From: throopw@sheol.UUCP (Wayne Throop)
Newsgroups: talk.origins
Subject: Holden Numbering: FAQs and figures
Summary: some common misconceptions about the Holden Number
Date: 27 Jul 92 23:31:02 GMT

>> mrjg8679@uxa.cso.uiuc.edu (Michael R James)
>> Has anyone looked at the HN for giraffes.

> From: news@fedfil.UUCP (news)
> Message-ID: <2834@fedfil.UUCP>
> Around 13 or so. 

Good grief.  Why wonder what the Holden Number is for some animal or
other?  It's very, VERY easy to calculate.  It's a measure of force
over cross section, so divide the total load (in lbs force) over a
cross section derived from the volume, in turn derived from the mass
(in lbs mass).  Or, for the giraffe:

                  2200 / 2200^(2/3)

The "^(2/3)" is what gets a cross section from the mass, by getting a
linear measure by taking the cube root, then getting an area measure by
squaring that.

Now, what UNITS the Holden Number has are bizarre, since Ted
specifies the load in lbs force and the mass in lbs mass.  But in the
end, the specific units don't matter, as long as the formula is
applied consistently.

Ted makes the error of calling this a "dimensionless number", a number
with no units.  This, of course, is very wrong, and demonstrates quite
clearly that Ted doesn't know what he's talking about.  From the
evidence, I tenatively conclude that Ted doesn't even know why the above
calculation works for exact proportional scaling, nor why it fails for
non-proportional scaling, because he claims both that it WORKS for
non-proportional scaling, and fails to give any reason WHY it is a
comparison factor used in weight-lifting events.

So, if you are wondering what the HN for some particular animal is,
look up the mass of the animal and calculate it for yourself.  It is
easy, and involves no messy measurements of the muscle sizes or limb
diameters of the animal itself.  (Ted did once show that the load per
total cross section in the upper segment of the four limbs of the
elephant on display at the smithsonian were roughly equal to the Holden
Limit.  Interestingly, Ted persists in calling this elephant "Jumbo",
despite the fact that that's not the elephant's name: don't confuse
Ted's reference with the actual elephant called "Jumbo", the remains
of which were destroyed in a fire some time ago.)


A related frequently-asked-question is normally posed in the form of a
"refutation" of Ted's theory about the "felt effect" of gravity.  Ted
claims that estimates made by others of the larger sauropod masses are
too small, and that he has better estimates that demonstrate his
beloved "felt effect".  An example is the seismosaur, which most
estimates place at less than 100 tons.  Ted claims that it should be 280
tons, and that the "felt effect" is what accounts for the incorrect,
lower estimates.

The incorrect rebuttal to Ted's position is "Well, even 80 tons is
still above the Holden Limit".  This is incorrect.  The Holden
Limit isn't a limit on weight, as we see from above, but a limit
on weight over cross section derived from mass.  Using 80 tons
for the weight, and 280 tons for the mass, we have

            160,000 / 560,000^(2/3)  ~= 24

Again, the Holden Limit doesn't work out to be a limit on weight...
it's a limit on weight per 2/3 power of mass, or force per
cross-section.  The reason Ted is wrong with his calculations for the
breviparopus and seismosaur are that the <100 ton weights are, in fact,
calculated by what Ted calls the "Archimidean method" (that is, by
estimating volume, and hence mass).

The simple fact is, Ted's estimates of the mass of these creatures in
particular are far, far too high, because he still hasn't acknowledged,
despite it being pointed out to him many, many times, that the average
Brachiosaurid is 4 times as voluminous (and hence massive) as the
average Diplodocid of equal length.  Ted's estimates are gotten by
calculating the volumes of these Diplodocid dinosaurs as if they were
Brachiosaurids (specifically, by scaling up McGowan's estimate for
Ultrasaurus, which is based in turn on earlier estimates by Coyle for
Brachiosaurus), and thus his estimates are off by factors of four or
so.  (In the case just discussed, a bit less.)

Also, be aware that when reading Ted's expositions, he tends to confuse
"mass" with "weight".  Basically, he uses "weight" for both things, and
you have to deduce from context which one he really means.

So, the moral is: calculate your Holden Numbers for yourself.  It's
easy, fun, and asking Ted to do it is silly.

A subordinate moral is: don't fall into the error of supposing the
Holden Limit is a limit on weight.  It isn't.
--
Wayne Throop  ...!mcnc!dg-rtp!sheol!throopw