Mass vs weight.

Relaxation, kinetic chaining and weight drop; the combination and interaction of these three mechanics creates the sine wave motion.

The emphasis on weight drop is probably the most obvious divergence from early karate-style Taekwon-Do, and used properly it is an effective way to develop 'easy' power, i.e. significant gains in impact with minimal exertion.

However, some of the traditional techniques gain nothing and some even lose power when performed with the sine wave motion.

That these moves are, and continue to be, performed with sine wave illustrates a lack of understanding of the physics involved in weight drop, and that for the most part these errors reduce to a conflation between mass and weight, or more accurately; between mass and apparent weight.

The Difference between mass and weight:

Mass is a measure of inertia, and inertia is the tendency of an object to resist any change in its motion. So; mass is a measure of an object's resistance to any change in its motion: the more massive a body, the greater the force required to alter its motion.

This resistance to change is independent of  direction or circumstance, a brick with a mass of 1 kilogram will have the same resistance to change whether it is sitting on the bottom of the ocean or drifting through interstellar space. The water pressure, friction and gravity acting on the deep sea brick are additional external factors, and do not influence the mass of the brick.

Weight is the force exerted on a body by gravity. For any object on the Earth's surface, it's weight is a downwards pull towards the earth's' centre of mass.

So; mass is an intrinsic quality of an object and operates equally in all directions, whereas weight is an external force acting on an object, and in only one direction.

Because weight is a force acting on a body, and not a quality of that body, it is not easily distinguishable from any other forces acting on that body. For example if I hand  you a brick, you can't accurately gauge the weight of the brick until I let go - I could be pressing it into your hand making it appear heavier than it is.

A more relevant example; if you stand on a scales and suddenly bend your knees a few degrees, the scales will register a weight fluctuation. The gravitational force on your body, your weight, did not change, but your apparent weight did.
Initially your body (from the knees up) went into free fall and was not exerting any force on the scales, so the scales registered lighter, but then you caught yourself and stopped your decent, and the scales registered heavier - even heavier than your true weight, before finally coming back to indicate your true weight.

Essentially you fooled the scales with a combination of your weight and a change in motion of your mass. Gravity accelerated your body downwards, and from the definition of mass we know that to stop a moving body requires a force. The combination of these two forces (your actual weight + the stopping force) registered as an increase in weight on the scales. When the movement of your body was brought to a halt, the additional force ceased and the scales again registered only your actual (true) weight.

The force you exert on the ground is your apparent weight, as we can see from the example above sometimes your apparent weight is the same as your actual weight, sometimes it is greater, sometimes less.

For practical purposes there is no functional difference between actual weight and apparent weight, and for this post it is enough to know that weight can be changed whereas mass cannot.

• Two bricks rest on a table, one brick has a mass of 1kg, the other has a mass of 2kg.
  In order to move the bricks a force must be applied to each, but the 2 kg brick will require a greater force be applied in order to move it the same distance as the 1kg brick.

• A single 1kg brick rests on the table, another 1kg brick is falling from a height. The falling brick has a dramatically increased apparent weight¹ due to a combination of actual gravitational weight and downward momentum.
  However, the force required to move either brick horizontally is exactly the same, as weight is irrelevant in the horizontal plane and mass, which is relevant, remains unchanged.

To translate this into martial relevance:
The simple act of dropping my mass can make me weigh as much as a larger person, but will not automatically grant his resistance to change in horizontal motion. Keep in mind that 'his resistance to change' is a measure of both how hard it is to move him, and how hard it is to stop him moving.

There are several examples in the Taekwon-Do tul that indicate a lack of understanding of this limitation of weight dropping. The most obvious is a front punch in the sitting stance, the most damning is the front punch in a parallel stance.
To understand just why this technique (punching from the parallel stance) is so especially flawed it is necessary to go back and examine how and when the weight drop does work


Weight drop works when the downwards momentum can be redirected. I built a machine to demonstrate a this redirection:

The downwards motion of the anvil is deflected by the rear leg. This leg is inflexible along its length, so it will not compress, but its is hinged close to its base allowing it to swing in an arc. The weight of the anvil forces the leg to move through its arc, and the leg forces the anvil to move horizontally. Because the arcing motion happens, by definition,  in both the horizontal and vertical planes, the two cannot be separated, so a greater downwards force will result in a greater horizontal force.

The angle of the rear leg is an important factor in this interaction. If the leg is standing at 90° to its base (i.e. completely vertical) then any any downwards force will act directly down its length and will cause no arcing motion. As the leg is positioned further from the vertical, the applied weight causes more arcing and in turn the arcing causes more horizontal motion.
At the other extreme, as the rear leg approaches a position parallel to the base (flat on the ground), the weight applied will have a great effect on the arcing motion, but that arcing motion will translate into very little horizontal motion as the arc also approaches it's limit in that direction.
The optimal leg-angle for translating downwards momentum to horizontal momentum is about 45°, halfway between the two ineffective extremes² .

So; in order to utilise weight drop in any direction other than downwards, a separate redirecting force is necessary, and the angle of this force is directly responsible for the effectiveness of the redirection.

It is worth noting at this point that this mechanic is just as important when not utilising sine wave or any other weight drop; to effectively put  your weight into any technique, or use your weight to brace or root your technique, you must have a foot on the ground behind your centre of mass.

In the case of the parallel stance front punch there is no redirecting force, as neither foot is placed behind the centre of mass with respect to the target. Worse still, because the sine wave in this position is generated by lifting the heels off the floor, as opposed to the usual knee spring, the body weight moves from the ball of the foot, at the height of the wave, to the middle of the foot as the technique finishes.
This means that the centre of gravity is moving away from the target during impact:

So not only does weight drop add nothing to this technique due to the lack of a redirecting force, but the action of rising and dropping from the ankles creates a counter-productive backwards motion, slowing the striking hand and removing body mass from the strike.

There are other movements within the tul that are not executed with sine wave, I would like to see the parallel stance punch added to their number. In fact, we could probably do away with the "ankle wave" in general, as it fails to add anything useful while doing a fine job of destroying the practioners balance.




Footnotes

¹ Technically the increase in apparent weight does not occur until the brick contacts the table, but that makes no difference here.

²  Under constant angular speed this would definitely be 45°, but in this case where gravity is accelerating the arc I imagine the optimal angle gets more acute, but not by much.

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.

• A similar paragraph appeared in a post on Dan Djurdjevic's karate/internal arts blog, but has since been amended. I rescued this line which was quoted in the comments section:

So, the longer your fist is in contact with the target, the less force it applies.

• JKD author Terri Tom makes this claim in her book The Straight Lead:

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.