The Physics of Football

Originally published on Physics Central

Football is a sport almost made for physicists. Newton’s three laws of motion are at work during every play and little things like the unpredictable bounce of the “prolate spheroid” – the football – can throw kinks into a game no physicist, player or fan ever saw coming.

Here’s how Bill Belichick, head coach of the New England Patriots, described the gridiron in Football Physics: The Science of the Game by Timothy Gay:

The action that happens on a football field involves mass, velocity, acceleration, torque, and many other concepts…

While some observers see only carnage and chaos, brilliant athletic performances and bone jarring collisions, the science-minded see the field as a working laboratory.

Newton’s laws of motion are the superstars of pigskin physics, explaining a lot of what goes on on the field. Newton’s first law tells us that an object either at motion or at rest tends to stay in that state of motion or rest. The heavier the object, the more it wants to stay in a steady state. Thus, a big linebacker is hard to push around.

How is it then that a little guy like a small defensive player can tackle a bigger running back? It’s possible thanks to two things: Torque, or the measure of rotational force, and a player’s center of mass, which is explained later.

To understand how torque works, stand next to a swinging door. First, push the door open with your hand on the opposite side from the hinges – about three feet from the axis of rotation or the imaginary line the door swings around. It opens pretty easily.

Now, place your hand very close to the hinges – close to the axis of rotation – and push again. It’s much harder this time to open the door. This is because you have more torque when you’re at a greater distance from the axis of rotation and a bigger torque is better at moving an object around that axis.

But torque alone isn’t responsible for the tackle. A player’s center of mass – the point where gravity acts on an object – also has to be considered. A player’s center of mass is near his stomach, roughly in the middle of the body. The center of mass is where the torque acts. The axis of rotation, the point the player’s body rotates around, is the player’s feet touching the ground.

When a player crouches down, keeping low, his center of mass is closer to the ground. Therefore, the potential torque is small. Imagine that the center of mass is like your hand on the door; it’s closer to the hinges – or the feet. This gives the player lower towards the ground the advantage. It’s harder to push him around his axis of rotation.

When the crouched player, whose center of mass is low, pushes on a standing or running player, whose center of gravity is higher, it’s easier to push the upright player around his own axis of rotation, since his center of mass is further away from the axis. More torque.

There are, of course, more forces at work in a tackle, so even the lowest of tacklers can still fail to lay out his target. Understanding torque, though, helps to understand how a little guy can take a big guy.