The perfect kick

If you’re a soccer fan, you’re familiar with this common sight: a penalty kick is in place, with a “wall” of defenders lined up in front of the goal, ready to leap to try to block the ball if it sails overhead. Mentally, you might be able to draw the parabola that would net that kicker a goal every time, but the calculations of guessing the path of the ball are surprisingly complex. Solving the problem involves fluid mechanics, and NCSA’s supercomputers are the perfect platform for simulating the path of a goal-producing kick.

Researchers from the University of Illinois Urbana-Champaign (U. of I.) have been using soccer balls to refine computational fluid dynamics (CFD) research methods. Shashwot Paudel, a doctoral student at U. of I., and Jinhui Yan, an associate professor in the Grainger College of Engineering Civil and Environmental Engineering Department, recently published their results in Computational Mechanics. Their research used NCSA’s Delta supercomputer to help them accurately predict a soccer ball’s flight path when kicked through the air.

“Modeling the full flight of a soccer ball from launching to landing is a challenging problem for existing computational fluid dynamics methods,” said Yan. “Our research aims to bridge this gap by developing a high-fidelity model that simultaneously solves the fluid flow and ball motion from the instant the ball is kicked until it lands. This allows us to capture the complete aerodynamic behavior of the ball under realistic game conditions.”

Yan and Paudel simulated a soccer free kick that depicts simultaneously how the ball moves through the air and how the air moves around the ball, tracking the ball’s translational and angular movements.

“We use a high-fidelity computational framework that couples fluid dynamics with rigid-body motion,” explained Yan. “The centerpiece of our approach is a monolithic overset method that we recently developed. This technique employs two overlapping meshes: a fine, boundary-fitted mesh that moves with the ball and a larger stationary mesh that represents the surrounding air.”

The team’s monolithic overset method divides and analyzes the space around the ball, enabling researchers to create a more natural and realistic simulation compared to previous methodologies.

“Traditionally, such problems require immersed boundary or boundary-fitted methods with complex mesh deformation or remeshing procedures,” said Yan. “In contrast, our method allows the use of a boundary-fitted mesh to represent boundary layers around the ball surface while allowing the ball to move freely in three dimensions without any mesh motion or remeshing. Moreover, unlike conventional overset methods that rely on iterative subdomain coupling, our monolithic formulation solves everything together, resulting in improved accuracy, efficiency and robustness.”

NCSA resources were paramount to our work. These simulations are computationally intensive. We are solving fully coupled fluid-object interaction systems, employing meshes with well over 29 million elements in some cases. Without the powerful supercomputer like Delta, this research would not have been possible.

–Jinhui Yan, University of Illinois

While research into soccer kicks may seem all fun and games, there are many ways this research could be used to develop better methodologies for other fluid mechanics questions.

“‘Banana kicks and other curved trajectories have long fascinated soccer fans, yet full-flight simulations of these motions remain rare, both experimentally and computationally,” said Yan. “We realized that our method is ideally suited to study this kind of problem. Soccer aerodynamics not only provides a fun and visually compelling test case but also represents a complex real-world example of moving-object aerodynamics – a common challenge across many engineering systems. By studying soccer ball flight, we can both advance the scientific understanding of sports aerodynamics and demonstrate our method’s capability for a wide range of engineering fluid-structure interaction problems.”

The monolithic overset method could be beneficial for researchers designing better, more efficient drones or for those aiming to create longer-lasting wind turbine blades. Both move through the air and create similar challenges for study as soccer balls do.

“Our work serves as a foundational computational tool with broad implications across sports and engineering,” said Yan. “In the sports domain, it can help coaches and players better understand kick strategies and assist manufacturers in optimizing ball design by studying how seam geometry, panel size and surface texture affect flight stability and curvature. The method can be applied to other ball sports, such as tennis and table tennis. Beyond sports, the same methodology can be applied to problems involving spinning projectiles, bio-inspired flying vehicles, or any engineering system where fluid-object interaction is critical.”

As a Ph.D. student at the University of Illinois, access to NCSA resources has been a game-changer. Being able to tackle computationally massive and ambitious problems means that our ability to solve problems and innovate is not limited by computing power. For both students and faculty, this resource can serve as the critical difference that turns complex research ideas from theory into practical reality.

–Shashwot Paudel, University of Illinois

As Yan’s research team continues to refine their methods, they plan to add new elements to their simulation.

“In reality, soccer balls are not perfectly rigid – they deform when kicked or when they strike the ground or goalpost. Our next goal is to extend this work to include contact dynamics and deformable bodies, enabling us to simulate more realistic in-game conditions.”

You can find an earlier related paper with more information about this research in Engineering with Computers.