Please, look here.

https://books.google.ru/books?id=TEZrZQiEB58C&printsec=frontcover&hl=ru#v=onepage&q&f=false

What do you think on the authorship of this book?

]]>Yesterday I’ve shown Neill’s presentation on “Hopes and Fears” as the last lecture in my course on biomechanics.

It seems to have gone fine. I’ve managed to explain every slide.

Most of the time I devoted to explanation of Kram & Taylor hypothesis and the first slide plotting

metabolic cost of transport in running together with mechanical energy of the center of mass (taken from Full & Tu, 1991).

The question which Neill definitely meant here is why the mass-specific cost of running falls as mass^(-1/3),

while mechanical energy fluctuations per meter per kilogram remain almost constant.

I am sure that Neill was greatly suspicious about Kram & Taylor hypothesis, because,

on the one hand, it is the only hypothesis that explains the sacral law of mass^(-1/3) decrease of the metabolic cost,

and on the other hand, it is based on a strange assumtion that the cost of muscular force overrides the cost of muscular work.

Thinking after the lecture on the problem, I’ve, seems to me, guessed the sacral puzzle of mass^(-1/3).

Just look.

What is the unit of mass-specific metabolic cost of transport?

Yes, it is Joule/(meter*kg) = Newton*meter/(meter*kg) = (kg*meter/second^2)/kg = meter/second^2

This is the unit of acceleration.

So, on the graph from Full & Tu, 1991 it is more adequate to place, instead of the plot of mechanical energy of the center of mass,

the plot of typical accelerations in running.

It is very easy to imagine the line of acceleration on this graph.

Indeed, acceleration = force/mass = (work/shift)/mass

Let it be the average vertical (antigravitational) acceleration of the center of mass in the contact phase.

The mass is the mass of the body, the force is the average vertical ground reaction force,

shift is the distance over which the force is applied and it is definitely proportional to leg length,

while work is proportional to muscular mass involved in antigravitational action.

Thus, acceleration ~ (muscular mass)/(leg length/body mass).

We can easily assume that in all running animals musculature is proportionately involved in mechanical work against gravity.

So, acceleration ~ 1/(leg length) ~ mass^(-1/3) ~ (mass-specific metabolic cost of transport)

Taking into account the same units of acceleration and cost,

it seems appropriate to estimate the efficiency by the ratio: (acceleration/mass-specific metabolic cost of transport)

Both of them fall as mass^(-1/3), and so the muscular efficiency is size-independent in fact.

What do you think about it? Would Neill be happy of this simple solution?

]]>http://movement.osu.edu/papers/AlexanderCV/RobertMcNeillAlexanderCV2005.pdf

This PDF contains the remarkable list of all his papers and books until early 2005. Of course, his work from 2005 onwards can be looked up on google scholar as:

https://scholar.google.com/scholar?as_ylo=2005&q=author:mcneill-alexander