Aerodynamics

Aerodynamics 1

Aerodynamics

A vortex is created by the passage of an aircraft wing, revealed by smoke.Vortices are one of the many phenomena associated to the study of

aerodynamics. The equations of aerodynamics show that the vortex is createdby the difference in pressure between the upper and lower surface of the wing.At the end of the wing, the lower surface effectively tries to 'reach over' to the

low pressure side, creating rotation and the vortex.

Aerodynamics is a branch of dynamicsconcerned with studying the motion of air,particularly when it interacts with a movingobject. Aerodynamics is a subfield of fluiddynamics and gas dynamics, with much theoryshared between them. Aerodynamics is oftenused synonymously with gas dynamics, withthe difference being that gas dynamics appliesto all gases. Understanding the motion of air(often called a flow field) around an objectenables the calculation of forces and momentsacting on the object. Typical propertiescalculated for a flow field include velocity,pressure, density and temperature as a functionof position and time. By defining a controlvolume around the flow field, equations for theconservation of mass, momentum, and energycan be defined and used to solve for theproperties. The use of aerodynamics throughmathematical analysis, empiricalapproximations, wind tunnel experimentation,and computer simulations form the scientific basis for heavier-than-air flight.

Aerodynamic problems can be classified according to the flow environment. External aerodynamics is the study offlow around solid objects of various shapes. Evaluating the lift and drag on an airplane or the shock waves that formin front of the nose of a rocket are examples of external aerodynamics. Internal aerodynamics is the study of flowthrough passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow througha jet engine or through an air conditioning pipe.

Aerodynamic problems can also be classified according to whether the flow speed is below, near or above the speedof sound. A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic ifspeeds both below and above the speed of sound are present (normally when the characteristic speed isapproximately the speed of sound), supersonic when the characteristic flow speed is greater than the speed of sound,and hypersonic when the flow speed is much greater than the speed of sound. Aerodynamicists disagree over theprecise definition of hypersonic flow; minimum Mach numbers for hypersonic flow range from 3 to 12.The influence of viscosity in the flow dictates a third classification. Some problems may encounter only very smallviscous effects on the solution, in which case viscosity can be considered to be negligible. The approximations tothese problems are called inviscid flows. Flows for which viscosity cannot be neglected are called viscous flows.

Aerodynamics 2

History

Early ideas - ancient times to the 17th century

A drawing of a design for a flying machine by Leonardo da Vinci (c. 1488). Thismachine was an ornithopter, with flapping wings similar to a bird, first presented in

his Codex on the Flight of Birds in 1505.

Humans have been harnessing aerodynamicforces for thousands of years with sailboatsand windmills.[1] Images and stories offlight have appeared throughout recordedhistory,[2] such as the legendary story ofIcarus and Daedalus.[3] Althoughobservations of some aerodynamic effectslike wind resistance (e.g. drag) wererecorded by the likes of Aristotle, Leonardoda Vinci and Galileo Galilei, very littleeffort was made to develop a rigorousquantitative theory of air flow prior to the17th century.

In 1505, Leonardo da Vinci wrote the Codexon the Flight of Birds, one of the earliesttreatises on aerodynamics. He notes for thefirst time that the center of gravity of aflying bird does not coincide with its centerof pressure, and he describes theconstruction of an ornithopter, with flapping wings similar to a bird's.

Sir Isaac Newton was the first person to develop a theory of air resistance,[4] making him one of the firstaerodynamicists. As part of that theory, Newton considered that drag was due to the dimensions of a body, thedensity of the fluid, and the velocity raised to the second power. These all turned out to be correct for low flowspeeds. Newton also developed a law for the drag force on a flat plate inclined towards the direction of the fluidflow. Using F for the drag force, ρ for the density, S for the area of the flat plate, V for the flow velocity, and θ forthe inclination angle, his law was expressed as Unfortunately, this equation is incorrect for the calculation of drag in most cases. Drag on a flat plate is closer tobeing linear with the angle of inclination as opposed to acting quadratically at low angles. The Newton formula canlead one to believe that flight is more difficult than it actually is, and it may have contributed to a delay in humanflight. However, it is correct for a very slender plate when the angle becomes large and flow separation occurs, or ifthe flow speed is supersonic.[5]

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Modern beginnings - 18th to 19th century

A drawing of a glider by Sir George Cayley, one of theearly attempts at creating an aerodynamic shape.

In 1738 The Dutch-Swiss mathematician Daniel Bernoullipublished Hydrodynamica, where he described the fundamentalrelationship among pressure, density, and velocity; in particularBernoulli's principle, which is sometimes used to calculateaerodynamic lift.[6] More general equations of fluid flow - theEuler equations - were published by Leonard Euler in 1757. TheEuler equations were extended to incorporate the effects ofviscosity in the first half of the 1800s, resulting in theNavier-Stokes equations.

Sir George Cayley is credited as the first person to identify thefour aerodynamic forces of flight—weight, lift, drag, andthrust—and the relationship between them.[7] [8] Cayley believedthat the drag on a flying machine must be counteracted by a meansof propulsion in order for level flight to occur. Cayley also lookedto nature for aerodynamic shapes with low drag. Among theshapes he investigated were the cross-sections of trout. This mayappear counterintuitive, however, the bodies of fish are shaped toproduce very low resistance as they travel through water. Theircross-sections are sometimes very close to that of modern lowdrag airfoils.

Air resistance experiments were carried out by investigatorsthroughout the 18th and 19th centuries. Drag theories were

developed by Jean le Rond d'Alembert,[9] Gustav Kirchhoff,[10] and Lord Rayleigh.[11] Equations for fluid flow withfriction were developed by Claude-Louis Navier[12] and George Gabriel Stokes.[13] To simulate fluid flow, manyexperiments involved immersing objects in streams of water or simply dropping them off the top of a tall building.Towards the end of this time period Gustave Eiffel used his Eiffel Tower to assist in the drop testing of flat plates.

Of course, a more precise way to measure resistance is to place an object within an artificial, uniform stream of airwhere the velocity is known. The first person to experiment in this fashion was Francis Herbert Wenham, who indoing so constructed the first wind tunnel in 1871. Wenham was also a member of the first professional organizationdedicated to aeronautics, the Royal Aeronautical Society of the United Kingdom. Objects placed in wind tunnelmodels are almost always smaller than in practice, so a method was needed to relate small scale models to theirreal-life counterparts. This was achieved with the invention of the dimensionless Reynolds number by OsborneReynolds.[14] Reynolds also experimented with laminar to turbulent flow transition in 1883.By the late 19th century, two problems were identified before heavier-than-air flight could be realized. The first wasthe creation of low-drag, high-lift aerodynamic wings. The second problem was how to determine the power neededfor sustained flight. During this time, the groundwork was laid down for modern day fluid dynamics andaerodynamics, with other less scientifically inclined enthusiasts testing various flying machines with little success.

Aerodynamics 4

A replica of the Wright Brothers' wind tunnel is on display at the Virginia Air andSpace Center. Wind tunnels were key in the development and validation of the

laws of aerodynamics.

In 1889, Charles Renard, a Frenchaeronautical engineer, became the firstperson to reasonably predict the powerneeded for sustained flight.[15] Renard andGerman physicist Hermann von Helmholtzexplored the wing loading of birds,eventually concluding that humans couldnot fly under their own power by attachingwings onto their arms. Otto Lilienthal,following the work of Sir George Cayley,was the first person to become highlysuccessful with glider flights. Lilienthalbelieved that thin, curved airfoils wouldproduce high lift and low drag.

Octave Chanute provided a great service tothose interested in aerodynamics and flyingmachines by publishing a book outlining allof the research conducted around the world up to 1893.[16]

Practical flight - early 20th century

With the information contained in Chanute's book, the personal assistance of Chanute himself, and research carriedout in their own wind tunnel, the Wright brothers gained just enough knowledge of aerodynamics to fly the firstpowered aircraft on December 17, 1903, just in time to beat the efforts of Samuel Pierpont Langley. The Wrightbrothers' flight confirmed or disproved a number of aerodynamics theories. Newton's drag force theory was finallyproved incorrect. This first widely-publicised flight led to a more organized effort between aviators and scientists,leading the way to modern aerodynamics.

During the time of the first flights, Frederick W. Lanchester,[17] Martin Wilhelm Kutta, and Nikolai Zhukovskyindependently created theories that connected circulation of a fluid flow to lift. Kutta and Zhukovsky went on todevelop a two-dimensional wing theory. Expanding upon the work of Lanchester, Ludwig Prandtl is credited withdeveloping the mathematics[18] behind thin-airfoil and lifting-line theories as well as work with boundary layers.Prandtl, a professor at the University of Göttingen, instructed many students who would play important roles in thedevelopment of aerodynamics like Theodore von Kármán and Max Munk.

Faster than sound - later 20th centuryAs aircraft began to travel faster, aerodynamicists realized that the density of air began to change as it came into contact with an object, leading to a division of fluid flow into the incompressible and compressible regimes. In compressible aerodynamics, density and pressure both change, which is the basis for calculating the speed of sound. Newton was the first to develop a mathematical model for calculating the speed of sound, but it was not correct until Pierre-Simon Laplace accounted for the molecular behavior of gases and introduced the heat capacity ratio. The ratio of the flow speed to the speed of sound was named the Mach number after Ernst Mach, who was one of the first to investigate the properties of supersonic flow which included Schlieren photography techniques to visualize the changes in density. William John Macquorn Rankine and Pierre Henri Hugoniot independently developed the theory for flow properties before and after a shock wave. Jakob Ackeret led the initial work on calculating the lift and drag on a supersonic airfoil.[19] Theodore von Kármán and Hugh Latimer Dryden introduced the term transonic to describe flow speeds around Mach 1 where drag increases rapidly. Because of the increase in drag approaching

Aerodynamics 5

Mach 1, aerodynamicists and aviators disagreed on whether supersonic flight was achievable.

Image showing shock waves from NASA's X-43A hypersonic research vehicle inflight at Mach 7, generated using a computational fluid dynamics algorithm.

On September 30, 1935 an exclusiveconference was held in Rome with the topicof high velocity flight and the possibility ofbreaking the sound barrier.[20] Participantsincluded Theodore von Kármán, LudwigPrandtl, Jakob Ackeret, Eastman Jacobs,Adolf Busemann, Geoffrey Ingram Taylor,Gaetano Arturo Crocco, and EnricoPistolesi. Ackeret presented a design for asupersonic wind tunnel. Busemann gave apresentation on the need for aircraft withswept wings for high speed flight. EastmanJacobs, working for NACA, presented hisoptimized airfoils for high subsonic speedswhich led to some of the high performance

American aircraft during World War II. Supersonic propulsion was also discussed. The sound barrier was brokenusing the Bell X-1 aircraft twelve years later, thanks in part to those individuals.

By the time the sound barrier was broken, much of the subsonic and low supersonic aerodynamics knowledge hadmatured. The Cold War fueled an ever evolving line of high performance aircraft. Computational fluid dynamics wasstarted as an effort to solve for flow properties around complex objects and has rapidly grown to the point whereentire aircraft can be designed using a computer.

With some exceptions, the knowledge of hypersonic aerodynamics has matured between the 1960s and the presentdecade. Therefore, the goals of an aerodynamicist have shifted from understanding the behavior of fluid flow tounderstanding how to engineer a vehicle to interact appropriately with the fluid flow. For example, while thebehavior of hypersonic flow is understood, building a scramjet aircraft to fly at hypersonic speeds has seen verylimited success. Along with building a successful scramjet aircraft, the desire to improve the aerodynamic efficiencyof current aircraft and propulsion systems will continue to fuel new research in aerodynamics.

Introductory terminology• Lift• Drag• Reynolds number• Mach number

Continuity assumptionGases are composed of molecules which collide with one another and solid objects. If density and velocity are takento be well-defined at infinitely small points, and are assumed to vary continuously from one point to another, thediscrete molecular nature of a gas is ignored.The continuity assumption becomes less valid as a gas becomes more rarefied. In these cases, statistical mechanics isa more valid method of solving the problem than continuous aerodynamics. The Knudsen number can be used toguide the choice between statistical mechanics and the continuous formulation of aerodynamics.

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Laws of conservation

Control volume schematic of internal flow with one inlet and exit including an axialforce, work, and heat transfer. State 1 is the inlet and state 2 is the exit.

Aerodynamics problems are oftensolved using conservation laws asapplied to a fluid continuum. Theconservation laws can be written inintegral or differential form. In manybasic problems, three conservationprinciples are used:

• Continuity: If a certain mass offluid enters a volume, it must eitherexit the volume or change the massinside the volume. In fluid dynamics, the continuity equation is analogous to Kirchhoff's Current Law in electriccircuits. The differential form of the continuity equation is:

Above, is the fluid density, u is a velocity vector, and t is time. Physically, the equation also shows that mass isneither created nor destroyed in the control volume.[21] For a steady state process, the rate at which mass enters thevolume is equal to the rate at which it leaves the volume.[22] Consequently, the first term on the left is then equal tozero. For flow through a tube with one inlet (state 1) and exit (state 2) as shown in the figure in this section, thecontinuity equation may be written and solved as:

Above, A is the variable cross-section area of the tube at the inlet and exit. For incompressible flows, density remainsconstant.• Conservation of Momentum: This equation applies Newton's second law of motion to a continuum, whereby force

is equal to the time derivative of momentum. Both surface and body forces are accounted for in this equation. Forinstance, F could be expanded into an expression for the frictional force acting on an internal flow.

For the same figure, a control volume analysis yields:

Above, the force is placed on the left side of the equation, assuming it acts with the flow moving in a left-to-rightdirection. Depending on the other properties of the flow, the resulting force could be negative which means it acts inthe opposite direction as depicted in the figure.• Conservation of Energy: Although energy can be converted from one form to another, the total energy in a given

system remains constant.

Above, h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and is the viscous dissipationfunction. The viscous dissipation function governs the rate at which mechanical energy of the flow is converted toheat. The term is always positive since, according to the second law of thermodynamics, viscosity cannot add energyto the control volume.[23] The expression on the left side is a material derivative. Again using the figure, the energyequation in terms of the control volume may be written as:

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Above, the shaft work and heat transfer are assumed to be acting on the flow. They may be positive (to the flow fromthe surroundings) or negative (to the surroundings from the flow) depending on the problem. The ideal gas law oranother equation of state is often used in conjunction with these equations to form a system to solve for the unknownvariables.

Incompressible aerodynamicsAn incompressible flow is characterized by a constant density despite flowing over surfaces or inside ducts. A flowcan be considered incompressible as long as its speed is low. For higher speeds, the flow will begin to compress as itcomes into contact with surfaces. The Mach number is used to distinguish between incompressible and compressibleflows.

Subsonic flowSubsonic (or low-speed) aerodynamics is the study of fluid motion which is everywhere much slower than the speedof sound through the fluid or gas. There are several branches of subsonic flow but one special case arises when theflow is inviscid, incompressible and irrotational. This case is called Potential flow and allows the differentialequations used to be a simplified version of the governing equations of fluid dynamics, thus making available to theaerodynamicist a range of quick and easy solutions.[24] It is a special case of Subsonic aerodynamics.In solving a subsonic problem, one decision to be made by the aerodynamicist is whether to incorporate the effectsof compressibility. Compressibility is a description of the amount of change of density in the problem. When theeffects of compressibility on the solution are small, the aerodynamicist may choose to assume that density isconstant. The problem is then an incompressible low-speed aerodynamics problem. When the density is allowed tovary, the problem is called a compressible problem. In air, compressibility effects are usually ignored when theMach number in the flow does not exceed 0.3 (about 335 feet (102m) per second or 228 miles (366 km) per hour at60oF). Above 0.3, the problem should be solved by using compressible aerodynamics.

Compressible aerodynamicsAccording to the theory of aerodynamics, a flow is considered to be compressible if its change in density withrespect to pressure is non-zero along a streamline. This means that - unlike incompressible flow - changes in densitymust be considered. In general, this is the case where the Mach number in part or all of the flow exceeds 0.3. TheMach .3 value is rather arbitrary, but it is used because gas flows with a Mach number below that value demonstratechanges in density with respect to the change in pressure of less than 5%. Furthermore, that maximum 5% densitychange occurs at the stagnation point of an object immersed in the gas flow and the density changes around the restof the object will be significantly lower. Transonic, supersonic, and hypersonic flows are all compressible.

Transonic flowThe term Transonic refers to a range of velocities just below and above the local speed of sound (generally taken asMach 0.8–1.2). It is defined as the range of speeds between the critical Mach number, when some parts of theairflow over an aircraft become supersonic, and a higher speed, typically near Mach 1.2, when all of the airflow issupersonic. Between these speeds some of the airflow is supersonic, and some is not.

Supersonic flowSupersonic aerodynamic problems are those involving flow speeds greater than the speed of sound. Calculating thelift on the Concorde during cruise can be an example of a supersonic aerodynamic problem.Supersonic flow behaves very differently from subsonic flow. Fluids react to differences in pressure; pressure changes are how a fluid is "told" to respond to its environment. Therefore, since sound is in fact an infinitesimal

Aerodynamics 8

pressure difference propagating through a fluid, the speed of sound in that fluid can be considered the fastest speedthat "information" can travel in the flow. This difference most obviously manifests itself in the case of a fluidstriking an object. In front of that object, the fluid builds up a stagnation pressure as impact with the object brings themoving fluid to rest. In fluid traveling at subsonic speed, this pressure disturbance can propagate upstream, changingthe flow pattern ahead of the object and giving the impression that the fluid "knows" the object is there and isavoiding it. However, in a supersonic flow, the pressure disturbance cannot propagate upstream. Thus, when thefluid finally does strike the object, it is forced to change its properties -- temperature, density, pressure, and Machnumber -- in an extremely violent and irreversible fashion called a shock wave. The presence of shock waves, alongwith the compressibility effects of high-velocity (see Reynolds number) fluids, is the central difference betweensupersonic and subsonic aerodynamics problems.

Hypersonic flowIn aerodynamics, hypersonic speeds are speeds that are highly supersonic. In the 1970s, the term generally came torefer to speeds of Mach 5 (5 times the speed of sound) and above. The hypersonic regime is a subset of thesupersonic regime. Hypersonic flow is characterized by high temperature flow behind a shock wave, viscousinteraction, and chemical dissociation of gas.

Associated terminology

Areas around an airfoil where Potential flow theory (A), boundary layer flow theory (B),or turbulent wake analysis (C) apply.

The incompressible and compressibleflow regimes produce many associatedphenomena, such as boundary layersand turbulence.

Boundary layers

The concept of a boundary layer isimportant in many aerodynamicproblems. The viscosity and fluidfriction in the air is approximated asbeing significant only in this thin layer.This principle makes aerodynamicsmuch more tractable mathematically.

Turbulence

In aerodynamics, turbulence is characterized by chaotic, stochastic property changes in the flow. This includes lowmomentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time.Flow that is not turbulent is called laminar flow.

Aerodynamics in other fieldsFurther information: Automotive aerodynamicsAerodynamics is important in a number of applications other than aerospace engineering. It is a significant factor in any type of vehicle design, including automobiles. It is important in the prediction of forces and moments in sailing. It is used in the design of large components such as hard drive heads. Structural engineers also use aerodynamics, and particularly aeroelasticity, to calculate wind loads in the design of large buildings and bridges. Urban aerodynamics seeks to help town planners and designers improve comfort in outdoor spaces, create urban

Aerodynamics 9

microclimates and reduce the effects of urban pollution. The field of environmental aerodynamics studies the waysatmospheric circulation and flight mechanics affect ecosystems. The aerodynamics of internal passages is importantin heating/ventilation, gas piping, and in automotive engines where detailed flow patterns strongly affect theperformance of the engine.

References[1] "...it shouldn't be imagined that aerodynamic lift (the force that makes airplanes fly) is a modern concept that was unknown to the ancients.

The earliest known use of wind power, of course, is the sail boat, and this technology had an important impact on the later development ofsail-type windmills. Ancient sailors understood lift and used it every day, even though they didn't have the physics to explain how or why itworked." Wind Power's Beginnings (1000 B.C. - 1300 A.D.) Illustrated History of Wind Power Development http:/ / telosnet. com/ wind/early. html

[2] Don Berliner (1997). " Aviation: Reaching for the Sky (http:/ / books. google. com/ books?id=Efr2Ll1OdqMC& pg=PA128& dq&hl=en#v=onepage& q=& f=false)". The Oliver Press, Inc. p.128. ISBN 1-881508-33-1

[3] Ovid; Gregory, H. (2001). The Metamorphoses. Signet Classics. ISBN 0451527933. OCLC 45393471.[4] Newton, I. (1726). Philosophiae Naturalis Principia Mathematica, Book II.[5] von Karman, Theodore (2004). Aerodynamics: Selected Topics in the Light of Their Historical Development. Dover Publications.

ISBN 0486434850. OCLC 53900531.[6] "Hydrodynamica" (http:/ / www. britannica. com/ EBchecked/ topic/ 658890/ Hydrodynamica#tab=active~checked,items~checked&

title=Hydrodynamica -- Britannica Online Encyclopedia). Britannica Online Encyclopedia. . Retrieved 2008-10-30.[7] "U.S Centennial of Flight Commission - Sir George Cayley." (http:/ / www. centennialofflight. gov/ essay/ Prehistory/ Cayley/ PH2. htm). .

Retrieved 2008-09-10. "Sir George Cayley, born in 1773, is sometimes called the Father of Aviation. A pioneer in his field, he was the first toidentify the four aerodynamic forces of flight - weight, lift, drag, and thrust and their relationship. He was also the first to build a successfulhuman-carrying glider. Cayley described many of the concepts and elements of the modern airplane and was the first to understand andexplain in engineering terms the concepts of lift and thrust."

[8] Cayley, George. "On Aerial Navigation" Part 1 (http:/ / www. aeronautics. nasa. gov/ fap/ OnAerialNavigationPt1. pdf), Part 2 (http:/ / www.aeronautics. nasa. gov/ fap/ OnAerialNavigationPt2. pdf), Part 3 (http:/ / www. aeronautics. nasa. gov/ fap/ OnAerialNavigationPt3. pdf)Nicholson's Journal of Natural Philosophy, 1809-1810. (Via NASA). Raw text (http:/ / invention. psychology. msstate. edu/ i/ Cayley/ Cayley.html). Retrieved: 30 May 2010.

[9] d'Alembert, J. (1752). Essai d'une nouvelle theorie de la resistance des fluides.[10] Kirchhoff, G. (1869). Zur Theorie freier Flussigkeitsstrahlen. Journal fur die reine und angewandte Mathematik (70), 289-298.[11] Rayleigh, Lord (1876). On the Resistance of Fluids. Philosophical Magazine (5)2, 430-441.[12] Navier, C. L. M. H. (1823). Memoire sur les lois du mouvement des fluides. Memoires de l'Academie des Sciences (6), 389-416.[13] Stokes, G. (1845). On the Theories of the Internal Friction of Fluids in Motion. Transaction of the Cambridge Philosophical Society (8),

287-305.[14] Reynolds, O. (1883). An Experimental Investigation of the Circumstances which Determine whether the Motion of Water Shall Be Direct or

Sinuous and of the Law of Resistance in Parallel Channels. Philosophical Transactions of the Royal Society of London A-174, 935-982.[15] Renard, C. (1889). Nouvelles experiences sur la resistance de l'air. L'Aeronaute (22) 73-81.[16] Chanute, Octave (1997). Progress in Flying Machines. Dover Publications. ISBN 0486299813. OCLC 37782926.[17] Lanchester, F. W. (1907). Aerodynamics.[18] Prandtl, L. (1919). Tragflügeltheorie. Göttinger Nachrichten, mathematischphysikalische Klasse, 451-477.[19] Ackeret, J. (1925). Luftkrafte auf Flugel, die mit der grosserer als Schallgeschwindigkeit bewegt werden. Zeitschrift fur Flugtechnik und

Motorluftschiffahrt (16), 72-74.[20] Anderson, John D. (2007). Fundamentals of Aerodynamics (4th ed.). McGraw-Hill. ISBN 0071254080. OCLC 60589123.[21] Anderson, J.D., Fundamentals of Aerodynamics, 4th Ed., McGraw-Hill, 2007.[22] Clancy, L.J.(1975), Aerodynamics, Section 3.3, Pitman Publishing Limited, London[23] White, F.M., Viscous Fluid Flow, McGraw-Hill, 1974.[24] Katz, Joseph (1991). Low-speed aerodynamics: From wing theory to panel methods. McGraw-Hill series in aeronautical and aerospace

engineering. New York: McGraw-Hill. ISBN 0070504466. OCLC 21593499.

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Further readingGeneral Aerodynamics

• Anderson, John D. (2007). Fundamentals of Aerodynamics (4th ed.). McGraw-Hill. ISBN 0071254080.OCLC 60589123.

• Bertin, J. J.; Smith, M. L. (2001). Aerodynamics for Engineers (4th ed.). Prentice Hall. ISBN 0130646334.OCLC 47297603.

• Smith, Hubert C. (1991). Illustrated Guide to Aerodynamics (2nd ed.). McGraw-Hill. ISBN 0830639012.OCLC 24319048.

• Craig, Gale (2003). Introduction to Aerodynamics. Regenerative Press. ISBN 0964680637. OCLC 53083897.Subsonic Aerodynamics

• Katz, Joseph; Plotkin, Allen (2001). Low-Speed Aerodynamics (2nd ed.). Cambridge University Press.ISBN 0521665523. OCLC 43970751 45992085.

Transonic Aerodynamics

• Moulden, Trevor H. (1990). Fundamentals of Transonic Flow. Krieger Publishing Company. ISBN 0894644416.OCLC 20594163.

• Cole, Julian D; Cook, L. Pamela (1986). Transonic Aerodynamics. North-Holland. ISBN 0444879587.OCLC 13094084.

Supersonic Aerodynamics

• Ferri, Antonio (2005). Elements of Aerodynamics of Supersonic Flows (Phoenix ed.). Dover Publications.ISBN 0486442802. OCLC 58043501.

• Shapiro, Ascher H. (1953). The Dynamics and Thermodynamics of Compressible Fluid Flow, Volume 1. RonaldPress. ISBN 978-0-471-06691-0. OCLC 11404735 174280323 174455871 45374029.

• Anderson, John D. (2004). Modern Compressible Flow. McGraw-Hill. ISBN 0071241361. OCLC 71626491.• Liepmann, H. W.; Roshko, A. (2002). Elements of Gasdynamics. Dover Publications. ISBN 0486419630.

OCLC 47838319.• von Mises, Richard (2004). Mathematical Theory of Compressible Fluid Flow. Dover Publications.

ISBN 0486439410. OCLC 56033096.• Hodge, B. K.; Koenig K. (1995). Compressible Fluid Dynamics with Personal Computer Applications. Prentice

Hall. ISBN 013308552X. OCLC 31662199. ISBN 0-13-308552-X.Hypersonic Aerodynamics

• Anderson, John D. (2006). Hypersonic and High Temperature Gas Dynamics (2nd ed.). AIAA.ISBN 1563477807. OCLC 68262944.

• Hayes, Wallace D.; Probstein, Ronald F. (2004). Hypersonic Inviscid Flow. Dover Publications.ISBN 0486432815. OCLC 53021584.

History of Aerodynamics

• Chanute, Octave (1997). Progress in Flying Machines. Dover Publications. ISBN 0486299813. OCLC 37782926.• von Karman, Theodore (2004). Aerodynamics: Selected Topics in the Light of Their Historical Development.

Dover Publications. ISBN 0486434850. OCLC 53900531.• Anderson, John D. (1997). A History of Aerodynamics: And Its Impact on Flying Machines. Cambridge

University Press. ISBN 0521454352. OCLC 228667184 231729782 35646587.Aerodynamics Related to Engineering

Ground Vehicles

• Katz, Joseph (1995). Race Car Aerodynamics: Designing for Speed. Bentley Publishers. ISBN 0837601428.OCLC 181644146 32856137.

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• Barnard, R. H. (2001). Road Vehicle Aerodynamic Design (2nd ed.). Mechaero Publishing. ISBN 0954073401.OCLC 47868546.

Fixed-Wing Aircraft

• Ashley, Holt; Landahl, Marten (1985). Aerodynamics of Wings and Bodies (2nd ed.). Dover Publications.ISBN 0486648990. OCLC 12021729.

• Abbott, Ira H.; von Doenhoff, A. E. (1959). Theory of Wing Sections: Including a Summary of Airfoil Data.Dover Publications. ISBN 0486605868. OCLC 171142119.

• Clancy, L.J. (1975). Aerodynamics. Pitman Publishing Limited. ISBN 0 273 01120 0. OCLC 16420565.Helicopters

• Leishman, J. Gordon (2006). Principles of Helicopter Aerodynamics (2nd ed.). Cambridge University Press.ISBN 0521858607. OCLC 224565656 61463625.

• Prouty, Raymond W. (2001). Helicopter Performance, Stability, and Control. Krieger Publishing Company Press.ISBN 1575242095. OCLC 212379050 77078136.

• Seddon, J.; Newman, Simon (2001). Basic Helicopter Aerodynamics: An Account of First Principles in the FluidMechanics and Flight Dynamics of the Single Rotor Helicopter. AIAA. ISBN 1563475103. OCLC 4762395060850095.

Missiles

• Nielson, Jack N. (1988). Missile Aerodynamics. AIAA. ISBN 0962062901. OCLC 17981448.Model Aircraft

• Simons, Martin (1999). Model Aircraft Aerodynamics (4th ed.). Trans-Atlantic Publications, Inc..ISBN 1854861905. OCLC 43634314 51047735.

Related Branches of Aerodynamics

Aerothermodynamics

• Hirschel, Ernst H. (2004). Basics of Aerothermodynamics. Springer. ISBN 3540221328. OCLC 22838329656755343 59203553.

• Bertin, John J. (1993). Hypersonic Aerothermodynamics. AIAA. ISBN 1563470365. OCLC 28422796.Aeroelasticity

• Bisplinghoff, Raymond L.; Ashley, Holt; Halfman, Robert L. (1996). Aeroelasticity. Dover Publications.ISBN 0486691896. OCLC 34284560.

• Fung, Y. C. (2002). An Introduction to the Theory of Aeroelasticity (Phoenix ed.). Dover Publications.ISBN 0486495051. OCLC 55087733.

Boundary Layers

• Young, A. D. (1989). Boundary Layers. AIAA. ISBN 0930403576. OCLC 19981526.• Rosenhead, L. (1988). Laminar Boundary Layers. Dover Publications. ISBN 0486656462. OCLC 17619090

21227855.Turbulence

• Tennekes, H.; Lumley, J. L. (1972). A First Course in Turbulence. The MIT Press. ISBN 0262200198.OCLC 281992.

• Pope, Stephen B. (2000). Turbulent Flows. Cambridge University Press. ISBN 0521598869. OCLC 17479028042296280 43540430 67711662.

Aerodynamics 12

External links• NASA Beginner's Guide to Aerodynamics (http:/ / www. grc. nasa. gov/ WWW/ K-12/ airplane/ bga. html)• Aerodynamics for Students (http:/ / www. aerodynamics4students. com)• Applied Aerodynamics: A Digital Textbook (http:/ / www. desktopaero. com/ appliedaero/ preface/ welcome.

html)• Aerodynamics for Pilots (http:/ / selair. selkirk. bc. ca/ Training/ Aerodynamics/ index. html)• Aerodynamics and Race Car Tuning (http:/ / www. 240edge. com/ performance/ tuning-aero. html)• Aerodynamic Related Projects (http:/ / www. aerodyndesign. com)• eFluids Bicycle Aerodynamics (http:/ / www. efluids. com/ efluids/ pages/ bicycle. htm)• Application of Aerodynamics in Formula One (F1) (http:/ / www. forumula1. net/ 2006/ f1/ features/

car-design-technology/ aerodynamics/ )• Aerodynamics in Car Racing (http:/ / www. nas. nasa. gov/ About/ Education/ Racecar/ )• Aerodynamics of Birds (http:/ / wings. avkids. com/ Book/ Animals/ intermediate/ birds-01. html)• Aerodynamics and dragonfly wings (http:/ / www. public. iastate. edu/ ~huhui/ paper/ 2007/ AIAA-2007-0483.

pdf)

Article Sources and Contributors 13

Article Sources and ContributorsAerodynamics  Source: http://en.wikipedia.org/w/index.php?oldid=458100375  Contributors: 124Nick, 21655, 2D, 89119, Aakashamistry, Abqwildcat, Acdx, Acroterion, Adsta01, AeroPsico,Al3209, Alansohn, Albedo, Ale jrb, Alexf, Alias Flood, Allagappan.gnu, Allahmuhammed, Anaraug, Andonic, Andy Dingley, AndyTheGrump, Anonymous Dissident, Anville, Anynobody,Ariadacapo, Arnero, Arpingstone, Art Carlson, Ashwin18, AtheWeatherman, Aude, AugPi, Avarame, BMF81, Bart133, Bartledan, Beetstra, BeteNoir, BilCat, Black Kite, Blaxthos, Blckavnger,Bleh999, Bluerasberry, BoKu, Bobo192, Bongwarrior, BoomerAB, Bowakowa, Bsadowski1, Burnside65, CAD6DEE2E8DAD95A, CWii, Cain6119, CambridgeBayWeather, Camw, Can't sleep,clown will eat me, Canyouhearmenow, Capricorn42, Carson56437, Ceoil, ChaosNil, Charles Matthews, Chris 73, Chrislk02, Citicat, Clarince63, Cmichael, Coffee and TV, Collins432,Cometstyles, Conversion script, Corpx, Crowsnest, D, DARTH SIDIOUS 2, DMurphy, Darth Panda, Davehi1, David R. Ingham, DerHexer, Dhaluza, Dinosaur puppy, Dolphin51, Dorftrottel,Douglass.auld, Doulos Christos, Drbreznjev, Durin, EMBaero, EdgeOfEpsilon, Edward321, Edwy, El C, Eleven even, Encyclopediarocketman, Epbr123, Eric-Wester, Ericd, Excirial,Fallthroughheat, FisherQueen, Flinkinshmorph, Fremsley, Friday, Funnybunny, Fæ, GRAHAMUK, Geoffrey Wickham, Giftlite, Gimmetrow, GirasoleDE, Gonzonoir, Graham87, GrahamN,Greatestrowerever, GreenEco, Gun Powder Ma, Gunter, GurraJG, Haemo, Hall Monitor, HamburgerRadio, Hashem sfarim, Headbomb, Hede2000, Hipertek, Hjmerkel, Hmrox, Hohum, Hotlorp,Hurricane111, Hydrogen Iodide, IdreamofJeanie, Infrogmation, Introductory adverb clause, Inwind, Iridescent, Ixfd64, J.delanoy, J8079s, JForget, Jagged 85, Jake Wartenberg, James086,JamesBWatson, Java7837, Jerzy, Jfiling, Jhsounds, Jmcc150, John, JohnI, Johnska7, Jpkotta, Jrockley, Julesd, Jusdafax, JustUser, Kazubon, Keilana, Kingpin13, KungFuMil, Kungfuadam, LKensington, LAX, LearnMore, LeaveSleaves, Leszek Jańczuk, Liftarn, Lights, Literacola, Lkent 009, Luk, Luna Santin, M0r4d, MER-C, Macduffman, MadScot, Magnus Manske, Mailer diablo,Mandarax, Maniadis, Marek69, Master son, Mathmo, Mattb112885, Matthew Desjardins, McSly, Mdh81235, Mechefan, Mentifisto, Michael Belisle, Michael Hardy, MichaelMaggs,Michaelas10, Mike1, Minimac's Clone, Mirwin, Mitch21236, Mlouns, Mmeijeri, Moink, Motorhead, Movcha, Mr swordfish, MrFish, Mrs.S.Reeves, Mxn, Mythealias, Ncmvocalist, NickNumber, Nickkid5, Nikai, Nimbus227, Nonforma, Nposs, Nsaa, Nuno Tavares, Oda Mari, Olivier, Onco p53, Onebravemonkey, Opelio, Orthografer, OverlordQ, Party, Penguinboy2, PerfectProposal, Peteypaws, Philip Trueman, Phydend, Piali, Pinkadelica, Pironman, Player00, Pmlineditor, Poeloq, Polly, Poony, PrestonH, PseudoSudo, Psycho Kirby, Pumeleon, Pvazteixeira,Pyrrhus16, Qst, Quantpole, QuantumEngineer, Quintote, Randywombat, Raven in Orbit, RayAYang, Raymondwinn, Rbeas, Remnar, RexNL, Rholton, Riana, Rigadoun, Rjwilmsi,Robomaeyhem, Roke, Rory096, RoyBoy, Rrburke, Ruleke, S, Salih, Salvo46, Saruman438, Sceptre, Scott14, Seangies, Semperf, Shirik, Skarebo, Slysplace, Smalljim, SmilesALot, Snoyes,Soliloquial, Solipsist, Someguy1221, Sonett72, Ssd, Ssd175, Stanley Ipkiss, Stardust8212, Steelpillow, Stizz, Svdmolen, T-9000, TBloemink, TGCP, THF, Tawker, Thatperson, The RamblingMan, The Thing That Should Not Be, The cattr, The sock that should not be, TheKMan, TheNeutroniumAlchemist, Tide rolls, Titoxd, Tobby72, Tomasz Prochownik, Tommy2010, Trakesht,Treecko1230, Treisijs, Tresiden, Trevor MacInnis, Trusilver, Uhai, Updogdude44, Useight, User A1, Utcursch, Vanka5, Venny85, VernoWhitney, Versus22, WPjcm, Walton One, Waltpohl,Warofdreams, Watterson6969, Weatherman1126, Why Not A Duck, Wikitanvir, Will Beback, William Avery, Wimt, Wolfkeeper, WoodyWerm, Xmnemonic, Yamamoto Ichiro, Yekrats,Yomattyyo, Youngoat, ZX81, ZeroOne, Zocky, Zzuuzz, 1009 anonymous edits

Image Sources, Licenses and ContributorsImage:Airplane vortex edit.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Airplane_vortex_edit.jpg  License: Public Domain  Contributors: NASA Langley Research Center(NASA-LaRC), Edited by Fir0002Image:Design for a Flying Machine.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Design_for_a_Flying_Machine.jpg  License: Public Domain  Contributors: AnRo0002,Czarnoglowa, Falcorian, Five-toed-sloth, G.dallorto, Mattes, Mdd, OldakQuill, Rilegator, 丁Image:Governableparachute.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Governableparachute.jpg  License: Public Domain  Contributors: Dbenbenn, Kilom691, MddImage:WB Wind Tunnel.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:WB_Wind_Tunnel.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Originaluploader was Axda0002 at en.wikipediaImage:X-43A (Hyper - X) Mach 7 computational fluid dynamic (CFD).jpg  Source:http://en.wikipedia.org/w/index.php?title=File:X-43A_(Hyper_-_X)_Mach_7_computational_fluid_dynamic_(CFD).jpg  License: Public Domain  Contributors: NASAImage:Conservation for aerodynamics.PNG  Source: http://en.wikipedia.org/w/index.php?title=File:Conservation_for_aerodynamics.PNG  License: Public Domain  Contributors: EMBaero(talk)File:Types of flow analysis in fluid mechanics.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Types_of_flow_analysis_in_fluid_mechanics.svg  License: Creative CommonsAttribution-Sharealike 3.0  Contributors: User:Ariadacapo

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