How Big Is A Windmill? - Glauert Revisited

The size-power relationships of a conventional wind-powered generator are important in selecting the correct size for various applications as well as in comparing different concepts. The obvious similarities to propellers and helicopter rotors suggest that helicopter technology might be used to improve wind generator performance, perhaps including development of a windmill airfoil. In a back-to-basics approach, this paper reviews the analyses of Glauert to determine basic size-power relations. The energy method of Wheatley developed for helicopter/auto-gyro performance prediction is then incorporated into the basic theory. Equations and charts are presented showing ratios of power output to the ideal power capability as functions of mean blade lift and drag coefficients, solidity and rotor tip speed ratio. It is found there is little possibility for improved performance by using improved airfoils. The effects of blade twist and planform are discussed. The basic assumptions of the Glauert theory are reviewed and means are suggested for achieving the basic power capability indicated by momentum theory. Rotor tip speeds, blade loadings, and disk loadings are indicated and a simplified chart is presented to size the rotor.