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Lets indulge in a bit of Mad Science, here.

Assuming the world described here: Making the Enterprise Fly (60% of earth's gravity, 50% denser atmosphere) what is the wingspan needed to allow an average adult human to fly?

Assume feathery wings, and that the resulting winged human needs to be able to fly well, not just founder through the air technically flying.

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    $\begingroup$ Keep in mind that wing area is what really matters, not just wing span. $\endgroup$ – Tim B Oct 20 '14 at 12:53
  • $\begingroup$ Truth, although wing height is rather severely limited by the height of the person. 175.3 cm on average for a male. $\endgroup$ – Danny Reagan Oct 20 '14 at 12:58
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    $\begingroup$ I think this would be a much more valuable question with normal earthlike conditions... $\endgroup$ – Liath Oct 20 '14 at 13:12
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    $\begingroup$ @Liath That question has been done. A lot, really: wired.com/2012/01/why-cant-humans-fly-like-birds $\endgroup$ – Danny Reagan Oct 20 '14 at 13:21
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    $\begingroup$ Wingspan is not the only limiting factor here. If you truly need to fly (not just glide) then you also need power. I do not believe human arm muscles are capable of providing that power in earthlike conditions (our stronger leg muscles are just barely strong enough, given proper gearing). Apparently, this would be possible on Titan: what-if.xkcd.com/30 $\endgroup$ – Caleb Hines Oct 20 '14 at 13:23
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According to google:

The largest species of bat are a few species of Pteropus (fruit bats or flying foxes) and the giant golden-crowned flying fox with a weight up to 1.6 kg (4 lb) and wingspan up to 1.7 m (5 ft 7 in).

It also tells us that

While the average body mass globally was 62 kg, North Americans weigh in at 81.9 kg.

You've said average at a gravity of .6g so we'll say use 38.

It's actually the surface area of the wing rather than the span which generates lift. Taking a big simplification we'll assume the bat has square wings. So assume our bat has an approximate wing surface area of about 2.9 square metres giving a surface area to weight ratio of 1.8.

We can scale up here... a 62kg at .6 gravity human would require a wing surface area of 68 square metres equating to a wing span of about 8.5 metres.

These are VERY rough calculations (for one I've never seen a bat with square wings) however I hope it illustrates that a human would require enormous wings in comparison to their height (not to mention that the wings would also add weight to the person which would also require extra wing!).

I've not taken into account the increased atmosphere because humans are a lot less aerodynamic than traditional flying creatures and we're not factoring in the weight of the wings.

Clearly your average human would need to lose a lot of weight for this to be even remotely possible, we're not talking about dieting... we're talking about lightweight bones, organs and muscles!

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    $\begingroup$ I've had a crack at this but I'm not 100% happy with this answer, if someone spots some maths mistakes please feel free to correct them! $\endgroup$ – Liath Oct 20 '14 at 13:06
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    $\begingroup$ Not to mention that humans lack the upper arm strength to continuously flap such heavy wings. $\endgroup$ – DonyorM Oct 20 '14 at 13:43
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    $\begingroup$ @DonyorM all in all I think we're better off with Leonardo's flying bike! $\endgroup$ – Liath Oct 20 '14 at 13:47
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    $\begingroup$ The human would have to gain considerable muscle mass, offsetting the gains made by having hollow bones. Look at any bird, huge jutting sternum and massive pectoral to body weight ratio. Unless of course the muscles could be made more efficient. The higher oxygen atmosphere present on earth many millions of years ago allowed giant dragonflies to fly. $\endgroup$ – superluminary Oct 20 '14 at 15:07
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    $\begingroup$ @NickNo, many modern depictions of both angels and demons, Harvey Birdman (Hanna-Barbera), Angel (Marvel Comics), Icarus (Marvel Comics), and many depictions of the Valkyries all come to mind as a humanoid form with wings that have nothing to do with the arms. $\endgroup$ – Brian S Oct 20 '14 at 21:51
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It really depends how fast you expect them to fly. But let's look at how your changed world will affect them.

The equation you're looking for is:

Area = (lift force)/(half velocity * velocity * air density * lift coefficient)

Or mathematically:

$$ A = \frac{L}{0.5 v^2 \rho C_L} $$

$A$ (area) is the number we're looking for.

$L$ (lift force) must be equal to the mass of the person, in order to support their weight. People on earth average 62kg. With all the exercise from flying, they might average a little lower in that world.

$v$ (velocity) is the take-off speed: the speed at which the forward movement through the air makes the lift cancel out the person's mass.

$\rho$ (air density) is specified as 1.5 times Earth's.

$C_L$ (lift coefficient) is approximately 1, and depends on the angle of attack and wing shape. You can assume their wings are decently well shaped, so can ignore this term. Changing this to make thrust is, basically, what flapping does.

Wing loading on an Earth hang glider is as high as 6.3 kg per square meter, and the takeoff speed is about 15 mph.

From the equation above, we can see that the wing area is proportional to mass ($L$), and inversely proportional to air density ($\rho$). In other words, wings need to be larger when there is more mass; and don't need to be as large when the air is denser.

So we can multiply the needed area by $\frac{0.6}{1.5} = 0.4$. So 6.3 kg per 0.4 m2, or 15.75 kg per square metre.

That's roughly a quarter of human bodyweight, so you'd need four square metres for an average person. Two square metres per wing. Assuming folded wings like birds have, that's certainly achievable.

Now, let's push the limits. Adults with anorexia have a BMI below 17.5. So let's aim for that, as the acceptable limit of thinness. When $M$ is mass, and $h$ is height, $ M = h^2 \times 17.5 $.

This scales with the square of height, so height is definitely not a good thing. So assume 1.5 m (approximately 4'11").

$$ 1.5^2 \times 17.5 = 39 \space\text{kg} $$

That needs only 1.25 m2 per wing!

Something else to note, though, is that lift improves with the square of the velocity, but linearly with area. So if you double the speed to 30 mph, you can quarter the area: in a 30 mph wind, you could hover in a trenchcoat.

If you halve the speed, you only need to multiply the area by $\sqrt{2}$: so for a normal weight person, you can have gliding at 7.5 mph with 2.8 m2 each side, which is still in the range of achievable, and means they could take off in a breeze or at a run, without needing to jump off a hill. For our petite skinny person, that's only 1.8 m2 per side.

Acrobatics would require higher velocities, but that's what a dive is for! :D

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    $\begingroup$ A detail this answer calls attention to is how important local windiness is to wing size. If you live on a windy coast and follow the air currents, you can get by with a lot smaller wings than if you live someplace with calm air. $\endgroup$ – ohwilleke Nov 17 '16 at 4:34
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    $\begingroup$ Hi Dewi. I edited your answer mainly for formatting. Please double-check to make sure I didn't accidentally introduce an error! $\endgroup$ – a CVn Jun 24 '17 at 19:49
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    $\begingroup$ @MichaelKjörling Great work: I learned much about SE formatting from it, and every single edit was a significant improvement: thank you! You edited with a light touch, maintaining tone but firming up the style throughout. Your single line of clarification was needed, and perfectly done. I'd welcome you as an editor any day! To me, as a programmer, single character variable names are sinful, as good code needs no lookup table to make intuitive sense to even a lay reader on the first pass. But with both versions, the answer now caters to both audiences! :) $\endgroup$ – Dewi Morgan Jun 26 '17 at 15:36
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    $\begingroup$ While I definitely agree that single character variable names are often bad, it isn't necessarily so when the quantities involved have well-established symbols, such as $\rho$ for pressure or $A$ for area. That said, I'm not arguing against you here. $\endgroup$ – a CVn Jun 26 '17 at 19:41
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    $\begingroup$ @DavideTesta Sounds like you just described applying a different coefficient of lift ($C_L$). When $C_L$ grows larger, $\cfrac{L}{x C_L}$ grows smaller, so $A$ grows smaller, so you need less wing area -- which is consistent with having a relatively smaller wing span. $\endgroup$ – a CVn Jun 27 '17 at 7:47
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Humans can fly quite well with wings the size of a typical hang glider. Of course they are doing soaring flight rather than flapping, but then the largest species of birds mostly soar. (As did the even larger pterosaurs like Quetzalcoatlus.) See e.g. condors, albatrosses, etc.

Soaring puts limitations on their lifestyle and habitat. They'll need to live near the tops of cliffs or hills, and in windy regions.

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The only way humans could ever fly is by being little flying angels! Let me explain:

What if you allowed some sort of genetic mutation to the human DNA so that our growth stops very early, around 4 years old.

It might have some minor impact on our cognitive functions since our skull would have smaller volume. You might solve that by also modifying our DNA so that our head is bigger in proportion to our body size. Also modify our DNA so that we have wings, and the appropriate muscle and cardio-vascular system to move them fast enough to fly.

Our body weight would then be around 15-20kg, similar to an albatros. Then flying on earth (1G) would seem possible.

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  • $\begingroup$ //It might have some minor impact on our cognitive functions since our skull would have smaller volume// if you can bio-engineer us smaller then it's not unreasonable to assume you can also engineer a larger head to body ratio to whatever might be appropriate or needed : of course there are issues of pelvis to head ratios for birth so you might want to adjust the pelvis in some manner as well (unless you're going for 100% cesarean births). $\endgroup$ – Pelinore Dec 7 '18 at 2:17
  • $\begingroup$ ^ or perhaps adjust the growth pattern so the head grows more after birth than it does now. $\endgroup$ – Pelinore Dec 7 '18 at 2:22

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