From: tlode@nyx.cs.du.edu (trygve lode)
Subject: Re: Holden, Jumbo, and the Fenykoevi elephant
Organization: Nyx, Public Access Unix @ U. of Denver Math/CS dept.
Date: Mon, 5 Oct 92 05:42:44 GMT

In article <718245000@sheol.UUCP> throopw@sheol.UUCP (Wayne Throop) writes:
>
>- square-cube cross section estimation inter-species
>
>Ted is fond of saying that he has measured and found that
>his predictions of cross section derived from the Holden Number hold
>when comparing Kazmaier and the Fenykoevi elephant.  I was looking
>at the photograph of that elephant in AF&F, and noted that
>it would exceedingly difficult to get a circumference of the actual
>major muscles driving the legs, and easy to make the mistake of
>taking the measurement below the "elbow" of the front leg,
>or below the "hock" of the rear leg.  That is, to take the measure
>above the apparent "knees" yet below the next joint up.

[...]

>Working from the photograph, I get 500 in^2 or so of total cross
>section, by making the *incorrect* measurement, and 2400 in^2
>when making the measurement more correctly.
>
>Therefore, I tentatively conclude that Ted's measurements which he
>claims show that his square-cube scaling successfully relates human to
>elephant (and biped to quadruped) cross sections are off, perhaps by as
>much as 3-to-1 in cross section, or 1.7 or so times off in linear measure.

[...]

>Also, anybody know Kazmaier's measurements?  I have something like
>71 in^2 per thigh, cross section.  It may be an underestimate...
>
>( Yes, I realize there are difficulties in estimating muscle
>  cross sections from outside circumference measures.  Nevertheless... )

Actually, it's quite difficult to estimate muscle cross-sections 
involved in a movement based on limb circumference for a few more
reasons.  Perhaps most importantly, the principal muscles involved 
in any multi-joint limb movement (squat, bench, or bent row, but 
not curls) are located in the torso rather than in the limb itself--
the gluteus maximus is both larger and stronger than the combined
heads of the quadriceps; the pectoralis major and anterior deltoid
are considerably larger than the triceps; and the latissimus dorsi
is much larger than the biceps.  Quadrupeds frequently show a much
greater disparity--try, for example, to estimate the strength of a
horse by comparing the cross-section of its limbs with those of a
human.

Further, a lot of muscle attachments are, to use the technical term,
just plain dumb.  Considering the squat again for a moment, the 
biceps femoris both provides hip extension (what you want) and knee
flexion (exactly what you don't want); during the performance of the
lift, a good portion of the strength of the quadriceps is spent 
fighting the biceps femoris.  Further, one of the heads of the 
quadriceps (the rectus femoris) performs both knee extension and
hip flexion, so a portion of the effort of the gluteus maximus is
used simply to fight against the rectus femoris.  Technically, we
should count the biceps femoris and rectus femoris as extensors in
this movement (at which point we've included all the large muscles
of the thigh), yet we're certainly not getting the effective force
that we would expect from that many square inches of muscle tissue,
because a lot of it is operating at cross-purposes.  This suggests
two things:  1)  animals with better designed muscle attachments
could lift much more weight per square inch of muscle tissue and
2) if a divine creator was involved in the selection of human muscle
origin and insertion points, we can conclude that this creator
failed its mechanical engineering courses very badly.

Trygve