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.

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

3.   Evading

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.

Damage: Dealing It, Avoiding It

Science Concepts: kinetic energy, work, momentum, impulse, integrals, derivatives

“If you think I look bad, you should see the other guy!” This common phrase, sometimes spoken sarcastically, reflects a fundamental principle of fighting, which is the one who receives the least damage “wins”.  The goals in a fight are to inflict damage and avoid taking it.  There is a lot that goes into achieving those goals.  What I’ll address here is the damage inflicted when a strike is landed.  Sorry, no joint locks or grappling slams today.  I’m going to assume, for the sake of discussion, that the attacker (whether that is you or your opponent) has landed a strike in the desired location.  So, assuming that happens, if you’re dishing it out then how do you maximize the effect, and if you’re dishing it in then how do you minimize the effect?  (A little forewarning: this one is going to get really nerdy.)

Harder, Better, Faster, Stronger

Daft Punk got it right.  Harder, better, faster, and stronger are all unique and separate things.  Speed is great, but without structure behind it, then there’s no strength in the strike (which is fine, by the way, in knife fighting).  You can have structure and strength in your movement, but if you move slowly then you won’t be knocking out too many people even if you manage to hit them.  A speeding feather riding a gust of wind isn’t going to hurt you and neither will a slow rolling car (assuming it doesn’t roll over you).  We need both speed and strength.  This is where momentum comes in…

The Science

Momentum is the product of an object’s mass and its velocity, often written p = mv.  (Aside: You may be wondering why ‘p’ is used for momentum.  Let’s ignore the fact that using ‘m’ would just be confusing since ‘mass’ already uses that.  Newton originally used the word ‘impetus’ to describe the quality we now know as momentum. The Latin for ‘impetus’ is ‘petere’, which means “to go to; to seek.”  So, ‘p’ is for ‘petere’.  Etymological nerdery completed.)  You might guess that I’m getting at the point that both speed and mass are important for striking.  You’d be right, but that’s only a tiny part of the picture.

Momentum is necessary for striking, but consider this: simply by existing on planet Earth you have huge amounts of momentum.  You have mass (some of you more than others) and are on a planet that is speeding around the sun, which is in a solar system speeding around the galaxy, which is traveling at ridiculous speeds across the universe.  “Ah,” you say, “relative momentum is the key.”  That’s a move in the right direction, but still not quite there.  If I’m in a car that gently accelerates me up to 60 mph, then it has taken me from a relative momentum of zero (to the ground) and up to 60 mph times my mass.  My momentum at the end of that is huge, but I wouldn’t say that my body was devastated from the “strike” the car gave me.  Time is important.  If we change the momentum of something very quickly, then we’re talking about serious impact…or as they say in physics, “impulse.”

Impulse is the measure of the change of momentum over time.  Here’s a quick derivation of the formula:

F = ma                    , Newton’s 2^nd law of motion

F = m Dv/t               , a = Dv/t by definition of acceleration (see my post on Physics)

F t = m Dv               , multiplicative inverse and multiplication property of equality (ok, now I’m just being a pedantic jerk)

Now m Dv is the change in momentum (the Greek letter delta, ‘D’, is commonly used in math to indicate the change in a value.  Think of Dv as (v₂ – v₁).), and that is equal to force times time.  Now we are getting somewhere.  If you change the momentum, say of someone’s face, by applying a large force in a little time then you can bet that it’s going to hurt.  But what if the same force is applied over a larger amount of time?  Depending on how much large the time interval is, it might not hurt at all.  This is where the concept of “rolling with the punches” comes from.  When on the receiving end of a strike, if you loosen up and move your body back with the punch so it doesn’t hit full force all at once, then the force is dissipated over a longer period of time, which reduces the maximum force you feel at any one time.  Consider the following graphs.

Both graphs show force vs. time.  In the graph on the left, the force is dealt in a short interval of time, spiking the graph above the pain level.  Receiving this type of strike hurts.  The graph on the right is an example of what happens when you roll with the punches.  The blue areas of the graphs are equal (or at least they’re supposed to be…just pretend), and the area is the amount of impulse experienced.  This comes from the Calculus version of the impulse equation above:

∫F dt = m Dv

This almost gives us the whole picture.  “There’s more?!” Yes, there’s more science, but the conclusion is worth it.  Now, when someone rolls with the punch, they are applying some force to the fist.  If they weren’t, then they’d just be moving backwards until the punch hit them full force.  So, the force has to be dissipated a little at a time, but how should you do that exactly?

We know that the incoming strike has both mass and velocity, which means that it has kinetic energy, which is the energy an object has due to its motion.  Work is when a force is applied to an object that then moves in the direction of the force.  Kinetic energy and work are the final pieces of the puzzle that we need.  The formula for kinetic energy is KE = ½ mv².  The formula for work is W = Fd.  So, if the incoming punch has kinetic energy, then the face needs to do work to dissipate that energy.  That gives us the equation W = F_avgd = ½ mv².  To stop the incoming strike, the guy rolling with the punch will need to provide an average force over a distance d.  You could also think of the average force as the impact force felt by the face (remember that every action has an equal but opposite reaction).  The greater the distance is the smaller that average force can be.  So, impulse told us that we need to increase the impact time and the energy equations told us that we need to increase the impact distance (to avoid taking damage, that is).  Those two conclusions both being true isn’t all that surprising.  What is interesting about the energy equation is this: when striking, velocity is a much bigger factor than mass.  I can say this because of the squared velocity.  Let’s consider a qualitative example.

Suppose puncher A has a mass m and puncher B has a mass m/2.  Also suppose that puncher A punches at v m/s and that puncher B punches at 2v m/s.  So, puncher B has half the mass, but twice the velocity.  The momentum equation will tell us that both punchers have the same momentum on their punches.  However, the energy equations tell a more complete story.  The punch from A has a kinetic energy of  KE_A = ½ mv² .  The punch from B has a kinetic energy of is

KEB = ½ (m/2)(2v)² = (m/4)(4v²) = mv² = 2KE_A.  So, B’s punch has twice the kinetic energy of A’s punch, which means that someone will need twice the distance to “roll with the punch” or they’ll just have to feel twice the average impact force.  This explains why Bruce Lee had such devastating strikes despite his small size.

Conclusion

There was a lot of math and physics getting here, but the results were quite useful.  First, we noted that both mass and velocity matter when striking.  In particular, we want to change the momentum of our target in as little time as possible.  If we’re getting hit, then we want the impact to last as long as possible.  Finally, based on the energy equations, we saw that even though mass and velocity matter in striking, velocity matters more.  So, when you’re practicing, learn good form to have structure that will allow you to use the mass of your body in your strikes and from there ... get faster!

Striking Structure (with pictures!)

Science concepts: vectors, torque, Newton’s 2^nd and 3^rd laws of motion, static structures

Striking is a quintessential part of most martial arts.  Different martial arts strike differently.  Knife hand chops, ridge hand strikes, hammer fist strikes, backhands, punches, kicks, elbows, knees, head butts…the list goes on.  There are seemingly many kinds of strikes, but they really only boil down to a handful of different categories.  As Hock Hochheim says, “a strike is either going to be straight or curving and either committed or hit-and-retract.”  Here, I’m only concerned with the actual structure of the attack.  So, I’m not going to worry about whether a strike is committed or non-committed.

For any strike to be effective, you need the correct structure.  Otherwise, some of your effort is wasted.  There are quite of a few scientific concepts involved here.  So, let’s dive in.

The Science

Punching is what most people are familiar with.  So I’ll use a straight punch and a hook punch as my examples, but know that the same principles apply to kicks.  Elbows and knees work on the same principles too, and they’re even easier to apply because there are fewer joints involved.

The Straight Punch

Let’s start from the business end of the punch: the knuckles.  How should the knuckles make contact with the target?  Having already covered vectors, I’ll bet you can make a good guess.  As with many problems involving vectors, we define our axes first. 

 Here, the axis that is parallel to surface of the contact point is the “wasted” axis (red axis), and the axis that is perpendicular to the surface of the contact point is the “useful” axis (green axis).  Now, break the vector of the incoming fist’s motion (blue vector) into components along these axes (red and green components...take note of my superbly mediocre mspaint skills).  Hopefully, the axis names make the point for me here.  Any motion that is parallel to the surface is wasted.  This kind of motion is what produces strikes that glance off of the target.  Only the perpendicular motion affects the target.  So, this is our first structural insight: hit perpendicular to the surface for maximum effect.

When that perfectly landed punch makes contact, the target impedes the motion of the fist.  This is a phenomenon described by Newton’s 3^rd law of motion, which states that for every action there is an equal but opposite reaction.  Informally, the target pushes back on the fist.  Where does that force go?  That depends on your structure.  Let’s now focus on the next joint in this chain of effects, the wrist.  Just like the knuckles ran into the face, the forearm runs into the hand.  We can do the same thing that we did early, define our axes, break the incoming vector into components, and see how much is useful and how much is wasted.

We see in the first picture, that some of the incoming force is wasted.  Actually, it’s worse than wasted.  It’s harmful.

I had mostly done Taekwondo as my primary martial art all the way through college.  After college, my roommate and I got a punching bag, the kind that has a plastic stand that you fill with water.  I had spent years kicking and punching the air and always pulling my strikes when sparring because control was paramount.  I was excited to finally get to hit something and see what kind of damage I could do.  We filled it up with water and I started hitting full force.  Kick, kick, kick, punch……..ow!  For the first time ever, I punched something as hard as I could.  At that speed and force, any little structural flaw was going to be felt in a big way.  Like the picture above, my wrist was bent down, ever so slightly, but that meant that the force from my forearm didn’t transfer into my hand.  It sent my forearm past my hand, but my knuckles were firmly planted on the bag.  Therefore…sprained wrist.  It’s not a mistake I’ve made twice.  Lesson learned: align your forearm bones with your hand bones.

This principle applies all the way up the arm.  Keep things in line if you want the force to transfer properly.  This is also the reason that martial arts instructors will tell students to extend their arms when doing straight punches because it puts the strain on the bones rather than the muscles, which might give way.

This is all well and good, but the astute observer will note that the force transfer doesn’t stop at the shoulder.  It has to go somewhere.  Well, it wants to take your shoulder straight back.  To prevent this from happening, we use our core muscles.  This is where all the linear force gets converted, at least partially, into torque.  I say “partially” because it depends on the angle of your spine relative to direction of the punch.  If you were leaning forward a bit, then some of the force transfers straight down the spine and the rest of it tries to torque the spine backwards.

Light blue is linear force transfer; Yellow is linear force that is converted to torque (about the hips).

The abs and other core muscles counter that torque (orange) to keep your torso from rotating backwards.  As long as the torque provided by the abs is equal to the torque resulting from the punch's linear force, the torso will remain steady.  It should be noted that the longer the torso, the more torque necessary to balance this out.  Tall guys, beware.

But we’re still not done.  Remember Newton’s 3^rd law.  If the abdominal muscles are torquing the torso forward, what are they basing off of to apply that torque?  And where does that linear force that went straight down the spine go?  The answer to both of these is “the legs”.  Now, just like the arms, if the structure is right, then the force gets transferred through the bones.  If not, then the muscles have to apply torque to make sure that you don’t fall over.

In this stance, I'd have to apply virtually all of the torque with my toes to counteract the force of the punch.
The idea is so ridiculous that I can't even keep a straight face for the picture.

Where does the buck stop?  In the ground.  The foot does the final transfer of linear force and torque into the ground, and the massive size of the planet takes care of the rest. I may have covered the structure of the punch from fist to foot, but the punch is produced in the opposite way.  The power or base of the punch comes from the ground.  If you have a good structure that transfers the reaction force from the contact back into the ground, then you’re not going to buckle.  His face will.

Again, the blue arrow represents the linear force, the yellow arc represents the transferred torque from the punch that
will tend to tip me backwards, and the orange arc is the counter-torque supplied by my foot to make sure
that I remain upright and balanced.  The ground takes care of things from there.

 This is another key point:   ultimately, you want your punch to come from the ground.

The Hook Punch

There are actually a lot of variations on hook punches for various situations, but I’m going to cover the one that allows for the greatest bone structure involvement.  Just like the straight punch, you want to make contact perpendicular to the surface.  Similarly, you still need your forearm and wrist aligned to minimize the amount of forearm muscles you need to use to stop yourself from spraining your wrist, like me.  For those things to be true, your knuckles, wrist, and elbow need to be lined up.  The elbow is what pushes the fist into the target. 

Blue is the applied force (note the alignment).  Yellow represents the consequential torque.
Orange, again, represents the counter-torque.

This is where things get different from the straight punch.  At this point, it’s all about torque, which is going to come from the muscles.  The amount that the elbow is bent is very important.  If the elbow is fairly extended, then the bicep needs to supply enough torque to transfer the force into the fist without the elbow buckling under the impact.  If the elbow is too bent, then we lose velocity, the ability for the elbow to push the fist, and the tricep muscle needs to engage to prevent the elbow from buckling under the impact.  To avoid these two extremes, go to the middle with a perfect 90 degree bend.  (NOTE:  I am not claiming that hook punches done without this 90 degree bend will not be effective.  I’m just making a claim about ideal bone alignment for transferring force.  If having to engage your bicep is worth it to you to gain some range on your hook, then by all means swing for the fences.  Just be aware of the trade off.)

This makes things easy on the arm muscles, but just like the force in the last example, the torque has to go somewhere.  The pectoral muscles end up being next in line.  This isn’t so bad since it’s a very large muscle, comparatively speaking.  This means that the torso now feels the torque, and just like the last example, the torque ultimately ends up in the feet and the ground.  The reaction force goes to the elbow and converts to torque (because of the 90 degree angle).  That torque is applied to the shoulder via the humerus.  The shoulder and chest muscles counter that torque, which then results in a torque in the hips that also need to be countered.  The feet counter that torque and the ground takes it from there.

Having good contact with the ground is essential.  Imagine doing a hook punch on someone while you’re standing on ice or while wearing roller skates.  The punch would end up rotating your body rather that transferring all of that motion into the target.

The Other Side

Knowing the proper structure to deliver a strike has another benefit.  It allows you to notice when your opponent doesn’t have proper structure for absorbing a strike.  The phrase “caught on your heels” is used in boxing to describe a structure that is leaning back rather than sinking down and forward.  If you’re leaning back, then there’s no way to absorb an incoming strike.  You just take it and get knocked over.  We don’t want to be receiving a strike in that situation, but we definitely want to be delivering one if the other guy is in that situation.  Watch for poor structure in your opponents to determine the best time to deliver a strike.  In another post, I’ll cover how to produce poor structure in your opponents.

Structure Tip

Some of you may have seen or heard of the “sun fist” (not to be confused with Sunkist). 

Good for punching

Good for thirst quenching
Also, "it's different because of the spelling" (Eddie Izzard) 

(Actually, there is not a nice one-to-one relationship between the name “sun fist” and my intention illustrated here.  If you call this something else, then just assume that’s what I meant and don’t get hung up on nomenclature.) I saw someone do this in a class I was teaching and tried to correct him because I thought he was doing a less extreme version of this:

He then had me make a fist and said he would try to bend my wrist and that I was to prevent him from doing so.  He was able to bend it fairly easily.  Then he had me make a sun fist and repeat the exercise.  He couldn’t bend my wrist this time.  It wasn’t just that he wasn’t trying as hard either.  I actually felt the structural difference.  It felt stronger.  To confirm, I repeated the exercise with several other people.  This time, I was the one trying to bend the wrist.  Sure enough, the sun fist was stronger.  It almost seemed like magic.  Seeing as how I wasn’t prone to believing about the mystical and mysterious aspects of martial arts, I spent a fair chunk of the rest of the class analyzing my hand.  Then I realized why the sun fist was working.  Luckily, my hands are fairly lean, which revealed the essential anatomy.  It turns out that the sun fist, by positioning the thumb knuckle (the one by the web of the hand) up closer to the back of the hand, allowed for an additional tendon to tighten and provide support.  In particular, the extensor pollicis longus tendon. 

This picture is from http://anatomyproartifex.blogspot.com/2011/06/dorsal-hand-dorsal-foots-fraternal-twin.html
and is the clearest and best illustrated picture I could find for the extensor pollicus longus.
Props to the one who runs that blog.

This made me happy because it meant that I didn’t have to tuck my thumb in, which I still didn’t like, even though it’s only slightly in the sun fist.  I just position my thumb alongside my index finger and flex that tendon.

The thumb is pressed up against the index finger.  Note you can really
see the flex of the extensor pollicus longus tendon here.

If only I’d known this before I sprained my wrist!  This little tip will allow the force of your punches to transfer through your knuckles better and avoid bending your wrist.  I believe this is the secret to the attribute known in MMA as “heavy hands”.  Sure, some guys just have meatier hands, but the weight difference is actually quite minuscule.  The ability to punch with good structure is a much bigger factor than a couple of ounces of weight difference.

Conclusion

By applying this knowledge, you could really punch in just about any wacky way you want as long as your structure can transfer the force of the punch into the target.  This knowledge should also affect how you hit various targets.  The head can be a tricky target.  Getting that perpendicular shot can be difficult when your opponent is bobbing, weaving, and shuffling around.  Knowing what it takes to make a good punch (and a bad one!), you can choose at the last moment whether or not to follow through or pull back to avoid injuring yourself.  Traditional martial artists are always talking about having good structure and stances, and they’re right.  Though the set of good stances is much bigger than most people realize and it changes with the situation.  Learn to feel your way through good structure and you’ll do well.

Quick and Dirty Physics Primer

Before I can dive into the martial arts and how the science applies, I need to at least introduce some concepts from physics.  If any of this sounds completely confusing to you, then you may want to find an alternate source to get a deeper explanation.  I recommend khanacademy.com.  The following text is a bit dry for the typical martial artist.  So, you can skip it if you want, but you may need to come back to understand later articles.

Displacement, Velocity, and Acceleration

Displacement (which is like distance and will be treated as such in most situations here) is one of the fundamental concepts in physics.  Space exists.  Displacement is the measure of how far apart two points in space are.  For example, “that punch missed me by 3 inches”.  Here, “3” would be the measure and “inches” would be the unit of measure.

What happens when we put time in the mix?  When we go a distance over a period of time?  Then we get velocity (which is like speed and will also be treated as such in most situations here).  For example, if a person runs 100 meters (m) in 12 seconds (s), then their (average) velocity is 100m/12s = 8.33 m/s.  In general, the units for velocity are distance divided by time (distance/time).

Most people are familiar with the standard of testing an automobile’s “0 to 60” time, which means “the amount of time it takes a car to go from 0 mph to 60 mph”.  Just like velocity was a difference in displacement divided by time, acceleration is a difference of velocity divided by time.  So, a car that goes from 0 mph to 60 mph (note that ‘mph’ means miles/hour, which is distance divided by time) in 5.2 seconds has an acceleration of (60mph – 0mph)/5.2s = (26.8224m/s – 0m/s)/5.2s = 5.16m/s² = 11.54mph/s.  The whole “seconds squared” unit is sometimes hard for people to grasp.  So it helps to think of it this way: the car can increase its speed by 5.16 m/s per second.

For those of you who know calculus, acceleration is the derivative of velocity, which is the derivative of displacement (all with respect to time).

Force

No, I’m not talking about Star Wars or “force fields” (well technically…oh nevermind).  I’m talking about physical forces.  Gravity is a force.  Atoms are held together by various forces.  Pushing someone involves applying a force.  This is something that is highly applicable to fighting.

According to Sir Isaac Newton, force (commonly depicted with the capital letter ‘F’) is equal to mass times acceleration, or more succinctly: F = ma.  Much like distance, mass is another fundamental measure of the physical universe.  It specifically measures the amount of matter an object has.  Note that this is different from “weight”, which can change depending on the force of gravity (like on the moon).  I also want to highlight the importance of this concept by pointing out that the formula, F = ma, is the second of Newton’s three laws of motion (the first being inertia and the third being that every action has an equal but opposite reaction).

Vectors

Early, I said that displacement was like distance and velocity was like speed.  Vectors are what make them different.  Distance and speed are known as “scalars”.  They are represented only by a single quantity (5 meters, 55 miles per hour, etc).  Vectors, however, are represented by two quantities: magnitude and direction.  So, 5 meters might become 5 meters to the left.  55 miles per hour might become 55 miles per hour North. 

Understanding the concept of vectors is extremely important for fighting.  As you may have guessed, forces are vectors.  We don’t just push people.  We push them in a direction.

Conclusion

I realize that all of that text was really light on the fighting and martial arts, but just like studying any subject, you need to understand the vocabulary and base concepts before you can absorb any of the really good stuff.  The next post will be juicier.  I promise!

The Science Behind Martial Arts: Introduction and Purpose

What is this all about?

I love martial arts, and I love science.  I also love teaching, and I believe that by looking at martial arts from a scientific perspective, I can teach people to become proficient in martial arts in relatively little time.  Now, when I say “science” I’m not talking about vague claims about “power” and “speed”.  No, I’m talking about the details: formulas, vectors, integrals, solving equations, etc., and how understanding those things can quickly help anyone to master the art of fighting.  By applying some established knowledge from various areas of science, you can take a shortcut to martial mastery.  Skip all of the stuff that is provably ineffective, and focus only on things that can be scientifically shown to work.

Could you achieve the same effectiveness the “old fashioned way” by just practicing a lot?  Yes.  However, most people don’t have the time for that kind of trial and error process, and even then many of them are simply parroting what they’ve been taught and don’t understand why a technique works or how to modify it for a new situation.  I advocate that understanding the scientific principles behind martial arts will allow you to progress more quickly and become more adaptable in a fight (competitive or defensive).

Why should you listen to me?

I’m generally not a fan of touting my own skills and credentials, but seeing as how there is an ocean of self-proclaimed experts to choose from and I really believe I have some valuable information that I want people to devote their limited time and attention to, I see no alternative.  So, let me explain why I’m qualified to talk about both martial arts and science.

I started doing Taekwondo (TKD) and Judo back when I was 9 years old.  I did it for a few years, then stopped for a few years, then I started again (back at white belt, though I really shouldn’t have…my choice) and got up to brown belt.  I did TKD on and off throughout college, getting approximately 5 total years of practice under my belt (I’m an engineer…bad puns are required).  After college, I joined a Hapkido school that also taught a fair amount of ground fighting.  I was there for two years and did A LOT of sparring.  Black eyes, bloody noses, and split lips were the norm, and I loved it.  I would have stayed with that school, but I moved out of state and got involved in another school.  This school claimed to practice “reality-based” martial arts.  There was a lot of grappling, weapons, street tactics, trapping, and the like there.  Eventually, I left to start a dojo with a friend where we emphasized modern fighting tactics with influences from traditional ninpo taijutsu.  My “style” has evolved to be anything that works for me.  I take what’s useful and ignore the rest, which makes answering the question, “which style do you practice?” a somewhat difficult one to answer accurately in any short span of time.  In any case, I’ve been doing modern reality-based fighting for the last 8 years or so.

As far as ranks that I’ve achieved that are worth mentioning:

•       Level 11 in the Scientific Fighting Congress (SFC*) Unarmed program (equivalent to 2^nd degree black belt)
•       Level 11 in SFC Knife
•       Level 10 in SFC Pacific Archipelago Combatives (PAC), which includes a lot of Kali and Silat and fighting with two weapons in hand
•      4^th degree black belt in tactical ninjutsu (which focuses mainly on taijutsu, Filipino martial arts, Silat, and JKD)

(There are a number of honorary ranks I have received as a result of several of the above as well as a collection of certifications for various systems that I’m now certified to teach, but that’s not the point.  The point is that I am qualified to train people in the use of their hands, knives, and sticks, award them black belts for it, and have their black belts be recognized by an international organization [http://www.forcenecessary.com/fighting-instructors/us-sfc-combat-instructors-2/].)

I've also done some training with JKD instructor Tim Tackett, and I draw most of my JKD drills and techniques from his teachings.

What about my scientific credentials?  While not as impressive as the above (or at least, I think so), I do have some experience with science.  First, I have an engineering degree from The Ohio State University (with extra emphasis on the “the”… it’s required). I got good grades.  I also took ridiculous math classes that the orientation people said that engineers had no business taking, which of course meant that I had to.  I’ve also spent the last five years tutoring high school and college kids in math and physics.  I’ve tutored math from algebra 1 up to multi-variable calculus and differential equations.  I’m comfortable with physics up through college level electricity and magnetism, though that particular topic won’t be necessary for what I’ll be covering here.  The point here is that I’m very comfortable with classical mechanics -- comfortable enough to teach other people how to do it.

I’m also very logical, almost to a fault (actually, my wife would probably argue that I make it all the way there ;-) ).  I like deconstructing concepts and finding the common elements in order to better categorize a topic.  My degree is actually in computer science and engineering.  So, much of that desire for structure and abstraction comes from my software engineering skills.

Combining all of these things, I’m in a fairly unique position to deconstruct, simplify, categorize, and communicate the essentials of martial arts/fighting.

But aren’t “martial arts”, you know, an art?

Yes and no.  It’s really just like anything else.  Seeing the science behind the art is a matter of comprehension.  From a casual observer’s perspective, all martial arts might appear to be more art than science (or maybe just pure chaos!), but that’s only because they don’t see the structure and principles at work.  Once those principles are understood, what used to seem like chaotic motion of fighters becomes structured and predictable.  Is that to say that there’s no “art” aspect to fighting?  Not at all.  I’ve tried my hand at many skills in the past and was proficient, for a time, in most of them.  However, martial arts is the only one in which I would label myself an “artist”.  What do I mean by “art” though?  I define “art” as a means of self-expression through a medium.  In my case, I can express myself through fighting.  I can be playful, angry, happy, sad, or just about any other emotion and have that emotion come out in the way I fight while still being effective.  After expressing myself through fighting, I could then scientifically analyze what I did and demonstrate all the scientific principles at work to other people.  The science of fighting is the toolbox and raw materials.  The art is the house that you build with them.  Rather than showing you how to build pre-designed houses, I’ll show you how to apply the tools to design and build your own house.  I’ll show you how to apply scientific principles so you can practice a style of fighting that works for your body.

What not to expect

Don’t expect me to trash particular fighting styles or systems or to provide any sort of hierarchy of effectiveness for different arts.  All systems that have been around for any significant amount of time have survived for a reason.  It’s important to know what those reasons are, both so you know when to apply the art and when NOT to apply the art.  I’m not here to step on toes.  I’m here to show you the principles that apply to all fighting, regardless of system or dogma.  People should be able to take this information and apply it in the art that they practice to become more effective.

That being said, I’ll probably criticize certain generic dogma here and there, but the goal will be to help people understand different arts better, not to try to change them.

What to expect

Since science is the main driving force (ah, the puns) behind these writings, things will get a bit nerdy.  I’ll do my best to separate out the really nerdy stuff from the application, but seeing as how I love both martial arts and science I humbly request that you read through the nerdy parts.  Martial arts is as much, if not more so, a brain activity than a physical activity.  So, it’ll be good for you.

Expect to see principles from math, probability, classical mechanics, engineering, physiology, sociology and psychology.  I’ll cover striking with all parts of the body (hands, feet, forearms, shins, elbows, knees, shoulders, hips, torso, and head).  I’ll also cover joint locks, throws, grappling (both standing and on the ground), weapons, multiple opponents, surrounding environments, essential fighting attributes and anything else that might come up in a fight.

This is going to be fun!  I have a huge list of topics that I want to cover eventually, but if anyone has a particular topic they’d like to see, just send me a message and I’ll see what I can do.

*  Hock has decided to rename his SFC program to "Force Necessary".  This is largely because he is tired of the overuse of the word "combatives" (even though he was the one who drove the word to popularity in the first place).  I prefer the SFC name...for the "science". :-)