Hi and
to the forum.
Unfortunately, the dynamometer figures are all that's available for the 3kW motors and this is the typical way of measuring the actual power output from a motor.
Without having a chart for your particular propellor showing the power requirement of the prop for given rpm it is difficult to know how much power you will need.
Also, the Power requirements for a particular RPM will vary significantly according to the speed of the boat, as the power being drawn to maintain a set rpm will be much greater when stationary and will reduce as the boat speed increases.
I think that the propellor should be suitably sized/geared to allow maximum speed at approximately 3,100 rpm, so that 4kW of output power will still be available at full speed.
If the gearing is too low
(or the pitch and/or diameter of the prop is too small) the motor will be unable to produce maximum power due to excessive rpm caused by insufficient load on the motor.
If the gearing is too high
(or the pitch and/or diameter of the prop is too large) the motor will be overloaded, causing it
(and the controller) to run hot and be very inefficient.
I presume that the hydrodynamics of a boat will be similar to the aerodynamics of a land vehicle
(i.e. the power is roughly proportional to the cube of the speed) which means that it would require eight times the energy to double the speed.
Therefore, doubling the speed would effectively reduce your available range by more than 75% and your battery duration by more than 87.5%!
Here's an easier to understand example:
If your fully charged battery can only power your boat for two hours at a steady 3 knots, it would have a maximum range of ~6 nautical miles.
However, the same fully charged battery would probably last ~15 minutes at a steady 6 knots, giving a maximum range of ~1.5 nautical miles.
I suspect that empirical testing will be necessary to determine how much power is actually required at different speeds by running the boat at various speeds and measuring the motor's power consumption.
Alan