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I know that we could never fly even if we had wings because we're not aerodynamic but if we were. How big ( length * width or area ) would they have to be? I would like a clear answer or at least an equation that is metric.

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marked as duplicate by Aify, ckersch, Hohmannfan, Brythan, Pavel Janicek Jun 2 '16 at 6:21

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ An answer to this question puts the area (\$m^2\$ at 1.8 times the mass (kg). $\endgroup$ – Brythan Jun 2 '16 at 3:23
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    $\begingroup$ I'm 100000% sure this is a duplicate, I just can't find it. $\endgroup$ – Aify Jun 2 '16 at 3:42
  • $\begingroup$ @Aify yes! Complete duplicate $\endgroup$ – Aarthew III Jun 2 '16 at 3:51
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Aerodynamics (if you mean lack of streamlining) is the least of our worries. I presume by flight you mean sustained horizontal flight in air densities similar to 5,000 ft ASL and 20 deg C temperature.

The two biggest problems are wing mass and strength and power-to-weight ratio.

Let's take a total mass of 100 kg as a starting point. Let's say half of that is wing. Figure a flying speed of 15 mph, or 6.7 m/sec, which is a bit less than the 20 mph produced by a 10 second hundred yard dash. Wing span is 8 meters, which allows each wing to fold into 2, 2 meter segments on the ground, and these are roughly comparable to the length of a person.

Here you can find an estimate for the power required to fly: $$P = \frac{W^2}{\rho v b^2} $$ where P is power, W is weight in newtons, \rho is air density, v is velocity, and b is wingspan. For the first cut, $$P = \frac{1960^2}{1\times6.7\times16} = 35.8 \text{ kw} $$ This just won't work. Here is a superbly fit 95 kg cyclist putting out 700 watts. In order for this to work, wingspan has to increase by a factor of 6. Really? 24 meters? 12 meters per wing?

Now look at wing construction. Assume a main spar with a 10 cm diam running the length of the wing, weighing 1/3 the total wing weight. That works out to 1 kg/m, with a density of 132 g/$m^3$, or about 1/7 that of water. A spar that long which will support 50 kg with that sort of density, and organic to boot, is going to be something of a challenge.

With a spar diameter of 10 cm, the frontal area of each wing will be 1.2 meters, for a wing cross-sectional area of 2.4 meters. The cross-sectional area of a person is about 1+ feet by 3- feet, or about 1/3 square meter. This is 1/8th the wing area, which is why our being aerodynamic really doesn't enter the picture.

So, at a first cut, a human flyer which flies at a sprint pace will have about an 80 foot wingspan. Good luck getting through doorways.

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