Rotational Motion

Rotational energy is used throughout all martial arts styles. Rotation is used extensively to increase power. For example, when a punch is thrown, extra power can be generated by rotating the hips. Rotational kicks, such as a jump spinning crescent kick or spinning side kick, can generate more power than the same kick without the rotation (and some, like the crescent kick, require rotation for all of their power!)

In general, however, most of these techniques gain power by increasing speed. If you rotate your hips, you are extending your reach, getting your body in a better position to strike, or using that motion to increase speed. If you are spinning, you are exclusively taking advantage of the greater speed. Circular motion allows humans to move faster without moving their center of gravity. Another way rotating the hips adds power is because it brings more of the body into play, thus increasing the mass used for the punch. A martial artist will use rotation very often, and it is useful to understand a little more about what is going on.

An object in motion rotates when it is accelerated toward a central point. Any object rotating in a circle must have a force pulling it toward the center of the circle. This force is f_c, and it is defined as:

Equation 1:

f_c = central force, m = mass, a = acceleration, r = radius

The central force, f_c, is the inward force required to keep the mass, m, moving in a circular path. Much of the power in this type of attack is generated from speed. For equation 1, the force f_c is not the force that is used to strike a target. The velocity of a spinning kick is still governed by the previous equations. The force f_c is instead the force a martial artist would feel on their leg, pulling outward, as the kick is thrown. Some martial arts weapons, such as weighted chains or nunchukas, will experience this more noticeably than the fist or leg. The faster they are spinning, the more force is required to keep the center of rotation still.

Figure 6 - Rotation of p

Figure 6 shows the forces involved in an object rotating about a point. Our object, p, will want to remain at rest or remain in motion if no forces are acting on it. Object p has a velocity vector, A, at the instant this "picture" of our little object is taken. At this particular instant in time, p wants to continue exactly as it is, and that is to move directly along A. If it does so, it will fly off into space. In order to make it move along the circle, we have to have a force, which is along B, that essentially pulls p toward the object q. Since every action has an opposite reaction, q will also feel a force along B in the opposite direction. Imagine that B is a string, our hand is q, which is holding the string, and p is an object tied to the end of it. If we swing p around in a circle, p feels a force toward our hand (which is q). However, you also feel a force toward the object, because it wants to move along A. How does this effect us? In most rotations, we don't necessarily have to worry the force along B. What martial artists care about is A. In any instance in time, p has a velocity. Figure 4 shows the various forces involved in a rotation from a wheel kick:

Figure 7 - Rotation from wheel kick

A wheel kick is almost all rotation, so it's easier to see what's going on. The martial artist rotates about a fixed center, and the striking point, the heel, is at a distant equal to the radius of the rotation. To get a wheel kick moving, the body has to exert a force on the leg to start its motion. To keep it in a circle, a force is required that pulls the foot toward the center, which you supply by simply being connected to your foot. As many martial artists have felt, however, that force does exists, because as you spin, your rotating leg will pull you off balance. Just as p wants to travel along A, your leg wants to stay in motion. Because you have a force pulling you toward p along B, you have to counter that force to perform any spinning technique. This is natural for many kicks, but I've seen a lot of students attempt the wheel kick without countering that additional force.

Once your foot is moving in a circle, your kick benefits from additional speed afforded by the rotation, not the acceleration toward the center. Given the fixed mass of your foot, the only thing you can do to increase power is to increase the velocity of your foot. To do this, you need to spin faster. It may not be obvious how to do this without some instruction, but now physics has given you an edge because you know what has to happen to improve your kick.

Rotational energy also uses principles of levers. Consider standing on a rotating cylinder.

Figure 8 - Rotation Around a Point

The velocity of the points further out on the cylinder move faster. Given these three velocities, the following expression holds true:

Now consider a roundhouse kick, which follows a similar principle. Because the roundhouse kick follows a circular path, and the foot is farthest from the center of rotation, it would be going the fastest. The same thing is true for a stick or a Bo staff. Blocking at the end of the stick will mean that the martial artist must absorb the full potential of the attack.

Figure 9 - Roundhouse Kick

Figure 9 shows a roundhouse kick. Because it moves in a circle (ie. hinges at the knee and moves around the body), the foot is the farthest point from the center of rotation. In this case, the martial artist maximizes the speed of the strike by using the top of the foot. Although the roundhouse kick is effective with other striking points, like the shin, it will be traveling slower because it is closer to the center of rotation. Although the shin may not have the speed of the top of the foot, it has additional mass, which can more than make up for it. Momentum, as we have seen, is the product of velocity and mass.

Rotational motion is one area where martial artists must heed physiological limitations. Although a rotating fist or foot is going the fastest if it far away from our body, there are a few factors that need to be considered. The arm or leg is not like a ball on a chain, where all the mass is at the end. The martial artist has to consider the effective mass (i.e. think of the ball on a chain, where almost all effective mass is in the ball) of the striking point, which is somewhat difficult to calculate exactly. The stiffness of the arm or leg and speed combine to form the effective mass at the striking area. Someone that just swings their arm will not have the same amount of power as someone who punches with the entire body, as the latter will significantly increase the effective mass of the striking surface. We are also limited because we have less power the farther we extend our fists and feet. Although we can swing our foot, like that weight on a chain, toward out target, it doesn't actually have much strength when it is extended. Thus, we have to balance when we need additional strength and when we can use rotation at its maximum efficiency.