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The basic principle of the firmware is the relationship _Motor power = assistance factor * human power _
Mechanical power is speed * torque
For the motor, this means: _Motor power = rotor speed * motor torque _
For human power, this means: _Human power = cadence * torque at the crank _
So we can write: _Rotor speed * motor torque = assistance factor * cadence * torque at the crank _
With a middrive motor, the rotor speed is always in a constant ratio to the cadence due to the internal gear Motor speed = gear ratio * cadence
Therefore, the cadence cancels out of the equation.
_Gear ratio * Cadence * Motor torque = Assistance factor * Cadence * Torque at the crank _
Solving for torque yields: _Motor torque = Assistance factor * Torque at the crank / Gear ratio _
The motor torque depends solely on the motor current and the motor constant KM. _Motor torque = Motor current * KM _
It follows that: _Motor current = Assistance factor * Torque at the crank / (Gear ratio * KM) _
The various constants in the formula can be combined into a single constant:
Motor current = System constant * Assistance factor * Torque at the crank