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 BetzJoukowsky limit. The analytic correction accounts for the effect that the non-uniform atmospheric boundary layer velocity distribution has on the BetzJoukowsky 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 100m rotor diameter at 80m hub height in a neutrally stratified boundary layer flow predicts a maximum power increase of 12%, depending on the approach terrain. Copyright (c) 2012 John Wiley & Sons, Ltd.