Modelling the effects of gun-recoil

[_RAAF_Stupot]

This should be an easy problem for anybody with high school physics to solve.

Remember, momentum is always conserved! Ignore air resistance!

Momentum = Mass x Velocity

What is the Mass of a 20mm (Hispano) round?
What is the Muzzle Velocity of a 20mm Cal round?

What is the Mass of a (say half-loaded) Spit MkV?
Assume the Spit is doing 200 kts.

That is all the info you need to determine by how much the Spit slows down after a single cannon round is fired.




Now, as far as the force and power of the recoil is concerned - this depends on how long the recoil is applied to the aircraft. That in turn depends on the length of the barrel of the cannon (assume that the round travels at 0.5 x muzzle velocity right through the barrel). Once the round has exited the muzzle, the recoil is effectively absent. (Ignore mass of propellant gases).


The force of the recoil = Mass of Round x Acceleration of Round

Acceleration of Round = Muzzle Velocity / Time through barrel



Power of recoil = Change of Kinetic Energy / Time through barrel

Kinetic Energy = 0.5 x Mass of Round x (Muzzle Velocity)^2


To make all these sums work, use consistent units....

Mass (Kg) Kilograms
Velocity (m/s) Metres per second
Time (s) Seconds
Force (N) Newtons
Energy (J) Joules
Power (W) Watts

Assume 1 knot = 1.8 km/h

I'm too tired to actually do these sums now, but this is a good problem for anybody doing High School physics that has exams coming up.