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Bumblebee aerodynamics

The other day I heard someone repeat the legend that it was aerodynamically impossible for a bumblebee to fly.

Well, I don't know if I can debunk the urban legend because I have heard several versions regarding its origin. I can, though, explain why it is easy to come to the improper conclusions with regard to bumblebee aerodynamics.

The apocryphal story I have with regard to the legend is that an aerodynamicist worked up the aerodynamics of the bumblebee on a lark, and found, based on his assumptions (i.e., flat plate aerodynamics over the wing, a certain beat frequency and airspeed [indicating an oscillatory angle of attack on the wings], imposition of the Kutta condition, etc) that the power requirements were far beyond the capacity of bumblebee flight muscles to provide. Moreover, the wings were stalled through a large percent of their flap cycle, yielding horrendous L/D penalties. He confided his result to another during a reception to which the press had been invited; it was overheard by a member of the press, and the rest was media history. The aerodynamicist was reported to have realized an error in his [tacit] assumptions later during the event, but the damage had been done.

As I said, an apocryphal tale.

The key to understanding bumblebee (and dragonfly and butterfly and mosquito) aerodynamics is in understanding bumblebee airfoils. If you imagine a bee's wing, with its veins and undulations in cross section, the first question that comes to mind is, "why would anyone pick such a horrible airfoil and try to fly with it?" Of course, individual bumblebees have little choice in the matter, but mother nature *could* have chosen another design. Bees have been part of the biosphere since the late Cretaceous (they co-evolved with the flowering plants). If another insect were to develop, which could fly and pollinate flowers with greater ease than the bee, it would have had a survival advantage and taken over (it should be noted that bees have several other survival advantages as well).

So why isn't there a bee-sized insect out there with a NACA 64-series airfoil?

The answer is scaling. At the sizes of bee wings, the bumpy-looking wing cross section is actually a very efficient airfoil. The key is to recognize that at bee dimensions, Reynolds numbers are low! Many of the fluid dynamic assumptions students use in the study of airfoils do not hold up (since few airliners are built to bee dimensions, the assumptions are still fine for most of us aerocritters). Once you have a higher Cl airfoil, the L/D goes up and power requirements go down.

And, voila! the bee flies!

This is what our hapless hero realized, too late to hold the presses (if you believe this version of the story).

Actually, at small scale, and low Reynolds numbers, a surprising variety of structures become quite good flying machines. Perhaps one of the oddest is gossamer. Certain species of spiders have taken to the air by spinning web and holding it aloft. Once picked up by the breeze, these spiders can travel great distances and achieve fairly respectable altitudes. Often, these spiders travel en masse, and meld their webs into a flying spider colony (a few cases of UFO sightings in the 50's were attributed to gossamer).

Airborne bacteria have developed even stranger schemes...

Brent Wellman
U.S. Army Aeroflightdynamics Directorate, Ames Research Center

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