What Runners Can Learn From Cheetahs

Usain Bolt may be looking to cement his Olympic track legacy at this year's London games, but in a competition for world's fastest sprinter, it's the cheetah that takes first place. Though pitting the Jamaican athlete against the speedy cat may not be a fair comparison—especially since in 2009 a cheetah named Sarah bested Bolt's record-breaking 9.69-second 100-meter dash by a good 3 seconds.

While running at the leisurely pace of 9 m/s the cats used 2.4 strides per second, but when they sped up to 17.8 m/s they used 3.2 strides per second. Greyhounds on the other hand, sprinted with 3.5 strides per second regardless of how fast they were going.

Path traveled by runner's center of mass

As the runner runs along, his center of mass follows a parabolic arc, as shown in the figure above. This parabolic path is due to the force of gravity acting on the runner between foot strikes with the ground. These foot strikes propel him through the air in a shallow arc, up until the time he lands with his other foot, at which point he pushes off the ground with that foot, which then sends him once more through the air with his center of mass following a parabolic arc. The force that the runner pushes off the ground with serves as an initial launch force which causes his center of mass to follow a parabolic arc, as predicted by Newton's second law and the equations of projectile motion. The greater the force Fx, the greater the horizontal running velocity, and the longer the arc length, hence the faster the runner will run. .

Arm Swinging

Arm swinging is an important part of running. It serves to stabilize the body. To illustrate this consider the figure on the left. As the runner's left foot strikes the ground, he pushes off with a force Fx. This force causes a torque T1 to be exerted on his body which tends to rotate his torso in the direction shown. To correct for this rotation the runner simultaneously swings his arms in the direction shown which exerts a counter torque T2 on his body which tends to rotate his torso in the opposite direction. The generation of this counter-torque helps keep his body stable and facing forward as he runs. Similarly, When his right foot strikes the ground the situation reverses, and his arms must swing in the opposite direction to before to induce a corrective torque which once more helps keeps his body facing forward. Keeping your arms bent while running makes it easier to swing them. Think of a swinging pendulum. A short pendulum is easier to swing than a long pendulum, and by analogy your arms are easier to swing when they are bent. When we run we do all this without thinking. It is a completely automatic set of movements.

Forces generated during running

Consider the figure below showing the profile view of a runner on a flat horizontal surface. The forces are indicated. This figure shows the forces acting on a runner when he is pushing off the ground with one of his feet. The force Fx is the horizontal force due to the contact between the runner's foot and the ground, and the force Fy is the vertical force due to the contact between the runner's foot and the ground. The force Fg is the force due to gravity which pulls down on the runner. This force acts through the center of mass of the runner, represented by the purple dot. During a run the force Fy is greater than Fg in order to lift the runner off the ground as he runs. The force that drives the runner forward is the propulsive force Fx. Running speed is directly related to the magnitude of this force. An Olympic sprinter can push off the ground with a total peak force of more than 1000 pounds (with a time averaged Fx equal to about 200 pounds, which is less than the peak Fx). In contrast, the average person can apply 500-600 pounds of total peak force.