Only a few researchers have studied why American football flies such a unique trajectory, navigating through the air with remarkable precision, but also swerving, swaying, and even drooping as it heads down. Now, ballistics experts at Stevens Institute of Technology have, for the first time, applied their understanding of artillery shells to explain this unique motion, creating the most accurate model yet of football’s spiraling flight.
“When a quarterback makes a good helical pass, the trajectory of the ball is remarkably similar to that of a cannonball or bullet, and the Army is pouring enormous resources into studying the way these projectiles fly,” explained John Dzielsky, one of Stevens’ research. Professor and mechanical engineer reported for work in The Open Journal of the American Society of Mechanical Engineers for Engineering. “Using well-understood ballistics equations, we have been able to model a football flight more accurately than ever before.”
In fact, Dzielsky said, while the ballistics equations themselves aren’t terribly complex, the motions they expect can be. The equations contain many terms that represent all the ways air might affect projectile motion. The first challenge is to consider each variable in turn to determine which variables are important when used in a new or different context.
Dzielsky and co-author Mark Blackburn, a senior research scientist at Stevens, first took a holistic approach — modeling everything from quarterback control to the effect of crosswinds, to the effect of Earth’s rotation — and then derived equations that stripped the factors that didn’t. Significantly affect the course of the football journey. For example, during a 60-yard lane, the Earth’s rotation changes the lane’s end point by only four inches. “It turns out that the rotation of the Earth doesn’t have much of an effect on the football pass – but at least now we know that for sure,” Dzielski said.
Modeling a football journey sheds light on what separates good passes from bad passes. Not only did Dzielsky and his colleagues show that a helical pass can swing at a slow rate or at a fast rate (or a combination of both), but they were also the first to calculate what these frequencies are in football. If the football wiggles slowly, it is well thrown. If he wiggles quickly, the quarterback either twists his wrist (like turning a screwdriver) or pushes it sideways while releasing the ball. The wrist may be sprained due to an injury to the midfielder.
“The midfielders and coaches already know this intuitively, but we were able to describe the physics at work,” Dzielski said.
The other, more surprising finding was that the Magnus Effect, which causes a baseball to slip or deflect due to changes in air pressure, has remarkably little effect on a spinning soccer ball. Dzielsky explained that the soccer ball rotates along the wrong axis to create the Magnus effect, so any deviations in the flight path must come from a different source, such as lift caused by the ball’s angles in the air. “A lot of people think that a soccer ball is deflected to the left or right because of the Magnus effect, but that’s not the case at all. The effect of the Magnus force is twice that of the Earth’s rotation,” he said.
In addition, Dzielski and Blackburn showed, for the first time, that this deflection is closely related to the reason why the ball ends up nose-down at the end of a pass when it is thrown with its nose up.
Although Dzielski’s and Blackburn’s work represents the most accurate model of football’s flight path to date, Dzielski cautioned that more work remains to be done. Because the soccer ball rotates and tumbles as it travels, it is nearly impossible to use wind tunnel studies to accurately record the aerodynamics of a moving soccer ball. “This means that we do not yet have good data to enter into our model, so creating an accurate simulation is impossible,” he said.
In the coming months, Dzielsky hopes to find funding for tools that can capture aerodynamic data from a free-flying soccer ball in real-world conditions, not just in wind tunnels. “This is the only way we will be able to get the kind of data we need,” he said. “Until then, there is a precise — and precise — way of modeling a footballIts trajectory will remain elusive.”
John Dzielsky et al., Modeling American football dynamics and spin-induced stability, ASME Open Journal of Engineering (2022). doi: 10.1115/1.4054692
Stevens Institute of Technology
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