The claim that bees should not be able to fly came from a dinner-table sum

Most explanations of the aerodynamics of bee flight stop at the point where it starts to matter. This one carries on.

The origin of the claim

The story traces to a conversation in the 1930s between a French entomologist and an engineer who ran a quick calculation over dinner. The engineer applied standard fixed-wing aerodynamics to the bee's wing area and body mass and found the numbers did not work. It was a back-of-the-envelope estimate offered informally, and the assumptions it used were plainly inappropriate for a flapping wing.

Neither man appears to have concluded that bees cannot fly, which would have been a strange conclusion to reach while watching one. The anecdote escaped into general circulation and lost every qualification it started with, which is the ordinary fate of such stories.

Why the calculation failed

Fixed-wing aerodynamics assumes a rigid aerofoil moving steadily through the air at a constant angle, which describes an aeroplane reasonably well. An insect wing does none of this, beating rapidly, twisting along its length and reversing its angle at each end of the stroke.

The air around a flapping wing never reaches a steady state, so the standard equations are being applied to conditions they do not cover. Applying the wrong model and getting an impossible answer is a result about the model rather than about the animal. The correct response to such an answer is to check the assumptions, which is exactly what happened, though it took decades.

What the wings actually do

A flapping wing at a high angle of attack sheds a vortex along its leading edge, and that vortex stays attached and generates substantial extra lift. The wing also passes through the disturbed air left by its own previous stroke, recovering energy that a fixed wing would simply lose. Rotating the wing at the end of each stroke produces additional lift through a mechanism related to the spin of a ball in flight.

These effects are unsteady by nature and cannot appear in a calculation that assumes steady flow. Together they account for the lift that the original estimate could not find.

How it was worked out

High-speed photography made it possible to see what the wings were actually doing, which the human eye cannot resolve at those frequencies. Researchers also built scaled mechanical wings operating in fluids chosen to reproduce the relevant flow conditions at a size that could be measured. Those models allowed forces to be measured directly at each point in the stroke rather than inferred from the animal's behaviour.

Where the story actually begins, computational fluid dynamics later reproduced the same effects, giving an independent line of evidence.

The result is one of the better-understood problems in animal flight, which is the opposite of what the anecdote implies.

Why the story is so popular

It is used to suggest that scientists are frequently confounded by nature, which is a comforting idea for anyone who dislikes being told things. It also appears in motivational contexts, where the bee is praised for flying in defiance of the experts. That reading requires the scientists to have made a confident public claim, which they did not, and requires the bee to be unaware of it, which is difficult.

The anecdote has been repeated in advertising and in speeches for decades, which has given it far more circulation than the correction. It is a rare case where the myth is specifically about science being wrong, which makes it unusually resistant to being corrected by scientists.

Printing a correction has a poor record of taking a myth out of circulation.

What it is actually good for

It is an excellent illustration of a model being applied outside its domain and producing a nonsense answer. That happens constantly in engineering and science, and recognising it is a genuine skill rather than an embarrassment.

Where the story actually begins, the bee is not defying physics; a rough estimate was defying the situation it was applied to. The correct lesson is about checking assumptions, which is considerably more useful than the one usually drawn. It also happens to be a good story about what a high-speed camera can do to a forty-year-old argument.

The takeaway

The sum was right and the assumptions were wrong, which is a different thing from nature defeating physics.

The satisfying version of a story is the one that travels, which is the whole problem.