without the stress of deafening explosions.
that deafening explosion is caused by air pressure. In the case of most cannons this pressure is caused by rapidly expanding gases, in the case of an air powered cannon... it will still be caused by the rapidly expanding gas.
Thus making an artillery shell air powered wont reduce noise.
Secondly, an air compressor requires energy which your going to have to store and transport, be it giant battery or fossil fuel generator or what, it doesnt matter.
Self propelled artillery shells store the energy in chemical form, and have the required amount of energy ready to go. Just load, arm, and fire.
A compressor would be much bigger, and require an equal amount of power. Unless it were nuclear powered, I doubt the fuel for the compressor would weight less than the chemical fuel powering todays shells.
What I mean is, if you took the weight of the 'gunpowder' on the shells, and the weight of eanough whatever fuel source you used for the compressor to fire the same amount of shell, the 'gunpowder' would weigh less.
Then the weight of the compressor and its generator would be an added setback.
Thus, todays self-propelled shells are compact, cheap, and easy to move around.
A compressor is big, expensive, hard to move, and could easily be destroyed. Imagine 1 armour peircing round incapacitating a whole artillery battery.
The barrels might have to be longer, but a recoil mechanism wouldn't be neccessary.
Why not? Are you familliar with Newton's laws? By conservation of momentum if I shoot a shell forward, something has to gain backward momentum...
EDIT: basicaly a compressed air cannon and a normal cannon work under the same principle: high pressure air rapidly expands forcing the projectile out of the barrel at high speed. The only difference is one uses a compressor to compress the air, the other makes use of an endothermic chemical reaction and Gay-Lussac's gas law.
-Andrew