Physics of a Roundhouse Kick

The martial arts have fascinated many people for generations, most notably through films such as those of Bruce Lee and even Chuck Norris. Often, the martial arts are associated with gravity-defying jumps and kicks. One of these kicks that has always interested me is the spin-kick, or the roundhouse kick.

For this Physics News, I looked specifically at the spin-kicks of the Thai form of martial art known as Muay Thai, although these kicks are generally quite consistent in their form and function across different schools of martial art. It has been shown that Muay Thai roundhouse kicks are about as deadly as being clubbed by a baseball bat (generating around 480 pounds of force per strike).

As elucidated in the diagram to the left, the physics of a spin-kick follows the general rules of uniform circular motion. The foot, which is the object at the edge of the circle, is trying to move in a tangential manner to the circle, but a force is exerted inwards towards the body (center of rotation) that is keeping the foot in circular motion.
Keeping in mind Newton's third law, every action has a reaction, so for the force moving inwards towards the body that is keeping the foot in circular motion, there is a force exerted by the body against the leg, thereby canceling out the two forces. This then makes it so that the mass of the foot, with the force of gravity acting upon it, has to be overcome for the kick to be kept in a spin. This is when we try to do spin-kicks, we tend to fall forwards before completing a full spin.

This additional force that has to be applied to over come the mass of the foot is the torque, which is the tendency of a force to rotate an object about an axis or a fulcrum. Torque is defined as:

τ = r × F

where,

τ = torque
r = length or radius of the arm lever
F = magnitude of the force applied

Now that we know how a spin-kick is maintained in a spin, we can move on to the additional factor that makes spin-kicks so deadly. This is where the power equation comes in:

P = Fd / t

= τ x ω

where P = power,
τ = torque,

ω = angular velocity

We can then deduce from this equation that the faster the spin of the kick, the more power it is likely going to generate upon hitting the opponent. Moreover, because the torque is determined by the radius of the lever (or Muay Thai fighter's leg, in our case), it is to the fighter's great advantage the he or she extend his or her leg as far as possible, so as to generate as much power as possible.

The picture on the left shows a fighter (in black) extending his foot so as to achieve maximum radial proportion. He is also twisting his body so that his leg is swinging at an angle, which contributes to the angular velocity with which the leg rotates.

For additional information and live-action demonstrations of Muay Thai spin-kicks, see the following video:
http://www.youtube.com/watch?v=gyb2iUVY0oQ&noredirect=1