The importance of velocity in the striking arts.
Karate works primarily as a result of strikes by kicks and punches of one kind or another. Yet, each fighter is unique in their size, flexibility, age, strength, and experience. Despite these variables, one concept affects all fighters in maximizing the power of a strike and stands out as a universal unifying concept: the velocity of the striking weapon.
Many people believe that the power of a strike is simply a function of mass multiplied by velocity. Rather, mass times velocity merely describes momentum. The formula for momentum is:
p = m x v
In this formula, p represents momentum, m represents mass, and v represents velocity on impact. Note that momentum is a directional concept (or "vector" quantity): it requires a direction in order to be understandable and complete. You cannot accurately describe momentum without taking into account the respective directions of the various objects which happen to be in motion during the collision.
The mass in the above formula refers to weight at a certain altitude. A given mass would weigh a little more in Death Valley since it is closer to the center of the earth, and a lot less on the moon, since it is a long way from the center of the earth (and closer to the center of a smaller mass, the moon). The velocity in the formula is speed--not acceleration in the sense of an increasing speed; it is the final speed of the moving object at the moment of impact. Impact, however, is not instantaneous. Impact is spread over a period of time, however short.
In a collision of two objects inside a closed system (i.e., a system in which we can account for everything), the sum of all momenta is conserved, in conformity with Newton's Third Law. In billiards, the cue ball stops upon impact with another ball and this ball is propelled with the identical momentum of the cue ball (except for any loss of momentum to friction). Principles of momentum allow us to predict the direction and speed of objects upon their colliding with each other. However, in any combat utilizing the striking arts, the essential question is not whether and in what manner an opponent may cause you to move in a certain direction. In karate strikes, momentum is simply not a controlling factor. This seems by common experience to fly in the face of reason. Immediately, the picture comes to mind of a 250 pound giant planting his fist into your face. After recovering consciousness, you think to yourself, "I definitely felt that punch." And true enough, if you are hit with a properly thrown punch by a 250 pound opponent who knows how to deliver a punch, it's going to hurt, a lot. But the mechanism inflicting the pain was not from application of the opponent's momentum against you. It is not momentum which creates "work" on your body; it is kinetic energy (KE).
What is Power?
The unit of measurement for power is the watt, one of which is equivalent to one joule of energy per second. In physics terms, then, power constitutes the rate at which energy is transmitted. Since impact is never instantaneous, in a car collision, for example, the "crumple effect" of newer models disburses the impact over many multiples of the period of time experienced by older cars with rigid steel frames. The crumple effect thus cushions the blow by spreading it out over time. A vehicle's air bag works in a similar fashion, spreading the stopping of the car occupant's body over: (1) a period of time from impact with the bag through deflation, thus slowing down the moment of impact, and (2) an area in space (the surface of the air bag versus the surface of the shoulder restraint).
With regard to the first factor, a boxer's "taking a punch" by throwing his head in the direction of the punch operates to disburse the absorbed energy over a period of time. One reason why cupping a hand behind the head of an opponent at the moment of a strike to the face is so effective is that it forces the impact into a brief moment of time, not spread out over milliseconds by the opponent's head moving away from and with the strike. Similarly, an impact to an opponent's forehead (a relatively hard target) versus an impact with his or her abdomen (a softer target, with more "give" than his forehead) will lessen the time in which the impact acts on the target and thus deliver more destructive power.
The implications of the second factor are due to the fact that the larger the striking mass surface area at the point of contact, the wider the disbursal of the kinetic energy, thus diffusing the blow. This is why, in karate, a dragon's head (a fist with a protruding middle knuckle backed up by the thumb) is such an effective striking weapon, since it focuses all of the striking force over an area roughly four square centimeters, versus the more common Himalayan ram punch (a conventional fist shape), which has roughly eight times more striking surface, resulting in less force per square centimeter by a factor of eight. This is also why striking with the tip of a kubeton (a small wooden or metal rod held in the hand) creates such a destructive impact.
Kinetic Energy as Destructive Power
The standard unit of measurement for KE is the joule. One joule is equal to the translational KE produced by one kilogram times one meter squared per second squared. (Translational KE is the energy due to linear motion from one location to another.) And recall that power is measured as a rate in watts--joules per second.
Imagine having the choice between: (1) being hit by a 4,000 pound truck traveling at one mph, or (2) being hit by a one pound baseball traveling at 4,000 mph. If you wanted to live, you would choose to be hit by the truck. The truck would tap you with its bumper and bump you out of the way. The high-speed baseball would tear a hole through your body and keep on going. The momentum of each object, however, is identical: 4,000 units (m x v). Why, then, does the 4,000 mile per hour baseball have so much devastating energy when compared with the much heavier truck? The answer lies in the difference between momentum and KE.
KE is defined in physics as the work needed to accelerate a body from rest to its current velocity. Having gained this energy during its acceleration, the body maintains the KE unless its speed changes. KE varies dramatically from momentum. KE is "scalar," meaning that it does not have a directional component. Whatever KE a certain body in motion possesses, it is the KE regardless of direction. Most significantly, the mathematical formula for KE greatly differs from the formula for momentum. While the formula for momentum is p = m x v, in calculating KE the formula is:
KE = _ m x [v.sup.2]
The simplicity of this formula belies KE's enormous significance on the impact of moving objects on other objects. While incremental increases in mass yield increases in KE in direct proportion to the resulting mass, incremental increases in velocity yield increases in KE by the square of the resulting velocity. When recently I became aware of this principle of physics, I was immediately in awe of the ramifications. If the velocity of the striking object is doubled, the KE available for release against the target increases by four times. If the velocity is tripled, the available KE increases by nine times, and so on. The reality of this holds dramatic consequences in the striking arts.
Why does KE increase with the square of the velocity? First, without motion, there is no KE. And second, it becomes exponentially more difficult to accelerate any object to higher and higher speeds. If it takes five joules of work to move a 10 kilogram object at a speed of one meter per second (10 x 1 x 1 divided by 2 = 5), it takes 20 joules of work to move the 10 kilogram object at two meters per second (10 x 2 x 2 divided by 2 = 20), and 45 joules of work to move the 10 kilogram object at three meters per second (10 x 3 x 3 divided by 2 = 45). This exponential relationship between velocity and KE is unlike the linear relationship we've seen with velocity and momentum, or with mass and KE.
In the Heat of Battle
Negative work of the same magnitude is required to return the body to a state of rest from any given velocity. In the case of a punch, the "negative work" to slow it down to its original zero kinetic energy is, primarily, the target impacted by the punch. The same work that went into accelerating the fist will be required to return the body to a state of rest from that velocity.
But what if the blow does not land? If a 200 pound opponent, for example, is moving quickly directly at you, all of his or her weight and speed creates not only a momentum, but KE. If he suddenly needs to redirect in response to your move against him, he must overcome his own directional movement, by applying work, to slow down, stop, or change directions; this work needed is proportional to the square of his velocity. This is why punching "in the air" is so hard on a fighter's body. The identical work required to accelerate the fist to its terminal speed is required to slow the fist down to a stop at the end of the fighter's punch.
The implications of the KE formula mean that a car traveling at double the speed of an identical vehicle will take four times as much distance to brake to a stop. Now consider two trucks--a light truck and a heavier truck--traveling with identical momenta (and therefore different speeds). Because of the work-energy principle, it takes more work to stop the light/faster truck than to stop the heavier/slower truck. The fact that the light/faster truck has more KE than the heavier/slower truck demonstrates that it is KE and not momentum or mass which decides strike effectiveness, or controls the stopping and changing directions of a fighter.
We can now see why the explosive energy of the high speed baseball from the earlier example would have immensely more KE upon impact than the slow-moving truck. For the slow-moving truck, the KE calculation is 4,000 x 1 x 1 divided by 2, or 2,000 units of KE (joules require translation into kilograms and meters per second and it will suffice to use "units" for this comparison). For the high-speed baseball, the KE calculation is 1 x 4,000 x 4,000 divided by 2, or 8,000,000 units of KE. The baseball therefore has 4,000 times the KE of the slow-moving truck, despite the fact that the momentum of the baseball and that of the truck are identical!
Karate in Motion
Imagine that instead of thrusting a side kick at the heavy bag, you approach the heavy bag at a jog, jump up and deliver your side kick. Your entire body is moving forward in the process of the flying side kick. This means that the velocity of your body toward the bag is added to the velocity of the thrust of your kick, and that combined velocity is squared in the KE calculation. The result: a dramatic increase in KE. Additionally, your entire body weight in the flying side kick becomes a component of the mass impacting the bag during the side kick, resulting in the added benefit of a heavier mass impacting the bag.
If the velocity of the foot's knife edge hitting the bag has, for example, doubled, in relation to the velocity of a sidekick from a stationary (though pivoting) base foot, then by virtue of the increased velocity alone, KE has increased by four times. Consider the difference between a rear leg knee kick from a stationary position versus one preceded by an explosive step-drag, or even an explosive, forward-moving chicken kick. In fact, simply driving off the forward foot, while bringing the rear leg up for a knee kick, increases the overall system velocity, and hence, significantly increases the KE in a knee strike.
The following table shows renowned professor of kinesiology Vladimir Zatsiorsky's findings on body-part mass as a percentage of overall body mass for various parts of the human body:
BODY PART % OF TOTAL MASS--MALES % OF TOTAL MASS--FEMALES HEAD 6.9% 6.7% TRUNK 43.5% 42.6% UPPER ARM 2.7% 2.6% FOREARM 1.7% 1.4% HAND 0.6% 0.6% THIGH 14.2% 14.8% CALF 4.3% 4.8% FOOT 1.4% 1.3%
Imagine striking an opponent's chest with a rear hand straight thrust punch. A male weighing 80 kilograms using mass from a combination of his fist, upper arm, forearm, and half his trunk would use approximately 27% of his total body mass, or 21.6 kilograms of body mass, to strike. Let's say his first attempt achieves a speed of 5 meters per second. 21.6 x 5 x 5 divided by 2 = 270 units of KE. With greater effort, the fighter next increases the speed of impact to 6 meters per second. Now, the KE calculation is 21.6 x 6 x 6 divided by 2 = 389 units of KE. By increasing the speed by 20%, he has generated a 44% increase in the force of his blow upon impact. If he strikes at 10 meters per second (generally considered the approximate top speed of a straight thrust punch from a stationary position), he has attained a 100% increase in velocity. 20 x 10 x 10 divided by 2 = 1,080 units of KE, or four times the KE on impact. Not a bad rate of return on investment! To make every blow as forceful as possible, remember velocity counts.
Remember too that since KE increases by velocity squared, so too does the work required to generate that increase. In running, the work required to run at 10 miles an hour is four times as much as the work required to jog at 5 miles an hour. The role of speed in the work-energy principle goes far to explain the physical exhaustion a runner feels after interval workouts, and the relatively brief lengths of time sprinters can perform at top speed. The fact that the body switches over to anaerobic energy systems at high speeds is a result of the vast amounts of energy required to maintain them. The upside is that the velocity you generate pays off in spades not only in power, but in your increased overall fitness level and caloric use as well.
lawabiding (Member): Mysteries of Karate 12/4/2008 9:07 PM
This is a fascinating subject, and Jack Forbes' article is very readable and extremely informative. Karate has always been such a mysterious subject to so many people, wondering if and how it really works. Understanding the relationship between kinetic energy and velocity takes me a long ways in appreciating the power of an effective karate strike or kick. This seems to be the first article that really analyzes the role of the velocity of the striking weapon in creating power in karate. This information should be understood by every martial artist in the striking arts, and any martial arts film buff.
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|Publication:||Running & FitNews|
|Date:||Jan 1, 2008|
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