Professor Sir Alfred George Greenhill of the British Royal Military Academy, who devised a formula for determining twist rate which, simplified here, multiplies the square of the bullet diameter by 150 and then divides the result by the length of the bullet, and looks like this: (C x D2) ÷ L = T.
C is a constant, 150; D2 is bullet diameter multiplied by itself, L is bullet length and T is the result, twist rate. Using it is simple; let’s stick with our 5.56 mm/.223 Rem. example. The bullet diameter is .244" and length of a 55 grainer is .740". Following Greenhill:
- Step 1—Finding D2: .244 x .244 = .05953
- Step 2—Finding C x D2: 150 x .05953 = 8.9295
- Step 3—Divide result by bullet length: 8.9295 ÷ .740 = 12.06
So, 1:12.06-inch, rounded to 1:12-inch, is our standard twist rate for the .223 Rem. 55-grain bullet.
Doing the same for an 80-grain bullet 1.075" long:
- Step 1—Finding D2: .244 x .244 = .05953
- Step 2—Finding C x D2: 150 x .05953 = 8.9295
- Step 3—Divide result by bullet length: 8.9295 ÷ 1.075 = 8.306
Rounded, 1:8-inch twist is Greenhill’s indicated twist rate for 80-grain bullets. As shooters have discovered, the reality is that a 1:8-inch twist can be marginal for a .223 Rem. 80-grain bullet, working better with some makes than others, and that a 1:7-inch twist may work better. What’s up with that?
Plug and play math
John Maynard converted Greenhill’s formula into a chart in 1962.
The shortcoming of Greenhill’s formula is that the professor developed it for elliptical (football-shaped) subsonic lead projectiles (he was more into rifled cannons). Though it applies surprisingly well for rifle bullets with muzzle velocities up to about 2,800 fps (for higher velocities, we can substitute 180 for 150 in the constant C, which results in slower twist rates), it isn’t perfect. Others have offered their own (pardon the pun) twists on Greenhill. The
Miller twist rule, formulated by Don Miller and published in 2005, refines Greenhill a bit by including bullet weight. The tweak takes into account the lighter-for-length jacketed, hollow point and homogeneous metal bullets invented since Greenhill developed his formula.
Though Greenhill and Miller may appear complex to those who believe numbers and letters are a devil’s mix, they are both actually simple “plug n play” tools where you plug in your variables, such as bullet length, into the correct place and then let a simple hand calculator do the math. If that’s still too much math, a twist table by John Maynard published in the 1963
Gun Handbook provides an instant, follow-the-lines visual graph. “The graph will not work properly for bullets of other than all-lead or lead-and-gilding metal construction,” Maynard accedes, “but who shoots solid bronze pills today?”
WinGyro by gunsmith John Knight is a
free software program that performs twist rate calculations. There’s also the McCoy “McGyro” algorithm drag/twist calculator. You might try the Bowman-Howell
software calculator, which requires simple inputs of bullet length, diameter, muzzle velocity and a provided specific gravity density value assigned to copper, brass, lead or steel (the longer version of Greenhill’s formula included specific gravities, as well). It improves upon Greenhill’s formula, which lacks a velocity term, but apparently is not as accurate as Miller across a broader range of muzzle velocities and bullet shapes.
As a final matter of curiosity, how fast do bullets spin, anyway? That depends upon twist rate and muzzle velocity. A 5.56 mm/.223 Rem. bullet fired at 3,000 fps from our National Match AR-15 with a 1:7-inch twist exceeds 300,000 rpm. While we don’t need to know that, we do need to know what bullets our rifles will stabilize, and if we don’t have computers or calculators handy, we can figure it out reasonably well ourselves with pencil and paper—and Greenhill’s formula.
