PHYSICS OF KARATE

A cure for a headache? What kind of forces are required to break rocks, bricks and boards and
how does this karate instructor break these tiles with his head without injury?

I began my career in Kyokusin Kai karate at the Black Eagle Federation Dojo and also as an astronomy lecturer at the Hansen Planetarium in Utah. Through time, I ended up in the geological sciences and also in Shorin-Ryu Karate and Kobudo. I was fascinated by physics but rocks became some of my best friends, whether I was out collecting them to break with my hands, or studying them to find a new gold, diamond or colored gemstone deposit..

In many of my classes, I like to refer to Sir Issac Newton and his formulas. Particularly F=ma²  (force equals mass times acceleration squared). To generate force in our punches and kicks, we must try to find ways to increase our acceleration as our mass is going to be constant. But there are things happening to acceleration that most of us have a difficult time grasping.

For instance, a TV program, Stan Lee's Superhuman showed one individual who had incredible strength for his mass and could break hammers, wrenches, and even roll up frying pans with little effort just using his hands. Then there is the incredible martial art known as Juko-Ryu Kijutsu, where martial artists learn to develop incredible striking power along with accepting full-force strikes that extend way beyond the border of amazing. On Fight Science a couple of years ago, Dai-Soke Sacharnoski and Hanshi Kirby Roy of Juku Kai International demonstrated this amazing art. Somewhere they found a giant MMA practitioner who was 6'8" and weighed 280 pounds who agreed to hit Kirby in the throat with a shuto (edge of hand). The measured force of the strike to the throat was 650 pounds - it should have crushed his windpipe, but it didn't do a thing to Kirby. Then he kicked Kirby in the testicles (no protection) and Kirby accepted the kick with absolutely no effect (1100 pounds of force, more than 1/2 ton!) and all it did was hurt the MMA practitioner's leg. How?

Shitai Kori (body hardening) at the Gillette, Wyoming dojo.

Florin Diacu discusses the forces of a traditional karate punch in an article “On the Dynamics of Karate” and answers some of these questions providing some very interesting concepts supported by physics. According to Diacu, the energy generated by a punch (zuki) is best examined using the following equation:

E_T = E_P + E_K + E_R

Total energy = potential energy + kinetic energy + rotational energy

Which can be written as: E=mgh + 0.5mv² + 0.5mr²w²  

This formula considers potential energy, kinetic energy and rotational energy generated by a zuki.

Here, m is the mass used during punching, g is the gravitational constant {32 feet/second² (9.8 m/s²)}, h is the difference in height from the initial position to a position where the zuki strikes its target {when stepping forward the body may drop 6 to 8 inches (15 to 20 cm) while delivering a punch according to Diacu}, v is the velocity of the fist, r is the radius of the fist, and w is the angular velocity of the fist’s rotation (something that is uniquely characteristic of a karate punch).

First, it should be obvious that the larger the person, the more powerful the punch as long as all other factors are the same (which they are not, but its an assumption that we need to consider). Thus, the greater the mass, the greater the potential energy (energy increases linearly with mass).

Soke Hausel accepts a full force kick to groin
at University of Wyoming half-time. The force
of this kick was estimated at several hundred
pounds of pressure - so how do traditional
Okinawan martial artists survive these feats? And
how can he smile? This martial art was created
by Dai Soke Sacharnoski of Juko Kai International

So let’s use a subject, a karate-ka we will call 'Toshio'. If Toshio is twice as heavy as another karate-ka by the name of Miyagi, then Toshio has the potential to produce twice the amount of energy as Miyagi based on this single variable. That is quite a difference, particularly if Toshio spent a lot of his past time in the dojo training rather than in front of the TV eating snacks.

However, we do not put all of our mass into a punch, and the mass of the punch may better be represented by the mass of one’s arm. Since a typical arm is only about 10% of our body weight, this dramatically decreases the amount of mass used in a punch (this is a simplification – because when we use a proper rooted stance to the floor or ground, or move forward using much of our body weight in a punch by rotating our hips, this will also increase the energy of a punch). At the Arizona School of Traditional Karate we also try to get some of our body mass moving forward with strikes, or pull an attacker into our strikes to increase the mass variable. Even so, lets just consider the arm as the only mass that is involved in a punch. Now we will assume that Toshio weighs 155 pounds and Miyagi weighs only 100 pounds (both of them gave up snacks and starting training regularly in the dojo), then Miyagi must punch only 18% faster to achieve the same force as Toshioka learns through proper technique to get more mass into a punch with proper hip rotation as well as by moving his/hers body forward with the punch.

(2) The lower the drop, the greater the energy, by remaining at the same height (h) when punching will result in energy conservation. This is one reason why we work hard in karate to keep our shoulders at the same height while stepping forward. This relates to the first part of the formula, which considers potential energy, which is a substantial source of energy since it considers the entire mass of the body.

 (3) The greater the velocity, the greater the energy. The greater the velocity of the fist, the greater the amount of energy generated. This is very important in that velocity quadratically influences energy (by a factor of four)! This means that if Toshio and Miagi have the same mass and Toshio’s punch is twice as fast as Miagi’s, then Toshio can produce 4 times more energy with his/her punch! This is one of several reasons why karate punches and kicks are so effective. When breaking rocks and boards, maximum velocity is achieved at the point of impact producing maximum force. Based on high-speed movies taken of black belts at Cleveland State University the average speed of their punches was about 23 feet/s (7m/s).

(4) The effect of fist rotation is negligible. The effect of fist rotation is negligible in increasing the overall energy of a punch according to Diacu.  This is not surprising as the purpose of the rotation is primarily for efficiency of punching and for linear movement in order to obtain the greatest possible velocity over the shortest amount of distance.

To show the effects of fist rotation (rotational energy), Diacu describes a person weighing 155 pounds. This black belt will have arm weight of 15.5 pounds, an average punching speed of 23 feet/second at the point of impact, a fist rotation of 5 π rad/second (the fist rotates 180^O in 0.2 seconds), a fist radius of 1.2 inches, and a drop in height of about 7.9 inches which will result in

E_P (Potential Energy) = 137.2 J (joule; 1 J=0.239 calories) {100 ft-pounds}

E_K = 171.5 J {130 foot-pounds}

E_R= 0.78 J {0.58 foot-pounds}

E_T=309.48 J {228.3 foot-pounds}

This shows that rotational energy accounts for only 0.25% (one-quarter of a percentage point) of the total energy – a very small amount!

(5) The greater the distance, the greater the time. This should be obvious that it takes more time to travel a greater distance. This implies that a person’s punch can reach its target faster than a kick due to the shorter distance that it needs to travel.  However, kicks can generate more power. The leg, which is longer than the arm, has more mass and a little more time to accelerate. A leg may weigh as much as 20% of the body mass.

According to Diacu, a typical black belt’s zuki may have a velocity of 18.7 to 32.5 feet/second (5.7 - 9.9 m/s), whereas a typical mae geri may have a velocity of 32.5 to 47.2 feet/second (9.9 - 14.4 m/s), a shuto 32.8 to 45.9 feet/second (10 - 14 m/s), maewashigeri 31.2 to 36.1 feet/second (9.5 - 11 m/s), and ushirogeri about 34.8 to 39.4 feet/second (10.6 - 12 m/s).

(6) Kicks may generate more energy than a punch For a person of 155 pounds (70 kg) may generate as much as 228.3 foot-pounds of total energy with a punch. But how much can this person generate with a kick?

Assuming a leg may be 20% of the total body weight. Thus for a 155 pound person, a leg is about 30.9 pounds (14 kg) and a good kick may have a velocity of 39.4 feet (12m/s). Thus the kinetic energy of the kick alone is 743.5 foot-pounds (1008J). This is more than 4 times the kinetic energy of a punch by the same black belt. 

Uncle Al – Sketch by Soke Hausel.

 Conclusions. So why don’t we use more kicks than punches?  The distance is shorter to the target using a punch, kicks are also more difficult to sight on a target, they are easier to avoid, and if properly done, some punches can generate a tremendous amount of knockdown power when done correctly with the right amount of snap, focus, hip rotation, and balance. 

At out dojo in Mesa Arizona, our Arizona School of Traditional Karate, we teach traditional martial arts for adults. No person and in particular, no woman in the Phoenix valley should be without self-defense training – it is dangerous here. And with democrats running around, one must be prepared for anything. You can find out more about us by visiting our dojo in Mesa and learning about our international martial arts association. We practice traditional karate as it has been taught for the past few hundred years in Okinawa, we strive to be the best people we can be, learn some Japanese, focus on traditions of the dojo and Budo, and strive to meet interesting people and have a great time sharing our art.

Our training center is open to the public - we focus on Adults and Families. Come learn the traditions of Okinawan Karate & Kobudo. Much of the class is conducted in both Japanese and English to help students learn Japanese. We also teach meditation, philosophy and martial arts history interjected in karate classes. Check out our class schedule and join us in our pursuit of force and karate.

Teaching a little Karate, Physics and Geology at the University of Wyoming.