How Big Would Wings Need to Be for Humans to Fly
Aerospace engineer here.
Like UnholyDemigod said, humans cannot produce the power required to flap wings of this size, but let's look at gliding flight.
Lift is generated through 2 main mechanisms. The first is from airflow hitting the lower part of the wing, "pushing" the wing up (almost like a sail); this is Newton's third law at work. The second mechanism is the generation of a low pressure zone on the upper surface of the wing, this is formed due to airflow accelerating over the convex shape of the upper surface (faster air leads to lower static pressure).
A wing generates lift that is proportional to its surface and to the dynamic pressure of the incoming airflow:
L=liftcoefficient*1/2*density*velocity^2*surfacearea Since your man weighs 190 pounds, we need a lifting force equal to 190 pounds, or 845 Newtons. The lift coefficient is a value denoting the lift-creating capabilities of the wing. This value is found by using complex analytical or numerical methods, but for simplicity let's assume a value of 1. At sea level the air density is around 1.225 kg/m3. If we then assume that the man is able to run 3 m/s with this contraption mounted on his back, we can easily solve the equation.
This leads to a wing area of 153 m^2, or 1647 sq ft. With an aspect ratio 12, which is not uncommon for glider-type aircraft, that leads to a wing span of 43 m. Almost the width of a football field.
This wingspan is obviously unfeasible, so how to improve it? Looking at our lift equation, we see a very convenient way of increasing our lift. We could increase our speed, and since the speed is to the power of two it will have a very large impact.
Let's say that our man jumps off a cliff. He can easily reach a velocity of about 10 m/s (22 mph) if he is facing down with his wing. Redoing our calculation, keeping the other variables the same, gives us a wing surface of only 14 m^2. That's a huge improvement, but it's still too big, especially when we consider our high aspect ratio wing would give a span of 13 meters.
To remedy this we go back to our lift equation again, and decide that we have to increase the lift coefficient. Usually this means countless hours of analysis and wind tunnel testing. Needless to say, it's very expensive. The easier way to increase the lift coefficient is simply to increase the angle of attack of the wing, this means to point your wing more upwards. Problem is, if you point it too high up, the airflow going over your wing won't be able to "stick" to the surface. In other words, your wing stalls and you fall out of the sky.
Since we are smart we know that if our wing is short and the front edge of is angled sharply backwards, so that it looks like a triangle from above, we can reach much higher angles before stalling. (Vortex lift on wikipedia, for those who are interested) We also know that if we increase the curvature of our wing, we increase the speed of the air going over the top side of the wing. This also increases the lift coefficient. In the end, when we are done designing, we get a new lift coefficient of 2.0. Great!
We redo our lift calculation, and find the new surface area. It's only 7 m 2 (75 sq ft) now! But remember, our wing is no longer a high-aspect ratio wing, we changed that to increase our maximum angle of attack and our lift coefficient. Now it's what we call a delta wing, and it's much more stub. In fact, it kinda looks like this.
Edited to correct a blunder in the aspect ratio calculation. Thanks fourhandedwarrior! And to clarify dimension of football field.
How Big Would Wings Need to Be for Humans to Fly
Source: https://www.reddit.com/r/askscience/comments/sxz8v/how_big_would_wings_have_to_be_to_facilitate/
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