Re: pinhole peregrine falcon question

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From: Paul Doherty (pauld@exploratorium.edu)
Date: Thu Oct 04 2001 - 09:06:10 PDT 

Message-Id: <l03110710b7e236c4b7de@[192.174.2.173]>
Date: Thu, 4 Oct 2001 09:06:10 -0700
From: Paul Doherty <pauld@exploratorium.edu>
Subject: Re: pinhole peregrine falcon question

Hi Regan

The terminal velocity of a person is 120 mph in the spread eagle position
(maximum air resistance) and 200 mph in the dive position (minimum air
resistance)

Now Assume a spherical person and a spherical falcon:

Terminal velocity occurs when the force of gravity, mg, is equal and
opposite to the air friction force. which is proportional to the cross
sectional area of the object moving through the air, and to its velocity
squared (it also depends a little on the shape of the object.)

The mass of a human is 100 times the mass of a falcon so the cross
sectional area is 16 times (100 to the 2/3 power) as big

so m1/m2 = A1V1^2/A2V2^2 or V1/V2 = sqrt(M1A2/M2A1) = sqrt(6) = 2.5

And the terminal velocity of the human should be 2.5 times the velocity of
the falcon.

BUT this all assumes spherical people and falcons
remember that "small" effect of the shape of the object. By streamlining
the shape you can easily make up for this factor of 2.5 and make the
terminal velocities equal.

Paul D

Paul "But it is more complicated than that!" Doherty,
Senior Staff Scientist, The Exploratorium.
pauld@exploratorium.edu, www.exo.net/~pauld

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