6. Acting State of Force

In the preceding chapter we studied the chief forces used in judo practice and arrived at a conception of force. But when we apply force to a body, many different effects are produced according to the points at which force is applied and to the direction in which it works. The same thing can be said for the number of forces to be applied. In this chapter let us study what effects are produced by a force, or forces, working under a variety of conditions. We shall lean how to apply them most effectively in judo.

The principle of transmissibility of force

In Figure 48 a string is attached to a block placed at the point P. Let us suppose that force F acts on the block by pulling the string along the line represented by the arrow. Force F acts at three places along this arrow: M, N, and 0. We wish to displace the block from the point P to the point Q. We exert force F first on point M, then on point N, and finally let it push point O. Then the same effect is produced three times, and the block is displaced from point P to point Q.

By these experiments we realize that, provided the applied forces act along a single straight line and their magnitude and direction are the same, the same effect will be produced at whatever point on the straight line where they may be applied. The result is usually called the principle of the transmissibility of force. Let us observe a few applications of this principle to judo practice.

In Figure 49 the opponent (B) has leaned forward. Provided P1= P2—P3 and the three forces act alike along the same line (l), the cause that makes him lean forward may be considered as the push of an external force, P3, the force P1, with which you (A) pull, and the force P2, with which he advances.

Composition of forces

The principle of ju is one of the most important things in judo, as we have observed in Chapter 1. It teaches us to throw the opponent by making use of his force. For instance, if you apply a force to him in the right direction, since he moves in the same direction with his own force, the force that throws him equals the sum of both forces. If you apply the force in the opposite direction to that of his force, the effective force is the result of your force minus his force. Under the principle of ju, to use force in that manner results in a complete waste of your energy. But if you pull him to the right front corner simultaneously as he moves to the right, in what direction is he compelled to move?

Look at Figure 50. Let us attach a string to the point 0 on block M. Now let us move the block by pulling the string. Let F1 represent the pull of the string. Now let the force F1act on the point 0. The point 0 will then be displaced from its present position to the point 0'. Complete the parallelogram OAO'B with the line 00' as the diag­onal. Let OA, 00', and OB represent respectively the three forces Flt F2, and F3. OA can represent the magnitude and direction of force F2; 00'y those of the force F1; and OB, those of the force F3. We already know that if force F1 acts on point 0, point 0 will be displaced from its present position to point 0'. If the two forces F2 and F3 act on point 0 simultaneously, how does point 0 move?

Point 0 moves with the same velocity along the diagonal 00' to point 0' and coincides with it. Therefore we can understand that the same effect will be produced whether a single force F1 acts on point O or the two forces F2 and F3 act on it simultaneously, if these forces represent respectively the three lines of the parallelogram. Thus we may take the two forces F2 and F3, acting together, as a single force F1.

The single force F1 is usually called the resultant of the two forces F2 and F3. When the single force F1 acts on the point 0, we may consider it as the two forces F2 and F3 acting on it. For this reason the two forces F2 and F3 are called the components of the force F1. This fact is called the principle of the parallelogram of forces. Now let us consider the application of this principle to judo.

In Figure 51a the opponent (B) is about to advance toward you (A) with the intent of grasping your lapel. In Figure 51 & he has advanced his upper body by force, and you have retreated a step backwards. Now harmonize your motion with his. You pull him for­ward and down by force Q while force P acts on him. Then the two forces P and Q act on him together, producing a larger motion in his body. The force is the resultant F. In Figure 51c the direction and magnitude of the force that makes him bend forward is shown by the resultant (F) of the two forces P and Q.

Decomposition of forces

When we pull a sled with a heavy load, we find that the longer the rope attached to the sled, the smaller the force needed to pull it. This is the result of the decomposition of the pulling force. Let us complete a parallelogram of force with the length of the rope as the diagonal. (See Figure 52.) Take into account that force F, which pulls the sled, works along a horizontal line. Then you will notice that the smaller the angle 0, the larger the force (F3) to pull the sled becomes.

52. Decomposition of forces.

53. Modified kami-shiho-gatame uses larger vertical compo­nent.

54. Kami-shiho-gatame uses smaller verti­cal component.

The longer the rope, the smaller the angle becomes. Let us see how this principle is made use of in grappling techniques. To press your opponent most effectively against the mat, you must make use of the force that works vertically. Therefore it becomes im­portant to make the vertical force larger. Look at Figure 53. The momentum will be produced when you press your chest against his. And it will work along the line of your center of gravity, CC, and resolve into two components. So, to make the vertical force larger, you must put the center of gravity in the highest position, since the smaller the angle O', the larger the vertical component becomes. Thus we can say that modified kami-shiho-gatame (Figure 53) is a more effective technique than kami-shiho-gatame (Figure 54).

55.  Moment of force operates to open a door.

56. Arm of moment.

The moment of force

We have previously stated that different effects are produced according to the points to which force is applied. Why is this true? The reason is that a moment of force is produced whenever a force is applied at any point of a body besides the center of gravity.

Look at Figures 55 and 56. The door in Figure 55 is going to open because the force P' acts on the handle of the door. In Figure 56 you (A) are about to throw your opponent (B) by pulling him down and forward. His right big toe serves as a fulcrum, just as the hinge of a door does.

Does the same law work in both cases ? You will note that the handle of a door is placed as far as possible from the hinges, since the door can thus be opened with the minimum amount of force. In Figure 55 the handle is placed at the distance L’ from the hinge. If the handle is placed only halfway from the hinge, twice the previous force will be required.

From this experiment we find that when a force is exerted on the door, the efficiency of this force changes according to the point of application. The product of the acting force and the distance between the axis and the line of action of a force is called the moment of force. Thus the moment of force in opening the door in Figure 55 is P'L', and the moment of force in rotating the opponent in Figure 56 with his right toe as a fulcrum is PL. The distance between the axis or the fulcrum and the line of action of force is called the arm. When a bar works as an arm, we call it a lever.

57. Moment of force becomes larger when arm is longer.

Let us study the arm in more detail. In Figure 57 the distance be­tween the fulcrum and the line of action of force is a straight line drawn perpendicularly from the fulcrum to the line of force. Suppose a sandbag, C, is suspended from point 0 and that three forces equal in magnitude, P1, P2, and P3, act on it. P1is acting on C per­pendicularly. In the case of P1, the arm we see is CO, because P1 acts on it perpendicularly. In the case of P2, the arm OB is drawn per­pendicularly from the point O to the line of force P2. In the case of P3, the arm is OE for the same reason. Thus in Figure 56, if the acting force P does not act on the opponent (B) perpendicularly from the fulcrum O, the arm becomes OD, the line drawn perpendicularly from the fulcrum O—that is, the toes of the right foot of the opponent (B)—to the line of action of the force P. From this experiment we know that the larger the force acting on the opponent, the larger the moment of force. In the case of the arm, the moment of force becomes larger when the arm is longer.

In judo we use this principle more in grappling than in throwing. This is true because in throwing techniques we usually grasp the opponent by the sleeves, the lapel, or the upper parts of the chest. In grappling, the part of the opponent's body that should be grasped is decided by the actions of the competitors. Thus the use of the moment of force in throwing techniques is difficult to see. But in grappling, its use is very obvious. For instance, look at kami-shiho-gatame in Figure 54. The arm of the moment of force is short. To make it longer, you must hold your opponent down on the mat with your abdomen (see Figure 53), stretching both your legs outward in a V position.

60. Arm of moment: type 3.

Look at Figure 58. A straight bar is called a lever when it is used to pry up a heavy weight or a fixed object in order to take advantage of the moment of force. The fixed point 0 of the bar is called the fulcrum. Point A, where the bar is in contact with the force (weight) that is acted upon or resisted, is called the point of exertion. Point B, where the force is applied to the bar, is called the point of application.

Levers can be classified into three types, as shown in Figures 58, 59, and 60. The type that we use in grappling is the one that has the point of exertion A between the fulcrum O and the point of application

B,         as illustrated in Figure 59. Refer to the explanation of grappling

techniques in Chapter 8 for further information.

What happens when you grasp your opponent by the sleeve and lapel and pull him forward? Look at Figure 61. The point of applica­tion of your pulling force is the point B on the upper part of your opponent's body. His right toes serve as a fulcrum. On the other side, the point of application of his gravity, which is opposing your pull, is the point A on the mat, vertically under the center of his gravity,

C.        This point is thus the point of exertion in relation to your force.

61. Arm of moment in judo. A: point of exertion.

B: point of application C : center of gravity

O : fulcrum

is

62. Vertically   applied   pressure strong; horizontally applied pres­sure is weak.

Let us now consider body movement. If you read the first part of Chapter 5 again, you will find that the human body is based and built on the principle of the moment of force. Look at Figure 37 again, keeping in mind the types of lever shown in Figures 58, 59, and 60. When you bend your elbow joint, the part to which one end of the biceps is attached becomes the point of application B; the hand repre­sents the point of exertion A; and the elbow represents the fulcrum O. In this case the arm OB is shorter than the arm OA. Therefore, if you wish to lift a block by bending your elbow, the force that you must exert must be greater than the weight of the block. When the location of the fulcrum is changed, however, the point of exertion A will move inversely faster than the point of application B.

The construction of the human body directs it to rely on speed rather than to economize its force. Look at okuri-ashi-harai in Figure 84. You can sweep your opponent's foot quickly and easily. However, you must exert a strong force that comes from the waist and ab­dominal region, and you must make use of your opponent's weak points by twisting and bending his joints. For another example, see juji-gatame in Figure 122.

A jujitsu master once said: "A human body must be handled under the principle of a lever." As Figure 62 shows, if you press an object with the back of a fork held horizontally, the pressing force will be weak, but if you press vertically with the tines along the curve of the fork, the force will be stronger.

The moment of a couple

If you (A) and your opponent (B) are holding each other as shown in o-soto-gari (Figure 85), what force will you exert on him to make him fall backwards? You will probably find two ways to do this. The first way is to exert force F alone on the upper part of his trunk. In this case you should move fast and with controlled strength in order to prevent him from escaping by stepping back with his right foot. If he cannot do this in time, he will fall backwards. The second method is to exert two inverse forces on the upper part of his trunk and the lower extremities. There are many such instances in judo, including o-soto-gari (major external reaping), o-uchi-gari (major inner reaping), and harai-tsurikomi-ashi (lifting foot sweep). (See Figures 63 and 64.)

What do we mean by a couple? If the two forces P and Q are equal in magnitude and opposite in direction, the pair is called a couple. Let us study its nature.

The moment of a couple is the product of one of the forces and the distance between their lines of action. Figure 65 is an illustration of the moment of a couple. Point O is the fulcrum, and the distance between the fulcrum and the lines of action of the applied forces P and Q are L and I, respectively. Then the moment of P with respect to the fulcrum O equals PI, and the moment of Q with respect to the fulcrum equals QL. Therefore the sum of the moments of the forces is determined as follows:

moment=PI+QL

P=Q moment=P(l+L)

By acting on a rigid body, a couple cannot displace it; it can only let it rotate about the fulcrum. If another external force acts on the fulcrum together with the couple, the body will move in the direction of the force, rotating about the fulcrum.

Why is a couple effective? Look at Figure 64. Since the opponent's posture has been broken to his left back corner, he will fall on his back if you push him with your right hand and reap his left leg for­ward (his weight rests on the heel) with the lower part of your right leg. This technique is called o-uchi-gari.

63. Moment of a couple in o-soto-otoshi (major leg drop).

64. Moment of a couple in o-uchi-gari (major inner reaping).

65, Moment of a couple.

Why is a couple more effective in making the opponent fall on his back, as in the above-described technique, than a single force applied to the upper part of his body ? The answer is that the moment a couple is applied, the opponent's left foot is reaped away from the mat, and at the same time his body drops down on the mat. But when a single force is applied on the upper part of the opponent's body, his body does not immediately drop down on the mat. It first begins to rotate toward the back with the heel as a fulcrum. Hence it takes longer to complete the throw, and the longer time gives the opponent an oppor­tunity to defend himself from your attack.

Let us now study an instance where the application of a couple should be avoided. If you try to apply o-soto-gari (Figure 85) before your opponent's posture has been broken, his body will not move. The reason for this is that one part of the couple that works to reap his leg is nullified by the friction produced between his sole and the mat when you try to reap his leg from the mat. Therefore, in such a case, you must change your technique and use the reaping leg only to step behind his leg while pushing strongly against the upper part of his body.

Your pushing force can become larger, since your attacking energy is not divided into two. This technique is called o-soto-otoshi. However, you must make sure that pushing precedes reaping in order to throw him backward successfully. O-soto-otoshi is a technique based on a block-and-push type of throw that is unlike the reaping type of action in o-soto-gari.

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