[Unclenick]

My second sentence should simply have been, "That accelerates the gun to a higher rearward velocity". That would have cleared the ambiguity.

Originally Posted by Jimro

you can see my point that barrel time isn't the deciding factor in impact

Actually, that was the point I was trying to make. Your earlier sentence made me think you had that confused, when you said:

Originally Posted by Jimro

But you missed the point, VELOCITY is dependent on TIME.

You should have written: "…VELOCITY is dependent on TIME, IF the FORCE is constant and the MASS is unchanged". And that's pretty much where I was going, too. Change the time OR the force OR the mass and you get a different acceleration over a different time with different resulting final velocity. The length of the barrel being constant is assumed.

You and I should get together and write a textbook. Between us we'll get it edited correctly in the end.

Slightly OT, but relevant to the discussion: One of the confounding things for people trying to keep their rifle loads tuned is that velocity and barrel time don't always track well enough to do that. You can't just change powders and load to the same velocity and be tuned because the barrel times won't match. If you pick a charge of a fast powder and a companion charge of a slow powder that both produce the same velocity with the same bullet in the same rifle, the fast powder charge will produce the shorter barrel time.

The above happens because, even though both charges have the same average pressure over the bullet trip down the bore, the fast powder achieves that average with a higher peak pressure and lower muzzle pressure. It therefore does a greater portion of its acceleration earlier in the bullet's trip, letting the bullet cover the remaining bore length at a higher average velocity. The slow powder has a lower peak pressure and a higher muzzle pressure, so it spreads the acceleration out more over the length of the barrel, and the bullet velocity just catches up to the fast powder bullet velocity at the very end of the journey.

So barrel time has a pressure profile dependency, with average pressure being the integral of the powder pressure function with respect to either time or bullet base position in the tube. Since the average pressure comes out the same for both the fast and slow powder at the end, the resulting imparted momentum and transferred final energies are still the same.

"First contemplation of the problems of Interior Ballistics gives the impression that they should yield rather easily to relatively simple methods of analysis. Further study shows the subject to be of almost unbelievable complexity."

Homer Powley