Indian-Origin Student at American University Resolves Century-Old Mathematical Challenge
Indian-Origin Student at American University Resolves Century-Old Mathematical Challenge
Developed by British aerodynamicist Hermann Glauert, this problem has been fundamental to aerodynamics research for many years.
Divya Tyagi, a graduate student in aerospace engineering of Indian descent at Pennsylvania State University, has made an impressive advancement by revising a century-old mathematical challenge. Her creative approach streamlines the intricate problem, enhancing its accessibility and facilitating further exploration.
Tyagi, having completed her bachelor’s degree in aeronautical engineering, is now advancing her education by pursuing a master’s degree while engaging in innovative research in the field of computational fluid dynamics (CFD).
Indian student Divya Tyagi at Penn State University has cracked a 100-year-old math problem, which will enable higher efficiency in wind turbines. pic.twitter.com/YtkJXZkmtp
— Hindutva Knight (@HPhobiaWatch) March 18, 2025
Developed by British aerodynamicist Hermann Glauert, this problem has been fundamental to aerodynamics research for many years. Tyagi builds upon Glauert’s findings, revealing new opportunities in wind turbine design that had not been investigated before, as stated on the official Penn State University website.
Sven Schmitz, who serves as an adviser and co-author to Divya Tyagi, pointed out that Hermann Glauert’s foundational research focused exclusively on optimizing the power coefficient, a metric that evaluates the effectiveness of converting wind energy into electrical power.
Glauert’s study overlooked the overall force and moment coefficients affecting the rotor and failed to account for the influence of wind pressure on the turbine blades, particularly regarding their bending under stress.
“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,” says Divya.
Schmitz noted that Tyagi’s creative solution, grounded in the calculus of variations, provides an impressively straightforward yet effective framework. This mathematical method facilitates constrained optimization, empowering researchers to effortlessly investigate new dimensions of wind turbine design.
“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,” says Schmitz.
“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. 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,” he adds.
Tyagi’s innovation is expected to lower expenses and enhance wind energy generation. She noted that even a slight enhancement of one percent in the power coefficient could significantly boost a turbine’s energy production, potentially supplying power to an entire community.
