Lift is a result of pressure differences and depends on angle of attack, airfoil shape, air density, and airspeed. The pressure is the normal force per unit area exerted by the air, and the net force manifests itself as pressure differences. The pressure on the lower surface of an airfoil pushes upward harder than the reduced pressure on the upper surface pushes down, resulting in lift.
The angle of attack, the angle between the chord line of an airfoil and the oncoming airflow, is a key factor. A symmetrical airfoil generates zero lift at zero angle of attack, but as the angle increases, the air is deflected downward, resulting in more lift. However, increasing the angle of attack beyond a critical point causes the airflow to separate from the upper surface, reducing lift – a condition known as stall. Airfoil shape, particularly the amount of camber (curvature), also affects lift, with increased camber generally increasing the maximum lift at a given airspeed.
Mathematical theories of lift are based on continuum fluid mechanics and the fundamental principles of physics, including conservation of momentum, conservation of mass, and conservation of energy. The Navier–Stokes equations (NS), representing these conservation laws, provide the most accurate theory, but practical calculations often rely on the Reynolds-averaged Navier–Stokes equations (RANS) to account for turbulence. Simpler theories, like inviscid-flow equations, offer approximations but may be less accurate, particularly at angles of attack above stall.
The Kutta–Joukowski theorem relates the lift per unit width of a two-dimensional airfoil to the circulation of air around it. This theorem, alongside the momentum theorem for a control volume, demonstrates how lift is manifested as both momentum fluxes and pressure differences.
Lift is proportional to the density of the air and approximately proportional to the square of the flow speed. The lift also depends on the size of the wing, being generally proportional to the wing's area.
An airfoil produces a pressure field in the surrounding air, which extends beyond the wing itself. This pressure field results in a slight increase in pressure on the ground beneath an airplane, creating a force equal to the total aerodynamic lift and the airplane's weight. This ensures that the net force on the atmosphere as a whole is zero, with no integrated accumulation of vertical momentum.
The flow around a three-dimensional wing creates wingtip vortices, which combine with vortex sheets from the trailing edge to form a horseshoe vortex system. This system influences the velocity field around the wing and contributes to lift-induced drag. The velocity perturbations caused by this system are produced by the pressure field, and are consistent with the Kutta–Joukowski theorem.