The Energy in the Wind: Air Density and Rotor Area
A wind turbine obtains its power input by converting the force of the wind into a torque (turning force) acting on the rotor blades. The amount of energy which the wind transfers to the rotor depends on the density of the air, the rotor area, and the wind speed. Wind energy in a slice of air
The cartoon shows how a cylindrical slice of air 1 metre thick moves through the 2,300 m 2 rotor of a typical 1,000 kilowatt wind turbine.
With a 54 metre rotor diameter each cylinder actually weighs 2.8 tonnes, i.e. 2,300 times 1.225 kilogrammes.
Density of Air
The kinetic energy of a moving body is proportional to its mass (or weight). The kinetic energy in the wind thus depends on the density of the air, i.e. its mass per unit of volume.
In other words, the "heavier" the air, the more energy is received by the turbine.
At normal atmospheric pressure and at 15° Celsius air weighs some 1.225 kilogrammes per cubic metre, but the density decreases slightly with increasing humidity.
Also, the air is denser when it is cold than when it is warm. At high altitudes, (in mountains) the air pressure is lower, and the air is less dense.
Rotor Area
A typical 1,000 kW wind turbine has a rotor diameter of 54 metres, i.e. a rotor area of some 2,300 square metres. The rotor area determines how much energy a wind turbine is able to harvest from the wind.
Since the rotor area increases with the square of the rotor diameter, a turbine which is twice as large will receive 2 2 = 2 x 2 = four times as much energy. The page on the size of wind turbines gives you more details.
© Copyright 1997-2003 Danish Wind Industry Association
Updated 25 June 2003
http://www.windpower.org/en/tour/wres/enerwind.htm
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