Hi, good post
Here wiki link explained that rocket engine can get 70% energy efficency and if the rocket travel at the same speed as exhaust gas then all that energy is converted to kinetic energy:
What do you you think about that link?
Also I think gun can get much higher than that as diesel engine can get to 60% and pressure in gun chamber is much higher than piston engine.
I heard that burning temperatures is the worst factor contributes to barrel erosion. Could you explained about this a little?
Hmmm. Interesting.
What the wiki-author means by 'propulsive efficiency' is the actual energy imparted to the burning fuel stream leaving the rocket nozzle vs the initial chemical energy stored in the rocket fuel.
What I mean by 'propulsive efficiency' is the energy imparted to the projectile (not a complete rocket assembly) as it is the projectile which is being fired at the target.
Also, there is also a mis-conception here, as guns impart energy to their projectiles by pressure from the burning gasses, with chamber pressures as high as 50,000+ psig.
So as an example for a 155 mm (6 inch) gun/howitzer the base has an area of A = pi * r^2 in this case:
A = 3.14 * 3^2
A = 28.27 square inches
So the propulsive force is gun chamber pressure of 50,000 lbs / in^2 * 28.27 in^2
F = 1,413,716.7 lbs! (wow!)
Rockets on the other hand rely on ejecting mass at high speed out the back nozzle to accelerate the projectile.
This is called THRUST and generates a propulsive IMPULSE, and is less efficient than accelerating a mass initially by pressure (up to certain ranges and velocities).
If I remember correctly, it is expressed as a change in momentum p, where p = m * v (mass x velocity).
So (change in momentum) dp/dt = m * dv/dt + v * dm/dt. (derivative of a product)
The first part of this is Newton's second law; F = m * a, where a = dv/dt. (acceleration)
The second part is the IMPULSE, = v * dm/dt where the change in momentum is produced by a stream of mass, (the rocket fuel) ejected a the rocket's exhaust velocity, v.
This is the basic rocket equation.
The problem is that the rest of the rocket casing/staging is superfluous or rather, added baggage and mass needed to contain the propellant to accelerate the projectile.
In a gun, what will matter to the target is the projectile, and although a great enormous rocket assembly flying at you might seem impressive, for short ranges, it is a rather difficult and wasteful way to get that projectile on target.
Just look a the small quantity of propellant a gun (say a 52 cal 155 mm howitzer) needs to fire its 50 kg High Explosive ERFB-BB round to a range of 50+ km vs the vast amount of rocket propellant needed to fire a similar missile warhead the same range and you will see the vast difference in efficiency between a gun and rocket over these relatively modest ranges.
Comparing a gun to an engine works up to a point, the fact is most large marine diesel engines have maximum efficiency when the stroke is around 3.5 times the bore, any more and friction losses outweigh gains.
In a 52, 60 or longer caliber gun barrel, the friction problem gets worse.
And to impart maximum energy to the projectile, the propellant must be low-temperature and slow-burning exerting a prolonged 'push' onto the projectile.
Still there is the matter of diminishing returns, as longer and longer gun barrels do not provide the same degree of energy to the projectile.
As to the barrel erosion, I would think that's rather obvious, as high temperatures melt and erode the metal inside the gun's chamber and barrel, wearing out the gun.