Meet Divya Tyagi, the Penn State student who cracked a 100-year-old wind energy equation, boosting turbine efficiency – The Times of India

A Penn State engineering student has made a remarkable breakthrough in wind energy research, revisiting and refining a 100-year-old equation that could lead to more efficient wind turbines. Divya Tyagi, an Indian-origin aerospace engineering graduate, tackled a complex problem first posed by British aerodynamicist Hermann Glauert in 1926, improving it in a way that could have significant implications for the renewable energy sector.
Tyagi’s work, published in Wind Energy Science, refines Glauert’s third-order polynomial, which has been central to understanding how wind turbines extract power from the wind. The original equation helped determine the optimum axial induction factor, but Tyagi’s new approach not only simplifies the problem but also enhances its accuracy. This breakthrough could lead to wind turbines that produce more energy, potentially powering entire communities more efficiently.
A step towards more efficient turbines
The original equation by Glauert, although instrumental in wind turbine design for nearly a century, focused solely on the maximum power coefficient — the efficiency with which a turbine converts wind into energy. However, as reported by the PennState, this model did not account for the total force and moment coefficients acting on the rotor blades, which are essential to understanding the stresses on turbines under operational conditions.
Tyagi, working under the guidance of Professor Sven Schmitz at Penn State, expanded the equation to include these forces, which are crucial for designing more durable turbines. Her method uses calculus of variations to present a simpler, more transparent solution to the problem, while also incorporating the important bending moments and thrust forces that act on the turbine blades. “The real impact will be on the next generation of wind turbines using the new knowledge that has been unveiled,” said Schmitz, as quoted by the PennState.
A breakthrough in wind energy design
Tyagi’s findings offer practical benefits for wind turbine design. Her refined model can help engineers optimise rotor blade shape, twist, and angle, ultimately improving the energy output of turbines. A small improvement in the power coefficient — as little as 1% — can have a substantial impact on energy production. “Improving the power coefficient of a large wind turbine by just 1% could notably increase a turbine’s energy output, potentially powering an entire neighbourhood,” said Tyagi, as quoted by the PennState.
Tyagi’s work not only opens the door to improved turbine efficiency but also fills a gap in rotor disk theory by providing the first exact analytical integrals for thrust and bending moment coefficients. This marks a significant step in understanding how turbines interact with wind, offering new opportunities for innovation.

From undergraduate research to real-world impact
The breakthrough began as Tyagi’s undergraduate thesis for the Schreyer Honors College at Penn State. For her research, she was awarded the prestigious Anthony E. Wolk Award for the best thesis in aerospace engineering. Despite the challenges of solving a highly mathematical problem, Tyagi dedicated 10 to 15 hours each week to her research, which paid off in this groundbreaking result. Tyagi’s work could transform wind turbine design and efficiency for the future of renewable energy.
The full impact of her work on global wind energy production remains to be seen, but the significance of her achievement cannot be understated. With continued research and development, Tyagi’s innovations could lead to more efficient, cost-effective wind turbines, helping to meet the growing demand for sustainable energy solutions.