Physics for the Martial Artist

[JusticeZero]

This post was originally published as an article in a dedicated KarateForums.com Articles section, which is no longer online. After the section was closed, this article was most to the most appropriate forum in our community.

As martial artists, we strive to perfect our use of our bodies as weapons, attempting to master the techniques needed to deliver powerful, destructive blows and unbalancing, graceful throws. It is amazing, then, how so many martial artists have little understanding of the physics of force, velocity and balance which their techniques rely on. Many people fear the mathematics they see associated with it, and while mathematics are a vital life skill, the important thing is to understand what the mathematics are trying to say. As every person and every situation is a little bit different, each technique a martial artist does will have countless tiny fudge factors, so there is no point to trying to calculate each movement down to some spurious level of so-called accuracy when it is the principles that matter.

Force, Power and Energy

What is force? Force is the power to move you. Or anything else. It is the power to make things happen. Push, pull, break, whatever. And we want to make things move or break.

Force, power and energy are all concepts that are close together and only slightly different. Power is how quickly something, such as your muscles, can put useful energy, in this case kinetic energy, out along a direction (or vector) which, when it actually connects, will be measured as a force of impact.

There are two kinds of force that we care about: acceleration and peak impulse. Acceleration is how much force is applied over the entire movement, and peak impulse is the fastest and strongest instant of force over the entire movement, usually the moment the hand or foot first makes contact.

A technique that applies a lot of acceleration will move or control the target. This includes push-kicks, throws and the like; if the technique is supposed to shove a bag or a partner into the wall, it uses acceleration. This acceleration is measured by how much force is delivered, times how long the force is maintained. They will all have some prolonged contact and be designed to deliver that force and that contact over a long area of space in order to keep speeding them up as long as possible.

Techniques that use peak impulse attempt to break the target. These include punches, hard kicks and the part of a throw that is done by the floor. The intention here is to focus force over the smallest possible measure of time and/or space in order to damage the material struck.

Imagine a roll of produce bags at the grocery. If you take one and pull, you can unreel the entire roll. But by taking one and yanking at it swiftly, you can tear one bag off of the roll without disturbing the rest. This is the power of peak impulse. Matter – a plastic bag, a piece of wood, a bone or whatever else – is made up of molecules and atoms. In a solid, they all are bound together; if you try to pull it apart, it tries to pull together, and if you push it, it pushes back. You can imagine it being made of little pieces hooked together with springs or rubber, like a net. Push or pull gently on it, and the whole thing moves. But if you quickly yank on a little bit of that structure hard, the bonds next to it might come apart before the rest of it can be made to move.

Muscle, bone, wood, and everything else will have slightly different properties of how well it is bound together and how much force is needed to break it apart, but it's all matter. The "springs" connecting the molecules in a piece of glass might be short, stiff and brittle, where the "springs" in a piece of foam are long, soft and forgiving.

The problem we face is how to deliver the force we need to create the effects we want. For every action, there is a reaction; if you push something, your hand is pushed back. There is no delay here. It makes no more sense to talk about "snapping back before the force rebounds" than it does to talk about wanting to leave home before your car – which you are the owner and driver and sole passenger for – leaves without you. There is no "force moving into the target" followed by a separate "force reflected back from the target," there is just one force, one impact. Likewise, there is no connoisseur distinction between different kinds of kinetic energy; a unit of force is a unit of force is a unit of force. Because of this, a major measure of how much energy your technique can deliver is also a measure of how hard it will be to move you backward by pushing on your punch or kick.

There are several strategies of how to push back against your technique to make these work. You can use raw inertia, of course; just the fact that your body has mass can be used to resist the force of your technique. However, many techniques also take advantage of movement, gravity or structure.

It takes force and time to accelerate any mass, like yourself. You could just push something away from your center of mass. Effective techniques, though, involve more forces than just that. Either the amount of power needed to push you away from the target needs to be increased or the property of the impact – usually the speed, or the surface area through which the force is transmitted – needs to be changed so that you can focus more force into the target where you want it to go.

Concentration Over Space

A knife is an extreme example of focusing an impact in terms of space. The actual force applied by the blade is low. However, that force is applied to a very small amount of matter. Say you are cutting into a turkey. The knife is pressed against the meat and might only have a small amount of pressure, but each of the molecules directly under the blade is being pushed with a large share of this force. The blade slices, pulling each of the molecules of turkey under the blade and ripping them away from their neighbors; as they do, a gap is made into which the pressure behind the knife guides the blade. At the bottom of each gap, the blade lands upon more molecules of turkey, and the process continues until a sheet of cooked bird has been cut away.

Or you might stab with the knife, focusing that energy onto a vastly tinier point. The structure of that one tiny piece of turkey into which the knife was jabbed has no hope of stopping a tiny number of blade molecules from crashing through them and severing the binds between the molecules of meat. The force behind the knife didn't need to be great, and the knife didn't need any great speed. The solidity of the knife point and the huge concentration of force did the work.

In many arts, the structure of the fist is examined; the knuckle is used in hopes of concentrating the speed and power of the punch over the surface area of two or possibly three of the joints of the hand. This, of course, means that the structure of the hand must be strengthened through training and structure so that those joints, and the bones and fingers surrounding them, can withstand the force of the impact.

Kicks, too, can concentrate force in space. The shin, ball of the foot and heel all provide relatively small surface areas backed by rigid bony structure; shoes add heels and possibly toes. Elbows and knees serve a similar function. The palm, too, can concentrate force at the heel of the palm.

Additionally, force can be concentrated in the body of the target. If a limb is forcefully moved beyond its normal range of motion, this can cause the joint to be hyperextended and damaged.

Concentration in Time

A movement can focus an acceleration over a short period of time, resulting in a higher peak impulse force. One example of this can be found in the hammer. A carpentry hammer is lifted, then allowed to fall with a small assist from the muscles of the carpenter. It accelerates for a distance, then makes contact with the nail. The hammerhead is flat, has no give and covers the surface of the nail all at the same moment, accelerating the nail with a sharp peak impulse of power to drive it into the wood.

Meanwhile, a martial artist turns their body around, twisting and unloading by whipping their foot through the air in a long circle to blast a small pad out of the hands of their training partner.

The key here is speed, and a focused, singular impact.

To achieve this speed, you need room to accelerate, and ways of focusing that speed. Spinning techniques are one way of achieving this; if you spin your body around a central point – over your base foot, maybe – and extend your foot, the foot covers a long distance very quickly. If you throw a 360 spin kick in a complete circle, through the magic of grade school mathematics your shoe will travel a little more than six times the length of your leg in that short period of time.

If your foot was in the air for half a second, and your leg is three feet/a meter long, that means that your foot averaged more than thirty six feet (or twelve meters) each second, or about twenty-eight miles an hour. That's an average, and it was stopped at the ends, so in the middle, where your target is, it is probably closer to fifty. A leg at that speed has a lot of momentum, and being hit with it will put a large peak impulse into the target at the point of impact.

More linear styles will concentrate on packing a lot of acceleration into a short distance, using gravity, leg strength and the like to get as much mass moving into the target as fast as possible. The principles are still the same.

Gravity

On Earth, everything is trying to move downward, speeding up at just under 22 miles per hour (MPH) each second (9.8 m/s/s). Everything – people, flowerpots, birds, water or whatever – has to stop itself from accelerating downward by pushing against something under it.

People usually use legs for this, which also let us move around by letting us fall in the direction we want to go then catch ourselves, over and over again. We do this with a practiced shift of our weight and lifting of one foot from the ground, stretching out with our heavy legs and unbalancing ourselves further from our center of gravity to plant our other foot on the ground where we plan to fall. Through lots of practice, this feels stable to us.

But if we are prevented from putting a foot under oneself, if we are guided out to a position where our center of gravity is far from our only support, we are suddenly subject to this acceleration. Those who do not have techniques of how to fall will accelerate at this 22 mph/second until they meet the hard ground and experience a sharp peak impulse of deceleration as the ground suddenly pushes them away. Others know how to fall, using techniques to distribute this impact over time and distance to resisting the ground over a period of time and changing the velocity of the fall into lateral movement.

Some techniques use this acceleration in other ways. If you step into a technique, you are using gravity to move yourself and help power a technique. If a kick has you drop your torso away from the target, it might be using that fall to rotate your hips and legs upward into the target. If our technique brings our striking limb above the target, then drops back down into it, our striking limb is being accelerated by gravity.

Structure

Another way of resisting the power of our own techniques is by bracing oneself against something, such as the ground. If a style uses a "deep" stance, then punches upward along the line of the stance, then they have braced the force with their leg. The striker is no longer limited by their own mass and inertia in terms of how much power they can in theory direct into the target, though they may still be limited by the practicality and speed of the techniques, and maybe by the traction their shoes can generate against the ground.

Each joint must be aligned and used for this to work most effectively; anything not in line with the force being applied might end up being turned aside by the power of the technique.

Targets and What That Means

People are not Muppets, made from a block of sponge rubber. People have bones, blood and internal organs inside them, a wide variety of different materials and material properties. Force is not "projected into the target," nor is it delayed or anything else. A vector of force is a vector of force, of course, and no more. But just as how our body structure matters for our ability to apply this force, so too does the body structure of our target change what our techniques do.

Bones are rigid; they can be broken, but even if they are not, their rigidity means that a technique which strikes a bone might cause parts of the body behind the bone to be struck by the now-moving bone, even targets not directly in line with the original technique. Blood vessels full of liquid are concentrated near the surface of the skin, and an impact with a large surface area and high peak impulse, despite not being concentrated enough to break bones, might still cause this non-compressible fluid to force itself against blood vessels and create large bruises or otherwise affect muscle and nerve tissue. Different points of impact and different properties of the impact can have very different effects, and many of our techniques take that into account.

People are not point masses. Techniques cannot be meaningfully compared by any single raw measurement of kinetic energy. Nor, however, can they be relegated to the realm of the mysterious and inexplicable. It is important to understand how our techniques work and what factors might make them work better, without being tempted to measure them with some oversimplified tool or "scientific" measurement or retreating into vagueness. The universe is no longer mysterious, and the principles underlying everything we do are readily available for anyone to understand and use.

It is no more acceptable to retreat into mysticism or to trust in pseudo-scientific gadgetry to understand how our basic techniques work than it is to sell quackery or pseudo-scientific fads to our students when they search for advice on diet and strength training. We should no more accept mystical explanations of force transfer than we should accept an old-style training regimen involving painful and injurious "partner bounce stretches" which we now know to be counterproductive at best. It is our duty to understand these basic principles of physics and to analyze our techniques in terms of the understandings we have of the real workings of the world.

[Patrick]

Thank you for the submission, Justice.

Patrick

[CredoTe]

Now there's a bit of scientific explanation of martial arts! Great article!

As an engineer, I like being able to put any technique I'm shown to the test against physics/scientific fact. If a technique doesn't make common sense (fighting sense) or physics/scientific sense, how can it possibly be used to defend oneself? Because some "sensei" says it's based upon some "ancient mystical energy or technique"? Puh-leeeeze...

Karate/Tode is based upon Tii; Tii was invented by educated people who had the best grasp of physics and the human physique/anatomy in the Okinawan culture for their time. While there was some spirituality put into their art (meditation, etc), the actual Tii techniques were based purely on their best understanding of physics/scientific fact (and how the human physique relates to it) at the time.

In fact, Tii had no kata, and thus no "mysterious techniques" or ambiguities, until after the need to preserve the art secretly. Even then, the only "kata" that existed in Tii were in Okinawan folk dances that contained the movements and techniques of their art (which needed a skilled, trusting instructor to decipher for the student).

[DWx]

Wow this is a really great article Justice.

Certainly in my experience, people get bogged down by almost pseudo-physics - they take snippets of things like F = MA and misunderstand and misapply it.

[sensei8]

Now, that's a solid piece of writing!! Concise, and well researched!! It was everything that an article should have when approached as with the MA in mind.

SOLID!!