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Old April 13, 2010, 03:02 PM   #12
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Join Date: January 27, 2010
Location: Norfolk, VA
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Someone suggested looking at the Greenhill formula. I've done that, and part of the problem is that the typical form of the Greenhill formula that's used is a simplified version of his complete formula (which I haven't found yet), and the constant 'C' in the formula (usually defined as 150 or 180, depending on projectile speed) hides a lot of assumptions and approximations.

I've found an article from the November issue of the International Journal of Impact Engineering that contains the full derivation of Greenhill's original formula and not just the final simplified version, but it will take a few days to get the article in-hand. In particular, I think that the "moment of inertia" parts of the calculations assume a cylindrical projectile (longer than it is wide). If you were to replace those equations with the equations for a sphere (which has the same moment of inertia about all three major axes), I think the effect of rifling will diminish greatly, if not cancel out altogether.

I'll know more once I've looked at the full derivation of the Greenhill formula and dug back into my fluid mechanics textbooks, but I think that the only reason spherical projectiles benefit from rifled barrels is that a) they're not really spherical, and b) they're not perfectly smooth. I believe that if a projectile is in fact nearly round, and uniformly smooth over its surface, its exterior ballistics are not going to be affected by whether or not it's spinning during flight.
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