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I've noticed that most every quadcopter drone I see uses outrunner BLDC motors like this:

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Why is that? What unique advantages to outrunners have that make them better than inrunners for multirotors?

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The difference between outrunner and inrunner BLDC (brushless DC) motors is that an outrunner's rotor is outside the stator while an inrunner's rotor is inside the stator.

enter image description here (cit.)

In general, outrunners create more torque and rotate slower than inrunners, which usually have less torque and rotate significantly quicker. The two different designs are possible because it is relatively easy to conceptualize how to flip the order of the stator and rotor within the motor due to the fact that no mechanical commutation is necessary, unlike in a brushed motor.

Whichever side of the motor (outside or inside) that is the stator is far thicker than the other because the orientation of the coils on the stator contributes a lot of depth. Outrunners trade increased torque for decreased rotation rate because the electromotive force between the magnets and coils acts roughly at the air gap between them, which is further from the center of the motor in an outrunner, resulting in an increased moment arm and more torque. (remember that τ = F x r where τ is torque in Nm, F is the force, and r is the distance from the rotational axis)

This increased torque is critical because the BLDC motors have no gearboxes between them and the propellers, which require decent amounts of torque to spin. In other systems, motors could use gearboxes to trade speed for torque, but the requirements of multirotors to be as efficient and lightweight as possible don't allow for them to be installed.

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