Are the Forces During a Gunshot Balanced and Optimized by Barrel Length?

[thetexan]

My understanding is this...

a. The force acting to recoil the mass of the rifle and the mass of the shooter combined is equal (give or take small other masses such as gas) to the force acting to push the bullet down the barrel.

b. This means that all of that force you feel in your shoulder is the same as that acting on the tip end of that bullet as it enters the target (minus loss of energy during flight).

c. Since the the expanding gas is what is driving the bullet down the barrel you would think, at first, that the longer the barrel the more opportunity the gas has to accelerate the bullet. However, there comes a point where, when considering the friction between the bullet and the barrel, the gas no longer can accelerate the bullet and at that point the friction becomes a slowing factor. Therefore the point where this occurs determines the ideal length of the barrel...any shorter and the gas escapes before it finishes it acceleration...any longer and the friction of the barrel begins to decelerate the bullet absent the push from the gas.

Am I thinking correctly?

thanks,
tex

 

[Nugatory]

Am I thinking correctly?

Pretty much, yes.

The details can get complicated: The force on the bullet is equal to the cross-section area of the bullet times the pressure behind it; as the bullet moves forward the volume increases and the pressure decreases; heat is transferred to the barrel which lowers the pressure; the combustion of the propellant is not instantaneous so the pressure may continue to build even after the bullet starts moving; and so forth. But you've got the basic concept down.

 

[.Scott]

Even with a frictionless barrel, there would come a point where lengthening the barrel would slow the bullet.
The bullet is compressing the air in the barrel in front of it while the pressure in the barrel behind it decreases. Given a long enough barrel, the bullet would begin to decelerate - and perhaps even reverse direction.

 

[thetexan]

Yes. There will be some point where all of the factors come into equilibrium and after that point we're losing ground.

 

[A.T.]

However, there comes a point where, when considering the friction between the bullet and the barrel, the gas no longer can accelerate the bullet and at that point the friction becomes a slowing factor.

Right. If you want to build a super-cannon, you need multiple charges along the way (multi-charge gun):
http://en.wikipedia.org/wiki/V-3_cannon

 

[bahamagreen]

Some of the force is spent imparting the spin of the bullet (rifling in the barrel).