Concept

Flapping flight — where it appears

Flight produced by beating wings rather than by a wing held at a steady incidence. The stroke is only a few chord lengths long, so the circulation never reaches its steady value and the mechanisms that hold the animal up are unsteady ones.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as leading edge vortex — the same set of essays touches all of them, so they are one junction rather than several.

One calculation is about the animal; the other is about how fast it happens to be going. The mean lift coefficient required of each animal's wings, computed two ways, on a log scale. Treating the wings as fixed and flying them at the animal's forward speed gives answers spanning a factor of 29 — from 0.88 to 26 — because the number is governed by a speed that has nothing to do with how the animal makes its lift. Doing the flapping arithmetic gives answers spanning a factor of 1.90. And in a hover the fixed-wing calculation has no answer at all: there is no dynamic pressure, and no coefficient however large will do. That is the version of the famous claim that is actually true, and it is a statement about the calculation rather than about the bee.

The bee that cannot fly

The claim has a traceable origin and the calculation behind it was a real calculation done with the wrong velocity. Doing it with the right one gives a number an aerofoil might plausibly produce — and still leaves a gap, and the gap is what took another sixty years to close.

misconceptions · Bumblebee $Where four insects have to turn round. Wagner's function — the fraction of its eventual circulation a wing has built after a stated distance of travel — with the half-stroke of each of four insects marked on it. Every one of them reverses while the curve is still climbing, so no insect wing ever reaches the circulation a steady calculation assigns it.$

A calculation with no memory in it

The bee calculation is famous for using the wrong velocity. Done with the right one it still falls short, and the reason is structural: a quasi-steady sum is a statement about a wing that has always been going, and an insect's wing travels between two and five chord lengths before it turns round.

misconceptions · Bumblebee

Named alongside it

The objects these essays reach for when they reach for this one.

Blade-element Leading edge vortex Quasi-steady Borrowed measurement Circulation Hover Induced velocity Lift coefficient Memory kernel Model limit Model validity Reduced frequency

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