# Power consumption for an in-wheel motor

I'm trying to estimate the power consumption of an in-wheel electric motor. I used the formula

$$P = T\cdot\omega + K_m\cdot T^2$$

where T is the torque, ω is the motor angular velocity and $$\K_m\$$ is a constant who takes into account power electronics and motor copper losses. I plotted the power over time.

Is this the right way to calculate the power consumption? How can I treat this topic in a not too detailed but exhaustive way?

All the best.

• "not too detailed" and "exhaustive" seem mutually contradictory to me. Which do you want? – Dave Tweed Dec 6 '18 at 13:15
• @DaveTweed exhaustive is good – Manuel Dec 6 '18 at 13:35
• Normally, the motor constant Km applies to copper losses in the motor only. – user28910 Dec 6 '18 at 14:58

## 1 Answer

A large part of the losses are proportional to current squared and thus proportional to torque squared. There is a small amount of power consumed when the controller is energized but the motor is stopped. There are some friction and windage losses that are proportional to speed and speed cubed and much influenced by torque. The controller switching losses are proportional to both speed and torque. The motor has some iron losses that are proportional to speed and some power of speed.