Hi giguana
My 36V Ezee NiMH was about 41.5-42V hot off the charger when new IIRC & down to 36-36.5V when it cuts out at full discharge, the low voltage cut out on Ezee controller about 31 or 32V I think?
I haven't used lithium, but think they have a slightly higher voltage freshly charged (they are 37V 'nominally') though they have been less suitable for supplying high currents, power supply cutting out under continuous heavy load/high power needs, due to either voltage drop in the controller or their 'management' system cutting out power. The Ezee lithiums now have a different management system intended to reduce occurrences of cut-out.
Regarding torque, as I understand it a direct-drive hub motor (no gearing) like crystalyte 400 or bionx would be less efficient & use rather more power at low speed than a geared hub motor like the 8fun in the Ezee Quando for example (for the same wheel size & max rpm of motor) so yes a high speed ungeared motor would use more power & less efficiently going uphill, but on the flat or only marginally uphill might be marginally more efficient due to zero loss through gears
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I'd say that with either motor type its best to keep some momentum if possible because highest efficiency is always at higher motor revs, but on hills and/or at higher speed that must be balanced with the power required to go that speed
and climb a hill, so in pratice there is an optimum speed for any given bike, motor, rider & battery combination which in all honesty you'd probably have more success finding it by experience & intuition as by any calculation you might try!
Don't forget to regulate your tyre pressures, check your chain & keep you battery cosy & warm too!
I tend to try to keep a constant speed & throttle setting, more or less, on the flatter bits & for gentler uphill gradients I tend to try to keep the throttle constant & pedal a bit more, even if speed drops slightly: that way I've a better idea of the power usage & my overall range. Range wise, I know I can get about 30 or more miles at 15mph & 15-20 miles at 20mph or so in my gently undulating terrain, so I can juggle speed & range accordingly. The speed you use on hills & how much pedal assist you give too is a much bigger factor with respect to range than speed/pedal assist on the flat.
Forgot to say, you can use the motor as much as you like on fast downhills since little power used at max revs anyway, also NiCad batteries are apparently the best for high power use because they can give all their power in a very short time - except they contain toxic cadmium, so use is being discouraged.
Hope thats useful & correct, and a happy new year to you
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Stuart.