Conflicts In Betz Limit and An Alternative Approach for Wind Turbines

Abstract

The popularly accepted Betz limit for wind turbines calculates that the incoming wind speed can be reduced to only a third, and efficiency can be at most 59.3 %. This paper suggests that Betz may be based on the paradoxical derivation and assumption that wind speed at the turbine is the average of the incoming and outgoing wind speeds. This average speed is regardless of the distance of the turbine inside the expanding wind stream. Contrary to Betz, turbine energy could be largely from wind deceleration close to the blades and not far away at the input and output. This may give large discrepancies when the outgoing wind speed is much lowered. In this paper, separate cases of constant deceleration and a conically increasing section have been studied. Betz equations may not address the fluid mechanical issues of wind determining efficiency of wind turbines. An accurate measurement of incoming and outgoing air temperatures may verify that much of the wind energy is being converted to heat, which Betz does not consider. The alternative to Betz may be to consider two (not three) cross-sections of incoming and outgoing winds. Reducing outgoing air speed too much will lead to too large an outgoing area, which may be a better approach to finding the practical limits of wind turbines.