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The recent spam thread on physics gave me the interesting idea of
trying to analyze various things we see in anime with real world
physics.
Unless people think this is either a horrible idea or consider it spam
(since it's not a fanfic) and don't want it on the FFML, I plan to
have an analysis each week or two. As for the first installment, I
give a very rough analysis of the Tenshin Amaguriken in Ranma 1/2.
Any corrections or suggestions are welcome.
Physics in Anime
Yoo C. Chung (wacko@laplace.snu.ac.kr)
Copyright (C) 1997 Yoo C. Chung
This work may be redistributed freely without modification in
an electronic medium. No part of this may be used or reproduced
(except for the case stated explicitly in the previous) for any
purpose whatsoever without the permission of the author.
1.1 Tenshin Amaguriken
The Tenshin Amguriken (also called the Chestnust Fist) is a martial
arts technique which is capable of throwing a great number of punches
in a very short time.
1.1.1 Rough Analysis
Let's say that the forearm has a mass of m, the forearm travels
a distance of d when throwing a punch, and that punches are thrown
at a rate of n.
For the sake of simplicity, assume that the arm is always moving
at a constant speed, and changing the direction of the arm happens
instantaneously. Since the arm moves a distance of 2dnt in time
t, the speed of the arm v is
v = 2nd (1.1)
Then the impulse J that the arm must receive when changing the
direction the arm is moving is
J = 2mv = 4nmd (1.2)
_
Then the average force F that must be exerted on the arm is
_ 2
F = Jnt/t= 4mdn (1.3)
Since this is a very rough analysis, we can assume the minimum
average power P needed for the technique to be
_ __ 2 2 3
P = Fv = (4mdn )(2nd) = 8md n (1.4)
From the above equation, we see that a slight increase may result
in a larger than expected force and a much larger than expected
energy consumption.
Let's see what we get when we put in actual numbers. Let's say
that the forearm is 1 kg, the forearm travels 0.5 m when throwing
a punch, and that 100 punches are thrown per second. Then we obtain
the following figures.
v = 50 m/s
J = 200 kg m/s
_
F = 20000 N
_
P = 1 MW
The average speed that the arm moves is 50 m/s, which isn't much
of a big deal. However, the average force that needs to be exerted
is very large. Since an average person weighs 60 to 70 kilograms,
it is enough force to sustain the weight of about 30 people. This
is rather extraordinary, but someone might conceivably be able
to do this in the real world.
Also, if the Tenshin Amaguriken is sustained for one second,
the amount of energy used is about 240 kcal, which is about ten percent
of the energy an average person uses in a single day. The amount
of energy consumed by the person performing the technique would
probably be a lot more higher, since the efficiency of muscles
are not particularly high.
So, if the force needed to use the Tenshin Amaguriken can be
conceivably exerted by someone in the real world, why don't we
see anyone in the real world performing the technique? One reason
is that the above force is the *average* of the force exerted.
The peak would be magnitudes of order higher, and would probably
be impossible for any human in the real world to exert. Another
reason is that it is questionable whether human muscles can produce
the necessary energy in so short a time.
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