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Can an airfoil generate enough lift, if it is contained in an enclosed space, to lift the enclosed space? Assume that there would be sufficient airflow over the foil to generate lift if it was not in an enclosed space to lift the airfoil and the enclosed space if it were externally attached. enter image description here

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    $\begingroup$ This is a bit unclear, but I'd say "no". After all, wings are tested in wind tunnels and the wing doesn't lift the whole tunnel building off the ground. $\endgroup$
    – FreeMan
    May 5 at 17:53
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    $\begingroup$ Does a car get lighter (total weight on wheels decrease) when a bumblebee at rest in the car takes off into flight? (Assume windows closed.) Is the answer different if the windows are open? $\endgroup$ May 5 at 18:02
  • $\begingroup$ @quietflyer, how is it akin to perpetual motion? $\endgroup$ May 5 at 18:07
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    $\begingroup$ If it’s recycled then there will be forces on the enclosure getting it turned around. If it’s vented then it not a closed space anymore $\endgroup$
    – Jim
    May 5 at 18:28
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    $\begingroup$ Clearly this is how the most basic of alien designs, the saucer, stays airborne. $\endgroup$
    – Therac
    May 5 at 22:31

8 Answers 8

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Consider Newton’s third law - for any action there is an equal and opposite reaction. If the action is to lift the enclosure then what is the reaction? It has to be pushing against something. You might just as well hope to levitate by pulling your own bootlaces.

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    $\begingroup$ Good comparison. Or pushing up on the inside of a box and expecting the box to rise into the air. $\endgroup$ May 5 at 23:46
  • $\begingroup$ The air going past the airfoil pushes the airfoil up, and goes down. A few moments later, it hits the bottom of the tube, pushing the tube down. $\endgroup$
    – user253751
    May 6 at 13:45
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    $\begingroup$ A system like this would also be a reactionless drive and violate the law of conservation of momentum. $\endgroup$
    – John Ray
    May 9 at 2:09
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Can an airfoil generate enough lift, if it is contained in an enclosed space, to lift the enclosed space?

If this were possible, the enclosed structure would rise up through the atmosphere without creating any downwash at all. It's intuitively clear that this would not be possible.

In fact, some upwash would be created by drag on the exterior walls of the enclosed structure as it rises up through the atmosphere. This would be inconsistent with the principle of conservation of momentum.

If you had the enclosed structure supported above the ground on a stand, and someone came and took away the stand at exactly the same instant the fan inside the enclosed structure started blowing air over the airfoil and (theoretically) creating lift exactly equal to the weight of the enclosed structure ( + airfoil), so that the vertical speed of the enclosed structure remained at zero even with the stand removed, the conservation of momentum argument would no longer apply. Still, it's intuitively clear that this enclosed structure could not hover above the ground without creating any downwash.

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    $\begingroup$ Well, if you define the "system" as equal to the enclosed space, then there is no downwash extending beyond the boundaries of the "system". So it seems to me intuitively clear that the "system" as a whole cannot support itself above the ground. Maybe another answer can explain it better. But the point is that if the "downwash" from the blades is not leaving the boundaries of the "system", then something--such as the walls of the enclosed space-- is interrupting it. And that interaction exerts a downward force on the walls of the enclosed space. Which cancels out the airfoil lift force. $\endgroup$ May 5 at 19:24
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    $\begingroup$ Think of it this way @KevinMcDowell, if you were standing outside this enclosed space, how would you detect that the airfoil inside was producing lift? Some exterior force would need to act on the structure as a whole to cause it to rise, what would that force be? $\endgroup$ May 5 at 19:31
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    $\begingroup$ "Lift from an airplane wing is not acting against the ground, else we'd feel it." If that was true, then ground effect would vanish. We humans don't feel it only because the airplane is so high and the downwash so diffuse by the time it reaches us. aviation.stackexchange.com/q/51879/31425 $\endgroup$ May 5 at 20:13
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    $\begingroup$ @KevinMcDowell, Of course there's downwash, have you never seen videos of people getting blasted by the downwash of low flying aircraft? $\endgroup$ May 5 at 22:35
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    $\begingroup$ @KevinMcDowell Lift from an airplane wing is acting (eventually) against the ground, therefore, we do feel the downward pressure of airplanes passing overhead. It's just spread out over such a large area that it's barely even measurable. $\endgroup$ May 5 at 23:58
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Another way to get to the correct answer of "no" is that all your designs have wing sections in a tube. Any low pressure created on the upper surface of these sections is replicated on the bottom of the tube just above, cancelling any lift generated. What you have made is a venturi, not a lifting device.

btw In option 2 no airflow beyond leakage is possible as there is no outlet. You just pressurize your container.

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You need to first understand what is lift in this situation.

In all 3 diagrams. Lift is the force between the airfoil and the enclosed space. The lift will generate a force that pulls the airfoil towards the ceiling of the space and away from the floor. It has nothing to do with the relationship of the enclosed space and the outside world.

This situation is exactly the same as you pulling a rope on the floor:

Pulling a rope attached to the floor

Is it ever possible to lift the floor you are standing on by pulling on a rope attached to it?

Once you see it this way it is obvious that you cannot lift yourself by pulling on a rope attached to the floor. The only way for it to work is to step outside the floor onto the ground around it - only then can you lift the floor because you are now generating a force (lift) against the ground instead of against the floor.

Similarly, if you fully enclose the air it will not lift the space around it. You need to let the air have access to the space outside the enclosed space in order for it to work because you need to generate lift relative to the outside instead of relative to the enclosed space.

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  • $\begingroup$ The real problem may be air flow within the container. But if we put, say, stators on the floor or something to prevent a vortex ring from forming, and the room was infinitely large and light, I wonder. But having air flow in one end and out the other would be better. $\endgroup$ May 6 at 8:03
  • $\begingroup$ @RobertDiGiovanni The free-body diagram does not change even in that case. How do you lift the floor you are standing on? It is actually kind of possible but only momentarily - using an impulse. You can't lift the floor but you can make it bounce. Imagine instead of pulling on the rope you put a heavy weight on the open end and swing it vertically. With enough energy input you can make the floor bounce from the ground (it's how phone vibrators work). Similarly if you can make the air quickly rush from the floor to the ceiling you can momentarily make the container bounce $\endgroup$
    – slebetman
    May 6 at 12:24
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    $\begingroup$ @RobertDiGiovanni If you have access to an infinitely large room, you have an infinite amount of air to accelerate downwards and that air can go an infinite amount of time without hitting the room and pushing it back down. Note that we do have an infinitely large room called the universe. $\endgroup$
    – user253751
    May 6 at 13:47
  • $\begingroup$ @slebetman (academic pursuit only) if you had a pulley attached to the cieling? My interest is in the greater efficiency of the prop vs propwash force down. Sort of like a turbine that can pull itself into the wind. But in a closed system, the vortex ring will form. Interesting the 1 might lift and spin, but way less efficiently than an open system. $\endgroup$ May 6 at 15:05
  • $\begingroup$ This is turning into another "if an airplane was on a treadmill..." $\endgroup$ May 7 at 1:38
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In short, no. A aerofoil works by creating a region of high pressure below the wing and low pressure above, this provides lift.

In the enclosed system, we still have high pressure below and low pressure above the aerofoil but countering that we have normal atmospheric pressure above and below the contining tube with both providing a net downward force which equals and cancels the upward force experienced by the aerofoil.

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Sure, depending how you define "Lift"

Option 1, no way. You could possibly make it leap into the air by sloshing the air around violently enough, but that's unlikely, unsustainable, and too much of a stretch of the definition.

Option 2, sure. If your wing is near enough to the exit, it could redirect the air down, which will push the system up. It's hard to imagine that providing enough lift to fly.

Option 3, maybe. If you implemented it in a way that drives significant pressure changes, you might be able to get a pressure differential that causes the diffusing structure to lift up.

In both Option 2 & 3 though, the wings basically don't matter. The wind tunnel is acting as an overly-elaborate airfoil.

So. Does that count?

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Expanding on @pilothead's answer, remember that the airfoil generates lift by creating a low pressure area above the wing. This low pressure area isn't just lifting the wing up, it is pulling in air and whatnot from every direction. The airfoil lift's because it is part of the "whatnot". In your enclosed space, roof of your enclosure is also part of the "whatnot" and the exact same amount of force placed on the upper surface of the wing is placed on the enclosure above the low pressure area, pulling it downward.

Basically, it means that since the low pressure area is inside the enclosure, it can't lift the enclosure. You would need a low pressure area above the enclosure in order to lift the enclosure.

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Option one is a fully closed system so its center of gravity will not (in steady state) be affected of the internal fans and wings

Since all flow is inward bound in option two it would either go to zero or pressure would go to infinity, so no lift.

But for option three, since the geometry produces circulation around the upwards facing tube-bends, it might actually lift off. Not perhaps because of the wings but rather because of the geometry of the tubing and the fans.

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