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

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.
Γ = 2.445C_L = 1.212ideal flow with the Kutta condition applied6° incidence 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.

 the upper surface is 1.7% longerso equal transit needs the flow over it 1.7% fasterit is actually 76.5% fasterthe premise is false and the number it predicts is wrongsurface lengths and speeds measured on the solved field6° incidence 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.

 too little — the flow whips round the edgeΓ = 0.93the Kutta value — it leaves smoothlyΓ = 2.67too much — the rear stagnation point is on topΓ = 4.81ideal flow — three admissible solutions, one physical8° incidence 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.

 lift at zero incidenceC_Langle of attack, degreesslope6.84 / radthin-aerofoil theory: 6.28the difference is thicknessideal flow with the Kutta condition, no stall modelattached flow only 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.

 a uniform streama doublet alonestream + doublet = a circleideal flow — superposition holds because the equations are linear 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.

 lift 3.393= ρUΓ = 3.400drag 1.5e-16 — still zeroideal flow — no shape, only circulationΓ = -3.4 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 — inviscid, irrotational, steadyno circulation 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.

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