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Aerodynamics for
Engineering Students
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Aerodynamics for
Engineering Students
Sixth Edition
E.L. Houghton
P.W. Carpenter
Steven H. Collicott
Daniel T. Valentine
AMSTERDAM•BOSTON•HEIDELBERG•LONDON
NEWYORK•OXFORD•PARIS•SANDIEGO
SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO
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Preface
This volume is intended for engineering students in introductory aerodynamics
courses and as a reference useful for reviewing foundational topics for graduate
courses.
Thesequenceofsubjectdevelopmentinthiseditionbeginswithdefinitionsand
concepts and then moves on to incompressible flow, low speed airfoil and wing
theories,compressibleflow,highspeedwingtheories,viscousflow,boundarylayers,
transitionandturbulence,wingdesign,andconcludeswithpropellersandpropulsion.
Reinforcingorteachingfirsttheunits,dimensions,andpropertiesofthephysical
quantitiesusedinaerodynamicsaddressesconceptsthatareperhapsboththesimplest
and the most critical. Common aeronautical definitions are covered before lessons
ontheaerodynamicforcesinvolvedandhowtheforcesdriveourdefinitionsofair-
foilcharacteristics.Thefundamentalfluiddynamicsrequiredforthedevelopmentof
aerodynamicstudiesandtheanalysisofflowswithinandaroundsolidboundariesfor
airatsubsonicspeedsisexploredindepthinthenexttwochapters.Classicalairfoil
andwingtheoriesfortheestimationofaerodynamiccharacteristicsintheseregimes
arethendeveloped.
AttentionisthenturnedtotheaerodynamicsofhighspeedairflowsinChapters6
and7.Thelawsgoverningthebehaviorofthephysicalpropertiesofairareapplied
to the transonic and supersonic flow speeds and the aerodynamics of the abrupt
changes in the flow characteristics at these speeds, shock waves, are explained.
Then compressible flow theories are applied to explain the significant effects on
wings in transonic and supersonic flight and to develop appropriate aerodynamic
characteristics.Viscosityisakeyphysicalquantityofairanditssignificanceinaero-
dynamicsituationsisnextconsideredindepth.Thepowerfulconceptoftheboundary
layer and the development of properties of various flows when adjacent to solid
boundaries create a body of reliable methods for estimating the fluid forces due to
viscosity. In aerodynamics, these forces are notably skin friction and profile drag.
Chapters on wing design and flow control, and propellers and propulsion, respec-
tively,bringtogetherdisparateaspectsofthepreviouschaptersasappropriate.This
permitsdiscussionofsomepracticalandindividualapplicationsofaerodynamics.
Obviously aerodynamic design today relies extensively on computational meth-
ods.Thisisreflectedinpartinthisvolumebytheintroduction,whereappropriate,of
descriptionsanddiscussionsofrelevantcomputationaltechniques.However,thistext
is aimed at providing the fundamental fluid dynamics or aerodynamics background
necessaryforstudentstomovesuccessfullyintoadedicatedcourseoncomputation
methodsorexperimentalmethods.Assuch,experienceincomputationaltechniques
orexperimentaltechniquesarenotrequiredforacompleteunderstandingoftheaero-
dynamicsinthisbook.Theauthorsurgestudentsonwardtosuchadvancedcourses
andexcitingcareersinaerodynamics.
xv
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xvi Preface
ADDITIONAL RESOURCES
A set of .m files for the MATLAB routines in the book are available by visiting
the book’s companion site, www.elsevierdirect.com and searching on ‘houghton.’
Instructors using the text for a course may access the solutions manual and image
bank by visiting www.textbooks.elsevier.com and following the online registration
instructions.
ACKNOWLEDGEMENTS
The authors thank the following faculty, who provided feedback on this project
throughsurveyresponses,reviewofproposal,and/orreviewofchapters:
AlinaAlexeenko PurdueUniversity
S.FirasatAli TuskegeeUniversity
DavidBridges MississippiStateUniversity
RussellM.Cummings CaliforniaPolytechnicStateUniversity
PaulDawson BoiseStateUniversity
SimonW.Evans,Ph.D WorcesterPolytechnicInstitute
RichardS.Figliola ClemsonUniversity
TimothyW.Fox CaliforniaStateUniversityNorthridge
AshokGopalarathnam NorthCarolinaStateUniversity
Dr.MarkW.Johnson UniversityofLiverpool
BrianLandrum,Ph.D UniversityofAlabamainHuntsville
GaryL.Solbrekken UniversityofMissouri
MohammadE.Taslim NortheasternUniversity
ValanaWells ArizonaStateUniversity
ProfessorsCollicottandValentinearegratefulfortheopportunitytocontinuethe
work of Professors Houghton and Carpenter and thank Joe Hayton, Publisher, for
theinvitationtodoso.Inaddition,theprofessionaleffortsofMikeJoyce,Editorial
ProgramManager,HeatherTighe,ProductionManager,andKristenDavis,Designer
areinstrumentalinthecreationofthissixthedition.
Theproductsofone’seffortsareofcoursetheculminationofallofone’sexperi-
enceswithothers.Foremostamongstthepeoplewhoaretobethankedmostwarmly
forsupportareourfamilies.CollicottandValentinethankJennifer,Sarah,andRachel
andMary,Clara,andZachT.,respectively,fortheirloveandforthecountlessjoys
that they bring to us. Our Professors and students over the decades are major con-
tributorstoouraerodynamicsknowledgeandwearethankfulforthem.Theauthors
sharetheirdeepgratitudeforGod’sboundlessloveandgraceforall.
CONTENTS
Chapter 1 Basic Concepts and Definitions
Chapter 2 Fundamental Equations of Fluid Mechanics
Chapter 3 Potential Flow
Chapter 4 Two-Dimensional Wing Theory
Chapter 5 Wing theory
Chapter 6 Compressible Flow
Chapter 7 Airfoils and Wings in Compressible Flow
Chapter 8 Viscous Flow and Boundary Layers
Chapter 9 Flow Control and Wing Design
Chapter 10 Propulsion Devices
Appendix A Symbols and Notation
Appendix B Air Properties vs. Altitude
Appendix C A Solution of Integrals of the Type of Glauert's Integral
Appendix D Conversion of Imperial Units to Système international d’unités (SI Units)
Bibliography
Index
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CHAPTER
1
Basic Concepts and
Definitions
“Toworkintelligently”(OrvilleandWilburWright)
“oneneedstoknowtheeffectsofvariations
incorporatedinthesurfaces....Thepressuresonsquares
aredifferentfromthoseonrectangles,circles,triangles,or
ellipses....
Theshapeoftheedgealsomakesadifference.”
fromTheStructureofthePlane–MurielRukeyser
LEARNING OBJECTIVES
• Reviewthefundamentalprinciplesoffluidmechanicsandthermodynamics
requiredtoinvestigatetheaerodynamicsofairfoils,wings,andairplanes.
• Recalltheconceptsofunitsanddimensionandhowtheyareappliedtosolving
andunderstandingengineeringproblems.
• Learnaboutthegeometricfeaturesofairfoils,wings,andairplanesandhowthe
namesforthesefeaturesareusedinaerodynamicscommunications.
• Exploretheaerodynamicforcesandmomentsthatactonairfoils,wings,and
airplanesandlearnhowwedescribetheseloadsquantitativelyindimensional
formandascoefficients.
1.1 INTRODUCTION
The study of aerodynamics requires a number of basic definitions, including an
unambiguous nomenclature and an understanding of the relevant physical proper-
ties, related mechanics, and appropriate mathematics. Of course, these notions are
common to other disciplines, and it is the purpose of this chapter to identify and
explainthosethatarebasicandpertinenttoaerodynamicsandthataretobeusedin
theremainderofthevolume.
AerodynamicsforEngineeringStudents.DOI:10.1016/B978-0-08-096632-8.00001-1 1
(cid:13)c 2013ElsevierLtd.Allrightsreserved.
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2 CHAPTER 1 Basic Concepts and Definitions
1.1.1 Basic Concepts
Thistextisanintroductoryinvestigationofaerodynamicsforengineeringstudents.1
Hence, we are interested in theory to the extent that it can be practically applied
to solve engineering problems related to the design and analysis of aerodynamic
objects.
The design of vehicles such as airplanes has advanced to the level where we
require the wealth of experience gained in the investigation of flight over the past
100 years. We plan to investigate the clever approximations made by the few who
learned how to apply mathematical ideas that led to productive methods and useful
formulas to predict the dynamical behavior of “aerodynamic” shapes. We need to
learn the strengths and, more important, the limitations of the methodologies and
discoveriesthatcamebeforeus.
Althoughwehaveextensivearchivesofrecordedexperienceinaeronautics,there
arestillmanyopportunitiesforadvancement.Forexample,significantadvancements
can be achieved in the state of the art in design analysis. As we develop ideas
related to the physics of flight and the engineering of flight vehicles, we will learn
thestrengthsandlimitationsofexistingproceduresandexistingcomputationaltools
(commerciallyavailableorotherwise).Wewilllearnhowairfoilsandwingsperform
andhowweapproachthedesignsoftheseobjectsbyanalyticalprocedures.
The fluid of primary interest is air, which is a gas at standard atmospheric con-
ditions. We assume that air’s dynamics can be effectively modeled in terms of the
continuumfluiddynamicsofanincompressibleorsimple-compressiblefluid.Airis
a fluid whose local thermodynamic state we assume is described either by its mass
densityρ=constant,orbytheidealgaslaw.Inotherwords,weassumeairbehaves
aseitheranincompressibleorasimple-compressiblemedium,respectively.Thecon-
cepts of a continuum, an incompressible substance, and a simple-compressible gas
willbeelaboratedoninChapter2.
The equation of state, known as the ideal gas law, relates two thermodynamic
propertiestootherpropertiesand,inparticular,thepressure.Itis
p=ρRT
where p is the thermodynamic pressure, ρ is mass density, T is absolute (thermo-
dynamic)temperature,andR=287J/(kgK)orR=1716ft-lb(slug◦R)−1.Pressure
andtemperaturearerelativelyeasytomeasure.Forexample,“standard”barometric
pressureatsealevelisp=101,325Pascals,whereaPascal(Pa)is1N/m2.InImpe-
rialunitsthisis14.675psi,wherepsiislb/in2and1psiisequalto6895Pa(notethat
1It has long been common in engineering schools for an elementary, macroscopic thermodynamics
coursetobecompletedpriortoacompressible-flowcourse.Theportionsofthistextthatdiscusscom-
pressible flow assume that such a course precedes this one, and thus the discussions assume some
elementaryexperiencewithconceptssuchasinternalenergyandenthalpy.
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1.1 Introduction 3
14.675psiisequalto2113.2lb/ft2).Thestandardtemperatureis288.15K(or15◦C,
whereabsolutezeroequalto−273.15◦Cisused).InImperialunitsthisis519◦R(or
59◦F,whereabsolutezeroequalto−459.67◦Fisused).Substitutingintotheidealgas
law, we get for the standard density ρ=1.225 kg/m3 in SI units (and ρ=0.00237
slugs/ft3 inImperialunits).Thisisthedensityofairatsealevelgiveninthetableof
dataforatmosphericair;thetableforstandardatmosphericconditionsisprovidedin
AppendixB.
Thethermodynamicpropertiesofpressure,temperature,anddensityareassumed
tobethepropertiesofamass-pointparticleofairatalocationx=(x,y,z)inspace
at a particular instant in time, t. We assume the measurement volume to be suf-
ficiently small to be considered a mathematical point. We also assume that it is
sufficientlylargesothatthesepropertieshavemeaningfromtheperspectiveofequi-
libriumthermodynamics.Andwefurtherassumethatthepropertiesarethesameas
thosedescribedinacourseonclassicalequilibriumthermodynamics.Therefore,we
assume that local thermodynamic equilibrium prevails within the mass-point parti-
cleatxandtregardlessofhowfastthethermodynamicstatechangesastheparticle
movesfromonelocationinspacetoanother.Thisisanacceptableassumptionforour
macroscopicpurposesbecausemolecularprocessesaretypicallyfasterthanchanges
intheflowfieldweareinterestedinfromamacroscopicpointofview.Inaddition,
weinvokethecontinuumhypothesis,whichstatesthatwecandefineallflowproper-
tiesascontinuousfunctionsofpositionandtimeandthatthesefunctionsaresmooth,
thatis,theirderivativesarecontinuous.Thisallowsustoapplydifferentialintegral
calculustosolvepartialdifferentialequationsthatsuccessfullymodeltheflowfields
ofinterestinthiscourse.Inotherwords,predictionsbasedonthetheoryreportedin
thistexthavebeenexperimentallyverified.
To develop the theory, the fundamental principles of classical mechanics are
assumed.Theyare
• Conservationofmass
• Newton’ssecondlawofmotion
• Firstlawofthermodynamics
• Secondlawofthermodynamics
Theprincipleofconservationofmassdefinesamass-pointparticle,whichisafixed-
massparticle.Thustheprinciplealsodefinesmassdensityρ,whichismassperunit
volume.Ifamass-pointparticleconservesmass,aswehavepostulated,thendensity
changescanonlyoccurifthevolumeoftheparticlechanges,becausethedimension
ofmassdensityisM/L3,whereMismassandLislength.TheSIunitofdensityis
thuskg/m3.
Newton’ssecondlawdefinestheconceptofforceintermsofacceleration(“F=
ma”). The acceleration of a mass-point particle is the change in its velocity with
respecttoachangeintime.Letthevelocityvectoru=(u,v,w);thisisthevelocityof
amass-pointparticleatapointinspace,x=(x,y,z),ataparticularinstantintimet.
