To start let’s examine a little more thoroughly some of what has been presented elsewhere about this topic and make clearer the meaning of some familiar terms:
Speed x 3
Much has been made of the importance of speed for the martial artist and indeed it is important for several reasons, some of which are not often directly recognized and exploited in training. Let’s start first with these less discussed reasons and then later re-examine the reason most often presented for a martial artist to have speed.
The two additional reasons for using speed both take advantage of the law of inertia. One concerns the inertia of the target and the other concerns our inertia and how it effects the force of our tool.
The law of inertia states that a stationary body remains stationary unless acted upon by a force. Inertia is easily seen in the trick of pulling a tablecloth out from under a table full of dishes: pull too slowly and the dishes come along with the table cloth, but yank fast enough and the tablecloth will be out from under the dishes before their inertia is overcome and they can start to move. (Please don’t try this, especially if they’re not your dishes - pulling a napkin out from under a spoon would be safer.)
For our training, let’s first examine exploiting the inertia of the target. If we hit a target too slowly the energy of the initial contact will start the target moving away from the remaining energy of the impact (as happens in a push kick). The faster the impact the more energy will go into the target before it can move away. This is most obvious with
loosely suspended, and free-standing targets, but it is just as important for heavier targets if energy is not going to be wasted. A heavy bag, when kicked solidly, will often swing away from the kicker, which means some of the energy of the kick went into pushing the bag. When kicked with a sufficiently fast kick the bag will bend around the foot and finish by “dancing” on its chain as the energy which went into the bag is dissipated.
This effect can also be seen in some board breaking events when the number of people needed to hold for a successful break is proportional to how slow the kick is. With proper speed, two people should be enough to hold for a three or four board break. If the people holding get knocked back it is because the technique is too slow and is pushing instead of snapping. Only part of the kicker’s energy is going into the actual impact, the rest is being used to push the target away. Unfortunately, this lack of speed will be masked with mechanically braced targets as long as enough mass accompanies the slow speed. Few real-world applications of our techniques, however, are wall or platform braced (just try to get a mugger to stand still against a wall for you), and we will not be able to effectively transfer our energy into the target if our training exercises do not take this inertial effect into account.
Inertia shows up for our bodies also, because the faster a tool can be accelerated, the faster it will be going before our own body is pushed back by reaction force. Seeing how this works for our bodies can easily be demonstrated by shutting a car door: stand feet together close to a car door which has been pushed up to the latch. Without leaning, push your hand slowly against the door. You will push yourself backwards and the door will not latch. Push a little faster and you may get the first of the two catches to engage before you get pushed away. Push very fast and you can probably get both latches engaged and remain standing vertically in place. This means that your power went into moving the door rather than into moving you.
EXPERIMENT 1. This can also be practiced as an exercise with a partner. Stand with your feet together half an arm length away from your partner who is standing sideways in front of you with their feet together. Without leaning into them, try pushing against your partner’s shoulder at different speeds and notice the varying results. Try doing this with different size partners, and also while standing on one leg. This exercise will be used again later in this paper to demonstrate several other points.
Now for those definitions mentioned earlier, and that other reason:
Energy is defined as the capacity to do work. Gravity, stretched or compressed springs, rotating objects (from atoms to solar systems), among other things, all can be used to perform work. Work is a measure of the energy transferred when an object is moved.
Power is the capacity to do work (or transfer energy) in a given amount of time. If twice as much work can be done in a given amount of time (or if the same amount of work can be done in half the time), it means twice as much power is available.
If a hill is steep and long enough we may have just enough energy to bicycle to the top before we have to stop. Somebody else the same size as us may be able to pedal to the top in half the time it takes us before they run out of oomph. Since we’re both the same size and we both made it to the top of the same hill using the same bike we both did the same work and used the same amount of energy, but the other person had twice the power, because they could perform the same work in half the time. Same amount of energy used, but twice the power produced. We’ll see how later.
Right now with these definitions in mind let’s revisit the most often used reason for using speed.
As is often quoted: Kinetic(motion) Energy = ½ mass x velocity2. Increase the mass by 40% and there will be a 40% increase in energy, but increase the speed by 40% and there will be a nearly 100% increase in energy. Since we would seem (more about this later) to have a limited ability to make our fists or feet heavier on the spur of the moment, increasing our tool’s speed is often presented as an important way to increase our tool’s energy. Of the different kinds of energy that exist, this energy formula is only concerned with the amount of energy in a moving object (usually viewed as a fist or foot, for our purposes). It is not a measure of power, but only a measure of the energy in the moving foot (for instance). It does not indicate how the foot got to be moving, how much energy was used to get it moving, or how much work it will actually do. This formula tells us that a moving foot has energy, but gives no indication as to how it got to be moving. Two different feet moving at the same speed may have taken very different amounts of power to get to that speed. This formula does not help us know how to directly improve our results, it just says that more speed is better (or more mass for that matter).
The three reasons discussed above (being able to increase the impact on the target by using it’s inertia, increasing our power transfer to our tool by using our own inertia and the squared increase in energy of a moving object) all make speed very important, but speed is the end result of how we use ourselves and is of major concern only to what we are hitting. Concentrating on final speed itself is not the key to improving final speed since it usually places attention on the arm or leg which is not where the power best begins, nor is it the largest potential contributor of power to the technique. More important for improving our performance is to focus on the process which leads to speed.
Acceleration > Speed
Gasoline contains energy and a moving car has energy, but studying the gasoline or how much energy there is in the moving car will not help you figure out how to make the energy of the gasoline perform work to move the car. If you realize that an engine is needed to transform the energy of the gasoline into the energy of a moving car, then you probably also recognize that some engines work better than others - some get more power for their size, others use less gasoline for the same performance. To understand why this is so, you would need to study how engines work. Similarly, we all contain energy and we all know how to work, and by focusing on how we work, we can discover ways to improve our performance - whether power or stamina. To improve our kicking effectiveness we will benefit from focusing on what our body can do to increase the speed of the foot. And increasing speed is the very definition of acceleration.
Speed, or velocity, is the distance covered in a particular direction in a certain amount of time, such as 32 feet/second. Acceleration is the change in speed in a given amount of time, such as 32 feet/second/second. In the speed example, the object will be moving 32 feet/second after the first second, and will still be moving 32 feet/second after the next second and 32 feet/second after the third second and so on. In the acceleration example, the object will be moving 32 feet/ second at the end of the first second, 64 feet/second at the end of the 2nd second, 96 feet/second after the 3rd second, etc. Since at a constant velocity the object moves the same distance each second, the energy transfer is the same from second to second, but the accelerating object covers more distance each second and so for acceleration the energy transfer is constantly increasing. Significantly however, nowhere in the above formula for energy is acceleration mentioned. Yet, acceleration is the process which leads to speed, and is what we need. Now, where does acceleration come from?
The final velocity of an object (a fist or foot, for instance) is ultimately determined by how quickly, and for how long, it can be accelerated. And the rate of acceleration is dependent on the nature of the force behind the object. Although energy is used to generate a force, only a force, not energy or power, is directly involved in the acceleration of a mass: Force = mass x acceleration (F=ma). In the case of a dropping ball, gravity is the force. In the case of your accelerating fist or foot, you are the force. Only a force can change the speed or direction of an object. And changing the speed and directions of objects is what we are doing in performing Taekwon-do.
Energy > Force > Power
To summarize: First there has to be energy, without it nothing can be done. But just having energy is not enough. Gasoline can be spread and burned to make a warming fire, or it can be confined in a small space and ignited causing an explosive force. The first way of using the energy does not usually get much work done, but by focusing the energy the second way can move quite a lot.
So from energy, force needs to be created. And from force the power to do work can be created. We could use our energy to create a force to push against a wall and work up quite a bit of sweat, but if when we stop pushing on it the wall is still in place no work is considered to have been accomplished since nothing was moved. And, as we learned from the earlier definitions of work and power, since nothing was moved no work was done so no power was demonstrated to be available. I know, I know: it was “hard work” pushing against the wall, but that was for us, the outside world was unmoved.
So being able to focus energy to create force is important, but, just as with some engine designs, some ways of using energy creates more force from less energy than others do thus making more horsepower possible from less fuel. Paying attention to how the force is created will get more force from less energy. Paying attention to how the force is applied will ensure that more is accomplished with the force available. Some ways and applications are more effective than others. Some people work better and others work harder. Being somewhat lazy, I’d rather make sure I’m doing things the most effective way I can before I have to actually work harder. To do this we must have a better understanding of what force is and how it works.
Although the effects of forces can often be seen, the forces themselves usually cannot be. Because so much of this discussion deals with forces, it will be useful to have a way of representing them to make it easier to “see” some of the interactions being examined. This will also provide a means for the reader to understand future situations they may wish to analyze themselves in order to improve their performance.
Force is considered a vector quantity which means it has magnitude(strength) and direction(focus). In comparison, heat is energy, but has no direction, a moving ball has energy and direction, but cannot accelerate by itself. The two force characteristics of direction and magnitude can be drawn as vectors which look a lot like arrows, but with a very important difference: the arrowhead still indicates the direction, but the length is proportional to the strength of the force; if it’s twice as long, it’s twice as strong:
Force vectors only indicate direction and strength: they do not indicate motion or distance. If one force is equally opposed by another force they will be in equilibrium and there will be no change of position, i.e., no motion. Think about pushing on that wall again: your pushing force had direction and strength, but there was no motion or distance traveled.
If the force pushing up in your legs (vector of a certain length pointing upward) exactly equals the force of gravity (a vector of the same length but pointing down), adding the two vectors tip to tail shows that they cancel out and there is no motion - you are just standing there. When one force weakens, the equilibrium is then broken and there will be acceleration according to the direction of the stronger force, and the final magnitude will be the difference of the two strengths. If the force in your legs becomes weaker (shorter vector pointing up) then adding this tip to tail to gravity’s vector will leave a short vector pointing down: you will be dropping to the floor. If you generate more upward force in your legs than gravity exerts, the longer vector will add to gravity’s vector leaving a short vector pointing up which indicates the strength of your lift or jump.
For now we will ignore any intentional opposing forces and only consider the unbalanced forces which result in movement.
If more than one force is at work on an object at one time, the vectors are first added together tip to tail (in any order). Then by connecting the starting point of those added vectors to the point where they finish reveals the resulting direction and strength of the combined forces on the object. You can draw a vector arrow pointing to the right of a particular length, say 1 inch, representing a force being applied to a ball. Now to the end of that vector draw another one pointing up also with a force 1 inch long, representing something else pushing the ball with the same force upward. Now go back to the beginning of your first vector arrow and draw a line connecting to the end of the second vector you drew. This length and direction shows that the ball will experience a slightly greater force than either of the two forces alone, but in a direction 45 degrees to the starting forces.
As can be seen, additional forces can strengthen, weaken, and/or change the direction of any initially intended force.
The ancient Egyptians, Greeks and Romans had a practical understanding of forces sufficient enough to allow them to do some pretty amazing engineering from their predictions of those forces. This can be seen in the various monumental constructions, such as pyramids, aqueducts and coliseums, which they built, some of which have lasted for centuries.
The method of adding forces used in the examples above has been known for 400 years since the work of Simon Stevin, and countless bridges, buildings and other structures have been designed using it. The relationships of force, acceleration and mass have been understood and exploited since Isaac Newton formalized the three laws of classical mechanics 300 years ago. These laws of inertia, force, and action and reaction, and the mathematics behind them, have been used to understand, and design, engines, cars, and supersonic aircraft, and can be used to explain the forces in any stationary or moving system.
These principles are considered laws because they can be (and have been) tested and proved many times by careful observation of the properties and terms in them. They are used everyday in the work of thousands of architects and engineers. These laws apply to all moving bodies, including ours. Since no exceptions have surfaced so far in three centuries, no new untested ideas need to be proposed to explain Taekwondo’s techniques and movements. These laws are more than sufficient to show us ways to improve our performance, to reveal things we may be doing which are hurting our performance, and to better explain the reasons behind many martial art training principles.
Checking forces in our training
So, let’s look at how these vectors can illustrate the forces at work in some simple examples from our training:
Adding the force vector of a downward attack (a knifehand, hammerfist or kick, for example) tip to tail with the force vector of a body dropping from flexing knees, not too surprisingly, results in an increase in the total impact force, as seen by the longer vector pointing downward.
Adding the force vector of an upward attack (upward punch or overhead kick, for example) with the force of a body drop downward, will result in a shorter vector pointing up and therefore a decrease in the total impact force.
Adding the force of a forward attack (punch, thrust or kick) with the force of a body drop, will slightly increase the strength of the attack force (shown by the slightly longer line that results compared to the forward attack by itself), but it will also radically change its direction, and therefore reduce the effectiveness of the attack at its intended angle of impact.
Taking a slightly more complex, but hardly uncommon situation for a beginning student where a forward punch vector is added to a downward vector representing a dropping body, is then added to a backward vector representing an arching back. Drawing the sum line from the beginning of the first vector to the end of the last vector demonstrates the final change in direction and decreased force of the resulting forward punch.
Note also that even if the body drop portion is removed from this example, adding together just the forces of the punch and the arching back demonstrates the need for a strong center so that the body does not flex at the waist and subtract force from the forward-directed tool (more about this later).
These examples demonstrate a major reason why some people use more energy to produce less power than others: some of the forces they are producing are canceling and/or misdirecting some of their other forces. This fact demonstrates the need to pay attention to how we focus our various forces for an intended task.
Force cannot exist without acceleration and vice versa. They are inextricably linked by the relationship, force = mass x acceleration. The maximum magnitude of our acceleration is partially determined by our muscle’s ability to contract and our joints’ ability to handle the energy without damage (especially critical if the technique abruptly changes direction along its path). Physical conditioning can increase our muscle strength and contraction speed, and proper exercise can increase our joint strength and flexibility. But, unless our brute strength is focused properly by skill, much of our body’s physical efforts can be canceled or misdirected.
mass x acceleration = \/ = mass x acceleration
Or, in other words, for any given amount of force there is always a trade-off between mass and acceleration: if the mass is increased, then the acceleration will decrease, and if the mass is decreased then the acceleration will increase. The force vector shown above could represent the force in our dropping body or in our downward kick: if our leg were 1/10 of our body mass and the leg acceleration were 10 times faster than gravity then the force would be the same as the whole body dropping under gravity’s acceleration. It makes no difference to a force if it is going to be used to accelerate a small mass at high acceleration or a large mass at a slower acceleration. BUT our expectation of moving a large mass or a small one unfortunately often makes a significant difference in how we use our bodies to generate that force. When expecting to move a large object we usually prepare ourselves differently and start using different muscles than when we are moving a small object even when we are supposedly intending to move it as quickly as we can. Performing a technique against extra resistance or weight will often let us better see if we are using the optimum muscle sequence and pathway for that technique.
EXPERIMENT 2: A) stand in a left walking stance with the right fist extended in a forward punch and the left fist at your hip. Have a partner stand in front of you and hold the wrist of the extended fist while putting their other palm against the fist at your waist. While your partner holds on strongly (enough to strongly challenge you, but not to live-or-die frustrate you), pull back the extended fist while you punch forward with the fist at your hip. If you are trying to punch just with your arms you will probably have difficulty completing the motion at first, and your body will start searching for other ways to add to the effort. When you have adjusted the way you use your body and can do this punch reasonably well against a strong resistance (if you are having trouble, a helpful hint will be given shortly), try moving the one fist from the hip up to a starting position on the waist and try again against the same amount of resistance and compare the effort to the hip starting position; then try starting the fist from the shoulder against the same resistance and feel the results.
B) Try doing a side kick while somebody holds on to the cuff of your pants in such a way that it will pull out of their hand only if you move strongly enough (no torn uniforms, please)
C) Try performing a sidefist strike while holding onto a dumbbell.
All of these approaches increase the feedback of what your body is doing when you perform techniques. You will likely find that there are additional muscles you could be using, that some positions are more difficult to generate a force from, and that some portions of your motions are jerky which puts the joints at long-term risk of being damaged. All of these discoveries will still apply when the resistance or weight is removed because we are still dealing with the same potential amount of force (force = mass x acceleration). Increasing the mass just proportionately slowed down the acceleration and increased the obvious loads on our joints, making it more obvious what our body was doing. With enough repetition, any improvement in body use can be transferred to the light-load condition of just using the tool by itself, as long as we stay aware of our whole self.
It is quite possible to work harder without much increase in results. In fact, as we have seen in the above vector samples, if the effort is not well focused it is even possible to work harder with a decrease in results. Too often effort is confused with effect. It is the efficiency of movement which concerns us here, and it affects the tool’s acceleration and even, as will be explained later, the final mass at impact. An increase of efficiency allows an increase in delivered power using the same effort as expended before, or it allows the same amount of power as delivered before to be achieved with less effort, resulting in increased stamina. It is the nature of the force used which will determine how much power can be produced from the energy we have. Creating the force comes before power. A little bit of understanding and practice can give us some “free” power and stamina. Want some?
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