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The concept of a wind turbine is not new technology, however, in a day and age where renewable energy is popular, the interest in wind turbines has increased dramatically. This project investigates multiple aspects of a wind turbine and will derive the maximum power efficiency of an ideal wind turbine, first introduced by Albert Betz in 1919. This project will also calculate the size of a wind turbine at maximum efficiency given certain parameters and determine the optimum outlet velocity as a function of wind speed to maximize the mechanical energy produced. These equations will be derived by using concepts from physics and calculus, which will result in determining the optimal efficiency of an ideal turbine to be 59.26%; this is referred to as The Betz Limit.

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Mathematics Commons




Arcadii Grinshpan, Mathematics and Statistics

Scott Campbell, Chemical and Biomedical Engineering

Problem Suggester:

Scott Campbell