In case you haven’t noticed, the NASA Perseverance rover landed on Mars. Yeah, it’s kind of a big deal. But there’s something special about this rover — it brings with it a flying autonomous vehicle. Yes, it’s got a drone…on Mars. It even has a name. It’s called Ingenuity.
OK, so there was a bunch of research and development that went into designing and building a drone (you can call it a helicopter if that makes you happy) that can not only survive a rocket launch. It can also survive the cold environment on Mars — OH, and it can even fly on Mars.
So, what’s so special about flying on Mars? There are two big differences compared to an Earth-based flight:
- Gravitational field. The gravitational field on Mars is lower than on Earth. Earth has a surface field strength (g) of 9.8 Newtons/kilogram, but on Mars it’s 3.7 N/kg. With a lower gravitational field, you don’t need as much upward thrust to fly. That’s a good thing.
- Density of the atmosphere. The density of air on Earth is 1.2 kilograms/meter³, on Mars it’s 0.02 kg/m³. A rotary aircraft (quad-copter or helicopter) flies by pushing air down. With a lower density of air, you don’t get as much thrust. This is a bad thing.
But don’t worry, I have a model for the power requirements to fly something with a rotor. Here is my very brief explanation (my original calculation comes from the power estimation for a human powered helicopter).
The Physics of Hovering
It starts with air (I’m using the generic term for air so that it’s just the stuff in the atmosphere). If you take air above you and push it down, the air will push back up on you because forces are always an interaction between two things (this is that whole Newton’s Third Law thing). The value of this force from the air depends on the mass of air and the speed that it’s thrown down (also, the time it takes to get up to speed — but that also depends on the speed).
This means that the two important aspects of drone flight are the size of the rotor and the speed of the air. With a bigger rotor, you are increasing the mass of the air that gets thrown down (for a larger change in air-momentum) and you would get more thrust. Also, the faster you throw the air the greater the air-momentum.
If the aircraft is hovering, then this thrust force must be equal to the weight (from the gravitational force) of the helicopter. This gives the following expression.
In this equation, ρ is the density of air. A is the total area of the rotors and v is the speed of the air. Oh, g is the local gravitational field — I forgot about that. From this, I could find the required air speed for the drone (or for the Mars helicopter) to hover. You can see from this expression that the drone won’t need as much thrust since the gravitational field on Mars is lower. However, it will need a greater air speed because the density of the atmosphere is also lower.
But what about the power? If it requires greater power to fly then the drone won’t be able to stay up in the air for very long — or will need a bigger battery. The power is defined as the change in energy divided by the change in time. The change in energy will be due to the increased kinetic energy of the air (both the kinetic energy and the time interval depend on the air speed). Putting this together, I get the following expression for power:
In order to actually calculate the power, I would first use the thrust equation for hovering and find the air speed. With that, I can plug into this formula to calculate the power.
How Long Would a DJI Mavic Mini Fly?
For my real drone, I am going to assume that it’s the DJI Mavic Mini — because this is the drone that I have. Check it out.
What do I need to know about this drone? I need, the following data:
- Rotor Area: Each rotor has a diameter of 0.117 m and there are 4 of them. This gives a total area of 0.043 m². Note: I used this image to get the rotor diameter.
- Mass: This one is easy. The Mavic Mini was designed to be just under 250 grams (because of FAA stuff). This gives it a mass of 0.249 kg.
- Battery Storage: The Mavic Mini has a battery listed at 2400 mAh with a voltage of 7.2 V. Converting this to a better unit, I get 6.22 x 10⁴ Joules.
So, let’s plop this thing down on the surface of Mars (and assume it survives the extreme cold). I can first calculate the air speed needed to hover (using g = 3.7 N/kg and air density of 0.02 kg/m³. This gives an air speed of 46.3 m/s (calculations are below).
Now I can use the air speed to determine the power required to hover. On Mars, it would take 21.2 Watts. Finally, using this power and the energy stored in the battery I can calculate the hover time. I get a flight time of 48 minutes. But I think that’s wrong. Here are my calculations in python.
It just seems too long of a flight time — so I also ran the numbers for flying on Earth. The Mavic Mini will not fly for 87 minutes. So, I guess I just need to include some efficiency term in there. But if I just make a comparison between times, it looks like the Mini would fly for about half the time as it would on Earth. I think you could possibly get 10 minute flight time. Honestly, I’m sort of surprised it would work at all.
There is the mars helicopter. What if you just used a drone you could buy? DJI Mavic mini