Wind power is great because once you set it up, it’s pretty much just there giving you power. Of course, it needs wind to operate and the faster the wind, the more power you get. However, there is a theoretical maximum power described by Betz’s Law. I’m going to derive that maximum power.
The Idealized (and wrong) Power
It’s not terrible to do this the wrong way. It at least gives a basic idea of the power from a turbine. Imagine that I have a turbine with a rotor area A. Wind moves into the turbine with a speed v. We can visualize this wind as a large cylinder of air.
This cylinder has a length of vΔt (since the air moves this distance in some time interval — even if we don’t know the time). Since the final air velocity is zero, the kinetic energy of this air all goes into the power of the turbine.
Using the density of air (ρ = 1.2 kg/m³) and the volume of a cylinder, we can find the ass.