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

Aerodynamic centre — where it appears

The point on a section about which the pitching moment does not change with angle of attack. It sits near the quarter chord for a thin section in subsonic flow, and its position is what decides whether an aircraft is stable in pitch.

Named by 6 essays across one field — each of them below, with the objects they name alongside it.

Finding the aerodynamic centre by sweeping the chord. How fast the pitching moment changes with incidence, plotted against where along the chord the moment is taken. The curve crosses zero once, and that crossing is the aerodynamic centre — the single point about which pitching the wing does not change the moment.

Where the lift acts

Lift gets drawn as an arrow, and an arrow has to start somewhere. The pressure is spread over the whole surface, so the choice of where to put the arrow is free — except that exactly one point on the chord has the property of not changing its answer when the wing is pitched.

circulation · Moment 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.

circulation · Thin-aerofoil The downwash approaches twice the value at the wing — from above. The downwash behind an elliptically loaded wing of aspect ratio 8, as a multiple of the induced angle at the wing itself, against distance in spans. Every account of tail sizing quotes a factor of two here. Two is the value at infinity: the trailing legs of the horseshoe system contribute a factor (1 + x/√(x² + a²)) which is one at the lifting line and two far downstream. Close behind, the bound vortex dominates and the field is much larger, and the curve comes down to its limit. A tailplane sits two or three chords behind, which on this wing is 0.31 of a span — where the factor is 2.46, a quarter above the number in the formula.

The surface in the wake

A wing has no opinion about its own incidence, which is why it needs a second surface behind it. How much that surface is worth depends on how much of the wing's downwash it is sitting in, and the factor of two everybody quotes for that is the value at infinity — where no tailplane has ever been put.

circulation · Moment How the weight is shared between the two surfaces, against the centre of gravity. The wing's load and the tail's, for an aeroplane in level flight, against the static margin. The two must sum to the weight and their moments must cancel, and those two equations decide the split. At a forward centre of gravity the tail carries down and the wing carries more than the weight; the crossing is where the tail carries nothing.

More lift than weight

An aeroplane in level flight is drawn with one arrow up and one arrow down, equal and opposite. That equation collapses the whole configuration onto one number, and it is not true of any aeroplane with a tail behind it: there are two surfaces, two equations, and the second decides the split.

circulation · Trim Rolling effectiveness against dynamic pressure. The rolling moment an aileron produces, as a fraction of what it would produce on a rigid wing. It falls from one, passes through zero at the reversal pressure, and goes negative: beyond that point deflecting the aileron down rolls the aeroplane the other way. There is no oscillation anywhere in this figure and no frequency — it is a static failure.

The control that works backwards

Divergence is the static aeroelastic failure everybody names, and a wing with its elastic axis at its aerodynamic centre cannot diverge at any speed. It can still reverse — deflect the aileron down above a certain dynamic pressure and the aeroplane rolls the other way — because the aileron's own nose-down moment is there whatever the elastic axis is doing.

circulation · Flutter 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.

circulation · Thin-aerofoil

Named alongside it

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

Pitching momentModel limitThin-aerofoil theoryCirculationStabilityStatic marginCamberDownwashLift coefficientTail volumeTrimAeroelasticity

All concepts