Introduction to Aeronautics - A Design Perspective

476 Pages·2004·12.9 MB·English

by  Brandt

Introduction to Aeronautics:
A Design Perspective
Second Edition
StevenA.Brandt
U.S.AirForceAcademy
ColoradoSprings,Colorado
RandallJ.Stiles
ColoradoCollege
ColoradoSprings,Colorado
JohnJ.Bertin
U.S.AirForceAcademy
ColoradoSprings,Colorado
RayWhitford
RoyalMilitaryCollegeofScience
andtheCranfieldInstituteofTechnology
UnitedKingdom
EDUCATIONSERIES
JosephA.Schetz
SeriesEditor-in-Chief
VirginiaPolytechnicInstituteandStateUniversity
Blacksburg,Virginia
Publishedby
AmericanInstituteofAeronauticsandAstronautics,Inc.
1801AlexanderBellDrive,Reston,VA20191-4344
AmericanInstituteofAeronauticsandAstronautics,Inc.,Reston,Virginia
1 2 3 4 5
LibraryofCongressCataloging-in-PublicationData
Introductiontoaeronautics:adesignperspective/StevenA.Brandt...[etal.].–2nded.
p. cm. – (Educationseries)
Includesbibliographicalreferencesandindex.
ISBN1-56347-701-7(alk.paper)
1.Airplanes–Designandconstruction. 2.Aeronautics. I.Brandt,StevenA.,1953- II.Title.
III.Series:AIAAeducationseries.
TL671.2.I64 2004
629.134(cid:1)1–dc22 2004005844
Copyright (cid:2)c 2004 by the American Institute of Aeronautics and Astronautics, Inc. All
rightsreserved.ThisworkwascreatedintheperformanceofaCooperativeResearchand
DevelopmentAgreementwiththeDepartmentoftheAirForce.TheGovernmentofthe
UnitedStateshascertainrightstousethiswork.PrintedintheUnitedStatesofAmerica.
Nopartofthispublicationmaybereproduced,distributed,ortransmitted,inanyformorby
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notresponsibleforanyinjuryordamageresultingfromuseorreliance,nordoesAIAA
warrantthatuseorreliancewillbefreefromprivatelyownedrights.
Nomenclature
A =streamtubecross-sectionalarea
=aspectratio,b2/S √
a =speedofsoundinair, λRT;linearacceleration,dV/dt
b =wingspan
C =finitewingorwholeaircraft(three-dimensional)dragcoefficient, D/qS
D
C =finitewingorwholeaircraft(three-dimensional)induced(duetolift)
Di
dragcoefficient
C =wholeaircraft(three-dimensional)zero-liftdragcoefficient
CD0 =equivalentskin-frictioncoefficient
Cfe =finitewingorwholeaircraft(three-dimensional)liftcoefficient, L/qS
L
C =finitewingorwholeaircraftpitchingmomentcoefficient, M/qSc
M
c =wingorairfoilchord;specificfuelconsumptionusedfor
reciprocatingengines
c¯ =wingmeanaerodynamicchord
c =airfoil(two-dimensional)dragcoefficient,d/qS
d
c =airfoil(two-dimensional)liftcoefficient,l/qS
l
c =airfoilpitchingmomentcoefficient,m/qSc
m
c =thrust-specificfuelconsumptionusedprimarilyforturbineengines
t
c =wingrootchord
root
c =wingtipchord
tip
D =wingoraircrafttotaldrag
D =wingoraircraftinduceddragordragduetolift
i
D =wingoraircraftzero-liftdrag
0
d =airfoildrag
E =wavedragefficiencyparameter,comparesactualtoidealwavedrag
WD
e =wingspanefficiencyfactor
e =aircraftOswald’sefficiencyfactor
O
F =force
f =airspeedcompressibilitycorrectionfactor
h =altitude
i =incidenceangle
k,k =induceddragtermcoefficient,1/(πe )
1
k =camberinfluencecoefficientininduceddragterm
2
L =finitewingorwholeaircraft(three-dimensional)lift
l =airfoillift;overalllength,especiallyofthefuselageortheentireaircraft
L =wholeaircraftrollingmoment
M =wingorwholeaircraftpitchingmoment;Machnumber,V/a
m =airfoilpitchingmoment
N =normalforce,yawingmoment
xix
n =loadfactor
P =staticpressure;power,TV
P =poweravailable
avail
P =powerrequired
req
P =specificexcesspower,V(T −D)/W
S
q =dynamicpressure, 1ρV2
2
R =range;idealgaslawproportionalityconstant(P =ρRT)
Re =Reynoldsnumber,ρVx/µ
r =turnradius
S =referenceplanformarea,usuallytheareaofthewingplanform
S =canardplanformarea
c
S =horizontaltailplanformarea
t
s =distancealongapath
T =thrust;temperature
T =thrustavailable
avail
T =thrustrequired, D
req
t =time
u =x-axiscomponentofvelocity
V =velocity(magnitude)
V =horizontaltailvolumeratio,Sl /Sc
H t t
V∞ =freestreamvelocityvector
v = y-axiscomponentofvelocity
w =z-axiscomponentofvelocity
X =forcecomponentalongthex axis
x =axisofcoordinatesystem,whichisfrequentlyalignedwiththeaircraft’s
longitudinalaxis
Y =forcecomponentalongthe y axis
y =axisofcoordinatesystem,whichisfrequentlyalignedpositiveoutthe
aircraft’srightwing
Z =forcecomponentalongthezaxis
z =axisofcoordinatesystem,whichisfrequentlyalignedpositivedown
Greek
α =angleofattack;thrustlapse,T/T
SL
αa =absoluteangleofattack,α−αL=0
αl=0 =airfoilzero-liftangleofattack
αL=0 =wingzero-liftangleofattack
β =sideslipangle;weightfraction,W/W
TO
(cid:6) =dihedralangle
γ =flight-pathangle;ratioofspecificheats,1.4forair
δ =controlsurfacedeflectionangle
ε =downwashangle
η =mechanicalefficiency
(cid:11) =wingsweepangle
λ =wingtaperratio
µ =airviscosity;rollingfrictioncoefficient
ρ =airdensity
τ =shearstress
φ =bankangle
ω =angularvelocity,rateofrotation
Math
∞ =largestpossiblenumber,usedasasubscripttodenoteagreat
distanceaway
(cid:5) =parallelto
⊥ =perpendicularto
Preface
ThistextbookandtheaccompanyingAeroDYNAMICsoftwarewerecreatedfor
useasresourcesforteachingbasicdesignmethodsinconjunctionwithanintro-
ductory course in aeronautics. That these two topics can coexist and reinforce
eachotherinanintroductory-levelcoursehasbeenprovenby11yearsofexpe-
rience with a course taught to the entire student body of the United States Air
ForceAcademy(USAFA).Thebookwaswrittenforuseinteachingstudentsin
theirfirstthreeyearsofpost-secondaryeducation,sounderstandingofthederiva-
tionsandanalysismethodsisfacilitatedbypriorknowledgeofcalculus,classical
physics,andengineeringmechanics.However,thematerialispresentedatalevel
thatshouldbeunderstandablebyadvancedhighschoolstudents.
The text begins with an entire chapter devoted to the motivation, methods,
andhistoryofengineeringdesigningeneralandaircraftdesigninparticular.The
designmethodsdescribedarecommonlyusedthroughoutindustry,butmostofthe
examples given are specific to aircraft design. The reasoning behind placing the
designchapterfirstisidenticaltothereasoningthatmotivatesteachingdesignin
conjuction with basic aeronautical engineering concepts. Typically, engineering
students spend their first two or three years learning basic math, science, and
engineeringanalysismethodswithouthavingmuchopportunitytoseewhereall
thisknowledgefitsintheworkthatengineersdo.Mostengineeringstudentshave
chosen engineering as their major because they want to learn how to design.
ExperienceatUSAFAhasshownthatlearningaboutdesignfirstmotivatesstudents
tolearnthetheoryandanalysismethodsthattheyneedinordertodesign.Chapter1
does not describe any analysis methods in detail, but simply describes where
analysisfitsinthedesignprocess.Subsequentchaptersintroduceanalysismethods
anddescribewhytheyarenecessarytoolsoftheaircraftdesigner.Inotherwords,
Chapter1establishesaframeworkoroutlineoftheaircraftdesignprocess,then
Chapters2–8fillintheanalysismethodsneededineachdesignstep.
Chapter 2 introduces analysis methods, which apply to static fluids, and de-
scribeshowthesemethodscanbeusedintheconstructionofpressuremeasurement
devicesandamodeloftheatmospherethatengineersuseasastandardreference.
Chapter3teachesanalysisofmovingfluidsandshowshowthesemethodsareused
topredicttheliftanddragexertedbyfluidsonbodiesmovingthroughthem.Chap-
ter 4 expands the lift and drag prediction methods to include three-dimensional
effects of finite wings and whole aircraft, and gives an example of how these
methodsareusedtopredicttheaerodynamiccharacteristicsofamodernjetfighter
aircraft. In Chapter 5 the reader learns how knowledge of an aircraft’s aerody-
namics, engine thrust capabilities, and the laws of physics are used to predict
its performance capabilities, or in other words the ability of the aircraft to meet
a customer’s needs. Chapter 5 also discusses constraint analysis, a method used
tochooseaircraftcharacteristicssuchthattheaircraftcanmeetcustomerneeds.
xv
Chapter 6 introduces stability and control concepts, and further describes static
longitudinalstabilityanalysisasasimpleexampleofhowthestaticanddynamic
stability of an aircraft in all six degrees of freedom is analyzed. Chapter 7 dis-
cusses the fundamentals of structural design and analysis and presents a simple
structuralsizingexample.Chapter8dealswithsizing,determininghowlargean
aircraftneedstobeinordertoflyaparticularmissionwithaspecifiedpayload.
Thisdiscussionincludesanintroductiontomissionanalysismethodsthatareused
todeterminetheamountoffuelrequiredbyanaircrafttoflyamission.Chapter8
alsodiscussesasimplemethodforpredictingaircraftpurchaseandoperatingcosts.
Oncestudentshavemasteredthebasicaeronauticalengineeringmethodspre-
sented in Chapters 1–8, they are adequately equipped to tackle simple aircraft
designproblems.Chapter9explainshowallofthemethodsareusedinthecon-
ceptualaircraftdesignprocess.TheAeroDYNAMICsoftwarethatcomplements
this text provides user-friendly aircraft geometry modeling and design analysis
tools that greatly facilitate the working of such problems. Chapter 10 is offered
tosupportstudents’firstdesignexperiencesbypresentingcasestudiesofthede-
velopmentofthreewell-knownaircraftdesignsandadiscussionoffutureaircraft
designpossibilities.Thesediscussionsfocusontheimpactoftechnology,politics,
andtheeconomyoneachaircraft’sdesignprocess.
The material in this textbook and the AeroDYNAMIC software is sufficient
to support a university-level course of three to six semester hours. At USAFA,
Chapters1–6areusedinathree-semester-hourcoursetaughttotheentirestudent
body. The material in Chapters 7–10 is taught at USAFA in later courses taken
onlybyaeronauticalengineeringmajors.
StevenA.Brandt
May2004
Table of
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Chapter1. DesignThinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 DesignMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 DesignExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 DesignandAeronautics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 BriefHistoryofAircraftDesign . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.7 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.8 MoreDetails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter2. OperatingEnvironment . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.1 DesignMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2 CharacteristicsoftheAtmosphere . . . . . . . . . . . . . . . . . . . . . . . 42
2.3 PressureMeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4 StandardAtmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.5 CommonUsesoftheStandardAtmosphere . . . . . . . . . . . . . . . . . 51
2.6 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.7 MoreDetails—MolecularCollisionsandAerodynamics . . . . . . . . 54
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Chapter3. AerodynamicsandAirfoils . . . . . . . . . . . . . . . . . . . . . . . 61
3.1 DesignMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 BasicAerodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 BasicAerodynamicsApplications . . . . . . . . . . . . . . . . . . . . . . . 66
3.4 ViscousFlow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.5 AirfoilCharacteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.7 MoreDetails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
xi
Chapter4. WingsandAirplanes. . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.1 DesignMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 Wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3 High-LiftDevices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.4 WholeAircraftLift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.5 WholeAircraftDragandDragPolar . . . . . . . . . . . . . . . . . . . . . 128
4.6 Mach-NumberEffects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.7 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.8 MoreDetails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.9 WholeAircraftAnalysisExample . . . . . . . . . . . . . . . . . . . . . . 162
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Chapter5. Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.1 DesignMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.2 EquationsofMotion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.3 Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.4 DragCurves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.5 Lift-to-DragRatio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.6 PowerCurves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
5.7 CurveShifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.8 Glides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.9 Climbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.10 RangeandEndurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.11 TakeoffandLanding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
5.12 Turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
5.13 V–nDiagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
5.14 EnergyHeightandSpecificExcessPower . . . . . . . . . . . . . . . . . 233
5.15 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
5.16 MoreDetails—ManeuverabilityDiagramsand
ConstraintAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
5.17 PerformanceAnalysisExample . . . . . . . . . . . . . . . . . . . . . . . . 253
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
Chapter6. StabilityandControl . . . . . . . . . . . . . . . . . . . . . . . . . . 267
6.1 DesignMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
6.2 Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
6.3 LongitudinalControlAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . 275
6.4 LongitudinalStability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
6.5 DynamicLongitudinalStability . . . . . . . . . . . . . . . . . . . . . . . . 285
6.6 Lateral-DirectionalStability . . . . . . . . . . . . . . . . . . . . . . . . . . 287
6.7 DynamicLateral-DirectionalStability . . . . . . . . . . . . . . . . . . . . 293
6.8 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
6.9 MoreDetails—CalculatingStabilityParameters . . . . . . . . . . . . . 300
6.10 StabilityandControlAnalysisExample:F-16AandF-16C . . . . . 305
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Chapter7. Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
7.1 DesignMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
7.2 SolidMechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
7.3 TypesofStress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
7.4 Loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
7.5 StructuralLayout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
7.6 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
7.7 ComponentSizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
7.8 StructuralSizingExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
7.9 WeightEstimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
7.10 FiniteElementAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
7.11 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
Chapter8. Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
8.1 DesignMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
8.2 InternalLayout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
8.3 StructuresandWeight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
8.4 GeometryConstraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
8.5 MissionAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
8.6 SizingEquation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
8.7 WeightFractionMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
8.8 WeightandBalance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
8.9 MissionAnalysisandSizingExample. . . . . . . . . . . . . . . . . . . . 367
8.10 AeroDYNAMIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
8.11 Cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
8.12 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
Chapter9. PuttingItAllTogether:ConceptualAircraftDesign . . . . 379
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
9.2 Overviewofthe12Activities. . . . . . . . . . . . . . . . . . . . . . . . . . 380
9.3 CustomerFocus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
9.4 DesignSynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
9.5 GeometryModelingandEngineeringDrawing . . . . . . . . . . . . . . 383
9.6 AerodynamicAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
9.7 PropulsionAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
9.8 ConstraintAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
9.9 MissionAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
9.10 WeightAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
9.11 Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
9.12 CostAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
9.13 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
9.14 PerformanceReporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
9.15 PuttingItAllTogether . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395