Saturday, June 29, 2013

The contact time fallacy

In martial arts, as in most endeavours, if you don't understand what it is you are trying to do then your chances of doing it correctly diminish.

Our understanding of how the physical world works is profound, classical physics is unlikely to be overhauled at any point; physical interactions on the human level are completely covered by the Newtonian model. It is probably fair to say that most people have some understanding of the laws of motion and conservation of energy, even those that couldn't articulate it as such.
Scientific understanding has become not just commonplace, but the lingua franca of describing the functioning of the world around us.
For example: I would be surprised if anybody, on finding a window in their house broken, would find it easy to accept the explanation that 'it just broke' or that it broke because the house is cursed. A bird collision, a stone kicked up by a passing car, a sudden temperature variation, these are things we can accept, because they involve physical forces.

It is with this mindset then that modern practitioners attempt to understand their traditional martial arts.
The billiard-ball type physics needed are not particularly difficult to understand, but applying them can be tricky. The apparent simplicity of both the laws of motion and of the equations for force and momentum can lead to a lack of logical rigour, and this carelessness can in turn lead to conclusions that would not stand if they were not couched in scientific jargon; we can sometimes blind ourselves with science.

About five years ago an article appeared in Irish Fighter magazine where a kung-fu instructor explained how the retraction of a punch added to the impact.
His logic ran like this:

The power of a strike is measured by its momentum.
Momentum= Mass x Velocity.
The strike travels towards the target with speed V1 and retracts with speed V2
Velocity at turning point (full extension before retraction) = V1 + V2
Momentum = Mass x (V1+V2)


This is a disaster.
The velocity of the strike at the turning point is zero; in order to go backwards we must stop going forwards, we can't do both at once. So the momentum at full extension is zero.
Worse still, according to this logic the speed of a body after impact, V2, contributes to that impact.
If this was true you could smash your prized glass coffee table by lifting up your cup quickly. The target of a strike would need to wait and find out just how fast the weapon is going to retract be before it knows how hard it has been hit!

This may be a garbled mess,  but it is far from unique. In fact it is closely related to a much more common martial-physics fallacy; the fallacy of contact time.

This fallacy generally takes the form: Impact is a force delivered onto a target in a short time, as opposed to a push which delivers a force over a longer time. Therefore, if we decrease the time element of the impact by withdrawing the attacking tool we effectively increase the impact.

Some examples form the martial arts fraternity;

  • From Marc McYoungs excellent nononsenseselfdefense.com:
Another reason that you need to withdraw (your fist) is the retraction lessens the duration of the impact, which means that the power is delivered all at once. This instead of over a protracted period of time --  as happens with a push.
So, the longer your fist is in contact with the target, the less force it applies.
By changing the direction of your hand, you actually increase the impulse, thereby increasing the force required to change direction. Think about it, Stopping your fist requires a certain impulse. Changing direction after stopping your fist actually requires additional impulse. And if the time of contact, or time during which you apply force, is kept to a minimum, the force at impact will be even greater.
This last example is interesting because it ties two major mistakes together and illustrates their common root. The fallacy of contact time appears in its familiar form in the last line "And if the time of contact...is kept to a minimum, the force at impact will be even greater", and I'll get back to why this is a fallacy in a moment.

Previous to this is the line: "Changing direction after stopping your fist actually requires additional impulse", does this concept seem familiar?
It should, Ms Tom is arguing here that the speed (as mass is constant) of the retraction of a strike adds to the impact, the same idea presented by the kung-fu instructor at the beginning of this post.
Ms Tom put more work into understanding the physics, the fault in her reasoning is harder to spot and is maybe more forgiveable, but it is equally wrong.

Changing direction after stopping your fist actually requires additional impulse.
If I punch you in the face, and you simultaneously slam your face into my fist and push it backwards, then yes, the additional impulse provided by the forward motion of your face will increase the force of impact.

But if you don't move towards me and I pull my own hand back, using the muscles in my arm, then where is this supposed additional force of impact coming from? As I previously noted, a strike must stop going forward in order to go back. Yes, there is a change in momentum involved in retracting the hand, but it starts from zero (remember that  momentum is zero at full extension) and travels back towards me.
Contrary to popular myth, my arms don't actually explode/implode in all directions at once. Arms either extend or retract, not both simultaneously.

And this is where the root lies; who is doing the work? in what direction? and when?
Two bodies moving towards each other can cause a collision, two bodies moving away from each other cannot cause a collision.
  1. During impact if both bodies are moving towards each other, the force of impact will be increased.
  2. During impact if either body is moving away from the other the force of impact will be decreased.
  3. Anything that happens after impact is irrelevant to the force of the impact, simply because it happens after impact, effect follows cause not the other way around.

So back to the fallacy of contact time.

If I pull my arm back during impact, before its forward motion is fully arrested by the collision, and thereby shorten the time in contact,  then point 2 applies; I am lessening the force of impact. This is called pulling a punch.

If I pull my arm back after the collision is resolved, then point 3 applies; The retraction has no effect on impact at all.

If I don't pull my arm back, and leave my fist in contact with the target for another ten minutes, point 3 still applies; the impact is unaffected.

This is why the measure of contact time tells us exactly nothing about the impact that occurred during that time, and why withdrawing the tool in order to increase impact is misguided at best and counter-productive at worst.

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