Originally Posted by
cplager
But it's not the same power as defined by the formula. That's the point. (I agree in terms of biomechanics, it is the same power).
Let's concentrate on this, and hopefully all the other tings fall into place.
Where you are mixing everything up is that the force in Prathmann's equation is
not the force applied by the rider on the pedals. It is the force applied by the back wheels on the ground, that is pushing the bike forward.
And in your example those forces between back wheel and ground are different for each example. So for example when going at 30 mph the force is 2 times smaller than at 15 mph. Multiplying that with the speed gets you to the same power.