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Power requirements are so non-linear, and battery life and range increases so much at lower speeds, I don't see hull speed as being my normal cruising speed.

I'd want enough power to achieve hull speed against chop or a head wind, in case of emergency, but I can't see myself carrying enough battery to do it very long.

The math predicts a smooth curve - lower power means lower speed and longer range. But it's almost certain that there will be certain power levels that are more efficient.

I don't, though, think that anyone could predict where they will be. I'll need to experiment.
The variability in propeller performance and battery performance is why I recommend choosing a single operating speed. That is a flat water, light wind speed. I suggest using something near hull speed so that the drive can then cope with wind and waves etc. without the hull coming to a stop.

My experience building electric drives is not great but two things were learnt. Firstly a propeller spinning at a chosen rpm provides a constant thrust. How that translates to boat speed depends on everything from how clean the prop and hull are to headwinds and waves. Secondly motors are most efficient operating at full design speed. Following that principle, slowing the motor down means the motor can run for longer on a battery but it is not likely to travel further. (That assumes all speeds are within the power curve of the propeller.) This issue is confused by the characteristics of batteries. The amps/hrs available from a battery and how that changes with state of charge is probably more significant than motor efficiency. Lithium batteries are more predictable than lead acid.

What I found was that the problem got more and more complex as I was building. In the end I chose a propeller and a battery and built the drive to give approx 80% of hull speed for as long as possible. My customer then chose different batteries and messed up all my testing and planning.
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