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Lecture Notes




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121 Proc. Okla. Acad. Sci. 56: 121-124 (1976) ON THE AERODYNAMICS OF WINDMILL BLADES Martin C. Jischke University of Oklahoma, Norman, Oklahoma The optimum twist of a windmill blade is examined on the basis of elementary blade-element theory. For a given wind speed and blade angular velocity, it is shown that the maximum power efficiency is achieved when the blade is twisted according to a program that depends upon the variation of the sectional lift and drag coefficients with angle of attack. Results for a typical airfoil cross-section show that the optimum angle of attack decreases from the maximum-lift-coefficient angle of attack at the blade root to greater than eighty percent of this value at the blade tip. INTRODUCTION The energy crisis in the United States has caused a considerable growth of interest in alternative sources of energy in the past few years. Among the several energy sources being explored, wind energy ― a form of solar energy ― shows much promise in selected areas of the United States where the average wind speeds are high. These areas include the Aleutian Islands, the Columbia River Basin, the Atlantic Coast of the New England states, the southeast boundary of Texas, and the Great Plains area, which includes most of Oklahoma. Estimates of the potential contribution of wind power to the energy needs of the nation vary from as low as five percent to as much as one hundred percent. While the latter figure is suspect, it is clear that in the high-wind-speed regions of the country, wind power can, if properly developed, become a significant energy source. Initial estimates suggest that electrical power can be developed from the wind at a cost of approximately $400 per installed kilowatt as compared with $250 to $400 per installed kilowatt for fossil fuels. While energy storage remains problematic for wind power, it would seem that the environmental benignity and low operating costs of wind power coupled with the growing costs of fossil fuels will make wind power increasingly attractive in the future. The utilization of the energy in the winds requires the development of devices which convert that energy into more useful forms. This is typically accomplished by first mechanically converting the linear velocity of the wind into a rotational motion by means of a windmill and then converting the rotational energy of the windmill blades into electrical energy by using a generator or alternator. For purposes here, we can thus view the windmill as a mechanical device for extracting some of the kinetic energy of the wind and converting it into the rotational energy of the blade motion. This is accomplished, in detail, by having the blades oriented at some angle to the wind so that the wind blowing past the blades exerts an aerodynamic force on them and thereby causes them to rotate. The question that naturally then arises is: at what angle to the wind should the blades be set? That is, is there a best angle? This, of course, implies ...





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