# Physic

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Volume 1

JOURNAL OF HOW THINGS WORK

Fall, 1999

JON CHANANIE

In recent years, the ancient eastern art of Karate-Do (a Japanese word, literally

translated as “the way of the empty hand”) has become popular in the western world.

Karateka—practitioners of Karate—often break boards, cinderblocks, and other solid

materials in order to demonstrate the strength that their training develops. Much can

be said of the history and culture associated with the expansion of martial training, but

this essay—it is, after all, a physics paper—will examine the collision mechanics of a

hand strike to a solid target like a board.

That large objects moving at high speeds hit harder than smaller objects moving

more slowly goes without saying. In attempting to break a board, a karateka seeks to

hit the board as hard as possible. It therefore follows that the karateka should move

his or her weapon (for the purpose of this paper, the hand) as quickly as possible in

order to hit as hard as possible. But what makes for a “hard” strike? Two ways exist to

answer this question, both equally accurate. The first looks at the collision in terms of

Force (F) is

times

(t) (put another way, acceleration is the derivative of velocity with respect to time),

force is the derivative of momentum with respect to time. Equivalently, force times

time equals change in momentum, or

because momentum is a conserved quantity. It can be neither created nor destroyed,

but is passed from one object (the hand) to another (the board). The reason for this

conservation is Newton’s third law of motion, which states that if an object exerts a

force on another object for a given time, the second object exerts a force equal in

magnitude but opposite in direction (force being a vector quantity) on the first object

for the same amount of time so the second object gains exactly the amount of

momentum the first object loses. Momentum is thus transferred. With ∆p a fixed

quantity, F and t are necessarily inversely proportional. One can deliver a given

amount of momentum by transferring a large force for a short time or by transferring

small amounts of force continuously for a longer time.

Why, then, move should the karateka swing his or her hand with as much velocity

as possible? Because if the hand is moving quickly, it is likely to decelerate (strictly

speaking, accelerate in the direction opposite to its direction of travel) more quickly in

response to the force the board exerts on it upon collision, as per Newton’s third law.

If the amount of time involved in the transfer of momentum is therefore small, the

amount of force that will be transferred to the target all at once will be large. This

sudden transfer of a lot of force causes the part of the board that is struck and which

therefore experiences that force to accelerate. If that part of the board accelerates

© 1999 Jon Chananie

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Volume 1

JOURNAL OF HOW THINGS WORK

Fall, 1999

enough relative to other parts of the board (which are generally held still by the

cinderblocks on which the boards are placed), breakage occurs.

This same phenomenon can be analyzed in terms of

object of mass

ignoring the negligible amount of energy lost as thermal energy (heat), the amount of

energy in the system lost to deformation damage (∆E) is given by the following:

2

(1−

1

2

2

∆

⋅

⋅

2

(

1

2

where

is a function of the hardness or softness of the colliding objects, which along with

velocity determines impulse. If hard objects collide (for a perfectly inelastic collision,

a small amount of time while soft objects colliding (for a perfectly elastic collision,

Difference in how long momentum takes to transfer and therefore in force at a given

instant is why hitting a pillow with the fleshy part of the hand hurts much less than

hitting a brick with the knuckles.

As ∆E is proportional to the square of velocity, the more velocity the hand has, the

more energy will be transferred into the board. In the simplest possible terms, if the

board is infused with more energy than its structure can handle, it breaks. More

rigorously analyzed, energy transfer causes the board to dent. This process of

transferring energy is

of the board that is struck dents a sufficient distance, it will break. Since the distance

it dents depends on the energy transferred to it and the amount of energy transferred

depends on the velocity of the karateka’s hand, a high-speed strike is most likely to

break the board.

Any martial artist who has ever struck a board with improper hand technique can

attest to the physical pain associated with such impact. The human had is a complex

system of bones connected by tissue, and much can be said about the importance of

proper hand alignment in breaking. From the standpoint of physical science, however,

what is crucial about hand position upon impact is that all formulae for force,

momentum, and deformation energy are for a given unit of

amount of striking surface on the hand involved in collision with the board, a karateka

minimizes the area of the target to which force and energy are transferred and

therefore maximizes the amount of force and energy transferred per unit area.

Consider a martial artist capable of striking with 190 joules (J) of energy. A typical

human hand is about 6 inches long including the fingers and 4 inches across, which

means that a strike with the entire hand disperses those 190 J over 24 square inches,

about 7.92 J per square inch. If, however, the karateka strikes with only the fleshy part

of the palm, about 2 inches across and 1.5 inches long, the 190 J will be dispersed

over only 3 square inches. That strike will deliver about 63.3 J per square inch,

inflicting many times the amount of damage the whole hand could—the same amount

of energy dispersed over a smaller area delivers more energy per unit area. This is

© 1999 Jon Chananie

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Volume 1

JOURNAL OF HOW THINGS WORK

Fall, 1999

why martial artists seek to use as tiny a striking surface as possible in not only hand

techniques, but also kicks, elbows, and other strikes as well.

Karate black belts often advise white belts before their first attempt at breaking

not to try to break the board, but to break the floor under the board. This is to ensure

that the hand does not decelerate prior to contact with the target, a mistake that

beginners, fearful of injury and therefore mentally hesitant, often make. High velocity

of the hand is critical to successful breaking, and data taken from high-speed movies

of karateka show that maximum hand velocity is achieved when the arm reaches

approximately 75% of extension. Intuitively, this makes sense. Since the hand cannot

move forward a distance greater than the length of the arm, it must have a velocity of

0 at full arm’s length extension. It follows that the hand must decelerate well before

the arm is fully extended. Advising beginners to attempt to hit an imaginary target

25% of their arms’ length on the far side of their targets would therefore be more

precise than the typical encouragement to aim for the floor, but the physical principle

is the same: maximum hand velocity is achieved when the point of focus of the strike

is well beyond the surface of the target.

Note that

transfer alike: all three are directly proportional to mass. Since a human being’s mass

for the time it takes to deliver a strike is constant—a karateka with a body mass of 70

kilograms before a strike will have a body mass of 70 kilograms after the strike—

mass is often and erroneously dismissed as a constant in the equations for force,

momentum, and impulse. What matters is not the karateka’s body mass, but how

much of that mass is involved in the strike. A body mass of 70 kilograms is beyond

the karateka’s immediate control; how many of those 70 kilograms contribute to the

strike is very much within the karateka’s control. It is therefore crucial not to use the

arm alone to extend the weapon and hope for sufficient force and energy to break the

target. The entire body should be used by snapping the hips and pushing with the legs

in the direction of the target. This explains why boxers are seldom knocked

unconscious by jabs, where little more than the mass of the arm contributes to the

punch, but are frequently knocked out by hook punches where the entire mass of the

body is thrown behind the punch. The same principle of using the entire body mass to

deliver a blow applies in breaking techniques as well.

Consider now the breaking process from the perspective of the target. When the

force of the strike is applied to the board or cinderblock, it accelerates in response to

that force. The key is that it does not accelerate uniformly—those areas where the

force is applied (the center of the target, if the strike is properly aimed) accelerate

much more than the outer regions of the target which are held in place by large

cinderblocks. This localized

strike, initiates the rupture. Strain is functionally the loss of height of the target that

occurs when the top surface is compressed and the bottom surface stretched. Because

© 1999 Jon Chananie

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Volume 1

JOURNAL OF HOW THINGS WORK

Fall, 1999

of their molecular compositions, materials such as wood and cinderblocks withstand

compression better than stretching. This is why the target begins to split at the bottom.

A clean break occurs when the crack reaches the upper surface of the target.

1. Bardosi, Z., “Kintematical Movement Evaluation of the Straight-line Karate

Techniques.”

2. Bloomfield, Louis A.,

York: John Wiley & Sons, Inc. (1977).

3. Walker, Jearl D., “Karate Strikes.” American Journal of Physics 43, 845-849

(1975).

4. Wilk, S.R. et al., “The Physics of Karate.” American Journal of Physics 51, 783-

790 (1983).

© 1999 Jon Chananie

4

JOURNAL OF HOW THINGS WORK

Fall, 1999

**THE PHYSICS OF KARATE STRIKES**JON CHANANIE

*University of Virginia, Charlottesville, VA 22903***1 Introduction**In recent years, the ancient eastern art of Karate-Do (a Japanese word, literally

translated as “the way of the empty hand”) has become popular in the western world.

Karateka—practitioners of Karate—often break boards, cinderblocks, and other solid

materials in order to demonstrate the strength that their training develops. Much can

be said of the history and culture associated with the expansion of martial training, but

this essay—it is, after all, a physics paper—will examine the collision mechanics of a

hand strike to a solid target like a board.

**2 Force, Momentum, and Deformation Energy**That large objects moving at high speeds hit harder than smaller objects moving

more slowly goes without saying. In attempting to break a board, a karateka seeks to

hit the board as hard as possible. It therefore follows that the karateka should move

his or her weapon (for the purpose of this paper, the hand) as quickly as possible in

order to hit as hard as possible. But what makes for a “hard” strike? Two ways exist to

answer this question, both equally accurate. The first looks at the collision in terms of

**force**and**momentum**; the second looks at the collision in terms of**energy**.Force (F) is

**acceleration**(a) times mass (*m*): F =*m·*a. Momentum (p) is masstimes

**velocity**(v): p =*m·*v. Since acceleration measures change in velocity over time(t) (put another way, acceleration is the derivative of velocity with respect to time),

force is the derivative of momentum with respect to time. Equivalently, force times

time equals change in momentum, or

**impulse**(∆p): ∆p=F· t. This is significantbecause momentum is a conserved quantity. It can be neither created nor destroyed,

but is passed from one object (the hand) to another (the board). The reason for this

conservation is Newton’s third law of motion, which states that if an object exerts a

force on another object for a given time, the second object exerts a force equal in

magnitude but opposite in direction (force being a vector quantity) on the first object

for the same amount of time so the second object gains exactly the amount of

momentum the first object loses. Momentum is thus transferred. With ∆p a fixed

quantity, F and t are necessarily inversely proportional. One can deliver a given

amount of momentum by transferring a large force for a short time or by transferring

small amounts of force continuously for a longer time.

Why, then, move should the karateka swing his or her hand with as much velocity

as possible? Because if the hand is moving quickly, it is likely to decelerate (strictly

speaking, accelerate in the direction opposite to its direction of travel) more quickly in

response to the force the board exerts on it upon collision, as per Newton’s third law.

If the amount of time involved in the transfer of momentum is therefore small, the

amount of force that will be transferred to the target all at once will be large. This

sudden transfer of a lot of force causes the part of the board that is struck and which

therefore experiences that force to accelerate. If that part of the board accelerates

© 1999 Jon Chananie

1

Volume 1

JOURNAL OF HOW THINGS WORK

Fall, 1999

enough relative to other parts of the board (which are generally held still by the

cinderblocks on which the boards are placed), breakage occurs.

This same phenomenon can be analyzed in terms of

**energy transfer**and resulting**deformation damage**. Given and object with mass*m*1 at rest (the board) and anotherobject of mass

*m*2 (the karateka’s hand) moving at velocity*v*upon impact andignoring the negligible amount of energy lost as thermal energy (heat), the amount of

energy in the system lost to deformation damage (∆E) is given by the following:

2

(1−

*e*)*m*⋅*m*1

2

2

∆

*E*=⋅

⋅

*v*2

(

*m*+*m*)1

2

where

*e*is the coefficient of restitution, which measures how elastic the collision is. Itis a function of the hardness or softness of the colliding objects, which along with

velocity determines impulse. If hard objects collide (for a perfectly inelastic collision,

*e*=0), they will accelerate one another quickly, transferring a large amount of force ina small amount of time while soft objects colliding (for a perfectly elastic collision,

*e*=1) transfer smaller amounts of energy to one another for longer periods of time.Difference in how long momentum takes to transfer and therefore in force at a given

instant is why hitting a pillow with the fleshy part of the hand hurts much less than

hitting a brick with the knuckles.

As ∆E is proportional to the square of velocity, the more velocity the hand has, the

more energy will be transferred into the board. In the simplest possible terms, if the

board is infused with more energy than its structure can handle, it breaks. More

rigorously analyzed, energy transfer causes the board to dent. This process of

transferring energy is

**work**(W). Work is force times distance (d): W=F· d. If the areaof the board that is struck dents a sufficient distance, it will break. Since the distance

it dents depends on the energy transferred to it and the amount of energy transferred

depends on the velocity of the karateka’s hand, a high-speed strike is most likely to

break the board.

**3 Striking****Surface**Any martial artist who has ever struck a board with improper hand technique can

attest to the physical pain associated with such impact. The human had is a complex

system of bones connected by tissue, and much can be said about the importance of

proper hand alignment in breaking. From the standpoint of physical science, however,

what is crucial about hand position upon impact is that all formulae for force,

momentum, and deformation energy are for a given unit of

**area**. By minimizing theamount of striking surface on the hand involved in collision with the board, a karateka

minimizes the area of the target to which force and energy are transferred and

therefore maximizes the amount of force and energy transferred per unit area.

Consider a martial artist capable of striking with 190 joules (J) of energy. A typical

human hand is about 6 inches long including the fingers and 4 inches across, which

means that a strike with the entire hand disperses those 190 J over 24 square inches,

about 7.92 J per square inch. If, however, the karateka strikes with only the fleshy part

of the palm, about 2 inches across and 1.5 inches long, the 190 J will be dispersed

over only 3 square inches. That strike will deliver about 63.3 J per square inch,

inflicting many times the amount of damage the whole hand could—the same amount

of energy dispersed over a smaller area delivers more energy per unit area. This is

© 1999 Jon Chananie

2

Volume 1

JOURNAL OF HOW THINGS WORK

Fall, 1999

why martial artists seek to use as tiny a striking surface as possible in not only hand

techniques, but also kicks, elbows, and other strikes as well.

**4 Point of Focus**Karate black belts often advise white belts before their first attempt at breaking

not to try to break the board, but to break the floor under the board. This is to ensure

that the hand does not decelerate prior to contact with the target, a mistake that

beginners, fearful of injury and therefore mentally hesitant, often make. High velocity

of the hand is critical to successful breaking, and data taken from high-speed movies

of karateka show that maximum hand velocity is achieved when the arm reaches

approximately 75% of extension. Intuitively, this makes sense. Since the hand cannot

move forward a distance greater than the length of the arm, it must have a velocity of

0 at full arm’s length extension. It follows that the hand must decelerate well before

the arm is fully extended. Advising beginners to attempt to hit an imaginary target

25% of their arms’ length on the far side of their targets would therefore be more

precise than the typical encouragement to aim for the floor, but the physical principle

is the same: maximum hand velocity is achieved when the point of focus of the strike

is well beyond the surface of the target.

**5 Use of Body Mass**Note that

**mass**is a co-efficient in the formulae for force, momentum, and energytransfer alike: all three are directly proportional to mass. Since a human being’s mass

for the time it takes to deliver a strike is constant—a karateka with a body mass of 70

kilograms before a strike will have a body mass of 70 kilograms after the strike—

mass is often and erroneously dismissed as a constant in the equations for force,

momentum, and impulse. What matters is not the karateka’s body mass, but how

much of that mass is involved in the strike. A body mass of 70 kilograms is beyond

the karateka’s immediate control; how many of those 70 kilograms contribute to the

strike is very much within the karateka’s control. It is therefore crucial not to use the

arm alone to extend the weapon and hope for sufficient force and energy to break the

target. The entire body should be used by snapping the hips and pushing with the legs

in the direction of the target. This explains why boxers are seldom knocked

unconscious by jabs, where little more than the mass of the arm contributes to the

punch, but are frequently knocked out by hook punches where the entire mass of the

body is thrown behind the punch. The same principle of using the entire body mass to

deliver a blow applies in breaking techniques as well.

**6 Specifics of Impact**Consider now the breaking process from the perspective of the target. When the

force of the strike is applied to the board or cinderblock, it accelerates in response to

that force. The key is that it does not accelerate uniformly—those areas where the

force is applied (the center of the target, if the strike is properly aimed) accelerate

much more than the outer regions of the target which are held in place by large

cinderblocks. This localized

**strain**, the response to influence of**stress**imposed by thestrike, initiates the rupture. Strain is functionally the loss of height of the target that

occurs when the top surface is compressed and the bottom surface stretched. Because

© 1999 Jon Chananie

3

Volume 1

JOURNAL OF HOW THINGS WORK

Fall, 1999

of their molecular compositions, materials such as wood and cinderblocks withstand

compression better than stretching. This is why the target begins to split at the bottom.

A clean break occurs when the crack reaches the upper surface of the target.

**Works Consulted:**1. Bardosi, Z., “Kintematical Movement Evaluation of the Straight-line Karate

Techniques.”

*Proceedings of the Eighth International Symposium of the Society of*

Biomechanicsin Sports, July 3–9, 1990, Prague, Czechoslovakia, 23-30 (1990).Biomechanicsin Sports

2. Bloomfield, Louis A.,

*How Things Work: the Physics of Everyday Life*. NewYork: John Wiley & Sons, Inc. (1977).

3. Walker, Jearl D., “Karate Strikes.” American Journal of Physics 43, 845-849

(1975).

4. Wilk, S.R. et al., “The Physics of Karate.” American Journal of Physics 51, 783-

790 (1983).

© 1999 Jon Chananie

4

# Document Outline

- Introduction
- Force, Momentum, and Deformation Energy
- Striking Surface
- Point of Focus
- Use of Body Mass
- Specifics of Impact