THE PHYSICS OF STRIKING

When you strike an object or person (either by punching or kicking) what exactly are the factors controlling how much force that strike will have? The physics of this process are well understood and agree perfectly with the techniques used and recommended by martial art instructors in Tae Kwon-Do and Karate. The basic technique is :

1) With the least possible muscle tension, accelerate the striking surface towards the target as quickly as possible.

2) Just before impact, tense all the muscles concerned with the body framework so that as the impact happens the body is as rigid as possible.

How does this technique result in enough destructive force for a trained person to break pieces of ice the size of breeze blocks? What is the difficult part of this technique that prevents even the strongest novice from performing the same feats? Part of the answer to these questions lie in areas such as physical strength in the right muscles, confidence and the ability to use these attributes efficiently due to superior concentration and will. Questions on these aspects can only really be answered by an experienced martial artist and those answers will probably involve at least four years of hard training! The rest of the technique is down to physics and muscle control.

Newton's Second Law: The rate of change of a body's velocity is proportional to the net force acting on it and takes place in the direction of that force.

Force = Mass x Acceleration (Mass is the constant of proportionality)

Newton's Third Law : Forces acting between bodies in contact are equal and opposite.

(Newton's first law is really only a special case of his second law)

With integration we can rewrite Newton 1 as :‑ F x dt = M x dv where :

F is the average force applied during the time interval

dt is the time interval

M is the mass

dv is the difference in velocity before and after the time interval

When the fist (of mass M) collides with a target that cannot move away quickly (either because it is very heavy like a person or because people are supporting it with their bodies), that object must decelerate the fist from whatever velocity it had before it came into contact with the target (say V) to rest in a very short time (dt). To do this it must provide a force (F) which is equal to (M x V) / dt . If the target cannot provide this force, the fist will continue on until F x dt finally adds up to M x V some time later. In the case of wooden boards this 'continuing on' simply bends them. If they have to bend too far however, the back surface (which is then under tension) will split and the board will break. In the case of person's body, this 'continuing on' will probably cause internal damage as organs are forced to move out of the path of the fist. If the target was a 40 ton block of steel however, it would have no problem providing the necessary stopping force instantly and by Newton 3 that force would have only the contact points on the fist to act on. This would probably result in damage to the fist.

The three factors resulting in possibly damaging force being demanded from the target are therefore:

1) Mass of the attacking object.

2) Velocity (speed) of the attacking object on impact.

3) The amount of time the object takes to stop the attacking object from continuing. In most cases this can be measured as a distance before damage occurs.

The basic technique of striking in terms of these factors will be explained using the example of a forward punch.

At the moment of impact we want maximum mass and speed. To achieve the speed, we accelerate the fist from rest towards the target by applying a force F with the muscles. Newton 2 tells us that F = M x A so A = F / M. In other words, for a set force F (which we can only improve by getting stronger) we will get a larger acceleration (and thus impact speed) if the mass M is low. On impact though, as we have stated, we want the maximum possible mass for the target to have to decelerate. How can the mass of the striking object be changed from small (while the body accelerates it) to large (while the target decelerates it)?

If the fist, forearm, shoulder etc. were made from a solid material such as metal and welded together, the mass of the striking object would simply be the masses of each of these parts added together. If however, these parts of the body were only connected by string or wires, the mass of the striking object would be that of the fist alone. In reality, the body is connected by bones, joints and muscles which is a situation between the two extremes. When the muscles are tensed, the body acts more like one solid object. When the muscles are relaxed, the body acts more like separate parts. What happens in a correct punch is this :

1) The body is kept as relaxed and 'disconnected' as possible to keep the effective mass of the fist down while it is accelerated towards the target.

2) 'Just before impact' the whole frame is tensed to get as close as possible to the 'one solid unit' state with maximum effective mass and hopefully the same velocity of the striking surface.

If the tension is applied to early, the effective mass of the fist rises early which reduces the acceleration and, thus, final speed on impact. If the tension arrives too late, the effective mass of the fist is low and it will have less effect. To achieve the most efficient timing, strength, tension and posture to exploit this technique (which only lasts a fraction of a second) is not something that is learnt easily. Without the evidence of destruction demonstrations, the fact that it could be learnt at all would, I think, be in doubt.

Some other strikes used in martial arts exploit the two other factors - speed and impact time - more than the 'strongest' attacks such as the side kick and forward punch which rely on the above technique very strongly. Extra speed on impact can be achieved in some cases by extending the limbs in rotation much like a sling-shot or golf swing. Other strikes exploit the very short time of impact caused by hitting with a part of the body which is very rigid such as the elbow or head.