[buchanan]

The shaft diameter calculation based on peak power should be valid for a machine already moving at the speed at which peak power is developed. There are a couple of other considerations, though.

1) You have to check that the torque is available to accelerate the mass of the machine from a standing start at the chosen drive ratio (diameter). Otherwise your bot just sits on the launch pad and smokes. This calculation should be fairly easy, though.

2) The rate of acceleration must be taken into consideration if you want to (and you should) optimize elapsed time rather than simply a top speed there may not be time/distance to reach. Improved acceleration from a smaller shaft trades off against reductions in top speed. This is a somewhat harder problem, but certainly solvable, though I'm personally too lazy to do it. As a practical matter other factors argue for a far more conservative value than this optimization would give anyway.