Flight Dynamics Principles, Second Edition: A Linear Systems Approach to Aircraft Stability and Control

491 Pages·2007·3.4 MB·English

by  Michael V. Cook

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Flight Dynamics Principles
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Flight Dynamics Principles
M.V. Cook
BSc, MSc, CEng, FRAeS, CMath, FIMA
Senior Lecturer in the School of
Engineering Cranfield University
AMSTERDAM•BOSTON•HEIDELBERG•LONDON•NEWYORK•OXFORD
PARIS•SANDIEGO•SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO
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Secondedition2007
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Contents
Prefacetothefirstedition ix
Prefacetothesecondedition xi
Acknowledgements xiii
Nomenclature xv
1. Introduction 1
1.1 Overview 1
1.2 Flyingandhandlingqualities 3
1.3 Generalconsiderations 4
1.4 Aircraftequationsofmotion 7
1.5 Aerodynamics 7
1.6 Computers 8
1.7 Summary 10
References 11
2. Systemsofaxesandnotation 12
2.1 Earthaxes 12
2.2 Aircraftbodyfixedaxes 13
2.3 Euleranglesandaircraftattitude 18
2.4 Axestransformations 18
2.5 Aircraftreferencegeometry 24
2.6 Controlsnotation 27
2.7 Aerodynamicreferencecentres 28
References 30
Problems 30
3. Staticequilibriumandtrim 32
3.1 Trimequilibrium 32
3.2 Thepitchingmomentequation 40
3.3 Longitudinalstaticstability 44
3.4 Lateralstaticstability 53
3.5 Directionalstaticstability 54
3.6 Calculationofaircrafttrimcondition 57
References 64
Problems 64
4. Theequationsofmotion 66
4.1Theequationsofmotionofarigidsymmetricaircraft 66
4.2Thelinearisedequationsofmotion 73
v
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vi Contents
4.3Thedecoupledequationsofmotion 79
4.4Alternativeformsoftheequationsofmotion 82
References 95
Problems 96
5. Thesolutionoftheequationsofmotion 98
5.1 Methodsofsolution 98
5.2 Cramer’srule 99
5.3 Aircraftresponsetransferfunctions 101
5.4 Responsetocontrols 108
5.5 Accelerationresponsetransferfunctions 112
5.6 Thestatespacemethod 114
5.7 Statespacemodelaugmentation 128
References 134
Problems 134
6. Longitudinaldynamics 138
6.1 Responsetocontrols 138
6.2 Thedynamicstabilitymodes 144
6.3 Reducedordermodels 147
6.4 Frequencyresponse 158
6.5 Flyingandhandlingqualities 165
6.6 Modeexcitation 167
References 170
Problems 171
7. Lateral–directionaldynamics 174
7.1 Responsetocontrols 174
7.2 Thedynamicstabilitymodes 183
7.3 Reducedordermodels 188
7.4 Frequencyresponse 195
7.5 Flyingandhandlingqualities 200
7.6 Modeexcitation 202
References 206
Problems 206
8. Manoeuvrability 210
8.1 Introduction 210
8.2 Thesteadypull-upmanoeuvre 212
8.3 Thepitchingmomentequation 214
8.4 Longitudinalmanoeuvrestability 216
8.5 Aircraftdynamicsandmanoeuvrability 222
References 223
9. Stability 224
9.1 Introduction 224
9.2 Thecharacteristicequation 227
9.3 TheRouth–Hurwitzstabilitycriterion 227
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Contents vii
9.4 Thestabilityquartic 231
9.5 Graphicalinterpretationofstability 234
References 238
Problems 238
10. Flyingandhandlingqualities 240
10.1 Introduction 240
10.2 Shorttermdynamicmodels 241
10.3 Flyingqualitiesrequirements 249
10.4 Aircraftrole 251
10.5 Pilotopinionrating 255
10.6 Longitudinalflyingqualitiesrequirements 256
10.7 Controlanticipationparameter 260
10.8 Lateral–directionalflyingqualitiesrequirements 263
10.9 Flyingqualitiesrequirementsonthes-plane 266
References 271
Problems 272
11. Stabilityaugmentation 274
11.1 Introduction 274
11.2 Augmentationsystemdesign 280
11.3 Closedloopsystemanalysis 283
11.4 Therootlocusplot 287
11.5 Longitudinalstabilityaugmentation 293
11.6 Lateral–directionalstabilityaugmentation 300
11.7 Thepoleplacementmethod 311
References 316
Problems 316
12. Aerodynamicmodelling 320
12.1 Introduction 320
12.2 Quasi-staticderivatives 321
12.3 Derivativeestimation 323
12.4 Theeffectsofcompressibility 327
12.5 Limitationsofaerodynamicmodelling 335
References 336
13. Aerodynamicstabilityandcontrolderivatives 337
13.1 Introduction 337
13.2 Longitudinalaerodynamicstabilityderivatives 337
13.3 Lateral–directionalaerodynamicstabilityderivatives 350
13.4 Aerodynamiccontrolderivatives 371
13.5 NorthAmericanderivativecoefficientnotation 377
References 385
Problems 385
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viii Contents
14. CourseworkStudies 390
14.1 Introduction 390
14.2 Workingtheassignments 390
14.3 Reporting 390
Assignment1. StabilityaugmentationoftheNorthAmericanX-15
hypersonicresearchaeroplane 391
Assignment2. Thestabilityandcontrolcharacteristicsofaciviltransport
aeroplanewithrelaxedlongitudinalstaticstability 392
Assignment3. Lateral–directionalhandlingqualitiesdesignforthe
LockheedF-104Starfighteraircraft. 396
Assignment4. AnalysisoftheeffectsofMachnumberonthelongitudinal
stabilityandcontrolcharacteristicsoftheLTVA7-A
Corsairaircraft 401
Appendices
1 AeroTrim–ASymmetricTrimCalculatorforSubsonic
FlightConditions 405
2 DefinitionsofAerodynamicStabilityandControlDerivatives 412
3 AircraftResponseTransferFunctionsReferredtoAircraftBodyAxes 419
4 Units,ConversionsandConstants 425
5 AVeryShortTableofLaplaceTransforms 426
6 TheDynamicsofaLinearSecondOrderSystem 427
7 NorthAmericanAerodynamicDerivativeNotation 431
8 ApproximateExpressionsfortheDimensionless
AerodynamicStabilityandControlDerivatives 434
9 TheTransformationofAerodynamicStabilityDerivativesfroma
BodyAxesReferencetoaWindAxesReference 438
10 TheTransformationoftheMomentsandProductsofInertiafrom
aBodyAxesReferencetoaWindAxesReference 448
11 TheRootLocusPlot 451
Index 457
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Preface to the first edition
WhenIjoinedthestaffoftheCollegeofAeronauticssomeyearsagoIwaspresented
withawellworncollectionoflecturenotesandinvitedtoteachAircraftStabilityand
Controltopostgraduatestudents.Inspectionofthenotesrevealedtheunmistakable
signsthattheirrootsreachedbacktotheworkofW.J.Duncan,whichisperhapsnot
surprisingsinceDuncanwasthefirstProfessorofAerodynamicsatCranfieldsome
50yearsago.Itisundoubtedlyaprivilegeand,atfirst,wasverydauntingtobegiven
the opportunity to follow in the footsteps of such a distinguished academic. From
thathumblebeginningmyinterpretationofthesubjecthascontinuouslyevolvedto
itspresentformwhichprovidedthebasisforthisbook.
Theclassicallinearisedtheoryofthestabilityandcontrolofaircraftistimeless,it
isbrilliantinitsrelativesimplicityanditisverysecurelyanchoredinthedomainof
theaerodynamicist.Sowhatisnew?Theshortansweris;notagreatdeal.However,
todaythematerialisusedandappliedinwaysthathavechangedconsiderably, due
largelytotheadventofthedigitalcomputer.Thecomputerisusedastheprincipal
toolforanalysisanddesign,anditisalsotheessentialcomponentofthemodernflight
controlsystemonwhichalladvancedtechnologyaeroplanesdepend.Itisthelatter
developmentinparticularwhichhashad, andcontinuestohave, amajorinfluence
onthewayinwhichthematerialofthesubjectisnowused.Itisnolongerpossible
toguaranteegoodflyingandhandlingqualitiessimplybytailoringthestabilityand
controlcharacteristicsofanadvancedtechnologyaeroplanebyaerodynamicdesign
alone.Flightcontrolsystemsnowplayanequallyimportantpartindeterminingthe
flyingandhandlingqualitiesofanaeroplanebyaugmentingthestabilityandcontrol
characteristicsoftheairframeinabeneficialway.Thereforethesubjecthashadto
evolveinordertofacilitateintegrationwithflightcontroland,today,theintegrated
subjectismuchbroaderinscopeandismorefrequentlyreferredtoasFlightDynamics.
Thetreatmentofthematerialinthisbookreflectsmypersonalexperienceofusing,
applyingandteachingitoveraperiodofmanyyears.Myformativeexperiencewas
gained as a Systems Engineer in the avionics industry where the emphasis was on
thedesignofflightcontrolsystems. Inmorerecentyears, inadditiontoteachinga
formalcourseinthesubject, Ihavebeenprivilegedtohavespentverymanyhours
teaching the classical material in the College of Aeronautics airborne laboratory
aircraft.Thisexperiencehasenabledmetodevelopthematerialfromtheclassical
treatmentintroducedbyDuncanintheearliestdaysoftheCollegeofAeronauticsto
thepresenttreatment,whichisbiasedtowardsmodernsystemsapplications.However,
thevitallyimportantaerodynamicoriginsofthematerialremainclearandforwhich
Icantakenocredit.
Modern flight dynamics tends be concerned with the wider issues of flying and
handlingqualitiesratherthanwiththetraditional,andmorelimited,issuesofstability
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