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According to this site, NASA produced a public domain painting representing what the Olympics could look like on a lunar colony. In the upper right of the picture, there are people flying by flapping wearable wings. Given Moon's gravity with Earth's atmospheric pressure in a lunar colony dome, like the one shown here, could this be possible? How much force would you have to push down on your arms to take off? Would taking off be feasible, or is just gliding?

Lunar Olmpics

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Yes, in a word. Would have to get more details to add to this... –  PearsonArtPhoto Jun 4 at 13:37
    
Relevant XKCD: what-if.xkcd.com/30 –  gerrit Jun 4 at 14:22
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@gerrit: I just love how "there is an xkcd that might be intresting too" mutated to the standard phrase "relevant xkcd". We might want to think about "is already answered as xkcd" as a close reason –  PlasmaHH Jun 4 at 19:31

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The lift force you would need to produce would have to be equal (stable flight) or greater (take off) than the force pulling you back towards the moon. If your mass is average for a male at 62kg, the force from the lunar gravity would be F=ma, = 62kg x 1.622m/s2 = 100N (almost exactly).

lift force = 0.5 x density x lift coefficient x area x velocity^2

This is as far as you can really calculate without specifying shape/size of the wings etc. However this site shows that the human arm can exert around 50N -60N (that's per arm). So with the correct design it seems like you have 1.1 times the required force available. This all ignores the mass of the wings themselves, the percentage of force that is applied in the appropriate direction etc, it at least implies you would be able to hover on the spot until you get tired. I suppose doing so would become comparable to the world record for treading water - after 85 hours you'd be pretty bored.

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With numbers that close, it seems wing design is going to be critical for the experience. I wonder how getting a running start would help. Also to consider would be the range in arm motion and muscles required and the duration of muscular exertion forces needed during the flapping motion. –  TK-421 Jun 4 at 18:36
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That's true. Although, the values quotes for arm strength are average of a typical male. So you could expect an athlete to perform significantly better. Getting a running start would definatly help, I'd guess that you might even be able to run and take off into a glide (given the right wing profiles ofcourse). –  FraserOfSmeg Jun 4 at 19:42
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Your guy can't fly. You're showing that it takes all the guy's got to fly--but after making a flap he has to move his arm back for the next one. Is he really going to be able to reposition 10x as fast as he flapped? The athlete has a chance, though. –  Loren Pechtel Jun 5 at 3:36
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It looks like this assumes that the you have to be able to produce a thrust:weight ratio >= 1 in order to fly. But you don't; wings are more efficient than that. It's straightforward to create a wing with a lift:drag ratio of 10, and much higher ratios can be achieved with careful attention. Calculating the thrust available from a flapping motion is rather a complicated exercise, but the fact that human-powered sustained flight is possible (if unwieldy, and requiring extreme athletics) on Earth suggests that it would be straightforward in a 1 atm environment on the moon. –  pericynthion Jun 5 at 5:44

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