Large Wind Turbine

Power in the wind

Energy in the wind is the kinetic energy it contains. For certain mass of air, the kinetic energy can be calculated by the formula below.

Energy = 1/2 X Mass X (Velocity)^2

It can be easily shown that the power of the wind flowing through a certain area is given by

Power = 1/2 X Air Density X Area X (Velocity)^3

Where

Power is in watts
Air Density is in kg/m3
Area is the cross-sectional area of the flowing air in m2
Velocity is in m/s

At sea level and at 15 degrees Celsius, dry air has a density of approximately 1.225 kg/m3. varying with pressure and temperature. Air density decreases with increasing altitude.

It can be seen that the power in the wind is proportional to the cube of the velocity, and is proportional to the swept area of the turbine rotor. However, only a fraction of this power can actually be extracted by the rotor.