An airfoil (in American English, or aerofoil in British English) is a specially shaped cross-section of a wing or blade, used to provide lift or downforce, depending on its application. Airfoils have a characteristic shape which is that of a curved streamline, with a rounded leading edge and a sharp trailing edge.
For an understanding of the various ways of explaining lift, see lift. This force can be harnessed to lift an aircraft. Alternatively, an airfoil in an inverted position will create a downward pressure on an automobile or other motor vehicle, improving its traction and reducing its likelihood of becoming airborne. Both the horizontal and vertical tails are made with airfoils as well. Airfoils are also found in propellors, fans, and turbines. Sails are also airfoils, and the underwater fins of sailboats, such as centerboards, are also lifting foils and operate on the same principles as airfoils (technically they shoould called hydrofoils, but this term as already been taken; generally they are just referred to as "foils").
It is important to note that any thin object at an angle of attack with respect to the airflow, such as a flat plate or a bridge, will generate lift; there is nothing "magic" about the shape of an airfoil. However, the airfoil shape ensures that lift is generated with the minimum of drag, so it is important for efficiency.
The optimal design of airfoils has been much-studied, and is a key element in aerodynamics. Different applications will call for a different airfoil - there is no one "true" airfoil design. A supercritical airfoil, with its low camber reduces transonic drag divergence, while a symmetric airfoil may be more suitable for frequent inverted flight. New airfoil design techniques continue to develop.
Various systems have been devised to describe and characterise airfoils - the most common and prevalent is the NACA system. Before this, various ad-hoc systems were used. An example of a general purpose airfoil that finds wide application, and predates the NACA system is the Clark-Y.
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