Computational Modelling and Simulation of Aircraft and the Environment: Platform Kinematics and Synthetic Environment, Volume 1

This first volume of Computational Modelling of Aircraft and the Environment provides a comprehensive guide to the derivation of computational models from basic physical & mathematical principles, giving the reader sufficient information to be able to represent the basic architecture of the synthetic environment. Highly relevant to practitioners, it takes into account the multi-disciplinary nature of the aerospace environment and the integrated nature of the models needed to represent it. Coupled with the forthcoming Volume 2: Aircraft Models and Flight Dynamics it represents a complete reference to the modelling and simulation of aircraft and the environment. All major principles with this book are demonstrated using MATLAB and the detailed mathematics is developed progressively and fully within the context of each individual topic area, thereby rendering the comprehensive body of material digestible as an introductory level text. The author has drawn from his experience as a modelling and simulation specialist with BAE SYSTEMS along with his more recent academic career to create a resource that will appeal to and benefit senior/graduate students and industry practitioners alike.Content: Chapter 1 Introduction (pages 1–23): Chapter 2 Platform Kinematics (pages 25–62): Chapter 3 Geospatial Reference Model (pages 63–136): Chapter 4 Positional Astronomy (pages 137–195): Chapter 5 Geopotential Fields (pages 197–235): Chapter 6 Atmosphere (pages 237–278): The End of the Beginning......Page 20 Synthetic Environment......Page 33 Aerospace Vehicles......Page 36 Line of Sight......Page 43 Earth-Centred Axis Systems......Page 45 Orientation......Page 47 Flight Axis System......Page 57 Vector Differentiation......Page 63 Poisson’s Equation......Page 65 Frame Rotation via Quaternions......Page 67 Relationship between Quaternions and Euler Angles......Page 72 Actual Latitudes, Longitudes and Altitudes......Page 81 World Geodetic System WGS84......Page 99 Geodesic Trajectory......Page 117 Geodesic Length......Page 118 Meridian Distances......Page 119 Rhumb Lines......Page 121 Forward Projection......Page 131 National Grid of Great Britain......Page 134 Universal Transverse Mercator UTM Grid......Page 137 Projection Geometry......Page 138 Night Sky......Page 155 First Equatorial Frame......Page 158 Frame Transformations......Page 160 Mean Time......Page 161 Diurnal Cycle......Page 162 Terrestrial Time......Page 170 Inertial Frame......Page 174 Rotating Frame......Page 175 Precession......Page 176 Coordinate Transformations......Page 178 Kepler’s Laws......Page 179 Anomalies and Kepler’s Equation......Page 184 Orbital Elements......Page 187 Planetary Data......Page 190 Planetary Trajectories......Page 193 Mean Sun and the Equation of Time......Page 198 GPS Almanac Model......Page 202 GPS Ephemeris Model......Page 203 Two-Line Elements......Page 205 GPS Constellation......Page 207 Final Comment on Geopotential Models......Page 214 Applications of Gauss’s Theorem......Page 215 Poisson’s Equation and Laplace’s Equation......Page 216 Generic Solution of Laplace’s Equation......Page 217 Apparent Gravity: Spherical Earth......Page 219 Apparent Gravity: WGS84 Ellipsoid......Page 221 Gravitational Moments......Page 222 Earth Gravitational Model EGM96......Page 223 MacCullagh’s Formula......Page 225 Earth Flattening or ‘Oblateness’......Page 228 Cartesian Components of Gravity......Page 230 WGS84 Gravity Formula......Page 231 Earth’s Magnetic Field......Page 232 World Magnetic Model WMM2005......Page 235 Approximate Dipole......Page 239 EGM96 and WMM2005 Spherical Harmonics......Page 242 Recurrence Formulae......Page 243 Weather Systems......Page 253 Standard Definition......Page 258 Generalised Definition......Page 259 Köppen-Geiger Classification......Page 272 Gas Constant......Page 277 Humidity......Page 279 MATLAB......Page 295 Getting Started......Page 296 Getting Help......Page 297 Where?......Page 300 Numbers: Variables and Literals......Page 302 Arithmetic......Page 306 Logic......Page 309 M-Files and Functions......Page 311 Creating Graphs......Page 314 Summary of Appendix A......Page 316 Types of Data......Page 318 double’......Page 320 char’......Page 321 cell’......Page 322 struct’......Page 323 function_handle’......Page 325 Syntax......Page 328 Top-level Function Definition......Page 329 Method Statements......Page 330 Control Statements......Page 331 If’ Statements......Page 332 Switch’ Statements......Page 333 For’ Statements......Page 334 While’ Statements......Page 335 Exception Handling......Page 336 Interfacing......Page 337 Generic Functions......Page 340 Recursive Functions......Page 341 User-defined Classes......Page 342 Naming Variables......Page 346 Acronyms and Abbreviations......Page 347 Top-Level Structure......Page 348 Program Interfacing......Page 349 Statements......Page 350 Operator Precedence......Page 351 File Precedence......Page 352 Summary of Appendix B......Page 353 Specialist Agencies of the United Nations......Page 354 International Organisations......Page 355 US Government Organisations......Page 358 UK Government Organisations......Page 360 European Organisations......Page 361 Open Projects and Consortia......Page 362 Bibliography......Page 364 Index......Page 368 Computational Modelling and Simulation of Aircraft and the Environment An in-depth discussion of aircraft dynamics modelling and simulation This book provides a comprehensive guide to modelling and simulation from basic physical and mathematical principles, giving the reader sufficient information to be able to build computational models of aircraft for the purposes of simulation and evaluation. Highly relevant to practitioners, it takes into account the multi-disciplinary nature of aerospace products and the integrated nature of the models needed in order to represent them. Volume 1- Platform Kinematics and Synthetic Environment focused on the modelling of a synthetic environment in which aircraft operate and its spatial relationship with vehicles that are situated and moving within it. This volume focuses on the modelling of aircraft and the interpretation of their flight dynamics. Key features: Includes chapters on equations of motion, fixed-wing aerodynamics, longitudinal flight and gas turbines, as well as an opening chapter that presents an overview of flight modelling and a concluding chapter that presents a number of additional topics such as aircraft structures and embedded systems. Serves as both a student text and practitioner reference. Follows on from previous Aerospace Series titles, offering a complementary view of vehicles and systems from the perspectives of mathematics, physics and simulation. This book offers a comprehensive guide for senior, graduate and postgraduate students of aerospace engineering as well as professional engineers involved in the modelling and simulation of aircraft.

This first volume of Computational Modelling of Aircraft and the Environment provides a comprehensive guide to the derivation of computational models from basic physical & mathematical principles, giving the reader sufficient information to be able to represent the basic architecture of the synthetic environment. Highly relevant to practitioners, it takes into account the multi-disciplinary nature of the aerospace environment and the integrated nature of the models needed to represent it. Coupled with the forthcoming Volume 2: Aircraft Models and Flight Dynamics it represents a complete reference to the modelling and simulation of aircraft and the environment.

Chapters include:

• Computational Modelling

• Platform Kinematics

• Geospatial Reference Model

• Positional Astronomy

• Geopotential Fields

• Atmosphere

• Appendices (an Introduction to MATLAB and Data and Functions).

All major examples within the book are implemented using MATLAB, and more high level, detailed mathematics is contained within the appendices in order to render the main body of the material digestible as an introductory level text. The author has drawn from his experience both as a modelling and simulation specialist with BAE Systems along with his more recent academic career to create a resource that will appeal to and benefit senior/ graduate students and industry practitioners alike.

This book is a comprehensive reference on deriving and developing computational models from basic physical & mathematical principles, giving the reader sufficient information to be able to represent the basic architecture of air vehicles and their embedded systems and to then be able to apply those models in analysis and simulation. This book provides a comprehensive guide to the derivation of computational models from basic physical mathematical principles, giving the reader sufficient information to be able to represent the basic architecture of air vehicles and their embedded systems.