The design and analysis of the wings of aircraft is one of the principal applications of the science of aerodynamics, which is a branch of fluid mechanics. In principle, the properties of the airflow around any moving object can be found by solving the Navier-Stokes equations of fluid dynamics. However, except for simple geometries these equations are notoriously difficult to solve and simpler equations are used.
For a wing to produce lift, it must be oriented at a suitable angle of attack. When this occurs, the wing deflects the airflow downwards as it passes the wing. Since the wing exerts a force on the air to change its direction, the air must also exert an equal and opposite force on the wing.
An airfoil (American English) or aerofoil (British English) is the shape of a wing, blade (of a propeller, rotor, or turbine), or sail (as seen in cross-section). Wings with an asymmetrical cross section are the norm in subsonic flight. Wings with a symmetrical cross section can also generate lift by using a positive angle of attack to deflect air downward. Symmetrical airfoils have higher stalling speeds than cambered airfoils of the same wing area but are used in aerobatic aircraft as they provide practical performance whether the aircraft is upright or inverted. Another example comes from sailboats, where the sail is a thin membrane with no path-length difference between one side and the other.
For flight speeds near the speed of sound (transonic flight), airfoils with complex asymmetrical shapes are used to minimize the drastic increase in drag associated with airflow near the speed of sound. Such airfoils, called supercritical airfoils, are flat on top and curved on the bottom.
In 1948, Francis Rogallo invented a kite-like tensile wing supported by inflated or rigid struts, which ushered in new possibilities for aircraft. Near in time, Domina Jalbert invented flexible un-sparred ram-air airfoiled thick wings. These two new branches of wings have been since extensively studied and applied in new branches of aircraft, especially altering the personal recreational aviation landscape.
^Halliday, David; Resnick, Robert. Fundamentals of Physics (3rd ed.). John Wiley & Sons. p. 378. ...the effect of the wing is to give the air stream a downward velocity component. The reaction force of the deflected air mass must then act on the wing to give it an equal and opposite upward component.
^"If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the body" "Lift from Flow Turning". Glenn Research Center. Retrieved 2011-06-29.
^"The cause of the aerodynamic lifting force is the downward acceleration of air by the airfoil..." Weltner, Klaus; Ingelman-Sundberg, Martin. "Physics of Flight – reviewed". Goethe University Frankfurt. Archived from the original on 2011-07-19.
^"...consider a sail that is nothing but a vertical wing (generating side-force to propel a yacht). ...it is obvious that the distance between the stagnation point and the trailing edge is more or less the same on both sides. This becomes exactly true in the absence of a mast—and clearly the presence of the mast is of no consequence in the generation of lift. Thus, the generation of lift does not require different distances around the upper and lower surfaces." Holger Babinsky How do Wings Work? Physics Education November 2003, PDF
^John D. Anderson, Jr. Introduction to Flight 4th ed page 271.
^"Supercritical wings have a flat-on-top "upside down" look". NASA Dryden Flight Research Center.