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Can a helicopter trapped in a bubble generate lift?

I understand that it is a closed system, and should not. However, the equations for lift seem to rely on one simple thing: a pressure gradient. Conceptually I cannot reason out why this would be prohibited within a bubble.

Further, I imagine that the helicopter might be tethered to the bubble, and if lift is generated - that it would also lift the bubble. Perhaps even by adjusting the position of the tether, the lift force could be translated in to horizontal thrust, etc.

And...a slight extension of the same idea that I am curious about: if we made the bubble a slightly open system (perhaps by cutting a small opening on the bottom). Would it be possible to regulate the environment barrier between the inside and outside of the bubble, with the hope of maintaining proper atmosphere inside the bubble to continue generating lift?

I thought of this question while watching a movie that shows a helicopter not being able to climb past a certain elevation to rescue hikers on Mt. Everest. Like a divers "bell" helmet - could the helicopter have "pulled off" the rescue if it were trapped inside of a bubble that maintained atmospheric pressure for the spinning blades to act upon? That way it could climb, theoretically, to any elevation.

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    $\begingroup$ You should distinguish clearly between lifting the helicopter relative the bubble and moving the system (copter and bubble) relative the outside world. $\endgroup$ – dmckee --- ex-moderator kitten Dec 10 '16 at 18:23
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    $\begingroup$ Mythbusters did this EXACT experiment for a model helicopter inside a closed container. @sapbucket, do a Google search and watch the video for more details. $\endgroup$ – David White Dec 10 '16 at 18:43
  • $\begingroup$ I think the mythbuster program was based on the old 500 pigeons in a truck story, being forced to fly to "lighten" the load over a weak bridge. $\endgroup$ – user108787 Dec 10 '16 at 19:00
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No, the helicopter will be lifting itself relative to the bottom of the bubble. If you attach a tether between the helicopter and the bubble, then the force exerted by the helicopter will go to increase the tension of the tether - it will not move the outside of the bubble.

The force it uses to lift itself has to be outside of the entire thing it is lifting. Think of it like this: What the helicopter is doing is moving a chunk of air from above it to below it, and the the helicopter goes up to take the place of the moved air. In order to lift the bubble, it would have to be moving a chunk of air from above the bubble to below it, which it can't do just be swirling the air on the inside.

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