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