How a Wing Generates Lift

This is a test article — just an example while I prepare the real Notebook pieces.

Ask why a wing lifts and you often get the "longer path on top" story, which turns out to be wrong. A cleaner picture is this: the wing turns the air, and turning air is what produces lift.

Air turns at the leading edge

As the flow reaches the wing it splits and curves sharply around the rounded leading edge. Hugging the upper surface, it keeps bending and leaves the trailing edge aimed slightly downward. The wing has deflected a stream of air downward, and by Newton's third law the air pushes back on the wing — upward.

Seen as a whole, this bending is a net rotation of air around the wing: the flow moves a little faster over the top and slower underneath, as if a weak vortex were bound to the wing. That bound rotation is the heart of the matter.

Curved streamlines need a pressure difference

The link between "the air curves" and "there is a force" is geometric. Whenever a streamline follows a curve of radius $R$, something must supply the centripetal acceleration, and the only thing available is a pressure gradient across the flow:

$$\frac{\partial p}{\partial n} = \rho\, \frac{V^2}{R}.$$

Pressure rises as you move away from the centre of curvature. Over the top of the wing the streamlines curve downward, with their centre of curvature below them, so pressure falls as you approach the surface — a suction. The tighter the curve (smaller $R$), the steeper the gradient and the stronger the pull. This radius-of-curvature view is the one Babinsky uses to explain lift without invoking equal transit times.^[1]

Circulation makes it quantitative

The rotation around the wing is measured by the circulation $\Gamma$, the integral of velocity around a loop enclosing the section. The Kutta–Joukowski theorem ties it directly to lift per unit span:

$$L' = \rho\, V_\infty\, \Gamma.$$

What fixes the value of $\Gamma$ is the Kutta condition: the flow must leave the sharp trailing edge smoothly, and only one amount of circulation lets it do that. Set that, and the lift follows.^[2]