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

Circulation and lift

Where lift actually comes from. The Kutta condition, the Joukowski aerofoil, and lift derived rather than asserted.
Γ = 2.445C_L = 1.212ideal flow with the Kutta condition applied6° incidence

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.

 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

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

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.

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

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.

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