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.

On the other hand...

In Taekwon-Do, the use of the reaction hand is almost universal. It is used as a counterweight during the execution of most strikes and blocks. And it based on one of the simplest and most universal physical laws we have; Newtons third law of motion:

When a body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.

In the case of the reaction hand, the relevant interaction is between the reaction hand/arm (body A), and the centre of mass (body B), which is located at the centre of the body, slightly below the navel.

From the third law we see that:

1. When the hand is pushed outwards from the centre of mass, the centre of mass is also pushed away from the hand.¹
2. When the hand is pulled towards the centre of mass, the centre of mass is also pulled towards the hand.
3. When the hand accelerates laterally with respect to the centre of mass, the centre of mass gains momentum in the opposite direction. This is also true at any instant where the hand is orbiting the centre of mass.

The Encyclopaedia of Taekwon-Do:

"Another reaction force is your own. A punch with the right fist is aided by pulling back the left fist to the hip."

This seems pretty straight-forward, between the three applications of the third law I have stated here, and the reaction force quote form the encyclopaedia, it should be easy to understand the use of the reaction hand.

But a little research shows that this is widely misunderstood, and often written off as trivial.
The reason for this is simple; if you don't begin by understanding the laws of motion you wont know when you are violating them. The vast majority of us start form the above quote where the punch is 'aided', or similar instruction from a teacher, which, despite being correct, tells us exactly nothing about how the left fist aids the right punch.
And on that vague foundation we make assumptions, and those assumptions may, and do, lead to misunderstandings.

The following are each examples of either misunderstanding, misapplication, or both:

1.

From C'hang Hon Taekwon-Do Hae Sul by Mr. Stuart Anslow:

"However, when there is an actual opponent, the equal and opposite reaction takes place within the opponent themselves, so where as in training, the reaction hand has a purpose, in combat this purpose is voided..."

Mr. Anslow's understanding appears to be that the purpose of the reaction hand is to stop or slow the technique, just as hitting a target would stop or slow the technique.

This is one of the errors that contribute to the contact-time fallacy; the idea that  stopping a punch yourself (pulling a punch) is the same thing as having it stopped for you (hitting a target).

Mr.Anslow is wrong here, but his mistake is probably based on an explanation given by General Choi himself in his encyclopaedia, which also incorrectly reverses the role played by the reaction hand.

The encyclopaedia is not the only book that has the physics right on one page and backwards on another, and before I look at Choi's mistake I'll take a look at a very similar situation in a much more recent publication.

 2.

This time its First Grandmaster Rhee's 'This Is Taekwon-Do Vol.1' in the firing line.

In fact, This is Taekwon-Do Vol.1 has an excellent introductory section on the reaction force, and has a couple of examples that very clearly demonstrate how it works.
However, it also has a classic mistake in the very first example given, the example of the front punch;

Reaction force diagram from This Is Taekwon-Do by Grandmaster Rhee.Ki Ha

"One arm pulls whilst the other pushes around the pivoting points which are the spine and hips, you are using opposing sides of your body to generate power. If you simply punched without the reaction hand moving, you would only be using power from one side of your body."

This explanation, with the help of the top-down diagram, states that the action arm and reaction arm work together to rotate the body, and this rotation increases the power of the punch.

But this is clearly pulling yourself up by the bootstraps; the action of the arms rotates the body, the body rotation aids the action of the arms, which rotates the body, which aids the arms..... it's an infinite loop.

If we look at this model with the third law of motion in mind we can see that the action arm and reaction arm both work together to turn the body in the opposite direction:

• As the punch goes forward it pushes the action side of the body backward.
• As the reaction hand is pulled backwards it pulls the reaction side of the body forward.  

This would rob the punch of power, instead of aiding it.

This is not a trivial point. I think it is exactly this broken model, specifically treating the front punch as something that develops its power through rotation about a central axis, that has led many martial artists from Taekwon-Do and Karate to abandon the use or understanding of reaction force.

This is the first learned and most obvious use of the reaction hand, and if it is doing exactly the opposite of what it is supposed to be doing, then it is no surprise that it never really feels right to the practitioner.

A better model tells a different story.
The action performed when executing a front punch is more akin to a closing door, with the reaction hip remaining largely stationary as the opposite 'action' hip comes forward.
The centre of mass lies between these two points and so travels forward with the action hip. This is how we get body mass into the strike, not by rotating around the centre of mass, but by moving the centre of mass in the direction of the strike.

The purpose of the reaction arm is to pull the body forward, even as the punching arm attempts to push it back. This is the counterbalance; the striking arm robs us of forward momentum, the reaction hand adds forward momentum.

This application of reaction force is so deeply embedded in Taekwon-Do that nearly every formal technique has been designed around it.
The trajectory of the reaction hand usually attempts to mirror the trajectory of the action hand,  so in Won Hyo, for example, we see the reaction hand pulled across the chest to the opposite shoulder rather than to the hip for inward knife-hand strike in the L-stance.

In the encyclopaedia Choi adds an additional reason to bring the hand to the opposite shoulder instead of the hip:

3.

From The Encyclopaedia of Taekwondo:

"Incorrect: The attacking tool is over extended, passing the point of focus, because the other fist is pulled to the hip instead of the shoulder."

It would be easy to interpret this to mean that the purpose of the reaction hand, when pulled to the shoulder, is to stop the strike at the point of focus, and this is probably where Mr. Anslow picked up the idea.
But that's not a valid interpretation, simply because that is not the purpose of the reaction hand. Instead, Choi is giving an additional reason why the to-the-hip reaction is less suitable for this strike.

The claim Choi is making here is that pulling the fist to the hip will cause that hip to move backwards, resulting in an unwanted rotation of the torso.
Unfortunately this is the same faulty physics found in the earlier front punch example. No amount of reaction force will push that hip back, because the reaction force is operating in the opposite direction; it is pulling the hip forward.

In fact, pulling to the hip works well here, but pulling to the shoulder works better as it more closely mirrors the lateral trajectory of the strike at the moment of impact.

Hiki-te.

Using the reaction hand as a counterweight, as something to pull against, ties in perfectly with a concept borrowed from Karate; hiki-te, the pulling hand.

In many, though not all, techniques the reaction hand can be used to grab and pull the opponent into a strike. The mechanic is the same as the standard reaction hand, but now the opponent provides much better anchorage for pulling into the strike, while the pulling action also unbalances and/or positions the opponent.

I won't argue that using the non-striking hand is always best utilised as a counterweight, pushing, pulling, holding and guarding are all options, though a good guard is not near as important in self defence as it is in combat sport. But that's a point for another post.

My favourite example of  reaction force use is Lee Morrison in action. Partially because he does it so well, but also because Lee really does not like traditional martial arts (making him an impartial judge of traditional technique, if not a downright hostile one) and is interested only in what works for him.

Take a look here, specifically watching the reaction hand and how he pulls it both to the side (not to the hip, but that's a matter of degree) and to the opposite shoulder/chest, at different times:

Footnotes.

1. I'm treating the hand as a kind of point mass representing the mass of the whole arm, which is probably the original convention, hence 'reaction hand ' instead of 'reaction arm'.

change and infallibility

I had the recently had the privilege of training with Grandmaster Paul Cutler. During one of the breaks we were discussing the various changes that have crept into the tul, some of which are exaggerations - often propagated as the result of tournament judges favouring stylistic flourishes, others have been introduced by the technical committees of the various ITF groups. GM Cutler commented that we should not alter Taekwon-Do from General Choi's original teachings. This was an-off-the-cuff remark and I have no idea how invested the Grandmaster is in this point of view, but it is certainly not an uncommon idea in the world of ITF Taekwon-Do.

I run the risk of stating the painfully obvious when I say that nobody is infallible;¹ not the pope, not Bruce Lee and not General Choi.

Many martial arts, including the arts that Taekwon-Do is built upon, have been refined for generations, in some cases development has spanned centuries. There is no reason why Taekwon-Do cannot also benefit from continued development, especially when you consider that Choi was a revisionist; he made huge sweeping changes to the his art. Addressing the implications of these changes is another job in itself.

Choi was a great martial engineer, his mechanics are worked out to an incredible degree. But there is at least one significant error in his application of physics.² At some point that will need to be fixed.

In addition, Choi's structural/mechanical accomplishments have come at a price; the tactical aspect of Taekwon-Do is sorely lacking. This is almost certainly inherited in part from Shotokan katate, Taekwon-Do's 'mother art' and greatest influence. Additionally, the absence of a thorough tactical framework may be a symptom of a more abstract approach to striking, something I hope to explore in a future post.

There is a growing movement of  karate instructors working hard to re-interpret the kata and rediscover the practical tactical applications that they represent. Taekwon-Do also needs to develop this aspect of the art, in harmony with Choi's structural work. Already  there are  many instructors out there pushing this work forward.

There is plenty left to be done in developing this martial art.
Seen in a certain light, from a certain angle,  Choi's greatest contributions to his art are a starting point, a martial arts construction kit. Building a truly comprehensive art may well including revising some of the work that has gone before, but then Taekwon-Do is built on revisions, as is all human knowledge.

Footnotes:

1. Possibly Milla Jovovich is infallible.

2. There are several instances where sine wave is used in stances where weight drop will not contribute to power generation, and a few cases where it will actually remove power from a strike. As far as I can tell these errors are due to a conflation between mass and weight.

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.