A windmill takes energy from the wind (fluid) and produces power. The maximum theoretical power is 16/27 of the wind’s power this is known as the “Betz limit”. The wind’s energy, because it is moving, is in the form of kinetic energy and if all the energy was captured by the propeller or rotor there would not be an airflow consequently it can be said that the “lost” energy is used to keep the air flowing.

The maximum power available P is equal to –

K x D x A x V3

Where
K is a constant (Betz Limit)
D is the density of air (kg/m3)
A is the swept area of the blade (m2)
V is the velocity of the wind (m/s)

It can be seen that by doubling the velocity of the wind the available power is increased eight times (2×2x2) and by doubling the blade diameter the available power is increased four times. When the power required is known and estimating the efficiency of the machine it is possible to size the rotor for the average wind speed available. Equally the efficiency that manufacturers claim can be calculated. It should be noted that when calculating the power available the efficiency of the total system should be used, that is, not only the generator and gearbox but also the transmission and storage.

Wind turbines have “rated outputs” which give the best output at a particular wind speed. But this output must not be taken to mean power available i.e. rated output x hours, as the wind speed is not constant and will vary from around 1/10 to 1/3 of the figure.

Efficiencies achieved in practice are much less than the theoretical 59.3%(16/27), that of a traditional windmill with a small number of sail-like blades is a little over 5%. However since wind is often available in practically unlimited quantities, this “efficiency” can become of little significance.