Non-uniform velocity distribution effect on the Betz-Joukowsky limit

A simple analytic correction is derived for the maximum efficiency of an ideal wind turbine rotor, the Betz-Joukowsky limit. The analytic correction accounts for the effect that the non-uniform atmospheric boundary layer velocity distribution has on the Betz-Joukowsky derivation. The maximum power coefficient predicted by using the atmospheric boundary layer velocity profile is slightly higher than that predicted by using a uniform velocity distribution. The application of the correction to a 100 m rotor diameter at 80 m hub height in a neutrally stratified boundary layer flow predicts a maximum power increase of 1-2%, depending on the approach terrain.