Path: utzoo!utgpu!attcan!uunet!seismo!sundc!pitstop!sun!decwrl!labrea!agate!violet.berkeley.edu!dean
From: dean@violet.berkeley.edu (Dean Pentcheff)
Newsgroups: sci.bio
Subject: Re: Squirrel Questions
Summary: Drag for small mammals
Keywords: drag terminal velocity
Message-ID: <14804@agate.BERKELEY.EDU>
Date: 29 Sep 88 03:49:36 GMT
References: <22811@mordor.s1.gov>
Sender: usenet@agate.BERKELEY.EDU
Followup-To: sci.bio
Organization: University of California, Berkeley   Department of Zoology
Lines: 41

In article <22811@mordor.s1.gov> lip@s1-amid.UUCP () writes:
>	I once saw a squirrel jump with a drop of over six feet (onto
>a carpeted floor, I might add), and run off as if nothing had
>happened. Is such durability typical of small animals? If so, then it
>would be an outcome of the square-cube law, in which smaller animals
>have a larger drag force (~area~length^2) per unit mass
>(~volume~length^3).

Well, no, not quite.  It turns out that (at the sort of sizes and
speeds that concern a falling squirrel) drag is proportional to the
cross sectional area perpendicular to the fall direction and the
velocity squared.  To be pedantic:
				     2
	drag = 0.5 * C  * rho * S * U
		      D
where C-sub-D is the "drag coefficient" and is a fudge factor that
accounts (more or less) for shape differences, rho is the density of
air, S is the cross sectional area, and U-squared is the velocity
squared.

The mass falling in gravity results in a force, countered by the drag
force (which increases as the _square_ of velocity).  Note that for the
small mass of a squirrel, the drag force quickly becomes very high,
slowing the animal.  The animal quickly reaches "terminal velocity",
where the force from gravity = the force from drag and the animal stops
accelerating.  It turns out (and, yes, the experiment was done) that
you can drop a mouse from a five-story building with no harm to the
mouse - it probably reached terminal velocity around the second story.
The situation should be similar for squirrels, particularly given their
fuzziness (which should yield a high drag for their mass).

If you're interested in a readable account of the relevant biology and
physics, see Vogel, S. (1981) Life in moving fluids.  Willard Grant.

-Dean


Dean Pentcheff        dean@violet.berkeley.edu

To acquire imunity to eloquence is of the utmost importance to the
citizens of a democracy.                          Bertrand Russell