Some excellent PDF's on the physics of Taekwondo

Flash movie on science of power

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 is how far the fist is displaced from the hip to the chin along a vector.

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 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 of the fist = displacement of the fist  / time required to complete the displacement

Acceleration of the fist  = change in velocity of the fist / time required to achieve the final velocity.

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 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.

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 is basically the fist's weight.

• Acceleration is how quickly the fist increases in velocity.

• Velocity is how fast the fist is moving.

• Displacement is how far the fist moves.

• 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, skin, muscles, and joint 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 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?