Optimal, robust, and benign horizontal and vertical axis wind turbines

Abstract

The remarkable success of fixed speed and pitch ‘propellers’ in tapping the gusting and shifting wind begs explanation. Glauert's two-dimensional analysis of ‘horizontal axis wind turbines’ was an incomplete aside to aviation propeller theory in 1935, but is now the basis of most ‘Hawt’ algorithms. A very simple windmill optimum is found for his ‘blade element momentum’ theory, even for the movement inclined to the wind in ‘vertical axis wind turbines’. Optimizing the two-dimensional ‘Vawt’ pitch cycles for high speed ratios matches the best Hawt power. Making the optimum ‘robust’ to variation of the wind further discovers a Hawt blade element chord and fixed pitch with a very broad quartic optimum around the design wind and ‘benign’ avoidance of high aerodynamic load coefficients further from it; and finds a fixed cycle of pitching to give a benign quartic Vawt.