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It’s a pretty safe bet that you won’t hear any football coach utter this phrase: “That’s the way the prolate spheroid bounces!”
Yet, that’s one reason why football is so unpredictable and fun.
A football’s shape is called a prolate spheroid, which is a spheroid with a polar diameter longer than its equatorial diameter. While a true prolate spheroid has rounded edges, a football has pointed ends. Again, however, this makes the game exciting.
Unlike a baseball, basketball or soccer ball, a football can have some crazy bounces. That’s because of its shape.
Michael Kruger, a physics professor at UMKC, proposed an experiment where you would drop a soccer ball.
“Put a ruler against a point on a soccer ball where it’s going to hit (the ground),” Kruger said. “If the ruler is parallel to the floor, the ball will bounce straight back up. No matter how you put the sphere (soccer ball), this is the same.”
The ruler becomes the tangent, which is a line sharing a common point with a curve or surface and being the closest linear approximation of the curve or surface at that point.
Next up, Kruger used a football. It also can bounce straight up, but it has to land on its long axis. More often than not, the ball will bounce away from a person who drops it.
“The ruler no longer is parallel to the floor and that will not bounce back up,” Kruger said.
Timothy Gay notes in his book Football Physics: The Science of the Game that the shape of the football also can affect the spin.
“The football’s prolate shape also means that when it hits the ground with one of its points, a relatively large torque can be exerted on the ball’s center of mass,” Gay wrote. “In contrast, most of the force exerted by the ground on a soccer ball is the vertical force, which passes through the ball’s center.
“This means it has no leverage on the ball, so it can’t change its spin. The rotation of a football can change dramatically if one of its points is the first part to make contact with the ground. This change in the ball’s tumbling motion can add significantly to the punt returner’s difficulties, but it can also complicate the job of the offensive players trying to down the ball.”
History of a football
Popular Mechanics researched the history of the football in competition, and found that the first game in 1869 used a round ball like a soccer ball.
In 1874, a rugby-type ball was used in a contest between McGill University and Harvard University. The magazine noted that the new ball looked like a watermelon. It stayed roughly that way until 1912.
“That year, a new set of rules for college football transformed the game ball from the watermelon-shaped ball to an oversize version of today’s modern football,” the magazine wrote. “The pros soon followed. The ball now weighed 14 to 15 ounces, its long axis was set between 28 and 28 1/2 inches and its short axis (around the middle) between 22 1/2 and 23 inches.…
“In 1935, the NFL shortened the ball’s short axis to between 21 1/4 and 21 1/2 inches. The ball’s length was shortened that year to between 11 and 11 1/4 inches, and the amount of air that it could hold was set at 12.5 to 13.5 psi. Its long axis of 28 to 28 1/2 inches, however, did not change. These dimensions remain today, as does the ball’s shape, which has been called a ‘prolate spheroid’ since 1890.”
To reach Pete Grathoff, send e-mail to pgrathoff@kcstar.com
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