Airfoil 1

Airfoil

Examples of airfoils in nature and within various vehicles

An airfoil (in American English) oraerofoil (in British English) is theshape of a wing or blade (of apropeller, rotor or turbine) or sail asseen in cross-section.

An airfoil-shaped body moved througha fluid produces an aerodynamic force.The component of this forceperpendicular to the direction ofmotion is called lift. The componentparallel to the direction of motion iscalled drag. Subsonic flight airfoilshave a characteristic shape with arounded leading edge, followed by asharp trailing edge, often withasymmetric camber. Foils of similarfunction designed with water as theworking fluid are called hydrofoils.

The lift on an airfoil is primarily theresult of its angle of attack and shape.When oriented at a suitable angle, theairfoil deflects the oncoming air,resulting in a force on the airfoil in thedirection opposite to the deflection.This force is known as aerodynamic force and can be resolved into two components: Lift and drag. Most foil shapesrequire 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 which results in lower pressure on one sideand higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli'sprinciple, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on thelower surface. The lift force can be related directly to the average top/bottom velocity difference without computingthe pressure by using the concept of circulation and the Kutta-Joukowski theorem.[1][2][3][4]

Airfoil 2

Introduction

Streamlines around a NACA 0012 airfoil at moderate angle of attack

Lift and Drag curves for a typical airfoil

A fixed-wing aircraft's wings, horizontal,and vertical stabilizers are built withairfoil-shaped cross sections, as arehelicopter rotor blades. Airfoils are alsofound in propellers, fans, compressors andturbines. Sails are also airfoils, and theunderwater surfaces of sailboats, such as thecenterboard and keel, are similar incross-section and operate on the sameprinciples as airfoils. Swimming and flyingcreatures and even many plants and sessileorganisms employ airfoils/hydrofoils:common examples being bird wings, thebodies of fish, and the shape of sand dollars.An airfoil-shaped wing can createdownforce on an automobile or other motorvehicle, improving traction.

Any object with an angle of attack in amoving fluid, such as a flat plate, a building,or the deck of a bridge, will generate anaerodynamic force (called lift) perpendicularto the flow. Airfoils are more efficientlifting shapes, able to generate more lift (upto a point), and to generate lift with lessdrag.

A lift and drag curve obtained in windtunnel testing is shown on the right. Thecurve represents an airfoil with a positivecamber so some lift is produced at zeroangle of attack. With increased angle ofattack, lift increases in a roughly linearrelation, called the slope of the lift curve. Atabout 18 degrees this airfoil stalls, and lift falls off quickly beyond that. The drop in lift can be explained by theaction of the upper-surface boundary layer, which separates and greatly thickens over the upper surface at and pastthe stall angle. The thickened boundary layer's displacement thickness changes the airfoil's effective shape, inparticular it reduces its effective camber, which modifies the overall flow field so as to reduce the circulation and thelift. The thicker boundary layer also causes a large increase in pressure drag, so that the overall drag increasessharply 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 spin-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

Airfoil 3

thickness to minimize the chance of boundary layer separation. This elongates the wing and moves the point ofmaximum 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 sensitiveto angle of attack. A supercritical airfoil has its maximum thickness close to the leading edge to have a lot of lengthto slowly shock the supersonic flow back to subsonic speeds. Generally such transonic airfoils and also thesupersonic airfoils have a low camber to reduce drag divergence. Modern aircraft wings may have different airfoilsections 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 edgeflap acts similarly to an aileron; however, it, as opposed to an aileron, can be retracted partially into the wing if notused.A laminar flow wing has a maximum thickness in the middle camber line. Analyzing the Navier-Stokes equationsin 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 ahigher cruising speed is possible. However, with rain or insects on the wing, or for jetliner speeds, this does notwork. Since such a wing stalls more easily, this airfoil is not used on wingtips (spin-stall again).Schemes have been devised to define airfoils — an example is the NACA system. Various airfoil generation systemsare also used. An example of a general purpose airfoil that finds wide application, and predates the NACA system, isthe Clark-Y. Today, airfoils can be designed for specific functions using inverse design programs such as PROFOIL,XFOIL and AeroFoil. XFOIL is an online program created by Mark Drela that will design and analyze subsonicisolated airfoils.[5]

Airfoil terminology

Airfoil nomenclature

The various terms related to airfoils aredefined below:[6]

• The suction surface (a.k.a. uppersurface) is generally associated withhigher velocity and thus lower staticpressure.

• The pressure surface (a.k.a. lowersurface) has a comparatively higherstatic pressure than the suctionsurface. The pressure gradientbetween 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.A key characteristic of an airfoil is its chord. We thus define the following concepts:• The leading edge is the point at the front of the airfoil that has maximum curvature.[7]

• The trailing edge is defined similarly as the point of maximum curvature at the rear of the airfoil.• The chord line is a straight line connecting the leading and trailing edges of the airfoil.• The chord length, or simply chord, , is the length of the chord line and is the characteristic dimension of the

airfoil section.

Airfoil 4

Different definitions of airfoil thickness

An airfoil designed for winglets (PSU90-125WL)

The shape of the airfoil is defined using the following concepts:• The mean camber line is the locus of points midway between the

upper and lower surfaces. Its exact shape depends on how thethickness is defined;

• The thickness of an airfoil varies along the chord. It may bemeasured in either of two ways:

• Thickness measured perpendicular to the camber line.[8][9] Thisis sometimes described as the "American convention";[8]

• Thickness measured perpendicular to the chord line.[10] This issometimes described as the "British convention".

Two key parameters to describe an airfoil’s shape are its maximumthickness (expressed as a percentage of the chord), and the location ofthe maximum thickness point (also expressed as a percentage of thechord).

Finally, important concepts used to describe the airfoil’s behavior whenmoving through a fluid are:

• The aerodynamic center, which is the chord-wise length aboutwhich the pitching moment is independent of the lift coefficient andthe angle of attack.

• The center of pressure, which is the chord-wise location about which the pitching moment is zero.

Thin airfoil theory

An airfoil section is displayed at the tip of thisDenney Kitfox aircraft, built in 1991.

Airfoil of Kamov Ka-26 helicopters

Thin airfoil theory is a simple theory of airfoils that relates angle ofattack to lift for incompressible, inviscid flows. It was devised byGerman-American mathematician Max Munk and further refined byBritish aerodynamicist Hermann Glauert and others[11] in the 1920s.The theory idealizes the flow around an airfoil as two-dimensionalflow around a thin airfoil. It can be imagined as addressing an airfoil ofzero thickness and infinite wingspan.

Thin airfoil theory was particularly notable in its day because itprovided a sound theoretical basis for the following importantproperties of airfoils in two-dimensional flow:[12][13]

(1) on a symmetric airfoil, the center of pressure and aerodynamiccenter lies exactly one quarter of the chord behind the leading edge(2) on a cambered airfoil, the aerodynamic center lies exactly onequarter 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 symmetricairfoil of infinite wingspan is:

where is the section lift coefficient,

Airfoil 5

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 tothe 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.[14]

Derivation of thin airfoil theory

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 airfoilColors:

Black = laminar flow,red = turbulent flow,

grey = subsonic stream,blue = supersonic flow volume

The airfoil is modeled as a thin lifting mean-line(camber line). The mean-line, y(x), is considered toproduce a distribution of vorticity along the line,s. By the Kutta condition, the vorticity is zero at thetrailing edge. Since the airfoil is thin, x (chord position)can be used instead of s, and all angles can beapproximated as small.From the Biot-Savart law, this vorticity produces aflow field where

where is the location where induced velocity isproduced, is the location of the vortex elementproducing the velocity and is the chord length of theairfoil.

Since there is no flow normal to the curved surface ofthe airfoil, balances that from the component ofmain flow , which is locally normal to theplate—the main flow is locally inclined to the plate byan angle . That is:

This integral equation can by solved for , afterreplacing x by

,as a Fourier series in with a modifiedlead term That is

(These terms are known as the Glauert integral).The coefficients are given by

Airfoil 6

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 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 varywith angle of attack, i.e.,

Notes[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, pp. 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 inmagnitude, direction, or both. Changing the velocity creates a net force on the body" "Lift from Flow Turning" (http:/ / www. grc. nasa. gov/WWW/ K-12/ airplane/ right2. html). NASA Glenn Research Center. Archived (http:/ / web. archive. org/ web/ 20110705131653/ http:/ /www. grc. nasa. gov/ WWW/ K-12/ airplane/ right2. html) 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 (http:/ / user. uni-frankfurt. de/ ~weltner/ Flight/ PHYSIC4. htm),

[4] "...if a streamline is curved, there must be a pressure gradient across the streamline..."Babinsky, Holger (November 2003), "How do wingswork?" (http:/ / www. iop. org/ EJ/ article/ 0031-9120/ 38/ 6/ 001/ pe3_6_001. pdf), Physics Education,

[5] XFOIL (http:/ / web. mit. edu/ drela/ Public/ web/ xfoil/ )[6] 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.[7] Houghton, E. L.; Carpenter, P.W. (2003). Butterworth Heinmann. ed. Aerodynamics for Engineering Students (5th ed.). ISBN 0-7506-5111-3.

p.18[8] Houghton, E. L.; Carpenter, P.W. (2003). Butterworth Heinmann. ed. Aerodynamics for Engineering Students (5th ed.). ISBN 0-7506-5111-3.

p.17[9] Phillips, Warren F. (2010). Mechanics of Flight (2nd ed.). Wiley & Sons. ISBN 978-0-470-53975-0. p.27[10] Bertin, John J.; Cummings, Russel M. (2009). Pearson Prentice Hall. ed. Aerodynamics for Engineers (5th ed.). ISBN 978-0-13-227268-1.

p.199[11] 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[12] Abbott, Ira H., and Von Doenhoff, Albert E. (1959), Theory of Wing Sections, Section 4.3[13] Clancy, L.J. (1975), Aerodynamics, Sections 8.1 to 8.8, Pitman Publishing Limited, London. ISBN 0-273-01120-0

Airfoil 7

[14] Aerospaceweb's information on Thin Airfoil Theory (http:/ / www. aerospaceweb. org/ question/ aerodynamics/ q0136. shtml)

References• Anderson, John, D (2007). Fundamentals of Aerodynamics. McGraw-Hill.• Desktopaero (http:/ / www. desktopaero. com/ appliedaero/ airfoils1/ tatderivation. html)• University of Sydney, Aerodynamics for Students (http:/ / s6. aeromech. usyd. edu. au/ aero/ thinaero/ thinaero.

pdf)• Batchelor, George. K (1967). An Introduction to Fluid Dynamics. Cambridge UP. pp. 467–471.

External links• UIUC Airfoil Coordinates Database (http:/ / www. ae. uiuc. edu/ m-selig/ ads/ coord_database. html)• Database with airfoils (http:/ / www. worldofkrauss. com/ foils/ search)• Airfoil & Hydrofoil Reference Application (http:/ / www. skias-engineering. gr/ index.

php?option=com_content& task=view& id=19& Itemid=47)• The Joukowski Airfoil (http:/ / math. fullerton. edu/ mathews/ c2003/ JoukowskiTransMod. html)• Chard Museum (http:/ / www. chardmuseum. co. uk/ Powered_Flight/ ) The Birth of Powered Flight.• FoilSim (http:/ / www. grc. nasa. gov/ WWW/ K-12/ airplane/ foil2. html) An airfoil simulator from NASA.

Article Sources and Contributors 8

Article Sources and ContributorsAirfoil  Source: http://en.wikipedia.org/w/index.php?oldid=523957779  Contributors: 9258fahsflkh917fas, ABF, AHands, Aaggrreenn, Akradecki, Albertktau, Ali K, Andy Dingley, Antilived,Ariadacapo, Arnero, Arpingstone, Ashchap, Avé, B, Baddy007309, Ballon of pi, BigJohnHenry, Bigbluefish, BorgHunter, BozMo, Brookie, Can't sleep, clown will eat me, Canadianshoper,Canterbury Tail, Carlossuarez46, Ccrummer, Chiefmanzzz, ChrisMP1, Clappingsimon, Cnilep, Cocoaguy, Coconuts00, CommonsDelinker, Comrade009, Crowsnest, D1ma5ad, DBManley,Davidjagoe, De728631, Decltype, Derekyang1, Dhaluza, Doggyt658, Dolphin51, Doprendek, Duxwing, EagleFan, Emt147, Epbr123, Epipelagic, Everyking, F l a n k e r, Fawcett5, Fluzwup,Fresheneesz, Funandtrvl, GRAHAMUK, Garylhewitt, Giftlite, Gilamonster, Gilliam, Glenn, Gracefool, Grafen, Gwernol, HCA, Headbomb, Hlucho, Hschilling, Interiot, Isnow, IstvanWolf,J.delanoy, J04n, JForget, Jamison Lofthouse, Jarnopons, Jenslekman, Jhbdel, JidGom, Jjdreese, Jvhertum, Kallemax, Kazvorpal, Kirk Hilliard, Lao Wai, Lee, Lesnail, LindsayH, Linmhall,Linuxlad, Luís Felipe Braga, MER-C, Mark.camp, Marsian, Martial75, Mbw5014, McSly, Meggar, Mini-Geek, Mmeijeri, Mooglemoogle, Moogwrench, Morganw, Mostly water, Mr swordfish,Mrb712, N328KF, Nabla, Nahallac Silverwinds, Neelix, Nightscream, Nil0lab, Nowa, Nymphii, Omit, P199, Patrick O'Leary, Petebutt, PhilipO, Prari, R'n'B, Raghith, Raymondwinn, Rbeas,Reliableforever, ResearchRave, Rmosler2100, Robofish, Robophilosopher, Rowmn, Ryanmac06, Rylee118, Senthilvel32, Ser Amantio di Nicolao, Silivrenion, Slay3r 1.2.5, Some Wiki Editor,Some standardized rigour, Sonett72, SpookyMulder, StuRat, Svart0, The High Fin Sperm Whale, Tohd8BohaithuGh1, Totensiebush, Unused0030, Van helsing, Vgy7ujm, Vifar55, VolodymyrB,Wavelength, Wereon, Wildthing61476, Wjbeaty, Wjejskenewr, Wknight94, Wxlfsr, Xiegui117, Xmnemonic, Zammy flames, ZeroOne, Zoicon5, 288 ,حيا ,.אריה ה anonymous edits

Image Sources, Licenses and ContributorsFile:Examples of Airfoils.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Examples_of_Airfoils.svg  License: Creative Commons Zero  Contributors: User:AriadacapoImage:Streamlines around a NACA 0012.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Streamlines_around_a_NACA_0012.svg  License: Public Domain  Contributors: MichaelBelisleImage:Lift drag graph.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Lift_drag_graph.JPG  License: GNU Free Documentation License  Contributors: Original uploader wasMeggar at en.wikipediaFile:Wing profile nomenclature.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Wing_profile_nomenclature.svg  License: Creative Commons Zero  Contributors: User:AriadacapoFile:Airfoil thickness definition.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Airfoil_thickness_definition.svg  License: Creative Commons Zero  Contributors: User:AriadacapoImage:PSU-90-125.PNG  Source: http://en.wikipedia.org/w/index.php?title=File:PSU-90-125.PNG  License: GNU Free Documentation License  Contributors: DhaluzaImage:denney.kitfox.g-foxc.arp.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Denney.kitfox.g-foxc.arp.jpg  License: Public Domain  Contributors: Arpingstone, Denniss,PeterWDImage:Helikopter forgószárnyának keresztmetszete 2.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Helikopter_forgószárnyának_keresztmetszete_2.jpg  License: CreativeCommons Attribution-Sharealike 3.0  Contributors: Zátonyi Sándor (ifj.)Image:Aerofoils for different aeroplanes.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Aerofoils_for_different_aeroplanes.svg  License: Creative CommonsAttribution-Sharealike 3.0  Contributors: Arnero

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