Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Series

Thin-aerofoil — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Four camber lines, and the angle at which each stops lifting. Four mean lines on the same chord: symmetric, a circular arc, a four-digit line with its crest at forty per cent, and a reflexed line whose tail turns up. The zero-lift angle beside each is computed from that line's own slope by quadrature and is a property of the shape alone — no incidence, no speed, no thickness enters it. The symmetric line's is exactly zero, the arc's is −2m to ten decimal places, and the reflexed line's is positive: it needs to be pointed up before it stops lifting.

    Where lift starts

    A wing at zero incidence is not a wing making no lift. The angle at which a section stops lifting is a property of its camber line and of nothing else — not of its thickness, not of its speed, not of the air — and it is an integral anybody can take.

    part 1 · circulation
  2. Two camber lines, one lift and one moment. A NACA 2412 mean line and the same line with a fourth harmonic added to its slope. They are eight tenths of a per cent of the chord apart, which is forty per cent of the section's own camber, and they have the same lift and the same pitching moment at every incidence — to the last bit of double precision.

    Three numbers out of a camber line

    Thin-aerofoil theory takes a whole function and returns a lift and a moment. Only three coefficients of that function survive: two camber lines matched in the first three, and eight tenths of a per cent of chord apart, have the same lift and the same moment at every incidence and load distributions thirty-seven per cent apart.

    part 2 · circulation
  3. The camber lines that carry them. The camber lines that carry the four loads at their ideal angles, heights in chords at a design lift coefficient of one. The uniform load's line is symmetric about mid-chord, 5.52% high; tapering the load over the last fifth moves the peak to 0.515 of the chord and raises it to 6.79%; tapering it over the whole chord, a = 0, puts the peak at 0.323.

    A load carried to the trailing edge needs a hook

    Thin-aerofoil theory runs backwards: ask for a chordwise load and it returns the camber line that carries it. Ask for the simplest load of all, the same everywhere, and the line comes back with a vertical tangent at both ends. The one at the nose is the price of a clean entry; the one at the tail is the Kutta condition being broken, and the hook it makes is what a Gurney flap is. Every NACA a-series line is a way of not paying it.

    part 3 · circulation

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