Torsion Artillery

arms & armour, Vol. 12 No. 1, Spring 2015, 67–89

Performance of Greek–Roman Artillery Cesare Rossi Sergio Savino Dept. of Industrial Engineering, University of – “Federico II”

Arcangelo Messina Giulio Reina Dept. of Engineering for Innovation, University of Salento, Lecce

The main throwing machines invented and used by the Greeks and adopted, more widely, by Roman armies are examined. The kinematics and dynamics of both light and heavy Greek–Roman artillery are used in order to accurately assess its performance. Thus, a better understanding is obtained of the tactics and strategies of the legions of the Roman Empire as well as the reasons for some brilliant campaigns. Reconstructions of a repeating catapult, considered to be the ancestor of the modern machine gun, are also presented. The development of the mechanical design of such machines is discussed and pictorial reconstructions proposed. keywords  ancient throwing machines, history of warfare, catapults, Roman weaponry.

Introduction It is well-known that the Roman legions took advantage of a skilled corps of e­ ngineers during their campaigns. Perhaps the best example is represented by the most famous Roman engineer: Vitruvius (Marcus Vitruvius Pollio 70–80 BC to after 15 AD). He authored the very famous engineering treatise De architectura, whose 10th book was dedicated to the war machines. Moreover, Vitruvius probably was a high officer (praefectus fabrum) of the corps of military engineers during the campaigns of Julius Cesar in Gallia and in Britain. His considerable knowledge of the field of military engineering, allowed the legions to have a considerable advantage as far as both tactics and strategy were concerned. In fact, the possibility of rapidly built roads allowed legions to be quickly moved, while the wide number of different war machines including rams, siege towers and other siege engines, throwing machines etc., gave the legions a big advantage over

© The Trustees of the Armouries 2015

DOI 10.1179/1741612415Z.00000000050

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less technologically developed peoples that represented the largest part of the world of those times. Among these engines, the throwing machines are particularly interesting. They represented the ancient artillery, both light and heavy, and included pieces to be used in the sieges for static warfare and pieces to be used in open field battles as heavy artillery and as infantry support gun or battalion gun. This is why so many authors have studied ancient throwing machines.1–22 Therefore, it is interesting to study both the kinematics and the dynamics of these machines in depth in order to assess their performance, and, thus, to better understand the tactics and strategies of the legions and of the Roman Empire and, consequently, the development of some brilliant campaigns and battles. These engines are described as Greek–Roman since, generally, they were invented by the Greeks but standardized for mass production and widely used by the Romans. In addition, this study reveals that the knowledge of mechanics was surprisingly advanced, although this field is probably less well than others because archaeological finds are less evident, smaller and sometimes unrecognized.

The motors First of all, it is necessary to describe the motors of these throwing machines. It is well-known that one of the first throwing devices was the bow, which works on the principle of flexion. Essentially, an elastic rod is flexed to store elastic energy and, when released, the rod s this elastic energy to a projectile as kinetic energy. The early throwing machines, capable of throwing stones and big arrows or javelins, were built on the same principle. In Figure 1 some pictorial reconstructions of these flexionbased throwing machines are represented1,2. In Figure 1A and 1B the pictorial reconstruction of static flexion motor catapults are shown; in Figure 1C a gastraphetes, a type of big crossbow, is depicted. Throwing machines, whose motor is based on the elastic energy generated by the flexion of a rod, cannot generally reach a high level of performance because such a motor does not allow heavy projectiles to be thrown with a relatively high velocity. Therefore, in the third century BC, a different kind of motor became common in practically all the artillery pieces: the torsion motor, which was small and powerful and provide a superior performance. The Greeks from Syracuse developed the first catapults, as the result of engineering research funded by the tyrant Dionysius the Elder in the fourth century BC.2,3 Special mathematical and technical skills were necessary to build and maintain a catapult. All the surviving catapult specifications imply that an optimum configuration was indeed reached. Archimedes, either invented or improved a device that would remain one of the most important forms of warfare technology for almost two millennia: the catapult. Later, during Alexander the Great's times, catapults were the big advantage for conquering central Asia. The last major improvement in catapult design came in later Roman times, when the basic material of the frame was changed from wood to iron. This innovation made

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figure 1  Flexion throwing machines.

possible a reduction in size, an increase in stress levels and a greater freedom of stroke for the bow arms. The new open frame also simplified aiming, which with the wood construction of the earlier machines had been limited, particularly for close moving targets. Therefore such artillery pieces, powered by torsion motors, are considered in more depth.

The torsion motor This motor consisted of a strong wooden square frame, reinforced by iron straps, divided into three separate sections. The central section was used to insert the shaft of the weapons, whereas the sides were for the two coils of twisted rope. These coils were made by a bundle of elastic fibres: bovine sinews, horsehair or women’s hair23; the latter natural fibres had the best mechanical properties and were the most widely used. In Figure 2, a motor of a Roman catapult is shown; on the left a specimen found in Xantem, Germany, is reported, in the middle a pictorial exploded view1,2, and a bundle of fibres on the right. Design rules and concepts were practised extensively by the engineers of ancient times leading to machine design from single machine elements to the design of a machine as a whole system. One of the main steps was represented by the establishment of the optimum ratio between the diameter and the length of the coil.1–3 Inside the coils, arms were fitted; at the other end of each of the arms, a rope was affixed, like the ends of an archery bow. The last major improvement in catapult design was achieved during the Roman Empire when the most stressed components

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figure 2  Propulsor of a Roman catapult: remains found at Xantem, Germany (left) and reconstruction (right).

of these machines were made by metal (iron and bronze) allowing a reduction in size, an increase in the maximum stress levels and greater freedom of travel for the bow arms.3 The design of Greek–Roman throwing machines was based on a module, i.e. the diameter of the modiolus marked in Figures 2 and 3. Probably, the first ancient scientist who stated the relationship between the weight of the projectile and the modulus diameter was Archimedes of Syracuse. From Philon of Byzantium24 to Vitruvius,25 all the throwing machines designers and theoreticians say that this relationship is: D = 1.1 ⋅ 3 100 ⋅ m (1) where D is the diameter of the modiolus (hence of the hair bundle) in digits (1 digit ≈19.5 mm) m is the mass of the projectile in minae (1 mina ≈ 431 g). According to ancient engineers, (e.g. Philon of Byzantium and Vitruvius), the design of the machines was modular: all the main components and parts were sized as a multiple or a sub-multiple of a modiolus. Thus, even if only a part of an ancient machine is found, it is still possible to evaluate the weight of the projectile and its energy. That is to say, once the diameter of the modiolus was stated as described, all the other main dimensions of the machine were referred to this dimension. Figure 3 shows a scheme of a ballista and a particular of the frame with the modioli.

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figure 3 Schematic drawing of a ballista.

As for the design of this machine, Vitruvius24 is meticulous in giving the ratios between the diameter of the modiolus and all the other main dimensions of the machine: A = 7D, B = 3+ ¼D, C ~ 0.5D (this datum is deduced by some relicts), E = 1D, F = 4D, d1 = 9/16D, diameter of the arm near the bundle, and d2 = 7/16D, diameter of the arm near the rope. From the results, we deduce that the bundle length L was 7 times its diameter D. If we consider that about ¼D of the hair bundles are reasonably blocked in the modioli, we can consider that the coil of fibres that really were twisted by the arm A had a ratio L/D = 0.5. The L/D ratio between the length of the bundle and its diameter was decisive for obtaining the maximum energy from the bundle itself. Figure 4 summarizes some of the results on a model of the fibres bundle.1,5 In the upper part of Figure 4 the maximum bundle torsion (beyond the tensile stress limit) as a function of L/D ratio is reported. In the lower part of Figure 4, the energy that is possible to store in a bundle is reported as a function of the bundle rotation for a few L/D ratios and for a given value of the Young’s modulus. In Figure 4, the maximum elastic energy which corresponds to a given stress limit is also reported. All the graphs were obtained considering the same bundle volume, i.e. bundles in which it was possible to store the same energy; that is to say, the horizontal line marked with ‘Emax’ represents the elastic energy that corresponds, for each bundle, to a rotation over which the external hair stress exceeds the proportionality limit. If operating arm rotation angles and bundle L/D ratios are considered for ballistae and catapults, from Figure 4 it is possible to conclude that those machines were designed with ancient engineers having a thorough understanding of the mechanics

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figure 4  Effect of varying the bundle L/D ratio.

of those devices. From Figure 4, it is evident that the higher the L/D ratio, the wider the arm rotation must be in order to store the maximum possible elastic energy in the bundle. Moreover, from the figure it is noted that the lower the L/D ratio, the greater the slope of the curve. As far as this aspect is concerned, we can observe that steeper slopes correspond to a faster release of energy when throwing the projectile. This last aspect is similar to what happens for firearms where, with heavy projectiles, slow burning powders are used whereas with light projectiles, quick burning powders are used. This suggests that high L/D ratios for the bundle could have been used for machines throwing heavier projectiles and, perhaps, with higher efficiency.

The torsion artillery The term ‘torsion artillery’ is used to refer to those throwing machines whose motor was the torsion elastic bundle described in the previous paragraph. First of all, a few words must be said about terminology. The word catapult comes from the Greek (κατα = through and πελτη = shield). During the Roman Empire the word catapulta was used for a machine that throws darts, while the word ballista (from the Greek βαλλω = to throw) was used for a machine that throws balls. During the Middle Ages the words were used with the opposite meaning: ballista for a dart throwing machine and catapult for a ball throwing one. Another throwing machine was part of the Greek–Roman armies: the onager. In contrast to the previous machines that gave to the projectile a rather smooth trajectory, the onager (in Latin onagrum) had a high-arcing ballistic trajectory. Finally, it must be said that ballistae and catapults,

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from a mechanical and architectural point of view, were quite similar, having the same mechanical architecture represented in Figure 3. The onager, however, was rather different.

The ballista Figure 5 shows a pictorial reconstruction of the ballista,1,2 according with the data by Vitruvius.25 Around the second century BC, Biton of Byzantium tells about an important improvement in throwing machine design. According to several authors,8,20,21 many machines begin to be built having a new design often called ‘palintone’, from the ancient Greek root πάλιν (palin) that means newly. In these ‘new’ machines, the arms are mounted inside the mainframe, whereas in traditional machines (called euthytone) the arms were outside the mainframe. The palintone design, obviously, allowed larger rotations of the arms with the probable advantages reported above. Figure 6 shows schemes of the euthytone and of the palintone design. In Figure 7, a pictorial reconstruction of the great ballista, the remains of which were found in Hatra (actually al-Hadr in Iraq) is represented.8 The latter was a gigantic machine designed to throw very heavy projectiles (up to 33 kg for some relics) and, according to what was computed in Figure 4, its arms had a wider rotation. Moreover, from the relics, it was found that the bundle casings were designed for bundles having an approximate L/D ratio of 9.8, 20

figure 5 Pictorial reconstruction of the ballista of Vitruvius.

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figure 6 Schemes of A the euthytone and B the palintone machines.

figure 7  Pictorial reconstruction of the great ballista of Hatra.

Using the information that Vitruvius gives about its dimensional design, kinematic and dynamic models of such machines were obtained1,5 and, thence, the elastic energy stored in the bundle was calculated, giving a measurement of the performance of these machines. The results1,5 showed that these machines threw stones having a muzzle velocity of about 104 m s–1 for the euthytone and about 124 m s–1 for the palintone. The projectile trajectories from this type of machine were computed by using a simple model for the air drag force R: R=−

1 Cv ρ V2A v 2

(2)

where Cv is the drag coefficient for a rough sphere ≈ 0.5, ρ is the mass density of the air = 1225 kg m–3, V is the speed (module with its unit vector v) of the projectile, and A is the area of the projectile’s cross section.

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The differential equations governing the motion can be obtained by projecting along the classical horizontal rightward, x(t), and vertical upward direction, y(t), the following vector equation: 1 m a (P) + Cv ρ VA V(P) − m g = 0 (3) 2 where P is the vector configuring the position of the projectile for any instant of time. Equation (3) was numerically solved. Equations 1–3 were applied in the following examples. Euthytone ballista A medium-sized ballista consisted of a throwing projectile having a mass of 10 Roman minae = 4.31 kg in the form of an almost spherical stone of about 149 mm diameter. Because the computed initial velocity of 100 m s–1 was almost the maximum value for such a machine in very good condition, it seemed more realistic, for a machine used in battle, to consider an initial velocity of 95 m s–1 giving an initial energy of about 10% lower than the maximum energy that the machine could achieve. Table 1 gives examples of range figures, including the angle of elevation θ, the range, the maximum height reached by the projectile, the velocity at the impact Vf, the angle at the impact β, and the time of flight Tf for elevation angles θ of 5°, 10°, 20° and 30°. Figure 8 shows the trajectories for the same conditions. Palintone ballista For the palintone, a 10% decrease in the maximum energy was also considered, thus the projectile initial velocity was assumed to be 118 m s–1. Because this machine architecture was often conceived for large machines, a 40 minae = 21.55 kg projectile consisting of an almost spherical stone having about 254 mm diameter was considered. Table 2 and Figure 9 give the corresponding range figures and trajectories. As for the terminal effect of those projectiles, it is interesting to observe the holes produced by stone balls thrown against the walls of the city of Pompeii8 during Lucius Cornelius Silla’s siege in 89 AC. One such hole is shown in Figure 10; each ruler mark is 10 cm, so the holes have a diameter of almost 150 mm, i.e. the same as the projectile considered for the example given in Table 1 and Figure 8.

figure 8 Trajectories for the euthytone (axes expressed in metres).

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TABLE 1 EUTHYTONE BALLISTA RANGE FIGURES FOR A PROJECTILE MASS = 4.31 KG, INITIAL VELOCITY 95 M/S θ (deg)

Range (m)

hmax (m)

Vf (m s–1)

β(deg)

Tf (s)

5

141.6

3.3

79.8

5.6

1.6

10

252

12.3

70

12.3

3

20

406.2

43.7

59.7

27.1

6

30

491

87.3

56.9

41.3

8.4

TABLE 2 PALINTONE BALLISTA RANGE FIGURES FOR A PROJECTILE OF MASS = 21.55 KG AND INITIAL VELOCITY 118 M S–1 θ (deg) 5

Range (m)

hmax (m)

Vf (m/s)

β(deg)

Tf

221

5.1

110.7

5.5

2

10

396.5

19.2

89.1

12

4

20

645.1

68.7

76.6

26.5

7.5

30

785.5

137.6

73

40.5

10.6

figure 9 Trajectories for the large Palintone.

The Catapult, the Scorpio and the Carrobalista As previously reported, the term catapult refers to a machine that throws big darts or javelins but, substantially, there were no significant differences between the mechanical architecture of the ballistae and the catapults. Small catapults, used as light field artillery pieces, were called by the Romans scorpio, literally scorpion, probably because its arrows acted like the stinger of that animal. Among these relatively small machines, two were particularly interesting: the repeating catapult and the carroballista. The repeating catapult The repeating catapult was among the ancestors of modern machine guns, being a truly automatic weapon. It was described by Philon of Byzantium6–10 and can be considered as a futuristic automatic weapon that throws 481 mm long darts. The machine was attributed to Dionysius of Alexandria and was, apparently, used around the first century BC; it was part of the arsenal of Rhodes that may be considered as a concentration of the most advanced mechanical kinematic and automatic systems

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figure 10  Holes caused by the impact of ballistae projectiles.

of the time, many of which show working principles and concepts that are still considered modern. The machine was described ‘in modern times’ by Bernardino Baldi,29 but the first studies on it were carried out by a German officer, Erwin Schramm,30 who built a model of it at the beginning of the XX century giving unquestionable demonstration of its potential during the testing performed before the Kaiser. There were some later proposed studies on this device.6,7,31 All the reconstructions proposed have almost the same working principle. In the first phase of the working cycle, the operators had to turn the windlass in a direction to charge the weapon and at the end of this phase the missile was thrown. The operators then turned the windlass in the opposite direction in order to carry the mechanism back to the starting configuration. With this way of operating, among other things, once one cycle was started, it was difficult to stop or to pause it because, in the first half of the cycle, the torsion motor was charged and no non-return device could be used because the windlass had to be free to rotate in both directions. Such a working principle had some disadvantages: it was not efficient, it was difficult to operate during a battle and it was dangerous for the operators. Conversely, a mechanism that was operated by turning the windlass always in the same direction of rotation and the presence of a non-return mechanism could have greatly simplified all the operating sequence by the operators, increasing both the rate of fire and the working safety. Thus, it would have been possible to stop the working sequence at any stage. Finally, the whole mechanism would have been automatic from a wider point of view. Therefore, we proposed a rather different reconstruction and working cycle,2,10 based on the translation of the original description by Philon of Byzantium.6,7 It should be pointed out that ancient Greek has no technical terms: for instance in Ta Filonos Belopoika 75, 33–34 the chainmail is called πλτνθτα, ‘little brick’, and the teeth of the chainmails are called περονατς, ‘fin’. Hence, the description left to us by Philon, although readily understood, was not written to eliminate all doubt because it lacks a technical glossary and an analytic style.

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figure 11  Pictorial reconstruction of the automatic catapult.

A pictorial reconstruction of the repeating catapult is shown in Figure 11. The repeating device consisted of a container holding within it a number of arrows, a cylinder feeding device and movement chain. Figure 12 shows another pictorial reconstruction with some details of the mechanism. The details that permit operation of the whole cycle by rotating the windlass always in the same sense of rotation are shown. According to Philon and to other authors’ reconstructions, the arrows A were located in a vertical feeder M (Figures 13 and 14) and were transferred one at a time into the firing groove by means of a rotating cylinder C activated alternatively by a guided cam, in turn activated by a slide. The guided cam is represented by a helical groove in the rotating cylinder in which a pin connected to the slide is located. Hence, a simple rotation of the crank was sufficient to move the cylinder, the slide, the slide hooking mechanism and the trigger mechanism. The cycle repeated automatically without interruption or inverting the rotation of the sprocket until the magazine was empty, a magazine that could be reloaded without suspending firing. In Figure 12, the slide S and the pentagonal wheels P are also represented. The difference between our reconstruction of this device and the previous ones is mainly in the reload sequence: it was previously supposed that the crank handles had to reverse the rotation for each strike, whereas we have assumed the direction of rotation was always the same. This seems more realistic because, in this way, the ratchet could have worked correctly and the rate of fire could have been maintained quasi constant. Figure 13 also shows the feed mechanism compared with the one of the Gatling machine gun; the latter is considered as the first (1862 U.S. patent) machine gun and

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figure 12  Details of the mechanism.

figure 13  Details of the mechanism (left and centre); Gatling gun mechanism (right).

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figure 14 Technical drawing of the repeating catapult.

its working principle is still used for modern aircraft automatic weapons. Figure 14 shows a technical drawing of the device.10 From a ballistic perspective, the speed of firing must have been an average of five strokes per minute, very little compared with modern automatic weapons, but certainly impressive for that time. In order to compute the performance of such a machine, according to ancient engineers,24,25 calculations were made starting from the length of the arrow S. The diameter D of the modiolus is: D = S/9(4) The ratios between the diameter of the modiolus and all the other main dimensions of the machine are the same as those already considered. For the arrow weight, reasonable values are between 100 and 150 g. Figure 15 shows the projectile velocity plotted versus the arm position for arrow weights of 100, 150 and 200 g with a cross section of a circle of 32 mm diameter1. The air drag coefficient in equation 2 was assumed to be Cv =0.35; the performance was computed by using equation 3. The results are summarized in Table 3. The ballistic trajectories of such a small scorpio are reported in Figure 16.

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figure 15 Projectile velocity as a function of the arm position.

figure 16 Trajectories for a repeating catapult (small scorpio). TABLE 3 REPEATING CATAPULT RANGE FIGURES; PROJECTILE MASS = 150 G, INITIAL VELOCITY 65 M/S Range (m)

hmax (m)

Vf (m/s)

β(deg)

Tf (s)

5

70.6

1.6

60

5.2

1.1

10

132.5

6.1

56

11

2.2

20

229.1

22.8

50.8

23.5

4.3

30

289,8

46.9

48.8

36

6.2

θ (deg)

The carroballista The carroballista was the first example of an infantry support gun (or battalion gun) that was much later developed in modern (eighteenth–twentieth century) warfare. Figure 17 shows some pictures of this machine from the Trajan and Marcus Aurelius columns and from De Rebus Bellicis (an anonymous treatise of the IV–V century AD). From a historical point of view, the Roman imperial carroballista was developed in the first century AD and represents the earliest example of mobile artillery. It was very similar to the cheirobalistra or manubalista,8,14 but was mounted on a cart in order to provide a quick deployment of the artillery piece to give close support to infantrymen. This explains why, according to several reports,8,32,33 each of the Imperial Roman Legions was equipped with about 24 of these machines. Moreover, such a lightweight, powerful and, in particular, highly movable war machine was probably developed after four Roman Legions were surprised in an ambush in the

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figure 17  A and C: Trajan’s column; B Aurelian column; D: De Rebus Bellicis (Trans. XVI Sec.)

figure 18  Bas relief and scheme of the carroballista.

forest of Teutoburgo;33 such highly movable and powerful machines would have been decisive in such conditions. Thus, the carroballista was an effective example of an infantry support gun in the open field. It is also surprising to consider the modernity of the concept that consisted of providing the legions with a battalion gun for close support about 1900 years ago. Based on some of our previous studies1,2,5 and on those of others,8,14,15,32 we assume that this ballista (Figure 18) was based on a palintone design shown in Figure 6B.

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figure 19  Schematic diagram of the machine.

As it shown in a previous study,5 this design, having the arms inside the main frame of the machine, is more efficient because the rotation angle of the arms is wider than that of a euthytone. Therefore, it is reasonable to assume such a design for a machine that had to develop sufficient power in small dimensions. The main dimensions of the machine suggested previously8,14,18,32,33 are given in Figure 19; moreover, the most probable torsion motor of these machines was made by a helical torsion spring,22 as shown in Figure 19. This type of motor was compatible with the technology at that time and was small and powerful enough. For such a machine, an initial velocity of 104 m s–1 was computed for a projectile of 200 g.34 In order to evaluate the projectile range, we considered two possible projectiles: a 200 g lead ball 32 mm in diameter, and a bolt having about the same mass and cross section, similar to those reported in Figure 20. Trajectories for the bolt for an initial velocity of 104 m s–1 are given in Figure 21, which shows that the trajectories are rather flat. Thus, there is a high probability of hitting the target even when there are some errors in estimating the real distance of the target itself. Tables 4 and 5 give the range figures for a lead sphere and a bolt, respectively. For comparison, 650 J is the energy of a 3.6 g bullet fired by a NATO 5.56 × 45 cal. ordnance rifle at 300 m from the muzzle, whereas 500 J is the energy of a 8 g bullet at the muzzle fired by 9 × 19 cal. NATO ordnance pistol. Because those modern bullets are much lighter than the ballista projectile, their translational momentum, hence the shock at impact, is much lower than the projectiles thrown by the carroballista.

The onager The onager was a rather mysterious ancient war machine, about which there is very little information available in the ancient literature. Even Vitruvius25 does not mention it. Some detail about a monoanchon can be found in the 5th book, named Belopoeica, of the treatise on the mechanics Mechanike syntaxis (Compendium of Mechanics) by Philo of Byzantium (ca. 280 BC – ca. 220 BC); it is described as a throwing machine having only a big arm instead of two little arms.24 No further mention is found until the fourth century AD when Ammianus Marcellinus (325/330–after 391) describes it in detail and names it onagrum,34 from the latin onagrus meaning donkey, probably because its working principle was similar to the kick of a donkey. It is interesting to recall that inside the city of Pompeii, for instance, several stone balls were found that were larger than the holes on the walls that were made by the impact of the projectiles thrown by the ballistae. Those big balls had been thrown

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figure 20  Roman bolts: A. The only intact specimen of a Roman ballista bolt ever discovered was excavated in Dura Europos, Syria, http://alexisphoenix.org/ballista.php; B. A modern reconstruction weighting about 195 g; C. A bolt head found at Ham Hill, Great Britain by Dr Chris Evans, from the Cambridge Archaeological Unit, Photo by, Yale University Art Gallery, from Greek and Roman Artillery 399 BC–AD 363, by Duncan Campbell, http://hillforts.466ad. co.uk/ham-hill-p2.html and http://imgbuddy.com/roman-ballista-bolts.asp.

figure 21 Trajectory of the bolt.

by the onagers of Silla and had jumped over the walls of Pompeii during the siege in 89 BC.25 A pictorial reconstruction of the onager is shown in Figure 22 and the working principle of the machine is given in Figure 23. The onager comprised a single arm (A in Figure 22) that is inserted into a bundle of yarns made from woman hairs.1–11,23 This bundle is the torsion motor of the machine,

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TABLE 4 RANGE FIGURES FOR THE LEAD BALL Range (m)

Vf (m s–1)

Impact energy (J)

5

165

84.4

712

10

290

72.5

526

15

385

65.3

426

Elevation angle (deg.)

TABLE 5 RANGE FIGURES FOR THE BOLT Range (m)

Vf (m s–1)

Impact energy (J)

5

172

89.3

797

10

310.6

79.4

630

15

421

72.7

529

Elevation angle (deg.)

figure 22 Pictorial reconstruction of the onager and detail of the linkage of the sling.

figure 23 Working principle of the onager.

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which gives an elastic couple (C in Figure 23) to the arm. On the other end of the arm, a sling holds the projectile. One of the sling ropes is fixed to the arm and the other rope is linked by means of a ring that is put on a pin (F in the detail of Figure 22); the axis of this pin can be set with a desired angle γ with respect to the axis of the arm. Finally, a capstan rotates the arm to charge the torsion spring and, hence, the machine. When the trigger is pushed, the arm is released and it rotates because of the couple given by the torsion motor. The projectile is released by the sling when its ropes are approximately aligned with the pin axis because in this condition the ring of the sling climbs over the pin. Thus, by changing the angle γ, the initial throwing angle of the projectile and its initial velocity can both be set. In order to evaluate the performance of an onager, a machine having the following dimensions was considered: length of the arm, 2.2 m; length of the sling, 1 m; weight of the projectile, 17.44 kg (=40 Roman minae), comprising a stone sphere of approximately 237 mm diameter. A mathematical model of tise machine was developed and, by solving the differential equations, the dynamical behaviour of the machine itself was computed. In turn, this allowed the projectile initial velocity to be calculated under several different working conditions. Finally, the range figures were computed by means of equations 2 and 3. The range of this throwing machine could be adjusted both by changing the angle γ and by changing the bundle torque, that is to say by releasing the arm from a different starting position. To illustrate this, two examples, varying the releasing angle γ and the bundle torsion are reported: Ranges by varying the releasing angle γ The results in Table 6 and Figure 24 refer to the same bundle torsion (θund = 110°), and different θr (i.e. by assuming a different releasing angle γ between the finger and the arm). In the range figure tables, in addition to the range, the following data are reported: θr arm angular position when the projectile is released; V0 projectile initial velocity; α projectile initial direction; hmax maximum height reached by the projectile; Vf projectile velocity at the impact; and β the angle of the projectile at the impact. Ranges by varying the bundle torsion The results in Table 7 and Figure 25 refer to almost the same angle γ between the finger and the arm but the range is varied by changing the bundle torsion (θund).

figure 24 Onager trajectories, θund =110°.

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From the previous tables and figures, it is possible to observe that this war machine was capable of effective performance allowing a considerable projectile to be thrown with sufficient energy to clear the walls. Moreover, it is interesting to note that, generally, the range could be adjusted by changing the angle γ; on the other side, the range can be also adjusted by changing the bundle torque obtaining ‘flatter’ trajectories than previously. If a comparison with modern howitzers can be made, we could conclude that the methods of adjusting the range essentially corresponds to both a variation of the gun barrel elevation and of the weight of the firing charge.

Conclusions An overview of all the artillery of the Greek and Roman armies is presented; these war machines were used from the third century BC until the fall of the Roman Empire

figure 25 Onager trajectories, θr = 95°.

TABLE 6 ONAGER RANGE FIGURES, θUND =110°

V 0 (m s–1)

α(°)

65

35.72

73.99

63.8

57.3

33.9

74

75

43.66

65.1

132.2

74.6

40.2

67

θr (°)

Range (m)

hmax (m)

V f (m s–1)

β(°)

85

52.3

52.5

229.7

80.1

45.7

55.5

95

61.4

32.46

293.5

50.5

50.6

36.7

TABLE 7 ONAGER RANGE FIGURES, θR =95°

V 0 (m s )

α (°)

Range (m)

hmax (m)

V f (m s–1)

β(°)

75

29.1

29.69

71.4

10.4

27.7

30.6

85

37.67

30.64

118.7

18.1

34.8

32.3

95

46.78

31.5

179.5

28.9

41.5

34

θr (°)

–1

105

56.41

32.18

252.8

42.3

47.7

35.8

115

66.57

32.71

337.2

59.3

53.4

37.6

88

CESARE ROSSI et al.

and some of them survived until the Middle Ages. Examples of the performance of these ancient artillery pieces are based on the functional reconstruction of these machines that allowed their kinematics and dynamics to be obtained. The performance of these machines showed their reliability and sometimes their surprising efficiency. The authors hope that this study provides a useful contribution to the understanding of ancient warfare.

Notes 1

C. Rossi, ‘Ancient Throwing Machines: a Method to Compute Their Performances’, Mechanism and Machine Theory, 1–13 (2012), 51. 2 C. Rossi, F. Russo, and F. Russo, Ancient Engineers’ Inventions – Precursors of the Present. Series: History of Mechanism and Machine Science, Vol. 8. (Dordrecht: Springer, 2009). 3 T. G. Chondros, Archimedes (287–212 BC) History of Mechanism and Machine Science 1, Distinguished Figures in Mechanism and Machine Science, Their Contributions and Legacies, Part 1. Edited by Marco Ceccarelli, University of Cassino, Italy (Dordrecht Springer, 2007). 4 T. G. Chondros, ‘The Development of Machine Design as a Science from Classical Times to Modern Era’. Proceedings of HMM 2008, International Symposium on History of Machines and Mechanisms (Dordrecht: Springer, 2008). 5 C. Rossi and S. Pagano, ‘Improvement in Ballistae Design from Eutitonon to Palintonon: A Study on the Mechanical Advantages’, Journal of Mechanical Design, Transactions of the ASME, 135 (8) (2013), 1–7. 6 E. W. Marsden, Greek and Roman Artillery Historical Development (Oxford: Oxford University Press, 1969). 7 E. W Marsden, Greek and Roman Artillery: Technical Treatises (Oxford: Oxford University Press, 1971), pp. 106–84. 8 F. Russo, L’artiglieria delle legioni romane (The Artillery of the Roman Legions, in Italian). Ist ed. (Rome: Poligrafico e Zecca dello Stato, 2004). 9 F. Russo, Tormenta Navalia. L’artiglieria navale romana (Rome: USSM Italian Navy, 2007). 10 C. Rossi and F. Russo, ‘A reconstruction of the Greek–Roman repeating catapult’, Mechanism and Machine Theory, 45 (1) (2010), 36–45. 11 F. Russo, Le baliste dell’Impero. Cenni storici, reperti, tavole ricostruttive. Vol. 18: La grande Balista di Hatra. Ed. ESA (Naples: ESA, Torre del Greco (2009). 12 E. Shramm, Die antiken Geshützen der Saalburg, 1918. Reprint (Bad Homburg: Saalburg Museum, 1980). 13 W. Soedel and V. Foley, ‘Ancient Catapults’, Scientific American, 240 (1979), 150–60. 14 A. Iriarte, ‘Pseudo-Heron’s cheiroballistra a(nother) reconstruction: I. Theoretics’, Journal of Roman Military Equipment Studies, 11 (2000), 47–75.

15

A. Iriarte, ‘The Inswinging Theory’, Gladius, 23 (2003), 111–40. 16 D. Baatz, ‘Recent Finds of Ancient Artillery’, Britannia, 9 (1978), 1–17. 17 M. C. Bishop and J. C. N. Coulston, Roman military equipment from the Punic Wars to the fall of Rome (London: B. T. Batsford, 1993). See reviews of this book by Boris Rankov in The Classical Review (New Series), 44 1994), 137–38, and by Matthew Bennett, Roman Military Equipment Greece and Rome (Second Series), 41 (1994), 79–81. 18 R. Harpham and D. W. W. Stevenson, ‘Heron’s Cheiroballistra (A Roman Torsion Crossbow)’, Journal of the Society of Archer-Antiquaries, 40 (1997), 13–17. 19 V. G. Hart and M. J. T. Lewis, ‘Mechanics of the Onager’, Journal of Engineering Mathematics, 20(4) (1986), 345–65. 20 V. G. Hart and M. J. T. Lewis, ‘The Hatra Ballista: A Secret Weapon of the Past?’ Journal of Engineering Mathematics, 67 (2009), 261–73. 21 M. Lahanas, ‘Ancient Greek Artillery Technology from Catapults to the Architronio Cannon’, available at . 22 P. G. Molari, G. Angelini, A. Canzler and P. Sannipoli P. 2012. ‘Ricostruzione della balista imperiale Romana – un piacevole viaggio fra fantasia, storia, tecnologia e progettazione’, University of Bologna, 2012. p. 40. DOI 10.6092/unibo/amsacta/3306. 23 Appianus Alexandrinus, Wars against Carthage, liber VIII, 160 A.D.; available in English at . 24 Philo of Byzantium (III Century BC) Mechanike syntaxis (Compendium of Mechanics), in particular that part called Belopoeica where torsion artilleries are described. 25 Vitruvius, De Architectura, liber X, c. 15 B.C.; available in English at . 26 Qiang Xiao, Jeff Schirer, Fred Tsuchiya and Dehua Yang. Nanotensile Study of Single Human Hair Fiber. Hysitron Incorporated 10025 Valley View Road, Minneapolis MN 55344. Available at: <www. hysitron.com/Portals/0/App%20Notes/BIO13ANr1. f.pdf>.

PERFORMANCE OF GREEK–ROMAN ARTILLERY 27

L. Tonelli, Tecnologia Tessile – Fibre tessili, filatura, Vol. 1 (Milan: Hoepli, 1950). 28 F. Manna, Note sulle funi Metalliche (Naples: Unviersity of Naples, 1966). 29 B. Baldi, Heronis Ctesibii Belopoeka, hoc est, Telifactiva. Augusta Vindelicorum, typis Davidu Frany. 1616. Available at . 30 E. Shramm, Die antiken Geschütze der Saalburg 31 Soedel and Foley, 150–60. 32 Molari P. G. 2013. ‘Dal fregio della Colonna Traiana argomenti per ricostruire la balista imperiale romana’, Proceedings of Colonna Traiana MCM – Accademia di Romania in Roma 7–8 June 2013. In press

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33

F. Russo and F. Russo, ‘La lezione di Teutoburgo’, Archeo, 295 (2009), 54–61. 34 F. Penta, C. Rossi, and S. Savino, ‘Mechanical behavior of the imperial carroballista’, Mechanism and Machine Theory, 80 (2014), 142–50. 35 Ammianus Marcellinus (IV Century A.D.) Res gestae. 36 F. Russo F. 2011. Attenti all’asino. Archeo, 311 (2011), 90–95. 37 C. Rossi, Guest editorial. ‘On Designs by Ancient Engineers’, Journal of Mechanical Design, Transactions of the ASME, 135(6) (2013), 1–2. All web addresses have been rechecked by accessing on 26 March 2015.

Notes on contributors Cesare Rossi graduated in 1973, focusing on humanities. In 1979, he received the Mechanical Engineer Degree cum Laude at the University of Napoli – “Federico II”, and became Professor of Mechanics for Machines and Mechanical Systems there in 2000. His main research activities are on the topics of tribology, rotor dynamics, mechanical vibrations, chaotic motions in mechanical systems, robot mechanics, and video applications for robotics. For several years he has researched the history of engineering and cooperates with other researchers in the field mainly involving Technology in the Classic Age (in which he has taught PhD courses at other Italian universities. He is currently Chair of the IFToMM, Italy and a member of its Permanent Commission for the History of Mechanism and Machine Science. Arcangelo Messina received the Mechanical Engineer Degree cum Laude at Politecnico di Bari in 1991, and a PhD in Mechanical Engineering. He became Professor of Mechanics for Machines and Mechanical Systems at the Università del Salento, Italy in 2006. His main research activities are on the topics of mechanical vibrations, composite materials, mechatronic systems, signal processing in mechanical systems, damage detection and modal analysis. Giulio Reina received the Mechanical Engineer Degree cum Laude at Politecnico di Bari in 2000, and a PhD in Mechanical Engineering. He became Assistant Professor of Mechanics for Machines and Mechanical Systems at the Università del Salento, Italy, in 2005. His research focuses on the topics of field robotics, vehicle dynamics, and vision systems in robotics. Sergio Savino received his Mechanical Engineer Degree at the University of Napoli - “Federico II” in 2001, and a PhD in Mechanical Engineering. Currently Research Assistant of Mechanics for Machines and Mechanical Systems at the University of Napoli - “Federico II”, his main areas of research are video applications for robotics, and the history of mechanism and machine science. Correspondence to Cesare Rossi. Email: [email protected]

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