Many thanks for quick replies. Great forum. I weigh 12 stone and live in rural Wiltshire. I believe many 250 watt rated motors can actually deliver 700 watts or more. Would this not be enough if torque multiplied by drive through multi gears?
I'm afraid not, the Quando I mentioned has internal gear reduction and has a nominal peak power of 720 watts, but in fact has been measured at 1000 watts gross peak power. I live in the North Downs and have a few 25% hills, one 33% hill and only yards from my home a stretch of 22.5%, so plenty of experience of what's possible. The 14% mentioned is a much as it can do unaided
Your 12 stones is just over 76 kilos, plus a typical e-bike weight of 24 kilos brings the gross climb weight to 100 kilos For climbing unaided a 25% hill at the lowest comfortable balance speed of 5 mph, that calculates to an absolute minimum of 570 watts of continuous power rating, a bit over double the legal figure.
However, that's still not enough, since you specified that the bike must achieve 15.5 mph easily, but the slowest a motor geared for that will give that maximum power is about 7 to 8 mph, depending on the motor design. Below that the power starts to tail off. To get that 570 watts continuous at a 5 mph climb speed, the continuous power rating of the proposed motor would have to at least 850 watts, over three times the legal limit.
The equation I've used for simplicity is:
Pu = 9.81MVgG
where Pu is the power needed in Watts, M is the total mass of the rider, bike and cargo expressed in kilograms, Vg is the ground speed in metres per second and G is the gradient expressed as a fraction that is the elevation changed over the distance travelled.
I've made a tiny addition to the watts to account for rolling resistance and frictions.
For steeper gradients such as 25%. G should really be changed for:
sine [tan-1(rise/run)]
but I haven't bothered since your requirement clearly cannot be met anyway.
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