People will tell that there is no air, and this is why we cannot. But if I read on the internet, there is air in space, much less, but still something.
for example, 100 km - 0.0000006 times as much air as on the surface. 1000 km - 0.000000000000025 times as much air as on the surface. even on 36000 km there is something (0.0000000000000000015 times as much air as on the surface or 30000 atoms per 1 cubic decimeter).
Talking practically: NASA already built a prototype of the helicopter which will fly on Mars where the atmosphere is the same as 30 km high on The Earth.
if I take some software to calculate propeller thrust like this Propeller Selector and I calculate this very particular practical example. If I take this propeller which cost 50 euro and this engine which cost 9 euro, then I can fly up to 30 km with only 381 Watts of power for 8140 rpm. Fly I mean it will produce 1 kg thrust, which enough to hold 29 grammes engine, 349 grammes propeller and let say 500 grammes for the power source (we can even use a solar panel for it). Calculations are shown in the picture below:
and the same configuration will fly (produce same 1 kg thrust) on the surface with only 47 Watts of power and just 1000 rpm.
if I go forward, I can calculate that to fly on 100 km I will need 25 meters (1000 Inches) diameter propeller and just about 800 Watts of power with rotation speed 500 rpm.
I general, we just need big enough propeller, and because of very low air pressure, we will not need a lot of power to make it rotating fast. Also, we can make propeller very thin, because it should not be very strong, because of low pressure as well. Another point, that we can use different propellers for different altitudes, like many stages rockets.
Ultimately, if we make a few kilometer size propeller we can theoretically even fly to Mars and other planets. There are still 30000 atoms per 1 cubic decimeter in space.
Thank you, everyone, for very valuable comments. I will do exact calculations with the real propeller, motor and solar panel to see how high we can go.
The main problems as I understand is the weight of propeller + power source and strength of the material of propeller.
Real calculation of helicopter with solar panels :)
If I take this real propeller which is 6.5 kg and 70 Inch diameter, this real motor with 1600W power and these row solar panels with the weight with the weight 4.5 kg for 1350 Watt (or 1 kg gives 300 Watt) and I add 50% of mass of the solar panel to the mounting of them.
My calculation with the same program (Propeller Selector) shows that it can fly up to 5km taking into account mass of propeller, the mass of motor, the mass of solar panels, the mass of solar panel mounting, max motor power, max propeller rpm, max motor rpm.
If solar panels would be 10 times lighter, then 20 km can be reached.
So far I see only 2 problems:
The weight of the solar panel. If we can make it 10 times lighter, then we can reach much higher altitude.
This program can give wrong results for altitude more than 5-10 km.
Other problems from comments:
- Rotor speed higher than orbit speed. Calculation shows that it is not necessary and Karman line depends on aircraft weight. So, if we make very lite aircraft/airplane from non-existing/"future invented" material (carbon epoxy, etc), then Karman line will be higher than 100 km.
- Shock wave when propeller parts are moving faster than sound. One comment was, that it is not a big problem if air density is very small. So we can start with low speed on the ground and reach high speed propeller when we reach higher altitude.
- The strength of the material. In my last picture with 25 m (1000 Inch) propeller, if I calculate acceleration and g-force it will be 3500g, yes, 10 times more than normal helicopters (Mi-26 helicopter with 32 m propeller and 132 rpm). But, pistol inside V8 formula car 1 engine works with 8500g, than it is kind of feasible). Maybe they do not do it for real helicopters, because of sound speed, but as I told before, it does not matter at high altitudes.