Mathematics behind wind turbines

A mathematical conundrum of building the most efficient wind turbine is one that many mathematicians have attempted to solve. In the early 20th century, Hermann Glauert, a British aerodynamicist, first came up with a solution to it; however, the solution was not perfect as it excluded the effect of various forces during the actual operation and considered the wind turbines as a single disc. Recently, an undergraduate student at Pennsylvania State, Divya Tyagi, created an equation that answered the conundrum. He utilised the calculus of variations to approach this challenge. Rather than varying only one parameter, it varies the entire function to find the optimal solution. By using this technique, Tyagi rewrote Glauert’s solution and included the effects of downward thrust on the turbine blades and the effects of the blades bending at their roots. This, therefore, helped the engineers to design the most efficient wind turbine.