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Suppose I am a super-being. From the outside I look and act exactly like an ordinary human. My flexibility of limbs is the same as that of a human so I can't shape-change or bend my arms unnaturally.

My superpowers are strength, speed and endurance. I can move my arms, hands, fingers as fast as I like. My skin is tough so I won't get burned up.

Assuming I have no equipment and am dressed only in an ordinary (but extra-strong) bathing suit, how fast do I have to flap my arms (and or legs) in order to fly? What is the best kind of motion for flight through the air, swimming or flapping?


Assumptions

I am strong enough and fast enough to perform the required movements continuously for say half an hour.

I am not damaged by the stresses and strains of my efforts.

I am of average weight, height build etc. for a human. From the outside, no one can tell the difference simply by looking.

Gravity and other conditions are Earth-normal for me and I have no powers of levitation apart from what I can achieve by moving my limbs.

I can jump for take-off but I can't cover long distances without flapping. I need to fly and maintain constant height and velocity** for at least half an hour and that would be impractical if I simply jumped.


Notes

In case anyone objects that my super-powers require magic. That may be so but all the magic is contained within my body. I can't reach out and change the forces of nature such as gravity. I can only affect what is inside my skin and I can't change my mass.

** I've recently edited the requirement to constant height and velocity for clarity.

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    $\begingroup$ You can't. It's not a question of speed. It's a question of aerodynamics. Flapping your arms does not generate lift. $\endgroup$
    – Mary
    Jan 3 at 23:09
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    $\begingroup$ @Mary - What about doing a super-fast breast stroke then? $\endgroup$ Jan 3 at 23:17
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    $\begingroup$ I'm convinced @Mary is right. It's easy to push against water compared to atmosphere. Flapping your arms with super speed would create a lot of noise and might create localized atmospheric interference, but an arm simply can't push enough air at any speed to displace the weight of the body. Even if you didn't flap and converted to a swimmer's motion to scoop air on the down-stroke but minimize resistance against the up-stroke... I can't feel the suspension of disbelief on this one. The surface area of a bird's wing vs. its weight is enormous compared to a human. $\endgroup$ Jan 4 at 3:50
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    $\begingroup$ With enough thrust pig can fly, you need very strong superhuman level strong... farts. Then use the flapping to signal the ground crews your progress. $\endgroup$
    – user6760
    Jan 4 at 4:27
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    $\begingroup$ @JBH If you move your arms fast enough, in theory the Reynolds number should increase to the point where it would be more like you were swimming than flying. But there's the pesky sound barrier in the way. You would also need arms made of unobtanium and a fuel source made of unobtanium. Either way, expect to be flapping your arms far faster than a hummingbird does. $\endgroup$
    – DKNguyen
    Jan 4 at 23:47
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My superpowers are strength, speed and endurance. I can move my arms, hands, fingers as fast as I like. My skin is tough so I won't get burned up.

Why fly at all? Just run and jump. If you are sufficiently fast, and strong, you can just do an extraordinary long jump (take that Olympic athletes) that would look like you were flying to anyone on the ground. But really, who cares if you generate lift? You are effectively flying, because you have cleared buildings and the like and are moving as the crow flies. Of course, this would lead to the consequence of not really being able to change direction once airborne since you aren't an airfoil. And you might smash through some buildings with a poorly timed leap on your way up or down. But let's assume that crashing into and/or smashing through buildings is just harmless fun for you.

But people might still be convinced that you are in fact flying, when in reality you are just falling on a predetermined trajectory. I mean, go watch an airplane, would you know that it was flying or falling unless it did something that would require an airfoil like turning. It could have been launched by a catapult miles away, and going to land miles away for all you know.

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  • $\begingroup$ Also, you can make swimming motions as you fall, and tell people that you are able to swim through the air to try and convince people that you can fly, but you know the truth, you are just jumping. $\endgroup$
    – Ryan
    Jan 4 at 23:40
  • $\begingroup$ Thanks. I did mention (and eliminate) that in my assumptions. The problem is that I want to maintain constant speed and altitude. For example I could help my neighbours by crop-spraying their fields or I could do search and rescue over the sea when it's too rough for helicopters. Without hovering ability it would be very hard to locate a lone survivor in a lifebelt. Also, it would be very difficult, if not impossible, to jump out of the sea if I landed in the wrong spot, or if I was trying to carry the survivor. $\endgroup$ Jan 4 at 23:45
  • $\begingroup$ I suppose that's true but with sufficient speed, you could get yourself into an extremely low earth orbit until the air friction slowed you down enough to land. I take your point that you would want to hover, and that wouldn't really solve your problem. But in theory you could stay up for longer than half an hour with just a jump without expending any extra energy. $\endgroup$
    – Ryan
    Jan 5 at 0:00
  • $\begingroup$ Your other option is to move the world off of earth. Then the atmosphere can be more dense than on earth. Allowing you to "swim" through the atmosphere. The laws of fluid dynamics would allow such a thing if the atmosphere was denser. There isn't much difference between flying and swimming other than the density of the medium. In such a world flight would have been discovered much earlier and more animals would naturally be capable of flight too. $\endgroup$
    – Ryan
    Jan 5 at 0:10
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So...you'd need some sort of suit.

I suppose this could take any one of many forms (autogyro, base jump wingsuit, etc.) to change your aerodynamics. Then the flapping or pedaling of arms and/or legs would be used as your source of power. As stated by Ryan, you could also make long jumps and use your wingsuit to direct your fall/glide. This wouldn't be totally unassisted flight, but due to the weight and aerodynamics of a human body, flight is impossible without a bit of help, at least so far as I understand. Unlike a bird, which has shaped wings, our arms have relatively the same shape on top and bottom, meaning that flapping generates as much downforce as upforce-flying with our arms is like lifting yourself up in a bucket by its handle.

IF you must have only a bathing suit: take it off. Free and breezy is the way to go; use that strategically oversized suit to make yourself a small parachute or airfoil. Jump and glide. Repeat. You will be the freshest, least sweaty superhero, even if you do have to suffer the indignity of superhero names like Butt-boy™ or Ballbouncer™.

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  • $\begingroup$ I don't really like the idea of any kind of equipment. If my clothes could somehow be converted without too much trouble and they aren't too bulky when worn, then that's a possibility. I reckon my hands could act like small wings. They can form an aerofoil shape and the angle can be changed. I'm sure some lift is available that way. $\endgroup$ Jan 5 at 19:02
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You can't. Like Mary said in the comments, it's not a matter of strength, it's a matter of aerodynamics.

In order to fly you need to generate lift, and for that you need an appropriate surface. Wings are good for that because they deflect air just the right way. For a human arm, air goes right through it on both sides. The amount of lift is negligible. You could move your arms at supersonic speeds and you'd still be stuck on ground.

A whole human body can have enough lift to stay afloat if there is a very strong wind coming from below. This is the basis for a certain attraction in some amusement parks, called vertical wind tunnel:

A person floating inside a vertical wind tunnel

You know how that works. In order to fly, your hero would have to generate that amount of wind. No amount of arms flapping will generate that because of aerodynamics, so the next think you consider is blowing down like Superman. Realistically that doesn't work either, because you just can't store enough air in your lungs to pull that off continuously. And if you do it in puffs, you'll be sucking much the same air that you blow.

Alternatively the hero could blow downwards really fast. The same principle of rockets works here - you will have as much momentum up as the momentum of the gas going down. You will see flames or plasma coming out of the hero's mouth, but the hero will go up really fast. That would allow some time for filling in the lungs again, and then another blow in the direction opposite that you wanna go. This would allow for sustained flight.

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You can jump, and when you jump you don't flap your legs like a fly does with its wings. Raise your arms once, really slow... Then lower them down fast enough to move more air than you weight.

How fast would it be? Fast enough to create a hole of emptyness in the air where your arms are traveling... So over sonic speed. Your arms will sound like gunshots.

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  • $\begingroup$ I like the idea of the gunshot sound. It will probably sound like an automatic weapon, excellent. I think what you are suggesting is quite a lot like the breast-stroke when swimming. You can push your arms forward when close together but extend them for the down-stroke. $\endgroup$ Jan 5 at 18:59
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Congratulations, You're a Human Hummingbird

Ok, so this idea is plainly ridiculous, but I don't think it's technically impossible. First rule:

  1. Humming Birds Flap their wings in a figure eight

That's going to be your MO too. You should expect to do exactly the same thing with your body in the air that you would do in the water in order to tread water, so you're going to be moving your arms in small figure eights at your sides below your shoulders and possibly as low as your waist.

  1. Hummingbirds flap their wings up to 70 times per second

That's a lower bound for how fast you have to move your arms, but there's a few important things to remember:

Firstly, your arms are more aerodynamic than a humingbird's wings. How much more aerodynamic is not really something I know enough fluid dynamics to calculate, but I think it's fair to assume that they are at least 3 times as aerodynamic as hummingbird wings as a result of width and shape. Thus, we should triple that speed to 210 beats per second.

Secondly, wingspan in flying birds typically increases at a rate roughly equivalent to the squareroot of an animal's weight. Ok, so a hummingbird has a wingspan of around 6 centimeters and weighs around 5 grams. We'll assume that you have a wingspan of around 1.5 meters (25 times the hummingbird), and you weigh 75 kg to keep the math easy (15,000 times the hummingbird). This means your wingspan is around 5 times too short for the work you need to do. Squareroot that because the area of your wings increases with the square of your wingpan and it's the area of your wings that does the work, and you get a new flapping speed rounded to 500 beats per second.

If you are moving your hands in tiny figure eights at your side 500 times per second, I expect they are moving at least 30 cm a flap, or 150m/s (335 mph for us imperial measurement fans).

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  • $\begingroup$ I don't fully understand your calculation. However the speed of movement you suggest is not a problem - bump it up to 1000 bps if you like. P.S I wasn't me who downvoted. $\endgroup$ Jan 5 at 21:33

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