in fact, a slightly curved trajectory because of the vertical component of the impulse force.
A circular momentum is generated when the body rotates around a vertical axis going through the center of gravity. The spring of the rear leg, the reaction force, and the force of the abdominal region are used to create a rotation of the hips, shoulders, and head in horizontal planes. The circular momentum is increased when the body is first twisted in the opposite direction, in a winding up motion, and by the antagonistic action of the hands (push-pull type of motion). These principles are used primarily in circular techniques.
A pendular momentum is generated when the hips swing backward and forward in a vertical plane going through the center of gravity. The pendular motion of the hips is used mainly in direct kicking techniques.
Concentration of force
The importance of the hips and abdominal region cannot be overemphasized. Because muscular force is of a cumulative nature, as many muscles as possible must be used in the motion (obviously these muscles have to be convergent and not antagonistic). Because of the reaction law, the long and flexible muscles of the extremities have to rest on the stronger and more stable muscles of the body to produce an effective result. Of all the profound muscles, the waist muscles are the strongest and therefore they must be contracted first to support the next closest muscles which in turn support adjacent long muscles and so on to the extremities of the body used for punching or kicking. The movement has to be executed fast to generate a high momentum. For the arm or foot to move quickly, muscles have to be strongly contracted. But if the muscular tension is kept throughout the motion, it will slow it down. Therefore the initial contraction of a muscle should be followed by a decontraction while the fist travels. At the time of impact, the muscles have to be tightened again to straighten the joints of the arm, insuring the maximum transmission of force. Otherwise, the reaction force will cancel out the force of the elbow. These periods of intense contraction and decontraction have to be well coordinated and it is only through intensive practice that one can develop a feeling for the right time at which the contraction or decontraction of the muscles should take place.
The relation between the force and the momentum is given by the equation: Momentum=M x V=FxT, T being the time during which the force F is applied to produce the momentum M x V. In the execution of a punch, M would be the mass of the fist; if M and V are constant, it can be seen from this equation that the force will increase when T decreases .
Thus the shorter the time, the greater the force generated. As a result, the force should be concentrated in as little time as possible. Therefore, speed being directly proportional to force, it is conceivable that a person of smaller physical structure (who is generally capable of greater speed than his counterpart of a larger structure) is able to create enough force to match and possibly supercede the force of a much larger man. Thus, it is said of a karate practitioner that size has no bearing on capability in the fighting art.
In modern karatedo, not only are the hips used in linear, circular, or pendular motions, but also the shoulders and head. This horizontal counterbalancing of the head and shoulders, added to (A) the horizontal pendular motions, (B) horizontal and vertical motions of the hips, and (C) circular motions of the feet, increases the momentum of the back counterbalance motion of the elbow. This supports and enhances the executions of the hand technique. This support counterbalance theory is particularly of importance in the Kenkokan system, where the motion is not stopped at the time of impact, but, in fact, followed through. With this, the acceleration of the striking mass is increased and thus creates a greater force M X A, A being the acceleration). Other reasons for using follow-through motions will be given in the next paragraph.
The reaction force
The reaction force is that which results from the application of a force to a specific point and directly opposes the initial impact. If you kick on the ground with your foot, using your muscular force and gravity, it creates an upward force in your foot and body which can be reutilized in another direction. It is this reaction force which is used by high jumpers when they stamp on the ground before jumping. It is used in karatedo in much the same way. The ground is kicked just before punching or kicking and the reaction force is transmitted through the body to the fist or the foot, adding a momentum proportional to the force of the kick on the ground [when there is no loss of momentum. (If the ground is soft it may' absorb part of the energy generated by the kick.)]
While the reaction force can be used positively, it can also have detrimental effects. When hitting a target, a reaction force results, which may lessen the force of your blow. This is why a strong stance is needed and explains the advantage of using follow through motions rather than stopping on impact, because the reaction force is completely nullified by the continuing momentum of the technique.
The law of reaction is applied in many different ways, as, for example in the use of antagonistic muscles. It is well known that the contraction of the biceps will produce an extension of the triceps (these muscles are called antagonistic muscles). This property can be turned to account in karatedo. Before kicking, the heel is raised backward, almost to the buttock, extending the fore-muscles of the thigh. When the heel is thrown forward, not only are these muscles strongly contracted, but the foot describes a longer trajectory and in doing so, gathers more momentum.
The reaction principle is also utilized in push-pull types of motion. If you are punching with your right fist, pull your left fist back to the side of your left hip. When kicking, pull your hands back to your waist or downward on each side of your body. In fact, a technique is not completed until after the blow has been pulled back. The punch or the kick has to be executed and retracted at the same speed and in a single continuous motion to take full advantage of the action reaction principle.
Inner power
This is perhaps the most important single source of power of the human body and also the most difficult to generate because it requires the coordination of physical as well as physiological principles. Physically, the inner power is the result of the force of the abdominal muscles located below the diaphragm. They are the strongest muscles of the body and take a prominent part in the transmission of force as they link the upper and lower body. When the abdominal muscles are contracted, the whole body becomes one single mass concentrated around its center of gravity; thus, in momentum MxV transmitted to the striking extremity, M represents the total weight of the body. Abdominal muscles must thus be contracted right at the beginning of the motion to solidify the body into one mass, on which, step by step, other muscles are going to rest to transmit the striking force.
The force of the abdominal region is developed by correct breathing and use of the centripetal pressure of the abdominal muscles. The proper way to breathe is to inhale deeply from the nose, lifting the diaphragm and filling up the lower abdomen (tanden) with air. The breath should then be held in the tanden and the abdominal muscles should contract to create an antagonistic pressure called centripetal pressure. This is truly the source of inner power. The lower abdomen should always remain slightly tensed, filled with ki, in a position of equilibrium between the centrifugal force excited by the breathing and the centripetal pressure of the abdominal muscles. This kind of respiration provides a constant massage of the internal organs (liver, spleen, and stomach) and facilitates blood circulation by pushing back to the heart like a pump, the blood irrigating the lower part of the abdomen. The movement of the diaphragm relaxes the solar plexus which is an important nervous center, and as a result, the functions of the central nervous system are better controlled and the mind becomes more serene.
Another effect of abdominal respiration is the lowering of the center of gravity. In normal respiration, the chest is inflated and the shoulders are lifted, thus the center of gravity moves up. Breathing with the lower part of the diaphragm creates a centripetal pressure by which the internal organs are pushed downward and the center of gravity is lowered considerably, thereby increasing the stability of the body.
Distance, timing, and speed
These three factors are lightly correlated and are extremely important for the transmission of a maximum force to the point of impact.
Distance refers, in this paragraph, to the length of segment joining the striking part and the target. Your reach is important for this particular technique. If this