# The Physics of Karate Strikes HTML version

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 m1 at rest (the board) and another
object of mass m2 (the karateka’s hand) moving at velocity v upon impact and
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:
(1
)
2(
2
mm
∆ =
1
2
v
2
mm
)
1
2
where e is the coefficient of restitution, which measures how elastic the collision is. It
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,
e=0), they will accelerate one another quickly, transferring a large amount of force in
a 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
3 StrikingSurface
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 the
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