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Essay:The Sine wave Theory of Taekwondo
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There is a concept in Tae Kwon Do, introduced by General Choi Hong Hi called the sine wave. It has been introduced as part of a scientific theory that claims to use physics to explain the use of a bobbing up and down motion combined with a forward movement to produce power instead of using the hip twist that is used by just about every other martial art out there. General Choi was a great man and a great martial artist but he was no scientist. Here is where the sine wave concept breaks down: The equation given in the encyclopedia on page 47 of volume 2 is;
P = 1/2mv^2 Where P = power m = the mass v = velocity. However this is not the scientific formula for power, it is the formula for kinetic energy. Not power. Power would be the change in kinetic energy divided by time. Another formula that has been used on a school’s website is;
P = 1/2mv2 + mgh Where; mgh = 0 for no sine wave. g = the acceleration due to gravity and h is the height. This formula is used to attempt to show that a downward motion affects a horizontal motion. The + sign in the formula indicates that the 2 terms are independent of one another (one does not affect the other), if they were dependent then the terms would be multiplied. This is a valid equation for the total energy of a strike but only applies (when mgh does not equal 0) to movements that have a downward component, e.g. a downward punch or low section side kick. It is an accepted scientific theory that for objects moving under the influence of gravity, the horizontal and vertical components of the movement do not affect each other.
Another correct formula for power is;
P = W/t Where W = work done By eliminating time (making it =1unit in seconds, minutes etc.), concentrating on the RHS of the equation and using the definition of work you have:
W = F*d*cos(theta)
Where F = the applied force, d = the distance moved and cos(theta) = the cosine of the angle of movement in relation to the applied force. A cosine wave is just a sine wave shifted by 90 degrees. For any angle smaller than 90 degrees or larger than 0 degrees cos(theta) = <1, which can be seen when dragging an object along the floor by a rope. When the rope is at an angle it is harder to move the object than if the rope was along the ground. For an angle of 90 degrees (the dropping of the hips in the sine wave movement) cos(theta) = exactly 0. In other words the pure downward motion contributes absolutely nothing to the power generated horzontally. This is simple physics which is called Newtonian mechanics.