This university student refined a 100-year-old math problem

Divya Tyagi, a graduate student in aerospace engineering at Pennsylvania State University, has refined a century-old mathematical problem, simplifying its form and broadening its applications in aerodynamics, according to a blog by Penn State.

Divya developed an addendum to a problem originally posed by British aerodynamicist Hermann Glauert, offering a new approach to optimising wind turbine performance.

According to the blog, Divya's research, which began as an undergraduate thesis at Penn State's Schreyer Honors College, was published in Wind Energy Science. Her work focuses on determining the ideal aerodynamic conditions for maximising wind turbine power output. Unlike Glauert's original formulation, which only considered the maximum attainable power coefficient, a measure of a turbine's efficiency, Divya's refinement accounts for the total force and moment coefficients acting on the rotor, including how turbine blades bend under wind pressure.

Sven Schmitz, a professor of aerospace engineering and co-author of the paper, noted that Glauert's work did not consider downwind thrust forces or the structural loads that turbine blades endure. Divya's approach, based on the calculus of variations, provides a clearer mathematical framework that allows researchers and engineers to explore new aspects of wind turbine design. Schmitz believes that her findings could influence the next generation of wind turbines and be incorporated into classrooms worldwide, as per the blog.

Divya Tyagi sees her work as a step towards improving wind energy efficiency and reducing costs. She highlighted that even a 1% increase in a turbine's power coefficient could significantly enhance energy output, potentially supplying power to an entire neighbourhood. Her efforts earned her the Anthony E. Wolk Award for the best undergraduate aerospace engineering thesis at Penn State.