The Bee’s Knees

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According to 20th century folklore, the laws of aerodynamics prove that the bumblebee should be incapable of flight, as it does not have the capacity (in terms of wing size or beats per second) to achieve flight with the degree of wing loading necessary. The origin of this claim has been difficult to pin down with any certainty. John McMasters recounted an anecdote about an unnamed Swiss aerodynamicist at a dinner party who performed some rough calculations and concluded, presumably in jest, that according to the equations, bumblebees cannot fly.

In later years McMasters has backed away from this origin, suggesting that there could be multiple sources, and that the earliest he has found was a reference in the 1934 French book Le vol des insectes; they had applied the equations of air resistance to insects and found that their flight was impossible, but that “One shouldn’t be surprised that the results of the calculations don’t square with reality”.

Some credit physicist Ludwig Prandtl (1875–1953) of the University of Göttingen in Germany with popularizing the idea. Others say it was Swiss gas dynamicist Jacob Ackeret (1898–1981) who did the calculations.

In 1934, French entomologist Antoine Magnan (1881-1938) included the following passage in the introduction to his book Le Vol des Insectes:

Tout d’abord poussé par ce qui se fait en aviation, j’ai appliqué aux insectes les lois de la résistance de l’air, et je suis arrivé avec M. Sainte-Laguë à cette conclusion que leur vol est impossible.

This translates to:

First prompted by what is done in aviation, I applied the laws of air resistance to insects, and I arrived, with Mr. Sainte-Laguë, at this conclusion that their flight is impossible.

Magnan refers to his assistant André Sainte-Laguë, a mathematician.The calculations that purported to show that bumblebees cannot fly are based upon a simplified linear treatment of oscillating aerofoils. The method assumes small amplitude oscillations without flow separation. This ignores the effect of dynamic stall, an airflow separation inducing a large vortex above the wing, which briefly produces several times the lift of the aerofoil in regular flight. More sophisticated aerodynamic analysis shows that the bumblebee can fly because its wings encounter dynamic stall in every oscillation cycle.

Additionally, John Maynard Smith, a noted biologist with a strong background in aeronautics, has pointed out that bumblebees would not be expected to sustain flight, as they would need to generate too much power given their tiny wing area. However, in aerodynamics experiments with other insects he found that viscosity at the scale of small insects meant that even their small wings can move a very large volume of air relative to the size, and this reduces the power required to sustain flight by an order of magnitude.

Another description of a bee’s wing function is that the wings work similarly to helicopter blades, “reverse-pitch semirotary helicopter blades”.

Bees beat their wings approximately 200 times a second. Their thorax muscles do not expand and contract on each nerve firing but rather vibrate like a plucked rubber band.

~ Wikipedia

Just because you can’t fly, doesn’t mean you can’t fly.

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