” The relationship between an object’s mass (m), it’s acceleration (a) and the applied force (F) is F=ma. Acceleration and force are vectors; in this law the direction fo the force vector is the same as the direction of the acceleration vector” Newton’s Second Law of Motion
“For every action there is an equal and opposite reaction” Newton’s Third Law of Motion
Before I start all the “karatespeak”, discussing what I consider the basics of karate, I need to set the tone: I consider karate to be nothing but basic physics applied to the physical human body. There is nothing mystical about it at all: we are attempting to create lethal ballistic weapons out of our own bodies. In fact, even if you are not studying karate and your favourite martial art is one of the “twisty-bendy” arts like judo or aikido, you are still learning how to apply force to another physical body and throw it to the ground. Kind of like a catapult throwing a rock.
Coming back to our old favourite term “Ikken Hissatsu” or “one punch kill”. If we are adherants to the belief of “ikken hissatsu”, then our goal in karate is to create the absolutely most devastating attacks or blocks possible. If we are successful in creating those techniques we will actually be applying traditional Newtonian physics as it applies to projectile dynamics. Our fists, feet, arms and legs will be the projectile, while our body will be the weapon. I really like this particular image and use it frequently in my classes; it works in just so many ways.
When one of our techniques lands on an opponent, what exactly are we delivering to their body that inflicts damage? We are delivering energy, pure and simple. In the case of a projectile, that energy is “kinetic energy”. On impact the fist is decelerated (negative acceleration) by the body of the opponent. The kinetic energy of the fist is translated into the body ( the law of conservation of energy) as a wave as the body is compressed by the fist. Kinetic energy becomes destructive energy. There are only two things that dictate how much kinetic energy that punch carries: mass and velocity. Kinetic energy is defined as KE=0.5 times mass times the square of the velocity. Two important things the karateka must take from this: you need to have mass (body mass) behind the attack and the energy of the punch goes up exponentially as your punching speed improves.
Another thing you need to consider is how focal that force may be: spread the force over a large area and it may be easily absorbed by the enemy as a push; concentrate that force into a small area and you possibly multiply the penetration and the focal damage by a huge multiplying factor. The force is increased by focusing it into a small surface area ( the main reason a woman in spike heels always should be considered armed and dangerous!!) I am talking about hitting with a fist versus a slap: the fist hits with a very limited surface area, focusing the delivery of KE into a small point, versus the slap which spreads it over a large area. This point is useful in two ways: you know now that a fist will likely cause more damage to a focal area and a slap will be better to use if you do not want to be arrested the next day: the slap is less likely to leave a lasting impression.
Others will prefer to trot out the F=ma equation: this works too and is very useful if you want to discuss “shocking power”. In this equation we are really discussing deceleration rather than acceleration: specifically the deceleration of my fist by the opponent’s body. More force will be used by my opponent’s body to decelerate my fist if it is going very fast and I have all my body behind it versus if I am just using my arm at slothfully slow. Note here the only two things on my side of the equation that matter are the velocity of my fist and the amount of body mass I put behind it (also known as momentum). The other side of the equation is my opponent’s body: how long does it take to absorb the shock of my fist? If I hit his bony, hard face, the fist stops quickly, shocking his head back hard and possibly causing a concussion. If I hit his pudgy, soft fat belly, my fist sinks in, gliding to a halt after a couple of inches of deceleration. I would expect this blow to be more of a push rather than a smack down. On the other hand, maybe my opponent is a trained boxer and he anticipates the head punch. Here he may roll with the punch, riding the punch back and absorbing the blow by moving his head (knowing as “slipping”). Again, here my punch decelerates slowly, becoming a push rather than a shock. Again, the point here is that the F=ma equation involves my technique velocity, the mass I throw behind it, and how fast my opponent stops it with his face.
How then, does my ability to accelerate my technique (punch, kick) have anything to do with the force of the impact? Think about it guys: you need to accelerate the punch maximally so it is at terminal velocity once it impacts. If you are incapable of accelerating your punch and it hits slow, then the deceleration on impact is far from impressive.
The concept of “terminal velocity” needs to be addressed briefly. Maximum or terminal velocity occurs about from the middle of the punch path to about the last third or last quarter. At full extension of the punch your fist is actually slowing down as a protective reflex of your body; it is not really practical to overextend and destroy your own elbow in the midst of a life and death fight. Every fighter needs to consider this when he is throwing a real punch in a real fight (or against a heavy bag or makiwara); the impact point is short of full extension while full extension represents a point inside or past the target. This explains why we are admonished to strike through a target rather than at a target.
Consider the term mass in the F=ma equation (or the KE= 0.5m v squared.): this equation implies that a fighter needs to involve as much of his body mass as he can behind the punch or kick. This also implies that the mass is aligned well behind the technique and the limb involved can deliver the entire mass movement directly without folding or absorbing the impact along it’s axis. The visual on this would be the destructive force of a linear projectile (missile) versus the destructive force of a sponge of the same mass: one will spear rigidly through the target while the other folds on impact, absorbing much of the KE back into it’s mass. The message here is that your limb and your body have to be aligned on impact and kept that way through to completion.
Let’s consider the Newton’s third law now: for every action there is an equal and opposite reaction. This implies if I hit some opponent, he is actually hitting me back ( via my fist: remember his face is decelerating my fist). If I am more rigid than my opponent and my mass is able to penetrate along it’s line of attack, then my opponent will crumple or be projected away from me. If my opponent ( or the solid makiwara) is more rigid than I, then I will crumple and bounce back. Anyone that has ever misapplied a solid side thrust kick has discovered Newton’s third law: you tend to bounce off the target and fall down if your side thrust kick is not extended enough that you can drive in off the supporting leg. This brings up an important point: for the most part you need to be driving in these techniques while well braced on the floor by the driving leg. Without contact with the floor to brace your body on impact, then you are likely to absorb the impact reaction into your body and bounce off the opponent rather than vice-versa. This little point explains why hockey players fight the way they do: on a slippery surface you have to brace yourself by grabbing the opponent with one hand while you hit with the other; otherwise you will just slide away on impact. In some fights the degree of contact with the ground (friction) may have some importance: certainly a slippery gravel parking lot at a roadside beer joint presents a much different situation than the hardwood floor of the traditional dojo.
Some authors prefer to use the term Impulse (J) to explain force delivery in karate. Impulse is a term used to describe the amount of change of momentum of a moving object when a force is applied to it. This change in momentum may be a change in velocity or in the direction of movement. Momentum is described by the equation of p (momentum)= mass(m) times velocity (v). Impulse is defined as J(impulse)= F(force) times t (time). This equation is very specific in what it is saying: an object’s directional velocity (vector) will alter a specific amount when a directional force is applied for a specific period of time. If you apply a different force, then J is different. If you apply that force for a different period of time, then J is different. On the other hand force and time are completely independent of each other: applying a punch for a shorter period of time does not, by any means, increase the force of the punch. The only possible way to increase the force of the punch is to increase mass or increase velocity: an increase of either one of those will increase the KE of your punch and increase the momentum of your punch. I repeat: force and time are completely independent of each other. If you were to apply a great force to the opponent for twice as long as you normally do, the impulse on him would be greater and the change in his momentum would be twice as much. Argue all you want, but that is exactly what the equations mean, nothing else.
The F=ma equation explains why a shorter impact period may cause more damage far better than the impulse equation. You are best to ignore anyone using the impulse equation to justify “snapping” punches and the like: they either are purposefully cheating or they do not understand simple physics. There is a justification for snapping techniques (they tend to be faster, thus more velocity, and they can set you up quicker for another devastating technique), but the Impulse equation is not by any means the true justification.
We should look at the term “center of mass”. Within a system of inter-related particles (ie: our bodies) the center of mass is the point at which the system’s mass behaves as if it were concentrated. For the human body this point occurs slightly below the navel and just above the pubic symphysis; in martial arts this is called the “seika tanden” or, for simplicity, the “tanden”. The Chinese practitioners call this the “Tan Tien” or “Dantien”. We need to consider this point because when we apply force or have force applied to us, for the most part rotation of our mass will tend to occur around this point. Control of our center of mass is synonymous with control of our stability. A low center of mass tends to favour increased stability (to lower the center of mass you usually have to broaden your base: the most stable point would likely be lying down: the center cannot fall any farther and the base is at it’s widest). Raising your center of mass tends to decrease stability and favour mobility ( you need to narrow your base to raise the tanden, thus allowing gravity to help movement). The standard “stances” of martial arts are all about raising or lowering your center of mass: long, low and stable versus high, short and mobile. The karateka always has to play mobility versus stability when performing: obviously maximizing both would be preferable. Training to maximize both stability and mobility may justify training to move quickly and powerfully in a standard long stance such as zenkutsu dachi (front stance). Since the body tends to rotate on the tanden, this also explains much of our effort to maintain a strict upright posture: any deviation off the upright alters the lever arm action around the tanden and thus lends itself to instability. Consider a take down (throw) and attack of the downed opponent: if you throw your opponent and lean over his prone body, your own mass will tend to pivot head first around the tanden as your upper body weight drops down. This is especially true if your opponent is grabbing you and pulling you over, helping that leverage. If you maintain your upright posture and drop down by bending your legs and naturally lowering the tanden as your opponent falls, then there is no leveraged force applied around your center and you are far more difficult to throw.
We should also consider the physics of lever arms. A simple lever is a mechanical device that rotates on an axis such that a force applied at one end will produce work at the other. Practically all the bones in the body are mechanical levers with the muscles acting as a complex pully system to do work. Most of the bones in the body act as third class levers: the fulcrum is the joint, the muscle is the force and is applied along the axis of the bone, while the resistance is applied at the far end of the bone in the form of whatever work the limb may be doing. This arrangement allows for speed of action, and greater range of motion, but does require a relatively large amount of force to move even a small amount of resistance. This arrangement actually provides negative mechanical advantage in favour of range of motion and speed. The mechanical advantage of the limb actually decreases as it extends:this is one part of the reason that an extended arm is much weaker than a flexed arm. The astute readers here will also understand why most throws and joint manipulations are done at very close quarters: it keeps the lever arm of the karateka’s limbs shorter and thus far stronger. The speed of action part of this equation also explains the utility of coiled and uncoiled kicks and strikes. Consider the movement of a kicking leg at the hip joint: a ninety degree flexion of that joint represents only about six inches movement. Take that same movement two and a half feet away at the foot end of the leg: the foot moves through a far greater distance (range of motion) to cover that same ninety degree arc; obviously the foot must be moving at a greater velocity than the hip joint. The coiling action of the leg tends to magnify this action by creating the radial acceleration effect at the hip and knee simultaneously. Furthermore, the coiled leg activates both the hip flexors to move the limb at the hip joint and the femoral muscles to extend the limb at the knee: the net effect is to take a small, fast arc and suddenly extend it into a large fast arc. Large is better.
One point that needs to be said here (I hope some of you are already saying it): this is all about physics happening to a limited physical body. Whenever we consider the limitations of the physical body we have to consider how our own muscles act as they provide the force that works our living system of levers. The muscles are made up of a series of interlocking “ratchet” or “Velcro” like units called sarcomeres. Under the influence of neurological input, energy from oxygen and nutrients, and various enzymes, our muscles activate or relax these ratchets, increasing the amount of relative overlap between the halves of the interlocking ”teeth”: maximal overlap represents maximal contraction, while minimal overlap represents relaxation. The most efficient range of the muscles is at the mid range: neither maximally contracted nor completely relaxed. This interaction explains why most of our techniques, especially blocks, are most efficient at the middle range, when our limb is at about ninety degree flexion. ( I would bet that ninety degree extension on a punch is about the point when our punch is accelerating maximally and approaching terminal velocity) .
One last thing I would like to discuss with regards to physics as it applies to martial arts: vectors. A vector is a term that describes motion or force in a specific direction. Take for example a bullet launched from a gun pointed at a 30 degree angle upward. The force from that gun created by explosion of the gun powder and the resulting expansion of the exhaust gasses behind the bullet has a vector of 30 degrees upward. The bullet also has a velocity vector of thirty degrees upward. Now, on the other hand, by applying simple geometry this vector can be broken down into components: a force of thirty degrees upward will have component going directly upward at ninety degrees and a component going directly forward at zero degrees. Continuing on this topic there will also be other vector forces applied to that bullet. There will be the force of gravity which is always ninety degrees downward (which acts to counter the upward component of the trajectory from moment the bullet leaves the gun). Then there will be the force of air resistance acting to slow the bullet along the horizontal axis. There may also be a second form of air resistance from any cross wind blowing that may act to both slow the bullet and force it off it’s trajectory with sheer force. Sounds pretty complex doesn’t it? How does it apply to karate? Consider a front snapping kick: the foot travels from the floor to it’s target on the body: the direct line is forward and up. That foot has a trajectory and a vector, thus it has vector components both forward and upward. When teaching students most instructors will have noticed that students miss one or the other of these components: some students fail to have any forward vector in the kick and thus just balance on their support leg while kicking practically straight up, while others fail to lift their leg at all and basically kick forward along the floor. The better students recognize early on that a good kick has both upward and forward vector components. Similar analogies can be made for just about all our techniques: thrusting techniques usually have mostly forward vectors while snapping techniques often have both forward and angular vectors. Thinking in this way may not help in actual training, but it certainly does help an instructor recognize student’s shortcomings in many techniques.
Consider all these ideas and perhaps add to them outside the dojo: deep thoughts about Newtonian physics while you are training out on the hardwood is absolutely innappropriate and likely to get someone hit and hurt.