THE GREENHILL FORMULA
There are some elaborate computer programs to calculate bullet length to rifling twist, but there is a very simple method that works with a pocket calculator or even paper and pencil — The Greenhill Formula. The Greenhill formula for determining twist rates was the work of Sir Alfred George Greenhill, a mathematics professor at Cambridge University who later served as an instructor at the Woolrich Military Academy from 1876 to 1906. Greenhill discovered that the optimum twist rate for a bullet is determined by dividing 150 by the length of the bullet in calibers (100ths of an inch).
The number 150 is a good choice since it allows a useful margin in the calculations. Most twist rates that are close to the formulated ideal will usually work well. The beauty of this formula is that it works very well for lead or jacketed bullets. Weight does not appear to be a critical factor. Shape and design do not seem to have that much effect either up to velocities of 2200 fps and to a degree, above this. To compensate for increased rotational speed at velocities over 3000 fps some authorities recommend a slightly reduced twist rate. Although velocity does not appear to be considered within this formula, it is included in the rotation segment in a concealed form.
Assume a 1-12″ barrel firing a bullet at 1000 fps. This equals 1000 rotations per second. At 2000 fps the rotations per second double. Higher velocity yields a faster spin and is thus considered in the calculations, although it is not specifically mentioned. The most recent interpretations of Greenhill opt for a slightly faster twist with the higher velocity cartridges in the belief that erring on the side of over-stabilization is better than under-stabilization that may result in a tumbling bullet.
The popular 223 Remington is a good candidate for study. Rifles for this cartridge are currently available with the following twist rates — 1-7″, 1-8.5″, 1-9″, 1-10″, 1-12″ and 1-14″. To apply the Greenhill Formula using the original 55 grain bullet yields the following, for one brand of full metal jacket (FMJ) military type bullet measuring .647″ in length. The bullet diameter is .224″, which divided into the length of .647″ gives 2.89 calibers long. Dividing 2.89 into 150 yields a figure of 51.90 or an ideal twist rate of one turn in 51.90 calibers. Multiply 51.90 by the bullet diameter (.224″) equals one turn in 11.63″ for this particular bullet.
The original twist for the 223 caliber M-16 rifle is 1-12″. In its wisdom (?) the Army decided a heavier (longer) bullet was necessary and the M-16A1 is bored with a 1-10″ twist. The new military bullet will not stabilize in the 1-12″ barrels. Bullets as heavy as 70 grains are available for the .223 Remington. For a 70 grain bullet measuring .785″ in length, .785 ÷ .224 = 3.50. 150 ÷ 3.50 = 42.86 or one turn in 42.86 calibers. 42.86 X .224 (i.e., the bullet caliber) = 9.60.
Thus a twist of 1-9″ or 1-10″ is required to shoot this bullet accurately, while a 1-12″ will not stabilize it and as for a 1-14″, forget it. There are other factors involved, such as the amount of bearing surface on the bullet, velocity and barrel length. In some cases bullets that are not well matched to twist rate can be made to function. For example, a short, 40 or 45 grain bullet, in a 223 with a fast twist of 1-9″ or 1-10″, will perform, if the powder charge is cut back. By decreasing the velocity, you can keep the bullet from tearing itself apart. This might be called a limited success, since in the manner of the .22 Short in the 22 Long Rifle barrel, accuracy will likely suffer.
Applying the Greenhill formula can save time and money not spent on ammunition that won’t shoot well. It can serve as a useful guide when it comes to buying a gun or having one custom barreled if you know in advance what kind of shooting you will be doing and thus what kind of bullets you will use.
About the Author: Bill Chevalier has been involved in the reloading industry for more than 30 years. Working closely with the National Rifle Association, Bill helped develop the NRA's Certified Course in Reloading. More than 1000 NRA instructors are now certified to teach reloading.
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