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From: throopw@rtp47.UUCP (Wayne Throop)
Newsgroups: net.origins
Subject: A matter of scale
Message-ID: <187@rtp47.UUCP>
Date: Sat, 14-Sep-85 15:31:50 EDT
Article-I.D.: rtp47.187
Posted: Sat Sep 14 15:31:50 1985
Date-Received: Sun, 15-Sep-85 23:57:08 EDT
Organization: Data General, RTP, NC
Lines: 54

I'd like to sort of reason-test a simple-minded scale-up from human size
to "Ultrasaur" size.  Basically, in a simple-minded scale up, horizontal
distances scale by F^1.5, while vertical distances scale by F, where F
is H1/H2, the ratio of height after to height before.

Now, in the case of the Ultrasaur, Ted Holden gives figures of 30 feet
high at the shoulder, and 300,000 pounds.  A human (when you turn one
into a quadroped), is about 3 feet high at the shoulder, and 250 pounds.
Thus, the vertical scale factor F is 10, and the horizontal scale factor
is (gasp) 31.6!  (I note in passing that the weight scales about right
also:  250*10^3 ~= 300,000.  Why did I give our starting quadroped a
weight of 250 pounds?  Because I turned the arms of a 200 pound, 6-foot
man into legs to match the hind ones.)

Well, this is indeed ridiculous, since it means that the poor reptile
would need knees more than twelve feet thick!  However, this
simple-minded scale-up is (so far) overlooking some important factors.
First, this scale up would allow the mumble-saur to have loading factors
on its limbs similar to those of a human.  Second, I am ignoring the
advantages of leverage gained in having thicker limbs.   I'll estimate
leverage factors and additional loads, and back off of the 30-times
horizontal factor a little.

Now, a human knee, (just looking at an example here), is applying muscle
power on an arm 2.5 inches, delivering power to an arm ~20 inches long.
Our initial scale up has the mumble-saur applying on a 6-foot arm, and
delivering power to a 15-foot (or less) arm.  This is about a 3-to-4
times increase in force due to leverage.  Can we reduce the diameter of
the knee by a factor of (say) 3, and still not exceed the tearing limit
of muscle and ligament?  This would make the knee 4 feet across,
handling 9 times as much force as the human knee.  The wear-and-tear on
the knee would be that of a human weighing (hmmm, four human-designed
knees, supporting 250 pounds, so over two times 9) 1125 pounds (or a
human knee working in 4.5 Gs).

Now this borders on the impossible, but doesn't seem to me to be out of
the question.  There are still some factors favoring the mumble-saur
that we haven't addressed.  For example, our mumble-saur wouldn't be in
any *muscular* distress.  The problem is strictly one of the ability of
his bones and skeleton handling the stress without breaking.  And I
haven't addressed the actual geometry of the mumble-saur knee.  I simply
used human geometry and scaled it.  An actual mumble-saur could get a
fair extra margin from altered application of stress to the limb by
varying the geometry (for example, humans balance weight on top of the
leg, while the sauropod slings the weight between, leading to much
smaller legs, as seen in existing quadropeds).

Now, this back-of-an-envelope scaling excersise points up the fact that
the Ultrasaur is an impressive beast, and that the larger sauropods are
pushing the limits of possible size in a 1-G gravity, but it *doesn't*
show that it is impossible.  On the contrary, I'd say it shows that it
is (just barely) possible.
-- 
Wayne Throop at Data General, RTP, NC
<the-known-world>!mcnc!rti-sel!rtp47!throopw


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