Muzzleloader 101


The Greenhill formula is T=150 x D^{2}/R, where T is the Twist rate, D is the diameter of the bullet, and R is the length of the bullet. 150 x diameter squared divided by bullet length = required spin Example for a .45 caliber bullet .60 inches long: 150 x .45 x .45 divided by .60 = 50.6 inches So, for the example bullet, a spin rate of 1:50.6 or faster is required The formula can also provide us with the maximum bullet length which can be stabilized by a given barrel twist. The formula becomes: 150 x diameter squared divided by twist rate Example for a .50 caliber barrel of 1:48 twist: 150 x .50 x .50 divided by 48 = .78 inches. The barrel will stabilize a bullet .78 inches long, or shorter. Keep in mind that Greenhill's Twist Rate Formula isn't applicable to round projectiles, and it's really not ideal for any projectile that isn't at least 2.5 or 3 times longer than it is wide. You really can't use Greenhill's formula for round balls. The only reason it gives you a result at all is that you're using the common simplified approximation of Greenhill's Twist Rate Formula. If you use the full and complete version, entering the dimensions for a round ball (length and diameter are equal), the equation "blows up" and basically gives an infinite twist length (i.e. zero twist). The reason is, a spherical projectile can't be dynamically "stable" or "unstable", since the center of pressure and center of gravity are always at the exact same place  the center of the ball. That's why the twist rate formula fails. The only reasons that twist is actually beneficial for round balls (surface imperfections, density variations, and the slight deformation as the ball goes through the barrel) aren't modeled anywhere in Greenhill's calculations. The reason that the simplified version gives you a result you can use is that it actually recommends more twist than you need, and since there aren't any negative consequences of using too much twist with a solid lead projectile, the calculated twist length works. But that's more of a happy coincidence than anything else. 



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