Researchers Are Using Soccer Balls and Supercomputers to Push the Limits of Computational Fluid Dynamics

Researchers at the University of Illinois Urbana-Champaign are turning an everyday sports object—the soccer ball—into a powerful scientific tool to improve how engineers simulate complex airflows. By combining advanced computational fluid dynamics (CFD) techniques with the massive computing power of NCSA’s Delta supercomputer, the team has developed a highly detailed way to predict how a soccer ball moves through the air from the moment it is kicked until it lands.

At first glance, predicting the path of a soccer ball might seem simple. Anyone who has watched a free kick curve around a defensive wall has an intuitive sense of the arc the ball should take. But beneath that familiar trajectory lies a web of complicated physics involving airflow, rotation, turbulence, drag, and lift. Accurately capturing all of these effects at once has long been a challenge for traditional CFD methods.

The research team, led by Jinhui Yan, an associate professor in the Grainger College of Engineering, and Shashwot Paudel, a doctoral student at the university, set out to close this gap. Their findings were recently published in the journal Computational Mechanics, presenting a new way to simulate the full flight of a soccer ball with unprecedented accuracy.

Why Soccer Ball Flight Is Such a Hard Problem to Solve

A soccer ball in flight is not just moving forward. It is also spinning, interacting with air at very high speeds, and continuously changing how that air flows around it. These interactions create aerodynamic forces such as drag, which slows the ball down, and lift, which can cause it to curve sideways or dip unexpectedly.

Traditional models often simplify the problem. Many rely on empirical formulas that estimate drag and lift based on experimental data, then plug those values into relatively simple equations of motion. While useful, these models cannot fully capture what happens when airflow and ball motion influence each other at every instant.

What Yan and Paudel wanted was a method that simultaneously solves for the motion of the ball and the motion of the air around it. This kind of tightly coupled simulation is known as a fluid–structure interaction problem, and it is among the most computationally demanding challenges in engineering.

The Monolithic Overset Method Explained

At the heart of this research is a technique known as the monolithic overset method, developed by Yan’s group. In simple terms, the method divides the simulation space into two overlapping regions.

One region uses a fine, boundary-fitted mesh that closely follows the surface of the soccer ball. This mesh moves with the ball and is detailed enough to capture thin boundary layers and subtle flow features near the surface. The second region is a larger, stationary mesh that represents the surrounding air.

What makes this approach stand out is that both regions are solved together, in a single, unified system of equations. Unlike conventional overset methods, which require iterative back-and-forth communication between different parts of the domain, the monolithic approach treats everything as one problem. This results in better accuracy, improved numerical stability, and greater computational efficiency.

Using this framework, the researchers were able to track not only the ball’s position, but also its rotational motion, while simultaneously resolving the airflow and vortices that form around it.

Supercomputing Power Makes It Possible

Simulations of this complexity are far beyond what a typical workstation can handle. Some of the models used by the team involved meshes with more than 29 million elements, each representing a tiny piece of air or surface geometry.

To handle this massive workload, the researchers relied on the Delta supercomputer at the National Center for Supercomputing Applications (NCSA). Without access to such resources, running fully coupled, high-resolution simulations of a soccer ball’s complete flight would simply not be feasible.

This access allowed the team to explore realistic game conditions, including different initial speeds, spin rates, and comparisons between a real soccer ball and a smooth sphere. These comparisons revealed how surface features like seams and panels significantly influence airflow and trajectory.

What the Simulations Reveal About Soccer Kicks

One of the most visually striking aspects of the simulations is how they capture vorticity, the swirling motion of air behind the ball. These vortices play a key role in side-to-side deviations, helping explain why a spinning ball can bend dramatically in midair.

The simulations also highlight why so-called banana kicks are so difficult to model accurately. Curved trajectories emerge from a delicate balance of spin, speed, and airflow separation, and small changes in any of these factors can lead to noticeably different outcomes.

By modeling the entire flight, rather than isolated moments, the researchers can see how aerodynamic forces evolve continuously from launch to landing.

Beyond Soccer: Why This Research Matters

While soccer provides an engaging and relatable test case, the broader implications of this work extend far beyond sports. Many engineering systems involve objects moving through air while interacting with fluid forces in complex ways.

For example, drones experience coupled airflow and body motion that affects stability and efficiency. Wind turbine blades must endure unsteady aerodynamic loads over long periods. Even bio-inspired flying vehicles rely on precise fluid–structure interactions to function effectively.

The same computational framework used to simulate a spinning soccer ball can be adapted to study these systems, making this research a foundational contribution to the field of CFD.

Applications in Sports Science and Equipment Design

In the sports world, the findings could help coaches, players, and manufacturers better understand how design choices and techniques influence performance. By adjusting parameters such as seam geometry, panel size, and surface texture, manufacturers can study how different designs affect flight stability and curvature before ever producing a physical prototype.

The method is also applicable to other ball sports, including tennis and table tennis, where spin-induced aerodynamics play a crucial role.

The Next Step: Adding Deformation and Contact

Despite its sophistication, the current model still makes one important assumption: the soccer ball is perfectly rigid. In reality, balls deform when kicked, when they strike the ground, or when they hit the goalpost.

The research team plans to extend their framework to include contact dynamics and deformable bodies, enabling simulations that are even closer to real match conditions. Incorporating deformation will add another layer of complexity, but it will also unlock new insights into how energy transfer and material properties influence ball behavior.

A Powerful Tool for Future Research

For Paudel, the project also highlights the importance of access to high-performance computing for early-career researchers. Being able to tackle computationally intensive problems opens the door to innovation that would otherwise remain theoretical.

As the team continues refining their methods, their work stands as a clear example of how advanced computation, fundamental physics, and even sports can come together to push scientific boundaries.

Research paper:
Paudel, S., et al. High-fidelity simulations of full-flight soccer ball aerodynamics using a monolithic overset approach, Computational Mechanics (2025).
https://doi.org/10.1007/s00466-025-02705-2