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The Physics of Karate Strikes

Volume 1
Fall, 1999
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
p=F· t. This is significant
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
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 = a. Momentum (p) is mass
times velocity (v): p = 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 (