[pct-l] Ultralight as a must?

Yoshihiro Murakami completewalker at gmail.com
Sun Sep 30 19:02:04 CDT 2012


Dear Stefan

Please input following words in Google search window:
site:mailman.backcountry.net/pipermail/pct-l "The meaning of walking model"
I posted several times the walking model, which was proved to simulate
human walking by empirical studies.


I introduced the walking model and make several explanation in my
hiking handbook <---this is a brief translation from my new handbook.

Kuo, A.D. ( 2007 ) The six determinants of gait and the inverted
pendulum analogy:A dynamic walking perspective. Human Movement
Science, 26, 617-656.

by Kuo( 2007 )

The energy consumption is predictable mathematically by the following formula,

WR =(1/8)f^3s^4

WR is work rate (energy consumption per 1 kg in weight),  f is
standardized frequency of pitch, and s is standardized step length.

This model was proved by the walking experiments. The mathematical
estimation of energy consumption was very similar to the real energy
consumption.

Several reasoning can be done by simple arithmetics.

WR is proportional to the fourth power of the step width and the third
power of frequency of pitch. In other words,  step width has stronger
influence to energy consumption. When you walk in high speed, it is
better to increase frequency of pitch, then the increase of energy
consumption is minimum.  It might be a similar mechanism in running,
then the high frequency pitch running is recommended in the
long-distance runnings such as the marathon.

The dynamic walk model is based on  weightless legs, then assuming
the step width be minimum and frequency of pitch be maximal, the
energy consumption decreases near zero.

In a real world, there in no weightless leg.  The energy consumption
also increases by the twists of the waist.  The most efficient walking
speed is found to be 4-5km/h, then the energy consumption is minimum (
There are many experiments in Ergonics, for ex. Abe, D., Yanagawa, K,
& Niihata, S.  2004  Effects of load carriage, load position, and
walking speed on energy cost of walking.  Applied Ergonics, 35,
329-335.)

WR is a energy consumption per 1 kg in weight per time. In other
words, as for the energy consumption of the person weighing 60 kg is
60 x WR, and  the energy consumption of the person weighing 70 kg is
70  x  WR . So the energy consumption is estimated by weight  x  WR.
The total energy in a day is also simply calculated by weight x  WR  x
walking time.

As for the energy consumption, assuming step width and the frequency
are constant, if you carry 20% of body weight backpack, then the
energy consumption is ( body  + backpack ) weight x WR, that is 1.2 x
WR.  It is a very simple relation.

Now, another reasoning. ---20%body weight backpack and without backpack

If the energy consumption of 20% backpack condition is equal to
without-backpack condition,  how should we tune our gait.  If you walk
without a backpack, your energy consumption is  ( body weight ) x 1/ 8
 x f^3  x s0^4.   If you walk with a 20% body weight  backpack, your
energy consumption is  ( body weight + backpack weight ) x 1/ 8  x f^3
 x s2^4.

s0 is a step width in without backpack, and s2 is a step width in 20%
backpack condition.

If we can walk with the same energy in the both condition.
( body weight ) x 1/ 8  x f^3  x s0^4 = 1.2 x ( body weight  ) x 1/ 8
x f^3  x s2^4.
then by simple arithmetic,  we can conclude s2=0.956s0.

That is if you walk carrying 20% body weight backpack with 95.6% step
width as compared to without backpack condition, your energy
consumption may be equal to the without backpack condition.


Another reasoning: ultralight hiker (10%body weight backpack) vs heavy
trucker(40% body weight backpack)

Assuming, an ultralight hiker who carries a 10% body weight backpack,
and  a heavy trucker who carries a 40% body weight backpack, the body
weights are equal.

If they walk  same time  with same step width and pitch, then  the
energy consumption of ultralight hiker is 1.1, and that of heavy
tracker is 1.4,  Then the heavy trucker needs energy of 1.27 times of
the ultra light hiker.

If they walk same time with different step widths(s1, and s4),
assuming frequency of pitch is constant. Assuming an ultra light hiker
and the heavy trucker walk with the same energy consumption at the
same time. Then,  1.4s4^4=1.1s1^4,  It becomes s4=0.943s1

That is the energy consumption becomes equal to that of the ultralight
hiker at the 94% distance of the ultra light hiker. In other words,
the heavy trucker can prevent physical consumption if he make distance
a little short.

I am very sorry for you all. The simple reasoning based of recent
walking model indicated the the influence of backpack weight is not so
large as you expected. It may be within 5% when walking gait is tuned.
 You cannot walk double distance if you halve the backpack weight. The
endurance training is needed.


-- 
Sincerely
--------------- --------------------------------------
Hiro    ( Yoshihiro Murakami  村上宣寛 )
facebook  http://www.facebook.com/completewalker
Blogs  http://completewalker.blogspot.jp/
Photo  https://picasaweb.google.com/104620544810418955412/
Backpacking since about 1980 in Japan
JMT, 2009, 2010, 2011(half), 2012
Handbook of Hiking (in Japanese ) will be published in 2013
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