Recoil Buffering Physics Explained

[Microcephalus]

Ciao people

I'm having trouble wrapping my mind around the physics of the follwing:

A cannon fires a 1 kg cannonball that leaves the barrel at 1000 m/s

The cannon weighs 1000 kg.

Now, conservation of momentum suggests that the residual velocity of the cannon would be 1·1000 + 1000·v = 0 → v = -1 m/s

Fine. Now to my problem:

The 1000 kg mass is not really the cannon, it is just that bolt (?) thing that recoils and spits out the empty shell.

That is in turn connected to the actual cannon via a spring. We can assume that the actual cannon is rigidly connected to a big honking warship, so we can say that the mass of the cannon is infinite and the spring has to absorb all the kinetic energy of that bolt.

I would assume that the spring has to absorb E=½mv² = ½·1000·1² = 500 Joule energy?

Is this correct?

I'm confused because the cannonball seems to have the kinetic energy ½·1·1000² = 500 kJ - a thousand times more - and somehow that strikes me as odd and suspicious. I seem to recall something about large warships drifting sideways substantially after a firing off a full broadside salvo, which would suggest that they get charged with a lot more kinetic energy than a paltry promille of what the cannonballs get. Or am I wrong?

Anyway, if that bolt thing recoils 1 m to eject the empty shell, and then snap back into the barrel, the spring(s) would need to absorb those 500 J over that 1 m. If the spring excerted a constant force, that force would be E=F·s → 500/1 = 500 N.

In reality, a spring is more likely to increase its force linearly over distance, so the maximum force would be 1000 N if it ramps constantly from zero.

Now to the really confusing part - I don't really have the muzzle velocity of the cannonball. I just know the force exerted on it when it shoots off.

The cannonball is sent off with a 50 kN force. That should accelerate it to 1000 m/s in 10 m according to v²=2·a·s and during 0.02 s according to s = ½·a·t². The same force would hit the bolt - 50 kN on a 1000 kg mass gives a = 50 m/s². During 0.02 s is 0.01 m, and 1 m/s speed. So the bolt is kicked back during one centimeter and then brought to stop in the next 99. Okay, seems legit.

Here's where my brain dislodges - why is it that the cannonball is sent off with 50 kN force while the recoil is only like 1000 N? Doesn't that kind of go against what old man Newton said?

 

[kurtlesker]

that's because the cannon ball force is instantaneous instead of constant. Once the cannon ball loses contact with the cannon there is no force. might be easier to think in terms of momentum conservation. to actually spring compression distance as a function of time is kind of difficult...

 

[256bits]

The cannonball is sent off with a 50 kN force. That should accelerate it to 1000 m/s in 10 m according to v²=2·a·s and during 0.02 s according to s = ½·a·t². The same force would hit the bolt - 50 kN on a 1000 kg mass gives a = 50 m/s². During 0.02 s is 0.01 m, and 1 m/s speed. So the bolt is kicked back during one centimeter and then brought to stop in the next 99. Okay, seems legit.

Here's where my brain dislodges - why is it that the cannonball is sent off with 50 kN force while the recoil is only like 1000 N? Doesn't that kind of go against what old man Newton said?

there is two parts to your dilema.

The gases in the barrel push equally on the cannonball and the bolt, so in your case 50kN, but only for a fraction of a second.

The 1000 N force you are talking about is the force need to stop the bolt from moving, and that what the spring provides, but for a longer duration.

 

[Microcephalus]

Thanks, I think the picture is clearing in my head now.

The 50 kN does kick on the bolt, briefly. The 1000 N is then required to catch the motion, over extended time. We're not breaking any Newtonian laws here.

Also, it is fully acceptable that one mass gets less kinetic energy than the other.

 

[Bob S]

See the effect of a recoiling howitzer cannon at

OUCH!

 

[Microcephalus]

Ouch indeed.

What is that recoiling component called in english, really? I google for cannons and howitzers but the closest I found was "bolt". Breech?

English is not my primary language and I never did any military service so the nomenclature and taxonomy of guns is not quite my forte.

 

[Bob S]

See annotated breachblock in 3rd photo of howitzer in

http://www.bravecannons.org/the_gun/m1a1.html

 

[haruspex]

the cannonball seems to have the kinetic energy ½·1·1000² = 500 kJ - a thousand times more - and somehow that strikes me as odd and suspicious. I seem to recall something about large warships drifting sideways substantially after a firing off a full broadside salvo, which would suggest that they get charged with a lot more kinetic energy than a paltry promille of what the cannonballs get.

Don't worry about the energy - as you say a lot of that is dissipated in the spring.
The recoil momentum of 1000 kg.m/s is conserved all the way to the warship.
The Japanese Yamato class battleship weighed 72000t and fired 1.4t shells.
Don't know the muzzle velocity, but 1000m/s is about the right order of magnitude for 40km range.
So the recoil speed of the ship from a single shell would be about 2 cm/s.