From: throopw@sheol.UUCP (Wayne Throop)
Newsgroups: talk.origins
Subject: Re: The Holden number
Summary: Ted's formula is correct only for exact proportional scaling
Date: 06 Apr 92 01:13:23 GMT

Scott H Mullins has been asking about the derivation of the formula
for the infamous Holden Number:

> smullins@cidmac.ecn.purdue.edu (Scott H Mullins)
> Message-ID: <1992Mar26.142843.26018@noose.ecn.purdue.edu>
> It looks to me like you just made
> this up off the top of your head. Why is the 2/3 power significant? 

> smullins@cidmac.ecn.purdue.edu (Scott H Mullins)
> Message-ID: <1992Mar30.222851.10369@noose.ecn.purdue.edu>
> I will ask again: Where did the 2/3 power come from? I think you made this
> up to match your own assertions.

It turns out that Ted actually more-or less answered this in the "still
waiting for answers" thread.  Here's an excerpt from what Ted has to
say:

> news@fedfil.UUCP (news) (Ted Holden)
> Message-ID: <2696@fedfil.UUCP>
>>  I don't understand, could you clarify this for me please?
> You lose power-to-weight ratio as you get bigger...  weight goes up in 
> proportion to volume, which is a cubed figure.  Strength and every other 
> measure of efficiency go up only in proportion to various squared figures.
> Strength in particular is proportional to cross-section of bones and muscles.
> Two-thirds power of body weight is a kind of a general average of body
> cross-section, and for this reason is the natural scaling factor for lifting
> events.  

Ted doesn't mention it explicitly, but volume (assuming constant
density) is proportional to mass, which in turn (assuming constant
gravitational acceleration) is proportional to weight.  Thus, the
two-thirds power is simply the square-cube scaling factor.  The units of
the Holden Number (far from being "dimensionless" as Ted has incorrectly
claimed several times in the past), are therefore force over area. 

What Ted absolutely refuses to believe (but which is nevertheless the
case) is that square-cube scaling of the simple sort he is doing only
applies to animals of uniform density and shape.  Since human
weightlifters (all being human) are indeed very roughly all the same
density and shape, the square-cube scaling factor applies to them quite
well. 

The problem is that Ted claims this "generalized cross section"
nonsense, which is demonstrably not true.  His calculation of "about 27"
as the Holden Limit is flawed, because he doesn't take account of
quadruped vs biped differences, limb leverage differences, and the
inaccuracy of the "squat" weightlifting events as a model. 

These things have all been pointed out to Ted for more than four years,
and he has yet to understand and agree to these simple facts.  I don't
expect him to start now. 


PS: Recently, Ted claimed that Ultrasaurus' weight by volume
measurements was 360000 lbs, and that the weight given in the Guiness
Book of Records was (probably) from footprint depths, and thus
underestimated because of his also-infamous lessened Felt Effect of
Gravity.  Thus, the lighter weight measured by the GBR (of 100-140 tons)
is what accounts for the Ultrasaurus' existance.  Ted apparently didn't
do his arithmetic: this has the Ultrasaurus, even in Ted's Antedeluvian
Wonderland, having a Holden Number somewhere between 40 and 55. 

This is not too surprising.  The last time Ted proposed this solution
to the discrepency of his weights to forces derived from track
depths and the like, he didn't do his arithmetic about the volume
of the Seismosaurus, confusing diplodocids and brachiosaurids
as he is wont to do.
--
Wayne Throop  ...!mcnc!dg-rtp!sheol!throopw
Newsgroups: talk.origins