Four kinematic elements form the basis for a quantitative solution to a long-standing paradox as to why the nose of a spiral-shaped football follows the trajectory of the ball. Photo credit: LLNL
The hallmark of a perfectly thrown football is a tight spiral of the tip around the trajectory of the parabolic flight path. Why the tip follows the trajectory has been a paradox for some time. A team of researchers, including physicist Willy Moss of the Lawrence Livermore National Laboratory (LLNL), provided a simple solution to this paradox in an article published as Editor’s Selection in the American Journal of Physics.
Moss – together with lead author Richard Price from the Massachusetts Institute of Technology (WITH) and co-author Tim Gay of the University of Nebraska – distilled the physics into two simple equations that could be solved numerically. The solution explains why the tip of the ball follows the trajectory of the ball.
“If you were to stick a pen on the nose of a spinning football in flight, you would see the nose spiral around its direction of motion as it flies, not a single point in the middle,” Moss said. “The combination of gravity, wind force on the soccer ball, and gyroscopy is key to this paradox. But a numerical solution alone still doesn’t help anyone understand why the ball is doing what it is doing. ”
The numerical solution illuminates a simple qualitative explanation based on the strange behavior of gyroscopes.
“Gyroscopic motion is not intuitive, even for physicists,” said Moss. “Just accept the following behavior as fact: when a gyroscope rotates vertically and you press the top with your finger, it moves left or right, at right angles to the pressure, not the direction of the pressure. This is exactly what is going on here. ”
Due to gravity, the ball’s axis of rotation is usually slightly inclined, which means it is not in the same direction as its trajectory. The only exception is the case of a perfectly thrown spiral pass the moment the ball is thrown. As the ball moves through the air, wind force pushes against the ball in the direction opposite to its trajectory. The wind pressing on the inclined ball works like a finger pressing on a gyroscope. The spinning ball moves at right angles to the impact and wants to follow a circular path – so-called “precession” – around the current trajectory. The nose of the ball draws a circle around the direction of the wind speed that changes constantly as gravity changes the trajectory.
By focusing on the gyroscopic behavior and the interaction of the wind-driven torque with the trajectory of the ball, the researchers were able to develop a quantitative solution that characterizes the movement of a football in flight. The quantitative solution presented in this article contains four key kinematic elements: the speed at which it spins, two different types of wobble – nutation and precession – and its trajectory.
“I’ve been interested in this paradox for a while,” said Moss. “I’ve known Tim for 50 years. We played college football together. We finally have to publish a paper together. It’s long overdue. ”
Reference: “The American Football Tight Spiral Pass Paradox: A Simple Solution,” by Richard H. Price, William C. Moss, and TJ Gay, August 19, 2020 American Journal of Physics.
DOI: 10.1119 / 10.0001388
