Recoil Energy Calculations

[saefroch]

I think I know how one would calculate recoil energy from just the projectile, use conservation of momentum to find the velocity of the cannon based on that of the projectile, then calculate kinetic energy from that, right?

What I'm confused/lost on is how one can calculate recoil based on the expanding gas travelling out the barrel. Normally, I can see how this could be negligible, especially with a high-mass projectile, but with my Trident it's not. There is only slightly more recoil shooting a 11/32" ball bearing than there is with no projectile. So... how does one calculate recoil energy produced by an expanding gas?

[inonickname]

Well, you should be able to calculate the mass of the gas fairly easily... And I suppose use a value roughly that of your projectile speed as the velocity value?

[Ragnarok]

Normally, I can see how this could be negligible

Less so than you might think, with spudguns. Lots of high density air expanding as far as possible - yeah, that's a lot of momentum.

So... how does one calculate recoil energy produced by an expanding gas?

Calculate mass of gasses (air, or an air/fuel mix will be around 1.2-1.3 grams per litre at atmospheric pressure) then multiply by their speed of sound. This is a close enough approximation to the velocity of the gasses to be sufficient. (And yes, the gasses will be moving faster than the projectile!)

This gives you the momentum of the gases, so then add the momentum of the projectile. Divide by launcher mass to get recoil velocity. Solve kinetic energy equation for launcher mass and recoil velocity. Simples.

[saefroch]

Dang. I guess it really could be that easy... thanks!

EDIT: I just got a recoil energy of 0.0937 joules. I don't think that's right. Can somebody check it?
Using:
Mass of cannon: 7lbs
Mass of projectile: 2.75 grams
Velocity of projectile: 912fps
Chamber volume: 5.388in^3
Chamber pressure: 1,000psig

I'm converting all my units correctly... I think.

[linuxexorcist]

The trident's piston probably has a lot more mass than a .36" BB, and probably contributes to recoil more than said BBs will, that's where I'd look for your recoil, not the moving gas

[saefroch]

Wouldn't the recoil from the piston be in the forwards direction though? We'd be looking at impact force there, which I also have NO IDEA how to calculate. I can mass my piston tomorrow on a friend's kitchen scale, it's too light to mass on my bathroom scale .

[linuxexorcist]

The piston's recoil would be forward, at first, but when it comes to a stop at after actuating, it works like a little hammer

i know how to calculate the impact energy, but not the force, it's just the kinetic energy of the actuating piston (Ek=mv^2), the majority of that energy will be transferred into the trident and your shoulder, unless there's a bumper to mitigate the force of impact

[Ragnarok]

The piston's recoil would be forward, at first, but when it comes to a stop at after actuating, it works like a little hammer.

No. Because it is being accelerated, AND being brought to a stop within a contained system, it has no actual recoil. A "kick" maybe, but no recoil - in the same way that a springer air rifle just jolts, rather than actually recoiling.

@saefroch:I get a result of 2 Joules.

0.00275 kg projectile at 278 m/s = 0.76 Ns
88 cc chamber at 68 atmospheres = 0.0078 kg gas. At 340 m/s = 2.65 Ns
0.76 + 2.65 = 3.42 Ns (yes, I know it doesn't add like that, but I'm rounding the numbers here)
3.42 Ns recoil on a 3.2 kg launcher = 1.1 m/s recoil.
1.1m/s ² * 3.2 kg / 2 = 2 Joules, rounding to the appropriate number of significant figures. (One, as the launcher mass was only given to one.)

[saefroch]

Okay, thanks for the help. I don't know what I did wrong, but I have a feeling I misplaced a decimal, because I tried it again and got pretty much what you got.

significant figures

Yeah... I need a better way to weigh things around here. Anyway, thanks for the help!