Airfoil Lift

It turns oncoming air downward. By accelerating air over the curved upper surface and deflecting it down at the trailing edge, the wing imposes a momentum change on the airflow. Newton's third law gives an equal-and-opposite reaction lifting the wing. Bernoulli's principle describes the same physics in pressure terms — faster flow, lower static pressure.

Both — they describe the same phenomenon. Bernoulli relates pressure to velocity; Newton relates force to momentum change. Bernoulli alone (the "equal transit time" myth) is wrong because particles do not have to meet at the trailing edge. Correct explanation: circulation around the airfoil creates the velocity differences that produce the pressure pattern that produces the force.

The angle between the chord line of the airfoil and the relative wind. Increasing angle of attack increases C_L roughly linearly until the critical angle, beyond which flow separates and lift collapses (stall). Pilots manage AoA via pitch control. Modern airliners cruise around 2–4° AoA, climb at 8–10°, stall warnings trigger near 14–17°.

At high angles of attack, the adverse pressure gradient on the upper surface causes the boundary layer to separate. Lift drops sharply, drag rises, and recovery requires reducing AoA. Stall characteristics depend on airfoil thickness, camber, and Reynolds number. Aircraft are designed so the wing root stalls before the tip, preserving aileron control.

A dimensionless number that captures the aerodynamic efficiency of a shape at a given AoA, independent of size or speed. C_L of a typical thin airfoil is 0.1 per degree of AoA up to stall, peaking around 1.2–1.6. High-lift devices — slats, flaps — boost C_L_max to 2.5–3.0 for landing. Symmetric airfoils have zero lift at zero AoA; cambered ones generate lift at zero AoA.

Lift on a finite wing creates trailing wingtip vortices that tilt the local lift vector backwards, producing induced drag proportional to C_L². High aspect ratio wings (gliders, U-2) reduce induced drag by minimizing wingtip effects relative to span. Winglets achieve a similar effect by recovering some vortex energy. Induced drag dominates at low speeds; parasitic drag at high speeds.

Compressibility dominates. Above Mach 0.7, shock waves form on the upper surface, pressure distributions shift, and lift coefficient drops while drag spikes (transonic drag rise). Supersonic airfoils are thin and sharp-edged with very different lift mechanisms — pressure differentials across oblique shocks rather than smooth Bernoulli flow.