THE GREENHILL FORMULA
Twist is measured in the number of inches for one complete turn of the rifling in the barrel. For example, many 30 caliber rifles have barrels with a twist of one turn in 10 inches.
For a given twist rate and diameter, there is a maximum length of bullet that may be stabilized.
If the bullet is too long, or the twist is too slow, the bullet will not stabilize and will go through the target making a hole that is somewhere between oval and the side view of the bullet.
When the bullet makes an oval hole, we say that it is “tipping”. When the hole starts to be real long and to look like a side view of the bullet, we say that the bullet is “keyholing”. It is not uncommon to find that best accuracy at slow velocities is accompanied by slight tipping of the bullet. (Tipping is also called "yawing")
The Greenhill formula was designed around the stability = the ability to keep the sharp end going frontward, of low velocity lead bullets.
Bullet stability is affected by several variables not included in the Greenhill formula.
Bullet stability is slightly affected by velocity, faster bullets are slightly more stable than slower.
Stability is affected by bullet density; an aluminum bullet won't be stable at Greenhill length and linotype (less dense) bullets are less stable than lead bullets.
Stability is affected by the density of the medium the bullet is going through-generally air, but sometimes meat or water. Bullets are slightly more stable at high altitudes where the air is thin, than at sea level; and are much less stable going through denser mediums such as meat or water. Most of the time Greenhill does a remarkably good job of explaining the relationship between caliber, twist and bullet length required for bullet stability.
The Greenhill formula is an approximation showing the relationship between rifling twist rate, maximum bullet length, and caliber. For any caliber and twist there is a
maximum bullet length that will stabilize. For any caliber and bullet length there is a
minimum rifling twist that will stabilize that bullet. By algebraic fiddling we can solve for either twist or length. Here is the formula set up to solve for maximum bullet length.
The Greenhill Formula is: L = (150/twist) * (caliber squared)
Where L is the maximum length of bullet that will be stabilized in inches; twist is the number of inches required for one turn in the rifling; and caliber is the bullet diameter in inches.
This table shows the maximum bullet length by caliber/twist combinations. For example, a .308 caliber barrel of 10" twist will stabilize a bullet that is a maximum of 1.42" long.