An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of a wing, blade (of a propeller, rotor, or turbine), or sail (as seen in cross-section).

An airfoil-shaped body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the direction of motion is called lift. The component parallel to the direction of motion is called drag. Subsonic flight airfoils have a characteristic shape with a rounded leading edge, followed by a sharp trailing edge, often with a symmetric curvature of upper and lower surfaces. 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 angle of attack and shape. 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. 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.[1][2][3][4]

Examples of Airfoils
Examples of aerofoils in nature and within various vehicles. The dolphin flipper at bottom left obeys the same principles in a different fluid medium; it is an example of a hydrofoil.


Streamlines around a NACA 0012
Streamlines around a NACA 0012 airfoil at moderate angle of attack
Lift drag graph
Lift and drag curves for a typical airfoil

A fixed-wing aircraft's wings, horizontal, and vertical stabilizers are built with airfoil-shaped 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 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 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 have potential for use 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 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, 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 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 spinstall. 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 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 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.[5] 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., graphite fiber) and machined metal methods were 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.[6]

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. Today, airfoils can be designed for specific functions by the use of computer programs.

Airfoil terminology

Wing profile nomenclature
Airfoil nomenclature

The various terms related to airfoils are defined below:[7]

  • 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).[8]
  • 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, , is the length of the chord line. That is the reference dimension of the airfoil section.
Airfoil thickness definition
Different definitions of airfoil thickness
An airfoil designed for winglets (PSU 90-125WL)

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.[9][10] This is sometimes described as the "American convention";[9]
    • Thickness measured perpendicular to the chord line.[11] 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:

Thin airfoil theory

An airfoil section is displayed at the tip of this Denney Kitfox aircraft, built in 1991.
Helikopter forgószárnyának keresztmetszete 2
Airfoil of Kamov Ka-26 helicopters

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-American mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others[12] 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.

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 flow:[13][14]

  1. on a symmetric airfoil, the center of pressure and aerodynamic center are coincident and lie 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:

where is the section lift coefficient,
is the angle of attack in radians, measured relative to the chord line.

(The above expression is also applicable to a cambered airfoil where 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:

where 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.[15] In the mid-late 2000's, however, a theory predicting the onset of leading-edge stall was proposed by Wallace J. Morris II in his doctoral thesis.[16] Morris's subsequent refinements contain the details on the current state of theoretical knowledge on the leading-edge stall phenomenon.[17][18] 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.[19] 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

Aerofoils for different aeroplanes
From top to bottom:
• Laminar flow airfoil for a RC park flyer
• Laminar flow airfoil for a RC pylon racer
• Laminar flow airfoil for a manned propeller aircraft
• Laminar flow at a jet airliner airfoil
• Stable airfoil used for flying wings
• Aft loaded airfoil allowing for a large main spar and late stall
• Transonic supercritical airfoil
• Supersonic leading edge airfoil
  laminar flow
  turbulent flow
  subsonic stream
  supersonic flow volume

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 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 where

is the location where induced velocity is produced, is the location of the vortex element producing the velocity and is the chord length of the airfoil.

Since there is no flow normal to the curved surface of the airfoil, balances that from the component of main flow , which is locally normal to the plate – the main flow is locally inclined to the plate by an angle . That is:

This integral equation can by solved for , after replacing x by


as a Fourier series in with a modified lead term

That is

(These terms are known as the Glauert integral).

The coefficients are given by


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 and , 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 'quarter-chord' point 0.25 c, by

The aerodynamic center, 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.,

See also


  1. ^ "...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." In: Halliday, David; Resnick, Robert, Fundamentals of Physics 3rd Edition, John Wiley & Sons, p. 378
  2. ^ "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". NASA Glenn Research Center. Archived from the original on 5 July 2011. Retrieved 2011-06-29.
  3. ^ "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, archived from the original on 2011-07-19
  4. ^ "...if a streamline is curved, there must be a pressure gradient across the streamline..."Babinsky, Holger (November 2003), "How do wings work?" (PDF), Physics Education, 38 (6): 497–503, Bibcode:2003PhyEd..38..497B, doi:10.1088/0031-9120/38/6/001
  5. ^ Croom, C. C.; Holmes, B. J. (1985-04-01). Flight evaluation of an insect contamination protection system for laminar flow wings.
  6. ^ Holmes, B. J.; Obara, C. J.; Yip, L. P. (1984-06-01). "Natural laminar flow experiments on modern airplane surfaces". Cite journal requires |journal= (help)
  7. ^ Hurt, H. H., Jr. (January 1965) [1960]. Aerodynamics for Naval Aviators. U.S. Government Printing Office, Washington, D.C.: U.S. Navy, Aviation Training Division. pp. 21–22. NAVWEPS 00-80T-80.
  8. ^ Houghton, E.L.; Carpenter, P.W. (2003). Butterworth Heinmann (ed.). Aerodynamics for Engineering Students (5th ed.). p. 18. ISBN 978-0-7506-5111-0.
  9. ^ a b Houghton, E. L.; Carpenter, P.W. (2003). Butterworth Heinmann (ed.). Aerodynamics for Engineering Students (5th ed.). p. 17. ISBN 978-0-7506-5111-0.
  10. ^ Phillips, Warren F. (2010). Mechanics of Flight (2nd ed.). Wiley & Sons. p. 27. ISBN 978-0-470-53975-0.
  11. ^ Bertin, John J.; Cummings, Russel M. (2009). Pearson Prentice Hall (ed.). Aerodynamics for Engineers (5th ed.). p. 199. ISBN 978-0-13-227268-1.
  12. ^ Abbott, Ira H., and Von Doenhoff, Albert E. (1959), Theory of Wing Sections, Section 4.2, Dover Publications Inc., New York, Standard Book Number 486-60586-8
  13. ^ Abbott, Ira H., and Von Doenhoff, Albert E. (1959), Theory of Wing Sections, Section 4.3
  14. ^ Clancy, L.J. (1975), Aerodynamics, Sections 8.1 to 8.8, Pitman Publishing Limited, London. ISBN 0-273-01120-0
  15. ^ Aerospaceweb's information on Thin Airfoil Theory
  16. ^ Morris, Wallace J., II (2009). "A universal prediction of stall onset for airfoils at a wide range of Reynolds number flows". Ph.D. Thesis. Bibcode:2009PhDT.......146M.
  17. ^ Morris, Wallace J.; Rusak, Zvi (October 2013). "Stall onset on aerofoils at low to moderately high Reynolds number flows". Journal of Fluid Mechanics. 733: 439–472. Bibcode:2013JFM...733..439M. doi:10.1017/jfm.2013.440. ISSN 0022-1120.
  18. ^ Traub, Lance W. (2016-03-24). "Semi-Empirical Prediction of Airfoil Hysteresis". Aerospace. 3 (2): 9. doi:10.3390/aerospace3020009.
  19. ^ Ramesh, Kiran; Gopalarathnam, Ashok; Granlund, Kenneth; Ol, Michael V.; Edwards, Jack R. (July 2014). "Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding". Journal of Fluid Mechanics. 751: 500–538. Bibcode:2014JFM...751..500R. doi:10.1017/jfm.2014.297. ISSN 0022-1120.


External links

Angle of attack

In fluid dynamics, angle of attack (AOA, α, or ) 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 moving. Angle of attack is the angle between the body's reference line and the oncoming flow. This article focuses on the most common application, the angle of attack of a wing or airfoil moving through air.

In aerodynamics, angle of attack specifies the angle between the chord line of the wing of a fixed-wing aircraft and the vector representing the relative motion between the aircraft and the atmosphere. Since a wing can have twist, a chord line of the whole wing may not be definable, so an alternate reference line is simply defined. Often, the chord line of the root of the wing is chosen as the reference line. Another choice is to use a horizontal line on the fuselage as the reference line (and also as the longitudinal axis). Some authors do not use an arbitrary chord line but use the zero lift axis where, by definition, zero angle of attack corresponds to zero coefficient of lift.

Some British authors have used the term angle of incidence instead of angle of attack. However, this can lead to confusion with the term riggers' angle of incidence meaning the angle between the chord of an airfoil and some fixed datum in the airplane.

Angle of incidence (aerodynamics)

On fixed-wing aircraft, the angle of incidence (sometimes referred to as the mounting angle) is the angle between the chord line of the wing where the wing is mounted to the fuselage, and a reference axis along the fuselage (often the direction of minimum drag, or where applicable, the longitudinal axis). The angle of incidence is fixed in the design of the aircraft, and with rare exceptions, cannot be varied in flight.

The term can also be applied to horizontal surfaces in general (such as canards or horizontal stabilizers) for the angle they make relative the longitudinal axis of the fuselage.

The figure to the right shows a side view of an airplane. The extended chord line of the wing root (red line) makes an angle with the longitudinal axis (roll axis) of the aircraft (blue line). Wings are typically mounted at a small positive angle of incidence, to allow the fuselage to have a low angle with the airflow in cruising flight. Angles of incidence of about 6° are common on most general aviation designs.

Other terms for angle of incidence in this context are rigging angle and rigger's angle of incidence. It should not be confused with the angle of attack, which is the angle the wing chord presents to the airflow in flight. Note that some ambiguity in this terminology exists, as some engineering texts that focus solely on the study of airfoils and their medium may use either term when referring to angle of attack.On rotary–wing aircraft, the AoA (Angle of Attack) is the angle between the airfoil chord line and resultant relative wind. AoA is an aerodynamic angle. It can change with no change in the AoI (Angle of Incidence). Several factors may change the rotor blade AoA. Pilots control some of those factors; others occur automatically due to the rotor system design. Pilots adjust AoA through normal control manipulation; however, even with no pilot input AoA will change as an integral part of travel of the rotor blade through the rotor-disc. This continuous process of change accommodates rotary-wing flight. Pilots have little control over blade flapping and flexing, gusty wind, and/or turbulent air conditions. AoA is one of the primary factors determining amount of lift and drag produced by an airfoil.

Clark Y

Clark Y is the name of a particular aerofoil 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. The airfoil has a thickness of 11.7 percent and is flat on the lower surface aft of 30 percent of chord. The flat bottom simplifies angle measurements on propellers, and makes for easy construction of wings.

For many applications the Clark Y has been an adequate airfoil section; it gives reasonable overall performance in respect of its lift-to-drag ratio, and has gentle and relatively benign stall characteristics. But the flat lower surface is not optimal from an aerodynamic perspective, and it is rarely used in modern designs.

The Clark YH airfoil is similar but with a reflexed (turned up) trailing edge producing a more positive pitching moment reducing the horizontal tail load required to trim an aircraft.


In aeronautics, downwash is the change in direction of air deflected by the aerodynamic action of an airfoil, wing or helicopter rotor blade in motion, as part of the process of producing lift.Lift on airfoil is an example of application of Newton's third law of motion - the force required to create the downwash is equal in magnitude and opposite in direction to the lift force on the airfoil. Lift on an airfoil is also an example of the Kutta-Joukowski theorem – the Kutta condition explains the existence of downwash at the trailing edge of the wing.

Drag coefficient

In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.

The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.

Ground-effect vehicle

A ground-effect vehicle (GEV), also called a wing-in-ground-effect (WIG), ground-effect craft, wingship or in Russian: ekranoplan, is a vehicle that is designed to attain sustained flight over a level surface (usually over the sea) by making use of ground effect, the aerodynamic interaction between the wings and the surface. The type is typically intended to operate from water like a flying boat, but some can operate over any flat area such as frozen lakes or flat plains similar to a hovercraft.

Gurney flap

The Gurney flap (or wickerbill) is a small tab projecting from the trailing edge of a wing. Typically it is set at a right angle to the pressure-side surface of the airfoil

and projects 1% to 2% of the wing chord.

This trailing edge device can improve the performance of a simple airfoil to nearly the same level as a complex high-performance design.The device operates by increasing pressure on the pressure side, decreasing pressure on the suction side, and helping the boundary layer flow stay attached all the way to the trailing edge on the suction side of the airfoil.

Common applications occur in auto racing, helicopter horizontal stabilizers, and aircraft where high lift is essential, such as banner-towing airplanes.It is named for its inventor and developer, American race car driver Dan Gurney.

Headwind and tailwind

A tailwind is a wind that blows in the direction of travel of an object, while a headwind blows against the direction of travel. A tailwind increases the object's speed and reduces the time required to reach its destination, while a headwind has the opposite effect.

In aeronautics, a headwind is favorable in takeoffs and landings because an airfoil moving into a headwind is capable of generating greater lift than the same airfoil moving through tranquil air, or with a tailwind, at equal ground speed. As a result, aviators and air traffic controllers commonly choose to take off or land in the direction of a runway that will provide a headwind.

In sailing, a headwind may make forward movement difficult, and necessitate tacking into the wind.

Tailwinds and headwinds are commonly measured in relation to the speed of vehicles — commonly air and watercraft — as well as in running events — particularly sprints.

Joukowsky transform

In applied mathematics, the Joukowsky transform, named after Nikolai Zhukovsky (who published it in 1910), is a conformal map historically used to understand some principles of airfoil design.

The transform is

where is a complex variable in the new space and is a complex variable in the original space. This transform is also called the Joukowsky transformation, the Joukowski transform, the Zhukovsky transform and other variations.

In aerodynamics, the transform is used to solve for the two-dimensional potential flow around a class of airfoils known as Joukowsky airfoils. A Joukowsky airfoil is generated in the complex plane (-plane) by applying the Joukowsky transform to a circle in the -plane. The coordinates of the centre of the circle are variables, and varying them modifies the shape of the resulting airfoil. The circle encloses the point (where the derivative is zero) and intersects the point This can be achieved for any allowable centre position by varying the radius of the circle.

Joukowsky airfoils have a cusp at their trailing edge. A closely related conformal mapping, the Kármán–Trefftz transform, generates the much broader class of Kármán–Trefftz airfoils by controlling the trailing edge angle. When a trailing edge angle of zero is specified, the Kármán–Trefftz transform reduces to the Joukowsky transform.

Kutta–Joukowski theorem

The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil and any two-dimensional bodies including circular cylinders translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated. The theorem relates the lift generated by an airfoil to the speed of the airfoil through the fluid, the density of the fluid and the circulation around the airfoil. The circulation is defined as the line integral around a closed loop enclosing the airfoil of the component of the velocity of the fluid tangent to the loop. It is named after Martin Kutta and Nikolai Zhukovsky (or Joukowski) who first developed its key ideas in the early 20th century. Kutta–Joukowski theorem is an inviscid theory, but it is a good approximation for real viscous flow in typical aerodynamic applications.

Kutta–Joukowski theorem relates lift to circulation much like the Magnus effect relates side force (called Magnus force) to rotation. However, the circulation here is not induced by rotation of the airfoil. The fluid flow in the presence of the airfoil can be considered to be the superposition of a translational flow and a rotating flow. This rotating flow is induced by the effects of camber, angle of attack and a sharp trailing edge of the airfoil. It should not be confused with a vortex like a tornado encircling the airfoil. At a large distance from the airfoil, the rotating flow may be regarded as induced by a line vortex (with the rotating line perpendicular to the two-dimensional plane). In the derivation of the Kutta–Joukowski theorem the airfoil is usually mapped onto a circular cylinder. In many text books, the theorem is proved for a circular cylinder and the Joukowski airfoil, but it holds true for general airfoils.

Leading edge

The leading edge is the part of the wing that first contacts the air; alternatively it is the foremost edge of an airfoil section. The first is an aerodynamic definition, the second a structural one.

As an example of the distinction, during a tailslide, from an aerodynamic point of view, the trailing edge becomes the leading edge and vice versa but from a structural point of view the leading edge remains unchanged.

Lift (force)

A fluid flowing past the surface of a body exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow.

If the surrounding fluid is air, the force is called an aerodynamic force. In water or any other liquid, it is called a hydrodynamic force.

Dynamic lift is distinguished from other kinds of lift in fluids. Aerostatic lift or buoyancy, in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, blimps, dirigibles, boats, and submarines. Planing lift, in which only the lower portion of the body is immersed in a liquid flow, is used by motorboats, surfboards, and water-skis.

Lift coefficient

The lift coefficient (CL) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area. A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. CL is a function of the angle of the body to the flow, its Reynolds number and its Mach number. The lift coefficient cl refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

NACA airfoil

The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA). The shape of the NACA airfoils is described using a series of digits following the word "NACA". The parameters in the numerical code can be entered into equations to precisely generate the cross-section of the airfoil and calculate its properties.

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 of the airfoil. The pitching moment on the wing of an airplane is part of the total moment that must be balanced using the lift on the horizontal stabilizer. More generally, a pitching moment is any moment acting on the pitch axis of a moving body.

The lift on an airfoil is a distributed force that can be said to act at a point called the center of pressure. However, as angle of attack changes on a cambered airfoil, there is movement of the center of pressure forward and aft. This makes analysis difficult when attempting to use the concept of the center of pressure. One of the remarkable properties of a cambered airfoil is that, even though the center of pressure moves forward and aft, if the lift is imagined to act at a point called the aerodynamic center the moment of the lift force changes in proportion to the square of the airspeed. If the moment is divided by the dynamic pressure, the area and chord of the airfoil, the result is known as the pitching moment coefficient. This coefficient changes only a little over the operating range of angle of attack of the airfoil. The combination of the two concepts of aerodynamic center and pitching moment coefficient make it relatively simple to analyse some of the flight characteristics of an aircraft.

Rib (aeronautics)

In an aircraft, ribs are forming elements of the structure of a wing, especially in traditional construction.

By analogy with the anatomical definition of "rib", the ribs attach to the main spar, and by being repeated at frequent intervals, form a skeletal shape for the wing. Usually ribs incorporate the airfoil shape of the wing, and the skin adopts this shape when stretched over the ribs.

Richard T. Whitcomb

Richard Travis Whitcomb (February 21, 1921 – October 13, 2009) was an American aeronautical engineer who was noted for his contributions to the science of aerodynamics.

Supercritical airfoil

A supercritical airfoil is an airfoil designed primarily to delay the onset of wave drag in the transonic speed range. Supercritical airfoils are characterized by their flattened upper surface, highly cambered ("downward-curved") aft section, and larger leading-edge radius compared with NACA 6-series laminar airfoil shapes. Standard wing shapes are designed to create lower pressure over the top of the wing. The camber of the wing determines how much the air accelerates around the wing. As the speed of the aircraft approaches the speed of sound, the air accelerating around the wing reaches Mach 1 and shockwaves begin to form. The formation of these shockwaves causes wave drag. Supercritical airfoils are designed to minimize this effect by flattening the upper surface of the wing.

The supercritical airfoils were suggested first in Germany in 1940, when K. A. Kawalki at Deutsche Versuchsanstalt für Luftfahrt Berlin-Adlershof designed airfoils characterised by elliptical leading edges, maximal thickness located downstream up to 50% chord and a flat upper surface. Testing of these airfoils was reported by B. Göthert and K. A. Kawalki in 1944. Kawalki's airfoil shapes were identical to Richard Whitcomb's. Hawker-Siddeley in Hatfield, England, designed in 1959–1965 improved airfoil profiles known as rooftop rear-loaded airfoils, which were the basis of the Airbus A300 supercritical wing, which first flew in 1972.In the U.S., supercritical airfoils were studied in the 1960s, by then NASA engineer Richard Whitcomb, and were first tested on a modified North American T-2C Buckeye. After this first test, the airfoils were tested at higher speeds on the TF-8A Crusader. While the design was initially developed as part of the supersonic transport (SST) project at NASA, it has since been mainly applied to increase the fuel efficiency of many high-subsonic aircraft. The supercritical airfoil shape is incorporated into the design of a supercritical wing.

Kawalki's research was the basis for the objection in 1984 against the US-patent specification for the supercritical airfoil.

Vortex generator

A vortex generator (VG) is an aerodynamic device, consisting of a small vane usually attached to a lifting surface (or airfoil, such as an aircraft wing) or a rotor blade of a wind turbine. VGs may also be attached to some part of an aerodynamic vehicle such as an aircraft fuselage or a car. When the airfoil or the body is in motion relative to the air, the VG creates a vortex, which, by removing some part of the slow-moving boundary layer in contact with the airfoil surface, delays local flow separation and aerodynamic stalling, thereby improving the effectiveness of wings and control surfaces, such as flaps, elevators, ailerons, and rudders.

Classical simple machines
Compressors and pumps
External combustion engines
Internal combustion engines


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