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Originally Posted by buchanan
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.
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I
set up the differential equation and found an analytical solution. You can see the effect of acceleration, which is interesting and instructive.
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As a practical matter other factors argue for a far more conservative value than this optimization would give anyway.
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I tend to agree. Compared to variations in motor performance, friction, battery voltage, and whatever else, it's probably not the major factor in determining what the real-world result will be. But still interesting and instructive.