Rotor Efficiency and Betz limit

Betz limit is defined as the maximum fraction of the power in the wind that can theoretically be extracted, usually given as 16/27. or by other words that the maximum value for the power extracted from the wind is 0,59 or 16/27 of the total power in the wind.

An airstream moving through a turbine rotor disc cannot give up all of its energy to the blades because some kinetic energy must be retained in order to move the airstream away from the disc area after interaction. In addition there are frictional effects, which produce heat losses. Thus, a turbine rotor will never extract 100% of the wind's energy.



As the air stream interacts with the rotor disc and power is extracted, the air stream speed is reduced by an amount described by the axial interference factor, a. This is the ratio of the upstream to the downstream wind speed. Equation below show the power using the axial interference factor.



by substitution, the power co-efficient Cp may be defined


By differentiating with respect to a, the maximum value of Cp occurs when a = 0.33. so we can find that, Cp,max = 16/27 = 0.593 Cp,max = 16/27 = 0.593

this known as Betz limit,