What is the formula used to determine the optimum barrel length for a firearm?

---

Request for Question Clarification by tutuzdad-ga on 16 Mar 2006 06:58 PST

According to this article the optimum barrel length is relative to the
"twist rate" of the projectile, or number of complete revolutions the
grooves make in one inch of barrel length. A 1 in 10, or 1:10, would
be one complete turn in 10 inches of barrel length. Please let me know
if the formula on this page answers your question:

LOAD FROM A DISK
http://www.loadammo.com/Topics/July01.htm

tutuzdad-ga

Here's a link you might try:
http://nerfhaven.com/homemade/boltsniper_far/

   It records one person's project to design & build a rifle from
scratch with ammunition with PVC pipe elements. I'm not sure how
helpful it'll be to you, but it does have related formulae, and I
think it's interesting.

The problem with this question is if you are trying to maximize muzzle
velocity as well; I'm fairly certain that nearly all barrels are cut
well short of the optimum length concerning velocity as a concession
to portability. Bullets accelerate because of the pressure
differential between the front and rear of the slug as a result of the
expansion of gasses created when the propellant burns. If a longer
barrel is used the bullet is allowed more time to accellerate before
it leaves the barrel, the only opposing force would be friction. Thus,
to maximize muzzle velocity the barrel would the length where the
acceleration due to the pressure differential and the force due to
friction become equal: this is not very practical for any handgun.

So if everything asides from the barrel is a given, intended muzzle
velocity must be decided first to calculate the necessary barrel
length with which to achieve it, then the pitch of the rifling can be
determined from the length. If you were to assume the slug was
flawless the number of turns could be dictated solely by the maximum
rotational speed it could withstand before pulling itself apart--it
isn't perfect though, so a formula derived from empirical data like
the one on the page tutuzdad-ga linked is necessary.