# Physics of Power

## Definitions

• Vector. A vector is a straight line from point A to point B, such as the line your fist travels when moving from your hip to an opponent's chin. Any deviation from the straight line will result in a loss of power.
• Displacement. Displacement is how far the fist is displaced from the hip to the chin along a vector.
• Distance. Distance is how far the fist actually travels during the punch, which includes any stray movements from the vector and its return travel back to the hip.
• Speed. Speed of the fist is measured using the distance it moves, which includes any extraneous movements away from the vector. Velocity is measured using displacement of the fist, which only uses travel along the vector and in only one direction.
• Velocity. Velocity of the fist = displacement of the fist  / time required to complete the displacement
• Acceleration. Acceleration of the fist  = change in velocity of the fist / time required to achieve the final velocity.
• Force. Force of the fist = mass of the fist (including arm and some of torso) x acceleration of the fist. As it applies to the punch, force is of no concern if it misses the chin. If it strikes the chin, then an important consideration is the amount of pressure the fist applies to the chin.
• Pressure. Pressure of the punch = force of the fist / striking area of the fist. Thus, the smaller the striking area of the fist, such as the first two knuckles versus the entire front of the fist, the greater striking force.

# Force Equation

Actually, the equation for force involves more than just mass and acceleration. The full equation is F=ma+cv+kx. This longer equation takes other variables into consideration, such as wind resistance, gravity, friction within joints, muscle tension, and energy lost through heat. This longer equation for force contains 6 parts: (mass x acceleration) + (velocity x displacement) + (damping x stiffness)

• Mass. Mass is basically the fist's weight.
• Acceleration. Acceleration is how quickly the fist increases in velocity.
• Velocity. Velocity is how fast the fist is moving.
• Displacement. Displacement is how far the fist moves.
• Damping. Damping accounts for force that is dissipated by flexible surfaces and structures contacting each other. Damping occurs when there is weakening in the structure of the punch. When the fist impacts the chin, it cause the skin, muscles, and joint to collapse somewhat, which dampens, or reduces, the force of the punch. If the fist is covered in boxing glove, the striking force is reduced by dampening effect of the glove's padding. Some damping also occurs when the body oscillates. Since the body is mostly water, it oscillates when shaken by the reaction to the action of the punch. Damping is also caused by friction. Muscles generate heat by the friction of rubbing against each other, which uses up energy. Energy is also wasted by other types of friction, such as the arm rubbing against the body during a punch.
• Stiffness. Stiffness is how rigid the fist and arm are at impact. The stiffer the fist and arm are on impact, the greater the striking force. The hardness of the striking surface increases the force delivered because reaction force will not be absorbed, thus, the knuckles of the hand strike harder than the knife hand.

Mass of the punch may be increased by using muscle tension to add the masses of the shoulder, torso, legs, and feet to the mass of the punching arm. Generally, speed decreases as effective mass increases, but, by using a sequential application of forces, such as arm, then shoulder, then hip snap, and then leg thrust, the fist is snapped out similar to a whip, without adding mass that may slow speed of the punch. Then, at moment of impact, the body tenses and adds the mass to the punch.

Focus is when a full-power, full-speed technique is aimed to terminate a point in space. Focus is not just terminating the technique at the point in space; it is also a simultaneous contracting of all muscles to add all the power and mass of the body to the technique. Maximum power occurs when all muscles of the body contract at impact. Since the impact force of a technique equals the mass times the acceleration of the attacking weapon, to reach maximum force, you must be loose and relaxed as a technique starts and progresses so you may achieve maximum acceleration, and then contract all the muscles to achieve maximum mass. Since the technique stops at the point of focus, maximum force of the technique occurs at a point just millimeters before the point of focus. After maximum power point, the fist is decelerating. Without the contraction, maximum power is not reached; therefore, if an opponent moves into a technique that was intended to stop just short of contact, the attacker can lessen the force of the impact by not contracting into the technique. When sparring, the point of focus is just short of the surface of the chin, so the opponent is not harmed. In an actual attack, the focus point is internal of the chin, so that fist is at maximum velocity when if strikes the surface of the chin and thus strikes with maximum force.

Taking all this into consideration, which punches harder, a large person or a small person? The large person has bigger muscles and more mass, but it requires more muscle power to move the greater mass so acceleration and velocity of the punch is reduced. The smaller person has smaller muscles and less mass, but the acceleration and velocity of the punch is greater. This, striking pressures of the two punches may actually be equal. The striking force of a speeding bullet and speeding locomotive may be equal, but which would you rather be hit by?

A larger person has more reach, more mass to absorb blows, and more strength. The farther a punch travels, the more time it has to accelerate, so a larger person with longer arms may generate more power. However, it takes more time to cover the longer distance, which may give the smaller person time to avoid or block the punch. John Jerome, in his work The Sweet Spot in Time, states that large, muscular athletes are generally faster than smaller, thinner people when moving about. So, in general, a large person hits with more force than a small person.

The momentum of an object is its mass multiplied by its velocity. By adding up the momentum of all individual objects in a system, the system's total momentum can be calculated. In a "closed" system, the net momentum never changes. This is a useful fact when analyzing an impact, because we know that the total momentum of the system will be the same after the impact as it was before the impact, even though the momentum of its parts may have changed. Momentum is a "vector" quantity, which means that two equal masses moving in opposite directions with the same velocity have zero net momentum.

Energy takes many forms, such as the kinetic energy of a moving mass. Energy is a "scalar" quantity, which means that two equal masses moving at the same velocity have the same total kinetic energy, regardless of their direction of movement. The kinetic energy of an object is equal to half its mass times the square of its velocity.

Energy, like momentum, is always conserved. However, sometimes it changes from kinetic energy, which is easily observed by measuring velocities and masses, to other forms that are harder to measure, most notably heat. The process of changing kinetic energy to heat is usually damaging to the material being heated. If the material is human tissue, it can be crushed, torn, or broken by the conversion of kinetic energy to heat. If the material is wood, it will break. A process that slowly or gradually converts kinetic energy to heat is usually called friction. A process that suddenly converts kinetic energy to heat is called an

## Examples of inelastic collisions

• Example 1: When billiard balls collide at normal speeds, they suffer no measurable damage because their collisions are almost perfectly elastic. All collisions conserve momentum, but only elastic ones conserve kinetic energy. So, if one ball with a certain velocity strikes a stationary ball on-center, it will transfer all of its momentum and kinetic energy to the stationary ball, stop, and cause the other ball to move away at the same velocity as the striking ball. If a perfectly elastic Taekwondo student struck a perfectly elastic target, the target would fly off undamaged, but with lots of kinetic energy, perhaps sustaining damage when it hits the floor.
• Example 2: If, instead of hard balls, we use balls made of soft clay, then, when one ball strikes a stationary ball, both balls will mush together and move away with half the velocity of the striking ball. The kinetic energy before the collision is MV2/2. The kinetic energy after the collision is MV2/4. Half of the kinetic energy has gone into damaging the balls. Since both balls are equally damaged, each ball got damaged in the amount MV2/8.
• Example 3: If a hard ball strikes a stationary clay ball, only the clay ball will be damaged. Therefore, all of the lost kinetic energy MV2/4 went into damaging the clay ball.
• Example 4: If a clay ball strikes an anchored hard ball, all the momentum of the clay ball will be transferred to the earth, and all of its kinetic energy MV2/2 will be expended in damaging the clay ball. This is twice the damage of example 3, and four times the per-ball damage of example 2.

Therefore, as a Taekwondo student, you should be as elastic as possible as protection against damage. Proper focus unites the bones, muscles, tendons, and ligaments into a structure that is better able to distribute forces elastically (non-destructively), such as pre-stressed concrete does in buildings. It also means that an onrushing opponent who is impaled on a well-rooted reverse punch will sustain more damage than a stationary opponent. The effect of having a firm stance is most important when the opponent is stepping toward you, therefore, your best strategy for causing damage is to wait for the opponent to step toward you with an attack, deflect the attack, and then use a well-rooted reverse counter punch. Colliding elastically does not transfer any kinetic energy, so it should be avoided. An inelastic collision with the target transfers kinetic energy that damages the target rather than your striking limb. You want your victim to be damaged, not pushed backward. To cause maximum damage to an opponent, targets should be chosen for their inability to respond elastically. The ability of a target to respond elastically depends on its structure, the speed of the impact, and the area of impact pressure.

All tissues have a range of pressures over which they are capable of responding elastically. The transition from elastic response to inelastic response is called "yielding." As pressure builds in a collision between two objects, both objects are initially elastic. A striker strives to have a larger elastic domain than the target. Once the target yields, the pressure between the two objects stops increasing and starts decreasing. When we consider momentum rather than pressure, the speed at which your technique travels has a greater effect upon the collision than the mass of the technique. Therefore, maximize speed to maximize damage. If purpose of a technique is to break bone, then use a high velocity impact with a small target area. If purpose of a technique is to cause internal damage, then use a technique that will transfer momentum.

## Sources

Everett, P.C. (1996). When Worlds Collide.

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