Re: what are the laws govering kicked footballs?

I love sports physics questions. And as a former punter in high school, I know a few things about punting. Footballs have some very peculiar air flight behavoirs because of their shape. Much of sports projectile problems involve the shape of the flying object and properties of the air it is moving through.

With a punt, 3 things are important: angle of attack, tightness of the spiral, and the air conditions.

Angle of attack works similarly to simple physics projectile problems. The angle of release (kick) will determine range and height. Typically around a 45 degree angle give the best range with a football kick, but hang time is often more important. So typically the kick is at around 50 degrees.

The shape of a football is ellipsoid. It will have two natural(Eigen) values of its angular momentum: end over end and tight spiral. The spiral is essential. The ball presents a lower drag coefficient if it spiraling rather than tumbling. The drag on a projectile will make its return or drop flight different than its rise flight path. No longer will the ball travel in a symmetric parabola, but the peak of the flight will be closer to its landing point than its starting point. Try working an easy projectile differential equation with a drag proportional to velocity and the results will flop right out.

The weather or air conditions will have a great effect on hangtime. Although, the weather probably has more effect on the person than the anything. Cold days are harder on hang time because the ball does not "spring" off the foot as easily.

A properly punted football will "turn over." That means the leading nose of the ball will always be the leading nose. Usually, with a punt, the leading nose is higher on the upward path and higher on the lower path. If the leading nose is up on the downward path, then the ball is presenting a wider face to the air-thus more drag, less distance. If the ball turns over and presents a small area for the downward path, it will travel slightly farther.

Sincerely,
Tom Cull
"Fan of Ray Guy"