Science concepts: shear force, moment of inertia, F = ma, torque, anatomy
“Repeat after me,” said the second highest ranking black belt instructor in my taekwondo school. “I am a legend...” We all repeated, but he continued. “…in my own mind.” He paused to let us finish repeating his statement. His point was that we viewed ourselves as spectacular fighters, as I believe many martial artists do. A lot goes well for us in our mental theater when beating down our imagined opponents. Or maybe it’s just me, but I doubt it. In our day dreams, our strikes all have devastating effects on the bad guys, but the fact of the matter is that running parts of your body into certain parts of other people’s bodies can really hurt you. Here, I attempt to address some of the more common ways that martial artists hurt themselves on other people. My assumption is that if you enjoy martial arts the way I do, then you’re hoping to be able to continue practicing when you’re 70 years old. As a side note, I went to a Dan Inosanto seminar a few years back. Despite him being 70+ years old, I’m pretty sure he could still whoop me. So, let’s look at a bunch of wrong ways to do martial arts and how we can train for longevity.
Let’s Take It From The Top!
I have to start somewhere and a top down approach is as good as any.
One of the techniques of choice for fighting soccer players everywhere, the headbutt can be a devastating strike but not just for the recipient. Sure, the skull is shaped well for structural integrity. The likelihood of you breaking your skull from impact against another person is slim. The skull isn’t what I’m worried about. I’m worried about the brain. You know…that (roughly) three pound organ inside your skull that RUNS YOUR ENTIRE BODY. The reason your skull is so great at distributing force is because protecting your brain is critical to your well-being and your survival. That doesn’t mean that you should use it as an impact weapon.
Let’s look at the science. Anatomically, the skull is not perfectly smooth on the inside. There are little jagged edges. They’re small…but jagged. Now let’s consider the physics of the headbutt. You thrust or swing your head towards the target, accelerating your skull and brain up to max speed over a “large” distance (3 to 18 inches). When you make contact, your skull decelerates from its max speed back down to zero in a couple centimeters. This spells bad news for your brain. Imagine that your skull is a car and your brain is a baby in a car seat that’s not strapped in. Smashing your car against another car is not going to go well for the baby. I’m going to stop the analogy there because the imagery is too gruesome, yet it is accurate. Your brain will splash (this is an official neurology term…brain splash) against your skull, which has those jagged edges. So your brain suffers blunt trauma and potential tearing.
“But I don’t feel any pain when I headbutt!” Yeah, there’s a reason for that. While the brain may be made up of nerves, not all nerves are designed for feeling touch sensations. There are no pain receptors in your brain. This is good and bad. It’s good because that way you won’t get a tickly sensation every time you turn your head. It’s bad because you can bludgeon it and not realize that YOU’RE GIVING YOURSELF BRAIN DAMAGE. Heck, one of the ways to knock someone out is to give them that brain splash. When you headbutt, you do that to yourself.
Here’s a tip: don’t ask the brute of a martial artist that has been smashing his head against things for years about headbutting, ask a brain doctor.
My advice is to avoid putting your brain into a highly accelerated or decelerated frame of reference.
The elbow is a very hard part of the body, which is what makes it such a great striking tool. Some arts, like Muay Thai, are known for their myriad elbow strikes. It’s a great blunt instrument, but it comes with caveats. Some people might say that “the sharper the striking surface you can use, the better.” Typically, I’d agree, but not in the case of elbows. To illustrate why, I have a personal story to share.
Years ago I was spending a lot of extra time at the dojo. We had some 180 pound, tall heavy bags that were great for striking practice. I was doing a lot of elbows, striking with the point of the elbow for maximum pressure on the target (Pressure = Force / Area). In class, we were also working on ground fighting, which meant that my elbows often rubbed against the ground. All of this contact on the tip of my elbows began to agitate my bursa. Prior to this incident, I didn’t even know bursa existed.
|The bursa is a gelatinous cover over the tip of the elbow|
When my elbow began to look like it swallowed a golf ball, I decided to look it up. The swelling after class was at least an inch (no exaggeration) above where my elbow should be. Much like this:
I waited several days for it to go away on its own, but it didn’t. It was terribly painful and was disrupting my sleep. I ended up going to the emergency room. They drained it with a syringe and gave me some antibiotics (which actually resulted in another crazy story…but for another time).
Needless to say, I changed the way I did elbow strikes. Rather than striking with the tip, I strike with the final inch or two of my ulna bone or with the very bottom of the tricep tendon area when doing downward/backward elbow strikes.
After doing some searching online for “bursitis” I learned that plumbers often get bursitis in their knees because of all the rubbing from crawling under sinks. If you want to train for longevity, don’t irritate your bursa. By not striking with the very tip of your elbow, you also get the added benefit of reducing the risk of chipping a bone, which thankfully has never happened to me but it does happen.
Fists seem to be the weapon of choice for unarmed combatants. Despite the commonality of punching, it’s actually somewhat difficult to do correctly. In Hock’s Unarmed Combatives program, punching doesn’t show up until level 5 (level 10 = black belt). It’s preceded by finger strikes to the eyes, forearm strikes, elbow strikes, and hammer fists. Punches have a relatively small margin of error regarding structure (link to structure article) because of all of the joints involved.
But let’s put all of that aside for the moment and assume that you can perform a punch perfectly. Things can still go badly for you if you hit the wrong target. For a large number of psychological and sociological reasons, people like to aim for the head. There’s some wisdom to taking out the head in a fight. However, remember earlier when I talked about the skull’s ability to absorb force well? Yeah, that’s going to work on your fist if you hit the hard, immovable part. Just look at the anatomy here: fist vs cranium.
Domes are basically meant for distributing force. So, when the comparatively tiny bones of your fist slam into the bone that protects one of the most critical organs of the body, things go badly for the fist. Just do an image search online for “boxer’s fracture” to see what kind of goodness awaits the fist swinging head hunter.
The fist is a great weapon. Just don’t run your fist into anything structurally stronger than it and you’ll be ok.
Knee strikes are actually, for the most part, safe to do. I’m really only thinking of one particular knee strike, which is somewhat rare. Although, all of that stuff on saving your bursa applies here too, though your knee is likely to be much sturdier than the elbow. The strike of concern is the one where the knee is swung from the outside/open position to the center, which uses the medial (inside) part of the knee to strike. To see why, look at this picture of a knee.
When striking this way, you’re smashing the medial collateral ligament (MCL) against the target. That’s bad all on its own. Speaking of knee ligaments, the torque put on the knee happens in a direction that the knee isn’t meant to go. Forward/backward movement for the knee? No problem. Side to side? Not so good. Also look at the cartilage. When the knee impacts something sideways the tibia and femur will put a shear force on the meniscus. The meniscus is designed to be squished not sheared.
Without good, healthy knees your martial arts options are very limited. Take care of them.
Shin to Shin
I, like many people, was looking forward to the rematch of Anderson Silva against Chris Weidman. The first time was a bit of a fluke because Silva got too cocky. With skill like his, he can afford to be fairly cocky. He just went a bit too far. I figured that the loss would make him come back as fierce as ever. No more toying with his opponents. He had something to gain by winning this time, and it showed. He was intense, pressuring, and fast. Unfortunately, he was a bit too fast. I knew what happened before he even set his foot down after the kick. I’d seen that motion before. It was the motion of a foot and knee out of sync. Sure enough, Anderson Silva snapped his shin. It was empathetically painful and heartbreaking all at the same time. I wanted to see what he could do, and now I probably wouldn’t get the chance.
Now, like I said, I’d seen this kind of break before, but the break got a lot of media play because it was Anderson Silva during a title fight. So, people talked about it, and it got me thinking. “What happened to cause the break?” I searched for videos of leg breaks and compared them to Silva’s. I found a common element. You might think it has to do with the way the defensive shin is raised, but that defense doesn’t result in a break more often than not. No, the common element in the breaks was in the kick. Every single instance of someone breaking their shin was because they didn’t rotate their support foot. By not rotating the support foot (I can just hear my TKD instructors shouting at me now…”PIVOT!”) the hips can’t rotate over, which means the kicking shin moves roughly at an upward 45 degree angle putting the flat of the kicking shin against the edge of the defensive shin. That is the key factor in whether or not the shin breaks.
Imagine taking two equal length 2x4 planks of wood and hitting the thin edge of one against the wide edge of the other. Which do you think will break, if any? The wide edge will lose every time. This is due to bending stress. The maximum bending stress that a particular object can endure before undergoing irreversible deformation is of particular interest to us. A wire hanger is fairly springy, but if you bend it too far then it gets stuck that way. Bones are similar, but they’re not as springy. The maximum bending stress that an object can undergo depends on what it’s made out of and its dimensions relative to the load being applied to it, but enough of defining terms…
There is A LOT of math that goes into these formulas and I can already feel your boredom creeping in. So, I’ll get to mathematical punchline. The formula for bending stress experienced by a material is:
s = M y/Ix
M = The bending moment at the load point
y = The distance to the neutral axis
Ix = The second momentof area about the neutral axis
M and Ix have further formulas to break down into. The formula for M is based on Hooke’s Law and expands to different things depending on the situation. I’m going to assume that the shin can be approximated by a cantilever beam with the “fixed” point being the knee.
Mmax = dF
F = The load force being applied
d = The distance from the load point to the fixed point (the knee)
I will assume that the shin bone can be loosely approximated to have a rectangular cross section (a wide side and a thin side). For our situation, the load is applied parallel to the height.
Therefore, Ix comes out to
Ix = wh3/12
w = The width of the rectangle
h = The height of the rectangle
Now, this formula for Ix is where my intuition comes from. Notice how only one of the directions gets cubed? That means that one direction is more important than the other for determining bending stress.
The final piece is the ‘y’. The neutral axis is going to be near the middle. So, we can say that y = h/2. Putting it all together we get
(My apologies for the ugly notation...re-writing it by hand might make things easier to read if you actually care to see what's going on.)
Whew! Ok, what does all of this mathematical and engineering craziness tell us? Let’s handle the numerator first. We see that the higher the load force, the more bending stress there is. That makes sense. We also see that we get more bending stress the farther from the knee we hit. This makes sense if you think of the load as a torque that uses the shin as the effort arm. Now for the denominator we see the dimensions of the rectangle/shin. As elements of the denominator get bigger, the bending stress gets smaller. That means that thicker objects experience less bending stress. This makes intuitive sense. The interesting thing is that the height, which is the amount of material the load force is trying to push down through, has a bigger impact on the bending force by a power of 2.
So, now imagine two similarly structured shin bones hitting each other (like the 2x4 example) where the wide side of one hits the narrow side of the other. The formula tells us that the one that impacts on the wide side will experience a greater bending stress. If that bending stress gets too high, then someone isn’t walking home.
What’s the lesson after all of that pontificating? Well for one, don’t kick people in the shin with your shin, but if you do use the narrow edge of your shin by rotating your support foot.
Top of the Foot
The advice on the fist vs skull issue applies here, for sure. Definitely don’t kick people in big, hard bones with your dainty little meta-tarsals if you don’t want a swollen and/or broken foot. That being said, there’s something else to be careful about when kicking. This is a lesson I had to learn the hard way. The learning came slowly because the injuries were never so bad that they lasted more than a few days. Eventually though, I became wise enough to stop hurting myself with my kicks.
In my five years of TKD, we focused a lot on the round kick. Being a 6’ 4” lanky guy, I was able to use rotational inertia and angular momentum to my advantage for firing off hard and fast round kicks. I was trained to use the top of my foot as the weapon “for maximum reach” I was told. That works great in theory, when kicking into the air, and when pulling your kicks in point sparring. Where it doesn’t work is on a heavy bag or an opponent that has decided that blocking your kick by meeting it with direct force. That’s a fact I discovered on several occasions, resulting in slight sprains.
Let’s think about this. I’m told to point my toes to avoid breaking them on contact. That’s good advice but doesn’t go far enough. By pointing my toes, I extend all of the muscles on the front of my lower leg. When the top of my foot hits a target, Newton’s 3rd law of motion comes into effect. The strength of my kick is received in full reaction back to my foot, and since I’m making contact on the top of my foot it torques my ankle to extend even further than it already is. The ankle only goes so far before the ligaments get sprained. Now, the body has a built in way to reduce this kind of torque on the ankle. It’s the muscles on the front of the lower leg. You know, the ones that I extend for the kick, preventing them from flexing? Yeah…I sort of dug myself into a hole with that one. The problem is even worse for me because my feet are so big that I provide an even longer effort arm for the torque. Maybe small footed people don’t have this problem.
Gaining an extra six inches or so on my kick is great and all, but I feel that the negatives outweigh the positives. Kicks that contact at the top of the foot are at a slight disadvantage because the ankle gives way during impact, increasing the time of impact. It would be better to make contact with the bottom of the tibia. That part of the bone is HUGE by comparison to the meta-tarsals. All of that stuff above about bending stress can be used in your favor if you use the right part of your body, and either end of the tibia works fantastically.
Well, that was a lot of text. Hopefully, the physics, engineering, and anatomy references were enough to convince you to refine your techniques to avoid hurting yourself when you strike. And if that isn't enough for you, then take my personal history of injuries as anecdotal evidence of how NOT to do things.
Here’s the TL;DR summary:
- Don’t use your head as an impact weapon
- Be nice to the bursa on the tip of your elbow
- Don’t punch the head unless you can hit at the nose or below
- Don’t use the inside part of your knee to strike
- Don’t hit with the wide part of your shin; rotate your support foot for proper form
- Don’t smash your feet into hard targets; prefer the bottom of the tibia for kicks