# Projectile acceleration in barrel

## Main Question or Discussion Point

Another gun-related question:

I'm building a pneumatic airgun and I'm trying to find out what pressure/barrel lenght I have to use for a given muzzle velocity. I've done a bit of number crunching but I keep coming up with insane barrel lenghts, and that's not even considering any friction. Here's what I did:

I want to accelerate a 0.2 gram 6mm bb to a velocity of 300m/s using compressed air.

I take a pressure difference of 30 bar (3,0 * 10^6 Pa) so a total pressure of 31 bar and a surface area of 2.83 * 10^ -4 m^2. P = F/A, therefore F = PA

3 * 10^6 * 2.83 * 10^ -4 = 84,9N, so when I initially pull the trigger the air pressure is pushing my bb forward with 84,9N of force. If the pressure behind the bb at the moment I pull the trigger is 31 bar and at the moment it exits the barrel is 1 bar, this leaves me with an average force of 84.9/2 = 42,45N.

a = F/M (where a = acceleration), F is 42.45 and M = 2 * 10^ -4, 42.45/2 * 10^ -4 = 212250 m/s^2

At that rate of acceleration, my bb reaches 300 m/s after accelerating for 0.0376 seconds. The thing is, by then it has already traveled 300/2 * 0.0376 = 5.64 meters, which is a bit unpractical.

Modern air rifles use a lot less air to accelerate much heavier projectiles to similar velocities with 50/60cm barrels.

What am I doing wrong here?

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OldEngr63
Gold Member
Well, for one thing, even if your receiver is charged up to 31 bar, the pressure behind the bb will not instantaneously jump to 31 bar.

Secondly, as the bb moves down the barrel, the volume behind the bb is constantly increasing. You can't expect to keep a steady 31 bar in that volume at all times.

You need to give some thought to the fluid flow problem here.

I did not check your numbers; there could be other errors as well, but the one above strikes me as the big one.

it might help to think in terms of energy instead of acceleration and time.
.2 grams = .0002kg
KE=1/2mv2 so...
(3002)(.0002)(1/2)=9 Joules
Joules = force * distance so...
9=42.45x where x is the length of the barrel, so, about 4.7 meters

clearly you need more pressure. CO2 is a commonly used propellant and has a vapor pressure of 60 bar at 22 degrees C. If that pressure were maintained over the length of the barrel it would be more like 1.2 meters.

• cheekibreeki
it might help to think in terms of energy instead of acceleration and time.
.2 grams = .0002kg
KE=1/2mv2 so...
(3002)(.0002)(1/2)=9 Joules
Joules = force * distance so...
9=42.45x where x is the length of the barrel, so, about 4.7 meters

clearly you need more pressure. CO2 is a commonly used propellant and has a vapor pressure of 60 bar at 22 degrees C. If that pressure were maintained over the length of the barrel it would be more like 1.2 meters.
How did you get those numbers? if E = F * S then 9 = 42.45 * x, then 42.45x = 9, then x = 9/42.45, x = 0.212. According to that formula the lenght of the barrel should be only 21.2 cm instead of 4.7 meters. ???

sophiecentaur
Gold Member
At that rate of acceleration, my bb reaches 300 m/s after accelerating for 0.0376 seconds. The thing is, by then it has already traveled 300/2 * 0.0376 = 5.64 meters, which is a bit unpractical.

Modern air rifles use a lot less air to accelerate much heavier projectiles to similar velocities with 50/60cm barrels.
That's nearly Mach 1. Can that possibly be correct? You can see the pellet as it goes away from you, unlike a .22 rifle bullet.
The limit for the energy of a legal air gun is only 12ft lbs, affair

That's nearly Mach 1. Can that possibly be correct? You can see the pellet as it goes away from you, unlike a .22 rifle bullet.
The limit for the energy of a legal air gun is only 12ft lbs, affair
Actually, there is no legal limit here in the Netherlands. And yes, using an airSOFT gun, which generally shoot around 70-120m/s, you can see the bb fly away, but I'm not building an airsoft gun. I'm building an air rifle, 6mm is just for the concept gun.