higher speed, with

lurdetermined,

the

pressure

drag

Hmits as yet on forward

edges exceeds the separation drag on after surfaces.

In this case, the exposed edges are best faced aft. If

a reasonable degree of smoothness

required,

a cement

filler

or a rivet

is

also

cement

is

applied in the region abaft the exposed trailing edge,

diagrammed at 2

An verse"

in Fig. 75. C.

exposed plate edge if it

lies

is

considered "trans-

within 30 deg of a line normal to

the adjacent water flow, indicated at 3 in the figure.

In some quarters, however, chamfering

HULL SMOOrriNESS AND FAIRING

See.

T53

and

filling of

exposed edges

is

called for

if

they

within 70 deg of the normal to the flow.

lie

In fact,

it is

711

be a more important factor than easy water and where expense is usually not an item

flow,

good design, and probably worth

to

be considered, the outer surfaces of metal

while from the point of view of fuel saving during

hulls

chamfer exposed corners or to add filler along exposed edges, indicated in Fig. 75. D, even though these edges lie generally

hand grinding. The depressions are then

the

of a vessel, to

life

CASE 3. WORKING LIMITS ON STRUCTURAL ROUGHNESS FOR EDGES GENERALLY PARALLEL TO THE FLOW APPLYING TO SHIP SPEED RANGES OF Tq
to Paae, Within

is

Normal

—s-Q

30 deg Each Wo^

1

are

freed

often

Case

3

The exact flow directions all over a ship surface are not known too well, despite the advances of recent years in the techparallel to the flow.

C and

somewhat

This

75. D.

filler is

as

shown

in

heavier than

water so that the additional displacement volume of the filled coves is less than the corresponding weight. In other words, the filler does not carry its own weight. The extra displacement weight, coupled with the extra expense, possibly may be justified only in a ship running at a T„ greater than about LO or LI, F„ > 0.3 or 0.33, or in case there is only a small margin of power for a specified

niques of observing and recording flow around a

The

leveled

and the whole surface given a high degree of by troweling on a cement or filler which adheres firmly to the metal for long periods without repair or attention. On certain large ships the coves associated with riveted lapped seams and butts have been filled by applying the same type of cement. The filler is tapered off to zero thickness at a distance from the cove equal Figs. 75.

Working Limits on Structural Roughness,

by

projections

fairness

to 4 or 5 plate thicknesses,

Fig. 75.D

their

of

minimum

Unfortunately,

speed.

the

smoothest

metal

shell

by the application

and heaving motions of a ship in waves, even though not violent, add motion components which change the flow

surface can be well-nigh ruined

directions relative to the ship surface.

agent like varnish or enamel, and when this dries hard, the minor projections are minimized by

model.

This

pitching, rolUng,

not the place to discuss the matter of applying shell plates on a metal ship to produce a hull surface that is fair and without waviness, is

as contemplated

by the

lines

drawing. It

is

a

proper design procedure, however, to emphasize the necessity for accomplishing this if the con-

of

poor anticorrosive or antif ouling coatings.

When

the antifouling coating contains a self-leveling

the self-smoothing action of the coating around

them. This thins the freely flowing material over the projections and thickens it over the hollows. For the reasons explained in Sec. 5.21, the roughnesses which project through the laminar sub-

struction phases of shipbuilding are to keep pace

layer are primarily responsible for the roughness

with the design phases. Riveted flush seams and butts, with a single

as indicated

strap inside, lack the rigidity and the reliability of

lapped riveted joints,

symmetry

despite

the

of

of both, because of the stretchable butt

strap in between. Sad experiences with

vessels

oil

leakage

bottoms

of

proves that this method

of

in the single-strapped butts of the

numerous

lack

achieving

external smoothness is structurally unsound. The remedy for it in riveted construction, namely double butt straps, is structurally good but hydrodynamically "unsmooth." Welded

butts are the real answer, especially for large,

high-powered, or important vessels which run at Tj values in excess of LO, and of which a high propulsive performance

On

is

demanded.

yachts, where glistening appearance

may

drag.

The laminar sublayer

of Sec.

thickness 6i (delta)

is,

by the formulas of Fig. 5.R and those 45.10 on pages 104-105 of the present

volume, a function of the kinematic viscosity j'(nu)

bow

of the water, of the .-r-distance of the ship,

and

of the speed

V

from the

of the ship.

This speed, or the relative velocity [/„ of the undisturbed water, is by far the most important factor. It is the reason

surfaces

on

large,

fast

why rough ships

or gravelly

generate

large

even when the roughness heights are minute with respect to the ship size. The ABC ship under design in this part of the book is in what may be called the fast-speed class, with a Taylor quotient r„ of 0.908 and an F^ of about 0.27. It is worth while, therefore, to eliminate all irregularities in the plating which come into friction

resistances,

HYDRODYNAMICS

742

contact with the water during normal running.

This

calls for all

All seams,

underwater butts to be

flush.

lapped and riveted, are to be as

if

nearly as practicable parallel to the lines of flow in their respective regions. Tliis

especially the

is

case in the leading 0.2 or 0.3 of the length

and

IN SHIP DESIGN

Sec. 75.4

ing surfaces with a reentrant angle not less than

about 80 deg, and the flow

is

generally parallel

to the intersection of these surfaces,

required, for

hydrodynamic reasons at

the cove thus formed.

does

its

own

The water

no

B

along

in this case

fairing, explained in Sec.

diagram

fillet is

least,

6.7

and

Common

in the after half or two-thirds of the run. If this

illustrated in

regions, lying at angles greater than

can not be accomplished the seams in these about 30 deg to the flow, should be faired with a suitable filler

examples of intersections of this type are to be found where shaft struts enter the hull, diagrammed in Fig. 36. B for a pair of V-struts and

compound

in Fig. 73. F for the

In

as described earher in this section.

the length, flush

fact, for the leading 0.2 of

welded plating throughout promises the best possible service performance.

75.4 Fillets.

The Utilization of Casting The working of generous

or

Welding into

fillets

the coves or inside corners of castings for hull

components is almost mandatory as a matter of good foundry practice. Furthermore, many inside corners occur where thin sections meet heavy sections. Proper gradation in the distribution of material

calls

for

transition

regions

that

are

improved by the use of large-radius corners. Four pairs of corners filleted in this manner are shown around the strut hub in Fig. 73. F. When large appendages and structural parts which form a portion of the outer hull are made up as weldments, good design precludes the use of masses of welding beads in inside corners. Certainly not enough beads can be added to produce the equivalent of the generous-radius fillets in a large casting. If fillets in weldments are really necessary, for hydrodynamic reasons, they should be worked into the adjacent structural parts, more or less independent of the welding. It may be necessary either to machine the fillets into the weldment or to modify the design so that excessive weld metal need not be deposited. An example of this design is illustrated in Fig. 73. F, where stubs for attaching the strut arms are incorporated in the strut-hub casting. are cast integral with the stub

75.5 Fillets.

Comers

Inside

As

Requiring

background

design features

fillets

Negligible

information

discussed

The

arms and the hub.

in

this

for

the

section,

the

principal characteristics of flow about longitudinal discontinuities are described in Sees. 8.2, 27.8,

and

28.2, particularly that

long chines and coves. It

is

quantitatively the effect discontinuities

encountered around not possible to assess

of

these

longitudinal

by any method yet developed, or to

give design rules with numbers.

When

flow takes place past two fixed intersect-

ABC

of Fig. 6.D.

arch-stern ship. Similar

where small skegs, horns, and the like project below the main hull. A not-socomnion example, but one of much greater size, is the long right-angled cove formed where a large deck erection, such as a conning-tower fairwater, rises from the flat superstructure or upper deck of a submarine. The longest and the most common pair of coves are those to be found intersections occur

alongside a single-plate type of roll-resisting keel.

Both reentrant angles are of the order of 90 deg, yet the sharp cove at the intersection with the hull appears not to develop excess resistance or

to interfere with the keel performance.

For reentrant angles design

is

of less than 80 deg, good a matter partly of judgment and partly

There is a blocking effect at the and this effect increases rapidly as the acute angle becomes smaller. On the one hand, the water can do its own blocking and slowing down. On the other, a fairing can be added to the inside corner, provided the leading and trailing of circumstances.

inside corner,

ends of the fairing can themselves be faired. In the case of movable appendages attached

from a hull, such as rudders under the stern, or diving planes with small hull clearances, it is not practicable, nor is it necessary, to fit fairings. A similar case is that of the retractable sound dome which, when in use, is lowered bodily below the keel of a ship through a hole only slightly larger than the planform of the dome. If no separation or eddying is to be expected abreast or behind the dome, there is no particular need for fairing the 90-deg inside corner where the dome meets the hull. Taking account of the variation in translational velocity under the keel, due to the boundary layer, does not change the situation or require any means of improving the flow along the to or projecting fitting

close

inside corners.

75.6 The Fairing of Appendages in General. Supplementing the foregoing, there are given here a few design notes applicable to the fairing

HULL SMOOTHNESS AND FAIRING

Sec. 7'y.7

743

There appears to be no more excuse for leaving exposed the heads and nuts of bolts connecting the palms of rudder stocks and rudders, considering the infrequency with which they are disturbed or removed. Certainly it is incongruous to smooth and fair everything else in the vicinity but to leave a half-dozen or dozen of these sharpcornered

fastenings

ISBSR, 27

May

projecting

the

flow

1954, p. 10 of Advt]. In the

same

into

fashion

it is inconsistent to shape a strut or a rudder section to some very special streamUned form and then to plaster it with thick plates of zinc which must make the water wonder what the

naval architect or shipbuilder expects of it. Fig. 75. E is a good illustration of what not to do in the

way

of roughening the surface of a horn and a rudder lying in the outflow jet of a propeller.

75.7

Recessed Lifting and Mooring Fittings. apply a veritable

It is frequently the practice to

multitude of external padeyes,

clips

with

lifting

and eyebolts to the shell plating in the run. These permit the easy and quick attachment of lifting devices and tackle for the handhng of propeller blades, rudders, exposed shafts, and other demountable underwater parts when in dock. The practice is by no means limited to small vessels, or to those of slow and medium speed. Many, if not most of the fittings are under water eyes,

Fig.

of

75.

E Roughnesses and Discontinuities ox RuDDEB Horn and Ruddeb

appendages

a

problems are

in general. Specific

discussed in the sections following.

There is no excuse, from the point of view of hydrodynamics and propulsion, and little reason from the structural standpoint, for fitting external strut-arm pads with their bases projecting beyond

at the designed-load draft, particularly

stern-wave crest

when

the

an age which is blessed with welding and other improved methods of attaching structural parts to each other. At times the pads must be mounted external to the shell, as on some wooden vessels.

taken into account. Individually, the pressure drag resulting from each of these fittings is small, but collectively they present a formidable impediment to the motion of the ship. Furthermore, many of them throw spray when underway. They give anything but a neat, trim appearance to a run which is supposed to embody everything that the naval architect

The

and the shipbuilder have learned about stream-

the fair surface of the ship. This

is

especially true

in

projecting edges are then reheved with a

large radius on the forward edge sides,

and along the

Floor

lining in the past several decades.

The handling

supplemented by a long taper on the after

side of the pad.

Plate

on

flight

decks that

must remain smooth, and the

tight

fits

of aircraft

Takes

Lifting

Load

Shell Plotinq |

Alternative

is

Recessed

Liftinij

Fitting

3 Fig. 75.F

|

-J

'2 ~

I

1

Recessed Lifting Fittings

of air-

HYDRODYNAMICS

744

—

jtl

—

Elevation from

Outside

--.

IN SHIP DESIGN

Sec. 75.S

of the propeller hub. This requirement

the assembly drawn at least

important part of

1

in Fig. 75. H.

continuous

this

met in Not the

is

form

fair

the easy curve at the forward end, Avhere the diameter of the assembly has to increase from the is

diameter of the shaft to one nearly three times as large. The shght decrease in diameter from the forward end of the assembly back through the propeller Normol

hub conforms

to the pattern of the

flow lines in the inflow jet and contributes a

Vertical Section U> 5liell

inward component of velocity which partly compensates for the centrifugal force due to induced rotation in the jet at the propeller. When a propeller is located abaft a large skeg or long slight

G

Fig. 75.

Recessed Mooring Bitt

craft-carrier hulls in canal locks

development

have led to the

a number of recessed fittings for and mooring. Two types of simple,

of

lashing, lifting,

welded, recessed lifting fittings are diagrammed in Fig. 75. F, adaptable to shell

plating.

dolphin

is

A

single

any position or slope of recessed bitt or Dutch

depicted in Fig. 75. G.

passed through the designed

as

may

strap

is

easily

and an eye is the bitt. While

off

an abovewater installation this be used in positions which are under

water at some load conditions. 75.8 Fairing the Enlargements Around Exposed Propeller Shafts. The hubs of shaft struts, the external or exposed couplings of the propeller shafts passing through them, and the hubs of the

by these

reduction

of radius through the a natural consequence of the tapering form of the skeg or bossing. It is natural

hub

is

kind to give the propeller blades a reasonable amount of rake but the designer of the Prinz Eugen propellers did not see fit to do so. in cases of this

Good design

lifting fittings

quickly thrown over or lifted

dolphin

A

bossing this

propeller

water flow

for

calls for

minimum

leading to traihng edge of this or an equivalent assembly. There should be no sharp discontinuities such as are

sometimes encountered when the leading fairing in front of a cyhndrical strut is made of straight conical form. If such an assembly can be expected to remain completely submerged under all except the most severe

hub

in waves, the maximum be at the propeller hub. If a large not required there for other reasons

pitching

conditions

as units. In other words, the leading fairing, the

diameter

may

enlarged strut-hub body, the propeller hub, and the trailing fairing are treated as parts of a single

diameter

is

body. They should, theoretically, form a continuous streamlined surface for a considerable length

design illustrated.

propellers carried

along the shaft

axis.

One

shafts require fairings

it

may

be in the strut hub, as in the German

Direction

solution for the fairing

an assembly is represented by the design of these parts on the wing shafts of the World War II German cruiser Prinz Eugcn, illustrated in Fig. 75. H. The fact that the maximum diameter of the integrated fairing combination is considerably larger than that of the strut hub is not to be taken as an indication of good or recommended design. This shape was adopted for many German men-of-war of the 1930's and 1940's. Its use can

and easy

resistance

the use of curved profiles from

of

Flow

Manifestly,

the

farther

Moximum Diameter

of

Foirinij

2.77^mes

of such

aft

i5

Shoft

I

\J)iometer

Tonqent 'Lie5 0t32de(j 1

Foinnq on Outboard Shafts, Germon Cruiser PRINZ. EUGEN '

*'"^ S'^""'

Center

be justified, at least partly, by the following line of reasoning.

The of

a

effects

factor,

best flow to the root sections of the blades

screw is

where the interference and uniform flow is a useful

propeller,

are large

obtained

when

the structure surrounding

the propeller shaft bearing and the strut hub is absolutely fair for a rather long distance ahead

Fig. 75.H

Fairings for Strut and Propeller Hubs

HULL SMOOTHNESS AND FAIRING

Sec. 7''.P

maximum

that this

diameter occurs in the assem-

bly the greater must be the slope of the fairing abaft

it,

unless a blunt-ended cap

The ends

For high-speed ships, a propeller hub fairing long enough to eliminate entirely the^'swirl core described in Sec. 23.14 and illustrated in Fig. 23. K would probably have to extend for one or more propeller diameters abaft the hub. This is on the basis that the core is generated entirely by the water set in rotation by friction around the hub. In practice, such an appendage is out of the question, especially as the propeller hub fairing must also clear any rudder placed in the outflow jet. There are two compromises available

One

here.

hub

to give the profile of the propeller

is

fairing a range of slope angles

from about

maximum of about 22 deg,

terminating

15 deg to a

continuities need

used.

is

the fairing in an ogival form having a radius of about 0.1 the radius of its larger end. Variations of such a form are drawn in full and broken lines at 2 in Fig. 75. H. The other compromise, on the basis that the swirl core is in reality the combined

vortex of the several blade-root vortexes,

is

to

terminate the fairing in a square end at about

hub diameter d. This is also shown on Fig. 75. H. Further comments on propeller-hub fairings and caps are given in Sec. 70.14. Exposed sleeve-type couphngs on a propeller shaft are partly faired by trimming off the ends of the sleeves themselves. This has the added advantage of a gradual transition in the combined rigidity of the sleeve and the shaft. The result is 0.7 to 0.5 the propeller

745

rotating shafts need not be large and these dis-

have no detrimental

effects.

of non-ferrous journal sleeves

onto steel shafts generally

lie

shrunk

within other

fair-

may

abut rubber or other protective coverings around the portion of the shaft which would otherwise be exposed to sea water. In any case they are relatively thin and need little or no fairing of their own. The fairing of intermediate strut hubs follows the general lines suggested in other paragraphs of this section, as does the fairing of propeller hubs ings.

If

not,

they

abaft skegs or bossings.

Water-lubricated

bearings

shaft

require

a

continual longitudinal circulation of liquid through

bearing when the ship is underway. An opening around a rotating shaft and just inside a fixed leading-edge fairing of oval or ogival shape

the

is

in a region of -fAp, sufficient to force the

Any — Ap

through.

fairwater helps to bearing.

may

The

fairing

water

occurring abaft a trailing

draw water ahead

aft

through the

of a shaft-bearing

hub

rotate with the shaft, as does the propeller

hub of the arch-stern ABC ship in Fig. 74. L. A beU-mouthed strip around the bearing hub, shown in that figure, then serves as a scoop for the lubri-

cating and cooling water.

A

hole in the center of

hub serves to draw the water out of the after end. 75.9 The Fairing of Propeller Hubs in Front the fixed fairing abaft the bearing

of Simple or

Compound Rudders.

For a propeller

placed immediately ahead of a simple or com-

a stress concentration in the shaft of diminished

pound-type rudder, or ahead of a rudder hung on a fixed rudder post, the propeller hub is faired

magnitude at the ends

neatly by a swelling of the fixed portion, by a

A

of the sleeve.

flange-type shaft coupling exposed to the

water

all

around

may

be enclosed in a substantial

casing of fair form, about as illustrated in Figs. 73.

H

and

74. L.

If

the fairing rotates with the

shaft as in the latter figure,

wax

it

may

be

filled

or other preservative to protect the

with

mechan-

ical parts of the coupling. If it is stationary, as in

Fig. 73. H,

it

can be "pointed" slightly on the

upstream side and given a streamlined tail of sorts on the downstream side, following the general shape of the short bossing diagrammed in that figure. So far as known, it makes little hydrodynamic difference whether the transition from the stationary to the rotating parts, and vice versa,

occurs in a parallel or cylindrical

portion of the enlargement, or at

its

beginning or

projection extending forward from the post, or

by both.

A

rudder of the balanced type, with

its

stock axis intersecting or lying close to the pro-

be notched moderately on forward edge, cutting into the balance portion, to provide clearance for a conical or ogival peller shaft axis, can its

propeller fairing cap of reasonable length.

One form

of fixed fairing for

a propeller hub,

worked into a deep horn or into the fixed portion of a compound-type rudder, is embodied easily

in the transom-stern design of the illustrated in Figs. 66. Q, 67.U, 74.K,

ABC

ship,

and 74.N.

Rope and

cable guards to protect the opening between the rotating propeller hub and the fixed fairing, as well as removable sections of the latter to facihtate taking off the propeller shaft nut and

ending, next to the shaft surface.

the propeller, are readily incorporated in a fixed

for

fairing of this type.

Gaps required working clearances between fixed fairings and

HYDRODYNAMICS

746

When

the propeller shaft bearing

abaft the propeller, as

is

is

placed

done on many high-speed

motorboats and on the arch-stern design of the ABC ship, this bearing may be carried by a partial skeg, a deep horn, or a fixed rudder post, extending down abaft the wheel. The rudder is usually mounted as a hinged flap along its after edge. The fairing assembly is then composed of the following parts, reckoned from forward: (1)

Leading

fairing, rotating

the propeller (2)

Propeller

with the shaft and

hub hub

Propeller shaft bearing housing with rope guard and water scoop on leading end which may (4) Fairing for bearing housing, extend aft into the flap or moving portion of the (3)

rudder.

On

the

fairing

is

ABC

ship,

with twin rudders, a fixed

mounted abaft the

strut barrel or

hub

IN SHIP

DESIGN

Emergence

Points.

fairing.

The

simplest and the cheapest

bearing,

up to the after stern-tube and pass the rotating shaft out through

a clearance hole in the shell plating.

A reasonable amount of fairing, with no increase in

displacement volume and

Exposed

Shafts

at

little

added cost and

achieved by adding a pair of removable shaped plates to enclose a free-flooding space

weight,

is

between the hull and the

shaft.

These extend

for

a short distance abaft the hull opening, indicated

no enlargement or which must be drawn past the fairing, the complication of bolting on a nonwatertight fairing which must be removed frequently for examination of the hull underneath is obviated by extending the framing locally and at

1

in Fig. 75.1. If there is

flange on the shaft

proper, in the of

is

recess within the hull,

incorporating

Fairing

method

to omit the fairing altogether, build a watertight

Fig. 74.L.

The

which

shafts

emerge, as do most of them, at small angles with the adjacent hull surface represent a problem in

supporting the propeller bearing, indicated in 75.10

Sec. 75.10

Exposed

the fairing plate into the

manner shown

shell

at 2 in Fig. 75.1.

On

a large or medium-size vessel the free-flooding

Mechanical Clearance

Around Shaft

Not Less Thon 4 and Preferoblu^ 5 Shaft Diameters

—

^

Section at A-A

with

Near Side FairinQ

Plate

Removed

Section ot

J-

B-B

with Near Side Plate.

Fia. 75.1

Two Types

of Hull Fairing Around Exposed Propeller Shafts

f?emoved

c.

HULL SMOOTHNESS AND FAU^ING

Sec. 75.12

space

inspected by entering the hole through

is

which the shaft

The

one which

withdrawn.

is

method

best

may

member

hull,

Since the adjacent shell plating and the framing

and

contribute a large portion of the actual rigidity

eliminate an intermediate strut

is no reason why their scantlings can not be increased to permit fining of the skeg or bossing ending as required for easy flow into the propeller

otherwise required,

from the

747

deflection or vibration of a large skeg or bossing.

of fairing at this point,

is

to build a short bossing out

terminating in a single-arm strut

An

carrying a shaft bearing.

fairing of this type

was incorporated

excellent

there

position. Actually, the

optimum

solution of this

Bathdesigned World War I destroyers of the U. S. Navy. Despite the small clearances around the shaft tube within the ship, it is preferable that a short bossing of this type be made completely watertight and an integral part of the hull. Design notes and rules covering these short

particular design problem

bossings are given in Sec. 73.9.

67.24.

The Termination of Skegs and Bossings. 75. 1 1 The endings of short skegs and short bossings are

The phenomenon

subject to separation drag

detrimental effects are discussed in Sec. 20.10.

surfaces

these

in the

the slopes of the

if

appendages

exceed

is

not necessarily to

unduly but to shape it in such a manner that the periodic and transient stiffen the structure

forces acting

upon

The matter

it

are diminished.

of shaping the endings of skegs

and

bossings in profile to provide the necessary aperture clearances

75.12

is

discussed in Sees. 67.23 and

Precautions Against Air Entrainment. of

entrainment and

air

its

certain

This section mentions methods of eliminating the

angles with the flowlines. So far as known, the

formation and the trapping of air bubbles around

critical

of

values of these angles depend primarily

upon the hydrostatic

pressure.

They

are of the

order of 13 to 14 deg at the surface and perhaps

20 deg at a submergence depth of 20

ft

or more;

see also Sec. 46.2.

deep skegs on single-screw vessels, of large skegs on multiple-screw vessels, and of long bossings usually lie immediately ahead of the propellers. Their terminations must be fine else the eddying and other disturbances created behind them are carried directly into the propeller discs without an opportunity for smoothing out the flow. The square, blunt sternposts of cheaply built cargo vessels are particular offenders in this respect, despite the slow speed of both the ship and the propeller. Indeed, it is only because of this slow speed that unfair surfaces of this kind can be tolerated. The flexibility afforded by modern knowledge techniques

members

known

in

the present state of the art.

The most ship

is

direct cause of trouble on a

merchant

the multitude of air bubbles which pass

over the shell diaphragm of a fathometer or

The terminations

and

the underwater hull, as well as they are

in

of

the

casting

of

or in the assembly of these

structural

members

as

weldments makes available to the ship designer a ready means of fining the terminations of skegs and bossings. Indeed, a shining example of excellent bossing terminations, even by modern standards, was designed and built into the S.S. Talamanca class by the Newport News shipyard in about 1930. Fig. 73. G is traced from some of the

Newport News drawings, with the permission of the Newport News Shipbuilding and Dry Dock Company. Sufficient rigidity can rarely

a heavy terminal

member

be incorporated in prevent lateral

to

echo-sounder, usually installed in a horizontal position under the bottom.

The bubbles

interfere

with the sonic pressure waves emanating from and impinging upon such a diaphragm so that

depth readings are not satisfactory. For smoothwater operation at deep or load draft the best position for such a diaphragm is well forward, say in the first 0.1 or 0.15 of the length. This is ahead of the point where the flowlines from the stem, in the vicinity of the bow-wave crest, pass

under the

ship.

The

down

flow diagrams of Chap. 52

illustrate this feature for a great variety of hull

shapes. For operation in waves, especially

when

the forefoot emerges, or for operation in ballast there is practically no diaphragm position on the sides or under the bottom which is entirely free of air interference or light-load condition,

or air blanketing.

Design rules for guarding against problems of entrainment are limited by present knowledge

air

to the following: (a)

Avoid projections on the hull which face

downward and which can

A

trap air

when

the

bow

downward-facing ledge as narrow as the thickness of a projecting shell plate is sufficient to take some air bubbles down with it. Projecting edges of fenders are worse in drops during pitching.

HYDRODYNAMICS

748

respect because they extend farther from

this

the

sliip's side.

(b) Avoid an.v semblance of a flat bottom forward beneath which air may be caught and buried under the hull when the forefoot emerges and then plunges heavily during wavegoing. The air is

carried aft

from

this region, along the

bottom

of

the ship, by the relative motion of the water. practicable, the water-injection (c) Wherever

openings on the under side of a ship are to be kept free of streams of air bubbles. Usually, these

by the ship waves in smooth-water operation and carried along under the ship in

are trapped

more-or-less well-traveled routes.

The

routes can

IN SHIP DESIGN

Sec. 75.13

This +Ap been larger for an opening longer in the direction of flow. In any case it would be sufficient to start a flow into the opening if a circuit for the liquid

q

= 0.5pUl

would undoubtedly have

.

were provided. In the design of closed-bottom recesses to create minimum drag, one obvious solution is to offset the downstream edge inward, away from the water flow, depicted at 3 in Fig. 75.J. S. F. Hoerner indicates that a setback at this edge

equal to 8 per cent of the depth of the downstream face, when combined with a square, flush corner at the upstream edge of the recess, reduces the

by an appreciable amount [AD, 1951, Reheving the downstream edge

overall drag

be determined reasonably well in a circulatingwater channel by injecting a small stream of air at any point around the bow where water appears to be falUng on itself (as in a breaking bow-wave crest) and tracing the route of the bubbles

Fig. 4.22, p. 56].

visually or photographically.

recesses are few,

manner, for a hull opening, involves and possibly local trimming of framing members. This is an expensive item on any kind of metal hull. If the

in

this

special shaping of the shell plating

and the openings

large, as for

the hopper-door recesses under a dredge,

Venting holes in keels, for the escape of air trapped below them, are described in Sec. 73.19

and

it

may

be worth while to incorporate this setback in the downstream edge of each of them. It is not recom-

illustrated in Fig. 73.0.

Air leakage to rudders, propellers, and the like is prevented by overhanging portions of the stern, by Jenney fins, and by similar devices, described elsewhere in the book.

Direction of Flow Over Surfoce

-*-J)epth -

A shallow recess, illustrated at 1 in Fig. 75.J, is defined here as one which has a depth —h below

It has

auxiUary

a closed bottom, so there flow into or out of

licjuid

is

I

[""^i^Cj the Flow * For the

Lo'^OLft

Frontal

any shallow

is

b^r Wdth

'^'^'"°" **^*

Thot of Reciancjle

of

Openinq

^<^

is

ABCD

AD&F

is -§-

For Low Broq, Keep e Short and

Ratio -g- Lorqe

it.

1

Judging principally by results of flow tests for inlet openings in the shell, such as condenser scoops,

Breodjh

[>^

Area of Downstream Face

Aspect Ratio

no

' I

Shown;

Recess or Gap Area

the fair solid surface less than either its breadth b across the flow or its length e in the direction of flow.

_

Vi

T^L"Ie"^qThT~~

Design Notes for Shallow Recesses.

75.13

as a Whole.

V iscous /Mixing and

Retardation

recess of appreciable length

may be expected to have on its downstream face, in diagram C of Fig. 7.J and at

in the direction of flow

a

stagnation

illustrated at

point

Q

diagram 2 of Fig. 75.J. The presence of ram pressure on such a surface, facing forward, means large -|-Ap's and added drag. Other

Q

in

+Ap Reqion

ot and

Near Stoqnation Point Q.

features of the flow are discussed in Sec. 8.3.

W. Froude found in the early 1870's, when experimenting with a pressure speed log for ships [Brit. Assn. Rep., 1874, p. 256], that if a circular pipe as small as 0.04

ft in

Schematic Streamlines

diameter was fitted

square to and terminated flush with a

flat

surface

was mouth of the the ram pressure

parallel to the direction of liquid flow, there

developed a small pipe,

amounting

to

+Ap

within the

about 0.04 of

Fig.

75.J

Definition and Flow Sketches fob Shallow Recesses

HULL SMOOTHNESS AND FAIRING

Sec. 15.14

mended that

the shell at the leading edge of the

opening or recess be bulged outward solely to move the stagnation point and the +Ap's out-

ward from the forward-facing surface at the trailing edge. In any case, do not chamfer, relieve, or set back the leading edge of the recess. According to Hoerner, this approximately doubles the drag

upstream and downstream edges both flush and square. The effect of depth-width or length-depth of a recess with

and of setback as well, bound up with boundary-

ratios of shallow recesses, is

rather intricately

layer thickness recess;

and velocity

recess on the hull.

common-sense

The

one,

way

of the

best design rule here

which

as shallow as operating

permit.

profile in

possibly also with the position of the

If

the recess

is

is

to

make

is

the

the recess

and service conditions large and the trailing

edge can be set back to reduce the area exposed

or fairing procedures.

respect

is

749

An

excellent guide in this

the group of data on the drag of surface

irregularities

assembled by

S.

F.

Hoerner [AD,

1951, pp. 49-54].

By and large, it is not difficult to achieve the smoothness called for by specification requirements or to design proper fairings. Indeed, it is often easier, if the job is planned properly from the start, to make a ship or its parts fair, well adapted to easy water flow around them, than to make them abrupt or irregular. The difficulty arises, first, 'in making good engineering compromises between initial cost and maintenance on the one hand and improved service performance on the other hand. The second difficulty is convincing all those concerned with the design and building of the ship that the refinements apparently justified by improved service performance are really worth while. All too often, it is feared,

means do it. what might be termed

the designer and the shipbuilder look upon efforts

aspect ratio for the openings of recesses, Hoerner

as either outright compromises or trivial details

jumps

short gap, lying across the stream. It "penetrates

not worthy of their attention. In too many cases the shipbuilder looks upon these efforts as nuis-

deeply into the longitudinal groove" formed by a gap lying with its long dimension parallel to

ances and the ship owner as additional means of draining his pocketbook.

to 4-Ap's,

As

by

all

for the effects of

states that the "flow

easily" across a wide,

to provide smoothness

the stream, or within 10 deg of the parallel direction [AD,

1951, p. 56]. Because of the

higher drag" in the latter case, should,

if

practicable,

"much

the designer

place a recess with

its

shortest dimension parallel to the flow.

75.14 Practical Problems in Achieving Underwater Smoothness and Fairness on a Ship. In the matter of hull smoothness and fairing, the

problem

of the conscientious ship designer re-

who must and energy. The

sembles closely that of the executive carefully apportion his time

is not to pass over all the but to know which details are of sufficient importance to justify his attention. Similarly, the

executive's solution details

ship

must know which roughnesses how much time and trouble to fairing, and what will be the effect of

designer

and to incorporate

fairings

In yachts, sleek appearance above water

is

almost more important than smoothness under water. Several centuries of experience with

them

prove that when the designer and builder and the artisans realize the importance of smoothness, it is

achieved at no great increase in cost and time.

New

tools

are

designed,

new techniques

are

and new procedures utiUzed which make it relatively easy to smooth up the yacht hull when it is known in advance that it must be smooth. What has been done with yachts can be accomplished with merchant and other vessels. The designers and builders take pride in the increased speeds of modern ships. They will take pride in their smoothness as soon as they and all developed,

require smoothing,

others concerned are convinced that the necessity

devote to

for

neglect to incorporate the necessary smoothing

smoothness increases as the square of that

increased speed.

CHAPTER

The Design

76

of Special Hull Forms and

Special-Purpose Craft 76.

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 16.1

751

moment not be interested in special-service craft, it may be useful for him and give him

and types now

valuable ideas to read through the various re-

orienting the reader's

quirements and the design comments and rules

which follow. Design features applicable

the

in this chapter.

With

these thoughts in mind, the unusual forms

TABLE To make

this table

in this chapter.

Hull Proportions and Features

76.a

Classification op Special

world are

in general use throughout the

classified in

Table

76.a, as

mind

to the discussions

to

an aid in

shallow

and

restricted waters, without regard to vessel type.

Hull Forms and Special-Puhpose Craft

complete and comprehensive, special types of vessels are included whose design

is

not discussed

HYDRODYNAMICS

752 certain

as well as

important features of

self-

propelled craft intended to operate in confined waters, are discussed in Chap. 72. Special features in the design of tugs, towboats, pushboats, and self-propelled lighters, as well as

and floats, are under the general

non-self-propelled barges, scows,

covered in Part 5 of Volume

III,

subject of Towing.

The Design of Fine, Slender Hulls; 76.2 Canoes, Racing Shells, and Fast Launches. As long as watercraft are required to be propelled by manpower and as long as men have to handle remain a demand for a and small weight compared to its speed and carrying capacity. Such a demand is met by the birchbark canoe of the American Indian and the kayak of the Eskimo.

them there

or carry

will

craft of small resistance

Canoes

of greater fineness

but also

of greater

up of large and still used by many peoples of the world. These are driven by as many as a hundred paddlers each [111. London News, 9 Jul 1955, p. 81]. It is entirely probable weight,

dug out

parts, are

that

still

many

of single logs or built

in existence

of these fine-ended designs evolved

from a desire to minimize water disturbance and

TABLE

IN SHIP DESIGN noise

Sec. 76.2

when hunting. For

the craft paddled

by

—

one or two persons, a reduction of resistance and thrust is far more personal and important than

—

is an engine available to drive it. Dixon Kemp, in his book "A Manual of Yacht and Boat Saihng" [Cox, London, 3rd ed., 1882], devotes Chap. XXVI, on pages 374-381, to "Canoeing." It contains drawings and rather

if

there

detailed descriptions of a considerable

number

of

and American canoes. A storj-- and excellent photographs of canoes and kayaks built by the natives of northwestern North America are found on pages 77-79 of the February 1917 issue of the Pacific Marine Review. Some historical and technical data on the canoes of America are given by H. I. Chapelle ["American British

Small Sailing Craft," Norton, New York, 1951, pp. 36-38]. Design features of the modern lightweight canoe, the small-boat version of the long, slender ship, and still popular as a pleasure craft, are discussed and presented by R. P. Beebe [Rudder, Jan 1954, pp. 49-53, 82]. This article illustrates five typical canoe midsections. The ultimate in fineness and reduction of both friction and pressure resistance is achieved by

Comparative Form and Performance Data for Two Types of Manually Propelled Ckaft and One Mechanically Propelled Vessel

76.b

These data are taken from published information by F. H. Alexander (see the reference quoted in the text) and by K. C. Barnaby [INA, 1950, p. J13]. The circular-constant parameters are those of R. E. Froude; see Appendix 1. For comparison with the 8-oared shell, a single-oared shell is about 1 ft wide, and weighs about 28.5 lb, without crew.

Item

Length on LWL, ft Beam, extreme, ft Draft,

(estimated)

ft

Displacement, tons, with crew

V

(estimated),

Wetted

ft'

surface, ft^

Speed, kt Speed, ft per sec

Value of® Value of (S) Value of (g) Value of© Value of

V/Vl

Value of A/f

j»,

tons for 100-ft length

Resistance, lb Resistance, plus

still-air Z).5a

,

lb

.

.

Resistance per ton of displacement, lb Resistance ratio. Friction /Total .

Value of

(C)

.

.

.

.

.

.

.

8-oared

Whaleboat,

Cross-channel

Racing Shell

10 oars

Steamer

62.0 2.0 0.5 0.81 28.4 109.5 10.0 17.0 20.2 11.78 6.025 1.34 1.27

28.0 6.85

320.0 40,0

1.70 59.5 133 6.7 11.33 7.17 8.73 3.58 1.34 1.27

1,850 64,750 12,510 22.75 38.4 7.97 7.76 3.78 1.34 1.27

3.5

77.5

56.5

77 90.0 95.0 0.95 1.162

81

87,300

47.6 0.51 1.662

47.2 0.40 1.469

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.2

TABLE

76.C

Data on Fast Launches and Torpedoboats Prior to

753 1905

HYDRODYNAMICS

754

IN SHIP DESIGN

maximum

76 J

Sec.

are of interest to a designer. These craft did not

make

plane in a strict sense, despite the T^ values of

portions which were developed through the years

some of them are shown in Plate 190 of the reference. Deck plans and waterUne planforms are drawn on Plates 191 and 192, while photographs of some of the boats underway are reproduced on Plates 193-197. Other successful yachts and launches of this tj'pe were designed and built by N. G. Herreshoff. A few of them are described and illustrated by 4.0 or more. Midsections of

when

still

represent the furthest point reached in the

development

of

fine-ended

displacement-type

craft. Their shapes are almost necessary for hulls which are not permitted to create large surface disturbances when moving rapidly ["Speed Without Fuss," The Motor Boat and Yachting, Sep 1956, p. 423]. These shapes may very well become useful for certain requirements not yet presented to the naval architect. Speaking of the future, the requirements of the early years of mechanical propulsion for a craft which could be driven swiftly yet easily and smoothly, such as a pleasure launch or yacht, may be expected to continue as long as mechanical propulsion is utilized. When another cycle of human behavior rolls around, the former demand for a quiet craft, gliding gracefully yet rapidly, may well be repeated. Jet and rocket propulsion may, in the years ahead, be appUed to slender displacement forms for certain particular duties rather than to the skimming and planing forms now associated with high speeds over the water. Pounding and slamming on planing craft, even in small waves, may well set a limit on the ultimate speed at which

their hulls will hold together.

Except for the additional wetted surface unL/B or L/H ratios, and the

avoidable with large

extra friction resistance involved, the

shape for a

optimum

reduce the pressure resistance due to wavemaking and separation to a minimum, is

one which

L/B 15.

hull, to

ratio

This

is

definitely fine

and

slender.

The

may is

then exceed 10 and even approach not easy to accomplish in a small

which needs space for the crew, passengers, propelling machinery, and some useful load but must have metacentric stabihty as well. A satisfactory compromise between lengthbeam ratio and absolute length is determined by the speed-length quotient T^ or the Froude number F„ at which the craft is expected to craft,

speed.

The

lengths and pro-

high-speed

was the predominant type for small, craft are given by C. H. Crane

[SNAME,

1904, pp. 321-326; 1905, p. 369].

of is

this

them

are listed in Table 76. c.

Some

The B/H

ratio

frequently amenable to some variation but

only rarely,

if

at

all,

it is

that the propulsion perform-

ance can be improved by departing from the proportions listed in the table.

With the length-beam and beam-draft propor-

L. F. Herreshoff [Yachting, Sep 1950, pp. 26-27].

While these vessels had shapes no longer considered stylish or efficient, they represented, and

its

tions likely to be found the

may become small,

in

optimum, the draft

a small proportion of the length; so that

fact,

it

provide shape of well below the

difficult

is

rudder area in an blade except by projecting sufficient

to

efficient it

baseplane.

With the

large

L/B

ratios

mentioned here

it is

easy to keep the waterline run slopes below 11 or 12 deg and thus to eliminate all possibiUty of separation at the stern. Attempts to save resist-

ance by cutting

off

the stern and

its

wetted surface

are rarely successful unless the transom so formed

kept out of water at all speeds. Working reverse curvature into the buttocks and terminating them

is

tangent to the at-rest the occasional

wave

WL

is

good design provided

slap under the stern can be

accepted. However, any curvature of the stern buttocks, convex downward, develops under them and drags the stern down, with

— Ap's all

the

disadvantages of excessive trim by the stern. Special problems are involved in the design of

high-speed

craft

running

at

1.8,

F„

=

"inter-

so-called

ference" speeds in the range of T^

=

1.3

to

0.39 to 0.54, where a practically con-

hump is shown by Fig. 66. B. The design problems involved are discussed at some length by E. Rolland, on the basis of designs of former years by N. G. Herreshoff and E. W. Graef [ATMA, 1951, Vol. 50, pp. 443^62; tinuous resistance

an English translation of this paper is available at the David Taylor Model Basin]. Ultra-High-Speed Displacement Types. 76.3 Despite the insistent modern demand for ultrahigh-speed ships to carry cargoes or other useful loads, reckoned by the hundreds or the thousands of tons, relatively Httle

thorough and systematic

investigation has been devoted to the displace-

ment type

of hull driven at speed-length or

Taylor

quotients T^ exceeding 2.0 or 2.2, F„ greater than

about 0.60 or

The

0.66.

100-ft Turhinia of C. A. Parsons

made 34

kt in the 1890's, and the 100-ft steam yacht

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 7r,.4

Arrow, designed by C. D. Moshei', reached the unprecedented speed of 45 kt a few years later.

For displacement-type vessels to reach T, values of 3.4 and 4.5 was remarkable, and still is, but the useful loads carried by each were extremely

1908, PI. 87]. Fig. 76.A shows the fines of a

small.

An

early form of the

German

schnellboote (fast

a displacement- type craft intended to maintain high speed on the high seas in heavy boat),

weather,

is

[26 Oct-2

described and illustrated in Schiffbau

Nov

1921, pp. 112-116].

A

set of small-

round-bottom craft is included During World War II the Germans

scale lines of this in the article. built

75b

view of the low speeds at which these vessels formerly traveled, that the emphasis has been on capacity and cargo handling rather than on hydrodynamics. R. Curr gives the lines of a Great Lakes bulk ore carrier of a half-century ago [SNAME,

and operated a considerable number

of these

so-called S-boats of a later version [Rupp, L. A.,

NavTechMisEu Rep. 338-45 of 23 Aug 1945; K., Handbuch der Werften, 1952, pp. 37-42]. The David Taylor Model Basin made Biiller,

numerous tests following World War II of TMB model 3993 representing some of these craft [TMB Rep. 628 of Jan 1948 and other reports]. Although by no means cargo carriers in the accepted sense of the term these craft did carry an appreciable useful load, and they performed admirably in such rough-water areas as the English Channel and the North Sea. They may well

World some 40 years later, similar to the design covered by SNAME Resistance Data sheet 90. J. J. Henry gives a considerable amount of statistical and other data on Great Lakes bulk ore vessels in his paper "Modern Ore Carriers"

War

[SNAME, 1955, pp. 92-95], but here again the emphasis is on features other than hydrodynamics. Table 76. d lists five more vessel types and supplies supplementary information on hull proportions and features and form coefficients. Discrepancies between the two tables are due generally to lack of precise definition of the terms listed. The bibliography of 24 items at the end of the Henry paper, a number of which apply to oceangoing vessels with few draft and beam limitations, is supplemented by the references which follow: (1)

and

faster versions,

207

(2)

Narrow, Blunt-Ended Vessels; Great Lakes Cargo Carriers. Limitations on beam and draft imposed by canal locks, drydocks, pier facilities at loading and unloading ports, and shallow water along the route produce a ship form that is abnormally elongated, especially if the 76.4

is

The result is a series of among which may be hsted

other American and its towed barges of European rivers, and the bulk-cargo the American Great Lakes. Only the of

the large carrier of

Volume

In the past, these limitations have produced

enough to make them manageable in the confined waters in which they operated or to enable them to be self-propelled with some reasonable degree of efficiency. The Great Lakes freighter has benefited from a great deal of attention, devoted both to its construction as whittled

(5)

(6)

(7)

off just

well as its design. It

is

perhaps not strange, in

paper,

although

H. C, and Lindblad, A., "Stresses on Vessels Lakes Due to Waves of Varying Lengths and Heights," SNAME, 1922, pp. 77-82. The text and PI. 13 contain some data relating to

Lindblad,

A.

"Some Features

F.,

of the

Lake Freighters,"

Affecting

SNAME,

the

1923,

Cross, A. W.,

SNAME,

The paper

1928, pp. 51-62

and

Pis.

around a description of steamer Harry Coulby, having an Lb^l oi 615.2 ft, a S of 65 ft, a displacement of 19,092 long tons and a speed of 11.3 kt. Fisher, C. R., and Kennedy, A., Jr., "Turbine Electric Drive as Applied on the Great Lakes Cargo Ships," SNAME, 1928, pp. 235-248 and Pis. 135-138. This paper on propelling machinery is

built

the

III.

box-like or block-shaped vessels, with the ends

This

of

Sadler,

41-51.

self-propelled craft are considered here; the others

are discussed in Part 5 of

119-133.

Moments

1905, pp. 187-

pp. 37-49 and PI. 9 (4)

the Erie and

canals, the river steamer

Pis.

Economy

the American (freight) car float, the self-propelled cargo-carrier

and

SNAME,

hydrodj'namio design. (3)

high.

widely varying types,

"Longitudinal Bending

I.,

of the Great

Long,

carrying capacity

W.

primarily structural, gives principal dimensions of the Victory and the Elbert H. Gary.

carrying larger pro-

portions of useful weight.

Babcock,

Certain Lake Steamers,"

serve as the starting point for the development of larger

II design of

(8)

gives a considerable amount of hull design and ship performance data on the steamer Carl D. Bradley. Workman, J. C, "Shipping on the Great Lakes," SNAME, HT, 1943, pp. 363-376 Baier, L. A., "The Great Lakes Bulk Cargo Carrier; Design and Power," SNAME, Great Lakes Sect., 1947, Vol. 55, pp. 385-390. On p. 390 of this paper the author gives a list of 25 references pertaining to the Great Lakes bulk cargo carrier. Mathews, S. T., "Resistance and Propulsion Tests on a Model of a Lake Freighter," Div. Mech. Eng., Nat. Res. Council, Ottawa, Rep. MB-137, 3 Jul

1951

HYDRODYNAMICS

756

IN SHIP DESIGN

Sec. 76.4

24-ft Bilqe t?adiu3-3.75 ft,

* 0.0625

Buttock Rise of Floor-

Bx

025

ft, -o-

0.0042 Bx

-o- 0.0125 Bv Lenqth of. Parallel Middlebody = 330 ft.-o 0542 L^^ Maximum- Area -Section ot Midlenqth of Middlebody, - 478 L^Lfrom FP Lenqth of Entrance- 126 ft,=0 0.207 L^l Lenqth of Run - 139 ft, -o- 0228 L^l i-E °^ Entrance- 45.7 deq, Ir=374 dec^ Lenqth Overall- 620.0 ft Lenqth Between Perpendiculars - 605.0 ft Lenqth on Keel- 595.0 ft Lenqth on 24-ft I)WL= 609.0 ft

Tumble Home- 0.75

ft,

Position of

Beam, Molded Fig. 76. a

(9)

(10)

Body Pian, U.

S.

600

ft

"C4 Conversion to Great Lakes Ore Carrier Tom M. Girdler," SNAME, Gulf Sect., 19 Oct 1951; abstracted in SNAME Member's Bull., Jan 1952, p. 20 Cowles, W. C, "New Ore Carrier Philip R. Clarke,"

MESR, 19.52, p.

Jul 1952, pp. 62-81; also

MESR, Dec

72

Service,"

MESR,

Oct 1952, pp. 50-63; also

Dec 1952 "Steamer Edward B. Greene Becomes Cleveland-Cliffs

Flagship,"

MESR,

the

MESR, Nov

New 1952,

pp. 38-50 (13)

Nov 1952, pp. 16-19, 30. This article describes the conversion of the C4-S-B2 vessel

Schaeffner, C. R.,

(11) Zuehlke, A. J., and Rankin, G. F., "Largest Lakes Self-Unloader, the John G. Munson, Goes into

(12)

Depth, Molded- 35.0 ff

Maeitimb Commission Design L6-S-A1 of Great Lakes Freighter

"Conversion Job, King Size (Joseph H. Thompson),"

Naut. Gaz.,

Marine Robin,

utilizing only the after portion.

"600-Foot Lakes Ore Carriers Built in East Coast Shipyard," Mar. Eng'g., Jan 1953, pp. 36-47; describes the first vessel of the Johnstown class (15) "The 690-Foot Ernest T. Weir," Mar. Eng.'g., Apr 1954, pp. 36-46; also Mar. Eng'g., Dec 1954, p. 60 (16) Downer, H. C, "Ore Carrier Richard M. Marshall," Mar. Eng'g., Jun 1954, pp. 44-60 on the Lakes (steamer George M. (17) "Largest Humphrey)," Maritime Reporter, 15 Nov 1954, p. 27 (14)

(18)

De

Rooij, G., "Practical Shipl)uilding," 1953, Figs.

799 and 800 on

p. 373.

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. T6.4

The

following

vessels of the

and

SNAME RD

sheets apply to

Great Lakes bulk ore-carrier type,

refer to the loaded condition:

Sheet

amber

Length,

Beam,

Draft,

Displ.,

Speed,

757

1

:i3

^^

.S

o)

.

J.

1

Sec. 16.4

760

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.4

761

%.

^

Fig. 76.B

Gkeat Lakes Ore Carrier

George

M. Humyhrey

in Building

Dock

Photograph by Denny C. Harris, Cleveland, Ohio. The 5-bladed propeller is of built-up construction. Note the fine skeg ending up under the stern. The aperture on the centerline at the stern is the hawsepipe for the stern anchor.

Summarizing the hull-design problem resolves itself into:

the owners and operators for the highest possible ratio of useful load to total displacement, in the full-load

Achieving the required carrying capacity with the minimum length and wetted surface (b) Holding the sinkage down to the minimum (a)

practicable value

Shaping the ends to keep down the pressure resistance due to wavemaking, separation, and (c)

the Uke.

The wavemaking

condition,

is

generally such that the

stern can not be fined sufficiently to eliminate all

separation,

axis

of

a

even at depths as low as the

single

propeller.

separation drag kept large

by

Not only

is

this limitation

the

but

the possibihties of air leakage to the propeller, its consequent loss of power, vibration, and

with

noise are aggravated.

a can never be a large part

pressure

resistance,

at

Hmiting T„ of, say 0.7, of the whole unless the bow is deliberately made too blunt. On the other hand, the separation drag can be excessive. These hulls are therefore in the class where the major part of the fining needs to be done at the stern. The demands of

It appears that a not-too-wide transom stern, with an immersion in the load condition of only a foot or so, might be a partial answer to this problem. The transom sheK can be mde enough

to guard against air leakage to the propellers and it can be used to make up the displacement

volume

lost

by

fining the skeg forward of the

HYDRODYNAMICS

762 single propeller.

On

ships of the

maximum

permitted by turning basins and pier all this

length

facilities,

length could be put into the waterline.

76.5

The Design

of

Dry-Cargo Vessels with

Somewhat

Box-Shaped Holds.

similar

to

the

and to the canal and not unlike the box-shaped watercraft Sec. 76.15, is the vessel which is required to

long, narrow, blunt-ended vessel,

boat, of

house rectangular, box-shaped, dry-cargo spaces within the boundary of a ship-shaped hull. In some respects the design problem resembles that of a newsprint carrier in which the storage space is required, almost literally, to be larger than the dimensions of the outer shell! Vessels of the rectangular- or box-hold type

which railway cars are stowed on tracks at levels from the bottom of the holds to and including the upper deck [Burrill, L. C, "The Design and Construction of the Rail-Car Carrying Steamship Seatrain," NECI, 1929-1930, Vol. XL VI, pp. 179-204 and Pis. VI, VII; MESR, (a) Seatrains, in

1952, front cover]

Cargo-container craft, in which the cargo

(b)

consists

almost exclusively

of

metal shipping

containers in the form of cubes and parallelepipeds. For these vessels the cargo,

when loaded

and unloaded, as well as when transported, may be stowed instead on pallet boards suitable for handling by fork-lift trucks. The combination of pallet and material carried by it is usually of box shape. So-called trailer ships, in which the cargo

(c)

box or body portions of trailer minus the tractor portions [Mar. Eng'g., Apr 1954, pp. 48-49, 60; Jan 1955, pp. 57-58, 74]. consists of the

trucks,

These ships are designed on the principle that all

holds are to be truly rectangular, with

floors or

The boundaries side

flat

decks and vertical sides and bulkheads. are

all

to be flush on the hold

and to stand at right angles to each

other.

Actually, instead of designing a ship hull of normal

form and arranging cargo holds inside it, the holds are laid out first and the ship envelope is drawn around them. The hydrodynamic design problem becomes one of fashioning such an envelope so that it has the greatest practicable fullness coefficient but is not too difficult to drive. The box-shaped holds can not be raised appreciably to help with the hull

shape because of the consequent loss of volume

and the

raising of the center of gravity of the

No

cargo.

Sec. 76.5

design rules are available for develop-

ing an acceptable underwater form under these

conditions except the general principles of achieving reasonably good flow around

all

parts of the

and a reasonably uniform pressure distribution. The comments in Chaps. 8, 27, and 28 relative to the flow around and the behavior of straight-element and discontinuous-section forms hull

are of value here.

Achieving practically a rectangular

maximum

transverse section presents no problem because successful ships are

By

0.99 or more.

now

Cx values

built with

using a

of

inner bottom and

flat

placing a vertical wing-tank bulkhead inboard of

the shell on each side, the transverse section of the

hold

include:

Aug

IN SHIP DESIGN

is

To

completely rectangular.

obtain the greatest length of this

full rec-

tangular section^ the cargo holds must occupy all of

the fullest portions of the length, leaving

the tapered portions at the ends to

accommodate

the propelling and auxiliary machinery and miscellaneous equipment. It is

by no means necessary

interfere with the best hold space

up

to break

by the

or

installa-

tion of a midship deckhouse, as has been the practice on tankers

many

decades.

vessel

may

and ocean-going ore ships

The whole

for

central portion of the

be kept clear for hatches, cargo-

handhng gear, and deck loads, if desired, by moving the machinery and accommodations all the way aft. This was done on the large Swedish tanker Oceanus [SBSR, 16 Dec 1954, p. 20 of advt.; Motor Ship, London, Jan 1955, p. 460] and is shown by J. J. Henry in his "Artist's (and presumably Naval Architect's) Conception of a Modern Ore Carrier" [SNAME, 1955, p. 57]. 76.6 The Design of Straight-Element Hulls. Other than to obtain the special V-bottom shapes for high-speed motorboats and other planing craft, the straight-element form defined in Sec. 27.1 is used to facihtate hull construction.

This involves not only reductions in cost, time, and effort but in the amount and kind of fabricating equipment required. Depending

upon the

structure of the boat or ship the transverse frame

members may be made up around

the

periphery,

plating

may

be

made

of straight

the

planking

developable,

single curvature only, or there

may

segments or

shell

embod3ang

be a combina-

tion of both. If ease of construction

is

a pre-

dominating factor, the shape of the underwater hull, and perhaps also that of the abovewater hull, must conform to the limitations of the

DESIGN OF SPECIAL-PURPOSE CRAFT

Sen. 76.r>

amateur or inexperienced builder, to the lack of equipment in small plants, or to the necessity for rapid and economical fabrication and erection. often convenient to replace the sharp

It is

corners of polygonal sections with rounded corners

but in this case the corners lying along any diagonal must generally be of fixed radius if rapid production methods are employed. The principal design requirement for straightelement hulls is that the chines (and coves) shall lie in the adjacent lines of flow in such a manner that water does not cross these external dis-

The

principles set forth in Chaps. 4, 27,

and

manner in which water flows are employed to estimate the

52, concerning the

around a

ship,

direction which the water take. It is well to

draft ratio

is large,

may

be expected to

remember that, if the beammost of the flow goes under the

bottom. In the present state of the art

it is

not always

easy to predict the flow around hulls of unusual shape. Fortunately,

it is

possible,

even with small

models, to check the flow directions experimentally

on a straight-element form, so that the

designer can obtain an idea of the flow pattern

while the hull form

is still sufficiently

"plastic"

to be changed readily.

For the best performance a cove

line is

not

placed where the water flowing around the ship is

relative speeds are low the chine line can depart from the hues of flow to facilitate construction. For a sailing yacht which is almost never upright when moving through the water, the shape of the underwater hull varies with the angle of heel, as do the lines of flow for that particular heel. The flow may also vary for the speed or

range

of speed corresponding to that heel, because of the considerable wavemaking. Never-

required to cross

it.

Fortunately, this

is

con-

be expected that, by simple flow means, a chine line may be found

theless, it is to

tests or other

which

continuities.

763

the chine angle approaches 90 deg but as the

fits all

these flow positions rather well.

The maximum number

of chines

lines of flow.

The

chine positions therefore can

favor the lines of plating or the type of framing to be used.

Frame

sections which are nominally straight be given a slight outward bow or camber, corresponding to the camber in a weather deck. This is not enough to involve forming or furnacing.

may

Metal plating applied to lies flatter,

slightly

held to perfectly straight frame

waviness, than

of a projecting chine,

lines [Baier, L. A., unpubl. Itr. to

inert water carried along in the cove

and the

usually shallow depth of the reentrant portion. If a chine

extends above the designed waterline

in the entrance, it is generally necessary that the

when projected on the centerplane with the craft at rest and reckoned with respect to the at-rest WL, be reasonably large, slope of the chine,

to insure upward dynamic lift when pitching and encountering waves and to throw spray clear

A suitable range of angles of slope exposed forward chines of planing craft, apphcable to all straight-element forms, has not as yet been laid down. However, a series of chine shapes and positions, based partly on the intended of the hull. for

service

and partly upon the maximum T^ and is to run, is shown in Fig.

F„ at which the craft 77.1.

bowed frames

or perhaps one should say with less

siderably less important than for a similar crossing

because of the sensibly

(or coves)

which can be worked longitudinally into a hull is Umited only by the number of strakes desired to meet construction requirements. As many as five chines on each side have been employed successfully in some hulls, illustrated by the body plans of Figs. 27. B and 68. J. As the projecting corners in multiple-chine sections approach 180 deg there is less need for placing them exactly in the

if

HES

of

4

Aug

1950].

The degree to which a hull surface may vary from one which is exactly of single curvature depends upon the size of the surface in question compared to the size or the area or the shape of the sheet or plate of which that surface is to be made. A wooden plank may be bent, twisted, and sprung out of its natural shape, fastened to the frame of a boat, and left in its sprung shape for years provided it is not too wide or too thick for the shape to be impressed upon it. A wide sheet or plate of metal may often be pulled and stretched to make it conform slightly to a second degree of curvature. A wide sheet of plywood, assembled in the flat, may not respond to such treatment without definite and detrimental cracking.

The minimum number

the straight-element form facilitates con-

one at each diagonal bulge, as in the hull of the well-known

struction in

flat-bottomed

advantageous to incorporate

skiff,

of chines

is

punt, or dory. In this case

If

any particular

case, it

it

is

equally

into the above-

HYDRODYNAMICS

764

Body Plan of World War II ConcreteHull Steamer, U. S. Maritime CoiMmission

Fig. 76.C

Design Cl-S-Dl

water body. Indeed, the use of straight sides, plumb or sloping slightly, is standard on

either

many

ships in which straight elements are not

otherwise employed.

The elements

of greatest practical benefit are

the straight and level sheer

line, utilizing

a section

and the straight or ridge-type deck-beam lines described in Chap. 68. Examples of straight-element ship forms which have been designed and constructed in the past are described and illustrated in the following: of constant depth,

(1)

U.S.

Navy

plan

is

landing craft

LCI

(L).

The

shown by E. A. Wright,

original

SNAME,

body 1946,

Fig. 14, p. 384. (2)

World War

TABLE

76.e

tions FOR

This

Maritime Commodel 3745M. A

II concrete steamer, U.S.

mission, Cl-S-Dl design,

TMB

Hull-Form Parameters and ProporWorld War II Concrete Steamer

craft, of

the U. S. Maritime Commission Cl-S-Dl

had transverse joined by short arcs. design,

Length between perps.

sections

made up

of straight lines

IN SHIP DESIGN

Sec. 76.7

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.R (14) Johnson, Eads,

"Ferryboats,"

SNAME, HT,

1943,

pp. 172, 174, 179 (15) Stephens, E. O.,

"Thames (Dumb) Barges," INA,

1945, pp. 170-184 (16) Holt,

W.

Vessels,"

"Admiralty

J.,

INA,

Type Motor Fishing

1946, pp. 295-307

(17) Wright, E. A., "A Pattern for Research in Naval Architecture," SNAME, 1946, p. 374, particularly

LCI

body plan in Fig. 14 on p. 384 Wartime Prefabrioation Methods Employed hi the Construction of Small (L) original

R.

(IS) Aitlcen,

"Special

L.,

Vessels," lESS, 1947, Vol. 90, pp. 246-288, 322-344.

(19)

(20)

Gives many diagrams of small vessels with straight frame segments. Emerson, A., "Experiment Work on Merchant Ship Models During the War," NECI, 1947-1948, Vol. 64, pp. 289-332, esp. p. 320 Van Lammeren, W. P. A., Troost, L., and Koning, J. G.,

RPSS,

1948, p. 110

R. W., and Ward, L. W., of Nine Double-Chine Simplified Hull Forms," Univ. Michigan Thesis,

(21) Thiel, P., Jr., Johnson,

"The Resistance and Waive

May

1948.

The

introduction gives a

list of

straight-

element-form vessels built and in service. (22) During World War II a considerable number of small cargo vessels, 173 to 176 ft long, were built with straight-element sections and double chines along

One such vessel is shown in the National Geographic Magazine, Jul 1948, p. 88. (23) Bayard, N., "Stock Sloop," The Rudder, Feb 1950, p. 44. This craft has 4-sided polygonal frames, from keel to gunwale. It is not known whether the hull the bilges.

surfaces are developable. (24)

Simpson, D. S., "Small Craft, Construction and Design," SNAME, 1951, pp. 554-611, esp. Fig. 21 on p. 580. On page 558 the author comments that:

"As the size increases (above 50 or 60 ft) there would appear to be an excellent field for the doublechine hull form, especially for vessels that operate

under varying displacement and trim conditions and in rough waters. There is little difference from the molded (rounded) form in hull characteristics but the double chine with its straight frames and warped (developable) shell surfaces can be built with much less equipment and at a considerable saving in cost." (25)

Williamson, B., double-chine

SNAME, corner

1950, Fig. 19, p. 21 shows

endings

developability of these surfaces (26)

Examples

on is

of straight-element barge

barges.

and

lighter hulls,

with resistance data, are to be found on sheets listed hereunder:

RD

Sheet number

The

not known.

SNAME

765

HYDRODYNAMICS

766

BODY

IN SHIP DESIGN

Sec. 76.8

PLAN

PROFILE

Chine Lencjth Fig. 76.D

(3)

Lq

Diagram Illustbating Layout of Developable Surfaces for a Small V-Bottom Boat

First establish arbitrarily the deck edge at

(6)

To

get the proper rounding and fullness of

U

side or sheer profile, the chine profile, the baseline

the forward deck, the apex

and the chine planform by drawing them in the customary manner for orthogonal projection. It is necessary to draw the sheer profile of the deck in approximately its proper

the forward portion of the side,

in the profile,

and farther Its position (7)

Apex

A

aft is

in the profile, for

is to be lower than the apex S in the profile.

fixed presently.

bottom Lc ahead of

in the profile, for the conical

located about 0.2 or 0.25

relation with respect to the chine profile. In the

surface,

example given by Hartman and utilized here, the baseline in the profile happens to coincide with

the chine beginning C. Its vertical position below the chine beginning determines the depth of the

the centerline in the plan view. It

forefoot

is

required to

deck edge in plan, the keel profile, and the stem profile, and to make the orthodox lines drawing with section lines and buttocks. (4) For laying out the side, place the apex S in the profile at a height of about 0.5 to 0.75 times the chine (or overall) length Lc above the chine beginning C at the stem, and slightly forward of find the

that beginning (0.1 (5)

Place apex

Lc

in the figure)

T in the plan

and

apex in the

and the rise of floor in the forward sections.

Apex

B

in the plan is located opposite

apex

A

and across the centerline from that side of the bottom to be drawn. It is positioned laterally at about the distance 0.5 Be from the centerhne. (9) Divide the chine length Lc into a convenient

number

of

equidifferent

station

lengths;

there

are four such lengths in Fig. 76. (10)

(opposite apex S

in the plane of the projection of that

(8)

is

Draw

a side generatrix from the point

along the chine profile at Sta. straight line from

F

1

to the apex S. This intersects

D in the profile.

plan view) at a distance from the centerhne, on the same side as the plan view to be drawn,

the sheer line already drawn at

approximately equal to the length of the halfchine beam IZ at the transom

by drawing a straight hne from view to apex T

(11)

Lay down

F

by laying down a

the plan view of this generatrix

F

in the plan

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.8

(12) Project the point

D in

the profile

downward

FT, intersecting it at D. one point in the plan view of the deck

(23)

Draw

to the latter generatrix

profile to

This

upward

is

edge at the side. FD in the profile and FD in the plan view are two projections of the same straight line in the side of the boat at the forward quarter. (13) Starting similarly

with points P, N, and Z in

the chine profile, find the plan contour of the

deck edge at the side abaft the point (14)

To

bow a

D in the plan.

get the fullness of side required at the

shorter and fuller cone

made by having the

is

used. This tran-

element of the new cone coincide with the last element of the old cone; for example, FDU and FDS in the profile. This means that the apex U in the profile sition is

first

on the generatrix FDS. Apex V is laid down on the generatrix FDT opposite apex U. must (15)

lie

From

a selected point

draw

H in the

chine profile

HJ

on a straight generatrix toward the bow-profile apex U. This straight line intersects the sheer Une at J in the profile. (16) From the point H on the chine in the plan view, opposite H in the profile, draw a straight line to apex V (17) Project J in the profile downward to the generatrix HV, which it intersects at J in the plan view. This is another point along the deck forward,

edge in the plan. (18) Continue in this manner until sufficient points in the forward deck edge are available to

M

767

H

a line from

on the chine

apex A. Project the point

until

it

M in the plan

intersects the generatrix

in the profile.

This

is

in the

HA

at

another point on the

manner

keel profile. Continue in this

until all

points along the keel profile are determined. (24)

To

assist in delineating the after portion of

the bottom and to help in preparing the lines

draw a buttock Bj at about 0.4 beam Bc/2 (or draw several them). Then draw the generatrix QB and

drawing

later,

times the half-chine of

proceed as before.

To draw (25)

The

the buttock B, in the profile:

generatrix

PYB

in the plan view inter-

sects the buttock Bi at the point

W.

Project this

point upward, intersecting the (same) generatrix

PYA in

the profile at

desired buttock.

W.

This

is

The remaining

one point on the points are

same manner. To draw the waterline WLi

drawn

in the

(26)

view, the generatrix

FDS

in

the plan

in the profile intersects

this waterfine at the point R. Project

R downward FDT in

until it intersects the (same) generatrix

R of the plan view.

This is one point on Continue in the same manner to find remaining points. (27) To draw the customary body plan, it is possible to lay down the projections of the deck edge, the chine, and the keel on a transverse the point the

desired

waterline.

permit drawing this line for the entire length (19) As an aid in dehneating the deck edge aft

plane, using the station offsets of the other

the plan view a waterline WLi is drawn through the hull in the profile, parallel to the baseline. By estabUshing the approximate outline of the transom, half of which is indicated in the

on the body plan, using the B in the plan and the vertical height of apex A in the profile. The

in

body plan, it is possible to lay down the point E on the plan view and to determine another point along the deck edge

ET. Another way

aft,

lying on the generatrix

to do this

is

to extend the

chine for a station or two abaft the transom and follow the regular procedure. (20)

To

line in the

B

plan view from

F

draw a

on the chine to apex

in the plan, intersecting the centerHne at

(21) In the profile,

draw a

chine to apex A. Project to its intersection

K

K in K is

generatrix FA. Point

line

from

K

F on

in the plan

the

upward

the profile with the one point on the keel

profile.

H

on the (22) Draw a line from another point chine in the plan view to apex B; it intersects the centerline at the point

(28)

M

Draw apex

transverse offset of apex

transverse projections of the two apexes for the

drawn in the same manner but they are not shown in Fig. 76.D. (29) From the known point F on the body plan, where the chine crosses Sta. 1, draw a generatrix side are

to the apex 0.

FGO

determine the keel profile, first

two

views

The point

G where this generatrix

crosses the section line for Sta. 0.5

is

then

found by stepping off (1) the offset from G in the plan view to the centerline or (2) the height from the basehne to G in the profile, along the fine FGO. Sufficient points for drawing this and all the other section lines are found by continuing this operation. The section fines, when drawn, are found to have the usual shape for a develop-

able surface, slightly convex outward.

may

not

have the shape that the designer intended.

He

When

the process

is

finished the boat

HYDRODYNAMICS

768

IN SHIP DESIGN

take care of some special situation which arises

may then shift the various apex positions and go through the dehneation process all over again.

after the vessel

Even the most experienced

blister

designers of small

craft with developable surfaces find this necessary, but with practice it is possible to perceive when the developed shape is departing from that visuaUzed, and to correct it before too much work is put into an undesired delineation. In the example described, the chine is used as a directrix for both the bottom and the side. Only two cones were used for the side but three, four, or more could have been used to give the side a

greater tumble

home

aft or for other reasons.

Five cones, four above the side and one below it, are employed for the 23-ft high-speed boat drawn

on page 30 of the Werback reference In fact, the apex can continue to shift from

in Fig. I cited.

one generatrix to the next, following a continuous curve in space, provided that the apex always remains clear of (outside of) the portion of developed surface that is to be worked into the boat. Reduced to their utmost simplicity, portions of developable surfaces

can be

flat or

cyUndrical.

In these, cases, the traces of given generatrixes are parallel to each other in all three views of an

Sec. 76.9

is built. The ship which has a added to the outside of its hull, as in Fig. 76. E, whether it is a vessel M'hich needs torpedo protection or more beam and displacement, or a submarine which needs external ballast tanks attached to its pressure hull [USNI, Feb 1955, p. 159], calls for the use of design

principles that are essentially the same.

Actually,

if

certain basic

principles are fol-

lowed, rather amazing discontinuities of this type, in the

way

and the

of saddle tanks, thick fender strakes,

like,

can be worked into underwater

sections without incurring too

pressure

resistance.

much

friction or

may

These principles

be

stated as follows: (a)

The chine lines are to be so placed that the when flowing around the ship at the speed

water,

and under the conditions considered most important, follows but does not have to cross them (b) When there are "offset" surfaces between chines and coves, illustrated in diagram 3 of Fig. 76. F, which are of appreciable area when projected on a vertical transverse plane,

make the

it

appears

projected areas facing aft about

orthogonal projection.

wise to

Considering the importance of the bottom shape in a V-section craft with chines, both the keel line and the chine may be established at

equal to those facing forward, even though the

the outset and used as a pair of directrixes. The procedure in this case, somewhat more involved

than that described, is covered in an unpublished paper by L. K. Losee, reference (e) listed at the beginning of this section. Mr. Losee is, at the time of writing (1955), on the staff of the Bureau of Ships of the U. S. Navy Department. 76.9 Design of Discontinuous-Section Forms Chap. 28 explains that it Blisters and Bulges. is

frequently convenient to incorporate disconan vmder-

tinuities in the transverse sections of

water

hull, either to simplify

construction or to

actual offset surfaces do parallel the lines of flow.

For example, in the body plans of the German submarine U-111 in Figs. 28.B and 28.C, the projected area of the offset surfaces between the chines and the coves in the forebody is of the same order of magnitude as the area of those in the afterbody. There is no known hydrodynamic justification for this rule; only the engineering

intuition of the author. (c)

The lower

offset surfaces of

discontinuous sec-

near the water surface, are shaped to parallel the general surface-wave profile at the selected speed. Otherwise they will lie at angles to the streamlines and may produce areas of tions,

if

separation. (d)

It is desirable

to limit the sides or offset

surfaces of a cove, at least those lying perpendicular or nearly so to each other, to the

minimum

practicable widths. This can frequently be ac-

complished by sloping or cutting away the edge the projecting portion beyond the region where a right-angled connection is required for structural reasons, indicated in diagrams 1 and 2 of

Re-entrant Fig.

/>nqle 100 deq

Midsection of World War II German Cruiser Prinz Eugen with Busters

76.E

of Fig. 76.F. (e) The reentrant angle at the bottom of a cove should be as large as practicable; in no case

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.9

should this angle, measured on the water

769

side,

less than 90 deg. If the reentrant angle of a cove is much larger than 120 deg and approaches 180 deg, the position and direction of the cove, with reference to the adjacent streamlines, is

be

not too important.

The discontinuities should fade out at the (f) ends and merge gently into the fair form of the hull (g)

Shell openings on ducts or pipes leading into

the hull proper are best kept clear from the region

underneath the offsets in discontinuous This is particularly true where both sides of the cove slope upward, forming a possible trap for air. Such a cove in the entrance may easily collect air coming down from the region close

sections.

of the

bow-wave

may

continuity

crest.

The length

of the dis-

be so great that this

and released where the cove slopes upward. readily carried along

air is

not

in the run,

Although they represent longitudinal disconof relatively

tinuities

bulged fender sirakes

small transverse section,

may

be classed with small

bulges and blisters. Discussing structural matters

moment, the combination of simplicity of and greater efficiency

for a

construction, ease of upkeep,

dictates the use of heavy, single-thickness fender strakes, conforming to the adjacent hull shape or

bulge,

instead

They may

of

built-up

external

fenders.

below the surface waterline on submarines, as at 3 in Fig. 36. N and at 1 in Fig. 73. Q, or at or near the waterline on tugs, sketched in Fig. 68. J. Diagrams 4 and 5 of Fig. 76. F illustrate several types of bulged fender strakes, not including one of circular-arc section. These may be worked in as part of the hull plating, either above or below water, and in a fiat or curved side. lie

Bhstered fender strakes should involve not-

Fig. 76.F

Design Details for Discontinuous Sections

When

designing a blister to be added to an

existing ship, available,

for

these

which the Hues of flow are

may

be used for guidance in

laying out the coves, chines, knuckles, and other longitudinal discontinuities. It must be expected,

main

hull plating. As far as practicable they should follow the actual lines of flow as modified

however, that the addition of a blister of relatively large volume may change the flow pattern around the combination. A check test is called for at an early design stage to insure that the flow around

by surface waves,

the ship-and-blister assembly

too-small reentrant angles where they join the

especially at that speed for a given ship at which low resistance is considered If bulged fender strakes must of be placed at the waterline the dis-

important. necessity

turbance to surface wave action must be accepted. It

will,

when blister sections are down suitable cove traces which

should be possible,

sketched

in,

when

to lay

the blister

is

along the resultant lines

very nearly of flow. This is partic-

in place, lie

A

special case arises

when

is

satisfactory.

external bhsters are

—

—

added locally and usually temporarily in the form of boxes, pontoons, and the like to give added buoyancy, or transverse metacentric stabihty, or both, to a hull which must be floated through a region of exceptionally shallow water, or which must be held upright when lifted to a draft corresponding to that acceptable for the

[MESR, Jun

ularly true

shallow-water area

an awkward bump upon

Oct 1954, p. 58]. It is sometimes necessary to tow a vessel thus

if the blister, as it should, fairs reasonably well into the original hull and does not make it.

1952,

p.

53;

HYDRODYNAMICS

770

IN SHIP DESIGN

Sec. 7r,.10

supported, either before or after entering the

coast or, like whale catchers, they travel from

shallow water, through a region of deep water.

Norway to the Antarctic and back every whaUng season.

The towhne

tension for such an operation

must

be approximated and the protuberances, with their connections to the main hull, must be able to withstand the forces and moments due to waves and to the motion of the buoyed-up hull in waves. No systematic design data are available for use in .situations of this kind but the problem is one readily and simply handled by a model basin which possesses a model of the ship to which the protuberances are to be attached. 76.10 Vessels with Fat Hull Forms. Length of hull, which is an asset when striving for speed and propulsive efficiency, becomes somewhat of a Uabihty when first cost, compactness, hull stiffness, maneuverability, and habitability are important factors. This is especially true for craft which are small compared to the

minimum

lockers, passageways,

and access

Sailing yachts,

small fishing craft,

tugs,

sizes for berths,

for the crew.

work

and similar vessels are, more often than not, fat and chubby. Icebreakers are larger

again for

pointed out by Ambrose Hunter ["The Art Trawler Planning," Ship and Boat Builder and Naval Architect, London, Feb 1953, pp. It is

of

259-260] that fishing vessels in general: (I)

Are similar to tugs in that they have to tow and trawls, yet have to possess

fishing gear, nets,

a high free-running speed (II) Are akin to lightships in that they spend more time stopped at sea than any other type (III) Are hke sailing yachts in their resistance to drifting, ease of handling, and extreme maneuver-

ability.

Specific

from D.

S.

hydrodynamic requirements adapted Simpson [SNAME, 1951, p. 561] and

R. F. Symonds [SNAME, 1947, pp. 381, 384] include the following, together with appropriate

comments concerning

design:

boats,

displacement-

(1) Adequate metacentric stability, both static and dynamic, for all conditions of loading, includ-

to 500 or more, with

ing the top weight of a coating of ice over every-

0-diml fatness ratios of 17.5 and above. Their

thing above water. This coating may amount to 20 tons or more. Metacentric stability is outside the scope of this book; see PNA, 1939, Vol. 1, Chap. Ill, pp. 99-137, and other standard

vessels

in

this

Their

category.

length quotients run

up

length-beam ratios are invariably small, generally less than 5 and sometimes as small as 3. Figs.

66.

D

and

66.1

indicate

that separate

design lanes, or branches of regular lanes, are

needed for these craft. The two lanes of Fig. 66. A each have branches of this kind. They are omitted from the latter figure partly to avoid compUcation and partly because insufficient data have been collected to locate them properly. In general, data for existing craft in the fat and

chubby category are widely

scattered.

unfortunate that the Taylor Standard Series was not extended to embody fat forms It

is

having displacement-length quotients A/(0.010L)^ in excess of 250, corresponding to a fatness ratio V/(0.mLY of 8.77. Partly to fill this gap there are given in Sec. 56.6 the results of an analysis of miscellaneous model-test data on fat forms made by R. F. P. Desel and J. T. Collins. Requirements and Design Notes for 76.11 Fishing Vessels.

references. (2)

Moderate change

(3)

More than adequate

going ability, at

all

features are covered in Part 6 of (4)

Easy motion

form

in reasonably

whether a wintry, rock-bound

they work five miles

off

rough water, over a range of

(5) Reasonably dry decks, accepting spray but no breaking seas or solid water, over the range of speeds mentioned in (4), so that fishing can proceed even in bad weather. The design comments of item (3) apply.

but not water

craft,

III.

well.

Ability to slow

ocean-going

These design

Volume

speeds where fishing gear can be handled. The design comments of (3) preceding apply here as

(7)

robust,

wave-

to provide a good working plat-

fish

essentially

or above-average

speeds which can be main-

tained in the heaviest weather.

SNAME,

1951, p. 561]. Large or small, they are

between extreme entering and

when

leaving the fishing grounds

all types and by the requirement that they must "keep the sea and work on it, all the year around, and in all weathers" [Simpson, D. S.,

Fishing vessels of

sizes are characterized

of trim

operating conditions, such as

(6)

Extra-large freeing ports or freeing slots in

the bulwarks, screened to hold men, gear, and

down

or to heave to while

retaining steering control, so that the vessel can

be held in any desired position in wind and waves

DESIGN OF SPECIAL-PURPOSE CRAFf

Sec. 76.12

submergence of the propeller and rudder, under wavegoing conditions, to give them a hold on the water and to render the vessel fully manageable Sufficient

(8)

Minimum

J.O.Trauncj Model

Ship Lcnqlh -

19.51

540 q IV m -o- 6401

771

ft

beam-bZ7m-o 2057_ft Meon Drofl- 2.354rTr*T72

ft

when broadside or when hauling in gear and nets from abeam. The effect of driftresisting keels is discussed in Sec. 36.15; some design rules for them are included in Sec. 73.19. The drift-resisting effect of a deep hull, like that (9)

drifting

of

nearly so to the wind and sea, as

New

of the pilot boat

36.K,

is

York illustrated in Fig.

appreciable.

(10) Positive

stability

conditions; this

of route

Volume III (11) Ample speed

load

all

3.11

for running to

This feature

fishing grounds.

under

discussed in detail in Part 5 of

is

is

Ax" 10.347 m^

rather closely

Cx

related to the provision of a reasonably high

free-running speed for tugs. It fishing vessels,

powered

like

tugs,

is

minimum

is

said in the foregoing about

importance. In other words,

it

ratio

is

of

little

can be as high as

beam does not

increase resist-

ance

The

(c)

It

center of

buoyancy should be well

possible that the position of the

is

aft.

maximum-

area section should also be abaft midlength. (d)

Differences in the block coefficient

0.55, (e)

have

The

little

(f

(g)

,

below

or no influence

Cp is of great imoptimum value of about 0.575

Transom sterns act to reduce resistance The half-angle of entrance, or the waterline

.slope

(h)

Cb

prismatic coefficient

portance, with an

is in this region, should be low

Parallel

middlebody and sharp shoulders are

to be avoided. Fig. 76. of Traung's models.

ft

Traung's Model 340a

Data from the Japanese fishing-vessel standard and summarized in Sec. 56.4.

series are referenced

The fitted

multiplicity of longitudinal fender bars

on some

steel trawlers to

by heavy

prevent damage

banging probably more objectionable from a maintenance standpoint than for the added resistance which they cause. A construction much to be preferred from all points of view is described to the shell plating

along the side

and

is

illustrated in Sec. 73.22

76.r.

It

embodies heavier

complete absence of

form

fishing gear

and shell

Figs.

73.Q and

plating and a

applied appendages in the

all

of fender bars, fender shapes,

and fender

strips.

A combination of controllable propeller and swinging tubular rudder or Kort nozzle, designed for astern as well as

ahead propulsion,

excellent combination for a fishing craft.

required for other reasons.

Enlarging the

32

J.-O.

resistance

The displacement-length

(b)

IN.

O.TOI

are invariably over-

and shaft power to meet the several requirements, there is no more excuse for unnecessary resistance and Uttle more excuse for unneeded power in a fishing vessel than in a craft of any other type. With respect to fishing vessels as a class, Jan-Olof Traung has come to the following conclusions concerning the effect of form parameters on resistance, based upon analyses of tests on a considerable number of models [Int. Fishing Boat Congr., Paris and Miami, Oct-Nov, 1953, "Outline to a Catalog of Fishing Boat Tank Tests"]: (a)

o

=

Body Plan, European Fishing Boat,

Fig 76.G

why

one reason

for their size.

While nothing

-H-'2.56

and from the

G illustrates the lines of one

an Such

is

a combination, designed by the Swedish naval architect Jan-Olof Traung, is illustrated and described in Motorship, New York, Jun 1950, pages 42 through 44.

Modem Bibliography

on Fishing on the design and construction of fishing vessels, say for the period following the year 1930, is very extensive. This is not surprising because, although the average fishing vessel is less than 100 or 125 ft in 76.12

Vessels.

Partial

The modern

length, the

literature

number of t3T)es and kinds is incredibly

large.

An

insight into the great breadth of this field

and the variety

in it

is

afforded

by a reading

of

the excellent recent book entitled "Illustrations

772

HYDRODYNAMICS

IN SHIP DESIGN

of Japanese Fishing Boats."

Although pubUshed

Tuna

by the Fisheries Agency

of Japan, in 1952, the

man primarily responsible for it is Atsushi Takagi, Chief of the Fishing Boat Section of the Fisheries Agency.

Among

Sec. 76.12

Clippers

Trawlers and Sealers

Whale Catchers and Exploration

Fisheries Research

Vessels.

other information the Historical

book contains the following: (1)

Simimary tables of the Japanese fishing by types of vessels and kinds of engines, made up of some 23 or 24 categories

Owen,

and General "Outstanding

G.,

New

England Types

(a)

Fishing Boats, Whalers, and Yachts,"

fleets

HT,

Tabulated characteristics of 42 typical vessels, from whale factory ships to fisheries training

(2)

"Ships and Sailing Albums," Book 4, Kalmbach Publishing Co., 1027 No. Seventh St., Milwaukee 3, Wis. Describes New England fishing schooners.

(3)

Cunningham, D.

(b)

boats, giving general information, principal di-

mensions, capacities, form coefficients, and related data for light- and full-load condition, as well as

(4)

37 entries for each vessel Forty photographs of typical fishing vessels, both large and small (d) Technical data on 50 typical fishing vessels, comprising general arrangement plans, lines drawings, displacement and other curves, machinery and piping arrangements, fishing gear arrangements, refrigeration installations, and the like. The data presented are not the same for all vessels. The largest vessel has 15 plates of data; the least important vessels 3 and 4 plates. (e) All dimensions are in the metric system.

(5)

full-scale trial data;

B., "Notes on Trawl Fishing," lESS, 1948-1949, Vol. 92, pp. 260-330 Hardy, A. C, "Seafood Ships," Crosby, Lockwood & Son, Ltd., 20 Tudor St., London, E.C.4., 1947 Symonds, R. F., and Trowbridge, H. O., "The

Development

(c)

Atlantic," (6)

"A Review

(7)

D.

S.

(9)

"Pacific

which follow are under the headings:

and General

Model Tests Design and Construction Small Vessels

Miller

Freeman

Publications,

Washington. (10) Articles about fishing boats, but with fewer drawings,

Columbia

St.,

Seattle

4,

are published in:

Fisherman,"

Goffstown,

Atlantic

Inc., 71

(11)

Freeman

Columbia

St.,

Seattle

4,

The U.S. Government Fish and publishes

the

Review." This

monthly is

Inc.,

Washington

25,

Publications,

Washington. Wildlife

"Commercial

Service

Fisheries

by writing to the Department of the Interior,

obtainable

Service at the U.S.

Model

Fisherman,

New Hampshire

"Pacific Fisherman," Miller

D.C.

Tests

ships."

specific references

Historical

1951, p. 582

Motor Boat,"

Inc., 71

(12)

The

Con-

London, Apr 1952

There are many references to be found under the heading "Fishing Vessels" in the Engineering Index Summaries of the SNAME Member's Bulletins, dating from 1946 to the present Many journals publish news on current trends in fishing-boat design and construction. Generalarrangement drawings of new fishing boats can normally be found in every issue of the following

"Atlantic

for convenience

of the British Fishing Industry,"

journals:

is

and factory

the North

Yachting Magazine, 205 East 42nd Street, New York 17, N.Y. The Rudder, 9 Murray Street, New York 7, N.Y. "Fishing Gazette," Fishing Gazette Publishing Corporation, 461 Eight Ave., New York, N.Y.

tions,

trawlers

in

1947, pp. 359-384

Simpson gives 8 references to papers and on fishing and fishing-boat design in

SNAME, (8)

is "Fishing Boats of the World," edited by Jan-Olof Traung and published by Fishing News,

important to emphasise that 'Fishing Boats of the World' is not meant to be a book on naval architecture. It is a book dealing with that part of fishing boat design which is missing from all textbooks on naval architecture, and it is so written and presented that everyone concerned with building fishing boats can find its illustrations and information of practical value. It is not suggested that the book contains information about every type of fishing boat, but it does provide a comprehensive survey of a great number of boats, from beach landing craft to modern

Beam TrawHng

articles

A more recent informative book, of international

"It

of

SNAME,

tinental Daily Mail,

scope,

London, 1955, through A. J. Heighway PubhcaLtd., Ludgate House, 107 Fleet St., London, E.G. 4. The following explanatory paragraph is copied from the letter forwarding the first of these books from the Food and Agriculture Organization of the United Nations:

of

SNAME,

1943, pp. 145-151, 163-164

listed

(13)

Nordstrom, H. F., "Forsok med Fiskcbiitsmodcllcr (Tests with Fisliing Boat Models)," SSPA Rep. 2, 1943; English summary on pp. 30-32 and 5 references on p. 29 Traung, Jan-Olof, "N^gra Erfarenheter FrSn Tank-

med FiskebS,ter (Some Ex-periences of Tank Unda Maris, Goteborg Yearbook of the Nautical Museum, 1947-1948. The paper carries a summary in English on pp. forsok

Tests with Fishing Boats),"

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.12

65-68 but there

a complete English version in BSRA Transl. 58. A very comprehensive paper, with a list of 40 references on pp. 62-63. "Skarpning av FiskebS.tars Jan-Olof, (14) Traung, Fijrskepp (Finer Entrances for Fishing Boat Hulls)," Goteborg Yearbook, 1948; translated by the

is

BSRA

Traung, Jan-Olof, "Svenska Tankforsok med Fiskeb&tsmodeller (Swedish Tank Tests with Fishing Boat Models)," Norwegian Shipping News, 1949, No. 9; translated by the BSRA sheets for fishing vessels (16) There are SNAME available as indicated hereunder. Some form coefRoients and proportions are listed under "TRL" on page 35 of SNAME Tech. and Res.

(26

"Modern Development of the Herring Drifter," SBSR, 30 Apr 1942, pp. 468-470. Gives outlines

(27

"4rcterMs-Shrimp Trawler with New Idea," Motorship, New York, Jul 1947, pp. 26-28, 30. Length 108 ft, beam 25 ft, and designed draft 7 ft. Dyer, J. M., "The Development of the Columbia River Gill-Net Boat," SNAME, Pac. Northwest Sect., Oct 1947

of profiles, with freeboard

body

(15)

(28:

RD

Shows

Length,

Beam,

Draft,

Speed,

ft

ft

ft

kt

number

HI

Trawler Trawler Trawler Trawler Trawler Trawler Trawler

123 125

126 127 142 157

130

110.5 144.4 227.5 59.2 119.8 124.7

28.5 22.48 27.1 38.55 16.96 25.67 24.6

12.5

13

10.69 12.8 17.18 5.12 11.0 11.48

11 11

transom (33

1943,

(36

A.,

FAO

Fishing

1951,

Food and Agricultural Organization International Documents Service,

Bulletin,

(37:

(25a) Traung,

Jan-Olof,

tecture,"

FAO

"Fisheries

and

(38:

(39:

(4o:

(41

in

published

FAO World Fisheries by the FAO Headquarters in the

Abstracts,

Rome.

Dec

"Twin

Steel Diesel Shrimpers,"

sterns.

F.,

J.

"The

Fishing,

SNAME,

W.

J.,

Processing Vessel

Pac. Northwest Sect., 27

"Northwest Yards Launch Fishing

May

1951, pp. 44-45.

Clippers

Snyder, G., "Stability of Tuna Clippers," SNAME, Pao. Northwest Sect., 3 May 1946 Mann, C. F. A., "Sun Traveler— A 121-Foot Tuna

Mar

1948,

52

"Tuna purse

seiner Santa Helena,"

Diesel Prog.,

"New Baby Tuna-CUpper C. F. A., Conqueror," Diesel Prog., Feb 1949, pp. 30-31 Petrich, J. F., "The Tuna Clipper," SNAME, Mann,

North. Calif. Sect., 31 Mar 1949 Pugh, M. D., "The Tuna Clipper Carol Virginia," Motorship, New York, May 1949, pp. 18-19 Mann, C. F. A., "Tuna Clipper Mermaid," Diesel Prog., Sep 1949, pp. 42-45 Mann, C. F. A., "Mary E, Petrich World's Largest," Diesel Prog., Oct 1949, pp. 40-41. Describes and illustrates tuna clipper with an overall length of 150 ft, a beam of 34 ft, a depth of 16 ft, and a

maximum

speed of 13.75 kt. A., "Tuna Clipper Hortensia-Bertin," Diesel Prog., May 1950, pp. 54-55

(43:

Mann, C. F.

(44:

Barbour, H.

(45:

Tuna Clipper," Diesel Prog., Sep 1950, pp. 46-47 Mann, C. F. A., "A Temporary Lull in Tuna Clippers

Fisheries Bulletin, 1955, Vol. VIII,

No. 4 (in English), FAO, United Nations, Rome. (25b) A good review of current literature on fishing-vessel design and construction throughout the world is given

(42:

of the

Naval Archi-

Processing

Jun 1948, pp. 41-42

Jan/Feb and Mar/ Apr

2960 Broadway, New York, N.Y. Henschke, "Schiffbautechnisches Handbuch W., (24) (Shipbuilding and Ship Design Handbook)," 1952, Section on "Fishing-Vessel Design," pp. 592-613 U.N.,

A.,

Clipper for San Diego," Diesel Prog.,

Pao. Northwest Sect., 26

Traung, Jan-Olof, "Improvement of Fishing Vessels,"

Granberg,

p.

569, 571, 574-579, 581 (23)

Goodrich,

Tuna (35:

of

"ScantUngs for Small Wooden Vessels," Aug 1950 (22) Simpson, D. S., "Small Craft, Construction and Design," SNAME, 1951, pp. 554-611, esp. pp. 561-564 on the trawler, and drawings on pp. 564-

R.

F.

Craft," Diesel Prog.,

ments.

SNAME,

Fish

Pac. Northwest Sect., 9

Diesel Prog., Jan 1951, p. 47. These vessels are 54 ft long by 16 ft beam by 6 ft depth, with wide

(34;

(21) Smith,

Coast

"Pacific

SNAME,

Mann, C.

pp. 95-103 (18) Spanner, E. F.,

Motor Fishing Vessels for the Herring Industry Board," SBSR, 5 Jun 1947, pp. 566-567. Lines drawings are given of two 65-ft experimental herring drifters, based on previous model e.xperi-

with large

(32

12

"Seaworthiness and Stability of Trawlers and Drifters," Joint mtg. INA and lESS, 24 Sep 1946. Abstracted in SBSR, 26 Sep 1946, pp. 354-356; 3 Oct 1946, pp. 381-382. (19) Holt, W. J., "Admu-alty Type Motor Fishing Vessels," INA, 12 Apr 1946, pp. 295-307

65-ft vessels

(3i:

10

INA,

and

1949 Robison, D., "Diesel Draggers," Diesel Prog., Apr 1950, pp. 56-57

Design and Construction

"New Type

Nickum, G. C, Vessels,"

12

11

sheer, as well as

sterns.

Deep Sea," Apr 1951

(17) Taylor, A. R., "Fishing Vessel Design,"

(20)

several 60-

transom (30;

Type

and

plan.

"Presenting a Group of Fishing Vessels Powered by GM-Diesels," Diesel Times, Mar 1948, pp. 7-8.

(29

Bull. 1-14, Jul 1953:

Sheet

773

Small Vessels

(46:

J.,

"Marilyn Rose,

Pacific's

Newest

Ends with Diesel Powered Modego," Diesel Prog., Jan 1951, p. 53 Hanson, H. C, "The Tuna Clipper of the Pacific," SNAME, 1954 Spring Meeting. This is a wellillustrated and informative paper; see also SNAME 1954, pp. 30-42. For the 130-ft vessel whose

HYDRODYNAMICS

774

IN SHIP DESIGN Exploration Vessel,"

data have been worked out for a 17-ft draft:

Sect.,

L = S = £) =

130 ft 30 ft

L/B

ratio

=

4.33

S///

=

ratio

17 ft

A/(0.010L)3 = 494 F/(0.10L)3 = 17.32

1.76

A = 1,085 long Cb = 0.648

tons

V = hr

11.7 =0=

Mann,

Fireboats or Firefloats.

76.13

1947, pp. 359-384, esp. pp.

371-384 on Trawler Design (48) Shearing, Douglas, "152-foot Ti-awlers for French Fishing Industry," Diesel Prog., Feb 1948, p. 56, with photograph of trawler Clair de Lune. Single is ft,

of

200/60

variable pitch, with

D

of 8.83

and 4

is

11 kt with

=

blades.

Speed

ft,

P n

3.33 rps.

Sealer (Terra Nove) on Maiden Voyage, Diesel Prog., Feb 1948. Lqa is 140 ft, B is 28 ft, and D is 14 ft. Speed is 9 kt. (50) French fishing trawler Saint Joan, Proc. Am. Merch. Mar. Conf., 1949, p. 292. A photograph shows rather well the form of the hull amidships and the form of the run, with the single propeller and (49) Diesel-engined

rudder.

Oct 1949, pp.

(51) Diesel trawler Giidrun, Diesel Times,

Length

1-2. (52)

is

115

ft

and beam 23

139. This vessel has a length of 185

30.5

a depth of 16 ft, and a speed of 13.63 kt. H. E., "Large Trawlers," INA, Apr 1954;

ft,

(53) Jaeger,

May

1954 issue of The Motor Ship, London, pp. 62-63. abstracted in the

Fireboats

as

the earliest of mobile special-

from the In Europe these vessels are normally

vessels themselves nor the class will ever be large,

type

the

yet

problems

it

interesting

is

complex

the

for

poses in naval architecture and marine

engineering.

The service requirements involving hydrodynamics, listed hereunder, are adapted from a paper by A. D. Stevens [SNAME, 1922, pp. 137-141 and Pis. 44-52], from a group of excellent articles

in

Motorship [New York,

May

1950,

pages 17-57], and from a more recent paper by

D.

S.

They

Simpson [SNAME, 1951, pp. 564-568]. down more or less in the order of

are set

their importance: (a)

Instant availability and prompt arrival at

the

fire.

This involves free-running speeds of 11

to 14 kt, in the present stage of development,

ft.

Trawler," SBSR, 31 Jan 1952, p. ft, a beam of

"A Powerful Motor

among

called firefloats. It is probable that neither the

SNAME,

of 6.175

Oct 1947

service vessels, dating in the Americas

Symonds, R. F., and Trowbridge, H. O., "The Development of Beam Trawling in the North

propeller

Northwest

Pan.

C. F. A., "Diesel Ship John N. Cobb," Diesel Apr 1950, pp. 40-41.

a class are

Trawlers and Sealers

Atlantic,"

SNAME,

Prog.,

mi per

10.16 kt

Cw = 0.88 Cx = 0.88.

Cp = 0.732

(60)

1870's.

(47)

Sec. 76.13

curves of form arc given in Fig. 11, the following

depending upon how far the craft has to travel from its station.

Extreme maneuverability, involving a high

(b)

degree of handiness, rapid response, and ability to

move

in almost

any

direction. In particular,

the boat must be able to steer and maneuver

Whale Catchers

when backing.

(54)

Matthews, L. H., "South Georgia: The British Empire's Subantarctic Outpost," 1931, pp. 123, 125-126

(55)

Granberg,

Dec

W.

(57)

"Diesels go

Whahng," Diesel Prog., wooden vessels,

North Pacific whaling. Norway's New Whale-Catcher Ships, Nautical Gazette, Jan 1951. Mentions a 16-kt speed with a brake power Pb of 2,400 horses. Whale catcher Setter II, SBSR, Feb 1952, p. 55. This vessel has an Lqa of 177.5 ft, an Lpp of 160 ft, a depth D of 17.5 ft, and a mean draft, fully loaded, of about 15.6 ft, including a bar keel 115 to 140

(56)

J.,

1949, pp. 34-35. Describes ft long, for

about 0.62 ing

is

1,080

and the (58) Shearing,

The displacement correspondlong tons. The trial speed is 15.3 kt,

ft

deep.

"The Whaler Enern," Diesel

Prog., Sep 1953, pp. 36-37. This vessel has an

LoA a

D

of 210

ft,

of 18.33

engine

is

an Lpp of 186.5 ft.

ft,

a

B

of 33

ft,

and

The brake power of the single rpm or 3.75 rps,

2,700 horses; n is 225 V is 16-17 kt.

and the speed

Fisheries Research (59)

and Exploration Vessels

Hanson, H. C, "The Conversion

at the discharge nozzles

of Pacific Fisheries

only a moderate say not in excess of 6 deg, when all fire-

(d) Stiffness sufficient to give list,

fighting

nozzles

are

directed

abeam, and discharging at (e)

full

horizontally

and

capacity

and for power should to the fire; an

Flexibility of drive for propulsion

pumping. The greater part

of the

be available for taking the vessel

equally large portion should then be available for (f)

vessel has a single screw.

Douglas,

(c) Ability to stay put in the position and at the heading desired, under the reaction forces exerted

pumping water. Freedom from clogging

suctions

if

only slightly exceeding

must

also

of

the

fire-pump

the boat has to operate in water depths

These suctions and debris floating

its draft.

remain clear of

ice

at or near the surface. (g) Ability to push or pull on vessels in an emergency, like a tug. This involves propulsion devices with large disc areas or equivalent-disc

areas Aa

In terms of screw propellers this means

DESIGN OF SPECIAL PURPOSE CRAFT

Sec. 7r,.J5

775

jamming

that they are neither too small nor too heavily

to prevent the craft from

loaded

when running free. Too much attention need not be paid to a hull of minimum free-running resistance, if other

piles

(h)

draft should be a minimum consistent with other characteristics (5) There should be no excessive keel drag or (4)

and the hke.

filling

may

to

be accepted

if it

leads to a better all-around

firefighting craft.

Harbor icebreaking

(i)

features,

called for; see

To

achieve maneuverability and handiness in of possible fires:

70 to 80 to 90 ft are adequate. Lengths of 110 and 120 ft are approaching the extreme; 125 ft possibly the

SNAME, (2)

maximum

[Parsons,

H. de

B.,

1896, p. 49].

The length-beam

ratio should not exceed 5.0.

between 4.0 and 4.5. (3) The sides should have continuous curvature, as for a tug, to enable the heading to be changed readily when the vessel is alongside a pier or another ship. The ends should be well rounded. Preferably

it

should

so placed as

in the propeller outflow jets.

reaction forces at the discharge nozzles or

H and by the example given later in this section, can be very large. They are counteracted by one or more of the following indicated numerically

(1) The craft should not be too large. Depending upon the pumping capacity required, lengths of

is

lie

monitors, illustrated pictorially in Fig. 76.

Sec. 76.26 following.

and around scenes

out of the lateral plane at either end

The rudders should always be

The if

between

The

more important features are thereby improved. As a rule, the pumping requirements call for plenty of power so that a not-too-high hull drag

(6)

itself

lie

Fig. 7b.

H

procedures or devices: (7) Constantly moving the fireboat or holding it on a certain heading with its propulsion device (s) turning over. This may involve a corresponding shift of the water streams to keep them playing on a desired spot of the fire. (8)

Passive

drift-resisting

keels,

described

in

These are a help at times but they are not adequate for all possible Sec. 36.15, or the equivalent.

situations. (9)

The

provision of one or more swinging or

rotating-blade propellers. This method, however,

T. Lunyley With Jeis in Action Photograph by Lawrence Barber, Portland, Oregon

Honolulu Fireboat Abner

HYDRODYNAMICS

776

necessitates either an accepted projection of the swinging propellers and rotating blades below the hull or cutups in the hull forward and aft to

accommodate these devices. There is generally not room within the vessel, nor would there always be room under it, for retractable propellers of any kind. The cutups involve an increase in thrust deduction and a loss of efficiency but there are several successful apphcations of this kind.

A

ferryboat installation, equally appli-

is that on the Virginia ferry Northampton, where a Voith-Schneider rotatingblade propeller under the bow supplements the twin propellers at the stern [Motorship, New York,

cable to a fireboat,

New

York,

Aug

may

(10) It

1950, pp. 26-27, 43].

at times be possible to turn a few

of the jets in the opposite direction, to balance

some

of the reactions

from the

firefighting jets

Concentrating the monitors near midlength of the vessel avoids the turning or swinging moments set up when monitors near the ends (11)

IN SHIP DESIGN

Low turbulence,

a more "solid" jet, and projection more water to a greater distance is achieved by slowing down, straightening out, and quieting the water immediately ahead of the nozzle. There of

is

insufficient information available in connection

with Fig. 76. are

carrying

to indicate

in

that

how

far the five jets

Nevertheless,

case.

the

photograph clearly reveals that a considerable amount of water is dissipated in the form of spray and would probably never reach a fire into which the jets were directed. The reader who is

may W. Howe, and

interested in this aspect of fireboat design

consult a paper

by H. Rouse,

J.

D. E. Metzler, entitled "Experimental Investigation of Fii'e Monitors and Nozzles" [ASCE, 1952, Vol. 117, pp. 1147-1188]. Improved designs recommended for nozzles and monitors are shown in Fig. 3(c), Table 1, and Fig. 21 on pages 1152, 1172, and 1174, respectively, of the reference cited, and in Fig. 76.1 of the present section.

An arrangement of underwater reaction jets might be thought more efficient for holding the fireboat in position because these would impart momentum to some of the surrounding water in same

H

Jet Diameter Dj

are playing.

the

Sec. 76.13

direction as the jet. It

is

to be

Nozzle

remem-

bered, however, that neither force nor pressure

is

communicated backward through a fiquid jet, at least not for distances more than a few times the jet diameter.

The

reaction force

is all

developed

when

accelerating the water in the nozzle, so the

force

is

against it

made no

some

greater

fixed obstacle

into the water.

When

by playing the

jet

nearby or by directing

the nozzle reactions are

used to augment the propulsive thrust to get the fireboat free of a hot spot in an emergency, playing the jets horizontally into the air gives

Referenced

One important

Monitor Recommended by the Iowa Institute OP Hydraulic Research

feature of fireboat design in-

hydrodynamics

has to do with the monitor nozzles. This is measured by the percentage of the total quantity flow of water that can be delivered per unit time at the greatest possible distance from the nozzle, reckoned on the basis of the quantity rate passing through the nozzle. A jet which disintegrates on its way to the fire or which has a short trajectory is inefficient. Breaking up of the jet in the air, as well as failure of the water to "carry," is a func-

In the design recommended by the

efficiency of the

tion of the turbulence existing in the water its

in

Improved Design of Fixed Fire-Fighting

Fig. 76.1

the greatest reaction.

volving

See Rq,2I the Text

For Further Details

upon

entrance into the large end of the nozzle.

illustrated here, there are

removing

turbulence,

one

IIHR and

two honeycombs in

the

stand

for

and

another in the barrel. Flow in the 90-deg corners is

facilitated

nozzle

is

by the guide vanes shown. The

simpler than, and superior in perform-

ance to orthodox designs.

To

obtain an idea of the reaction exerted by

the vertical swiveling part of a monitor, comprising a nozzle fed from a horizontal 90-deg branch

on each

side,

assume that the barrel fed by these

DESIGN OF SPECIAL-PURPOSE CRAFT

Scr. 76.11

branches

is

than 2

orifice, slightly larger

diameter

J^TPB

^

2g

Assume

EH,

n 29

2g

per

ft

sec",

specific

(76.i)

that the salt water being

weight

w

and that the pumping pressure psi.

1950, pp. 65-66]

{9Vnf

further that the acceleration of gravity

32.174

pumped has a 150

produces a 2-in

.

energy equation [Rouse, H.,

is

in,

As the same water passes through = (672')FB.rrei = 97^ From the

jet.

both, Fjet

g

and that the nozzle

of 6-in diameter,

of 64 lb per ft^,

in the barrel

is

Then 64.35(150)144

2gps

/

\w(9'

-

fQ4

V

1)

=

16.5

64(80)

whence Vj = 9(16.5) = 148.5 fps. As the feeding branches come into the barrel at right angles,

AV is also

148.5 fps, reckoned in the jet direction.

Then F„

,

upward and both balances

forces

moment of moment of the

the

these

By lift

negative

buoyancy. Tipping the submarine over on its side, in imagination, produces the fireboat equipped with both bow rudder and stern rudder. Swinging the leading edges of both rudders toward the fire produces a lateral force to counteract the nozzle reaction force. It is to be remembered, however, that the hft produced by the bow rudder, without the benefit of a propeller outflow jet, varies directly as the first power of the rudder angle and as the square of the water velocity past it. A 4-kt current might easily give the required lateral force forward, with not too great a rudder angle, whereas this might be difficult to obtain, with a large rudder angle, in a 1-kt current.

Appended

is

a brief

of references relating to

list

supplementing those mentioned at the

fireboats,

is

are exerting positive Uft.

adjusting the angles, the

the force on the vertical-swiveling

nozzle assembly,

777

the leading edges of both sets of planes point

beginning of this section:

F„ = pQAV Parsons, H. de B., "Fire-Boats," Cassier's Mag.,

(i)

=

1.9905

r i48.57r(l)^ 144

L

1 148.5

=

958

May lb.

1896, pp. 28-45. This article carries a con-

siderable

J

amount

of historical

data and

many

illustrations.

The

horizontal

reaction

on the fireboat

is,

(ii)

data on 24 fireboats

cosine of the angle of elevation of the nozzle

above the horizontal. The transverse reaction on the boat is the horizontal reaction times the sine of the angle which the nozzle makes with the boat centerline. It is sometimes necessary to hold a fireboat reasonably stationary in space in a tidal current or flowing river. The propulsion devices turning over slowly furnish the necessary force to breast the current but there remains the problem of holding the craft transversely against the waterjet reaction forces

if

An

yaw

C.

C,

"Centrifugal-Pump

Fire-Boats,"

1908, pp. 211-228 and Pis. 116-121 Seattle Fireboat Alki, Diesel Prog., Mar 1949, p.

(v)

Robison, D., "Milwaukee's

43

New

Fire Boat Deluge,"

Diesel Prog., Oct 1949, pp. 24-25. The overaU length is 96.58 ft, the waterhne length is 93 ft,

and the molded beam

is

23

ft,

with a draft of 6.75

ft.

(vi)

Houston Fireboat Captain

Crotty,

MESR, Dec

1952,

pp. 86, 112

Fireboat John D. McKean for New York City, Mar. Eng'g., Feb 1953, pp. 79-80; Sep 1954, pp. 54-58; SBSR, Int. Des. and Equip. No., 1955, pp. 68-69. The Lqa is 128.75 ft, the L^l 125 ft, the B 30 ft, the D 14.25 ft, and the H^^^ is 9.25

(vii)

New

(viii)

"The World's Fire-Fighting Boats," SBSR,

slightly

the stern planes a slight dive angle; in this position

West,

(iv)

the

toward the direction of the fire and balance the transverse yawing force against the combined nozzle reaction forces. However, the design situation here is exactly comparable to one frequently met with in submarines, where it is necessary to hold the vessel at about zero trim and at a given depth against relatively large amounts of positive or negative buoyancy. For negative buoyancy this is done by giving the bow planes a slight rise angle and

II,

SNAME,

the monitors are playing at

expert boat handler can possible

SNAME,

and III give detailed dating from 1875 through I,

1895. (iii)

right angles to the current direction.

fireboat

Parsons, H. de B., "American Fii'e-Boats," 1896, pp. 49-64. Tables

roughly, the nozzle-assembly reaction times the

ft;

there are 2 screws. Int.

Des. Equip. No., 1956, pp. 61-65.

76.14

Propelled

Distinguishing Design Features of Self-

Dredges.

A

self-propelled

suction

an example of a ship acted upon by other than hydrodynamic (and dredge, while digging,

is

aerodynamic) forces. This is because practically all of them draw up the bed material through one or more drag pipes, inchned aft and downward.

HYDRODYNAMICS

778

Each

of these pipes

has a scraper of some sort

and a large mouth adjacent to through which the bed material is carried by

at its lower end it

suction, suspended in a powerful stream of water.

At

upper end, possibly also at other points length, the drag pipe is hinged or swiveled about a horizontal, transverse axis. The scraper and the pipe may thus be lowered to the desired depth when digging or drawn up above the baseplane (and the waterplane) when the dredge is running free. its

along

its

dredges may have two drag outboard on either side, or a single pipe, lowered through a long center well. A diesel-electric twin-screw hopper dredge of the latter type, having a length of 290 ft and a beam of 58 ft, is illustrated in the technical hterature [SBSR, 8 May 1952, p. 48; also 9 Apr 1953, p. 42]. Most large model-basin estabUshments have tested models of self-propelled dredges (for example, models 3132, 3175, 3597, 3633, and Self-propelled

pipes, one

TMB

3779),

and some

of

them have made

resistance

tests of drag-pipe assemblies at various attitudes

and speeds. Unfortunately, however, much

of

this information is so speciahzed that it has not

found

its

hterature.

way into the technical and reference The drag encountered by the scraper

units depends

upon the nature

of the bottom,

the depth of cut being made, and other factors.

The ahead

resistance

occasioned by the

mouth

and the

lateral forces

of the drag pipe

when

scraping on the bottom, and the hydrodynamic

moving not exactly com-

resistance of the inchned drag pipe(s)

ahead through the water, are parable to the towhne tension on a tug or to the wind force on a sailboat. Nevertheless, the dragpipe resistances and scraper forces caU for increased propeller thrust and they may interfere with steering.

A

self-propelled

dredge

usually

scrapes

or

dredges in shallow water, with a small bed clearance. Furthermore, it necessarily scrapes at slow

more than the usual rudder effect it under control and moving in the desired lanes. This means that the rudder(s) must be of greater-than-normal blade area and that they must be placed in the outflow jets of

speed, so that is

required to keep

propellers, to provide the necessary lateral forces

at low speeds.

Aside from

ground and hydrodynamic and their gear, the principal resistance components pecuUar to selfthe

resistances of the drag pipes

propelled dredges are the pressure drags developed

IN SHIP DESIGN by the

Sec. 76.14

form under the hopper doors. If the doors, opening downward, are not to swing below the baseplane the recesses are unavoidably deep. The greater the hopper capacity of the dredge the discontinuities in the bottom, in the

of large recesses

more

recesses there are.

Hopper-door recesses in the bottoms of selfpropelled dredges of a half-century ago are illustrated by T. M. Cornbrooks [SNAME, 1908, PI. 140], where one port and one starboard row is indicated. Each recess is 4.42 ft wide and about 3 ft deep vertically. There are 6-in by 6-in by 5/8-in angles all around the lower edge of each recess, projecting both into the recess and below the bottom of the ship. The two rows of recesses are shghtly over 6 ft apart, measured to their inboard edges. Recesses in later designs of dredges are similar, indicated by the hnes drawings of

SNAME RD Technical

sheet

103 and of

Memorandum

The whole the bottom

ETT

Stevens

100.

subject of hopper-door recesses in is

discussed in Chap. VIII, pages

213-250, of the Scheffauer reference hsted near the end of this section. Several conical

valves of a

new type

dump

are illustrated in this refer-

They practically ehminate the large hopperdoor recesses and the hydrodynamic resistance generated by them. Most self-propelled suction dredges, with their limited draft and large underwater volume, have large B/H ratios. That of the 247-ft hopper dredge ence.

described in

SNAME RD

sheet 103

is

3.08, at

load draft. For other vessels of this type it is 4.5 or more. At reduced draft, as when returning

from the dumping ground to the dredging the

B/H

This type of hull definitely

calls for

a twin- or

[SNAME,

1947, pp. 97-169]. easier to shape a twin-screw stern of

multiple-skeg stern It is

area,

ratios are considerably larger.

much beam and

small draft with double skegs than with a normal form. Further, there is every reason to anticipate a better flow around the twin skegs, although the resistance may suffer because of the increased wetted area. Certainly it is far simpler to hang twin rudders abaft twin skegs carrying propellers than to mount them under a normal-form stern of generally V-shape. As an indication of the percentage of time during which a self-propelled seagoing suction dredge is large

running to and from the dumping grounds, T. M. Cornbrooks shows that for a working period of about 7.5 days, during which time the dredge made 44 complete round trips, it was outward

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.16

bound to the dumping ground and inward bound traveUng like a normal about 31 per cent of the total time

to the dredging area, vessel, for

[SNAME,

1908, p. 249].

Since the

dumping ground must

of necessity

(12) Scheffauer,

Dredge;

be some deepwater area where the refuse will not interfere with navigation in the future, and since

"The Hopper Development and Operation," Engineers, U.S. Army, Washington,

C.

F.

(editor-in-chief),

Its History,

Off. of Chief of

Gov't. Print.

may

be rather well out to sea, self-propelled dredges must possess a reasonable amount of freeboard, sheer, and reserve buoyancy. A brief list of references, limited almost exclusively to seagoing, self-propelled dredges of the it

779

There are two 27.5-inch diameter suction pipes, one on each side, with swivel joints below the waterline. The pipes are 72 ft long and the vessel can dredge in water up to 50 ft deep. There are twin spade rudders and 9 hopper doors under the bottom.

Off., 1954.

An

extensive bibliography

given on pages 375-376 of this reference. The following is taken from the Preface on page ix, as

is

applying to this book: "It

is

not a manual by the use of which a novice

may

design a dredge, but rather a guide for the use of those who may be engaged in the construction and

hopper type, follows:

operation of plant of this character." (1)

(2)

(3)

Robinson, A. W., "Hydraulic Dredging," Cassier's Mag., Nov 1896, pp. 37-47 Cornbrooks, T. M., "Sea-Going Suction Dredges," SNAME, 1908, pp. 247-249 and Pis. 140-146

"The United

States Suction

American,

Scientific

494. This vessel

Jun

1

Dredge New Orleans," and p.

1912, front cover

had a single centerline drag pipe, on the scoop to help break up the

(4)

with water jets mud in the river bed. Styer, W. D., "Hydraulic Seagoing Hopper Dredges,"

(5)

Vaughn, H.

SNAME,

(6)

(7)

1924, pp. 28-48 B., Jr.,

"Seagoing Hydraulic Hopper 1941, pp. 262-299

Dredges," SNAME, Barakovsky, V., "The Dredgers," Schip en Werf, 10 and 24 Jan 1947 Freeh, F. F., "Design and Construction of Seagoing Hopper Dredges with Special Reference to Essayms," SNAME, Phila. Sect., 27 Apr 1949. Abstracted in the publication Motorship, New York, issue of Sep 1949, beginning on p. 38. See

MESR, Dec. 1952, pp. Mar 1954, pp. 48-57.

also

74-75,

and Mar.

Eng'g., (8)

McCarthy, E. W., "Hopper Dredge Barranquilla) for Government of Naut. Gaz.,

Mar

(Ciudad de Colombia,"

1950, pp. 14-15, 37. This

is

a

twin-screw dredge having a hopper capacity of 1,000 cu yd, an overall length of 240.5 ft and a

speed of 11 (9)

The

kt.

general

features

of

six

shallow-water

hopper-type

self-

dredges

are

described and illustrated in Diesel Times,

Apr

twin-screw

propelled 1951. This

article also describes the seagoing, self-

propelled, twin-screw hopper dredge Pacific, built in 1937, as well as the self-propelled

hopper dredge

There

(ID)

1951-1952, Vol. 95, Part 6, pp. 438-484, esp. pp. 463-474; also Part 7, pp. 485-491. Paper is con-

cerned only with self-propelled dredges. There are

no diagrams

of

hopper recesses or doors but there them on pp. 472, 483.

are discussions of (11)

French suction dredger Charles

May

LoA 309 Lbp 291

Be

Belleville,

MENA,

1952, p. 221

49.25

D

ft

H 13.83 ft in fresh water

19.75 ft

Hopper capacity

is

35,310

ft^

a constant

Box-Shaped

demand

Vessels.

which has the customary barge,

hghter, or scow but which

for a craft

is

able to

move

itself

from place to place without the services of a tug. Very often an equally important requirement is that the craft be simple, cheaply or rapidly built, or both, with hull boundaries having easy curva-

ture or else none at

all.

The ultimate in this respect

was probably reached by the so-called "rhino ferries" of World War II, built up in the field by bolting together standard steel boxes having the form of rectangular parallelepipeds.

The requirements

for

this

group treat the

being definitely secondary to the load-carrying characteristics, yet they are of httle practical use unless they can be seK-propelled. The answer to this problem is to propulsion

characteristics

as

flat sides and by outboard drives he below the bottom

accept the square corners and the to push or pull them, or both,

with propellers whose discs plane of the box. Swinging these propellers about a vertical axis solves the problem of steering, backing, sidUng, and maneuvering, all at once. Lifting them up about a horizontal axis solves the shallow-water, repair, and maintenance problem. The complete power plants, in packaged units

that for

float, are inserted in

them

niches or slots provided

box assemblies, or are attached any convenient manner.

in the

temporarily in

A power unit with a rotating-blade propeller might be used to propel a box-shaped craft, except that the vertical blades projecting below the plane of the bottom of the box would be vulnerable in shallow water. 76.16 Self-Propelled Floating

Drydocks. A drydock which can propel itself in the open sea at a reasonable speed when nominally unloaded, which can maneuver after a fashion, floating

ft

ft

is

the carrying capacity of

Sandpiper, built in Montreal and used on the

Lake Maracaibo Bar in Venezuela. Low, D. W., "Considering Dredgmg Craft," lESS,

Self-Propelled

76.15

HVDRODVNAAriCS

780

Fig. 76.J Official

U.

propellers,

S. if

Aerial View of U.

S.

TN SHIP

Navy

ARD

DESIGN

Type Floating Drydock

Navy photograph. The

gate which closes the stern is hinged horizontally along its lower edge. Screw fitted for self-propulsion, would be close to the extreme stern and just inboard of the outside of the dock.

and which can control itself when hove to heavy weather, has all the principal attributes a ship, and is so classified here. Basically,

in

cargo, with the disadvantage that the "cargo"

of

one package, extending below the water as well as above it. The self-propelled floating drydock also may be considered as a partly submersible ship with a large, U-shaped,

it

resembles a single-ended car ferry or a "seatrain" in its ability to

accommodate a bulky, heavy

generally

all

in

is

DESIGN OF SPliCIAL PURPOSE CRAFT

Sec. 76.17

781

open docking recess and a tail gate, or as a singlesection floating drydock with a ship bow and the

intended for the propellers of

same

the after outer corners of the stern,

tail gate.

The question

whether any floating drydock should be self-propelled is not at issue here. These notes are included for the benefit of a designer who may be called upon to lay out a self-propelled craft of this type, whatever its service or purpose may be. As a rule, he will be called upon to work on a craft which is not suitable for self-propulsion but must be made so

by

of

his resourcefulness or ingenuity.

An

early form of self-propelled floating drydock with Ruthven hydraulic propulsion was illustrated by Vice-Admiral Sir E. Belcher many years ago [INA, 1870, pp. 197-211 and Fig. 2, PI.

I].

It

seemed

logical

at that time to use

hydraulic jet propulsion since the dock had to be

equipped with pumps in any case to handle the water in its various compartments. A similar type of drydock, proposed by G. B. Rennie [INA, 1883, Vol. XXIV, p. 225ff] was intended to be propelled by six hydrauhc jets on each side, indicated on Plate

A

XV

reproduced in Fig.

forward of the

A

The

positions originally

ARD

1

were under slightly

tail gate.

not-too-blunt bow, illustrated in the Bureau

of Ships Journal photograph,

drydock or any craft of

is

a necessity if a shape is to

this general

be self-propelled at a reasonable speed without an inordinately large propelling power. Assuming a 420-ft waterline length a nd a n upper limit of speed of 10 kt, T, is 10/V420 = 0.488, F„ = about 0.145. From Fig. 66.1 the optimum waterline entrance slope is 32 deg but since the graph relatively steep in this region the slope could be raised to 40 deg or more if other more important

is

requirements forced this change.

A floating drydock requires considerably more bed clearance, or water under it, than the ships being docked. Since the dock is often moored close inshore, generally in areas not useful for operating ships, the overall draft must be kept to a minimum. This complicates the problem of where to put the propulsion devices while retaining a reasonable

degree of efficiency in their operation.

of the reference.

dock with one screw propeller outboard at each after corner was proposed by L. Clark in a somewhat later paper, supplemented by some comments of W. Froude [INA, 1877, Vol. XVIII, PL XIV, Figs. 2 and 3; also discussion on p. 196]. Froude reminded the author (Clark)

A

similar

multiple-arch type of stern, similar to the

single-arch stern described in Sec. 67.16, appears to

offer

the best promise

of

good propulsive

efficiency while maintaining the stiffness necessary

any floating drydock. Such a stern would have a profile corresponding

in the floor structure of

approximately to that for the single-arch

that:

stern "If

76..I.

you put a screw

run at

all,

any the screw becomes

close to a ship, cut off without

the propulsive effect of

pellers could be large

floating

drydock

(ARD

1),

cap-

handUng a destroyer of the middle 1930's, was designed by the Bureau of Yards and Docks of the Navy Department and built for the U. S. Navy in 1934. This dock was designed to accommodate propelling machinery and propellers for self-propulsion but was never so fitted. It had an overall length of 393 ft, a beam of 60 ft, and a depth of 33 ft, with a maximum draft when flooded of 30 ft. Bow and stern views of this dock were published at that time and later [SBSR, 23 Aug 1934, p. 200; Motorship, New York, Apr 1950, p. 27; Mar. Eng'g., Apr 1954, p. 110, shows able of

a stern view of the larger

ARD

8,

Lqa = 486

ft,

B = 72 ft]. A bow aerial

view of an ARD floating dock appears on the front cover of Bureau of Ships

Journal for April 1953.

A

stern aerial view

is

ABC

M

and 67.0. The procompared to the fight draft,

in Figs. 67.

as their upper tips could extend above the

absolutely nil."

A ship-shaped,

shown

WL.

They would be protected excellently all around, and they could even be made accessible for inspection and repairs by flooding the forward dock tanks. The multiple skegs should give excellent

stability

of

route,

and the multiple

rudders abaft them equally good maneuvering characteristics.

The

design of a ship-shaped floating drydock embodying skegs or rudders or

for towing only,

both at the stern, is discussed in Part 5 of Volume III, under the design of towed craft. for Temporary Bows of 76.17 Design Emergency Running and Towing. A design

problem akin to that of shaping a bow for a self-propelled floating drydock is laying out a temporary bow on a ship which has lost its own bow. Towing or pushing a vessel terminated at its forward end only by a flat watertight bulkhead is

an extremely precarious operation.

A

danger-

HYDRODYNAMICS

782

IN SHIP DESIGN

Sec. 76.18

ously heavy load can be built up on the immersed

sketched at 4 in Fig. 76. K, should suffice for

area of such a bulkhead by dynamic action of the water, even at low speeds. Indeed, a vessel with

reasonably rapid travel. If head seas are likely

only a portion of its bow caved in, but with a hole by which the dynamic pressure at that point

any amount that

is

transmitted to the boundaries of the flooded

portion, can develop high

dynamic loads on those

boundaries, indicated by diagram

1

of Fig. 76. K.

A vessel damaged in this manner can and should be towed with the undamaged end foremost, even to the extent of towing stern first, without benefit of the steering effect of a rudder at the trailing end. A photograph of a large tanker without a bow, being towed in this manner, is reproduced in Shipbuilding and Shipping Record [5

Jun 1947,

propeller

is

p. 559].

Under these conditions the

permitted to free-wheel,

if

practicable.

A

combination of square leading and trailing ends, such as might be encountered on a transomstern destroyer with its bow broken off, may result in some yawing or weaving during a towing operation. However, if the damaged vessel is towed with its good end foremost, the holding bulkhead should remain intact and the ship

should stay afloat. If the

bow

is

damaged

or missing,

and

it is

home under its own bow is found adequate.

desired to bring the vessel

power, a rather blunt false

Straight sides and an entrance slope of 45 deg.

to be encountered, a rake to the false

bow

sides

found practicable up to 15 deg or so pays for itself in easing the impact loads on the flat surfaces. Because of the flat sides on the temporary bow, it can be expected that the wavegoing loads on the hull, at reduced speed, will be at least as large as on the undamaged vessel at normal speed. With a well-constructed false bow of the type illustrated in diagrams 3 and 4 of Fig. 76. K and in reasonably smooth water, it should be possible to make at least one-third the speed to be expected with the undamaged vessel. In fact, vessels have made ocean crossings under their own power with false bows very much blunter than the one depicted in diagrams 3 and 4 of the figure. One such ship was the U.S.S. Selfridge (DD 357), which had its bow blown off in the South Pacific during World War II. Fig. 76. L shows the vessel in a floating dry dock with the false bow completed. A photograph of the vessel under way in this condition is reproduced in the Bureau of Ships (U. S. Navy Department) Journal for May 1953, page 12. A varia76.18 Floats for Pontoon Bridges. tion of the box-shaped, load-carrjdng barge or fighter is the moored float intended to support is

—

Hydrostatic Pressure

Bulkhead is Auqmented b-; B'ynomic Pressure +Ap Developed at Blunt Bow on

Biacjrame

1,2,

IrrtQct

and 4 Represent Plan Views Waterline

at About the Surfoce

Any Rake up to 15

of

deo

IS

Probably

Benefit in

RouQh Woter

Fig. 76.

K

Schematic Design for Tempor-vry Bows of Damaged Vessels

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 16.19

783

mooring gear. In the case of rivers at flood stage, the pontoon may lie at an angle to the current even though when moored at a normal stage it may have been in line with the current. For floats or pontoons which are open and undecked, adapted for nesting inside each other in transit, adequate freeboard possesses an importance only slightly less than that of low drag. If the floats are moored in relatively shallow water, the bow-wave crests are augmented. of the

Furthermore, when floats are placed close to each other along the bridge, the water flows at augmented speed between them, with a consequent dropping of the water level there. Even though

wave crests at bow and stern may be high, each float drops bodily in the water, as does the simple ship in diagram 1 of Fig. 29. B.

the

Yacht-Design Requirements; Some Sailing- Yacht Design. Yachts, defined as craft intended for pleasure, recreational, competitive, or ceremonial purposes only, may be classified first by size: 76.19

Aspects

Fig. 76.L

Temporary Bow Fitted to U.

(DD

S. S. Selfridge

357)

photograph. The waterhne slopes of bow are very large, much larger than are recommended for a craft required to make a transocean crossing under its own power.

Official

U.

S.

of

Navy

this particular

(1)

manner

100 or 125

Medium, over 50

ft in overall

proper but not exceeding 125 of

pontoons for temporary bridges. In general these pontoons must carry their loads in swift streams or rivers, on the surface of which wind waves of considerable height and magnitude are often formed. The problem here is not exactly comparable to that of a towed craft carrying the same weight at the same speed, equal to the velocity of the river current, because the pontoon may not be entirely free to trim. Furthermore, the pontoon is usually anchored by a cable or chain which leads downward at a considerable angle and exerts an appreciable downward component of force at the bow. For almost any river, the current velocity at center exceeds the mean current speed, because of the retarded flow in the boundary layers along the sides and over the bed. In a

in

ft

overall

hydrodynamic design purposes these

are essentially displacement-type ships. (2)

large fixed weights over water, in the

Large, exceeding

length. For

(3)

Small, under 50

By be

ft

length of hull

ft

m overall length

of

huh.

type and method of propulsion they

may

classified as:

(a)

Displacement-type,

only,

mcluding water

signed (b)

by the

propulsion

These are usually de-

rules applying to larger vessels.

Semi-planing

mechanical

type,

only, including airscrews (c)

mechanical

jets.

and water

propulsion

jets

Planing type, mechanical propulsion only,

including airscrews, water

jets,

gas

jets, rockets,

and the hke (d) Sailing

yachts

with

auxiliary

mechanical

propulsion (e)

Sailing yachts without mechanical power.

the

wavemaking drag may exceed the friction drag. Since the downstream pull on each pontoon varies as the second power at least of the current velocity, and possibly as some higher power, the increase of current velocity from any

The

design notes in Chaps. 66 through 75 of

this part should suffice for the hull

and propdev

medium yachts with The semi-planing and

swift river the

design of the large and

source whatever

is

mechanical propulsion. planing craft of groups (b) and (c) preceding are classed as motorboats, for which design procedures and rules are set down in Chap. 77. Some features of sailing-yacht design are discussed subsequently

The

is

in this section.

it

not to be regarded hghtly. an important factor because the type, strength, and arrangement

overall drag

affects

Leaving aside for the moment the

sailing

yacht

HYDRODYNAMICS

784

which is intended purely for racing, certain general and detail requirements apply to all yachts:

Appearance

(i)

principal one.

is

usually a major item,

To be

if not the a true yacht, a craft must

look like a pleasure rather than a utihty craft. Styles, tastes, and fashions vary with individuals and change with time. No one but the owner can say whether he wants a 3-kt houseboat to look like a Roman chariot, or whether he wants a 40-kt speedboat to look Uke an airplane, (ii) Accommodations for engaging in manifold activities, even on a small craft. At first sight, this and the preceding item appear far removed from hydrodynamics but they involve freeboard, sheer, air and wind resistance of the hull and upper works, and other features having to do with maneuveiing and wavegoing. (iii) Speed in smooth water, coupled with endurance and fuel capacity at some specified speed (iv) Abihty to travel safely, and not too uncomfortably in waves, to ride out storms when hove to, and to negotiate passages through inlets and rivers with currents, tide rips, and choppy water (v) Useful load-carrying capacity, generally on a

usable-volume

rather

This item commodations. basis.

(vi)

is

than

a

weight-carrying

closely related to that of ac-

Maneuverability, like other items to follow,

by the prospective owner but can never be overlooked by the naval archiis

usually not specified

This includes the ability to handle the craft, usually with a very large part of its volume out of water, in high winds blowing from un-

IN SHIP DESIGN

(x) As is customary for all other sets of requirements in the book, items not related to hydrodjmamics are omitted.

The renowned yacht designer and builder Nat G. Herreshoff laid great emphasis on quiet smooth running in all his craft, and devoted much time and attention to achieving this end. WhUe of the noise made by mechanically propelled

most craft

comes from the main and auxiliary machinof the vibration and rough running well have a hydrodynamic origin. No specific

much

ery,

may

design rules are given here for insuring quiet

smooth operation

in a yacht. It is pointed out only that these features are by no means negUgible

and relaxa-

in a craft intended for pleasure, rest, tion.

A

sailing

yacht usually receives

makes

driving force and

its

the designer, and

it is

its

greatest

when

highest speed

running at a large angle of heel. It

is

the aim of

often possible, so to shape

the hull as greatly to increase

its effective

length

in the heeled position. This in turn, acts to decrease

the speed-length or Taylor quotient or the Froude

number and

make the

to

as the propelling thrust

yachts,

when driven

of

to

1.2

is

more easily Most sailing

vessel drive

increased.

hard, reach Taylor quotients correspondmg to a Velox wave

1.3,

length (from bow-wave crest to

first crest

follow-

somewhat greater than the waterline length

ing)

mth

at rest,

To

tect.

zero heel.

some

illustrate

of these features. Fig. 76.

M

a body plan of a one-design saihng yacht,

is

having a waterline length of 32.0 nished by Olin

favorable directions.

Sec. 76.19

J.

Stephens,

II,

ft,

kindly fur-

of the firm of

Practically any yacht which expects to run open water should have adequate metacentric height for a large range of stabihty. For the sailing yacht there should be a positive righting moment at 80 deg angle of heel. This means a reasonable width of deck on the lee side, high watertight coamings, self-baihng cockpits, and no internal ballast which can shift when rolling or when heeled to the extreme angle, (vii)

in

(viii)

A

distribution of weights as nearly amid-

ships as possible, to keep

down

the polar

moment

Actually,

ot

30

when He

of inertia of the

whole craft about the pitching axis

For the saihng yacht, the maximum practicable performance as to speed, freedom from leeway, and steering with the craft running at an angle of heel, when the underwater body is definitely and drastically asymmetric about any (ix)

longitudinal axis

Wo»e

the

the Yocht

de(),

Trovelinq

Inclined

Woterlii

for Heel of

is

So Post that

30

Profile Alters

ot which the DisplQ

the Surface Woterplone

deg.

Volume Equals That

Apprecioblij

1

Upriijht Conditic

Constructic

Sections

Fig.

76.M

Body Plan op Sailing Yacht with Inclined Waterline

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.19

Spai'kman and "plan there is

Stephens,

Inc.

On

this

785

body

drawn an inclined waterUne for a when the main deck edge touches

heel of 30 deg,

the water on the low side, for the condition in

which the inclined volume volume V.

V

equals the upright

Diagram 2 of Fig. 76. N gives a half-waterline shape with the yacht upright; diagram 1 shows the whole waterline shape in the inclined position just described. This shape, corresponding to the intersection of the hull with the level of the undisturbed water at rest, is definitely unsymmetric, even about a diagonal line

drawn from

the stem to the extreme after end of the inclined

Waterline Offsets Are Measured from Intersection of Plane of

Undisturbed

401

S>

Shape

WL length.

case only, with the water surface undisturbed

by any waves whatever. The dynamic situation when sailing is far different, even in smooth water. At their top speeds these craft generate a very pronounced Velox-wave system, with high crests at bow and stern and a deep trough amidships. The immersed length of the inclined waterline is then considerably longer than that shown in diagram 1 of Fig. 76.N, and its shape is probably much different. There is a similar difference between the at-rest inchned section-area curve and the corresponding yl-curve when underway. This difference may be greater than between the upright and inclined A-curves of diagrams 4

and 3, respectively, of Fig. 76.N. While considerable research has been and is being carried on relative to the overall resistance and propulsion aspects of saUing-yacht design and performance, this should be extended to cover the wave profiles and lines of floAV at various angles of heel. Put in another way, attention should be focused as much on the flow patterns around the hull when underway as on its form coefficients, section-area curves, and other parameters. All too often the latter apply only to the upright condition, with the vessel at rest. In the few modern books on saUing-yacht design there is little

discussion of the hull characteristics in

the inclined condition [Skene, N. L., "Elements of

Yacht Design," 5th

Sec. 29.8 mentions a

Allen

covering

ed., 1944, Fig. 45, p. 75].

much

older paper

some phases

of

this

by R. C. subject

-13

Station^

The Waterline Lenqth

m

is the Station Lenqth the Upriqht Position. For the 30-de<j Heel Position the Reference Lenqth L3 is olso theL^L

1.0

analysis apphes to the static

Desiqne

Yocht Upriqht

1.0

WL, when measured parallel to the ship axis. If measured along the diagonal broken line in diagram 1 of Fig. 76.N it is about 1.012 times The foregomg

of

Waterline with

WL has very nearly the same length as the upright

the upright

of Yocht

3j 2.0

waterline. For this particular yacht, the inchned

Woter Surface and Plane of Symmetry

HYDRODYNAMICS

786

to the center of resistance of the underwater hull.

Manj^ saUing yachts have transom

sterns.

these craft, where the propulsive power

is

On

limited

to that which can be derived from the wind, the

shape and position of the transom may be of greater relative importance than on a high-speed motor yacht or a destroyer. At slow speeds the transom must definitely be kept out of water, to avoid the separation drag abaft it. At higher speeds it may be possible to accept the added drag, especially if some of the deflection drag behind the bow-wave crest can thereby be eliminated.

ratio

In

its

appear in the design of sailing them may be mentioned the

ratios

Among

yachts.

ratio.

new

and the

sail-area

to

wetted-surface

simplest terms, the ballast ratio

ratio of the total weight of ballast,

is

the

both inside and

outside (portable and fixed in the keel), to the total scale weight of the yacht. It ranges

from

for a

same order

magnitude

of

ratios against load

worked up instance, an

water

fine

excellent

formance to windward

made-good

divided

is

basis is

obtained

angles,

characteristics

Tank

been assumed by some yacht

due largely to friction, so that speed and actual wetted area are the major factors. They are indeed factors but it is doubtful that they are the major ones. They are in the semi-planing range

is

certainly not the only factors.

D. Philhps-Birt presents a discussion which, though appUed to a sail-and-power craft called a motor sailer, embodies a number of useful comments on saihng-yacht design in general [Rudder,

As an

May 1955, pp. 12-15, 46-55]. indication of the type of unpublished

data available on saihng-yacht design, and of those to be expected in the not distant future, the followmg is quoted from an article by A. B. Murray of the Experimental Towing Tank, Stevens Institute of Technology [Yachting, Dec 1946, pp. 62, 110]:

"However, a system of correlation has been worked up which provides a useful yardstick of performance for sailing yachts of all sizes. Upright resistance, speed-made-good, leeway angle, stability, and balance are put into coefficient forms which eliminate the effect of differences in length

close-hauled speed-

few

fixed values of

have been prepared

for a large

number of means

new design,

besides indicating performance

trends.

"Another step was taken when a method was set up to compare three important characteristics on the basis of hull alone without effect of sails or center of gravity .

position. This

compares hull resistance, leeway angles and

longitudinal center of lateral resistance for three heel

and

angles at a standard speed tions of boat length.

of the

sail

By

stability

which are func-

separating hull characteristics

power, a more

critical analysis

may

bo

made

problem."

76.20

collect

Bibliography on Sailing-Yacht While no attempt has been made to all the published and unpublished referBrief

ences relating to the design of sailing yachts the

may

find the following brief bibliography

useful and interesting from a historical

and general

Harvey, J., "On the Construction and Building of Yachts," INA, 1878, Vol. 19, pp. 150-158 Kemp, Dixon, "A Manual of Yacht and Boat Sail(2) ing," Cox, London, 3rd ed., 1882 Kemp, Dixon, "Fifty Years of Yacht Building," (3) INA, 1887, Vol. 28, pp. 232-246 Nixon, L., "Yachts in America and England," (4) SNAME, 1894, pp. 261-277 Kemp, Dixon, "Yacht Architecture: A Treatise on (5) the Laws which Govern the Resistance of Bodies Moving in Water; Propulsion bj' Steam and Sail; Yacht Designing; and Yacht Building," Horace Cox, London, 3rd ed., 1897. This is a veritable treatise on naval architecture in most of its phases. Crane, C. H., "Some Thoughts on the Design of (6) Modern Steam Yachts," SNAME, 1903, pp. 57-65 Erismann, M. C, "The Effect of the Universal Rule (7) in Recent Yachts," SNAME, 1906, pp. 223-241 Warner, E. P., and Ober, S., "The Aerodynamics of (8) Yacht Sails," SNAME, 1925, pp. 207-232 and Pis. 133-146 Fox, Uffa, "Sailing, Seamanship, and Yacht Con(9) struction," 1934 (10) Baier, L. A., INA, 1934, pp. 107-108. Gives a brief discussion of form variations for sailing yachts. (11) Stephens, W. P., "Yacht Measurement," SNAME, 1935, pp. 7-42 (1)

designers that the hull resistance of a sailboat

if

for a

tested boats. These charts give immediately a

information standpoint:

It has probably

characteristics. For on which to compare per-

by \/Z

factor in the design of purely displacement types.

sailboats

chart

By similar methods, stability, leeway and balance may be compared. Charts of all these

reader

small

increased. Plots of the

other performance

for

which run fast enough to generate large dynamic lifts and which approach planing speeds, although it is also a to

is

make a convenient

true wind speed.

Design.

primarily

resulting ratios are of the

for comparison of hull resistance. Similar coefficients are

but the scheme remains the same. saU-area to wetted-surface ratio appUes

The

for all lengths of boats, tending

to be smaller as the boat length

from the

The

resistances of the full size boat

few selected fixed speed-length ratios are divided by

the displacement in tons.

upon the beam and other factors. There are rather elaborate ways of defining ballast, by modern racmg rules, 0.25 to 0.35 or more, depending

Sec. 76.20

and displacement. Upright

for evaluating a

Several

ballast

IN SHIP DESIGN

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.21 (12) Burgess,

C. P.,

SNAME,

"The America's Cup Defenders,"

1935, pp. 43-70

B., "On the Building of a Yacht," Yachting, Mar, Apr, May 1935 (14) Davidson, K. S. M., "Some Experimental Studies of 'the Sailing Yacht," SNAME, 1936, Vol. 44, pp. 288-344. There is a bibliography on pp. 303-

H.

(13) Nevins,

(33)

"Thoughts on Yachts and Yachting,"

Uffa,

1939 (17)

(18)

Stephens, W. P., "Traditions and Memories of American Yachting," 1942 Owen, G., "Outstanding New England Types of Fishing Boats, Whalers, and Yachts," SNAME,

HT,

1943, pp. 151-164

N.

(23)

L.,

New

Mead,

investigated by tests of models. "Symposium on Sailing Yacht Design," isfew

Engl.

Sect.,

May

18

SNAME, SNAME,

1948; see

1948, p. 90

C, BNA,

(24) Barnaby, K.

1954,

2nd

ed., pp.

244-256,

Arts. 165-169 as follows: (165) Sail Propulsion (166)

The Gimcrack

New

Norton,

York, 1951 (27) Barkla, H. M., "High-Speed Saihng," INA, 1951, Vol. 93, pp. 235-257. This is one of the few papers in

Testing,"

INA,

11

and Ware, B.

a

"Yacht

Oct 1956

Beam That Makes

Asymmetric

76.21

Forms.

Hull

Although

which are buUt to travel upright, a marine architect sets out to design a vessel which has an underwater hull of different breadth and shape on the port and rare, for ships

they do

exist.

When

starboard sides of the construction centerplane,

he wants to be sure that his unusual creation will be acceptable and serviceable. Among the asymmetric-hull craft which have performed exceedingly well, not only for years but for centuries, there may be mentioned: (a) The saUuig yacht and the sailing vessel. Although almost invariably designed to have symmetry about the centerplane when at rest, they always present an asymmetric form to the water when heeled and propelled at any apprecia-

The

by the wind.

These employ asymmetric hulls to eliminate centerboards, leeboards, and similar devices, as described in Sec. sailing canoes of Oceania.

They make use them the required degree of

24.21 ,and illustrated in Fig. 24. M. of outriggers to give

metacentric stability under (c)

The gondolas

sail.

of the canals

The

individual

hulls

usually asymmetric about their

basis.

catamarans

of

(d)

of

literature which tackles the yacht design on a fundamental, analytic

and lagoons

of

Venice, described briefly in Sec. 24.21

technical

the

problem

E.,

the Boat Go," Yachting, Jan 1957, pp. 146-147, 285 (36) Crane, C. H., "What Limits Speed Under Sail?" Yachting, Mar 1957, pp. 53-56, 100, 102. (35) Scheel, H., "It's

(b)

and "Lead" (169) Sail Area and Power to Carry Sail Barnaby, K. C, "Progress in Marine Propulsion, 1910-1950," INA, 1950, pp. J14-J15 Chapelle, H. I., "American Small Saihng Craft; Their Design, Development and Construction," (168) Centre of Effort

(26)

Allan, J. F., Doust, D. J.,

able speed

Sail Coefficients

(167) Sail Plans

(25)

(34)

practical applications of the asymmetric hull are

"Elements of Yacht Design," DoddYork, 1944 (20) Herreshoff, L. F., "The Common Sense of Yacht Design," The Rudder Publishing Co., New York, 1945. In two volumes. (21) Aupetit, A., "Essais de Yachts (Tests on Yachts)," ATMA, Jun 1946, Vol. 45, pp. 433-452 (22) Murray, A. B., "Towing Tank Developments," Yachting, Dec 1946, pp. 60-62, 110, 112. Abstracted in SBSR, 9 Jan 1947, p. 37. Devotes a considerable amount of discussion to sailing yacht design problems which have been or should be (19) Skene,

is

list of

Davidson, K. S. M., "Model Tests of Sailing Yachts," The Rudder, Aug 1937, pp. 14-15, 56, 58

(16) Fo.x,

1955 issue, pp. 66-70, 112, 114. Davidson, K. S. M., "The Mechanics of Sailing Ships and Yachts," Surveys in Mechanics, edited by G. K. Batchelor and R. M. Davies, Cambridge University Press, 1956, pp. 431-475. There 17 references on p. 475.

304, 312. (15)

787

Yachting, pp. 58-61, 94-98. Part II appears in the Mar 1955 issue, pp. 71-75, and Part III in the Apr

own

are

construction

centerlines.

Bay Saihng

(28)

Douty,

(29)

Morwood, John, "Saihng Aerodynamics," Morwood,

(30)

Denes, Gabor, "Yacht Research," The Motor Boat and Yachting, Dec 1954, pp. 524-525

J.

Vessels,"

F.,

"History of Chesapeake

SNAME,

Ches. Sect., 29

Nov

1951

Several

other

cases

present

themselves

in

practice:

123, Cheriton Rd., Folkestone, Kent, 1953

(31)

Yacht Research Council

(32)

of

Great Britain. Photo-

work shown in The Illustrated London News, 4 Dec 1954, p. 1009. Chapelle, H. I., "The Search for Speed under Sail: An Outhne of the Development of Yacht Design in America Until the 20th Century," a series of several articles beginning in the Feb 1955 issue of graphs

of

experimental

(e)

The

long, slender ship

which becomes shghtly

bent due to collision or other major damage. When the expense of straightenmg it appears exorbitant, the marine architect may be called upon for an opinion as to whether it really needs straightening or not. (f)

Ships to ferry, to tend, or to house operating

aircraft,

such as airplane tenders and aircraft

HYDRODYNAMICS

IN SHIP DESfGN

Sec. 76.22

which the various mstallations and

the pressure resistance are exerted in a vertical

the weights can not be balanced transversely (g) Ships for special operations which have

longitudinal plane through the center of buoyancy,

elaborate and expensive apparatus installed on

propelling thrust

one side only.

centerhne, there

carriers,

in

which appears reasonable, but that the resultant is

exerted along the construction

a constant

is

moment due

to

these forces alone which acts to swing the ship

asymmetry designed into a measured conveniently by the follo^ving:

The degree is

of

hull

(i) The port and starboard partial beams, measured in the same way as for the half-beam on a normal symmetrical vessel (ii) The percentage of the maximum beam by which the center of buoyancy CB is shifted from its normal centerplane position. This is measured by the transverse distance between the CB and a

vertical longitudinal plane through the construc-

tion centerhne, as

compared to the maximum

beam. (ni)

The percentage

volume which

is

of

shifted

the total displacement

from one side

of the hull

toward the wide side. Unless the length-beam ratio is less than 5 or 6, this constant turning moment is fikely to be of small consequence although it will always be of the same sign. It is wise to augment the steering control for a ship of this type over that provided for a normal design. The augment may equal but need not exceed the percentage by which the center of

buoyancy

is offset,

described in (u) preceding.

Design Problems in Multiple-Hulled It sometimes happens that a large beam Craft. can be accepted for the purpose of carrying objects which are bulky and awkward to handle but 76.22

relatively light in weight. It

may

be possible to

to the other, relative to the vertical longitudinal

improve the metacentric

plane through the construction centerline. For example, if 53.7 per cent of the underwater volume lies on one side of that plane and 46.3 per cent

bution in a craft by utilizing two or more widely

on the other side, the percentage of asymmetry in volume is (53.7 — 46.3)/2 or 3.7 per cent.

The numerous form ratios of various areas

coefficients

based upon

and volumes to the areas

same manner asymmetric as for the symmetric ship. A few notes may be set down for the design of asjrmmetric hulls which are to be built that way, parallelepipeds are calculated in the for the

based upon the usual demand for reasonable if not minimum power, maximum speed, and acceptable maneuverability of the asymmetric vessel, correspondmg to those for one that is symmetrical: (1)

The

CG

is

to be found in the

same

vertical

plane as the CB, offset from the construction centerplane toward the wide side, with the vessel upright and carrying the designed load (2) The CB and the CG should, whenever practicable,

have essentially the same

offset for load

conditions fighter than the designed, to insure that the ship remains upright at all drafts and

trims (3)

spaced but narrow hulls instead of one wide hull. The term catamaran is in this book restricted to craft which have two hulls of approximately equal

Based upon a construction centerplane that

passes through the hull terminations at the bow and stern, the propulsion devices are usually, but

not necessarily mounted symmetrical to that plane (4) On the assumption that both the friction and

size.

An

have one main of

or volumes of the circumscribing rectangles or

stabfiity or load distri-

outrigger canoe

is

considered to

hull only; the outrigger

auxfiiary-displacement

device

is

a form

corresponding

float of a flying boat or having one main hull and one supplementary hull abreast on either side is known as a trimaran. The side hulls may be of approximately the same .size or they may be smaller

somewhat to the wing-tip seaplane.

A

craft

than the main hull. In view of the many possible uses for towed or self-propelled craft mth multiple hulls no attempt is made to set down their requirements here. The crux of a suitable design of water craft in

two separate hulls must move along by side, is the shaping of the region between the two hulls. Only rarely can the hulls be made sufficiently short and narrow, compared to which

easily, side

spread, that they may be considered as independent bodies, hydrodynamically speaking. If they are slim enough to produce relatively narrow velocity and pressure fields, they may still be long enough to cause interferences between theii'

the surface-wave patterns between the hulls, as shown in Fig. 76.0. The diverging crests of the inside Velox wave systems will meet each other

on or about the construction if there were a thin plate mounted vertically between the hulls in that plane.

and be

reflected

centerplane, just as

DESIGN OF SPECTAL-PURPOSF. CRAFT

Sec. 76.22 Huli

p-Extreme Beam

Beom-.

Outside Phrtiol

Beam

poorly handled

789

may

even capsize. This means that the burden of preventing leeway falls on the leeward hull. Like the flying proa or the sailing canoe of Oceania, described and illustrated sail. If

it

and Fig. 24.M, the leeward hull should therefore be flat (or nearly so) on the outside and cambered in planform on the inside. This means that whatever speeding up of water occurs in the venturi section between the two in Sec. 24.21

starboard

Construction Centerplane'"

Hull

Direction of Motion for Both

DioQrQms»-

/of

Ends

of

Reflected

^—

Crests

of the

of

Waves

Crests

of

-Diverqinq Waves

^..^a^rr7777777//////\'k////^77777Z7^;;^i:^

\

Starboard

Hull

|

Approximate. "xDirection '"

Rudder

of

Motion of End^\of

Crests of

Fig.

DiveroinQ ^-^ Waves

ajjd Design Sketches Catamarans

76.0

Definition

Thus instead

fob

of the inside crests of the Velo.x

system from the port hull traveling across toward the stern of the starboard hull they are reflected on the construction centerplane of the catamaran and travel back toward the stern of the port hull, whose bow genei'ated them. Considering the small projected area of each hull against which a stern-wave crest could push it is perhaps wise, if possible, to have this reflected crest just clear the stern.

Assuming

that,

as illustrated in Fig. lO.B, the crest Unes diverge

an angle

about 20 deg to the construction centerplane of each hull, Fig. 76.0 indicates that the spread between the hulls should be at at

of

the waterline length times the natural tangent of 20 deg, or about ^.Z^ALwl The waterline beam of each hull, port plus starboard, depends greatly upon the amount of weight that must be carried on a given length, least

and upon the permissible draft. It may vary from about O-OGLrt^ on a sailing catamaran designed to reach a Taylor quotient T, of 3 or 3.5, to 0.12LjfrL

,

0.l5LwL

,

or

more on a

craft for

more

utiUtarian purposes.

catamaran is sail-propelled, the lee hull immersed more deeply when underway than when at rest, and the weather hull less deeply. Despite the seemingly large spread between the hulls, the craft heels somewhat to leeward under If the

is

an advantage. It increases the magnitude —Ap's on the windward side of the lee hull, which rides deeper in the water than the windward hull. On the other hand, the clear space between hulls must not be too small, else a blocking effect takes place there. With a catamaran assembly of the type shown in Fig. 76.0, the clear space between them should be not less than 3 or 3.5 times the maximum waterline beam of each hull. If the catamaran is mechanically propelled the planforms of the hulls are apparently not too important provided the speed-length quotient T, is not too large. Each hull may be symmetrical about its own centerplane, or each may be flat on the inside, as best suits other features. Because of the ever-present difficulty of obtaining sufficient usable and protected volume within the hulls of a catamaran, these huUs may be flared rather sharply above the waterline, especially on their insides. Bracing the two hulls against twisting in waves is a structural problem but determining the loads and forces involved is one of hydrodynamics. Unfortunately no method has yet been devised hulls is

/\pproximate Direction of Motion

for calculating their values.

Catamaran

hulls with flat bottoms,

if

properly

shaped, can be reUed upon to produce some dynamic lift, as in a planing craft. However, the aspect ratio

bottom

is

usually too small to permit the

of such a hull to act as

an

efficient

planing

surface. It is sometimes reported that the "tunnel" formed by the inboard surfaces of two catamaran huUs and the under surface of a large, horizontal deck structure joining them has a special shape. It is intended that the blocking effect of the air trapped in this tunnel will provide a -f-Ap under the deck and lift the assembly partly out of the water. Something of this kind might take place at values of T^ = 5 or more, but even then it is

most uncertain. G. H. Duggan designed and built an unusual form of saihng yacht, the Dominion of 1898, in

HYDRODYNAMICS

790

IN SHIP DESIGN

Sec. 76.23

which two canoe-shaped hulls were combined with a shallow scow type of hull. A small body plan of this craft, accompanied by a photograph of it under sail, is published in Yachting [Dec

most cases have to back

for

distances out of or into their

slips.

1946, p. 72]. In this case, however, the designer

variety of needs

did not have to concern hmiself too air flow

much with

between the hulls because at

its

higher

speeds the craft sailed at a large angle of heel,

with only the leeward "canoe" in the water. Sec. 25.23 contains a number of references to catamarans and trimarans in the modern (1955) technical hterature. Older Uterature goes back at

Dixon Kemp's "A Manual of Yacht and Boat Sailing" of 1882 [Cox, London, 3rd ed.]. In Chap. XXVI of this book, pages 348-356, entitled "Double Boats," Kemp describes and least as far as

illustrates

a number of catamarans, including by N. G. Herreshoff in 1876 and the

several built

Grasemann and G. W. McLachlan mention two ships designed

years following. C.

P. for

relatively

The

long

latter are

definitely special-service vessels.

Because they are intended to it is difficult

fill

such a great

to formulate general

requirements for the hydrodynamic design of ferryboats. A few of these, covering their special features, follow.

For double-ended (1)

vessels:

maximum beam, and draft, contemplated shps Abihty to start and stop promptly, at large Limiting length,

for existing or (2)

values of acceleration and deceleration, for cutting

down

the running time, for maneuvering, and for

emergency stopping (3)

Excellent steering and maneuvering charac-

teristics.

Most

ferries are required to cross tidal

currents at large angles. Furthermore,

them

cross the

most

normal routes of water

of

traffic

English Channel service, each having twin hulls.

nearly at right angles.

The Castalia, built by the Thames Ironworks Company m 1874, had two half hulls with the inboard sides vertical. The Express, a more successful venture, buUt by Messrs. Andrew Leshe and Company at Hebburn-on-Tyne in 1878, had

Great metacentric stability because all the is above the main deck and it is well to hmit the fist when the vehicle loads are not symmetric or when the passengers all rush to one side. This happens usually when the vessel is

two complete

hulls

["Enghsh Channel Packet

Boats," Syren and Shipping Ltd., London, 1939]. C. J. Wickwire describes the 35-ft catamaran

designed and built by D. and A. Locke of Detroit,

based upon careful design studies supplemented by model tests [Lakeland Yachting, Jul 1953, pp. 28, 40-41]. The extreme beam is 12 ft; the individual hulls, flat on their outboard sides and

cambered on

beam

of 4.5

their inboard sides,

ft.

practice which

each have a

Certain notes relating to modern

may

be found useful in the design embodied in a paper by R. F. Turner entitled "Catamarans, Past, Present and Future" [SNAME, Pearl Harbor Sect., 13 Sep 1955; abstracted in SNAME Bull., Oct 1955, pp. of catamarans are

Requirements for and References on Ferryboats. While most double-ended vessels, whether self-propeUed or not, are intended for 76.23

the short-haul transportation of people, creatures, their use

is

not neces-

type of service. They are therefore considered here primarily as vessels which must operate equally well in either direction. There are, to be sure, many one-direction car and train ferries, running on longer routes, which load over the bow or stern and which in sarily restricted to this

carrying only part of

its full

load

[SNAME,

1926,

pp. 228-229]. (5)

Large

the abovewater body for in-

flare in

creasing the metacentric stabiUty as the load

displacement and the draft increase

Mar 1939, p. 109] (6) An unnecessarily height

is

large transverse metacentric

to be avoided because

the vessel to yield and to strikes the "racks" its slip

[MESR,

it

does not permit

roll readily

when

it

on either side when entering

[Stevens, E. A.,

SNAME,

1896, p. 100]

Large longitudinal metacentric stabihty, to prevent the ends from being depressed unduly when the weights are concentrated there, in loading or unloading [DuBosque, F. L., SNAME, (7)

1896, pp. 95-96]

31-32].

and objects as ferryboats,

(4)

useful load

Large deck overhangs, sponsons, and the because the useful load is one of volume rather than of weight. At the same time the overhangs must be kept clear of wind waves and the ship's own waves. (8)

like,

For single-ended (9)

No

excessive

vessels: flare

under the car-deck or

vehicle-deck level, to cause pounding and slam-

ming when wavegoing (10)

If

required to back into, or out of long

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.23

adequate steering ability when running in

slips,

either direction

run in the open

(11) If intended to

sea,

or enough protection for that deck,

I

off of

on

191

p.

particulars

at

both ends, to keep menacing quantities of water

and Prins

Helsingborg, Storebaell,

enough

freeboard at the open end(s) of the car or vehicle deck,

791

1908-1909, Vol. LII, pp. 180-193 and Pis. X-XIV. This paper describes and illustrates the ferries hsts

22 Danish

of

"A

(a)

Stevens, E. A.,

New York (b)

"Some Thoughts on the Design

Ferryboats,"

SNAME,

209 and Pis. 46, 57 DuBosque, F. L., "Speed Trials Ferryboat,"

SNAME,

and stern

(i)

HT, 1943, Fig. 6, p. 170. The Boston Harbor ferryboats

which has

and

174 ft with a hull beam of 40 ft

(j)

1902, pp. 15-21

and

Pis. 1-3.

Elect.

(k)

The

Name

L.

(1)

Slip,

Admty.

tons

Coeff.

per cent

Coeff.

Length,

Cincinnati

Netherlands

Edgewater

217 200 203 173

0.34 0.42 0.36 0.42

900 952 825 687

"The above data

16

18.5 18.5 14.5

154 133 144 173

SBSR, 14 Apr

—diameter

8 ft 10.03 ft 10.19 ft 26.4 square

stern

Projected area, each

forsok

(e)

Stevens,

boat Bremen," E. A., Propulsion,"

(f)

DuBosque,

SNAME,

F.

SNAME,

(p)

Motorship,

(q)

S. S.

Ferry Boat 1905, pp. 1-7 and Pis. 1-4

SNAME, L.,

"A

1906, pp. 7-29.

The

Ferry-boat,"

table on pp. 11-12

gives principal dimensions of ferryboat (g)

(t)

Hammonton.

Olsen, H. M., "Danish State Railway Ferries," lESS,

Apr

E.,

1943,

"Modeli-

(Model Experiments with 7, 1947. Summary in Enghsh. York, Aug 1950, pp. 15-29, 36-43 Farja

Aug

1950, pp. 33-35;

1952, pp. 42-45 sheets 27, 84, 100,

and 150

Ferryboat Pvt. Joseph F. Merrell, MESR, Feb 1952, p. 61, showing wave profile; also Dec 1952, p. 85. This vessel is 290 ft overall by 277.5 ft on the 14.25-ft WL, by 69 ft over guards by 49 ft beam of hull at 14.25-ft draft. Propeller Z) = 20 ft and draft is 13.17 ft in normal operating condition. Great Lakes carferries Spartan and Badger, Mar. Eng'g., Mar 1953, pp. 42-57

D

H A (u)

New

SNAME RD

B

in

Fire-proof

1938, pp.

SSPA, Rep.

Vacationland, Diesel Prog.,

also

1903, pp. 1-14

"Some Problems

med en

a Ferry),"

LoA

Stevens, E. A., "Progressive Trials of Screw Ferry-

May

SNAME, HT,

(o)

ft."

(d)

1938, p. 495; also 5

pp. 165-196, 378-380, 386-387 Nordstrom, H. F., and Freimanis,

173 ft 34 ft

bow

a midship section

Johnson, Eads, "Ferryboats,"

(s)

Pitch,

is

(n)

(r)

9 ft, 6 5/8 in 687 tons 5,764 square ft

128

PI.

590-591

"Dimensions of Edgewater:

Length on water-line Beam on water-line Draught to base on trial Displacement to base on trial Wetted surface to base on trial

1926, pp. 225-226].

San Francisco Bay ferryboat Hayward. Mitchell, E. H., "The Design and Propulsion of Fast Double-Ended Screw Vessels," INA, 1928, pp. 88-102 and PI. X

are close appro-ximations only."

P. 17.

Propellers

SNAME,

and Green, C, "Some Considerations in Ferryboats," SNAME, 1926, pp. 217-

(m) Ferry Lymtngton with Voith-Schneider propulsion,

ft

Bremen

Double-Ended Ferryboats," Amer. Inst. Coast Conv., Sep 1925. The

of the

following quo-

Block

The hull depth is 15.33 ft. The two propellers,

ft.

service draft 9

Design of 248 and Pis. 119-130.

SNAME,

DispL,

and

Engr., Pac.

Gross, C. F.,

Pis.

tations are taken in full

W.

and the

sion for

from this reference, p. 15: "The following is the approximate performance of several vessels of this class at about that speed:

Flaherty

illustrated in

general conclusions arrived at in this paper are

Stevens, E. A., and Paulding, C. P., "Progressive Trails of Screw Ferryboat Edgewater,"

SNAME,

attached to two shafts bolted together amidships, have a diameter of 7.5 ft and a pitch of 10.5 ft. Kennedy, A., Jr., and Smith F. V., "Electric Propul-

32-35 (c)

bow

1921, pp. 826-830. The vessels are long overall and 57 ft wide over the guards,

of

a Screw-Propelled

its

MESA, Nov

reprinted in of

Lieid.

Ralph J. Columbo are described and

1893, pp. 192-

1896, pp. 93-104

12

propellers carried at the ends of a fin

keel e.xtending below the hull; see also

78,

went to some pains to Ust the specific design requirements which may be expected for such a craft. Supplementary requirements are given by F. L. DuBosque and E. A. Stevens in two papers describing screw-propelled ferryboats for New York harbor [SNAME, 1896, pp. 93-104 and Pis. 32-35; SNAME, 1893, p. 192]. Other useful references on this subject are: pp. 381-412],

and

are

Wyckoff, C. D. S., MESA, Oct 1921, pp. 750-751. This article describes and illustrates the diesel-

Diesel-Electric

Paddle Ferry-boat" [lESS, 1934-1935, Vol.

there

ferries;

electric ferryboat Poughkeepsie,

E. Denny, in a paper

Table

entries per vessel. (h)

it.

M.

Christian.

the principal dimensions

= = = = =

=

0.656

410.5 59.5 24.0

ft

Cb

ft

Ps =

ft

V = ISmphor

18.5

ft

Twin screws

7,000 horses, normal

15.66kt

8,860 t

Ferry Carabobo for Venezuela, Mar. Eng'g., Dec 1953, p. 76; Dec 1954, p. 73

LoA Lpp

B

= = =

162 ft 161.67 42 ft

D = ft

H

=

A =

12

ft

Sh 850

t

HYDRODYNAMICS

792 (v)

Crown pp. 58-59; Dec 1954,

San Diego-Coronado

Apr

1954,

LoA = 242. 13 Lpp = 230 ft

B

over guards

B of D =

ft

=

City,

ferrj'

65.13

79

= 46 ft 17.25 ft approx. = 11.5

H

ft

p.

Mar. Eng'g.,

A =

hull

995

IN SHIP DESIGN

Sec. 76.24

both propellers must exert thrust simultaneously to accelerate the craft at the high rates If

required for short runs, or to drive

it

at the re-

quired speed, the type of propelUng machinery ft

preferably such as to permit varying the rates

is t

and delivering the maximum power is done by:

of rotation (w) Lengthened ferry Princess Anne, Mar. Eng'g., Jul

to each propeller. This

1954, pp. 66-67, 81. After conversion,

350

ft

B

Lpp = 340

ft

D =

Lqa

=

over guards

H (x)

(y)

=

59

and

propeller, connected

single 10.5-ft

Characteristics of Propelling Plant

and

Propulsion Devices for Double-Ended Vessels.

When

simplicity of propelling plant

requirement,

as

usually

occurs

is

a primary

described in

Sec.

of rotation.

33.8,

This means, as

propulsive coefficient

is

hkewise low. This situa-

was described admirably by F. L. DuBosque, well over a half-century ago, and it has improved tion

little, if

any, since that time:

"The usual speed of this boat in ferry service is 11 miles per hour, and at this speed it requires 20 per cent more power to propel the boat with two screws than with one screw pushing, and 69 per cent more power to propel the boat with the screw at the

bow than

at the stern.

same power could be put into one screw at the as is used by the two screws, the speed would be

If the

stern

increased from 11 miles to 11.53 miles per hour. It clear, therefore,

that the

bow screw

is inefficient.

is

When

(generators)

and pumps are

not installed for each motor.

Uncoupluig the bow propeller and permitting

(3) it

to free-wheel, while the vessel

by the

stern propeller. This

is

is

driven entirely

possible only

if

either propeller can deUver the necessary power.

uneconomical as it seems because of fraction and greater propulsive efficiency for the stern propeller. To be sure, it requires the fitting of some kind of clutch, fluid couphng, or free-wheehng device between the prime mover and each propeller. Model tests with ferryboats having all three methods of propulsion, carried out in the Swedish It is not as

the higher

State (a)

(b)

wake

Model Basm

at Goteborg, are described in:

Nordstrom, H. F., and Freimanis, E., "ModeUforsok med en Farja (Model Experiments with a Ferr}')," SSPA Rep. 7, 1947. Summary in EngUsh. Nordstrom, H. F., and Edstrand, H., "Propulsion Problems Connected with Ferries," SSPA Rep. 17, 1951. Entirely in English.

that neither propeller

runs at an efficient advance coefficient, and the

shafts

electric,

dynamos

separate

on ferryboats

are coupled firmly to the same shaft so that they

by separate

hydrauhc, or other type of drive in which individual motors on each propeller shaft are driven from a central generating plant. This is not too difficult even though

designed for short runs, both end screw propellers

run at identical rates

Utihzing an

(2)

diameter propellers at each end of the vessel. The power which can be applied to each propeller is about 3,000 horses; 10 per cent of this is delivered to that propeller which is at the bow on any one run and 90 per cent to that at the stern. The trial speed is 15 kt at 171 rpm. De Rooij, "Practical Shipbuilding," 1953, Figs. 801 and 802 on pp. 374-375.

76.24

Providing a separate prime mover for each

(1)

ft

Ferry Cameron, Mar. Eng'g., Aug 1954, p. 63 Automobile and passenger ferry Evergreen State; see Mar. Eng'g., Jan 19.55, p. 70; Diesel Progr., Mar 1955, pp. 40-41; Diesel Times, Nov 1955, p. 7. Said to be one of the largest ferries of its tjrpe in the world, with a length of 310.17 ft, a beam of 73.17 ft over the guards, a beam of 53.5 ft at the waterline, and a depth of 23.25 ft. At a draft of 15.0 ft it displaces 2,022 tons. There is a dieselelectric drive to separate shafts

(z)

=

19.1ft 10.5 ft.

For a ferryboat which travels bow first on its runs, which enters its shps either bow first or stern first, and which is handicapped by narrow slip clearance, cross winds, loose ice, and the hke, an admirable solution is to employ an under-thebottom rotating-blade propeller at the bow. This may supplement one or two rotating-blade propellers or screw propellers at the stern.

The bow

augments propulsive power when desired, provides powerful lateral forces and steering effects at the bow, and creates a backward flow of water at the head of the ship when entering a shp, so as to clear out debris and ice [Virginia propeller

under way, it thrust a column of water against the bow of the boat at a velocity equal to the shp ratio of the screw, and considerable power is absorbed through friction of the blade surface; but a ferryboat's bow becomes its stern at each succeeding trip, and it is therefore impossible to dispense with the forward screw" [SNAME,

ferry Northampton, Motorship,

1896, pp. 94-95].

when underway.

The

1950, pp. 26-27, 43]. this

arrangement

is

that,

if

York,

Aug

drawback to

the rotating-blade

and are not used to they must always be idled

propellers are not retractable,

help propel the vessel,

New

principal

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.25

Brief design rules for feathering paddlewheels

on a double-ended ferryboat are given in Sec. 71.7. It is emphasized in Part 5 of Volume III, under the discussion of retardation and acceleration, that to be able to start and stop properly, the propulsion devices of a ferryboat must have a thrust-producing area,

Ao

equal

equivalent to

or

in Fig. 15. G, that is large in

size of the vessel. If

these

must have a

comparison to the driven by screw propellers

relatively large blade area as

well as a large diameter.

Sometimes the necessary

blade area can be achieved only by increasing

SNAME,

the propeller diameter [DuBosque, F. L., 1896, p. 103].

76.25 Design Notes for Ferryboat Hulls and Appendages. The relatively large metacentric

793

the designed waterline of the ferryboat Cincinnali, described in reference (b) of Sec. 76.23 preceding.

A

complete set of lines for a double-ended ferryboat taken from Het Schip, issue of February 1929, is reproduced to small scale by W. P. A.

van Lammeren, L. Troost, and J. G. Koning [RPSS, 1948, Fig. 195, p. 289]. Because thrust deduction is developed both abaft the bow propeller and forward of the stern propeller, it is important if both work simultaneously that the hull be fined as ticable abaft

and ahead

much

as prac-

of these propellers. This

fining should extend for at least 2 and preferably 3 propeller diameters abaft and ahead of the respective propeller discs. Actually, the form of

hull adjacent to screw-propeller positions

and the

height required for a ferryboat calls for a large

propeller clearances are determined for each end

designed

by the rules of Sees. 67.23 and 67.24, on the basis that that propeller pushes from the stern. The resulting design should be entirely adequate for a propeller which pulls from ahead. The combination of length to afford adequate space on deck, large waterUne area for metacentric stabifity, and fining of the ends results in a block coefficient Cb that is extremely low compared to its value for the average cargo vessel. The first table accompanying reference (c) of Sec. 76.23 shows a range of Cb from 0.34 to 0.42. Because of the full waterline endings, described elsewhere in this section, and of the large speedlength quotients at which modern ferryboats run, the heights of the bow- and stern-wave crests are factors to be reckoned with in design. The necessary clearances must be provided above the wave profile and under the sponsons or supports for the deck overhang, as well as the necessary freeboard for normal running. In addition, there must be some assurance that a heavily loaded vessel will not take water over the main deck when encountering or passing through

waterline,

with respect to

in

all

loading

conditions,

displacement volume. Because the cargo to be carried is one of volume rather than of weight, the length and beam are also its

large with respect to the displacement volume.

This means a small maximum-section and a rather large beam-draft ratio. It

area,

may

be expected that with

small

maximum-section

its

coefficient

large waterline

coefficient,

and

relatively shallow draft the ratio of the wetted

huU to the factor \^¥L be large. This means a large wetted-surface coefficient Cs perhaps so large as to be off the

surface S of a ferryboat will

,

graph in Fig. 45.G. Rather clever shaping of the waterhnes is called for to achieve a fineness at the ends which will avoid undue pressure resistance because of wavemaking forward and excessive pressure resistance due to separation aft, yet which will provide the square moment of area about the pitching axis called for by (7) of Sec. 76.23. If this can not be accompUshed, it is usually the hull resistance which has to suffer. Fig. 76. P is a plot of half of scale of the

3-ft

6-ft

9-ft

12-a

15-ft

propeller,

Buttocks

I

Fig. 76.P

Half-Body Plan and Half- Waterline foe

New York

Ferryboat

Cincinnati

HYDRODYNAMICS

794 high waves

Feb

Dec

made by another

1951, p. 28;

MESR, Feb

1952, p. 85;

vessel [Naut. Gaz.,

1952, p. 61;

Mar. Eng'g., 1954,

this case the encountered

wave

bow wave. Running

the ship's

is

p.

MESR, In

12].

superposed on

over shoal spots

IN SHIP DESIGN

mth

ferryboat

Sec. 76.26

a plated-in sponson.

additional buoyancy and righting

emergency,

by waves and

gives a far

it

affords in

foreign objects,

cleaner appearance to the

Some

and meetuig the unexpected waves which often

craft as a whole.

come along

to these sponsons are found in Sec. 68.12

at inopportune times

can greatly

reduce the nominal main-hull freeboard above these crests. Solid water over the large deck areas

Fig. 68. K.

at the ends can be disastrous.

is

Double-ended and double-direction craft are invariably fitted with double steering rudders. Because of the excessive torque imposed on a bow rudder if it is allowed to SAving and to take

page

an

eliminates fouling of a long row

it

of strut supports

and

It

moment

An

notes and sketches relative

and

admirable view of the hull of the

ferryboat Evergreen Stale, embodying this feature,

November

published in Diesel Times,

1955,

3.

The

hulls of

many

ferryboats lend themselves

this kind, to be

A few of found on ferryboats in service,

its

are illustrated in

SNAME, HT,

inefficiency as a steering device, for the reasons

and 20 on pages

172, 174,

part in the steeling action, to say nothing of

to the use of straight-element forms.

explained and illustrated in Sec. 37.11 and Fig. 37. G, it

is

preferable to lock the rudder mechanic-

1943, Figs.

9, 11,

and 179, respectively. Special Problems of Icebreakers and

76.26

An

Iceships.

icebreaker

is

a special-service vessel

ally at the

end which happens to be the bow. The steering control to that rudder is disconnected or de-energized, a centering pin is dropped into the top of the rudder, and the vessel is steered only with the rudder at the after or trailing end. For this reason, each rudder is required to provide the entire control necessary for maneuverability

breakmg up and making its way through heavy floe ice, pack ice, and soM sea ice. It makes navigable lanes for other vessels as well as for itself. Indeed, it may be called upon to tow other vessels through these lanes, or to push on another icebreaker ahead of it when the going

of the vessel.

involving great power on a limited length and

Even though as

it

located in a propeller outflow

should be, the rudder(s)

should be relatively large, to enable traffic,

to

and leave

maneuver promptly its

jet,

of a ferryboat it

to dodge

in a fog, to enter

berth in a cross tidal current, and

need be. Ice guards and rope guards are often fitted ahead of bow rudders and abaft stern ones. If these extend continuously around the outer rudder profile, from the hull above to the rudder shoe below, they form effective rope guards [Graemer, L., Schiffbau, 11 Oct 1911, Fig. 4, to turn around,

if

and Pis. 1-2; WRH, 15 Dec 1939, p. 381]. However, if they are bent inward accidentally, even only shghtly, they foul the rudder and prevent its swinging. They have one advantage

p. 4,

that they create a separation zone of sorts in

which the larger part of the rudder blade lies, so that excessive torque is not apphed continually on a rudder at the leading end of the vessel. Conversely, they may vibrate transversely because of alternate eddies shed abaft them. It is therefore best to

make such a

guard,

if fitted,

a

sort of prolongation of the sides of the rudder

blade.

There is much to be said in favor of supporting a long, wide deck overhang on each side of a

capable

of

particularly

gets

rough.

exceptional sturdiness,

very

fit tie

is

such that

Like a tug,

can carry

it

it

is

its

often called

own

upon

services.

to deliver

forward (and astern) thrust at or near

zero speed. This thrust, furthermore,

to overcome forces other than

dynamic

duty,

useful load, either in weight or volume,

other than that required for

maximum

primary

Its

its

is

required

own hydro-

resistance, just as its structure

is

required

to withstand forces other than those imposed

upon

An

it

in wavegoing.

and constructed adapted to traveling in heavily iced waters without the necessity for breaking solid ice and making its own water lane. It is intended to be capable only of withstanding ice impact and traversing an ice field which has previously been broken up by an icebreaker or by natural causes such as wind and swell. As a rule, the iceship is of more-or-less normal form, although it may have a Maier bow, intended to ride up on and break through not-too-tliick ice. Its hull plating iceship is a vessel designed

for, or

thick at the waterline belt, at least, and its framing is heavily reinforced. It is, in fact, designed and constructed for carrying cargo or for some other primary mission. Its abiUty to make its way through and to withstand not-toois

heavy

ice is purely

secondary ["Ships for Arctic

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.26

Use" (designations T-AKD-1 and T-AK270), Maritime Reporter, 15 Sep 1955, pp. 11-13]. No specific requirements other than the general functions Usted in the two paragraphs preceding are given for icebreakers and iceships because the service varies rather widely.

A

vessel suitable

and convoying large vessels through the Northwest Passage, for example, is for breaking a lane

entirely

unsuitable

for

clearing

out

a

small

harbor and working around slips. The details of ship handling in various kinds of ice are mentioned in a

number

of the references of Sec. 76.27

following, but are given in

more methodic fashion

in the 1948 Edition of the British Antarctic Pilot,

Chap.

I,

pages 42-54, under "Ice Navigation."

While the process of bucking ice is in no sense a hydrodynamic action there are major hydrodynamic problems involved. Considering the solution of these problems and the selection of design features for an icebreaker (not an iceship) in somewhat the same order as in Chaps. 64 through 68 for a surface ship, the appended list supplements one previously given by D. R. Simonson ["Bow Characteristics for Ice Breaking,"

ASNE,

the smaller vessels are not intended to break ice as thick as retiuired for the larger ones.

More important than

the length of an ice-

length-beam ratio, which must be small for superior maneuverability in driving through leads in the ice. When forcing its way into a harbor or inlet the ship must go around breaker

is its

corners, or must back and fill and turn to clear an open space for other vessels. The icebreaker may even have to back up or turn around to free convoyed vessels that have become stuck in the ice

behind

it

[Sokol, A.

E.,

USNI,

May

1951,

p. 482].

Fortunately, the very large

beam

the length needed for this purpose to clear a lane wide

enough

for a

is

relative to

also required

convoy following

behind. This lane can not always be straight, so the corners

must be cut

off for

longer vessels in the

rear.

A

beam-draft data for a large number wide variations with weight displacement. Considering only those vessels whose performance is known

study

of

of icebreakers (and designs), reveals rather

to be good or excellent, ratio with weight

1936, Vol. 48, pp. 249-254]:

795

W

(or

optimum values of L/B A) may be taken from

the vicinity of the curved broken line in Fig. (1)

(2)

(3) (4) (5)

Waterline length

76. Q.

Normal displacement Length-beam and beam-draft

ratios

5.50

Engine power Thrust available from the propeller(s) at low

500

speeds (6)

Transverse section shape

(7)

Number and

(8) (9)

position of propellers

Forebody shape Appendages.

These items have to be balanced against carrying capacity, steering and maneuvering qualities,

allowable draft, and economical power.

The length

mum

525

is

limited to the practicable mini-

so that the vessel can

work to advantage The waterline

in open-water spaces of small size.

length and the weight are also important because they largely determine the downward icebreaking

which can be exerted at the bow when the pushed up on the ice and the vessel lifts forward, usually by an angle less than 5 deg.

force

latter is

Although there are limited authentic data for it appears obvious from a consideration of the mechanics involved, presented by D. R. Simonson in the reference cited, and by R. Rune-

analysis

berg in references

(2)

and

(5) of Sec. 76.27,

that

This ratio increases from about 3.6 in

HYDRODYNAMICS

796

diameter propellers with tip submergences great

enough to

With drafts

should

clear surface ice.

these small it

is

be

L/B

ratios

and

relatively deep

natural that the block coefficients

low

and

the

displacement-length

quotients or fatness ratios high.

The Cb values

are of the order of 0.5 and the 0-diml fatness ratios range

from 8 or

less to

about

15.

Like a tug, the icebreaker has waterlines, both above and below the DWL, which are well

curved throughout. These enable

to follow

it

desirable leads or to extricate itself

when tem-

porarily caught.

The the

ship often has to back

maximum

off,

stop,

and gain

possible speed ahead in a short

distance so that

its

momentum

can be added to bow up over

the thrust forces to push the ship's

the ice. This means an ample reserve of power and propellers that are large enough to develop

very high thrust values. In certain kinds of ice the friction of a thick pack may exceed the water friction around the hull, especially at low speeds.

On the basis that it is usually desirable to break the ice without too much charging or ramming, the thrust to keep the ship going at low speeds in ice (say 3 kt) and at high real-shp ratios or /-values is a function of the propellerdisc area, the propeller power, and the overall 26

24 22

IN SHIP DESIGN

Sec. 76.26

DESIGN OF SPECIAL PlIRrOSF. CRAFT

Sen. 7r,.2r,

a slope of 85 deg should suffice for "all ordinary ice-breakers." H. F. Johnson, in 1946, sa3's that the slopes for the flaring sides of the midship

and 80 deg. A pronounced tumble home above the DWL is desirable to prevent the foulmg of top hamper when working around other vessels. One other feature of the abovewater body not to be oversection should be between 70

looked at this point

when heavily

the

is

minimum

freeboard

loaded. Entirely aside from wave-

going requirements, a reasonable amount of hull extending above the ice level is required to insure that, if held fast in the ice, the ship is not over-

whelmed by overriding rising

floes

above the water

and pressure ridges Nansen's Fram,

level.

although undamaged by lateral squeezing in its drift over the Arctic Ocean in 1893-1896, never-

It

has since been found that when the ice

is

up and drawn down under the bow by the inflow current from the bow propeller, without damaging the propeller, thin enough to be broken

then the latter

of great assistance.

is

When

a

thick layer of heavy snow hes on top of a relatively thin layer of sea ice the abovewater

bow

banks the snow up in front of it until finally the ship can no longer force its way through. The procedure then is to break up the ice by small increments and to suck both ice and snow down and under the ship, finally ejecting it behind. A

bow

propeller or propellers are of great assistance

here as well. If the ice

is

bow

so

heavy that as the

is struck by huge blocks, these blows are Uable, not only to bend or break the propeller blades but to bend

"Farthest North,"

the shaft or to dislodge the thrust bearing inside

January 1895 [Nansen,

F.,

1897, Vol. II, pp. 47-60].

The

powered steel icebreakers of the 1890's and 1900's were almost mvariably equipped with bow propellers, as were many of those of later years. This was on the theory that, after the breaker's bow had ridden up over a thick ice layer and broken it into chunks, partly by impact and partly by sheer weight, the inflow current to the bow propeller (s) would draw the ice down under the ship. The outflow current would push it aft under the ship, leaving the bow free to break more ice. It may be well to remember, however, that when F. E. Kirby of Detroit introduced the first bow propeller on the icebreaking car ferry St. Ignace for the Straits of Mackinac in 1888 [Runeberg, R., ICE, 1900, Vol. CXL, pp. 109-129], it was to perform an entirely different function. Faced with the problem of getting a ship through ice that was piled in layers all the way down to the channel bed, Kirby held the icebreaker's bow to the ice with a powerful stern propeller early, heavily

while the

bow

propeller, going astern, forced a

current of water into the ice mass ahead to loosen

When some

was loosened, the bow propeller was set to drive ahead, whereupon the inflow current produced by it drew loose ice from the mass and pushed it aft. After the ship advanced until it was again stalled, the process was it.

are designed.

was nearly overwhelmed and sunk by coming in sLx feet deep over the rail on 3-7

theless ice

797

knowing why things are done when new ships

of it

Following Kirby's success, bow prowere fitted to many icebreakers, whether faced with the same operational problems or not. This is another example of the importance of repeated. pellers

ship rides

up on

the

it

propeller

the ship.

The meaning

under

of the foregoing is that,

conditions which

may

change from day to day,

the ship needs a

bow

propeller or propellers or

encumbered by them. Although the mechanical problems seem almost insurmountable, especially for such heavy-duty machinery, it may nevertheless be possible at some time in the future to develop a housing bow propeller for an icebreaker. This might be a 2-bladed affair, made controllable and reversible from within, with else it is

having thick sjonmetrical not in use the blades could be feathered fore and aft and the whole propeller drawn backward into a shallow recess in a lower nearly

flat

sections.

blades

When

vertical portion of the stem. This

would support

the blades and hub against the impact of heavy blocks of ice striking from ahead. for use the

bow

When

desired

propeller with its shaft could be

pushed forward a short distance by an internal hydrauhc or equivalent mechanism. With the blades then turned to the desired angle, the propeller would be instantly available for pulling the ship ahead, sucking blocks of ice down clear of the upper part of the bow, or helping to back

the ship out of a jam in the ice. While the thrust deduction due to positive differential pressures +Ap abaft the bow propeller of an icebreaker is of no more than second-

ary consideration, the free passage of broken ice through and abaft the wheel calls for the same fining of the hull behind the propeller as would

be the case were

it

used for normal propulsion.

HYDRODYNAMICS

798 Indeed, the

bow

propellers of the ferryboat

and

although installed for entirely different normal functions, involve many of the of the icebreaker,

same hj^drodynamic

principles in their action.

The

comes in handy for clearing loose ice out of the head of its slip. For the designer faced with the problem of considering one or two bow propellers, or of designing an icebreaker with them, a most useful document is SSPA Report 20 by H. F. Nordstrom, H. Edstrand, and H. Lindgren, entitled "Model Tests Avith Icebreakers." It was published m 1952 and is entirely in English. Whether a bow propeller is fitted or not, D. R. Simonson mentions in the reference cited earher

ferryboat

bow

propeller often

in this section that it is often necessary to

fill

out what would be the forefoot, just above the order to obtain sufficient displacement baseline,

m

volume forward. The resulting bow profile corresponds somewhat to that of an icebreaker with a bow propeller. The vertical stem portion extending for a distance above the keel performs another useful service in that

it

prevents a

vessel with a constant slope of about 30 deg in

bow profile from riding up so far on a deep accumulation of ice cakes that it can not be backed off. The vertical portion of the stem acts also as the

a cutter to loosen up the lower layers of ice in deep windrows. Fig. 76.S shows the vertical

Fig. 76.S

Bow Quarteu View

IN SHIP DESIGN

Sec. 76.26

portion of the stem abaft a

bow

propeller position.

This portion should be retained, as previously noted, even without a bow propeller. The peg-top underwater sections, the tumble home above the waterline, and the massive bossings are also well

shown

in the figure.

The forward buttocks should be sloped as much or more than the bow profile, extending back to the section of maximum beam, so that the whole forward part of the ship acts effectively to break ice. The characteristics of the forebody should be duplicated as much as possible in the afterbody since the vessel will be required to

break ice when backing. The follo\ving is quoted from page 254 of the

Simonson reference: "It

is

desirable to

work the same angles

into

the

buttocks of the fore body to obtain equalization of lifting forces when the ice carries past the bow without breaking clear of the hull. As for the frame sections, they should show a marked flare at the waterline to relieve the crushing force of the ice."

It is obvious that vessels having V-shaped midship and other sections similar to those of icebreakers, with their large bulge radius, possess httle in the way of roll-damping characteristics. Without roll-quenching devices of some kind

they

ment

roll

deeply and heavily, to the great detriWhen the beam-draft

of their habitability.

of Hull of an Icebreaker of the Wind Class

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.27

moderately large they also

ratio is

unless the polar

moment

fore-and-aft rolling axis

The usual type

roll

Underwater inlets and discharges for the cooling water of heat exchangers are often shut off by

sharply

about the

of inertia

ice cakes resting across the

is large.

ice

Any type of retractable projection is almost as vulnerable. Plate-type keels, as distinguished from those of triangular section,

icebreakers carry fuel and other liquids

connections could be plugged temporarily and where the system could be filled with mud, silt,

wing tanks connected by pumps. Shifting these liquids from one side to the other produces enough heehng moment to rock the vessel and help free it from the ice. If sufficient power and weight could be spared to make this certain

or sand.

Published model-test data on icebreaker hulls are rather meager. There signer

roll-quenching

active

Protection against large blocks of ice striking

a single propeller at the stern is afforded by fitting one or more fins, generally horizontal, ahead of

Icebreakers.

1952, pp. 778-779; 25 Theia,

The Motor

1952, p. 831;

M.

S.

Since the flow of water along such a skeg fins

should

lie

is

(5)

aft

in the natural

streamhnes, as determined from model lines of flow

and as checked by

A

methods.

tufts

or

above the other,

parallel to the shaft

fins,

producmg more nearly

hne and

in

a

axial flow in ice-free

circulating-water

such

channel.

of icebreakers

and iceships are

tected integral

after

with

a

fashion

the

hull,

by

They

in-

preferably

projecting

downward

tabulation

contains a great deal of miscellaneous tabulated At the time of writing (1955) only the table

are pro-

horns,

comprehensive

in these tables date

avoid separation and eddying ahead of the wheel.

Rudders

really

on pages 22-23 and 26-34. The ships described from 1871 to 1938. The book appears to cover the theoretical and analytical aspects of icebreaker design rather well, and it

The

fins require fining to

variably completely submerged.

first

114-116 contains 44 entries for 39 icebreakers and same year (1946) I. V. Vinogradov pubhshed in Moscow a Russian book entitled "Vessels for Arctic Navigation (Icebreakers)," which has a rather complete list of tabulated data

checking in the design stage, preferably on a trailing edges of all

tabulation of dimensions,

iceships. In the

water. Such a layout, however, requires careful

model

first

appears to be that of H. F. Johnson [SNAME, 1946, pp. 112-151]. A large 3-page table on pages

one

extending forward for perhaps a propeller diameter, might have a beneficial propulsion effect in

The

of the fist in the latter part of this section.

The

equivalent

"ladder" of three or four

available to the de-

published in 1952 by

These data are contained in a single table on page 285 of reference (2), pubhshed in 1889; otherwise the small tables of data are somewhat scattered throughout both references.

Ship, London, Jan 1954, p. 458].

and upward, the

is

characteristics,

Dan, SBSR, 19 Jun

Dec

20,

and other data on icebreakers was made by R. Runeberg in references (2) and

the propeller, projecting on each side from the centerline skeg [M. S. Kista

SSPA Report

H. F. Nordstr5m, H. Estrand, and H. Lindgren, entitled "Model Tests with Icebreakers." This is abstracted in SBSR of 5 June 1952, pages 726-728; the Swedish report is, however, entirely in EngUsh. 76.27 Tabulated Data and References on

the natural rolling period,

tanks thus formed would go far toward making the icebreaker a more hvable ship in the open sea. the

dis-

charged into this box is cooled by contact with the shell before it is used over again. Similar water boxes are fitted on vessels required to operate in very shallow water where the outboard

be added at the start of each voyage and used to quench roll until such time as they are bent over or stripped off by the ice.

shift in the order of half

Water

circulating lines can be connected.

may

Most

openings or by broken

lodged in the strainers. It is customary to provide a water box inside the shell to which the

of roll-resisting keel is vulnerable

in the ice.

in

799

data. of

contents has been translated into English. of Congress number is VM451.V5. Table 76.f contains some dunensions, propor-

heyond the rudders and below their tops, so as to break up the ice when going ahead or astern and

The Library

prevent blocks from wedging themselves between the top of the rudder and the hull. To meet the they exacting maneuverability requirements

tions,

and

characteristics of

modern

icebreakers,

should be larger than normal but are often just the opposite, to make them less vulnerable to

supplementing the 1946 list of H. F. Johnson. These data were gathered from pubhshed sources so they are incomplete and in many cases inconsistent. This is due partly to a lack of strict

damage from the

definitions of displacements, powers,

ice.

.

and other

— 800

HYDRODYNAMICS

IN SHIP DESIGN

TABLE

Sec. 76.27

76.f

Dimensions, Proportions,

All dimensions are, unless otherwise stated, in ft to the proper power. All

General

Name

of Vessel

powers are in English

nF.STON

Sec. 7r,.27

OF SPECIAL PITRPOSF CRAFT

AND Form Data for Icebreakers horses.

AH weights and

Elbjom

displacements are, so far as can be learned, in long tons of 2,240

lb.

801

HYDRODYNAMICS

802

IN SHIP DESIGN

Sec. 76.27

TABLE Proportions and Form Coefficients {<2onUnucd)

Name

of Vessel

—

76.f-

Sec. 76.27

(Continued)

Elbjorn

DESIGN OF SPECIAL-PURPOSE CRAFT

803

HYDRODYNAMICS

804

IN SHIP DESIGN

terms and partly to incomplete descriptions of the terms for which numerical quantities are given. In any case, the new tables provide a framework for filling hi missing data in the future. In a number of cases new icebreakers have been built to replace old ones and have been given exactly the same names. There follows a selected list of references on ice, icebreakers, and iceships, giving what are beUeved to be the principal sources of information. Except for the

Vmogradov book

of 1946

of 42.5

ft.

Sec. 76.27

When

fully loaded, the draft

25

is

ft,

and the corresponding displacement 2,000 t. However, the displacement given is much too small for the dimensions. Although not specifically named in the reference, this vessel appears to be the Errnack.

There are three propellers

aft

and one propeller

forward, driven by four engines having a combined (indicated?) power of 10,000 horses. It is believed to have been designed by Admiral Makarov. On page 1223 it states that "The stern of the ice breaker is cut to form a recess, into which the stem of another vessel can be securely lashed, and thus obtain the utmost protection from her powerful

and the Schiffbau

references, these are all hi English.

consort." (1)

"Bibliography on Ice of the Northern Hemisphere," H. O. Publ. 240, Hydrographic Office, U.S. Navy,

(4b)

1945 (2)

"On Steamers for Winter Navigation and Ice-breaking," ICE, 1888-1889, Vol. XCVII, Part III, pp. 277-301 and Pis. 3-5. These plates show arrangement plans and lines drawings for the

Runeberg, R.,

ships

Bryderen,

Express,

Boat

"Ice

No.

(5)

Swan, H. F., pp. 325-332 Erniack and Runeberg, R.,

Frictional resistance caused of

by change

metacenter

of

about the

Sampo

CXL,

Sect.

pp.

I,

The

plate embodies an arrangedrawing of the Aegir, complete lines drawings of the St. Marie and Sampo, and forebody lines drawings of twelve icebreaking vessels, built between 1871 and 1896. Runeberg discusses the bow propeller, which was apparently introduced by F. E. Kirby on the Straits of

literature

Displacement

1899, Vol. 41, tells

"Steamers for Winter Navigation and

ment plan and

this reference appears to

Ice-breaking by a continually progressing steamer Ice-breaking power of a steamer when charging Effect produced by the continued working of the engine

Pis.

the Finnish icebreaker

109-129 and PL

2"

be the first one in the on this subject. Runeberg tackles the design problems involved in icebreaking from an analytic point of view and develops formulas covering the various operations under:

and

Ice-breaking," ICE, 1900, Vol.

(driven by paddles!) and a projected steamer for the Finland Government. It seems incredible but technical

INA, LIX-LXII;

"Ice-Breakers,"

Mackinac (6)

4.

lines

ferry St. Ignace in 1888.

"Icebreakers for the Port of Stockholm," the Ship-

(now SBMEB), Jan-Jun 1914, Vol. X,

builder

pp. 55-57. LoA = 200 ft, Lpp = 188 ft, Bx = = 21.5 ft. The ship has one large stern 55.75 ft,

D

propeller plus one smaller is

(7)

some drag

The Russian

motion

in

bow

icebreakers Sviatogor and Alexander are

illustrated in Schiffbau, 11

(vertically).

Engineer,

also in

propeller; also there

the keel.

Feb 1920, pp. 402-403;

London, 26 Deo 1919. Some

details are:

These sections are followed by discussions entitled "Details of Construction" and "Particulars of Some Ice-Breaking Steamers." Among the latter are the Express, Isbrytaren, Oland, Bryderen, Em. Z. Svitzer, for

3 screws,

and a proposed steamer the Finland Government.

Starkodder, Ice-Boat No.

2,

(5)

LoA 99.2 LirL 90.52 21.64

hereunder.

Magazine, Jul 1897, Vol. XII, p. 326, shows the stern view of a vessel in a drydock at Newport News. From all indications this ship is an icebreaker. In any case it has a very large beam, a considerable amount of tumble home all around, and is fitted with two huge 4-bladed propellers

Cassier's

(8)

(9)

A

"gigantic Russian ice crusher"

is

mentioned

latter reference this vessel

1898. It

is

305

ft

was launched on 29 Oct

long and 71 ft beam, with a depth

325.48 ft 297.0

ft

stem screws,

screw Lqa 85.64 Lwl 83.20

B

71.0 ft

19.45

m= m= m=

1

bow

280.98 ft 272.98 63.81

ft ft.

The midsections of these vessels, shown on page 404 of the Schiffbau reference, are of the typical pegtop shape, with a large tumble home above the DWL. Flodin, J., "Ice Breakers," Mar. Eng'g., Sep 1920, pp. 707-712 Kari, A., "The Design of Ice-Breakers," SBSR, 22 Deo

1921, pp. 802-804. is

Some

of the information

included in Mr. Kari's book

entitled "Design and Cost Estimating of Merchant and Passenger Ships." The reference discusses static and dynamic icebreaking, length, lengthbeam and length-depth ratios, and gives various formulas useful for design and for predicting the

in

ASNE, Aug 1898, Vol. X, pp. 917-918; also ASNE, Nov 1898, Vol. X, pp. 1222-1223. According to the

m = m = m =

given in this article

with fan-shaped blades. The propellers are of the built-up type with securing bolts or nuts that project prominently from the hubs. It is believed to be Russian. (4a)

2

all aft

B

Runeberg's comments and conclusions in this reference are somewhat modified by those in a later ICE article by hun, dated 30 Jan 1900, reference (3)

Alexander

Sviatogor

(10)

performance of a ship designed elsewhere. "Swedish Ice Breaker of 2,450 Tons Displacement and 6,000 I.H.P.," SBSR, 12 Mar 1925, p. 310

(11) "(Russian)

Ice Breaker Krisjamis Valdcmar,"

Shipbuilder, Jul 1925; abstracted in

The

ASNE, Aug

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.27

SBSR, 4 Mar

pp. 611-612;

192.'5,

1926, pp. 247-

A small sketch showing the general hull shape and the principal dimensions of this vessel is found in WRH, 22 Jan 1929, Fig. 9, p. 30.

particulars

"Konstruktionsbedingungen fur die in Eisgang und Eisbrechdienst zu verwendenden Schiffe (Construction Specifications for Ships Going F.,

Through

and

Ice-Breaking Service)," WRH, 22 Jan 1929, Vol. 10, pp. 27-31 (in German). Comments in English on this article are to be Ice

(13) Icebreaker

R.

Railway

of

SBSR, 20 Nov 1941, pp. 481-484, 491 "The Ice-breaker Ernest LaPoinie," SBMEB, Jan

(33)

and channel-surveying vessel built in Canada for the Canadian Department of Transport. Wasmund, J. A., "Coast Guard Ice-Breaking

1942, pp. 13-18. This

Vessels,"

1930, p. 610.

Lbp

ft,

The displacement

B

the

60

ft,

D

31

is ft,

5,034

H

Hammar, H.

G.,

Intended for

t,

the

19.5

(35)

(36)

Feb 1932 Ymer," SBSR, 25 Aug

1932, pp. 175-177 Ice Breaker Ymer's

Particular Attention to the

Aug

VIII, Stockholm,

Main

Plant,"

1932, following

ref.

(38)

Part

(15)

V., and Ericson, N., "Federal Ice Ymer's Machinery Equipment, with Emphasis on the Propelling Machinery," Part IX, Stockholm, Sep 1932

Breaker

Ymer

(9,000

B.H.P.

Machinery),"

1933, pp. 165-167

"Japanese Ice Breaker Soya Maru," MESA, May 1933, pp. 162-164, 182. Gives particulars, trial data, and photographs. (23) Hohnberg, G., "Federal Ice Breaker Ymer's Trial Runs," Teknisk Tidskrift, Stockhohn, Jan 1934 (22)

(24) Gouljaeff, N., "Ice Breakers,"

SBMEB, Mar

(40)

(Icebreakers)," Moscow, 1946 (in Russian) Outboard profile of Swedish icebreaker with diesel drive, having controllable twin propellers aft and one small screw propeller forward, is shown in AM,

"Machinery Installation of the Wind Guard Icebreakers," ASME, 29 Nov-3 Dec 1948, No. 48-A-lll Finnish Government Icebreaker Into, with 12,000 B.H.P. Machinery," Motor Ship, London, Aug

plans. Ship has

two bow and two stern

LoA = 212.88 ft Lpp = 185 ft B, molded = 36.75

H, as cargo

y = ft

cargo

Mendl, W. V., "Ice Breakers," pp. 543-544. Gives formula that can be broken. Sisu,

A

SBMEB,

as

(iceship)

a

=

Rooij (pronounced Rooy), G., "Practical Shipbuilding," H. Stam, Harlem, Holland, 1953, Fig.

De

Apr

Jun 1954, Vol.

Oct 1938,

Macy, R. H., "Icebreakers," USNI,

Voima. Dept., (46)

SBSR, 6 Feb

of Icebreakers,"

1941, pp. 127-128. This gives general

Aug

Bureau

of Ships Journal,

Navy

MENA, Aug

1954,

1954, pp. 2-6

Canadian Icebreaker Labrador,

pp. 293-294. Gives general particulars and an out-

1940, Vol. 66,

board

"The Design

1955, Vol.

(45) "Ships Against Ice,"

pp. 669-674

R. Munro,

130, pp. 655-657. Abstracted in

LXVII, pp. 13-14. These references give data on the Thule, Elbjom, and

IME, Jan

Motor

pp. 22-24. Finnish particulars of vessel, with 1939,

Gives arrangement plan and photographs.

(30) Smith,

capacity

vessel

16 on p. 19, Art. 208 on p. 372, and Fig. 798 on icebreakers in The Shipping World, 30

for thickness of ice

Diesel-Electric Ice Breaker,"

London,

icebreaker.

(29)

18.083 ft

(44) Article

cutter).

Ship,

=

1,200 tons (43)

SNAME, 1937, pp. 81-114. Describes cutters Escanaba, Algonquin, and Raritan (110-ft harbor

"The

vessel

12 kt

Deadweight

(25)

(28)

propellers,

with a motor power of 4 times 3,500 horses. (41) Kassell, B. M., "Russia's Icebreakers," ASNE, Feb 1951, pp. 137^152 (42) "A Motorship for Arctic Waters (Kista Dan)," SBSR, 19 Jun 1952; pp. 829-831

pp. 143-150. Gives a bibliography of information on icebreaker design.

(27)

icebreakers.

"Vessels for Arctic Navigation

V.,

1950, pp. 166-167. Includes particulars of vessel, discussion of machinery, profile and arrangement

1935,

Simonson, D. R., "Bow Characteristics for Ice Breaking," ASNE, 1936, pp. 249-254 (26) Hunnewell, F. A., "U.S. Coast Guard Cutters,"

modern

Class Coast

Motorship, Jan 1933, p. 366 (20) "Ice-Breaker Goeta Lejon," SBMEB, Feb 1933, p. 91 Ymer" for Swedish Government, (21) "Ice Breaker Motorship, London, Apr 1933, pp. 7-14; also

MESA, May

I.

(39) Thiele, E. H.,

Special (19) "Ice

Vinogradov,

Jul 1948, p. 26

(18) Christofferson,

Breaker

"Coast Guard's Diesel Powered Ice-Breakers," Motorship, London, Jun 1945, pp. 562-566, 604 Johnson, H. F., "Development of Ice-Breaking Vessels for the U.S. Coast Guard," SNAME, 1946, Vol. 54, pp. 112-151. A very complete paper, summarizing development to date and describing the design of

(37)

and Ericson, N., "The Federal Machinery Installation, with

(17) Christofferson, V.,

propellers,

MESR, Apr 1945, pp. 142-145. Includes a history of icebreaking vessels and gives

G.,

(16) "Diesel-Electric Ice-Breaker

bow

particulars of various icebreakers.

"The Construction of Cargo Vessels Winter Traffic and Navigation in

1931, p. 175 "Federal Icebreaker Ymer," Teknisk Tidskrift, Stockholm, Part I, Jan 1932; Part II,

(15) Halldin,

1944, pp. 184-186. Includes

(34) "Ice-Breaker Design,"

ft.

SBMEB, Mar

Ice,"

a twin-screw ice-breaking

propulsion motors, speed control, and power requirements.

Indicated power 2 times 3,250 horses. (14)

MESR, Dec

is

discussions of hull construction,

1929, p. 116.

McLean, for the Hudson Bay the Canadian Government, MESA,

is

suggests

(31) "Icebreakers,"

B.

Nov

260

Mar

icebreaker,

(32)

in

found in Marine Engineer,

typical

length-beam and beam-draft ratios, and gives a formula for thickness of ice that can be broken.

251.

(12) Judaschke,

805

a

for

(47)

profile.

of sLx icebreaking cargo vessels for Russia, being built in Holland, is illustrated and described in

One

HYDRODYNAMICS

806

MENA, Aug

pp. 288-290. These vessels have a single screw driven by a 7,000-horse electric

1954,

motor turning at 150 rpm.

LoA Lpp

= =

425 387

B = D =

ft ft

at this draft vessels

=

have a

it

H

ft

Deadweight

6,500 tons.

profile

27.63

7 =

ft

capacity

15 kt. These

resembling almost exactly

that of a regular icebreaker. (48)

"Ingalls Launches

Most Powerful Icebreaker," Mar.

Eng'g., Oct 1954, p. 58 (49)

"The Twin-Screw

Diesel-Electric Ship General San Martin; an Ice-breaking, Research and Supply Vessel for the Argentine," SBMEB, Feb 1955, pp. 108-109; also The Motor Ship, London, Jan 1955, p. 432, and MENA, Dec 1954, pp. 480-481. The last reference contains photographs of the bow and stern of the vessel in the building dock

(50)

and a photograph of the completed ship under way. "Diesel-Engined Soviet Icebreakers," The Motor Ship, London, Feb 1955, p. 503. Illustrates and describes the three vessels of the Kapetan Belousov class, as well as

(51)

the two 12,840-t icebreakers

now

on order (1955). Abstracted, with outboard profile, in IME, Jun 1955, Vol. LXVII, pp. 86-87; see also SBSR, 6 Sep 1956, pp. 313-315. "Icebreaker with 12,000-B.H.P. Machinery," The Motor Ship, London, Dec 1956, p. 362

Lo A ,273

ft

H, mean 22.33

LwL

,

260

ft

A, 4,950 t

Bex

,

63.75

76.28

ft

Hydrodynamic

Amphibians.

It

due largely to

its

Pb (normal), Design

ft

10,500 horses.

Features

of

may

be expected that the future will find more and more peacetime uses for a good combination of water craft and land vehicle, notwithstanding that its development to date is first

wartime usefulness. Indeed, the of Donald Roebhng

successful "alhgator"

was used originally in 1933, in the otherwise impenetrable expanse of the Florida Everglades, for rescuing hurricane victims and downed aviators.

During the recent war

its

descendants

served as means of carrying medical supphes and

even as mobile hospitals. Refitted World War II DUKW's are already serving as combination

and salvage craft, equally useful on dry land and in the water [Rudder, Aug 1952, pp. 24-25]. There is no reason why they should not be useful as ship-to-shore package and perfireboats, rescue,

sonnel carriers in out-of-the-way places where ships must anchor off and where there are no

shore

Sec. 76.28

soft

enough

it

acts as a hquid;

if

mud.

If it is

hard enough, as

a sohd.

61.58

36.79

=

IN SHIP DESIGN permissible "holiday" for travel in

facilities.

For these duties an amphibian must:

(b) Have an adequate reserve-buoyancy ratio, not only for wavegoing but for the bank require-

ment

of (f) following. This is more important in an amphibian than in a surface vessel because the former can rarely be ship-shaped or have much of a weather deck. (c) Maintain the reserve-buoyancy ratio throughout the design and construction period. This means that the total scale weight can not exceed the weight of the hghtest water displaced by the buoyant volume up to the safe working waterhne. Judging by some bitter experiences of the past, it means that an ample weight margin must be

included in the preliminary design. (d) Possess adequate freeboard to guard against water from the crests of its Velox waves. With a blunt bow and full form, these crests may be high. (e) Limit its water speed to 1/3, 1/4, or possibly a smaller ratio of its maximum land speed (f) Be able to drop down or run up a bank having a slope of at least 30 deg with the horizontal, both below and above the water surface. An amphibian, in the form of a wheeled or tracked vehicle which can propel itself along the surface of the water, or of a boat which can run on dry land with wheels, tracks, or the equivalent, can hardly be expected to have a high degree of propulsive efficiency when running in either medium. If the primary object of the design is to produce a load- or passenger-carrymg vehicle, a watertight body to give it flotation may be a clumsy encumbrance. Shaping this body to ease the water flow around it and at the same time to incorporate a pair of paddletracks, one or more screAV propellers, or a paddlewheel involves compromises Avhich must be worked out for each particular case. Applying wheels or tracks to an object designed primarily as a water craft is no less of a special problem. Fig. 76. T shows how clumsy such a craft can look and still perform well as an amphibian. This is not the place to advance arguments for or against the use of wheels or tracks for travehng on land, through sand and mud, or over submerged reefs. There might be some reason for

discussing the relative merits of propellers

paddletracks (a) Run in and on any kind of Hquid or sohd medium, from fresh and salt water to dry land, or any combination of these two. There is no

way

if

and

the form of the craft were in any

standardized. It may, nevertheless, not be

amiss to

list briefly

and precautions

the advantages, disadvantages,

to be observed in adapting

and

OF SPECIAL-PURPOSE CRAFT

m'.SK.N

Sec. 76.28

lllllll

807

good performance provided water can flow easily to it, either from the side or under the bottom. will give

in nil fin

The

central paddlewheel

is specially adapted catamaran type. It is simple mechanically, is easily constructed, maintained, and repaired, and is reasonably efficient

(3)

to divided-hull craft of the

for

shallow-water craft. It

lumbersome, and heavy I

1)

The sternwheel

is

is

admittedly bulky,

for the

power

delivered.

indicated only for raft-like

craft designed for traveling in extremely shallow

water (5)

One Type of Tracked Amphibian

Fig. 76.T

U. S. Navy photograph. Note the M-shaped paddles or cleats on the two moving tracks and the relatively close spacing of these paddles along

Official

the tracks.

employing one of the several possible methods water propulsion:

of

A

water

phibian

is,

jet to propel

with

its

space than can be devoted to

might serve for a lighter

The paddle track has

the advantage that the

installation

is

utihzed for run-

ning on both the water and the land, including propulsion as well as maneuvering. If

it is suffi-

and durable it is satisfactory for extended land travel but not for high speeds ciently strong

ashore unless

can somehow be rubberized.

it

Balancing this present shortcoming

is

the great

advantage that the track furnishes the only

known adequate and

acceptable propulsion in

ammore

resistful

it.

Such a device

craft.

(6) The amphibian driven by a paddlewheel of some kind or by one or more screw propellers needs a good rudder. Probably it needs more than

one to approach (1)

same mechanical

a heavy,

ducts, likely to occupy

the

maneuverability

the

of

which can change its track speeds or even go astern on one track while gomg ahead on the other. Rudders in amphibians tracked

vehicle,

propelled

by paddlewheels

or screw propellers

are almost of necessity placed in the outflow jets

from those propulsion devices. (7) Despite its clumsy form, maneuverability of an amphibian may not be too difficult to achieve because the length-beam ratio of such a contrivance is usually about 3 or 4 and rarely exceeds 5.

the complete range of media from clear water to

hard ground, growths, and

comprising

mud

silt,

sand,

vegetable

of all possible consistencies.

The screw propeller is adapted only for use media having the consistency of water. Undoubtedly, it is the most efficient of the propulsion devices, and capable of producing the highest speeds at which craft of this kind can travel in water. The propeller can be housed and at the same time protected in a tunnel under the stern of the craft, similar to that on a shallow-draft

Despite the fact that an amphibian

is

of

practical use unless it can travel in water,

no

it is

(2)

possible that whatever water-propulsion device

in

is fitted

vessel.

An adaptation

propeller

is

possible.

of the It is

outboard or swinging even practicable to

provide, as John Ericsson did for the American auxihary sailing ship Massachusetts in 1845, a propeller carried

verse

plane

by an arm swingmg

[Isherwood,

B.

F.,

in a trans"Engineering

Precedents for Steam Machinery," Vol.

II,

pp.

When

working it is swung down so that below or at least abaft the hull. When not working it is swimg up, well clear of the ground and inside the frontal or transverse 213-220].

the propeller

is

projected area of the vehicle.

The screw

propeller

to

it

may have

to play a secondary role

to the land-propulsion gear. Because of the variety of possible configurations, not

much can be

said

emmust have a reasonably

as to design for water propulsion except to

phasize that the water

good path to flow to whatever propdev is fitted. Because of the interference effects described in Sec. 32.2, the cleats on moving paddletracks always give the best performance when they are spaced as far apart as the considerations of ground or land travel permit. Although the water-excludmg portion of an

amphibian may look more hke a covered wagon than a boat or ship, the law of Archimedes still apphes. The craft sinks in the water untU the weight of water displaced equals its scale weight. Because of the relatively high bow-wave crest and deep folloAving trough created by the amphibian body when running at moderate speed.

HYDRODYNAMICS

808

and because it has a prow which resembles that of a scow more than that of a boat, the provision of adequate freeboard at the running attitude particularly

is

important.

possible to calculate

empirical

of

This

and there

is

is little

data for reference.

Towing and

are definitely indicated. Fortunately,

when the and when

almost wholly due to pressure the wavemaking aspects are to be studied, tests can be accomplished in any of the small model is

76.29

Vessels Designed for Beaching.

reported that the course of

its

Chmese junk became,

It

is

in the

long development, a rather more than

is

because of the almost

use of a non-watertight forepeak and a watertight

bulkhead at its after end stemmed from the hopelessness of keeping tight the hull seams around the stem with constant beaching. While the shallow-draft sternwheel river steamers of America were not designed expressly for beaching they were eminently adapted for tying up along the river banks and handling cargo whenever the occasion demanded and wherever there was a bank suitable for the purpose. Like the amphibian, therefore, the first craft designed for collision

transferiing cargo directly to a bank or beach were engaged in peaceful pursuits. The need for peacetime landing craft may be expected to continue as long as shore facilities lag behind

needs.

Requu-ements for vessels to carry heavy, bulky, and expensive cargo for landing directly on the beach must state the:

Minimum

Minmium depth

for keeping one

end

of the

craft waterborne or, conversely, the distance within which the ship shall approach the water's

edge at the beach

Range

conflicting requirements of (1) acceptable for

ocean voyages and

(2)

shallow draft with trim by the stern for landing

may

be met by the same procedure as for ships in

and for tankers traveling light, that is, by the use of liquid (water) ballast. This can be

of tide or

Strength and direction of tidal and other

currents at the

pumped out it

just before landing at the beach or can be shifted aft to give the desired trim.

bow, adapted to landing on broad, sand beaches but wholly unsuited for of a broad, flat, shallow

The only reasonable solution to this impasse appears to be the use of liquid ballast, liquid fuel, or liquid cargo in the forward part of wavegoing.

the vessel.

The bow

bank or beach

Wind waves and

surf to be encountered

Percentage (approximate) of the useful load which can be devoted to changing the trim of the craft to accommodate the depth and slope of the beach

is,

by

means, pushed down as far

this

as possible, in an effort to keep the flat portion

always under water, so that slamming does not occur there. The hquid is shifted aft when approaching the beach, to hghten the vessel forward

and to accommodate the slope of the beach. Proposals are made from time to time for a landing craft to be fitted Avith

bow

propellers

and to run in waves with the deep end forward. This sounds attractive but has the disadvantage of a high thrust-deduction fraction for screw propellers positioned ahead of the hull, as well

as inadequate submergence and racing because

ampfitude of pitch at the bow when

traveling in waves.

A form well adapted to operation in reasonably rough water and to running in toward shore through heavy swells and surf is one having a flattened W-section, similar to a pair of inverted-

vee

water level to be expected at and during the landing

(f)

The

wavegoing behavior

of the large

slope of beach wherever a landing

needs to be made

(e)

a pier or quay.

design. This involves the almost inevitable use

routes. In fact, it

(d)

foregoing requirements are in addition to

supposed that the ancient

and wharves along the

(c)

The

those for a ship of normal design which lands at

A much worse problem is not so easily solved by the compromises often encountered in ship

craft

total lack of piers

(b)

in

traffic

passable landmg

(a)

Relative importance of landing on a beach compared to maintaining speed and wavegoing the open sea.

ballast

basins.

human

Ser. 76.29

(g)

as

almost imbackground

simple self-propulsion tests of small-scale models

drag

IN SHIP DESIGN

hulls, like

two sea

Three projecting keels

sleds placed side

may

be

fitted

by

under

side. it

to

somewhat as longitudinal stabilizing fins and to resist slewing, yawing, and broaching. In addition, act

the three keels provide great lateral stability

when beached,

to say

nothmg

of

tribution of the beaching load.

circumstances

the

surfaces under the

absence

of

bow might

an excellent disUnder certain flat,

horizontal

defer or ehminate

slamming. Under other sea conditions, especially

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 7 6.30

It is impossible,

809

within the space allotted in

do more than describe briefly certain problems encountered in this hydrodynamic design, having to do primarily with operation submerged. One seldom finds these problems discussed scientifically in any kind of literature. A statement of them, with their present solutions (or lack of solutions), should not only broaden the outlook of the marine this book, to

special

architect engaged in the design of surface vessels

but also give him a more penetrating insight into the influence of hydrodynamics on the design of kinds and sizes of water craft.

all

It might be thought strange, not for so many other missing shipoperation requirements, that no basic requirements for submarine vessels have ever been

Requirements.

I.

Landing Craft with Inverted V-Bottom AT Stern Official U. S. Navy photograph. The small auxiliary rudder forward of the strut is for control when backing. The hole in the rudder permits withdrawing of the Fig. 76.U

propeller shaft without unshipping the rudder.

driven hard, the W-sections forward might

if

produce large accelerations and decelerations, as sled. The under side of the stern of a landing craft with a single inverted vee of small slope is illustrated in Fig. 76. U. Although it has to date (1955) been used on small vessels only, there is a great advantage in having hydraulic jet propulsion available under does the sea

were

it

formulated and published. Those which follow are sketchy but they may at least serve as the

groundwork for development in the future. They are based upon a possible, even though seemingly remote utilization of the submarine vessel for peaceful purposes. No attempt is made to go into detail or to insert numbers in these requirements:

Submerge and emerge, while stationary

(a)

or

dimensions

under way, when initially on the surface or submerged. This may or may not have to be accomplished within a given interval from the "execute" signal, starting from a given set of conditions as regards ballast water carried and percentage of reserve buoyancy. (b) Run submerged at a given nominal depth, throughout the complete speed range, without varying up or down more than a given amount

G. de Rooij ["Practical Shipbuilding," 1953, Figs. 791 and 792 on pp. 368-369]. Model test data for

from that depth (c) Run submerged, throughout a given speed range, without exceeding specified trim angles

the bottom

By

when

getting off a

bank

or beach.

directing the jet forward, toward the region

where the bow is aground, it is extremely useful washing away the sand or soil and freeing

for

the vessel easily.

General arrangement drawings and principal of landing and beaching craft of intermediate size (LCF and LOT) are given by

four models of landing craft are found on

RD

SNAME

sheets 38, 40, 43, and 44.

76.30

Common

Some Hydrodynamic Design Problems

There are no books, literature, which discuss the design of submarine vessels [Hay, M. F., "The Design of Submarines," SNAME, 1909, pp. 233-255]. The hydrodynamic design alone involves matters of diving and surfacing, dynamic equilibrium, speed and propulsion, .maneuvering, and wavegoing, both surface and submerged. Diving and surfacing involve in turn the flooding, venting, and blowing of the main ballast tanks which provide the reserve buoyancy of the submarine when it is on the surface. to All

and there

is

Submarines.

little

technical

(by the

bow

or stern) for the series of speeds

Maintain a given depth, within specified hmits, when the excess of static weight or buoyancy reaches a certain limiting amount, generally a percentage of the total weight or buoyancy, (d)

at

all

(e)

submerged speeds above a certain minimum Hold a given depth and maintain a level

fore-and-aft attitude, within not-too-close limits, when underway submerged at a very slow speed,

than a certain maxmium. This is the operation as hovering. The speed is so low that dynamic control is rather weak. Change depth, either up or down, within (f)

less

known

a given elapsed time from level running at the original depth to level running at the new depth.

HYDRODYNAMICS

810 within

certain

diving-plane

speed,

of

limits

angles, fore-and-aft inclination of the vessel,

buoyancy

excess static weight or

Change course

(g)

and

a horizontal

in

when submerged, from the

direction

small angles involved

normal steering to turns of 180 deg or more good wavegoing performance as a

in

(h) Possess

including

surface vessel, for personnel

the craft

is

reasonable

who may be on deck

either stopped or

safeguards

at sea,

when

underway

Provide adequate freeboard in the surface for access hatches leading to the pressure hull which may be open when underway (i)

condition,

IN SHIP DESIGN

the underwater hull design is abovewater design to msure acceptable wavegoing performance, the same as for the surface ship. While it is perfectly possible for a properly sealed submarine to plow through surface waves instead of riding over them, it suffers from much the same retardation as would a surface vessel under similar circumstances. Most of the space between the inner and the outer hulls is devoted to the provision of added buoyancy when the vessel is on the surface. In fittings. Similarly,

tied into the

this condition the water-excluding

Rest on the bottom for appreciable periods, and possibly travel along the bottom.

as diving trim at full buoyancy,

Physical Arrangement. To serve as a background for a discussion of hydrodynamic design problems of a submarine there must be some knowledge of the principal physical features of this type of vessel. It is possible but not likely that a further half-century of development will modify somewhat the physical arrangements of

modern

the

(1955)

modern,

relatively

One such design, shown by G. de Rooij

design. is

["Practical Shipbuilding," 1953, Fig. 42 on p. 29

and

Fig.

788

the back of the book.

A

brief

when the

vessel is

on the

The

result is

surface, the inner

appendages are raised above the level water by a volume equal to that of the main-ballast tanks, between the mner and outer hulls and below the surface waterline. This main-ballast-tank volume divided by the inner or pressure-hull volume is thus the reservehull

and

its

of the surrounding

buoyancy

ratio in the surface condition.

customary, on double-hulled submersibles, for the main-ballast tanks to extend above the surface waterline in diving trim. In fact, this is It

is

usually necessary,

to

provide adequate

initial

above the surface waterline adds to the reservebuoyancy volume of the pressure hull and of all water-displacing appendages and objects above

distinct

hulls,

taking

into

consideration

the

underwater and the abovewater portions as units performing distinctly different functions. The always-buoyant inner or 'pressure hull is of a form best adapted to resist external hydrostatic pressure, with practically no regard for the ease with which it could, as an independent unit, be driven through or along the surface of the water. The outer hull is a ship-shaped envelope built around the inner or pressure hull, designed to minimize resistance of the combination for surface propulsion and to provide spaces between the hulls for water-ballast tanks and fuel tanks. The portion of the outer hull lying below the waterplane in surface condition, indicated in diagram 2 of Fig. 37. C and in the schematic of Fig. 76.V, fulfills exactly the same function for a submarine as for a surface vessel.

section

is

that,

its

on the surface, called a

itself

submersible in this book, possesses two rather

with

all

metacentric stability and a safe range of positive stability. The volume of the main-ballast tanks

is

a good account of

It

external appendages.

plus

is

equal

is

given in Sec. 203 on page 368]. submarine which is also required to give

description

The

m

of the

volume of the inner hull

to the water-excluding

(j)

II.

volume

outer hull up to the surface waterline, in what

known

or at anchor

7630

Sec.

generally designed in the necessarily

clearance,

access

more regard between

same manner, for

hulls,

machinery and special

The

the waterplane.

vertical hatching of Fig.

76.V indicates this volume in schematic fashion. A rather complete general discussion of these features, including the matters of equilibrium of

static

and

forces

of

metacentric

discussed subsequently in this section,

by A.

Nov

I.

McKee

1929; also

the U.S.,"

[Bu

C and

is

given

R, Tech. Bull. 8-29,

"Development

SNAME, HT,

stability

of

Submarines in

1943, pp. 344-355].

When the craft submerges, sea water must be admitted to the main-ballast tanks to destroy the buoyancy which lifted the pressure hull above the water in the surface condition. For a vessel having a water-excluding displacement when submerged of say 3,000 tons, the weight of water to be admitted to the main-ballast tanks

may

Furthermore, to permit flooding with this water, the air in the mainballast tanks must be vented to the atmosphere. exceed

1,000

Admitting

tons.

this

much water and

venting an

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.30

I

811

Wood-Slat Decklor Perforoted- Metal Deck for Ventino of Superstructure

Hatch Freebocird

Fig. 76.V

Schematic Section op Double-Hulled Submersible Showing Main-Ballast Flooding and Venting Arrangements and Buoyant Volumes

equal volume of

air,

while at the same time

exercising control of the flooding

among a number

and venting

of separate tanks, involves a

given a large tumble

beam

of the flat or

rather elaborate system of large flood valves in

than 0.7 of the

the lower part of the outer hull and correspond-

waterplane.

ingly large vent valves along the tops of the

main-ballast tanks,

indicated

schematically in

Fig. 76.V.

Somewhat

similar

water-handhng systems

required for taking aboard, shifting

what

is

known

pumping

out,

are-

and

as variable-ballast water

within the pressure-proof boundaries of the submarine.

The

admission, discharge, and transfer

water serve as compensation for the expenditure of useful weights such as food, stores, and lubricating oU; for the taking aboard of additional of

weights; and for the moving of these weights fore and aft and transversely within the pressure-proof boundaries to suit the mission of useful

the vessel.

Because a submarine is not burdened with deck hatches and rarely requires personnel to work on deck at sea, except possibly for a limited region amidships, its freeboard to the superstructure deck can be much lower than that of a surface vessel. With this low freeboard it is expected that soUd water will be taken aboard. Several expedients are adopted for unloading this water expeditiously. The topside is vulnerable

home and

the deck edges

are often well rounded into the side, so that the

cambered deck

maximum beam

is

rarely

more

at the surface

The deck forward, excluding the rounded turtleback on each side, may be not more than 0.5 times the beam at the corresponding section. The perforations and slots in the deck, placed there to provide rapid venting of the free-

means away the deck load of water before it during an up pitch and dashes against

flooding superstructure volume, afford a of sluicing

sUdes aft

the deck erections amidships.

The freeboard at the extreme stern may be diminished to zero, so far as wavegoing characteristics are concerned. If, however, the surface speed is high enough to produce a crest of appreciable height on the stern wave, the outer hull should be carried up at least to the top of this crest, with the vessel in running trim.

The

flooding ports or openings along the lower

edges of the superstructure volume, just above the surface waterline, represent an unsolved problem as far as combining rapid flooding of the superstructure with surface

waterline

minimum drag along

is

concerned.

A

the

continuous

flooding slot along the lower edge of the superstructure, used at various times, is not

able

solution

because

of

the

an accept-

relatively

large

HYDRODYNAMICS

812

quantities of stationary water which can enter there.

by

When

these are picked up and accelerated

transverse

parts housed loss of

members and other

structural

mthin the superstructure a

energy

The volume

useless

involved.

is

of

water occupying certain small

free-flooding spaces below the surface waterplane,

rarely to be found on surface craft,

as

is

considered

a part of the ship weight which must be

must be displaced around these spaces the same as around the other parts of the hull. In one respect these several volumes of water are treated as though they were carried along. Outside water

blocks of

ice,

frozen in place. If the free-flooding

spaces have external openings in regions where there hull,

is a pressure gradient on the outside of the a flow of water through the spaces takes

IN SHIP DESIGN

Sec. 76.30

motion. Combined, these render the equalization of weight and buoyancy B a matter of hydro-

W

dynamics as well as hydrostatics. Admitting and expelling variable-ballast water in suitable quantities and at the proper locations as the submarine is moving can take care of the preponderant hydrostatic inequalities between and B. However, the hydrodynamic inequalities usually vary in magnitude with ship speed. They, as well as the undetermined {W-B) values, are normally compensated by vertical forces derived from hydrofoil action of the diving

W

planes. It is found that an amazing variety of submarine forms are afforded adequate control in rising and diving by the usual arrangement of bow and

stern planes.

place because of this pressure gradient. Energy

expended in setting up and maintaining

this flow,

generally of an eddying character and invariably is energy lost so far as the propulsion submarine is concerned.

undesirable, of the

III.

Equilibrium of Static and Dynamic Forces-

In a surface vessel, nature takes care of the balance between the hydrostatic weight and

buoyancy

forces

by adjusting the

latter so as to

equal the weight force imposed by the crew.

the weight

is

increased

If

by loading something

aboard, the vessel sinks to provide the additional

buoyancy. In a submerged submarine the buoyancy force is usually fixed by the total volume of the water-excluding structure and external parts, combined with the density of the surrounding water. The crew then has to make the necessary internal adjustments in the weight force, by admitting or expelling or shifting variable-ballast water, if equilibrium is to be maintained. While it is possible for the primary static forces of weight and buoyancy B to be balanced by taking in or pushing out variableballast water, this is the exception rather than the rule in submerged opei-ation. It is rarely possible to achieve an exact balance of primary hydrostatic forces, and moment as well, when underway beneath the surface. In addition there are vertical dynamic forces and moments gen-

W

when the vessel is underway by the lack symmetry of the outer hull about any longitudinal horizontal plane, by the presence of deck erections and appendages, and by small inclinaerated of

tions of the fore-and-aft axis to the direction of

and Pendulum Stability. The adequate metacentric stability when in the so-called "awash" condition, during either diving or surfacing, undoubtedly involves a time element to a small degree, and hence partakes of the nature of hydrodynamics. There are free surfaces in most if not all of the main-ballast tanks at some time or other during flooding or blo\\'ing. Each tank is in communication with the sea and only indirectly with its companion tank on the opposite side of the vessel. For this reason it is necessary to reckon a loss of correspondIV. Metacentric

problem

of

BM

ing only to the square

moment

surface in each tank about

its

of area of the free

own

fore-and-aft

and not about the longitudinal axis of the vessel. As a practical matter the time element enters particularly in the blowing-down operation while surfacing. This requires some minutes, dining which time the loose water in each mainballast tank is in direct communication with the sea through the flood valves at the bottom of the tank. There must be sufficient control over axis,

the compressed air delivered to the main-ballast

tanks on the two sides to hold the vessel in a sort of average upright position,

by a heavy beam

down

sea,

even when acted upon

with water surging up and

in the tanks.

For a consideration of the forces and moments involved in maneuvering submerged it is necessary to realize that the submarine in that condition has no effective or intact surface -waterline = and area (and no loose water), so that the metacenter coincides with the center of buoyancy CB. What holds the submerged submarine upright is the fact that the center of

BM

M

C

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec. 76.30

A

"Surfoi

BuoyancN; Force

B

-

813

few features already kiarned from them are

discussed in Sec. 15.0 and illustrated in Fig. 15.

under

flexible-fin propulsion.

However,

in

an

effort to

copy features that

will

be helpful in submarine design, two obstacles present themselves. They have not yet been sur-

Up^^

Stern

-->_J^uM Axis

mounted.

Arm

Restoring

The

mechanism known, man has not discovered the exact method by which the fi.sh or first is

that, while the general

of fish propulsion Submarine Acts Qs a

the sea

Pendulum with Weight at

CG

and Support at

CB

mammal

is

achieves

its

highest speeds or

Manimethods must be known and understood before they can be copied or utilized. For s-wims rapidly for long periods of time. festly, these

76.W Sketch Illustrating Pendulum Stability OF Submerged Submarine in Plane of Symmetry

Fig.

example,

it is

asserted that, in order to maintain

a speed of 20 or 25 kt while converting food gravity

CG

always

lies

below

combined

the

energy into propulsion energy and motion at the

center of buoyancy and metacenter. This gives

highest rate

known as pendulum stability, with G always below M, illustrated in Fig. 76.W. Any moment of weight forward or aft of the

to

the vessel what

submerged

CB

is

causes the vessel to trim in that

direction until the center of gravity

underneath the center of buoyancy. offset

may

the vessel

external

A

small

result in a large trim angle unless the

necessary correction

When

directly

is

is

moment,

is

made

inclined

to the

CG

position.

submerged by some

either in heel or in trim, there

always a pendulum-type restoring moment acting to level it off at an equilibrium attitude. When underway, this moment is superposed on is

the hydrodynamic moments.

V. Hull Shape and Propulsion. repeatedly raised, propulsion

is

The

question

is

when submarine shape and

discussed,

why

the submarine de-

signer should not take advantage of the develop-

ments

of nature, involving a process of evolution

through untold millenniums. He is why he does not copy some sort of aquatic fish or mammal, such as the shark or the porpoise, or even the whale. These creatures extending

known

to be, for their

size,

capable of prodi-

gious speeds, exceeding 20 kt in spurts for the

porpoise and the whale.

They make

these speeds,

at least in the case of the porpoise, with

what

seems to be effortless ease. The achievements of fish and aquatic mammals, in the matter of propulsion and maneuvering and related operations, have been the subject of scientific, engineering, and physiological study for three-quarters of a century or more. Research along these lines

is

continuing, steadily

if

slowly.

known

not do

weight in small

fish

every

seems certain that the animal does

this, at least

such high speed. It

while traveling continually at is

as inefficient as

if

man, a porpoise would have

to

his entire

half hour. It

also asserted that a pigeon,

some man-made

airplanes,

would have to carry along an internal-combustion engine with a power of several horses, in order to

make its known speed through The second is that for the

the

air.

great majority of

creatures in this category, propulsion

inherently

upon

in addition to

Certainly,

is

motion

swimming

of

at the high relative speeds

body undulations.

has

a

not

yet

based

body as a whole, the fins, tail, and flukes.

flexure of the

desired always involves

invented

Man

submarine structure

which can withstand great hydrostatic pressures and house a powerful propelling plant, while at the same time possessing great flexibility and capable of generating S-shaped undulations which travel along its length.

Actually, because of their varying environment

questioned as to

are

consume

and

their different needs, fish

often

rather

poorly

and mammals are by modern

streamlined

hydrodynamic and aeronautic standards. If it becomes necessary, on a submarine, to depart from a good streamline shape, that of some fish or

mammal

could be accepted.

VI. Maneuvering Submerged. ing, as (1)

Transient and steady motions in a straight

line parallel to the (2)

The term maneuver-

used here, involves:

submarine axis

Steering and turning in a plane that

zontal or nearly so

is

hori-

1

HYDRODYNAMICS

814 (3) Rising,

diving,

and

depth-keeping

in

a

vertical plane. of the vessel

are involved in each case, as contrasted to a

smaller underwater volume for the surface ship.

submerged to a depth h

times

its

hull height h,

surface above

it

is

of the order of several

the effect of the free

negligible.

This situation

is

contrasted with that of the surface ship, sur-

rounded by an air-water interface upon which gravity waves can be formed. Heel when turning, usually only an inconvenience on a surface vessel, can introduce vertical forces and moments on a submarine which affect its trim attitude and perhaps its depth of submergence. Unless the submarine carries a topside rudder of the type described in Sec. 37.14 and illustrated in diagram 2 of Fig. 37. C, the same steering rudder that "handles" the normal lateral area on the surface must, for horizontal steering and turning submerged, "handle" the greater lateral area of the entire bulk of the submarine. One feature related to both speed and propulsion and to maneuvering requires mention. Unlike a surface vessel the speed and propulsion requirements for a submerged submarine can not be dissociated from those of trim and attitude. In other words, it is useless for a submarine to be able to travel at a certain speed submerged unless the vessel can be held at the desired attitude and depth at that speed. 76.31

Lightships

Light

or

Vessels.

The

design of a lightship or a light vessel, whether

manned

or unattended

when on

station, repre-

some extremely interesting problems in hydrodynamics, which have benefited from only sents

sporadic scientific study in the past.

A

few of

these are discussed here, in rather limited scope.

Stated

briefly,

the requirements for a lightship

are for a vessel that shall: (1)

Display the necessary Ughts or other identifiboth abovewater and underwater

cation, send out

and perform These are best accomplished when the vessel is upright and at zero trim although they must be carried out under all

Sec.

that the vessel maintain

is

minimum

Exert the

(3)

The bulk shape and bulk volume

If

IN SHIP DESIGN

charted position.

consistent with mooring cable or when subjected to wind, or current, or both

other characteristics, line,

its

76J

on

pull,

its

(4) Be free of violent or undesirable yawing under the influence of wind or waves or both (5) Reduce the motions of rolling, pitching, and heaving to a minimum consistent with other requirements and the wavegoing conditions to be encountered. This is to reduce fatigue of personnel and wear and tear on equipment, whether the

vessel

is

Be

(6)

manned

or

unmanned.

able to propel itself at reasonable speed

and to maneuver,

if

the vessel

of this type.

is

The lightship is in a class with the life-saving boat discussed in Sec. 76.32 with respect to its abiUty to remain on station, completely operative except for

its

when

propulsion plant,

vessels of its size (and larger)

all

other

are required to

seek shelter in port. Its freeboard coefficient or freeboard-to-length

ratio is

much

greater than that of

any other type

of craft except a life-saving boat. Similarly, the

reserve-buoyancy ratio is very large, perhaps even larger than that of the latter craft. Lightships may have much more than the usual

amount

of sheer, especially forward, unless the

more deck height, for its whole would be customary in other vessels

vessel has one

length, than of its size.

While low resistance in a lightship when moored in a seaway is one of the major requirements, some of it may be sacrificed to permit the use of special features furthering the vessel's mission.

One such

feature

is

a set of extremely wide stayed by auxUiary

roll-resisting keels, possibly

struts extending

from near the outer edges of

the keel to the adjacent hull [SBSR, 17 Jan 1935,

Another would be an effective pitchdevice, provided a successful one could be devised for this type of vessel. Indeed, anything which assists in damping any part of the wavegoing motion is a useful feature, whether p.

66].

damping

manned

sonic signals, transmit radio signals,

the craft

similar functions.

provided, is almost never a primary feature, but the drag exerted by the stationary propeller in a current should be held to the minimum practicable amount. In only a very few cases does the technical literature contain reasonably complete principal dimensions, hull parameters, form coefficients, and other characteristics of lightships. Table 76.g

ship-motion conditions. (2)

Remain

afloat

and operable and on

station,

invariably an exposed one, regardless of the state of the sea and of the wind and weather. In fact,

the worse the conditions, the more necessary

it

is

Self-propulsion,

if

or unattended.

Sec.

7631

1

DESIGN OF SPECIAL-PURPOSE CRAFT

815

HYDRODYNAMICS

816

embodies the rather meager information of this type which could be collected for six lightship designs dating from 1881 through about 1914. Additional information and data, on old as well as modern vessels, are to be found in the brief list of references which follows: (a)

Body plan

of Elbe lightship,

(b)

(c)

=

with a

B/H

ratio of

and a rise of floor of 24 deg, is shown in Schiffbau, 26 Jun 1912, pp. 715-722, PI. .3 Idle, G., "The EfTect of Bilge Keels on the Rolling of Lightships," INA, 1912, pp. 103-123 and Pis. IX-XI. Figs. 10-13 on PI. X illustrate by flowlines the assumed motion of the water around the ship hull and around the bilge keels when rolling. Cook, G. C., "The Evolution of the Lightship," SNAME, 1913, pp. 97-118 and Pis. 52-63. Gives considerable historical data. Shows arrangement plans, body plan, and lines of self-propelled U.S. Lightship 94. Principal dimensions and hull coefficients are listed in Table 76. g. The wedges of immersion and emersion are intended to be nearly 25.25/12.46

2.03,

equal. The bilges are very slack. The full-load displacement at 18.58-ft draft is about 1,072 t. Static stability is a maximum at about 60 deg, and very

100 deg. The roll-resisting keels are of The Ship-

large at

triangular section, 1.5 ft wide. See also

builder (now

SBMEB), Jan-Jun

1914, Vol. X, pp.

215-220. (d)

Cooper, F. E., Liverpool Eng. Soc, The Shipbuilder (now SBMEB),

Mar

1914; also

Jan-Jun

1914,

X, pp. 295-296. Describes the non-self-propelled light vessel Alarm, whose dimensions are listed in Table 76. g. The bilge keels extend for 0.6L and are about 1.2 ft wide. New Lurcher No. 2 Lightship, Diesel Prog., Mar Vol.

(e)

192, p. 59 (f)

(g)

(h)

New New

Mar. Eng'g., Apr 1953, p. 45 Ambrose Lightship, Mar. Eng'g., Sep 1953, p. 85 Lightship Kish Bank, illustrated in SBSR, 27 Jan 1955, p. 36, has a centerline hawsepipe just above the for mooring on station plus a regular hawsepipe on each bow with port and starboard bower anchors and separate chains. The Motor Boat and Yachting, Aug 1954, p. 357, shows a photograph indicating extreme local sheer at the bow. Light vessel Osprey, SBMEB, Jun 1955, pp. 417-418; SBSR, 30 Jun 1955, p. 841. This non-self-propelled ship has an overall length of 136.42 ft and a beam Overfalls Lightship,

of 25

ft,

mooring

(j)

with "exceptionally large bilge keels." The is by 1.75-in chain, attached to a 4-ton anchor, with port and starboard 1.5-ton

from vessels

in distress it

be required for Presumably general design requirements exist for these craft but none have been located in the technical literature, especially none that relate directly to hydrodynamics. The following specifications appear to meet these needs: will

(1)

The

craft .shall be able to operate in the

matter how severe (2) The boat shall be self-righting without crew, when rolled to any angle of heel up to 180 deg (3) It shall be virtually unsinkable; in other words, it shall remain afloat, even when moder-

damaged The reserve-buoyancy

ately (4)

shall

ratio, with crew only, be exceptionally large, preferably of the

3. The wind resistance inherent in abovewater volume is accepted. With all the rescued personnel which can crowd aboard, the reserve-buoyancy ratio shall be not less than

order of 2 or

this large

1.0.

(5)

of

There shall be a covered deck at both ends, arched or turbleback form, designed to reUeve

itself of

water and spray which comes aboard well

of

subjected to a succeeding load

is

water

(6) All cockpits and depressions in the weather deck shall be self-baihng, with the boat carrying its crew and the maximum number of rescued

personnel (7)

The

free-running speed, without passengers

but with crew and

full fuel

and

erably, within the overall fair surface of the hull. it

shall

be possible to operate them jiust aground, or

with the boat

when directly alongside a larger vessel. (9) The fore-and-aft position of the propulsion be such

they continue to running under heavy

76.32 Life-Saving or Rescue Boats. The hfe-saving or rescue boats discussed in this section are the self-propelled craft which are based on shore .stations, or on large station ships afloat.

devices

They

with other recjuirements listed

by passenger

be

It shall be not less than 10 kt, in smooth water and no wind, and preferably 12 kt or higher. (8) The propulsion devices shall be housed, pref-

In any case

e.xclude the lifeboats carried

stores, shall

sufficient to reach a disaster scene expeditiously.

in shallow water,

793 and 794 and Sec. 206 on pp. 369, 373.

open

sea or to stand by in practically any weather, no

anchors in reserve. Rooij, G., "Practical Shipbuilding," 1953, Figs.

appears that life-saving

home or shore stations many years to come.

boats operating from

mushroom

De

Sec. 76.32

personnel can be taken aboard another vessel. Despite improved methods of removing personnel

before the craft

DWL

(i)

IN SHIP DESIGN

and other vessels, intended only to remain afloat and stay together on the scene until the rescued

shall

produce

thrust

when

that

pitching conditions (10)

The

draft shall be the

minimum compatible

DESIGN OF SPECIAL-PURPOSE CRAFT

Sec.

7632

(11)

The type and

rudder(s)

taking suction from the bottom of the boat must

shall

be such that steering or maneuvering control

be able to work in water-mud or water-sand

boat

of the

is

position

maintained at

the

of

all

times, regardless

mixtures.

A

of the state of the sea.

from item (1) preceding that these boats represent very nearly the ultimate in the wavegoing performance required of any vessel at sea. It might almost be said that life-saving boats should float and remain upright when all other craft sink or turn bottom side up. To achieve requirements (1) and (4) they are distinguished by very large freeboard at the bow and stern, usually very nearly equal at both ends, by a very large sheer, and by a very large volume of abovewater reserve buoyancy, often in the form of closed compartments intended for buoyancy only. The self-righting requirement (2) means that the boat should have positive transverse metaIt

clear

is

centric

or

positive

pendulum

inclined to amj 'position in

roll.

It

stability

when

should not only

and 180 deg but should be capable of rolling completely over (360 deg), without serious damage, if caught by a breaking beam sea. right itself from heel angles between 90

Cockpits and other depressions exposed to the weather are rendered self-bailing by making them watertight, with freeing slots passing out through the sides or down through the bottom. Some water enters through these slots when the boat pitches and rolls but the

amount

is

small, usually

only enough to cause slippery footing or to freeze

817

Gill

screw propeller,

fitted inside

an internal and dis-

duct, taking suction through a grating

charging through a rotable "deflecting nozzle,"

sometimes used for a lifeboat installation [SBSR, 27 Jul 1939, pp. HI, 113]. Figs. 59.Da and 59. Db show the general arrangement and method of operation of the Hotchkiss and Gill is

propellers, respectively.

pointed out in reference

It is list

(o) of

the attached

that rescue-boat speeds of the past, usually

not exceeding 8.5 kt, are no longer considered adequate. Speeds up to 20 kt, to be incorporated in German life-saving boats under design at the time of writing (1955), will call for a rather modification in the double-ended form which has been standard since the days when all these craft were propelled by oars. Transom sterns of moderate width are indicated for speedlength quotients exceeding about 1.2 or 1.3. It is possible that the high-speed, round-bottom, drastic

transom-stern patrol boat of small size, already developed into a craft capable of withstanding

extremely heavy weather, may be found suitable life-saving boats meeting the requirements

for

beginning of this section.

listed at the

Appended

a brief

is

list of

references relating

to life-saving or rescue boats. Although by no means complete it will give the reader some idea

problems involved:

of the design

into objectionable ice in cold weather.

On

certain life-saving boats of older design,

which were not required to be self-righting, it was customary to fit one or two projecting appendages, resembhng roll-resisting keels, along the bulge on each side. These were slotted so that, in the event the boat turned bottom side up, the survivors could use them as hand rails. In fact these appendages were wide enough to serve rather well as roll-resisting keels, despite the

cut through them. There

is

(a)

(c)

To meet

specification (7), propulsion

may

the

Reynolds advocated the use of models J., "Experiments with Lifeboat Models," INA, 1890, pp. 263-283 and Pis. XIV and XV. Reserve-buoyancy ratio of craft in the period 1862-1890 varied from about 0.75 to 2.1. Bamett, J. R., "Motor Lifeboats of the Royal

somewhat general terms.

Everett, H. A., "Stabihty of Lifeboats," SNAME, 1913, pp. 133-143 and Pis. 73-82. While this paper applies to lifeboats as carried on larger vessels, it contain interesting information for the designer

(e)

making a study of life-saving craft. Bamett, J. R., "Recent Developments in Motor Life-boats," INA, 1922, pp. 283-290 and Pis.

(f)

Bamett,

be by

with impellers entirely inside the hull, are often employed. Any type of propeller or impeller

Investigating

Corbett,

in (d)

or guards for the lower portions of the hull.

ducted propellers, approaching pure hydraulic-jet propulsion, or by screw propellers working in tunnels of suitable shape. Hotchkiss propellers,

of

National Lifeboat Institution," INA, 1910, pp. 112-119 and 129-139; also PI. X. This paper contains the principal lifeboat requirements, expressed

self-

two pairs of roll-resisting keels, to improve the wavegoing performance and to serve as fenders

"On Methods

fessor

(b)

righting rescue boat could not be fitted with one or

O.,

Qualities of Lifeboats," Manchester Literary and Philosophical Society, 14 Dec 1886, in which Pro-

hand holes

no reason why a

Reynolds,

XIX-XXII J.

R.,

"Motor

Life-boats

of

the

Royal

National Life-boat Institution," INA, 1929, pp.

225-236 and

Pis.

XXIII and XXIV

HYDRODYNAMICS

818 (g)

IN SHIP DESIGN

The two "Moyens de sauvetage modemes (Modem

Ghiradi, L.,

Methods

of Lifesaving),"

(i)

Design

of

ATMA,

Institution Lifeboats,"

(j)

482^83 "The German Lifeboat

(k)

Self-righting,

National

Lifeboat

SBSR,

15

May

1947, pp.

SBSR,

USNI, Dec

illustrated in

L., Pengelly,

Naval

"Theoretical

5 Jun 1947,

Guard

lifeboat

is

craft

A

(n)

H.

S.,

and Sims, A.

Architecture,"

1953,

J.,

pp.

The Bremen

is

ft.

a beam of 13.75 ft, and The brake power is 2 times 120 horses;

first

is

Each

(p)

of the larger boats built expressly for (q)

ft,

is

lifeboats

20 kt.

of these rescue craft carries a smaller or

"daughter" boat in an inclined trough set in the stem, enabling the smaller boat to be launched and hauled aboard at will. The "daughter" boat is 16.42 ft long and 6.5 ft wide. Although the righting arms are large when the boats are incUned to 90 deg, apparently neither of them are intended to withstand rolling completely

having a range of 238 miles at 8.38

kt.

and

all lifeboats

in general.

11 kt.

is

signed top speed

German

in

for British lifeboats in particular

ft,

the Helgoland. It has an overall length a beam of 17.75 ft, and a draft of 4.75 ft. The brake power is 2 times 300 horses and the deof 73.75

further discussion of British and

diesel engines,

a converted steel huU having an

overall length of 57.42

work

of the larger

"The Future of the R.N.L.I. Lifeboat," SBSR, 30 Jun 1955, pp. 828-829. This article discusses a number of requirements and features for lifeboat design and indicates the probable future trends

(o)

newest types of German lifesaving "cruisers" for

The

stem

desired to launch or to take aboard

SBSR, Int. Des. and Equip. given by G. No., 1955, pp. 67-68. The new British Coverack class are 42.5 ft long, with twin screws driven by

rescue work. These craft are "of a larger, faster, and more powerful t3rpe than previously used."

rescue

it is

Wood

181-183

the top speed

when

for sea-rescue work, of the period 1954-1955, is

1948, p. 1552

(m) "German Lifesaving 'Cruisers'," SBSR, 13 Jan 1955, pp. 41-43. This well-illustrated paper describes the

draft of 4.58

carried in

the smaller one.

non-sinkable Coast

Attwood, E.

Bremen are

is

trim-control device to depress the Service,"

pp. 556-557

(1)

There

one balanced rudder abaft each by a skeg bar which serves as a guard for both propeller and mdder. Between the port and starboard skeg bars there is mounted a horizontal hydrofoil which serves as a

1932, Vol. 36,

Royal

propellers of the

side tunnels.

propeller with its lower pintle carried

pp. 83-104

"Improved

life-

boats.

165-166 (h)

Sec. 76.33

over and righting themselves, as for the smaller

Motor lifeboat Insulinde, Zeit. des Ver. Deutsch. Ing., 13 Apr 1929, pp. 499-503; WRH, 22 Apr 1930, pp.

"Fast German Rescue Ship (Herman Apelt)," SBSR, 25 Aug. 1955, p. 259 (illustration). Length, 66 ft; beam, 15 ft; speed, 17 kt. "A New Watson Class R.N.L.I. Lifeboat," The Motor Boat and Yachting, Feb 1956, pp. 62-63.

76.33

Special-Purpose

Craft

of

the Future.

one can predict the uses, not now dreamed of, to which water craft will be put in the future. It is certain, however, that the creation of new forms or the adaptation of existing forms to these uses is to be done most efficiently by the application of hydrodynamic knowledge, as has been the

No

aim

in this book.

;

CHAPTER

The

77

Preliminary Hydrodynamic Design of a

Motorboat 77.1 77.2

77.3 77 4 .

77 5 77.6 77.7 77.8 .

Scope of This Chapter General Considerations Relating to Motorboat Design Special Design Features for Small-Craft Hulls Design Notes for Displacement-Type Motorboats Semi-Planing and Planing Small Craft Operating Requirements for Planing Forms General Notes on the Powering of Small Craft .

.

.

.

Analysis of the Principal Requirements

.

.

Tentative Selection of the Type and Proportions of the Hull

77.11

First Space

77.12

First

77.13 77.14

First

.

77.20 77.21 77.22

Interdependence of Hull-Design Features Layout of the Lines for the ABC Planing-

843

Type Tender Design Check on a Basis of Chine Dimen-

843

77.25

Selecting the Hull Features; Section Shapes

.

Rise-of-Floor Magnitude and Variation

.

.

Chine Shape, Proportions, and Dimensions Buttock Shapes; The Mean Buttock ... Trim Angle and Center-of-Gravity Position Use of Trim-Control Devices Spray Strips Stem Shape Deep Keel and Skeg; Other Appendages

.

.

A

Scope of This Chapter.

.

846

77.26

Second Estimate of Shaft Power, Based Upon

77.27

Effective Power Running Attitude and Fore-and-Aft Position

77.28

First Space

77 29 77 30

77.31

Weight Estimate for the 18-Knot Hull Power Estimate for the 18-Knot and 14-Knot Conditions Selecting the 18-Knot Hull Shape and Char-

77.32

Layout

Heavy Weights Layout

of the

.

827

850

First

.

ABC

Round-

Bottom Tender Example of a Modern Round-Bottom UtilityBoat Design Design for a Motorboat of Limited Draft

77.33

832 835 836 837 839

77.34 77.35 77.36 77.37 77.38 77 39 77.40

Design of Control Surfaces and Appendages Third Weight Estimate Self-Propelled Tests for Models witii Dynam-

77.41

Partial Bibliography on Motorboats

.

motorboat

.

Estimate of Screw-Propeller Characteristics

.

Propeller Tip Clearances; Hull Vibration

.

Still- Air

Drag and Wind Resistance

.... .

ic

853

854

of the Lines for the

831

840 841 842 842

852 853

First

acteristics

828

847

18-Knot Round-

Bottom Hull .

827

Procedure Second Weight Estimate Approximation to Shaft and Brake

.

of the

825 826

Weight Estimate; Weight-Estimating

Power 77.15 77.16 77.17 77.18 77 19

823 823 824 824

Layout of the 24-Knot Planing

Hull

77.23 77.24

sions

Principal Requirements for a Preliminary

Design Study 77 9 77 10

819

820 822

Lift .

.

.

855 858 858 859 859 862 862 863 864 865

is

design of a planing hull. Chap. 13 discusses basic

defined in this chapter as a mechanically pro-

planing phenomena and Chap. 30 the behavior

having a length of about 110 ft (33.5 meters) or less, running at a Taylor quotient r, greater than 1.0, F„ > 0.3, and of a general type which may or may not include the fishing vessels and yachts of Sees. 76.11 and 76.19. The treatment here is limited to craft driven by screw propellers. The motorboats may be supported wholly or in part by water buoyancy or by dynamic lift on the hull proper. In other words, they may be of the displacement, the semi-

of actual planing craft.

77.1

pelled

craft

planing,

supported

or

the

craft

fuU-planing are

in

a

type.

Hydrofoil-

separate

category,

discussed in Chap. 31 and partially covered

by

the limited bibhography of Sec. 53.9.

As introductory material

for

notes

on the

set of

Some

quantitative data

and planing and a rather lengthy references are given in Chap. 53. Notes for

on dynamic

lift

guidance in determining whether a craft designed to meet a given set of requirements is to be of the displacement type, or whether it is to be a semi-planing or a full-planing form, are found in Sec. 77.10 of the present chapter.

One aim

of this chapter is to collect

and

cor-

performance and design information applicable to motorboats in general, supplementing the large-ship data set down in earlier chapters. Sec. 77.41 contains a partial bibhography relating to smaU-craft, yacht, and motorboat design. It is to be hoped that, in the

819

relate certain small-craft

HYDRODYNAMICS

820

not distant future, an enterprising small-boat designer will present a much more extensive

summary and

and useful

digest of all available

information, as N. L. Skene did some years ago in his

book "Elements of Yacht Design," and Simpson and P. G. Tomalin did more

as D. S.

[SNAME,

recently

1951, pp. 554-611; 1953, pp.

590-634].

Manifestly, this

it is

not possible to compress into

chapter, with its illustrative examples,

all

fundamentals that have appeared in each of several books on the design of motorboats, Usted in the bibUography of Sec. 77.41, to say nothing of the valuable information in the multitude of technical papers and articles on this subject. It endeavors only to cover certain hydrodynamic features of motorboat design in a manner similar to the coverage of the principal features of large-ship design in Chaps. the

essentials

and

IN SHIP DESIGN

Sec. 77.2

which the speeds are usually restricted to T, values less than 2.0 or 2.5, F„ < 0.60 or 0.74, the comments as to water flow and ship behavior of Chaps. 24, 25, and 26 of Part 2 are vahd for

regardless

of

at least

size,

for

all

craft

large

enough to carry an adult human. Except for certain limitations on small craft because of the accommodations which have to be provided for

human

beings of nearly constant dimensions, the

design

rules

and

considerations

set

forth

in

Chaps. 66, 67, and 68 of Part 4 apply to small craft as well as to large ones.

W.

F.

Durand

pointed out as long ago as 1907, in his book "Motor Boats; A Thoroughly Scientific Discussion of

Their Design, Construction, and Operation"

Mar. Eng'g., London and

[Int.

New

York, 1907,

Library of Congress number YM341.D9] that: ".

.

.

the selection of principal dimensions, hull coeffi-

and parameters, underwater form, and the size and form of appendages is handled in almost exactly the same way as for a large vessel." cients

64 through

It

68.

stresses

the

differences

in

and procedures necessitated by size, as well as by the presence of a major supporting force other than buoyancy in the form of dynamic lift. As an illustration of the use of the data presented and the procedures described, there are characteristics

the difference in

included in the chapter the preliminary hydro-

dynamic designs alternative

of

two motorboats,

specifications.

One

two

to

involves

a fast

semi-planing hull and the other a high-speed

full-

planing hull.

General Considerations Relating to MoFor water craft of all kinds there is little difference in behavior \vith size if care is taken to maintain dynamic similarity of flow. This is done when a self-propelled free-running model, or a pilot model large enough to carry one 77.2

torboat Design.

more persons, is built as part of the development work on a large project. Dynamic similarity or

of flow is not fully realized if model tests include towing of the model of a mechanically propelled craft but exclude self-propulsion tests of that

model, its

when driven by a

small-scale replica of

propulsion device. This matter

is

discussed

further in Sec. 77.40. Since similarity of flow

almost

never

endeavoring to

completely ruii

achieved,

as

is

when

simultaneously at the same

number and of the Reynolds model and ship, similarity is maintained for that flow which is considered the most important. This is the basis of the whole

values of the Froude

number

for both

technicjue of ship-model testing.

Considering vessels of the displacement type.

The

—and unfortunately also —hes in estimating the total

principal difference

a principal difficulty

weight

of the finished small craft,

especially

if

some new type. There is another difference, discussed in Part 6 of Volume III under Wavegoing, in that the short wind and ship waves to be met by a motorboat or motor cruiser are considerably steeper than the long waves having the same ratio of wave length to ship length for a of

it is

large vessel.

The motorboat has wavegoing adventures, even in waters that are

considered sheltered. Velox

waves from passing vessels of larger size or greater speed are steep and sometimes troublesome, as are the waves stirred up in shallow areas by sudden squalls and storms. As a rule, the slowing down of motorboats in shallow and restricted waters is taken for granted, so that no special hull shapes are required for these conditions.

Motorboats

of the semi-planing type represent

a considerably more difficult design problem than those of the displacement type. The change of

when underway becomes a major design parameter and the necessity for an accurate estimate of the weight becomes much more acute. Moreover, there is a rather wide variety of possible hull shapes from which the proper choice has to be made. It must be admitted that in the past these problems have not had the benefit of the systematic empirical and practical study, to say nothing of the scientific and analytic research trim

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.2

that has been devoted to the design of larger

time comes, the hydrodynamic other aspects of semi-planing motorboat

ships. Until this

and

design will not be adequately covered, in reference

books or elsewhere. In the design procedure for a full-planing craft it is necessary to emphasize the large and numerous differences between the design problems for a displacement craft, set forth in Chaps. 6G, 67, and 68, and those applying to a planing motorboat: (1)

In the

first

Rr/W,

is

of displacement,

7?,.

/A

or

higher than for a displacement-type

craft, often

Rt/W

the total resistance in

place,

pounds per long ton

by two orders

for a tanker

may

of

magnitude. Whereas

be 4 or

5, for

a liner 10

and for a destroyer or similar high-speed craft up to 130 or 150, the Rt/W value for a motorboat with a T, of 5 or 6 is 700 or 800, indicated clearly by Fig. 56.M. The latter figure or 12,

represents a ratio of say 750 to 2,240, or roughly

one-third of the total weight. (2) In the second place, the buoyancy force corresponds to practically the entire weight of a displacement-type vessel, whereas for a planing

craft it

only

may

be not more than one-third or perhaps of the total weight. The

one-thirteenth

remainder

is

dynamic

lift.

its

and

its pitching and wavegoing behavior

behavior when planing,

porpoising characteristics, its

slamming

its

loads, as well as its controll-

ability, stability of route,

and heel when steering

and turning. (4) For a destroyer or similar high-speed vessel running on the after side of its own bow wave the slope drag

may

be as

much as 0.01511'", correspondOn a motorboat,

ing to say 30 or 35 lb per long ton.

before planing is reached, it may be as high as O.lOH^or more, corresponding to say 225 lb per ton. (5) The actual wetted surface of a planing craft diminishes rapidly as the speed increases, until at

designed speed

it

may

be only one-third or

less

of the at-rest value (6)

The

still-air

accompanied by large vertical forces. Furthermore, the abovewater volume and exposed area of a motorboat increase with the speed, as the craft rises out of the water.

The planing-boat

design problem

resistance

of

a large

ship

is

hydrodynamic resistance but in an ultra-high speed motorboat it may approach that resistance in value, and be rarely a large percentage of the

is

not only

vastly different from that of the displacementvastly more intricate, with and interactions of major effect. In perhaps no other branch of water-craft design is there so great a dependence of each design feature upon all the others. A 10 per cent increase in displacement of a vessel supported only by buoyancy means that it sinks somewhat deeper in the water and runs at slightly reduced speed but it retains essentially the same underwater form and gives about the same performance. A

type craft but

is

interrelationships

10 per cent increase in weight of a planing craft prevent it from planing at all, and from

may

designed

reaching more than half of

its

A

of the

slight

change in shape

which supports the only prevent

its

craft

full

speed.

bottom surface

when planing may not

planing but double

its

running

trim by the stern. Another slight change in bottom shape, hardly large enough to be noticeable, may lift it to planing position but may render it actually dangerous to handle at high speed.

The

planing-craft designer

reconcile himself to learning,

(3) The shape of the bottom of a displacementtype craft usually affects only its pressure resistance but may and often does have an effect upon maneuvering and wavegoing. In a planing craft the bottom shape affects its ability to plane at all,

821

must accordingly and understanding,

what amounts almost to an entirely new science and art. Fortunately for him, dynamic lift and other planing phenomena have also called for intensive study and experimentation on the part of aeronautical engineers and aerodynamicists who have been designing seaplanes and flying boats for the past half-century. Many more minds and hands were concentrated on the problem than would have been the case if the naval architect had had to go it alone. The attainment of superior hydrodynamic performance is perhaps of greater importance in small pleasure craft than in small utility craft. A person who builds or buys a boat and runs it for sheer enjoyment expects to have fun and not trouble. He is in a position, as when buying an automobile, to pick

and choose, and to be

satisfied

with nothing

but the best. For the same reasons, appearance may likewise be more of a factor than it is on a larger vessel, although as a rule not more important than performance in the water. Even a racing yacht must fines. A skipper who is proud of her racing record must also be proud of her

have pleasing

HYDRODYNAMICS

822

appearance.

He must

like to

look at her as well as

to sail her.

Many modern motorboats, and small sailing yachts as well, are of the V-bottom, hard-chine type, as contrasted with the round-bottom craft discussed in earlier chapters of Part 4. The fast, hard-chine, full-planing craft

may have

stepless

hulls or hulls with double or multiple steps. In

the former,

there

a single bottom surface

is

generating dynamic

terminating in a single transverse edge at the stern. In the latter there are two or more separate lift-generating surfaces, each with its own sharp downstream edge. In some cases the sharp, deep edges of steps may lift,

IN SHIP DESIGN

Sec. 77.3

than 6 kt is likely to be unacceptable in any pure power boat and more is generally needed. For this reason the values of T^ for non-planing craft rise from a minimum of 1.3 to a maximum of 1.5 or more, F„ in excess of 0.45 [Phillips-Birt, less

The Motor Boat and Yachting, Apr

D.,

1953,

p. 158].

The

(7)

larger change of trim for small craft at

Vision ahead, and fairly must be maintained at all trim

their designed speed. close aboard,

angles to be encountered in the speed range.

The

(8)

importance of aerodynamic

increased

loads with high absolute motorboat speeds, and

the effects of natural Avinds on high abovewater

run in diagonal directions, both fore-and-aft and

structures

transversely.

Special Design Features for Small-Craft

(9) The types of hull construction and building procedures are of considerably greater variety

The

than for large

77.3

Hulls.

design

small-craft

of

hulls

under

This

vessels.

of

is

importance to

about 110 ft (or 33.5 m) in length requires particular emphasis on certain features of lesser relative importance on large vessels. Among these

the hydrodynamic problem because of the possi-

are:

dicted

(1)

The normal

a

size of

human

adult and the

more-or-less fixed deck heights, headroom, berth

and bunk

messing spaces, seating room, areas, and stowage facilities resulting therefrom. A skiff, for example, must have enough stability so that a man can stand up in it without risk of capsizing. A motorboat passages,

biUty that the finished weight

estimated weight.

dynamic

Uft

is

may

exceed the

the calculated or pre-

If so,

not sufficient to raise or to

trim the boat to the position or attitude where

hydrodynamic resistance is power and thrust available.

matched

its

by the

sizes,

The

access

minimum

considerations of Sec. 77.2 combine with

the special features mentioned in this section to

render the preliminary design of a motorboat of the semi-planing or full-planing type exceedingly

metacentric

complex as compared with that of a large displacement-type vessel. W. P. Walker describes the situation admirably by saying that:

stabUity with scale as the vessel becomes smaller, especially when certain factors or parameters

that the smaller the ship the greater are the problems

can not have bunks smaller than a given size.

(2)

The diminution

in

transverse

remain constant. This is the reason why, when sailing in the same wind, a model yacht has to have a much larger and heavier ballast keel in proportion to its hull than the full-scale prototype. (3)

The

increased space required for handling

and stowing relatively larger items of equipment on deck. A dinghy carried for safety purposes is much larger in proportion than a lifeboat on a larger vessel. (4)

The

huU and

upper works on a small craft, because the fixed deck height is large with respect to the hull size (5)

The

increased inconvenience from spray with closer

relative speeds,

to

the

water,

with

higher

and with heavier impact loads

from slamming at those speeds (6)

The

.

.

(he) considers it

one of the parado.xes of his profession

associated with its design,

relatively larger

T,

= V/VL

or F„

values at which most small craft run. Anything

.

.

."

[lESS, 1948-1949, Vol. 92,

p. 304].

The

large

number

of successful displacement-

and planing boats in service proves that they can be designed. However, the embarrassingly frequent poor performers and downright failures leave most designers with a type, semi-planing,

distinct sense of uncertainty in the behavior of

their next product

proportionately larger area of

everything

".

if it is

different

from what has

already been built and run.

The pubUshed

design comments and notes some extent from this uncertainty, as well as from the lack of a straightforward procedure or sequence of operations by which one can actually design a boat. However, they can be greatly improved if experienced designers are able to find time and are willing to write down, systematically and in detail, the most reliable suffer to

PRELIMINARY DESIGN OF A MOTORBOA E

Sec. 77.5

and useful information data,

when made

in their possession.

These

available to the profession at

large, will surely lead to

improvement and prog-

ress.

The present fore,

effort is to

be looked upon, there-

as only a beginning in the application of

823

The ends have

people on board.

to be filled out

more than on a large ship, where spaces for man and his requirements are more readily provided. Some additional design information which apphes to certain kinds of motorboats and small craft,

together with appUcable references,

and

is

given

h3'drodynamics to the design of small craft. 77.4 Design Notes for Displacement-Type

in Sees. 76.2

Motorboats. There has been a major change in what may be termed the "normal" form of the motorboat in the course of a half-century. The fine, slender launches of the 1900's and the 1910's have become the much fatter transom-stern forms of the 1930's, 1940's, and 1950's. This major change in shape has left the marine architect with httle save his own resources in the design of a displacement-type motorboat. W. F.

It is difficult to define a semi-planing craft, or to

Durand's design procedure of 1907, embodied in the book referenced in the first part of Sec. 77.2, differed but little from that of a Uner of about the same proportions. Indeed, the analysis undertaken for the preparation of Chaps. 66, 67, and 68 still leaves the marine architect with unfinished spaces and missing design lanes on the following: (a)

Fig. 66.A; the design lane for fatness ratios

should have an upward branch, not indicated on that plot, for relatively high values of ¥/{0.lQLY

above 1.0 66.D shows the upper portion only of a lower branch into which the value of the maximum-section coefficient Cx drops rapidly for yachts, tugs, fishing craft, and other small vessels. This is because of the need for large deck space, for wide beam to give metacentric stabihty, for a deep keel with which to resist drifting, or in the range of T, (b) Fig.

for other reasons. (c)

beam Bx

manner

in

which the

diminishes to a limiting or

minimum

Fig. 66.E illustrates the

average value of about 2 or 3

ft

as the vessel

Semi-Planing and Planing Small Craft.

77.5

limit,

7G.3.

by a

description in words, the range of

variables within which a small craft of this type is

best located, as

appropriate

is

because of the wider beam of small vessels the waterUne slopes at the entrance branch off into a lane of their own, for the present not

were. Until something

more is

assumed to be one mtermediate between a displacement type and a true- or full-planing type, without specifying the speed range too closely. Put ia another way, the craft is of the semiplaning type, when:

becomes appreciable with more than 5 per cent of the latter. It may, in fact, become the controlling factor in its design and perform-

The dynamic

(1)

lift

respect to the weight of the boat, say

ance.

The

(2)

total resistance

Rt becomes more than

10 or 15 per cent of the total weight

The

(3)

craft trims

by the stern at

W

its

designed

speed and the center of gravity CG at this speed is at least as high with reference to the undisturbed water surface as when the boat is at rest (4) Roughly, the speed range Hes between T, values of 2.0 and 3.0, F„ between 0.60 and 0.89. This corresponds to the upper part of the inter-

mediate range of Fig. 29.D.

A

somewhat more

semi-planing craft

is

practical

way

to say that

of defining

it is

a

the round-

bottom version of a high-speed planing craft, more suitable than the latter for moderate weights carrying purposes and for continuous operation

heavy weather.

in

The length used

length diminishes to zero

it

devised, a semi-planing craft

in semi-planuig craft design

when

is

at rest,

(d) Fig. 66.1;

the waterMne length of the vessel

too well defined.

with the loads on board specified for the designed condition, the same as for a displacement-type vessel. The change of level or of trim that occurs

A graph given by D.

PhiUips-Birt ["The Design

of Small Power Craft," The Motor Boat and Yachting, London, Apr 1953, pp. 158-162] for the selection of prismatic coefficient Cp on a basis of a given T,

= V/ "s/L Ues well above the design

lane of Fig. 66.A for large vessels. This

is

un-

doubtedly due to the need in small craft of finding space for all that must be carried, including the

when running

at designed speed or below

is

taken into account here.

The (a) its

(b)

'Un

craft is of the fuU-planing

The dynamic

lift is

not

type when:

the controlling factor in

design and performance

The

total resistance

Rt

per cent of the total weight

rises TI^

above 10 to 15

to a range of from

25 to 75 per cent or more of that weight

HYDRODYNAMICS

82-1

CG

The

(c)

position

at the planing speed rises above its

when the

craft

is

at rest, reckoned with

IN SHIP DESIGN

Sec. 77.6

It should be no higher than the speed at which a displacement-type hull of the same approximate

an inordinate amount

respect to the level of the undisturbed water

size begins to require

surface

power.

designed-speed range lies above T", (d) The values of 2.5 or 3.0, F„ > 0.74 or 0.89. This corresponds to the range given in (1) of Sec.

(3) To achieve successful wavegoing performance a planing hull must plane at a speed so far below

30.2, subject to the quaUfication given there.

its

A

fifth

criterion

a semi-

differentiating

for

planing from a full-planing type of boat

is

that

used at the Expermiental Towing Tank, Stevens Institute of Technology. It is based on the fact that the full-planing type is always built with chines at the outer edges of the bottom. Here a full-planing condition

the water breaks

is

away

defined as that in Avhich

cleanly from the chine for

the entire length of the boat.

No

water curls up

over the chine and wets either the sides or the

transom.

A sixth criterion is that given in

(3) of Sec. 30.2,

illustrated graphically in Fig. 30.B. This defines

the full-planing speed as that at which there is a sharp reduction of the exponent n in the formula

Rr = kV: The

length used for planing-craft design pur-

poses varies. It

may

be:

the cruising range that in a seaway

planing characteristics.

If

it will

the craft

of

maintain

is

involun-

slowed to below that speed it should at once regain its planing position upon an increase in speed. This factor is of the most vital importtarily

ance. For example,

if

a planing hull must travel if it has a

at 14 kt to reach planing speed and

sustained cruising speed of only 16 kt, the adverse

only a small or moderate sea Avill suffice down to below the planing speed

effect of

to slow the craft

planing

of 14 kt. It will struggle along, alternately

back below hump speed. Such a craft is, in the words of Teller, "neither a successful planing boat nor an honest displacement boat."

and

falling

(4)

If

the planing craft

is

deliberately throttled

must have as good wavegoing performance as the best displacementtype hull. OtherAvise, if the planing boat experiences power-plant failure in a gale or has to be slowed because of fog or any other cause, it is no to below planing speed,

it

longer a seagoing vessel.

The

(i)

chine length

Lc

,

projected upon the

baseplane (ii)

The waterline length Lwl at normal when the craft is at rest The overall length Lqa

load and

trim (iii)

This matter

is

must be as

from pound-

free

size, running at the same speed. no seagoing vessel.

same

it is

not a weight-

is

carrying vessel, in the sense of a cargo ship. Its

should be restricted to carrying special equipment, certain types of cargo in an emergency, or so-called premium loads, where the expense

use

Operating

Requirements

for

Planing

normal requirements for speed, maneuverabihty, good wavegoing behavior, and adequate stability, the same as for any other small craft. The items listed and discussed here are adapted from those previously published by C. R. Teller [Motor Boating, New York, Ann.

in addition to the

Show Number At

hull

Finally, the true planing craft

(6)

discussed further in subsequent

Forms. There are a number of operating requirements peculiar to all planing forms which call for consideration ahead of the particular requirements of the owner and operator. The former are

(1)

hull of the

Otherwise

sections.

77.6

The planing

(5)

ing and slamming as the best displacement-type

less

(Jan), 1952, pp. 66-68, 247-249]:

than planing speed, that

is,

when

running as a displacement-type boat, the planing craft must be as seaworthy as the best displacement boat. Otherwise it is no seagoing vessel. (2) The speed at which the craft passes the humpresistance region and begins to plane must be low.

involved

in

transportation

saving in time.

An

example

excellent

may

boat

these

illustrating

Indeed, the planing craft

by the is an

justified

is

aircraft rescue

features.

well be regarded

more nearly as a seaplane or flying boat than as an ordinary boat. If the fljdng boat is overloaded it can not and will not take off from the water. If

the planing craft

not take

off

is

overloaded

it

likewise will

and plane.

General Notes on the Powering of Small of powering for motorboats and other small craft is touched upon here 77.7

Craft.

The general subject

briefly, as

a preliminary discussion of quantitative

power estimates

The designed

in Sees. 77.14

or

minimum

and

77.26.

speeds for which

motorboats are powered are usually those to be

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.S

made

in

specified,

with

the

(|uLet

water,

either

fresh

or

salt

as

with a clean, smooth, new bottom, and propelling

machinery

delivering

its

rated power or some specified fraction thereof, corresponding to the 0.95 factor of Sec. 69.9.

important for the naval architect as well

It is

as for the marine engineer to realize that because of the limit

on mean effective pressure

in

the

any reciprocating internal-combustion engine can produce its rated power only at a certain rate of rotation. At a lesser rotating speed, the power is less. Furthermore, it may not be possible for the engine to deliver its rated power cylinders,

at a higher rotating speed than that for which

designed or adjusted. This makes

it

it is

most impor-

tant that the small-craft propeller be one which, at a desired boat speed, absorbs exactly the engine

fuel,

77.8 Principal Requirements for a Preliminary Design Study. The craft selected as the running example in this chapter is a small motor tender for the ABC ship designed in Chaps. 64 through 68. The first step in the preliminary hydrodynamic de.sign of this motorboat is to outline the mission of the craft; in other words, to state

motorboat, just as a modern tug or fishing vessel is overpowered, but not for exactly the same reasons.

Motorboat overpowering resembles more

nearly, in fact, the gross overpowering of the

modern is

(1955) passenger automobile. Engine

longer and wear and tear

powers.

is

reduced

less at

The engine power actually required

greater part

of

the time

is

life

for the

delivered reliably

even though the engine may be somewhat out of adjustment or the fuel may not be up to standard. For these reasons, and others not mentioned, powering allowances are as necessary for a small craft as for a large one. It is

to cover the (a)

power needed

customary

boat structure,

if

in items (1)

to a period of at least six

wood, corresponding months in the water and

Roughening

of the

bottom surface because of uneven

rusting, pitting, oxidizing, flaking, peeling,

and fouling by marine organisms

—The

craft described in these specifications

is

to:

Serve as a power launch for and to be carried on board the ABC ship whose requirements are set forth in Tables 64.a through 64.g (2) Serve as an all-weather tender for the ferrying of

and miscellaneous portable from ship to shore and vice versa, under special conditions where the ship must anchor or lie-to.

personnel, incidental packages, articles

WEIGHT AND hoisting

it

LIMITATIONS—To ABC ship the boat is to:

SIZE

on board the

permit

(3) Have a gross hoisting weight not exceeding 25,000 lb, including a full supply of fuel, other consumables, parts,

tools,

and two crew members, the latter assumed to weigh Hoisting is to be by a single hook on the ship.

350

lb.

(4)

Be capable

of stowage, in a secure position for travel

on the weather deck either forward of or abaft the passenger accommodations (5) Have an overall length not exceeding 40 ft. at sea,

is

Be capable

(6)

to:

of carrying

one of the following items, or of all three, not exceeding

any reasonable combination 3,000 lb in weight: (a)

(b)

Twelve passengers plus a maximum crew of four Cargo in packages or luggage, in total weight not and in total volume not to exceed 125

to exceed 2,300 lb

maximum crew of four Eight passengers and a maximum crew of four, plus

plus a

ft',

(c)

one

litter

(7)

Provide protection from rain, wind, spray, and sun

patient

for all passengers

(8)

and

cargo.

Achieve a speed

of:

18 kt in smooth water with a half-load of fuel, a crew of two, and two passengers and their personal baggage (a)

(b)

Reduction of propelling-machinery efficiency and output because of wear and tear, low grades (d)

77.a. It is followed

SPEED AND ENDURANCE—The craft shall be able to:

speed.

calking,

Table

(1)

carrying capacity, over

and above design requirements, are not in this category. Logically, they must be paid for separately, either in increased power or reduced (c)

MISSION

two seasons

Unavoidable increases in weight with time in service, because of adding new equipment. for increased

(2) of

CARRYING CAPACITY AND ACCOMMODATIONS

(b)

Demands

and

TABLE 77.a—Motor Tender for ABC Ship; Principal Hydrodynamic and Other Requirements

—The tender

of

in the weather, covering at least

it is

for these

for:

Increase in weight due to thorough Avetting

of the

what

required to do. After consultation with the owners and operators of the large vessel, this is set down

output, less the transmission and shafting losses.

More power absorption means that the engine and propeller both have to speed up to make the powers match, if indeed this can be done. It is customary to overpower the modern

825

and excessive time between overhauls (e) Damage to blades of propulsion devices from numerous causes, probably of more frequent occurrence on small craft than on large ones. of

14 kt in smooth water with a

full

load of fuel and

cargo. (9)

Run

at full power for six hr without replenishing fuel.

a

HYDRODYNAMICS

826

TABLE SAFETY—The The

(10)

77.a— (Continued)

following requirements apply:

fuel used in the

power plant

shall

be diesel fuel

or its equivalent; no type of gasoline or equally volatile fuel is permitted

remain afloat and upright if completely swamped, with crew, passengers, and cargo on board. The cargo may be considered as 50 per cent permeable, and the special flotation volume as fully intact. (12) Drinking water and emergency rations for sixteen persons for two days are to be carried (13) Safety and operational equipment as required by regulations of the U. S. Coast Guard for operation in semi-protected ocean waters.

The tender

(11)

shall

OTHER REQUIREMENTS (14) It shall be possible to warm up and run the power plant for a short period before the boat is hoisted out (15) The boat shall preferably bank inward on turns in

normal steering

The

craft shall possess adequate steering control in head or following seas (17) It shall not pound or slam excessively, so as to risk injury to the boat structure or to the crew and passengers, when running in rough water at speeds in excess of 10 kt (18) The design and construction shall be rugged and substantial, suitable for hard service and reliable operation (16)

either

IN SHIP DESIGN (g)

Materials of construction

(h)

Method

of attaching the single-ring hoisting

sling.

Analysis of the Principal Requirements.

77.9

Before starting the design proper it is well to analyze the requirements, in terms of the back-

ground already gained

ABC

ship.

fixed for

and F„ values

are:

r«

Fn

T, Fn

items

for weight,

endurance,

safety,

in items (3)

and other

through

features,

develop as the design proceeds. prospective operators wish an alternative

the same general requirements as in Table 77. but to run at a higher maximum speed with less carrying capacity.

down

in

Table

The

is

the principal and the alternative designs: (a)

Type

of hull,

whether displacement, semiHowever, a conference

planing, or full-planing.

ABC

ship

operation,

all-

with the prospective operators of the brings

out

that

= =

=

2.30(0.2978)

2.30

=

0.685

18 kt

18/6.083

=

2.96(0.2978)

2.96

=

0.881

24 kt

T, F„

= =

24/6.083

=

3.95(0.2978)

3.95

=

1

.

176.

Nothing is said in the specifications about running trim; that is, change of trim when underway. Excessive trim by the stern, resulting either from placing the useful load too far aft, or

detail requirements are

77. b.

noted that complete freedom is left to the designer with respect to the following, for both It

14/6.083

Speed

(18). Still other

design prepared for a craft to meet substantially

set

= =

carrying capacity,

may

The

14 kt

Speed

Speed

by requirements embodied

in the preliminary design

The

overall length of 40 ft is both the principal and the alternative designs. To achieve the load- and volume-carrying capacities required, it is almost a certainty that the stern will have to be of the transom type. From an examination of the pubUshed data for other motorboats an average length for the waterhne at rest may be estimated as 37 or 38 ft; the lower value is on the safe side. Its square root is 6.083. Based upon the speeds in item (8) of Table 77.a and item (b) of Table 77.b, the T, of the

in salt water.

speed,

Sec. 77.9

reUabUity

of

weather behavior, and load-carrying performance of the craft are considered of paramount importance. Speed can be sacrificed if need be. Hull proportions, principally the L/B ratio but more important still, for actual stowage on the ship, the maximum beam (c) Hull draft or hmiting draft (d) General shape and appearance of hull (b)

(e)

Power plant and power

(f)

Number

of propellers

TABLE 77.b— Motor Tender for ABC Ship; Requirements for Alternative High-Speed Design An alternative design of motor tender is to be prepared having the general requirements of items (1) through (14) plus (18) of Table 77.a, modified by the following: Carrying capacity of six passengers plus a crew of all having an average weight of 170 lb per person, plus a cargo of packages or luggage weighing not in excess of 900 lb and having a volume not in excess of 50 ft', plus (a)

two,

a two-thirds load of fuel (b) Speed, 24 kt minimum, in quiet water, with the load of item (a) (c)

Run

(d)

The boat

two hr without refueUng bank inward on turns when running

at full power for shall

in

the planing range

The

craft shall possess adequate steering control in head or following seas (f) It shall not pound or slam excessively, so as to risk injury to the boat structure or to the crew and passengers, when running in rough water in the planing range (g) The craft shall not porpoise at any operating speed. (e)

either

Sec. 77.11

PRELIMINARY DESIGN OF A MOTORBOAT

827

from too much squat, increases the power unnecessarily and leads to impaired maneuvering and wavegoing. On the other hand, the craft with only the crew on board, but with full fuel, should not trim unduly by the bow. Better still, it should not trim by the bow at all. Since the steering is to be entirely by hand, the rudder(s) must trail under all running conditions.

Freedom from pounding and slamming

in

both

designs calls for V-sections in the lower f orebody,

with appreciable rise of floor. The speeds in all cases approach those for planing, especially at

Hght loads, hence the buttock lines aft should be straight or only very shghtly convex downward. 77.10 Tentative Selection of the Type and Proportions of the Hull. For the principal design it appears practicable to shape one hull that will run well at both 14 and 18 kt. However, the total weight displacements will be different for these two speeds because of the different useful loads of items (8) (a) and (8)(b) of Table 77.a. The underwater portions of the hull will thus be some-

what if

different in the

two

conditions, especially

the trim changes between loadings. It

ex-

is

25

ZO

15

Speed,

kt

Ranges op Size and Speed for Round-Bottom and V-Bottom Craft

Fig. 77.A

Adapted from the data

of

D. De Groot, referenced

in

the text.

bination for the

ABC

tender hes shghtly inside

the round-bottom region in the figure.

Because the design

of

a planing craft represents

what might be termed the general case, embodying

18-kt condition

practically all the variables to be encountered in

be the controUing one in the principal design. The 24-kt craft, to run definitely in the planing range, is destined to have an entirely different hull. From Sec. 77.9, the T, value for an 18-kt design of 37-ft length is below 3.0. If the whole available length of 40 ft overall is used, the length will be about 39 ft and the T, value 2.88. A semi-planing type of hull is tentatively indicated. This, combined with the important requirement for excellent wavegoing performance, points to a round-bottom hull as the preferred shape. For the faster 24-kt boat, running at a T, of the order of 4.0, well within the planing range, a hard-chine, V-bottom hull is called for. These will hereafter be called, for convenience, the round-bottom boat and the V-bottom or

lajdng out and selecting parameters for small

pected,

nevertheless,

that the

will

WL

This is not to make the but to avoid introducing entirely new features into the story at points which would break up the reader's line of thought. craft, it is

described

problem more

first.

difficult

The round-bottom

design procedure then becomes one of simplifying that for the general case. First Space Layout of the 24-Knot Plan77.11

The

ing Hull.

the

ABC

first

actual step in the design of

tender, as for

determine about

how

paper, showing proposed internal-space layouts. Sec. 77.3 points out that these craft are relatively

human and his accommoThey must, therefore, almost

a basis of quiet-water resistance, D. De Groot says that "the upper limit for the advantageous use of the U-form (round bottom) hes somewhere about F/a/L = 3.25" [Int. Shipbldg.

dations

.

.

Progr., 1955, Vol. 2, No. 6, p. 70]. Fig. 77.A is adapted from De Groot's diagram, showing the round-bottom and V-bottom regions in graphic form. However, the dividing hne in his plot corresponds to a T, of about 3.13; this was not changed in the adaptation. The 18-kt 37-ft com-

to

usually free-hand on ruled or Ught-lined coordinate

small in proportion to a

.

is

meet the design requirements. This is done by making a series of sketches to a convenient scale,

full-planing boat.

On

any motorboat,

large the boat has to be to

afloat.

invariably be designed on a volume basis rather

than a weight-carrying basis. The size of the boat is determined, not so much from those dimensions which will, with a normal form, give enough volume displacement to float the weight to be carried as from the positions of the boatshaped boundaries which wiU enclose the various spaces and units needed to meet the specification requirements. Several separate space studies are

HYDRODYNAMICS

828

IN SHIP DESIGN

Sec. 77.12

arranging the various principal units, the accom-

worked into spaces not useful for anj^thiug else. Their volumes should, if practicable, be so placed that the swamped boat is supported at or about

modations, and the service

zero trim.

perhaps a dozen oi' more, especially when the designer is allowed some latitude in (lesiniblc,

For craft over 25

facilities.

or 30 ft in length the pre-

ft

liminary space layouts

may

involve two or more

deck plans, one for the weather deck and another for the space below deck. A boat-shaped hull sketched around these spaces affords a rough idea of the principal dimensions such as overall length, beam, and depth of hull. Profiles based on these hull sketches indicate the positions

and

sizes of

houses or other erections projecting above the

weather deck. Having the general size and shape, or perhaps one might say the minimum size and shape, the designer proceeds to incorporate certain other features in the sketches such as

minimum freeboard and sheer, freeboard at or near the bow, and profiles of the bow and stern. He shows crew and passengers, as well as "cargo"

Fig. 77. B

ABC

A

smaller boat, 35 ft in

and 32

ft

long on the waterline,

overall length

appeared to be sufficiently roomy but with an estimated weight of 18,000 lb its displacementlength cjuotient of 245 was too high. The boat shown in the figure, with a waterhne length of 35 ft, provides room enough to meet the requirements of Table 77. b and is not too heavy for its length.

unless

for

show

minunum dimen-

sketch.

It

does not

within the limitations established by the owner and operator. 77.12 First Weight Estimate; Weight-Estimating Procedure. The second step in the design

oversize in case of doubt.

fire

in

by the

to

specifications

known, the spaces for propelhng can be roughed in,

auxiliaries

The

hull

or subdivision bulkheads are

The buoyancy tanks

flotation

fitted into a craft of the

is

necessarily represent the best arrangement pos-

structure usually presents no problem at this

required.

by the

that the spaces called for

represented

considered

nevertheless

is

the powers and sizes of the en-

gine(s) are not yet

stage,

The layout

purely preliminary. Its sole purpose

can be

them

for the

larger than necessary.

sions

leaving

made

craft 40 ft in overall length, with an estimated displacement weight of 25,000 lb, was somewhat

positions.

machinery and

last of several

planing-type tender. These indicated that a

in the present case, in their proper or proposed

Even though

was drawn from the

layout and arrangement sketches

or

compartments

an emergency can usually be

sible

of the planing-type craft

is

make

to

a preliminary

weight estimate of the complete boat, in operating condition and with the full useful load on board. Trace

of

De&iqned Waterline at rest In

Second Arronqe-

ment Sketch

^ '^

\.

/

L

^

T^^J

Movino Engines Forward and Passenqers Mt to

Make Them

More Comfortable and to Place Heavy

Removable

Sections to Permit Liftinq Out

FP Fig. 77.B

Weiqhts Over

Enqmes

Sketch of Tentative Space Layout fok V-Bottom Tender for

Stotlons

ABC

Ship

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.12

may

be handled in several ways. All of them, like that used for the ABC ship in Sec. 66.4,

This

involve weight estimates for a craft which in

a distinctly nebulous

situation

more difficult,

state.

reliable

is still

To make

this

pubhshed informa-

tion as to the weight percentages of the various groups and detailed information as to the actual scale weights for

motorboats are much scarcer

corresponding data for large vessels. A start in this direction has recently been made by E. Monk ["Weight and the Motor Boat," Yacht-

than

ing,

Jan 1955, pp. 118-120]. The graphic data

presented by

Monk, comprising a

between waterline length at for

relationship

and total weight wooden pleasure boats, are embodied in the rest

lower broken-line curve of Fig. 77. C.

The

full-fine

829

HYDRODYNAMICS

830

IN SHIP DESIGN

Sec. 77.12

ob

Fn'WT

Froude Number

1

-1=-

USEFUL LOAD FUEL-

/

:=!:

/

FUEi:'

MACHINERY and ELECTRICAL

1—4—

IPMEifr, ,5T0RE5,

OUTFIT

::=^=1 ::i

Toylor Quotient Jcf '^j^ 12

1.0

Fig. 77.D

1.6

1.4

I,

20

'

2Z

'

24

'

26

'

2.8

3.0

the fuel rate for the two 215-horse engines proposed is about 0.5 lb per brake horse per hr, so that 430 lb of fuel is required for both engines for

a 2-hr run. Since the owner has had no previous service experience with a tender of this kind, it seems mse at this stage to allow for a considerablyenlarged fuel capacity, say about tmce that actually required.

With an assumed weight amounts to 860/6.2

6.2 lb per gal, 860 lb of fuel

of

=

138.7, or say 140 gal. A further study of the probable service required of this tender reveals that, despite the increased capacity, it may be neces-

sary under some circumstances to return to the parent ship for refuehng before the day's work done. There may be times when this will be extremely inconvenient, so another 50 gal is added to the fuel capacity for good measure, is

bringing the total capacity to 190 gal, or 1,178 lb. The weights reasonably well known at this stage are: (1) Useful load, from owner's requirements, six passengers at 170 lb plus 900 lb of packages,

1,920 lb

Weight

ready to run, 5,300 lb (3) Fuel; although the owner requires only twothirds capacity on board for the designed speed, the full capacity is hsted here, 1,178 lb (4) Crew, two persons at 170 lb, 340 lb. of engines,

The known weights 18,000 still

-

3.6

5B

4.0

4.2

M

46

4.4

4.8

5.6

5,2

54

i,b

Percentage Disteibution op Principal Weights for Seven Moderate- to High-Speed Craft

quirement in item (c) of Table 77.b calls for a 2-hr supply at full power. Under these conditions

(2)

3.4

3.E

8,738

=

total 8,738 lb, leaving 9,262 lb for the weight groups

to be considered.

One method

of

making a preliminary weight

estimate of the remainder, with the craft not yet

roughed out in the form of lines or structural drawings from which weights can be calculated, is to use a weight-percentage diagram such as that of Fig. 77.D. Here the percentages of seven weight groups, making up a total of 100 per cent

on a basis of Taylor quotient T^ (and f„) for seven different planing craft for which reasonably reliable data are available. Only a general pattern of weight distribution is apparent for any of the boat types, for the complete boat, are plotted

because of great differences in the operating functions of the various craft, hsted in Table 77. c.

For the ABC planing-form tender, with an assumed WL length of 35 ft, the Taylor quotient T, = 24/\/35 = 4.05. The only reference craft of Fig. 77. D with a T, of about this value is the

D

24-ft personnel boat, designation

of the table

Here the combined total of useful load, fuel, and machinery (including electrical items) is 52.5 per cent, working down from the top in Fig. 77.D. For the craft being designed the

and the

figure.

corresponding percentage

is

8,738/18,000

=

48.5,

leaving 51.5 per cent for the hull, hull fittings,

equipment and Stores, and margin.

electrical

and electronics

gear,

What

appears at this stage to be a reasonable

subdivision of the 51.5 per cent

is:

(a)

Hull, 28 per cent or 5,040 lb

(b)

Hull

fittings,

9 per cent or 1,620 lb. This must if they are built in and

include the hoisting shngs

carried as part of the boat structure.

— Sec. 77.13

PRELIMINARY DESIGN OF A MOTORBOAT TABLE

77.C

The data in this table supplement those set down graphically upon the waterline length, where this is known.

Function of boat

831

Weight Distribution for Different Motorboat Types in Fig. 77. D.

The Taylor

quotients listed are based

HYDRODYNAMICS

832 brake power required

is

about 430 horses.

When

rigged for direct drive and fitted with hydraulically

operated chitches, with

lubricating

all

carried in the engine sumps, the weight lb per engine or 5,300 lb total.

liquids in the engines is

With an increase too

much is

This includes

all

first

It

estimate.

in the ratio of hull weight to

from 0.28 to

0.33,

it is

clear that

additional fuel can not be carried

percentage of margin fuel

oil

2,650

and the piping systems.

the same as was used for the

total weight of

is

is

if

also to be increased.

the

The

therefore limited to the 140 gal necessary

to run both engines at full

weight

power

for 4 hr. Its

=

868 lb. Hull fittings usually account for an unreasonably large proportion of the total weight for small boats because many of these parts are of standard 140(6.2)

is

and constant weight for a rather wide range A good value for a twin-screw planing boat of 35-ft waterline length seems to be about size

of boat sizes.

8 per cent of the total.

The planing boat under therefore

many

design

is

a tender,

usual items of equipment are not

no bunks or mattresses minimum and only a small quantity of drinking water need be carried. A low percentage of weight assigned to required. For example,

are needed. Stores can be held to a

the stores group, say only 3.0 per cent of the total,

appears adequate.

The customary amount tronic

as 800

To

equipment

is

of electrical

and

elec-

called for. This is estimated

lb.

avoid overweight, the most

common

fault

an ample margin is mandatory. At this stage a good 10 per cent of the total of the preceding groups is none too much, or about 9.5 per cent of the resulting total. A summary of the groups of the second weight of planing motorboats,

estimate follows: Hull

=

0.33(18,000)

=

IN SHIP DESIGN

Sec. 77.14

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.14

ment

vessel, it is

imperative to i^now, very early

about how much shaft (or brake) and the approximate weight of this machinery. Perhaps because it has been customary to make direct power estimates in the past, as distmguished from indirect estimates based upon effective power and propulsive coefficient, there are more shaft (or brake) power estimating procedures available to the motorboat designer than to the one who undertakes to in the design,

power

is

called for

design a large ship. Unfortunately, these

many

methods usually give as many different answers, and sometimes the answers vary widely among each other. Moreover, the observed data upon which these procedures are based also vary in reliability,

because

principally

of

the

lack

of

proper instrumentation and techniques whereby shaft powers for small craft may be measured accurately on

trial.

In the late 1920's and early

Charles Ross undertook a lengthy research project in an effort to measure the brake power of small-boat internal-combustion engines 1930's

Sir

by recording the rate of rotation and measuring the rate of fuel consumption with extreme care. Unfortunately the project was never finished nor were the results

of the

work written up

for publi-

The designer is therefore left with the hope that when a given engine is put into a boat cation.

it will

deliver the

shaft at rated

same brake power

rpm

that

it

did

when

at the output it

ran on the

factory test stand.

One power

of the simplest direct estimates of is

the table and the dimensional

brake

"K"

formula of K. C. Barnaby [BNA, 1954, Table 40

100

90 30 TO

60 50

«

833

HYDRODYNAMICS

834

Taylor quotient r„ less than 2.0. This is below the planing range for most motorboats. C. E. Werback has developed still another dimensional relation, derived originally by G. F. Crouch, of the following form: of the

where the

K^

coefficient

by

given

Sec. 77.14

taken from a table reproduced here as

is

PhilUps-Birt,

Table 77.e. N. L. Skene uses a formula almost exactly the same as Eqs. (77.i) and (77.iii), with the alternative forms

(ft)

= C

7(kt)

IN SHIP DESIGN

(77.ii)

F

TF(lb)

iPs

Y

(horses)

Transposed for deriving the shaft power of the other quantities it becomes

Fs

W

(horses)

(lb)

7'

in

terms

The

(kt)

TF/(0.010L)^

(ft)

(a)

required for taking

is

(lb)

(77.iv)

(horses)

=^(M_5imph)

(horses)

C

values of Skene's coefficient

(77.iva)

range from:

(77.iia)

CVL;,^

Analysis of this method indicates that a family of curves for various displacement-length quotients

P.

^^ \Pb

(mph)

off

180 to 185 for high-speed runabouts

190 to 205 for multiple-step or shingled hydroplanes (c) 210 for single-step hydroplanes of good design (b)

220 for small sea sleds to 270 for the largest

.proper values of the coefficient C. However, on

(d)

the basis that displacement-length quotients for good planing craft are of the order of 200 or

and most

slightly less, Fig. 77. F gives a

graph for selecting

efficient sleds

240 to 250 for small, three-point hydroplanes ["Elements of Yacht Design," New York, 1944, (e)

p. 222].

A value of C = ABC tender.

185 appears appropriate for the

Five of the methods listed give first approximations to the shaft power as follows, based upon an estimated weight, at this stage, of 19,000 lb or 8.482 tons, a speed of 24 kt, a waterline length hy,!^ of 35 ft, a T, of 4.056, and an P„ of is on Approximate Meonline. There Should Be Q FomllyCurves for Various DisplQce-_

This

1.208:

Only. of

ment-Lenqth Quotients Taylor Quotierrt Tq=

ill

'

liinlnnl

Method of K. C. Barnaby, Table 77.d. With a boat of the Y-chine, stepless type, 35 ft long, and I.

YlVh =

L

K^

is 3.4.

AND Weight

II.

at Tj values greater than 2.5 and not exceeding

A

^=

8.482

Method

of P.

Du

P^ =

Crouch- Werback Formula and Graph FOR Relating Shaft Power to Length, Speed,

Fig. 77.F

C

4.056,

Then

J.O

3.0

1.0

50

t^

-^^ =

422.6 horses.

Cane, Fig. 77.E. The ratio is estimated conserva-

of (IF in lb)/(PB in horses)

tively at 43.

Then

6.0.

D. PhiUips-Birt gives a dimensional formula exactly the same as K. C. Barnaby's (Eq. 77.i) the total for relating the brake power P^ weight W, and the speed Y ["The Design of Seagoing Planing Boats," The Motor Boat and Yachting, Jan 1954, p. 29]. This takes the alter,

Pb =

(IF in lb)/43

=

19,000/43

Ps

(horses)

=

F

(lb)

F^

C'VL^^

(77.iii)

(let)

=

(77.iiia)

(horses)

=

356.9.

is

estimated as

(72)'V35

/

Pb

is

(ft)

19,000(24)'

= i^.^/f^^^^ W (long tons)

442 horses.

III. Method of Crouch-Werback, where C taken as 72 from Fig. 77.F, and Eq. (77.iia) is

native forms F(kt)

=

From

this the

brake power Pb

356.9/0.95 or 375.7 horses.

— PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.15

TABLE The

values set

1954, p. 29).

77.e

down

Values of tub Piiillips-Birt Powering Coefficient Ki

here arc taken from a table published

by D.

in

Phillips-Birt [The

Equation

835 (77.iii)

Motor Boat and Yachting, Jan

HYDRODYNAMICS

836

IN SHIP DESIGN This

sections.

is

Sec. 77.16

often

an

important

design

consideration.

Straight entrance sections,

depicted at

1

in

have many of the disadvantages of both the concave and convex types with few of their advantages. Straight segments are often used in sections near the stern where the rise of floor is a minimum and there is little difference between the various section types. In regions of high rise-of-floor angle, they are used only for ease of Fig. 77. F,

Some

Rise-of-Roor Annie j£

Nominal

For All

construction.

The yoke -Hr^Holf-Sidinq Fig. 77.

'^Possible Modification

G Four Types of Typical Forebody Sections for Planing Craft

rough water there is heavy pounding and slamming, accompanied by either a reduction in speed or a risk of damage to the boat and injury to the personnel.

Better performance in rough water

by

raising the chine forward

rise of floor

is

obtained

and increasing the

but this change increases the resistance

and involves a sacrifice of smooth-water speed. Running into a wind, the concave forward section keeps the boat dry because the water is thrown to the side with little spray and disturbance. In heavy weather, entrance sections which are fine as well as concave result in heavy pitching. They give little reserve buoyancy and they are still subject to pounding and slamming. Boats with convex sections, sketched at 4 in Fig. 77. G, and of a type to be found in developable bottoms, have higher smooth-water resistances than those with concave sections. The water climbs up the side more easily and does not separate cleanly from the chine, resulting in greater wetted area. This type of section is much better for wavegoing because, like the round-

or inverted-bell section,

drawn at 3

good compromise. It gives the excellent wavegoing performance of the round-bottom entrance but retains the sharp angle at the chine to throw the water off cleanly, thus holding down the wetted area. It provides adequate reserve buoyancy, an ample rise of floor, and a constantly diminishing flare with vertical distance above the base, to prevent slamming and pounding. By using a high chine forward, the entrance sections are kept fine enough to avoid too great a hook at the chine corner where water could be trapped in a slam. in the figure, offers a

The rounded

portion near the centerline acts to

deflect the water

under the bottom and give

reasonably quick planing with good flow lines. Bell-shaped sections produce less spray than the

pure convex type. They have the disadvantage that they are more difficult to construct, they involve slightly higher building costs, and they

can not be worked into developable surfaces.

They have

slightly greater resistance in

smooth

water than the low-chine concave sections, due to the greater wetted surface, but probably less resistance than pure convex sections. 77.16

The

Rise-of -Floor Magnitude and Variation.

expressed as a sectionan important characteristic

rise of floor or deadrise,

slope angle ;8(beta),

is

of a planing boat.

In

fact, its choice influences

bottom form, it presents a constantly decreasing the oncoming (and upcoming) water as the bow pitches down. Pounding and slamming are

many

other features of the underwater and above-

water

hulls.

reduced considerably or avoided altogether. The

considerations the smaller the rise-of-floor angle

flare to

convex section builds up reserve buoyancy and As might be expected, boats with convex sections will not plane as rapidly or as readily as those with concave acts to ease the pitching motion.

From pure

planing and dynamic-lift

the better; in other words, the barn-door type of flat surface is the best load-carrying

inchned device.

As the

bottom and the dynamic

rise-of-floor angle of the

increases, the resistance increases

diminishes.

sections.

lift

Convex sections throw considerably more spray and make the boat wetter in a wind. The fitting

In the case of racing motorboats of the stepless type, havmg a continuous bottom terminating in

of spray strips, described in Sec. 77.20, largely

the transom edge, this bottom

overcomes these disadvantages. Convex sections forward give more internal volume than concave

practically

At other times

is

often

made

has a shape approximating that of an inverted deck with a flat.

it

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.17

small camber. Excessive slamming and pounding in

waves are accepted

ultiinate in speed. 4.8,

in the effort to rcat'li the

At Froude numbers

Taylor quotients of 15 or

IG,

the

of 4.5 or

minimum

the chine the attention

Planing

is

taken for

the

sinc(;

Clement ["The

SNAME, May 1951; "Hull Form of Stepless Boats," SNAME, Ches. Sect., 12 Jan

minimiuii of bottom surface in contact with the spray, like the pounding,

has received

Analysis of Stepless Planing Hulls,"

Ches. Sect.,

The

it

early 1950's at the hands of E. P.

pressure and friction drag are achieved with the water.

837

are valid hydrodynamic reasons for devoting to

.3

paper Clement approa(!hes the

1955]. In his 1955

granted as an unavoidable characteristic of ultrahigh-speed performance. If the craft jumps com-

planing-boat design problem by using the chine

pletely out of water because of impact with the

jected area

crests of waves, this too is accepted providing

certain loading factors on the chine area as the fundamental design parameters. However, the lack of comprehensive and reliable full-scale performance data renders this scheme something less than adequate at the present time (1956). For convenience, Clement has embodied the data of

the stabilizmg

fin,

the lower blades of the propeller,

and the rudder can be kept reasonably well

in the

water.

Obviously, a planing boat with a

does not

make a

flat

bottom

satisfactory boat for all-around

length

Lc

,

beam Be

the chine

Ac

,

,

the chine pro-

the chine planform shape, and

new

High rise of floor is necessary forward for wavegoing and for low resistance at speeds below planmg. Some rise-of-fioor angle is necessary in the bottom aft to provide dynamic stability of rovite and proper steering qualities, although the angle required at the extreme stern is small. Thus most planing boats are built with what is known as a twisted or warped bottom, with a decreasing rise-of-floor angle from forward aft.

the referenced 1951 and 1955 reports in a

D. Phillips-Birt gives the following typical values

mention either of them specifically, are given by D. Phillips-Birt ["Motor Yacht and Boat Design," London, 1953, Fig. 51, p. 147]. The graphs of Fig. 77. H are adapted from curves 1 and 2 of the reference cited. Ratios of Lw^/BcfM^^) between 3 and 4 are typical of modern planing craft. In fact, many of the smaller boats, 20 to 25 ft in length, have ratios less than 3. For the ABC tender of 35-ft waterUne length a maximum beam at the chine of about 10 ft is indicated. The

service.

for these angles:

Amidships, 14 to 18 deg, flattening along the run to 2.5 to 4 deg at the stern [The Motor Boat and Yachting, Jan 1954, p. 28; "Motor Yacht and Boat Design," London, 1953, p. 148].

G. A. Guins states, in the paper listed as reference (16) of Sec. 77.41, that the minimum rise-of-floor angle found necessary for satisfactory

longitudinal stability

is

7 deg, together with a

are

built

with an ^un-

twisted bottom, embodying a constant rise-of-

from amidships to the stern. Compared to the warped bottom, the constant-slope bottom usually gives less rise of floor amidships and more at the stern. The untwisted bottom has the lower smooth-water resistance of the two, but its use floor angle

may

Boat"

[TMB

Nov 1956]. maximum chine beam Bc(Mai)

Rep. 1093,

Nevertheless, the

serves as an excellent starting point for deter-

mining the proper transverse dimensions of a planing craft. Good design graphs of what appears to be a maximum chine beam on a basis of waterline length, although the author does not

fore-and-aft position of the point of

long tapering skeg.

Some planmg boats

report entitled "Analyzing the Stepless Planing

lead easily to other unfavorable character-

chine

beam should

lie

maximum

in the range of 0.55 to

0.65L„,i abaft the FP. If

kept

good planing full to

is

ranging from 0.80 to 0.90 of Bcdnao stern

is

also beneficial to steering

However,

beam

desired the chine

is

the stern, with a value at the transom

in

rough

weather,

following sea, too wide a stern

•

when

A

especially

may

wide

planing. in

a

cause broach-

such as poor location of the center of

ing or sudden sheering from one side to the other.

buoyancy or bad steering qualities. Most smallboat designers seem to find it easier to obtain good planing-boat performance with the twisted bottom than with the constant- slope type. 77.17 Chine Shape, Proportions, and Dimensions. Inasmuch as the sensibly flat bottom of a

This condition is aggravated if the craft is running below planing speed. To improve wavegoing behavior and steering under these conditions, it is advisable to tuck in the sides at the stern to say

planing craft, within the boundaries of the chine, produces practically all the dynamic lift, there

planing craft, are shown by E. P. Clement ["Hull Form of Stepless Planing Craft," SNAME, Ches.

istics

0.65 to 0.75 of the

maximum beam

at the chine.

Acceptable chine planforms, at least for larger

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 77.17

PRELIMINARY DESIGN OF A MO TORBOAT

Snc. 77.18

other hydrodynamic reasons, the following general

design rules are given,

based on a 10-station

waterline length and the craft at rest at the

designed load and trim:

839

or 7 to the stern. There should be no concave

curvature in this region. (5) The chine Hne from Sta. 6 or 7 to the stern should be parallel to or have only a slight slope

upward and forward with respect to the (1)

The

chine height at Sta.O, above the designed

waterline at rest, should be at least O.OQLwl

If

a small pleasure boat the chine can be higher, up to 0.13L,tl above the designed waterline, because the pay load is small and the the design

is for

(6)

The

chine depth at Sta. 10 should be about

O.OlOLfTL to0.030Z/,pi below the designed waterline (7)

If

the boat

volume is relatively unimportant. happens that pay-load capacity is important then a low chine height may be necessary to get additional internal volume, at a sacrifice of

be used. Indeed,

rough-water performance. (2) Large boats can operate satisfactorily with

Fig. 30.

lost internal If it so

less chine

height forward than can small boats,

because the small, steep waves usually encountered have less influence on the rough-water

performance of the larger craft (3) The chine should He above the at-rest waterline from Sta. at the FP to a point somewhere between Sta. 3 and Sta. 5 (4) The chine line should be straight from Sta. 6

Fig. 77.1

at-rest

waterline. Large slopes are to be avoided.

is

intended for smooth-water

operation only, a lower chine height forward can if

smooth-water speed

ant, a lower chine height (8)

Spray

A

cially at

is

is

import-

desirable in that region.

strips of the general

form shown

in

should be fitted along the chine, espe-

the forward sections and preferably along

the entire length. This matter

is

discussed

more

fully in Sec. 77.20.

77.18

Buttock Shapes; The Mean Buttock. in the bottom of a planing

The buttock shapes

important that some repetition is emphasizing them. With the straight floor segments customary in V-bottom planing craft are so

justified in

Dimensionless Chine-Elevation Diagrams for Six Types and Sizes of Planing Craft

HYDRODYNAMICS

810

boats the fore-and-aft shapes of the buttocks are largely determined

when

by the shape

of

the chine,

projected on the centerplane. This

is

true

IN SHIP DESIGN

Sec. 77.19

and an unattractive appearance when viewed from outside results in discomfort to passengers

the boat.

may

It

with the

actually interfere

from

particularly in the afterbody.

steersman's

The shape and position of the buttock at about one-ciuarter beam on each side of the centerhne, often called the mean buttock, is used by some as one of the characteristic parameters of a planing craft [Clement, E. P., "Hull Form of Stepless Planing Craft," SNAME, Ches. Sect., 12 Jan

Moreover, the possibility of porpoising is greater with the larger trim angles. As a practical compromise the running-trim angle of a planing craft is usually kept below 2 or 3 deg; the greater resistance and lower speed inherent in this lesser trim are accepted. Limiting the trim to these

1955, pp. 2-3].

small angles requires that the center-of-gravity

Straight buttocks in the wetted region, where

be the

avoid negative differential pressures under the

ing.

suction and excessive trim by the stern.

The effect

of concavity in the buttocks

is

under the

described in the section following.

Convex buttock

lines

under the afterbody act

— Ap's,

but the convexity is sometimes unavoidable. Successful planing boats have been and can be designed with slightly convex buttock to develop

lines in the run,

control

but they require careful attention

station.

would otherwise

This in turn acts to prevent porpois-

case.

There are many advantages

running

in level

aside from those just mentioned,

afterbody, reckoned with reference to the water

underneath,

the

position be farther forward than

the dynamic pressures are generated, reduce or

afterbody. These in turn act to prevent bottom

vision

when

the force

and moment to achieve the smaller trim angle by a trim-control device external to the planing under surface of the hull proper. The slope drag called by some the induced drag, and are applied

—

illustrated in Fig. 53.

A— is

carrying ability of the boat

and

it

diminished, the loadis

greatly increased,

usually behaves better in waves. Trim-

control devices to accomplish this are discussed in

to other features of the design, such as the center-

Sees. 30.11

of-gravity location, because of the negative

hsted here for the convenience of the designer:

lift

and 37.24 but the principal kinds are

generated under the bottom.

mentioned previously in item (4) of Sec. to be discussed in item (1) of Sec. 77.19, and the designer is cautioned here that slight downward hooks in the buttocks near the stern are to be used vnih caution. They often produce erratic and sometimes even dangerous It is

77.17,

it is

performance. 77.19

Trim Angle and Center-of-Gravity Posi-

tion;

Use

and

practical

of

Trim-Control Devices. considerations

Theoretical

relating

to

the

running trim of a planing craft are rather thor-

oughly discussed by A. B. Murray [SNAME, 1950, pp. 658-692], It is customary, in analytic

and design work, to express the trun in degrees; this is the form employed in the present chapter. It would be preferable, if the full-scale data for it

could be readily derived, to express the trim

as a linear distance over the boat length, as

is

(1)

A wedge

side of the

manner that

extreme after end, or a bottom in such

forms a downward "hook" of

it

variable angle at the extreme after ends of the

buttocks terminating on it. The thickness of such a wedge, and the angle it makes with the

bottom on the full-scale boat, still require to be determined by cut-and-try methods. The wedge must be applied with caution because too much wedge action and vertical lift at the extreme stern are liable to have a disastrous effect

upon

the steering, especially in a following sea. (2)

The

controllable

flap,

with

its

variable

"hook" angle, probably requires for best performance something better than a shnple mechanical device which holds it rigidly in any selected position.

a gas or with

position.

(3)

For most planing boats, the ideal planing angle for least smooth-water resistance lies between 4 to 6 deg by the stern. This much trim often

briefly

for large vessels.

its

controllable flap hinged to the

Measuring the sinkage or rise at the bow and stern would give the naval architect a direct measure of the amount by which the center of gravity shifts its vertical done

or "shingle" applied to the under

bottom at

mentioned in performance

(3)

of

The Plum

described

yielding device, loaded with

Plum

stabilizer

improve the both the boat and the trimfollowing, should

when

control device

in

A

liquid, similar to the

in waves.

stabilizer,

Sec.

37.24.

many

j'^ears

whose action

is

explained

This was developed and

ago [Motor Boating, Mar and has benefited by a

1928, pp. 16-17, 54, 134]

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.20

amount

great

John Plum,

development by the inventor,

of

in the period 1945-1955.

From

the

produced amazing increases in the capabilities of a planing craft as compared with boat performance without trim control. however,

first,

(4)

it

Surface propellers, such as those fitted to sea

and propellers on ultra-high-speed racing motorboats which become surface propellers at high speed, exert an upward lift at the disc position which acts as a trim-control device. In fact, some planing craft with surface propellers are not able to get through the hump speed and to plane without their help. sleds,

(5)

some form

It is possible that

of auxiliary

may

be found useful in the future for trim control but no practical device of this kind is as yet developed. subsurface hydrofoil

841

In the absence of more extensive chine data it has been customary to indicate the fore-and-aft

CG

position as a fraction of the

WL length from

at the waterline beginning or from the

Sta.

extreme stern. The chine planforms of all singlestep planing craft terminate at the transom, and the chine planforms approximate a shape that is rather well standardized. Referring the CG to the

WL

at-rest

termination

therefore a reasonable

is

enginee ring p rocedure. The LCG values for the two test conditions reported by Clement on Plate 6 of the reference

and

cited are O.b'ilLwL

C.

W.

Spooner,

0.567L,i^i

states that t he value of

also of

LCG)

respectively.

,

Jr., in refe rence (26) of Sec.

LCB

77.41,

(and presumably

varies from about 0.53Ln^z, at a T^

of 1.5 to 0.58L[F£, at or

above a T,

of 3.0.

He reports

that successful high-speed designs have had the

Because of

rather specialized nature, no

its

trim-control device

planing-form

considered for the

is

and

tender,

it

is

not

ABC

discussed

further here.

Lacking the trimming

effect of

a trim-control

CB

as far aft as Q.^SLwl

stern

and V-drives to the

Moving the

CG

with engines

,

in

the

propellers.

forward reduces the running

trim and lessens the risk of porpoising but at the expense of increase in wetted length and

and-aft position of the center of gravity

wetted area. The effect on the total resistance depends upon the variation of friction and pressure resistance with trim angle, indicated by graphs similar to those in Fig. 77.0 of Sec. 77.26.

fuU-planing craft must

At low trims the

an auxihary

device, of surface propellers, or of hydrofoil, effect of

and neglecting

buoyancy,

CP

moment

the

apparent that the foreCG of a

lie

close to the center of

dynamic lift on the wetted the bottom. There is no direct, practical

pressure

area of

method now this

it is

for the

CP

of the

available

position on

(1955)

determining

for

must be with reference to some part

an actual boat.

estimated, therefore,

It

total resistance usually increases

but this is not to be taken for granted by any means, as witness the beneficial effect of trimcontrol devices.

77.20 Spray Strips. The form, position, and function of spray strips are well described and

of the planform, on a basis of expei'imental data from models. The chine planform, projected on the baseplane, is the logical element to use, and

generously illustrated by R. Ashton

the center of area of this element

flying boats to

reference point in

it.

is

the logical

Unfortunately, the chine

area has not been in use long enough, or to a sufficient extent

to build

optimum

among

up a fund

planing-craft designers,

of reference data indicating

relative fore-and-aft positions of the

center of the chine area and of the

CG. E.

P.

Clement gives some performance data for several types of motorboats with the CG abaft the center of chine area ^c by from 2.1 to 11.1 per cent of the chine length Lc ["Hull Form of Stepless Planing Boats," SNAME, Ches. Sect., 12 Jan 1955, Pis. 6-8, 10].

On

Clement gives a plot in the

manner

4 c/y^'^,

of

Plate 9 of the reference

CG

positions expressed

described, related to the ratio

based on data from half a dozen models

of large planing boats.

Memo first

keep spray out of the

pellers, are excellent illustrations of

less

[ETT

Tech.

Feb 1949]. These devices, probably employed on multi-engine seaplanes and 99,

major hydrodynamic

effects

offset pro-

the more-or-

produced by

not almost insignificant physical features. Spray strips are most important along the

minor,

if

forward portion of the boat. usually beneficial to

fit

them

However,

it

is

for the full length.

to advantage on all hulls, round-bottom as well as V-bottom with chine, except perhaps for forms with concave sections and low chines which have extremely sharp chine corners. On certain round-bottom craft they can also be used as fender strakes. Spray strips usually result in a sUght increase in resistance at low and cruising speeds. However,

They can be used

their

many

beneficial effects

disadvantage. They:

outweigh this slight

HYDRODYNAMICS

842

Decrease resistance at planing speeds Deflect spray roots and random water sharply

(a)

(b)

the sides

off (c)

Reduce spray throwing

(d)

Provide a positive lift in the forward part of boat which helps counteract any diving

the

moment Reduce, in round-bottom boats, the large at full speed sometimes climbs high up the side toward the deck edge. The spray root and spray accompanying this wave can be troublesome at times. (e)

bow wave which

IN SHIP DESIGN

Sec. 77.21

three "highly capable and well-known designers,"

supplemented by design sketches on page 27. Fortunately for the designer, spray strips are in the nature of appendages which can be adjusted in form and position to produce the best effect without either major or minor changes in the hull. 77.21 Stem Shape. Up to a speed-length quotient T, of 2.0, F„ of O.GO, the stem of a displacement or semi-planing type of boat should be nearly plumb. This takes advantage of all the waterline length possible, without increasing the hull weight to provide an overhang. For a higher T, and F„ the forefoot should be cut away, starting above the waterline, to get the bow wave under the boat as much as possible and to lessen sheering in a seaway [Spooner, C. W., Jr., "Speed and Power of Motorboats," unpublished manuscript dated Oct 1950 (in library)]. For pleasure craft of all three types discussed ,

TMB

matter of appearance is not There is some objection, from this standpoint, to a stem which rakes downward and forward under any trim or running condition. To prevent this, the stem must have a rake downward and aft, when at rest, of at least 6 deg, and possibly as much as 7 or 8 deg. 77.22 Deep Keel and Skeg Other Appendages. Most motorboats carry a centerhne keel that is rather deep, compared to the flatness of the bottom. This keel terminates aft in a skeg through which passes the shaft tube and shaft for an engine and propeller that happen to be located on the centerline. Examples are the small planing motorboat of Fig. 30.A and the larger roundbottom utility boat of Sec. 77.33 and Fig. 77.T. Besides acting as a support and fairing for the centerline shaft the skeg serves as a deep vertical fin which gives the boat dynamic stability of route and facilitates steering by serving as a sort of fulcrum about which the rudder moment is applied. For high-speed racing motorboats this in this chapter the

Fig. 77.Ja

Model of Large V-Bottom Craft

Running Without Sprat Strips The displacement-length quotient A/(0.010L)' for this hull is SO. It is being towed here at a Tq of 3.5. The spray root climbs up the side and the spraj' rises higher than the deck.

to be overlooked.

;

Fig. 77.Jb

Model op

Fig. 77. Ja

Running With

Spray Strips

The spray

roots

and the spray are thrown to

either

The speed-length quotient T, the same as for Fig. 77.Ja but the bow is lifted slightly

side, well clear of the hull. is

higher.

The photographs. Figs. 77.Ja and 77. Jb, reproduced from the Ashton report referenced at the beginning of this section by the permission of the Experimental Towing Tank, Stevens Institute of Technology, offer an excellent pictorial means of comparing spray formation on a planing-huU model, mth and without spray strips. There are many other pairs of photographs in the Ashton report which give similar comparisons for both models and full-scale motorboats, and which show the beneficial effect of the spray strips. The Appendix to the referenced ETT report by R. Ashton contains design comments from

skeg is reduced to a small, thin metal fin, generally forward of midlength, which also serves as a fulcrum about which the swinging moment exerted by the rudder

is

applied.

There are no known rules

for positioning

and

shaping this skeg, unless it is desired to have it extend far enough below the keel to serve as

mechanical protection ahead of the propeller. Many such skegs are included on published drawings of motorboats but a designer consulting

knows whether the skegs them are good or othermse.

these drawings rarely

shown

in

PRELIMINARY DESIGN OF A MO'IORBOAT

Sec. 77.2-f

Rudders 74.11.

for

motorboats are discussed in Sec.

Comments upon

the fairing of external

pads for the attachment of strut arms to wooden motorboat hulls are given in Sec. 75.6. 77.23 Interdependence of Hull-Design FeaThe principal hull-design features of a tures. planing craft are mvich more dependent upon each other than are those of a displacement-type vessel, just as the latter are

much more

intimately

843

Even though, as described presently, be necessary later on to change slightly

larger ship. it

may

the water-surface level on the hull to effect a

balance between weight and buoyancy rather

than to draw a new set of

the original

lines,

waterline (or waterplane) serves a definite purpose in

proportions,

dimensions,

establishing

parameters while the

and shape

size

and

of the hull

are being worked out.

the desirable features pertaining to each individual parameter, and then working out a compromise

ABC tender as an assumed as a starter that all the requirements can be met on a WL length of 35 ft. A horizontal waterline of this dimension is at the drawn to a convenient scale, with Sta. FP or waterline beginning and Sta. 10 at the AP or waterhne ending. The latter is also the transom position on the centerline. The shape of

to produce the nearest approach to the desired

the hull

overall performance that can be estimated during

stage,

than are the corresponding features of an airplane. For a planing craft the beam, the chine height, the rise of floor, and the type of tied together

sections are all related

hand

A

and must go hand

in

in fashioning the boat.

proper design procedure involves selecting

the preliminary design. Often several different types of section may be used to advantage along the length of a boat.

Yoke

sections forward easily

transform into convex or straight sections aft. Concave sections are often employed forward to obtain good planing characteristics, transforming

and aft where needed for the machinery plant and for tanks to carry liquids. Convex forward sections lend themselves to an easy transformation to straight sections where the rise of floor is small. compromises are made when Still greater selecting features favorable to both seakindliness and planing. In many boats the seakindly roundinto convex sections amidships

space

is

used in the entrance, transforming into the hard-chine efficient planing hull in the run. The reverse of this is sometimes encountered, but there appears to be no advantage in such an hull

form

is

arrangement [Phillips-Birt, D., The Motor Boat and Yachting, Jan 1954, p. 27]. 77.24 Layout of the Lines for the ABC PlaningType Tender. With the comments of the preceding sections as a background the designer is now ready to lay down a tentative set of lines. He must anticipate that this set may be only the first of a half dozen or more, in his search for a shape that best meets the design requirements. For this reason it is well to start with a scale just large enough to permit measuring lengths, areas, angles, and slopes with reasonable accuracy. The first line to draw is a waterUne for the profile and the bow and stern elevations. The designer is advised to work to this waterUne as a sort of fixed reference plane, the

same as

for a

Using the planing-type

example,

it is

is

to be based, but only generally at this

upon the arrangement sketch

The next

step

and to position

DWL. A

is it

to

of Fig. 77. B.

the shape of the chine

fix

vertically with respect to the

tentative chine line

is

drawn according

to the rules previously discussed: (a) Chine height at the FP. Because of the good wavegoing performance desired the chine height at the FP is made greater than the value of O.OQLwL previously mentioned in item (1) of Sec. 77.17. This allows finer sections forward with less probabifity of slamming and pounding. A

chine height of 0.07ZLwl appears adequate. (b) Chine height at the AP. A tentative value

-0.02lL,^z,

is

.

(c) Straight chine fine from Sta. 7 aft, for the aftermost 0.3 of the length as projected on the centerplane, (d) Chine,

crosses the

DWL between

4 and

Stas.

5.

then laid out on The plan view of the chine the basis of the preliminary arrangement sketch is

As a rule, the maximum chine beam within the range of 0.55 to 0.65Lwl abaft the FP. For the ABC tender it is placed at Sta. 6, or at O.QOLwt, abaft the FP. The maximum of Fig. 77.B.

should

chine

fie

beam

is

gives a ratio

tentatively selected as 10 ft, which of 3.5. This is typical for a

Lwl/Bc

craft, for

which the

varies from 3.0 to 3.6.

The beam

modern high-speed planing ratio

Lwl/Bc

made about 0.9 the Subsequent fairing of and working over the design produces a

at the transom ending

maximum beam, the lines 5c(Max)

of

or 9

10.04 ft

is

ft.

and a chine beam at the

transom of 8.96 ft. In this design a wide stern

is

chosen because

844

HYDRODYNAMICS

IN SHIP DESIGN

Sec. 11.24

PRELIMINARY DESIGN OF A MOl'ORBOAT

Sec. 77.24

the boat will operate most of the time in sheltered harbors or rivers. In addition, it improves the steering

A

when

next drawn in the elevation. It is so placed with reference to the chine as to give a rise-of-floor angle amidships in the range of 14 to 18 deg. At the stern the range

from

is

1

is

to 4 deg. If constant rise-of-floor

no twist in the afterbody be of the order of 6 to 9 deg. The lines of two motorboats of good performance published by L. Lord ["Naval Architecture of Planing Hulls," 1946], in Fig. 41 on page 89 and Fig. 43 on page 92, have constant rise-of-floor angles of 5.8 deg and 9.2 deg, respectively. Those of one planing boat whose Unes are pubUshed by D. D. Beach [The Rudder, Jan 1954, p. 38] average about 8.3 deg. The sections are next sketched in. For the is

desired, with

bottom, the angle

may

81

was to decrease the risc-of-floor the run of the boat. Every effort was

angles in

made

planing.

tentative keel Kne

angle aft

The net

effect

to keep the buttock lines straight in the

run, especially abaft Sta. 7.

The

sections were then redrawn with the

same volume was calculated. The volume below the DWL was found to be sUghtly more than needed, but a uniform decrease in draft of about 0.21 ft along the whole length gave the correct volume. A lifting of the whole boat in this manner is usually general characteristics, and the

found acceptable, because hull

AP

The

revised

+0.073 IL^t and at

is

—0.0211Lwl The relocated chine new designed waterhne between Stas.

it is

crosses the

4 and

FP

hull

the changes in the

all

are favorable.

characteristics

chine height at the

the

new

5.

convex

Next, the fore-and-aft position of the center of buoyancy CB is determined, and a check is made with available data such as those presented at the end of Sec. 77.19 to determine whether

sections in the run.

the

these

As previously mentioned, give volume forward but still

acceptable for good planing-boat design. If the

ABC

tender, sections of inverted-bell shape are

forward,

suitable

sections

into

fairing

slightly

allow the water and spray to break the chine.

They mil probably

cleanly at

off

result in slightly

smooth water, but should

greater resistance in

CB

lies

mthin a range

CB is not less than from the FP, the

CG

of

position found

more than 0.65L„.i, can probably be placed

0.55Z/nr£ or

CG

within that range so that the craft will float at

give improved wavegoing performance. Sections

the draft and in the attitude desired

with slightly convex bottom segments are favored

If

aft,

more

as they provide

hull

volume and allow

lower mounting of the engines.

When check

is

a tentative of the volume of the hull up to the

made

in,

When

was first tender the volume was found rest.

is

when

at rest.

as far forward as 0.45LH^i from the

FP, or as far aft as 0.70L^z,

the hull will have

,

to be reshaped to correct this condition.

the sections are sketched

designed waterline at

CB

the

craft is liable to porpoise

the

CG—are

too far

if

the at-rest

The

CB —and

aft.

After making the necessary shifts in the section

this

done for the ABC to be smaller than that corresponding to a weight of 19,000 lb of salt water. It would have been necessary to increase the draft about 0.5 ft to support the estimated boat weight. This was unacceptable as it lowered the chine too far and it altered the wavegoing characteristics intended

and other hues, and checking the volumes and CG positions, the lines are faired and drawn, including the abovewater body to the main-deck

for the forward sections.

curve,

Increasing the volume required the following

edge.

or

1:4

submergence

chine

at

the

increased to 0.0275Lwl or 0.962 ft chine crossed the between

DWL

Sta. 4. It

was

still

.

AP

The Sta.

was

revised 3

and

a straight line from Sta. 7 to

the stern at Sta. 10. (2)

The depth

of the keel

below the

DWL

was

increased shghtly (3)

The

position

chine forward remained at the same

mth

respect to the

DWL.

final result for

shown curve

box. This

drawn

is

is

the

ABC

in Fig. 77. K.

drawn

The

planing-form section-area

in Fig. 77. L, in the usual

supplemented by the

B/Bwx

Bwx/2 length L^l

so that the half-beam

equal to one-fourth the waterline Holfthe

The

is

A/Ax

changes: (1)

The

tender

is

HYDRODYNAMICS

846

Design Check on a Basis

77.25

of

IN SHIP DESIGN

Chine Di-

mensions.

I

I

I.I

I

I

Form of Stepless

:t

Ploninc)

Boats,*

5NAME,

Ches.Sect

l2Jan

^1

I955,PI. 12

how

the characteristics already determined for the tender compare ^\'ith the available chine

ABC

data plotted by E. P. Clement ["Hull Form of Stepless Planing Boats," SNAME, Ches. Sect.,

There are

TMB

listed

and

dimensions

in

derived

planing-form tender,

of

the

o

Motor Yachts

•

PT

Boots,

World Worll

Rep. 1093, Nov 1956]. Table 77. f the principal

characteristics

I

1000 to

Adopted from E.P Clement,' Hull

background and reference data to enable a new planing craft to be laid out on a basis solely of the chine dimensions and characteristics. It is

12 Jan 1955; also

I

I

met

D.iaplocement,

proportions, and position, there are insufficient

nevertheless useful at this point to ascertain

I

I

36 40 44 48 52 56

28 32

20 24

16

12

Despite the logical nature of the procedure and the various design data given in Sec. 77.17, based upon the chine dimensions,

Sec. 77.25

40

30

20

10

ABC

50

Bisplocement,

by the methods

Fig. 77.

M

l
60

80

70

or thousands

90 cff

100

120

110

pounds

Vaeiation op Chine Ratio Lc/Bc

described in the sections preceding. Included in

With Displacement

the table are some of the ratios used as parameters by Clement, based upon the actual dimensions

The dimension Lc is the projeoted length of the chine and Be is the mean width of the projected chine planform. The displacement corresponds to the buoyancy volume with the boat at rest. The solid line represents a tentative

of the craft

whose

As a check

lines are depicted in Fig. 77. K.

of these

dimensions and ratios with

meanline for the data plotted here.

the data given by Clement in the reference cited. Figs. 77.

Plates

M and 77. N have been adapted from his

12

standard

and

13,

Ac/V^^^

Using

found to be 413.7 ft'. This is considerably larger than the projected area of the chine, 334.6 ft', of the actual boat of Fig. 77. K. If this larger value of A c is divided by the actual chine length, the mean chine beam Be is found to be 413.7/36.65 or 11.29 ft. If, on the other hand, this larger area is used in combination with the Lc/Bc ratio of 3.86, the fore-and-aft chine length comes out as

notation.

the

tentative

total

M

With a fore-and-aft chine Lc of 36.35 ft from Table 77.f, the mean chine beam Be = 36.35/3.86 = 9.417 ft. With the Lc/Bc ratio of 3.86, Fig. 77.N is entered along the bottom scale and a ratio of

the meanline shown. length

The

= LwL =

LoA

Lc

principal dimensions, characteristics,

38.0

V =

ft

=

44.484

36.35

296.7

Ax = Le =

ft

ft';

ft.

and other data listed here are

35.0 ft

of chine

39.96

is

Chine Chabacteristics and Other Features of Proposed Fuli^Planing Tender fob

77.f

The Ac is

taken from the meanline.

value of ¥''' from Table 77.f

weight of 19,000 lb for the full-planing tender, is entered along the bottom scale and Fig. 77. a value of the ratio Lc/Bc of 3.86 is taken from

TABLE

of 0.3 is

with necessary changes to

for the craft

lines are

shown

ABC

Ship

in Fig.

77.K.

standard salt water

ft' in

10.56

whose

ft"

0.57LwL

,

from

FP

to section of

maximum

area

W

= 19,000 lb A = 8.482 long tons T, = V/VL = 24/V35 = 4.057 A/(0.010L)' = 197.8

4jf of at-rest waterline

Ac

¥'!' F2/3

Ratios Based upon the Chine Dimensions: Ac/Vi' = 334.6/44.484 = 7.522

Be mean, Ratio

of

334.6/36.35 = 9.205 /{Brake Power Pb at designed speed)

over chines,

Weight

W

of chine, projeoted,

= Ac/Lc =

= =

6.6696

ft

44.484

ft^

Le/Be =

36.35/9.205

= =

=

281.9

ft-

334.6

ft^

3.949

ft

=

19,000/430(est.)

44.19

Weight TF/(Brake Power Pb) = 19,000/450 (to be installed) = 42.22 Center of projected area of chine, Ac Ues at 0.532LirL abaft the FP Rise of floor at midlength of Lwl = 18.25 deg; at AP = 3.75 deg ,

LCB = 0.5ML^L or 20.79 ft abaft the FP LCG is assumed to be in the same fore-and-aft position, corresponding to 3.29 ft abaft midlength of the designed waterline or 14.21 ft forward of the

AP.

Sec. 77.26 6

PRELIMINARY DESIGN OF A MOTORBOAT

8-17

— HYDRODYNAMICS

818

mean chine Strictly than Be

the designed speed, the afterbody

beam

is

9.46

ft,

slightlj^ less

.

IN SHIP DESIGN

The

Srr. 77.26

dynamic-lift coefficient, assuming a con-

stant rise-of-floor angle of

speaking, Murray's data are not applicable to the present case, because they are derived from

{Cdl)»

/3,

is

2Cl Cl

— O.opV'B'

angle

/3. models with a constant rise-of-floor However, they are used here by taking as the

reference angle

angles

at

13

transom. This

mean

the

of the rise-of-floor

midlength section and

the is

0.5 (18.25

+

The speed coefficient, based on beam of the afterbody, is Cv =

at

the

3.75) or 11 deg.

the

mean

chine

=

J'^'-'^''^ \/32. 174(9 .46)

referenced paper but

ATTC

C,

TABLE

77.g

The data

Col.

is

the boat

of-floor angle of

V

=

2.324

(77.vi)

is

notation. It

calculations.

/3

=

is

required for the resistance

To determine

it,

enter the lower part

of Fig. 53. B in Sec. 53.4 with the average rise-of-

The load coefficient, also based on the afterbody mean chine beam, is expressed as C^ in Murray's the

W

on the basis that the entire weight of is supported by dynamic lift. Data so derived are certainly on the conservative side. The dynamic-lift- coefficient {Cdljo for a ri.seThis

represented by Cld in

floor angle

/3

of 11

deg and the value {Cdl)^ of

The derived value of {Col) a = 0.155. The sum of the friction resistance Rp and the

0.1298.

residuary resistance is

Rr

is,

the total drag force

opposing motion, represented as the

W

19,000

wB^c

64.043(9.46)'

=

0.3504

(77.vii)

and J

sum

of the

However, as it is not always practicable or possible to determine forces 7

in Fig.

13. C.

Resistance Calculation for Full-Planing Tender Hull of Fig. 77.K bt Murray's Planing-Surface Data

referenced in the heading of this table are found in Fig. 53.B, Sec. 53.4.

— PRELIMINARY DESIGN OF A MOIORBOAT

Sec. 77.26

TABLE The data

77.h

Calculation for CENTEn-OF-PuEssonE Location fob Fuli^Planing Hull op Fia. 77.K by Murray's Planing Surface Data

referenced in the heading of this table are found

ir

819

HYDRODYNAMICS

850

and the T„ at designed speed is 4.057. From the referenced graph the minimum resistance per pound of weight for a displacementtender

197.8

is

length quotient of 160 to ISO

is

0.123

cor-

lb,

responding to a resistance of 2,377 lb for a displacement of 19,000 lb. From Fig. 77.0 the minimum resistance predicted, at a trim angle d of 3.25 deg, is 2,320 lb.

The LCB

of the

boat at rest

is

found, by routine

methods, to be approximately 0.594L„.l abaft the FP. By Table 77.f, the center of the projected chine area is found to be 0.532L,rL abaft the FP. The CB thus lies at slightly more than 6 per cent of

LwL

This

close to

is

abaft the centroid of the chine area.

an average value as indicated by

Form

E. P. Clement ["Hull

Boats,"

SNAME,

of Stepless

PL

ft

Then

LCG =

abaft the FP, or 14.21

the transom.

To run

position on the

=

0.594L,rL ft

0.594(35)

=

forward of the lie

P.5

With a

horses.

trans-

mission loss of say 5 per cent in the shafting and bearings, the brake power Pb required to be

by the engines is 414/0.95 = 436 horses. This independent estimate compares well with the first approximations to the shaft power in Sec. 77.14, where it was found that two engines, delivered

each delivering a brake power of 225 horses, would be adequate for the purpose.

K. C. Barnaby gives a few average values the propulsive coefficient

j/p

Appx.

[INA, 1943,

126]:

1, p.

25-ft motorboats, average

motorboats, average

(b) 50-ft

of

as applying to craft

in the category being considered here

(a)

book

Barnaby's

"Basic

about 0.58 about 0.59.

t]p is tjp is

Naval

Architecture"

[1954, Art. 191, Fig. 100, p. 306] contains a

graph

20.79

of average

tjp

values which indicates a propulsive

AP at CP

coefficient

of

only about 0.45 for single-screw

at a steady trim the

bottom must

Sec. 77.27

absence of a better value, the shaft (or better, the propeller power Pp) is

Pe/vp = 207/0.50 = 414

9].

be assumed that the CG of the boat laid out in Figs. 77. B and 77. K lies directly above the center of bu oyancy CB when the craft is at rest.

power

Planing

Ches. Sect., 12 Jan 1955,

may

It

IN SHIP DESIGN of 0.50 in the

approximately

craft

50

long.

ft

lengths of 1,000

Since this graph extends to ft

it

may

not be intended to

under the CG position in the hull. From the upper graph of Fig. 77.0, the running trim for this CG position is found to be about 4.9 deg by

cover motorboats.

the stern. At this trim the total resistance

Rr

situation at this stage relative to the probable

is

position of the proposed craft with reference to

from the lower 2,500

set of graphs of that figure

by Murray take no drag of the hull and upper

resistance data given

account of the still-air works above the DWL. To predict this value for the ABC tender, it is necessary to estimate the transverse projected area above water. A rough calculation from Fig. 77. B gives 60.2 ft^. For the still-air drag the designer may use the dunensional formula Dsa = 0.0044^7' [S and P, 1943, p. 52], where D is in lb and V is in kt. Substituting, Dsa = 0.004 (60.2) (24)' = 138.7 lb. Other coefficients for this formula are given in Sec. 54.7. Based upon the rule given by H. F. Nordstrom [SSPA Rep. 19, 1951, p. 15], the resistance of well streamlined appendages for a twin-screw motorboat need not exceed 7 per cent of the bare-hull total resistance. An estimated value is then 0.07(2,500) = 175 lb. Still-air drag and wind resistance for motorboats are discussed further in

2,500

power

total resistance -I-

is

when

its

To

Rt

+

Dsa

+

^app

=

-I- 175 = 2,813.7 lb. The effective then 2,813.7(24)1.0889/550, or about

138.7

207 horses. Assuming a propulsive coefficient

t/^

visualize the

running attitude

planing, the designer proceeds to predict

certain features.

Among

these are the change in

CG

elevation of the center of gravity

with speed,

the fore-and-aft position of the center of pressure

CP

and

of the

CG, the dimensions and shape

of

the wetted bottom surface, the position of the

probable impact area in waves, and the best positions for the heavy weights in the boat.

There are at

least

two methods

the vertical position of the boat

determining

of

when underway

at full speed with respect to the level of the sur-

rounding undisturbed water. One is to make use of a diagram such as that given by A. B. Murray in Fig. 2 on page 658 of his referenced paper, or in Fig. 29.

D

of

Volume

I of

the present book, for a

about the same size and shape. Although Murray's diagram referenced in this case is for 40-ft V-bottom motorboats it full-planing

craft

of

should serve reasonably well for the

Sec. 77.37.

The

Heavy Weights.

the surrounding water and

lb.

The

Running Attitude and Fore-and-Aft Po-

77.27

sition of the

which

ABC

tender,

on the waterhne and 38 ft overall. At the designed speed of 24 kt, equivalent to 27.6 mph, tlie rise of the center of gravity above its at-rest position is approximately 0.7 ft, or is

35

ft

— PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.27

0.0175 of the 40-ft length. For a craft 38 ft long the rise of the CG would be about 0.G7 ft.

Another method

is

boat at

profile of the

an elevation designed speed and in

to lay out its

or its

predicted position and attitude with respect to

the undisturbed smooth water into which

advancing.

One

detailed

method

plane 14.21

ft

of

Sec.

follow.

mean wetted

77.26

in

a

by

is

4.9 deg

by the

B

Col.

of

stern.

Table

centerplane the point of intersection of the spray-

undisturbed

the

of

(77. ix)

It is probable that this length is a function of the local rather than of the average chine beam rise-of-floor angle. For the ABC planing tender these are taken as the local chine beam at

and

Sta. 5, equal to 9.96

ft,

and the

local rise-of-floor

angle at midlength, equal to 18.25 deg. Then, for a trim 6 of 4.9 deg.

somewhat above the water surface.

Li

=

This

(9.96)(0.3298)

=

1.22(9.96)

=

3.1416(0.0857)

On

is,

77. h,

ft.

lies

/3

tan 9

If

The

According to B. V. Korvin-Kroukovsky, D. Savitsky, and W. F. Lehman [ETT, Stevens, Rep. 360, Aug 1939, Fig. 15, p. 36] the forward edges of the wetted area of a planing craft when underway are defined by the bases of the spray roots under the bottom. These extend generally in two straight lines from a point on the keel to points abaft this on either chine. When the wetted area on one side of the hull is projected on the root base with the chine

851

(planing surface beam) tan

transverse

length L„,s at this trim angle

by interpolation from

level

^

forward of the AP, the correspond-

ing running attitude

21.4

which

CG and the CP tentatively located

the procedures

is

of accomplishing

this is described in the paragraphs

With the

it

_

the basis of perfectly

flat

surfaces, with constant angle

/3

12.2

ft.

V-shaped bottom and no twist, the

wetted length of the keel should equal the mean wetted length L^s plus half the length L^ For the ABC tender this is 21.4 ft plus 6.1 ft or 27.5 ft. This wetted keel length is laid off along the keel, forward from the AP, terminating at the point .

K

in Fig. 77. P.

ft less 6.1 ft

The wetted

or 15.3

ft.

chine length

This distance

is

21.4

is laid off

along the chine, also forward of the AP, terminating at the point C.

The diagonal broken

line

KG in

the figure forms the locus of the spray-root bases

on each breaks

side.

off

transom

Taking

for granted that the

water

cleanly along the chines, and that the

clears to its lower edge, the

wetted area

illustrated schematically in the small

hes entirely under the after portion of the V-

figure

pubhshed by A. B. Murray as a part of "The Hydrodynamics of Planing Hulls" [SNAME, 1950]. The mean wetted length Lws measured generally

bottom, indicated by the hatched area in the

Fig. 10 on page 665 of his paper

figure.

situation

is

,

mean buttock at the quarter-beam, mean of the wetted length of the and the wetted length along the chine. The

parallel to the is

the arithmetic

keel

between these two lengths, indicated Stevens, Report 360, is estimated by Eq. (17) on page 14 of that report, namely difference

as Li in

ETT,

The

drawn

Mean Buttock from Centerplane

Calculated Trim

is

4,9 deo b\

15

-^-2 30

ft

\

K

is

placed at the level of the sur-

in,

picturing the position and attitude of

the hull with respect to the undisturbed water level. Fig.

77.P

is this profile for

the

ABC

full-

planing tender, with dimensions and explanatory notes.

[Proposed Offset of

point

rounding undisturbed water, and the craft is trhnmed 4.9 deg by the stern. Its profile is then

E'ye

Position of

the Stern

Water Surface

—

\*

Fig. 77.P

^Mean Welted Lencjth is^

b^ calcuialion,

Lws

214 ft

f^CP

Position

for

Normal

H^dronomic Pressures

on Bottom,

14.21

ft

Forword of

Diagbam Showing Pbedicted Running Position and Attitude op Planing Tender at Full Speed

FP

P

HYDRODYNAMICS

852

Assuming a suitable vertical position of the in this case 0.5 ft above the DWL, the at-rest and underway CG positions are placed on the

IN SHIP DESIGN

Sec. 11 2R

Despite the fact that this item has received

little

Plum

CG,

attention in the technical literature, John

drawing, in a transverse plane 14.21 ft forward of the AP. Scaling the rise of the CG due to the

and others who have produced high-speed planing craft which give reasonably satisfactory behavior under these severe conditions maintain that the proper adjustment of the fore-and-aft location of

forward speed of 24 kt from the original of Fig. 77.P gives 0.81 ft, as compared to the 0.67 ft derived from the Murray reference earlier in

the heavy weight groups, and the control of the

the section.

superior wavegoing performance than

Two

now

some consideration. The first is the question of whether or not the steersman at the control station can see ahead other features

over the

bow

require

in this running attitude. Fig. 77.

indicates that with the stem carried all the

up to the forward deck direction

just

is

way

line,

vision in a horizontal

possible

from the proposed

control station. In order to see clearly to a point

on the water surface some 90

proper trim angle, are more important factors in

shape of the

any par-

To

give the naval architect a more reliable background in ticular or special

hull.

and to furnish him with better design an intensive and thorough study of the of weight location and trim control should

this respect rules,

effect

be carried out at the earUest opportunity. 77.28 First Space Layout of the 18-Knot

Round-Bottom Hull.

For the round-bottom tjT)e motorboat selected tentatively in Sec. 77.10 as the one best suited for the 18-kt speed, the requirements of Table 77. a indicate

ahead of the steersman, his line of sight would have to be depressed about 5 deg, indicated by a broken line in the figure. Clear vision at this angle would necessitate rounding the stem head and using some reverse sheer forward. The second matter is one of appearance. A planing boat running at full speed with a trim of the order of 5 deg by the stern seems to be struggling along, as though it could not quite get through its hump speed. The same boat, running at the same speed but with a trim of only some 2 deg, gives that delightful impression of smooth, effortless running which is the aim of every motorboat designer and builder and the hope of every owner and operator. Few among those who ride or watch seem to reahze, or to be concerned, that the resistance and power may be less at 5 deg than at 2 deg trim by the stern. If level running becomes of more importance than

40 ft long is unnecessarily large and that the weight hmit of 25,000 lb need not even be approached. A second arrangement sketch, reproduced in Fig. 77. Q, reveals that a transom-stern hull of 35-ft waterline length is ample to contain the necessaiy spaces and volumes without

efficiency of propulsion, a trim-control device of

crowding.

some kind

is

Sees. 36.26

and 37.24.

Taylor quotient 2\ at 14 For 18 kt it is 3.042, F„ = 0.906. From the utihty-boat curve of Fig. 77. C, the total weight should be not in excess of 18,000 lb or 8.036 tons. Using the PhilUps-Birt Eq. (77.iiia) of Sec. 77.14, the 14-kt speed, and the proper value of K2 from Table 77. e.

ft

clearly indicated, as described in

If this

area

is

well forward of the

boat receives an up-pitch

moment

as

it

CG

the

crest.

If,

the result of slamming on

wave

make

this speed with a half-

passengers and their personal baggage. It must,

however, be able to accommodate, at the slower speed of 14 kt, any of the items listed in (6) of

Table 77. a and to run for 6 hr at full power. In short, it must have power enough for the 18-kt load and speed, but room enough for the 14-kt load.

as

Sketching a preliminary arrangement indicates, it did for the full-planing boat, that a hull

For is

this length the

2.366,

F,,

=

0.705.

strikes

however, the impact forces are applied more or less underneath one of the heavy weight groups such as the propelhng machinery, every

that the craft must

load of fuel and a crew of two, as well as two

kt

The next step is to estimate, possibly from a diagram such as Fig. 77. P, about where the impact area will be under the bottom when the craft runs at high speed through relatively short waves.

of semi-planing

Pb

(horses)

=

V^

(kt)

W (long tons)

(14)^(8.036)

=

201.

(2.80)'

crests is limited

be remembered that at the 18-kt speed

to a compression of the structure between the engine bearers and the bottom of the boat, with an effective reduction in pitching

the useful load (and the total weight) will be

moment.

moment

generally

It is to

considerably less than 8.04 that one of the

t.

It

HN-10

appears for the diesel engines

!ser.

PRELIMINARY DESIGN OF A MOTORROAT

1130

853

/Trace of Desioned Waterline

In Second Layout

Enqme

Should

Be Moved Forward and Passengers Aft to Provide More Comfort for

Them

Weather Protection

Over Corqo

and Boqt^Qqe '*-

not

Shown Here

Desiqned" Woterlineot rest

96765|43ZIF|P mentioned in

Sees. 77.13

and 77.14

for installa-

tion in the 24-kt planing tender, with a

maximum

brake power of 225 horses, may be sufficient for the round-bottom tender. At least, it will be used for a first weight estimate. 77.29 First Weight Estimate for the 18-Knot Hull. A first weight estimate is made by using a few known weights plus reasonable percentages (from Fig. 77. D) of the estimated gross weight of 18,000 lb.

These

are, in lb:

18-kthull (1)

Pay

(2)

Diesel engine, one

load, including crew

equivalent,

and (3)

oil

HN-10

14-kthuU

1,000

3,000

2,650

2,650

or the

including water

in the engine

Fuel for 6 hr at

Stations

Sketch op Tentative Space Layout for Round-Bottom Tender for

Fig. 77. Q

power, reckoned as 0.5 lb per brake horse 338 (half per hr full

675

Pb =

ABC

Ship

HYDRODYNAMICS

854 Assuiiiiiig

a

tiaiisinissioii loss of 5

necessary brake power

is

178/0.95

IN SHIP DESIGN

per cent, the

Characteristics.

=

cus.sed

187 horses.

IV. Skene's Eq. (77.iva) of Sec. 77.14 does not

apply to round-bottom forms. Instead he gives a graph of the dimensional ratio P/W^'^ on a base of 7\ = V/'\/L, where P is in horses is in tons (presumably of brake power) and ["Elements of Yacht Design," New York, 1944,

W

Fig. 147, p. 295].

W

is 6.071 t, For the 18-kt boat, where For T, = 3.042, the value of P/W'^" from Skene's graph is 25. Then P = 25(8.20) = 205 horses. is 7.187 t, (b) For the 14-kt boat, where W'^" = 9.98. For T, = 2.366, the value of P/W'^"

(a)

Then

P =

13(9.98)

=

130 horses. This

design

The

G. TomaUn [SNAME, 600, for displacement-type vessels]

The nomogram

1953, Fig. 7, p.

of P.

shaped to run well at either the sustained

maximum

Here, however,

it

is

it

not possible to install

enough power to reach the higher speed at the heavier load condition. This limitation would

modern

(1955) reciprocating,

draft.

=

174 horses.

is

semi-

con-

sidered good boat design, therefore, to shape the hull for the heavier load condition

165/0.95

all

planing as well as full-planing craft. It

For the 18-kt boat, Aveighing 13,582 lb, a predicted shaft power Ps of 195 horses. Then Pb = 195/0.95 = 205 horses. (b) For the 14-kt boat, weighing 16,099 lb, a predicted shaft power Ps of 165 horses. Then

Pb =

.speed

was considered better design to fashion it for the higher speed. Although it was known that the ship would run for much of the time at reduced load and draft, the design was laid out for full load and full draft. speed,

gives: (a)

high-

found to control the engine power to be installed but for the selection of hull features the heavy-load condition is used. For the ABC ship itself, where the hull at its designed full-load displacement could have been is

internal-combustion power plants, to V.

dis-

intended to run at

different displacements.

apply, at least with

seems very low.

is

speed light-load condition

W

13.

The round-bottom

these sections

two speeds, at

or the

TF'^' is 8.20.

is

in

Sec. 77.31

and the deeper

Although the alternative design

of the

ABC

tender, running in the lower range of speeds,

is

have a round bottom it is nevertheless of the semi-planing type. For this reason, as well as to give it adequate metacentric stability and to to

provide a better internal arrangement, a wide-

H. F. Nordstrom for determining The effective power Pe Fig. 48 of SSPA Report 19, 1951, is a good one for craft of this type but unfortunately it does not extend far enough for chart of

beam

either the 18-kt or the 14-kt designs considered here.

From

the foregoing

light-load condition

amount

it is

is

manifest that the 18-kt

the one which controls the

power required. Of the empirical Crouch-Werback formula is only 187 horses, and is decidedly low. Those of the Skene graph and of the Tomalin nomogram are identical and low, but to a lesser degree. The identical predictions of the K. C. Barnaby and of engine

estimates, that of the

Philhps-Birt formulas, 251 horses, are higher than

the average by a greater amount. Despite these

appears safe at this stage to make use of one HN-10 engine or its equivalent, with a rated brake power Pu of 225 horses.

variations,

it

All the foregoing estimates are based upon the brake power Pb at the engine coupUng, and upon the designed (maximum) speed V and weight

W of the complete boat. 77.31

Selecting the 18-Knot Hull Shape and

hull

As a

,

10

is

first

again favored. guess, a

ft is selected. It is

maximum

waterline

beam

of

placed at Sta. 6 or at O.QQLwl

from the FP. At the 14- to 18-kt speeds at which this craft will run, a narrower stern is favored than for the 24-kt full-planing hull. Following seas are more of a problem in steering the slower craft and the liability of broaching is greater. The transom width is tentatively selected as only 0.75j5.y or 7.5 ft. A waterline is then sketched in, avoiding any hollow in the entrance portion. D. Phillips-Birt recommends certain optimum prismatic coefficients for small craft in the range of T,

1.3 to 1.8 ["The Design of Small Power The Motor Boat and Yachting, Apr 1953,

from

Craft," p. 160].

of the

While the lowest T^ value

ABC

tender

is

for this version

2.366 for 14 kt, Phillips-

Cp = 0.69 is used as a starter. 35 ft and a weight displacement of 7.187 t, the underwater volume V is 251.4 ft^ and the maximum-section area is Birt's value of

For an Lwl

Ax =

of

251.4 Cp{L,r,)

~

(0.69)(35)

=

10.4

ft'

Sec.

PRELIMINARY DESIGN OE A MOTORHOAT

77J2

about the same as for the 24-kt planing-type tender, the beam is about the same, This area

is

and the length

is

The

exactly the same.

keel

boat in Fig. 77. K, at the is therefore used as a guide in drawing a similar profile for the roundof the 24-kt

profile

bottom

of

bottom

the hull proper,

craft.

The depth

position of the section of

at

the

maximum

fore-and-aft

area

is

extrem(!ly valuable but almost

equally rare.

Layout of the Lines for the ABC RoundLaying out the underwater lines for the semi-planing motor tender being designed 77.32

Bottom Tender.

here calls for following the general principles set forth in previous sections for this operation on

about the same as for the faster boat. There is no general or special rule concerning

full-planing craft. Fashioning the abovewater hull

is

ft,

the longitudinal position of the section for a boat of this type.

maximum-area

To

afford a clean

run toward the transom it should, however, not lie abaft the midlength of the waterline. It is preferably placed slightly forward of that point. For the design in question it is taken at 0A7Lwl from the FP. Any small-craft designer welcomes the opportunity to study the hull shapes fashioned by others, even though he may have little intention of follomng or copying any of them. Sources of a considerable amount of these data are listed here

based upon considerations of wavegoing, good from the control platform and other operating requirements, convenience of the passengers and crew and, last but not least, appearis

vision

ance. Specifically, the first three steps involve roughing in the maximum-section contour, laying out a designed waterline, and sketching a pre-

liminary section-area curve,

much

as they did for

ABC ship design in

Chap.

06.

the large

(a)

"Some Tests with Models

waterline

tentatively as 0.05 ft

lated model-test data. Text

(d)

F.,

SSPA Rep.

19,

1951.

is

in English.

"Cruceros y Lanchas Veloces," Buenos Aires, 1951. The text is in Spanish, as yet untranslated (1957), but the lines drawings are understood

(b) Baader,

J.,

by any naval architect. Beach, D. D., "Power Boat Form," The Rudder, Jan 1954, pp. 38-43, 90. The author gives lines drawings of seven modern hull forms, with the practical and the hydrodynamic reasons for their hundreds of lines drawings of modern motorboats are to be found on the pages of yachting and

(d) Literally

motorboating magazines, most of them mentioned in the references of Sec. 77.41.

extremely unfortunate that,

^vith

such a

wealth of published data at hand, a motorboat renders himself vulnerable by rarely knowing whether the shape he is using for guidance is a good one or not. In other words, he seldom knows a fraction as much about the good or bad performance of a boat as he knows about its physical shape and other features from the published lines, arrangement drawings, photographs, and descriptions. As an example of what should be done with published material, D. S. Simpson includes a sketchy body plan of a round-bottom motorboat, but gives rather full comments on the behavior of the actual craft in designer

10.0

ft.

(c)

The designed waterline beam at the transom AP) is 7.5 ft The maximum-sectio n area is 10.4 ft' The value of LMA is 0.47L,^,, reckoned

(or at the

(e)

,

from the

The

FP keel

profile

tender, at the

bottom

(f)

of

the 24-kt full-planing

of the hull proper, is to

be

used as a guide.

The

first

layout of the maximum-area section Bwx) indicated

(actually taken at the position of

various features and characteristics.

is

beam Bwx is

from the FP. The half-siding at the bow may be taken

of Small This pubhcation gives the body plans of many round-bottom forms, together with their section-area curves and tabu-

Vessels,"

It

The maximum

Its fore-and-aft position is O.GOLwi, (b)

Nordstrom, H.

Summariz-

ing from Sec. 77.31:

for convenience:

(c)

kind

of this

855

1050, pp. 081-082). Information

selected

as 1.65

(a)

[SNAME,

service

that the initial beam of 10 ft was too large and that the keel line used for guidance lay too near the at-rest waterplane. The floor lines in the

bottom had too smaU a rise to insure reasonable freedom from pounding. The bottom slope was in fact smaller than for the corresponding sections of the full-planing form. Unfortunately there appears to be no set of minimum values to be used as a design criterion for selecting a proper rise-of-fioor angle for this type of boat. The combination of wide beam and shallow underwater body produced an extremely sharp curvature at the turn of the bilge. Indeed, the section had the appearance of one taken from a hard-chine hull in which the

maximum-area

chines had simply been rounded

second layout the keel line

beam was

was lowered.

oS.

For the

decreased and the

856

— PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77 J2

Skot.ching

a

designed

icMitativc

watcrliiie

through the three points given in the summary is no way of knowing whether it is a good one until the sections are drawn. Before this can be done, there has to be a tentative section-area curve from which to work. Before sketching such a curve for a normal form of motorboat it is necessary to fix its termination at the AP. Here again there are few design rules for selecting an immersed-transom area Au but the immersed draft Hu should not exceed the values given in Table 67. d. For a speed of 18 kt, it is about 1.15 ft; for 14 kt, about 0.695 ft. Probably it should not exceed 1.0 ft in the present presented no problem, but there

With a transom beam Bu

case.

average draft of say 0.6 4.5 is

ft^

and A^/Ax

ft,

0.43.

is

of 7.5 ft

and an

the value of

A

Au

sketched in roughly through the three

known

points and a check on the probable volume obtained. It should be about 6.07 (35) or 212.5

Many

is

section-area curve

is

ft'.

of the descriptive articles hsted in Sees.

and 77.41 include section-area curves with the hull lines. These may be used by the designer 77.31

as guides.

new and deeper keel an assumed designed waterline, and a

Starting again with a profile,

tentative

curve,

section-area

sketching of the

sections at the various stations

may

proceed.

When

drawing these sections a distinct effort is njade to keep the buttocks in the run as straight as possible. Even though the craft is not intended to plane at the designed load, this shape may be relied upon to encourage planing at the higher speeds, under loads (total Aveights) that are somewhat lighter than those specified.

TABLE

77.i

857

When

the section areas correspond roughly to the section-area curve ordinatcs, and the rise of

each appears to be adequate to prevent pounding, with convex sections in the entrance floor of

and not-too-sharp transverse bilge curvature, the designer may proceed to add the abovewater body. The main deck edge at the side is drawn to give a moderate flare in the forward sections, a slight flare in the midship sections, and some tumble home in the stern sections. Unless deck space

is

required in service, the extremely wide

decks seen in

many motorboat

designs do

slamming when waves under this overhang. For the ABC round-bottom tender the stem is made more nearly plumb than that of the planing tender. This provides a greater waterline length on a given overall length, with lower resistance at the speeds below planing. Upon completion of the shaping and fairing easily lead to dangerous strike

two was found that the volume under the tentative waterUne at rest was slightly greater than that required by the heavyload of 16,100 lb of salt water. Rather than to draw a third set of lines the designed waterline was lowered to give the correct volume. The final for this craft, involving the preparation of

successive sets of lines,

it

W

faired lines are reproduced in Fig. 77.R.

All the revised characteristics and parameters were checked to make sure that they were satisfactory. They are listed in Table 77. i.

A

final section-area

portions,

down

curve of the usual 1:4 pro-

and a curve

of

B/B^x

ratio, are laid

in Fig. 77. S, together with the fore-and-aft

Hull Characteristics and Other Features of Proposed Round-Bottom Tender for ABC Ship

The principal dimensions,

characteristics,

and other data Hsted here are

for the craft

whose

lines are

shown

Speed Data 14 kt at

T, r,

full load;

18 kt at light load;

= V/Vl = = V/Vl =

2.366 3.042

Hull Parameters

LCB = Cp

=

0.5S0LwL from the

251.4/(35)(10.6)

in Fig. 77. R.

Bwx = 9.3 ft Bu of transom = 7.3 ft y = 251.4 ft' in standard salt water Ax = 10.6 ft^ Aw of at-rest waterline = 250.9 ft^ Hu of transom = 0.87 ft at rest

= 37.07 ft LwL = 35.0 ft Bx = 9.04 ft W = 16,100 lb A = 7.188 long tons A/(0.010L)3 = 167.6 LoA

V = V =

little

but add weight and require exaggerated flare in the forward sections. The latter may, in turn,

=

FP Cx C„

0.678

35/9.30 = 3.763 Bfj = 0.785 B^x lE of entrance = 21 deg; ir of run, at transom corner,

L/B^x =

=

5.75 deg.

10.6/9.04(1.7)

250.9/35(9.04)

LMA =

0.47Z/

= 0.690 = 0.793

— HYDRODYNAMICS

858 Holf the - B

Beom B^x

^^

Drown

to a Scoie of One-Quorter the

Unqth

Lu/i_

IN SHIP DESIGN extreme draft

is

Sec. 77 J3

often determined

by the

size

'

and

the

of

position

vertical

propeller(s)

and

rudder (s). The bottom of the skeg or rudder shoe may be the lowest projection but if so it is lower

than the bottom

of the propeller tip

circle

to

give protection to the latter.

When

the draft

ditions, or Fig. 77.S Duiensionless Watebline-Offset and Section-Akea Cukves for Round-Bottom Tender OP ABC Ship

positions

of

maximum

the

ordinates

of

each.

This completes the preUminary hydrodynamic design of the ABC round-bottom tender, as

worked out in this chapter. 77.33 Example of a Modem Round-Bottom Utility-Boat Design. An example of a roundbottom design for a motorboat somewhat larger than that of the ABC tender is the 50-ft open utihty boat designed recently (1954) by C. E. Werback. Fig. 77. T is a body plan of this craft and Table 77. j lists its characteristics for the light- and full-load conditions.

TABLE 50-FT

Dimensions and Other Data for the 77. Round-Bottom Utility Boat of Fig. 77.T j

Light displacement, 24,500 lb Speed, 13.5 kt

=

Full-load displacement, 48,000 lb

10.937

=

t

21.784

t

Speed, 10.5 kt

LoA

Be

=

50.02 ft

(over guards)

=

14.48 ft

Lk^l = Bwx =

48.0 ft

12.02 ft

DWL

= 6.2 ft Freeboard at FP above Freeboard amidships = 4.1 ft Freeboard at AP = 4.02 ft Draft to bottom of skeg = 3.92 ft Radius at full power =145 miles Brake power, one 165-horse diesel engine Fuel, 170 gallons _ At 13.5 kt, T, = V/\/L_= 1.950 = = 1.517 At 10.5 kt, T, A/(0.010L)' at full load = 21.78/0.1106 = 197.2 Ratio of (Ih/Ps) at full load = 48,800/165 = 296.0 lb

V/^L

is

it is

limited

may

more tunnels

be recessed upward

just as they are in larger

tunnel-stern shallow-draft vessels. Usually, however,

there

insufficient

is

down

tunnel roof

length

to

drop the

to the plane of the designed

waterline abaft the wheel, so the after end of the

upper portion of the tunnel is exposed. In certain speed-length ranges, particularly just below hump speed, the change of trim and squat for most motorboat forms is large. Shallow water exaggerates this situation because of the increased steepness of the waves, generated either by the boat's own motion or by natural winds. It must not be expected, therefore, that a boat which has a draft of x ft when at rest may be able to run, under a variety of conditions, in water of x ft depth without scraping along or striking on the bottom. When working up the characteristics of a shallow-draft motorboat the designer may, with what appears to be a reasonable first weight estimate, convert this weight to volume of the liquid in which the craft is to run. Then on the basis of a tentative waterline area and shape, he may determine the mean draft necessary to give the displaced volume, assuming first that this draft is constant under the entire waterline area. As a first approximation, the maximum draft of the hull proper may be taken as equal to 3 times the mean draft. Additional draft needed to provide dynamic stability of route, or mechanical 48.0

ft

Beom, maximum on waterline, 12.02 Displacement Full Lood, 48,

This craft has buttock lines that are very nearly straight in the region from Sta. 8 to Sta. 12, or for the aftermost third of the length. The

by operating con-

desired to give the propellers

protection, they

into one or

Lenqth on Waterline,

per horse.

minimum

some

when

ft

WL5

rise-of-floor angle at Sta. 4, one-third

from the bow, exceeds 8 deg. The transom beam to maximum waterline rather large for a round-bottom boat but

of the length

ratio of

beam

is

in this case

it

provides additional room within

Wcterlme Buttock

Spocmq

Spacing l_

15

1.0

the hull. 77.34 Draft.

Designed Speed ot

Design for a Motorboat of Limited For a motorboat of normal design, the

Fig. 77.T

15

..

Full

Lood, 10.5 kt

YV/Vl

ft for all

at 'this 'speed. 1.517

Body Plan op 50-Foot Utility Boat

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.36

protection to the propener(s) and ruddcr(is),

added to the

is

liuU draft.

(1)

The speed

of

859

advance Va

is

0.95 (21) kt. In

the units required for the chart. Fig. 77. U, this

This estimate, plus a preliminary layout of the

is

0.95(24) (1.15)

=

24.84 mph.

and rudder(s), and an estimate of the sinkage at the stern, indicates roughly whether

delivered directly to

the limiting-draft conditions can be met.

per shaft, from the calculation at the end of

propeller(s)

Because

of the small

immersion

of its surface

and the small trim by the stern at runs, a sea-sled type of motorboat may

(2)

The

shaft power, considered here as the

Sec. 77.26.

On

tiie propeller, is

power

207 horses

the basis that the engine

is

rated

propellers

for sea-level

which it be admirably suited to operation in waters of limited depth. A 75-ft cruising yacht of the seasled type, in which the extreme draft is of the

of (b) preceding is 1.00, for a boat to be operated always at sea level. Strictly speaking, since the 24 kt is a maxunum trial speed and not a sustained speed, the sustained-load factor should also be 1.00. However, it seems wise, as in the case of the ABC ship described in Chap. 69, to limit the power at designed speed to about 0.96

order of only 3.5

Apr

[Yachting, 77.35 teristics.

ft, is

illustrated in the literature

1950, p. 62].

Estimate

For the

of

Screw-Propeller Charac-

selection of preliminary screw-

propeller characteristics for a motorboat, use

is

here of a nomogram developed by W. E. Fermann, issued by the Marine Division of the Federal-Mogul Corporation, and used since 1943 by the Bureau of Ships of the U. S. Navy Department. The diagram is reproduced as Fig. 77. U. On the facing page there are instructions for its use, supplemented by an example worked out

made

ABC

for the 24-kt planing type of

Use

tender.

Fermann nomogram

of this

requires that

three of the principal quantities be known: (a)

The speed

advance Va

of

of the propeller,

expressed as miles per hour, where

mph. The value

Va

1

kt

=

is

Tomalin gives a

types. P. G.

special

for determining the factor (1

—

w)

nomogram

[SNAME,

1953, p. 602]. (b)

The

power Ps delivered

shaft

at each pro-

may

be taken as 0.95 times the rated brake power P^ of the engine connected to that peller.

This

propeller.

Fermann

The

accompanying the

instructions

to the brake

power times the

mission

the

modifier

times

propeller

a

is

equal

efficiency of trans-

times

sustained-load

barometric

a

factor.

The

product of the last three factors is given as an average of 0.90 for gasoline engines and 0.85 for diesel engines. (c)

The

rate

of

for transmission losses

and taking the nearest round figure, the shaft power delivered at each propeller is assumed to be 210 horses. (3)

The

engines are designed to run at 2,500

rpm

at rated full power.

Only when

special

performance

justifies

the

custom-made motorboat propeller, conforming to a design drawn up in accordance with big-ship methods such as described in Chap. 70. Normally, a propeller is selected from stock, having the desired number of blades, diameter, pitch, and mean-width ratio. cost is

it

77.36 tion.

possible to install a

Propeller Tip Clearances; Hull Vibra-

For a

craft of the displacement type the

no more than the nominal turbulent boundary-layer thickness 5 (delta), determined for an a;-distance equal to that from the stem to the propeller position and for a speed V equal to the highest boat speed expected. Using the ABC round-bottom tender propeller-tip clearance need be

as an example, the .r-distance to the propeller

about 33

ft.

At a speed

per sec in standard salt

is

say 14 kt or 23.65 ft water, R^ from Table 45.b of

about 60 (10*^). Assuming that the flow is fully turbulent and interpolating between the graphs of Fig. 45. C, the value of 5 at the propeller is is

chart state that the shaft power

to

maximum. Allowing

of the order of 3 per cent

1.15

reckoned as 0.90 the speed V of the boat for a single-screw craft with a fine run and 0.95 times that speed for twin-screw craft, whether of the planing or round-bottom of

of the

operation the barometric modifier

rotation in

propeller turns. This

is

rpm

at

which the

equal to the engine

rpm

for direct drive.

Taking the twin-screw 24-kt planing type tender as an example:

ABC

about 0.3 ft. The data plotted there are for fresh water but the values would not change materially for salt water.

For a planing craft, the R^ length is somewhat shortened because of the diminished wetted length along the keel. For the ABC planing tender, running at 24 kt or 40.53 ft per sec, the mean wetted length is just under 22 ft, giving an R^ of about 66 (lO**) in salt water and a 5 at the propeller position (from Fig. 45. C) of the order of

r

HVDRODVN.\i\riC,S IN SHIP DESIGN

860

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PRELIMINARY DESIGN OF A MOTORROAT

Sec. n.3C,

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HYDRODYNAMICS

862

Here the .r-distance involved is slightly than the mean wetted length, because the propeller is to be forward of the transom. Without any more than instinctive or intuitive knowledge of viscous flow, boundary layers, or wake velocities, N. G. Herreshoff buUt many 0.2

ft.

less

and

successful high-speed launches, yachts,

tor-

IN SHIP DESIGN

boat, with the center of its "sail" area in the

proper fore-and-aft position, is usually more important than on a large vessel. Chap. 54 contains sufficient information for an estimate of the still-air drag of the hull and deck erections of a small craft. Sec. 77.26 contains a

computation

pedoboats in the half-century between 1870 and 1920 Mith extremely small tip clearances [Herre-

ABC

"N. G. Herreshoff and Some of the Yachts He Designed," The Rudder, Mar 1950, pp. 33-35; Sep 1950, pp. 26-27, 56-58]. He was fully as conscious as are modern marine architects of the advantages of smooth running and the need for holding vibration to a minimum. There is some question, therefore, as to whether radial or hull tip clearance is an important feature

dages.

shoff, L. Francis,

in a small craft [Tomalin, P. G.,

SNAME,

1953,

The

structural scale effect, which causes a small

more

than a geometrically similar large one oj material,

may

the

rigid

same

vibration than on a large vessel. Nevertheless,

seems wise on any small

it

craft, regardless of size,

not to reduce the tip clearance below 0.083 ft (1 mch) or, at the most, 0.0625 ft (f inch) [Lakeland Yachting,

On

all

May

and on most utihty craft as well, comfortable riding and freedom from vibration acquire an importance comparable to that on large vessels. P. G. Tomalin has discussed this matter at some length

[SNAME,

1953, pp. 610-613] so that

considered necessary only to reference 77.37

Still-Air

mentioned

it

it is

here.

Drag and Wind Resistance.

item (6) of Sec. 77.2 that in an ultra-high-speed motorboat the still-air resistance may approach the hydrodynamic resistance in magnitude. In any type of motorboat, with It is

by

in

far the greater part of its total

the water surface, neither the

volume above

still-air

drag Dsa

The

small craft are: (1)

Deep

(2)

Vertical stabihzing fin on an ultra-high-speed

craft, to

keel or skeg, or a combination of the

act.

Many

(3)

Propeller shaft(s), usually exposed

(4)

Shaft struts for supporting propeller bearings.

These

may On

be either forward of or abaft the proultra-high-speed

Aires, 1951, Fig. 104, p. 130]. (5)

Steering rudder(s)

(6)

Inlet scoops for cooling water to the propelhng

machinery; see Fig. 34 on page 42 of the Baader reference just cited.

The deep fins

keels or skegs act partly as stabilizing

to give the

prevent

skidding

craft

and

stability

of the

upper works on a motor-

of

sideslipping,

route,

they

and

they [Fig. 265

probably add some roll-quenching effect on p. 328 of the Baader reference listed in preceding].

Practically,

they

serve

as

(4)

partial

housings for centerline propeller shafts and as a

when grounding. There appear to be few design notes or rules in the literature other than those given by D. PhillipsBirt ["Motor Yacht and Boat Design," 1953, protection for the hull

dynamic difficulty. tered on such an appendage

Proper design

the propeller

is

it can still become important maneuvering. When the drag in a beam wind creates a swinging moment that, for example, always causes the craft to fall off and swing downmnd, the crew may have difficulty holding it in a hove-to position, head to both wind and

sea.

craft

sometimes carried by a swivel fitting on the rudder [Baader, J., "Cruceros y Lanchas Veloces (Cruisers and Fast Launches)," Buenos bearing

pp. 65-66].

for

types of these are

shown by J. Baader on pages 115, 119, 322-325, and 341 of the reference listed under (4).

nor the wind resistance i?wind is ever a negligible or an inconsiderable part of the total resistance. If it is not a major factor in resistance and powering at cruising speeds

two

provide a sort of fulcrum about which the

moment can

rudder

1952, p. 20].

small boats buUt for pleasure purposes,

drag for the planing-type of

Design of Control Surfaces and Appenprincipal control surfaces and appendages on a motorboat or other self-propelled

peller.

render the hull less susceptible to

of this

tender.

77.38

p. 611].

structure of a given material to be

Sec. 77.37

Exposed propeller shafts of shallow draft are

in a high-speed craft a constant source of hydroThe drag normally encoun-

aggravated by the it, where the ambient pressure is too small to develop a pressure gradient which will cause the water to close in abaft the shaft. Further, the ditch, hole, or separation zone extends aft into and through the ditch or hole in the water

propeller disc.

The only

is

made by

design solution here,

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.39

short of eliminating the shaft altogether or raising it

out of the water at speed,

to

is

make

it

as small

as possible in diameter.

the

Because the shaft struts of motorboats are usually short, and because they gain in relative rigidity with decrease in size, due to the structural scale effect,

it is

863

Prepared by the Chris-Craft Corporation for the Bureau of Ships of the U. S. Navy Department,

frequently possible to

make them

entries for the light-load condition alone occupied 56 tabulated sheets. Of the large weight groups, the machinery is

usually the heaviest. itself

may

Indeed,

the

weight

fuel

be appreciable. Only rarely

is

a motor-

of the single-arm type [Phillips-Birt, D.,

"Motor Yacht and Boat Design," 1953, p. 124; Baader, J., "Cruceros y Lanehas Veloces (Cruisers and Fast Launches)," Buenos Aires, 1951, Fig. 47, p. 60]. Design notes for motorboat rudders are dis-

boat designed unless there is a propelling plant ready to put into it. The engine and its attached components usually have been built, tested, and weighed, so that the designer knows just what figure to set

cussed in Sec. 74.11. Additional notes are given

machinery manufacturer. The

by D.

and 68

Phillips-Birt on pages 67

of the

reference just cited.

Third Weight Estimate. Having seton the general arrangement and equipment and the principal details of hull, machinery, and appendages of a motorboat design, it is now 77.39

tled

make

possible to

a more reliable estimate of the

weights, using smaller parts

and groups than

those listed in Sees. 77.13 and 77.29. Moreover,

when

this stage of the preliminary

design

is

hydrodynamic

reached, detailed arrangement layouts

and sketches of the framing and structure will have been started. These will include rough drawings of the revised internal arrangements, drawn to a scale considerably larger than those of Figs. 77.B and 77. Q, as well as framing layouts

showing the tentative scantlings,

and

characteristics of

and some

of the hull It

now time

is

many

The sUngs

77.29.

tenders,

that of the hull structure, including fastenings

but excluding hull fittings. As the largest unknown item it deserves the most attention in the weight estimates. Lacking reliable information concerning previous construction or faced with a novel design for which weight data probably do not

both below and above water, then multiply this area by an average weight of hull planking or plating, framing,

for

deck,

for

hoisting

Indeed, the hulls themselves

them

in

and out

example,

the

ABC

may

require

of the parent ship.

third weight estimate involves a more-or-

less detailed listing of all

the principal parts in

each group, and a calculation of the weight of each. Instead of the 8 items of Sees. 77.13 and 77.29, there should be more nearly 80. Even 180 items are not too

example,

Navy

many

at this stage.

the weight

As an

calculations

for

excellent

a U.

52-ft rescue boat, with direct drive,

of appreciable area,

(c)

flats,

and

for internal bulk-

and platforms

Calculate the weight of the deckhouses and

deck erections (d) Estimate the weight of what might be termed hull trim, such as guard rails, fenders, rubbing rails,

spray

strips, chafing pieces, doublers,

and

foundations for main and auxihary machinery.

By a somewhat different procedure, the designer

and 31 groups

may: (e) Rough out the structure by drawing the usual midship section, \vith its scantlings, supplemented

by several other

typical sections, sho-wing the

structure at those points in (f)

Calculate the weight of

typical section basis of length.

some all

detail

the parts in each

and draw a weight curve on a area under this curve repre-

The

sents the hull weight.

S.

em-

bodied 24 separate weight groups for the light-load condition, 30 groups for the hoisting-load conditions,

if

heads,

strengthening to take the constant wear and tear

The

and reinforcing

Follow the same procedure for the weather

(b)

carried partly rigged in the boats,

if

of hoisting

Calculate the area of the hull boundaries,

(a)

involve weights not normally included under hull fittings.

the designer can:

exist,

of the principal parts

determine,

by the

fuel has a weight

is known within close limits, so that when the fuel capacity is fixed, the designer can set down a second fixed figure for the fuel weight. The largest single remaining weight group is

sizes, positions,

whether the hull proper of the round-bottom ABC tender is hable to weigh more than the 34 per cent of the total weight allowed for it in Sec.

for the units furnished

density that

of the details.

to

down

for the full-load condition.

Certain features are of great importance in the weight estimate; first, that they be included and second, that the estimated weights assigned final

to

them be adequate. To enumerate and

explain:

HYDRODYNAMICS

8f)l

the hull

If

(1)

wood,

built of

is

it

inevitably

absorbs a certain amount of moisture as soon as launched, no matter

it is

by paints and soakage.

how

well

it is

similar coatings. This

protected is

called

The moisture can be absorbed above the

waterline from rain and spray, as well as below

that

line,

from

routine

immersion.

It

adds

directly to the weight of the boat as built.

Woods

same kind and grade vary if of the same moisture content. A boat is more likely to be buUt of heavy pieces than light ones, unless a (2)

of the

rather widely in weight, even

made. Wooden boats conby the same builder, have been known to vary plus and minus 10 per cent in weight in the course of a building program extending over a year or more. (3) For a design that is different from one for which adequate weight data are available, or for one that is novel, no naval architect can estimate accurately, in advance, the weight of the various parts, nor can he list all the parts that the builder (or he) will put into the boat by the time deliberate selection

structed

it is

to

is

the same drawings,

finished

operator, crew,

templated or allowed for in the design. When the performance of the boat suffers as a result, the designer is usually the one who has to take the initial blame. (5) New technologic developments bring into being certain items of equipment, such as radar, which may not have been in existence or even thought of when the design was completed. It is for this reason that numerous combatant vessels have been designed with margins to take care of increases in weight throughout most of the life of the vessel.

small-boat designers and builders have an utterly attitude

the amount wooden hull can and and exposed to the

concerning

(weight) of moisture which a

does absorb

by C. C. Walcutt [Yachting,

1955, pp. 64-65, 108-110].

The number

of motorboat designs of the past which the total weights have been underestimated is no less than appaUing. The finished weight has been known to exceed the weight estimate by 10 per cent or more, and the speed to be 10 per cent below the predicted value, solely for

because of overweight. Despite the time, labor, and expense involved, correct motorboat design

procedure

calls for

estimate. This

is

the making of a detailed weight possible as soon as the design

arrangements and hull structure is and equipment is made, and decisions have been rendered as to just what gear the boat is to carry. of the hull

essentially complete, the list of fittings

77.40 Self-Propelled Tests for Models with Djmamic Lift. An exception to the procedure set down in Sec. 1.5 of the Introduction to Volume I is justified

here to emphasise the necessity for

the self-propulsion of models of craft in which the forces or

moments generated by the propulsion

devices are likely to be large compared to those

when

afloat

elements. It has long been recognized that even

The

lift.

various velocity and pressure fields and forces set

up by the propulsion devices are of such magnitude in proportion to the other forces acting that

they can not be neglected in an endeavor to determine the resistance and running attitude of the full-

For high-speed vessels this running most important because the slope large in proportion to the hydrodynamic

scale craft.

attitude

drag

is

is

drag.

A

example of the intowed model test alone is that

never-to-be-forgotten

adequacy

of the

of the sea sled described in Sec. 30.13. Indeed,

the

lift

force produced

by the

surface propellers

at the stern of a craft of this type

The element of soakage in a wooden hull needs much more emphasis than has been given to it in the past. It is perhaps safe to say that many unrealistic

May

Sec. 77.40

generated by buoyancy or dynamic

The owner,

and others are certain to add weights which were never con(4)

IN SHIP DESIGN are vividly presented

may

be so

necessary to reduce the trim and the overall resistance that unless the propellers are running

enough to produce this force the craft may become nearly inoperable. It may, in effect, have only two speeds, full speed or stop, with an infast

abiUty to run satisfactorily or efficiently

when

slowed down. It

was

for

many

decades the practice, when

the best of paint and enamel coverings will not

stepping up the observed resistance of models of

prevent this absorption. It is perhaps not so weU that a plastic coating on one surface only will not prevent absorption through the other.

full-planing craft, to ignore the friction resistance

known

The astounding weight

reductions recorded by drying and weighing a small sailboat hull, where the weight ranged from 375 lb wet to 275 lb dry,

The total observed resistance was multipUed by the cube of the scale ratio, with the usual allowance for water density, to predict the resistance of the prototype. This was on the basis that the wetted surface diminished appreciably entirely.

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.41

when planing, and

possibly also on the assumption

that the surfaces of any type of planing craft

would always be smooth. It is now found far preferable, and far more accurate, to expand the observed data to full scale in the same manner as for a large, displacement-type vessel [Peters, S. A.,

SNAME,

1950, p. 682].

"Furthermore, there

is need for the development of equipment and techniques for self-propelling models of planing craft, if guesswork is to be eliminated from estimating engine power requirements, and maneuvering

characteristics" [Curry, J. F.,

77.41

Bibliography

Partial

Sec. 53.8 gives a partial surfaces,

SNAME,

dynamic

list of

lift,

1950, p. 688].

on

Motorboats.

references on planing

and planing

craft.

The

emphasis here is on the analytical and empirical aspects of predictmg performance rather than on the practical aspects of design. A few references from Sec. 53.8 are repeated here, but for the most part the items listed in the present section contain design notes and information of direct practical use. Furthermore, the references apply to displacement craft and to round-bottom motorboats of the semi-planing type, as well as to full-planing boats of

(7)

Speed Motor Boats," INA, 1927, Vol. LXIX, pp. 121-143 and Pis. X and XI (8) Richardson, H. C, "Aircraft Float Design," Ronald Press, New York, 1928 (9) McKenzie, Ian L., "The Powering of High-Speed Motor Yachts," SBSR, 16 May 1935, pp. 554-557 (10) Nicolson, D., "High-Speed Motor Craft," NECI, 1937-1938, Vol. LIV, pp. 98-118 and Pis. I and II; also pp. D25-D32; abstracted in SBSR, 13 Jan 1938, pp. 39-40. This paper is devoted to a description of the design and construction of ultra-highspeed motorboats having lengths of from 22 to 75 ft and Taylor quotients 7', of from 6.97 to 3.94. The single graph of power-weight ratio on a base of speed in kt begins at 35 horses per pound and 35 kt and extends up to over 150 kt. (11) Hadeler, W., "Motortorpedoboote-Schnellboote (Motor Torpedoboats-High-Speed Boats)," Zeit. d. Ver. Deutsch. Ing., 12 Aug 1939, pp. ^17-924. An English version of this paper is given in Transl. 88, Jan 1940. (12) Miller, R. T., Johnson, V. D., and Towne, S. R., "The Design of a High-Speed Torpedo Boat," Thesis, Webb Inst. Nav. Arch., New York, Apr 1940

TMB

N. L., "Elements of Yacht Design," New York, 1944. While much of this book is devoted to the design of sailing yachts, there is a considerable amount of information relating directly to the

(13) Skene,

design of motorboats and small powered craft. on Resistance, This is especially true of Chap.

many

XV

kinds. (1)

SNAME,

PL 94 of this paper gives speed-rpm, speed-sUp, speed-power, and other curves of the launch Vingt-et-Un II, designed by Crane. See also Yachting, Jan 1952,

pp. 224-240.

1904, Vol. 12, pp. 321-325.

(14) Lord, L.,

Crane, C. H., "Problems in Connection with High-

Speed Launches," Pis. 190-197.

of Planing Hulls," York, 1946 (16) Guins, G. A., "The Design of Pleasure Planing Craft (15) Lord,

The

first

1905, pp. 365-373 and three of these plates give

and fast launches of that time. Durand, W. F., "Motor Boats;

A

Thoroughly

and Operation," International Marine Engineering, London and New York, 1907, L. C. No. VM 341. D9 Luders, A. E., Sr., "Model Experiments and Speed Trials of 60-ft Motor Cruiser Kalhmar II," SNAME, 1913, Vol. 21, pp. 177-180 and Pis.

rise-of-floor angle for satisfactory longitudinal sta-

(17) Baier, L. A.,

May

"Model Experiments on Express High Speed-Length Ratio Deadrise Tj^pe Proves Superior to Round BUge Model Resistance of Appendages Investi-

Gamon, T.

work

A.,

(18) Thiel, P., Jr., Johnson,

—

United States.

AM, New York,

"The

and Wake of Nine Double-Chine SimpHfied Hull Forms," Thesis, Dept. Nav. Arch, and Mar. Eng'g., Univ. Mich., Ann Arbor, May Resistance

gated," Inter. Mar. Eng'g., Aug 1918, pp. 473-476 Smith, R. Munro, "The Design and Construction of Small Craft," pubKshed by The Technical Section, Association of Engineer and Shipbuilding Draughts-

men, 96, St. George's Square, Westminster, London, 1924. A considerable number of reproductions of this book have been distributed in the

"Power-Length-Speed,"

1948, pp. 34-35. Covers relatively slow-speed craft of lengths from 40 to 100 ft, speeds of

9 to 12 kt, weight displacement 50 to 300 t. R. W., and Ward, L. W.,

Cruisers of Deadrise Type; For

(6)

New

bifity is 7 deg.

110-112 (5)

"Naval Architecture

boat sizes is not given. Best rise-of-floor angle "for spray deflection and soft riding" found to be 38.5 deg at FP and 21 deg at 0.3L from FP. Minimum

Scientific Discussion of their Design, Construction,

(4)

L.,

from Model Studies," SNAME, Pac. Northwest Sect., 13 Sep 1947; abstracted in SNAME Member's Bull., Jan 1948, p. 18. Author found by tests on small models that the best value of the ratio [(average waterhne length) /(average waterline beam)[ is 2.63 for work in rough water. Range of

SNAME,

midsection shapes, outboard profiles, waterlines, and deck plans of a number of small torpedoboats (3)

"Elementary Considerations of Planing Hull SNAME, Phila. Sect., 18 Oct 1946

Design,"

Cornell Maritime Press,

p. 62. (2)

pp. 181-209, Chap. XVI on The Hydroplane, pp. 210-223, and Chap. XVII on Screw Propellers,

"High Speed Gasoline Launches,"

Crane, C. H.,

SOf)

Nicolson, D., "Design and Construction of High-

(19)

1948. The models forming the subject of this thesis have certain characteristics of motorboats. Peters, S. A., "Development of the Motor Torpedo Boat," SNAME, Ches. Sect., 3 Nov 1948. Abstracted in SNAME Member's Bull., Jan 1949, p. 21.

HYDRODYNAMICS

866 (20) "Tests

of

Twenty Related

IModels

of

IN SHIP DESIGN

V-Bottom

TMB

EMB

Motor Boats, Series 50," Rep. R-47, Revised Edition, Mar 1949. This report was originally number 170 in the ETT series, issued on 28 Oct 1941, under the authorship of K. S. M. David-

(30) Latimer,

Coast Guard 13 Oct SNAME Member's Bull., Jan 1952, p. 18. This paper describes and gives drawings and photographs of a rather wide variety of sizes and types of motorboats, from 18 to 52 ft in length. Most of the paper is devoted to a description

by modern standards. There are

many

low, because of laminar flow on

(21)

(22)

of the models.

of the

are plotted as contours of total model

resistance per lb of displacement,

or

Rt/W,

as

contours of running trim angle in deg of model wetted surface, and of other factors. Locke, F. W. S., Jr., "An Empirical Study of Low Aspect Ratio Lifting Surfaces with Particular Regard to Planing Craft," Jour. Aero. Sci., Mar 1949, Vol. 16, No. 3, pp. 184-188 Ashton, R., "Effect of Spray Strips on Various PowerBoat Designs," ETT, Stevens, Tech. Memo. 99, Feb 1949. This report is generously illustrated with excellent photographs of both models and full-scale motorboats, showing the spray formations very clearly. The appendix contains useful design comments, with sketches a rather unusual feature for a report of this kind. Korvin-Kroukovsky, B. V., Savitsky, D., and Lehman, W. F., "Wetted Area and Center of Pressure of Planing Surfaces," ETT, Stevens, Rep. 360, Aug" 1949. This is the Sherman M. Fairchild Publication Fund Paper 229, issued b)^ the Inst. Aero. Sci., New York, N. Y. Du Cane, P., "High-Speed Small Craft," Cornell Maritime Press, 1950. This book embodies, in 21

(24)

comment and design data on machinery, equipment, operation, and trials, in the size range up to 130 ft in length and in the speed range above 15 kt. chapters, informative

(31)

"N. G. Herreshoff and Some

He Designed," The Rudder. This comprises a series of articles, subdivided into about 12 chapters, which ran more or less regularly through the years 1949 and 1950. (26) Spooner, C. W., Jr., "Speed and Power of Motorof the Boats

Boats up to a Speed-Length Ratio of Three," unpubl. manuscript dated Oct 1950; available in the (27)

TMB library

Murray, A. Hulls,"

B.,

"The Hydrodynamics

of

Planing

SNAME,

1950, pp. 658-692. This is a most informative and useful paper for the practical naval architect. There is a bibliography of 19 items on

embodying three

40-ft utility boat,

Nordstrom, H. F., "Some Tests with Models of Small Vessels," SSPA Rep. 19, 1951 (in English). Data are given, with body plans and graphs, embodying test results on 27 different models of round-bottom and V-bottom boats (with chines).

values of propulsive coefficient. (32)

Simpson,

D.

S.,

"Small Craft,

SNAME,

Design,"

Construction and

1951, pp. 554-582. This paper

devoted mostly to the larger craft in the smallgroup, although many of the excellent comments in it apply to the motorboat group as well. is

vessel

design

(33) Savitsky, D.,

"Wetted Length and Center

of Pres-

sure of Vee-Step Planing Surfaces," Inst. Aero. Sci., Sep 1951, S. M. F. Fund Paper No. FF-6. This report also carries ETT, Stevens, number 378. It lists 24 references on pp. 25-27.

"Some Notes on Steering of High-Speed Planing Hulls," SNAME, Pac. Northwest Sect., 27 Sep 1952; abstracted in Member's Bull, Jan 1953, p. 35

(34) Grenfell, T.,

SNAME

(35) Phillips-Birt, D.,

W. and

J.

"Motor Yacht and Boat Design," Co., Ltd., Chatham,

MacKay and

England, 1953. A splendid addition to the scant on the problems and compromises of power boat design. There are chapters on size, speed, behavior, accommodation, appearance, stability, construction, hull form, powering, propellers, planing boats, and examples in design. American distributor, J. de Graff, Inc., 64 W. 23rd St., New York 10, N. Y. (36) Phillips-Birt, D., "The Design of Small Power Craft; Design Problems to be Solved by the Naval Architect," The Motor Boat and Yachting, London, Apr 1953, pp. 158-162. This excellent article, like all the papers and books of this author, gives an incredible amount of general information in a small space. This reference covers, in addition to literature

general comments, the following:

"The Analysis

Planing Hulls," SNAME, dies. Sect., 3 May 1951 (29) Baader, J., "Cruceros y Lanohas Velooes; Su Dinamica. Propulsion y Navegacion (Cruisers and Fast Launches; Their Hydrodynamics, Propulsion, and Operation)," Buenos Aires, 1951 (in Spanish). This appears to be by far the most comprehensive book of Stepless

on the subject of motorboats and sailing craft, of small to moderate size, that has ever been pubIt includes a considerable amount of information on naval architecture in general and some data on hydrodynamics in particular. It is lished.

USCG

pages 15 and 16 the report gives data as to the resistance of appendages and the probable

p. 680.

(28) Clement, E. P.,

of

Ches. Sect.,

On

hulls,

(25) Herreshoff, L. Francis,

SNAME,

vai'iations.

—

(23)

"Characteristics

P.,

1951. Abstracted in

indications that the observed resistances are too

The data

J.

Powered Boats,"

son and A. Suarez. Unfortunatelj', the parent form chosen for this series has a chine that is considered too low forward,

Sec. 77.41

generously illustrated, with drawings and graphs that are nothing less than superb.

Design requirements Speed and power

Power and

hull proportions

Hull form Principles of engine installation Seaworthiness and stability.

Tomalin, P. G., "Marine Engineering as Applied to Small Vessels," SNAME, 1953, pp. 590-634. This paper gives a number of nomograms and other data useful for the designer of small craft. (38) "Boats Today," Universal Motor Company, con(37)

PRELIMINARY DESIGN OF A MOTORBOAT

Sec. 77.41

and descriptions of 101 interesting boats created by 53 American and Canadian naval architects, Oshkosh, Wis., 1953 taining detailed designs

(39) Sliaw, P. S., National Researcli Council of

112.0

Whaler,"

MB-172, "Results Landing

Nov

Craft,

"The Design

(40) Phillips-Birt, D.,

Boats;

A

"Unusually of a 27-ft

May

of

27-ft

small craft have natural rolling

stiff

beam

seconds. In

Sea-Going Planing

seas these will also be the

of

encounter will be greater,

amounts depending on the

ship's

"While the period

of encounter

is

longer than

the boat's natural rolling periods, small craft tend to roll in the period of the waves.

an amazinglj' small space. The

often than large vessels,

in

They

are,

by the

prevailing sea rather than their hull form."

bilge or chine?

Displacement and shape

(50)

of section

Beam The planing

angle

Calculating the power required

Stepped

ETT

Stevens Tech.

Memo.

These

8.54-ft

percentages for 12 groups in the total weight of an

covering

PT

a

boat,

74.81-ft

TMB

Press, 1955

covering

26-kt,

by

model

a 30.18-ft by

twin-screw

pleasure

is

"Fundamental Design of Stepless Planing Motor Boating, New York, Feb-Jun 1956. a comprehensive paper which appeared

after the writing of the present chapter

had been

On page

54 of the June 1956 issue there is given an outline of the design procedure for stepless planing craft, in 26 operations. Reprints of the five parts of this paper may be obtained completed.

Boats," Inter. Shipbldg. Prog., 1955, Vol. 2, No. 6, pp. 61-80. There are 9 references on page 77 of this paper.

"Small Craft-Stabihty and SeaJul 1955, p. 110. Says that

147,

1.34^ft,

Temple

This

"average cruiser." (47) Clement, E. P., "Hull Form of Stepless Planing Boats," SNAME, Ches. Sect., 12 Jan 1955 (48) De Groot, D., "Resistance and Propulsion of Motor-

SBSR, 28

116,

model 917 " 'The Motor Boat and Yachting' Manual," London,

Hulls,"

hulls, as well as

sheet

by

ETT

(54) Stoltz, J.,

D.,

sheet

3.17-ft, 40-kt,

cruiser,

percentages for 10 weight groups in the hull only

kindliness,"

by

SNAME RD

(53)

(49) Phillips-Birt,

lb.

3592-1 i'52)

E., "Weight and the Motor Boat," Yachting, Jan 1955, pp. 118-120. The author gives typical

V-bottom and round-bottom

10,500

is

WL SNAME RD 13.22-ft

Bobbs-Merrill, Indianapolis, 1954

of

by twin screws and twin

DWL

(51)

Monk,

10.21 ft

These craft are of the V-bottom type, with hard chines and slightly hollow floor sections. The chine at about 0.30L from the line crosses the forward termination.

(44) Corlett, E. C. B.,

(46)

=

craft are driven

reverse gear

profiles considered

"Trends in Very High-Speed Craft, Part 1," The Motor Boat and Yachting, Sep 1954, pp. 386-388; Part 2, Oct 1954, pp. 446-447 Mason, J., "The Complete Book of Small Boats,"

19.0 ft

19.833 ft

engines of 2,500 horses (shaft power) each. The weight of each engine (presumably dry) and its

71,

in the design of these boats.

= =

H, extreme, = 6.083 ft L/B = 67/19 = 3.526.

M., "Modern Design and Construction Methods as Applied to 95-Ft Patrol Boats," SNAME, 1954, pp. 643-687. Figs. 2-5 on p. 644

body plans and bow

67.0 ft

D, molded, amidships

(43) Phannemiller, G.

(45)

71.375 ft

B, molded B, overall

dynamic and practical reasons for their various and characteristics. Jacobs, W. R., "Comparison of Hull Resistance for 'Standard Series' Ships, V-Bottom Motorboats and

give four

=

LwL =

Beach, D. D., "Power Boat Form," The Rudder, Jan 1954, pp. 38-43, 90. This is an excellent resume of seven typical modern powerboat forms, represented by lines drawings in each case, with the hydro-

Flying Boats," Apr 1954

"Design Features of Fast Patrol Boats," The Motor Ship, London, Aug 1955, pp. 208-209. The principal dimensions and characteristics are:

LoA

hulls.

features

(42)

more

the condition of

forced rolling, their motions governed

Planing

(41)

by

speed and

course.

following subjects are covered:

Round

1.75

usual. This

the period

Their Chai'acteristios," The Motor Boat and Yachting, Jan 1954, pp. 26-31. This article gives a large amount of technical information and some all in

= G.14,andGM =

periods of encounter, while in quartering seas

Discussion of the Different Types and

design rules,

L/fi

was very much better with

means that under a wide range of seagoing conditions, the wave period will exceed that of the boat. The period of a 100-ft wave is about 4j seconds; that of a 250-ft wave is 7

1954

RCN

ft,

periods as short as 3 J- seconds, and 5 to 6 seconds

of a 27-ft Preliminary Pro-

Dimensions," 25

peller

of a 27-ft

on a Model

MB-173, "Full Scale Trials on the Motor Seaboat," 4 Jun 1954

18.25

110.0 ft, B = 21 ft, L/B = 5.24; "very much lower weights and gi-eater GM." The following is copied from the reference:

is

with

B =

L =

Canada

1953

of Tests

ft,

Later D-class

ft.

Reports as follows:

MB-162, "Results of Tests on a Model Motor Cutter," 6 Nov 1953 MB-164, "Results of Tests on a Model

8f)7

L =

Fairmilo B-class rolled uiicoiiifortahly with

from Motor Boating, 572 Madison Ave., York 22, N.Y. (55)

Clement, E. Boat,"

"Analyzing the Stepless Planing Report 1093, Nov 1956.

P.,

TMB

New

CHAPTER

78

Model-Testing Program for a Large Ship Preliminary

78.1 78.2

Model-Test Data Desired for a Major-Ship Design Model-Test Notes for Preliminary ABC Designs Use of Stock Model Propellers for First Self-

78.3 78 4 .

Propulsion Tests

Displacement and Draft Conditions

78 5 78.6 78.7 78.8 .

....

Resistance Tests

Wave

Profiles and Lines of Flow Flow Observations with Tufts; Sinkage and

Trim; 78.9 78.10

Wake

Open- Water Propeller Tests

Preliminary.

78.11

868

78.12 78.13 78 14 78.15 78.16 78.17

869 870 871 872 873

Progress of the hydrody-

namic design, on paper,

is

suspended when:

Neutral Rudder Angle and Maneuvering Tests Controllability Tests in Shallow Water ... Wavegoing Model Tests Vibratory Forces Induced by the Propeller Reporting and Presenting Model-Test Data Te.st Results for Models of the ABC Ship

876 876 877 877 877 879

Comments on Model Data

879

.

.

.

.

.

Tests and Analysis of

Proposed Changes in Final Design of ABC Ship Comments on Illustrative Preliminary-Design Procedures of Part 4

78 18 .

874 875 876

Vectors

Self-PropeUed Tests

78.1

868

78 19 .

for the tests relating to

896

898

maneuvering and wave-

going.

Many

(a)

As many

much

as

features have been developed,

of the behavior has

and

been predicted, as

the state of the art permits, working from refer-

ence books and data only (b)

The

design has been narrowed to say two

alternatives, for

The

design

is

so novel that predictions of its

probable performance can not be

made on a

basis of existing data or experience.

This

is

is

which an evaluation on paper

indicates no preference (c)

marine architects are not famihar with of an up-to-date ship-model testing plant and do not reahze how much assistance can be rendered in confirming or modifying a ship design. A typical test schedule the

the stage at which to

capabilities

some detail. Model-Test Data Desired for a Major-

therefore described in 78.2

Ship Design. The specific model-test data listed here are intended to confirm, or other-wise, the corresponding data predicted in the course of the preliminary hydrodynamic design, worked up in

make towing and

model tests. Few ships, especially an untried design, can be built so quickly and cheaply that some time and expense devoted to model testmg is not worth while. Durmg World War II a model test worked into a total preliminary-design period of less than one week made it possible to eliminate one propeller, one shaft, and one propelhng plant from what had originally been a triple-screw layout. For a vessel of the si^e of the ABC ship, and for a design with its unusual features, a series of tests embracing

the preceding chapters of Part

4.

These cover,

briefly:

self-propelled of

everything within the capacity of the modern model basin estabhshment is considered well justified. It is both good naval architecture and good advance uisurance. Such a program, laid out in this chapter, was actually carried through for the ABC design at the David Taylor Model Basin before this volume was completed, except

(a)

Resistance of the hull,

ages (bare hull), and then

first

without append-

mth them

(b) Sinkage and trim of the hull; this may be measured on the hull either when it is bare or with appendages (c) Wave profile and flow pattern around the hull, first without appendages, to determine the traces of the roll-resisting keels and to check other features; later -with appendages and with the propeller (s) working

(d)

Wake

vectors or flow directions at positions

selected for the

arms

of struts to support propeller

bearings, as a guide to orienting or tmsting these

arms into the (e)

Wake

lines of flow

vectors at the propeller position (s),

with struts, bossings, or other appendages in place ahead of the propeller(s)

868

.

MODEL-TESIINC;

Sec. 78.3 (f)

all

PROGRAM FOR

Shaft power required to drive the hull with appendages, rate of rotation of the propeller(s),

and other self-propulsion factors, first with stock propellers (s), and then with propeller (s) designed especially for the hull

Open-water and

(g)

peller(s)

cavitation

data

on

pro-

designed specially for the hull

(h)

Determination of the proper neutral angles

for

multiple

rudders;

observation

dynamic

of

stabihty of route and maneuvering character-

a free-running model; controllability when backing istics, Avith

Wavegoing performance of the hull, when meeting waves from ahead and being overtaken by waves from astern Shallow-water and restricted-channel behavior (j ) (k) Nature and magnitude of the periodic vibration forces imposed on the hull by the propeller. (i)

displacement

It is not

always possible or advisable to conduct

these tests or to

make them

in the order given.

For example, the preliminary design resisting keels should not

keels be fitted to the

model

of

roll-

and in the sections

following.

is

10,

Transom-stern,

single-skeg; called transom

stern for short (2)

niinimiim

schedule.

As is customary at model-testing establishments, the models are to be built to the molded lines

shown on the drawings, with no allowances

for shell plating.

The appendages, only a part of which are shown on the drawings available at this stage, are expected to consist (a)

of:

Cutwater applied to the forward edge is

appendage and

is

not to be in place during the

bare-hull tests. (Actually

ABC

of the

considered in the nature of an

it

was

in place

on the

model bow)

(b) Roll-resisting keels, of shape, size, transverse

but a different afterbody. These are designated for convenience as: (1)

8f)9

ix; oiilled for. Tiic;

position,

such as might be embodied in a request for a complete set of model tests. There are two separate ABC hull forms to be tested. Each has the same forebody, forward of Sta.

not

1

until after lines-of-flow

on the bare hull indicate their proper positions. In the case of hull designs with offset skegs and tunnels it should be known from the flow tests that there is no cross flow under the skegs, eddying alongside them, or separation and eddying in the tunnel before shafts and struts are fitted and self-propulsion tests are made. Model-Test Notes for Preliminary ABC 78.3 Designs. Rather than to give the preliminary notes and to describe a detailed model-test schedule in general terms, apphcable to any case, the data prepared for model tests of the prehminary designs of the ABC ship are quoted

The wording

1

be completed nor the

observations

in full in this section

will

1'

SI

model weight for the partly loaded condition, approximately 1,650 lb for a 20-ft model, should be sufficient to care for the necessary midship bulkheads and connecting bolts; see the last paragraph of Sec. 78.5. The models may be made of wood or wax provided they will be suitable for the entire test

stem. This

all

A

Arch- or tunnel-stern, with double skegs;

called arch stern for short.

Two separate models may be made or one bow may be bolted to either of two sterns. So far as can be determined at present, model tests at displacements less than about 0.8 the designed

and fore-and-aft extent to be determined

only after lines of flow have been taken for both hull shapes. In

view

of the

contemplated width on the ship and

of the roll-resisting keels, 3.5 ft

0.1373

ft

on the model,

it is

desired that the keel

trace on the hull be determined

by

flags or

vanes

at a distance from the hull as well as by lines of flow on the hull. These traces should extend at least (c)

from

Sta. 6 to Sta. 14.

Rudder horn and

single rudder for the tran-

som-stern design. These latter are to have a contra-shape, designed to recover rotational

but they are to be omitted in their entirety from the bare-hull transom-stern model. Drawings showing these

losses in the propeller outflow jet,

appendages are to follow. for

the arch-stern model.

The double rudders and

the skegs on this model

(d)

Double rudders

are to be adapted for maneuvering tests to be conducted subsequently, involving movable blades

with stocks that can be turned from the deck. Only the unbalanced tails of these rudder blades, above the level of the lower edges of the skegs, are to be fitted to the bare hull; these may be in dummy form. The balanced foils below the lower edges of the skegs are to be added subsequently as appendages, or else the dummy upper portions are to be

rudders (e)

removed and the movable maneuvering

fitted.

Bottom anchor and

recess

—

— HYDRODYNAMICS

870

Cooling water intake scoop and discharge for to be reproduced.

(f)

main condenser are not

The ratios,

principal

dimensions,

and design parameters

form for the

coefficients,

ABC

ship,

at this stage of the design, are listed for the

information and convenience of the Model Basin Table 78. a. A set of drawings ultimately

staff in

furnished the

Model Basin, with

ing figure numbers,

A

few words

pomt

is

their correspond-

hsted in Table 78. b.

of explanation are inserted at this

for the benefit of the reader

who may have

noted shght numerical discrepancies here and there in the tabulated data and in the text. For example, the bare-hull volumes and displacements for

transom-stern

the

designs,

and

arch-stern

as listed in Table 78.a,

from those in Table

78. c.

ABC

differ

slightly

Any one who

has de-

signed a ship, or a house, or a machine, appreciates that the design

is

constantly developing, with

TABLE

78.a Principal Dimensions, Ratios, and Coefficients for the ABC Design These data apply to the design at the point where model

tests are requested.

SNAME RD

sheets.

hull,

molded, at the

first

furnished to the

Dimensions,

They are modified slightly in the The figures given apply to the bare stage in the design when they were Taylor Model Basin.

IN SHIP DESIGN

TABLE

Sec.

ISA

78.b List of Drawings Furnished to THE Model Basin in Connection With the Model-Test Program fob the ABC Ship

5

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 78.5

While tests with a stock propeller i'uniisli cmly an approximation to the shaft power and rate a range of ship speeds, they serve to confine the range of the probable wake and of rotation for

thrust-deduction fractions within rather narrow With average values inside these Umits it

limits. is

power and

possible to recalculate the shaft

may

the tip clearanc(!

the 1.0

871

to a
!«! loss

planned, these two propellers

ft originally

are considered suitable for the preliminary

propulsion

tests.

than

The

self-

larger wheel has a rake of

but some brief sketching

approximately 6 deg

aft,

indicates that this

small enough not to interfere

with

its

is

performance ahead of the four strut arms.

rate of rotation for a propeller other than the

It appears, therefore, that a standard waterlinc

stock model by the short method described in

model length

Sees. 70.21 through 70.38. is

The

propeller designer

able to undertake a final design with far

assurance than the

if

In view of the relatively large wake velocities to be expected around the inside of the tunnel in

fractions

and other

sented in the alternative

ABC

and

designs, 20

necessary to determine the availability

two stock wheels which have the same scale ratio as the two models. Assuming that the ship models are to have an LwL of 20 ft, ample for the testing of a prehminary of

if

the propellers are sufficiently large, the

scale ratio X (lambda)

is

510/20

=

25.5.

the arch-stern design, a reduced pitch for the outer blade sections of the propeller

Since there are two propeller diameters repre-

design

of 20 ft can be used. The scale ratio then fixed at 25.5.

more

wake and thrust-deduction

ft, it is

is

he were forced to approximate

design factors by less precise methods.

24

X

This gives

indicated.

This

prevents

is

definitely

overloading

the

tip

regions and the formation of strong tip vortexes.

TMB

Since

model propeller 1986 was designed normal stern and

for a single-screw vessel with

has constant pitch for 0.5 to 1.0 R, heavily loaded in that region

it

will

be rather

when run under the

arch-stern model. 78.5

Displacement and Draft Conditions. The

ABC models are to be run at a relatively advanced

values of X"' of 5.0498, X' of 650.25, and X' of

stage of the prehminary design,

Dividing the propeller diameters by 25.5 gives 0.7843 ft, or 9.412 in, for the 20-ft wheel and 0.9412 ft, or 11.294 in., for the 24-ft

what appendages are to be carried and their sizes and shapes are rather well determined. Their total volume is readily calculated, as is the additional volume below the 26-ft DWL due to the

16,581.4.

wheel.

The

preliminary propeller design by

first

the chart method, similar to that described in Sec. 70.6, indicates

optimum P/D

and

ratios of 0.975

(A later calculation, quoted in gave an optimum P/D ratio for the transom-stern wheel of 1.02). With 4-bladed propellers the blade width need not be large nor the thickness great. Reasonably modern blade sections, of airfoil type near the hub and ogival type near the tips, are available in stock, as are propellers with small or zero rake. An examination of the TMB stock hst reveals two right-hand 4-bladed propellers having the

shell plating. It is

when

it is

decided therefore to run

in the designed-load condition at a

known

all tests

model weight

1.045, respectively.

correspondmg to the

full in

with plating and all appendages, when floating at the designed waterUne in salt water having a specific volume of 34.977 ft^ per long ton of

Sec. 70.6,

following characteristics:

Item

Diameter of model

propeller, in

Full-scale diameter for X of 25.5, ft

Pitch-diameter ratio

Mean-widtii ratio Blade-thickness fraction

2,240

lb,

prescribed.

apparently

The corresponding full-scale diameters

is

to

have no carry no

There are several reasons illogical

for

this

procedure:

.

.

98 0.238 0.038 .

1 1 40 24 22 1 05 0.213 0.047

and

appendages in the bare-hull condition, it may be expected to float shghtly deeper than the designed draft when ballasted to the total weight

1986

.

to be built to the molded

representation of plating,

TMB

.

is

lines of the respective hull design, is to

229/t

9 652

finished ship weight,

at 59 deg F, 15 deg C.

Since each model

TMB 20

total

.

are shghtly

than contemplated in the hull design. However, as it appears that the 20-ft wheel for the transom-stern hull is on the small side, and as

larger

further study of the tunnel stern indicates that

Tolerances and unavoidable errors in fairing fines, in making the early volume calculations, and in shaping the model render it (1)

the preliminary

almost a coincidence when the model

floats at

exactly the correct draft

due to the added volume and normal appendages is usually insignificant. For the two ABC hulls, the change is less than 2 inches on the ship. (2)

The change

in draft

of the shell plating

— HYDRODYNAMICS

872

TABLE

78.C

Weight and Volume Data for

Model Resistance Tests All resistance tests in the designed-load condition are to be run at zero trim fore

and

aft.

All figures given are subject to

designs proceed but wiU be

model resistance

made

tests are run.

minor changes as the firm before the

first

IN SHIP DESIGN

Sec. 7S.6

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 7S.7

Fig. 78.B

The

subscript

namely 20.5

"W"

kt.

TMB Model 4505 at a Speed Corresponding to 20.5 kt for the Ship TMB model number on the legend signifies that the model is made of wax.

following the

This range corresponds to about

6 through 22.5 kt for the ship; 1.18 through 4.46

kt for the model. The reason for the emphasis on the low-speed range is to: (1) Determine the deep-water resistance corresponding to the low speeds necessary for the ABC ship in the canal leading to Port Amalo and

in the river leading to

Port Correo

Determine rather accurately, in the bare-huU condition, the separation drag in the range below that at which wavemaking occurs. (2)

Even though

may be

stimulation

considered

necessary by the David Taylor Model Basin to insure turbulent flow over practically the entire

area of the model hulls practicable,

made

some

is

it

resistance

desired that,

if

measurements be

in the low-speed range without turbulence

stimulation of any kind.

The

shell plating at

and at a speed corresponding to the ship

trial

speed of 20.5 kt. The lower can-iage platform furnishes a reference for estimating visually the sinkage and trmi (by the bow) 78.7

Wave and

Profiles

when underway.

and Lines

of Flow.

Wave

be taken on both models, bare-hull condition, at a speed corresponding to 20.5 kt for the ship, 4.06 kt for the model. The wave profile is to include the

profiles

lines of flow are to

profile across the

transom. (See Fig. 66. R).

For all resistance and self-propulsion tests the model speeds are to be noted at which the transom clears; in other

words,

when

the entire area of the

transom is exposed to the air. Undoubtedly this will be different for the two types of stern. If necessary to determine this clearing speed the model is to be run faster than that corresponding to 22.5 kt. (See Sec. 78.19). It is desired that the lines-of-flow observations

both ends

of the

ABC

ship

to be welded, with butts and laps both flush. For the remainder of the length the strakes of plating are to be raised and sunken, with welded butts and riveted seams. All excrescences are to be kept to a minimum, and fairmg is to be careful and thorough. A type of bottom coating is to be used that is either self-levehng or inherently is

smooth. It is beheved, therefore, that a roughness allowance AC;? of 0.30(10"^), to be applied to the

ATTC

1947 or Schoenherr friction values,

is

ample to represent the new, clean-bottom condition of the ship.

The usual photographs

of

both models under

the towing carriage are to be taken, at zero speed

and at speeds corresponding to 20.5 kt

for the

when run bare and then when run

ship, 4.06 kt for the model, first

without the cutwater, appendages. Figs. 78.A and 78.B are reproductions of the photos of the transom-stern model, at zero speed

hull,

with

all

Fig. 78.C

Bow-Quarter View of Transom-Stern

Model Showing Lines of Flow by Chemical Means The photograph is inverted of the flow.

to afford better visualization

HYDRODYNAMICS

874

IN SHIP DESIGN

Sec. 78.8

when driven at the model point of self-propulsion by the stock propeller. Still flash photographs suitable for reproduction are to be taken from

and from underneath both sterns. These are to be supplemented by motion-picture photographs if any unusual flow conditions are alongside

encountered. It

be possible to swing the double

should

rudders of the arch-stern model to observe the

change in flow

-with

rudder angle.

Smkage and trim measurements

Stern-Quarter View of Transom-Stern Ship, Showing Lines op Flow BY Chemical Means

Fig. 78.D

Model op ABC

are to be taken at the FP and AP on both models through the complete range of speeds covered in the tests. These data are to be recorded when both the bare-hull

and

tests are run.

at the hull surface mclude practically the entire

The hues should begin

length of the model. far forward as Sta.

if

1

practicable, but in

case not farther aft than Sta. 2.

as

any

They should

all the way to the stern. Fitting-room photographs are to be taken of the hull to show, as graphically as possible, the

extend

lines of flow resulting

from these

tests.

The

usual

comparison ^vith pubhshed data on sinkage and The data mth appendages are to enable the full-scale thrust measurements on the ship to be corrected for the weight component of the shaft, propeller, gear,

are to be determined for both types of sterns. In

be made on a body plan. For determining the proper positions for the roll-resistmg keels, flag indicators are to be mounted along the bilges on the model, extending from the side for a distance equivalent to about

stern

3 ft for the ship. Figs. 78. C of

TMB

and 78.D are bow and stern views model 4505, inverted from the positions

as photographed,

flow as revealed

showing the surface

by a chemical

lines

indicator.

of

The

when measured,

traces derived from the model,

and other rotating parts [SNAME,

1934, pp. 151-152]; see also Sec. 59.16. The wake vectors at the propeller-disc positions

view

also to

mth-appendages resistance

bare-hull data are required for

trim.

projection of the flowhnes on the transverse plane is

the

The

of the small hull clearance

and the

still

under the transom

smaller tip clearance inside the

tunnel of the arch stern, consideration is to be given to the use of the 5-orifice spherical-ended pitot tube, with its

smaUer head,

for determining

the wake vectors, in place of the 13-orifice tube with the larger head. In any case, the head

should not be so large as to interfere mth or modify the floAV it is intended to measure.

For the transom-stern model the wake observaoutward to cover a halfbeam at least as wide as that of the ship section tions are to be extended

heavy hues of Fig. 66.R in Sec. 66.28. Fig. 78.C shows clearly how the water at the sides of the bow sections sweeps around and flows along under the bottom. The upward-

shown

are those

and-aft

flow

in the

alongside

indicated clearly

m Fig.

the

centerline

skeg

is

78. D.

78.8 Flow Observations with Tufts; Sinkage and Trim Wake Vectors. Before any appendages are added to the arch-type stern, flow observations between and around the skegs are to be ;

made

in

the

circulating-water

tufts attached to the model.

channel,

using

It is particularly

desired to learn whether there

is

any evidence

of separation along the roof of the tunnel or of

under the bottoms of the skegs. Flow observations with tufts are to be made on both models in the circulating-water channel cross flow

Fig. 78.E

Model,

The dark tufts of

Underwater Profile of Arch-Stern

TMB 4505-1, in Circulating- Water Channel irregular streaks represent flow positions of

dark yarn attached to the model surface.

MODEL-TESriNG PROGRAM FOR A SHIP

Sec. 78.9

Fig. 78.F

Fish-Eye View of Arch-Stern Model in Circulating- Water Channel

Some

cross flow

is

visible

under the

flat

bottom

of the side skegs.

abreast the propeller disc. (This was not fully

make SP

accomplished; see Fig. 60. M).

partly loaded condition.

Actually, the transom-stern model was not checked for flow in the circulating-water channel because of the good flow pattern indicated on the bare-hull model. The work schedule was such that the circulating-water test of the arch-

TMB

stern

were Figs.

model was not made until all appendages fitted and the model was self-propelled. 78. E and 78. F are through-the-water photo-

graphs of the after portion of the ABC archstern model, 4505-1, taken in the circulating-water channel. Other than a slight

TMB

cross flow

under the

TMB

flat

bottoms of the skegs,

It

model with appendages, when both towed and self-propelled,

are plotted in Fig. 58.B.

survey data are plotted in Fig. 60. in Fig. 60.N. 78.9

Self-Propelled Tests.

tests are to

Wake-

M and analyzed

be run on both models, carrying

appendages except the

condenser

intake

TMB

all

and

2294 and

1986, over the range of speed specified for the resistance tests.

The displacements

indicated in Table 78.c. It

is

Df

that the

correction

[Bu

sion tests allow for a roughness of the clean,

applied to the

C

1933, pp. 37-38] for all self-propul-

ATTC

No overload When the results

values.

ACf

new

of 0.30(10"^),

as

1947 or Schoenherr friction

tests are required.

of the foregoing tests have been worked up and evaluated, a new propeller will be designed and built for the most promising

A

the alternative designs.

of

propulsion tests

is

new

set

of self-

to be run, over the range of

speeds specified for the resistance tests: (1)

At the

full-load displacement, draft,

and trim

condition (2) At the partly loaded conditions, with displacement, draft, and trim by the stern to be as

specified subsequently.

Fitting-room photographs are to be taken of the Self-propulsion

discharge, using stock propellers

7,

ship corresponding to a

the water passes easily and regularly through the

tunnel and around the skegs. Sinkage and trim data on the transom-stern

desired

is

R Bull.

and

with the stock propellers in the

tests

are to be as not necessary to

sterns

and

after quarters of

both models to show

the shape of the hull and arrangement of appendages.

propeller for the transom-stern ABC designed in Chap. 70 by the Lerbs short

The new ship

is

method.

The

A new model was not built to this design.

stern appendages on

the transom-stern

HYDRODYNAMICS

876

IN SHIP DESIGN

Sec. 7S.10

the double rudders and to obtain certain turning characteristics. This model,

selected design for the

ABC

if

it

represents the

hull, is to

be

self-

new model propeller; otherwise propeller. The weight displacement,

propelled with the

with the stock draft, trim,

and the

like are to

be for the designed-

down

in

neutral rudder angle for each rudder

is

load condition with appendages, as set

Table

78.c.

The

by a special test, first on the basis of the optimum steering characteristics when running ahead, and then on the basis of good steering and minimum propeller power for driving the ship in straight-ahead motion. Rudder angles for maneuvering tests are to be reckoned from these neutral angles. Free-running maneuvering tests are to be to be determined

carried out in the equivalent of deep water, to

determine:

The complete turrung path through a 180-deg

(a) Fig.

Fish-Eye View of Arch-Stern Model 78. G 4505-1, Looking Up and Aft, With All

and 20 kt, model speed between 3.86 and 3.96 kt, with rudders at 35 deg; see item (34) of Table 64.e

Appendages in Place

model are shown in Fig. 67.J of Sec. 67.13; those on the arch-stern model in Fig. 78. G. 78.10 Open-Water Propeller Tests. It is as-

sumed that

for

the stock propellers hsted in

Sec. 78.4, the open-water propeller-test data are

available.

The new model is

to be characterized

iir

measured and checked, and some quantitative

The new model

between the and Volume III, the latter covering the subject of maneuvering, none of the tests listed here were made on either model. Because

of the interval elapsing

publication of

78.12

Volume

II

Controllability Tests in Shallow Water.

model and the steering-gear motor arranged for distant manual control. If it so happens that these tests can be conducted in shallow water, when the model is ready, the depth dition described in Table 78. c, -with the

propelling motor

24-ft (ship size) propellers should be free of cavitation if the bottom of the transom is kept in the water in the one case and the tunnel is kept full of water in the other. There appears to be no need of conducting cavitation tests on a model propeller designed for either type of huU. If assistance can be furnished from the Design Office for the purpose, the new propeller is to be

surface finish.

propeller was designed but not hence there are no test data for it. Neutral Rudder Angle and Maneuvering 78. 11 Tests. Tests are to be conducted with the archstern model to determine the neutral angle for built,

as

arch-stern model, under the designed-load con-

David

predictions indicate that both the special

its

when turning

open water,

and the

values obtained for

of heel

Controllability tests are to be carried out for the

Taylor Model Basin.

The

The maximum angle

ABC

following the standard procedure of the

20-ft

(b)

in (a).

propeller intended to be de-

signed and built specially for the selected hull design

including advance, transfer, and tactical diameter, at an approach speed of between 19.5 turn,

to correspond to a full-scale depth of 40 ft, ft. Otherwise, the tests are to

is

model depth 1.78

be conducted in the shallowest depth available.

The model (1)

shall then:

Execute a crash-back maneuver.

From a

straight approach path at a speed corresponding

to 20.5 kt, 4.06 kt for the model, the propeUing is to be reversed within 3 sec, about 15 sec

motor

for the ship,

and an astern torque appUed, as

nearly as practicable equal to 0.8 of the ahead torque for 20.5 kt. The rate of propeller rotation astern

is

to be, as nearly as practicable, not in

excess of 0.5 of the ahead rate for 20.5 kt. Obser-

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 78.15

made

vations are to be position,

rotation, (2)

Be

torque,

thrust

of the successive ship if

practicable,

rate

of

and other pertinent data. at a

speed corresponding to 20.5 kt, with neutral rudder angle and no perceptible swing, to determine whether or not the model deviates progressively

from

its course,

as

it

would

if it

had dynamic

instability of route. (3)

Be run ahead

in a speed range corresponding

to 10.25 to 20.5 kt for the ship, 2.03 to 4.06 kt for

model,

the

determine

to

Maximum

characteristics.

its

general

rudder

steering

and

angle

maximum yaw,

if practicable, are to be observed but no special instrumentation need be provided

for this test. (4)

Be run

astern at speeds varying from

kt for the ship,

to 8

to 1.58 kt for the model, to

demonstrate that it will turn as directed by the rudder (s). The rate of propeller rotation is not

0.55

ft for

(b)

when running ahead

left to itself,

(a)

vLb'

=

L,y

,

510

877

510

12.42

ft

LwfiO, corresponding to an

Lw =

=

corresponding to an hw

=

hwr

17

ft

for

ft

Such other proportion as may appear advisupon before starting the tefsts. The angle of encounter is to be 180 deg (ship heading directly upsea), but a few runs are to be made at angles of encounter of deg (foUomng (c)

able and be agreed

or overtaking sea).

photographs are to be made of the model extreme up- and down-pitch positions, in regular waves of a length which produce the worst ship behavior. 78.14 Vibratory Forces Induced by the Propeller. In view of the unusual forms of the alternaStill

at

tive sterns for the tip clearances

ABC

ship, as well as the small

it would be extremely some indication of the propeller-

contemplated,

useful to have

excited vibratory forces to be expected on the

limited for this test.

However, at the time of writing (1955) the instrumentation for this purpose is still being developed by the David Taylor Model Basin hull.

78.13

Wavegoing Model Tests.

model at

least 6 or 7 ft long is to

A wavegoing be constructed

to the hull shape which proves superior (to have

under

the lower propeller power) in the self-propelled

H-8.

tests.

This model

is

to be fitted with all 'principal

erections above the

main deck

level,

it is

Technical and Research Project available, vibration tests can be

included in a model test program. 78.15

in block

form, as well as with the following appendages:

SNAME

When

Data.

Reporting and Presenting Model-Test

Except

for the notes concerning reproduc-

tions of the model-test data, this section (a)

(b) (c)

(d)

Cutwater Rudder horn on the transom-stern model

Rudder (s) Bower or abovewater anchor. The

vicinity of this anchor

is

work

of

a large-model-basin

It is

planned that

SNAME

Resistance Data,

Propeller Data, and Self-Propulsion

Data sheets

be made up (by the Design Office; in this case, the author and his assistant) for the tests of both models and of the special model propeller built for the selected model. Sufficient data are to be observed and recorded to enable the results to be presented in the form described for the items following. The data hsted are to be presented separately for each model will

is

to be so weighted that the longi-

is about 0.23L, reckoned about an assumed LCG of 0.505L from the FP. If possible without special instrumentation, an estimate is to be made of the natural pitching period of the model in quiet water, for angles not exceeding plus and minus 10 deg. The natural rolling period of the model, for an initial heel of the order of 30 deg, is hkewise to be determined

in quiet water.

and model

propeller:

(1) Curves of effective power Pe and friction power Pp both bare hull and mth appendages, for the fully loaded and partly loaded conditions, ,

be towed through simple regular waves by a gravity dynamometer, loaded to give a constant pull as required to tow the model at a speed corresponding to 20.5 kt for the ship in smooth, deep water. The waves are to vary in length from 0.5 to 2.5L, 255 ft to 1,275 ft full scale.

in requesting this

hull in the

to be represented rather

tudinal radius of gy ration

The model

written

estabUshment.

closely to scale.

The model

is

generally in the wording that would be employed

is

to

The wave height of each system is to be:

including calculated values of the wetted surface

S

for each condition.

The value

previously stated in Sec. 78.6,

is

of

ACf

,

as

to be taken as

0.30(10"'). (Curves of effective power Pe for both models of the ABC ship are given in Fig. 78.Nc on page 892 and in Fig. 78.1).

.

HYDRODYNAMICS

878 (2)

Curves of

power

effective

Pb

calculated for

the Taylor Standard Series model of identical

ATTC 1947 friction data, with a ACp equal to that for the actual models, and the reworked TSS data of M. Gertler (this work is to be done by the Design Office). The proportions, using the

TSS

curve is to cover the full-load condition only. (These curves are not plotted but "angleworm"

EHP)

curves giving the ratio (EHP/Taylor

are

found in Figs. 78. Jc and 78. Kc on pages 882, 885). (3) Body plan showing hues of flow in entrance

and run, wave zones

if

profile,

determined,

location

and

separation

of

other

flow

details.

.

IN SHIP DESIGN (in

Sec. 78.15

ally.

60.M

(Fig.

gram) (7) Curves

adapted from the

is

TMB

power Pg

of shaft

Pe

Pp), effective power

Pe/Ps

n, ratio of

fraction

wake

t,

for each propeller,

(or

,

(or propeller

Pe/Pp), thrust-deduction and real-slip ratio Sr

fraction w,

,

model when driven by and (2) the propeller of

(1)

the stock

special design.

(These are reproduced in Fig. 78.1 for the archstern model and in Fig. 78. Nc for the transomstern model,

when driven by the stock

propellers

given in Figs. 52.U and 66.R).

(8) Open-water characteristic curves of jjo and IOKq on a base of advance number

78.8). (5)

Curves

FP and L on a

of sinkage of

bow and

stern, at the

the AP, plotted as fractions of the length

base of both T, (= V/VL) and F„ (These are plotted for the ABC transom-stern hull in Fig. 58.B and for the arch-stern hull in .

Fig. 58. C, for

both the towed and the self-pro-

pulsion conditions. is

A

discussion of the differences

included in Sec. 58.2).

(6)

Transverse section at the propeller position

'0

0.1

0.2

0.3

0.4

0.5

0.6

power

rate of propeller rotation

only).

Photographs of pertinent features of the flow tests with tufts. (See Figs. 78.E and 78.F of Sec.

dia-

.

(Reproductions of the transom-stern plan are

(4)

wake

the plane of the propeller disc), with

vectors and components indicated diagrammatic-

,

Kr

,

the propeller of special design. (See Fig. 78.

H

TMB

TMB

propeller 1986

propeller 2294.

The

and

Fig.

78.Mc

for

H

Characteristic Curves of

TMB

for

propeller designed in Chap.

70 was not tested as a model). (9) Plot of successive positions of ship during a 270-deg turn at a specified speed (between 19.5 and 20 kt for the ship) and with a 35-deg rudder

angle. (This test

was not

carried out)

(10) Controllability in shallow water.

ABC

(No

test

was made on

either

(11) Plot of

wavegoing-speed ratio on ratio of

0.7

0.6

0.9

model)

i.O

I.I

1.2

Advance Coefficient J- \^/(nD) Fig. 78.

,

J, for

Model Propeller

1986,

Derived from Open- Water Tests

Sec. 18.17 b

MODEL-TESTING PROGRAM FOR A SHIP

879

HYDRODYNAMICS IN SHIP DESIGN MODEL RESISTANCE DATA

880

qHiP S

'Sin'y

S.

7^.nR'x

MODEL NO APPENDAGES. F^EMARKS.

z

0.2

Pfi'.lfi:^,

PASSFNGFR

Ifi'S?.-^

CARm

?n

fi

TON KNOTS

45nR

STEM

CUTWATER

DEE P

.WATER

WATER

COND. STILL( 97271

MODEL

MATERIAL

BASIN SIZE 963' .MODEL LENGTH.

TFST

P

nATF

70°

TMB W ATER

LABORATORY RASIN

Sec. 78.17

I

X S 'X 22' l

20.0 OCT. 53

TEMP

MODEL FINISH TURBULENCE

F

_WA^ WAX NONE

^''2

5.0498

A^650 25 )\

^ 16, 581

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 7S.17

L/B,

6.97B

Bv/H_

2.793

A/(nnini

f

7/(O.IOOL) ^

Q.

C^

i74-qf;

n

4.371

.

621

0.717

.

950

Q.822 n.643

By/Bn^ -H^/Hm

fi

ni

s/v '^ s/j!al_

6.533 15.62

0.5R9

"PA-

0.612

Sllfi 2/,

'PVA-

LOOP

.MAX. IMB/B^_LQQ3

1.0028

.MAX. WLB/B)( I.003

I

o no

0.8 25

BKW/B^

0.048

0.740

BR/B..

0.147

Q.623 633

0.619

PR/By,

O.OI4

Q.8I2

HS/B..

O 021

-Cp..^

0.935

0.724

KB/H

0.557

EXPANDED 1

Aj^/A^

C...-

-Cpg

881

AND COEFFICIENTS

RATIOS

RESISTANCE

DATA

C, 'IL-

0.449 0.908

HYDRODYNAMICS

882

EXPANDED FOR a.

X LU (£

o _J >•

0.

I

UJ

IN SHIP DESIGN

RESISTANCE CURVES 400-FOOT LENGTH

Sec. 78.17

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 78.17

883

MODEL RESISTANCE DATA SHIP

510

J2l08

S.S. Passenger

26.'086,

Cargo, 4505-1

16, 675

20

,

MODEL NO APPENDAGE S Half Rudders. Stem REMARKS Arch Stgrn ^ 0. c

~ •5-0.

(

5

to n

knot

Culwoler

LABORATORY __XMB Deep Water basin BASIN MOnFI

SIZE 963'

LENGTH

TEST_6_DATE

51*

20.'0

30

Oct.

66 WATER TEMP. watfr cond. siiii 1.97?,?) 22'

MODEL

MATERIAL

MODFI

FINISH

53 TURBULENCE

Wax Wox None

25.5

A A'^ z

a'

5.0498

650.25

a' 16,581

_

HYDRODYNAMICS

884

RATIOS L/Bx-

6.978

Bv/H.

2.802

MO.OIOLr V/(n i

mm

/v''' 3

S/?^^ 3

g8

C|

0.723 0.825 0.655

"pv'PA-

PF-

f 4.396 6. 105

0.935

6.938

0.623

0.612

0.597

-^PVE-

IN SHIP DESIGN

Sec. 78.17

COEFFICIENTS

-Hv /HuBKW/B)^

CpR-

0.938

1.002

.MAX. IMB/Rx 1003

1.0028

.MAX. WLB/BxL2Q3 0.528 C.„

0.048

0.462

BR/By

0.147

0.908

0.631

.DR/Bx-

0.014

0.827 0.727

.KB/H_

^WA-

16.61

s/IEL.

Co

125.

0.952

AND

HS/Bx0.557

EXPANDED RESISTANCE DATA 400

.FT.

DIMENSIONS A 8043.2 TONS S.W.

RX

57.32

-FT.

V 281

H

20.46

.FT

S

TRIM

i

REMARKS.

.FT

FOR

400

FT

LENGTH

LBS

SEcVfT.'*

T 59 °F

BASIS. Schoenherr

FRICTION

328

.FT.'

/O

1.9905

29.786

_FT.2

V

1.2817 x10-^

.

FT.2/SEC.

Sec. 7S.17

MODEL-TESTING PROGRAM EOR A SHIP

EXPANDED FOR D-

X

UJ tr

o _i

\ a.

X

RESISTANCE CURVES 400

FOOT

LENGTH

885

HYDRODYNAMICS

886 Direction

IN SHIP DESIGN

Sec. 78.17 Plane of Propeller

of

Disc

RotQtio

Fig. 78.L

Fig. 78.0

sistances

Rt

is

EMB

Model Propeller

a plot of the observed total re-

for the transom-stern model,

TMB

4505, both with and without turbulence stimulation. Apparently, stimulation is not required on

do the stimulating devices (short studs) have any effect on the measured resistance. Included in the diagram is a plot of the dimensional ratio Rt/V^, where Er is in lb and V is in kt. It is customary at the David Taylor Model this model, nor

Basin to make this as a check whUe the resistance testing It staff

is

in progress.

was noted and commented on by the

members

TMB

responsible for testing these models

that their performance during the test runs was

uniformly excellent. the models settled

When

down

measuring resistance,

quickly, allowing rapid

adjustment of the pan weights. Once the correct weight was established there was Httle oscillation of the resistance scriber from the zero Une. In the self-propulsion tests the actual D/o weights used on the pan agreed very closely with the calculated Df values, resulting in remarkably low AD/ corrections [C and R Bull. 7, 1933, pp. 37-38]. This consistency and reliabiUty, for both

models,

is

2294

believed to be due directly to the fact

that separation around the hull

is

limited to the

region abaft the transom and that the separation

points at the water surface always

lie

having waterhne slopes both

less

exactly at

On

a form and greater than

the outer corners of the transom.

the critical slope for separation, the separation points

may and undoubtedly do

at slightly

lie

run at the same speed. The positions depend upon the "history" of the viscous flow, on a distance basis, reckoned from

different positions for each

the

bow of The

tion.

the model back to the points in quesseparation

points

may

not

remam

fixed during the constant-speed portion of a run,

and they may not be opposite each other, on the two sides of the model. The chemically traced flowlines on the surface transom-stern model, depicted in Figs. 78.C and 78.D of Sec. 78.7, reveal definite flow patterns. There appears to be no uncertainty on the part of the water as to the paths that it is to dark follow. There are no excessively wide, of the

traces indicating undesirable slowing region.

up

in

any

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 78.17

PROPELLER 9-2$

DIAMETER, D NO. BLADES,

4

Z

HUB DIAMETER,

H

RAKE ANGLE

Q

REMARKS

TEST DISC

Vq

2.08

ROTATiriN

RIGHT

5

.

PROPELLER

TEST

kt,

ARFA Aq 73.169 jn^

REMARKS ABC

SHIP DATA

D

^

20.51 ft

f.

VESSEL,

U.S.

DIAMETER,

11.29

A[-

36.364

Q.497 =

11.14

jn

RATIO d

200

rpm

0.238

/"

m

0.982

0.0491

tg /n

NAVY

CHARACTERISTICS

np

,

P/D

ft.

DESIGNED

EMB

EXP AREA,

EXP AREA

9.08

R

HAND

SALVAGE

FOR

LABORATORY

50

070

TANGFNT

NATURAL

QR ICI NA LLY

DATA

0.180

ri/n

deg

2294 to

PITCH, P AT

ft

MODEL PROPELLER NO

ft

1.667

DESIGNED

DESIGN

3.696

in^

ft.

l^gxis/D

1088

Ap

30.994

AREA RATIO

0.4 24

rpg

PROJ. AREA,

PROJ.

9.652

D

P^ 20.13

rpm

ft.

=

jn

jn'

115

BLADE- SECTION DIMENSIONS AND RATIOS Trailing

Leading

Edge

Edge

I.

Face

Base Chord 7 Stations

Entrance

Chord SECT

c

Length

3 Stations

HYDRODYNAMICS IN SHIP DESIGN OPEN-WATER TEST DATA _LMB

BASIN

WATER FOR

Vo

T

60

Vo=

470'

SIZE

_deg 4.06

X

p

F kt.

and

42.'7 X

I4.'7

19383

Hq.

TEST NO

lb- sec^/ft'*

10.58

rps^

riATF

I

V

Sec. 18.17

I

2109

R „ at 0.7 R

7

APR.

194?

xio'^ft^/sec =

0.368

,10^

Sec. 7S.17

MODEL-TESriiNG

PROGRAM FOR A

SHIP

889

CAVITATION TEST DATA TUNNEL JET .deg F AIR

Vo

CONTENT

TEST

VAPOR pressure,

e

DATE

NO

.Ibs/ft2

.METHOD OF MEASUREMENT

/?_

Jb-sec2/

f

t4

HYDRODYNAMICS

890

IN SHIP DESIGN

SELF-PROPELLED 5IO'«73.08'i( 26'.I63. 16573 T

SHIP S.S.

PASSENGER

APPENDAGES KEELS.

DEEP

4Fir).S

BASIN

RUDDER.

MODEL

STEM

SIZE

CUTWATER MOnFI

MODEL SCHOENHERR

FRICTION

FORMULATION

WETTED

SURFACE, WITH APPENDAGES

-

MODEL DATA

TM

ARnRATORY

CARGO. 20.5 KT racjin

MODEL NUMBER

BILGE

I

B

RESISTANCE DATA

WATER

9K3'i(

SI' x

PROP. DATA ??'

20.'0

LENGTH DISPL.

2177

TRIM

Q

TIIRR

ft

V

TEMP

1.937! 1.

1133

lO^ACp ft'

INBOARD

REMARKS Hq IN

and

PROPELLER(S) n

101.33

ARF FT.

RFVOLUTIONS

DIAMETERS PITCHES ROTATION _

NO(S)

TMB 2294

9.652 9.475 R H

MODEL- SELF-PROPELLED TEST

RESULTS

SHEET.

SHEET

STIM.

WATER

Ihrw/i ft

SCHOENHERR

74.608

Sec. 78.17

NONE &fi

deg

F

Ib-sec^/ft**

XIO'^ ft^/sec

Q-^

OUTBOARD

Sec. 78.17

MODEL-TES'l ING

PROGRAM FOR A

SHIP

891

HYDRODYNAMICS

892

IN SHIP DESIGN

Sec. 18.17

FULL-SCALE SHIP AND WATER CHARACTERISTICS; DATA AND CURVES L

510

Bx

73.08

_ft

H

26.193

-ft

ft

16573

t,

FULL- SCALE

INBOARD

DIAM._

S W,

OF

PROPELLER

S

48 51 4

A

25.5

Tn

yt^ 908

34.977 DATA

ft^

.^/

t

/O

AT

20,5 T

5_9

t"'

I.99Q5

Ib-sec^/ :2/f^^ f

2fil7

.X 10^ ft^/sec

kt

deg

R,

1378

F

Fn

-XIO«

0.270

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 7S.17

self-propulsion

test,

The

optimistic.

893

the

was unduly

estimate

calculation of Sec.

using

60.8,

K. E. Schoenherr's formula [PNA, 1939, Vol. II, p. 149], was not made until after the hull form had been completely fashioned and a stock propeller had been selected for the first SP tests.

Groph of

—

Even

7

5

then, the predicted value of

w was

0.255,

considerably higher than the test value of 0.190

from

Figs.

78.Nb and 78.Nc.

The estimated thrust-deduction

(3)

fraction

I

of

used in Sec. 66.27, is close to the value of 0.30(0.7) = 0.21, derived by Eq. (60.vi) from K. E. Schoenherr's simple formulas [PNA, 1939, Vol. 0.20,

II,

Bare

Hull

I

-r-

/

o

With Stimulation

+

Without Stimulation

pp. 149-150] on the basis of using a streamlined

rudder.

JOodel Resistance,

-6

When

ABC

the transom-stern

for contra-rudders in Sec. 60.9, the

would have been 0.255(0.5) 1.0

1.4

1.8

2.2 2,6

3.0

34

Model Speed

3.8 4.2

4.6

5.0 5,4

56

the transom-stern design, repre-

TMB

model 4505, and analyzing the

speed-power differences between the values calculated on paper and those predicted from the model tests,

new

^-value

0.128. Utilizing illus-

trated in Fig. 67. V, and taking account of the

The off-surface vanes mounted along the bilges hkewise showed no uncertainty as to the proper water direction. The bilge-keel traces deduced from them are remarkedly fair. first

=

the stern shape of the hull by the method

Plot op Total Resistance R^ and of Ratio RtIY"^ for TMB Model 4505

Takmg

had

6.2

V, kt

Fig. 78.0

sented by

hull

been fully shaped, and it was known that a contra-rudder was to be fitted, a smaller value of t was selected. Takmg the coefficient 0.5 hsted

certam features stand out:

rudder, the predicted thrust-deduction fraction

from the upper graph of Fig. 60. P was 0.135. There appeared to be little justification for anticipating a low ^-value of 0.07, as was actually derived from the self-propulsion tests. Neverthethe hull efficiency

less,

by using a wake

assess the effect of the transom in advance. In it was known that a sizable bulb was to be used at the bow but it was questionable whether this bulb would be beneficial at the low T, of 0.908. Actually, the effective power P^ is about 3.5 or 4 per cent lower than the TSS effective power at that T^ (2) The wake fraction w of 0.30 used for the transom-stern hull in the shaft-power estimate of Sec. 66.27 was derived from the best available data on the self-propulsion of single-screw models. It was admittedly optismistic; indeed, since a value of only 0.190 was achieved in the model

the second place,

of 1.161,

estimated

and a thrustdeduction fraction of 0.135, is remarkably close to the value of 1.148 derived from the self-propelled model-test data of Fig. 78. Nb. The hull efficiency of 1.143, estimated at an early stage of the design and set down in Sec. 66.27, is Ukewise remarkably close to

was both conservative and optimistic to estimate, as was done in Sec. 66.9, that the resistance would be no lower and no higher than that of the Taylor Standard Series hull of the same proportions. In the first place, it was difficult to (1) It

-(]„

(4)

fraction of 0.255

both these

figures.

The estimated Pe/Ps

ratio or

r;?

value of

about 0.74 of Sees. 66.9 and 66.27 was admittedly somewhat random and even more hopeful. The higher -qp of 0.761 from the model tests may be due to the care with which the afterbody and skeg were shaped, in an effort to achieve good flow to the wheel. On the other hand, it may be ascribed to the use (a)

The

of:

contra-fashioning of the rudder-support

skeg and the rudder, which had not yet been decided upon when the power estimates of Sees.

.

66.9 (b)

and 66.27 were made

A

propeller diameter

somewhat

A

larger than

diameter of 0.7 the draft, one of the simple rules, would have been 0.7(26) = 18.2 ft, whereas the corresponding diameter was 20.51 the average.

ft for

the stock propeller used.

HYDRODYNAMICS

894

A

(c)

centerline skeg that

IN SHIP DESIGN

was unusually thin and

narrow, in a deliberate effort to cut down the thrust deduction. A designer may well question the usefulness or the validity of an estimating procedure, recommended for use in the paper stage of a preliminary design, which says (in Sec. 66.27) that 16,930 horses will be required at the shaft at the designed speed while the test results of a self-propelled

=

^r(App)

The

(iv)

Sec. 78.17

=

(1.05) (166,322)

174,638

thrust-deduction fraction

area factor 0.172 from Fig. 67.V and entering the

upper graph of Fig. 60.P, is 0.135. This procedure takes account of the presence of the rudder in each case. The estimated value of the propeller thrust

T is

174,638/(1

-

0.135)

=

201,894

horses. Allowing

say 2 per cent for the resistance of a scoop not fitted to the model, and for power to drive the circulating water through the condenser of the plant, the model prediction corresponds to a reduction of some 19 per cent in the estimated power. Conversely, the calculation represents an increase of about 25 per cent in the

main propelling

power predicted by the self-propelled model must be remembered, however, that Uttle or nothing was known of the shape or details of the hull when the first and larger estimate was

The wake

(v)

undertaken. Actually, a third approximation or estimate

power should have been made ABC ship after the hues had been drawn, the appendages designed, and the stock propeller selected. This could have been done while the model was being built. With data available as hsted hereunder, the procedure and for the

of the shaft

=

When

(i)

manner

the

been

decided,

(for

the clean,

66.9

is

roughness

new

hull)

allowance

of 0.4(10"')

ACf

of Sec.

reduced to the value of 0.3(10"')

Sec. 78.6. This

0.3)(10"')

C„

of plating the hull has

the

=

means that C^ + ^Cp is (1.470 Adding the value

1.770(10"').

from Sec.

66.9,

3.016(10"').

Then

of 1.246(10"')

1.770)(10"')

=

Ct

is

of

+ of

(1.246 4-

Rr = ip/2)V'SCT

= =

lb.

predicted from the

15.29 kt or 25.82 ft per sec.

The ram-pressure

load over the disc area of

the 20-ft ship propeller

With a

(vii)

=

T from

thrust

=

(p/2)AoFi

is

0.99525(25.82)'(0.7854)(20)'

208,609 (iv)

qAo

=

1b.

preceding of

= T/{qAo) 201,894/208,609 = 0.968. This is somewhat less than the value of 1.287 predicted in Sec. 66.27. 201,894

lb,

the thrust-load factor Ctl

=

means that the real efficiency of the propeller be somewhat higher than previously esti-

It

will

mated.

The rate of known at the

(viii)

rotation of the ship propeller

not

stage at which this approxima-

tion

is

made.

assumed that

It is therefore

is

its real

based upon the reasoning of Sec. 34.4. Consulting Fig. 34.B with the Ctl value of 0.968, the predicted real efficiency tjo efficiency will be O.Srji

is

,

0.665.

With a w-value of 0.254 and a i- value

(ix)

the corresponding

-

(1

-

0.135)/(1

rjn

is

0.254)

—

(1

=

of 0.135,

—

i)/il

0.865/0.746

w)

=

=

1.160.

Assuming an i/K-value of 1.02 from K. E. Schoenherr [PNA, 1939, Vol. II, p. 150], the estimated propulsive coefficient (1.160)1.02 (x)

=

(550) (0.787)

166,322

horses.

ijp

is

=

'r}o{vH)vR

0.665

0.787.

The predicted

(0.99525) (34.62)'(46,231) (3.016) (10"') lb.

=

20.5(0.746)

(vi)

transom-stern

results are outlined briefly in the following:

w

fraction

Schoenherr formula, using Eq. (60.ii) and the ship and propeller dimensions at this stage, is 0.254. The speed of advance at 20.5 kt is 20.5(1 - 0.254)

shaft

test. It

=

174,638/0.865

model, from Fig. 78.Nb, indicate that the shaft

power need not exceed 13,250

1b.

using the

t,

=

shaft

power

is

i2j-(App)F/

=

174,638(34.62) /432.85

13,968

only 5.5 per cent greater than the

Ps

(ii) With the appendages designed, and with no condenser scoops to be added or cooling water to be circulated in the model, there is no longer any reason for doubling the calculated appendage-

13,243 horses derived from the model self-propulsion test. The r;^ of that test, at 20.5 kt, was 0.761

resistance increase of 4 per cent or for adding the

stock propeller used was 0.685 instead of the

full

scoop resistance, as was done in Sec. 66.9. of resistance for the appendages is

The augment

then taken as 5 instead of 10 per cent, (ii) to the (iii) Applying the 1.05-factor from

Rt

oi

(i)

preceding.

This

is

and the

t/s

only 0.968.

The

of

real efficiency of the

0.665 predicted by the estimate of

(viii)

Values of the propulsive coefficient

preceding. tjp

ABC

derived

transomstern model, for a range of ship speed from 9 to 23 kt, are plotted in Fig. 78.P. For comparison

from the self-propelled

test of the

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 78.17

Arrows Indicate -Desiqned Speeds I

r

Each Case

in

(I)

The procedure

895

for running the

model

self-

"1

propulsion test does not take full account of the increased roughness effect to be encountered on the ship as compared to that on the model, even when the ship hull is clean and new

I

I I

I

I

^G. Shor^ Design, ^193

I

EX- Ships

A

(II)

re-reading of the items previously listed

in this section indicates that all the differences

between the original calculated or estimated performance of the ship and the actual performance of the model are in favor of the ship design as represented by the model. IZ

14

13

15

16

17

18

19

20

Zi

22

3hip Speed, kt Fig. 78.P

vp FOB

Comparison of Propulsive Coefficient ABC Ship and Other Designs

Models of

there are plotted similar values for the arch-stern model, for the

TMB

ABC

model having a Cb of 0.60, and for three types of merchant vessels of outstanding performance, from Series 60

factors will carry over into the full-scale ship

on and at the magnitudes indicated by the

trial,

model

the period 1930-1955. Incidentally,

In other words, practically everything that has been done to develop the ship, from the time that it had principal dimensions and proportions only, has made it better than the "phantom" ship of the Taylor Standard Series form having the same proportions. To assume that all these favorable

Just

the Telfer merit factor of Eq.

Volume

based upon the model predictions from tests of the transomstern model, is (34.XXV) of Sec. 34.10 of

I,

shaft

test, is

expecting a great deal.

how much

TF(long tons)F^(kt)

=

model

0.61

L(ft)Ps (horses)

is

78.18,

tested

and

after

self-propelled

The lower graph

0.61

the transom-stern

510(13,243)

of Fig. 78.

ABC

the

new

Q

12.895

reveals that for

design the increase of

resistance for appendages, over

=

the modified

with

propeller designed in Chap. 70.

16,573(20.5)'

=

of

the preliminary design should perhaps be determined only after the model is modified as described in Sec.

M

of the indicated reduction in

power can be carried into the next stage

most

of the speed

range, averages about 5 per cent. This corresponds

made

an F„ of 0.2704, and an Fl is well above the meanline of Fig. 34.1, from which a value of about 9.5 was used for the first shaft power approximation of

to the estimate

of 0.07312, this value

However, in the vicinity of 22 kt ship speed, the effective power with all appendages is lower than the effective power in the bare-hull condition!

Sec. 66.9.

Since the ship will probably never run at this

For a r,

To

of 0.908,

return to an analysis of the behavior of the

transom-stern lated shaft

power

the foregoing of first cost

ABC

is

model, a reduction in calcu-

magnitude indicated

in

this

The

and operation. However,

it

means to

order, with

new weight estimate is in machinery and fuel weights, as well

as

displacement,

the designer that a overall

speed, except at light load

that are

appreciably

For a project that is being done thoroughly it may even mean a revision of the prehminary design and the running of additional model tests, on the basis that a revised hull of shghtly smaller volume will be as efficient as the diminished.

first hull.

However, before any radical steps are taken, the following items are to be considered:

when the immersed

hull has a different effective shape, the reason for

comforting from the point of view

of the

earlier in the present section.

anomaly

is

somewhat

of

an academic matter.

variations with speed in the ratio of

(1)

power with appendages to (2) bare-hull effective power shown by Fig. 78. Q indicate that the appendage resistance is probably related to wavemaking around the ship. Further than this effective

it

has not been possible to account for the unusual

feature described. It is considerably

more

difficult to

analyze the

TMB

model performance of the arch-stern design, 4505-1, because of its unusual hull shape and the almost total lack of reference data for such a form. Despite the drastic change in shape of the run from the normal transom stern, and an

HYDRODYNAMICS

896

IN SHIP DESIGN

16

14

Sec. 78.18

20

18

Ship Speed, kt Fig. 7S.Q

Desiqned Speed

Ratios of Effective Powers, With and Without Appendages, for Transom-Stern and ArchStern ABC Designs

The expected high wake

increase of bare-hull wetted surface of 5.8 per

cent over that of the bare transom-stern hull, the effective power

Pe

about 2 per cent lower than that of a Taylor Standard Series hull of the

at designed speed

is

same proportions. This

superi-

above the trial even more so than for the tran-

ority increases rapidly with speed

speed of 20.5 kt,

In

exist.

fact,

inside the arch did not

the w-value derived from the

was slightly higher than the anticipated value of 0.164. It was known that large thrust-deduction forces would be generated by tion fraction

the four strut arms lying in the outflow jet of the

som-stern hull.

Although the several appendages were designed with great care, the increase in resistance of 18 per cent due to them appears high. However, in

wetted areas of the exposed shaft, the strut hub, and the quadruple strut arms are not added to the bare-hull wetted area. Consequently, the pressure drag of these parts is certain to show up as a large augment of the specific residuary resistance Cr Subsequent discussion with designers of tunnel-stern shallowwater craft reveals that appendage resistances in this type of vessel are consistently high. this case the

.

When making

propeller calculations prepara-

propeller,

but

it

was hoped that these would be by the contra-

partly or wholly compensated effect

on these arms.

It is possible that there

as well as the thrust-deduction forces.

Nevertheless, the propulsive coefficient of over 0.68

is

extremely high for this type of stern, where

values of 0.50 are considered very good.

Analysis indicates that the real or working efficiency

tjq

of the large-diameter 24.22-ft pro-

peller at the designed speed of 20.5 kt is

0.750. This is higher

and 78.4, values of the probable wake and thrust-deduction fractions were determined by the Schoenherr formulas used for the transom-

cent, than the tjo for the 20.51-ft wheel model 4505 of the transom-stern ship.

in Sees. 70.6

On

this basis,

admittedly inadequate

but the only one available, the values derived were 0.273 for the wake fraction

for the arch stern

and 0.164 for the thrust-deduction fraction. For the designed or trial speed of 20.5 kt, the arch-stern self-propelled data from Fig. 78.1 are:

Propulsive coefficient np Wake fraction, 0.072

= P e/Ps =

Thrust-deduction fraction, 0.175 Hull efficiency rj^ = (1 - 0.175)/(1

=

0.889.

0.686

TMB

prior to the completion of the contract plans.

Nevertheless, the designer

it

is

who has

carried the

convinced that, given a

more time, he can modify and improve upon A few such improvements are

considerably.

In the 0.072)

of

Ship.

outhned here

-

about

6.5 points, or 9.5 per

Proposed Changes in Final Design of In the normal course of a building program for a multi-milhon dollar ship the design and model-testing procedure described in Part 4 represents only the early stages of the development

little

Effective power, 12,500 horses

by

78.18

ABC

ship along this far

Shaft power, 18,300 horses

were

upward components of velocity in the flow passing the two horizontal arms. This would have increased the appendage resistance appreciable

tory to selecting the stock propeller, mentioned

stern design.

self-

propulsion test was only shghtly more than onequarter of the estimated value. The thrust-deduc-

first

for the

ABC

ship.

place, the designed waterlines of

both alternative hulls have values of transverse moment of area It that are certainly on

square

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 78.18

the low side. Furthermore, the change of direction of the water flomng around and under the forward sections, forward of the ciuarterpoint at Sta. 5, is more abrupt than it should be. The almost obvious step is to widen the designed waterline still further in way of Stas. 3 and 4, following an

earher change, and to trim

away the

hull lower

in this region. This gives a better path to

The change the minimum value

reflected in a lowering

the water.

is

of

of the section coefficient

ahead

of the

forward quarterpoint. Sec. 67.10 is

rather

high for good design.

Sta.

this stage, a

10.3 or 0.515L.

The beam

at this section

(Sta. 10.6) fair ed to a value of 73.33 ft rather

73.0

The

ft.

As the

LMA

of

0.530L

design lane of Fig. 66.L

double

circle in

(it

still fell

hes to the

than

within the left of

the

that figure), and as the ship was

to have a transom stern which

made

it

easier to

obtain small waterline slopes in the run, this

The shghtly larger beam was accepted as the waterline curvature plot with this beam proved to have most of the desirable features. The final dimensions and coefficients of the ABC ships as built into the models

to find out just

now

they

The basis for this step what gives them the performance

have.

What

is

it,

for example,

thrust-deduction fraction

the

t

that

of

the

of 0.125 or 0.13 in the intermediate-.speed

range

to a remarkably low value of 0.07 in the normal

nearly constant

SNAME RD

sheets of Figs. 78.J

and 78.K.

wake

fraction

and propulsive

but the relative drops. There is a sUght

coefficient the hull efficiency rises

rotative efficiency

hump

in the

jj^

Cr curve

of the 400-ft ship in Fig.

T, of 0.68, probably because at this speed the ship is only some 2.5 Velox wave lengths long. There is a smaller but sharper hump at a 78. Jc at a

T, of about 0.83. For the 510-ft ABC ship the corresponding speeds are 15.4 and 18.7 kt. From Fig. 78.Nc it is noted that these humps occur

somewhat beyond the ends of the transition portions in the t and rfHT curves [where r^HT = ^^ = (1 - t)/{\ - w)]. Beyond 21 kt for the length

ship, at a T, of is

about 0.93, when the ship

approaching

propulsive efficiency

1.5

falls off,

wave as

it

lengths,

the

does in most

ships above the designed speed. However, the

superiority over the Taylor Standard Series hull, in

respect

to

resistance

and

effective

power,

increases in this range.

After the bUge-keel trace for the forebody had been determined on the model it developed that the combination of bilge-keel width shown on Fig. 73. N and the bilge-keel trace caused the outer edge of the keel to project beyond the in the upright position from Sta. 8 forward to about Sta. 6.5. The requirements of item (48) in Table 64.f call for no projections beyond the fair hue of the hull for the first 150 ft from the stem. Sta. 6.5 is about 166 ft from the FP. However, for ease in handling, the hull shape

DWL

(a)

to do to improve

transom-stern form to drop from a constant value

ABC

embody one

what

of the alternative designs?

also

should

is,

the hydrodynamic performance of either or both

value was accepted.

are given in the

7.5.

principal question

running range of 18 to 20.5 or 21 kt? With a

few details need to be watched but not necessarily corrected. One such relates to the midships portion of the designed waterline of the ABC ship. In the final fairing of the lines preparatory to making the model the maximum section fell at Sta. 10.6 or 0.530L rather than at

At

about Sta.

6.4 to

causes

attention to the fact that this

897

Retain the same leading-end taper but shorten

the keels, moving the leading ends aft from Sta.

is

down

calls

(c)

of the following modifications:

Determine whether the widenhig

of the

DWL

in the entrance, proposed earlier in this section,

would bring the present keels within the

DWL

limits. If not,

A

search for improvement obviously calls for

a careful determination and rather close study of the wave profiles and flow patterns around the hull

and into the propeller at the 16- and 18-kt

speeds, perhaps also at the 21-kt speed.

The fact that, despite an increased wettedsurface area of 5.8 per cent, the resistance of the arch-stern bare hull drops below that of the transom-stern bare hull at 28 kt, where the T, is about 1.240, is well worth looking into. The remarkably low resistance of both hulls in the 23- to 25-kt range indicates that these forms might well find application to shorter, high-speed vessels.

On the basis that, of the two alternative sterns, the transom-stern arrangement has selected itself, so to speak, the owner-operator now has two choices. Either

Taper the forward end of the keels to a greater extent and reduce the width back to at least

he may:

(b)

Sta. 8

(1) Hold the speeds originally called for, adhere to the schedule already set up, and reduce the

HYDRODYNAMICS engine power by a substantial amount, of the order of 15 or more per cent, or he

may

Step up the schedule, retain the engine power origmally estimated, and increase the ship speeds, (2)

both sustained and

trial.

The background

for

this

involves

decision

hydrodjTiamics in onlj^ a small way but it is useful to discuss that small mfluence. Consulting the speed-power curves of the transom-stern design in Fig. 78.Nc, and assuming no scale effect

between model and the ship can

make

ship, it is safe to

assume that power of

21.1 kt with a shaft

16,000 horses, retaining the former limit of 0.95

times the

maximum

designed shaft power. Step-

ping up the sustained speed to 19.5 kt, at which about 10,750 horses are required for deep-water,

clean-bottom conditions, means that this speed

IN SHIP DESIGN prising the large

Sec. 7S.19

ABC

ship of the early chapters

and the motor-driven tenders of Chap. 77, are carried only far enough to demonstrate the use of the various graphs, diagrams, and rules embodied in the text. The Hmited treatment in these chapters is by no means to be taken as an indication that the preliminary hydrodynamic design for an actual ship can or should be limited to that set down in this volume. Problems of maneuvering and of wavegoing are discussed more fully in Volume III, Parts 5 and 6, respectively. For example, considering first the features commented upon in the present chapter, relating to the ship

itself:

apparent from the position of the wave profile observed on the transom-stern model and drawn on the afterbody portion of Fig. 66.R that (1)

It is

can be achieved with a power expenditure of

the transom did not clear at the designed speed,

only 67.2 per cent of the 0.95-maximum limit.

despite previous indications to the contrary. In

This

fact, it did

stUl conservative planning.

is

At the 21.1-kt speed the Pe/Ps ratio drops to 0.75, and the hull efficiency vht to 1.14, with only small changes in the t and w values. At the 19.2-kt speed these factors have about the same

not clear fully until the speed was far

m excess of any speed that the ship could reasonably have attained.

The

reason appeared to be

the large upward component of flow in the water just below the lower edge of the transom. Never-

may

a resistance some 4 per cent less than that of a Taylor Standard Series model of the same proportions there appeared to be no reason for changing the existing transom stern without the benefit of a further extended study. In any further development of this design, studies of the separation drag abaft the transom, mentioned in (2) of Sec. 78.6, should be pursued.

not be sufficient to make the increased power economically worth while.

lower (horizontal) strut arms in the arch-stern

values as at 18.7 kt. In other words, the ship

is

running efficiently, in the higher range, so far as speed and power are concerned. The rpm's increase from 110 to 114 at the higher trial speed but this permits smaller and Ughter gears than stUl

were originally involved. To be speed

is

slightly over 4 per cent

The

sure, the sustained

increased only 0.8 kt, an increase of but

from 18.7

kt.

This

history of mechanically driven vessels, ex-

tending back for more than a century and a is

half,

replete with instances of re-engining at greater

may have been due to inand in displacement. Much of it was undoubtedly to reduce fuel consumption by the use of more efficient machinery. Not a Uttle was carried out to increase the sustained speed, so as to keep pace with newer ships. The economic features are not discussed here, but the ship that benefits the most by this re-engining is the one which has a speed margin designed into the hull in the first place. It is a good sign, in a way, that powers.

Some

of this

creases in load

the

ABC

a better performer at higher speeds than at the speed for which it was designed. 78. IQ

ship

is

Comments on

Illustrative Preliminary-

Design Procedures of Part 4. The illustrative examples worked into Part 4 of the book, com-

theless, ^\ith

(2)

The

so-called neutral positions of the

two

design should have been estabhshed before the

design of the quadruple strut-arm and hub assembly was finished and this appendage was added to the model. The small-scale assembly could readily have been constructed to permit changing these positions on the self-propelled model, or some special means could have been provided whereby the flow in this region could have been observed in greater detail during the circulating-water-channel test. (3)

No

attempt

is

made

required to

move

book to power that would be

in Part 4 of the

calculate or estimate the

the necessary

amount

of cooling

water through the main condenser at the designed ship speed.

Considering next a few of the ship features in the early chapters of this part, and not Avorked out adequately there:

mentioned

MODEL-TESTING PROGRAM FOR A SHIP

Sec. 78.19

made

Furthei' studies should be

(i)

of the internal

arrangements, supplementing the discussion in Sec. 66.32, to enable the vessel to float at the

mtermediate-load 66. T.

indicated

waterlines

in

Fig.

These should be combined with studies

of

able,

899

the lowest speed at which the 24-kt

of

V-bottom

would actually plane, when carryload. This would indicate whether the craft could still run in the planing range if slowed by wind and sea, as mentioned ing

hull

the

specified

the effect of the variable weights, hi each of the

in (3) of Sec. 77.6.

proposed arrangements, upon the bending moments imposed on the hull structure,

(b) For the examples cited, involving motorboats which are to be in the water only for the hours in which they are required to run, the additional weight due to water soakage is not a problem. Nevertheless, this item must be considered for motorboat designs in general. (c) It is possible that for a motorboat, on which the propelling machinery receives much less care than on a large vessel, the reduction from maximum rated power to maximum sustained usable power should be considerably larger than 5 per

Estimates should be made of the effective

(ii)

and shaft powers and probable speeds in the variable-load conditions, for both deep and shallow water (iii)

The sinkage

of the

bow

at designed speed,

indicated on Figs. 58. B and 66. R,

The widening

as proposed in the

improve (iv)

A

is

rather large.

of the designed waterline forward, first

part of Sec. 78.18, should

this situation.

study,

much more comprehensive than made of the effect of

that of Sec. 60.15, should be

fouling on the total resistance, on the

thrust-deduction

and the propeller

fi'actions,

(or shaft)

wake and

the propeller thrust,

power.

There was no time or opportunity to design, lay out, and test a third alternative stem for twinscrew propulsion of the ABC ship, as mentioned in Sec. 69.5 on page 571. With respect to the preliminary hydrodynamic designs of the two small motor-driven tenders for the

ABC

ship, serving as the illustrative designs

treatment given there is likewise abbreviated. For a well-rounded project, even of this limited scope, a number of additional items should be considered: in

Chap.

(a)

A

77, the

determination, by the best methods avail-

cent of the former, as

recommended

for large

vessels (d)

For

the

particular

illustrative

examples

a comprehensive preUminary design should include a check on the fore-and-aft trim with full fuel and crew but with no cargo or described,

passengers (e)

An

adequate preKminary design for a fuU-

planing boat should include an estimate of the vertical

and pitching moments

forces

to

be

expected from propulsion devices carried at the stern

Definite steps should be taken to reduce the (f) running trim of a 35- or 40-ft motorboat which, as indicated in the early stage of the preliminary

design for the

ABC

The trim hmit

tender,

is

as great as 5 deg.

in this respect probably should

diminish as the absolute size of the boat increases.

APPENDIX

1

Symbols and Their Titles Xl.l X1.2 X1.3

General List of

Symbols and

Titles

Abbreviations for Positions and Conditions

Xl.l

General.

This appendix

lists

.

all

900 900 911

the

symbols employed in the text of Volume II except for a few used and described or defined locally and not having general application. It is identical, except for one or two deletions, a few additions, and minor modifications in titles, to the list of symbols and their titles in Sec. XI. 5 of Appendix 1 of Volume I, pages 597-611. Notes relating to prior approval of these symbols, subscripts for use with them, the method of indexing, and abbreviations accompanying them are found ui Sees. Xl.l, X1.2, X1.3, and X1.4 on pages 596-597 of Volume I and need not be repeated here.

much more comprehensive and terms, with complete definitions, in the form of a "Nomenclature for Hydrodynamics as Applied to Ship Design," will appear It

list

is

expected that a

of symbols

16

Greek Alphabet.

X1.4

Abbreviations for Physical Concepts Having

X1.5 X1.6

Abbreviations for Units of Measurement

Scalar Dimensions Circular Constant Notation

.

.

911 912 913

— SYMBOLS AND THEIR TITLES

X1.2

Sec.

— of a screw propeller Ap —Area, projected blade, a screw prooutside the boss or hub Ap Au— Propeller D. W. Taylor, ^0

^Area, disc,

of

peller,

coefficients of

,

When T

dimensional in character.

n

Ib-ft,

revolutions per sec,

is

Va

Q

in lb,

is is

is

in

in ft per sec,

P and D are in ft, Ap = (P/D) (55.0330,,)/ - s^y and Aa = (P/D)(8.7587Cr)/(l - s„)'

and (1

[Taylor, D. W., S

and

P,

1943, p. 101;

vertical

movable control

—Area, —

a rudder or other

of

surface, lying generally

projected, of stern diving planes of

a submarine Au Area, immersed transom, projected on a transverse plane; this does not necessarily correspond to that embodied in the area ratio fn of D. W. Taylor

A

tr

—Area,

in

ship,

the body

after perpendicular

waterplane, of a ship floating on

—Area, maximum transverse

Ax

5„

—Beam at the chine, at any designated a V-bottom planing craft jBc(Mnx) — Beam at the chine, maximum, wherever occurring on a planing craft Be—Beam, extreme, wherever occurs on the main above or below the designed waterline Bm —Beam, designed waterline, at midlength between perpendiculars Bp Bu— Basic propeller design variables of D. it

hull,

,

is

Ad/A^

maximum

is in ft

—Beam, designed area Brx—Beam, maximum, underwater body, wherever Bwx—Beam, maximima,

to

the

of

ler

Ax

ratio, referred

som is at the AP, this is the value of / dA/dL Rate of change of section

— dA/dx—Rate

the tran-

at the

B/Bx

h

tip

change of section area with

tip

cantilevered

at designed waterline,

occurs along the length

—Aspect

ratio of a hydrofoil of

when

any

—Ratio

beam

of the designed waterline

maximum

at the section of

Bx/Hm — Ratio, draft H^f

Bx/d

;

—Ratio,

Bx/Hx maximum

area;

area

beam-draft, is

based

on

the

the alternative form

beam-draft, at the section of

Bx/dx

is

the alternative form

c

— Celerity or velocity of a wave with respect

referred

it

occurs,

=

VgLw/{2T)

—

Chord length of an airfoil or hydrofoil, such an expanded propeller-blade section, a rudder blade, a fin, or other device; alternative symbol I c

as

—Breadth or width in general —Span of a hydrofoil, to when

the immersed or occurs

any section to the designed waterline beam

at

area with

to cartesian coordinates

h

it

of it

to the undis turbed hquid in which

distance along the x-axis of a ship,

s^Y'

AP.

length along the ship of

ft.

kind; also b^/An

mean If

are in

waterline, at the section

wherever

peller

area

D

and

maximum

b^'/Aproi

maximum

P

designed waterhne, of the immersed

Bx

of

ratio of

—Immersed-transom-area

in revolutions per sec,

is

Bu = (I>/P)(9.4835VCr)/(l - s^y

—

ratio of a screw pro-

A u/Ax

per sec, and

Bu Beam,

a screw pro—Expanded-area Al/{LHm) —Lateral-area ratio a surface ship Ap/Ao—Projected-area ratio of a screw propel-

to the section of

n

Bp = {D/P){23.772VCo)/{l -

peller

As/Aa

in Ib-ft,

transom

area

—Developed-area

is

and

using a lower-case subscript

section of

Q

in lb,

y-z plane, preferably indicated in the latter case

A WA —Area, waterplane, of afterbody Awe —Area, waterplane, of entrance A WF —Area, waterplane, of forebody A WR —Area, waterplane, of run A IAx— Section-area ratio, referred

When T

Taylor, dimensional in character.

Va

underwater body of a ship floating on the surface; submerged body or ship such as a submarine, the maximum area as projected on the transverse

,

Bouss inesq number, expressed as U/ \^gRn

station, for

section, of the

for a

A^

in equilibrium with the gravity force

or not

W.

the surface; not to be confused with A,

as

is

Be

projected,

parallel to the ship centerplane

As

—Vortex spacing, longitudinal, a vortex B—Beam at the designed waterline, at any designated station B —Buoyancy force on a body or whether h

street or trail

PNA,

1939, Vol. II, p. 141].

Ar —Area,

901

tip, or

Ch

support to

—Shallow-water wave speed, in depth h —Critical wave speed or velocity in shallow

Cc

water of depth

h,

= wgh

HYDRODYNAMICS

902

— Celerity of an any medium Cm — Chord length,

elastic or

Cs

in

hydrofoil, or of the

mean

compression wave of

a

expanded blade sections

of

average,

or

a screw propeller outside the hub Chord length, root, of a Cr

—

hydrofoil; also the chord length at

— Chord length, Cx — Distance from point

of

tip, of

maximum

midspan

of a

lb,

P

Q

and

D

are in

the leading edge to the of

a

n

in Ib-ft,

is

Cp Crj

hydrofoil

=

=

52.889(P/Z))Cg

coefficient

—

of

lift

Ca

— Coefficient,

Admiralty; the value of the

dimensional expression A'''F7P,(or A'^^FVP^), where is the weight displacement in tons of

A

salt

water

Cb— Coefficient, native sjmabol

Cc

—

= V/iLB^Hx);

block,

alter-

5 (delta)

Coefficient,

NOTE under Cd Co— Coefficient,

cross-force,

=

C/{qAL); see

=

D/(().5pAUb)

=

Co— Coefficient,

and P, 1943,

is

=

torque,

dimensional and

D and R, U and V interchangeably.

It is also possible, for special

work, to substitute

A

any expression having the same dimensions, such as (BH), L^, B^, and H^, provided this is explicitly stated. The symbol q for ram pressure

for

signifies 0.5pf7j or

0.5pVr

.

=

S/VVL = S/VVL

— Coefficient,

drag or resistance, = NOTE under Cc In this particular case, the use of the wetted surface S is arbitrarily taken as the standard; the use of any other value equivalent to (length)^ is covered

Ct

= Cp

Rr/iqS)

by a

+

total

C„

;

see

.

special note.

efficient is

or

dimensional and

— Coefficient,

T/(n'D^P'). This cois

Cw — Coefficient,

— —

mean or average — drag, = Dp/(qS); see NOTE under Co Cj — Coefficient of reduction, of a rudder or Coefficient,

specific

called the &-Froude

=

load, of a planing craft,

W/{wB^); the symbol Cld

Cw

becoming obsolete.

speed, usually of a planing

= V/ y/gB; preferably beam-Froude number

preferred

is

designed

Coefficient,

=

waterplane,

Aw/{LBx); alternative s3Tnbol a (alpha) maximum section, Cx Coefficient, Ax/{BxHx) Cy Coefficient, relation, = Cp/Cw C,

Cp

Q/(n'Z)'P'). This

is

craft,

possible to use

PNA,

101;

— —

Cv

the mathematical expression for this coefficient, as for many others in the list, it is

p.

becoming obsolete. Ch Coefficient, residuary drag or resistance, = P«/(?S) = Ct - Cp; see NOTE under C^ Cs Coeffi cient, wetted -surface, dimensionless,

D/{qA)

NOTE:—In

;

S!,)Cr

1939, Vol. II, p. 141].

Cr— Coefficient, thrust, = drag,

-

8.4175(P/Z))(1

a hydrofoil section

C Cross force, normal to both the direction of motion or resultant liquid flow and the direction

in

and

ft:

[Taylor, D. W., S

—

is

in revolutions per sec,

is

measured parallel to the base chord Distance from the leading edge to the Cz position of maximum camber of the meanline of

section,

When T

Taylor, dimensional in character.

a hydrofoil

thickness

X1.2

Sec.

—Coefficient, yawing moment, = N/{qAL); see NOTE under Co Cp — Coefficient, prismatic, longitudinal, = V/(LAx)', alternative symbol 0(phi) Cp Cu— Coefficients, propeller, of D. W. Cn

,

cantilevered

symmetrical-planform hydrofoil Ct

IN SHIP DESIGN

— —

flow,

Coefficient,

=

shearing

stress,

in

=

viscous

r/q

—

friction

Cam -Coefficient, added mass, of entrained water around a body or ship, as related to the

control surface; the ratio of the actual torque

ship

on a ship rudder stock to the torque calculated for the same rudder angle and relative speed in open water

area inside a bilge diagonal to the area [L(BDI)]

Ck

— Coefficient,

rolling

moment,

=

K/{qAL);

NOTE under Cc Ci— Coefficient, Hft, = L/{0.5pAhUb) L/iqAn); see NOTE under Cd

— —

M/(qAL);

see

NOTE

under Cc

— Ccp —

Coefficient,

bilge diagonal; ratio of th e

center

pressure,

of

hydrofoil; ratio of (the distance

=

a

c)

— Coefficient, dynamic of = W/{qB"-) = 2{C^o)/Cl CtL — Coefficient of square moment Cdl

for

from the leading

edge to CP) to (the chord length

see

midlength section, Cm Coefficient, Am/{BmHm); alternative symbol /3(beta) pitching moment, Cm Coefficient,

mass Cbd Coefficient,

lift,

a planing

craft,

=

waterplane for pitch,

=

=

of area of

/^/[(L'B.0/12]

=

I^/

(0.083L'B;f)

CiT

—Coefficient

of square

moment

of area of

Sec.

SYMBOLS AND THEIR TITLES

X1.2

waterplane for

=

roll,

=

/7./[(J5.yL)/12]

/,./

— —

former

Clf

=

Coefficient, lateral area, Coefficient, load, of

W/{'wB^)] is

A,^/{LHm)

a planing

symbol

alternative

Cw

is

craft,

but

= the

preferred

— Coefficient,

local specific friction drag, as

distinguished from

Cf

,

the

mean

or average

coefficient

— Cp E— ¥e/{LeA^) Cp — ¥p/iL,AM) CpB — CpA

prismatic,

afterbody,

=

Coefficient,

prismatic,

entrance,

=

Coefficient,

prismatic,

forebody,

=

Coefficient,

Va/{LaAm)

F

Coefficient, prismatic, run,

= Vp/{LkAx)

= Cpr— Coefficient, prismatic, vertical, V/(AwHx) = Cb/Cw = (Cy.Cx)/Cn. alternative ;

symbol

<^

v

Cj.L— Coefficient, thrust-load, NOTE under Co

=

T/{0.5pAoVl);

see

CvM

— Coefficient,

virtual

mass, in transient

flow or motion conditions; the ratio of the mass

body or ship and the surrounding enbody or ship.

of the

trained water to the mass of the

This of

coefficient,

equal to

added mass Cam

CwA

,

— Coefficient,

is

LO

plus the coefficient

always greater than unity.

waterplane,

afterbody,

=

—

waterplane,

— Coefficient,

waterplane,

C w E Coefficient, Awe/{LieBx)

=

entrance,

— Awr/{LrBx) C ws —

Coefficient,

forebody,

=

waterplane,

run

=

wetted surface, of D. W. Taylor, = S/ "v/AL, where A is the displacement in tons of 2,240 lb of salt water of sp.gr. L024 (35.075 ft^ per ton) and L is the mean immersed Coefficient,

length in ft

CpvA

— Coefficient,

H

vertical, is

after-

the draft at

—

length of the entrance

— Coefficient,

differential

slope,

total;

H

vertical, is

fore-

the draft at

Dw — Drag,

run

and

all

other

types

of

wind; the downwind force exerted wind on a body or ship, to be

relative

distinguished from the axial component ffwiod

—Diameter steady-turning path —Diameter, d/D —Boss or hub diameter fraction a screw propeller for a ACp — Roughness allowance, DsT

of

tactical

Dxact

of

specific,

body

or ship, to be

plate,

added to the smooth,

flat-

turbulent-flow specific friction resistance

coefficient

An

—Streamline

spacing

or

stream-tube

width, normal (transverse) to the direction of flow

— Differential pressure increase or decrease, resistance due to presAR —Augmentation sure from a propulsion device spacing, along the As— Equip flow direction diAU—Differential velocity increase or deAp

of

effects

otential-line

of

crease, finite

—

CpvR Coefficient, prismatic, vertical, run, = ¥r/{AwrII), where H is the draft at midlength of the

friction,

separation,

pressure,

ds,

prismatic,

= ¥f/{AwfJI), where midlength of the forebody body,

of

blade-circle,

finite

CpYE Coefficient, prismatic, vertical, entrance, Ve/{.AwbH), where H is the draft at midCpvF

H

— — — — during a test at the ship point self-propulsion Db — Diameter, of a paddlewheel De— Drag, separation, due to pressures in a separation zone Dp — Drag, friction D„ — Drag, hydrodynamic Di — Drag, induced Dp — Drag, pressure Dji — Drag, residuary, = Dt — Dp of a floating body on an Ds — Drag, inclined liquid surface the sum of the Dt— Drag,

dn,

prismatic,

body, = V a/{AwaH), where midlength of the afterbody

=

H

—

by the

A wf/{^fBm) CwR

rf— Draft of a floating body or ship; alternative symbols and T; is preferred dx Draft of a floating body or ship at the section of maximum area; alternative symbols Hx and Tx D Depth, molded, of a ship hull D Diameter in general; diameter of a body of revolution or of a propulsion device D Drag, as a force opposing motion in a liquid Df Towing force appUed to a ship model

drags due to relative liquid motion

A wa/{LaBm)

CwF

— Mean-width ratio of the blades of a Ct/cr — Taper ratio of a cantilevered hydrofoil d— Diameter, boss or hub, of a screw propeller

Cm/D

screw propeller

(fi.083B^L)

Cla Cld

903

e

—Base

of

example, log.

Napierian or natural logarithms; for

D

HYDRODYNAMICS

904

—Vapor pressure of water E— Energy; work E„ —Euler number or pressure =

p/q

(p

-

p»)/5

coefficient

=

= Ap/9 airfoil

trail

according

to

Rf = fSV";

W.

Froude,

the

in

equation

this is dimensional

—A function /— Ordinates, back and or of an hydrofoil /— Ratio the section area at an end perpen/

face,

airfoil

of

dicular to the section area at midlength. This

W.

D.

is

Taylor's "/" [S and P, 1943, p. 65]. Ratio of the section area A at the FP to

fs — midlength the section area Am fo — A function applying to a group of geometrically similar bodies or ships /b —Ratio of the section area A at the AP to sit

the section area

Au/Ait

A^

at midlength.

equal to /r only transom Hes at the AP. is

The

ratio

the immersed

if

Head,

of a planing craft

in

ha>

of infinite

submerged body or submarine, top to bottom, or deck to keel

—

hw/Lw Steepness ratio of a wave 77—Head, total, Bernoulli, = [Uy{2g)]

+

p/w

H—

+

the same as the Head, total, sjrmbol hr

Draft of a floating body or ship; alternative symbols d and T Shape factor of a boundary-layer velocity profile, = d*/d, where 6 is momentum thickness

H—

H^ — Draft,

aft; generally

measured at the

after

perpendicular

Hd— Drag,

keel, as

a vertical distance, repre-

senting a difference in drafts at the forward and

when

the keel line

is

extended

forward perpendicular

IJ

Hp — Draft,

Hm — Draft,

Hx — Draft h/B h/L

of

any given

blade, so that

Q = FJi for that blade Damping force F

— —Inertia force Fy — ^-Froude number;

mean, at midlength immersed transom at section of

native symbols dx and

propeller,

of

forward; generally measured at the

Hu— Draft,

exerted tangentially in the plane of the disc at

Ft,

extreme, wherever occurring along

beam = V/ 'VgB = the

is

CP

h;

the length

—Submergence-Froude number, where h = I'wgh = VI's/gh —Blade-disc force a screw

the depth of submergence,

of the

H

—Head, velocity, = U^/(2g) hv — Head, vapor, of a liquid hw — Height of a wave from trough to crest — Head of liquid an undisturbed stream extent A (pronounced hull height) — Hull height of a

= U/ 'VgL =

specifically,

R

total, Bernoulli, sjonbol

same as the

hu

He — Draft,

—Froude number; in general, Ft — 6-Froude number;

the radius

h,

the

;

to those perpendiculars

F„

F,,

X1.2

total,

and velocity hu

,

after perpendiculars

F— Force in general F—Freeboard

Froude number

Sec.

—Head, pressure, due to pumping, = pe/w, as distinguished from head due to gravity including hydrostatic hr — Head, pumping hp

— Camber of an or hydrofoil (6th ICSTS symbol); also m for meanline camber / — Frequency; eddy frequency in a vortex street or /—Friction coefficient of a surface in water, /

IN SHIP DESIGN hp

e

—Hull-height to

maximum

Tx beam

area; alter-

ratio of a

body

—Hull-height to length a body Hp/L—Slope a ship with a designed ratio of

of keel, in

drag; keel-drag ratio

—

Fi

specifically, the

volume

Froude number,

i Slope of a line defining a form, with reference to a specified or selected axis or plane; may be expressed as an angle in degrees or as a natural

tangent Ib

—Acceleration due to gravity = w/p G— Girth, measured generally from the

g

linear,

DWL

—Slope,

in

—Slope,

diagonal,

with reference to inter-

section of a diagonal plane Ie

—Depth in general; depth submergence h — Head, hydrostatic, hydraulic, or potential;

h

bowline or buttock, with reference

to baseplane

of

of

—Slope,

and the centerplane

waterline, in entrance, with refer-

ence to centerplane, neglecting local shape at the

a body or ship, such as a submarine

stem; alternative symbol {l/2)aj!

height or depth of liquid

reference to baseplane

ip

—Slope

of

floor

(bottom

of

ship),

with

SYMBOLS AND THEIR TITLES

X1.2

Sec.

—Slope, waterline, centerplane —Slope, section t/e

in run, with reference to

ships,

with reference to baseplane; this slope becomes greater than 90 deg in way of a tumble home line,

is

—Slope, waterline, general / —Square moment area that plane about an axis area II —Square moment Iff

of a plane surface

of

of of a waterplane about the transverse axis through CF, for pitching motion It Square moment of area of a waterplane about the longitudinal axis through CF, for

—

/jj

through an axis x-x in that plane

—Advance

J

number, or

coefficient,

Fx/(nZ)); F^/CnZ))

is

ratio,

=

the alternative

—Moment of inertia of the mass of a body or

ship; this is a true

moment

of inertia as

com-

pared to the square moment of area of a plane surface denoted by I Jl Moment of inertia of a body or ship for

—

pitching motion, about an axis transverse to the

plane of symmetry

—Moment inertia of a body or ship for about a longitudinal axis inertia about the J^ Jy J, — Moments and 2-body axes, respectively a body Jjj — Moment of inertia of the mass about an axis x-x Jabs X(lambda) — Absolute advance Jt

of

rolling motion,

x-,

of

,

,

Kr//fo—Thrust-torque

y-,

of

coefficient,

,

number, or

ratio,

= UA/iimD) = V A/{TrnD) =

factor

— Chord length of an symbol L— Length, the principal

I

= TD/Q

airfoil

or

hydrofoil;

c

sion of a ship;

any

longitudinal dimen-

characteristic length, specified

in detail; for special study, the length on the

surface waterline ship, at

—

WL

of the

immersed form

of a

any draft and trim

Lift as a force,

when generated by a com-

bination of circulation and uniform flow or by a deflected flow

—Length, afterbody, = L/2 — Length, projected, of the area bounded by the chine of a planing craft dynamic, due to planing action Ld — Le —Length, entrance, from FP to section of Lx Lc

Lift,

maximum

expression

J

T/{fm'D')

L

motion

—Square moment of area of a free-water surface, with axes defined for each case —Square moment of area of a plane surface Iw

UJ{nD) =

not yet worked out for the general case = coefficient, non-dimensional,

Kt—Thrust

alternative

in

rolling

905

a surface or area density factor and other relation-

area or to forward end of parallel

middlebody

—Length, forebody, = L/2 — hydrodynamic Lm — Length of model, as distinguished from ship length Ls Lp — Length, parallel middlebody, of constant shape and area Lr —Length, run, from section of maximum Lp

Lh

Lift,

area or after end of parallel middlebody to termination or other designated point

WL

— — or trough to trough to hydrodynamic for Lbf —Length, analysis, as defined LoA —Length, overall or extreme, wherever

Ls Length of ship, as distinguished from model length Lm Lw Length of a surface gravity wave from crest

crest

effective,

locally

fc—Constant of k

capillarity (6th

ICSTS symbol)

—Fractional value, at any point in a propul-

sion device, of the ultimate induced velocity Ui far astern

—Radius of gyration —Surface roughness height, average; height above a smooth reference surface —Radii of gyration about the and z-body axes, respectively a Hquid K—Bulk modulus K—Rolling moment about longitudinal x-axis non-dimensional, = Kq —Torque Ks —Equivalent sand roughness; requires also k

hill

fc

k^

,

ky

,

x-, y-,

fc,

of elasticity of

coefficient,

occurring on the main hull, in a direction parallel to the longitudinal axis Lpp Length between perpendiculars (6th

— — — WL —Length, on designed waterline beam-fineness L/Bx— Length-beam greater than unity L/D —Lift-drag depth-fineness L/D — Length-depth greater than unity L/D — Length-diameter or fineness

ICSTS symbol) Lws Length, mean wetted, of a planing LwL Length, on any given waterline

craft

Lr,

ratio;

ratio,

ratio

ratio;

ratio,

ratio of a

body

of revolution, greater

than unity

2

HYDRODYNAMICS IN SHIP DESIGN

906

—

L/h Length to merged body

m— Camber airfoil

hull-height ratio of a sub-

ordinates of the meanline of an

or hydrofoil section,

reckoned from the

base chord

m—Mass or ship,

in general,

= W/g;

mass

of

a body

= A/g

— —

m Metacentric height, = GM, for use in mathematical formulas m Strength of a source or sink, such that the total volume of Uquid per unit time flowing from a 2-dimensional source of unit depth is 2;rm and from a 3-dimensional source is 47rm lUx

—Camber ordinate, maximum, of the mean-

of a hydrofoil or

line

blade section, reckoned

from the base chord Merit factor of E. V.

M— Telfer, described in Sees. 34.10 and 60.13 M—Moment, pitching or trimming, about the y- or transverse body axis M„—Mach or Cauchy number, for relating the speed of a body around which flow is being studied to the speed of elastic waves in the surrounding liquid

— —

Mcs Moment exerted by a control surface about a principal axis of a body or ship TOx/c Camber ratio of a hydrofoil n n

—Index or exponent in general —Rate of angular rotation, speed, or velocity,

generally expressed as revolutions per unit time; alternative

symbol w(omega), generally expressed

as radians per unit time

—Tuning factor; ratio natural period T of T^ waves —Angular rate of rotation of a propulsion device open water An—Streamline spacing or stream-tube width, normal to the direction of liquid motion N—Moment, yawing, about deck-to-keel or n

of

ship motion to period of encounter

of

rio

in

Sec.

XI.

general; any force p—A pressure intensity per unit area Pa — Pressure, atmospheric Pc — Pressure, bubble or cavity Ph —Pressure, hydrostatic Pi — Pressure, impact Po — Pressure, ambient; see also Pah and p„ Pp —Pressure, pumping + Ph) = sum Pah —Pressure, ambient, = in

{jpA

of atmospheric

P-

and hydrostatic

pressures; see also

—Pressure, absolute —Pressure, ambient, of the Uquid in an un-

PAb. Pco

disturbed stream, at a great distance from a body or ship; this

is

an absolute pressure unless other-

wise indicated

±Ap—Pressure, tive,

differential, positive or negareckoned from the ambient pressure p„ Pitch in general; pitch of a propulsion

P—

device

P—Power

in general

—Planing number, = Dt/Ld Pb —Power, brake or towrope, = RV Pe —Power, Pf —Power, Pi—Power, indicated Pp —Power, propeller, = 2xQn; formerly known as deUvered power = 2irQn plus shaft Ps —Power, P„

effective

friction

shaft,

friction

power

Pj.— Power, Pef Pitch,

thrust,

= TV a = TVs

— when exerting zero net thrust P/D —Pitch ratio of a propulsion device q—Angular velocity in pitch about the y- or transverse body axis q— Dynamic pressure at a stagnation point Q; ram pressure, expressed by or (O.SpV^) flow in terms a Q— Quantity rate effective,

(0.5pf7^)

of

of

of

volume per unit time, where Q

liquid,

=

V/t; output

of a source or input of a sink

Q —Torque,

specifically,

torque applied at a pro-

—Friction of a surface in water, according to R. E. Froude S] — Amidships in general S]pp — Amidships, defined as the midlength between perpendiculars ^wL —Amidships, defined as the midlength on

Qo Torque of a propulsion device in open water Qs Spindle moment or torque, on a con-

waterline; alternative SJntrz,

exerted about the stock axis

coefficient

p

—Angular

longitudinal

velocity in roll about the x- or

body

axis

pulsion device

— — propeller Qcs — Control-surface

trollable

r

hinge or stock torque,

—Angular velocity in swing or yaw about the

deck-to-keel or 2-axis

}

SYMBOLS AND THEIR TITLES

X1.2

Sec.

R —A radius in general R — Resistance, as a force, r,

D

a liquid; alternative

—Reynolds number in general, = UL/v = Vhlv Rb — Reynolds number for propeller-blade secZ2„

where the velocity term

tions

is

the nominal

liquid velocity past the blade section

space term

and the

the expanded chord length at 0.7R.

is

Here FBUd, = {Vl + [2Tn{0.7R)f\''' and R, = [(Co.7ie)(FB,.ae)]/''. Rj d-Reynolds number, with the diameter or width D as the space term, = UD/v = VD/v x-Reynolds number, with distance x abaft i?i the leading edge as the space term, = Ux/v = Vx/v Rs 5-Reynolds number, with boundary-layer thickness 5 (delta) as the space term, = U8/v = VS/v Re Radius of curvature of path or turning

— — —

— Rf — Resistance to motion, friction Rh—Radius, hydraulic, of a channel; the area

circle

of liquid in a transverse plane divided

wetted perimeter Rj Resistance,

by the

ideal,

self

total,

tion,

and

sum

all

1

ratio, real

of the friction, pressure, separa-

other types of resistance due to

motion Rw Resistance due to gravity wavemaking ^wind Resistance, wind; the axial component of the force exerted by the relative wind on a

relative liquid

— —

true,

[F^/(n/-')]

1

-

of

in

= fL/U,

as the significant dimension, is

where /

the frequency of eddies shed behind a body

and forming a vortex street or trail Sj d-Strouhal number, based upon diameter

— = fD/U Sb — Surface, wetted, surrounding the bulk volume of a body or ship D. W. S/ VAL—Wetted-surface

D

as the significant dimension,

coeflBcient of

Taylor, where

A

is

the weight displacement in

tons of salt water, as defined under A/(0.010L)^;

the

sam e

as

Cws

S/y/VL —Wetted-surface

non-di-

coeflScient,

mensional; the same as Cs

S/F'^'—Wetted-surface

to (volume'^') ratio

—Temperature general D. W. Taylor, as applied —Terminal and a section-area curve; see to the shape —Thickness in general; thickness an in

t

— of a model run at the -propulsion point, = Rt — D, ship Rp —Resistance, pressure, due to forces acting normal to a surface Rr —Resistance, residuary, = Rt — Rf Rs — Orbit radius of the circular motion of a surface particle in a gravity wave Rs — Resistance, separation of a body or ship to Rt — Resistance, motion; the

= = — —Slip or [V,/{nP)] As—Equipotential-line spacing, equal to An, measured in the direction liquid motion S —Surface area general; surface, wetted S—Velocity, discharge, of stack or exhaust gases S„ — Strouhal number, in general Si — Z-Strouhal number, based upon length L Sr

opposing motion in for drag

907

ratio of

t

tg

ts

of

of

t

airfoil

or hydrofoil section

<—Thrust-deduction

fraction,

—Time general —Terminal

=

(T

-

Rt)/T

in

t

ratio of

Ie

W.

D.

Taylor, as applied

to the section-area curve at the

FP

[S

and P,

1943, p. 65] ta

—Thickness

of a screw-propeller blade, pro-

jected to the shaft axis; see

SNAME

Tech. and

Res. Bull. 1-13, 1953, p. 22 ifl— Terminal ratio of D. W. Taylor, as applied to the section-area curve at the AP, in the same

manner

as for ts

—Maximum thickness

of

any

selected hydro-

body or ship, along its a;-axis; to be distinguished from the downwind drag Dw

foil

Rso wave RsA

Draft of a floating body or ship; alternative and d symbols T Thrust; usually ahead thrust; specifically,

—Radius the —Resistance, of

rolling circle of a trochoidal

tx

section

r—

H

still-air;

the wind resistance

due to ship speed alone through

still

air

— thrust developed by a propulsion device T—Time or period a complete cycle; natural of

s—Space

or

distance

in

general,

along

a

straight line or curved arc s

—Specific gravity of a

liquid, non-dimensional,

represented by the ratio [Weight (or mass) of a given volume of the Kquid]/ [Weight (or mass) of

period of oscillatory ship motion of any kind

T,—Taylor quotient, = V/ VL, L in ft; this is dimensional J' (pronounced

{

the

same volume

Sa

—Slip

of

=

1

¥^

,

Ty

,

¥,

—

[V/{nP)]

F

is

in

toll)— Towline tension in general of towline tension

—Components

relative to the x-, y-,

pure water]

ratio, apparent,

where

kt and

a body or ship

and

z-axes, respectively, of

E

HYDRODYNAMICS

908

Te

— Period of encounter of waves, referred to —Thrust, exerted on a ship by a

a ship or other point

T

IN SHIP DESIGN

=

r(l

—

propeller direction —Velocity, linear component longitudinal or x-axis a body or ship general; U, V— Velocity or speed

u

of, in

of

specifically,

in

body or measurement

or speed of the

ship V, irrespective of units of

UAfVA, y E —Velocity

or axial speed of ad-

vance of a propulsion device, reckoned in the direction of motion of the device, = U — Uw = V - V^ = U{1 - w) = F(l - w) Ui Velocity, induced, at a great distance astern of a finite-length hydrofoil with circulation

—

Vg

Ur,

—Velocity

or speed, resultant, of the

flow approaching a hydrofoil, taking account of

induced velocity

—Relative impact or striking velocity —Velocity or speed, the blades of a propulsion device, = imD Uw Vw —Velocity or speed, wake, resulting Us Ut

tip, of

,

from

all

causes acting around a

body

or ship,

reckoned in the direction of motion

—

UjA Velocity, induced, axial; the axial component of the induced velocity at a selected point in a propeller jet with rotation UiT

—Velocity,

gential

induced, tangential; the tan-

component

of the induced velocity at a

selected point in a propeller jet with rotation Ua>

,

Fco

—Velocity

of the liquid in the undis-

turbed part of a stream or at a great distance

from a body or ship C/,—Velocity, shear,

by Vto/p Uotb

or

Uo

—Orbital

particle in a gravity

V

—Velocity,

linear

in viscous flow,

velocity

a

of

defined surface

gential, of the blades of a paddlewheel,

component body

U— Speed

measured and

at midheight of the blades for a radial wheel

at the blade-trunnion circle for a feathering wheel

Va

Ve

,

,

U

—Speed or velocity of advance of

a propulsion device, reckoned in the direction of

motion of the device, = F(l — w) = U{1 — w) Vi Schlichting intermediate speed, for analysis of shallow-water performance Vm Speed of model, as distinguished from ship

— — speed Vs Vo—Speed

of advance of a propulsion device open water; speed of a ship along the approach path just prior to entry into a turn Vr Ur Speed or velocity, resultant, of the flow approaching a hydrofoil Vs Speed of ship, as distinguished from model speed Vm V Velocity of sound in a medium Vt Towing speed of a tug in

—

,

— — — VsT —Speed, steady-turning Vw Uw —Speed or velocity,

wake, resulting from all causes acting around a body or ship, reckoned in the direction of motion F„ C/co Speed of the Uquid in the undisturbed part of a stream at a great distance from ,

—

,

a body or ship F (pronounced vol)

ume

of

—Volume; displacement vol-

a body or ship; alternative symbol V(also

pronounced vol) Va Volume, afterbody, of a ship ¥b Volume, bulk, as of a submerged submarine Ye Volume, entrance, of a ship ¥p Volume, forebody ¥p Volume, parallel middlebody Vr Volume, run

— — — — — —

F/(0.10L)' or V/(0.10L)'— Fatness or (volume-0.1 length) ratio. This is preferred to a length/volume ratio because it increases as the fatness increases, the same as the displacementlength quotient of D. quotient, where

F

W.

Taylor.

quotient T^ or speed-length is

in kt

and L

in ft; this is

dimensional

of,

in direction

or ship, positive

to starboard

V,

measurement

—Speed of ship in water of depth h —Velocity, nominal tanV° (F of blade

V/\/L — Taylor

wave

of transverse or y-a.xis of a

or velocity of the

circle)

tx/c, tx/l

U

XI.

V,,

roll

velocity of the liquid

V

liquid U, irrespective of units of

t)

—Period of heave To — Thrust of a propulsion device in open water Tp — Period of pitch Tjj— Period of Ts —Thrust, slope, exerted by gravity on a floating body on an inclined hquid surface Tw— Period of a gravity wave —Thickness ratio of a hydrofoil section to/D — Blade-thickness fraction of a screw Th

of

Sec.

speed of the body or ship

effective,

propulsion device,

2

A

s

or velocity in general; specifically,

w —Velocity,

component of, from deck to w— Wake fraction of Taylor, = (F (F - Ve)/V linear

of the z-axis of a ship,

in direction

keel

- Va)/V =

B

SYMBOLS AND THEIR TITLES

X1.2

Sec.

w— Weight density, or weight per unit volume, = W/V = pg Wf —Wake fraction, Froude, = (F — Va)/Va Wq —Wake fraction, determined from torque identity

—Wake fraction, determined from thrust identity W— Weight in general; displacement weight; weight or gravity force; scale weight of a body where W = mg or W—Wind velocity Wn—Weber number, relating to surface tension, = C7'L/k (kappa) = see NOTE under W — Wind velocity, relative to ship Wt—Wind velocity, true, over the earth's Wt

direction of

surface;

C^,

sometimes called the natural-wind veloc-

W — Wind velocity,

still-air,

sA

caused solely by

still air

— Longitudinal body positive forward 0-diml, of a screw propeller, —Radius = R/Rm^^ reckoned usually in an ahead Xo — Motion X

axis,

ratio,

x'

axis,

body y

or ship along

— —

symbol C w a Ratio,

linear or scale, full-size

of

hydrodynamic

its

longitudinal or a;-axis

force on a

X (lambda)

—Nominal angle of incidence on a control neglecting (1/2)q:b —Angle of entrance, shape at the stem; alternative symbol is —Angle of attack of a hydrofoil, hydrody-

ua

surface

half,

local oti

namic, measured from the attitude or position of zero hft to the direction of the resultant velocity, taking induced velocity into account

—Angle, neutral, between the zero-hft posiand the body or ship axes ao — Angle of attack of a hydrofoil, alternative symbol a^ as —Angle of attack of a hydrofoil, stalhng —Angle of attack of a hydrofoil, alternative symbol ao acR —Angle of attack of a hydrofoil, —Advance angle for a propeller-blade element, = tan"' [VA/{2irnR)] for the radius R —Angle bossing termination, extreme after ai^

zero-lift;

zero-lift;

ttz

critical

of

fi

distance,

any point

perpendicular

in the

to

the

boundary layer

of a

viscous liquid

floor if or "deadrise" in a planing craft; angle of

obliquity for a flat surface impacting a Uquid

—Angle of in turning —Coefficient, midlength section; alternative symbol Cm —Hydrodynamic pitch angle of a screw-prodrift

—Transverse body positive to starboard —Motion reckoned usually to starboard or to the right of the Y— Component of hydrodynamic force on a

peller

body

induced velocity into account

axis,

y

axis,

2/0

a;o-axis

z

or ship along its transverse or y-axis

—Vertical body positive from deck to keel —Shaft convergence, expressed as an angle axis,

Zc

or slope with reference to the centerplane, after

projection on the baseplane Zd

—Shaft

declivity, expressed as

an angle or

slope with reference to the baseplane, after projection

/3

fii

blade section at any radius R,

symmetry r (gamma,

S (delta)

z-axis

of

of

—Angular

surface from 5 5

of

its

capital)

— Circulation,

strength

of,

around a hydrofoil or body

of

of

—

—

axis of

taking

7 (gamma) Projected angle of roll 7 Dihedral angle, measured from the axis of a hydrofoil to a normal erected on the plane of

on the centerplane

—Motion Az— Sinkage a body or ship when moving on the surface a Uquid Z— Component hydrodynamic force on a keelward or body or ship along Z—Number blades in a propulsion device a (alpha) —Acceleration, angular a —Angle of attack a hydrofoil, geometric encounter of waves, between the a —Angle 2o

body or ship symbol

to model, greater than unity; alternative

edge, with reference to the baseplane; slope of

—Normal

surface, to

of ship

;S(beta)

direction, tangent to the sea surface

X— Component

and the direction a = 180 deg.

tion of a control surface

ity

the motion of a ship in

909 travel

motion. For a head sea, a Designed waterplane coefficient; alternative

ship,

C/'i)/ k;

wave

5

its

displacement of a control

neutral position

—Coeflacient, block; alternative symbol Cb —Thickness of a boundary layer in viscous flow —Advance ratio of D. W. Taylor, = nD/V a

When n is expressed in rpm, D in ft, and Va was done by Taylor, and equal to 101.33/7 as

bs axis

—Angle,

bow

.

in kt,

this ratio is dimensional

plane, with reference to ship

HYDRODYNAMICS

910

—Thickness of the laminar sublayer a —Angle, neutral, a control surface Sp —Angle, diving plane or horizontal control surface, with reference to body or ship axis reference to ship axis 8r — Angle, rudder, —Angle, stern plane, with reference to ship of

5l

viscous boundary layer

of

Sat

Avith

8s

axis 6* (delta

boundary

star)

—'Displacement

thickness

of

a

IN SHIP DESIGN

—Efficiency, mechanical = —Efficiency, propeller, in open {Kr/Ka)[J/{2T)] = (r„7„)/(2,m„Qo) —Efficiency, propulsive = Ps/Pp = VoVhtir —Efficiency, relative rotative, = vb/vo = Vb/vo —Efficiency, shafting 0(theta) — An angle in general —Angle of pitch or trim in a with 7/m

r]p

qji

—

^An increment or decreA(delta, small capital) ment; see also the combination symbols Usted under the letter D ACp (using small capital delta) Increment of specific friction resistance due to surface roughness

large capital)

—Displacement

6

weight

or scale weight, in tons of salt water (see item

—Momentum thickness

Br

ds

;

plane, of the

craft

or

A/(L/100)'— Displacement-

length quotient of D.

having a

W. Taylor

sp.gr. of 1.024 at

59 deg

equivalent to 63.863 lb per

ton of 2,240

lb,

and

ft'

for salt

F

or 35.075 ft'

for a length

L

per

in ft; this is

dimensional and is equal to the displacement, in English long tons, of a geometrically similar ship ft

long

of a

body

or ship; alternative

symbol

V

(also

—

€(epsilon)

—Angle

—Drag-lift —Slope f

of

downwash

of the surface of a gravity

wave,

—Angle, vertical path, between the hori-

zontal plane and the velocity vector of the motion

CG

—Efficiency, general —Elevation, surface, a wave, with reference to a plane, usually the = Vb Ve — Efficiency, propeller, behind ship VoVr —Efficiency, gearing of

still-water level

,

rio

hull,

=

(1

-

0/(1

-

—Efficiency, ideal —Efficiency,

riK

in

J p.hB

ideal,

{imD)

=

design,

to

X

V a./

= VE/irnD)

— Ratio, linear or

body number

scale, full-size

1

or ship

greater

:20 model;

—Magnification factor in resonant motion — a doublet, or close-coupled = dynamic, —Viscosity,

;u(mu)

n Strength of source and sink

coefficient

of

r{i2M)/{dU/dy) j'(nu)

—Kinematic

viscosity,

coefficient of,

=

m/p l(ksi)

—Angle, tab, with reference to the control

surface on which p(rho)

it is

mounted

—Mass density, or mass per unit volume,

= m/¥ = w/g

~ ^)/l — Cavitation index, = —Cavitation index based on angular velocity, — e)/{0.5pn'D'') = for propeller —Cavitation index based on liquid o-(sigma)

(pAba

tests,

with jet rotation

propeller

—Angle, leeway, or of leeway —Coefficient, absolute advance, =

cn

Pe/Pt T],

w)

factor

X (lambda)

7)

77„— Efficiency,

of kinematic capillarity

the constant of capillarity

is

K—Goldstein

of a ship

q

skeg

take account of the number of blades

IX

of the

line of a contra-guide

— Coefficient

where k

k/p,

reckoned with respect to the horizontal r)(eta)

median

than unity; for example, 20th scale or alternative symbol a (alpha)

or sidewash

ratio of a blade section or hydrofoil

(zeta)

with reference to the ship center-

to model, generally expressed as a

pronounced vol) Vb Volume, bulk; alternative symbol Vb

6

K(kappa)

=

X,

V (pronounced vol) —Volume; displacement vol-

with reference to the ship center-

ending

water

or 15 deg C,

boundary layer

uj

c/-\

—Slope, —Slope,

of

plane, of the incident flow on a contra-rudder

following) gravity load on the water for a planing

A/(0.010L)'

refer-

divided by the length L.

Jo

and other factors

ume

ship,

the designed waterline at the end perpendiculars,

—

100

s

97

ence to the designed or normal attitude in the fore-and-aft plane. Its natural tangent is the algebraic difference of the changes in elevation of

=/:(-f)

A (delta,

Avater,

7)0

6

layer,

XI .2

Sec.


,


(pAb,

4

XI.

Sec.

velocity, for propeller tests,

SYMBOLS AND THEIR TITLES = (pAb. — e)/(0.5pFi) CB — Center of CE— Center of

—Surface tension —Indexes of dynamic stability of route —Cavitation index or number, 2(sigma, large capital) — Sum, summation T(tau) — Shear, intensity of internal, in the 0-

0-1

,

0-2

etc.

,

ffcR

critical

viscous flow of a liquid, proportional to (dU/dy);

shearing stress To

—Shear

effort,

boundary

—Angle,

geometric pitch or heUx, of a screw-propeller blade at any radius

—Angle of or reckoned about the longitudinal ship axis —Potential function such as a velocity = potential, where u = w = d

roll,

body or ship the wind blowing

of a

as for

sail

—

CF Center of flotation; geometric or moment center of the surface waterplane area A w

—Center

CG body

of gravity or center of

mass

of

a

or ship

CM, CMt

,

M— Metacenter, for transverse in-

clination

CMl Ml — Metacenter, ,

intensity in a viscous liquid at a

solid-surface <^(phi)

on a

911

buoyancy

for longitudinal incli-

nation

— pressure hydrodynamic forces CS —Static center; center resultant weight W and buoyancy B CCF— Center cross forces applied normal to

CP Center on a body

of

of

of

of

of

the direction of motion of the

CG

and normal to



d(t>/dx, v

d<j)/dy,

alter-



v

the direction of

lift

— — sarily at the center of area CWL— Construction waterline, as a position only 0-diml—Non-dimensional, as applied to phys-

CLA Center of lateral area of the underwater body, as projected on the plane of symmetry CLP Center of lateral pressure; not neceslateral

symbol Cpv

—Angle of yaw —Current or stream function —Radial stream function for a source — Radial stream function for a sink ^s — Stream function for the flow around ^(psi)

}p

apphed to flow having

1^0

ical expressions; also as

4'K

characteristics variable in one dimension only

a

stream form

w (omega)

—Angular speed or

velocity, generally

expressed as radians per unit time; alternative sjnnbol n, generally expressed as revolutions per unit time

0(omega, capital)

—Gravity

potential,

due to

the earth's gravity force.

XI. 3

—Two-dimensional, as applied to 3-diml — Three-dimensional, as applied to flow, shape, and the DWL— Designed waterline, as a position only FP—Forward perpendicular, designed LE—Leading edge MP—-Mid perpendicular PP—Between perpendiculars; pivoting point SK—Sink, as a drain for radial flow SO —Source, as a source of radial flow TE—Trailing edge TP—Towing point or towed point WL—Waterline in general; free-surface water2-diml

Abbreviations for Positions and Con-

ditions.

C — Center E—Separation

point on a body in a stream, where the relative flow velocity becomes zero at the body surface in the process of reversing direc-

like

point along the intersection of the

any

fine in

may

tion

K—Any

flow,

shape, and the like

or

condition, undisturbed

may

Sp.gr.

—

not be at the

by waves;

this

DWL

Specific gravity.

baseplane with the plane of sjonmetry

N—Neutral body

or ambient-pressure point

in a stream,

where

U = U„

—Origin of coordinates Q— Stagnation point on a

and p

body

=

on a

in a stream,

and the dynamic pressure equals the ram pressure q where the relative flow velocity

AP—After perpendicular, CA— Center of area

is

zero

designed

XI. 4

Abbreviations

for

Having Scalar Dimensions.

Physical

Concepts

The superposed bar

Pa,

or vinculum over the groups of letters in this section indicate that they represent scalar quantities,

measurable in orthodox units.

BD —Bilge-diagonal

offset, at any station, measured on the diagonal plane from the center-

line intersection to the hull surface

— HYDRODYNAMICS

912

BG — Pendulum

stability height, as of a sub-

when the

marine,

ne gUgi ble and

CM

waterplane area

surface

position

BMl — Metacentric radius for longitudinal inclimaximum

BDI —Bilge-diagonal

intercept,

wh en

PWL— Length

measured be-

measured at mid-

width,

of the parallel or straight-sided

portion of the designed waterline area, reckoned as a height

when

above the baseplane

projected to Bx/2; also called "deadrise"

and abbreviated

DR

RF/Bx

— Ratio,

XI .5

Abbreviations for Units of Measurement.

extended to the vertical at Bx/2

BKW — Bilge-keel

by

RF— Rise of floor at shell at section of maximum area

tween (1) the intersection of the bilge diagonal with the centerline at the designed waterline and (2) the intersection of this diagonal with the floor h ne,

to change trim, followed

appropriate unit

nation Bilge radius at section of

X1.5

taken as the midlength of the middle-

MCT —-Moment

radius for transverse

inclination

BR

is

Sec.

body.

CB

coincides with

BM, BMx —Metacentric

is

IN SHIP DESIGN

rise of floor to

beam.

BKW/Bx Ratio, bilge-keel width to designed water line beam at the section of maximum area; Blew is measured at midlength because it is

For convenience these abbreviations are placed in natural groups involving length, area, volume, weight, pressure, power, time, and the like, rather than in alphabetic order. The same abbreviation applies to both the plural and singular of the word(s) it represents. Periods are not inserted after any abbreviation or

usually greatest there

part thereof.

w herever this width is a maximum BD/BDI — Ratio, bilge-diagonal offset to bilge-

length or

diagonal intercept, at any station

—

BR/Bx line

—Ratio, bilge radius to designed water-

beam, at the section

of

maximum

area

PR— Dea drise; see last part of definition forRF

GM, GiMx — Metacentric height, transverse, CG to CM, for transverse inclination

from

GMl — Metacentric height, CG to CMl for longitudinal

longitudinal,

incUnation

,

HS— Half

siding at flat keel, wherever

maximum HS/Bx — Ratio flat keel,

of the greatest

wherever

section of

maximum

it is

a

half -siding at

occurs, to the

it

from

beam

at the

area

KB— Center of buoyancy above baseplane KG— Center of gravity above baseplane KM, KMt — Distance of metacenter above

KMl — Distance of metacenter above baseplane for longitudinal inclination

minimum, above

b asepl ane

KB/H — Ratio

of height of center of

buoyancy

above baseplane to draft

LCB — Longitudinal FP, in fraction

LCF— Longitudinal FP,

center of

of L; alternative

buoyancy abaft Lcb

center of flotation abaft

in fraction of L; alternative

LCG— Longitudinal

Lcf

Lea

LM A—Longitudinal position of section of maxiLma

area abaft FP, in fraction of L; alternative If

—inch sq —square inch sq —square foot —foot sq yd, yd^ — square yard yd—yard sq mi, mi^ — square mile fm—fathom mi—mile; nautical mile unless otherwise indicated mm —millimeter sq mm, mm^ — square millimeter cm — centimeter sq cm, cm" —square centimeter sq m, m" — square meter m —meter km —kilometer sq km, km^—square kilometer in

in, in" t^

ft

ft, f

—cubic inch millimeter —cubic foot cu cu cm, cm' — cubic centimeter cu yd, yd' —-cubic yard cu m, m' — cubic meter U.S. — gallon Imp. —gallon. Imperial, equal to 1.201 U.S. gal bbl — barrel

cu

in, in^

mm, mm^ — cubic ft, ft'

gal, gal.

center of gravity abaft FP,

in fraction of L; alternative

mum

Area

Length

cu

height at side,

listed here.

Volume

baseplane for transverse inclination

KS — Sheer

Trigonometric abbreviations are well known

and are not

a vessel has parallel middlebody, this

Weight kip — a thousand pounds —ounce kg—kilogram —pound —ton be further specified)

oz lb t

(to

6

SYMBOLS AND THEIR TITLES

XI.

Sec.

913

pounds per square inch; above atmospheric or gage pressure, unless otherwise

with the non-dimensional formulas which express their values as multipliers of well-known 0-diml numbers. Following these are the dimensional

specified

forms, as applied to English units of measurement.

Pressure lb in^, psi, psig

—

—pounds per square foot

lb in'

It is important that consistent units be employed in the formulas listed hereunder, as well as in all other pure formulas, containing physical concepts only. For example, in the English

14.2 lb in'

system of measurement, units should be lb, ft, and sec. The same value of g should be used for

lb ft^, psf

—pounds per square inch, absolute roughly atm —atmospheres of pressure, in units 14.7 kg cm" —kilograms per sq cm, in units of roughly psia

of

all

Moment

the expressions.

Angles and Arcs

or Torque

—inch-pound —foot-pound kg-m—kilogram-meter

—degrees arc —radians, 360/

in-lb

deg

ft-lb

rad

@

of

(2 tt)

Length-Displacement Constant. The ratio

of the length

L

of the ship to the length of the

same volume

side of a cube having the

placement

F

or

V

of dis-

as the ship.

Power

—horse, a unit power, English units unless otherwise specified hp —horsepower bhp —brake power, in English horses power, in English horses ehp — ihp — indicated power, in English horses php — propeller power, in English horses shp —shaft power, in English horses

h

of

in

effective

®

Speed-Displacement Constant. The ratio of V of the ship to the speed of a wave with

the speed

a length equal to half the length of the side of a

cube having the same volume of displacement or

V

V

as the ship.

V

Time and Rate

—micro second, one millionth a second ms—millisecond sec —second min—minute hr —-hour per second per sec —foot fps or per minute per min —foot fpm or —cubic foot per second cfm— cubic foot per minute cms — cubic meter per second ops — cycles per second gpm—gallon per minute per second hz —hertz, frequency rps — revolutions per second rpm —revolutions per minute mph —miles (generally geographical) per hour mps —meters per second kt — knot, one nautical mile per hour

2ir2

of

us

ft

(feet)

(feet)

ft

cfs

of

= V4ir

©

W,

displacement constant lOOOfi ¥'^

w

— — —

X L6 Circular Constant Notation. The several symbols of the circular constant notation of R. E. Froude and G. S. Baker are listed here,

to the displacement

v

®. Here

W

_9_

lOOOff

At

wV =

= wV.

V V' At

39.79Cj

where Ct is the total specific resistance coefficient based on ¥^^^ as the reference dimension. (L)

speed

Temperature

R

divided by the square of the speed-

1 cj^cle

deg degree deg C degree Centigrade deg F degree Fahrenheit.

3.545F,

One thousand times

Resistance Constant.

the ratio of the resistance

weight

=

VgV

Speed-Length Constant. The ratio of the V of the ship to the speed of a gravity wave

of length equal to half the length

© (p)

L

of the ship.

3.545F„

Speed-Prismatic-Length Constant. The ratio V of the ship to the speed of a wave

of the speed

6

HYDRODYNAMICS IN SHIP DESIGN

914

of length Cp{L), where Cp is the prismatic coeflBcient of the ship and L is the ship length.

stants, lb,

F

where

is

L

in kt,

is

S

Sec.

in ft, is

in

A ft^,

and Pe

horses:

V

=

\2-K

V

Wetted-Surface Constant. The ratio of the ship wetted surface S to the area of one face of a cube having the same volume displacement V or

V

=

0.3057 ^1/3

=

0.5834

V

2.5066

(s)

©

= 427.1^^^

©

=

1.055

©

=

0.746

©

=

as the ship.

—

o TI2/3

—

o V72/3

There are given hereunder the familiar dimensional expressions for the several circular con-

There

is

no Appendix 2

in this

V

Vl V Vc7(LJ

volume.

0.0935

XI.

in long tons of 2,240

is

s

is

in English

APPENDIX

3

Mechanical Properties of Water, Air,

and Other Media General Reference Data for Weights, Volumes, and Mass Densities of "Standard" Fresh and

X3.1 X3.2

Saltwater

X3.4

Other Mechanical Properties of Fresh and Salt Water at Atmospheric Pressure; Dynamic Viscosity and Surface Tension .

General.

X3.1

There are many

fluids.

water,

of

.

air,

published

and other common

The tabulated values shown, are

these sources,

in

all sufficiently precise for

the

usual problems in engineering design. Nevertheless it is disconcerting, to a student or especially to field to

an engineer, when shifting from one

another, say in a time of national emer-

gency when everyone is harassed, to encounter a group of different values for what is apparently a standard state of some medium. Furthermore, certain ratios in everyday use in naval architecture are by no means consistent when derived in several different ways. To clarify this situation for the marine architect a set of so-called "standard" values has been evolved, for both fresh

and

salt water.

in the sections

Elastic Characteristics of

X3.8

Mechanical Properties of Air and Exhaust Gases at Atmospheric Pressure and at Sea Level Mechanical Properties of Other Liquids and Gases Chemical Constituents of Sea Water

Common

They

are described

which

follow.

A

X3.10 X3.ll

of State of Fresh

921

922

Liquids

.

.

.

List of Pertinent References

and tabulated

set of standard

The

Salt Water.

mass

922 924 924 925

so-called standard unit weights,

densities, temperatures,

ities in

use for

and by model

many

specific grav-

were most part because they were round numbers, easy to remember, and easy to use. Indeed, if they approximated 1.0, they were often thrown away. That they were anything but consistent among themselves was not too important, because the deviations involved were generally of smaller magnitude than the overall precision of measurement of the various operabasins, at least in America,

selected for the

tions.

They began with 35

ft^

the use of the round numbers

per ton for sea water and 36

ft^

per ton for

These gave values of 64.000 lb per ft' for salt water and 62.222 lb per ft' for fresh water, based on long tons of 2,240 lb. Incidentally, because some seas in the world contain fresh water in their upper levels, the term "salt water" fresh water.

used in this book;

is

embodied in these "standard" water values are by no means necessary in making first and second approxima-

contrast to "fresh water."

five significant figures

and

years by naval architects

values for air already exists.

While the

and Salt

Water and Other

920

while often differing within the range of significant figures

X3.7

X3.9

sources of information concerning the mechanical properties

Data on Change Water

918

920

neering Units

X3.5

X3.6

915

Mass-Density Values of Fresh and Salt Water, in English and Metric Engineering Units Kinematic-Viscosity Values of Fresh and Salt Water, in English and Metric Engi-

X3.3

915

When

it

also stands in

round numbers were used, the

better

specific

tions or in the early stages of a ship design, they

gravity of salt water on a basis of fresh water came out as 36/35, or 1.0286. Since this was

lend themselves to the desk-machine calculation

larger than the ratio existing in

now almost

oceans,

universal in the later stages of a

ship design, or in the preparation of technical

of the

Model Basin,

half a century ago, adopted a smaller value of

reports.

1.024.

Reference Data for Weights, Volumes, and Mass Densities of "Standard" Fresh and

it

X3.2

most parts

the U. S. Experimental

The

origin of this figure

is

not

known but

was embodied in all the calculations of the 1910 edition of D. W. Taylor's "The Speed and Power

915

— 916

HYDRODYNAMICS TABLE

All data are for a

X3.a

water temperature of 59 deg

of 10.

Title

IN SHIP DESIGN

Sec.

X3.2

Reference Data for Standard Water

F

or 15 deg

C and

a latitude of 45 deg. All logarithms are to the base

— Sec.

MECHANICAL PROPERTIES OF AIR AND WATER

X3.2

TABLE The

X3.C

Standard Characteristics op the Water Used

basin water

is

assumed to be at an average temperature

Title

of

in

917

Several Model Basins in North America

68 deg F, 20 dcg C.

— 918

HYDRODYNAMICS

IN SHIP DESIGN

TABLE X3.e Mass Density of SALT WATER, 3.5 Per Cent Salinity,

Sec.

X5.3

Embodying Variation With Temperature

The values given are in English engineering units of slugs per ft'. They correspond to those adopted by the American Towing Tank Conference in 1939 and published in SNAME, 1939, p. 416. To convert them to pounds weight, multiply by the local acceleration of gravity g.

Temperature,

— Sec.

MECHANICAL PROPERTIES OF AIR AND WATER

X3.3

TABLE The

X3.g

Mass Density of SALT WATER,

3.5

values given are in metric engineering units of slugs per meter'.

Temperature,

919

Per Cent Salinity, Embodying Variation With Temperature

— HYDRODYNAMICS IN SHIP DESIGN

920

TABLE The values

X3.i

listed are for (lO^);- in meters^

figures in this table are

Fresh

Sec.

X3A

Kinematic Viscosity of Fresh and Salt Water, in Metric Engineering Units somewhat doubtful.

per sec.

The

salinity of the salt

water

is

3.5 per cent.

The

fifth significant

— Sec.

MECHANICAL PROPERTIES OF AIR AND WATER

X3.6

TABLE The data

X3.j

in this table, expressed in English engineering units, are taken

Temperature,

921

Mechanical Properties op Fresh Water at Atmospheric Pressure from H. Rouse [EMF, 1946,

p. 364].

— HYDRODYNAMICS

922

TABLE The data on vapor pressure

IN SHIP DESIGN

Data on Change of State op Fresh and Salt Water of fresh water are taken from H. Rouse [EMF, 1946, Table XI, p. 364]. The note

Sec.

X3.7

X3.1

concerning taken from page 67 of the book "The Oceans: Their Physics, Chemistry, and General Biology," by H. U. Sverdrup, M. W. Johnson, and R. H. Fleming, 1942. Table 29 on page 116 of the reference, not reproduced here, lists the "maximum vapor tension in millibars" over water of 3.5 per cent salinity for a range of temperature from —2 deg C to 32 deg C. the vapor pressure of sea water

Temperature,

T

is

— MECHANICAL PROPERTIES OF AIR AND WATER

X3.8

Sec.

mechanical properties of air at atmospheric pressure and at sea level, depending upon what

in the

source of his

consulted. A. H. Shapiro, in Volume I book "Compressible Fluid Flow," 1953,

is

pages 612-613, gives the following principal data, to

which supplementary data have been added:

Height above sea Temperature, T Speed of sound, c Pressure,

level,

h Oft

C

59 deg F, 15 deg 1,117 ft per sec 2,116.2 lb per

p

-

ft'

14.696 psi 29.91 inches of

Hg

o 759.7 mm. of Hg Mass

0.002378 slugs per

density, p

Weight density,

w

0.0765 lb per

Coefficient of viscosity,

ft'

ft'

3.719(10"') slugs per

^x

ft-sec

Kinematic

1.564(10"")

viscosity, v

per

ft^

sec.

Corresponding data for temperature from deg listed in Table X3.n.

For possible use

air,

F

over a range of

to 200 deg F, are

in wind-resistance calculations,

as well as for the design of stacks and other outlets to carry exhaust gases

and products

of

TABLE X3.m Bulk Modulus of Elasticity of Fresh AND Salt Water at Atmospheric Pressure are taken from H. Rouse [EMF, 1946, p.

The data

except that the value of

K for fresh water at

364],

100 deg

F

is

increased to 332,000 to agree with a faired curve of these values.

from

The X-value

this curve.

Temperature,

T

for 59

deg F, 15 deg C,

is

interpolated

923

— HYDRODYNAMICS

92-1

TABLE

X3.p

60

The data

IN SHIP DESIGN

Sec.

X3.9

Density Characteristics of Common Liquids and Gases Under Atmospheric Pressure at

in these tables are

Deg P

adapted from those given by H. Rouse [EMF, 1946, Appendix, Tables VII,

VII, p. 3581.

Liquids

Under Atmospheric Pressure at

60

Deg F

p. 357,

and

Sec.

MECHANICAL PROPERTIES OF AIR AND Wy\TER

X3.ll (a)

Chlorine

(f)

Potassium

(b)

Sodium Magnesium

(g)

Bromine

(h)

Strontium

(c)

(d) (e)

Sulphur Calcium

(i)

Boron

(j)

Silicon

I.

Chloride, Cl-

18.98 parts per thousand

SOr

Sulphate,

Bicarbonate,

Bromide, Br"

0.065

F~ Boric acid, H3BO3

0.0013

Fluoride,

II.

Sodium,

Na+

,

MgBr,

or

"Of

0.400

Ca"*""*"

alkali"

possible that

generators,

(1)

reason

why

may

book referenced previously:

(6)

(7)

(8)

be the

the analysis which follows does not

agree in certain respects with the data presented in the

(5)

condensers,

evaporators, heat exchangers, and the hke, some of the constituents are altered. This

1949, p. 75].

List of Pertinent References.

Refer-

of data in this

appendix are

listed

hereunder:

by the time the sea water,

the form of steam

[MESR, Nov

1949].

(3)

with these constituents plus its dissolved air and gases, is mixed up with shipboard machinery in

magnesium bromide, 0.01 percent. magnesium chloride is most objectionable

these, the

and magnesium hydroxide are found in the scale on evaporators may not mean that these compounds were present in the sea water being evaporated, in just that form [Brush, C. E., and Browning, R. C, "Notes on Prevention of Scale in Evaporators," SNAME, Ches. Sect., 21 Jan

(4)

is

or calcium carbonate, 0.01 percent

Just because calcium sulphate, calcium carbonate,

0.0133 parts per thousand.

figures in the original table, the total roughly 34.48 parts per thousand.

It

2.72 percent

.

Adding up the exact is

,

salt),

magnesium chloride, 0.38 percent magnesium sulphate, 0.17 percent

because it breaks down, forming hydrochloric acid, MgCl, + 2H2O = 2HC1 + Mg(0H)2 Other acids formed from these solids are: Carbonic, sulphuric, and nitric. These can be neutralized by compounding properly with

(2)

0.380

K"""

Strontium, Sr^^

or

and groups

10.57 parts per thousand

1.272

Calcium,

or

,

ences consulted in the preparation of the tables

0.026 parts per thousand.

Magnesium, Mg^^ Potassium,

MgClj

MgSOi CaCOa

X3.ll

0.14

follows:

NaCl, or sodium chloride (common

2.65

HCOs"

by weight, as

solids

These and the remaining data in this section are taken from the extensive information assembled by H. U. Sverdrup, M. W. Johnson, and R. H. Fleming in "The Oceans: Their Physics, Chemistry, and General Biology" [Prentice-Hall, Inc., New York, 1942]. Although the chemical compounds in sea water appear to be present in proportions that are remarkably constant, it is difficult to isolate and measure them by present methods of analysis. Table 35 on page 173 of the reference lists these constituents in two groups:

925

"Sea water contains about 3.5 percent of dissolved

(9)

Rouse, H., EMF, 1946, Appendi.x, pp. 357-365 Rouse, H., (editor), EH, 1950, AppendLx, pp. 10041012 Rouse, H., and Howe, J. W., BMF, 1953, Appendix, pp. 231-238 Eshbach, O. W., (editor), "Handbook of Engineering Fundamentals," Wiley, New York, 1st ed., 1936 "Landolt-Bornstein Physikalich-Chemische Tabellen (Chemical-Physical Tables)," edited by W. A. Roth and K. Scheel, Julius Springer, Beriin, 1923-1936 "Smithsonian Physical Tables," Smithsonian Institution, Washington, ninth revised edition. Vol. 88, 1954 "International Critical Tables," McGraw-Hill, New :

York "Handbook of Chemistry and Physics," Chemical Rubber Publishing Company, Cleveland Sverdrup, H. U., Johnson, M. W., and Fleming, R. H., "The Oceans: Their Physics, Chemistry, and General Biology," Prentice-Hall, 1942.

Inc.,

New

York,

—

APPENDIX

4

Useful Data for Analysis and Comparison X4.1 X4.2

General

Customary Units of Measurement in the English System X4.3 Ratios Between English Units of Measure-

General.

X4.4

926

X4.5 X4.6

926

ment; Standard Values

X4.1

926

Hydrodynamic

and

analysis

Conversion English-Metric and Ratios, Metric-English Ratios of Ship Parameters and Coefficients Frequently Used Numbers, Their Powers, and Logarithms .

some system

of measurement.

The

929 930 932

units of the

design can rarely proceed very far without getting

English engineering system, listed in Table X4.a,

into the realm of numbers, for expressing magni-

are used in this book unless indicated otherwise

tudes and intensities of one kind or another. The recent phenomenal growth in the availability of tabular material [Luke, Y. L., "Numer-

for a particular case.

ical Analysis,"

310], prepared

Appl. Mech. Rev.,

and published

Aug

1955, p.

and

for the scientist

the engineer in general, should find

its

counter-

part in an expansion of similar material for the

naval

architect

and

marine

engineer.

This

appendix, taken in conjunction with Appendix is

3,

considered a minor but appreciable beginning

and marine architect. X4.2 Customary Units of Measurement in the English System. It is customary, although not

for both hydrodynamicist

universal,

to

express

the

magnitudes

of

all

important physical terms or concepts in units of

TABLE Symbol

X4.a

The

"consistent" units of the English system

and the second. Ratios Between English Units of Meas-

are normally the pound, the foot,

X4.3

urement; Standard Values.

Most

of the ratios

between units used to express given concepts are simple numbers, learned in elementary school. Examples applying to the length concept are 1 yd = 3 ft and 1 mile = 5,280 ft. However, certain other relationships are not so simple, nor do they always remain fixed. One such ratio is

number by 360/2ir the

57.3.

of degrees in a radian, represented

=

57.2956, usually abbreviated to

Another familiar example

feet in

is

the

number

of

a nautical mile. This ratio has had a

Customary Units of Measurement

in

the English System

— Sec.

X4J

USEFUL DATA FOR ANALYSIS AND COMPARISON TABLE

The number

Ft per

sec

X4.b

of significant figures

Corresponding Values of Speed, in Four Different Units ia

limited to those used in rapid engineering calculations.

927

— HYDRODYNAMICS

928

TABLE For

T,

X4.C

this tabulation the corresponding values

= V/Vl

IN SHIP DESIGN

Sec.

X4.3

Correspondinq Values of Taylor or Speed-Length Quotient and Froude Number have been taken as

V/y/^ =

0.2978F/v'i and V/y/L = 3.S5SV/\/gL

Sec.

X4.4

USEFUL DATA FOR ANALYSIS AND COMPARISON TABLE X4.C— Continued

F„

= V/VgL

929

— HYDRODYNAMICS

930

TABLE

X4.d

Sec.

X4.5

Corbbspondinq Values op Displacbment-Lbnoth Quotient and O-Diul Fatness Ratio

The

A

IN SHIP DESIGN

conversion factors used here are described in Sec. X4.5.

Sec.

X4.5

HYDRODYNAMICS

932

whether they are dimensional or the concepts forming parts dimensional parameters are given certain

definite values

dimensionless. of

When

IN SHIP DESIGN

Sec.

X4.6

quently used in hydrodynamic ship-design problems, together with their frequently used powers

and with logarithms

of these

numbers

to the

then possible to express their relationships to the dimensionless values, for any given system of measurement. There are tabu-

base 10, are listed hereunder in a form to make them readily available for calculation purposes.

lated in this section certain ratios which occur

in

accepted values

frequently in

it is

the

treatment of hydrodynamic

problems in ship design. One such ratio in everyday use is that between the Taylor quotient T^ and the Froude number F„ By definition and accepted practice, T^ = .

YI \/L, where V is in kt and L in ft; by consistent =

units, F„

V/'s/^L, where

V

is in ft

per sec,

and L in ft. The ratio between Ta and F„ depends upon the "standard" value assumed for the acceleration of gravity g and the length of a nautical mile. At a latitude of 45 deg and at sea level, g is taken as 32.174 ft per sec''. For this book, 1 nautical mile is 6080.20 ft. g in ft per sec",

Then

^ F

(ft

per sec)

in Parts

1

and

12,

logio

144,

log.o

= =

1,728,

logio

=

3.23754

3.281 ft per meter.

logio

=

0.51601

logio

=

0.22760

logio

=

0.16643

logio

=

0.22732

0.2978

-^y^

=

1.07918

2.15836

SPEEDS AND VELOCITIES 1.6889 ft per sec for Ikt, in this book,

1.467 ft per sec for

1

mph,

(ft)

1

=

2.

LENGTHS AND AREAS

national knot, 1954,

V32.174L

\/gL

=

0.5921,

logio

=

9.77240

=

2.8524,

logio

=

0.45521

1.

0.2978r,

(1.6889)'

ACCELERATIONS =

3.358F„

0.2978

For rule-of-thumb work, T^

=

g

F„

0.3T„

and

=

32.174

ft

•\/32.174

10i^„/3.

1

Corresponding values of the pair T, and F„ and the pair F„ and T, are listed in Table X4.c, for a range sufficient to cover all design problems ,

and ships, small and large. Another conversion that needs to be made often is the one between D. W. Taylor's displacement-length quotient A/(0.010L)^ and the 0-diml fatness ratio F/(0.10L)^ A conversion

for boats

=

5.6722,

logio

= =

0.75375

=

0.17630,

logio

=

9.24625

per sec'

logio

1.50751

\/32.174

KINEMATIC VISCOSITY When Knu) =

1.2285(10"'), then 1

=

1.2285(10"')

When

V

0.8140(10')

then

1.2817(10"'),

=

factor has to be fixed here because of Taylor's 1

use of a specific gravity for salt water of 1.024, corresponding to a volume of 35.075 ft^ per long ton.

For converting from the displacement-length

quotient to the 0-diml fatness ratio, the former is multiplied by 0.035075 or divided by 28.510. To

=

1.2817(10"')

0.7802(10')

WAVE ACTION =

obtain values of the displacement-length quotient from the 0-diml fatness ratio, multiply the latter

by 28.510 or divide it by 0.035075. Table X4.d lists corresponding values of these two quantities. Used Numbers, Their X4.6 Frequently Powers, and Logarithms. The numbers fre-

is

accordance with the general subjects discussed

1.6878 ft per sec for inter-

1.6889F(kt)

^

For certain special numbers the grouping

= 6.2832

V2^ = 1

V2^

=

2.50663 0.39894.

2.2629 English units

1

.2493 metric units

Personal-Name Index In the case of persons having a great many actual envolume, only the most important are included.

in the

With a few

exceptions, the

names

Abbott, I. H., 74, 272, 606, 608 Abell, T. B., 39, 77, 440, 726 Acevedo, M. L., 86, 107, 109, 113, 130, 319 Acker, H. G., 564, 565 Ackeret, J., 579 Adamson, G., 271, 272 Aertsson, G., 98, 126, 279 Ahlborn, F., 35, 37, 141, 144 Airy, Sir G. B., 183 Aitken, R. L., 765 Akimoff, N. W., 39 Alexander, F. H., 752, 753 Allan, J. F., 131, 132, 608, 787 Allen, R. C., 785 Allen, W. G., 733 Allison, J. M., 270 Amtsberg, H., 126, 687 Amundsen, R., 796 Anderson, M. A., 331 Anderson, R. E., 74 Aquino, A. Q., 262, 368, 371 Archer, C., 796

Arnold, R. N., 82, 144, 150 Arnott, D., 549 Arthur, R. S., 184

Ashton,

R.,

255,

841,

842,

866

of people

Acknowledgements section

ning on page

tries in this

v, are

mentioned

Barnaby,

W.,

S.

xix,

154, 540

Barnett, J. R., 817 Barr, G. E., 336 Barry, R. E., 561, 711, 726

Bateman, H.,

130, 343

2, 4,

Bates, J. L., 228, 231, 236, 237, 355, 465, 700

Baule, A., 70

Baumann,

H., 440 Bayard, N., 765

Bazin, H., 129

Beach, D. D., 845, 855, 867 Beatty, K. O., Jr., 95 Beaufoy, M., 99, 187 Beebe, R. P., 752 Belcher, Sir E., 781 Bell, A. G., 272 Bell, L. G., 157 Bellante, E., 704 Benard, H., 6, 38, 141 Bengough, G. D., 122, 125

Benson, F. W., 205, 608 Benson, J. M., 272 Bergeron, T., 185 Berggren, R. E., 609 Bertin, L. E., 183 Betz, A., 25, 69, 71, 129, 337, 343, 533, 534, 607

Attwood, E. L., 175, 479, 818 Audren, V., 713 Aupetit, A., 787 Ayre, Sir Amos L., 316, 537

Bienen, Th., 607

Babcock, W. I., 755 Bacon, D. L., 82

Biermann, D., 141, 293 Bigelow, H. B., 172, 184 Biles, H. J. R., 279 Biles, J. H., 227 Bindel, S., 312 Binder, R. C., 2, 922 Bion, C. W., 764

Baler, L. A., 103, 104, 116, 127, 255,

Birkhoff, G., 4, 134, 158, 206, 216,

Baader,

236, 340, 579, 651-653,

J.,

658, 698, 724, 855, 862, 863, 866

553, 670, 672, 755, 763, 786, 865

Baines,

W.

217, 219, 221, 319 Bisplinghoff, R. L., 271

D., 104, 131

185

Baird, G., 336

Bjerknes,

Bairstow, L., 39

Bjerknes, V., 185

Baker, G.

Blake, F. G.,

S., 25, 39, 40, 95, 98, 99,

125, 132, 144, 234, 262, 269, 278-

280, 359, 415, 416, 465, 582, 585, 600,

608,

650,

660,

764,

913

Bakhmeteff, B. A., 130 Baldwin, F. W., 272 Ball,

W.

E., Jr., 51

Barakovsky, V., 779 Barbour, H. J., 773 Barkla, H. M., 269, 308, 310, 787 Barnaby, J. W., 157 Barnaby, K. C., 126, 280, 284, 375, 474, 478, 752, 787, 833, 850, 853

of this volume, begin-

not duplicated in this index.

J.,

Jr.,

158

Blanchard, U. J., 271 Blank, H., 416 Blasius, H., 104, 129 Bleuzen,

J.,

250

Block, W., 177, 179 Blum, J., 189

Borden, A., 51, 293 Bottomley, G. H., 719, 720 Bottomley, W. T., 157 Bowen, F. C., 571 Bowers, W. H., 155 Boyd, G. M., Jr., 271 Brabazon, Lord, 572 Bradlee, F. B. C., 571 Bragg, E. M., 242, 335, 336, 509, 640-642, 663, 664 Brahmig, R., 418, 437, 440 Brand, M., 42, 61 Brard, R., 39, 71, 250, 413, 416 Brazell, N. J., 367, 568 Brehme, H., 600 Breslin, J. P., 704 Bridge, I. C., 335, 336 Bridgman, P. W., 4 Briggs,

H.

B., 157

Briggs, L. J., 82

Brin, C. B., 337

Brodetsky, Brodie, J.

S.,

S.,

157

665, 674

Browne, A. D., 440 Browning, R. C., 925 Bruckhoff, 129 Brunt, D., 275 Brush, C. E., 925 Bryant, C. N., 129 Buchi, G., 337, 687 Buckingham, E., 4

Budd, W. I. H., 236, 474 Buermann, T. M., 271, 273 Biiller, K. J., 272, 273, 755 Bunyan, T. W., 433, 733 Burge, C. H., 565 Burgers, J. M., 129 Burgess, C. P., 228, 765, 787

Burke, A. A., 414 Burkhardt, J. E., 358, 572, 575, 580, 598 Burrill, L. C.,

144, 153, 158, 159,

338, 352, 374, 440, 579, 599, 605, 608, 609, 625, 630, 762

Burtner, E., 569

Bustard, E. E., 460 Cafiero, D., 413

Blumerius, R., 336 Bobyleff, 48 Boetcher, H. N., 156

Caldwell, A., 691, 715

Boie, C., 441

Carrier, G. F., 131

Bollay, W., 271

Cauchy, A.

Booth, H., 39

933

Calvert, G. A., 99, 359

CampbeU,

I. J.,

40, 42, 43

L., 183 Chambliss, D. B., 271

HYDRODYNAMICS

934 H. I., 752, 787 Chapman, C. F., 280 Chapman, F. H., 187, 204 Chapelle,

Charpentier, H., 4 Chartier,

C, 607

Christofferson, V., 805

Christopher, K. W., 331

Chu, H., 43, 45 Chu, P. C, 43, 45 Church, O., 77 Churmack, D. A., 276, 349 Clark, L., 696, 781

Claughton, H., 652

Clement, E.

P., 271, 837, 840, 841,

846, 850, 866, 867

Coales, J. D., 77, 195 Cockerill (Shipyard), 338

J.,

82

Cole, A. P., 439 Cole, F.

IN SHIP DESIGN

722 M., 4, 99, 129, 139, 243, 331, 467, 651, 787, 866 Davies, D. G., 329, 331 Davies, E. T. J., 272 Davis, A. W., 144 Davis, H. F. D., 125, 591, 592 Davidson, K.

Davis,

W.

S.

F.,

Dawson, A.

75,

704

J.,

135, 554, 674

De Groot, D., 154, 827, 867 de Luce, H., 236 Denes, G., 787 Den Hartog, J. P., 144

700, 736, 756, 792, 805, 809, 810,

J. T., 303, 305, 770 Comstock, J. P., 98, 416, 548 Conn, J. F. C, 113, 144, 311, 440, 596 Connelly, D. S., 651 Cook, F. E., 705 Cook, G. C, 816 Cook, S. S., 349 Coombes, L. P., 271, 272 Cooper, F. E., 816 Cooper, R. D., 144 Coqueret, F., 360, 553 Corbett, J., 817 Corlett, E. C. B., 572, 632, 650, 867 Cornbrooks, T. M., 778, 779

ColHns,

Cornish, V., 175, 183, 184

241 Couch, R. B., 117, 126, 139, 243, 378, 379 Cowles, W. C, 756 Cowley, W. L., 77, 195 Cox, O. L., 703 Crabbe, E. R., 82 Craig, R. K., 456, 565 Cramp (Shipyard), 234 Crane, C. H., 753, 754, 786, 787, 865 Cross, A. W., 755 Crouch, G. F., 834, 853 Crowley, J. W., 270 Crump, S. F., 147, 158 Cotterill, J. H.,

Cummins, W. E., Cunningham, D.

69, 71

B.,

772

Curr, R., 755

816

De

Rusett, E. W., 652 de Saint-Venant, J.-C. B., 183 de Santis, R., 650 Desel, R. F. P., 303, 305, 339, 770 de Verdiere, G., 242, 713 de Vito, E., 479, 496

262

Daily, J. W., 150, 159, 649

Eiffel, G., 293, 588,

589

Eisenberg, P., 42,

147,

155,

157,

292

Eisner, F., 130

EUis, J.

457 279

J.,

Ellis, R.,

W. M., Jr., 293, 704 Emerson, A., 153, 158, 195, 765 Epshteyn, L. A., 631 Ericson, N., 805 Ellsworth,

J., 807 Erismann, M. C, 786 Eshbach, O. W., 270, 279, 925, 928-930 Eustaze, S., 564 Everett, H. A., 237, 817

Ericsson,

Fage, A., 82 Fairbairn, W., 227 Farrell,

K.

Fauber,

W.

287

Dudebout,

Forbes,

A., 32, 70, 104, 129, 335,

Fea,

L.,

P., 285,

H., 269

579

Fenger, F. A., 536

Ferguson,

M.,

J.

Fermann, W.

Dudgeon, J., 531 Duggan, G. H., 789-790 Duncan, W. J., 4, 608 Durand, W. F., 73, 118,

Dyer, J. M., 773 Dyson, C. W., 589

511

Ferrell, J. K.,

Ferris,

W.

A. D., 125

Fottinger, H., 40, 47, 50, 61, 70

Fournier, Adm., 221

Fowler, H. 169, 180,

Fowler,

M.

S.,

39

E., 106

Fox, Uffa, 3, 276, 786, 787 Franklin, B., 337 Freeh, F. F., 779

Freeman, H. B.,

97, 152,

Easter, E. W., 673

Freimanis, E., 791, 792 Frick, C. W., 704

Ebel, F. G., 503

Froude, R. E.,

C, 184 Eckhardt, M. K.,

127,

116,

E., 588, 859

Forest, F. X., 236, 248, 301

337, 338, 479

607, 643, 820, 823, 865

98,

257, 274, 278, 280, 287, 314, 509,

95 T. E., 236, 502 Fisher, C. R., 755 Fisher, J. W., 154 Flachsbart, 0., 74 Flamant, G., 183 Flamm, O., 38 Fleming, R. H., 184, 185, 921, 922, 925 Flodin, J., 804 Flugel, G., 37, 78, 608 Foerster, E., 237, 359, 607, 674 Forbes, R. B., 571

227, 272, 321, 331, 335, 415, 564,

Dahlmann, W.,

T., 172, 184 Edstrand, H., 153, 157, 597, 609, 792, 798, 799 Edward, J., 764 Edwards, V. B., 674 Eggert, E. F., 47, 154, 244, 245,

687 Diehl, W. S., 270, 271, 291, 323 Dieudonnfe, J., 157 Dillon, E. S., 508, 513 Dimpker, A., 440 Diproso, K. V., 82 Dislere, 129 Dodero, E., 547 Doell, H. A., 579 Doherty, C. S., 271 Dorey, S. F., 635 Douglas, W. R., 537 Doust, D. J., 787 Douty, J. F., 787 Downer, H. C, 756 Doyere, C, 316 Dryden, H. L., 2, 4, 82, 131 DuBosque, F. L., 3ll, 790-793 Du Cane, P., 833, 834, 866 67, 371, 568,

865 Curry, M., 275, 276 Curry, W. H., 82 Curtiss, G. H., 269 Cutland, R. S., 131, 132, 325 J. F.,

Edmonson, W.

Fancev, M., 312

Dewey, D. R., 49 Dickmann, H. E.,

Currie, W., 561

Curry,

Eden, C. G., 39

158,

de Rooij, G., 228, 553, 558, 684,

C, 674

Collar, A. R., 342

Eckman, V. W., 185

510, 514, 684

Deacon, G. E. R., 184 de Berlhe, B., 673 de Bothezat, G., 141 Deetjen, R., 336, 648

Denny, Sir M. E., 311, 712, 791 Denny, W., (Shipyard), 241 Deparis, G., 358

Coffee, C. W., Jr., 273

Cohen,

C,

Darnell, R.

1,

157

99, 241, 457, 585,

586, 752, 906, 913

Eckart,

610, 627

Froude, W.,

3,

99,

129,

140, 183,

PERSONAL-NAME INDEX 185, 241, 306, 311, 370, 390, 440,

748, 781

W.

G., 70 E.,

211, 215, 216, 218,

Guins, G. A., 837, 865 Guntzberger, H., 286, 440 Gutsche, F., 80, 82, 85, 144, 579,

656

Gagnatto, L., 286 Gaillard, D., 183 Gamon, T. A., 865 Gannett, H., 660 Garabedian, P. R., 158 Garber, H. J., 49 Gardner, H. A., 125 Gardner, J. H., 336 Garibaldi, R. J., 438 Garthune, R. S., 413 Gates, S. B., 82 Gatewood, R., 183 Gautier, J., 242

Gawn, R. W.

607, 608, 687

Haack, M., 415 Haas, H., 532 Hadeler, W., 865 Hadler,

Hama,

334, 357, 378, 519

F. R., 132

Hamilton, Hamilton,

J.,

662

W.

S., 98,

Hammar, H.

L., 125, 153, 157, 158,

386, 585, 586, 608, 609, 631

596 Gerstner, F., 174, 182 Gertler, M., 42, 132, 223, 231, 301,

303, 318, 472, 878

Ghiradi, L., 818 Gilbarg, D., 158

H. W., 340 Gillmor, H. G., 331 Gill, J.

256

G., 805

Hancock, C. H., 49, 98, 416 Hankins, G. A., 4 Hannan, T. E., 609 Hanovich, I. G., 276, 349 Hansen, M., 129 Hanson, H. C., 547, 773, 774 Hanzlik, H. J., 703 Hardy, A. C., 279, 672, 653, 772 Harlemen, D. R. F., 185 Harper, M. S., 255 Harris, J. E., 125

Gilmore, F. R., 168

Harris,

R. G., 157

Harrison, M., 168

608, 609

I.,

J. B.,

Giroux, C. H., 665

Hart, M., 335, 647, 648, 689

Glauert, H., 18, 71, 343, 352, 609

Hartman,

Gleyzal, A. N., 441

Harvald, S. A., 243, 245, 246, 262, 359, 368-370

Goldstein,

S.,

Goodall, F.

79, 80,

2,

C,

105, 607

547, 671

Goodall, Sir S. V., 82

Goodrich,

773

J. F.,

Gouljaeff, N., 805

Graef, E. W., 764

Graemer,

L.,

Graham, D. Graham, D. Granberg,

794 609

J.,

705 773, 774

P., 125,

W.

J.,

Granville, P. S., 131

Gras, v., 336

Grasemann,

C.,

790

Gravier, G., 572

Gray, T. L., 666 Green, A. E., 167 Green, C., 791 Green, R., and H., 338 Greening, H. B., 685 Greer, J. F., 269 Grenfell, T. E., 725, 726, 866 Griffiths, R.,

523

Grim, O., 441 Gross, C. F., 791

Grunberg, V., 272 Grupp, C. W., 273 Gruschwitz, E., 98, 130 Guidoni, A., 272 Guillonde, L., 564

935

W.

Herrnstein,

H., Jr.,

141,

293

Hess, G. K., Jr., 441 Hess, R. L., 441

Hewins, E. F., 372, 704 Heyerdahl, T., 3, 698 Hidaka, K., 180 Higgins, T. J., 51 Hill, J. G., 82, 335, 688, 605, 609,

Hagan, H. H., 306, 364 Hagen, G. R., 722 Halldin, G., 805

Gebers, F., 38, 103, 130, 335, 336,

Ginzel,

S.,

219, 221, 608, 609

Fuhrmann, Fuller,

Guilloton, R.

G., 766

Harvey, E., 157 Harvey, H. F., Jr., 705 Harvey, J., 786 Harvey, J. F., 67 Havelock, Sir T. H., 67, 206, 207, 210-213, 215-219, 331, 391, 416, 440, 441

610, 616 Hind, J. A., 662 Hinterthan, W., 586 Hinz, M., 674 Hiraga, Y., 130, 267, 311 Hobson, C. A., 639 Hoerner, S. F., 272, 281, 291, 293296, 323, 727, 748, 749 Hogner, E., 132, 161, 184, 211 Hollander, A., 157 Holm, W. J., 126 Holmberg, G., 805 Holmes, G. C. V., 571 Holstein, H., 432, 440 Holt, W. J., 765, 773

Homann,

F., 131

Hook, C., 272 Hoppe, H., 98, Horn,

130, 262

F., 40, 47, 61, 109,

HI,

127,

319, 336, 607, 608, 687

Home,

L. R., 441

Hotchkiss, D. v., 339, 340

Hovgaard, W., 161, 266 Howard, R. G., 82 Howe, J. W., 2, 94, 141, 776, 925 Hsu, E.-Y., 42 Hubbard, P. G., 51 Hughes, G., 104, 132, 144, 279, 282, 286, 684 Hughes, W. L., 144 Hunnewell, F. A., 805 Hunter, A., 444, 770 Hunter, H., 144 Huntley, H. E., 4

Hawksley, T., 227 Hay, A. D., 141 Hay, J. S., 112,275 Hay, M. F., 764, 809

Hutchinson, J. F., 252

Hay, N., 51

Ijsselmuiden, A. H., 552, 564

Hayes, 337 Hayes, H. C, 144 Heoking, J., 634 Heckscher, E., 242, 416 Heiser, H. M., 416 Hele-Shaw, H. S., 20, 33, 36 Hellerman, L., 71 Helm, K., 336, 337, 416, 439 Helmbold, H. B., 343, 607 Helmholtz, H., 144 Henry, J. J., 228, 755, 762 Henschke, W., 276, 336, 360, 656, 687, 773 Herreshoff, L. F., 754, 787, 862, 866 Herreshoff, N. G., 669, 754, 784, 790, 862

Ikada,

Idle, G.,

816

Igonet, C., 242, 262, 704

S.,

360

Imlay, F. H., 273 Ince, J., Inui, T.,

183,208 222, 300

Ippen, A. T., 185 Irish, J. M., 154 C. O'D., 175, 287 Isherwood, B. F., 663, 807 Iselin,

Izubuchi, T., 257

Jacobs, E. N., 74 Jacobs,

W.

R., 215, 221, 867

Jaeger, H. E., 774

James, R. W., 176, 184 Janes, C. E., 259 Jasper, N. H., 349, 362, 500, 571

HYDRODYNAMICS

936 Jastram, H., 674 Jeffreys, H., 184 Joerg,

W.

L. G., 929, 931

Joessel, 74

Johnston, L., 270 Jones, B. M., 82

B.

D., 228, 283, 307, 634, 752,

786, 790

Kotik,

G., 98, 121, 125, 130, 131,

V., 126

Lovett,

Sir H., 2, 48, 71, 141, 181,

184, 185, 215, 420, 441 J. H., 130,

Lamonds, H.

256

95

A.,

Land, N. S., 272 Landweber, L., 16, 42, 102, 110, 128, 131, 132, 141, 301, 395, 396,

410, 422, 423, 427

Lang, H., 674 Langhaar, H. L., 4 Lankester, S. G., 144 Lap, A. J. W., 104, 132, 279, 312;,319 Latimer, J. P., 268, 866 Lattanzi, B., 704 Laubeuf, M., 244, 415

Lavine,

131, 132

J.,

I.,

Lavrent'ev,

930

M.

A., 184,

250, 313

Leehey,

273

P., 271,

Lefol, J.,

368

Legendre, R., 39

Lehman, W.

F., 266, 268, 271, 851,

866

Kinoshita, M., 218, 360, 734

Kirby, F. E., 336, 664, 797, 804 Kirchhoff, G. R., 208

Lerbs,

H. W.

Kito, F., 637

Levi-Civita, T., 184 131, 132

Klein, E., 144 Klikoff,

W.

Knapp, R.

A.,

42

T., 157, 158

Knight, M., 82

Knowler, H., 271, 272 Koch, J. J., 50, 431, 433-436, 440 Koning, J. G., 74, 75, 77, 130, 231, 244, 279-281, 290, 291, 319, 325,

272

Lavrent'ev, V. M., 222, 228, 229,

W.

S.,

E., 128, 287

Lovell, L. N., 335

Leland,

Klebanoff, P.

M.

Kretzschmar, F., 336 Kriimmel, O., 183 Krzywoblocki, M. Z., 131, 132 Kuethe, A. M., 82 Kurr, G. W., 704 Kutta, W., 25

Laute, W., 47, 98, 256

W.

Long,

Lord, L., 845, 865 Lorenz, H., 221 Losee, L. K., 765, 768

Lamble,

S.,

271, 866

82

Losch, F., 608

Laufer,

194

S., Jr., 132,

Jr.,

Krappinger, O., 336 Kreitner, J., 416

596, 607, 608, 650, 661, 739

Kennard, E. H., 33 Kennedy, A., Jr., 755, 791 Kent, J. L., 25, 40, 47, 204, 244, 279, 325, 415, 608, 764 Kermeen, R. W., 158 Kerr, W., 144 Keulegan, G. H., 184

Loeser, O.,

Loftin, L. K., Jr., 609

206, 216, 217, 221, 319

J.,

W.

Locke, F.

Kramer, K. N., 608

234, 279, 282, 337, 359, 372, 439,

Kielhorn,

206,

319, 369, 371, 851, 866 Kostyukov, A. A., 391 Kotchin, N. E., 272

Lamb, 438, 441, 580,

Kelvin, Lord, 71, 160, 161

J. J., 189,

V.,

Labberton, J. M., 574 Lackenby, H., 104, 113, 129, 205, 311, 325 Lagally, M., 69, 71, 141

585-587, 591, 600, 609 Kaplan, C, 42 Kapryan, W. J., 271 Karhan, K., 98, 131, 132 Kari, A., 804 Kassell, B. M., 805 Keeton, H., 182 Keith, H. H. W., 588 Keldysch, M. V., 272

Kendrick,

T. O., 570 Lock, C. N. H., 343, 416 Locke, D. and A., 790

A., 158

Laas, W., 178, 179

Joukowski, N., 84 Judaschke, F., 805 Jury, S. H., 49

Kempf,

Lisle,

W.

Konstantinov, Koppen, 276

215-217, 221, 262, 266, 268, 271,

Johnson, A. J., 434, 441 Johnson, E., 765, 791 Johnson, H. F., 796, 797, 799, 805 Johnson, J., 566 Johnson, J. B., 157 Johnson, M. W., 184, 185, 921, 922, 925 Johnson, R. W., 765, 865 Johnson, V. D., 865 Johnson, V. E., Jr., 159

Kemp,

Lindgren, H., 798, 799

713, 714, 765, 793

Korvin-Kroukovsky,

Johansen, F. C, 416 John, F., 441 John, W., 227 Johns, A. W., 221

Kaemmerer, 272 Kaemmerer, W., 335 Kane, J. R., 349, 437,

IN SHIP DESIGN

331, 375, 376, 416, 609, 650, 684,

237 E.,

47,

583,

605,

607-610, 619, 656

Lewes, V. B., 125 Lewis, E. v., 123, 126, 456, 508, 513 Lewis, F. M., 144, 335, 418, 426- 428, 430-433, 440, 580, 585, 588, 591, 592, 595, 597, 609, 637 Lewis, R. G., 40, 42, 43

Lewy, H., 158 Liddell, E., 465

Lindblad, A. F., 250, 509, 514, 755

W.

J.,

554

Low, D. W., 779 Lowery, R., 445 Luders, A. E., Sr., 865 Ludwieg, H., 608 Luke, W. J., 369, 370 Luke, Y. L., 926 Lundberg, S., 440 Lunde, J. K., 67, 161, 211-222, 391, 416 Lutzky, M., 144 MacMillan, D. C., 565 Macmillan, J. F., 548 Macovsky, M. S., 81, 147, 157 Macy, R. H., 805 Maginnis, A. J., 540 Malavard, L., 50, 51 Malglaive, P. de, 279 Mallock, 38 Mandel, P., 143, 147, 151, 288-290, 294, 295, 678, 691, 694, 714, 727, 729, 734

Mann, C.

F. A., 773, 774

Manning, G.

C., 161, 182

Marchet, P., 51 Markland, E., 51 Marmer, H. A., 184 Marran, F. L., 835 Marriner, W. W., 415 Marshall, D., 129, 144 Marussi, A., 180

Marwood, W. J., 433, Mason, C. J., 663 Mason, J., 867 Mason, M. A., 184 Mason, W. P., 157 Mathews, S. T., 755

434,

441

Matthews, L. H., 774 Matveyey, R. T., 274 Maxwell, C., 208

May,

A., 441 McAleer, J. A., 764 McAUster, F., 583 McCarthy, E. W., 779 McEh-oy, W. D., 157 McEntee, W., 47, 120, 125, 279, 579, 673, 764 McGoldrick, R. T., 236, 349, 431, 433, 437-441, 580, 600, 609 McGraw, J. T., 158

PERSONAL-NAME INDEX McKann, R. E., 273 McKay, D., 228 McKee, A. I., 810 McKee, P. B., 82

Nixon, L., 469, 786 Nolan, R. W., 279, 563, 564 Noonan, E. P., 438

Nordstrom, H.

McKenzie, I. L., 865 McKinney, E. G., 77 McLachlan, G. W. P., 790

McNown,

J.

S.,

42, 48,

515, 676

Mendl, W. V., 805 Metzler, D. E., 776 Meyer, E. R., 879 Michel, P., 359

W.

176, 184

J., Jr.,

Pitrc, A. S., 125, 279, 331

855, 920

Plessct,

W.

Normand,

H., 329, 414

J.-A., 157,

479

Norton, P. H., 82 Norton, H. P., 548

Melville, G. W., 237

Picrson,

Pinkerton, R. M., 74 Pistolesi,. E., 71

596, 679, 772, 792, 798, 850, 854,

Norloy, 152, 157,

P., 98, 250, 311, 388,

937 Piercy, N. A. V., 82

M.

S., 157,

158

Plum, J., 272, 852 Pluymert, N. J., 228 Poisson, S. D., 183 Pollard,

Nowka, G., 321, 445, 660 Numachi, P., 158

32, 70,

J.,

104,

Nystrom,

J.

Middendorf, 221

Ober,

786

Miedlich, P., 537

O'Brien, T. P., 609

Pommellct, A., 173 Pond, H. L., 157 Popper, S., 415 Posdunine, V. L., 153, 631 Pournaras, U. A., 271 Powell, J. W., 240

Millar, G. H., 269,

Oetling, J. J., 272

Prandtl, L.,

Miller,

734 609 Olsen, H. M., 791 Olson, C. R., 413 Olson, R. M., 158 Orlando, M., 702, 704

Nutting,

W. W., 272 W., 187, 188, 191, 204

Miehell, J. H., 189, 211, 219

270 R. T., 273, 865

(.)kada, S.,

Millikan, C. B., 129

Okeil,

Milne, D., 182

Milne-Thomson, L. M., 48, 69, 71, 185, 420 Minorsky, V., 358

2, 21,

25,

Mitchell, A. R., 333, 660, 667, 669672, 674

Mitchell, E. H., 791

Mohr,

E., 71

Monk, E., 829, 832, Moody, C. G., 178

833, 867

Moore, A. D., 67 Morgan, W. B., 338, 610, 627 Morris, H. N., 114, 132 Morwood, J., 787 Mosher, C. D., 755 Mossman, E. A., 704 MouUin, E. B., 431, 440 Mueller, H. P., 333, 337, 436, 594, 656, 658 Mueller, J., 157, 594 Munk, M. M., 71, 77, 214, 343

Munk, W.

H., 184

Munroe, F. A., Jr., 662 Murnaghan, P. D., 2, 4 Murray, A. B., 266, 268, 269, 271, 785-787,

Nakamura, Nansen, Napier,

S.,

866

300 797

P., 796,

J. R., 187,

Narbeth, Neifert,

847-851,

840,

207, 210, 227, 335

J. H., 187,

H.

S.,

547

R., 351, 361

Neuerburg, E. M., 427, 432 Neumann, G., 176, 184 Nevins, H. B., 787 Nevitt, C. G., 464, 465, 496 Nicholls, H. W., 424, 439 Nichols, H. J., 579 Niekerson, A. M., Jr., 241, 349 Nickum, G. C., 773 Nicolson, D., 658, 865 Neidermair, J. C., 170, 478, 496 Nikuradse, J., 114, 130 Nimitz, C. W., 558

M.

Prohaska, C. W., 428-436, 440, 441, 588, 589, 592-594

Parsons, Sir C. A., 153, 600, 678, 701, 754

Parsons, H. de B., 516, 775, 777 Parsons, J. P., 82

82

J.,

Peres, J., 50, 51 J.,

W. G.

440 A., 82,

270

Perry, B., 140, 271 Peskett, L., 228 Peters, S. A., 865

Petrich, J. P., 773

Phannemiller, G. M., 867 Phillips-Birt, D., 653, 786, 822, 823,

834, 835, 837, 843, 853, 854, 862, 863, 866, 867

Phipps, G. H., 210 Pien, P. C., 198, 218, 334, 357, 368,

374, 378, 519

J.,

184

Rabbeno, G., 632, 703 Rabl,

S. S.,

272

Randall, L. M., 704

Rankin, G. P., 756 Rankine, W. J. M., 68, 70,

xix, 39, 57-59,

117, 166, 183, 187, 194,

208-210, 219, 335, 368, 370, 443, 549, 708, 715 Rasmussen, A., 415 Rattray, M., Jr., 158

Rayleigh, Lord, Rayner, P., 410

Paulus, 328, 390, 415 Pavlenko, G. E., 222, 270, 313, 316, 319, 765 Payne, M. P., 129 Peabody, C. H., 103, 169, 227, 237, 240, 279, 370, 371 Peary, R. E., 796 Peebles, P. N., 49 Pengelly, H. S., 175, 479, 818

Perring,

Proudman,

Pugh, M. D., 773 Purvis, P. P., 241

Rawlins, T. E., 49

184

Paulding, C. P., 791

Perkins, A.

H. S., 705 H. N., 276, 552, 562

Preiser,

Prins,

Panagopulos, E. P., 241, 349 Parkin, B. R., 158

S.,

129-131,

Praznik, O., 474

Ormondroyd, J., 670, 672 Ormsby, R. B., Jr., 82 Osbourne, A., 372 Owen, G., 772, 787 Owen, P. R., 42 Owen, W. S., 228, 482 Ower, E., 565

Patton, R.

2, 40, 99, 125,

141, 607

E.,

Paterson, C.

129, 335,

337, 338, 479

4,

183

Reber, R. K., 43 Reed, T. G., 82 Reilly, J. R.,

704

Relf, E. P., 50, 141

Rennie, G. B., 781 Retail, R., 312

Rethy, 48 Reynolds, 0., 99, 129, 157, 817 Riabouchinsky, D., 4 Richards, G. J., 141 Richardson, E. G., 82, 144 Richardson, P. M., 95 Richardson, H. C., 270, 272, 865 Richter, E., 279, 565 Riddell, A. M., 687 Riebe, J. M., 77 Riegels, P., 42 Riehn, W., 335 Rigg, A., 259, 260 Roach, C. D., 334, 378, 390 Robb, A. M., 103, 160, 311, 390, 416, 486, 764 Robertson, J. C., 354, 596

HYDRODYNAMICS

938 Robinson, A. W., 779 Robinson, H. F., 228 Robinson, J. H., 351, 361 Robison, D., 773, 777 Robison, J., 183 Roebling, D., 806 Roeske, J. F., 228 RoUand, E., 754

Romani,

Schiffer,

Schlichting, H., 103, 125, 130-132, 181, 242

SchUchting, O., 391, 392, 394-396, 399, 410 Schlick, 0., 439

Schmidt, H. F., 703 Schmidt, W., 416, 586-589

L., 51

Romano,

P., 360,

Schmierschalski, H., 333, 655

553

Schneider, A. J. R., 158

Ronan, K. M., 270 Roop, W. P., 125, 679

Schoenherr, K. E., 74-77, 82, 102,

Roscher, E. K., 687, 688

Rosenberg, B., 49, 413 Rosenhead, L., 141 Roshko, A., 144 Ross, Sir

C,

130, 151, 153, 262, 279, 301, 336, '

833

Rota, G., 415 Roth, W. A., 925 Rothe, 221 Rotta, J., 131 Rougeron, C, 308 Rouse, H.,

2, 4, 8, 16, 25, 31, 48, 51,

73, 75, 85, 94, 104, 128, 130, 141

142, 152, 153, 157, 183, 208, 291,

615, 649, 676, 776, 777, 920-925

Rubach, H., 141 Rumsey, J., 337 Runeberg, R., 795-797, 799, 804 Runyon, J. P., 141 Rupp, L. A., 338, 349, 362, 500, 571, 579, 755 Russell, J. S., xix, 183, 207, 209,

227, 244, 651, 665 Russell,

N.

665

S-,

IN SHIP DESIGN

H. F., 272 M., 158

Schertel,

Russo, V. L., 236, 255, 282, 431, 695, 707 Ruthven, J., 338

369, 371, 374, 585, 587, 594-598, 602, 603, 607, 608, 610, 630, 634,

713, 720, 722, 893, 894

Schoeneich, 275, 279 Schokker, J. C. A., 427, 432

Smith, Smith, Smith, Smith, Smith, Smith,

A. G., 268 E. H., 575 F. v., 791 L. P., 152, 153, 586, 607, 631

R. A., 773 R. H., 42 Smith, R. M., 805, 865 Smith, S. L., 311, 422 Smith, W. W., 116, 126, 279, 285, 564 Smith-Keary, E. M., 650 Snyder, G., 773 Sokol, A. E., 795 Solberg, H., 185 Soloviev, U. I., 276, 349 Sottorf, W., 270-272, 279 Spanner, E. F., 773

Sentid, A., 656

Spannhake, W., 85, 704 Sparks, W. J. C., 205 Speakman, E. M., 227 Spencer, D. B., 347 Spooner, C. W., Jr., 268, 841, 842, 866 Springston, G. B., Jr., 271 Sprinkle, L. W., 155 Squire, H. B., 564 Sretensky, L. N., 217 Stalker, E. A., 564

Serrin, J. B., Jr., 158

Stanton, T. E., 129, 144

Seward, H. L., 394, 395 Seydell, 338 Sezawa, K., 221, 440

Stapel, G., 674

Shaffer, P. A., 157

Steel, D.,

Shalnev, K. E., 158

Steele, J. E.,

Schroder, P., 270

Sohubauer, G. B., 131, 132 Schubert, R., 271 Schultz-Grunow, F., 102, 130, 131 Schumacher, A., 179 Schuster, S., 416 Schutt«, J., 415 Schwabe, M., 141 Sedov, L. I., 271

Shannon,

J. F., 82, 144,

St.

150

Shapiro, A. H., 923

Sharman, C.

F., 49,

Denis, M., 139, 218, 243, 378,

421, 441

50

33

270 Steinman, D. B., 144 Stephens, E. 0., 765 Stephens, O. J., II, 784

W.

787

Sharp, G. G., 234, 564, 565

Stephens,

Shaw, H. R., 835 Shaw, P. S., 867 Shearer, J. R., 217 Shearing, D., 774 Shelton, G. L., Jr., 51

Stevens, A. D., 774

Salisbury, J. K., 105

Shepheard, Sir V. G., 125, 552, 563

Stivers, L. S., Jr., 74, 272, 606,

608

Sambraus, A., 271 Saunders, H. E., 331

Sherlock, R. H., 564

Stokes, Sir G. G.,

185

Sherman,

Stoltz, J.,

Sasajinaa, H., 114, 132

Shigemitsu, A., 47, 129, 241, 257, 311

Stracke,

M., 270 Siestrunck, R., 50, 51 Silovid, S., 312 Silverleaf, A., 609

Strassel, H.,

Sachsenberg, G., 272 Sadler,

H. C, 241, 255, 336, 415,

664, 683, 755, 764 Salet, G.,

Sassi, S.,

50

P.,

Shoemaker,

600

Savitsky, D.,

266, 268, 271, 851,

866 Sawyer, J. W., 131 Sawyer, W. T., 85 Sayre, C. L.,

Jr.,

Scarborough,

W.

271 G., 378, 565, 581,

597 Schade, H. A., 703 Schadlofsky, E., 418, 440

271

J.

Simmons, L. F. G., 77, 141, 195 Simmons, N., 158 Simonson, D. R., 795, 798, 805 Simpson, D. S., 228, 446, 469, 688, 765, 770, 772-774, 820, 832, 855,

Schaeffner, C. R., 756

866 Simpson, G.

Schafer, O., 98, 262

Sims, A.

Schaffran, K., 336, 586, 587

Skene, N. L., 785, 787, 820, 834,

Scheel, H., 787

835, 854, 865 Skramstad, H. K., 131 Slocum, S. E., 4, 607

Scheel, K., 925

Scheffauer, F. C., 778, 779

J.,

C.,

175,

684 818

P., 228, 786,

Stevens, E. A.,

Jr.,

125, 228, 279,

640, 790, 791

Stewart,

W.

C., 156

Stilwell, J. J., 271,

273 129,

183,

867

W.

L., 81, 147,

157

608

Streeter, V. L., 2, 43, 45, 67, 106

Streever, O.

J.,

Stuntz, G. R.,

705 Jr.,

334,

357,

378,

519 Styer,

W.

S.,

779

Suarez, A., 866 Siiberkrub, F., 336, 688

SuUivan, E. K., 236, 255, 282, 378, 565, 581, 597, 695, 707, 733

Sund, E., 319, 331

W. J., Jr., 707 Surugue, J., 51 Sutherland, W. H., 47, 255 Sverdrup, H. U., 184, 185, 921, 922, 925 Surber,

PERSONAL-NAME INDEX Swan, H. F., 804 Swan, J., 377 Symonds, R. F., 770, 772, 774

Troost, L., 74, 77, 104, 130, 132, 231, 279-281, 290, 319, 325, 343, 359, 370, 375, 576, 587, 597, 605,

Tachmindji, A. J., 350, 352 Taggart, R., 199, 200, 203, 205 Takagi, A., 300, 303, 772 Takahashi, W. N., 49 Talen, H. W., 132 Tanner, T., 82 Tasseron, K., 338, 579 Taylor, A. R., 773 Taylor, D. W., 4, 24, 40, 47, 59, 103, 180, 188, 204, 242, 248, 274, 298,

307, 317, 325, 331, 368, 407, 415, 467, 482, 485, 489, 493, 509, 517,

608-610, 621, 625, 650, 684, 713, 714, 765, 793

Troucer,

564

J.,

Trowbridge, H. O., 772, 774 Truscott, S., 271 Tulin, M. P., 158, 159, 632 Tupper, K. F., 416 Turnbull, J., 169, 182 Turner, R. F., 790

439, 440

Ward, C. E., 335, 659, 665, 672, 073 Ward, K. E., 47, 74, 270 Ward, L. E., 272 Ward, L. W., 765, 865 Ware, B. E., 787 Warholm, A. O., 243 Warner, E. P., 786 Warren, C. H. E., 273 Warrington,

Aken,

204

Watsuji, H., 552

Watts, Sir P., 415 Weaver, A. H., Jr., 255 Weber, E. H., 183

Valensi, J., 564, 565

van van van van van

J. N., 188,

Wasraund, J. H., 805 Watanabe, W., 440

UUyott, P., 49 Upson, R. H., 42 Ursell, F., 441

586, 620, 642, 678, 764, 901, 918

Taylor, G. I., 49, 50, 71, 157 Taylor, J. L., 125, 424, 430, 431,

939 Walker, V., 39 Walker, W. P., 113,311,822 Wallace, W. D., 144 WanlesB, I. J., 228, 237, 700

J. A., 338, 579,

637

der Hegge Zijnen, B. G., 129

135, 154, 231, 243, 262, 279-281,

Weber, W., 183 Weeks, A. F., 154 Wehausen, J. V., 81, 147, 157, 211 Weick, F. E., 343, 607 Weinblum, G. P., 71, 177, 188-194,

Teubert, O., 335, 640, 643, 648, 673 Thaeler, A. S., 228

290, 312, 319, 325, 375, 399, 465,

204, 206, 211, 215-219, 222, 323,

Thayer, E., 465 Theodorsen, Th., 630 Thews, J. G., 125 Thiel, P., Jr., 765, 865 Thiele, E. H., 805 Thieme, H., 205, 271, 564 Thomas, J. B., 764 Thompson, R. C, 481 Thomson, W., 182 Thorade, H. F., 184 Thornton, K. C, 537 Thornycroft, Sir J. I., 157, 673 Thorny croft (Shipyard), 338 Thorpe, T., 285, 287 Thurston, R. H., 187

605-607, 610, 631, 634, 650, 682,

Taylor,

640

S.,

Telfer, E. V., 3, 104, 125, 318, 319,

757

824

Teller, C. R.,

Tideman, B.

J., 99,

Driest, E. R., 4

K. T., 157 Lammeren, W. P. A.,

Iterson, F.

74, 113,

687, 706, 713, 714, 722, 726, 729,

421, 441 Weinig, F., 270, 272, 609 Weinstein, I., 271

765, 793

Weissinger,

485, 537, 540, 585-587, 596, 602,

Tietjens, O. G., 2, 37, 40, 130, 141,

272

608, 619

Weitbrecht, H. M., 114, 359, 371

595-597, 602, 605, 609, 610, 621,

Wendel, K., 417, 420, 427, 430, 431, 441

625, 656, 688

Werback, C. E., 765, 834, 853, 858 Weske, J. R., 703

van Meerten, 70

Van Van

Patten, D., 271, 272 Zandt, T. E., 71

Vaughn, H.

779

B., Jr.,

Vedeler, G., 479

Vennard, J. K., 2, Veres, G. A., 447 Vertens, F., 272

4, 8, 44, 76,

157

Vincent, S. A., 117, 231, 465, 474, 479, 483, 485, 553

103, 129

J.,

J. D., 312, 319, 360,

van Manen,

Vinogradov, Viskovid,

I.,

I.

799, 804, 805

V.,

157

West, C. C., 777 West, H. H., 547 Wheelock, C. D., 169, 170 White, M., 276 White, Sir W. H., 227, 331, 337, 415 Whiteley, A. H., 157 Wickwire, C. J., 787 Wieghardt, K., 131 Wigley, W. C. S., 206, 207, 211, 217219, 243, 244, 510

131, 153, 211, 228, 236, 248, 301,

Volpich, H., 335, 336, 355

Wilda, 221 Wilhams, E. B., 537 Williams, H., 125 Williams, M. E., 651

360, 374, 424, 429, 433, 440, 441,

von Doenhoff, A.

Williams,

Tingey, R. H., 600, 606, 608, 633,

Visscher, J. P., 125

634 Todd, F. H.,

Vladimiroff, A., 272 3, 99, 101, 126,

130,

485, 519, 631, 764

Todd, M. A., 189 Togino, S., 47, 241, 257, 311 Tollmien, W., 71

Tolman, R.

C., 4 Tomalin, P. G., 540, 820, 833, 854, 859, 862, 866 Toogood, 337 Torda, T. P., 416 Towne, S. R., 865

Townsend, A.

A., 131

Trask, E. P., 237

Traung, J.-O., 298, 300, 771-773 Trilling, L., 158

Volker, H., 686, 683 E., 74, 272, 606,

608

von Kdrmdn, Th.,

6,

38, 42,

130, 141, 607

von Larisch, Graf, 184 Vossnack, E.

Votaw, H.

J.,

427, 432

C., 181

Waas, H., 542, 670 Waeselynck, R., 158 Wagner, H., 270 Wagner, R., 38, 732 Walchner, O., 157 Walcutt, C. C., 864 Walker, R. J., 349

103,

W.

L.,

156

Williamson, B., 765 Williamson, R. R., 221 Wilson, R. C., 659, 673 Wilson, T. D., 227 Winter, H., 73, 82

Winzer, A., 422, 423, 427 Wislicenus, G. F., 25, 85, 649

Wood, G., 818 Wood, R. McK., 157, 343 WoodhuU, J. C., 441 Woolley,

Work, C.

J.,

Wormald,

183

E., 144

Workman,

J. C., J.,

448

755

HYDRODYNAMICS

940 Worthen, E.

P.,

704

Wright, E. A., 98, 99, 141, 286, 411, 413, 416, 764, 765 Wrobbel, J. F. K., 764 WyckoEf, C. D. S., 791

Yamagata, M., 359, 608, 734

Yamamoto, 764

T., 47, 241, 257, 311,

IN SHIP DESIGN

Yang, C. S., 374, 599, 609 Yarrow, A. F., 311, 331, 410, 669, 671, 673 Yarrow, H., 415 Yokota, S., 47, 241, 257, 311 Yoshida, E., 114, 132 Young, A. D., 42 Young, C. F. T., 125 Young, D. B., 293

Young, Young,

E., 42

T., 183

Zahm, A.

F., 25, 40, 129, 141, 419,

421 Ziloher, R.,

336

Zimmerman, 0. T., 930 Zimmermann, E., 170, Zuehlke, A.

J.,

756

176,

183

Ship-Name Index In addition to the ship names occurring in the text, there are listed here a few class names, such as "Export Line ships," to cover cases where individual ship names are not given.

In man}' cases the pages listed in this index contain only references to the subject of the abbreviated index entry, and not the subject itself. For example, under Allegheny in the column below, page 233 of this volume does not embody a reproduction of the body plan but tells where it may be found.

Berlin, old paddle steamer, wheel data, 335 Bismarck, battleship, bower anchor stowage on deck,

556 Bremen, German lifesaving "cruiser," 818 Bremen, hydrofoil-supported boat, 273 Bremen, New York harbor ferryboat, 791 Bridge, supply ship, displacement of appendages, 296 rudder area, 714 Bristol Queen, modern paddle steamer (1947), description of model paddlewheel tests and self-propelled model tests, 336 Britannia, pass'r vessel of 1840, general data, 228 Britannia, royal yacht, air-flow tests on model, 563

Abner T. Longley, Honolulu fireboat, 775 A. D. Haynes II, large river pushboat with long tunnels,

Brunsbiitiel,

669

Brunshausen,

with

single

Bryderen, early icebreaking steamer, 804

Akron, airship, achieving easy transition to parallel middlebody, 194, 196 boundary-layer measurements on model, 97 longitudinal potential flow around, 42 Alarm, lightship, 815, 816 Albert, vessel of 1853 with hydraulic propulsion, 338 Aldebaran, French minesweeper, towing tests, 312 Alexander, Russian icebreaker, 804 Algonquin, USCG icebreaking cutter, 805 Alki, Seattle fireboat, 777 Allegheny, pass'r-cargo vessel, standard body plan, 233 Altmark, fast tanker, ref data on parallel DWL, 231 Ambrose, lightship, 816 America, pass'r liner, ref data on parallel DWL, 231 multiple model tests, 502 section coeff in entrance, 516 self-propelled model test data, 379 Ammonoosuc, high-speed cruiser of 1867, self-propulsion model test data, 377 Amsterdam, triple-screw tug, 674 Antilles, pass'r liner, projecting bulb on, 510 Arctic, store ship, rudder area, 714

Bunker

Arcturus, shrimp trawler, 773

ARD

screwprop

well

abaft sternpost, 568

Aegir, early icebreaking vessel, 804

ARD

8, ship-shaped floating drydocks, 780, 781 1, Argonaut, U. S. submarine (of 1928), with crossed recessed anchors, 557 Arizona, battleship, projecting bulb on, 510 Arrow, ultra-high-speed displacement-type yacht, 755 Asheville, gunboat, displacement of appendages, 296

Ashworth, channel steamer, boundary-layer vel full-scale

profile,

98

wake measurements, 262

Augsburg, motorship, full-scale towing tests with rotatingblade props, 337 Aquitania, Atlantic liner of 1915, general data, 228

ATF-163,

fleet tug,

flow pattern around stern, 255

Badger, Lake Michigan car ferry, 791 Baltimore, (old) cruiser,

wave

profile, lines of flow,

248

Bangor, early ship of 1845 with machinery aft, 571 Benjamin Fairless, Great Lakes ore carrier, 758, 760 Berkshire, pass'r-cargo vessel, standard body plan, 233

941

Hill, fast pass'r-cargo vessel,

232 BB49-5/, 233

class, battleships (of 1919),

standard body plan, standard body plan,

body plan, 232 Cameron, ferryboat, 792 Captain Crotty, Houston fireboat, 777 Carabobo, Venezuelan ferryboat, 791 Carl D. Bradley. Great Lakes self-unloading bulk carrier, 755 Carmania, pass'r liner, ref to photos of triple screws, 521 Carol Virginia, tuna clipper, 773 Castalia, twin-hull channel steamer of 1874, 790 Cerberus, proposed semi-globular battery with underwater mushroom anchor, 558 Charles Belleville, French suction dredge, 779 Chaleaurenaull, French cruiser, photo of Velox waves, 240 Chester, (old) scout cruiser, displacement of appendages, 296 Chryssi, tanker, variation in blade thrust around disc, 349 wave profile at stern, 241 Cincinnati, double-ended ferryboat, body plan and DWL, 793 general dimensions and data, 791 towing tests of, 311 City of Erie, lake paddlewheel pass'r steamer, body plan, 663 general information on, 663 City of New York, old paddlewheel steamer, general data, 665 City of Paris, pass'r vessel, ref data on parallel DWL, 231 Ciudad de Barranquilla, hopper dredge, 779 Clair de Lune, 152-ft French trawler, 774 Clairton, cargo vessel, center-of-wind-pressure data, 285 effect of relative wind on bow, 281 full-scale thrust measurements of 1931, 310 lines of flow and wave profile in run, 252 boundary-layer measurements, 98 unpublished variation of thrust-load coeff with speed, 346 Clemson, destroyer, displacement of appendages, 296 Calijornian, cargo vessel, standard

TMB

HYDRODYNAMICS IN SHIP DESIGN

942 Cliffs Victory, fast

Columbia

Great Lakes ore

carrier, 758,

Dixie, destroyer tender, variation of residuary resistance

760

(old, of 1890), triple-screw cruiser, design notes,

521 stern arrangement, 237 Cormnodore Preble, early ship of 1845 with machinerj' aft, 571 Commonwealth, (old, prior to 1861) paddle steamer, general data, 665 Commonwealth, (new) paddle steamer, wheel data, 641, 643

standard body plan, 232 Concordia, old paddle steamer, wheel data for, 335

Eagle

Edgewater,

and

self-

data on parallel

DWL,

231

with straight-element hull, 764 Corsicana, tanker, ref data on parallel DWL, 231 Cossack, destroyer, full-scale trials in varied depths of ferryboat

water, 415, 416 City,

San Diego Bay

ferry,

Cuba, pass'r vessel, standard body C. W. Morse, paddle steamer, wheel data, 335 Cyclops, collier, standard body plan, 232

curves, 236

and

hull coeffs, 228

DWL,

model

self-propulsion

231

test data,

377

variation of residuary resistance with speed, 307

CS-Sl-Al cargo

CZ-SU

ship, ref

DWL, 231 DWL, 231

data on parallel

cargo ship, ref data on parallel

C-3 cargo vessel, body plan, 236 curve of propulsive coefficient, 895 ref data on parallel DWL, 231 variation of power with displacement and trim, 357 wake survey, 3-diml, on model, 361 CS-S-AS, reference data on parallel DWL, 231 C4-S-la, Mariner class with variations, 3-dimI wake surveys on models, 361-363 C4-S-A1 cargo vessel, ref data on parallel DWL, 231 C4-S-B2, converted to Great Lakes carrier, 756

D. C. Endert,

Jr.,

tests of, 311,

vessel,

ram

773

see Liberty ship

EC2-S-C1 cargo

vessel, ref

data on parallel

DWL,

231

Farragut, destroyer, effect of wind on bow, 281

rudder with short length on top, 710 Flandre, pass'r liner, projecting bulb on, 510

Flying Cloud, clipper ship, designed waterUne, 228, 230 Fram, polar expedition ship, 796 experience with ice over deck, 797

Froude, large independently powered model, test data, 371 wind-resistance tests on, 279

German

San Martin,

iceship for research

and supply, 801^

M. Humphrey,

Gimcrack battleship,

Great Lakes ore

carrier, 756, 758,

760, 761

standard body plan, 233

sail coefficients,

787

Glacier, icebreaker, general information, 801,

photo of Velox

Goeben,

German

803

battle cruiser, photo of Velox waves, 240

Geota Lejon, icebreaker, 805

waves, 240

Canadian

iceship, general data, 800,

Direklor Schliiler, triple-screw tug, 674 Dixie, fast launch

EC2-G-AW2;

George

or bulb, 510

Deluge, Milwaukee fireboat, 777

D'Iberville,

338 Ermack, early Russian icebreaker, 804 Ernest LaPointe, Canadian icebreaker, 805 Ernest T. Weir, Great Lakes ore carrier, 756, 758, 760 Escanaba, USCG icebreaking cutter, 805 Essayons, seagoing hopper suction dredge, 779 Europa, Atlantic liner, general data, 237 Evangeline, pass'r vessel, standard body plan, 232 Evergreen State, large auto and pass'r ferry, 792 plated sponsons on, 794 Export Line ships, 1930, curve of propulsive coefF, 895 Express, early iceship, 804 Express, twin-hull channel steamer, 790

803, 806

319

and processing

Delaware, battleship, projecting

Deutschland, small

572

aft,

Z. Svilzer, early icebreaking steamer, 804

General

312

fishing

Elbjorn, icebreaker, general information, 801, 803, 805

El Djezair, pass'r steamer with machinery

independently powered 72-ft model,

tests of Victory ship geosims,

Deep Sea,

Greene, Great Lakes ore carrier, 756 E. J. Kulas, Great Lakes ore carrier, added mass of entrained water in shallow-water areas, 433, 441 Elbe, Ughtship, 816 Elbert H. Gary, Great Lakes ore carrier, 755

sheer data, 549

of run, 234, 235, 236 Cl-S-Dl concrete steamer, body plan, general data, 764 self-propulsion model test data, 377, 378 C-S cargo vessel, body plan, hull coeffs and section-area

data on parallel

harbor ferry boat, 791

Enterprise, of 1853, with unsuccessful hydraulic propulsion,

Cl-A merchant ship, U. S. Mar Comm design, ref data on parallel DWL, 231 Cl-M-AVl small merchant vessel, body plan and lines

ref

New York

Empress of Britain, pass'r liner (of early 1930's), with two large and two small props, 573 Enem, large whale catcher, general information, 774

792 plan, 232, 233

principal dimensions

beam wind,

Edith, early ship with machinery aft, 571

Em.

Coverack, British lifeboat, 818

Croum

I patrol boat, effect of

Edward B.

Crnite di Savoia, pass'r liner, general data, 237

ref

World War

straight-element hull, 764

propulsion model test data, 379 smoke-exhausting arrangement, 564

Coquivacoa,

class,

286

Condi, French cruiser, photo of Velox waves, 240 Conqueror, small tuna clipper, 773 Constitution, pass'r liner, resistance, propeller,

with speed, 307 Dominion, scow-type yacht with tunnel, 789, 790 DUKW, amphibious landing craft, 806 DD 364 destroyer, ref data on parallel DWL, 231 DD 4BO-4BB destroyers (of 1919), standard body plan, 233 DD 692 class, U. S. destroyers, wind load on multiple-ship moorings, 128

by C. H. Crane, 753

802

Gopher Mariner, cargo ship, added-mass coefficient, 424 small-scale body plan, 236 Governor Miller, Great Lakes ore carrier, 758, 760

SHIP-NAME INDEX Greal Northern, triple-screw pass'r vessel,

body

plan, 237,

238

943

propulsion model teat data, 379 smoke-exhausting arrangement, 564 InsuUnde, motor lifeboat, 818

design notes on triple-screw hulls, 521 reference data on parallel DWL, 231

Into, Finnish icebreaker,

section coeff in entrance, 616

Iowa

standard body plan, 233 Greater Buffalo, Greater Detroit, lake paddlewheel pass'r steamers, body plan, 664

data on feathering paddlewheels, 336 general information, 663, 664 Greyhound, towed hulk, analysis of full-scale towing data, 103 presentation of original data, 129

towing tests by W. Froude, 311 towing tests in shallow water, 390 virtual-mass coeffs for straight-ahead motion, 440

Gudnm,

774

115-ft trawler,

Gwin, old torpedoboat,

full-scale change-of-trim data,

331

Hakuhasan Maru, cargo vessel, full-scale wind-resistance tests, 276 Hamburg, pass'r vessel, plates for measuring friction drag in side of ship, 130

retardation measurements on ship and model, 439 Hamilton, destroyer, full-scale change-of-trim data, 331 full-scale vibration measurements, 440

measured

310

full-scale thrusts,

TMB boundary-layer observations, Ky/A

with T,

,

Jack, 6-meter yacht, 785

Jackdaw, light-draft gunboat, 673 Jackdraw, (of 1863) unsuccessful hydraulic propulsion, 338 Jaycee, tug with straight^element hull, 765 Jean Bart, French battleship, tandem breakwaters on, 555 Jill, 6-meter yacht, 785 John Bowes, collier of 1852 with machinery aft, 571 John D. McKean, New York harbor fireboat, 777 John G. Munson, Great Lakes self-unloading bulk carrier, 756, 758, 760 John J. Rowe, triple-screw river towboat with Kort nozzles, 687 John J. Walsh, ferryboat with straight-element hull, 764

John N. Cobb, fisheries research vessel, 774 Joseph H. Thompson, Great Lakes ore carrier, 756, 758, 760 Johnstown class of Great Lakes ore carriers, 756, 758, 760 Jupiter, collier, rudder area, 714 Kaiserin Auguste Viktoria, pass'r

98

calculations,

variation of residuary resistance with speed, 307, 308 variation of

805 photo of Velox waves, 240 Iris, Royal Navy dispatch vessel, ship data, 227 Isbrytaren, early icebreaking steamer, 804 (old), battleship,

309, 310

variation of thrust-load coeff with speed, 344, 346

Hamilton, destroyer model, center-of-wind-pressure data,

285

wind on bow, 281 sample boundary-layer vel profile, 99 boundary-layer data, 98 unpublished wind-resistance tests, 279 Hammonton, New York harbor ferryboat, 791 Harry Coulby, Great Lakes ore carrier, 755, 758, 760 Harvard, coastwise pass'r vessel, body plan, 237 Hashike, Japanese ship, towing tests on model, 311 effect of relative

TMB

Francisco Bay ferryboat, 791 HD-4, early hydrofoil-supported boat, 272 Helgoland, German lifesaving "cruiser," 818 Helgoland, with twin rotating-blade propellers, 657 Helsinghorg, Danish railway ferry, 791 Henderson, transport, displacement of appendages, 296

Hayward, San

rudder area, 714 Hendrik Hudson, river paddlewheel steamer, general data, 663, 664 Herman Apelt, fast German rescue ship, 818 Heron, light-draft gunboat, 673 Heywood, naval transport, section coeff in entrance, 516 Himalaya, pass'r liner, recessed anchor stowage, 557 Hindenburg, merchant vessel, flow data close aboard, 98 Holger Dansk, icebreaker, general information, 800, 802 Hortensia-Bertin, tuna clipper, 773

Huntington, Ught cruiser, unexplained anomaUes of shallow-

water operation, 414 river paddle steamer, model tests of paddlewheel, 336

Hugo Marcus,

Ice Boat No. 2, early iceship, prior to 1888, 804 Independence, pass'r liner, resistance, propeller,

and

self-

liner,

wind-resistance

276

Kanawha, tanker, rudder area, 714 Kapetan Belousov, icebreaker, general data, 801, 803, 806 Kathmar II, 60-ft motor cruiser, speed trials, 865 Kish Bank, lightship, 816 Kista Dan, iceship with fins protecting propeller, 799, 805 Kon-Tiki, balsa-log raft, estimating hydrodynamic resistance, 3 with movable centerboard planks, 698 II, whale catcher, very high sheer at bow, 549 Krisjamis Valdemar, Russian icebreaker, 804

Konan Maru

Labrador, icebreaker, general data, 800, 802, 805 Lajayette; see Normandie LCF and LCT landing craft, 809 LCI{L) landing craft, 764, 765

Lebanon, naval auxiliary, rudder area, 714 Le Nord, channel paddle steamer, data on alterations to wheels, 335

Leviathan, Atlantic Uner (of 1914), standard

body

plan,

232 Leviathan,

British

aircraft

of

cruiser

Standard Series Lexington,

lines,

1890's,

source of Taylor

298

carrier

(of

1926),

displacement of

appendages, 296 Liberty ship, U. S. Mar Conmi design EC2-G-AW2, change-of-trim data, 328, 330 Lieut. Flaherty, Boston harbor ferryboat, 791 Lt. James E. Robinson, Victory ship, variation in thrust, torque, and transverse forces during a revolution, 350-352 3-diml wake surveys at light and intermediate displacements, 361, 364, 365 LSM 458, landing craft, towing vessel for YTB 602, 311 with Kirsten rotating-blade props, 311 Ducinda, paddle steamer, ship and model wave profiles, 241

HYDRODYNAMICS IN SHIP DESIGN

944 Lucy

Ashtoii, ex-paddle steamer, driven

of trim dviring ship trials,

by gas

jets,

change

estimated augment of velocity and resistance due to potential flow, 111-113 general dimensions and characteristics, 311 list

ness, 113

pitometer log boundary-layer traverses, 98 propulsion by gas jets, 311 tests of large family of geosim models, 319 thrust measurements, 310 Lurcher No. 2, lightship, 815, 816 Lusiiania, Atlantic liner, effect of full streamlining on

upper works, 279 for, 502 Ly-ee-Moon, use of hollow mast as ventilator, 566 Lymington, ferry with Voith-Schneider propulsion, 791 L6-S-A1 Great Lakes bulk carrier, body plan, 756 L.V43, L.V.74, L.V.94, U. S. lightships, 815, 816

extensive planning

Maainal, Kort nozzle tug, with openwork aftfoot, 518 airship; see

model

test

Allen, tanker,

DWL

of test reports, 311

permissible roughness height for hydrodynamic smooth-

Macon,

and ship-trial data, 378 photo of flow pattern, 255 Mary E. Petrich, large tuna clipper, 773 Mary Powell, river paddle steamer, cutaway forefoot, 668 designed afterbody waterline, 228 entrance slope, 667 general data, 663, 664 Massachusetts, early ship with lifting prop, 807 with machinery aft, 571 Massachusetts, fast pass'r-cargo vessel, standard body plan, 232 Maui, pass'r ship of 1917, with machinery aft, 571 Mauretania, (old, of 1907), Atlantic finer, extensive planning for, 502 powers on inboard and outboard shafts, 574 reference data on parallel DWL, 231 resistance of upper works, 561 wind-resistance calculations for, 276 wind-tunnel tests on above water model, 279 Mayflower, j'acht, displacement of appendages, 296 Melik, light-draft steamer, 673 Memphis, river steamer, general data, 665 Mermaid, tuna clipper, 773 Messina, hydrofoil-supported boat, 273 Meteor, research ship, stereoscopic wave photos from, 179 Minerva, paddle steamer, ship and model wave profiles, 241 self-propelled

Martha E.

325

Akron

Magenta, French battleship, photo of Velox waves, 240 Magiinkook, merchant ship with excessively full stern, 135 Maine, battleship of 1903, observed wave profiles, 239 Majestic, Atlantic liner of 1889, with overlapping screwprops, 540

Makrelen, torpedoboat, full-scale tests in varied depths of water, 415, 416 Malolo, pass'r vessel, section coefT in entrance, 516

standard body plan, 232 Manhattan, Atlantic Uner, body plan and general huU data, 236, 237 proposal for complete streamlining of upper works, 561 reference data on parallel DWL, 231 self-propulsion model test data, 379 Manhattan, twin-skeg design of U. S. Mar Comm, model data as follows: plan, 236

body

boundarj'-layer data, 99

contours of long'l wake velocity abaft skeg, 359 self-propulsion data, 379

Minneapolis, (old, of 1890), triple-screw cruiser, design notes on, 521 Missourian, cargo vessel, standard body plan, 232 Modego, tuna clipper, 773 Moltke, German battle cruiser, photo of Velox waves, 240

Monitor, hydrofoil-supported sailboat, 273 Monitor, U. S. ironclad of 1862, with under-the-bottom anchor, 558 Monocacy, river gunboat, displacement of appendages, 296

Monterey, pass'r liner (of 1932), self-propelled model test

and ship-trial data, 378 Moosehead, pass'r ferry, standard body plan, 233 Moreno, Argentine triple-screw battleship, 521 Morris, (old) torpedoboat, full-scale change-of-trim data, 331 Mt. Carol, standard body plan, 233 Mt. Clinton, standard body plan, 233

wake-survey diagram, 3-diml, 361

wave profile and lines of flow, 252, 253 Manning, USCG cutter, observed wave profiles, 240 Manukai, Manulani, cargo vessels with machinery aft, 571 Marie Henriette, channel paddle steamer, 336 Marilyn Rose, tuna clipper, 773 Marine Robin, C-4 converted to Great Lakes carrier, 756 Mariner class, fast cargo vessels, data as follows: body plan and wave profile, 236 curve of propulsive coeff on T, 895 ,

discharge opening for circulating water, 704

wind on bow, 282 on rudder, 733 principal dimensions and hull coeffs, 228 section-area curves, 236 speed and power from ship-trial data, 378 wavy bilge-keel traces, 255, 695 3-diml wake-survey diagrams, 361-363 Mariposa, pass'r liner (of 1932), reference data on section coeff in entrance, 516

submarine

(of

19301,

with crossed

recessed

anchors, 557

Natchez class of river towboats, 673 of 1863, with hydraulic-jet propulsion, 338 submarine (of 1930), with crossed recessed

Nautihis, Nautilus,

anchors, 557

Neptune,

collier,

effect of

wind and fouling

resistances,

279

rudder area, 714

New York harbor ferryboat, 791 New Mexico, battleship, mathematical fines for blisters, 187 New Orleans, suction dredge, 779 New York, pilot boat (of 1897), drift^resisting characterNetherlands,

pitting

231

Narwhal,

125,

effect of relative

DWL,

Napier, fast twin-screw launch by Yarrow, 753 Narvik, German destroyer, transom stern on model, 531

parallel

istics, 771 with deep V-sections, 515 New York, river paddle steamer, body plan, 663 cutaway forefoot, 668 slope, 667 entrance

DWL

SHIP-NAME INDEX general data, 664

Newton, cargo vessel with transom stern, 764 Normandie, Atlantic liner, contours of wake fraction abaft bossings, 359, 360 excessive vibration of structure, 365 expanded resistance data, 298 general dimensions and characteristics, 237 resistance, propeller, and self-propulsion data for model, 379 variation of residuary resistance with speed, 307 North Carolina, (old) heavy cruiser, tests of three geosim models, 319 Northampton, bay ferry, with bow rotating-blade prop, 776, 792 Northern Pacific, triple-screw pass'r vessel, body plan, 237, 238 design notes on triple-screw hulls, 521 standard body plan, 233 Northwind class of USCG and USN icebreakers, 796

Ocean

915

variation of residuary resistance with speed, 307, 308

Vulcan, cargo ship, report of sea trials in waves, 169

Oceamis, large tanker, with all deckhouses aft, 563, 762 Oland, early icebreaking steamer, 804 Old Colony, fast pass'r-cargo steamei', standard body plan,

232 light cruiser, displacement of appendages, 296 overlapping screwprops, 520, 541 standard body plan, 232 Oranje, pass'r vessel, double rows of discontinuous bilge

Omaha,

keels, 692 extreme tumble home, 552 smoke-stack tests on model, 564 wind flow over upper works, 562 wind-velocity vectors over hull and superstructures, 276 Oriental, steam yacht, variation of resistance with speed,

307

wave

profiles

and

Phelps, destroyer, effect of wind on how, 281

Philip R. Clarke, Great Lakes ore carrier, general data, 756, 758, 760 self-propulsion

model

test data, 377,

378

Piemonte, Italian cruiser, wave profiles, 240 Pioneer, shallow-water pushboat with arch-type stern, 527

bow bulb

Pola, light cruiser, large

Pomona

on, 514

Victory; see Tervaele

Poughkeepsie, ferry with propellers on

fin keel,

791

President Coolidge, pass'r vessel (of 1931), reference data

on

parallel

DWL,

231

President Tajt, pass'r vessel, ref data on parallel

Preussen, sailing ship, Princess

Vancouver,

of

DWL,

231

wave observations from, 178

Princess Anne, Chesapeake

Bay

792

ferry, lengthened,

steamer,

ferry

rotating-blade

propeller for exerting transverse thrust, 654 Prins Christian, Danish railway ferry, 791 Prim Eugen, heavy cruiser, body plan with blisters, 768 bower anchor stowage on deck, 556, 557 fairing caps for propellers, 601 fairing for strut and propeller hubs, 744 reference data on parallel DWL, 231 section at roll-resisting tanks, 238 shield on forward side of stack, 564 Proteus, collier, rudder area, 714 Pruitt, destroyer, thrust measurements on, 310 PT 20/54, hydrofoil-supported boat, 273 PT 8, fast motor torpedoboat, chine position, 838, 839

Puffin, early lightship (1887), 815 Putnam, destroyer, resistance augment due to fouling, 123 Pvt. Joseph F. Merrell, New York harbor ferryboat, 791

P1-S2-L2 pass'r vessel, P3-S2-DA1, U. S. Mar

wave photos from,

data on parallel DWL, 231 design of proposed pass'r

ref

Comm

liner (1949), general

Orion, collier, rudder area, 714

Oriskany, aircraft carrier, stereoscopic

How, 248, 249

lines of

wind-resistance test of model, 279

dimensions and characteristics,

228, 237

178, 179

Orizaba,

pass'r-cargo

vessel,

standard body plan, 232

Queen Mary, Atlantic

liner,

hmited ship data

for,

228

Orsova, pass'r liner, with special derrick posts, 566

Overfalls, lightship,

at inlet scoops, 703

816

Pacific, self-propelled

hopper dredge, 779

Pacific Trader, cargo vessel, full-scale

wake measurements,

262 wind-tunnel tests on abovewater model, 279

Panama, pass'r-cargo

vessel (of

reference data on parallel

DWL,

1939),

body

Paa-de-Calais, channel paddle steamer, data on alterations to wheels, 335

DWL,

231

Pennsylvania, tanker, body plan, wave profile, and lines of flow,

B. McLean, Canadian icebreaker, 805 Rex, pass'r liner, general dimensions and characteristics,

237

231

and self-propulsion test data, 378 launch by Electric Launch Co., 753

Pasteur, pass'r liner, ref data on parallel

Ralph J. Columbo, Boston harbor ferrj'boat, 791 Ramapo, tanker, displacement of appendages, 296 Rappahannock, store ship, rudder area, 714 Raritan, USCG icebreaking cutter, 805

R plan, 234

resistance, open-water,

Panhard, fast

and velocity measurements

Raleigh, light cruiser, pressure

Osprey, lightship, 816

236

and hull coefTs, 228, 236 section-area curves, 236 self-propelled model test data, 378 wake-fraction data, 368, 369 Pensacola, heavy cruiser, center-of-wind-pressure data, 285 effect of relative wind on bow, 282 large bow bulb on, 514

DWL, 231 Marshall, Great Lakes ore carrier, 756, 758, 760

reference data on parallel

Richard

M.

Rijeka, cargo ship, sea tests

of,

312

Rivadavia, battleship, triple-screw, 521 Rival, of 1870, with hydraulic-jet propulsion, 338 Roosevelt, polar expedition ship of Peary, 796

Ruytingen, lightship, 815

principal dimensions

S-boat,

German,

of

World War

IT,

chine position, 838

fast displacement-type craft, 755

Saint Joan, French trawler, 774 Salinas, tanker, center-of-wind-pressure data, 285 effect of wind on bow, 281 wind-resistance test of model, 279

HYDRODYNAMICS IN SHIP DESIGN

946 Salt

Lake

City,

heavy

cruiser, large

bow bulb

wind-resistance test of model, 279 Sampo, Finnish icebreaker, 804 San Fernando, San Florentino, single-screw

on, 514

Francisco, (old) cruiser,

wave

profile

and

tankers,

lines of flow,

248

German merchant vessel, body plan, 234 measurements on model in moving water, 98 full-scale thrust measurements, 310 open-water test data for model prop, 334 self-propelled model test data, 378

San

Francisco,

flow

stereoscopic Sore

wave photos from,

machinery

San Leandro,

177, 178

pass'r-cargo vessel

Francisco,

aft,

tuna clipper, 773 Russian icebreaker, 804 Szechenyi, paddle tug, with double wheels abreast on each side, 336 SI 19, German torpedoboat, change of trim in shallow water, 328 full-scale test in varied depths of water, 415, 416 increase in shallow-water resistance by inspection, 409 resistance and trim in varied depths, 390 S4-S2-BB3, U. S. Mar Comm design, ref data on parallel DWL, 231 S4-SE2-BD1, ref data on parallel DWL, 231 Traveler, 121-ft

Svialogor,

variation in torque during propeller revolution, 349

San

Sun

of

the 1910's, with

571

tanker, wind-tunnel tests of abovewater

Tagoog, paddle tug, with wheels on each quarter, 337 Talamanca, pass'r-cargo ship, excellent bossing termination, 684,

747

section coeff in entrance, 516

model, 279 Sandpiper, self-propelled hopper dredge, 779 Santa Ana, Santa Barbara, pass'r-cargo vessels, standard

body plan, 233 Santa Elena, merchant

ship, rough and smooth velocity 98 Santa Helena, tuna purse seiner, 773 Santa Luisa, pass'r-cargo vessel, standard body plan, 233 Santa Rosa, pass'r vessel, center-of-wind-pressure data, 285 effect of wind on bow, 281, 283 Santa Teresa, pass'r-cargo vtssel, standard body plan, 233 profiles,

Schuyler Otis Bland, cargo ship, body plan, hull coeffs,

and section-area curves, 236 and coeffs, 228 self-propelled model test data, 378

principal dimensions

use of largest practicable prop, 597 wake-fraction data, 368, 369 Sea Otter, small merchant ship, with under-the-bottom multiple propellers, 653, 654 Sealrain, general description, 762

sheer data, 549 Talbot, torpedoboat, full-scale change-of-trim data,

331 Tannenberg, merchant ship, contours of wake fraction at

prop positions, 359 open-water test data of regular and special ship props, 334 unpublished boundary-layer velocity profiles, 98 Tashmoo, river steamer, body plan, 663 general information, 663, 664 paddlewheel data, 642, 643 Tennessee, battleship, displacement of appendages, 296 resistance augment due to fouling, 123 Terra Nove, sealing vessel, 774 Terror, minelayer, self-propelled model test data, 379 self-propelled model test data when running astern, 388 wave profile and lines of flow, 252 3-diml wake-survey diagram, 361 Tervaete, Victory ship, results of fouUng on, 126 rodmeter velocity

profiles,

98

with temporary bow, 782, 783 Seraing I, of 1860, with "articulated" paddlewheels, 338 Seraing II, of 1860, with hydraulic-jet propulsion, 338 Setter II, whale catcher, 774 Sewell Avery, Great Lakes ore carrier, 758, 760

Teutonic, pass'r liner of 1889 with overlapping screwprops,

Sheikh, river gunboat, 673

Tirpitz, battleship,

standard body plan, 232 Sirius, French minesweeper, towing vessel for Aldebaran, 312 Sisit, Finnish icebreaker, 805 Snaefell, channel steamer, boundary-layer profiles on, 312 full-scale wake measurements, 262 Sobjornen, torpedoboat, full-scale trials in varied depths

Tjaldur, Danish warship, photo of Velox waves, 240

Selfridge, destroyer,

Siboney,

pass'r-cargo

vessel,

of water, 415, 416 Sotoyomo, tug, wave profile and lines of flow, 248, 249 Southern Cross, pass'r liner with machinery aft, 571 Southern Soldier, whale catcher, sheer at bow, 549

Japanese icebreaker, 805

Soya Maru, Spartan, Lake Michigan car ferry, 791 Stadt Wien, river vessel, Unes of, 336 Standard Arrow, tanker, standard body plan, 232 Starkodder, early icebreaking steamer, 804 St. Ignace, Great Lakes icebreaking car ferry, 797, 804 Louis Socony, tunnel-stern towboat, 674 Marie, Great Lakes icebreaking car ferry, 804 Storebaelt, Danish railway ferry, 791 Sultan, light-draft steamer, 673 St. St.

540 Theta, iceship with fins protecting propeller, 799

Thommen,

river steamer,

model

tests of paddlewheels,

336

Thule, icebreaker, general information, 800, 802, 805

Tom M.

Girdler,

bower anchor stowage on deck, 556

Great Lakes ore

carrier, 756, 758,

760

Truman 0. Olson, U. S. Army vessel with cycloidal rotatingblade props, 337 Turbinia, experimental turbine-driven craft, condenser-

scoop arrangement, 701, 702 photo at full speed, 244 proposed very thin prop blades, 600 single-arm struts, 678 ultra-high-speed displacement-type vessel, 754 Turret, turret ship with

machinery

Tyler, pass'r-cargo vessel, standard

Tl-M-BT

aft,

571

body

plan, 232

inland tanker, change-of-trim data from model,

328, 330

DWL, 231 data on parallel DWL, 231 sinkage in shallow water from model tests, 666 3-diml wake survey on model, 362 T2-SE-A1 tanker, change-of-trimdata from model, 328, 330 Tl-M-BTl

tanker, ref data on parallel

T-2 class tanker,

wave

profiles

ref

and

lines of flow at full-load

conditions, 256, 257

and ballast

SHIP-NAME INDEX U-lll, German submarine, "offset" surfaces on a discontinuous-section hull, 768 Vacationland, large quadruple-screw ferry, 791 Valley Transporter, large river pushboat with long tunnels,

669 Vanguard, battleship, with excellent anchor recesses, 557 Veritas, fast launch by Gielow, 753 Victory ship, U. S. Mar Comm design VC2-S-AP3, ohangeof-trim data for model, 328, 330 3-diml wake surveys at light and intermediate displacements, 364, 365 Victory, Great Lakes ore carrier, 755 Vingt-et-Un II, fast launch by C. H. Crane, 753 speed-power and other curves, 865 Viper, British gunboat of 1863, with twin screws, 338 Voima, icebreaker, general information, 801, 803, 805 Voltaire, French warship, photo of Velox waves, 240 V-1, submarine (of 1925), displacement of appendages, 296 VCS-S-AP3; see Victory ship

W.

Alton Jones, tanker, single-screw, 22,000-horse propulsion,

568

Wampanoag, high-speed model

cruiser

of

1867,

self-propelled

377 Washington, (old) armored cruiser, resistance and selfpropulsion test data, 378 Washington, battleship (of 1941), added mass of water around deep skegs, 438, 439 Waterwitch, of 1866, with hydraulic-jet propulsion, 337, 338 Welborn C. Wood, destroyer, condenser-scoop tests, 703 White Hawk, hydrofoil-supported boat, 272 test data,

947

Widgeon, minesweeper, displacement of appendages, 296 Wilfred Sykes, ore sliip, general data, 758, 760 self-propelled model test data, 378 variation of residuary resistance with speed, 307 class of USCG and USN icebreakers, machinery installation, 805 view of hull, 798 Windsor, cargo vessel, compound flare forward and aft, 552 Worden, destroyer, with successful deflection-type bossings, 686 Wrangel, destroyer, boundary-layer velocity profiles on, 98 full-scale towing tests, 311

Wind

XPDNC,

fast Herreshoff launch, 753

body plan, 237 Yarmouth, pass'r vessel, section coeff in entrance, 516 standard body plan, 232 Ymer, Swedish icebreaker, 805 Yudachi, Japanese destroyer, full-scale towing tests, 257, 311 resistance augment due to fouling, 123 YTB 500, harbor tug, full-scale thrust measurements, 310 open-water test data for fixed-pitch prop model, 334 variation of thrust-load coefficient with speed, 346 YTB 502, harbor tug, full-scale thrust measurements, 310

Yale, coastwise pass'r vessel,

towed by

LSM

458, 311 use of controllable propellers on, 338

ZS7,

German

destroyer,

screwprops, 635

with

corrosion-resisting

steel

Subject Index Appendix 1 of this volume contains an alphabetical list of symbols, letter groups, and abbreviations, with These features are therefore omitted from the subject inde.x. Rules Followed in Making up this Index. All principal words in the part headings, chapter headings, section headings, and te.xt and in some cases the figure captions and table headings are included in the subject index. In general, this takes in nouns and adjectives but not verbs, adverbs, prepositions, and articles. Abbreviations. To make the entries as descriptive and useful as possible, yet to keep them concise, abbreviations or short forms are employed, where necessary, for words that are familiar and frequently used. Plurals are formed by adding the customary "s" and "es" to the shortened nouns. Examples are the following: General.

their short titles.

—

Abbrev

—

SUBJECT INDEX Added mass

of entrained liquid; see

Mass

Adjustable features in propdev design, 578 fins on raft Kon-Tiki, 698

Advance

coefficient, calculation of for a screwprop,

Aeration of separation zones, 140 Afterbody buttocks, design of, 519 Air, and exhaust gases, mechanical properties

wind resistance

"Angleworm" curves, description of, 303 use of, 316 Anomalies, unexplained, in confined-water performance, 414

613

"Antilift" developed of,

922

of ships, estimated, 274

ship, estimated,

on models, 563

separation zones, 140 of,

arch-stern

915

classification

increase of with height above surface, 274

data from, 73 Airscrew propulsion, 658 Allowance(s), design and performance, 454 for ABC ship design, 456 estimated curvature, in friction-resist

wake

velocity

110

577

shadowing, for appendages in tandem, 292 graphs of, 123, 124 Alphabet, Greek, 900 specific fouling,

Alternative preliminary ship designs, preparation

of,'

501

806

Analogy, electric, bibliography on, 50 delineation of flow patterns by, 49, 67 Analysis, diagram, for wake-survey data of

ABC

ship,

367

for arch type of stern, 525

hydrodynamic ship requirements, 460 model-test data on ABC ship, 879 observed flow at screwprop position, 259 principal requirements for motorboat, 826 ship-design, useful data for, 926

TMB 3-diml wake-survey diagram, 362 wake behind a

ship, 261 wetted surface, 493 Analytical and mathematical methods, provements in, 219

necessary

im-

ship-wave relations, 217 Anchor, installation, under-the-bow, proposed, 558 mushroom, proposed for ABC ship, 558, 559 recesses, design of, 556 Anchored ship, friction drag of, 128 Angle(s), blade-helix, of screwprops, 340, 341 control surface, neutral, setting of, 736 entrance, of designed waterline, 479 hydrodynamic pitch, /3j, first approx for screwprop,

type of single-screw stern, 521 flow analysis for, 525 Area(s), -balance ratio, of a control surface, 721 bilge-keel, 692 control-surface, determining by new procedure, 715 first approx, for preliminary design, 713

maximum-,

neutral rudder, model tests for, 876

symm

hydrofoil,

section,

optimum

longitudinal position

of,

482 paddlewheel blade, finding, 642 340 expanded, finding, for new design, 602 of, 713-720 sail-, to wetted-surface ratio, for a yacht, 786

ratio(s) of screwprops, definitions of,

rudder, determination silhouette, of a ship

above water, 277

wetted, of a hydrofoil, 5

Arm,

615 second approx, 616 coeff data for

675 tandem, shadowing allowances for, 292 varjdng flow, 293 inception and effect of cavitation on, 145 large, resistance of, 295 lift data for bodies representing, 291 motorboat, design of, 842, 862 movable, design of, 706 resistance, calculation of, 288 for submarines, 295 individual, per cent, 289 overall, customary values, 288 scale-effect problems in connection with, 288

in

curve, section-; see Section-area

of predicting pressure resistance, 321

and press

290

295, 296

tandem, resistance of, 292 use of flow diagrams for positioning, 258 vibration of, design to avoid, 700 Aquino wake-fraction formula, 368 Arch stern, ABC ship, afterbody plan, 523 appendages for, 681

diagrams, 239

151

of,

short, definition of, 108

flow, abaft a screw propeller, 259

-of-attack

145

fixed, design of,

in ship design, 574

of,

of,

of drag,

ferryboat, design of, 793

on appendage drag, 292

hydrodynamic design

by type

fairing of, in general, 742

calcs,

roughness; see Roughness

craft,

design, 681

drag data for bodies representing, 291 effect of wake velocity on, 292

powering, and reserves, graphic representation, 576,

Amphibious

632

design of control surfaces and, for motorboats, 862

displacement

Airfoils, typical, test

for

ABC

cavitation on, occurrence

resistance of ships, estimating, 274 velocitj',

of,

Appearance features of hull sheer line, 547 Appendage(s), abreast and in tandem, modifications in drag for, 293 added-mass data for water surrounding, 438 and hull combinations, design of, 526

565

leakage, to screwprop, avoiding, 631

mechanical properties

and use

propeller, shaping of hull adjacent to, 536

passenger-ship model, 563 test techniques

d(,'f

gaps ahead of rudders, 712

currents around superstructures, 561-563

ABC

by surface props,

Aperture(s), and clcaranc-cM for propdevs, 537

entrainment, precautions against, 747 -flow pattern over

949

Angle(s), trim, for planing craft, 840

strut; see Strut

Arrangement, physical, of submarines, 810 Aspect ratio, data on effect of lifting surfaces with low, 866 effective, for fins and skegs, 698 ship hydrofoils, 83

HYDRODYNAMICS IN SHIP DESIGN

950

Assumptions, general, for added-mass calculations, 417 propelling raachinerj', 443 in calculation of wavemaking drag, 212 Astern maneuvering, rudders for, 735 Asymmetric body, distribution of vel and press around, 43 formed by sources and sinks, 46 propulsion, notes on, 651 Asynmietric hull forms, design notes for, 787 ATTC 1947 friction-resistance formulas, 102 meanline, 104 Attitude, changes of, for fat forms, 329 planing forms, variation with speed, 329 running and ship motion diagrams, 325 of planing craft, 850 predicted, of planing craft, 851 Augment of resistance see Thrust deduction Automatic flap-type rudders and planes, 735 Auxiliary propulsion for sailing yachts, 652 "Awash" condition of a submarine, occurrence of, 812 Axial-component wake-fraction diagrams, 358 velocity components in screwprop outflow jet, 260 Axis, stock, positioning rel to control-surf blade, 720 Axisymmetric bodies formed by sources and sinks, 42 ;

Bibliography and references, condenser scoops, 703

partial

and

selected,

on:

confined-water effects, 415 vessel design, 659 controllable propellers, 579 damping, vibration, and added-mass effects, 439-441 distribution of vel and press around hydrofoils, 81, 82 dredges, self-propelled, 779 dynamic lift, 269 eddy systems, 144 electric analogy for flow patterns, 50

ferryboats, (mostly double-ended), 790-792 fishing vessels, 771-774 fouling, 125 friction resistance, 128-132

geometric waves, 182-185 Great Lakes cargo carriers, 755, 756 hydrodynamics and hydraulics (books), 2 hydrofoil-supported craft, 271-273 icebreakers

Kort

and

iceships, 799, 804-806

nozzle, 687

Lagally's Theorem, 71 life-saving or rescue boats, 817, 818

816 mathematical lines for ships, 204 mechanical properties, air and water, 925 model propellers, open-water test data, 333-335 wind-resistance tests, 278 motorboats, 865-867 paddlewheels, 335-337 planing and planing craft, 269 lightships,

Back flow around

ships in canal locks, 414 Backing power from self-propelled model tests, 388 Baker (G. S.) model 56C, lines and resistance data, 234 Balance, buoyancy and weight, first longitudinal, 497, 498 Balance, degree of, in control-surface design, 720 portion of rudder, pressure field of, 711 ratio, area-, of control surface,

721

length-, of control surface, 721 weight, longitudinal, for light draft, 500 Balanced rudders, design notes for, 720

'running-attitude diagrams, 331 sailing-yacht design, 786, 787

screw-propeller design, 606-609

Ballast condition, estimated lines of flow in, 256 ratio for saUing yachts, definition of,

singing of propellers, 144

786

Barnaby (K.

sinkage and change of trim, 331 sources and sinks, 70

Baseplane and propeller-disc clearances, 540

Telfer

C.) powering coeflacient for small craft, 833 Barrel or basket area of rotating-blade propeller, 656

Basic concepts for calculations and predictions,

1

method

of predicting ship resistance, 318, 319

theoretical resistance calculations, 221, 222

factors in ship design, 442

theory of similitude, 4

screwprop design variables of D. W. Taylor, 586, 901, 902 Bates (J. L.) effective-power data for prelim design, 355 Beaching, keels; see Keels, resting vessels designed for, 808 Beam, and draft for preliminary design, 468 as a design feature in confined waters, 662 -draft influence on residuary resistance, 298, 299 -Froude number, definition and use of, 11 on ship length, dimensional graph of, 470 selection of, in a new design, 468, 470

WL, max, design lane for fore-and-aft position, 481 Bearing, thrust, relation between screwprop thrust and load at, 347, 348

Beaufort wind-velocity scale of U. S. Navy Dept, 284 Bed clearances in shallow-water operation, estimate of, 666 Behavior, probable, prediction for a prelim ship design, 459 shallow-water, first approx to, 501 ship, in confined waters, predicting, 389 Bibliography and references, partial and selected, on:

added-mass, vibration, and damping cavitation, 167-159 change of trim and sinkage, 331

straight-element ship designs, 764, 765

effects,

439-441

thrust and towing-pull measurements, 311, 312

tunnel stern vessels, 673 vibration, damping,

vortex streets or

and added-mass

trails, 141,

effects,

439-441

144

wake, 262 wake-fraction diagrams, 359, 360 wavemaking resistance, 217-219

waves, geometric and general, 182-185 subsurface, 185 yacht design, 786, 787 Bilge(s), diagonal, hull shape along, 517 keel(s); see Keels

prediction of flow pattern at, 255 radius, formulas for computing, 477 Blade (s), area, paddlewheel, determining, 642 circle of paddlewheel, definition of, 640 control-surf, positioning stock axis rel to,

curvature

of, for

proportions rotating-,

720

paddlewheel, 646

of, for

a paddlewheel, calculated, 641

propeller;

see

Propeller

(general

fication)

rudder, stock axis position relative to, 720

classi-

SUBJECT INDEX Blade(s), sorewprop, choice of number, 599 for ABC ship, 612 screwprop, edges, shaping

twin-screw, section shapes of,

606

vertical, as

helix angles, 340, 341

ABC

ship,

ABC

thickness, calculation for

Bow; see also Stem Bow, abovewater section shapes

design considerations for, 605

underwater, design of, 517, 768 projecting, design of, 517, 560, 561 Blocking effect between appendages, 293 Blunt-ended vessels, design of, 755 Boats, fishing, special reqmrements for, 770 life-saving or rescue, design of, 816 motor, design, general considerations, 820 high-speed planing, design data for, 823 Body(ies), and ship lines, mathematical formulas for, 187 any, determination of velocity around, 24 asymmetric, formed by sources and sinks, 46 isotachyls around, 45 velocity and pressure distribution around, 43 axisymmetric, formed by sources and sinks, 42 drawing streamlines around, 31 in unsteady motion, added mass of water around, 417 mathematic methods for delineating, 186 of revolution, cavitation data for, 151 pressure coefficients around, 42 refs to vel and press distribution around, 40-45 plans, ship, ABC, transom-stern, 491 arch-stern, 523 estimated flow pattern on, 255 shallow-water, 663, 664 single-screw, 234-236

"standard", 231-234

submerged, calc of bulk volume and wetted drag coefficients for, 322

surf,

322

pressure resistance as function of depth, 323 typical, representing appendages, drag of, 291

and vel and press diagrams, 31 streets, 141

yawed,

refs to flow patterns about, 38, 40 2-diml and S-dirnl, refs to vel and press data, 43-45

velocity

and pressure diagrams for, 43 and disadvantages, 677

Bossing(s), advantages

around

shafts, design of,

682

contra-guide or deflection type, design rules, 686 endings, adjacent to propdevs, design of, 536 or struts, selection of, 677 short, design of for

termination

of,

ABC

684, 747

at the, 551

shaping

of,

513

single-ended ovoid for, 514

systematic resistance data for, 510-512 diving plane(s), design rules for, 736 profile(s),

for

491

ABC

ship, 511

and free-running, design, 632,792

propeller(s), coupled

housing, design

of,

797

separate shafts for, 792 raked, possible advantages rudders, design

of,

507

735

of,

shaping, for confined waters, 667 snubbing of, for ease of construction, 508

temporary, design of, for damaged ships, 781 crest, height and position, estimate of, 244 lag of abaft stem, 245 Bowers (W. H.) cavitation criteria, 155 Box-shaped forms, self-propelled, design notes, 779 holds, design of dry-cargo ships with, 762

-wave

Bracket, shaft; see Strut Bracketing design technique, 458

twin-screw, 236

and vortex

95

by Ferguson, 511 anchor installation under the bottom, 558 cavitation, check on, 514 comparison of resist with that of normal bow, 512 design for ABC ship, 511 lanes for, 509 notes on, 508, 509 parameters, 485 rules of W. C. S. Wigley, 510 layout diagram, 513 for ABC ship, 510 position and proportions of, 485, 508-514

see also Bulge

vibrating,

of,

ship, 109, 110

bulb, analysis of Taylor resist data

Blasius friction-resistance formula for laminar flow, 104

various, flow patterns

ABC

on ship drag calculations, 213 variation with x-distance from stem, 95, 96 velocity profiles for two ships, 97 Boussinesq number, definition and use of, 16 effect of

shape, final, for ABC ship, 627 shaping by cavitation criteria, 621 shaping and finish, 633 strength and deformation, 634 -thickness distribution, 620 widths of, 340 cavitation diagrams for selecting, 605

;

on and prediction

-layer characteristics, data

ship, 627-629

section, selection of type, 605

Blister(s)

683

Bottom anchor

624

prediction of cavitation on, 149 profile, choice of, 602

skew-back, for raked, use of, 600

for, list of refs,

docking keels, 686

wetted surface, calculating procedure, 108 installation proposed for ABC ship, 558, 559 Boundary, change of added mass in unsteady motion near a large, 432

hollow-face, disadvantages of, 627

outline for

951

Bossing(s), transverse section shapes, 683-685

ship,

685

Brake horsepower ; see Power Breakwaters, deck, design of, 554 Bridges, pontoon, floats for, 782 Bulb bow; see Bulge(s)

;

Bow and

Stern

see also Blister

prediction of ship flow pattern at, 248-257

517 underwater, design of, 768 Bulged fender strakes, design notes for, 560, 769 Bulk modulus, fresh and salt water, 923 volume, calculation of, for a submerged body, 322 side, design of,

for a submarine, definition of, 457 Bulwarks, design of, 554 freeing ports and slots in, 554, 555

Buoyancy, balance, longitudinal, center

of, shifts

in

CG

first

approx, 497

position to suit, 498

HYDRODYNAMICS

952

Buoyancy, longitudinal center of, usual positions for, 486 reserve, requirements in design, 546 Burrill (L. C.) method to derive thrust and torque for a screwprop, 352 Buttock, lines, reversed curvature in, 492, 493 mean, for planing craft, 839, 840 shapes, for planing craft, 839 slope and curvature for confined water, 668 Butts and laps, shaping and facing of, 740, 741 Calculated and experimental

comparison

resist,

of,

for, 1

critical, 10, 11

on typical hydrofoil, 150 not involved, screwprop design procedure when, 625 number(s), definition of, 8, 11 in salt water, tables of, 147-149

limits

nomogram

for, 147,

150

of,

without, screwprop blade widths, 625 Celerity of trochoidal wave, tabulated data, 165-168

resistance, 86

overall wetted surface and bulk volume, 106, 322 performance of a screw propeller, 592, 613, 629 miscellaneous propdevs, 332 pressure resistance, mathematical methods for, 206 modern developments in, 210 resistance, theoretical, reference material on, 221 total, of a submarine and surface ship, 313 screw-propeller efficiency, expected, 629 ship design and performance data, 1 performance, practical benefits of, 220 pressure resistance due to wavemaking, 215 resistance, earlj' efforts, 207 thrust-load factor for a screwprop design, 613 of a screw propeller, 345 wave resistance, ship forms suitable for, 219 wavemaking drag, assumptions and limitations, 212 resistance, 215 components of, 216 Camber, deck, diagrams for, 554 selection of, 553 ratio, in screw-propeller design, 625 Canal(s), locks, predicting ship resistance in, 413 water-surface slopes in, 660 Canoes, design of hulls for, 752 Cargo carriers, Great Lakes, design notes on, 755 vessels with box-shaped holds, design of, 762 Cascade effects on hydrofoils, data for, 84 Casting fillets, use of for fairing, 742 Catamaran hulls, definition and design problems of, 788

and use

of,

7

Cavitation, bibliography, selected, 157-159

bulb, check on, 510

shaping, 621

circular-arc blade section

NSP, for 3-bladed screw of W. H. Bowers, 155

camber

lines,

623

propellers, 154

criterion, factors in, 146

data, for bodies of revolution, 151

symmetrical hydrofoil, 161 model screw propeller, 153 effect and inception, on ships and propellers, 145 on screw-propeller performance, 152 erosion, prediction of, 156 hub, and swirl core, prediction of, 155 typical, for

number,

relation of to pressure coefficient, 10, 11

on hydrofoils and propeller blades, 149 comments on propellers for, 631 propeller performance under, 156

friction drag, for a ship, 126

criteria, for blade-section

on ships and appen-

super-, design

for submarines, 295 blade and paddlewheel proportions, 641 effective and friction power, 354

definition

or

prediction

resistance, 288

Cauchy number,

effect of,

index(es), for three axisymmetrio body heads, 152 nomogram for, 150

occurrence of on ships and appendages, 145 photographing, on model and ship propellers, 153

ship behavior in confined waters, 389

appendage

and

dages, 145

216

Calculating, advance coefficients for a screwprop, 613

and predicting, basic concepts

IN SHIP DESIGN Cavitation, inception

Center of buoyancj^, height above baseline, 479 usual longitudinal positions of, 486 gravity, height above baseline, 479 position, long'l, for planing craft, 840 Center-of-pressure location, calc, for planing for hydrofoil,

craft,

849

80

planing form, 267 Center-of-wind-pressure data for typical ships, 285

layout for location,

Change

ABC

ship,

283

284

of state of water, data on, 921

trim; see

Trim

Changes proposed in

final

ABC

ship design, 896

Channel(s), calculation and use of hydraulic radius, 409 references to flow patterns in, 36, 39 restricted, prediction of ship behavior in, 409-415 slopes, water-surface,

data on, 660

steering in offset positions along, 413

Chart(s), design, for screw propellers, 584, 596

data from, 335 propeller-series, listing of,

comments

on, 589

584-588

preliminary design procedure, 592

requirements for, 584 Chemical constituents of sea water, 924 Chine(s), abovewater, design

comments

on, 560

dimensions, for motorboat design, 846 elevations, for planing craft, 839

placing of in straight-element forms, 763 shape, proportions, dimensions, for planing craft, 837

Chisel type of screwprop blade trailing edge, 636

Chordwise pressure distribution about hydrofoils, 81 proportions of control-surface sections, 722 Circular constant notation, 913 Circulation, and lift, spanwise distribution of, 83 formulas for calculating, 72 theory, application to screwprop design, 609 Clearance (s), aperture and tip for propdevs, 537 bed, in shallow water, estimate of, 666 hull, for paddlewheels, 645 propeller-disc and baseplane, 540 tip, for motorboats, 859 in tunnels, 669 Close-coupled rudders, design of, 726 Closures for rudder hinge gaps, 726 Clubbing of skeg ending at aftfoot, def of, 537

SUBJECT INDEX Coatings, propeller, to resist erosion, 635 Coefficient(s), added-mass, definition of,

419

estimate for vibrating ships and snrewpropa, 433,

436 advance, calculating for a screwprop, 613 and designed waterline shapes, 228 related data

shapes, for

on typical

ships,

223

DWL's, 228

ship parameters, ratios

953

Contra-guide bossings, design of, 686 skeg ending, design of, for ABC ship, 532, 534 WIj's, relation of to median line, 533 -horn for ABC ship, design of, 733 -rotating screwprops, design comments, 655 -rudder, design of, 729 -struts, abaft screwprop, layout, 682 -vanes, for paddlewheels

930

and sternwheels, positioning,

virtual-mass, 418, 419

688 proposed arrangement of F. Siiberkriib, 689 Control surface(s), and movable appendages, design of, 706 angles, neutral, setting of, 736 area, determining by new procedure, 715 first approx to, 713 design of, 706 structural, affected by hydrodynamics, 723 determining areas of various, 715 motorboat, design of, 862 Controllability model tests in shallow water, 876 Controllable features in propdev design, 578 propellers, list of references, 579 performance data on, 338 Conversion graphs, 931 ratios and tables, 928-930 Coordinates, ship, 0-diml representation of, 189, 190, 192 Cores, swirl, predicting, 155 Comers, inside, requiring no fillets, 742 Corrosion-resisting steel to resist propeller erosion, 635 Coupled bow propellers, design notes, 632

waterline, selecting, 478

Cove(s),

of,

and upper works, 279, 322 submerged bodies, 322 2-diml and 3-diml geometric shapes, 291 form, dimensions, and rel data on typical ships, 223

drag, for hulls

product, for screwprop blade sections, 617 maximum-section, selecting, 468, 469 moment-of-area, square-, of DWL, 478 pressure, or Euler number, 8 lift-,

relation to cavitation index, 10, 11

table

of, 27,

30

prismatic, longitudinal, selecting, 467 propulsive,

ABC

and other

determination ranges

of,

ships,

895

375

of,

376

section, along length, for

variation

ABC

517

ship,

517

of,

of typical ships, 516 specific, definition of, 5

thrust-load, variation with speed, 344-346

Complex

position

and shape, on discontinuous-section

forms, 560, 561

wind-drag, for ship types, 280

172

sea, synthetic, delineation of,

amphibious, hydrodynamic design

Craft,

of,

waves for design purposes, 171 Comparison and analysis, useful data for, 926 Components, major resistance, ratios of, 313

full-planing, design procedure for, 821

Compound

planing; see Planing

design

551 hydrofoils, test data from, 75 rudders, design notes for, 726 fairing propeller hubs forward flare,

Compromises

hydrofoil-supported, bibliography on, 271-273 multiple-hulled, design problems

of,

in ship design, general

of,

draft

for,

and displacement

comments, 444

model

special design features for,

822

750 818

tunnel stern, powering of, 672 ultra-high-speed displacement-type, design notes, 754

flow pattern for light or ballast, 256 in,

Conformal transformation, description and uses of, 25 Constant notation, circular, 913 Construction, adherence to design details, 459 mechanical, of screwprops, 633 Contour(s), maximum-section, layout of, 476 of Re/ A, typical, for TSS, 2«9 from Gertler-TSS data, 302 Rw for Japanese fishing vessels, 300 residuarj'-resistance coefficient Cr, 301-303 rudder, ABC ship designs, 728, 729 stem and stern; see Profiles stream-form, 2-diml, around single source, 52 Contra-features, for diving planes, 736 propdevs for use with, 579 '

of,

of the future,

871

probable variable-weight, 463 variable-load, screwprop submersion and trim wavegoing, limits for, 458 Confined waters; see Water(s)

825

special-purpose, classification of, 750

design tests,

for,

references to tabulated data, 228 semi-planing, design, 823

911

for

788

preliminary design study, requirements hydrodynamic design, 819

745

partial bibliographj' on, 703

Conditions, abbreviations

of,

small, powering of, 824

Concepts, basic, for calculations and predictions, 1 physical, having scalar dimensions, abbrev for, 911

Condenser scoops,

806

498

Crest see ;

Wave

Criteria for cavitation, blade-section shaping by, 621

factors in, 146

on screwprops, 154 separation and eddying, 133 Criterion, Goldstein, for face,

hydrodynamically smooth sur-

112

Taylor (D. W.), limiting depth for ship trials, 407 number, when occurring, 11 -speed ratio in shallow water, definition of, 393

Critical cavitation

nomogram

for,

395

wave speed and water depth, table of, 661 Crossed anchor chains and hawsepipes, use of, 557 Current(s), river, reference data on, 660 surface-water, due to natural wind, 287

Curvature, allowances in friction-resistance calcs, 110 buttocks, for confined-water operation, 668

HYDRODYNAMICS IN SHIP DESIGN

954

Design(s), appendage(s), motorboat, 862

Curvature, dimensiouless, measurement and plotting

196 flow, in screwprop blade, design corrections hull, and resistance, relation between, 194

movable, 706

of,

for,

625

for shallow-water design, 665

beaching vessels and landing bilge-keel, 692-694

notes on anah'sis, 195

bossings, contra-guide or deflection tj'pe, 686

0-diml, graphic determination, 196

fairing type, for shafts, 682 bow, propellers, 632 rudders, 735 temporary, for emergencies, 781 bulb bow, 508, 509 canoes, 752 chart(s), screw-propeller, 584 data from, 335 contra-guide skeg ending, 532 -horn for ABC ship, 733 -rotating screw propellers, 655 -rudder, 729 control surface(s), 706 motorboat, 862 structural, affected by hydrodynamics, 723 detail, adherence to in construction, 459 of underwater hull, 504 devices to produce vert and transv thrust, 654 discharge openings through shell, 701 discontinuous-section hulls, 768 displacement-type motorboats, 754, 823 diving planes, bow and stern, 736 dry-cargo vessels, 762 edges of appendages, leading and trailing, 675 equalizing powers of multiple propellers, 573 essence of, 444 facilities for abovewater smoke and gas discharge, 563 features, applicable to confined waters, 659 general, abovewater form, 546 hydrodynamic, of amphibians, 806 propeller, comments on, 596 self-propelled dredges, 777 special, small-craft hulls, 822, 823 supporting horns for rudders, 690 ferryboat hull and appendages, 793 final ABC ship, proposed changes in, 896 fins, fixed stabilizing, 697 torque-compensating, 699 fireboats or firefloats, 774 fishing vessels, 770 fixed objects in a stream, 675 screw-propeller shrouding, 687 stabilizing skegs or fins, 697 for conflicting steering requirements, 713 hydraulic- and pump-jet propulsion, 648

longitudinal, flowplane, 199

instruction plan, 198 of section-area curve, 199

radius

of,

2-diml, formula for, 195

on friction drag, 110 from nose to body, 196 value of fairness and, in ship lines, 193 0-diml, method of measuring, 196, 198 surface, effect

transition, gradual,

plot of

DWL for ABC ship,

506, 507

ABC

section-area curves for

ships, 544

Curve, section-area; see Section area Curved surface; see Surface

Cutwater

for

ABC

ships, 511

blunt stem, design Cycloidal propeller

;

676

of,

see Propeller, rotating-blade

Cylinders, drag of appendages approximating, 291

Damping

effects, partial

bibliography on, 439

Deck(s), camber, diagrams

for,

554

selection of, 553 details

and abovewater

profile,

553

straight-element ridge type, 554

Deduction, thrust; see Thrust Deep-water waves, relation to shallow-water waves, 180 Deflection of flow around separation zones, apparent, 139 -type bossings, design rules for, 686 Deformation of screw-propeller blades, 634

Degree

to avoid vibration, 700

as a compromise, 444 basic factors in, 442

estimated friction allowances for, 110

of balance of control surfaces,

Delineating, flow patterns

by

720

electric analogy,

49

mathematic, of section-area curves, 198 ship forms, mathematical lines for, 186 source-sink flow diagrams, 52 synthetic, 3-component, complex sea, 172-175

2-diml stream-form contours around single source, 52 Density, mass, reference data on, 94

"standard" fresh and

salt water, 915,

918

Depth(s), equivalent, of channels, def and calc given, 2 per cent speed reduction in, 403

of,

412

-length ratios of ship hulls, data on, 496 limiting, for ship trials,

2 per cent

from D. W. Taylor, 407 404 on pressure resistance, 323

resist increase,

submerged body,

effect

water, given, practical resist-speed cases involving, 396

ABC ship, appendages for arch-stern, 681 changes in final design, 896 motor tenders, additional design items for, 899 preliminary, model-test notes, 869 principal hull data, 870 roll-resisting keels, 695 abovewater section shapes, 551 alternative preliminary, preparation of, 501 amphibians, hydrodynamic, 806 anchor recesses, 556 and drag data for hydrofoils, 83 performance allowances, ABC ship, 454, 456

Design(s),

appendage(s), fixed, 675

craft,

808

minimum

thrust deduction, 541 reduction of drag, sinkage and squat, 661

galvanic-action protectors, 704 general, of the propdevs, 567

horns, supporting, for rudders, 690 hull(s), and appendage combinations, 526

752 paddlewheel diameter and position to, 643 water flow applied to, 545 hydraulic-jet propulsion, 648 hydrodynamic, effect of unrelated factors, 502 fine, slender, rel of

SUBJECT INDEX Design(s), of motorboats, additional items to consider, 899 problems of submarines, 809 second, modifications for, 896 improvements, field for future, 444 keels, bilge-, 692-694

for

ABC

ship,

for

rules, general, for

length, 470 bulb bows, JE values for, 509 Bwx positions, 481 Cp values, 466 Cx values, 469 displacement-length quotient, 466 fatness ratios, 466

L/B

ratios,

screw propeller, 582 bibliography, partial, 606-609 blade,

470

484

waterline, 480 ts of

DWL,

numbers

of,

for

ABC

ship,

612

'

positions, 483

terminal value

stern diving planes, 736

783

bibliography on, 786, 787 schedule for a ship, 444

695

parallel middlebody,

bow and

sailing yachts, aspects of,

beam on

LMA

maneuvering astern, 735

motorboat, 724

docking, drift-resisting, resting, 695 landing craft, 808 lane(s),

955

Design(s), rudder(s), close-coupled and compound, 726

509

shapes by Lerbs' short method, 627 width, 605 design references for circulation theory, 610

methods and procedures, 583, 596 prehminary, comments on features, 596 design procedure with series charts, 592 Schoenherr combination of steps, 630 wake-adapted, 609 second hydrodynamio, modifications for, 896 shallow recesses, notes on, 748 shells, racing,

WL entrance angles, 479

752

ship, basic factors in,

442

launches, fast, 752

definition of, 442

long, narrow, blunt-ended vessels, 755

guaranteeing performance of new, 459

motorboat(s), displacement-type, 823 general considerations, 820, 843 of limited draft, 858

on basis of chine dimensions, 846 motor tenders for ABC ship, principal requirements for preliminary design stud}', 825

movable appendages and control multiple-hulled craft, problems propellers, equalizing

surfaces, ,706

of,

powers

788 573

of,

-skeg stern, 531

paddletrack propulsion, 638 paddlewheel, details and mechanism, 645 feathering, for ABC ship, 644

hydrodynamics of, 638 variations from normal, 648 planing craft, check on basis of chine dimensions, 846 interdependence of hull-design features, 843 selecting hull features, 835

ABC ship, model-test notes for, 869 hydrod}'namic, of a motorboat, 819 of Part 4, comments on, 898 preparation of alternate, for a ship, 501

preliminary,

ship, steps in the,

460

procedure, for full-planing craft, 821

modification of normal, for hull with keel drag,

543 propdev(s), miscellaneous, 638 to

meet maneuvering requirements, 580

propeller(s), for supercavitation, 631

rotating-blade, 656

propelling machinery, effect

on

hull,

570

protectors, galvanic-action, 704

pump-jet propulsion, 648 rapid response to rudder action, 735 recesses, shallow,

hull, rel of

paddlewheel diam and propulsion

748

requirements, for a screw propeller, 583

ready-made, interpretation, 454 statement of principal, 446 rotating-blade propellers, notes on, 656 rudder(s), alternative sterns,

ABC

ship, 727

to,

643

hydrodynamics applied

442 major, model-test data for, 868 skegs, fixed, 697 smoke-stack, 564 sound-gear location, 705 special hull forms and special-purpose craft, 750 specs, involving hydrodynamics, formulation, 446 partial, for a passenger-cargo ship, 447 steps for Lerbs' short method for screwprop, 630 straight-element hulls, 762 bibliography on, 764, 765 adaptation to shallow-water vessels, 666 structural control-surface, affected by hydrodynamics, 723 strut, for exposed rotating shafts, 678 submarines, hydrodynamio problems, 809 surface propellers, 650 tandem screw propellers, 655 technique, bracketing, 458 torque-compensating fins, 699 tunnel stern, 669 underwater hull, detail, 504 unsymmetrical single-screw stern, 528 utility-boat, round-bottom, 858 wake-adapted screwprop, by circulation theory, 609 water inlet and discharge openings, 701 Designed waterhne; see Waterline parallel, reference data on, 231 waterplane, shape of vessel near, 504 Designer, first task of the, 446 ship, general problems of, 454 Detail, deck, and abovewater profile, 553 design, adherence to in construction, 459 notes on paddlewheel, 645 of underwater hull, 504 Developable hull surfaces, hnes for ships with, 765 to,

Devices, propulsion; see Propdevs trim-control, use of for planing craft, 840

HYDRODYNAMICS IN SHIP DESIGN

956 Devices, trim-control,

Plum

stabilizer,

840

Diagrain(s), analysis, wake-, for

ABC

ship,

367

Flow

flow; see

and knuckles, 560 on a rudder and horn, 743 transverse, in abovewater body, 561 Discontinuous bilge keels on liner Oranje, 692 Discontinuities, longitudinal,

Diagonal, bilge, hull shape along, 517

about hydrofoils, list of references, 78 analysis of, 239 flow and flow net, around various bodies, 31 for positioning appendages, use of, 258 upper works configurations, 276 lines-of-flow, typical, on ship models, 248 model surface-flow, analysis of, 250 polar, for hydrofoils, 75 list of references, 76

-section hulls, design of, 768 friction drag on, 127 Displacement, and draft conditions for model tests, 871 trim, effect of changes on resistance, 310 changes, effect on effective power, 355 -length quotient, first approx, 465, 466 relation to fatness ratio, 930, 932 of appendages, 295, 296 -tj-pe craft, ultra-high-speed,

pressure, details of, 9

motorboats, design

running attitude and ship motion, 325 trim and wetted surface, for planing craft, 851 source-sink flow, delineation of, 52 streamline, published, references to, 32 surface-flow, on models, anah'sis of, 250 velocity and pressure, around various bodies, 31 2-

and 3-diml bodies, 43

volume and

considerations

size,

of power, equal,

among

on hydrofoils, 81

radial thrust, of screwprop, first approx, 615

analysis of, 362

3-diml, 360

optimum, comments on, 597 paddlewheel, relation to hull design, 643 selection of, 597

schematic ship forms, 47 ship forms, prediction of, 257 Diverging waves, effect on calculated resistance, 220 Diving planes see Plane(s)

Docking keels, design

data on Great Lakes oreships,

695

Double- or multiple-chine hull form, design

typical ships, 223-228

blade and paddlewheel, calculating, 641 chine, design check of for motorboat, 846

planing craft, 837 physical quantities, 4 principal, first approx, 464

second approx, 475 ship, basis for selection,

457

transverse, for shallow-water running, 662

Dimensionless general equations for ship forms, summary of, 192 longitudinal curvature, graphic determination, 196 instruction plan, 198

numbers; see Number of,

of,

762

-ended ships; see Ferryboats propelling plant and propdevs for, 792 solutions to equations of motion, 6 Doublet, and circular stream form, 61 definition and use of, 18 Doubly refracting solutions, use in flow studies, 48 Draft, and beam for preliminarj' design, 468

568

limiting, of propdevs,

quantitative use

of,

sketches, 697 vertical bossings as, 686

icebreakers, 800-803

displacement conditions for model tests, 871 trim variations, estimated, for ABC ship, 481, 498 immersed-transom, 530 increased, with age, comments on, 566 limited, design for

motorboat

of,

858

square, for confined waters, definition

of,

393

variable, first statement, 483

variations, estimated, with variable weights, 481

7

Drag,

summary of data on, 8 representation of ship surface, 189 ship coordinates, definition sketch for, 189 surface equations, application of, 191

relationships,

Dip and dip

ratio of paddlewheel, definitions of, 639 Direction of rotation of propdevs, for ship design, 572 Disc, clearances for propellers; see Clearances of,

83

;

Differential pressures at screw propeller, data on, 343

drag

lift,

and pressure, about asymmetric body, 43 around bodies, references to, 44 body of revolution, 40 hydrofoils, and list of refs, 80, 81

velocity

Diameter, pitch-, ratio; see Pitch Diameter(s), hub and propeller-disc, 612 screw-propeller, Burtner formula for, 569 fqr hub, 601

propeller-,

448

and magnitude on planing-craft bottoms, 266 second approx, 616

flat,

of,

multiple propellers, 573

pressure, chordwise,

spanwise, of circulation and

rel

754

pressure, along a vee entrance, 48

TMB 3-diml,

Dimension(s), and 758-760

of,

Distribution, blade-thickness, for screwprop, 620

wake-fraction, at propdev positions, 358 -survey,

design

823

for,

291

274 wind on bow, 281

of ships, estimating,

resistance with

appendage(s), abreast, modifications classification effect of

wake

by

in,

293

type, 290

velocities,

292

abovewater hulls and upper works, 279 submerged bodies, 322 typical 2-diml and 3-diml geometric bodies,

coeff(s), for

291

and hub diameters, design

notes, 612

Discharge, abovewater gas and smoke, 563 openings, water, design of, 701 underwater, gas and smoke, 565 Discontinuities, estimating drag

air,

and

of,

294

graphs, typical, for hydrofoils, 73, 74 confined-water, design for reduction, 661

and spheres, 291 appendages, 291 and gaps, 294

cylinders, ellipsoids,

data for bodies

like

holes, slots,

SUBJECT INDEX Drag, data for hydrofoil planforms and sections, 83 due to ice, as for icebreal<ers, 794, 796 exposed rotating shafts, 293 fiat plates

and

291

discs,

for drawing streamlines, 31 technique, 50 Element, straight-; see Straight

hydrofoil, formulas for calculating, 72

543

modifications for appendages abreast, 293 pipes for suction dredges, 777, 778

predominant type, 290

classification of

rigging, design to reduce,

Elliptic ellipsoids, definition of,

appendages by,

of,

139, 321

slope, estimate of, 321

for,

hull, skeg,

methods

of,

31

the final design of screw propeller, 629 Dredges, self-propelled, special design problems, 777 Drift and leeway, estimated, due to wind, 286 -resisting keels, design of, 695 Drive, vertical-shaft, for screw propellers, 653 Dry-cargo vessels, design of, 762 Drydocks, floating, self-propelled, 779 Ducts and channels, refs to flow patterns in, 36, 37, 39 passages, friction data for water flow in, 105 amphibian, peacetime uses of, 806 Djmamic forces, equilibrium of static and, on submarine, 812 lift, and planing, quantitative data, 263 coefficient of planing form, graph for, 265 determination of, 264 self-propelled motorboat models with, 864 metacentric stability, check of, 553 definition of, 443 viscosity, and surface tension, 920 reference data on, 94

DUKW

196

design

contra-guide skeg, design

wind, irregular structures, formulas for, 276 lateral, 285 masts, spars, and rigging, 566 with wind on bow, 281 Drawing, final design, ABC screw propeller, 628 streamlines, various

nose outhne, formulas

Emergence points, faired shafts at, 746 Emergency running, temporary bow for, 781 Empirical data, use of in modern ship design, Endings, bossing,

motorboats, 862

43

around, 43

Elliptic ellipsoids, flow

566

separation, estimate and approx still-air, of

Electroanalogic methods, 51 Electrolytic tank arrangements, 49

friction; see Friction

keel, design of hull with,

957

Electric analogy, delineation of flow patterns by, 49, 67 bibliography on, 50

of,

xix

536

of,

532

Energy, in surface-wave system, calculation Engines, number and position of, 570

of,

163

English-metric conversion ratios, 928-930

English system, units in, 926 units of measurements, ratios between, 926 Enlargements around propeller shafts, fairing, 744 Entrained water, added mass of; see Mass Entrainment, air, precautions against, 747 Entrance, angle of designed waterline, 479 selection of section shapes in, 515

vee, pressure distribution along, 48

EPH

streamlined section (Ellipse-Parabola-Hyperbola),

678 Equal-velocity contours; see Isotachyl

Equalizing powers for multiple screw propellers, 573

Equations, and formulas, pure, use

xx, 7

of,

of motion, multiple solutions to, 6

summary

of general 0-diml, for ship forms, 192

0-diml ship-surface, application

of,

191

Equilibrium, static and dynamic forces, for submarine, 812 Erosion, cavitation, prediction and prevention of, 156 propeller, coating

and materials to

Estimating, added-mass

coefficients

resist,

for

635

vibrating

ships

and propdevs in confined waters, 433, 436 added mass of water in unsteady body or ship motion, 417

and wind resistance of ships, 274 bow-wave heights and positions, 244 air

Earthquake wave or tsunami, 181 Echo-ranging gear, design notes for locating, 705 Eddies, circulation strength of, in streets or trails, 142 references to flow photographs of, 37

Eddy

draft variations, 481 drift

and leeway due to wind, 286

effect of lateral channel restr in subcritical range,

410

and friction power, 354 flow at propdev positions, 258 effective

frequency, definition sketch for, 16 relations for vortex trails, 142

pattern for light or ballast conditions, 256

systems, references to, 144

Eddying, separation, and vortex motion, reference data, 133 Edges, leading and trailing, design of, 675, 676 screw-propeller blade, shaping of, 606 to prevent singing and vibration, 636 Effect, and inception of cavitation on ships and props, 145

forces

on a moored

ship,

287

hull volume, first approx, 471

metacentric stability, first, 478 power, first approx, for round-bottom motorboat, 853

propdev

efficiency,

332

resistance of discontinuities, 294

relative rotative, estimate of, 374

screwprop characteristics for motorboats, 859 thrust from insufficient data, 346 shaft power, second approx, for planing craft, 847 ship-wake fraction, 368 stern-wave heights, 245 thrust and torque variation per rev for screwprops, 348 total resist for submerged and surface ships, 313

screwprop, calculating expected, 629

weight, first approx, 463

scale; see Scale

Effective power; see

wake

Power

fraction, definition of, 615

Efficiency, ideal, shaft-power estimate

propdev, estimate

of,

by use

332

real, propeller, variation in.

333

Elastic characteristics of water, 922

of,

383

for planing craft,

828

1

HYDRODYNAMICS IN SHIP DESIGN

958

Estimating, weight, for round-bottom motorboat, 853 principal, second, for surface ship,

474

second, for planing-huU motorboat, 831 third approx, for motorboats, 863 Euler number, definition and use of, 8-1 Exhaust, gases and air, mechanical properties, 922 underwater, for propelling machinery, 545 Expanded-area ratio of screw propeller, 602 chord length of screwprop blade derived from meanwidth ratio, 340 Experimental and calculated ship resist, comparison of, 216

basic, in ship design,

welding, use of for fairing, 742

on raft Kon-Tiki, 698 ahead of movable rudders, 75, 77, 719 fixed stabilizing, design of, 697 flexible cantilever type, calc of added mass, 438, 439 fulcrum or stabilizing, on ultra-high-speed motorboats, 862

Fin(s), adjustable,

procedure, for motorboats, 828

Factor(s), absolute size, in

Fillet(s),

maneuvering requirements, 452 442

conversion, English-metric, 928-931

Jennej', to prevent air leakage to propellers,

Fireboats and firefloats, design problems, 774 Fire-fighting monitor, improved design, 776 Fishing vessel(s), bibhography on, 771-774

design

of,

770

Japanese, illustrations

standard

series,

of,

771, 772

Japanese, 300

and mooring, 743

merit, for predicting shaft power, 380

Fittings, recessed Ufting

reduction, for calculating added masses, 430

Five-screw (propeller) installations, notes on, 521 Fixed appendages, design of, 675 guards and fenders, design of, 699

section shape, for vibrating ships, 429 thrust-load, 343, 345

calculating for a screwprop, 613

variation with ship speed, 344-346 unrelated, effect on hydrodynamic design, 502 Faired principal ship lines, practical use of mathematical formulas for, 203

and

hull smoothness, achieving, 749 problems of, 738 appendages in general, 742 definition of, 738 designed waterhne of ABC ship, 200 enlargements around shafts, 744 exposed shafts at emergence points, 746 for inside corners, 742 hub, screw-propeller, 601, 744, 745 importance of, 738 mathematic, of entrance, ABC ship, 200-202 necessity for in ship lines, 193, 194 propeller hubs, 745 section-area curve, 198 ship lines by mathematic methods, 199 underwater, on a ship, problems in achieving, 749 Fairness and curvature, value of in ship hnes, 193 Fat forms, changes of attitude and trim, 329 hull forms, vessels with, 770 ships, resistance data for, 303-306 Fatness ratio, first approx, 464-466

Fairing,

DWL

i

objects in a stream, design, 675 screwprop shrouding, design of, 687 stabilizing skegs or fins, 697 Flap, controllable, for planing craft, 840

hinged, for closing propeller tunnels, 671

-type rudders and planes, automatic, 735 Flare,

compound, design procedure

strakes, design of, 560, 700 Ferryboat(s), hulls and appendages, design

requirements and references Fetch, for wind waves, 176 Fields, velocity

;

of,

793

790

and pressure around a

Filleting at inside corners, Fillet(s)

for,

for,

551

Fleet tug, displacement of appendages, 296 Floating dry docks, self-propelled, 779, 780 Floats for pontoon bridges, 782

Flooding spaces,

due to flow through, 323

free-, resistance

Floor, rise of, in mid- or maximum-sections, 476, 477

magnitude, for planing craft, 836 Flow, abaft a screw propeller, 259 adequate, to propdevs in confined waters, 668 air-, pattern, over ABC ship, estimated, 565 passenger-ship model, 563 analj'sis for arch-type stern, 521

and

force data for hydrofoils, 72

pressure around a hydrofoil, 80

around special forms, 46 in a liquid, formulas for, 7

around an irregular 3-diml bodj', ship, prediction of, 239

43, 46

special forms, 46

at propdev positions, determination

relation to displacement-length quotient, 930, 932

Feathering features, in propdev design, 578 paddlewheels, definition and design sketch, 640 propellers, design data for, 651 Fender(s), constructed as bulges, design of, 769 fixed, design of, 699

of,

358-366

estimated, 258, 259

screwprop positions, anal3'sis of observed, 259, 366, 367 back, around ships in canal locks, 414 curvature, in screwprop design, corrections for, 625 data, viscous, 86 summary of formulas for, 87 deflection around separation zones, apparent, 139 derivation of formulas for 2-diml and 3-diml, around sources and sinks, 17-24

hydrofoil, 82

742

see also Fairing

diagrams, about hydrofoils,

list

of refs, 78,

79

upper works, 276 ship, analj'sis of, 239

for

at strut-arm endings, 679, 680

source-sink, delineation of, 52

casting, use of, for fairing, 742

surface-flow,

738 fairing, and problems of hull smoothness, 738 root, for screwprop blades, shaping, 606

use of for positioning appendages, 258

definition of,

748

torque-compensating, design of one type, 699 Fine, slender hulls, design notes, 752

on model,

analj'sis of,

250

3-diml radial, data for constructing, 64 uniform, data for constructing, 65

SUBJECT INDEX Flow, equations

of,

double solutions

to,

and moment data for hydrofoils, 72 by ink trails around model, 138, 139 tufts on model, 137-139

force,

indicated

induced, in screwprop

jets,

343

into propdev positions, data on, 341 lines of,

determined from models, 248, 873

diagi'ams, typical, 248-250

under ship bottom, 253 liquid, general

formulas relating

to, 7

drawing of, 31 observations with tufts on models, 137-139, 874 off-the-surface, on models, interpretation of, 254 pattern(s), around geometric and other shapes, 31-33 ship forms, prediction of, 239 variation with Cx, 251 simple shapes, references to photos of, 34, 35 when yawed, 38, 40 simple ship forms, 39 source-sink pair, 2-diml, 54 stream-form shapes, formulas for calculating, nets,

67 typical hydrofoils, 78, 79

delineation of

by

electric analogy,

49

bibliography on, 50

around ship forms, 39, 40 or ballast conditions, 256

for ideal liquid light

in ducts

pairs, 58

bodies, 38, 40 255 on body plan, estimating, 255 prediction of, 239 source-sink, by colored hquid, 67 electric analogy, 67 graphic construction, 54 2-diml, around source and sink, 54 for three source-sink pairs, 59 for two source-sink pairs, 58 3-diml, graphic construction of around 3-diml source and sink, 62 photographs for hydrofoils, list of references, 79 potential, quantitative rel bet press and vel in, 25, 26 probable, at a distance from ship surface, 256 source-sink, delineation of, 52 studies, use of doubly refracting solutions for, 48 surface, on models, analysis, 250 through free-flooding spaces, resist due to water, 323 ship, at the bilges, prediction of,

under-the-bottom, on models, 253 viscous-, data,

and

friction-resistance calculations, 86

corrections for in screwprop design, 625

water, as apphed to hull design, 545

Flowlines, sketching, for

transom-stern

ABC

new

design, 494

ship,

495

moored

287 typical planing craft, definition diagram, 264 principal, on a planing craft, 264 static and dynamic, equihbrium of on a submarine, 812 thrust and toi-que, created by screwprops, 348 velocity, and pressure of natural wind, 284 vibratory, induced by propeller, 877 Fonn(s), abovewater, layout of the, 546 and shape data on typical ships, 223 asymmetric hull, 787 discontinuous-section, design of, 768 fat hull, design of, 770 ship, estimating,

geometric, separation around, 140 hydrofoil and equivalent, flow and force data for, 72

layout of the abovewater, 546 normal, modification for shallow water, 666 parent, choice of

of, for

ship lines, 488

Taylor Standard

223-225

Series,

planing, operating requirements for, 824

204 good performance, comparison of new design with, 496 predicting distribution of vel and press around, 257 schematic, distribution of vel and press around, 47 suitable for calculating wave resistance, 219

ship, geometric variation of,

of

simple ship, flow patterns around, 39 special, flow, velocity, and pressure around, 46

2-diml doublet, 61

and channels, 36, 37, 39 laying out around two source-sink photos of, around hydrofoils, 79 shapes and bodies, 34, 35 potential-, around bodies, 31 for ideal liquid around yawed

959

Force(s), on a

6

Flowplane curvature, longitudinal, 199 Folding propeller, design data for, 651 Force(s), and fiow data for hydrofoils, 72 exerted by or on bodies around sources and sinks in a uniform stream, 68 moment, and flow data for hydrofoils, 72

and design of, 750 and quadruple-screw vessels, 520 stream, circular, and the doublet, 61 contours and streamlines around 2-diml source, 52 hull, classification

stern, for twin-

shapes, formulas for calculating, 67 solid, definition of,

variety

of,

66

produced by sources and sinks, 67

2-diml, calculations for, 17

construction from line sources and sinks, 59 graphic determination of vel around, 57 3-diml, calculations for, 20 of, 62 molding a new, 488

graphic construction

underwater

hull,

Fonnula(s), for calculating circulation, hft, drag, 72 ship friction resistance, 99

stream-form shapes, 67 friction-resistance, for

smooth

plates, 102

general, relating to liquid flow, 7

mathematical, for delineating ship hues, 187 faired principal lines, 203 power, for planing-type motorboats, 834, 835 round-bottom motorboats, 853, 854 pure, use

of,

7

ship powering, for steady ahead motion, 354 stream-function and velocity-potential, derivation for

2-diml flows, 17 3-diml flows, 20

hydrodynamics, 2 of, 87 wake-fraction, of Aquino, 368 Schoenherr, 369 wind drag of superstructures, 276 Fouled-huU condition, estimated shaft power useful, in theoretical

viscous-flow,

summary

for,

385

Fouling, effects of ship resistance, prediction of, 120 factor, loeaUty, definition and use of, 122

HYDRODYNAMICS IN SHIP DESIGN

960 Fouling, factor, proposed table

Gas(es), and smoke discharge, abovewater, design, 563 underwater, comments on, 565

122

of,

references relating to, 125

graphs

resistance, allowances,

of, 123,

exhaust, and

124

factors affecting, 117

Fraction, hull-force, for control surfaces, 718

velocit.y,

of,

of miscellaneous propdevs,

Freeboard, and sheer for general service, 547 protected waters, 547

forms, separation

wavegoing, design values, 548

2-dimI and 3-diml, drag data

for icebreakers, 797

waves; see Waves

Geometry

Freeing ports in bulwarks, required area, 554, 555 Frequency, eddy, definition sketch for, 16 relations for vortex trails, 142 of trochoidal waves, data on, 165-168

propdev and hull vibration, relation

of,

of and flow around, 5 Gertler prediction of residuary resistance, 318 reworking of TSS data, 301-303 Gill axial-flow propeller, long'l section through,

580

1947 or Schoenherr, 104

on

128

126

straight-element and hulls,

discontinuous-section

specific, of

a liquid, definition

of,

87

and residuarj^, typical percentages, 314 wetted length and surface of planing craft, 268 bibliograph}', selected, 128-132

resistance,

from SNAME ERD sheets, 402 development of formulas for calculation of, of

99,

316

formula(s), comprehensive, 101 of a planing hull, 128, specific, tables of for

in turbulent flow, 102

268 models and ship, 101, 102

Froude friction-resistance formulas, 103 number, and 7",, tables of, 928 definition and use of, 11 ratio to Taylor quotient, 11, 928, 929, 932 submergence-, for transom sterns, 530

Greek alphabet, 900 Guard(s), and fenders,

755

fixed, design of,

699

rudder, for ferryboats, 794

Guide, contra-; see Contra-

and salt number as,

corresp to unit press, fresh

water, 28, 29, 916

expression of cavitation

11

Heavy

weights, long'l position in a planing craft, 850

and lateral wind moments, 285 Height(s), above surface, increase of wind velocity with, Heel, angle

of,

274 sheer, in fractions of

related to

wave

wave, and steepness to

wave

WL length,

549

steepness, 548 ratios,

169

length, ratios in ship design, 170

Helix angles, blade-, of sorewprops, 340, 341

tables of, 12-14

Full-planing craft, design procedure for, 821 -scale thrust and towing measurements on ships, 310-

Hillman straight-element shallow-water Hinge gaps, rudder, closures for, 691, 726

hull,

666,

667

Historical highlights, introduction of, xx

312 Function, stream, formulas for typical 2-diml flows, 17 3-diml flows, 20 radial, for 2-diml source-sink pair, 55

Funnel see Smoke ;

Future, special-purpose craft of the, 818 Galvanic-action protectors, design of, 704

Gaps, ahead of control surfaces, design of, 709-712, 735 rudders, 712 holes, and slots, drag data pertaining to, 294 rudder hinge, closures

5

Head(s), and pressures, ram, tables of, 28-30 axisymmetric, cavitation data for three types, 152

calculations, 86

smooth plate

of,

carriers, design notes,

tabulated hull data, 758-760

power, estimating, 354

for

K

Great Lakes cargo

127

summary

formulas,

339 Goldstein criterion, for hydrodynamically smooth surf, 112 factor for sorewprop, 616, 617

Graphs, conversion, English-metric and metric-English, 931 Gravity, acceleration of, var with latitude, 917, 918

data, water flow in internal passages, 105 craft,

of the ship, 0-diml, 189, 191

Geosims, definition

Friction allowances for surfaces of varjdng roughness, 115

ship, calculation of,

291

for,

variation of ship forms, 204

whale catcher, 550 tentative, 548

ratio(s), for

drag of moored

phenomena around, 140

shapes, added mass for, 419

deck, tentative graph for, 547, 548

ATTC

638

formulas relating to liquid flow, 7 hull features, determination of, 457 problems of ship designer, 454 Geometric bodies, drag coefficients of, 291

ship models, for maneuvering tests, 876

coefficients, specific,

stacks, 564

design features of abovewater form, 546

Free-flooding spaces, flow through, resist due to, 323 -running bow propellers, design of, 632

minimum,

mechanical properties, 922, 924

minimum, from

Gebers friction-resistance formula, 103 General considerations in preliminary ship design, 460

718 thrust-deduction; see Thrust deduction wake; see Wake rudder-force, definition

air,

-jet propdevs, data on, 337

for,

726

History of operation as basis for fouling, 119, 120

Hogner's contribution to Kelvin wave system, 161 Holes, gaps, and slots, drag data, 294 Hollow-face prop-blade sections, use and disadvantages of, 627 Hollows and humps in resist curves, 466, 467 supporting, for rudder, design notes, 690 Horn, Hotchkiss propeller, explanatory diagrams, 339 Housing bow propeller, design of, 797

Hovering, applied to a submarine, definition Hub(s), cavitation, predicting, 155

of,

809

SUBJECT INDEX Hub(s), diameters, and screwprop-disc, 612 screwprop, 601 sorewprop, fairing of, 601, 745 type of, 633

profile for surface ship,

in motorboats,

friction-resistance formulas, 104

Hull(s), abovewater,

comments on

drag coefficients

for,

wind-fiiction resist, 2S0'

279

proportions for strength, wavegoiiig, 496 adjacent to propdev positions, sliaping of, 536

and appendage combinations, design, 526 screwprop vibration frequencies, relation of, 580 asymmetric, design of, 787 blunt-ended, long and narrow, design of, 755 design, detail, of the underwater, 504 features, motorboat, interdependence of, 843 relation of paddlewheel diameter and position to, 643 water flow applied to, 545 discontinuous-section, design

of,

504

of,

506

vibration and jiropdcv frequencies, relation

vortexes, predicting, 155

Hughes

961

Hull(s), underwater, detail design

768

of,

volume, first estimate, 471 with keel drag, design procedure, 543 Humps and hollows in Rr curves, diagram, 467 Rt curves, diagram, 466 Hydraulic-jet propdevs, data on, 337 propulsion, design notes for, 648 radius, definition and sketch, 409 of channels, calculation of, 409, 412 Hydrodynamic(s), applied to ship design, 442 design, effect of unrelated factors, 502 of amphibians, 806 preUminary, of a motorboat, 819 problems of submarines, 809 second, modifications for, 896

formulation of design specifications involving, 446 of reference books on, 2 paddlewheel propulsion, 638 list

friction drag on, 127

endings adjacent to propdevs, 536 design of, 770

pitch angle ft of screwprop, first approx, 615 second approx, 616

features, determination of general, 457

-diameter ratio, 617 requirements of a ship, analysis

fat,

for planing craft, selecting, 835

ferryboat, design for, 793 fine

and

of,

460

principal, of a small craft, 825

slender, design of, 752

structural control-surface design, effect of on, 724

-force fraction for control surfs, definition of, 718

form(s), asymmetric, 787 special, classification

and design

of,

750

underwater, molding a new, 488 formulas for wind drag of irregular, 276 fouled-, condition, estimated shaft

power

for,

385

theoretical, useful formulas in, 2

Hydrodynamically smooth surface, criterion for, 112 Hydrofoil(s), compound, lift data and CP positions, 75-77 test data from, 75 distribution of velocity and pressure around, 80 drag data for, 83

inner, of submarine, definition of, 810

effective aspect ratio for equivalent ship, 83

laying out other types, 502

flow, force,

lines,

preparation for model

tests,

566

outer, of a submarine, definition of,

and use

of,

810

827-852

827 friction resistance of, 128 pressure, of submarine, definition and use of, 810 profile, underwater, 506 proportions of, for a surface ship, 464 selection, for motorboat, 827 resistance, total, calculation of, 313 round-bottom motorboat, first space layout, 852 weight estimate, 853 shape, along bilge diagonal, 517 and propulsion, on a submarine, 813 selection of for large ship, 476 for round-bottom motorboat, 854 in entrance and run, 515 ship, general formulas for wind drag of, 276 in unsteady motion, estimated added mass of water around, 417 rel of paddlewheel diam and position to, 643 small-craft, design of, 822 smoothness, fillets, and fairing, 738 straight-element, allowances for drag on, 127 bibliography on, 764, 765 design of, 762 surfaces, abreast screwprops, design notes, 672 type, selection of for motorboat, 827 first

space layout

of,

and moment data

for,

low-aspect ratio, empirical study

multiple-, craft design, 788

planing, design

580

859

72

of,

as lifting surfaces,

866 planforms and sections, design and drag data, 83 polar diagrams for simple, 75, 76 prediction of cavitation on, 149

-supported craft, bibliography, 271-273 symmetrical, cavitation and

lift

data, 151

leading and trailing edges, 676 typical, cavitation limits on, 150

flow patterns around, 78 test data from, 73 velocity

with

flat

and pressure fields around, 82 and round edges, data on, 73, 74

Icebreakers, bibliography on, 804-806

and design problems of, 794-799 minimum, 797 general data and references on, 799 tabulated data for modern, 800-803 definition

freeboard,

transverse section for, 796

and design problems, 794-799 method to predict shaft power, 383 liquid, velocity and pressure diagrams for, 31 Illustrative prelim design procedures, comments on, 898 Iirunersed-transom drafts and speeds, 530 Iceships, definition

Ideal efficiency

stern, design of, 529 Improvements in design, field for future, 444 Inception and effect of cavitation on ships and props, 145

Inclined bar, to

make

air-filled

ditch for prop shaft, 685

HYDRODYNAMICS

962

data on, 784 Increased, draft with ship age, comments, 566 resistance, limiting depth for 2 per cent, 404 Increasing the power and speed of an existing ship, 387 Inclined, waterlines

on

sailing j'achts,

Index, cavitation, definition and use

of, 10,

11

roughness, factors in, 114 Induced flow in sorewprop jets, 343 velocities in screwprop jets, data on, 343 Induction openings, positioning of for wavegoing, 701 Ink trail on ship model in circ-water channel, 138, 139 Inlet and discharge openings for heat exchangers, design,

701 openings, multi-vane type, 702

underwater, positioning to remain submerged, 701 Inner hull of submarine, definition and use of, 810 Installation, galvanic-action protectors, 704 Interdependence of motorboat hull-design features, 843 Interference effects, between blade sections in cascade, 84

wave, general rules for, 243 Intermediate speed ratio in shallow water, graphs of, 394 Internal passages, friction data for water flow, 105 shearing stresses in water along ships, 94 ready-made ship-design requirements, 454

Interpretation,

streamline traces and tufts, on ship models, 250-255

wake diagrams,

3-diml, at sorewprop positions, 362

Isotachyls around an ellipsoid midsection, 45 J-class sailing yachts, reference to lines drawings of, 228

Japanese fishing boats,

illustrations of, 771,

Jenney

fins,

772

300

-vessel standard series,

to prevent air leakage to propellers, 748

Jet(s), diameters, screwprop, ratio of inflow-outflow,

342

variation of with thrust-load coefficient, 343

augment of velocity at rudder positions, 707 axial and rotational velocity components in, 260

outflow,

position of multiple rudders relative to, 708 outlines for screwprops, inflow

and outflow, 343 337

-propulsion, gas or hquid, data on,

hydraulic, data on, 337

design notes on, 648

pump-, data on, 337 design notes on, 648

Joukowski

airfoil sections,

drag data

for,

84

Keel(s), bilge-, area, 692

design diagrams, 692, 693 of,

691, 692, 694

for

ABC

ship,

695

discontinuous, on liner Oranje, 692

gaps and offsets between sections, 692 structural considerations in design, 694 traces

by flow

streamlines, 692

transverse shape and section, 694 deep, of a motorboat, 842

docking, design

of,

695

sketches, 697 vertical bossings as,

686

drag, design of hull with, 543 drift-resisting, design of,

resting, design of, roll-resisting,

695

695

design of for

ABC

ship,

695

and in tandem, 692 position, type, number, 691 Kelvin wave system, modified by E. Hogner, 161 in parallel (abreast)

IN SHIP DESIGN Kinematic

viscosity, reference

data on, 94

values of for water, 919, 920

Knuckles, abovewater, design

Koch added-mass data

of,

560

for confined water, 434

Kort nozzle, definition sketch and design references, 687 Kramer's contours of ideal efficienc}', 614

Lackenby friction-resistance formula, 104 Lag of bow-wave crest, graph for, 245 Lagally Theorem, description of, 68 references on, 71

Laminar-sublayer thickness, in turbulent flow, 104, 120 variation with i-distance and speed, 105 Landing and beaching, vessels designed for, 808 Landweber local-friction-resistance formula, 102 Lap and Troost friction-resistance formula, 104 Laps and butts, shaping and facing of, 740, 741 Lateral wind drag, 285 moments and hull angles, 285 Launches, fast, design of, 752 Layer, boundary; see Boundary LCB, usual fore-and-aft positions of, 486 Leading edge(s) of appendages, design of, 675, 676 Leakage, air, to screwprops, avoiding, 631 separation zones, 140 Leeway, estimated, due to wind, 286 Length and long'l curvature in shallow-water design, 665 -balance ratio, control surface, 721, 727 -beam ratio for ships, 470 planing craft, 838 ship, first approx, 465 trochoidal wave, tables of, 165-168 waterline, first approx, 464 wave, to wave height, ratios in ship design, 170 wetted, of planing forms, 268 Lerbs' 1954 screwprop design method, for ABC ship, 611 summary of steps, 630 Level, change of with speed, 325 Life-saving or rescue boats, 816 Lift, -coefficient data for symmetrical hj'drofoil, 151 graphs, typical, for hydrofoils, 73, 74 product, for sorewprop blade sections, 617-619 data for bodies hke appendages, 291 -drag ratios for airfoils and hs'drofoils, refs on, 76 dynamic, bibliography on, 269-271 determination of, 264 quantitative data on, 263 self-propelled motorboat models with, 864 hydrofoil, formulas for calculating, 72 spanwise distribution of, 83 Lifting fittings, recessed, design of, 743 -surface correction factor, for sorewprop, 619 Light-load condition, estimated flow pattern in, 256 Lightships, or light vessels, design notes for, 814 Limen, of a rough surface, 112, 114 Limitations, present, of mathematical methods, 2 Limits for wavegoing conditions, 458 Line(s), choice of parent form for, 488 faired, use of formulas for, 203 fairing by mathematical methods, 199 hull, preparation for model tests, 566 layout, ABC planing-type tender, 843 round-bottom tender, 855 of constant pressure derived analytically, 218

SUBJECT INDEX Lme(s),

diagrams for ship models, 248 of flow, in ballast condition, 257 observed on models, 873 -of-flow

procedure for a ship, 432 change of, near a large boundary, 432 coefficients, definition of, 419

sheer, for various ship types, 550, 551

limitations of, 192

references relating to, 204

use of for ships, 186, 193 with developable surfaces, 765 sources and sinks, definition of stream functions, 60 use of for 2-diml forms, 59 Taylor Standard Series, 224 condenser Lips on scoops and discharges, 701-703

common,

elastic characteristics,

entrained, mass of; see

Mass

elliptic sections,

427

floating streamlined bodies,

422

geometric shapes, 419-423

reference data on, 94

and pressure diagrams mass, added; see Mass velocity

for,

31

mechanical properties, gases and, 924 velocity and pressure diagrams for, 31 Lissoneoid of Rankine, diagram of, 208 List; see Heel Load distribution, equalizing among multiple props, 573 Locality fouling factor, definition and use of, 122 Locating echo-ranging gear on merchant vessels, 705

propdevs on a ship, 368 propeUing machinery in a ship, 443, 570 Locks, canal, predicting ship resistance in, 413 Logarithmic propeller-series charts, 588-590, 593 Logarithms of numbers frequently used, 932 first,

LCB, with good

"standard" fresh and salt water, 915, 918 Masts, design to reduce wind drag, 566 Materials, propeller, to resist erosion, 635 Mathematical and 0-diml representation of ship surf, 189 calculation of wavemaking drag, assumptions in, 212 deUneation of section-area curve, 198 determination of selected points on ship, 203 entrance, ABC ship, 200-202 fauing of section-area curve, 198 formulas for deUneating ship lines, 187 faired fines, use of, 203 fines for ships, fimitations of, 192

DWL

practical use of, 186, 193

references for, 204

methods

497

center of buoyancy, usual positions for, 486 fit

effects, partial bibliography on, 439 entrained water around a ship in unsteady motion, 417 for bodies with fore-and-aft asymmetry, 422, 423

selected

ideal, flow patterns for, 31

gravity, to

ships, 433 data for large, thin, vibrating cantilever, 439 water around appendages and skegs, 438

modes of motion, 419-423 submerged spheroids, 422 Mass density, Hquids and gases, 924

922

flow, general formulas relating to, 7

Longitudinal, buoyancy balance,

liquid, calculation

estimated, for vibrating propdevs, 436

ship, mathematical, formulas for delineating, 187

Liquid(s),

963

Mass, added

hull lines, 498

for calculating pressure resistance,

delineating bodies

and

ships,

fairing ship fines, 199

necessary improvements

curvature, analysis, notes on, 195

in,

219

flowplane, 199

predicting pressure resistance, 321

in shallow-water design, 665

present fimitations

maximum-area

above water, design, 560 section,

optimum

heavy weights,

in planing craft, 850

(theoretical) surface waves,

data on, 160

Mathematics, proper use

of in engineering problems, 3

Maximum,

optimum

-area section,

long'l position of, 482,

483

prismatic coefficient, selecting, 467

497 weight balance of a Low-aspect ratio hydrofoils, behavior as lifting surfaces, 866 Low ship speeds, resistance data for, 306 ship, first,

Mach number,

definition and use of, 7 Machinery, propeUing; see Propelling Magnus Effect on exposed rotating shafts, 678 Main-ballast systems of submarine, description of, 811 Maneuvering, and steering, behavior, first approx, 501 swinging props for, 737 turning, model tests, 876 astern, rudders for, 735 behavior, first approx, in prehminary design, 501

diagram, for ship requirements, 451 requirements, absolute size as a factor

2

sections for ships, 191, 193

positions for, 482,

483 position,

of,

representation of ship surface, 189

0-diml, graphic determination, 196 discontinuities

206

186

in,

452

in ship design, 450

propdev design to meet, 580 submerged, on a submarine, 813 swinging props for, 737 Mass, added liquid, assumptions when calculating, 417, 418

-section coefficient, selecting, 468, 469

contour, layout, 476, 477

WL beam, best fore-and-aft position, 481 ratio of screwprop blades, formula for, 341 Measurement(s), abbreviations for units of, 912 Engfish units of, 926 ratios between, 926 Mechanical construction of screwprops, 633

Mean-width

properties, air

and

and exhaust

gases, 922

920 other liquids and gases, 924 water, air, and other media, 915 Mechanism, paddlewheel, design notes, 645 Median line of contra-guide features, 533 Merit factors, for predicting shaft power, 380 fresh

salt water,

Telfer, for ABC ship, 895 Metacenter, height above basefine, 479 Metacentric stability, and pendulum, on submarine, 912 dynamic, check of, 553 definition of, 443 first estimate of in preUminary design, 478

1

HYDRODYNAMICS

964

Meteorologic conditions affecting ship design, 448 Metric-English conversion ratios, 928-930

484 longitudinal position of midlength of, 483 systematic resistance data, 306 Miscellaneous propdevs, design of, 638 performance of, 339 Mode(s) of motion, added masses for selected, 419 of vibrating screwprop, 437 Model(s), ABC ship, test results for, 879 and ships, bibliography on confined-water effects, 415 observed resistance data for, 297 flow data, presentation and reporting of, 877, 878 lines-of-flow diagrams, 248-250

Middlebody,

parallel, design of, 483,

off-the-surface flow data, observation tation,

residuary

IN SHIP DESIGN Moored

ship, friction drag of, 128

Mooring fittings, recessed, design of, 743 Morrish formula; see Normand formula Motion(s), ahead, steady, ship-powering data diagrams, ship, 325

equations

of,

multiple solutions

vortex, reference data on, 133

wave, in shallow water, compared with deep water, 180 definition of, 819

design, general considerations, 820

preliminary hydrodynamic, 819 n-ith limited draft,

resistance data, observed, 297

screwprops, open-water tests, 632, 876 self-propelled tests, 377, 632,

875

backing power from, 388 on motorboats with dynamic lift, 864 use of stock screwprops for, 870 series, sj'stematic resistance data, 298

250

ship, analysis of the surface-flow diagrams,

wake around

or behind a, 259-262

diagrams for, 248 submerged, towing of, 322, 323 surface-flow diagrams, analysis, 250 test(s), controllability in shallow water, 876 data, ABC ship models, analysis and comments, tj'pical lines-of-flow

6

of, selected,

Motorboat(s), bibhography on, 865-867

and interpre-

variation with speed, 306-308

354

added liquid masses for, 419 vibrating screwprop, 437 unsteady, added mass of water around ship in, 417

mode(s),

264

resist, rate of

to,

for,

858

of, 823 round-bottom, first space layout, 852 weight estimate, 853 rudders, design of, 724 Movable appendages, design of, 706 Multiple, -hulled craft, design problems, 788 propellers, design to equaUze powers of, 573 rudders, single or, 708 -screw stern body plans, typical, 236

displacement-type, design

-skeg stern, design

of,

531

solutions to equations of motion, 6

Mushroom anchor

ABC

for

proposed

ship,

under-the-

bottom, 558, 559

NACA

blade-thickness forms, 621, 623 Narvik class transom stern, model, 531 Natural winds and waves, average relation between, 176 Nets, flow, drawing of, 31 Neutral control-surface angle for rudder(s), setting, 736 rudder angle and model maneuvering tests, 876 Niedermair wave, definition and use of, 170 Nomenclature; see Appendix 1 Nominal wake fraction, definition of, 615 Nomogram for cavitation index, depth, water speed, 150 critical-speed ratio in shallow water, 395 square-draft to water-depth ratios, 393 Normand (J.-A.) formula for height of CB, 479 Nose outhne, elliptic, formulas for, 196 Notation, circular constant, 913 list of sj'mbols, 900 Nozzle, Kort, definition sketch and design references, 687 Number(s), blade-Reynolds, definition and diagram of, 15 Boussinesq, def and use of, 16

DD

879 desired for large ship design, 868

on typical

ships, resistance from,

297

reporting and presenting, 877 rotating-blade props, 337 hull lines for, 566

maneuvering, 876 motorboats, with dynamic lift, 864 neutral rudder angle, 876 notes for preKminary ABC design, 869 open-water and self-propelled, 632 resistance data from, 297 self-propulsion, data from, 377, 875 wavegoing, 877 when backing, 388 testing methods, EMB, 129 program for large ship, 868 total resistance, variation with T,, 308-310 TSS, improving the performance of, 474 wave profiles, 241 wind resistance, 277, 278 bibliography of model tests, 278 Model 56C of G. S. Baker, lines and resistance data, 234 Modulus, bulk, fresh and salt water, 923 Moment (s), and forces on typical planing craft, 264 -coefficient graphs, typical, for hydrofoils, 73, 74 force, and flow data for hydrofoils, 72 lateral wind, and heel angle, 285 pitching, on hydrofoil, 80 principal, on a planing craft, 264 Moment-of-area of coefficient, selecting, 478 Monkey rudders, on sternwheel craft, 709 Moored ship, estimating forces on, 287

WL

Cauchj", 7 cavitation,

tables

and Euler, def and use of, and nomogram, 147-150

d-Reynolds, def of, 15 dimensionless, quantitative use

summary and

table

of,

of,

,

7

8

frequently used, powers and logs

Froude, def and use of

8, 10,

of,

931

1

tables of, 12-14

Mach, 7 of propelling engines, 570

propulsion devices, 567 roll-resisting keels, selecting,

screwprop blades, choice for ABC ship, 612

of,

691 599

11

SUBJECT INDEX Number(s), Planing, def and use Reynolds, calculation tables of, 88-94 variations

of,

IG

of,

15

483 resistance data, systematic, 300

Parameters, bulb-bow, 485

15

of,

Strouhal, application

Weber, def and use

of, 16,

of,

143

ship, ratios of coefficients and,

16

a;-Reynolds and 5-Reynolds, def

Objects, fixed in a stream, design

of,

of,

transom-stern, 485 Parent form see Form Passages, internal, friction data Pattem(s), flow; see Flow

15

Offsets, of frame stations, calc of,

675

from faired

lines,

TSS

of,

stream, construction of from line sources and sinks, 59

wave; see

tests, 632,

stability, definition of,

in variable-pressure inlet,

of ship, calculation of, 1

good, ship form, comparison of

701 Ovoid, 3-diml, construction, with single 3-diml source, 23

Paddletrack propulsion, design features, 638 Paddlewheel(s), bibhography on, 335-337 blade area, determining, 642 design, layout for ABC ship, 644 notes on hydrodynamics of, 638 variations from normal, 648 details and mechanism, design notes, 645 diameter, relation to hull design, 643 feathering, definition and design sketch, 640 performance data on, 335 profile, 241,

positioning and shape of contra-vanes abaft, 688 of,

design lane for, 480 reference data on, 231 middlebody, detail design, 483, 484

230

new

design with, 496

miscellaneous propdevs, 339

positioning to remain submerged, 701 Operating conditions, two or more, powering for, 388 requirements for planing forms, 824 Operation(s), in confined waters at supercritical speeds, 412 shallow-water, modification of normal forms for, 666 Optimum diameter for a screwprop, 597 Orbit radii of trochoidal wave, decrease with depth, 169 Orbital velocities for surface particles of trochoidal waves, 162, 166, 16S, 169 Outboard propulsion, with vertical screwprop drive, 653 Outflow jet, of screwprop, axial and rotational vel components in, 260 position of multiple rudders relative to, 708 Outline, expanded-blade, for ABC ship, 624 sketch, first, of a large ship, 486, 4S7 small craft, 827, 828, 852, 853 Outer hull, of submarine, definition of, 810 Overall problem of the ship designer, 454 ship appendage resistance, values for, 288 wetted surface of submerged body, calculation of, 322 Overboard discharges for heat exchangers, design notes,

Parallel designed waterline, definition

414

references to, 223

water tunnel, 334

and wave

in,

on controllable and reversible props, 338 paddlewheels and sternwheels, 335

876

and discharge, design, 701

position, long'l, rel to hull

stabiHty on submarine, 812

813

254

data from, 333-335

Openings, water

Wave

Pendulum and metacentric

Ogival heads or noses for appendages, 676

Open-water model screw-propeller

water How, 105

203

parent form, 225

Off-the-surface flow data on models, interpretation

for

Performance, allowances, design and, 454 for ABC ship, 456 confined-water, unexplained anomahes data, from jet propdevs, 337 screwprop design charts, 335

ship, 0-diml, representation of, 190, 192

for

030

;

Oblique tunnels for shallow-water craft, 670, 671 Obliquity of hull not used in calculating wetted surf, 108 Observations of flow with tufts, 874 Observed resistance data for models and ships, 297 Oceanographic conditions affecting ship design, 448 Offset running positions in channels, data on, 413

0-diml

965

Parallel middlcl)ody, longitudinal position of midlength,

643

new ship design, guaranteeing, 459 propdev, and power, lack of rehable data for confined waters, 411 predicting, 332

screwprop(s), effect of cavitation on, 152

under supercavitation, 156 220 Periods of trochoidal waves, tables of, 165-168 Persistence of wake abaft a ship, 261 ship, practical benefits of calculating,

Phenomena;

see particular kind desired

Photograph(s), flow, in ciro-water channel, 137-139, 874,

875 references to, 34, 35 of flow

about hydrofoils,

refs to,

79

stereoscopic, of ocean waves, 177, 179

Photographing cavitation on model and ship props, 153 Physical arrangement of submarines, 810 concepts having scalar dimensions, abbrev for, 911 Pioneers in marine architecture, mention of, xx Pitch angle, hydrodynamic, ft, first approx for screwprop, " 615 second approx, 616 -diameter ratio, hydrodynamic, for screwprop, 617 proper, for ABC ship, 620 screwprop, 598 variation with radius of screwprop, 598 Pitching moment on hydrofoil, 80 Plane(s), and rudder(s), positioning, 706 bow, general design rules, 736 diving, automatic flap-type, 735 bow, design of, 736 contra-features for, 736 positioning of in design, 706 diving, sections, selection and proportions, 722 stern, design rules for,

736

Planing, craft, bibliography, 269-271

bottoms, typical pressure distribution on, 266 design of, 823 forces on, definition diagram, 264 full-,

design procedure, 821

HYDRODYNAMICS IN SHIP DESIGN

966

Planing, craft, principal forces and

moments

Power(s), estimated,

264

on,

increasing the, of an existing ship, 387

maximum

space laj'out, 827 friction resist of, 128

hull, first

of

to maintain constant speed shaft, estimated,

shallow-water vessels, 663, 664 single-screw, 234-236

first

Plating, shell, approx to

volume

prediction

291

of,

of,

airfoils

of,

and

486

601, 633

hydrofoils, 75

358

factors for estimating, 358

of,

358 ahead motion, 354

388 in ship design, 574

of references, 76

Pontoon bridges,

vessels,

second approx, 493 estimate for planing craft, 847 third approx, ABC ship, 894 shallow-water, lack of reliable data on, 411 Powering allowances, for two or more operating conditions,

simple hydrofoils, 75 list

method, 383

for steady

specific smoothness problems, 739 Plots, 0-diml waterline curvature, 506, 507 Plum stabilizer for trim control on planing craft, 840

Points, percentage, definition

when wavegoing, 449

ideal-efficiency

approx, for a ship, 471

methods and

twin-screw, 236

drag

574

planing craft, 832 merit factors for predicting, 380

"standard", 231-234

Polar diagrams for

by

from similar

Plan(s), body, estimating the ship flow pattern on the, 255

flat,

of,

for fouIed-huU condition, 385

tender, layout of lines, 843

and

designed shaft, definition

numbers frequently used, 932

reserve, in propelling maohinerj', 575

number, definition and use of, 16 quantitative data on, 263 factors involved in, 263

Plates, circular

round-bottom motor-

formulas, for round-bottom motorboats, 853, 854

graphs of dynamic-lift coefficient, 265 operating requirements for, 824

ABC

for

lack of reliable data for confined waters, 411

forms, center-of-pressure location, 267

-type

first,

boat, 853

variation of attitude and position with speed, 329

floats for,

data, ship, for steady ahead motion, 354

782

Ports, freeing, required area for surface ships, 554, 555

reserves, graphic representation, 576,

Position{s), abbreviations for, 911

small craft, notes on, 824

center-of-gravity, longitudinal, for planing craft, 840

577

tunnel-stern craft, 672

engines, propelling, in the hull, 570

Prandtl-Schlichting friction-resistance formula,

longitudinal, center of buoyancy, 486

Predicting, attitude, running, of planing craft, 851

heavy weights in planing craft, 850 maximum-area, 482 paddlewheel, rel to hull and wave profile, 241, 643 planing craft, variation with speed, 329 propdev(s), data on flow into, 341

design rules for, 568

estimated flow

at,

wake diagrams

at,

258 358

propeller, analysis of flow conditions at,

691

running, predicted, of planing craft, 851 screwprop, analysis of observed flow at, 259

basic concepts underlying, 1

boundary-layer data for ABC ship, 109 cavitation erosion, 156 on screwprop blades, 149 curves of Rr and Pe, 308, 354 fouling effects on ship resistance, 120 pressure resistance, by analytic methods, 321

by merit

contra-vanes abaft paddlewheels, 688

at bilges, 255

by Gertler adaptation of TSS by Taylor TSS contours, 317 by Telfer's method, 318

resistance

superstructure and upper works, 561

underwater inlet openings, to remain submerged, 701 Potential flow, patterns around bodies, 31 ratio, for shallow water, definition of, 395 396 velocity-, expression, formulation of, 214 formulas for typical 2-diml flows, 17 of,

model

in canal locks, 413 sinkage and change of trim, 325

EMB methods,

388

velocity

brake, first approx, for planing-type motorboat, 832 distr, design to equalize, with multiple screws, 573

257

effective,

and

self-propelled

friction, calculation of,

tests,

354

effect of displacement and trim changes, 355-357 estimating, 354 use as estimate basis for motorboat, 847

equalization

among

multiple propdevs, 573

data, 318

speed and power of ships, by surface-wave profile, 246 thrust-deduction fraction, 369-371

3-diml flows, 20

Power (s), backing, from

380

flow patterns, 239

and planes, 706

stock axis rel to control-surf blade, 720

graphs

factors,

shallow-water resist by inspection, 408 ship behavior in confined waters, 389

Positioning, appendages, use of flow diagrams for, 258

rudder(s),

03

procedures and reference data, 1 propdev performance, 332 residuary resistance, from series data, 316 running position, of planing craft, 851 shaft power, 358

259

propelling machinery in a ship, 570 roll-resisting keels, selecting,

1

wake wave

129

and pressure distribution around ship form,

fraction,

368

profile around a ship, 246 wind resistance for ABC ship, 282

Preliminary design(s), ABC, model-test notes alternative, preparation of, 501 hydrodynamic, of a motorboat, 819

for,

869

SUBJECT INDEX Preliminary design(s), mptorboat, principal requirements for, 825

Profile(s)

for

comments on illustrative, 898 screwprop, with series charts, 592

procedure,

steps in the, 460

Pressure(s), and flow around a hydrofoil, 80 special forms, 46 in a hquid, formulas for, 41

28-30

of,

velocity diagrams around bodies, 31 for 2-diml

and 3-diml

bodies, 43

distribution about asymmetric body, 43

body

of revolution. 40

hydrofoil, 80

schematic ship forms, 47 ship forms, prediction

of,

257

2-diml and 3-diml bodies, references to, fields

44 around a hydrofoil, 82

relationships in potential flow, 25, 26

around special forms, 46 axial-, distr in screwprop inflow-outflow

jets,

343

of,

ship, 511

Prohaska added-mass data

coefEcient(s), def of, 11

distribution

ABC

underwater, 500 screwprop blade, choice of, 602 skew-back for ABC propeller, 627-629 ship-wave, typical, 239 small-scale, preparation of, 486 sketch of, 487 stern, 491 and rudder shape, 709 surface-wave, prediction of, 246 transom-stern ABC ship, 492 velocity, in ship boundary layers, 97 list of references, 98 wave, determined from models, 241, 873 from stereoscopic photos, 180 prediction of, for any ship, 246 sketching, for new design, 494 transom-stern ABC ship, 495 typical, for ships, 239 3-component, complex sea, 175 wind-wave, by modern methods, 177 Program, for model testing, for large ship, 868 hull,

section-area curve, 485

heads, ram, tables

967 bow, 491

around axisymmetric bodies, 42

relation of to cavitation index, 10, IJ

tables of, 27, 30

for shallow water, 434, 435 Projected area of hydrofoil, def of, 5 Projections, major abovewater, in the main hull, 560 Propdev(s), (of many kinds and types)

corresp to unit heads, fresh and salt water, 28, 29 diagrams, graphic, details of, 9

and

differential, at screwprop,

aperture and tip clearances, 537

adequate flow

data on, 343

distribution, along a vee entrance, 48

direction of rotation, 572

about hydrofoils, 81 on model afterbody, 258 planing-craft bottoms, 266 velocity and, around a hydrofoil, 80 an asymmetric body, 43 schematic bodies and ship forms, 44, 257 hull of submarine, definition and use of, 810 lines of constant, derived analytically, 218 chordT\nse,

efficiencies,

gas-jet,

miscellaneous, design

performance

number and type

mathematic methods of calculating, 206 by analytic methods, 321 modern developments in calculation of, 210

vapor, of water, 146, 147, 921

Rankine Ussoneoid, 208 of natural wind, 284

of,

25

284

Principal design req'ts for surface ship, statement of, 446

dimensions, coeffs, features, for typical ships, 223-228

approx, 464 second approx, 475 preliminary design requirements for motorboat, 825 analysis of, 826 weights, second estimate, for surface ship, 474 Prismatic coeflBcient see Coefficient Profile(s), abovewater, and deck details, 553 afterbody, arch-stern ABC ship, 524, 527 first

;

of,

638

339 567

411 predicting, 332 positions,

wind, location of center magnitude of, 283

of,

of, 638 performance, lack of reliable data for confined waters,

on a submerged

relationships, quantitative, in potential flow,

of,

paddletrack, design features

and limiting dimensions, 568

data on flow into, 341 estimated flow at, 258

of ship,

and force

^

data on, 337

hydrauhc-jet, data on, 337 45, 47,

prediction

variations along a

332

of,

general design of the, 567

body, 323

velocity,

estimate

for double-ended vessels, 792

observation on a rudder, layout for, 9 ram, for fresh and salt water, 28-30

ship,

confined waters, 668

design to meet maneuvering requirements, 580

bodies of revolution, 42

resistance, as a function of depth,

to, in

hull vibration frequencies, relation of, 580

shaping hull adjacent to, 536 wake diagrams at, 358 pump-jet, data on, 337 rate of rotation of, 572 torque, disadvantages of unbalanced, 579 type and number, 567 used with contra-devices, 579 Propelled, seU-

;

see Self-propelled

PropeUer(s), (general classification) efficiencies, Gill,

estimate

of,

332

longitudinal section through, 339

Hotchkiss, explanatory diagrams, 339 Kirsten-Boeing; see Propellers, rotating-blade limiting dimensions for a ship design, 568 materials and coatings to resist erosion, 635 multiple, design to equalize powers of, 573

photographing cavitation on ship, 153

HYDRODYNAMICS

968

Propeller(s), positions, for a ship design, 568

rotating-blade, "basket" diameter, 536

design notes, 656 test results on,

337

values of real efficiency, 333 shafts, design of bossings for, 682

exposed, fairing

of,

in cavitating range, 153 in variable-pressure water tunnel,

650

self-propelled tests with, 377, 632,

swinging, for steering and maneuvering, 737

ABC

ship, design of

by Lerbs' short

method, 611 disc

and hub diameters, 612

final design,

area ratios, 340

340 627

selection of, 605 of,

634

comparison fisting of, 584-588 requirements for, 584

and moments

of,

589

shafts, design of bossings for,

682

per,

348

exposed, fairing enlargements around, 744

shrouding, fixed, design

widths, 340, 605

687 single-bladed, comments on, 600 submergence in all operating conditions, 500, 571 submersion under variable-load conditions, 498

632

housing, design

performance data on, 338

revolution, variation of forces -series charts,

sections, hollow-face,

of,

under supercavitation, 156

reversible,

606

prediction of cavitation on, 149

bow, design

all times, 500, 571 outflow jet, augment of velocity at rudder position, 707 performance, effect of cavitation, 152

preliminary design with series charts, 592

blade(s), edges, shaping of, helix angles,

on self-propelled models, 592, 870

position, anal.vsis of flow at, 259

628

rake for blades, 612

strength

stock, use of

334

875

necessity for full submergence at

vibratory forces induced by, 877 PropeUer(s), screw,

mean-width ratio, formula for, 341 mechanical construction, 633 model, and ship, photos of cavitation, 153 open-water test(s), 632, 876 data, 333, 878

744, 746

singing and vibration prevention, 636 surface, design of,

IN SHIP DESIGN Propeller(s), screw, materials to resist erosion, 635

of,

797

cavitation criteria, 154

inception and effect

of,

145

characteristic curves, open-water test, 334, 878 of, 655 682 controllable, fist of references, 679 performance data on, 338 » corrosion-resisting steel, to prevent erosion, 635 coupled, design of, 632 design, 582 bibliography, 606-609 charts, data from, 335 circulation theory for, 609 comments for supercavitating range, 631 features, preUminary comments, 596 Lerbs' short method of 1954, summary of, 630 procedures, 583, 596 requirements for, 583 Schoenherr's combination of steps, 630 to exert vertical and lateral thrust, 654 designed to operate under supercavitation, 631 diameter, selection of and optimum, 597 disc and hub diameters, 612 -disc clearances, 540 drawing the final design of, 629 efficiency, calculating expected, 629 estimate of characteristics for motorboats, 859 thrust and torque variation per revolution, 348 expanded chord length from mean-width ratio, 340 feathering and folding, definition of, 651, 652 design data for, 651 flow abaft a, 259 free-running bow, design of, 632 hollow-face blade, use and disadvantages of, 627 hubs, diameter, 601, 612 fairing of, 745 hull surfaces abreast, 672 jet diameters, inflow and outflow, 342, 343

contra-rotating, design features -struts abaft, layout of,

of,

swinging, for steering and turning, design notes, 737 tandem, design features of, 655 thrust, approximation of from insufficient data, 346 relation to load at thrust bearing, 347, 348 tip clearances for motorboats, 859 submergence, adequate, 541 torque, unbalanced, compensating fins for, 699 disadvantages of, 579 under-the-bottom, 653 values of real efficiency, 333 vertical drive for, 653 vibrating, estimated added-mass coefficients for, 436 modes of motion, 437 vibratory forces induced by, 877

Voith-Schneider; see Propellers, rotating-blade Propelling machinery, for double-ended vessels, 792

general assumptions, 443 location of in ship, 570

reserve of power, 574, 575 t.vpe and design, effect on hull, 570 underwater exhaust for, 545 Properties, mechanical, of air and exhaust gases, 922 water, 915 fresh and salt water, 920 other liquids and gases, 924 Proportion(s), blade and paddlewheel, calculated, 641 chine, for planing craft, 837 chordwise sections, control surfaces, 722 hull, abovewater, for strength, wavegoing, 496 of a surface ship, 464 selection of for motorboat, 827 immersed-transom stern, 529 principal, second approx, 475 shape data, Great Lakes oreships, 758-760 icebreakers, 800-803 typical ships, 223-228 Propulsion, airscrew, 658

SUBJECT INDEX Propulsion, and hull shape for a submarine, S13 asymmetric, notes on, 651 auxiliary, for sailing yachts, 652

bow screwprops data,

self-,

and, 632, 792 on models of typical

377

factors, ship-and-model, for typical vessels, 380-382

performance data on, 337

hydraulic-jet, available performance data, 337

design notes, 648

Propulsive coefficient, of,

ABC

ships,

895

375

waterline

Pull, towing, measured on ships, 310 Pump-jet propdevs, available performance data on, 337

propulsion, design notes for, 648 craft, classification of,

750

750

of the future, 818

Pure formulas and equations, use of, xx, 7 Pushboat, Hillman, body plan and profile, 667

of, 27,

list of;

efficiency, variation in,

see

BibUography

source abbreviations

xx

for,

in specific coefficients, 5

Refracting solutions, use of in flow studies, 48 Relations, analytic ship-wave, features derived from, 217

Relationship,

quantitative,

between vel and press in

potential flow, 25, 26

Relative rotative efficiency, finding, 374

Requirement(s),

applying

formulation

of,

to

hydrodynamic

variation of total resistance with, 308-310 of,

11

Froude number,

design, ferryboats, 790 fireboats,

11, 928,

932

774

fishing vessels, 770 for screwprop, 583

Race, propeller; see Jet, outflow Racing shells, design of hulls for, 752 Radial flow diagrams, 3-diml, data for constructing, 64, 65 stream functions, 53 stream functions for 2-diml source-sink pair, 55 thrust distribution for screwprop, 615, 616 Radius, and pitch variation of screwprop, 598 bilge, computing, 477 hydraulic, definition and sketch, 409, 412 of channels, calculation and use, 409 of curvature, 2-diml, formula for, 195 Rake for ABC screwprop, determination of, 612 Raked screwprop blades, use of, 600 Ram pressures and heads, in fresh and salt water, tables, 28-30 Rate of rotation, in propdev and ship design, 572 screwprop, determining, 597 Ratio(s), area, of screwprops, 340

aspect; see Aspect

786 between English units of measurement, 926 bilge radius to beam Bx, 477, 912

ballast, definition of,

conversion, English-metric, 928-930

paddle blades, 639

features,

446

departures from letter of specifications and, 454

Quotient, speed-length, 11

dip, of

30

to length, 470

333 Recessed lifting fittings, design of, 743 Recesses, for anchors, design of, 556 shallow, design of, 748 Reduction factors for calculated added masses, 430 of 2 per cent speed in water of given depth, 403 Reference(s), area, length, or volume, definition of, 5 data and prediction procedures, 1 for properties of water, 915

terms

Quadruple-screw vessels, stern forms for, 520 Quantitative data on dynamic lift and planing, 263 separation, eddjdng and vortex motion, 133 Quantitative effect of shallow water on ship speed and resistance, 390 relationships between vel and press in potential flow, 25

relation to

beam

Real propeller

ranges of typical values, 376

Taylor, definition and use

and wave heights, 169 and press coefficients, tables

steepness, velocity,

and other

Protectors, galvanic-action, design of, 704

of,

reserve-bouyancy, 547

786 909 ship parameters and coefficients, 930 square-draft to water-depth, 393

pump-jet, available data on, 337 design notes, 648 submarine, 813

design

of refa, 76

scale, a(or X),

paddletrack, design features, 638

Purpose, special-,

and hydrofoils, list major resistance components, 313 pitch-diameter, for screwprop, 598 hydrodynamic for screwprop, 617 lift-drag for airfoils

sail-area to wetted-surface,

outboard, 653

determination

expanded-area, of screwprop, 602 fatness, first approx, 464 freeboard, tentative, 548

ships,

devices; see Propdevs

gas-jet,

969

Ratio(s), effective aspect, for ship hydrofoils

submarines, 809 life-saving or rescue boats, 816

hghtships, 814 principal, statement of,

446

propeller-series charts, 584

readj'-made, interpretation, 454

fundamental, for every ship, 443 hydrodynamic, analysis, 460 maneuvering, propdev design for, 580 ship size as a factor in, 452 operating, for planing forms, 824 prehminary design study of motorboat, 825 principal hydrodynamic, analysis of, 826 rescue or life-saving boats, 816

reserve-buoyancy, 546

secondary ship, tabulation, 452

713 submarine operating, 809 yacht-design, 783 Reserve and powering allowances, 576, 577 buoyancy, requirements in design, 546 of power, in propelling machinery, 575 steering, design for conflicting,

speed, desirability of, 574, 575 Residuary resistance see Resistance ;

HYDRODYNAMICS IN SHIP DESIGN

970

Resilient material in sorewprop tunnel roofs, 672

Resistance(s),

estimating, 274

air, of ships,

Resistance, surface ship, estimate Telfer's

method

of,

313

of predicting, 318

on models, 872

and drag with wind on bow, 281

tests

appendage, calculation of, 288 for submarines, 295 customary values, 2SS augment of; see Thrust deduction calculated, and experimental, comparison of, 216 for planing craft, 848 surface and submerged ships, 313 of appendages, 288 ship forms suitable for, 219 theoretical, references on, 221 changes of, with changes in displacement and trim, 310 components, major, ratios of, 313 data, from model tests of typical ships, 297 observed, for models and ships, 297 parallel middlebody variations, 306 systematic, from model series, 298 typical shallow-water, 389, 390 very fat ships, 303-306

theoretical calcs of, reference material on, 221

low speeds, 306 deep-water, found from shallow-water data, 400 discontinuities, estimating,

due to flow

294

in free-flooding spaces,

experimental and

323

calculated, comparison of, 216

fouling, factors affecting, 117

graphs

of,

123, 124

friction; see Friction

unusual forms, 3 depth for, 404 individual appendages, per cent, 289 kinds of for ships, summary, 313 large appendages, 295 limiting depth for 2 per cent increase, 404 overall, for appendages, 288 pressure, analytic methods of predicting, 321 mathematic methods of calculating, 206 modern developments in calculation of, 210 of submerged bodies as function of depth, 323 rate of variation of residuary (for model), with speed,

hydrodynamic,

of

increase, 2 per cent, Umiting

306 residuary, contours

from TSS, 299

prediction from Gertler data, 318

Japanese fishing-vessel series, 300 TSS contours, 316, 317 specific, from Gertler-TSS data, 302 variation of with speed, 306-308 on planing forms, 269 shallow-water, found from deep-water data, 400 predicting resistance by inspection, 408 quantitative effect of in subcritical range, 390 ship, early efforts to calculate, 207 in canal locks, predicting, 413, 414 predicting fouling effects on, 120 summarj- of kinds of, 313 slope, estimating, 321 specific, definition of,

5

-speed data, finding, for shallow water, 397, 400 determination of O. Schlicting in shallow water, definition diagram, 392 still-air

and wind, 278, 322 ships, estimate of,

and R-r/V"^ ratio for ABC ship model, 893 comparison of calculated and experimental, 217

total,

estimated, for submerged and surface ships, 313

methods of approximating, 315 of model and ship, variation with

T,,

308

per ton, for typical ships, 309 variation of with speed, 308, 310

on planing forms, 269 and residuary, 314

subdivision into friction

wavemaldng, calculation

of, 215 comparison of calculated and experimental, 216, 217 due to diverging and transverse waves, 220 tabulation of typical components, 216 wind, and CP layout for ABC ship, 283 ship still-air, 322 bibhography of model tests, 278 -friction, of abovewater hull, 280 models and testing techniques. 278 motorboats, 862 of irregular structures, formulas for, 276 ships, estimating, 274 prediction for ABC ship, 282 with wind on bow, 281 Response, rapid, to rudder action, design for, 711, 735 Resting keels, design of, 695

Restricted and shallow waters; see Water(s), confined Restrictions, lateral channel, in subcritical range, estimated effect,

410

Reversible features in propdev design, 578

performance data on, 338 Revolution, body of, cavitation data for, 151 velocity and pressure distribution around, 40 Reynolds number, blade-Reynolds and d-Reynolds, 15 propellers,

calculation

of,

15

tables of, 88-94

x-Reynolds and 5-Reynolds, 15 Ridge-type straight deck, 554 Rigging, design to reduce wind drag, 566 Rise-of-floor magnitude for planing craft, 836 River steamers, typical, general data, 664, 665 water-surface slopes and currents, 660 Roll-resisting keels see Keels Rolling periods, estimated, for ABC ship, 497 Root fillets for screwprop blades, shaping, 606 ;

Rotating-blade propeller; see Propeller (general classification)

Rotation, determining rate

of, for

screwprop, 597

and rate in propdev and ship design, 572 Rotational vel components in screwprop outflow jet, 260 direction

of, 374 Rough-hull condition, estimated shaft power for, 385 Roughness, allowances, determination of, 115 plot of three types, 100 tentative individual, 117 drag variation along length, 739

Rotative efficiency, relative, estimate

equivalent sand, 113

subdivision into five types, 314

submerged bodies and

torpedoboat, in shallow water, 390

friction,

313

allowances

for,

index, factors in, 114

on

flat surfaces,

115

SUBJECT INDEX Roughness, on a rudder and horn, 743 structural, working limits, 740, 74]

971

Schmidt type of flush inlet scoop, 702 Schoenherr combination of steps for screwprop design, 630

surface, practical, definitions of, 114

friction formulation, 100,

Round-bottom motorboat, first power and weight estimates, 853

specific friction-resist coefTs, partial tables of,

space layout, 852

ABC,

Schultz-Grunow friction-resistance formula, 102 855 858

laj'out of lines,

example

of,

Scoops, condenser, injection, design, 701 partial bibliography on, 703

Rudder(s), action, design for rapid response and plane areas, 715 positions,

to,

Screw or screw

735

propeller; see Propeller, screw

multiple-, sterns, 236

706

single-,

body

plans, typical, 234-236

and moment diagram, 717 angle, neutral, from model tests, 876 apertures and gaps ahead of, 712

three-

-area data for merchant-type ships, 714, 715

triple-, vessels,

automatic flap-type, 735 balance portion, pressure bow, design of, 735

twin-,

ship force

sterns, arch type, 521

general arrangement, 518

or flap-type, design

of,

726

water, chemical constituents

726

simple, faired propeller hubs forward

of,

745

ABC

520

of,

of,

172

924

waves; see Waves Seagoing; see Wavegoing 762 of,

452

Section(s), blade, screwprop, selection of types, 605

shapes, final, for

G. H. Bottomley, 719

flap-type; see Rudder,

of,

Secondary ship-design requirements, tabulation

ship sterns, 727

of horns for, 690 -fin assemblies of

for,

Seatrains, to carry railway cars, description

design notes for, 729

two

521

five-, installations,

Sea, complex, 3-oomponent, delineation of,

contra-; see Contra-

design(s) for

and

shapes of, 237, 238 and quadruple-, stern forms body plans, typical, 238

field of, 711

close-coupled and compound, design

compound

104

wake-fraction formula, 369

selecting hull shape, 854

tender,

utility-boat, design,

ABC

ship,

627

shaping by cavitation criteria, 621 coeff along length, variation of for ABC

compound

automatic, 735 for

102

local friction-resistance formula, 102

ship, 517

maneuvering astern, 735 and moment, lateral, by model

force

in entrance, for typical ships, 516 tests, 716,

717

proposed method of estimating, 715

control surfaces, chordwise proportions, 722

discontinuous; see Discontinuous

-force fraction, for control surfs, definition of, 718

half-, of five strut shapes,

hinge gaps, closures for, 691, 726 horns, design notes, 690 motorboat, design of, 724

huU, shapes of in design, 515 hydrofoils, symmetrical, leading and trailing edges, 675 maximum, layout of contour, 476, 477

position relative to screwprop outflow jet, 707, 708 positioning

of, in

shaping

and proportioning, 722

of, relative

single or multiple,

section coefficient, selecting, 468, 469

maximum-area, longitudinal position

design, 706

sections, selecting

to stern, 709

shape (s), abovewater, design

708

in,

predicted, of planing craft, 851

Russian ship data, tabulated, 229

of,

551

for planing craft, selecting, 835

shallow-water running, 662

234-238, 249, 252, 253

Running attitude, and ship motion diagrams, 325 planing craft, 850 predicted, of plam'ng craft, 851 position(s), and steering, offset, in a channel, 413

in entrance

and run, 515

strut-arm, for ultra-high speeds, 680 ship, mathematical, 191

small-scale, preparation,

sketch

of,

486

487

Section-area curve(s), dehneation, mathematic, 198 fairing of, 198 final, for

ABC

ABC

ship, 542,

543

planing-type tender, 845

Sail-area to wetted-surface ratio of yachts, 786

for

Sailing yacht(s), auxihary propulsion for, 652

round-bottom tender, 858 ship, 0-diml plot of, 544 preliminarj^ 485 reference data for drawing, 230 selection, sketching, and shaping TSS parent form, 224

design, aspects of, 783 brief bibliography on, 786,

483

factors for vibrating ships, 429

selection of section shape in, 515

shapes of typical ships

of,

roll-damping features in, 477 rudder, chordwise, selecting and proportioning, 722

torque and ship-turning moments, 720 tubular, conditions for, 726

Run,

679

787

Sand roughness, equivalent, 113 Scale effect, in predicting shaft power, 379-382

problems in appendage resistance, 288 Schedule, design, for a ship, 444 Schlichting, intermediate speed in shallow water, 392 O., shallow-water procedure, features of, 394 speed-resist determination in shallow water, definition diagram, 392

0-diml ordinates

of,

of,

482

226

Self-propelled box-shaped vessels, design notes, 779 dredges, design features, 777 floating drydocks, 779

model

tests,

backing power from, 388

HYDRODYNAMICS IN SHIP DESIGN

972 model

Self-propelled,

tests, curves,

377-379

when backing, 3SS

strut-arm section, for ultra-high speeds, 680 transverse, for shallow-water vessels, 662

data from, 377, S75 for screwprops, 632

motorboats, nith dynamic

lift,

864

use of stock screwprops, 870 Semi-planing small craft, design of, 823

Separation

133

criteria,

for buttocks, 136

waterlines, 135

detection

of,

drag, approx

321

of, around a ship, 139 on ship drag calculations, 213 phenomena around geometric forms, 140 zone(s), aeration of and leakage into, 140 apparent flow deflection around, 139

estimate

effect

extent

Ship(s),

136

of,

indicated

by

tufts, 137,

254

584 Japanese fishing-vessel, 300 model, residuary resistance from, 298, 316 standard, Taylor, contours of Rr/A, 298 Gertler reworking of, 301 parent form for, 223-225 section-area curves, 224 0-diml ordinates of, 226 0-diml offsets for, 225 systematic, resistance data from, 298 Shadowing allowances for appendages in tandem, 292 Shaft(s), and struts, exposed, design of, 678 exposed, fairing enlargements around, 744 requirements

for,

of at emergence, 746

rotating, drag of, 293

strut design for, 678

power; see Power propeller, design of bossings for,

682 744

fairing enlargements around,

Shallow and restricted waters; see Water(s), confined water; see Water(s), shallow Shape(s), abovewater

bow

characteristics for coeffs, for

ABC;

see

ABC

ship

and wind resistance, estimating, 274 analysis of wake around and behind, 248, 250, 254, 261 and models, bibliography on confined-water effects, air

omitted from wetted-surface calculations, 109 on ships, typical, 134 Series, charts, propeller-, comments on, 589 listing of, 584-588 modification of design procedure, 596 preliminary design procedure, 592

and

vessel, near DWL, 504 Shearing stress, internal, representative values for water, 94 Sheer and freeboard, for general service, 547 protected waters, 547 deck, for the sake of appearance, 547 length, 549 heights, in fractions of related to wave steepness, 548 ship types, 551 lines, 0-diml, for five Shell(s), plating, approx to volume of, 486 smoothness problems on, 739 racing, design of hulls for, 752 Shingle trim-control device on planing craft, 840

WL

136 of,

Shape(s), stem, at various waterlines, 508 of motorboat, 842

section, design of, 551

round-bottom motorboats, 854

415 observed resistance data

for,

297

propellers, effect of cavitation on, 145

behavior in confined waters, predicting, 389 boundary-layer characteristics, data on, 95 cavitation on, occurrence of, 145 data, Russian, tabulated, 229 typical, tabulated, 223-228 design; see Design designer, first task of, 446

general problems

of,

454

dimensions, basis for selection of, 457 existing, increasing the power and speed of an, 387 fat,

changes of attitude and trim, 329 very, resistance data for, 303-306

flow patterns; see Flow form(s), geometric variation

of, 204 mathematical methods for delineating, 186 of good performance, comparison of new design with, 496 predicting vel and press distribution around, 257 schematic, distribution of vel and press around, 47 suitable for calculating wave resist, 219 summary of 0-diml equations for, 192 hull, general, formulas for wind drag of, 276 submerged and surface, calculating resist of, 313 in unsteady motion, added mass of water around, 417

inception and effect of cavitation on, 145

DWL's, 228

proportions data, typical ships, 223

lengths and speeds, Reynolds

numbers

for,

lines,

chine, for planing craft, 837

mathematical, selected references, 204 use of, 186 mass, added, in unsteady motion, 417 mathematical methods for delineating, 186

designed waterhne(s), typical,

first

sketch, 479

228

geometric, added masses for, 419 vibrating, comparison with vibrating ship, 423

2-diml and 3-diml, drag data, 291 hull, along bilge diagonal, 517

and propulsion, on a submarine, 813 476 round-bottom motorboat, 854 835 shallow water, 662 in entrance and run, 515 selection,

for

section, for planing craft, selecting,

94

involving developable surfaces, 765

buttock, for planing craft, 839

model(s); see Models

model-testing program for large, 868 moored, estimating forces on, 287 motion; see Motion diagrams, 325 observed resistance data for, 297

operation in confined waters, design features for, 659

parameters and coefficients, ratios of, 930 performance, practical benefits of calculating, 220

SUBJECT INDEX Ship(s), persistence of

wake behind

a,

powering data for steady-ahead motion, 354 prediction of behavior in confined waters, 389

ending, contra-guide, design, 532 endings adjacent to propdcvs, 530

principal dimensions of typical, 223

requirements, fundamental, for every, 443 resistance; see Resistance skegs and appendages, added-masa data

for,

fixed stabilizing, design of, 697

motorboat, design notes, 842

438

multiple-, stern, design of, 531

speed and power increase for existing, 387 very low, resistance data for, 306 smoothness and fairness, achieving, 749

and wind

still-air

termination

resistance, 322

of,

191

friction drag calculation for, 126 mathematical and 0-diml representation probable flow at a distance from, 256

wetted, computation

of,

of,

189

T,,,

and

solids, 7,

8

for, 170,

171

prelim design study, requirements, 825 hydrodynamic design, 819-822 references to tabulated data, 228

semi-planing and planing, design

823

of,

special design features, 822

gas discharge, abovewater, design, 563, 565

minimum, 564 564

hulls,

of,

resist,

plans, 234-236

Sound gear on merchant

patterns,

864

vessels, location of,

705

by colored

liquid,

67

construction of 2-diml, 54 3-diml, 62

67 stream functions

electric analogy,

pair, 2-d)ml, radial

Source(s) and sink(s),

forces

exerted

for,

55

by or on bodies

around, 68

shallow and restricted waters, 328

line, definition

and sketches

of,

60

delineation of flow patterns around, 59

references to, 331

data, for four cargo ships in shallow water, 328-330

661 for,

Size, absolute, as a factor in

281

738

Source-sink combinations, derivation of <j)- and i^-formulas for flow around, 17, 20 references to streamline diagrams around, 39 flow diagrams, delineation of, 52

arrangement and designs, 518 unsymmetrical, design of, 528 Sink; see Source and sink Sinkage, and trim data from models, 874 in open, deep water, 325

of,

819

Source abbreviations for references, xx

stern, arch type of, 521

design for reduction

of,

660 555

Solutions to equations of motion, multiple, 6 to,

or multiple rudders, 708

Sinusoidal waves, formulas

rivers,

Solitary-wave speeds for shallow-water depths, 661

143 prevention on screwprops, 636 of screwprops, refs to, 144 Single, -bladed screw propeller, 600

body

Small craft, definition powering of, 824

Snubbing of stem; see Stem Soakage for wooden motorboat

Singing and vibration, apphcation of Strouhal number

-screw

and 294

for,

Smoothness, hull, and fairing, definition importance of, 738 hydrodynamic, criterion for, 112 problems, specific, 739 underwater, achieving on a ship, 749

3

and ordinates

drag data

holes,

masts, deck erections, drag and wind

of references for, 4

profile, abscissas

294

ports, freeing, required area of, 554,

and

stack(s), design,

Simple ship; see Ship waves for design purposes, 171 Simplified ship form; see Straiglit-element

Sine-wave

and

gaps,

gas velocit}',

Side blisters or bulges, design, 517 Silhouette area of a ship above water, 277 from abeam, typical surface-ship, 283 of,

resistance, 293,

underwater, 565

Short appendages, definition of, 108 bossing, shape for ABC ship, 685 Shrouding, fixed screwprop, design of, 687

list

on

thrust, estimate of, 321

water-surface, canals, channels, Slots,

Smoke and

waves, data on, 160 celerity, in liquids

and

varying water-surface, drag and thrust data, 321

D. W. Taylor for Umiting depth, 407 -turning moments and rudder torque, 720 and shape data, 223 proportions typical, resistance from model test data, 297 vibrating, comparison with geometric shape, 423 estimating added-mass coefficients of, 433 -wake fraction, estimated, 368 -wave interference alongside ship, 243 profiles, tj'pical, 239 relations, 217

Similitude, principles

propeller-shaft, effect

surface, of trochoidal waves, 163, 164

308-310

trials, criterion of

Shock-wave

DWL

resistance

106

total resistance, variation with

rudder support, design, 690 of, 747 Skew-back in ABC propeller blade profile, 627-629 screwprop design, 603, 604 Slime, formation of and effect on friction resistance, 118 Slope(s), at entrance, graph for, 479 in run, 480 of buttocks for confined waters, 668 partial, for

straight-element design, partial bibliography, 764 surface, and submerged, estimate of total resist, 313

equation, 0-diml, application

973

Skeg(s), added-masa data for water around, 438 deep keel and, design for motorboats, 842

261

170

maneuvering

Skeg(s), acting as docking supports, 690

req'ts,

452

multiple pairs, flow pattern around, 59 partial bibliography on, 70 two pairs, dehneating flow pattern for, 58 variety of stream forms produced by, 67

2-diml flow pattern around, 56

HYDRODYNAMICS IN SHIP DESIGN

974 and

Source(s")

smk(s"), 3-diinl, flow pattern around,

66

Space layout, first, for planing hull, 827 round-bottom motorboat hull, 852 Spanwise distribution of circulation and lift, 83 Spars, design to reduce T\ind drag, 566 Special and submerged forms, estimate of resistance, 313 -purpose craft, classification and design, 750 of the future, 818 -service vessel, preliminary hydrodynamic design, 750 gravity, of a liquid, def of, 5 resistance, def of, 5

smoothness problems, 739 of,

5

merchant vessel, 447, 449-453 involving hydrodynamics, formulation, 446

Specification(s), design, for a

partial, for a passenger-cargo ship, 447 ready-made, interpretation of, 454 ship, departures from letter of, 454 Speed(s), and power, effect of shallow water on, 390 increasing the, for an existing ship, 387 changes in level and trim with, 325 corresponding values, in four sets of units, 927

deep-water, from shallow-water resist-speed data, 400 economical and practical, in shallow water, 660 -length quotient, and F„, tables of, 928 variation of total resist with, 308-310

model residuary resist with, 306-308 reduction of 2 per cent in given depth of water, 403 rate of var of

requirements, for a

new

ship,

449

reserve, desirability of, 574, 575 -resistance determination of O. Schlichting in shallow

water, definition diagram, 392

306 solitary-wave, for shallow water, 661 supercritical, confined water operation sustained, discussion of, 455-457 very low, resistance data

at,

412, 413

forms, 269 Sponsons, notes on design of, 560, 561 Spray strips, for planing craft, 841 to counteract engine torque, 580, 699 Square-draft, definition and sketch of, 393 to water-depth ratio, 393 nomogram for, 393 Squat, and attitude diagrams, 325 of,

661

check

of,

553

definition of, 443

metacentric and pendulum, on submarine, 812 first estimate of, 478 pendulum, on a submarine, 813 range of, preliminary check, 553 Stabilizer, Plum, for trim control on planing craft, 840 Stabilizing fins, fixed, design, 697

notes on aspect ratio, 698

salt water, reference

data on, 915

tentative, for ship design

and evalua-

tion, 172

waves

for design purposes, 171

dynamic and, on submarine, 812 Steepness ratios in waves, data on, 169 Steering and maneuvering, behavior, first approx, 501 swinging propellers for, 737 in offset positions in channels, 413 requirements, design for conflicting, 713 Stem, blunt, cutwater for, design of, 676 construction of, 508 shape at various waterlines, 508 of motorboat, 842 Stereoscopic wave photos, 177, 179 Stern(s), ABC ship, rudder designs for two, 727 arch-, ABC design, appendages for, 681 arch type, flow analysis, 525 for single screw, design of, 521 bulb, proposals for, 599 contra-; see Contraguide, design notes for, 532 diving planes, design rules for, 736 forms for twin- and quadruple-screw ships, 520 immersed transom, design of, 529 multiple-screw, typical, 236 skeg, design of, 531

491

and rudder shape, 709 single-screw, arch type, 521

transom,

strut-arm shapes for, 680 values of, in four English units, 927 var of attitude and position of planing craft with, 329 model residuary resist with, 306-308 total and residuary resistance with, on planing

design for reduction

and

wave systems,

general arrangement, 518

for,

ultra-high, displacement-type craft, design of, 754

Stability, dj-namic metacentric,

fresh

profiles,

shallow-water, from deep-water resist-speed data, 397 quantitative effect of in subcritical range, 390 ship,

;

Static forces, equilibrium of

Specific coefficients, definition of, 5

terms, derivation and use weight, definition of, 5

Stack see Smoke Standard series; see Series use of in estimating ship drag, 298 values, for engineering concepts, in English units, 926 "Standard" body plans, 231-234

ABC

sMp,

profile of,

492

edge, flow under rounded, 531 in section-area curve, 485

Narvik class DD, 531 parameters for, 485 shaping of, 530, 531 tunnel, craft, powering of, 672 669 bibhography on, 673 unsymmetrical single-screw, design of, 520 -wave crest height and position, estimate of, 244 Sternwheels, performance data on, 335 Still-air and wind resistance of motorboats, 862 ship, 278, 322 Sting mounting for submerged bodies, 323 Stock(s), axis, positioning rel to control-surf blade, 720 model screwprops, for model self-propulsion, 592, 870' Straight-element hulls, bibhography on, 764 design of, 762 design

of,

vessels,

friction drag on, 127

use for shallow-water vessels, 666

ridge-type deck, 554 Strakes, bulged fender, design

of, 769 Stream form; see Form Stream fimction, for flow around rod and sphere, 41

formulas for 2-diml flows, 17 3-diml flows, 20

SUBJECT INDEX Steam

function, pattern for 3-diml sourco-sink pair, 66

radial, for 2-diml source-sink pair,

55

Stream patterns, 2-diml, construction of from line sources and sinks, 59 Streamline(s), delineation of around a single source, 52 various bodies, 31

2-diml sources and sinks, 54

3-diml sources and sinks, 62 derived analytically, 218 diagrams, from source-sink combinations, 39 published, 33

Surface(s), developable, drawing lines for ships with, 765

flow diagrams on models, analysis hull,

of

;

roughness, practical definitions

Street or

vortex,

trail,

6,

141

estimate of total resistance

mathematical and 0-diml representation probable flow at a distance from, 256

wave(s), profile on a ship, prediction

system, calculation of energy

94

189

of, for

new

Strips, spray, for planing craft, 841

appendages and bare

Strouhal number, application

calc for transom-stern

of,

16

Structural considerations, bilge-keel design, 694

of overall, for a

roughness, working hmits on, 740, 741

advantages and disadvantages, 677 arm(s), design, 678 drag of elliptic and streamlined sections, 291 position at strut hub, 680 section (s), leading and trailing edges, 676 placing in lines of flow, 678 shape(s) for ultra-high speeds, 680 half-sections of five, 679 selection of, 678, 679 bossings, or, selection of, 677 contra-, abaft sorewprops, layout of, 682 Subcritical range, effect of lateral channel restr in, 410 shallow water on resistance and speed in, 390 Sublayer thickness in turbulent flow, laminar, 104, 120 Submarine (s), bulk volume of, 322 design problems common to all, 809 Submerged and surface forms, est of total resist for, 313 body, calculation of bulk volume and wetted surface,

coefficient, 0-diml,

and data

for,

322

maneuvering of a submarine, 813 ship models, questionable practices in towing tests of, 322, 323 vessels, calculation of appendage resistance, 295 Submergence, immersed transom, Fj values for, 530 propeller-tip, necessity for adequate, in design, 500,

541, 571 Submersible, definition and description of, 810 Submersion, screwprop, and trim, under variable load, 498 inadequate, avoiding air leakage with, 631 Subsurface waves, bibliography on, 185 Supercavitating range, definition of and design for screw-

631

Supercavitation, screwprop performance under, 156 Supercritical speed; see Speed (s) Superficial or wetted area of a hydrofoil, 5

Superstructure(s), air-flow diagrams for, 276

and upper works, design of, 561 general formulas for wind drag of, 276

246 215

design, 493

hull, calculation of,

ABC

106-109

ship, 109

submerged body, 322

contours

106, 107

of,

computation for a ship, 106 diagram for a planing craft, 851

Strut(s),

pressure resistance as function of depth, 323

of,

in, 163,

theoretical, data on, 160

wetted, analysis

in,

of,

tension and dynamic viscosity, 920

Stress, internal shearing, representative values for water,

props

313 126

for,

friction-resist calculation for,

of screwprop blades, 634

coefficients

114

of,

-water currents due to natural wind, 287

Strength, abovewater hull proportions for, 496

322 drag

322

of,

ship, application of 0-diml equation to, 191

see Fairing

upper works, advantages and disadvantages, 561, 562

250

of,

abreast screvvprops, 672

hydrodynamically smooth, 112 overall, wetted, of submarine, def and calc planing, bibliography on, 269 propellers, design procedure for, 650

patterns around ships, references to, 39

Streamlining

975

Surface control; see Control

longitudinal curvature,

water

and length

of shallow-

665 of planing forms, 268 to sail-area ratio, 786 craft,

0-diml contours for calculation

of, 106,

107

Sustained speed, discussion of, 455-457 Swinging props for steering and turning, design notes, 737 Swirl cores, predicting, 155

Symbols and

their titles, 900 Symmetrical propeller-blade sections, design and use 605 Synthetic complex sea, delineation of, 172 Systematic wake variations, use of, 572

Tables; see item desired Tandem appendages, shadowing allowances screwprops, design features, 655

Tank,

for,

of,

292

electrol3ftio, for plotting equipotential lines, 31, 49 Tanqua viscous drag, definition of, 118 Tanvis viscous drag, definition of, 119 Taylor, D. W., criterion for limiting depth for ship trials, 407 friction-resistance formulas, 104 Standard Series, contours of TJ^/A for, 298 data, Gertler reworking of, 301-303 prediction of residuary resistance, 317 parent form for, 223-225 performance, bettering of, 465, 474 section-area curves, 224 superiority of for certain Cp values, 474 Taylor Standard Series, 0-diml offsets for, 225

and use of, 11 Froude number, 11, 932

quotient, definition ratio of to

tables of, 928, 929

Telfer extrapolation diagram, 320 friction-resistance formula, 104 method, list of references, 318-319 of predicting ship resistance, 318

HYDRODYNAMICS IN SHIP DESIGN

976 Telfer, merit factor for

ABC

Temporary bows, design

of,

ship,

Transition, gradual, abaft elliptic 3-diml nose, 196

895

sharp, between portions of VVL's, 197

781

Tender, planing-type, for ABC ship, lines, 843 requirements for, 826 round-bottom, for ABC ship, hnes, 855 requirements for, 825 Tension, surface, and dynamic viscosity, 920

Transom

Terminal values t for DWL's, design lane for, 509 Termination of skegs and bossings, 684, 747 Testing program, model, for a large ship, 868 techniques for wind-resistance models, 278 Tests, controllability, of model in shallow water, 876 model; see Model Theoretical surface waves, data on, 160 wave patterns on water surface, 160

Thickness, blade-, radial distribution for screwprop, 620 boundary-layer, variation with x-distance, 95, 96 laminar sublayer, in turbulent flow, 104, 120 variation with length and speed, 105 sea, delineation of, 172

Three-component complex

-dimensional flow around rod and sphere, 41 stream functions, diagram of, 41

wake-survey diagrams, 360 analysis of TMB, 362 -screw installations, notes on, 521 Thrust, bearing, rel bet screwprop thrust and load at, 347 calculation for a propeller, 347 -deduction fraction, determination by model tests, 879 estimate by "cylinder" method, 372, 373 for ABC ship, 542 of, from hull shape, 542 predicting, 369-371

prediction of

minimum, design

W. for,

J.

Luke, 369

slope, estimate of,

237, 238

of,

Trochoidal wave(s), deep water, data on, 166 definition drawing, 162 elevations and slopes of, 163, 164

orbital velocity in deep water, 162, 166, 168, 169 profile, ordinates for,

163

sketch of surface slopes, 164 system, formulas for, 162, 163

when towing, 346 344-346

factor, calculating, for a screwprop,

613

theory,

summary

of,

161

Troost and Lap friction-resistance formula, 104

data derived from, 345 measured, on ships, 310 screwprop, and thrust-bearing load,

Triple-screw vessels, typical shapes

orbit radii, change with depth, 169

321

-load coeff, variation per rev, for a screwprop, 349 5\ath ship speed,

Trimarans; see Catamarans

lengths, periods, velocities, 165-168

541

distribution, radial, of screwprop, 615, 616

due to water-surface

stern; see Stern

Transverse dimensions for shallow-water running, 662 discontinuities, above water, 561 force tests on models, in rudder tests, 716, 717 moment-of-area coefficient for DWL, selecting, 478 thrust, design of devices to produce, 654 waves, effect on calculated resistance, 220 Trials, ship, limiting depth of water for, 407 Trim, and displ, effect of changes on resistance, 310 draft variations, ABC ship, due to variable weights, 481, 498 resistance data for torpedoboat in shallow water, 390 sinkage on models, 874 angle for planing craft, 840 change of, effect on effective power, 355 for fat forms, 329 towed and self-propelled models, 327 in open, deep water, data on, 325-328 shallow and restricted waters, 328 on models, towed and self-propelled, 327, 874 with speed, 325 -control devices, use of for planing craft, 840 data, typical shallow-water, 390 diagram, running, for ABC planing-type tender, 849 propeller submersion and, under variable load, 498

rel bet, 347,

348

estimating from insufficient data, 346 slope, estimate of, 321

transv and vertical, design of devices producing, 654 var per rev for screwprops, est of, 348, 350, 351 Tideman friction-resistance data, 103

Tip clearances, for propdevs, 537 of propellers for motorboats, 859 submergence of screwprops, adequate, 541

symbols used, 900 Torpedoboats, old, general data on, 753 Torque, coeff, variation per rev on a screwprop, 350, 351 -compensating fins, design of, 699 unbalanced, of a propdev, disadvantages, 579 variation per rev for screwprops, est of, 348, 350-352 Towing, emergency, temporary bow for, 781 pulls on ships, measured, 310 Tracked vehicles as amphibious craft, 806 Tracks, paddle; see Paddletracks Trail or street, vortex, 6, 141, 142 Trailing edges of appendages, design of, 675, 676 Transformation, conformal, description and uses of, 25

Trough; see Wave(s) Tsunami or earthquake wave, 181 Tubular rudders, conditions calling for, 726 Tufts, model flow observations with, 874 partly reversed, view of, 137, 139 use of for determining flow, 137, 254 Tug, fleet, displ of appendages, 296 Tumble home, design data for, 551 Timnel(s),

in

multiple-skeg

sterns,

design

notes,

oblique, in shallow-water craft, 670, 671

stern (s), craft, powering, 672

Titles of

design

of,

669

vessels, bibliography on, 673,

Turn

674

of ship in loose or tight circle, 6

Twin-screw body plans, 236 vessels, stern forms for, 520

Two

or

more

solutions to equation of motion, 6

types of flow or performance, 6 per cent resist increase, limiting depth for, 404 speed reduction in water of given depth, 403 Type(s), huU, selection of for motorboat, 827

propeUing machinery, effect

of,

570

roll-resisting keels, selecting, 691

531

SUBJECT INDEX Ultxa-high-speed displacement-typo craft, design Unbalanced propdev torque, disadvantages, 579

of,

754

Under-the-bottom anchor installation, 558 screw propellers, 653 Underwater exhaust for propelling machinery, 545, 565 form, molding a new, 488 hull, detail design of, 504 profile, 506 ship smoothness and fairness, 749 Unequal power distr in multiple props, design to avoid, 573 Units of measurement, abbreviations for, 912 in English sj'stem, 926 ratios between English and metric, 926 Unsteady motion; see Motion Unsymmetrical single-screw stern, design of, 528 Upper works, air-flow diagrams for, 276 drag coefficients for, 279 shaping and positioning, 561 Useful data for analysis and comparison, 926 Utility-boat design, round-bottom, example, 858 Vanes, contra-; see ContraVapor pressure of water, 146, 147, 921, 922 Variable draft, first approx, 483 -load conditions, screwprop submersion and trim in, 498 -weight conditions, buoyancy, stability, weight data, 499 probable, first approx, 463 second statement of, 482 selected incUned WL's for, 499 Variation(s), attitude of planing craft with speed, 329 estimated draft for ABC ship, with variable weights, 481 forces and moments throughout screwprop revolution, 348 from normal hulls for shallow-water running, 666 paddlewheel design, 648 geometric, of ship forms, 204 model residuary resistance with speed, 306-308 parallel-middlebody, resistance data, 306 pitch with radius of screwprop, 598 pressure, along a Rankine lissoneoid, 208 rate of, model resistance with speed, 306 resistance with speed-length quotient, 308 on planing forms, 269 trim, weight, and volume, 310 rise-of-fioor, in planing craft, 836 section coefficient along length, 517 thrust-and torque per revolution for screwprops, 348 -load coefficient with speed, 344-346 total resistance with T,, 308-310

wake, systematic, use of, 572 wind force with heel angle, 285 velocity with height, 274 Vectors, wake, determined on models, 874

Vee entrance, pressure

distribution along, 48

Velocity and pressure diagrams around bodies, 31 2-

and 3-diml

bodies, 43

distribution around

body

of revolution, 40

hydrofoil, 80

schematic ship forms, 47 asj'mmetrio body, 43 ship forms, prediction of, 257

977

and pressure fields around a hydrofoil, 82 distr around 2-diinl and 3-diml bodies, 44 around body, determination of by flow net, 24

Velocity,

special forms, 40

2-diml stream forms, graphic determination axial-, distr in

screwprop inflow-outflow

jets,

of,

57

343

distribution around schematic ship forms, 47

on hydrofoil, 80 around a hydrofoil, 82 induced, in screwprop jets, data on, 343 liquid, determination of around any body, 24

fields

orbital, in trochoidal waves, 162, 166, 168, 169

potential, expression, formulation of, 214

formulas for typical 2-diml flows, 17 3-diml flows, 20 pressure, and force of natural wind, 284 relationships in potential flow, 25, 26 profiles in ship

boundary

layers, list of references,

98

typical, 97

and pressure coefficients, tables of, 27, 30 trochoidal waves, tables of, 165-168 wake, effect on appendage drag, 292 wind, increase of with height, 274 Vertical and transverse thrust, design of devices to produce, 654 bossings as docking keels, 686 center of buoyancy position, by Normand formula, 479 gravit}^ position, estimated, 479 drive for screw propellers, 653 thrust, design of devices to produce, 654 ratios

Vessels

;

and types and vortex streets, 141

see specific kinds

Vibrating bodies

geometric shape, comparison to vibrating ellipsoid, 423 screwprop(s), estimated added-mass coeffs for, 436

modes

of motion,

437

ship hull, comparison with vibrating elHpsoid, 423

estimated added-mass coefficients for, 433 Vibration, characteristics considered in design, 580, 598 frequencies, relation of hull

and

propeller,

580

motorboats, 859 of ship appendages, avoidance of, 700 partial bibliography on, 439 prevention of on screwprops, 636 problem in shallow water, handling, 673

hull, in

resonant, Strouhal number in, 143 Vibratory forces induced by propeller, 877

Virtual-mass coefficient, 418, 419 Viscosity, dynamic,

and surface tension, 920

reference data on, 94

kinematic, reference data on, 94

values for water, 919, 920 various fiquids and gases, tables

of,

919-922

Viscous flow; see Flow Volimie, bulk, calculation for a submerged body, 322 definition and description of, 454 distribution, tentative, for

ABC

ship,

-Froude number, definition of, 11 hull, first estimate, 471 of submarine pressure hull, discussion second approx for ABC sliip, 497 "standard" fresh and salt water, 915

Von Karman

498

of,

friction-resistance formula, 103

Vortex(es), hub, predicting, 155 motion, reference data on, 133

457

HYDRODYNAMICS IN SHIP DESIGN

978

Vortex(es), references to flow photographs spacing, long'l streets

and transv in a vortex

of,

Water(s), -depth to square-draft ratio, 393

37

street,

141

eddy-frequency relations, 142 references to, 144

trails,

schematic diagram

of,

mass-densitj' values

ABC ship, 367 around or behind ship or model, 248, 250, 254, 261

bibliography on, 262

TMB

3-diml, analysis of, 362 diagrams at propdev positions, 358 bibliography on, 359, 360 effective, definition of, 615 formula of Aquino, 368 Schoenherr, 369 graph of D. W. Taylor, 369 nominal, definition of, 615 ship-, estimate of, 368 patterns abaft ship-shaped bodies, 39

-fraction,

around

inlet

and discharge openings, design, 701

shallow,

and

366

systematic, 572

on appendage drag, 292 Water(s), added-mass coefficients for vibrating ships, 433 data for skegs in, 438 adequate flow to propdevs in confined waters, 668 air and, mechanical properties of, 915 confined, behavior in, first approx, 501 predicted, of a ship in, 389

of,

data

in,

328

389

design factors for, 666 features applicable, 659 drag, sinkage, squat, design for reduction, 661 effect(s),

bibliography on, 415

410 414 estimated added-mass coeff for vibrating ship in, 433 lack of reliable data on power and propeller performance in, 411 operation at supercritical speeds, 412 practical definition of, 389 predicting ship behavior in, 389 resistance curves of R. Brard for Suez Canal model, 413 running in, transverse section shapes for, 662 ship performance, unexplained anomalies in, 414 sinkage data in, 328 speeds, economical and practical, in, 660 straight-element hull for use in, 666 deep-, resist and speed from shallow-water data, 400 depth, given, practical resist-speed cases involving, 396 2 per cent speed reduction in, 403 limiting, of D. W. Taylor, for ship trials, 407 of lateral restrictions in subcritical range,

summary

of,

restricted; see Water(s), confined

behavior

in, first

controllability

approx, 501

model

tests in,

876

definition of, 389

on speed and power, 390 of, 414

effect of,

summary

estimated effect of lateral channel restrictions in subcritical range,

410

operation, modification to normal forms for, 666

resistance data, typical, 389

found from deep-water data, 400 prediction by inspection, 408 section shapes for, 662 speed from deep-water data, 397 transverse dimensions for, 662 vessels,

adaptation of straight-element form

666

-velocity effect

of trim

325

390 for,

vectors from model tests, 874

definition

in,

quantitative effect on ship resistance and speed,

ships, references to, 39

transom-stern ABC ship, 366 3-diml, 360-366 variations, behind ships, 259-262

change

323

of, 920 917-919

of,

mechanical properties of, 915, 920 open, deep, change of trim and sinkage restricted, definition of, 389 sea, chemical constituents of, 924

persistence of, behind a ship, 261

-survey diagrams, definition sketch torpedo, 366

to,

mechanical properties of, 915 standard or reference values for, 915-920

609

of,

anah'sis diagram for

diagrams,

922

kinematic-viscosity values

6

'Wake(s), -adapted screwprop, design

of,

elastic characteristics of,

flow through free-flooding spaces, resist due fresh and salt, data on change of state, 921

and vibrating bodies, 141

typical, 663

vibration problems

673

in,

wave(s), data, 181 relation to deep-water waves, 180 of, 392 "standard", mass density, volumes, weight, 915 reference data for, 915, 918, 920

speed, definition

vapor pressure

of, 146, 147,

921

Waterline(s), afterbody, transom-stern

beam, maximum, fore-and-aft curvature, 0-diml, of plots,

ABC

ship,

ship,

507

506

designed, fairing of for first

ABC

position, 481

sketch

of,

ABC

ship,

200-202

479

505 of ABC shape, 479 ships,

typical ships, 230 parallel, reference

data on, 231

inclined, for variable-weight conditions,

499

on saiUng yachts, data on, 784 length, first approx, 464 parallel, definition of, 230 design lane for, 480 shapes and coefficients, designed, 228 slope, at entrance, graphs for, 479 run, 480 stem shapes at various, 508 Waterplane^, coefficient, data for selecting, 478 shape of vessel near designed, 504 WaveCs), actual wind, tabulated data for, 175

bibliography on, 182-185 complex, for design purposes, 171

506

to,

SUBJECT INDEX Wave(s), conditions, tentative, for ship design, 172 crest, bow, estimate of height and poaition, 244 lag abaft stem, 245 deep-water, comparison with shallow water, 180 diverging, effect on drag, 220 earthquake, or tsunami, 181 geometric, references to, 182

and steepness ratios for design purposes, 169 bow and stern, predicted, 244 to wave length ratios for ship design, 170

height(s),

979

Wavegoing, requirements

Wavemaking, pressure

in ship design,

resistance

Weber number,

definition and use of, 16 Wedge-type trim-control device on planing

Weight(s), balance, longitudinal,

and evaluation,

172 transverse, effect

on drag, 220

trochoidal, definition drawing, 162

elevation

and

slopes of, 163, 164

length-velocity-period relations, 165-168 orbit radii, change with depth, 169 orbital velocity in deep water, 162, 166, 168, 169

sketch of slopes, 164

summary

of theory, 161

tables of lengths, periods, velocities, 165-168

tsunami or earthquake, 181 deep and shallow water, 180-182 wind, patterns and profiles by modern methods, 177 velocities in

tabulated data, 175

Zimmermann,

definition and use of, 176, 177 Wavegoing, abovewater hull proportions for, 496

conditions, limits for, 458

freeboard

model

548 877

for,

tests,

first

craft,

840

approx, 497, 498

for light draft, 500

estimate,

tentative "standard", for design

210

comparison of calculated and experimental, 217

conditions, variable-, 463

systems, Kelvin, modified by Hogner, 161

of,

due to diverging and transverse waves, 220 tabulation of typical components, 216

Kelvin system, 161 lengths, in deep and shallow water, 182, 183 miscellaneous, general data for, 181 ocean, stereoscopic photo of, 179 typical profiles, 178 patterns around 2-diml forms, 39 on water surface, theoretical, 160 profile(s), alongside models, 241 observed on models, 873 of ocean waves, from stereo photos, 180 ship, typical, 239 sketching, for new design, 494 synthetic, 3-component, complex sea, 175 surface, prediction of, 246 transom-stern ABC ship, 495 trochoidal, 163, 164 typical, for ships, 239 relations, analytic ship-, 217 to natural wind, 176 resistance calculations, ship forms for, 219 shallow-water, comparison with deep-water, 180 data on, 181 ship, data on, 160 simple and standard, for design purposes, 171 sinusoidal, formulas and ordinates for, 170 -speed, ratio in shallow water, definition of, 395 speed, solitary, for shallow water, 661 tables of, 165-168 steepness ratios encountered at sea, 169 stern-, estimate of height and position, 245 surface, theoretical, data on, 160

due to calculation

resistance, calculation of, 215

interference along a ship, general rules for, 243

subsurface, bibhography on, 185

449

first,

for a ship, 463

planing craft, 828

round-bottom motorboat, 853 second, for planing-hull motorboat, 831 third, for motorboats, 863 estimating procedure for motorboat, 828 heavy, longitudinal position in a planing craft, 850 principal, second estimate, 474 specific, definition of,

5 -speed-power factors for average vessels, 383 small craft, 824, 832, 853 "standard" fresh and salt water, 915 Weitbrecht equivalent sand roughness values, 114

Welding fillets, use of for fairing, 742 Wetted area of a hydrofoil, definition

of,

5

length of planing forms, 268 surface; see Surface

Wheel, paddle; see Paddlewheel propeller; see Propeller

Wheelock wave,

definition and use of, 169, 170 Width, blade-, of screwprops, 340 cavitation diagrams for selecting, 605 design of, 605 Wigleys (W. C. S.) design rules for bulb bows, 510 Wind, drag, and resistance, with wind on bow, 281 coefficients for ship types, 280 irregular structures, formulas for, 276 lateral, 285 masts, spars, rigging, reducing, 566 -effect calculations, examples for ABC ship, 282, 285 capsizing moments, 286 force, velocity, and pressure, nominal, 284 friction resistance of hull, comments on, 280 moments, lateral, and heel angles, 285 natural, surface-water currents due to, 287 force, velocity and pressure of, 284 relation to waves, 176 pressure, location of center of, 284, 285 magnitude of, 283 resistance, 322 and CP layout for ABC ship, 283 model(s), and testing, notes on, 278 typical, 277 of motorboats, 862 of ships, estimating, 274, 322 prediction for ABC ship, 282 still-air, 278 tests, bibliography of, 278 with wind on bow, 281, 282 velocitj', increase with height above water surface,

274-276 velocities

and Beaufort

scale of U. S.

wave(s), patterns and profiles by

Navy Dept, 284

modern methods, 177

HYDRODYNAMICS IN SHIP DESIGN

980

Wind, wave(s), systems, tentative "standard,"

for design,

tabulated data

sailing, auxiliary

propulsion

for,

652

yacht(s), design, bibliography on, 786, 787

lyi for,

175

Works, upper, positioning

of,

561

Yawed

notes for, 783 tabulated data on old, 228 bodies, references to flow patterns about, 38, 40

Yacht(s), -design requirements, 783 J-class, reference to lines

drawings

references to tabulated da:ta, 228

of,

Zimmermann wave,

228 •

definition

and use

Zone, separation; see Separation

of,

176, 177

siiiiiliiiii