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Barrel Natural Frequency 2021-01-03

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Posting this into Resources section for Jim Boatright.


I was asked several years ago by David Tubb to explain ballistically why crosswinds favored riflemen shooting barrels made with twist direction matching the crosswind direction--L to R winds favoring LH twist barrels, and vice-versa. I could find nothing in aeroballistics showing any asymmetry at all. Well, now I can explain the problem. It happens when the barrel length used is so long that the load being fired cannot be adjusted so that bullets exit the muzzle after its first halting of the muzzle's recoil-driven downward motion. Bullets fired from extra long barrels are always given a pitch-up (nose high) attitude and positive pitch-rate upon exiting the muzzle due to its downward motion.

The attached paper explains this problem in detail. An active Excel spreadsheet allows the reader to calculate the natural vibration mode frequencies for any set of barrel dimension and (isotropic) material specs. I did not address carbon fiber barrels nor muzzle attachments. I worked an example for a 44-inch, 8-pound, 4140 Cro-Mo steel, 50-caliber barrel firing an 850-gr bullet at 2722 fps from a 50 BMG cartridge. The maximum tunable barrel length turned out to be 32 inches in that example.

I mentioned David's solution which is to have matched pairs of LH and RH twist barrels available for each match.
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