JUDO AND AIKIDO ARE MARTIAL arts that demand an intuitive understanding of the physics of forces, torques, stability and rotational motion. This month I shall examine a few of the basic throws of these two forms of combat. Although I cannot convey fully the grace each throw requires, I can break it up into components that can be examined in terms of classical physics. The experiments I shall describe call for actual performance of the throws, but you should do them only under expert supervision. Both types of combat can be dangerous to you and your opponent.

In judo the main goal is to overcome your opponent's stability. The skill lies in the anticipation of his movements and the timing of your responses. The idea is to avoid forcing your opponent into a firm resistance to your throw that would pit your strength against his. A small but skilled judo player has a distinct advantage over a larger but unskilled opponent if a contest of strength is avoided.

Probably the best example of this advantage is the basic hip throw, which is most effective against a taller and slower opponent. In the normal judo competition you face your opponent with your hands grasping the lapels or shoulders of his uniform. To execute the throw you step forward with your right foot to a point between his feet, pulling him downward and toward your right. The throw works well if you have caught your opponent just as he has stepped forward with his right foot. He is still stable against a pull directly toward you, but he is considerably less stable against a pull to your right because of the position of his feet.

During your step forward you curve your body forward so that your head is at your opponent's shoulder level. Next you rapidly turn your left hip backward while pulling him onto your right hip. This should be the first body contact during the movement. If you continue the pull with your hands and the rearward turn with your left hip until you are facing in the same direction as your opponent, he will be rotated over your right hip and onto the mat.

Since you do not want to hurt your opponent in the sport, you maintain your grip on his uniform during the fall so that he lands on his left side and can slap the mat with his left arm during impact. The slap spreads the impact force over a larger area so that the stress on his ribs is not enough to hurt him. Part of the early training in judo involves timing the slap on the mat to coincide with the impact. The only time I have been hurt in the sport is when I failed to slap properly.

Timing and smooth execution are essential to the hip throw, but an understanding of the physics, particularly of the torques and the center of mass, is also necessary. Your opponent's center of mass is the geometric center of his mass distribution. It can be regarded as the point where the gravitational force acts on the body as a whole, which is why it is sometimes called the center of gravity. Your opponent is stable as long as his center of mass remains over the support area outlined by his feet. When he stands upright in a normal posture, his center of mass is approximately between his spine and his navel. Therefore he is stable until you force or trick him into moving his center of mass or into losing part of his support area.

Suppose during a throw you manage to move your opponent's center of mass forward of his feet. Even if you then no longer aid the throw, the gravitational pull on his center of mass creates a torque that might make him fall. To calculate a torque one must multiply two items: the force acting to bring about a rotation and the lever arm between the pivot point and the force. The lever arm is the perpendicular line from the pivot point to a straight line through the force. If you have made your opponent unstable, the force that can rotate him about his feet to the mat is the gravitational pull on him. I represent this force, which is merely his weight, by a vector pointing straight down from his center of mass. Here the lever arm is the horizontal distance between the pivot point at his feet and an extension of a vertical line running through the weight vector. The torque on an unstable opponent is the product of his weight and the lever arm. When your opponent is upright, the lever arm for his weight vector is zero and so the torque is zero too. When he is caught with his center of mass forward of his feet, the lever arm is no longer zero and the resulting torque causes his rotation. The longer the lever arm (the more he is leaning), the greater the torque. One of the objectives of judo is to trick your opponent into an unstable position so quickly that recovery is impossible. Once he is unstable you can continue the throw by applying another torque to him, one that will bring him to the mat long before he can even attempt to regain his stability.

During the hip throw you initially pull on your opponent's uniform to make him unstable. If you pulled directly toward you, you could not easily cause this instability because his center of mass would be moved over his forward foot. He could then maintain his balance by bending that knee. To make him unstable you would have to move his center of mass a relatively great distance until it was beyond his forward foot, but the motion would require a strong and prolonged pull, which he could counter quickly.

An easier way to make your opponent unstable is for you to pull to your right, because in that direction his center of mass must be displaced only a relatively short distance before it no longer lies over the support area. He will probably not be able to counter such a pull before the instability is established. Thereafter he will not be able to counter the continued rotation involved in the hip throw.

Your pull has an additional purpose. It curves your opponent's body so that his center of mass is brought forward to his navel or just outside his body. This new position will aid you in rotating his body over your right hip. Once body contact is made a new pivot point is established at your hip and your pull creates a new torque on the opponent, one that will cause the rotation over your hip. As before the torque is calculated by multiplying the force on the opponent by the lever arm between the line of that force and the pivot point. This time the force is your pull and the pivot point is your hip. Thus the hip throw gives rise to two torques on your opponent, one torque due to his own weight and unstable position and one due directly to the pull you are exerting on him. The throw begins with the first torque so that you can set up the second one without resistance from him.

Suppose you do not curve your opponent's body forward and bring his center of mass out to his navel. Then when you attempt to rotate his body over your right hip, a torque due to his weight will actually counter the torque from your pull on his uniform. Suppose he is still in an upright position when you make body contact and attempt to rotate him over your hip. The pivot point for the rotation is your hip; I shall apply it in determining the lever arms for both of the torques then acting on the opponent.

One of the torques is the product of your pull and the lever arm from your hip to the line through the vector of the pull. The other torque is the product of your opponent's weight and the lever arm from your hip to a vertical line passing through the opponent's center of mass. If your opponent is standing upright, the torque from his weight opposes the torque you are applying, since it attempts to rotate him in the opposite direction over your hip. To finish the throw you now must overcome the torque due to his weight, but the time required destroys your advantage in the surprise of the throw. Moreover, you must pit your strength against his.

When the hip throw is properly executed, you bring your opponent's body forward in a curve, move his center of mass out

to his navel and so decrease or eliminate the lever arm associated with his weight. The torque due to his weight is therefore diminished and you have a comparatively easy time rotating his body over your right hip. The throw works better on an opponent who is taller than you are because you can pull him downward into the proper curved posture more easily than you could an opponent who is your height or shorter. You can also more easily slide your right hip under a taller opponent. The lever arm of your pull on the uniform of a taller opponent will also be larger, thereby providing more torque to bring him over your hip.

The "major outer reaping throw" (it is called osotogari in Japanese) is somewhat easier to understand in terms of the rotational motions. As your opponent steps backward with his left foot you step with your left foot just to the outside of his right foot and pull downward on his uniform to force his weight downward on that foot. Your pull will also be toward his right rear so that his body is curved backward. He is already in an unstable position because your pull moves his center of mass to his right rear and away from the support area of his feet. He cannot escape by sliding his feet to the rear and regaining his balance because you have forced him downward. His instability results from the torque his weight creates around a pivot point at his feet, primarily his right foot. The lever arm runs between the pivot point and a line through his weight vector. Placing him in this position sets him up for the next part of the throw, in which you further remove his support area and apply a second torque to bring him rapidly to the mat.

You continue the throw by stepping with your right foot around and behind your opponent's right foot. Then you sweep your right hip and leg to your rear while you force his right side downward and to his rear, leaving him with virtually no support base. The two torques cause him to rotate about a pivot point on your right leg. Even if you did not continue to pull on him after sweeping his leg, he would rotate about your leg because his center of mass is being pulled down by gravity. Your downward pull provides another torque to hasten his fall. In this throw the two torques complement each other.

The "sweeping ankle throw" (okuriashi bari) removes your opponent's leg support in a similar manner. As he is about to

place his weight on his right foot in the course of a step forward or backward you sweep your left foot into that leg just above the ankle. Simultaneously you pull his uniform in his original direction of travel. Suppose he was moving forward, You pull forward (and so meet no resistance from him) as you sweep his right foot into his left one Even if he manages to keep his left foot on the mat, his support area is greatly reduced and is swept from under his center of mass. His weight vector through the center of mass provides a torque that will take him to the mat. If you lower your-body while maintaining your pull on his uniform, you will provide another torque that will rotate him to the floor. The pivot point is his left foot, and again the two torques complement each other.

Advanced judo classes teach methods of disabling an opponent on the mat. Most of these "hold downs" entail trapping your opponent on the mat with your weight positioned in such a way that he cannot roll over or rise even if he is stronger than you are. For example, in the "cross armlock" (udehishigi-jujigatame) you are positioned with part of your weight on the upper torso of your opponent on the mat. He not only is prevented from rising but also probably will not even move for fear of having his arm broken.

The maneuver originates when you are astride your opponent, who is on his back. When he raises his left arm to ward you off, you grasp his wrist with both of your hands, fall to his left side, throw your right leg across his neck and with your left knee raised drive your left ankle into his side. His left arm is pinned between your legs with the elbow downward. Even a gentle downward push on his wrist creates a tremendous torque on his arm around the pivot point where that arm crosses your right leg. He cannot sit up because your weight creates an overwhelming torque on him as he attempts to rotate his trunk about a pivot point at his hips. He also cannot free his left arm even if he is considerably stronger than you are. He could try to counter your torque on his arm by using his shoulder muscles, but they would pull on his arm at approximately the location of the pivot point and so their pull would have a short lever. As in most judo techniques, a person trained in creating the correct torques on an opponent has a tremendous advantage even if the opponent is much stronger.

Aikido is a relatively modern form of martial art that incorporates techniques from many of the other martial arts. It is distinguished by its firm code of avoiding injury to the opponent. Hence it is a form of self-defense rather than a sport. It involves no techniques that can be regarded as attacks. I think it is the most difficult of all the martial arts to learn. Its demands for skill, grace and timing rival those of classical ballet.

Aikido employs many of the same principles of physics that are found in judo. Suppose your opponent grasps your wrists from behind. In one of the aikido maneuvers you smoothly lower your body while bringing your wrists upward and over your head toward the front. Your opponent hangs on to your wrists but is brought forward by your descent and slight lean forward. His position is therefore unstable because his center of mass is now slightly forward of his feet. You rapidly draw your right leg backward and drop onto your right knee. Your arms and torso are brought forward and downward in a large arc. Because the first part of the motion induced your opponent to hold tightly to your wrists, he is now thrown over your body in a front somersault.

As in much of aikido, your opponent actually throws himself. He cannot prevent your forward motion because of the unstable posture in which you initially place him. Even if he has superior body weight, he cannot stop the motion by pulling downward on your raised wrists. In such a position he can pull only along the length of your arms. The torque due to such a pull is zero because there is no lever. Remember, the lever is the perpendicular from the pivot point (in this case your shoulder) to the line through the force. The line through your opponent's pull passes through your shoulder and therefore has no lever arm. Even if he is heavy or strong, he cannot rotate your arms once you have them properly over your head.

Many of the techniques of aikido employ the deflection of a force directed at you. Suppose your attacker throws a punch at your face. To stop the punch directly requires a large impact force, probably higher than 3,000 newtons. With such forces bones are likely to be broken. A wiser technique is to deflect the strike. Although a large force is necessary to stop the punch directly, only a small force is needed to deflect it. A force of 10 newtons may be enough to deflect a punch by a centimeter.

Although most followers of Western styles of fighting consider an attack to be an advantage, in aikido the attacker is at a distinct disadvantage because of the momentum of his strike. You can use his momentum to throw him to the mat. Suppose your attacker steps forward with his right foot and slashes at your face with the side of his right hand (a typical attack both in Western styles of fighting and in karate). You slide your left foot to the rear as you parry his slash with your left arm. The parry is meant to deflect the slash, not to stop it or even to slow it, since either effect would require strength from you. During the parry you guide your attacker's right arm downward into the grasp of your right hand. While still not fighting the forward momentum of his slash you pull him around in the circular motion you have begun with the withdrawal of your left foot. He was relatively stable against a pull directly forward because of his extended right foot, but he is highly unstable against a pull forward and to his left. In such a direction his center of mass does not have to be moved far before he becomes unstable against a fall. Therefore as you continue to circle you pull him in that direction. He now has two serious disadvantages. First, he is committed to a forward motion that would take a considerable force to stop, even from himself. Second, your pull and his motion are removing his center of mass from his base of support.

To complete the throw rotate your attacker's right arm downward while stepping to your left rear. Turn his wrist upside down and bend his hand around it. At this point it is impossible for him to prevent the throw. He is now off balance and completely unable to stop his own motion. He also cannot pull out of your grip because you have bent his arm at the wrist. Although his arms may be strong, he cannot prevent the torque you create when you push his hand around his own wrist. You bring him to the mat.

How would such a strike to the head be handled in karate? In the Korean karate style of tae-kwon-do I was taught to parry a slash with a powerful strike across the opponent's arm. Deflection was important but so was countering the slash with a large force. Force was working against force, and usually the stronger person won. (I was rarely that person.)

Circular motion is employed in aikido both for deflection and to aid in throwing an opponent off balance. Suppose someone approaches you from behind, reaches around your body and pins your arms to your sides. You should reach upward and hold his hands tightly to your chest while sliding your foot forward. The timing is critical because you want to move your torso forward at a rate matching the speed of your opponent. If you delay, you will lose the advantage of exploiting his momentum. If you move too fast, you will have to drag him forward. You must slide your right foot forward at the correct speed and then suddenly lean forward and rotate your body to your right.

The combination of your opponent's initial momentum and your rapid rotation throws him off to the right. He cannot prevent your throw because your lean forward brings his center of mass forward of his feet. He cannot release himself from the forward motion because of his established momentum, because you have pinned his hands and because of his grip around your arms. The centrifugal force on him during your rapid rotation is too large for him to deal with in his unstable position. Hence he essentially throws himself to the floor.

Two more examples of how aikido employs a small force to bring an attacker off balance entail stick fighting as it is taught in advanced classes. Suppose an attacker thrusts a long stick at your midsection, advancing with his left leg during the lunge and thrusting the stick horizontally, holding it with the palms of both hands down. It would be futile to try to stop the end of the stick. You rapidly step forward with your right foot so that the stick passes you on your left. (The agility to do this comes only with long practice.) As the stick passes you turn your body to face it so that you can grab it with both hands. Your left hand is forward of your attacker's outermost hand. Your right hand is between his hands.

In grabbing the stick your objective is not to stop its motion, which would require considerable force. Rather it is to deflect the lunge upward, around to your left in a circular motion and then up and over your attacker's head. Once he has committed himself to the forward lunge he can do little to prevent the deflection. He would need a large force to stop his momentum, and he cannot thrust horizontally to your midsection while pulling downward to prevent your deflection.

Once you have the stick over your attacker's head he is easily thrown. With his left foot forward he is highly unstable against a pull to his left rear because in that direction his center of mass must move only a short distance before it is no longer over his support area. When you have the stick over his head, you pull it downward over his back in that direction. He falls to the mat on his back and probably releases the stick.

Suppose you have a stick and a determined attacker rushes forward to grab its forward end. Allow him to grasp it but lead him with it (as if it were a carrot in front of a donkey) so that he continues his rush. Also lower your end to trick him into bending downward. Once he has committed himself to this awkward motion and is about to pass to your right you bring your end of the stick upward over his face and then downward over his back. If this motion is executed rapidly, he still has a strong grip on the stick and therefore is bent backward by your pull downward over his back and by the continued forward motion of his torso. The torque due to his own weight rotates him to the floor around the pivot point of his feet. His grip on the stick also provides a torque that rotates him. He actually throws himself to the mat because of his initial forward rush and a bit of trickery on your part.

Aikido has hundreds of techniques for employing such trickery against a determined opponent. In nearly all of them a small deflection force parries an opponent's thrust and then guides it so that he throws himself down. When I watch an aikido master defend himself the motion seems so fluid and effortless that I am inclined to suspect the opponent of faking when he falls to the floor. The fall is not faked. It looks that way because the master has spent years developing an intuitive feeling for the basic physics of forces, rotation and torques.

Bibliography

JUDO ON THE GROUND. E.J. Harrison, W. Foulsham & Co., Ltd., 1954.

AIKIDO AND THE DYNAMIC SPHERE: AN ILLUSTRATED INTRODUCTION. A. Westbrook and O. Ratti. Charles E. Tuttle Company, 1970.

ADVANCED TECHNIQUES. Morihiro Saito in Traditional Aikido: Sword, Stick and Body Arts. Minato Research & Publishing Co., 1973-74.

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