Suppose we want to make a drone fly on the Moon (the gravity on the Moon is 1/6 of that on Earth), only by making use of its rotors and air.
The drone is as light as possible ($m_{min}(kg)$, has dimensions $l(m)$ long, $w(m)$ wide $h(m)$ high. The rotor blades have an as big as possible length of $r(m)$ (which is of course smaller than the length $l$, ca va sans dire). The cylinders are as small and light as possible but big enough to give a constant air output for some time. Say the output of air is $a(kg/sec)$ at a speed of $v(m/s)$.
The cylinders inside the drone release their air through tubes that lead the air to an (as light as possible) construction of tubes with holes around the drone, out of which the air is sprayed towards the drone so there is a cloud of air around the drone (the mass of construction is included in the drone's mass).

To ignore ground effects we'll hang the drone high somehow and let it go as soon the rotors start and the air is released (zo the initial upward velocity is zero). Things are constructed in a way that no net momentum is given to the drone.

Can the drone get an upward lift while the rotor blades are rotating in the surrounding air? Although the air spreads out very fast (see a comment made this loss of air can be compensated by the air that's provided by the cylinders.

The air is in a steady-state (going towards the drone to be sucked out by the vacuum on the Moon). So the four rotor blades have an amount of air beneath them.

Now the most probable velocity of an atom (or molecule) is $\sqrt{\frac{2kT}{m}}$, and for air (at about 300 Kelvin, the velocity at which it escapes into the vacuum is about 1500 (m/sec). So what if we used cold helium at a temperature of, say 4,5 Kelvin, and sprayed the helium to constantly fill the gap left by the escaping helium. The speed of expanion would be reduced to about 200 (m/sec), taking into account the reduced $m$ in the formula just mentioned. The weght of the cylinders would be reduced (as would the lifing power though).

For sure, it has to work in outer space where no gravity is present.

It's not my intention to propose a new kind of propulsion technique. Obviously, letting a device fly in a vacuum is much more efficient by just putting thrusters on it. It's just the physics I'm interested in.

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    $\begingroup$ Ignoring the practicality of actually carrying enough air with you, how do you release air without giving it momentum mv? Air has mass, and to release it you have to move it which means you have to give it velocity. Might as well just aim the air straight down and forget the rotors. I don't think this would work even if you had a magical, weightless, infinite source of onboard gas until you released so much gas that the moon essentially had an atmosphere. $\endgroup$ – DKNguyen Oct 11 '20 at 23:12
  • $\begingroup$ @DKNguyen Of course you can use the air as a means of propulsion. Very simple. But I stated that the air that is pushed out doesn't give the drone momentum. $\endgroup$ – Deschele Schilder Oct 12 '20 at 0:02
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    $\begingroup$ And I'm saying that pushing is synonymous with giving something momentum, so saying that you are pushing something without giving it momentum doesn't compute in the same way a reactionless drive doesn't compute. If you can push something without giving it momentum you have a reactionless drive somewhere and should just use that instead. $\endgroup$ – DKNguyen Oct 12 '20 at 0:04
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    $\begingroup$ @DKNguyen You can let the air fly out from different containers symmetrically around the drone, so the net momentum given to the drone is zero. Many tiny containers spherically and symmetrically attached around the drone and all exhausting the same and constant amount of air per second. No net momentum is transferred to the drone. Note that in the question I mentioned containers. $\endgroup$ – Deschele Schilder Oct 12 '20 at 0:10
  • $\begingroup$ Hmmm, yeah that's a good point. That would deal with the momentum thing but I think the efficiency would be far too low, since it is so roundabout, to lift it unless gravity was almost nonexistent. And you would still never be able to carry enough gas. $\endgroup$ – DKNguyen Oct 12 '20 at 0:19

The question reveals a misunderstanding of how a drone stays aloft. In fact, a drone, helicopter, or airplane stays aloft by shoving air downward. That is, the upward force due to an airfoil moving through air is equal in magnitude to the downward momentum change per unit time in the air the airfoil is moving through. That momentum change is $v dm/dt + m dv/dt$ and amounts to a deflection of the air downward.

In the scheme you suggest, the rotors of the drone would "shove" air downward very inefficiently; and the drone would quickly run out of air. Better just to direct the air downward at high velocity right from the compressed air container through a suitable nozzle.

However, an even more practical approach would be to let the drone use lunar dust as reaction mass. The dust could be carried by the drone and accelerated downward electrostatically a little bit at a time to provide upward thrust. Whenever the drone runs out of dust, it lands and scoops up some more.

  • $\begingroup$ I'm not convinced. $\endgroup$ – Deschele Schilder Oct 12 '20 at 10:04
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    $\begingroup$ Please be more specific. What part doesn't make sense to you? $\endgroup$ – S. McGrew Oct 12 '20 at 12:17
  • $\begingroup$ The last part. This is completely different appraoch which doesn't adress the qustion. But meanwhile I upvted. $\endgroup$ – Deschele Schilder Oct 13 '20 at 12:01
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    $\begingroup$ Imagine a cloud of air in a vacuum. It will expand extremely rapidly in all directions (the average speed of an air molecule under standard conditions is ~1000 miles per hour!). Now set a propeller in the middle of the cloud and spin it. Most of the air never is touched by the propeller. At least half flies off upward; and a lot of it shoots off sideways. Only that small part of the air that happens to pass through the propeller gets "shoved" downward to produce thrust. $\endgroup$ – S. McGrew Oct 13 '20 at 14:10
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    $\begingroup$ Start with air in a small volume, each molecule moving in an arbitrary direction. As soon as the molecules have moved a distance equal to the diameter of the volume, they are essentially all moving away from the center. At a thousand miles per hour, with an initial volume of, say, 1 meter diameter, that occurs after about 5 milliseconds. The air cloud simply will not hang around in a vacuum! $\endgroup$ – S. McGrew Oct 13 '20 at 15:01

Absolutely not, other than possibly a momentary lift from ground effects when the gas is first released, it would not be able to lift the huge amounts of compressed air canisters it would take to create even a small area of uncontained atmosphere in the near complete vacuum on the Moon. It would be much more possible to direct the release of the compressed air downwards for lift rather than releasing it onto rotors to direct it downwards.

  • $\begingroup$ This is a comment, not an answer. $\endgroup$ – Deschele Schilder Oct 12 '20 at 0:03
  • $\begingroup$ ok I will expand on it. $\endgroup$ – Adrian Howard Oct 12 '20 at 1:04
  • $\begingroup$ This is still not a convincing answer. $\endgroup$ – Deschele Schilder Oct 12 '20 at 10:05
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    $\begingroup$ @DescheleSchilder Respectfully, I believe your question is being downvoted so vehemently being you're being so aggressive with people who are taking time out of their day to try to answer your question. Perhaps consider showing some respect for people with advanced degrees in physics trying to patiently explain to you the mechanics behind your proposed drone? $\endgroup$ – TheEnvironmentalist Oct 12 '20 at 22:40
  • $\begingroup$ @TheEnvironmentalist Where did I show agressiveness? Some answers were quite agressive. $\endgroup$ – Deschele Schilder Oct 13 '20 at 11:56

Let me add my two cents.

A number of people here have correctly remarked that if you just open the bottle at the bottom; air will flow out and you have made a small rocket that will run out of air very quickly, so that the rotor is useless.

However, there would be (theoretically) a parameter regime where your plan would work.

Given a certain weight $m_{min}$ for the drone, there would be a certain critical thrust $T=a.v>T_m$ required to lift it up. Now, consider being in a $T>T_m$ case, and let $a\rightarrow0$ (so that we don't waste too much air too fast) while $v\rightarrow\infty$. This is not a sustainable velocity from the pressure of the gas bottle alone. However, the propellor can be used to accelerate the air from $v_{out}$ to $v_{final}$. The achievable $v_{final}$ will only be limited by the power of the rotor, but if a good ultralight engine (and solarpanels or battery for power supply) is present, it should work.


Yes it will, BUT this is the stupidest way to build a rocket.

von Braun disapproves!!

I won't go into calculations if it can carry enough fuel, or what the velocity will be since I will prove, that your drone is a simple rocket, for which these relations are known.

We neglect the effect of the Earth atmosphere and start describing our drone in the vacuum. If air is released in a way, that it doesn't push the drone in any direction it is at least some small time nearby your propeller, before it disperses. In this small time at least some air could be pushed with a propeller in one direction, eg we get mass flow from the drone. This is the definition of ROCKET. It is pushing the flow of mass, which was before stored in the rocket and produces thrust. Its characteristics then depend on the mass flow $\Phi$, the mass of the rocket $m$, and flow velocity $v$.

From there, you can calculate all things as for a usual rocket, although it is so inefficient, that it wouldn't work in any real case. What would be the characteristics of such a theoretical-drone-powered-rocket motor is left as an exercise for the reader.

  • $\begingroup$ RELAX!!! The stupidest ways can lead to the most interesting roads...I was just asking. It's not meant to realize a new form of rocketeering. Just a thought experiment. Just for the sake of the physics involved. This is a physics site, not a rocket engineering site. What has von Braun gotta do with this question? How can he disapprove? He's not among us anymore. $\endgroup$ – Deschele Schilder Oct 12 '20 at 22:21
  • $\begingroup$ The drone I suggested isn't (by your own definition) getting it's thrust by the "fuel", as you call it, of the compressed air containers. The air provides the medium in which the rotors can give the drone an upward force. The energy source (the fuel) is the battery powering the drone. $\endgroup$ – Deschele Schilder Oct 13 '20 at 14:37
  • $\begingroup$ @DescheleSchilder, you can allways design shield so the ari wont escape the sourounding of propeler, except one direction in which propeler pushes it. You still wouldn't get any thrust from air escaping from container. This now lead us to the philosopical question: Is helicopter a rocket? $\endgroup$ – Vid Oct 13 '20 at 14:51
  • $\begingroup$ Why wouldn't you get thrust? In your contraption, you don't need the rotor blades anymore. The air will find it's way outside through the hole and give the entire construction an upward thrust. $\endgroup$ – Deschele Schilder Oct 13 '20 at 17:35

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