How much power can I get from the wind?

So how much power can I actually get from the wind? I turns out that the answer is not that simple, because there are a lot of factors at play. For instance wind speed, type and size of wind generator, efficiency of the generator etc.

So let us start by looking at the wind itself. The power in the wind is influenced by three factors, the wind speed, the area the wind is hitting and the density of the air.

So this sound logical to me. So air at sea level has a density of about 1.23 as you go higher the density decreases.

The formula to calculate the amount of watts of power in the wind is as follows:
Power in the wind(Watts) = 1/2 * rho * A * V^3
where:
rho = air density,
A = area in square meters
V = velocity in meters/second

So at sea level for a horizontally mounted propeller with a diameter of 2 meters and a windspeed of 5 m/s we get the following:
Area of the a circle = Pi * radius squared so for the propeller we get
Pi * 1^2 = 3.141
Power = 1/2 * 1.23 * 3.141 * 5^3
Power = 242 watts

Wow! that seems like a lot of power and as a result a smallish turbine in a moderate wind can produce a lot of power. Unfortunately, along came Albert Betz. He calculated that although there is all this pwer in the air you can't harvest it all, because it flows around things. So he mathematically proved that at best you can harvest just over 59% of the power.

So that gives us 242 * 0.59 = 142.78 watts

This is still not to bad, but then we need to take into account that the our generator is not 100% efficient. From what I can read a realistic percentage for a decent DIY wind turbine is around 35%.

242 * 0.35 = 84.7 watts

Luckily, if you look at the formula you will notice that wind velocity is cubed, so what this means is that as the wind increases we get a cubic increase in power.

At 35% efficiency at double the wind speed we get
1/2 * 1.23 * 3.141 * 10^3 * 0.35 = 676.1 watts

Now that looks much better.