A 100-year-old math problem has been solved, helping to improve wind turbine efficiency
Penn State University undergraduate discovered a novel approach to an old problem and made it possible for engineers to create more efficient winds turbines.
Because the real world can be a complex place, physicists often start by using the simplest possible approximation of a problem. They then refine it as necessary. Hermann Glauert was a British aerodynamicist who made the first attempts to optimize wind turbines in the early twentieth century.
For wind turbines, optimization is important because we need to maximize the amount of energy that can be extracted from a set of materials. Glauert’s solution provided an answer but assumed wind turbines to be solid discs that did not react to forces they encounter in real life. There have been numerous attempts since then to improve Glauert’s model. However, Divya Tiagi, an undergraduate at Pennsylvania State University, recently made a revolutionary leap. Tyagi, in a Wind Energy Science paper published by the journal, found a way that was much easier to increase complexity and sophistication.
Calculus of Variations (
Tyagi used a method called the Calculus of Variations. Normal calculus involves varying an unknown parameter to determine how it will affect the solution. You can then find the best solution to that particular problem. What if the solution is not known in advance? The calculus of variation is used in this case. You can vary the mathematical function to describe a range of problems, instead of changing a perimeter. It is important to arrive at a solution that can be applied in a wide range of different situations.
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Improve Wind Turbines (
) Tyagi revised Glauert’s original solution using this technique. Tyagi was able to apply the solution in more complex scenarios. Tyagi specifically included effects from the downwind thrust, which is the wind force blowing against the blades of the turbine rotor. Tyagi’s results also include the effect of the blades being bent at the roots by the wind pressure.
Tyagi created a formula that folds multiple factors that are important for real-life turbines. The engineers can use this simple solution to create the most efficient turbines. It is crucial to wind energy, because even one percent can be a huge difference. As an additional bonus, the wind turbines themselves are no longer solid discs.
Learn more: A low-toxic technique could help recycle wind turbine blades
Sources for Articles
Discovermagazine.com’s writers use high-quality peer-reviewed sources and studies for their articles. Our editors check for accuracy, scientific standards and editorial standards. Check out the following sources for this article.
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European Academy of Wind Energy. Glauert’s optimal rotor disc revisited: a calculus of variation solution and exact integrals of thrust and bending moments coefficients.
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Journal of Aeronautical History. Hermann Glauert FRS, FRAeS (1892 – 1934)
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Springer Nature. A History of the Calculus of Variations From the 17th to the 19th Century.
Paul M. Sutter, cosmologist and NASA advisor is the host of the podcast “Ask a Spaceman” as well as a U.S. citizen. Cultural Ambassador. Author of Your Place in the Universe, How to Die in Space and Your Place in the Universe.
