I'm trying to size a motor for an e-bike, but I'm confused as to what motor parameters determine the maximum torque that it can output (Kv or power in watts); I've found the following formulas:
Power (watts) = torque (Nm) * angular_velocity (rad/s)
also note that P = I(amps) * V(volts)
Torque (Nm) = Kt * I (amps)
Where Kt is the torque constant or (1/Kv), and Kv is rpm/volt
So let's say we have a 1000 watt motor with a Kv of 200, the motor operates at 24V. Let's also say that we're talking about a low rpm (60 rpm);if we multiply rpm by (2 * pi / 60) then we get angular velocity. Using P = I*V we can calculate the max current to be 41.6 amps.
So according to the first formula, with a low rpm of 60 we could get a torque of ~159 Nm at max power.
Using the second formula we get a torque of 0.208 Nm at max power
These are massively different, and would require changes to gear ratios, battery sizes, material choices, etc.
So my question is: which one is right? Is torque determined by the Kv of the motor? or is torque determined by the power rating of the motor?