Is there a physics reason why compressed air projectiles are more powerful than elastic launched ones?

Question

Is there a physics reason why compressed air projectiles are more powerful than elastic launched ones?

Answer 1

If the compressed air is IN the projectile, then the force of the escaping air is being exerted on the projectile for as long as there is a pressure differential.

With an elastic launch, once the projectile has left the launcher; there is no longer any (forward) force being exerted upon it.

Answer 2

But David N , what if the compressed air is not in the projectile itself  ( like in the case of air gun ) ?

Answer 3

Projectiles in Physics are only as powerful as the force you put behind the object you are making fly. In theory, you can make any projectile as fast as you like it with both materials and methods.

But to answer this question through calculations...

Rubber bands/springs use the fromula

Force = .5kx^2

k= Spring constant.

x= is the distance it is stretched.

In compression.

Force = PxA

P = Pressure

A = Area

It's like blowing up a balloon. As you blow up, the force is the same for the air and the elastic. As pressure goes up, the balloon gets tighter. Once the elasticity constant is stretched beyond its critical point. Pressure takes over and pops the balloon.

Since you can always increase the pressure in an experiment and you can't change a materials Elasticity/spring constant. Air is easier to use.

The reason you don't see that in the world today is because we have perfected our ability to compress air, rather then perfected the elasticity of materials. In addition, air is cheap in comparison to elastics.

We don't pay much to breath.  

Answer 4

Generally speaking, we can compress air more than we can compress a comparable spring.  From pV = nRT = K constant at a fixed temperature T as V --> v (the volume of air is compressed), where v < V, p --> P (the pressure goes up), where P > p, to maintain the constant RHS of the equation.  

Thus, the force on the projectile is F = PA = KA/v upon release giving the projectile a = F/m = PA/m = KA/mv acceleration off the muzzle.  As we can see, we get more acceleration for more compression to v.

Similarly F = k dX is the force on the same projectile m; so that a = F/m = k dX/m; where k is the spring constant and dX is the compression.  Set the two accelerations equal so that KA/mv = k dX/m.  Then we have KA/v = k dX and KA/kv = dX if the spring and the compressed gun are to have the same muzzle acceleration.

And now we are beginning to see why the spring has limits the compressed air does not.  A spring can only be compressed so far, depending on the diameter of wire in the coil.  Gas, when compressed from V --> v can be compressed considerably more v = (1/100) V is not uncommon.  But dX = 1/2 X is about the limit for an uncmpressed spring of length X.

The bottom line is that air can be compressed relatively more than a spring so that air has relatively more potential energy than a comparable compressed spring.  Of course, one can gin up a small air gun vs a very large spring and the spring would win, but it would not be a comparable spring...not a fair fight in this case.