Scaling up Ingenuity

The Ingenuity helicopter only weighs 4 lbs, but it has two rotor blades that are 4 feet long and rotate at 2400 rpm. That’s a lot more lifting surface and rotation speed than a similar sized copter on Earth would need.

So how much could it be scaled up? Is there a limit to how large a helicopter or drone could be and still fly on Mars?

You could always use the quad/hexa/etc.-copter approach. Scaling those is easy if you have a single-blade design that’s known to work. You need some structure between the different props, but that could be fairly light.

In fact it appears that JPL’s proposed next design does just that:

I don’t have very good intuition about the scaling laws of helicopter blades. Obviously they can be made to be quite long on Earth. On Mars, with the much higher speeds, I don’t know if you run into more serious issues with, say, vibration. It might be best to stick with the smaller rotors and use as many as required.

One limit is the tensile strength of the blades and fasteners. And you don’t want to approach those limits too closely. On Earth the blade tip can already become supersonic when the leading edge is sweeping forward. That’s at only 500 rpm or so for a smaller rotor.

I know jack about the subject, but didn’t I read somewhere that the speed of sound at the rotor tip is also a limit on RPMs? I imagine that wouldn’t be a problem on Mars.

ETA: weirdly, Mars has a lower speed of sound than Earth’s (at sea level). Which is not what I would have intuited. Nasa link

For ideal gases, the speed of sound is independent of pressure. So all that matters is the temperature and the fact that it’s largely CO2 instead of N2/O2. The fact that the pressure is 0.5% of Earth basically drops out of the formula.

Rotors can go supersonic, but that poses all kinds of problems (shockwaves, etc.), and isn’t too efficient. Ingenuity keeps its rotor tip speed under mach 0.7, which probably keeps the gas flow under mach 1 across all surfaces of the rotor.

If tip speed is the limiting factor, a large rotor gets easier–centripetal acceleration is \frac{v^2}{r}, so if v is constant, then the 1 \over r factor reduces the accelerations. But a large rotor also needs better stiffness to not sag, and is going to be harder to fold up for storage. I think this latter point might be the most significant factor; a multirotor can fold up in a way that doesn’t take much space.

For calculation, the air density on Mars is 1/100 that of earth, about equivalent to an altitude of 100,000 feet IIRC. But gravity is 40% of earth’s.

Perhaps a more useful scale up would be a blimp, if some way to create hot air or capture hydrogen could be devised.