Physics for martial arts

Yes, Physics is in the martial arts and you'd better get used to that idea. The hallmark of Western civilization is Science. So what's that? Science is a methodology for investigation, involving hypothesis (how's it really work?), open discussion (peer review), and reproducible tests. Commonly the knowledge that arises from Science is casually called Science, but really that is not the case. This has gone so far the now folks talk about the scientific method. well we do try to be indulgent of the unwashed masses. In any case, one big feature is reproducibility in a reliable way. After all, if you walk into a room, flick the light switch and nothing happens do you check the bulb and fusebox, or do you mutter that electromagnetism is just another theory?

The amount of Physics you need to understand what happens in martial arts is pretty low, but you won't be able to do techniques as reliably without knowing a bit. This page has the sorts of concepts I find I refer to all the time in martial arts classes. This is driven not by some effort to catalog everything, but what I find I need in my specific martial arts system, hakko denshin ryu aiki jujutsu.

Some people maintain that mysterious powers are the cause of their abilities. Usually this just means they can't explain what happens. Of course, being in communion with higher powers is in any case irrelevant: I've had no success at using some great supernatural force, no matter how much a few enthusiasts have coached me. So even if such a thing were real, it does not apply to me and I have to fall back on other ways to reliably reproduce the effects I am after.



In standard Newtonian Physics (you don't need anything else unless you are moving close to the speed of light and if you can do that, why are you studying a martial art?), force is defined as

F = ma

alias force = (mass) x (acceleration). You may get more force by increasing either mass or acceleration.

Here is a thought on the difference between so-called external systems (like karate) and internal systems like jujutsu. External systems tend to try and maximize the acceleration to generate force. Internal systems tend to emphasis root and connection to the floor, in effect allowing you to increase you mass -- your largest effective mass is how much force your legs can exert against the floor. This is not to say that both types don't attempt to juggle the other half of the product. Low stances in karate can help effectively increase mass and "shaking" (aka fa jing in Chinese or hakkei in Japanese) are really aimed at letting you accelerate without losing your root.


This is the measure of a force's tendency to produce rotation about a fixed point. This is found by multiplying the distance from the point by the force acting at 90 degrees to it. Generally, human bodies are designed for compression but not torque, so there are a lot of torquing motions.


This consists of two equal forces that are working parallel and in opposite directions on an object to induce a rotation. Turning a faucet or winding a clock are all examples of couples. Reaping throws fall into this category. This is applied in many different ways and is embodied in the concept of opposing forces or shearing as it is sometimes called.

Simple Machines

A simple machine allows a small force to overcome a larger force. They are referred to as simple, since they require only a single force. There are just a few basic simple machines and we use them and their variations all the time. We start with

The Lever

The load (L) is the object to be moved. The fulcrum (O) is the point of rotation and we denote by F the force applied to move the load. There are three classes of levers which are:

First class. The fulcrum lies between the load and the point of application. It looks like this: L----O-----F A standard textbook example is the see-saw. When you nod your head, this is a first class lever where the head is the load, the neck muscles supply the effort and the vertebrae are the fulcrum. First class lever change the size and direction of the force. If you have the fulcrum in the right place, you can lift a car by pushing down with one hand. Hip throws are this type of lever with the load as the lower body and the fulcrum is the thrower's hip. Here we see why using body weight to initiate the throw is such a grand idea: With the upper part of the receiver toppling, this effectively uses him to increase the force on his lower body. Since generally peoples upper body are heavier than their lower bodies, there is invariably enough force to throw the person. This accounts for their great power.

Second class. The load lies between the force and the fulcrum:O----L----F A bottle opener or wheelbarrow are the standard examples. On you, whenever you stand on tiptoe you are using a second class lever, where the balls of your feet are the fulcrum, you are the load and the calf muscles supply the force. Second class levers multiply the force, but do not change its direction. Throws of this sort are shiho nage, irimi nage, as well as throws where the lower body is blocked, such as with a foot pin. Most hip throws incorporate this type of levering action initially to get the opponent off-balance, then switch to another levering action.

Third class. The force is applied between the load and the fulcrum: O----F----L Tweezers are a standard example, as is swinging a baseball bat -- or a samurai sword. On you, your forearm works this way, where the load is the forearm, the fulcrum is the elbow and the force is generated by the biceps. Third class levers multiply motion but reduce the power. So while it takes a relatively large force, the load moves much further. Armbars and ankle bites are examples of this, as are most takedowns like kibusu gaeshi, in which the leg is fixed at the lower end and force is applied to the knee or hip to effect the throw -- this is because these throws are variations on armbar-type locking.

The Wheel

This is a continuous lever rotating in a circle about an axis. Force may be applied to the outside of the wheel to turn the axle (think steering wheel), making it a first class lever or the axle may turn to move a load on the rim, like car tires, making a third class lever.

Actually most joint locks in our system are wheels. In this case, the axis of rotation is the through the joint at the base of the thumb. The traditional way of explaining this is the talk about the power of the pinkie, since the pinkie follows the rim of this wheel. Consider our basic wrist escape, hakko dori. What happens at the Physics level is that the attacker is suddenly trying to hold onto the rim of a powerful wheel. This is not possible (have you ever tried to grab a spinning wheel?) A lot of the wrist manipulations in the system are devastatingly clever ways of exploiting the wheel (don't forget there are three dimensions and switching of directions judiciously has to be done.)

The Inclined Plane

This allows for lifting or lowering an object without having to move it vertically. Walking up a hill with switchbacks is using an inclined plane, vs. climbing straight up. Lifting like this does not often present itself in martial arts, but two variations of this are very useful indeed.

The Screw

This allows for a rotatry motion to be converted into a linear motion, such as forward or backwards. A screw is a continuous inclined plane. This is seen in many motions that involve the concept of maki komi. or wrapping. Another frequent way is when moving into the twisted stance, kosa dachi, in which the dropping, turning motion means you are the screw and the action on your grappled opponent is to pull him powerfully off-balance. Other screwing actions can occur in joint locks, like te kagami, in which the entire upper body will be moved by using uke's whole arm as the screw.

The Wedge

This allows a force to split. It is a moving inclined plane. A martial example is a simple parry or using hakko zeme as a counter to a punch. Most techinques where you displace some part of uke are wedges.

Other useful topics


The momentum of an object is defined as the product of its mass and speed. One fundamental fact is the conservation of momentum. This means that if two objects combine, their total momentum stays the same. Now, one caution is that this works as long as the enery in the system is not dissapated in some other form. For instance, in a car accident the energy might be used up deforming (crushing) one vehicle and the net momentum will be low. Billiard balls are not elastic so they tend to conserve momentum nicely. A practical issue for the martial artist is that when making contact with your opponent, you might lose a lot of momentum if your structure is not set right. This means that the force you are generating is dissipated into deforming your structure, rather than moving him.

For martial arts, we speak of getting the attacker caught in your momentum flow, that is to say, as you move, you transfer momentum to your attacker, moving him with you.


This occurs when force acts on an object and is defined as

momentum x time

Think of it this way. The when two objects are in contact, the longer they touch the more energy is transmitted from one to the other.


This is defined as


and you may therefore increase the pressure for a given force by reducing the area. karateka practice mightily to reduce the striking area so as to try and maximize the damage. Grapplers try to maximize the surface area so that the pressure can be had with less force.

Impulsive force

This is Pressure x time This is useful for most techniques actually, since you must be aware of the area of contact in order to transfer momentum to the attacker. This may be increased by maximizing the area and increasing the time. This explains why we emphasize moving a bit slower and sticking at all times.