Why do multirotors usually have four propellors?

I've observed that hover-capable drones almost always have four propellers. There are helicopters of course, which have two, but in general, the vast majority of UAVs seem to go with four propellers.

It seems to me intuitively that this must be less efficient: More points of friction, more wiring, more weight, etc...

Why is it that we see an overwhelming predominance of four propeller drones rather than, for instance, three propellers? Is it just because it's easier to control or gives a smoother flight? Or is there some physical reason?

With aircraft, there are 6 degrees of freedom (DoF) we want to control (roll-pitch-yaw, and x-y-z), but for hovering vehicles (i.e. rotorcraft) we can get away with controlling two degrees of freedom (x-y) by combining the 4 other degrees (roll-pitch-yaw + z).

There are many ways of controlling those four DoF, typically:

• helicopters, which use variable pitch blades and some combinations of main and tail rotors, to result in a combination which results in control over roll, pitch, yaw, and thrust
• tricopters, quadcopters, hexacopters, octocopters, etc..., all of which use their blades to control the roll, pitch, yaw, and thrust.

Somewhere it is inescapable that for stabilized flight on all four DoF you must have the ability to control each DoF. Mathematically, the quadcopter provides the lowest number of simple actuators that accomplish the job. Each actuator can work by simply speeding up or slowing down, whereas helicopters and tricopters require some other kind of actuation, usually a complex one. It turns out from a pragmatic viewpoint speeding up and slowing down motors is much more robust than changing angles of spinning blades.

Formally, it looks like this:

So quadcopters reign over helicopters and tripcoters because they're simple. Each axis is controlled by a certain combination of motor speeds and all axes are independent, i.e. when you increase thrust you don't have to also worry about changing the pitch.

So why not hexas, octos, etc...?

Hexacopters

Hexas can lift more, but provide no additional safety margin because there is no way to stabilize all four axes when an arbitrary motor goes out (there are certain configurations which can continue to fly if one motor out of a set of four fails, but cannot fly if either of the other two fail).

Hexas also are less efficient, since they use smaller propellers. (Without diving into blade theory, and simplifying somewhat, the most efficient blade is a single blade which is infinitely large and moving infinitely slowly.)

Hexas also have 6 motors for four degrees of freedom, so when they're all flat you get what is called an "overconstrained" system. You can actually angle them to interesting effect, e.g. CyPhy Work's LVL 1 drone.

Octocopters

Octos theoretically can continue to fly if any arbitrary motor fails, but in reality, you'll likely encounter blade stalling effects or other pathologies that will not allow the octo to sustain flight. This happens because the typical octo is loaded past the point where 4 motors can carry it safely. However, certain high-value vehicles, such as those carrying expensive cameras, are octos because it's cheaper to over-spec the octo's batteries and motors than it is to replace a \$50k camera.

Octos are also less efficient, for the same reason as hexas.

This is a very interesting question, and one that is always my favourite to answer.

Firstly, rotary aircraft commonly need an even number of propellers (though not always) or another way to counteract the inertia of the props. Think, for example, why helicopters have a propeller at the end of their tail boom; they need to counteract the rotational forces of the main prop (in a system, momentum must be conserved so without the tail boom, the rotor on top would cause the main airframe to rotate to counter the motion proportional to its mass).

So, to counteract this, you need the rotational inertia of the props to sum to zero to avoid motion, such as by having an even number of propellers, or you need a way to vector part of the thrust to counteract this motion, which you can see in tricopters where they have a servo on one of the rotors. This adds extra complication and points of failure, so it’s easier to go with an even number of rotors.

The reading that we have four instead of two rotors is that, as well as yaw, we also need to think about the pitch and roll axes. For a bicopter. If you want to yaw, you either need to vector the thrust, or decrease the speed of one of the directions of propellers.

The former of these requires servos which, again, adds extra complications, and the latter means that there is an imbalance of thrust, which will cause unwanted pitch or roll, depending on the orientation of the aircraft.

However, on a quadcopter, these problems disappear. We can have the rotation of each diagonal set of props matching each other. If we want to yaw, we increase the thrust in one set and decrease it in another. If we want to pitch or roll, we can decrease the thrust in adjacent props and increase the thrust in the other two, both while maintaining inertia and having no yaw motion (see the diagram below). We also have the added benefit of more thrust so a greater payload.

This can be scaled up with the same principle to aircraft with any even number of propellers so that there is redundancy - if one motor or prop fails, the others can compensate.

For anyone interested how an aircraft with an odd number of motors doesn’t need servos, I’ve found this interesting paper from MIT: https://people.csail.mit.edu/taodu/pentacopter_guide/guide.pdf

• @KennSebesta very true, I was just trying to give a simplified answer as the consensus on Meta seemed to be that delving too deep into the physics isn’t necessarily always the way to go. Also, I was generalising as whilst for R&D purposes there doesn’t always need to be an even number, it is true for most in the commercial and professional sector. Thank you for pointing that out, though - I’ll add an edit to clarify. Edit: I’ve just re-read my answer and I don’t see where I said that an even numbers was a requirement, only that it was an option. Could you please clarify what I should edit? Commented Apr 16, 2020 at 20:19
• @KennSebesta sorry - I deleted my other comment because it wouldn’t let me edit and I felt I came across as a little confrontational. Thank you for sharing the link to the link, I’ll take a look! Commented Apr 16, 2020 at 20:38
• @KennSebesta haha I’m glad I didn’t seem confrontational - I certainly didn’t intend to be! I don’t think you should worry about deleting your comments - they add extra context to my answer and that can only ever be a good thing! Commented Apr 16, 2020 at 20:46

Simplest answer I give to anyone who asks?: It allows full featured flight without ANY control surfaces, linkages, and any moving parts at all other than rotation of the motors. This is incredibly simple, cheap and robust and is a truly simple device as flying machines go. This is what makes quad designs so special over other types.

• Yup. Multis are really terrible aerodynamic platforms with very low efficiency, but the iteration time of fly to crash to fly is minutes, instead of weeks. Commented Apr 22, 2020 at 12:12
• Drones can't be a solid state device since motors require a gap between the spinning bit and the not spinning bit. See en.wikipedia.org/wiki/Solid-state_electronics Commented May 8, 2020 at 20:45
• uh, ya whatever about the 'solid state' thing. The point of the answer was to clarify that the ONLY mechanical part on a multirotor IS the motors making them simple as flying machines. Your wiki link is however a great bit of smartassery though. I've edited the answer to take out the offensive bit... thanks I guess.
– user251
Commented May 9, 2020 at 23:48

Four is the minimal number of propellers to control the attitude of an aircraft without having to use control methods other than just controlling the speed of each propeller.

The ONLY moving parts of a quadcopter are the rotors. And the only control method available is the precise control of the rotation speed of each rotor.

The least moving parts you have, the smaller is the chance of a failure.

Also, four props are the most efficient way to make the vehicle small. Given a fixed vehicle size constrain, to add more props you have to reduce each prop size, and it makes the prop less efficient. The bigger the prop, the more weight-to-power (efficiency) ratio increases. As a rough example: A single 10 inch prop will produce 1 kg of thrust using 100W, while a 5 inch prop needs 150W to produce the same amount of thrust.

As a curious fact: Helicopters has a "rotary wing" on top of it, not a "propeller". Helicopters can sustain flight even after an engine failure, because it's rotary wing will still produce lift, so it can glide like an airplane and land safely. Multirotors doesn't has wings, so it's propeller will NOT give any attitude control if a motor fails. To have redundancy, you need to add more rotors... But it's easier to make a more reliable rotor than to add redundancy to a multi-rotor aircraft... That's why most of multirotors out there have exactly four rotors.