Computational Modelling and Simulation of Aircraft and the Environment, Volume 2 E-Book

Dominic J. Diston

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Aerospace Series (PEP)
• Sprache: Englisch

Seitenzahl: 223

Veröffentlichungsjahr: 2024

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Table of Contents

Series Page

Title Page

Copyright Page

Preface

Aerospace Series Preface

1 A Simple Flight Model

1.1 Introduction

1.2 Flight Path

1.3 Flight Environment <20 km

1.4 Simple Propulsion Model

1.5 Simple Aerodynamic Model

1.6 Airspeed Definitions

1.7 Flight Model Architecture

2 Equations of Motion

2.1 Introduction

2.2 Spatial Reference Model

2.3 Aircraft Dynamics

2.4 Aircraft Kinematics

2.5 Initialisation

2.6 Linearisation

3 Fixed‐Wing Aerodynamics

3.1 Introduction

3.2 Aerodynamic Principles

3.3 Aerodynamic Model of an Isolated Wing

3.4 Trailing‐Edge Controls

3.5 Factors affecting Lift Generation

3.6 Lift Distribution

3.7 Drag Distribution

4 Longitudinal Flight

4.1 Introduction

4.2 Aerodynamic Fundamentals

4.3 Geometry

4.4 Wing/Body Combination

4.5 All‐Moving Tail

4.6 Flight Trim

4.7 Flight Stability

4.8 Trim Drag

4.9 Steady‐State Flight Performance

4.10 Dynamic Modes

5 Gas Turbine Dynamics

5.1 Introduction

5.2 Ideal Gas Properties

5.3 Gas Dynamics

5.4 Engine Components

5.5 Engine Dynamics

5.6 Engine Models

5.7 Gas Properties Data

6 Additional Topics

6.1 Introduction

6.2 Structural Models

6.3 Mass Distribution

Bibliography

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Selected Parameters for the International Standard Atmosphere.

Table 1.2 Interface Parameters in the Simple Flight Model.

Chapter 2

Table 2.1 ECEF‐to‐NED Rotations.

Table 2.2 NED‐to‐Aircraft Rotations.

Table 2.3 Flight Path Rotations.

Table 2.4 Airstream Direction.

Table 2.5 WGS84 Geometry.

Chapter 3

Table 3.1 Wing Geometric Parameters.

Table 3.2 Aerodynamic Properties for NACA Four‐Digit Sections.

Table 3.3 Numerical Approximations for Two‐Dimensional Flap Effects.

Table 3.4 Numerical Approximations for Three‐Dimensional Flap Effects.

Table 3.5 Further Numerical Approximations for Flap Hinge Moments.

Table 3.6 Numerical Approximations for Flap Hinge Moments.

Table 3.7 Approximations for Diederich Coefficients.

Chapter 4

Table 4.1 Wing Geometric Parameters.

Chapter 5

Table 5.1 Thermodynamic Processes.

Table 5.2 Turbojet Parameters.

Table 5.3 Derivation of Gas Conditions.

Table 5.4 Turbofan Parameters (Unmixed Cycle).

Table 5.5 Approximate Composition of Dry Air.

Chapter 6

Table 6.1 Internal Layout of Inertia and Stiffness Matrices.

Table 6.2 Extended Inertia and Stiffness.

Table 6.3 Internal Layout of Aircraft Inertia Matrix.

List of Illustrations

Chapter 1

Figure 1.1 Symmetric Flight Trajectory.

Figure 1.2 Symmetric Force/Moment System.

Figure 1.3 Generalised Flight Path Parameters.

Figure 1.4 Generalised Force/Moment System.

Figure 1.5 Thrust Performance for Simple Jet Engine Model.

Figure 1.6 Idealised Aircraft.

Figure 1.7 Wing Force/Moment System.

Figure 1.8 Variation of Lift‐Curve Gradient.

Figure 1.9 Aircraft in Straight‐and‐Level Flight.

Figure 1.10 Effect of Downwash on Horizontal Tail.

Figure 1.11 Variation of the Lift Distribution Coefficient.

Figure 1.12 Incremental Lift on a Wing Element.

Figure 1.13 Distribution Functions and their Integrals.

Figure 1.14 Changes in Lift Coefficient due to Flap Deflection.

Figure 1.15 Trailing‐Edge Control Surfaces.

Figure 1.16 Flap Effectiveness.

Figure 1.17 Dataflow for the Simple Flight Model.

Figure 1.18 Functional Physics and Dynamics for the Simple Flight Model.

Figure 1.19 Physics and Dynamics of a Generic Functional Block.

Chapter 2

Figure 2.1 Relative Orientation.

Figure 2.2 Vector Differentiation.

Figure 2.3 Reference Frames.

Figure 2.4 Aircraft Orientation.

Figure 2.5 Flight Path Axes.

Figure 2.6 Airflow Parameters.

Figure 2.7 Aircraft Flight Parameters.

Figure 2.8 Defining Flight Parameters at the Aircraft Datum and the Aircraft...

Figure 2.9 Dataflow for Dynamic Equations of Motion.

Figure 2.10 Rotation of an Aircraft about an Axis.

Figure 2.11 Dataflow for Kinematic Equations of Motion.

Figure 2.12 Generic Flight Condition.

Figure 2.13 Angular Velocities for Flight Equilibrium.

Chapter 3

Figure 3.1 Streamlines around a Wing Section.

Figure 3.2 Pressure Distribution over a Wing Section.

Figure 3.3 Uncambered and Cambered Wing Sections.

Figure 3.4 Forces on Uncambered and Cambered Wings.

Figure 3.5 Isolated Wing in Symmetric Flight.

Figure 3.6 Wing Lift Curves.

Figure 3.7 Centre of Pressure.

Figure 3.8 Aerodynamic Centre.

Figure 3.9 Aerofoil Cross‐Section.

Figure 3.10 Effect of Aerofoil Cross‐Sectional Geometry on the Aerodynamic C...

Figure 3.11 Idealised Swept Wing (Top Panel).

Figure 3.12 Idealised Swept Wing.

Figure 3.13 NACA Four‐Digit Section Geometry.

Figure 3.14 Empirical Correction for 2D Lift‐Curve Gradient.

Figure 3.15

C

D

0

Measurements for a Grumman Avenger.

Figure 3.16 Conceptual Model of Airflow over a Wing.

Figure 3.17 DATCOM Method for Determination of Drag Divergence Mach number....

Figure 3.18 Typical Aerodynamic Parameter Variation vs. Mach number.

Figure 3.19 Wing Profile Drag vs Sweep Angle and Thickness/Chord Ratio [NASA...

Figure 3.20 Trailing‐Edge Control Surfaces.

Figure 3.21 Flap Span Factor.

Figure 3.22 Correction Factor for Flaps.

Figure 3.23 Flap Chord Factor.

Figure 3.24 Flap Effectiveness.

Figure 3.25 Airflow Direction.

Figure 3.26 Wing Geometry in Sideslip.

Figure 3.27 Local Reference Frame.

Figure 3.28 Frame Orientation for Flexure.

Figure 3.29 Frame Orientation for Dihedral.

Figure 3.30 Frame Orientation for Flexure.

Figure 3.31 Sweep Correction Function.

Figure 3.32 Diederich Coefficients.

Figure 3.33 Wing Downwash and Tip Vortices.

Chapter 4

Figure 4.1 Typical Wing.

Figure 4.2 Idealised Aircraft.

Figure 4.3 Aircraft Planform Geometry.

Figure 4.4 Effect of Downwash on Horizontal Tail.

Figure 4.5 Flap Effectiveness.

Figure 4.6 Fuselage Partition for Multhopp’s Method.

Figure 4.7 Correction Factor

K

2

 − 

K

1

.

Figure 4.8 Upwash Gradient.

Figure 4.9 Engine Nacelle Geometry.

Figure 4.10 Aircraft in Straight‐and‐Level Flight.

Figure 4.11 Incremental Lift Force and Pitching Moment.

Figure 4.12 Typical Trim Drag Curve (left panel), Typical Trim Drag Curve (R...

Figure 4.13 Practical Limitations associated with Trim Drag (left panel), Pr...

Figure 4.14 Generalised Force/Moment System.

Chapter 5

Figure 5.1 Massflow Through a Streamtube.

Figure 5.2 Sound Propagation Through Dry Air at Sea Level.

Figure 5.3 Example Compressor Map.

Figure 5.4 Example Turbine Map.

Figure 5.5 Turbojet Schematic.

Figure 5.6 Turbojet Specification.

Figure 5.7 Turbojet Initialisation.

Figure 5.8 Turbojet Physics.

Figure 5.9 Turbojet Dynamics.

Figure 5.10 Modified Compressor Map.

Figure 5.11 Turbofan Schematic.

Figure 5.12 Turbofan Specification (Unmixed Cycle).

Figure 5.13 Turbofan Initialisation (Unmixed Cycle).

Figure 5.14 Turbofan Physics (Unmixed Cycle).

Figure 5.15 Turbofan Dynamics (Unmixed Cycle).

Figure 5.16 Boundary for Negligible Dissociation in Combustion (to Left of t...

Figure 5.17 Variation of Properties of Fuel/Air Combustion Products.

Chapter 6

Figure 6.1 Simple Transformation of Displacements and Forces.

Figure 6.2 Three‐Component Coupled Structure.

Figure 6.3 Simple Model of Wing‐Fuselage Structure.

Figure 6.4 Extended Wing‐Fuselage Model.

Figure 6.5 Extended Wing‐Body‐Fuselage Model.

Figure 6.6 Selected Aircraft Normal Modes.

Figure 6.7 Point Cloud for an Oblong Tank.

Figure 6.8 Point Cloud for a Wing Tank.

Figure 6.9 Point Cloud for a Wing Fuel Tank (50% Fill, 15‐degree Pitch Angle...

Figure 6.10 Height/Volume Relationship.

Figure 6.11 Fuel Density.

Figure 6.12 Example Fuel System.

Figure 6.13 Schematic of Geometric Parameters.

Figure 6.14 Fuel Distribution (50% Full, 0° Pitch).

Figure 6.15 Fuel Distribution (50% Full, 20° Pitch).

Figure 6.16 Fuel Schedule (or Burn Curve).

Figure 6.17 Typical Wing Structure.

Guide

Cover Page

Table of Contents

Series Page

Title Page

Copyright Page

Preface

Aerospace Series Preface

Begin Reading

Bibliography

Index

WILEY END USER LICENSE AGREEMENT

Pages

ii

iii

iv

xi

xiii

xiv

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

Aerospace Series

David Allerton. Principles of Flight Simulation

Allan Seabridge, Mohammad Radaei. Aircraft Systems Classifications: A Handbook of Characteristics and Design Guidelines

Douglas M. Marshall. UAS Integration into Civil Airspace: Policy, Regulations and Strategy

Paul G. Fahlstrom, Thomas J. Gleason, Mohammad H. Sadraey. Introduction to UAV Systems, 5th Edition

James W. Gregory, Tianshu Liu. Introduction to Flight Testing

Ashish Tewari. Foundations of Space Dynamics

Egbert Torenbeek. Essentials of Supersonic Commercial Aircraft Conceptual Design

Mohammad H. Sadraey. Design of Unmanned Aerial Systems

Saeed Farokhi. Future Propulsion Systems and Energy Sources in Sustainable Aviation

Rama K. Yedavalli. Flight Dynamics and Control of Aero and Space Vehicles

Allan Seabridge, Ian Moir. Design and Development of Aircraft Systems, 3rd Edition

Gareth D. Padfield. Helicopter Flight Dynamics: Including a Treatment of Tiltrotor Aircraft, 3rd Edition

Craig A. Kluever. Space Flight Dynamics, 2nd Edition

Trevor M. Young. Performance of the Jet Transport Airplane: Analysis Methods, Flight Operations, and Regulations

Andrew J. Keane, Andros Sobester, James P. Scanlan. Small Unmanned Fixed‐wing Aircraft Design: A Practical Approach

Pascual Marques, Andrea Da Ronch. Advanced UAV Aerodynamics, Flight Stability and Control: Novel Concepts, Theory and Applications

Farhan A. Faruqi. Differential Game Theory with Applications to Missiles and Autonomous Systems Guidance

Grigorios Dimitriadis. Introduction to Nonlinear Aeroelasticity

Nancy J. Cooke, Leah J. Rowe, Winston Bennett Jr., DeForest Q. Joralmon. Remotely Piloted Aircraft Systems: A Human Systems Integration Perspective

Stephen Corda. Introduction to Aerospace Engineering with a Flight Test Perspective

Wayne Durham, Kenneth A. Bordignon, Roger Beck. Aircraft Control Allocation

Ashish Tewari. Adaptive Aeroservoelastic Control

Ajoy Kumar Kundu, Mark A. Price, David Riordan. Theory and Practice of Aircraft Performance

Peter Belobaba, Amedeo Odoni, Cynthia Barnhart, Christos Kassapoglou. The Global Airline Industry, 2nd Edition

Jan R. Wright, Jonathan Edward Cooper. Introduction to Aircraft Aeroelasticity and Loads, 2nd Edition

Tapan K. Sengupta. Theoretical and Computational Aerodynamics

Andros Sobester, Alexander I.J. Forrester. Aircraft Aerodynamic Design: Geometry and Optimization

Roy Langton. Stability and Control of Aircraft Systems: Introduction to Classical Feedback Control

T. W. Lee. Aerospace Propulsion

Ian Moir, Allan Seabridge, Malcolm Jukes. Civil Avionics Systems, 2nd Edition

Wayne Durham. Aircraft Flight Dynamics and Control

Konstantinos Zografos, Giovanni Andreatta, Amedeo Odoni. Modelling and Managing Airport Performance

Egbert Torenbeek. Advanced Aircraft Design: Conceptual Design, Analysis and Optimization of Subsonic Civil Airplanes

Christos Kassapoglou. Design and Analysis of Composite Structures: With Applications to Aerospace Structures, 2nd Edition

Keith A. Rigby. Aircraft Systems Integration of Air‐Launched Weapons

Doug McLean. Understanding Aerodynamics: Arguing from the Real Physics

Mohammad H. Sadraey. Aircraft Design: A Systems Engineering Approach

G.D. McBain. Theory of Lift: Introductory Computational Aerodynamics in MATLAB/Octave

Plamen Angelov. Sense and Avoid in UAS: Research and Applications

John Valasek. Morphing Aerospace Vehicles and Structures

Peter Fortescue, Graham Swinerd, John Stark. Spacecraft Systems Engineering, 4th Edition

Reg Austin. Unmanned Aircraft Systems: UAVS Design, Development and Deployment

Roberto Sabatini, Alessandro Gardi. Sustainable Aviation Technology and Operations: Research and Innovation Perspectives

Grigorios Dimitriadis. Unsteady Aerodynamics: Potential and Vortex Methods

Dominic J. Diston. Computational Modelling and Simulation of Aircraft and the Environment, Volume 2

Visit www.wiley.com to view more titles in the Aerospace Series.

Computational Modelling and Simulation of Aircraft and the Environment

Volume 2: Aircraft Dynamics

Dominic J. Diston

University of Liverpool

UK

This edition first published 2024© 2024 John Wiley & Sons Ltd

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Dominic J. Diston to be identified as the author of this work has been asserted in accordance with law.

Registered OfficesJohn Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USAJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print‐on‐demand. Some content that appears in standard print versions of this book may not be available in other formats.

Trademarks: Wiley and the Wiley logo are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc. is not associated with any product or vendor mentioned in this book.

Limit of Liability/Disclaimer of WarrantyIn view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging‐in‐Publication Data Applied for:

Hardback ISBN: 9780470687116

Cover Design: WileyCover Image: © Andrei Armiagov/Shutterstock

Preface

Many years have passed since the publication of Volume 1, far more than ever intended or expected. This has been an inescapable consequence of a high workload elsewhere and, until recently, a general shortage of time caused by work/life imbalance. However, here it is … a range of material that covers some of the stuff that I have dealt with in a career that spanned approximately 43 years. In the 24 years spent at BAE SYSTEMS (and previously British Aerospace), I had the privilege of working on some of the most interesting and inventive areas of engineering that I could have ever wished for, as well as the privilege of working with some extraordinarily talented people. In the 19 years spent in higher education, I taught a wide range of aerospace subjects at the Universities of Manchester, Liverpool and Nottingham, as well as a short period at the Empire Test Pilots' School. So, this book is a digest of subject matter in the area of vehicle modelling and simulation. It focuses on the flight physics of fixed‐wing aircraft, with a short introduction towards the end of the book on systems modelling. This is all based on project work and taught modules that I have produced during my career. I have attempted to be thorough and interesting, although readers might not necessarily agree. However, it should provide more than enough information and interpretation to help develop specialised knowledge. I do not guarantee perfection, but I did employ my best endeavours to make this a worthwhile publication, albeit later than planned.

Aerospace Series Preface

The field of aerospace is multi‐disciplinary and wide ranging, covering a large variety of products, disciplines and domains, not merely in engineering but in many related supporting activities. The combination of these elements enables the aerospace industry to produce innovative and technologically advanced vehicles and systems. The wealth of knowledge and experience that has been gained by expert practitioners in the various aerospace fields needs to be passed onto others working in the industry as well as to researchers, teachers and the student body in universities.

The Aerospace Series aims to be a practical, topical and relevant series of books aimed at people working in the aerospace industry, including engineering professionals and operators, engineering educators in academia, and allied professions such as commercial and legal executives. The range of topics is intended to be wide, covering design and development, manufacture, operation and support of aircraft, as well as infrastructure operations and current advances in research and technology.

In the field of aircraft systems design, the application of computational models using commercially available modelling and simulation tools is widely practiced and taught in most university engineering degree courses. The use of such models provides the system designer with the ability to rapidly model their preliminary design concept and to exercise the model under many operational and failure scenarios. This approach allows the performance of the system to be assessed and enables the introduction of changes as required to refine the design. In this way, it is possible to validate the behaviour of the system before committing to the final detailed design – a valuable contribution to ‘right first time’ design.

Computational Modelling of Aircraft and the Environment, Volume 2 : Aircraft Dynamics is the sequel to Volume 1 which focused upon Platform Kinetics and Synthetic Environments and introduced a means of modelling the real‐world environment in which aircraft operate. This book continues the journey of providing a broad‐based text covering applicable mathematics and science in key domains required to create models to assist with the design of systems by summarising the essential elements of air vehicle modelling and simulation with a focus on the flight physics of fixed‐wing aircraft. It also introduces the development of representative flight models, deriving the equations of motion, fixed‐wing aerodynamics, longitudinal flight mechanics and the fundamentals of gas turbine dynamics. The final section builds upon the previous material through consideration of structural models, mass properties and physical system modelling, including the use of bond graphs. This book is a welcome addition to the Wiley Aerospace Series.

Peter Belobaba, Jonathan Cooper and Allan SeabridgeDecember 2023

1A Simple Flight Model

1.1 Introduction

1.1.1 General Introduction to Volume 2

Welcome to Volume 2 of Computational Modelling and Simulation of Aircraft and the Environment. This volume will present and explain the main theories that enable the dynamics of fixed‐wing aircraft to be modelled using mathematical and computational methods. The aim is to establish the heuristic basis for education in aeronautical engineering that provides a ‘handbook’ of concepts and interpretations, together with a formulary to support practical application. It is appropriate and convenient to commence with a simple flight model that brings together all the essential components without too much detail. This covers aircraft motion, atmosphere, aerodynamics, and propulsion. More detailed expositions are given in Chapters 2–5. These focus on Equations of Motion, Wing Aerodynamics, Longitudinal Flight and Gas Turbines.

The significant omission is lateral‐directional aerodynamics, apart from rolling a wing in flight (later in Chapter 1). This is because the formulary tends to be complicated and abstract, with no easily recognisable link to the underlying physics. Also, there is no inherent value in just repeating what other books [e.g. Pamadi] already provide. Also, supersonic flight is not discussed because it is a specialised area of aircraft design. The vast majority of aircraft are not supersonic.

The final chapter offers a brief introduction to several topics that are important in whole‐aircraft modelling but that sit outside the usual scope of flight physics. The discussion is brief because these subjects have substantial content and could easily expand to fill another two or three textbooks.

1.1.2 What Chapter 1 Includes

This chapter includes:

Equations of motions expressed with respect to flight path parameters.

Summary of the International Standard Atmosphere up to 20 km (roughly 50 000 ft).

Simple propulsion model that enables thrust calculations at given altitude and Mach number.

Simple aerodynamic model that is applicable to idealised wing geometry plus trailing‐edge flaps.

A short introduction to spanwise lift distribution for an idealised wing.

Aerodynamic model for wing/tail combinations (as an approximation to a complete aircraft).

A set of airspeed definitions.

One of many possible architectures for a flight model (i.e. a whole‐aircraft model).

1.1.3 What Chapter 1 Excludes

This chapter excludes:

Six degree‐of‐freedom (6‐DOF) equations of motion [go to

Chapter 2

].

Generalised wing configurations (e.g. taper, twist) [go to

Chapter 3

].

Flight mechanics of wing/tail combinations [go to

Chapter 4

].

Fuselage aerodynamic effects [go to

Chapter 4

].

Physics‐based models of gas turbines [go to

Chapter 5

].

Lateral‐directional aerodynamics [not covered by this book].

Supersonic flight [not covered by this book].

1.1.4 Overall Aim

Chapter 1 should provide ‘enough of everything’ that is needed to create a complete representation of aircraft flight behaviour, from ground up to 20 km and from low‐speed up to about 0.85 Mach number. This includes the essential flight physics without too much detail, such that computations can be verified by manual calculation and that parametric trend should be readily discernible. In short, this should provide a compact aircraft model for the purpose of preliminary concept evaluation and simulation.

1.2 Flight Path

The simplest possible flight path model is shown in Figure 1.1. This represents symmetric flight (with wings level) in a vertical plane. Motion parameters are defined at the centre of mass for an instantaneous pull‐up (which is turn in the vertical plane). Airspeed V is aligned (or tangential) with the flight path, which is normal to the radius of turn. The tangential acceleration varies the airspeed while the centripetal acceleration varies the flight path angle. The pitch angle θ defines the orientation of the aircraft horizontal datum and the angle of attack (AOA) is defined by:

(1.1)

where γ is the climb/dive angle. The rate of change of pitch angle is the pitch rate , such that

(1.2)

Figure 1.1 Symmetric Flight Trajectory.

The force/moment system is shown in Figure 1.2 (referred to the centre of gravity, CG). Thus, aircraft motion is governed by the following equations when aircraft mass is constant:

(1.3)

where m is aircraft mass, J is moment of inertia, X is tangential force, Z is normal force and M is pitching moment. Altenatively, these equations can be written as:

(1.4)

Figure 1.2 Symmetric Force/Moment System.

The forces X and Z are composed as:

(1.5)

where L is total lift, D is total drag, W is aircraft weight and T is the total nett thrust from all engines. For convenience, the thrust line is drawn through the centre of mass. Also, for convenience, the thrust is aligned with the velocity vector and not the aircraft datum. This is true if AOA is zero (which it rarely is) and almost true if AOA is small (which it usually is).

Currently, the flight path is constrained to lie within a single vertical plane, tracing a straight line course across the surface of the Earth. Horizontal turns would be useful! So, a reference system is defined for the Earth, with its axes aligned with North, East, and Down, shown in Figure 1.3. Flight path angles are defined as γ3 (setting the course direction), γ2 (setting the climb/dive angle), and γ1 (setting a rotation about the velocity vector). The resulting ‘flight path axes’ are shown as xyz. The vertical turn rate is now written as [cf. Figure 1.1] and a horizontal turn rate is introduced as . In fact, can be redefined as the variation in flight path angle measured in the plane of symmetry (which is inclined at an angle γ1 with respect to the vertical):

(1.6)

Figure 1.3 Generalised Flight Path Parameters.

The force/moment system is modified and extended, as shown in Figure 1.4. The lift vector is inclined at an angle γ1 with respect to the vertical. This generates the horizontal acceleration, thereby providing a bank‐to‐turn capability. Rotation about the velocity vector is produced by a rolling moment K about the velocity vector, such that the roll rate p is equal to .

The generalised equations of motion are given by:

(1.7)

(1.8)

where m is the aircraft mass, g is the gravitational acceleration, J1 is the roll moment of inertia, J2 is the pitch moment of inertia, and the other symbols have their previously defined meanings.

Figure 1.4 Generalised Force/Moment System.

The flight path angles are (γ1, γ2, γ3