Why do the techniques we are taught work so well?

An area of considerable interest (in my experience) among martial arts students is the
interface between karate and physics.  Are there any habits we've been picking up that actually make us less effective and should be corrected? What's a good scientific or quantitative way to assess these things? How should I strike to maximize the damage I will inflict, or to achieve the best balance of damage to time, or even to inflict exactly the right amount of damage and not do more than is needed? Etc, etc. With this post, I'm starting what will likely be a long-term investigation into some of these questions. I'll begin with some physics concepts and how they do and don't apply to what we do in karate Do.
We can start with Force. A more forceful blow will, of course, result in a more effective technique, just as your intuition would suggest. But how can we quantify force? What should we do to maximize the force we exert? Newton's second law, F = m a, tells us that "force" (measured in Newtons) is the product of mass and acceleration, but we must be cautious in how we apply this equation. It is tempting to read it as "a technique which is accelerating will be more forceful than one which is traveling at constant velocity", but that isn't the case. Consider a baseball pitch. Suppose you're standing 10 meters from a competent pitcher, who hurls a baseball at you. As soon as it leaves his hand, there's nothing continuing to accelerate it forward if we neglect air resistance, then the ball would travel at constant speed until it hit you. Constant speed - zero acceleration, which would imply zero force.
But that baseball would hurt, no?
If we factor in air resistance, then the ball is actually slowing down, so it has a negative acceleration along it's direction of travel. So F = m a, in this case gives us a negative force, which makes even less sense. Newton's second law is (of course) a good model of reality (i.e. correct for most intents and purposes), but we must be careful in how we interpret it, (more on force later).
I would argue that the main quantities that you want to look at to estimate the effectiveness of a karate Do technique are momentum, energy, and power (and concepts related to those, that I'll discuss in a moment).
Energy is a difficult term to define, because it can take so many forms. Let's go with "energy is the potential to cause change". If you're well rested and fed (have lots of energy), you can shovel a whole lot of dirt (or something), thereby rearranging the world around you. If you're exhausted, most of that dirt is going to have to stay where it is, because you don't have enough energy to move it. Similarly, a bullet that's traveling very fast (has a lot of kinetic energy) is going to rearrange whatever it hits more severely than one that's casually flicked off a table. Kinetic energy is equal to half of mass times velocity squared (so faster moving techniques have more kinetic energy behind them). Kinetic energy is definitely a useful quantity, but keep in mind that in a karate technique, there's a follow-through (or "impact" ) phase, where you're still using your muscles - there's more to this kind of impact than just the kinetic energy of your hand or foot right before it hits the target.
Energy is related to another physical quantity: Work. You can think of work as being the mechanical manifestation of energy. Shoveling all that dirt, for example, is doing work. More precisely, spending energy (that you get from your food, etc) to do mechanical work (physically moving and rearranging things). Energy is measured in Joules (or kilowatt-hours, as appear on your electricity bill, which are defined in relation to Joules).
Power is the rate at which work is done/energy is spent: amount work done per second, or energy spent per second (depending on what exactly you're measuring the power of). Power is measured in Watts, where a Watt is a Joule per second.
In practical terms, an effective technique, I argue, is one that does a lot of work very quickly. So both work and power need to be as high as possible. Why is it important to do the work quickly? Well, because slowly pushing someone backwards and smashing their rib cage with a side kick could be doing the same amount of work. Mathematically, work is force times distance. W = F d. Work is pushing something some distance, but it doesn't factor in time at all. If you push on the surface of an object, that force will be transferred through intermolecular forces through the entire object, causing the whole object to move. If you knock hard on the same surface, you get a vibration (sound). There's a sharp disruption in the intermolecular positions, and that disruption propagates through the material as a vibration (i.e. a sound wave). Hitting even harder, you might permanently deform the face of the object which you struck. The same applies, roughly speaking, to an opponent's body. The same amount of work done over a longer time will tend to move th
e opponent's whole body, but if done over a short period of time, the zone of impact must absorb more of the work (there isn't time for it to be redistributed), so you are more likely to break bone and destroy tissue. This explains why kime is so important. You want short duration, highly energetic impacts for maximum damage.
Okay, so for a damaging karate technique, you want do do a lot of work very quickly.
self defense 3 - Classical Martial Arts Centre - Toronto Central RegionPractically speaking, how do we increase work? W = F d. The d is easier to deal with - one way to increase that distance is by following your techniques through - ending the punch a little ways into the target, rather than right on the surface. But what about the F? I just finished explaining why Newton's second law is a bit tricky to apply in this context, so how do we figure out F? Well, unfortunately, it's a function of how muscles work. This article will be followed up with a second part, after I've found some solid information about what the force curve for typical muscles looks like. That being said, we all know on an intuitive level what more versus less force feels like. Whatever the exactrelationship is between a muscle's exerted force and it's length, rate of expansion, and whatever else it may depend on, we all know what it means to apply more force with muscles.  
What if your goal with a particular technique is to send the opponent flying backwards, more so than damaging internal tissues? In this case, what you're trying to maximize is probably impulse. Impulse is the average force of a collision multiplied by time. So a high impulse technique is a hard push that lasts a long time, rather than a "crack"-like brief explosion of delivered energy. Impulse determines the change in momen
tum after a collision, where momentum is the product of mass and velocity. So, the higher the impulse of a collision, the higher the end velocity of the opponent will be (this being reduced by their mass of course - heavier targets are harder to move).
As a final thought, some of the concepts discussed help to partially explain why rotating your hip to punch of kick harder is so effective (when compared with just using your limb muscles). When you throw more of your body into a technique, your effective mass (for the purpose of the collision) is higher. Colliding with your opponent's body stops your movement (a deceleration occurs during the collision), and F = m a tells us that the larger this deceleration and the larger the moving mass, the greater the force of the collision. The greater the force, the greater the work done because W = F d (assuming you follow through and actually end your technique a little ways past the surface of your target - so that you're acting through a distance). A technique with more of your mass behind it will also have a higher impulse for the same reason (higher Force), and so will send the opponent reeling harder. I believe there's more going on in the hip rotation than only this, but that's a discussion for another day.
The conclusions here should line up well with your intuition from your karate training. Throw your body into your techniques, use kime (which leads to quick, intense collisions) to cause damage. We can examine specific techniques in more fine-grained detail once we've got a quantitative grip on the behaviour of human muscles.
Sheldon - Classical Martial Arts Centre - Toronto Central Region - Martial Arts classes offered in Toronto - Adults and Children - Karate-Do, Jiu Jitsu, Self-Defense, Tai Chi Chuan, Chi Gung, Ba Gwa, Iaido, Jodo, Kobudo, Ancient Weaponry, Kali.Until next time!
Mr. Snyder, (Would be Nidan), holds an Honours Bachelor of Science (physics specialist program) from the University of Toronto."