Gun Recoil: Will Wall Impact Momentum & Velocity?

[RobRobinette]

TL;DR Summary

Does placing a gun against a wall to prevent recoil affect bullet velocity?

I know this is a basic question but it has me stumped.

If a gun is the same weight as its bullet and the gun is free to move when fired the momentum and velocity of the gun and bullet will be the same but in opposite directions.

If we put that gun up against an immovable wall and fire it will it increase the momentum and velocity of the bullet?

I know some (or all?) of the gun's momentum will generate heat in the wall but that's all I think I know.

Thanks in advance for the help.

 

[jbriggs444]

Summary:: Does placing a gun against a wall to prevent recoil affect bullet velocity?

I know this is a basic question but it has me stumped.

If a gun is the same weight as its bullet and the gun is free to move when fired the momentum and velocity of the gun and bullet will be the same but in opposite directions.

If we put that gun up against an immovable wall and fire it will it increase the momentum and velocity of the bullet?

I know some (or all?) of the gun's momentum will generate heat in the wall but that's all I think I know.

Thanks in advance for the help.

As long as the speed of sound in the very hot and highly compressed propellant gasses is fast enough to get to the bullet before it exits the barrel you would expect some effect, yes?

If the speed of sound is not that fast, the effect of the wall cannot catch up to the bullet.

Have you calculated the muzzle velocity of the bullet compared to the recoil velocity of the gun to try to figure out how much effect could be obtained at best?

 

[RobRobinette]

I'm sorry jbriggs, I don't understand how the speed of sound comes into play.

 

[jbriggs444]

I'm sorry jbriggs, I don't understand how the speed of sound comes into play.

The impact of the wall on the butt of the gun can only have an effect on the bullet after that effect has had time to reach the bullet. Such effects propagate at the speed of sound. [The speed of sound in the stock, in the steel of the firing chamber and in the expending propellant gasses. But we might choose to treat the gun as rigid and just concentrate on the propellant gasses].

The bullet is moving down the barrel of the gun. If it gets out of the barrel before the wall's effect arrives then the wall will not have affected the bullet.

 

[RobRobinette]

Something related to my question is called "limp wristing". A semi-auto pistol uses recoil to cycle the action and if a shooter does not hold the pistol firmly enough the recoil of the entire pistol prevents the action from fully functioning and results in a failed reload.

 

[RobRobinette]

Oh, I see now jbriggs. It would be the speed of sound through the gun right? Which would be metal for a metal pistol and wood or composite for a rifle. Let's assume a metal frame gun against a heavy metal wall.

 

[jbriggs444]

Oh, I see now jbriggs. It would be the speed of sound through the gun right? Which would be metal for a metal pistol and wood or composite for a rifle.

I've editted a little more detail into the prior post. I think it would be mainly the speed of sound in the propellant gasses which would matter. Barring a padded stock anyway. But to be fair, I do not have a good feel for the relative speeds of sound in wood, steel and hot gasses.

 

[RobRobinette]

Yes, I see. The effect has to travel through the frame of the gun then through the hot propellant gasses to reach the bullet.

 

[RobRobinette]

I used QuickLOAD, an internal ballistics calculator, to calculate some in-barrel bullet speeds. For a 357 Magnum pistol with a 4 inch barrel firing a 180 grain bullet, the bullet is going 200 ms at 2 inches down the barrel and 291 ms at the 4" muzzle. I googled the speed of sound through metal at 5960 ms.

It appears the shock wave through the metal frame will be almost instantaneous so I'm thinking the bullet's velocity will be affected, but by how much?

 

[RobRobinette]

3300k seems to be a good estimate of propellant gas temperature during the first half of bullet travel and around 3000k when the bullet is at 4 " (at the muzzle of the 4" long barrel).

Can we determine the original question with this new info?

 

[A.T.]

If a gun is the same weight as its bullet and the gun is free to move when fired the momentum and velocity of the gun and bullet will be the same but in opposite directions.

If we put that gun up against an immovable wall and fire it will it increase the momentum and velocity of the bullet?

Yes. Making the mass of the gun effecively infinite maximizes the amount of energy that goes into the bullet.

 

[jbriggs444]

I used QuickLOAD, an internal ballistics calculator, to calculate some in-barrel bullet speeds. For a 357 Magnum pistol with a 4 inch barrel firing a 180 grain bullet, the bullet is going 200 ms at 2 inches down the barrel and 291 ms at the 4" muzzle. I googled the speed of sound through metal at 5960 ms.

It appears the shock wave through the metal frame will be almost instantaneous so I'm thinking the bullet's velocity will be affected, but by how much?

At 3300 K, the speed of sound in air is about 1000 meters/second. The speed in propellant gasses should be similar.

We can put an upper bound on the effect by adding the recoil velocity of the gun to the nominal muzzle velocity of the bullet.

 

[RobRobinette]

So the upper bound would be a doubling of the bullet velocity, correct?

We would lose some energy to heat generated by the shock wave in the metal pistol frame and metal wall, correct? Any way to estimate that energy loss?

 

[RobRobinette]

Yes. Making the mass of the gun effectively infinite maximizes the amount of energy that goes into the bullet.

A.T., can you expand on that? How would that fit into the momentum equation?

 

[Nugatory]

If we put that gun up against an immovable wall and fire it will it increase the momentum and velocity of the bullet?

There is no such thing as an immovable wall - if there were, conservation of momentum would be violated when the bullet went one direction and the gun/wall doesn't move in the other direction. What's really going on is that the the wall is attached to the earth, which weighs about $10^{27}$ times what the bullet weighs - so as the bullet moves one direction with speed $v$, the Earth moves the other direction with speed $10^{-27}v$, an effect that is well and thoroughly undetectable.

Now if you do the algebra and remember that energy is also conserved (sum of kinetic energy $mv^2/2$ for the bullet and for the Earth is a fixed amount) you will find that the heavier the gun/wall/earth combination is compared with the bullet, the faster the bulet ends up moving. But it is worth doing the algebra to see for yourself.

 

[Nugatory]

We would lose some energy to heat generated by the shock wave in the metal pistol frame and metal wall, correct? Any way to estimate that energy loss?

You only need to if you're trying to calculate the total kinetic energy by subtracting those losses from the chemical energy released by burning the propellant. That's correct, but it's a lot of work. It's easier to just calculate the kinetic energy from the muzzle velocity of the bullet (which presumably you already know or can look up) - the answer won't be exact without your hypothetical wall but it will be within a fraction of a percent of right.

 

[RobRobinette]

Thank you Nugatory for the help. What I'm working on is trying to determine if the hold of a pistol has a measurable effect on bullet velocity. With a lightweight pistol with a strong recoil, like a titanium 357 Magnum revolver, will you lose bullet velocity with a frail person holding the pistol vs a big, strong handed lumberjack? If the big guy can slow the pistol recoil through a firm, strong grip how much velocity will will the bullet gain? Is it as simple as measuring gun recoil velocity difference between the two shooters and applying the difference to the bullet side of the equation?

The classic gun recoil theory says:
Gun recoil momentum = bullet momentum + gas momentum + "Jet effect" gas momentum

"Jet effect" is the acceleration of gasses out of the end of the barrel once the bullet "uncorks" the barrel.

How do we square that equation with preventing the gun from recoiling which adds momentum to the bullet?

 

[A.T.]

What I'm working on is trying to determine if the hold of a pistol has a measurable effect on bullet velocity.

It's much simpler to measure the bullet velocity and see. Trying to figure this out from theory, would involve the complex biomechanics of the hand and arm under a sudden load. And the result will rely on many shaky assumptions, so won't be very reliable.

 

[RobRobinette]

A.T., I'm trying to understand the basic physics involved. Can someone show an equation that shows the transfer of energy or momentum from the gun side of the equation to the bullet side?

For example, if we cut the gun recoil momentum in half by restraining its movement would most of that momentum shift to the bullet?

 

[jbriggs444]

So the upper bound would be a doubling of the bullet velocity, correct?

If the gun massed the same as the bullet yes. But that is unrealistic.

If you are going for unrealism, replace the bullet with a bolt threaded into the wall. The recoil velocity of the gun will increase considerably with such an arrangement. (I sure would not want to stand behind it). Much more than a mere doubling.

 

[jbriggs444]

For example, if we cut the gun recoil momentum in half by restraining its movement would most of that momentum shift to the bullet?

You are not cutting the gun recoil momentum at all. You are merely distributing it to the wall, to the house, to the foundations and to the earth. The effect is that now the bullet is pushing off from a nearly stationary weapon rather than a weapon that is recoiling at a few meters per second. Accordingly, the bullet may gain a few meters per second of velocity.

This actually increases the total momentum going into recoil. It must -- momentum is conserved. If the bullet goes faster, more momentum must be dumped into recoil.

 

[RobRobinette]

If it is not momentum then what energy is transferred from the gun to the bullet when the gun is restrained by the metal wall?

 

[jbriggs444]

If it is not momentum then what energy is transferred from the gun to the bullet when the gun is restrained by the metal wall?

What energy is transferred? The energy from the propellant gasses, of course.

One might think about the situation from an energy perspective. The energy provided to the bullet is a physics quantity called "work". Work is computed by multiplying an applied force by the distance over which that force is applied.

If we compare the work done in the case of a recoiling gun to the work done in the case of a stationary gun, we can see that the tip of the recoiling muzzle has moved. The bullet will have traversed less distance by the time it exits the barrel. Less work will have been done. Less energy will have been supplied to the bullet.Alternately, one might think about the situation from a momentum perspective. The momentum provided to the bullet is a physics quantity called "impulse". Impulse is computed by multiplying an applied force by the elapsed time during which that force is applied.

If we compare the impulse applied in the case of a recoiling gun to the impulse applied in the case of a stationary gun, we can see that the tip of the recoiling muzzle has moved. The bullet will have spent less time in the barrel when it exits. Less impulse will have been applied. The bullet will have less momentum.

Note that "energy" and "momentum" are not an either or. The bullet has both. If you know the bullet's mass and velocity then you can compute how much energy and how much momentum it has.

 

[RobRobinette]

I think I understand your work and impulse explanation. In the example where the gun and bullet weigh the same, 1/2 of the energy of the expanding gasses is used to move the gun and half is used to move the bullet and equal work is done between them. If we fix the gun against a wall then no work is done to the gun and the bullet is subjected to the force from the hot gas for 4 inches of travel instead of two so it gets twice the work applied. Sound reasonable?

jbriggs, I really appreciate you sticking with me. You're finally starting to get through (I think).

 

[jbriggs444]

I think I understand your work and impulse explanation. In the example where the gun and bullet weigh the same, 1/2 of the energy of the expanding gasses is used to move the gun and half is used to move the bullet and equal work is done between them. If we fix the gun against a wall then no work is done to the gun and the bullet is subjected to the force from the hot gas for 4 inches of travel instead of two so it gets twice the work applied. Sound reasonable?

Well reasoned in both cases.

 

[hutchphd]

But in the real world even a pistol is much heavier than the slug. At worst (no force holding gun), the recoil of the gun will reduce the speed of the bullet by at most $$\frac {m_{bullet}} {m_{gun}+m_{bullet}}$$. While your argument is indeed well reasoned, this will not be a very large diminution. As the gun is held more tightly, it has a larger "effective mass" and so the effect is even smaller ...

 

[RobRobinette]

Thank you very much hutch for clearing up the relationship between gun weight, gun recoil and muzzle velocity.

 

[RobRobinette]

jbriggs, I was thinking in terms of energy transfer and not in terms of work. I forgot you can expend energy trying to move something that doesn't move and no work is done. Thanks again for the excellent help.

 

[Shane Kennedy]

If the gun is prevented from moving, then all the energy goes into moving the bullet. The propellant pushes the gun and the bullet apart.

 

[John Archer]

In the real world, No, the small person holding the gun vs. a large person, the differences would be within the range of variables in each load (fire a gun 10 times, you will likely see 8-10 different speeds...all else being equal).
For the gun that weighs the same as the bullet vs. gun against a wall. Look at the forces on the bullet.
When the gun moves as fast as the bullet, in a 4" barrel, the bullet will move forward 2" before leaving the barrel.
In the gun+wall scenario, the bullet will be in the barrel for 4"(rounding).
so the bullet will indeed travel faster.
Again, in the real world, no normal bullet comes close to the weight of a normal gun. Add to that gun the weight/resistance of even a small shooter.
The lightest .357 revolver weighs 7000x the weight of the normal 125gn round it shoots.
a deringer weighs around 2200x as much as the bullet.
Add another 35000x for a 5lb arm.
So, yes, there is going to be a difference. The difference is likely too small to measure accurately.

 

[Joseph M. Zias]

I used QuickLOAD, an internal ballistics calculator, to calculate some in-barrel bullet speeds. For a 357 Magnum pistol with a 4 inch barrel firing a 180 grain bullet, the bullet is going 200 ms at 2 inches down the barrel and 291 ms at the 4" muzzle. I googled the speed of sound through metal at 5960 ms.

It appears the shock wave through the metal frame will be almost instantaneous so I'm thinking the bullet's velocity will be affected, but by how much?

Keep in mind that the total momentum has to include the gas leaving the barrel. The Lyman reloading book has the estimate in their equations and you can also find it with a web search. It is common for the gas to add 20% to the momentum.