Has anyone seen a math model for the acceleration curve a bullet sees after detonation and before exiting the muzzle?

I've been working on math modeling the time it takes for a bullet to go from the chamber to the muzzle.     So far, I've just assumed a constant acceleration.   I use that because the math is easy and I don't have any better approximation of the acceleration curve.

My final goal is to be able to predict a muzzle velocity  that will have the bullet exiting the muzzle when the muzzle is at a harmonic minimum node.

I've googled this but no luck so far.

thanks

use quick load.  There are way too many factors going into this to use a simple formula.  Bullet weight, Bearing surface, Powder burn rate, bore and groove surface area.

Quickload will run all that stuff.

Easiest way is load up 10 rounds at .2 increments and look for flat spots.

I don't think that will work for you because powder burn rates are not really fixed. Different conditions determine  average burn rate.

In all my different loads with one powder the burn rate varies greatly when matching MV.