## Wednesday, November 26, 2014

### Blocking Weapons and More

Science concepts: torque, Newton's 3rd law of motion

Seeing as how this past weekend I spent a whole day at a Hock SDMS (impact weapons) seminar, I figured that I'd write a little something relevant to that.

There are many aspects of physics that apply to stick fighting, but the first aspect of dealing with impact weapons that people should probably concern themselves with is blocking.  Though I should note, that any knowledge about the optimal way to block with a stick will help you to prevent your opponent from blocking well (by making sure that those optimal conditions are not present for the other guy).

### The Situation

Let's assume, for the sake of simplicity, that both you and your opponent have sticks.  Let's also assume that your opponent has swung his stick at your head and that you cannot safely evade in time, which would be preferable to blocking.  (We should also assume that you have offset your stick at a sufficient angle from the incoming strike so that the sticks aren't parallel and bounce right past each other.) Where on your stick should you take the impact and why?  Let's look at the science.

### The Science

At the moment of impact, we can treat the swinging motion of the opponent's stick as a linear force.  So we have a situation like the following:

 'd' is the distance from the impact force, F, to your hand, which is the thing providing the counter torque to prevent your block from collapsing
The physic principle at work here is simple.  The torque that your hand needs to provide to prevent the strike from collapsing is t = Fd.  So, the greater the incoming force, the more torque you need to provide...no surprise there.  And the greater the distance from your hand, the more torque you need to provide.  So, the physics says to block as close to the hand as possible to minimize the torque necessary to complete the block.  Now, for anyone who has done any amount of stick fighting knows just how unpleasant getting hit on the hand is (indeed there are plenty of people, myself included, that will actually aim for the hand).  So, the physics have to weigh in against the psychological desire to avoid impact against the hand.

To improve your odds of success, using both hands is advisable.  In fact, anyone who has done Hock's "increasing 12" stick drill (which accumulates up to someone striking at you as hard as they can on 12 different angles of attack in a single combo) has probably decided that using the double-handed block is a good idea.  You may think that putting two hands on the stick doubles your potential for getting your fingers crushed, but just try the "increasing 12" drill and see how you feel.  With a two-handed grip, we end up with this:

Now, the second hand is providing additional "helper" torque for the first hand.  The principle at work here is the same one used for building bridges.  If you were to turn the above diagram 90 degrees counter-clockwise and ignore the fact that there's a stick figure on the bottom, you'd basically have a force diagram for a car on a flat bridge.

The incoming force results in two reaction forces, one from each hand.  Since torque can be calculated around any point, we can look at the torque at each hand individually.  For the torque at the top hand, the reaction force at the bottom hand fights the torque of the incoming force.  For the torque at the bottom hand, the reaction force of the top hand fights the torque of the incoming force.  Two hands are better than one, clearly, but two-handed blocks are actually more than twice as easy as single-handed blocks.  Why?  Because instead of having to provide all the torque with the hand (the pinky side and the thumb side push the stick in opposite directions, basically), the torque is provided by two linear forces from the arms.

Think of it this way, when lifting heavy weight on a bench press would you use two hands for stability or just use one and let the tightness of the grip of the one hand stop the bar from rotating and dropping on either side?

### Applications

Knowing this is not only great for helping your defense, it's also great for helping your offense.  If you strike in a way so that the other guy can, at best, get the tip of his stick in place for the block, then your strike has a higher chance of getting through.  The same principle applies in the situation in which you grab your opponent's stick.  The applied force doesn't necessarily have to come from your weapon.  It can come from your hand.  The closer your are to the tip of his stick, the easier it will be to manipulate.

Though for practical applications, you really want to grab about half-way up his stick so that when you punch it forward, the tip of his stick moves with even greater velocity (this is leverage and angular velocity at work).  This balances the applied torque from your pushing hand and the leverage that multiplied the distance traveled by the tip of the stick versus your hand.

### Conclusion

This material may be fairly intuitive, but it is also fundamental to understanding all stick blocking.  The applications of this principle also extend to stick grappling, and there are even knife and unarmed applications from here too.  You just need to think about it a bit and you'll see it.

## Wednesday, November 19, 2014

### Breakfalls: How to avoid getting beat up by the ground

Science concepts: impulse, torque, friction

Taking people down to the ground is an essential part of most martial arts.  To train those techniques properly, our training partners need to know the safest way to fall.  Falling well is particularly important in grappling heavy arts like Judo.  Some Judo schools will spend upwards of 30 minutes per class working on this skill.

Over my years of training, I’ve been told and/or led to believe things about proper falling technique that just aren’t true or are half true.  I want to address the science behind the principles of breaking your fall.

Definition
Here I take the term break fall to mean any movement meant to reduce the painful impact with the ground.  A fall could happen as a result of a misstep, slip, trip, push, takedown, or throw.  I take this to include falling in place as well as rolling out (ukemi in Japanese martial art vernacular).

Core Principles
Getting hit hard is not fun.  When it’s the ground that’s doing the hitting, there’s not much you can do to counter it (gravity being a physical law and all that).  What you can do is break the impact up into smaller pieces so that no one piece actually inflicts injury.  This is largely a matter of impulse, which I’ve described in a previous post on dealing damage with strikes.  The same physical principles that apply to dampening impact from fists apply to the ground as well.

Another principle of break falls is to make contact with the ground using parts of the body that are less likely to be injured.  This generally means that you want to use soft, muscled/fatty (depending on your body composition…I’m not judging) parts of the body rather than bony parts.  This, more or less, is also because of impulse.  The more time that any given impact takes to change your momentum, the less painful it will feel.  In practice, this tends to provide several guidelines like “don’t let your head touch the ground” and “don’t roll along your spine” and “don’t ram your elbow into the ground”.

The Science
Let’s talk specifically about rolls since they’re more complicated than the “regular” breakfalls.  For now, I’ll assume that you have some amount of forward momentum (i.e. you’re not falling straight down).  This could be as a result of some kind of throw like a Tomoe-nage (otherwise known as the Captain Kirk throw).  If your body makes a single impact with the ground and then stops, then you take all of the organ-shocking impulse in one shot…not a good thing.  If you could cut that in half and take two impacts it would be better.  Keep cutting the impulse down with more impacts and you might just save yourself from some serious injury.

The ideal we’re shooting for is a wheel.  A wheel has a (virtually) infinite number of impact points with the ground as it moves forward.  The human body doesn’t really resemble a wheel (at least most people’s bodies don’t), but we can try to approximate it.  This is traditionally done by using the following body parts, in succession, as impact points: hand, forearm, upper arm/shoulder, upper back, middle back, lower back, glutes, foot, foot (the feet go in succession as well).  The back should be relatively round compared to the arms.  So, you get 8-10 contact points with the ground.  Now we’re talking.  Ten 10% strength impacts are definitely preferable to one 100% impact.

Realistically speaking though, not every point of impact is going to take exactly 10% as an equal distribution.  Nor would we want it to.  The feet are much better at taking impact than the hands are.  The glutes, being a large muscle, are good for taking impact, but probably not as good as the feet.  What we want is for each point of impact to take a small enough impact to avoid pain while dissipating the entirety of the impact.  That might mean putting 5% on each of the hand, forearm, and shoulder, then 15% on each of the upper, middle, and lower back parts, then maybe a 20% on the glutes, and 10% on each foot.  (These numbers are just off the top of my head…not a goal to shoot for.)

Assuming you know what your impact distribution should look like for your body (maybe your hands are super-awesome at taking impact compared to the average person), we can break the fall down into the appropriate pieces.

Like most of moves in martial arts, it will be helpful to break things up into vector components to see the effects.   There are a number of different scenarios to examine.  First, let’s look at what we don’t want to happen.

Though the motion of your center of mass is taking a parabolic trajectory through the air (by nature of the constant acceleration due to Earth’s gravitational pull), your instantaneous direction of motion is what to be concerned with.

 The thin black line represents the ground. The thick black line represents the trajectory of your center of mass. The gray arrows represent your instantaneous tangential velocity/momentum vectors.

 The blue line represents your forward most support. The red and green are the components of the momentum relative to the support.

The particular part of this that is important is the point on the ground that is directly in front of your instantaneous motion vector.  In relation to the picture above, this would be the point that the gray lines hit the ground, should they extend far enough.  Why is this point important?  Because if our contact point with the ground is ever beyond that point, then our motion will provide a downward torque rather than a forward torque.  This is bad.  Have you ever attempted a breakfall roll and ended up jamming your shoulder really badly or have your body crumple into the ground rather than roll nicely?  It’s probably because your contact point got out ahead of the motion vector-ground intersection point.  By putting that support point so far out, it causes a portion of your motion vector to torque down towards the ground.  Sometimes, if the points aren’t too far apart then your momentum will overcome this downward torque.  It still won’t feel comfortable on whatever the next joint up your body is.  [I opted to use drawings for this rather than get a picture of me doing it because the potential injury just isn’t worth having the real picture…just take my word for it or try it out yourself.]

Now, let’s consider the situation in which you put your support point somewhere between the motion-vector-ground intersection and the spot on the ground directly underneath your center of mass.

 (No trajectory here because it just clutters the picture at this point). The gray dot is where the gray line would intersect the ground, if it continued on. The top yellow dot represents your center of mass. The bottom yellow dot is the point on the ground directly under your center of mass.

This is going to have a different torque than the previous situation and certain effects on your vertical and horizontal motion.  Let’s break down the motion vector into components using the support point as our rotation point.

 Red and green are the component vectors, just like above.

This shows us that we will torque forward rather than down.  This is good, though the portion of the vector that goes towards torque isn’t huge here.  Much of the impact is being taken on this support point.  We could do better.

What if you put the support point behind your center of mass?  You’d end up with something like this:

This has a much bigger portion of the motion going towards torque, which is good…sort of.  The problem now is that the torque vector is angling you down at the ground again!  This support point does some of its job, breaking down the fall.  Where the support point that was too far forward took too much force at once, this point takes too little.  There’s a big portion of the impact still left over for the next support point.  Experience tells me that it’s either the shoulder or lower back that will usually suffer in these situations.  We could do better.

We’ve tried reaching way out.  We’ve tried reaching out in front of our center of mass.  We’ve tried reaching back behind our center of mass.  How about right under it (there's a Goldilocks joke in here somewhere...)?  We end up with a picture like this:

This actually looks pretty good.  The torque is taking us parallel to the ground (i.e. the non-ouchy direction) and a fair portion of the motion vector that isn’t too big is handled by the support arm.  This is the best of both worlds.

There’s another benefit in this situation.  The aspect that I’ve glossed over until now is friction.  You’ve probably assumed that your support point would actually stay put once placed on the ground.  Well, on a slippery surface that might not happen.  Imagine you’re doing the roll on wet ice.  If you reach out in front of yourself, then your hand might slip forward into the bad range and cause you to fall flat (I’m pretty sure you can see this in action at any mall ice skating rink if you watch long enough).  If you reach back, your hand could slip even further back, negating the benefits of the using the support point at all.  However, if you put the support point directly under your center of mass, then friction doesn’t even come into play.  Well, at the instant of contact it doesn’t come into play.  Once the angle changes it will start to be a factor, but it’ll be a very small one.  Friction is the force that fights against two materials from sliding on one another.  But it’s purely a reactive force.  If you don’t try to slide (i.e. you don’t have a horizontal force component), then friction doesn’t show up and isn’t relied upon.

Not to belabor the point too much, but what if my initial assumption wasn’t true?  What if you were indeed falling straight down?  Putting your support point directly under your center of mass might mean taking the full impact on whatever hits the ground first.  In that case, you actually do want to place your support point off to one direction or the other, depending on which way you can more easily make yourself approximate a wheel.

Rather than come up with video of my own to demonstrate all of the myriad ways this can happen, I found a good video on YouTube of a guy demonstrating various falls.

The Slap
Back when I was in Taekwondo and Judo, we did a lot of breakfalls.  When we did them (rolls or otherwise), each fall was accompanied with a loud hand slap on the ground.  The louder, the better.  There was a direct correlation between the loudness of the slap on the ground and the perceived quality of the breakfall.  We trained on fairly soft mats.  In the beginning, I questioned the slap, asking if it would work on hard ground.  I was assured by brown and black belts that it would.  They had years of experience and I was just a kid.  So, I believed them and didn’t really think much of it afterwards.  I allowed the doctrine to influence my technique.

Fast forward a few years to my Hapkido training.  I was at a seminar that was taught by a Korean grandmaster.  The guy didn’t speak a lick of English.  So, you know he was good (he was actually quite amazing.  I can only hope to be that agile at that age.).  We were doing seated backward breakfalls to warm up.  Now, the dojo also doubled as a dance studio.  So, the floors were hardwood, which they had placed some folding mats on for the seminar.  I was sitting in the back, on the last bit of mat.  I was doing my stereotypical, macho martial arts thing and slapping the mat really hard when I rolled back.  A few reps into it, my right hand had drifted slightly out to the right and found the edge of the mat.  When my fingers hit that wood floor, the pain was excruciating.  The bones hurt.  The joints hurt.  The skin hurt.  I honestly think that having my fingers cut off would have been less painful.

Of course, I couldn’t let any of this pain show.  That would have been contrary to the martial arts machismo.  However, I never forgot that pain.  All of the questions I had asked as a kid had now resurfaced in my, now post-college aged, mind.  After the seminar, I asked some of the Hapkido black belts about the issue of the breakfall slap.  They explained to me how to properly use my hands in a breakfall (though they admitted that some of the “traditionalists” want to hear a loud slap).

Now, I’ve heard many arguments for slapping hard and loud.  One that almost sounds convincing is the one that claims that the loudness of the slap is the dissipated energy from the fall.  With that logic, certainly louder is better.  It sort of makes sense, but if you look at the people who make this claim you’ll notice that they slap the ground after their torso hits the ground.  As a physics enthusiast, this tells me that they’re not dissipating energy from the fall at all.  Their adding energy by swinging their arms, which is where the loudness comes from.  And besides, anything they do after their torso has hit the ground isn’t really doing anything to protect them from the fall.  The fall has already happened at that point!  No, if you want your hands to be of any help at all, they need to touch the ground before your body does.  This makes sense from the physics perspective.  It also makes sense logically.

Friends don’t let friends do the macho breakfall slap.  (The video above doesn’t have sound, unfortunately, but I am virtually positive that the guy is falling very quietly.  Take a tip from the art of parkour: quieter impact is easier on your body.)

Some Tips
So, here’s the summary of the tips we get from the science plus a few “technique” tips I think will help.  First, try to make your body as round as possible when falling in order to maximize the number of contact points and therefore the number of pieces the impact is broken into.  Second, when rolling, try to keep your forward-most support point under your center of gravity.  For many people, this is approximately the stomach/chest area.  Third, to avoid hitting your head tuck your chin down to your chest and put your cheek to the shoulder of the arm that you aren’t rolling over.  Fourth, keep your feet tucked in close to your body as long as possible.  Many people open up too soon and end up having their knees and/or ankles slam against the ground, which stops all motion.  I’d much rather you converted the remaining motion into the horizontal direction so you can walk it off…literally.

Common Mistakes and Fixes

1. When rolling, if you go straight from your hand to your shoulder, then it means that your fingers need to point more backward.
2.  If your elbow hits hard to the point that you feel pain in your shoulder, then you are reaching too far forward.
3. If your lower back is sore, that means you need to arch your back more.  Make sure to tuck your head really far forward to get an arch in your spine.
4. If your feet are hitting the ground hard, stopping you from standing up out of the roll then you need to keep your knees bent and your feet close to your body for longer.  Wait until your feet touch before starting to extend your body.

Conclusion

If you’re like me, then you plan on training martial arts for a long time.  If you want to prevent unnecessary injuries (as opposed to the necessary ones…) then you need to learn how to fall properly.  Our training partners need to be able to practice the full motions of takedowns and throws just as much as we do, and we also need to know how to minimize damage to ourselves when someone successfully executes a move that would put us on the ground.  There are only a few scientific principles we need in order to do that.  Learn them.  Generalize and apply!

## Wednesday, November 12, 2014

### Joint Locks

Science concepts: torque (and a tiny bit of trigonometry)

Aikido.  Hapkido.  Jiu-jitsu.  Judo.  Brazilian Jiu-Jitsu.  Chin-na.  Dumog.  The list of martial arts in which joint locks play a prominent role is vast, and the paradigms are almost as diverse.  Small circles or big circles?  Smooth motions or violently snappy?  Certain arts tend to do joint locks a certain way.  Is this because there are just that many different joint locks, or are all of these systems simply expressing the same locks in different ways?  I would argue the latter.

Definition
Some people make a distinction between a “joint lock” and a “joint crank”, where a lock is immobilizing and a crank just hurts but the person can move to alleviate the pain.  For the sake of this topic, I’m going to lump them both together since the mechanics applied are largely the same and a crank can usually be turned into a lock by isolating a part of your opponent’s body to prevent it from moving (usually the next joint closer/proximal to the body).  For now, let’s consider a “joint lock” to be any movement that takes a joint beyond its comfortable range of motion, in any direction.

Deconstruction and Classification
There are only so many ways that joints can be locked.  The shoulder can be rotated too far up and too far down (I’ve seen this called “branch up” and “branch down” in certain Kempo systems).

 Branch Up "Concept" Lock Blue arrows are the applied force Red semi-circle is the resulting torque
 Branch Down "Concept" Lock

The elbow can be locked out straight or compressed too far (compression lock, which I’ll cover another time).

 Straight Arm Lock

 Compression locks can get complicated (physics-wise). There's a lot going on there that hurts.
The wrist, being a complicated joint, has several ways to hurt it.  It can twist too far to the right, too far to the left, too far forward, too far backward, and too far side to side. Here are just a few examples:

 Wow, that's a busy diagram There are basically to pairs of forces, each introduces some torque The torque arcs are in perpendicular planes if my awesome mspaint skills didn't make that clear

 I'll break this lock down into vectors down below

Fingers hurt with just about any direction to the extreme.  Hips are like shoulder, though the size of the bones and muscles make applying a lock very difficult.  The knees are much like the elbows.  The ankles are like the wrists, though only tend to hurt when twisting too far or pointing the toes too far.  Toes are just like fingers.  Just give them a good pull and you’ll probably break something.  The spine is structurally different than the rest of the joints, but it is still susceptible to twisting too far in just about any direction.

Core Principles
Fundamentally, joint locks involve moving one part of your opponent’s body relative to the rest of it.  If you move their wrist and the rest of their body comes along, then there’s no lock.  You’ve just moved them.  So, force needs to be applied in such a way that the rest of their body can’t move to compensate for the attempted lock, at least not fast enough to prevent the pain.  To do this, you almost always have to provide force in two directions.  (Ultimately, we really want to apply torque since all joints are pivot points.)  For example, when applying a standing arm bar, you pull up on the wrist while pushing down on the elbow.  To relieve the pain, the person usually throws their body down to keep their shoulder in line with their wrist and elbow (otherwise, their elbow will break).  That works until the ground prevents them from continuing…then you can break their arm.

This works for more complicated locks, too.  Consider the ubiquitous outside wrist lock (also pictured above).  The textbook application of it involves two pairs of two-way forces.

 "Turn it like a little steering wheel"

 The "death metal"' hand I have here is purely incidental

The first pair pulls the wrist away from the opponent and pushes the knuckles towards them.  The second pair involves pushing their wrist sideways towards the center and pushing the fingers towards the outside.
Since every joint lock involves two-way forces of some kind, then it would behoove us to understand the mechanics behind the principle.

The Science
Keeping all of these joint locks in mind, let’s do some physics for a bit.  We understand force (F = ma).  Force is what makes things change directions or speed.  In much the same way that force builds on acceleration, torque builds on force.  Torque is a twisting force that causes rotation (sounds like joint locks).  The formula is simple: t = Fd (physicists use t for torque, which is the Greek letter tau, because t was already taken [for time]).

Actually, this picture isn’t quite general enough.  We don’t always have the force being applied perfectly perpendicular to the effort arm.

 A little trigonometry is necessary here Who remembers SOH CAH TOA?

So, the formula is really t = (F cos q)d, which only accounts for the portion of the F vector that is perpendicular to the effort arm (recall that vectors can be split into components along arbitrary axes).

Let’s look at an example, which will build back up towards the standing arm bar.  If you apply an upward force on your opponent’s wrist, then you are applying torque over a distance of their entire arm.

But this doesn’t result in a lock because the shoulder doesn’t lock that way (unless you go really high with the arm, which is impractical).  We want to lock the elbow.  So we also need downward pressure on or near the elbow (pressing just above the elbow into the tricep tendon gives me the best results…leverage and pain compliance.  Yay!).  But how much do we need to press down to prevent the elbow from moving up when we push the wrist up?  It’s going to depend on whether or not your opponent is dropping down or not.  But let’s apply the formula to find out how hard to press.

Let’s assume that the “elbow hand” is half way between the “wrist hand” and the opponent’s shoulder.  Let’s also assume, for the time being, that the opponent is going to (dumbly and self-destructively) stay standing up.  Then the torque applied by the wrist-hand is t1 = F1 d and the torque applied by the elbow-hand is t2 = -F2 d/2.  The negative sign shows up in the second equation because the force is in the opposite direction and I’m taking “down” to be negative at the moment.  The “/2” shows up because the force is applied halfway between the wrist, which is d away from the shoulder, and the shoulder.  So, the total torque is  t = t 1 + t2 = F1 d - F2 d/2, which we want to be zero because we want to know how big F2 has to be to be to just barely stop the arm from moving up when the wrist is pushed up.  So, if F1 d - F2 d/2 = 0, then F1 d = F2 d/2, which implies that 2F1 = F2 (after a little algebra).  That means that the force on the elbow has to be twice as much as the force on the wrist, just to keep the arm in position.

Ultimately, we don’t want to just prevent the arm from moving up.  We want it to go down, preferably ending with their face hitting the ground.  That means that we’ll likely need to press more than twice as hard at the elbow than at the wrist.  To do that, you really need to get your body weight involved, which is something often missed by beginners who, consequently, can’t get this technique to work.

By applying the two torques in this way, the opponent either let’s all of that twisting force take up residence in their elbow ligaments, which have limited elasticity, or they move their body to alleviate the strain.  So, either you mechanically diminish their ability to fight, or you put them on the ground.  At which point, you can decide to mechanically diminish them anyway.  Win-win.

Some Tips
Here are a few tips to help augment the effectiveness of your joint locks.  First, when you apply torque to a joint, there’s a certain natural arc that the limb will want to move through that is comfortable for the body.  Don’t let them move through that arc.  Adjust the direction of the forces you’re applying so the limb moves in a tighter than natural arc.  Not only does this usually result in less physical movement on your part (making application faster), but it also tends to provoke the opponent to move the rest of their body to get back to that natural angle, which is far less painful.  Consider these two pictures:

 Natural Arc

 Too-Tight Arc Notice how Mike has to move his hips and tilt his torso to get away from the pain, whereas I moved very little compared to the natural arc version

This ties into the other tip I want to give you, which is that joint locks (and much of fighting) is about relative positioning not absolute positioning.  This means that you should adjust the pressure that you’re applying based on the way the opponent’s body is oriented.  Take the standing arm bar.  What if their elbow is pointed down instead of up?  The shoulder does rotate a fair ways around.  Well, this joint lock is meant to hyperextend the elbow.  So, push the elbow in a way that will hyperextend it, which in this case would be elbow UP and wrist DOWN, the opposite of before.  Some beginners (and non-beginners, on occasion) fail to make this distinction and don’t understand why a technique works for them sometimes but not others.  If the opponent rotates their arm a bit, then you need to follow it to maintain relative positioning.

Conclusion

I know that most people don’t like to bust out algebra if they can help it, but hopefully it wasn’t too bad. We may have solved some equations, but rest assured that doing so isn’t necessary during a fight.  We only do this to gain insights and understanding into what makes a technique work.  Once we have that understanding, we can both apply and teach the technique better because we know what needs to happen.  Then just practice the scientifically sound method for your techniques and let the repetitions sink in.

## Wednesday, November 5, 2014

### Basic Defense Concepts

Science concepts: Vectors, vector components, defining axes (and some torque)

Mr. Miyagi had it right.  You shouldn’t learn how to attack until you can guard yourself against incoming attacks.  Otherwise, your fight will end up looking like one of those amateur cage fights where neither person has any regard for their own well-being and just starts swinging for the fences hoping for a lucky punch.  It’s exciting to watch, but you don’t see a lot of that in the pro leagues and for good reason.

Four Levels of Defense
There are a myriad of ways to defend against attacks, but they can all be put into the following categories (in increasing order of preference):

1.   Blocking
2.   Parrying
4.   Intercepting

Blocking involves taking the full force of an attack on a part of your body that can take the damage with minimal negative consequences, usually an arm, leg, or large muscle like the lats.  This is the least desirable of the four, but it beats getting hit in the face.

Parrying is a more graceful version of a block.  Rather than taking all of the force of the attack on your body, you redirect the attack around you.  Compared to blocking, this is excellent.  The damage to your body is virtually non-existent, and you may even gain an advantage through unbalancing your opponent.

Evading is Mr. Miyagi’s preferred method of defense: “no be there”.  This method of defense is even better than parrying because it leaves all of your limbs available for counter-attacking.

Intercepting is Bruce Lee’s preferred method of defense, which is more along the line of “you’re not punching…I’M PUNCHING!”  This involves perceiving your opponent’s intention to attack through telegraphed movements or other signs and interrupting their attack with a quicker, more efficient attack.  The opponent starts first, but you finish first.  This is hard to achieve, but I will address it in a later post.

The Science
In this post, I’ll be focusing on the first two methods: blocking and parrying.  Both of them involve getting your hands (or whatever) on the incoming attack before it hits something that you’d rather didn’t get hit (face, gut, groin, etc.).  So, what’s the differentiator?  Force vectors.  The main difference between blocking and parrying has to do with the relative angle of the defensive limb’s motion to the offensive limb’s motion.  To illustrate, imagine someone is swinging a baseball bat at the side of your head.

 Here, Mike seems to be enjoying the prospect of smashing my face with a bat

A block might be to put your forearm up to take the force of the attack.  Sure, you can “roll with the punches”, which is a defensive tactic for reducing the maximum impulse (discussed here) of the attack, but you’re still taking a baseball bat to your forearm.  If I were a betting man, I’d put my money on the bat.  Now instead consider using your forearm to deflect the bat up and over your head (or down in front of your body, whichever makes more sense at the time).  You didn’t stop the bat.  You just prevented it from hitting your vital targets.  The bat’s force redirects around you so you don’t have to absorb it.

A block meets a force head on.  If the attack is coming from the left, then you push left.  If it comes from the right, you push right.  If it comes straight at you, you prepare to push forward into it.  This is good for stopping the movement of the attack, but it also means that all of the energy is transferred into your body.  There’s only so much a body can take before it breaks.  Meeting hard and fast attacks head on with blocking is a good way to discover how much your body can take.  I don’t recommend it if you can help it.

An ideal parry will tap an attack out of the way at a right angle (90 degrees, or an ‘L’ angle) to the attack’s motion.  In the bat example, tapping the bat up would be perfect if it were swung horizontally.  If instead the bat were swung straight down towards your head, then tapping it straight left or right would be ideal.  So, a pure parry is 90 degrees off of a pure block.  In the middle is a continuum sliding from one to the other.

Why not always use a pure and perfect parry?  Let’s go back to the bat example.  How confident are you that you can pop your arm straight up at just the right moment to get the bat to redirect over your head?  I don’t know about you, but I’ve been practicing this stuff for years and I’m not there yet -- at least not when a fast swinging bat is involved.  Instead you have to choose angle of deflection as close to 90 degrees to the attack as possible while still being able to make contact with the attack, which is going to depend on a lot of things: speed, distance, timing, luck, etc.

Vectors and Axes
A key idea when operating on vectors is the idea of equivalence.  Imagine simultaneously getting pushed from behind and from the left side.  Which direction would you go?  You’d go forward and to the right, just as if one person had pushed you from your back left side.

That’s vector equivalence.  Equivalence states that multiple vectors can be added together to create a single resultant vector.  This is useful for simplifying problems.  Equivalence also works in reverse.  If I have a single vector, which might be coming in at a funky angle that’s hard to do calculations on, then I can break it into more convenient pieces as long as those pieces add up to the original vector.  We’ll do that shortly.  (We’ll be doing this qualitatively so there won’t be any trigonometry involved.  Sorry to disappoint you.)

I often tell the students that I tutor in physics that they need to define their axes before they solve a problem involving vectors.  The same applies here.  That’s one of the things I like about physics, you can choose your axes in a way to make the math easy.  For the bat problem, let’s set one of the axes to be parallel to the defending arm and the other to be perpendicular to it as shown in the picture.

Labeling your axes is very important.  So, let’s call the parallel axis the “useful” axis and the perpendicular axis the “painful” axis.  Now, let’s take the vector of the bat’s motion and break it up into components that match up with our axes.  Hopefully, the naming of the axes is a big enough hint for you.  We want the angle of the block/parry to help minimize the “painful” component vector while still providing enough redirection to the bat to get it away from the head.

“Generalize and apply!”
Back at Ohio State, I took a number theory course with Professor Vitaly Bergelson.  He was a great teacher that showed the class mathematical insights into things that I never would have expected to find such beautifully simple yet impactful math.  He was also very brilliant and pushed the students to grow.  He would write a problem on the board and have us solve it. Then he would say “generalize and apply”, expecting us to formulate a more general version of the claim and use our first proof to guide us through the more general proof.  That idea of taking a concept, generalizing it, and applying the generalization in broader areas has served me well, and I advise you to do the same.

This very concept of perpendicular motion as a parry was something I realized after years of training specific defenses to specific attacks.  So, I’ve done some of the generalizing for you, but that doesn’t mean that there isn’t some bigger concept that this is just a special case for.

Above I used an example of a baseball bat swinging at the side of your head.  What about other swinging attacks?  What about straight attacks?  Take the idea and run with it.  Experiment and see what you find.