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Re: scaling laws



Thanks Hugh but I think this demonstrates my point. Besides
knowing that there is a greater surface area to volume ratio
for a mouse, one also needs to know that (a) rate of metabolism
is proportional to total blood volume, (b) heat generated is
proportional to metabolism, (c) heat loss is proportional to
surface area and (d) volume pumped by one beat of a heart
is proportional to total blood volume.

Or something like that.

____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301

-----Original Message-----
From: Forum for Physics Educators
[mailto:PHYS-L@lists.nau.edu] On Behalf Of Hugh Haskell
Sent: Friday, October 10, 2003 2:02 PM
To: PHYS-L@lists.nau.edu
Subject: Re: scaling laws


At 13:20 -0400 10/10/03, Robert Cohen wrote:

It doesn't appear to me that this "immediately" answers the
question of
why an elephant's heart doesn't have to beat faster. Don't
you have to
know something about metabolism? Or am I missing a more "immediate"
connection?

The smaller mouse has a much higher surface are to volume
ratio than does the larger elephant, hence the energy
generated within the mouse's body is much more easily
radiated away through the body surface. If both generated
heat at the same rate, either the elephant would fry itself
because it couldn't radiate the energy away as rapidly as
would be necessary, or the mouse would freeze itself
(figuratively) because it couldn't generate energy within the
body as rapidly as its body could radiate it away.

Humans may be a better example, because a baby is more nearly
a scaled down adult than a mouse is a scaled down elephant.
But the size difference isn't as great so the effect won't be
as great. Typical adult heart rates are around 70, while
those of infants are around 110-120. The difference can be
accounted for by the difference in surface to volume ratio
between infants and adults.

There is a nice book on scaling laws in biology called
"Newton Rules Biology," by C. J Pennycuick (Oxford, 1992),
that deals with these issues and more. There are lots of nice
examples of scaling as applied to biological systems in it.

Hugh