The Physics of Karate
Lab Ticket
* Read this lab write-up.
* Read the Condensed manual for the High Speed Camera. Located under the links
section of this course's web page.
* Write an outline of the procedure you will follow during your two-week
investigation.
There are two main parts to this experiment: measuring the amount of kinetic energy you
can put into your hand and measuring the amount of energy necessary to break a piece of
pine board. After completion of the lab you should be able to determine whether you can
break a pine board without injury to your hand. You are in no way required to break a
board but are welcome to try it after confirming that you theoretically can.
Equipment Provided:
1) High-speed video camera.
1) Two saw horses.
1) Load-Bearing board.
1) Dial indicator.
I. Introduction to the Physics of Karate
Karate is an ancient martial art that is believed to have begun on the island of Okinawa.
After invasion by the Japanese the islanders were forced to yield all of their weapons.
Consequently the islanders began training in empty-hand combat and developed
techniques for effective fighting without weapons. Modern scientific investigations of
these ancient techniques consistently find that they have been amazingly well designed.
Many of the techniques taught as conventional wisdom translate into precise physical
optimizations of human movement.
In the following you will investigate how a few of these techniques can be used to
break boards. The first section of the lab investigates the energy that you can deliver in
various punches. The second section is dedicated to finding out how strong pine boards
are. These sections can be approached in either order, so if there is a group already
working on the first section go ahead and work on the second one.
II. Energy in Your Hands
There is a stark contrast between eastern martial arts like karate and western styles of
fighting like boxing. Martial arts experts use very quick extremely controlled strikes to
injure their opponent and at the same time maintain their balance in case of
counterstrikes. In contrast western boxers use less controlled punches with long follow
through, designed to knock their opponents over. This difference in approach is important
to keep in mind as you investigate karate strikes.
The first part of this experiment is dedicated to finding out how much energy you
can deliver in a forward punch. A typical forward punch in karate is described below:
Let us consider a forward punch in which the attacker does not move his feet.
The fist starts at the waist with the closed palm upward, and as the fist is hurled forward,
it turns over until the closed palm is downward when the arm is fully extended. [1]
Practice this movement a couple of times. You may find it useful to pull your other fist
back as you punch. This rotates your hips and can add speed to the punch. However, be
aware of your balance, this technique is useless if you don't maintain balance.
1) Take a high-speed video of both you and your partner performing this punch.
While it may be tempting to use an extremely fast frame rate keep in mind
that you have to analyze this video and a whole bunch of frames that you
don't digitize is just extra baggage that will slow you down. A reasonable
frame rate is 500 frames per second. It is also a good idea to take the video
from the same side as the person is punching, that way you will be able to see
their fist in all of the frames. (As always be sure to have something in the
frame that you can use to scale the movie.)
1) Digitize your movies using the techniques described in the condensed manual
for the high-speed camera. In VideoPoint, set the frame rate to 500 fps by
clicking Select Frame Rate from the Movie menu.
1) What is the maximum speed that your hand reaches? How much energy is
your hand carrying at this point? The following table can help you to estimate
the mass of your hand (It is difficult to estimate a precise mass of your hand
because it is attached to your forearm. It would be reasonable to include some
of the mass of your forearm in the calculation of energy. However, keep in
mind that for the purpose of calculating whether you can break a board it is
safer to underestimate the energy that you can deliver with your hand. Thus
don't include the mass of your full forearm):
MALE SUBJECTS = [M] FEMALE SUBJECTS = [F]
HEAD 6.940% [M] 6.68% [F]
TRUNK 43.456% [M] 42.57% [F]
UPPER ARM 2.707% [M] 2.55% [F]
FOREARM 1.625% [M] 1.38% [F]
HAND 0.614% [M] 0.56% [F]
THIGH 14.165% [M] 14.78% [F]
CALF 4.330% [M] 4.81% [F]
FOOT 1.370% [M] 1.29% [F]
Table 1. The table above presents the mass of various parts of the human body for both
males and females given as percentages of total body mass. This data is from the findings
of Zatsiorsky, et. al.
One well-known piece of advice that karate instructors give their students
is to focus their punches into their target. Thus if you were striking another person
in the chest you would aim to terminate the punch about a fists length inside of
your opponent. Use the data you obtained in part 3) to evaluate this piece of
advice. There is actually an extremely useful and general analysis technique that
you can use in your evaluation of this advice, known as normalization. If you plot
the velocity of your punch vs. the position of your punch, measured from where
the punch began, you will have a good idea of where your punch attains its
greatest speed and consequently its greatest energy. However, if you were to
compare the position of this greatest speed to the position of your lab partners
greatest speed they are most likely going to be different. This is not very
surprising since you and your partner probably have very different builds and arm
lengths. If you want to make a more general statement of where the maximum
speed of a punch takes place, you would want to try and account for this
dependence on different people.
2) For this part of the analysis, we will need to move the data to Excel. To do
this, simply highlight the data from VideoPoint's table, copy it and past in
Excel. Plot the speed of your punch vs. the position of your punch. Do the
same for your partner. What are the positions when each of you reaches
maximum speed? Are they substantially different? Now, plot the speed of
your punch vs. the position of your punch divided by the total length of the
punch? What is different about this plot? Explain. Create the same plot for
your lab partner. Now, do the maximum speeds occur at the same normalized
position (or at least are they closer to the same)? In these final two plots you
have performed a normalization to total strike length.
The second strike you should evaluate is called the hammer fist strike. In the
hammer fist strike you clench your fist and raise it above and behind your head.
Then you quickly swing the fist down in front of you in a similar motion to a
smithy striking an anvil with his hammer. Most people can attain much higher
speeds with this strike then with the forward punch and it will probably be the one
you use to break the board.
3) Make another high-speed video of yourself executing the hammer fist strike.
Make one of your partner also. What is the maximum speed your fist reaches?
How much energy does your hand have at this speed? (If you are interested
you could develop a similar analysis of this strike as you did of the forward
punch.)
III. The Work Needed to Break a Board
In addition to knowing how much energy you can wield with you hands you need
to know how much work it takes to break a board. The two sawhorses, dial
indicator and load-bearing board will help you to measure this work.
1) Setup the two sawhorses so that their inner edges are about 26 cm apart,
leaving about 1cm of board overlapping on each side. Place one of the
clear (i.e. knot free) pieces of pine on the saw horses so that the grain of
the board runs parallel to the length of the sawhorses. Place a rod over the
center of the pine board and use the clamp and stand setup to place the dial
indicator on the rod. Calibrate the dial indicator so that it reads zero, since
the board has not been deflected yet. Now weigh the load-bearing board
and hang it from the rod. In your calculations, don't forget to include the
contribution of the load-bearing board to the work needed to break the
board.
2) Now, you can measure the work needed to break the board. Load five
kilograms onto the load-bearing board. The pine board will bend under the
weight and the dial indicator will measure this deflection. The pine board
does not stop bending immediately so wait for about three minutes and
then mark down the deflection. Ideally you would wait until the pine
board had completely stopped bending but this can actually take quite
some time. Repeat these steps until the board breaks.
3) Note that when you add 5 kgs to the load-bearing board the pine board is
deflected an amount x equal to the final reading of the dial indicator
minus the initial reading of the dial indicator. During this time the force
acting on the board is constant and equal to the total weight on the loadbearing
board. Use these facts to calculate the total work. Illustrate this
calculation graphically.
IV. Can You Break the Board?
In this section you will use the maximum velocity you obtained in the hammer fist strike
to evaluate whether you can break a board. Because the dynamics of your hands
interaction with the board is quite complex you should begin with a simplified model.
Think of the board as floating in outer space unsupported, this allows you to ignore the
effects of the sawhorses. Now, consider the situation, depicted below, in which your hand
with mass M comes in with velocity vo just below the velocity necessary to break the
board and collides inelastically with the board. In this situation the kinetic energy that
your hand loses results in two effects, the first is to accelerate the board up to its final
velocity (i.e. give the board kinetic energy) and the second is to deform the board. If the
energy that goes into deforming the board is greater than the work that it takes to break
the board then the board will rupture into pieces.
M
vo
m
a)
vm+M
b)
Figure 1. a) A mass M approaches a stationary board of mass m at velocity vo .
b) The mass M inelastically collides with the board accelerating it to a velocity
v and simultaneously deforming it.
1) Assume that the collision between the board and your hand is completely
inelastic. Use conservation of momentum to find the speed v of your hand and the
board after the collision in terms of vo , M and m.
2) As has been emphasized in lecture, energy is always conserved but there are many
forms that it can take on. Assuming that the only form of energy involved in this
collision other than kinetic is the energy stored in the deformation of the board
use the conservation of energy to determine how much energy went into the
deformation of the board. [Answer: Edeform =
1
2
mM
m + M




vo
2
]
3) Use the maximum velocity of your hammer fist strike that you found in II.5) to
calculate how much energy you can put into the deformation of the board. Is this
enough energy to break it? Note that the requirement for breaking the board is

Edeform  Wbreak (and not

KEhand  Wbreak ) since only some of the energy of your
hand goes to break the board.
Before breaking the board you have to evaluate whether you might be injured in this
process. Research has shown that an impulse leading to a 900 N force for 0.006 seconds
is enough to break a typical cheekbone.
4) If, as above, your hand makes an inelastic collision with the board resulting in a
final velocity v, what is the momentum change of your hand?
5) Suppose you have a failure of nerve because you are afraid of hurting yourself so
your hand slows down to a speed just below that which you need to break the
board. Assume that in this case the board brings your hand to a complete stop.
Calculate the momentum change of your hand.
6) Suppose that your hand is in contact with the board for about 6 ms (see [2]).
Using the results of 4) and 5) what is the maximum force your hand can feel if
you break the board? If you just barely fail to break the board?
7) If the injury you sustain is a function of the maximum force on your hand and if
you know theoretically that you can break the board, what is the consequence of
having a failure of nerve and slowing down your hand in mid-hit? Are you more
likely to be injured or less likely to be injured? Why?
Now, that you have all of the relevant information you should show your calculations to
the head lab instructor and he'll confirm that you can break a board. If you would like to
try it, go ahead and setup the sawhorses again and put a piece of pine on them. Be sure to
hit along the grain of the wood. Wood is ten times stronger against the grain and hitting it
this way could result in serious injury.
V. Some Possible Extensions
Here are some further ideas that you could investigate experimentally: I) See references
[1] and [2] for derivations of the deformation energy involved in these collisions. You
could use the high-speed camera to take video of your partner smashing a board and
determine to what degree the collision really was inelastic.
II) If you can find some dry semi-thin cinder block you could measure the work needed
to break it and show that you would be unable to break it.
III) References [1] and [2] also have some more involved theoretical models that are very
interesting.
[1] Walker, J. D. "Karate Strikes," AJP Vol. 43, 10, Oct. 1975
[2] Feld, M. S. et. al. "The Physics of Karate," Scientific American, pp. 150-158, April
1979.