Why Ingenuity drone has 2 coaxial rotors, not quad-rotor

When I first heard about Ingenuity I thought it will be quad-rotor because it's what seems to be easiest to operate (I say that because it's the most typical on-Earth amateur drone configuration). Then I found out its configuration is 2 coaxial rotors. Why? Is it because 2 are easier to keep working than 4? Lighter? More thrust?

• The very thin air means it's extremely difficult to get sufficient thrust and so needs to be as light as possible. If four rotors means four motors, that might have been a disadvantage, though maybe they'd me smaller, so.... dunno. Of course four motors and four rotors means more things can fail...
– uhoh
Feb 19 at 10:06
• Well, for one thing.. The speed of rotor is greatly limited by the sonic booms at the end of tip. A thin air means higher rotor speed, which probably makes the coaxial system win considering weight and power and electronics involved to drive them. Feb 19 at 10:32
• The only reason why we use Quadcopter drones is because they are proportionally very cheap to build, and the smaller/slower rotors are much more human friendly. Helicopters are vastly superior flyers, but they require very expensive mechanisms to handle the steering via pitch and collective control. In effect, they need to rotate each blade a bit, twice per revolution! With utter precision and reliability. This makes the minimum cost of a helicopter much more than the minimum cost of a quadcopter with similar lifting ability. Feb 20 at 18:23

[This is a thinly-sourced answer, for which I apologise. I spent a bunch of time looking for good sources but really failed to find anything very useful. The single best bit of information I found was this Veritaserum video, which is not something I'd normally want to cite (Veritaserum is wonderful, but videos seem like questionable sources in general). So I wrote a comment, but then I got interested and spent some time doing back-of-the-envelope sums, the results of some of which are below, and it all got way too long, hence this.]

I believe that at least four factors may be involved:

• helicopters are more efficient than quadcopters;
• helicopters are more inherently aerodynamically stable than quadcopters [questionable: see below];
• the rigid structure required to support a helicopter is much smaller than that required to support a quadcopter, and so can be lighter;
• related to this helicopters take much less storage space than an equivalent quadcopter.

Efficiency 1: fixed pitch vs variable-pitch

The way quadcopters work (or the way the ones we normally see work) is to have fixed-pitch blades, with the thrust from each set of blades being adjusted by adjusting their rotational speed. This is a horrible thing to have to do because it means that you need to be continually adjusting the rotational speed of the rotors, which costs you a lot of energy.

The way a helicopter works (and the way Ingenuity will work, as you can see if you look at NASA's 3D model of it is that the pitch of the rotors gets adjusted dynamically to control the lift (and also to create forward motion &c), while the angular velocity of the blades stays more-or-less constant.

Doing the latter thing is really a lot better than doing the former thing, especially when the rotors are long. And because the atmosphere of Mars is hugely less dense than Earth's, the rotors will need to be long. Other things being equal, the energy stored in a rotor goes like the cube of the length of it (assuming it has constant linear density, so the larger rotor is proportionally more massive than the smaller one), so this really gets horrible if you need big rotors that you need to speed up and slow down.

So quadcopters are great if the rotors can be rather small: they are mechanically simple, but they are not efficient, especially as the rotors get large.

This makes them, probably, rather bad choices for a solar-powered vehicle in an atmosphere with very low density.

One alternative would be to use a quadcopter with variable-pitch rotors: I'm not sure why this was ruled out but I can imagine extra weight, extra complexity (four sets of pitch-control mechanisms, and the mass of these may not scale down very well) being considerations.

Efficiency 2: rotor size

But this isn't the only sense in which a helicopter is better than a quadcopter. If you do a rather (very!) naive spherical-cow calculation, assuming a rotor blade which tapers uniformly to the centre (so most of the lift comes from near the tips), then if you assume a constant tip velocity $$V$$ (this is intended to represent the fact that you don't want the tips to be supersonic, so that constrains $$\omega$$), then you get a lift $$L\sim V^2 R^2$$, where $$R$$ is the radius of the rotor. So big rotors do significantly better than small ones.

(Here's how I got this: if you assume the chord at $$r$$ is $$\alpha r$$, and lift goes like $$k Av^2$$ where $$A$$ is area and $$k$$ is some fudge factor, then

\begin{aligned} dL &= k dA v^2\\ &= k \alpha r\, dr\, r^2\omega^2 \end{aligned}

So

\begin{aligned} L &= 2\int_0^R\, dL\\ &= 2k\alpha\omega^2 \int_0^R r^3\,dr\\ &= \frac{k\alpha}{2} \omega^2 R^4 \end{aligned}

But $$V = \omega R$$ so $$\omega = V/R$$ and finally

$$L = \frac{k\alpha}{2} V^2 R^2$$

But this is a naive calculation: the blade shape is in real life nothing like this, and the angle of attack varies along the blade of course. I am not an aeronautical engineer and am not competent to do the real calculation.)

However in the above I have simply neglected the mass of the rotor: I'm quietly assuming that you can make the mass of large rotors scale as no more than $$R^2$$ so that you can in fact extract much more useful lift from a large rotor than a small one.

This section really needs a proper treatment from someone who understands aerodynamics and the design of things like helicoptor blades, but I think that it is true, nevertheless: the lift you can get from a rotor goes better than linearly with its length.

Stability

[I now think what follows is questionable. First of all helicopters are only statically stable, so it's likely that dynamic stability (oscillations around the statically stable point, including possibly runaway oscilattions) needs to be dealt with. Secondly, since writing this I discovered that the two sets of blades on Ingenuity are independantly driven, so one possible failure could indeed be that a single pair of blades loses synchronisation with the other due to a motor or control failure, which would have catastrophic results. I am leaving the text below unaltered as I think it still has some use, just not as much as I thought it did.]

One nice thing about helicopters is that they're can be made to be aerodynamically statically stable. What this means is that if you have a helicopter which is hovering (say) and you swing it sideways somehow, it will swing back and after a while it will end up hovering again (probably not in the same place or at the same height). If that happens to a quadcopter it won't. This is why humans can fly helicopters without computer assistance, but they can't do the same for quadcopters.

However helicopters are (often? always?) not dynamically stable: they tend to oscillate around their equilibrium position and that oscillation can increase. I'm not sure about the dynamic stability of quadcopters: to some extent since they fail to be statically stable it's a moot point.

This is great for drones on Earth for the same reason that you want fighter aircraft not to be stable: you can servo the thing with a computer and get something which is extremely manoeuvrable, which is exactly what you want. Additionally because you're servoing it furiously it can make a very stable (yes!) camera platform: it won't swing about the way a helicopter would, so you can bolt the camera rigidly to the body of the drone. If something goes wrong with the computer, well, it crashes, but you can go and pick it up, or buy another one.

That's not the case with Ingenuity: if it crashes you can't go and pick it up. Worse: what if it crashes into Perserverance: that would be a very bad outcome indeed. A helicopter has much better failure modes: unless there is a mechanical failure in the cyclic pitch control (this is the bit that causes the vehicle to move horizontally: collective pitch control sends it up & down), any failure is likely to result in it going straight up or down: it's much less likely to hit something else, and much more likely that you can put it down gently under partial control and then work out what went wrong later.

[If you look up information on quadcoptor & helicopter stability there is a lot out there to back this up, but I couldn't find anything really citeable.]

Size & weight 1: quadcopters are heavy

One problem with a quadcopter is that you need a rigid structure which extends between the rotors. This is necessarily at least as large as twice the rotor radius, and it needs to be rigid so the rotors don't flap around, which would make it uncontrollable. Large rigid structures are, well, large, but they're also heavy.

For a helicopter with two counter-rotating rotors there's really no lower limit on how small the body can be: it needs to be large enough to hold the batteries and control electronics, cameras &c, but that's basically it. That means you can make it extremely light.

For a vehicle which not only has to fly from solar power in an extremely thin atmosphere, but has to be strapped to a spacecraft to get it to that thin atmosphere mass is really going to matter.

Size & weight 2: thermal considerations

[This is thanks to Dragongeek.] For a Quadcopter that's going to work at reasonable temperatures you can avoid some of the mass cost of the large structure you need by using it to contain electronics, batteries and so on. On Mars the temperature at night can get down to 180K (-90C) and just keeping everything warm is a really big issue. Indeed about two thirds of Ingenuity's power budget goes to keeping it warm at night (see the Veritaserum video above). So you really want to pack the electronics and batteries in the best way you can to keep them warm (from my, rather old, experience of dealing with low temperatures for military electronics the really critical thing will be keeping the batteries warm). The best geometry is a sphere, but a cube, which is pretty much what Ingenuity's body is, is not far off. They also do neat tricks like packing the electronics around the batteries as extra insulation for the batteries (I think there must be heaters in amongst the batteries, and also so the heat being lost from the batteries' heaters helps to keep the electronics warm on its way out.

In any case what you definitely don't want to do is to keep the electronics / batteries in the frame of the quadcopter: you need them all snuggled together for warmth.

Size & weight 3: quadcopters are big

One other problem with quadcopters is that, unless you plan to assemble the structure on arrival, they're also kind of big. I don't know the details of how Ingenuity is stowed under Perseverance, but I suspect strongly that being able to make the thing small mattered.

Here are two pictures which show how large a helicopter you can get in the same size as a given quadcopter. Here I've assumed the quadcopter is as small as it can be: the blades of the rotors just touch. The structure of the quadcopter is the black square (obviously this would be four beams, not a solid thing!), and the blades are the lines from the corners, with their swept area in pale grey. The helicopter is in blue, with its swept area in pale blue. I've just invented the size of the helicopter's body (and I've ignored its feet, which I should not have done).

The first picture has the worst case for the length of the helicopter blade that will stow in the same space as a quadcopter: this gives a blade which is $$\sqrt{3} \approx 1.7$$ times the length of the quadcopter blades.

The second picture has a better case from the point of view of the helicopter, the blade is now $$\sqrt{5} \approx 2.2$$ times the length of the quadcopter blades.

(There's a silly best-case for the helicopter, where the blade ends up $$1 + 2\sqrt{2} \approx 3.8$$ times the length of the quadcopter blades, but you would not stow the quadcopter like that.)

So I think it should be the case, because quadcopters have this big square structure, you can stow a much 'larger' (much longer bladed) helicopter in the same space.

Summary: helicopters win

I think it's pretty convincing that for a system which needs to fly in a very thin atmosphere, needs to be as light and small as it can be so it's not too expensive to get there, needs to fly autononomously, and for which any serious failure is terminal, that a helicopter is a significantly better choice than a quadcopter. But I'd like to see the design studies!

• Very good analysis! One thing I'd add (and that ties into the size/mass arguments) is the need for thermal protection. Due to the extreme cold that Mars reaches during the night and the fact that these temperatures can cause havoc to the electronics and especially the batteries, keeping all those internals in an insulated and heated container is much easier in with a helicopter configuration as the body shape gets closer to the ideal, minimum surface area, sphere-shape. In a more traditional multirotor layout you'd end up having motors and electronics at the ends of long arms Feb 20 at 14:51
• "One nice thing about helicopters is that they're aerodynamically stable". Helicopters are unstable, and hovering is a delicate maneuver (vortex ring state). See this article: "So, the helicopter, essentially, cannot maintain a steady flight regime. The pilot, piloting the helicopter, continuously has to act on the helicopter’s controls and create control moments, [...] to maintain the specified flight regime".
– mins
May 17 at 17:40
• Ingenuity has some added stability with the coaxial contra rotating rotors which speed and angle of attack are synchronized, else an anti-torque rotor would be required, another source of problems (like multiple un-synchronized rotors), specially because passive stabilization (weathercock) is not possible due to low density (actually low Reynolds number).
– mins
May 17 at 18:52
• @mins: one of the things that surprised me was that Ingenuity's two rotors are separately-driven (there are two motors). I assumed they'd be geared together but apparently not. I imagine if one motor fails the results would be, well, catastrophic!
– user21103
May 17 at 19:30
• Ah, I hope I'm not influencing too much here, I'm not really an expert in helicopter aerodynamics, but Simon is a helicopter pilot. Unfortunately he hasn't appeared for a long time. From my small knowledge, I agree with your analysis though.
– mins
May 18 at 11:39