Modeling the Dynamics of the American Football

a football on a football field

Department of Civil, Environmental and Ocean Engineering

Location: ABS 301 (w/ virtual option)

Speaker: John Dzielski, Stevens Institute of Technology


It is probably unnecessary to remark on the widespread interest in football in the United States, we all recognize there is a large measure of national interest in the sport. By “football,” we mean real football, not that sport where they chase after a round ball. Given the interest in football, one would think that a great deal is known about the dynamics and aerodynamics of footballs. That is not true. There appears to be only one experimental data set where all the important aerodynamic coefficients were measured (20 years ago), and of those important coefficients, there is only one additional report of measured drag data. The coefficients associated with damping of the football’s motion have never been measured, so a reliable analysis of the stability of the ball’s motion cannot be done. It appears that a correct calculation of the characteristic frequencies associated with the observable “wobble” associated with a spiral pass has never been published before this year (2022). In short, it appears there is almost nothing published that explains the motion of the football in the air. This presentation will describe recent work in applying mathematical models for spinning projectiles and bullets to the problem of understanding the motion of the football. People who understand ballistics have had the knowledge needed to explain the dynamics of footballs in flight for over 100 years. Because of that, our recent work is not really new, but we have explored in depth what the physical models for spun projectiles and the limited aerodynamic data can tell us about footballs in flight. In this talk, we will cover the equations of motion for a symmetric, spun body, and the aerodynamic effects that are expected to act on those bodies. The aerodynamic effects include the overturning moment, the lift and drag, the Magnus effect, spin/rotational damping, and even the Earth’s rotation. The presentation explains in turn how each effect is mathematically modeled. We discuss what experimental data exists to characterize the aerodynamic effects and what may be wrong with that data. We take each effect in turn and explain how they individually affect the motion of the ball in a long, spiral pass. The talk presents some limited simulation results, but we hope the main information that we convey is the connections between the mathematical models, the physics they represent, and the resulting motions of the ball.


a photo of John Dzielski standing outside with the NYC skyline in the background

John Dzielski earned a BS in mechanical engineering from Carnegie-Mellon University in 1982, and MS and Ph.D. degrees in mechanical engineering from the Massachusetts Institute of Technology in 1984 and 1988, respectively. He has more than 30 years of experience relating to the design, integration, and at-sea testing of autonomous undersea vehicle systems for various U.S. Navy missions. He has been involved in research related to supercavitating vehicles since 1995. Recently, he began applying his experience applying simulation-based analysis, synthesis, and validation processes to developing formal model-based system engineering methods and processes using SysML integrated with modern analysis and design optimization tools.

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To view the full list of seminar speakers for the Fall 2023 semester, visit the CEOE Seminars page.