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Old 09-27-2022 | 04:40 PM
  #49438  
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gigaplex
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Originally Posted by PDR
There isn't a simple formula to calculate motor power from resistance. Motors have counter-intuitive and complex behaviours. There is definitely a resistive element to stators, but for their intended purpose, they are dominated by inductive characteristics.

One of the really important things to remember is that essentially, a brushless motor in an RC car is not a DC device. Voltages and currents under any condition other than stopped are a very merry dance. Modern ESC's do a great job of dealing with that and hiding it from view.
There are 3 commonly described behaviours to an electric circuit: resistive, inductive and capacitive. In a pure DC circuit, they can very simplistically be modelled as resistors. In the real world, there are almost no pure DC circuits. The chunky wires from your battery to the ESC have all three characteristics, but that part of your car's circuit will have inductive/capacitive measures so low that they won't impact anything.

The stator is a very different beast. It is, by design, an inductor. It converts electric energy to a magnetic field. A resistor converts electrical energy to heat. Inductors are measured in units of Henrys (most motors have values in the single or two-digit micro-Henrys range). An inductor has dynamic resistance, called reactance (see https://en.wikipedia.org/wiki/Electrical_reactance), which changes according the change in electricity flowing through it. Its reactance is a function of frequency. So, the same inductor will have different resistance at different frequencies. Weird huh? Because of the way the magnetic field and the current flow interact, it's a time-shifting frenzy.

An example is if you measure the resistance of a power transformer, you'll end up with a pretty low value. Plug it into your electricity mains (240V here, since we're big and bold) with no load on the output and no power flows. Wut?? This is an inductor at work - the stator in a brushless motor is very similar.

Where it gets complimicated is that the frequency is not fixed or necessarily straightforward. The ESC switches the phases in sequence - maybe the frequency is then the same as the RPM? Close, but ESCs also use PWM (pulse width modulation), so it gets messy.

The design of the stator, the position and shape/strength of the rotor's magnet all affect how that magnetic field are formed. The rotor spins, making the field even more dynamic (back EMF is why motors don't accelerate for ever) and at this point, you just stick the darn thing on a dyno.

This collection of pages isn't bad at describing some of this stuff: https://c03.apogee.net/mvc/home/hes/...pc=foe&id=4571
At full throttle, the PWM doesn't apply. For the sake of discussing peak power, which will be at full throttle, we can ignore that aspect. Agreed with everything else though.
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