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Consider a toy helicopter that's floating(battery on) in the air. What's interesting was that it cost more energy for it to suspend at higher places. However, we knew that $F=mg$ thus the "thrust" or the "wind force" must be same since the only force acted on the toy helicopter was the gravity and the force from the air.

When it's very close to the ground, this was making a little bit sense since the air was kind of "compressed" by the ground. However, even when the toy helicopter was at say 2 or 3 meters high, or even 10 or 20 meters, this still appeared to be true. Compare to the size of the toy helicopter, for example, 0.1 m or 0.2 m, it doesn't quite make sense then, as the helicopter appeared to be high enough above the ground. However, the air pressure was obvious not a big influence at such occasion.

Question: Why it cost toy helicopter more energy to stay at higher place? and does this continuous forever?(in the case that the air pressure and gravity would not be taken into account, say a mile or so.)

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    $\begingroup$ I don't think that it requires significantly more power for a toy helicopter to hover at, say, 100 feet as opposed to 200 feet. The local air densities and temperatures should be about the same at the two altitudes, so the amount of power to hover should also be about the same at the two altitudes. This can be easily checked if you have drone like a DJI Mavic which allows one to see the instantaneous power consumption of the drone as it's hovering. In asking your question, I think that you're assuming a fact which you haven't justified or provided any evidence for. $\endgroup$
    – user93237
    Commented Feb 5, 2020 at 0:53
  • $\begingroup$ @SamuelWeir Thank you. I will give it a try sometimes. But just in a very common experience, the toy helicopter always ask one to push the power more so that it can goes higher, but it almost always slows down to certain attitude, until one push the control to tell it to spin faster. Isn't it? $\endgroup$ Commented Feb 5, 2020 at 0:58
  • $\begingroup$ Agree with Samuel Weir, I'd like to see some evidence of exactly how much more energy is required. Superficially, there shouldn't be much difference between whether the helicopter is 1 meter high or 10 meters high. $\endgroup$
    – Allure
    Commented Feb 5, 2020 at 1:46
  • $\begingroup$ @ShoutOutAndCalculate - If the toy helicopter (or drone) is hovering at a specific altitude and you want it hover at a higher altitude then, yes, of course you'll have to apply more power to get it to climb in altitude. But it will continue climbing and climbing (at least to the 400 feet legal FAA altitude limit of drones) if you don't back off on the power. I think that your belief that the drone naturally "slows down to a certain altitude" even without your backing off the increased power is probably due to your unconsciously reducing the power as the drone climbs higher and higher. $\endgroup$
    – user93237
    Commented Feb 5, 2020 at 4:56
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    $\begingroup$ Is the battery stable at the same voltage? electronics.stackexchange.com/questions/19107/… $\endgroup$
    – anna v
    Commented Feb 5, 2020 at 6:25

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When it's within a rotor length of the ground there is ground effect, so let's ignore that.

But as it goes up the air gets thinner, which means the rotors have to travel at higher speed to get the same lift. This doesn't cost more energy aerodynamically, but it does mean the motors have to turn faster. The power exerted by an electric motor (torque times rpm) has a maximum at a particular rpm and then it falls off, so the motor can't simply go much faster.

Airplanes like to travel at high altitudes because they can travel faster for the same lift and drag. (Of course there's a limit. The "Q-corner" or "coffin corner" is the big one.)

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