Math and Physics Review of Football

Math and Physics Review of Football

Math and Physics Review of Football 150 150 Deborah

Overview

The matchup between NFC West Champion Seattle Seahawks and AFC East Champion New England Patriots promises thrilling gridiron action during Super Bowl XLIX. Behind the scenes, principles of math and physics determine the shape of the ball itself, the running game, the passing game, and the kicking game.

Footballs and Ellipses

Many sports from basketball to tennis, golf, and baseball are played with spherical balls, based on circles. Football and rugby are played with balls that are based on ellipses. An ellipse has two axes, a long major axis and a short minor axis. When a solid is made by rotation around the major axis, it is called a prolate spheroid, the shape of a football.

Passes and Gyroscopes

One of the advantages to an elliptical ball is that it can be thrown accurately for long distances. Skilled quarterbacks such as Russell Wilson or Tom Brady throw accurate spiral passes to their intended receivers. The tighter the spiral, the more the spinning ball can resist drag. It acts like a gyroscope, keeping the ball on track along its intended path. If the pass is wobbly, the ball slows down because there is more area for air resistance.

Pythagorean Interceptions

Suppose a running back catches the pass and runs downfield. The distance to the end zone is 40 yards. The closest defender to the running back is 30 yards away at a right angle. In order to get close enough to tackle the runner and intercept the ball, the defender will have to run at an angle. The path will resemble a right triangle, and the distance the defender will have to run can be solved by using the Pythagorean Theorem. Let the side of triangle for the ball carrier be represented by a, and the side of the triangle from the carrier to the defender by represented by b. The path to intercept can be represented by c. Using the Pythagorean Theorem, a2 +b2= c2. In the example, 1600 +900 = 2500. The defender will have to run a 50 yard diagonal to catch up to the ball carrier.

 

Parabolic Punts

When a kicker punts the football, the ball follows a parabolic arc. It follows a vector with speed and distance. At the highest point of the parabola, the ball reaches its maximum height and speed. It begins to decline due to the force of gravity. The greater the force of the kick, the higher the highest point will be, and the farther the ball will travel before it bounces.

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