Twist Rate

Twist rate For best performance, the barrel should have a twist rate sufficient to stabilize any bullet that it would reasonably be expected to fire, but not significantly more. Large diameter bullets provide more stability, as the larger radius provides more gyroscopic inertia, while long bullets are harder to stabilize, as they tend to be very backheavy and the aerodynamic pressures have a longer "lever" to act on. The slowest twist rates are found in muzzleloading firearms meant to fire a round ball; these will have twist rates as low as 1 in 60 inches (1,500 mm), or slightly longer, although for a typical multi-purpose muzzleloader rifle, a twist rate of 1 in 48 inches (1,200 mm) is very common. The M16A2 rifle, which is designed to fire the SS109 bullet, has a 1 in 7-inch (180 mm) twist. Civilian AR-15 rifles are commonly found with 1 in 12 inches (300 mm) for older rifles and 1 in 9 inches (230 mm) for most newer rifles, although some are made with 1 in 7 inches (180 mm) twist rates, the same as used for the M16. Rifles, which generally fire longer, smaller diameter bullets, will in general have higher twist rates than handguns, which fire shorter, larger diameter bullets. In 1879, George Greenhill, a professor of mathematics at the Royal Military Academy (RMA) at Woolwich, London, UK[9] developed a rule of thumb for calculating the optimal twist rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape[10]. The eponymous Greenhill Formula, still used today, is:

where:    

C = 150 (use 180 for muzzle velocities higher than 2,800 f/s) D = bullet's diameter in inches L = bullet's length in inches SG = bullet's specific gravity (10.9 for lead-core bullets, which cancels out the second half of the equation)

The original value of C was 150, which yields a twist rate in inches per turn, when given the diameter D and the length L of the bullet in inches. This works to velocities of about 840 m/s (2800 ft/s); above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/s (2000 ft/s), a diameter of 0.5 inches (13 mm) and a length of 1.5 inches (38 mm), the Greenhill formula would give a value of 25, which means 1 turn in 25 inches (640 mm). Improved formulas for determining stability and twist rates include the Miller Twist Rule[11] and the McGyro program[12] developed by Bill Davis and Robert McCoy.

A Parrott rifle, used by both Confederate and Union forces in the American Civil War. If an insufficient twist rate is used, the bullet will begin to yaw and then tumble; this is usually seen as "keyholing", where bullets leave elongated holes in the target as they strike at an angle. Once the bullet starts to yaw, any hope of accuracy is lost, as the bullet will begin to veer off in random directions as it precesses. Conversely, too-high a rate of twist can also cause problems. The excessive twist can cause accelerated barrel wear, and also induce a very high spin rate which can cause high-velocity projectiles to disintegrate in flight. A higher twist than needed can also cause more subtle problems with accuracy: Any inconsistency within the bullet, such as a void that causes an unequal distribution of mass, may be magnified by the spin. Undersized bullets also have problems, as they may not enter the rifling exactly concentric and coaxial to the bore, and excess twist will exacerbate the accuracy problems this causes. Lastly, excessive spinning causes a reduction in the lateral kinetic energy of a projectile, thereby reducing its destructive power (the energy instead becomes rotational kinetic energy).

[edit] Bullet revolutions per minute (rpm) A bullet fired from a rifled barrel can spin at over 300,000 rpm, depending on the bullet's muzzle velocity (MV) and the barrel's twist rate. The general formula for calculating the rpm of a rotating object may be written as



where υ is the linear velocity of a point in the rotating object (in units of distance/minute) and C refers to the circumference of the circle that this measuring point performs around the axis of rotation. For a bullet, the specific formula below uses the bullet's MV and the barrel's twist rate to calculate rotational speed: 

MV(in fps) x (12/twist rate in inches) x 60 = Bullet rpm

For example, a bullet with a muzzle velocity of 3050 ft/s fired from a barrel with a twist rate of 1 in 7-inch (180 mm) (e.g., the M16A2 rifle) spins at ~315,000 rpm[13].

Excessive rotational speed can exceed the bullet's designed limits and the resulting centrifugal force can cause the bullet to disintegrate in a radial fashion[14].