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# Geoff's Bee

```Geoff,

I find some irony in your epistemological treatise of qlist #2028.
Specifically, the model you parse to examine the possible contributions and
conclusions is itself... ahem, flawed.  Although unstated, your model flies
perilously close to the oft repeated kernel of ignorance which goes, "There
is a big banner on the wall of the old Grumman Aircraft Corporation that
goes... According to all known aerodynamic laws, bumblebees can't fly!"
This statement is usually followed by a burst of canned, in-your-face,
laughter, and bad breath.

Although legend has the statement coming from a group of exhausted, bleary
eyed engineers, its origin is actually an early 20th century French
zoologist named Antoine Magnan, who lacked both training in aerodynamics
and an understanding of the scientific method.

What then, you are no doubt aquiver to know, explains the ability of the
bumblebee to fly?  Consider the equation for ornathroptic lift:  L =
Ad[0.12(snb)(snb) + 0.17 snbV]     Where A is the area swept in one flap, d
is air density, s is span, n is frequency of flap, b is amplitude of flap,
and V is airspeed.

During forward flight the second part of the equation comes into play as
airspeed, V, contributes to lift.  During hover V goes to zero and takes
the second part with it.  So at hover, for a given mechanism, our bee, his
ability to do so is governed by his capability to flap faster and/or
increase the amplitude of his flap, or, to be rigorous, to find some more
dense local air.  The constants, 0.12 and 0.17, are derived from the
characteristics of non-steady state, local flow field efficiencies.

So, Geoff, please remove this flawed model from your repertoire.

To which MSU does the "..pilot.msu.edu" in your address refer?  I am
willing to overlook the "pilot" regarding the above discussion, as "driver"
does not include total understanding of the physics of automobiles.

Regards, Gross Scruggs

Date: Sun, 5 Apr 1998 23:12:08 -0700
From: Geoff Jenkins <jenkinsg@pilot.msu.edu>
Subject: Dead Duds - sorry, but this just isn't physics...

Greetings All,

(Snip)

Take a bumblebee. Measure it, test it, apply (entirely reasonable, and
usually
accurate) aerodynamic models to it. (1) Theoretical conclusion: The
bumblebee
cannot fly. It weighs too much, its wings are too small and beat to slowly.
(2)
Practical observation: Bumblebees fly. (3) Logical corollary (assuming we
accept the physics of the aerodynamic model): (i) other factors, beyond the

model's scope, assist flight and/or (ii) the aerodynamic model does not
apply
well to small round insects with black and yellow stripes.

(Snip)

```