I was flying quads today and it just suddenly popped up into my mind — do the propellers all have to be the same size in quadcopters? Mine are, but What if two propellers were larger and the other two smaller? The drone would still be symmetrical, but would it have any effect on the performance of the drone? Could you explain the physics behind your answer?
The main point of a quadcopter is that it can be controlled by engine power using much simpler fixed-pitch rotors¹. Assuming this construction, you need to be able to separately adjust power of
- forward and rear set of propellers for pitch control,
- left and right set of propellers for roll control and
- clockwise and counterclockwise-rotating set of propeller for yaw control.
If you had two bigger and two smaller rotors, then one of the combinations would have the two bigger ones in one of the sets and the two smaller ones in the other. That would make it really, really hard to balance all the parameters to maintain appropriate controlability.
I think it might not be completely impossible, but it certainly makes no sense.
¹ Of course once you add cyclic and collective control, you can fly with one rotor only (well, two, or one with anti-torque rotor or jet) as most full-scale helicopters do, but then you've lost the simplicity of fixed propellers.
No, they don't have to be the same size. You could even fly with just two rotors - the Chinook does - the other pair would be needed for control only.
But having them all comparable makes it easier to design the quadcopter and keeps it generally more maneuverable.
No, you can fly a quadcopter using different rotor sizes. The smaller rotors would have to have a longer moment arm relative to the Centre of Gravity, and as @JanHudec points out the total rotational impulse in yaw direction must zero out as well.
So two pairs of counter-rotating rotors, correctly placed relative to CoG, would work.