Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
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The thread: Lift is circulation

Not shape, not equal transit times, not air pushed down in the way usually claimed. Lift is the circulation round the body, and the Kutta condition is what fixes it.

63 essays carry this thread — page 1 of 7.

Two parcels released together do not arrive together. The most repeated explanation of lift says that air parting at the leading edge must meet again at the trailing edge, so the longer upper path forces a higher speed. Released into the solved field, the upper parcel arrives long before the lower one — the premise is simply false, and the real speed difference is larger than it would require. What is taught wrongly

The story about air meeting up again

The most repeated explanation of lift says that air parting at the nose must rejoin at the tail, so the longer upper path forces a higher speed. The premise is false, and the speed it predicts is wrong by a factor of twenty.

 A Joukowski aerofoil at 6°. A cambered aerofoil in a uniform stream. The circulation is not chosen: it is whatever value makes the flow leave the sharp trailing edge smoothly, and that single condition fixes the lift. Circulation and lift

What actually holds a wing up

Not the shape, and not the story about air meeting up again behind. A wing lifts because there is circulation round it, and the sharp trailing edge is what decides how much.

 A Joukowski aerofoil at 8°. A cambered aerofoil in a uniform stream. The circulation is not chosen: it is whatever value makes the flow leave the sharp trailing edge smoothly, and that single condition fixes the lift. Circulation and lift

The sharp edge decides

Ideal flow round a wing admits infinitely many solutions, each with a different lift, and all of them exact. One extra requirement — that the air leaves the trailing edge instead of whipping round it — picks a single one.

 A control volume round an aerofoil. A rectangle drawn in the fluid around a lifting section. The arrows on the right-hand face show the downward velocity of the air leaving it, drawn to scale. Adding the momentum carried through all four faces to the pressure acting on them gives the force on whatever is inside, without the calculation ever going near the surface. What is taught wrongly

Air must be pushed down, and the usual sum is wrong

The momentum explanation of lift is the one physicists reach for, and it is right — a wing does hold itself up by throwing air downwards. The version usually given then does the accounting badly, and the face of the control volume it keeps turns out to carry the least of it.

 Ideal flow past a cylinder. A uniform stream past a circular cylinder in a fluid with no viscosity. The solution is exact and closed-form: streamlines part at a stagnation point, run round the surface and close up perfectly behind, and the pressure recovers to exactly what it was in front. Ideal flow

Flows add up

The equations of ideal flow are linear, so solutions can be laid on top of one another. A uniform stream plus a doublet produces a cylinder that nobody put there, and almost every classical result is built this way.

 A Joukowski aerofoil at 6°. A cambered aerofoil in a uniform stream. The circulation is not chosen: it is whatever value makes the flow leave the sharp trailing edge smoothly, and that single condition fixes the lift. Circulation and lift

The lift curve, and why it is a straight line

Lift against angle of attack is a straight line, it does not pass through the origin, and its slope is very close to a number that has no business being there. All three facts fall out of the theory.

 Ideal flow past a cylinder with circulation -3.4. A uniform stream past a circular cylinder in a fluid with no viscosity. The solution is exact and closed-form: streamlines part at a stagnation point, run round the surface and close up perfectly behind, and the pressure recovers to exactly what it was in front. Circulation and lift

Lift with no wing at all

A spinning cylinder has no camber, no aerofoil section and no trailing edge, and it lifts exactly as hard as its circulation says it should. Which settles what lift is caused by.

 Ideal flow past a cylinder. A uniform stream past a circular cylinder in a fluid with no viscosity. The solution is exact and closed-form: streamlines part at a stagnation point, run round the surface and close up perfectly behind, and the pressure recovers to exactly what it was in front. Ideal flow

Fast means low pressure

The trade between speed and pressure is the most useful relation in the subject and the most misused. Where it comes from, what it costs, and why the pressure over a wing is negative almost everywhere.

 The velocity field, arrows to scale. The same flow drawn as arrows. Scaled to the local speed the picture is honest and crowded; drawn all the same length it is legible and hides the very variation the figure is about. Flows and fields

Spin is not the same as going round

A whirlpool whose streamlines are perfect circles can have no rotation in it anywhere. A flow whose streamlines are dead straight and parallel can be rotating everywhere. Both statements are true, and getting them the wrong way round is the most expensive confusion in the subject.

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