An airfoil (in American English) or aerofoil (in British English) is the shape of a wing or blade (of a propeller, rotor or turbine) or sail as seen in crosssection.
An airfoilshaped body moved through a fluid produces a force perpendicular to the motion called lift. Subsonic flight airfoils have a characteristic shape with a rounded leading edge, followed by a sharp trailing edge, often with asymmetric camber. Foils of similar function designed with water as the working fluid are called hydrofoils.
The lift on an airfoil is primarily the result of its shape (in particular its camber) and its angle of attack. When either or both are positive, the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface. This velocity difference is necessarily accompanied by a pressure difference, via Bernoulli's principle for incompressible inviscid flow, which in turn produces the lift force. The lift force can also be related directly to the average top/bottom velocity difference, without invoking the pressure, by using the concept of circulation and the KuttaJoukowski theorem.
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A fixedwing aircraft's wings, horizontal, and vertical stabilizers are built with airfoilshaped cross sections, as are helicopter rotor blades. Airfoils are also found in propellers, fans, compressors and turbines. Sails are also airfoils, and the underwater surfaces of sailboats, such as the centerboard and keel, are similar in crosssection and operate on the same principles as airfoils. Swimming and flying creatures and even many plants and sessile organisms employ airfoils; common examples being bird wings, the bodies of fishes, and the shape of sand dollars. An airfoilshaped wing can create downforce on an automobile or other motor vehicle, improving traction.
Any object with an angle of attack in a moving fluid, such as a flat plate, a building, or the deck of a bridge, will generate an aerodynamic force (called lift) perpendicular to the flow. Airfoils are more efficient lifting shapes, able to generate more lift (up to a point), and to generate lift with less drag.
A lift and drag curve obtained in wind tunnel testing is shown on the right. The curve represents an airfoil with a positive camber so some lift is produced at zero angle of attack. With increased angle of attack, lift increases in a roughly linear relation, called the slope of the lift curve. At about 18 degrees this airfoil stalls, and lift falls off quickly beyond that. The drop in lift can be explained by the action of the uppersurface boundary layer, which separates and greatly thickens over the upper surface at and past the stall angle. The thickened boundary layer's displacement thickness changes the airfoil's effective shape, in particular it reduces its effective camber, which modifies the overall flow field so as to reduce the circulation and the lift. The thicker boundary layer also causes a large increase in pressure drag, so that the overall drag increases sharply near and past the stall point.
Airfoil design is a major facet of aerodynamics. Various airfoils serve different flight regimes. Asymmetric airfoils can generate lift at zero angle of attack, while a symmetric airfoil may better suit frequent inverted flight as in an aerobatic aeroplane. In the region of the ailerons and near a wingtip a symmetric airfoil can be used to increase the range of angles of attack to avoid spinstall. Ailerons themselves are not cut into the airfoil, but extend it. Thus a large range of angles can be used without boundary layer separation. Subsonic airfoils have a round leading edge, which is naturally insensitive to the angle of attack. For intermediate Reynolds numbers already before maximum thickness boundary layer separation occurs for a circular shape, thus the curvature is reduced going from front to back and the typical wing shape is retrieved.
Supersonic airfoils are much more angular in shape and can have a very sharp leading edge, which — as explained in the last sentence — is very sensitive to angle of attack. A supercritical airfoil has its maximum thickness close to the leading edge to have a lot of length to slowly shock the supersonic flow back to subsonic speeds. Generally such transonic airfoils and also the supersonic airfoils have a low camber to reduce drag divergence. Modern aircraft wings may have different airfoil sections along the wing span, each one optimized for the conditions in each section of the wing.
Movable highlift devices, flaps and sometimes slats, are fitted to airfoils on almost every aircraft. A trailing edge flap acts similar to an aileron, with the difference that it can be retracted partially into the wing if not used (and some flaps even make the plane a biplane if used).
A laminar flow wing has a maximum thickness in the middle camber line. Analysing the NavierStokes equations in the linear regime shows that a negative pressure gradient along the flow has the same effect as reducing the speed. So with the maximum camber in the middle, maintaining a laminar flow over a larger percentage of the wing at a higher cruising speed is possible. However, with rain or insects on the wing or for jetliner speeds this does not work. Since such a wing stalls more easily, this airfoil is not used on wingtips (spinstall again).
Schemes have been devised to define airfoils — an example is the NACA system. Various aerofoil generation systems are also used. An example of a general purpose airfoil that finds wide application, and predates the NACA system, is the ClarkY. Today, airfoils can be designed for specific functions using inverse design programs such as PROFOIL, XFOIL and AeroFoil^{[1]}. XFOIL is an online program created by Mark Drela that will design and analyze subsonic isolated airfoils^{[2]}.
The various terms related to airfoils are defined below:^{[3]}
Thin airfoil theory is a simple theory of airfoils that relates angle of attack to lift for incompressible, inviscid flows. It was devised by German mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others^{[4]} in the 1920s. The theory idealizes the flow around an airfoil as twodimensional flow around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite wingspan.
Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for the following important properties of airfoils in twodimensional flow: ^{[5]}^{[6]}
(1) on a symmetric airfoil, the center of pressure lies exactly one quarter of the chord behind the leading edge
(2) on a cambered airfoil, the aerodynamic center lies exactly one quarter of the chord behind the leading edge
(3) the slope of the lift coefficient versus angle of attack line is units per radian
As a consequence of (3), the section lift coefficient of a symmetric airfoil of infinite wingspan is:
(The above expression is also applicable to a cambered airfoil where is the angle of attack measured relative to the zerolift line instead of the chord line.)
Also as a consequence of (3), the section lift coefficient of a cambered airfoil of infinite wingspan is:
Thin airfoil theory does not account for the stall of the airfoil which usually occurs at an angle of attack between 10° and 15° for typical airfoils. ^{[7]}
The airfoil is modeled as a thin lifting meanline (camber line). The meanline, y(x), is considered to produce a distribution of vorticity γ(s) along the line, s. By the Kutta condition, the vorticity is zero at the trailing edge. Since the airfoil is thin, x (chord position) can be used instead of s, and all angles can be approximated as small.
From the BiotSavart law, this vorticity produces a flow field w(s) where
where x is the location at which induced velocity is produced, x' is the location of the vortex element producing the velocity and c is the chord length of the airfoil.
Since there is no flow normal to the curved surface of the airfoil, w(x) balances that from the component of main flow V which is locally normal to the plate — the main flow is locally inclined to the plate by an angle α − dy / dx. That is
This integral equation can by solved for γ(x), after replacing x by
,
as a Fourier series in A_{n}sin(nθ) with a modified lead term A_{0}(1 + cos(θ)) / sin(θ)
That is
(These terms are known as the Glauert integral).
The coefficients are given by
and
By the Kutta–Joukowski theorem, the total lift force F is proportional to
and its moment M about the leading edge to
The calculated Lift coefficient depends only on the first two terms of the Fourier series, as
The moment M about the leading edge depends only on A_{0},A_{1} and A_{2} , as
The moment about the 1/4 chord point will thus be,
.
From this it follows that the center of pressure is aft of the 'quarterchord' point 0.25 c, by
The aerodynamic center, AC, is at the quarterchord point. The AC is where the pitching moment M' does not vary with angle of attack, i.e.
An airfoil (in American English, or aerofoil in British English) is the shape of a wing or blade (of a propeller or ship's screw or sail) as seen in crosssection. It is passed through a fluid in order to provide either lift or downforce, depending on what it is used for.
