Dual optimum aerodynamic design for a conventional windmill

The theoretical possibility of designing the blading of a conventional windmill so as to match the optimum loading for maximum output at two different operating conditions (i.e., at two different values of the ratio of tip speed to wind speed) is investigated using the vortex blade element theory. The theory of optimum loading is developed, including the effect of profile drag. For the range of parameters considered, it is shown that the effect of profile drag on blade loading is quite small, although the effect on efficiency is significant. The simpler theory, neglecting profile drag, and first presented by Glauert, then is used to design three sets of blading which match the Glauert loading conditions at two conditions, tip speed ratios of 4 and 5. The first design is for fixed blading and the other two involve pitch changes of 1.5° and 2° between the two conditions, the latter two showing a moderate degree of taper and being more desirable from a structural design point of view. It is concluded that the possibility of designing blading having high efficiency over a considerable range of operating conditions exists and can be used.