Mystery "solved": how honeybees fly

Scientists found in the 1930s that they couldn't explain how bees
fly, and it has remained somewhat of a puzzle until recently.
[Only registered users see links. ]

[Only registered users see links. ] wrote:

In the cited article it is reported that "honeybees compensate for
short wingstrokes by beating their wings faster. This generates
aerodynamic forces every time the wings change direction that create
the requisite lift."

This is a nearly trivial consequence of two factors: (1) the wing
motion is driven by muscle tension, so the wings of all insects have
effectively the same Hooke's Law constant controlling thier oscillatory
frequency, and (2) a shorter wing has a smaller moment of rotational
inertia.

These two factors combine to approximately reproduce the relationship
of Galileo regarding the resonant period w(0) of a pendulum:
[Only registered users see links. ] (Eq. 4)
w(0) = sqrt(m*g*x/I)
where m is the mass of the wing, x is the distance between the center
of mass of the wing and the pivot point, I is the moment of inertia,
and g is proportional to the *Hooke's Law constant* of the wing
muscles.

It should be apparent that a longer, more massive wing such as that of
a large bee will have a longer period (i.e. lower frequency) than that
of a shorter, lighter wing such as that of a mosquito. Bees buzz;
mosquitoes hum; gnats whine.

The bee's wing generates forces moving through the viscous air on both
the downstroke and the upstroke due to the design of the hinge joint
itself. The wing swivels through a 45° - 60° angle on each stroke.
On the downstroke in level flight, the wing is essentially level,
generating almost pure lift. On the upstroke in level flight the wing
swivels to about a 60° angle of attack to generate almost pure thrust.
[Only registered users see links. ]

The *real* trick is that the angles are such that by tilting its body
the bee can direct its thrust more downward and hover. This only works
because the bee generates more lift that it needs to simply stay aloft.
http://digitalchocolate.org/images/4...ering-6106.jpg

The bee may also be able to adjust the *average* angle of attack of its
wings to assist it to hover:
[Only registered users see links. ]

Another point should be that bee flight and wing aerodynamics are
completely intractable to misguided applications of Bernoulli's
Principle. The Bernoulli Equation was derived using conservation of
energy considerations for (A) a laminar flow, (B) a non-viscous fluid,
and (C) a confined flow in a conduit. None of these assumptions apply
to flight - whether of fixed wing or movable wing systems.

The original attempt to describe the flight of bees using Bernoulli
were doomed from the start, hence the now-legendary conclusion that
'bees can't possibly fly, but they don't know that, so they go right
ahead and fly anyway.'

The 'mystery' is more a paradigm of the misapplication of a perfectly
good theory by someone who doesn't understand what it really means than
an exemplar of a mystery of nature.

Tom Davidson
Richmond, VA