Indian-Origin Student At US University Solves 100-Year-Old Math Problem

Divya Tyagi, an Indian-origin aerospace engineering graduate student at Pennsylvania State University, has achieved a remarkable breakthrough by reworking a 100-year-old mathematical problem. Ms Tyagi's innovative redesign simplifies the complex problem, making it more accessible and easier to explore. 

Originally developed by British aerodynamicist Hermann Glauert, the problem has been a cornerstone of aerodynamics research for decades. Ms Tyagi's work expands on Glauert's research, uncovering new possibilities in wind turbine design that were previously unexplored, according to the official website of Penn State University. 

"I created an addendum to Glauert's problem which determines the optimal aerodynamic performance of a wind turbine by solving for the ideal flow conditions for a turbine to maximize its power output," said Ms Tyagi.

Sven Schmitz, Divya Tyagi's adviser and co-author, highlighted that Hermann Glauert's original work concentrated solely on maximizing the power coefficient, which measures the efficiency of wind energy conversion into electricity. However, Glauert's research didn't consider the total force and moment coefficients acting on the rotor and also ignored the impact of wind pressure on turbine blades, specifically how they bend under stress.

"If you have your arms spread out and someone presses on your palm, you have to resist that movement. We call that the downwind thrust force and the root bending moment, and wind turbines must withstand that, too. You need to understand how large the total load is, which Glauert did not do," said Mr Schmitz, a faculty member in the Institute of Energy and the Environment. 

He remarked that Ms Tyagi's innovative solution, built on the calculus of variations, offers a remarkably simple yet powerful framework. This mathematical approach enables constrained optimisation, allowing researchers to explore novel aspects of wind turbine design with ease.

"The real impact will be on the next generation of wind turbines using the new knowledge that has been unveiled. As for Divya's elegant solution, I think it will find its way into the classrooms, across the country and around the world," Mr Schmitz said. 

He praised his student's determination and persistence in tackling the complex issue. "When I thought about the Glauert problem, I thought steps were missing and it was very complicated. There had to be an easier way to do it. That's when Divya came in. She was the fourth student I challenged with looking at it, and she was the only one who took it on. Her work is truly impressive," Mr Schmitz added. 

Ms Tyagi, who has finished her bachelor's degree in aeronautical engineering, is now pursuing her master's degree, and currently undertaking cutting-edge research in computational fluid dynamics (CFD). Her current project, funded by the US Navy, focuses on improving helicopter flight simulations and aviation safety.