Recover energy from a wheel

[rc4]

Hi,

The wheel:

http://en.wikipedia.org/wiki/Cycloid

roll up a tube with pressure inside it. The wheel turn on the ground but the tube is fixed (until it is roll up), one end of tube is fixed, other end is roll up by wheel. If there is no pressure at external, there is a work give from the tube, because the red trajectory seems to give a work ?


The force F seems to give a work:


Sure, there is a difference of surface inside/outside circle. But with a big radius for the wheel: 100 m, and a tube of 1cm the difference of surface is only of 6.28 cm and this don't depend of the radius. If I take a radius of 1000 m the difference of surface is always of 6.28 cm. But the works is not the same with a radius of 100 m or 1000 m, no ?