My bike has a L-ion 37v 10ah battery.
If I install the Cycle Analist and set it up to limit the maximun current discharge to 20a, which is the best GM motor for me: 36v500W or 36v750w?
Here's a little comparison between the 250W geared mini motor and the 500W Direct drive motor:
The 36V 250W mini geared hub produces 20.03Nm of torque @172.9rpm (23km/h or 14.3mph with 28" wheel).
To produce this torque it will draw 13.53Amps and consume 487Watts to output 362.5Watts @ 74% efficiency.
The 36V 500W non-geared hub produces 18.24Nm of torque @266.1rpm (35.5km/h or 22mph with 28" wheel).
To produce this torque it will draw 18.43Amps and consume 659.7Watts to output 508.1Watts @ 77% efficiency.
The geared motor will produce 8.68% more torque and use 26.2% less energy, but speed will be 35% slower.
At 362.5Watts output, the geared motor is working well above its 250W rating.
To answer your question, if you are limiting the available power to 740Watts (20x37) I think you might be better off running the 500Watt motor with an extra 80Watts than running the 750Watt motor with 235Watts less power.
(I've assumed the 750Watt motor will require an input of approx 975Watts to output 750Watts with same efficiency)
With a limited current of 20Amps, I would expect the geared 250W motor to give much better assistance up steep hills than the direct drive motors, providing it is able to cope with the strain.
(My rough calculations indicate the geared motor would produce 50% more torque than the direct drive motors)If you had a single speed bike with high gearing and pedalled up a very steep hill, you would soon be exhausted.
If the bike had low gearing you would go a lot further up the same steep hill before you needed to stop for a rest.
The same applies to hub motors, lowering the gearing
(by using a geared hub) will increase the torque and allow steeper hills to be climbed with the same amount of power, but at a slower speed!
Just something you might want to think about.
Alan