On a quiet afternoon in University Park, Pennsylvania, aerospace engineering student Divya Tyagi (22) sat buried in equations that had defeated generations of aerodynamicists. The puzzle, first posed more than a century ago by British pioneer Hermann Glauert, was central to understanding how wind turbines extract energy from the wind. What Tyagi found was a new way of looking at a foundational problem in turbine design.Her research, published in ‘Wind Energy Science’, offers formulas that could help engineers build safer, more efficient wind turbines. “Glauert’s work was brilliant, but there were aspects he didn’t explore. I wanted to see if there was another route,” she says.Early curiosityTyagi was born in Laguna Hills, California, to Indian immigrant parents, and grew up asking endless questions about how things worked. A STEM-focused high school nurtured her aptitude, but it was aviation that became her obsession. She remembers long hours at airport windows watching planes take off — aerospace engineering felt inevitable.At Penn State, she entered the Schreyer Honors College and joined Professor Sven Schmitz’s research group in her junior year. Schmitz had long wondered whether Glauert’s century-old optimization could be extended. Three students had tried and moved on. Tyagi stayed.Glauert’s problem defined the power coefficient, a measure of how efficiently a turbine converts wind energy into electricity. But the original model only prioritized power and ignored the structural forces acting on the rotor. Modern turbines must survive massive thrust and bending moments, especially offshore where blades are longer and winds are stronger. “Neglecting these loads might be acceptable in theory, but in the real world they determine whether a turbine survives high winds or fails,” Tyagi explains. The problem needed reframing, and Tyagi finally did it.Breaking new groundUsing the calculus of variations, she re-derived Glauert’s optimum and uncovered two previously unknown analytical solutions. These formulas express the thrust coefficient and root bending moment coefficient at maximum power. Researchers had long relied on approximations for these values, but Tyagi solved them in closed form.“In practice, turbines are not allowed to overload their structure. Knowing the loads at optimum performance helps engineers design better machines,” she says.Schmitz calls her approach “simple and elegant” and believes it will become widely taught. The implications are significant. Even a 1% rise in the power coefficient can power entire neighborhoods, and Tyagi’s formulas link the gain directly to structural stresses. Engineers can now optimize performance while respecting material limits, improving both efficiency and lifespan.Future constraintsTyagi’s next step is part two of her study, which looks at power extraction under limits on thrust or bending moment. Instead of asking how to maximize power, the question becomes how to get the most power without crossing safety thresholds.After completing her bachelor’s in 2024, she stayed at Penn State for her master’s as a US Navy-funded PIPELINE fellow. Her current work is in computational fluid dynamics, simulating how helicopter rotor wakes interact with airflows over ship decks. The goal is to improve pilot safety during landings. “It was a learning curve … after so much analytical work, but it is satisfying to see flow fields form on the screen,” she says.After graduating, Tyagi hopes to work in aircraft design or simulation. But her wind energy work could guide turbine engineers for decades. “Glauert’s work lasted a century. If my contribution adds something meaningful, maybe it will last too,” she says.
