Determining optimal barrel length for a projectile

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Determining the optimal barrel length for a firearm cartridge involves balancing factors like barrel whip, propellant burn, and rifling effectiveness. Longer barrels allow for complete propellant combustion and better stabilization of the projectile, but may introduce issues like barrel whip and friction that can reduce velocity after peak pressure. Conversely, shorter barrels minimize whip but may not provide sufficient length for complete burn and stabilization. For the M855 cartridge, a 20-inch barrel reportedly achieves maximum velocity, with shorter lengths resulting in decreased performance. Resources like the Speer Reloading Manual and research on interior ballistics can provide further insights into calculating optimal barrel length.
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Hello, I was wondering of anybody has a formula to determine the optimal barrel length for a firearm using a particular cartridge? For example, the M855 cartridge which has a 62gr. projectile and uses WC-844 propellant, which has a known burn rate etc.

The longer the barrel, the more susceptible to barrel "whip" the barrel would be; however, a longer barrel allows both the complete burning of the propellant as well as increased travel through the barrel's rifling which imparts spin on the projectile to stabilize it in flight...although I would think there would be a point of diminished returns where the friction of traveling down the barrel after peak pressure is achieved by the combustion of the propellant would perhaps slow the projectile down.

On the other hand, the shorter the barrel, the less "whip" should be encountered but the barrel must be of sufficient length to allow both complete burning of the propellant as well as allowing the rifling to impart enough spin on the projectile to stabilize it in flight.

For the aforementioned cartridge I used as an example...maximum velocity was apparently achieved with a barrel length of 20 inches, with an increasing drop in velocity with shorter barrel lengths.

I realize that this is ignoring rifling twist rates and other factors...I just am wondering if there is a formula out there which can be used to determine, to at least a ballpark value, optimal barrel length based on the specifics of a particular cartridge.
 
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Speer Reloading Manual has information on this, too. It is possible to tune a load such that you minimize group size.
 
Thank you for your replies.
 
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