[ivanjermakov]

I studied this subject when I was building FPV sim from scratch. I noticed that yaw action is often misunderstood, falsely believing that it's caused by a change in angular momentum (think reaction wheels).

There is a good SE answer about deriving net torques given each props' thrust force in less PhD language than this article: https://drones.stackexchange.com/a/416/11402

If anyone is interested in tackling UAV simulation, make sure to check out this prop/motor performance database, helped me a lot building a virtual drone with realistic properties (mainly motor thrust & torque): https://database.tytorobotics.com/tests

[fragmede]

Why does four seem optimal? Why not three or five? or eight?

[hnuser123456]

4, 6, and 8 are all fairly standard, as quadcopter, hexacopter, and octacopter, because you have a pair of motors rotating in each direction, which allows you to slow down all the motors spinning in one direction and speed up the others (as long as each set spinning the same direction is on opposite sides of the center of gravity), to maintain constant lift while yawing left or right.

Tricopters are possible as tilt-rotors, where you have two motors spinning opposite directions on mirrored sides, and the third motor is on the midline in front or back and able to tilt left and right. This allows the vehicle to control yaw despite having an inherent yaw imbalance in hover. I suppose you could do any odd number of rotors this way, and more rotors would mean less inherent yaw imbalance if there's only one extra motor spinning a given direction.

Two is possible if the payload hangs below the props, and the props are able to independently tilt.

One requires collective pitch and still at least a small tail rotor to cancel out the yaw, as a helicopter, but that is far more complex and fragile. But it is the most efficient, as fewer larger props are always more efficient than more smaller ones.

So four just turns out to be minimum to have no moving parts besides the props themselves, and still have full control authority, and the control logic is more straightforward than tilt rotors and such.

[montymintypie]

> Two is possible if the payload hangs below the props

I think this is incorrect, it's the somewhat unintuitive rocket pendulum fallacy.

[hnuser123456]

Here is a video of one: https://www.youtube.com/watch?v=qO747JB4Nr8

There's a few demonstrated here (26-32 seconds in): https://www.youtube.com/watch?v=vBsyFj8bEJk

And here's one that uses the ailerons instead of being able to tilt the motors: https://www.youtube.com/watch?v=L2fgL97rgK0

I could've sworn Peter Sripol built one while on Flite Test too, but I can't find it atm.

Looks like the rocket pendulum fallacy is about expecting meaningful passive stability from the location of the center of thrust vs center of mass, but even 2-rotors need to be able to tilt independently (or deflect thrust) for active control.

Theoretically this could still work even if the center of mass was above center of thrust, but the tilting/vectoring responsiveness would need to be very high. These RC models at least move so slowly that the air resistance of swinging back and fourth really does help dampen oscillations passively, but they all still have active flight controllers that are trying to keep angular velocity at zero without control input.

[montymintypie]

Sorry, I wasn't arguing against bicopters being possible, obviously something like the osprey exists.

> the air resistance of swinging back and fourth really does help dampen oscillations passively

But they don't swing back and forth like a pendulum (unless your PIDs are off) because of the center of mass, that is the entire issue with the fallacy.

[elictronic]

He specifically says if the motors independently tilt. This is active control. The Rocket pendulum fallacy is only valid for systems requiring passive stability.

Tandem rotor helicopters exist.

[montymintypie]

Rockets also have active control via gimballing motors. Bicopters tilt their motors to control pitch and yaw, roll is still governed by motor speed.

I was arguing against the COG of the payload, not of the existence of bicopters entirely.

[hnuser123456]

Too late to edit, but I meant cyclic pitch, not collective pitch.

[cpgxiii]

If you look at larger multi-copters, 6 and 8 are quite common since they allow for some redundancy, allowing for safe landing and/or continued flight following the failure of one of the rotors.

As other replies note, 4 is the simplest arrangement mechanically and control-wise, as the control math is quite simple (just rotor speeds/torque) and the only moving parts are the fixed-pitch rotors.

The minimum, as seen in real (and model) helicopters, is either two (approximately) constant-speed rotors with swashplate control, or one (approximately) constant-speed rotor with swashplate control and one tail rotor, either with (approximately) constant speed and variable pitch, or with variable speed. At the scale of real helicopters, two rotors may often be more powerful and efficient (e.g. CH-47, V-22) but the size and weight of the gearbox needed to transmit so much power is a significant contribution to the weight and cost of the helicopter, and thus having a single main gearbox is much lighter and cheaper. The notable difficulties of shaft drive between multi-rotor helicopters, particularly with distributed engines (see a number of V-22 issues) strongly discourages helicopters with more than 2 rotors.

[kurthr]

Not the OP, but due to neighboring rotor interactions an even number (or a single helicopter like lift rotor and a tail rotor ignoring airfoil lift possibilities) rotor makes design easier and improves performance significantly. Think of the rotors like gears meshed together and realize that an even number spins easily, while an odd number is locked.

Of course there are 6, 8, and larger numbers of rotors used in actual drones. The advantage of more rotors is that redundancy to failure can be built in, and that rotor tip speed for a given lift can be somewhat reduced at the cost of efficiency.