The power coefficient of windmills in ideal conditions

The windmill efficiency, also designated as the power coefficient, is defined as the ratio of the actual power output to the power present in the free stream of a fluid flowing through the same cross-sectional area. There are remarks in the literature to the effect that the power coefficient of actual windmills is very close to the ideal power coefficient or Betz limit of 0.5926. In this paper, the traditional basic assumptions in establishing the Betz limit are reviewed with mathematical derivation of the ideal power coefficient. It is concluded that the value of the ideal power coefficient is 0.89.