Hello !

I've tried the search motors but I don't know why, I mostly find awful explanations/strange translations, copied/pasted content.

I can't rent any bike near my location.

Me + my luggage + a child = 100kg. I can't find any resources explaining what weight a torque can really carry (especially with hills). Something like :

80kg - 5%hiill - 50Nm = 14kph (for example).

The torque computation is very straightforward: the tractive effort that pushes the bike uphill has to be at least as large as the weight force pushing you downhill.

In your example: 100kg (you+bike) *10N/kg (earth gravity)*0.05(5% hill) = 50 N tractive force.

To compute the torque needed at the rear wheel, multiply with the radius of your wheel. Let's assume it's a 700c wheel, so the radius is about 0.34m, so the torque needed is 17 Nm. For a 10% hill you need 34 Nm, for 20% about 70Nm. (% gradient is the tangent of the incline angle, the weight force pushing you downhill is going with the sine, but up to 20% the difference is negligible.)

For a hub motor, the torque at the wheel is the same as the motor torque (or gear output torque, for a geared hub motor). For a mid motor you have to multiply with the chain gear ratio. Motor torque = wheel torque * chain ring size / sprocket size, for example 17 Nm*38T/21T= 31 Nm needed from the motor.

To compute the speed with which you can climb the hill, divide the motor power by the tractive force needed, so 250W/50N = 5 m/s, or 18 km/h. This works as long as you are going slow enough that air drag does not play a role, up to about 15 km/h or so.

This is all based on the basic relations

- torque [Nm] = force[N] * lever arm [m] (or radius of a wheel),
- work = force * distance,
- power = work/time = force*speed,

and metric units make it all really simple.