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Is terminal velocity Terminal

We estimate the terminal velocity for a man falling in air. For air we have
equation50
We approximate the man to have cross sectional area 0.2 mtex2html_wrap_inline132 and mass m=70 kg. The corresponding terminal velocity is
equation52
(ps: I miscalculated this on the blackboard) This will typically be a lethal fall. We can estimate the distance required to reach the terminal velocity to be
equation57
This estimate neglected drag just asking after what distance a free fall reaches the terminal velocity.

Lets consider how this result scales with the typical linear dimensions of the falling object, L. We have tex2html_wrap_inline138 and tex2html_wrap_inline140 so finally
equation61
Thus if we consider a bug with typical dimensions L=0.005 m ie. 100 times smaller tha a human, its terminal velocity will be tex2html_wrap_inline144 times smaller than for a human ie. 14 mph. Hitting the earth at that velocity probably is harmless. Thus we now understand why a bug can fall from arbitrary heights without serious bodily injury. Its mass to area ratio is so small that the terminal velocity is not "terminal".



Collin Broholm
Mon Sep 29 10:16:07 EDT 1997