The Power of the Wind: Cube of Wind Speed
The wind speed is extremely important for the amount of energy a wind turbine can convert to electricity: The energy content of the wind varies with the cube (the third power) of the average wind speed, e.g. if the wind speed is twice as high it contains 2 3 = 2 x 2 x 2 = eight times as much energy.
Now, why does the energy in the wind vary with the third power of wind speed? Well, from everyday knowledge you may be aware that if you double the speed of a car, it takes four times as much energy to brake it down to a standstill. (Essentially this is Newton's second law of motion).
Power Content of the Wind
In the case of the wind turbine we use the energy from braking the wind, and if we double the wind speed, we get twice as many slices of wind moving through the rotor every second, and each of those slices contains four times as much energy, as we learned from the example of braking a car.
The graph shows that at a wind speed of 8 metres per second we get a power (amount of energy per second) of 314 Watts per square metre exposed to the wind (the wind is coming from a direction perpendicular to the swept rotor area).
At 16 m/s we get eight times as much power, i.e. 2509 W/m 2 . The table in the Reference Manual section gives you the power per square metre exposed to the wind for different wind speeds.
Power of the Wind Formula
The power of the wind passing perpendicularly through a circular area is:

P = 1/2   v3    r2

Where P = the power of the wind measured in W (Watt).
= (rho) = the density of dry air = 1.225 measured in kg/m 3 (kilogrammes per cubic metre, at average atmospheric pressure at sea level at 15° C).
v = the velocity of the wind measured in m/s (metres per second). = (pi) = 3.1415926535...
r = the radius (i.e. half the diameter) of the rotor measured in m (metres).
© Copyright 1997-2003 Danish Wind Industry Association
Updated 1 June 2003
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