Computational modelling and simulation of aircraft and the environment. platform kinematics and synthetic environment

372 Pages·2009·7.46 MB·English

by  Dominic J. Diston

Computational Modelling
and Simulation of Aircraft
and the Environment
Computational Modelling and Simulation of Aircraft and the Environment: Platform Kinematics and Synthetic Environment Volume 1 D.J. Diston
© 2009 John Wiley & Sons, Ltd. ISBN: 978-0-470-01840-8
Computational Modelling
and Simulation of Aircraft
and the Environment
Volume 1: Platform Kinematics and
Synthetic Environment
Dominic J. Diston
University of Manchester, UK
A John Wiley and Sons, Ltd., Publication
Thiseditionfirstpublished2009
(cid:2)2009JohnWiley&Sons,Ltd.
Registeredoffice
JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,
PO198SQ,UnitedKingdom
Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyfor
permissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com.
Therightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththe
Copyright,DesignsandPatentsAct1988.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or
transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,
exceptaspermittedbytheUKCopyright,DesignsandPatentsAct1988,withoutthepriorpermissionof
thepublisher.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynot
beavailableinelectronicbooks.
Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrand
namesandproductnamesusedinthisbookaretradenames,servicemarks,trademarksorregistered
trademarksoftheirrespectiveowners.Thepublisherisnotassociatedwithanyproductorvendor
mentionedinthisbook.Thispublicationisdesignedtoprovideaccurateandauthoritativeinformationin
regardtothesubjectmattercovered.Itissoldontheunderstandingthatthepublisherisnotengagedin
renderingprofessionalservices.Ifprofessionaladviceorotherexpertassistanceisrequired,theservicesofa
competentprofessionalshouldbesought.
MATLAB(cid:3)MATLABandanyassociatedtrademarksusedinthisbookaretheregisteredtrademarksof
TheMathWorks,Inc.
LibraryofCongressCataloguing-in-PublicationData
Diston,Dominic.
Computationalmodellingofaircraftandtheenvironment/DominicDiston.
v. cm.
Includesbibliographicalreferencesandindex.
Contents:Volume1. Platformkinematicsandsyntheticenvironment
ISBN978-0-470-01840-8(cloth)(v.1)
1. Airplanes—Computersimulation. 2. Airplanes—Performance—Mathematicalmodels.
3. Aeronautics—Systemsengineering—Dataprocessing. 4. Navigation(Aeronautics)—
Computersimulation. 5. Atmosphere—Computersimulation. 6. Gravitationalfields—
Computersimulation. 7. Sphericalastronomy—Dataprocessing. I. Title.
TL671.4.D572009
629.1301013—dc22
2009008333
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:978-0-470-01840-8
Setin9/11ptPhotinabyIntegraSoftwareServicesPvt.Ltd.,Pondicherry,India
PrintedintheUKbyAntonyRoweLtd,Chippenham,Wiltshire.
IN MEMORY OF
John Joseph Diston
Master Mariner
1925–2000
Contents
Preface xiii
Acknowledgements xv
List of Abbreviations xvii
How To Use This Book xxi
Series Preface xxv
Chapter1:Introduction 1
1.1 ComputationalModelling 1
1.2 ModellingandSimulation(M&S) 2
1.3 DevelopmentProcesses 4
1.4 Models 8
1.5 Meta-models 12
1.6 AerospaceApplications 14
1.6.1 SyntheticEnvironment 14
1.6.2 AerospaceVehicles 17
1.7 IntegrationandInteroperability 21
1.8 TheEndoftheBeginning 22
Chapter2:PlatformKinematics 25
2.1 AxisSystems 25
2.1.1 PlatformAxisSystem 25
2.1.2 LocalAxisSystems 25
2.1.3 Earth-CentredAxisSystems 27
2.1.4 Orientation 29
2.1.5 FlightAxisSystem 39
2.2 ChangingPositionandOrientation 42
2.3 RotatingAxisSystems 45
2.3.1 InertialandNon-inertialFrames 45
2.3.2 VectorDifferentiation 45
2.3.3 Poisson’sEquation 47
vii
viii Contents
2.4 Quaternions 49
2.4.1 MethodofConstruction 49
2.4.2 FrameRotationviaQuaternions 52
2.4.3 RelationshipbetweenQuaternionsandEulerAngles 54
2.5 LineofSight 56
Chapter3:GeospatialReferenceModel 63
3.1 SphericalEarth 63
3.2 SphericalTrigonometry 66
3.3 GreatCircleNavigation 72
3.4 RhumbLineNavigation 78
3.5 ReferenceEllipsoids 81
3.5.1 WorldGeodeticSystem(WGS84) 81
3.5.2 GeoidApproximations 82
3.6 CoordinateSystems 86
3.6.1 GeocentricandGeodeticLatitude 86
3.6.2 ParametricorReducedLatitude 87
3.6.3 CartesianCoordinates 89
3.6.4 ApproximateCartesianCoordinates 91
3.6.5 Latitude,LongitudeandAltitude 92
3.7 NavigationonanEllipsoidalEarth 93
3.7.1 DifferentialGeometry 93
3.7.2 Geodesics 96
3.7.3 GeodesicTrajectory 99
3.7.4 GeodesicLength 100
3.7.5 MeridianDistances 101
3.7.6 RhumbLines 103
3.8 Mapping 104
3.9 GeneralPrinciplesofMapProjection 104
3.10 MercatorProjection 109
3.11 TransverseMercatorProjection 113
3.11.1 ForwardProjection 113
3.11.2 NationalGridofGreatBritain 116
3.11.3 UniversalTransverseMercator(UTM)Grid 119
3.11.4 ProjectionGeometry 120
3.11.5 InverseProjection 123
3.12 ConformalLatitude 124
3.13 PolarStereographicProjection 125
3.13.1 BasicFormulation 125
3.13.2 UniversalPolarStereographic(UPS)Projection 126
3.14 Three-DimensionalMapping 127
3.15 ActualLatitudes,LongitudesandAltitudes 131
Contents ix
Chapter4:PositionalAstronomy 137
4.1 EarthandSun 137
4.2 ObservationalReferenceFrames 139
4.2.1 HorizontalFrame 140
4.2.2 FirstEquatorialFrame 140
4.2.3 SecondEquatorialFrame 142
4.2.4 FrameTransformations 142
4.3 MeasurementofTime 143
4.3.1 MeanTime 143
4.3.2 DiurnalCycle 144
4.3.3 UniversalTime 147
4.3.4 TimeZones 149
4.3.5 SiderealTime 151
4.3.6 TerrestrialTime 152
4.4 CalendarsandtheJ2000ReferenceEpoch 153
4.5 ChronologicalScale 156
4.6 AstrometricReferenceFrames 156
4.6.1 InertialFrame 156
4.6.2 RotatingFrame 157
4.6.3 Precession 158
4.6.4 CoordinateTransformations 160
4.7 OrbitalMechanics 161
4.7.1 Kepler’sLaws 161
4.7.2 OrbitalEnergyandVelocity 166
4.7.3 AnomaliesandKepler’sEquation 166
4.7.4 OrbitalElements 169
4.8 SolarSystemOrbitModels 171
4.8.1 PlanetaryData 172
4.8.2 PlanetaryTrajectories 175
4.8.3 MeanSunandtheEquationofTime 180
4.9 GPSOrbitModels 183
4.9.1 GPSAlmanacModel 184
4.9.2 GPSEphemerisModel 185
4.9.3 YUMAAlmanac 187
4.9.4 Two-LineElements 187
4.9.5 GPSConstellation 189
4.10 NightSky 190
Chapter5:GeopotentialFields 197
5.1 PotentialFields 197
5.1.1 Gauss’sTheorem 197
5.1.2 ApplicationsofGauss’sTheorem 198
5.1.3 Poisson’sEquationandLaplace’sEquation 199
x Contents
5.1.4 GenericSolutionofLaplace’sEquation 200
5.2 Gravitation 202
5.2.1 GravitationAttraction 202
5.2.2 ApparentGravity:SphericalEarth 202
5.2.3 ApparentGravity:WGS84Ellipsoid 204
5.2.4 GravitationalMoments 205
5.2.5 EarthGravitationalModel(EGM96) 206
5.2.6 MacCullagh’sFormula 208
5.2.7 EarthFlatteningor‘Oblateness’ 211
5.2.8 CartesianComponentsofGravity 213
5.2.9 WGS84GravityFormula 214
5.2.10 Geoid 215
5.3 Geomagnetism 215
5.3.1 Earth’sMagneticField 215
5.3.2 MagneticAttraction 216
5.3.3 WorldMagneticModel(WMM2005) 218
5.3.4 ApproximateDipole 222
5.4 GeopotentialComputation 224
5.4.1 EGM96andWMM2005SphericalHarmonics 225
5.4.2 RecurrenceFormulae 226
5.4.3 Cunningham’sMethod 229
5.5 FinalCommentonGeopotentialModels 235
Chapter6:Atmosphere 237
6.1 Overview 237
6.2 StandardAtmosphereModels 239
6.3 ISAConstantsandRelationships 239
6.4 GeopotentialAltitude 242
6.4.1 StandardDefinition 242
6.4.2 GeneralisedDefinition 243
6.5 VerticalStructureoftheAtmosphere 245
6.6 PressureAltitude 251
6.7 ReferenceAtmospheres 253
6.8 SeasonalVariation 255
6.9 ClimaticRegions 255
6.9.1 MIL-HDBK-310Classification 256
6.9.2 Ko¨ppen-GeigerClassification 256
6.10 AirDensity 260
6.11 WaterVapour 261
6.11.1 GasConstant 261
6.11.2 Humidity 263
6.12 WeatherSystems 272
Contents xi
Appendix A: Introduction to MATLAB 279
A.1 MATLAB 279
A.2 TheMATLABProductFamily 280
A.3 GettingStarted 280
A.4 GettingHelp 281
A.5 Where? 284
A.6 Numbers:VariablesandLiterals 286
A.7 Arithmetic 290
A.8 Logic 293
A.9 M-FilesandFunctions 295
A.10 Built-inFunctions 298
A.11 Constants 298
A.12 CreatingGraphs 298
A.13 SummaryofAppendixA 300
Appendix B: Data and Functions 303
B.1 TypesofData 303
B.2 DataTypeDescriptions 305
B.2.1 ‘double’ 305
B.2.2 ‘logical’ 306
B.2.3 ‘char’ 306
B.2.4 ‘cell’ 307
B.2.5 ‘struct’ 308
B.2.6 ‘function_handle’ 310
B.3 ProgramStructure 313
B.3.1 Syntax 313
B.3.2 ConditionalExecution 317
B.3.3 IterativeExecution 319
B.3.4 ExceptionHandling 321
B.3.5 Omissions 322
B.4 User-definedFunctions 322
B.4.1 Interfacing 322
B.4.2 GenericFunctions 325
B.4.3 RecursiveFunctions 326
B.4.4 PrivateFunctions 327
B.5 User-definedClasses 327
B.6 PracticalImplementation 331
B.6.1 NamingConvention 331
B.6.2 ProgramArchitecture 333