Small Wings

Space heroes who visit other planets have encountered alien beings who suspend themselves in the air with two small beating wings, each about 40 centimeters long, attached to their backs. These characters are less than a meter tall but probably have a mass of at least 20 kilograms. Could these wings suffice?

Answer

The small wings on such alien beings are probably much too small for a 20 kg body. One could argue that the planet’s gravitational force at its surface is much less than the value here on Earth, so the alien being’s weight is much less also. That may be so, and the proposition is not unreasonable. However, we still require a sufficient air density for the wings to do their work and a breathing atmosphere for our Earthling on the foreign planet’s surface. (After all, this example has the human standing there breathing without any special oxygen supply.)

We need to determine the required density of the atmosphere of this alien planet, assuming an adequate supply of oxygen molecules for breathing by our visiting human. Earth’s atmosphere at sea level has a total density of about 1.4 kg/m³, of which O₂ comprises about 20 percent by molecular composition. That is, 1 cubic meter of air weighs 1.4 kilograms. The remainder, of about 80 percent, is N₂, which has a molecular weight of 28, compared to 32 for O₂. For simplicity, we assume they have the same molecular weight, so we require an alien atmosphere to have about 0.3 kg/m³ of oxygen available for breathing.

The gravitational acceleration g′ at its surface determines the air density at the surface for a given molecular composition and air temperature profile. Most planets will have an acceleration not much different from the value of 9.8 m/s² here on Earth, as one can check out for the planets in the Solar System, for example. So the wings must be capable of exerting an upward force at least as great as the downward gravitational force in our example, the weight F = g′ m of the alien being with small wings, or 200 N if g′ = 10 m/s².

We assume that a very strong 20 kg individual can stretch out his arms horizontally to the side and push upward against two supports with about 200 N downward force to lift the body. However, this same individual will not be able to use small wings of the same length and perhaps just a little wider than the arms to beat against the air with equal effect. If you doubt this hypothesis, put some arm length wings on a strong person and observe how easily he or she can lift off and hover a few centimeters above the ground!

If the alien being were hollow inside so that its total mass is significantly less than expected for the body size, there may be no problem with hovering.