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:
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.
For those who just want a cheat sheet
Simplified from Sweeney, Gunsmithing Rifles, pp. 109-110
5.56 and other .22 centerfires:
|Bullet weight grains||Twist ratio 1:inches||Velocity|
|> 70||8||any practical|
|≤ 70||9||any practical|
|≤ 63||12||any practical|
|≤ 55||14||any practical|
|≤ 55||15||≥ 4100 fps|
|≤ 55||16||≥ 4300 fps|
Note that this is really for civilian use in “normal” climactic conditions. For military purposes where you must meet a +140ºF/-40ºF standard, you should go one twist increment slower per bullet weight increment, and understand that you will lose some ability to use weights at the extremes removed from your selected optimum round. Not much of a factor in a military application, where the fewer different DODAAC codes (ammunition stock numbers), the better, as far as the logistics elements are concerned.
7.62 NATO and other .308 centerfires:
|Bullet weight grains||Twist ratio 1:inches||Velocity|
|> 220||8||any practical|
|≤ 220||9||any practical|
|≤ 170||12||any practical|
|≤ 168||14||any practical|
|≤ 150||15||any practical|
Note again that this is for civilian/sporting/normal-climactic-conditions use. And that it applies to supersonic rounds only. You must redo the calculations for the slow, heavy bullets used in suppressed applications!
For those desirous of plug-in calculators:
- Vcalc offers an excellent and easy to use Greenhill calculator by Andrew Budd. Unfortunately no Miller calculator. https://www.vcalc.com/wiki/AndrewBudd/Greenhill+Formula+for+Optimal+Rifling+Twist+Rate
- Berger Bullets has a simple one that we believe to be based on the work of Don Miller and Bryan Litz. http://www.bergerbullets.com/twist-rate-calculator/
- JBM Ballistics offers numerous calculators. You can quickly get in over your head here if you don’t know what you’re doing, as we can attest. http://www.jbmballistics.com/ballistics/calculators/calculators.shtml
For those desirous of more sheet music:
- An interesting Usenet discussion of unknown vintage: http://yarchive.net/gun/barrel/rifling_twist_angle.html
- Miller for his part compared the Miller and Greenhill rules and five other equations and variants for estimating bullet stability (from which twist equations can be derived) in Precision Shooting in June 2009. That article can be found here: http://www.jbmballistics.com/ballistics/bibliography/articles/miller_stability_2.pdf