Horsepower & electric motors
I'm also a pilot and electrical engineer. With regard to horsepower, an electric motor can deliver much more than its rated power, BUT there is no such thing as a free lunch. The reason is that you can put up with short term heating as long as you don't fry the motor. You will be taking the power from the battery.
This means you can size the motor for cruise, and overload it short time for takeoff and initial climb. When speed and altitude permit, you throttle back to "cruise climb"/MECO power just like any other airplane.
Electric heating effects are proportional to the SQUARE of the current: "Twinkle, twinkle little start, power equals I (current) squared R (resistance)."
A motor on low voltage will put out the same power, but it will draw more current and usually fry itself. I work in a hardware store and we sell big, 240-volt air compressors; if you try to run them on 120 the thermal breaker in the motor will trip--that's the good news. The motor is trying to draw twice times the amps resulting in four times the heat.
--- Doug Drummond