Im still confused about hub motor max rpm and the impact of running a 36v motor with a 48v battery/controller?
Is the motor max rpm a constant regardless of the input voltage or does it also increase inline with the voltage supplied?
This seems like a good place to ask
Cheers..
btw links to homework/recommended reading are welcome
All electric motors have a constant called kV. It's a direct relationship between volts and rpm. When you change from 36v (10S) to 48v (13S), the motor will spin 30% faster. How fast it goes depends on the kV. A 36v that spins to 250 rpm has a kV of 250/36, so at 48v, it'll spin to 48x250/36 = 333rpm.
The kV comes from the back emf. When any motor turns with or without power, it becomes a generator. The faster it spins, the more volts it generates. The voltage generated is in the opposite direction of any battery voltage powering it, so it has the effect of reducing the applied voltage. At a certain speed (max rpm), the generated voltage is the same as the battery voltage, so the net voltage is zero and the motor no longer has any power to turn, which is why all motors have a max speed and the power ramps down as you approach it.
The controller fires pulses of power to the motor. The pulses have a width and a height. The height is the voltage (36v or 48v) and the width is the time the pulse lasts in microseconds. The energy provided in each pulse is proportional to the width times the height of the pulse, so there is 30% more energy in each 48v pulse compared with a 36v one, which manifests itself as more torque.
The current is controlled by the width and frequency of the pulses. The controller is not very sophisticated. The battery is connected directly to the motor, but is blocked by MOSFETs. The MOSFETS are nothing more than gates that open and close, so every pulse is the height of the battery voltage and the power/current is controlled by how long the MOSFET is open and closed.
Motors have an efficiency curve. They have low efficiency at low rpm and highest efficiency at about 75% of max rpm. If you increase the voltage from 36v to 48v, the rpm for best efficiency increases to 75% of the new max rpm, so it's not a good idea to increase the voltage if you only ride slowly. Generally, going from 36v to 48v doesn't make a big difference on efficiency, but going from 24v to 48v would or 36v to 72v.
There's no point in increasing the voltage of a crank-drive bike because it would make the cranks spin faster and reduce the motor's efficiency at your normal comfortable pedal speed. Instead, you should increase the current, unless you have a background in BMX and like to spin at 120rpm.