Very nice article about physics in Karate rwite by Giovani Di Maria for eeweb.com.
Read this!
The actions performed in karate respond to precise laws of physics and mathematics. Karate is based precisely on the exploitation of these rules to obtain maximum power from the human levers (arms and legs). The masters and students of martial arts, during their training in the dojo, spend a lot of time applying the tricks and tips of physics just to improve the power of their strokes. Let’s find out together some of the phenomena that can be observed in karate.
Karate: a collection of physics concepts
Karate is probably the sport in which the concepts of physics are applied with the greatest precision and frequency. All of the movements and strokes performed by the athletes are not random but are carefully studied to transmit maximum energy and receive fewer dangerous injuries to their body. If a shot is delivered correctly, it is potentially lethal and can kill a person. These potentialities of the human body are well-known by the wrestlers.
Some definitions
Before starting the analyses and simulations, it is useful to remember some technical definitions. In physics, each word has a precise meaning and cannot be exchanged for another:
- Force (N) — the action that causes a change in speed
- Weight (N) — a quantity derived from the International System that indicates the force with which a body is attracted by the force of gravity of Earth
- Mass (kg) — the measure of inertia; that is, of the resistance that the body opposes to all the variations of its state of rest or motion
- Speed (m/s) — the speed with which the position of a body changes. In karate, the average speed corresponds to the speed with which a technique is performed, while the instantaneous speed corresponds to the speed of impact.
- Acceleration (m/s2) — the speed with which the speed changes. If it assumes negative values, we have deceleration.
- Work (J) — the transfer of kinetic energy on a body, performed by a force when an object moves
- Energy (J) — the ability of a body to do work
- Kinetic energy (J) — the energy possessed by a body due to its movement
- Center of gravity — the point at which all the weight of the body is applied
- Pressure: (N/m2) — the ratio between an orthogonal force on a surface and its area
Speed is an essential element
In karate, the speed of movement plays an essential role, and the most important results could not be obtained if the bodies moved slowly. In other words, it is necessary to apply the maximum possible force at the moment of impact, and this can be achieved with such rapidity and precision at the same time, as can be seen in Figure 1. In this sequence of images, Bruce Lee sends all his weight in one place, with devastating results. All parts of his body move harmoniously and maximize the final energy. The system is equivalent to an object with a mass of about 60 kg (Bruce’s weight) launched at a speed of about 7 m/s, which has a kinetic energy of 1,470 J and an impact force of tens of thousands of Newtons. The 60-kg bag, as you can see, is thrown at a considerable distance.
Figure 1: Bruce Lee’s speed is devastating.
If Bruce Lee had been running at a speed of 1 m/s, his sack would have moved only a few centimeters, with poor results. Therefore, speed is the real ingredient in creating power, not mass. With a doubling of speed, the results would be shocking. The mass, of course, cannot be changed, because the parts of the body (fist and foot) are not modifiable. In Figure 2, we can see Bruce Lee hitting a 60-kg bag, with four different speeds:
- 1 m/s — The blow is barely perceptible and the bag oscillates only slightly.
- 2 m/s — The blow is a little stronger and the bag swings with greater amplitude, rising a few centimeters.
- 7 m/s — The blow is very strong and the bag lifts up to almost 2 meters from the ground.
- 10 m/s — The blow is very strong; the bag lifts up to several meters from the ground and also performs a revolution. This situation is at the limit of human possibilities.
The yellow graph describes the vertical position of the bag.
Figure 2: Athletes should train their speed of movement more carefully.
Now let’s see which of these situations possesses a greater kinetic energy, remembering that it is the energy that a body possesses due to its movement and is measured in joules. You have to choose between:
- Case 1 — A body with a mass of 4 kg at a speed of 10 m/s
- Case 2 — A body with a mass of 2 kg at a speed of 20 m/s
- Case 3 — A body with a mass of 8 kg at a speed of 5 m/s
To calculate the kinetic energy, the following formula is used:
The results are as follows:
As can be seen from the energy results, a doubling of the speed is always preferable to a doubling of the mass. A very light body, weighing only 2 kg, launched at high speed produces more kinetic energy and, therefore, more destruction (see Figure 3). The philosophy of the pistol bullet is based precisely on this point. Many fighters have the mistaken belief that “they can hit harder.” The energy of the blow can be increased by modifying two variables: the mass of the fist and its speed.
Figure 3: The speed of a body is more destructive than its mass
Impact dynamics
The impact is a violent collision between two bodies, usually endowed with speed. During the impact, there is a reciprocal transfer of energy, in the form of heat, work, deformation, or noise. For the calculation, it is necessary to determine the instantaneous deceleration; that is, the time in which a body passes from its cruising speed to zero. This is because each material reacts differently. If the impact surface is soft, the time will be longer than for an impact on hard surfaces. To calculate the impact force, it is necessary to know:
- The mass of the body
- The speed of the body
- The duration of the impact
It is quite difficult to calculate the deceleration time. It can range from a few hundredths of a second for a net impact on a hard surface to a few seconds for a soft landing surface. It is necessary to consider the geometry and structure of the bodies to verify whether it is an elastic or inelastic collision, and to evaluate the effects on the bodies and the relative deceleration due to the impact. To measure it practically, you can use special cameras with a very high “frame rate,” usually greater than 1,000 fps. In other words, the impact force will be different if, for example, a blow hits a piece of wood, an iron plate, a face, or a sponge. The fist of a good karateka can move at a speed greater than 10 m/s and can develop a destructive power greater than 700 kg/force. To calculate the force of the impact, the following formula is used:
Inelastic impact
In the inelastic collision, the momentum is conserved and the kinetic energy, on the other hand, is converted into deformation and heat. We can consider the punch hitting an athlete’s face as an inelastic impact (see Figure 4). Assume the following scenario:
- Mass “A” (head): 5 kg
- Speed “A”: 1 m/s
- Mass “B” (opponent’s punch): 0.6 kg
- Speed “B”: 15 m/s
From the velocity modules of the two masses, it is immediately understood that they are about to collide with each other, with surprising results. Let’s first calculate the kinetic energy of the two moving masses:
The kinetic energy of the entire system before the collision is equal to the algebraic sum of that of the two bodies:
Now it is necessary to calculate the speed of the entire system after the impact, in which the two bodies remain attached to each other, with the following formula:
Finally, we can calculate the kinetic energy of the entire system after the impact:
The kinetic energies measured are, therefore:
- Kinetic energy of the system before impact: 70 J
- Kinetic energy of the system after impact: 17.5 J
You immediately notice a difference in kinetic energy between the system before the collision and after the collision. In an inelastic impact, this difference in kinetic energy (52.5 J) is converted into deformation and heat (with consequent pain and injuries of the athlete who receives the blow in the face), unlike an elastic impact, in which the kinetic energy is preserved. The graph in the illustration shows a tremendous deceleration of the punch, lasting just 0.03 seconds. The impact force is devastating — about 400 N with an acceleration of about 60 g. Values over 6 g for a few seconds can cause very serious problems, from unconsciousness to death. In any case, the problem is very complex and there are many variables in reality. The following table summarizes, in a very general way, the human pressure limits above which damage to the body can be caused:
- 10,000 N (maximum force on the skull)
- 4,000 N (above this limit, the spinal column breaks)
- 700 N (maximum limit of a rib)
Figure 4: The head-punch system in an inelastic impact
Conclusion
The physics of karate is a very broad topic and should be deepened in several aspects. One could, for example, study the concept of balance or spinning strokes. All human and natural actions are governed by rigorous physical and mathematical laws, and their knowledge allows us to know all the behaviors of the quantities involved and to predict their effects, even in the long term. Those who know the movements of karate have real human weapons and know that their use could be lethal.
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