Twists of Fate, and Rifling

by Hognose

What separates the winners from the losers is how a person reacts to each new twist of fate.  -Donald J. Trump.

We’re not sure about twists of Fate, but a number of you have asked us about twists of rifling. The question usually comes in the context of AR-15 rifles and their clones, with rifling twists of 1:14. 1:12, 1:9, 1:8 and 1:7 all having been used.

Can you calculate optimum twist for a given caliber and projectile? Yes, you can. There are two equations that are commonly used, Greenhill’s and Miller’s.  Let’s start with the newer one, Miller’s, which was originally proposed in Precision Shooting in March, 2005:

http://www.jbmballistics.com/ballistics/bibliography/articles/miller_stability_1.pdf

Miller assumes a spitzer-pointed, boat-tailed projectile. In Imperial measurements:

T is twist
30 = a constant representing: standard atmospheric conditions, and a bullet speed of approximately Mach 2 (2800 fps at sea level in standard atmospherics). If you need real precision, Miller does provide more complete equations for that, but these approximations work for rifle velocities.
m = projectile mass, decimal grains
s = gyroscopic stability factor
d = diameter, decimal inches
l =  length in calibers (i.e. length is “l” times the caliber of the projo).

Greenhill’s rule dates originally to 1879, and is frequently used by gunsmiths as it is (or was. anyway) taught as part of gunsmithing school, repeated in Hatcher’s Notebook, and included in Patrick Sweeney’s rifle gunsmithing book among many others. Sir Alfred Greenhill of the Royal Armories at Woolwich developed a number of more complex equations. (More complex than Miller’s, too). But he also provided “Greenhill’s rule of thumb.” Sweeney describes this as follows:

“The length of the bullet in calibers, multiplied by the twist rate in calibers per turn, is 150.”

The constant 150 is good for velocities to about 2800 fps. For higher velocities, as often seen with small-caliber rifles, use 180.

Some notes on twist

As a rule of thumb, the more twist, the more stable the bullet. A bullet must meet a threshold of stability to be accurate. The less twist beyond minimal stability, the less accurate the bullet, in theory, but practical accuracy doesn’t drop off until a bullet is very overstabilized. In small calibers, varmint hunters will tell you a too-fast twist will cause bullets to self-destruct from centrifugal force before overspin hurts their accuracy.

You also need enough excess stability to account for atmospheric changes. As a rule, air density decreases with increased altitude above sea level, and air density decreases with rising temperatures. Less dense air needs less spin than more dense air. This is why the original AR-15 prototypes were found to lose accuracy during Arctic testing by the Air Force — important tests for guys who might have to defend ammo igloos in Iceland, antennas in Alaska, or missiles at Minot. These prototypes had barrels made by Winchester for Armalite in 1:14 twist, then the standard .22x varmint-rifle twist (no one pops prairie dogs in -20F weather). A change to 1:12 solved the problem, at least, for 53-55 grain bullets like those in what would become M193 ball ammunition. (Lighter weight tracer rounds have always been hard to stabilize and trajectory match in 5.56mm). The change to 63 grain ammunition drove the change to a 1:7 rifling twist.

These same calculations may not scale to all types of large-caliber, high-velocity artillery pieces such as tank guns. That’s because air is not truly dimensionless; air molecules don’t scale up as projectiles do. Aerodynamicists and exterior ballisticians can compensate for this scale effect by incorporating Reynolds Numbers in their calculations. For rifle ammo, it’s not necessary or useful.