Pressure in a soccer ball

Question:

How does the internal air pressure of a soccer ball affect how far and how fast it rolls?

Answer:

First of all we must set out a few things that are constant. Lets imagine that the ball is already rolling at a fixed speed and that the surface over which it is rolling is flat – like Astroturf (the synthetic surface used in this country for hockey pitches).

I think that the higher the pressure (within reason) inside the ball the further it will roll.

My reasons are:
(a) a firm ball will only touch the ground at one small area while a soft one will touch over a larger area. Now according to the laws of friction the area of contact should not matter but this case I think it will affect how far it goes. A smaller area, less friction and so a greater distance.
(b) If it is really soft it will not roll at all – simply flop over. The initial kinetic energy of the ball will not be sufficient to move the rubber skin over itself

Now lets consider how fast the ball might roll.
Once again I think that a firmer ball will roll faster after it has been given a specified initial impulse by either a kick or a push.

My reasons are:
(a) the air inside the ball is springy but if the pressure is low enough when you kick the ball the springiness will be less marked. I don't see the ball moving off at high speed. The low pressure air will 'absorb' the impact rather like a cushion. The ball will more or less stay where it is and the foot will simply sink into it!
(b) if the pressure is high then the energy of the kick will be transferred to the ball as kinetic energy. Very little will go into distorting the ball.

I think that you ignore the mass of the air within the ball in all cases as this is negligible compared with the mass of the 'skin' of the ball.

In an extreme case you could consider the ball as having a light rigid metal skin and so the impulse of the kick transfers a maximum amount of kinetic energy to the ball and virtually none to changing its shape.

Any bumps in the pitch you will have to think about the gain of potential energy as it rises up a bump. This will be more marked if the ball is not spherical, in other words if it the internal pressure is low enough so that the weight of the ball can distort it. I agree that if friction is ignored this should be returned as kinetic energy as it descends the other side of the hill but if there is friction then it will finally meet a hump that it cannot ascend.

I suppose that a very flabby ball is a bit like the crawler tracks on a tank when moving over the ground.