What Do a Submarine, a Rocket and a Football Have in Common?

Why the prolate spheroid is the shape for success

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NBC Learn's "The Science of NFL Football" episode about geometric shapes explores the differences between spheres, ellipses and prolate spheroids, and their impact on the game. The unique shape of the football, for example, contributes the dynamic nature of the ball itself, which can be thrown long distances in a tight spiral or bounce unpredictably on the field of play.

Baseballs, basketballs and many other sports balls rely on a spherical, uniform design that makes them easy to shoot, throw and hit. A football, however, owes its two-dimensional origin to the ellipse rather than the circle, giving the pigskin its prolate spheroid shape, which has a polar axis that is greater than its equatorial diameter. Thanks to its elongated nature, a football will spiral when thrown properly. The spin creates a gyroscopic effect, stabilizing the flight of the ball through the air.

This shape makes the football more difficult throw than a spherical ball. But, as a prolate spheroid, a football experiences less drag as it cuts through the air, which explains why you can toss a football farther than a spherical ball such as a basketball or soccer ball that is roughly the same size and weight. When a football is thrown with a bit of a wobble, as opposed to a tight spiral, it will not travel as far, because it presents more surface area in the direction of flight resulting in a greater degree of air friction, also called drag.

Improving the ball's original design has not proved easy. The best football shape would consider both reduced drag and trajectory stabilization, according to Tony Schmitz, an associate professor in the University of Florida's Department of Mechanical and Aerospace Engineering. "Right now, we have the pebbled surface and spiral motion that reduce drag," he says. Any design that "increases these effects could give improved 'flight' performance, but good luck making a significant change." The toy company Hasbro did make some interesting alterations in its Nerf lineup—its Nerf Vortex football has a tail, for example, which improves the distance it travels when thrown. How such a ball would travel when kicked is entirely different issue, of course.

Aircraft, submarines and rockets share the basic design principles as footballs in that their shapes are elongated in an effort to reduce drag. These vehicles are self-powered, however, and must be able to change direction mid-flight, so they cannot use the spinning gyroscopic effect that makes a perfectly thrown spiral such a thing of beauty.

As far as identified flying objects go, however, prolate spheroids cannot match the distance of one class of geometric shape: A flying disc (Frisbee) or ring (Aerobie) not only have slim profiles that reduce drag and rotation that increase stability, but they also create lift, enabling them to carry quite far. On a football field, a well-thrown Aerobie can easily go from end zone to end zone.