Karate Motion Efficiency Analysis
In this article I would like to describe the proposed title in view of the science of physics. The article will always give examples using 2 martial artists in action. When we deal with 2 martial artists for motion efficiency analysis (KMEA) we have several physical properties to deal with, such as: Force, momentum, impulse, torque, displacement, power, energy, work, mass, inertia, velocity, lever and so on.
In order to describe and categorize the KMEA, I will start with some basic definitions. One of the most important physical property is the force of a human being which is measured by the mass of the participant and multiplied by the acceleration of force (F = ma) or kg(m/sec2). The force is measured in Newton. 1 Newton (N) = 1 kgm/sec2).
Newton 2nd law of acceleration which states that when a body is acted on by a force, its resulting a change in momentum which takes place in the direction in which the force is applied, and is proportional to the force causing it, and inversely proportional to its mass. Change in velocity means acceleration or deceleration by a force which was applied.
In this case we are talking about a new physical property which is the momentum. The momentum (p) = mass x velocity or kgm/sec where m/sec represent velocity in case of linear motion. In case of rotary motion the equation is: L = Iω or I = kgm2/s and ω = rad/sec or (θ/sec). Where the “L” represents the angular momentum, the “I” represents the moment of inertia (angular inertia) the “ω” represents the angular velocity, “m” represents meter and “rad” represents radian, “θ” represents angle of a circle. The momentum represents the amount of motion possessed by a moving body. Thus, a body’s momentum can be changed by altering either its mass or its velocity.
Another important physical property is the impulse = force x time (J = Ft). In physics we talk about the impulse of force for a given time interval and is equal to the change in momentum produced over that time interval, i.e. J = m(vf - vi) where m = mass, vf represents the final velocity and vi represents the initial velocity. This impulse and momentum relationship derived from Newton’s second law. In sports there are two different impulse.
1. Controlled impulse refers to the muscle effort and bone leverage, as with the kicking leg. 2. Transmitted impulse occurs when, for example a karateka is about to take off for a flying side kick. The take-off leg acts against the floor, but the magnitude and direction of impulse is determined by the free arms and leg, and not through the take-off leg. The next physical property is the torque (T) or (Г) (moment of force or just moment). The torque is a force which produces a twisting or rotary motion about an axis of rotation. This force is related to the angular or rotational motion. Defining torque or moment by mathematical terms is the same; however, there is a little difference about understanding exactly the two terms.
Torque typically refers to the twisting motion, whereas moment is related to the bending or rotational action of a force. Torque (T) = Fd or Newton x meter (Nm) where, F represents the applied force multiplied by perpendicular distance (d) from the axis of rotation to the line of force action. The perpendicular distance is known as the torque arm, moment arm, or lever arm (). Fig. 1. Show different class levers.
As you can see in the first class lever the fulcrum is always between the effort and the load, resistance (weight) or gravity. The fulcrum is not necessarily must be exactly in the middle of the lever. In human mechanics the effort is represented by a muscle group in contraction. The weight can be represented also by a muscle group or by the gravity.
In the second and third class lever the fulcrum is always at the one end of the lever. In the second class lever the force arm (FA) is longer than the resistance arm (RA). In the third class lever the RA arm is longer then the FA. Second class levers are used for force. Third class levers are used more for speed.
Displacement is another physical property which is a vector quantity and refers to the distance where an object moved in a given direction. It is measured as a length of a straight line between the initial and final position. In karate we speak about distance instead of displacement which is strictly related to velocity. Distance is related to the speed. The speed in karate is not related to the distance, but is related to the timing e.g., how fast somebody can kick or punch an opponent.
Let’s analyze the following physical properties which are strictly related to each other such as; Power, Energy and Work. We can hear words from instructors or even athletes such as; hit with more power or you do not have enough power etc. We seldom hear the word force, why is this? Here is the explanation. Recall that force is an agent which can alter the state of a matter by pushing, pulling, twisting, sliding etc., and this agent is the product of the mass and acceleration. Power (P) defined as “the rate at which energy is expended or work is done.
The amount of power (P) delivered by a person depends on two components; force and velocity or speed (P = Fv). In other word if you have force which you do, and you have velocity more or less then you have power. In this way when an instructor says put more power in your hit, he/she meant, put more force or speed in your action. By the way force is almost omnipresent in any physical activity.
Recall that power is related to energy and work. Here we have another formula of the power which is: P = work/time. But how can we measure the work, here is the formula of the work (U) = F x displacement (s). The energy (E) =F x distance (d). As you can see the formula of the work and energy is very much interrelated and can be used almost unconditionally depending on the problem to be solved.
Speaking about energy, we know that there are many different kind of energy such as; chemical, electrical, light, wind, thermo-nuclear, water, and physical energy The linear kinetic energy (EKL) = 1/2 mv2 or kgsec2/2. The angular kinetic energy (EKR) = ½ Iω2. According to the law of thermodynamics, (conservation of energy), which states that in any system not involving nuclear reactions or velocities approaching the velocity of light, energy cannot be created or destroyed but can be lost. Yes you can lose or deplete your energy if you do not store the energy supply by the mean of meal and drink.
There are two kind of energy: Potential energy which is a stored energy in a body or system. The other one is the kinetic energy which is the energy of motion, which is defined as the work. So where is a motion such as a wind blow, the water fall, the karateka kick, and the chemical composition with its atoms and molecules that are in permanent motion there is a kinetic energy. In karate we deal mostly with kinetic energy. The kinetic energy comes from the potential (stored) energy.
Let’s give some examples about kinetic energy where the energy can be transformed. For example, a karateka will use chemical energy that was provided by food to hit and kick faster and to resist against tiredness during a long fight. If we do not take in consideration the friction of his feet against the floor he probably can maintain his speed during the entire bout. His energy has been converted into energy of motion (kinetic energy), but also his body just created heat energy by spending his calories. Supposedly who has a bigger mass probably has more energy using more calories to work etc.
I guess by now everybody with a little education knows about mass, inertia and lever arm. The question now is which physical property is the most important for a karateka to be efficient? How to analyze and when to put it in action to be most efficient during a sparring or a real fight. In the next pages I will give some indication purely by mechanical rules neglecting the most important factor for the victory which is the tactical preparation/actions before and during fight.
Calculations by the Newtonian (classical) mechanics.
Using any examples in biomechanics we use mostly Newton laws. Example 1: Calculate the kinetic energy (EK) of a 70 kg mass of karateka kicks from a natural position (both legs are parallel to each other) at 4 meters per second. (An expert karateka can even kick with a speed of 10 to 14 m per seconds). The distance is not specified and the speed has been registered as an average speed. We use the equation of EK = 1/2mv2. ½ (70kg) x 4 m/s2 = 560 Joules (the unit of measuring energy) or (N-m). (The kicking distance usually is about 95 cm or a little bit more than 1 meter).
Where should a good instructor concentrate when he uses biomechanical examples to give his students for the technical improvements? Recall that the beginning this article I mentioned about so many physical propertied. Here is my advice. Some physical properties are more related to each other such as momentum to impulse and work related to energy and to power. In this way the instructor can establish a very good reference method for examples. Also the karate instructor should know which physical property has the priority over the other(s). In karate the most important physical properties are and here I name just few:
Force, mass, speed, momentum, impulse and kinetic energy. Karate is practiced mostly with linear motions such as; straight front arm punch and the front kick. Even the roundhouse kick is somehow linear. Understanding the attack as a linear execution means that the opponents try straight contacts and do not turn away from the opponent as a diversion. Also there are no large movements such in Aikido, where half of the motions are angular.
In the following I will describe 4 kind of situation in dealing with karate motions: Nr.1. Two karateka is mostly in standing position and are very close to each other (they can touch each other simply by extending their arm’s or leg’s) Chika-ma in Japanese. The word ma = distance.
Nr. 2. Two karateka are farther from each other. The attacker must take a small step in order to reach his opponent Uchi-ma. Nr. 3. Two karateka are even farther from each other To-ma in Japanese. Nr. 4. One karateka grabs the opponent’s kimono in order to off-balance his opponent during a leg(s) sweeping execution.
Let’s analyze each possibility: Nr. 1. In this case the attacker (Tori) has the advantage by using correctly the impulse momentum-relationship. In this case the tori to be successful in his attack must create a large force using a very short time which will be possible by the short distance. By the way this kind of execution is the so said kime or focus in karate.
If the karateka use a longer time the speed will be maximum and in this way the force used could be less. By the way using a very high speed the impact will be devastating. Force will has less importance, because the speed will be maximum. At the time of impact the tori should withdraw his arm immediately; in karate terms is called a Snap-Punch which will create the most devastating effect. Why is this? Because the impulse required bringing something to a ‘stop’ and then, again in effect “throw it back” is much greater than the impulse which require merely to bring something to a stop.
Let’s examine Nr. 2. Uchi-ma positions. Because the distance is larger there is a possibility to accelerate the speed. The karateka must use his mass with acceleration (F = ma).
Example Nr. 3 where the distance is even greater. Any of the opponents should use a large step in order to be at punching or kicking position. Here in this example I use the possibility when both karateka simultaneously attack each other then;
A. Punch or kick each other.
B. One is the attacker (Tori) and the other one is defender (Uke) which counters at the same time with the attack.
What can happen in this case in terms of biomechanics? A) Both will have probably a large momentum (mv) and one which has the larger momentum either using the mass or the velocity will hurt the other one. In this situation we cannot talk about impulse (Ft), because they have approximately the same time of reaching each other for the impact force. B) In this case the tori must have a better impulse by using a longer time for the impact. The uke must have a shorter time for a better impulse which creates a better use of his force.
The following paragraphs will describe the force and time relation related to impulse. The importance of creating as large an impulse as possible is evident in the case of a baseball pitcher. The pitcher uses the longest time over which to apply the force to the ball before releasing it. Another example in baseball is the hitter which is often encouraged to follow-through when striking a ball. We can find the same example in tennis.
High speed films of the collision between bats/rackets and ball have shown that the act of following through serves to increase the time over which collision occurs. Surprisingly this prolonged time for hitting, favors not the force of the impact between the ball and the bat rather favors the change of the velocity of the ball. These two examples are more important for acquiring distance than impact force.
In karate however is a different story. The karateka must favor force over time. Where the force is larger and the time is shorter the impact will be devastating especially when the punching arm will be withdrawn or bounced off.
The withdrawn arm or in karate term Snap-Punch is which creates more devastating effect on the opponent. To demonstrate the time and force relations who are inversely proportional the following table will demonstrate this.
Let’s say we need to inquire 100 N for the maximal effect of a blow/throw/push.
|F x||t =||J|
|Force (N)||Time required||Acquired impulse|
|100 N||1 sec||100 units (max.impulse)|
|50 N||2 sec||100 units (max.impulse)|
|25 N||4 sec||100 units (max.impulse)|
|1 N||100 sec||100 units (max.impulse)|
Now let’s analyze a little bit the kinetic energy (EK) of both karateka: We use the equation described before in this article ½ mv2. Example Ba: related to the tori which have a mass of 70 kg and a velocity of 2.5m/s2. Then ½ (70) 2.52 = 218.75 Joules or N-m.
Example Bb: related to the uke; even he started at the same time and he is defending himself, the time for countering must be and will be shorter by focusing on his force in order to be effective. Uke’s mass 80kg, velocity is only 1.5m/s2. Then ½ (80) 1.52 = 90 Joules or (N-m). In the uke’s case the kinetic energy remains less than in the tori’s case. The tori still loses energy because the attack was diverted by the uke, by blocking and countering at the same time.
Example Nr.4. In this example where the tori grabs the opponent’s kimono in order to sweep the leg(s) of the uke many physical properties will be used. Here I enumerate them in order of importance in my opinion: 1. Distance 2. momentum (speed) 3. strength 4. balance 5. friction 6. leverage 7. impulse (minimal or non existent) 8. energy. This order of the physical properties can be different depending on the circumstances. I must specify that the speed, distance, balance and the lever are not physical properties.
Let’s describe a few words about each physical property: 1. Distance is primordial to approach the opponent’s safety space. Diverse feints and distraction must be use in order to grab the uke’s kimono. 2. Momentum must be used by giving priority to your velocity. 3. To use your strength in grabbing action to overcome a resistance of the opponent. 4. Using balance is two folded. Keeping your balance and the opponent’s balance for controlling him. Guiding the opponent in such a way to lose his balance.
5. Friction is always everywhere, when two forces act against each other and one is giving up by sliding. There are many kind of frictions, static/dynamic friction, rolling friction, sliding friction etc. In our case is the sliding friction is what happens. The tori’s leg which he uses for sweeping the uke’s leg must be very strong. 6. A karateka uses very seldom a leverage. Leverage cannot be used without contact to any other person or object. The tori has the opportunity to grab the uke’s kimono in different parts.
A. Grabbing on the collar is disadvantageous compared by grabbing on the sleeve. If you grab on the collar or on the shoulder, by pulling the opponent for losing his balance you have to deal with a large mass particularly the shoulder mass. By grabbing and pulling on the sleeve the task for off-balancing your opponent is easier, because you can maneuver easier a limb than a large body.
B. If you execute a sweeping technique without having contact on the sleeve, then the sweeping technique will be more difficult to carry out. In this case the tori must have a very good momentum and/or he must create feints which will induce the uke to lift up his front leg. By this way the tori can sweep uke’s both legs. The easiest case to sweep the front leg of the uke is when the weight proportion is more on the front leg then on the rear leg.
See the Fig. 2, a, b, c and d, shows the different kind of actions before and during foot sweeping. The impulse, has been described earlier, however again the kinetic energy will have an important role during fighting for a longer time period.
The following figures will show different levers such as First class lever and Second class lever.
Fig. 3. Represents 1st class lever where the axis is in the middle of the two forces (FA or effort arm and RA or resistance arm). At the 1st class lever the FA can be longer than the RA or vice versa in our case the FA is longer. Fig. 4. Represents 2nd class lever where the axis at the one end of the lever arm. In both cases the axis is at the coxo-femoral articulation of the karateka and is represented by a double large circle (O). The FA is always longer at the 2nd class lever.
For to better understand how this two different levers work it is important to describe some details about them: Interestingly the majority of the 1st class lever FA and RA acting mostly towards the same direction e.g., seesaw (both FA and RA acting downward towards the ground). In our case both forces act in opposite direction just like a scale working in an unbalanced position. The effort arm (moment arm) is stronger than the RA so the FA determines a rotation of the RA in the opposite direction. The shank and the thigh should work together as the FA (moment arm).
Looking at the Fig. 3. There are two “X” signs one is on the top of the shoulder and the other one is at the elbow pit. Recall that I mentioned if you use the grabbing position at or on the elbow pit the sweeping technique will be more successful. Another problem can occur if you grab the sleeve at the level of the wrist and try to pull to off-balance your opponent, you may not succeed because your opponent’s lever arm (RA) will not act in unison with the upper part of his body. In other words you will move only his arm.
Let’s turn our attention to Fig. 4. Here the FA is the same as at the Fig. 3. The RA forces particularly the biceps femoris, semitendinosus, semimembranosus act together by opposing to be in flexed position (the shank and the thigh). Also in addition the center of mass (CoM) of the thigh and the gravity act together as RA. Few more things I would like to explain here. You probably will ask, how can be established for the same kind of action two different class levers. To get the answer right to the point you should know that in mechanics the case is simple where the levers are represented by rigid bars. In human body the levers (representing the bones) are moved by muscles. Also there is controversy between biomechanists about establishing the exact lever system for each case in part.
These two lever examples are the author’s opinion. Levers are always established between two segments. In our case the 1st class lever involves three body segments such as the shank, thigh and the upper body part. But you can see that there are only two body lever parts: The whole leg and the upper body. In Fig. 4. The case is simple. There are two body link connections. There is a lot of to say about levers.
So far you found examples about energy, leverage, displacement/distancing. In the following I am giving some examples/calculations about impulse-momentum relationship.
Example Nr. 1. A karateka kicks a stationary punching bag. A technique is a roundhouse kick to the imaginary midsection of an opponent. The question is to find out the final impulse delivered by the bag to the kicking leg.
The karateka has a 70 kg body mass and has an initial momentum (p = mv) = 11 kg x 4m/s = p = 44 kgm/sec. The kicking leg force encounters a force from the impact of the bag which is an impulse (J = Ft) = 108 N x 1.5 sec = J = 162 Nsec. Since this impulse acts in the direction of motion, it changes the kicking leg momentum from 44 kgm/sec to 206 units (44 + 162 = 206). This is an initial impulse; the final impulse is encountered upon rebounding.
The bag creates an opposite force (Newton’s 3rd Law of Action and Reaction). This law states that in every action there is an equal and opposite reaction. However in our case of kicking a bag which is moving upon impact, the force which was delivered will not receive the equal force as in other case where the object is immovable. Taking into consideration the fact described above will result the final impulse force where the kicking leg can lose approximately 28 N. In this case the final impulse will be 162 N-sec – 28 N-sec = (J) 134 N-sec.
Example Nr. 2. A karateka hits a punching board (Makiwara in Japanese). We use his total arm length kg-force = 3.45 kg. He hits the makiwara with a speed of 5 m/s. It rebounds with a speed of 3 m/s. The contact time is 0.10 seconds. A). Determine the impulse with the makiwara. B). Determine the force of the makiwara on the punching fist.
Find the impulse. Given: m = 3.45 kg ; vi = 5 m/s; vf = 3 m/s; t = 0.10 s. Impulse = Momentum change = mΔv = m(vf – vi) = (3.45 kg) (-3 m/s – 5 m/s). Momentum (p) = - 27.6 kgm/s = Impulse = – 27.6 Ns (Ft).
The “-“ indicates that the impulse was opposite the original direction of motion. The Greek Δ sign indicates change. (Note that kgm/s is equivalent to Ns).
Find the force. Given: Ft then F = Impulse/t = (- 26.7 Ns) / ( 0.10 s) = Force = – 267 N.
In conclusion what can a karateka or instructor do to be sure that his/her karate techniques/motions are efficient? He should analyze the aforementioned examples adapted always to his karateka physical shape and somatotype.
If you have any comment, please send an email to email@example.com. Please visit our web site: www.sendo-ryu.com. Prof. Emeric Arus, Ph.D. is the Founder and President of the Int’l. Sendo-Ryu Karatedo Federation and the USA Sticky Hands Combat Jujutsu Federation.
Copyright © by Prof. Emeric Arus, Ph.D.