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An airfoil (
American English American English, sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. English is the most widely spoken language in the United States and in most circumstances ...
) or aerofoil (
British English British English (BrE, en-GB, or BE) is, according to Oxford Dictionaries, "English as used in Great Britain, as distinct from that used elsewhere". More narrowly, it can refer specifically to the English language in England, or, more broadl ...
) is the
cross-sectional Cross-sectional data, or a cross section of a study population, in statistics and econometrics, is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at the one point or period of time. The analy ...
shape of an object whose motion through a gas is capable of generating significant lift, such as a
wing A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is e ...
, a
sail A sail is a tensile structure—which is made from fabric or other membrane materials—that uses wind power to propel sailing craft, including sailing ships, sailboats, windsurfers, ice boats, and even sail-powered land vehicles. Sails ma ...
, or the blades of
propeller A propeller (colloquially often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon ...
, rotor, or
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin ''turbo'', meaning vortex) is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generating ...
. A solid body moving through a
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
produces an aerodynamic force. The component of this force
perpendicular In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', ⟂. It c ...
to the relative freestream velocity is called lift. The component parallel to the relative freestream velocity is called drag. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Airfoils can be designed for use at different speeds by modifying their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for
supersonic flight A supersonic aircraft is an aircraft capable of supersonic flight, that is, flying faster than the speed of sound (Mach number 1). Supersonic aircraft were developed in the second half of the twentieth century. Supersonic aircraft have been use ...
tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. Foils of similar function designed with water as the working fluid are called
hydrofoil A hydrofoil is a lifting surface, or foil, that operates in water. They are similar in appearance and purpose to aerofoils used by aeroplanes. Boats that use hydrofoil technology are also simply termed hydrofoils. As a hydrofoil craft gains s ...
s. The lift on an airfoil is primarily the result of its
angle of attack In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...
. When oriented at a suitable angle, the airfoil deflects the oncoming air (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and can be resolved into two components: lift and drag. Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack. This "turning" of the air in the vicinity of the airfoil creates curved streamlines, resulting in lower pressure on one side and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface. In some situations (e.g.
inviscid The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the in ...
potential flow) the lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta–Joukowski theorem.


Overview

The wings and stabilizers of
fixed-wing aircraft A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are dist ...
, as well as
helicopter A helicopter is a type of rotorcraft in which lift and thrust are supplied by horizontally spinning rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forward, backward and laterally. These attribu ...
rotor blades, are built with airfoil-shaped cross sections. Airfoils are also found in propellers, fans, compressors and turbines. Sails are also airfoils, and the underwater surfaces of sailboats, such as the
centerboard A centreboard or centerboard (US) is a retractable hull appendage which pivots out of a slot in the hull of a sailboat, known as a ''centreboard trunk'' (UK) or ''centerboard case'' (US). The retractability allows the centreboard to be raised ...
,
rudder A rudder is a primary control surface used to steer a ship, boat, submarine, hovercraft, aircraft, or other vehicle that moves through a fluid medium (generally air or water). On an aircraft the rudder is used primarily to counter adve ...
, and
keel The keel is the bottom-most longitudinal structural element on a vessel. On some sailboats, it may have a hydrodynamic and counterbalancing purpose, as well. As the laying down of the keel is the initial step in the construction of a ship, in Br ...
, are similar in cross-section and operate on the same principles as airfoils. Swimming and flying creatures and even many plants and sessile organisms employ airfoils/hydrofoils: common examples being bird wings, the bodies of fish, and the shape of sand dollars. An airfoil-shaped wing can create downforce on an
automobile A car or automobile is a motor vehicle with wheels. Most definitions of ''cars'' say that they run primarily on roads, seat one to eight people, have four wheels, and mainly transport people instead of goods. The year 1886 is regarded ...
or other motor vehicle, improving traction. When the wind is obstructed by an object such as a flat plate, a building, or the deck of a bridge, the object will experience drag and also an aerodynamic force perpendicular to the wind. This does not mean the object qualifies as an airfoil. Airfoils are highly-efficient lifting shapes, able to generate more lift than similarly sized flat plates of the same area, and able to generate lift with significantly less drag. Airfoils are used in the design of aircraft, propellers, rotor blades, wind turbines and other applications of aeronautical engineering. A lift and drag curve obtained in
wind tunnel Wind tunnels are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft ...
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 upper-surface 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 Parasitic drag, also known as profile drag, is a type of aerodynamic drag that acts on any object when the object is moving through a fluid. Parasitic drag is a combination of form drag and skin friction drag. It affects all objects regardless of ...
, so that the overall drag increases sharply near and past the stall point. Airfoil design is a major facet of
aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dy ...
. 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 Aerobatics is the practice of flying maneuvers involving aircraft attitudes that are not used in conventional passenger-carrying flights. The term is a portmanteau of "aerial" and "acrobatics". Aerobatics are performed in aeroplanes and glide ...
airplane. 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
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally ...
stall. 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. The cross section is not strictly circular, however: the radius of curvature is increased before the wing achieves maximum thickness to minimize the chance of boundary layer separation. This elongates the wing and moves the point of maximum thickness back from the leading edge.
Supersonic airfoils A supersonic airfoil is a cross-section geometry designed to generate lift efficiently at supersonic speeds. The need for such a design arises when an aircraft is required to operate consistently in the supersonic flight regime. Supersonic airfoil ...
are much more angular in shape and can have a very sharp leading edge, which 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 Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transoni ...
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 high-lift devices, flaps and sometimes slats, are fitted to airfoils on almost every aircraft. A trailing edge flap acts similarly to an aileron; however, it, as opposed to an aileron, can be retracted partially into the wing if not used. A laminar flow wing has a maximum thickness in the middle camber line. Analyzing the Navier–Stokes 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, some surface contamination will disrupt the laminar flow, making it turbulent. For example, with rain on the wing, the flow will be turbulent. Under certain conditions, insect debris on the wing will cause the loss of small regions of laminar flow as well. Before NASA's research in the 1970s and 1980s the aircraft design community understood from application attempts in the WW II era that laminar flow wing designs were not practical using common manufacturing tolerances and surface imperfections. That belief changed after new manufacturing methods were developed with composite materials (e.g. laminar-flow airfoils developed by Professor Franz Wortmann for use with wings made of
fibre-reinforced plastic Fibre-reinforced plastic (FRP; also called fibre-reinforced polymer, or in American English ''fiber'') is a composite material made of a polymer matrix reinforced with fibres. The fibres are usually glass (in fibreglass), carbon (in carbon-fibr ...
). Machined metal methods were also introduced. NASA's research in the 1980s revealed the practicality and usefulness of laminar flow wing designs and opened the way for laminar-flow applications on modern practical aircraft surfaces, from subsonic general aviation aircraft to transonic large transport aircraft, to supersonic designs. Schemes have been devised to define airfoils – an example is the NACA system. Various airfoil generation systems are also used. An example of a general purpose airfoil that finds wide application, and pre–dates the NACA system, is the
Clark-Y Clark Y is the name of a particular airfoil profile, widely used in general purpose aircraft designs, and much studied in aerodynamics over the years. The profile was designed in 1922 by Virginius E. Clark using thickness distribution of the German ...
. Today, airfoils can be designed for specific functions by the use of computer programs.


Airfoil terminology

The various terms related to airfoils are defined below: *The ''suction surface'' (a.k.a. upper surface) is generally associated with higher velocity and lower static pressure. *The ''pressure surface'' (a.k.a. lower surface) has a comparatively higher static pressure than the suction surface. The pressure gradient between these two surfaces contributes to the lift force generated for a given airfoil. The geometry of the airfoil is described with a variety of terms : *The '' leading edge'' is the point at the front of the airfoil that has maximum curvature (minimum radius). *The '' trailing edge'' is defined similarly as the point of maximum curvature at the rear of the airfoil. *The '' chord line'' is the straight line connecting leading and trailing edges. The ''chord length'', or simply chord, c, is the length of the chord line. That is the reference dimension of the airfoil section. The shape of the airfoil is defined using the following geometrical parameters: *The ''mean camber line'' or ''mean line'' is the locus of points midway between the upper and lower surfaces. Its shape depends on the thickness distribution along the chord; *The ''thickness'' of an airfoil varies along the chord. It may be measured in either of two ways: ** Thickness measured perpendicular to the camber line. This is sometimes described as the "American convention"; ** Thickness measured perpendicular to the chord line. This is sometimes described as the "British convention". Some important parameters to describe an airfoil's shape are its '' camber'' and its ''thickness''. For example, an airfoil of the NACA 4-digit series such as the NACA 2415 (to be read as 2 – 4 – 15) describes an airfoil with a camber of 0.02 chord located at 0.40 chord, with 0.15 chord of maximum thickness. Finally, important concepts used to describe the airfoil's behaviour when moving through a fluid are: *The ''
aerodynamic center In aerodynamics, the torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift and net drag applied at some point on the airfoil, and a separate net pitching moment about that point whose magni ...
'', which is the chord-wise location about which the pitching moment is independent of the lift coefficient and the angle of attack. *The '' center of pressure'', which is the chord-wise location about which the ''
pitching moment In aerodynamics, the pitching moment on an airfoil is the moment (or torque) produced by the aerodynamic force on the airfoil if that aerodynamic force is considered to be applied, not at the center of pressure, but at the aerodynamic center o ...
'' is momentarily zero. On a cambered airfoil, the center of pressure is not a fixed location as it moves in response to changes in angle of attack and lift coefficient.


Thin airfoil theory

Thin airfoil theory is a simple theory of airfoils that relates
angle of attack In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...
to lift for incompressible,
inviscid flow In fluid dynamics, inviscid flow is the flow of an inviscid (zero-viscosity) fluid, also known as a superfluid. The Reynolds number of inviscid flow approaches infinity as the viscosity approaches zero. When viscous forces are neglected, suc ...
s. It was devised by German mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others in the 1920s. The theory idealizes the flow around an airfoil as two-dimensional flow around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite
wingspan The wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip. For example, the Boeing 777–200 has a wingspan of , and a wandering albatross (''Diomedea exulans'') caught in 1965 had a wingspan o ...
. Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for the following important properties of airfoils in two-dimensional inviscid flow: # on a symmetric airfoil, the center of pressure and
aerodynamic center In aerodynamics, the torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift and net drag applied at some point on the airfoil, and a separate net pitching moment about that point whose magni ...
are coincident and lie exactly one quarter of the chord behind the leading edge. # on a cambered airfoil, the aerodynamic center lies exactly one quarter of the chord behind the leading edge, but the position of the center of pressure moves when the angle of attack changes. # the slope of the ''lift coefficient versus angle of attack'' line is 2 \pi\! units per radian. As a consequence of (3), the section lift coefficient of a symmetric airfoil of infinite wingspan is: : \ c_l = 2\pi \alpha :where c_l\! is the section lift coefficient, :\alpha\! is the
angle of attack In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...
in radians, measured relative to the chord line. (The above expression is also applicable to a cambered airfoil where \alpha\! is the angle of attack measured relative to the zero-lift line instead of the chord line.) Also as a consequence of (3), the section lift coefficient of a cambered airfoil of infinite wingspan is: : \ c_l = c_ + 2\pi\alpha :where \ c_ is the section lift coefficient when the angle of attack is zero. 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.Aerospaceweb's information on Thin Airfoil Theory
/ref> In the mid-late 2000s, however, a theory predicting the onset of leading-edge stall was proposed by Wallace J. Morris II in his doctoral thesis. Morris's subsequent refinements contain the details on the current state of theoretical knowledge on the leading-edge stall phenomenon. Morris's theory predicts the critical angle of attack for leading-edge stall onset as the condition at which a global separation zone is predicted in the solution for the inner flow. Morris's theory demonstrates that a subsonic flow about a thin airfoil can be described in terms of an outer region, around most of the airfoil chord, and an inner region, around the nose, that asymptotically match each other. As the flow in the outer region is dominated by classical thin airfoil theory, Morris's equations exhibit many components of thin airfoil theory.


Derivation of thin airfoil theory

The airfoil is modeled as a thin lifting mean-line (camber line). The mean-line, ''y''(''x''), is considered to produce a distribution of vorticity \gamma(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 Biot–Savart law, this vorticity produces a flow field w(x) where :w(x) = \frac \int_^ \frac\, dx' x is the location where 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 \alpha - dy/dx. That is: :V\; (\alpha - dy/dx) = w(x) = \frac \int_^ \frac \,dx'. This integral equation can be solved for \gamma(x), after replacing ''x'' by :x = c \cdot \frac, as a
Fourier series A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or '' ...
in A_n \sin(n \theta) with a modified lead term A_0 (1 + \cos (\theta)) / \sin(\theta). That is :\frac = A_0 \frac + \sum A_n \sin (n \theta)) (These terms are known as the Glauert integral). The coefficients are given by :A_0 = \alpha - \frac \int_^ \left(\frac\right) d\theta and :A_n = \frac \int_^ \left(\frac\right) \cos(n \theta)\; d\theta. By the Kutta–Joukowski theorem, the total lift force ''F'' is proportional to :\rho V \int_^ \gamma (x) \, dx and its moment ''M'' about the leading edge to :\rho V \int_^ x \; \gamma (x) \, dx. The calculated Lift coefficient depends only on the first two terms of the Fourier series, as :C_L = 2 \pi (A_0 + A_1/2). The moment ''M'' about the leading edge depends only on A_0, A_1 and A_2, as :C_M = - 0.5 \pi (A_0+A_1-A_2/2). The moment about the 1/4 chord point will thus be :C_M(1/4c) = - \pi /4 (A_1 - A_2). From this it follows that the center of pressure is aft of the 'quarter-chord' point 0.25 ''c'', by :\Delta x /c = \pi /4 ((A_1-A_2)/C_L). The
aerodynamic center In aerodynamics, the torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift and net drag applied at some point on the airfoil, and a separate net pitching moment about that point whose magni ...
, AC, is at the quarter-chord point. The AC is where the pitching moment ''M''′ does not ''vary'' with a change in lift coefficient, i.e., :\frac = 0.


See also

* Circulation control wing *
Hydrofoil A hydrofoil is a lifting surface, or foil, that operates in water. They are similar in appearance and purpose to aerofoils used by aeroplanes. Boats that use hydrofoil technology are also simply termed hydrofoils. As a hydrofoil craft gains s ...
* Kline–Fogleman airfoil * Küssner effect *
Parafoil A parafoil is a nonrigid (textile) airfoil with an aerodynamic cell structure which is inflated by the wind. Ram-air inflation forces the parafoil into a classic wing cross-section. Parafoils are most commonly constructed out of ripstop nylon. ...


References


Notes


Citations


Sources

* * * * * * * * * * * *


Further reading

* * *Ali Kamranpay, Alireza Mehrabadi. Numerical Analysis of NACA Airfoil 0012 at Different Attack Angles and Obtaining its Aerodynamic Coefficients. Journal of Mechatronics and Automation. 2019; 6(3): 8–16p.


External links


UIUC Airfoil Coordinates Database

Airfoil & Hydrofoil Reference Application


An airfoil simulator from NASA
Airfoil Playground - Interactive WebApp



University of Sydney, Aerodynamics for Students

Airflow across a wing (University of Cambridge)
{{Authority control Aerodynamics Aircraft wing design *https://engineeringjournals.stmjournals.in/index.php/JoMA/article/view/3639