[pct-l] The meaning of walking model

[Yoshihiro Murakami]

Dear American hiker

I am re-thinking about the Dynamic walk model, which was an expanded
mathematical theory from the inverted pendulum mode.

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

I am not specialized in Ergonomic, so I may misunderstand the meaning
of theory. But, I think this model describes important aspects of
hiking.

The energy consumption is predictable by the simple mathematical
equation as follows:
WR =1/8 f^3 s^4
where WR is work rate, f is normalized step frequency, and s is
normalized step length. WR is indicated as W/kg in in other pages. So
I think WR is energy consumption per 1kg body weight.

The prediction by the model:
The energy consumption per 1 kg body weight is proportional to the
third power of the step frequency and the forth power of the step
length.

The influence of step length is larger than step frequency. Then we
should increase step frequency when we want to walk fast as like
long-distance runners.

The dynamic walking model is based on the weightless legs. In reality,
the energy consumption increases by the twist of the waist and the
movement of the legs. So, there is a upper limit to the step
frequency.

WR expresses energy consumption per 1 kg in weight. Then,  for
example, the total energy consumption is estimated by very simple way.

When your body weight is 70kg, the energy consumption is WR x 70, when
your body weight is 60 kg, the energy consumption is WR x  60, ...

When you carry 20% body weight backpack, your body weight increases as
1.2 times. Then the energy consumption is WR x bodyweight x 1.2.

If you want to walk with 20% body weight backpack by the same energy
consumption to with no backpack condition,
Assuming :
step frequency is constant f,
step lengths are s0, s2, for each condition,
The energy consumption of no backpack condition is
WR =1/8 f^3 s0^4
backpack condition is
1.2 WR = 1.2 1/8 f^3 s2^4
When you want to walk same energy consumption of both conditions,
1/8 f^3 s0^4 =1.2 1/8 f^3 s2^4
Then, s0^4 = 1.2 s2^4
s2 = 0.956 s0

That is:
When you carry 20% body weight backpack, and when you set your step
length to 0.956 times of your step length with no backpack condition,
your energy consumption of backpack condition became equal to the no
backpack condition.
(Sorry, it was difficult to translate. please guess)




-- 
Sincerely
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Hiro    ( Yoshihiro Murakami  村上宣寛 )
facebook  http://www.facebook.com/completewalker
Blogs  http://completewalker.blogspot.com/
Photo  http://picasaweb.google.co.jp/CompleteWalker/
Backpacking since about 1980 in Japan
JMT, 2009, 2010, 2011(half).
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