Aircraft Flight Dynamics and Control

Wayne Durham, Virginia Polytechnic Institute and State University, USAWayne Durham is an Associate Professor Emeritus in the College of Engineering at Virginia Polytechnic Institute and State University. His area of research focuses on aircraft flight dynamics and control and he teaches a course (AOE 5214) on this subject at Virginia Tech University. He previously worked as a flight instructor at various Navy Schools in the US.

"Although not a replacement for Bernard Etkins' Dynamics of Atmospheric Flight or Mike Cook's Flight Dynamic Principles, it is an ideal companion book for students and those beginning their careers in flight dynamics and control." (The Aeronautical Journal, 1 June 2014)"Written by an author with experience as an engineering test pilot as well as a university professor, Aircraft Flight Dynamics and Control provides the reader with a systematic development of the insights and tools necessary for further work in related fields of flight dynamics and control. It is an ideal course textbook and is also a valuable reference for many of the necessary basic formulations of the math and science underlying flight dynamics and control." (Expofairs.com, 15 May 2014)

• Series Preface xiii Glossary xv1 Introduction 11.1 Background 11.2 Overview 21.3 Customs and Conventions 62 Coordinate Systems 72.1 Background 72.2 The Coordinate Systems 72.2.1 The inertial reference frame, FI 72.2.2 The earth-centered reference frame, FEC 82.2.3 The earth-fixed reference frame, FE 82.2.4 The local-horizontal reference frame, FH 82.2.5 Body-fixed reference frames, FB 102.2.6 Wind-axis system, FW 122.2.7 Atmospheric reference frame 122.3 Vector Notation 132.4 Customs and Conventions 142.4.1 Latitude and longitude 142.4.2 Body axes 142.4.3 'The' body-axis system 142.4.4 Aerodynamic angles 153 Coordinate System Transformations 173.1 Problem Statement 173.2 Transformations 183.2.1 Definitions 183.2.2 Direction cosines 183.2.3 Euler angles 213.2.4 Euler parameters 253.3 Transformations of Systems of Equations 263.4 Customs and Conventions 273.4.1 Names of Euler angles 273.4.2 Principal values of Euler angles 274 Rotating Coordinate Systems 314.1 General 314.2 Direction Cosines 344.3 Euler Angles 344.4 Euler Parameters 364.5 Customs and Conventions 384.5.1 Angular velocity components 385 Inertial Accelerations 435.1 General 435.2 Inertial Acceleration of a Point 435.2.1 Arbitrary moving reference frame 435.2.2 Earth-centered moving reference frame 465.2.3 Earth-fixed moving reference frame 465.3 Inertial Acceleration of a Mass 475.3.1 Linear acceleration 485.3.2 Rotational acceleration 495.4 States 535.5 Customs and Conventions 535.5.1 Linear velocity components 535.5.2 Angular velocity components 545.5.3 Forces 545.5.4 Moments 565.5.5 Groupings 566 Forces and Moments 596.1 General 596.1.1 Assumptions 596.1.2 State variables 606.1.3 State rates 606.1.4 Flight controls 606.1.5 Independent variables 626.2 Non-Dimensionalization 626.3 Non-Dimensional Coefficient Dependencies 636.3.1 General 636.3.2 Altitude dependencies 646.3.3 Velocity dependencies 646.3.4 Angle-of-attack dependencies 646.3.5 Sideslip dependencies 666.3.6 Angular velocity dependencies 686.3.7 Control dependencies 696.3.8 Summary of dependencies 706.4 The Linear Assumption 716.5 Tabular Data 716.6 Customs and Conventions 727 Equations of Motion 757.1 General 757.2 Body-Axis Equations 757.2.1 Body-axis force equations 757.2.2 Body-axis moment equations 767.2.3 Body-axis orientation equations (kinematic equations) 777.2.4 Body-axis navigation equations 777.3 Wind-Axis Equations 787.3.1 Wind-axis force equations 787.3.2 Wind-axis orientation equations (kinematic equations) 807.3.3 Wind-axis navigation equations 817.4 Steady-State Solutions 817.4.1 General 817.4.2 Special cases 837.4.3 The trim problem 888 Linearization 938.1 General 938.2 Taylor Series 948.3 Nonlinear Ordinary Differential Equations 958.4 Systems of Equations 958.5 Examples 978.5.1 General 978.5.2 A kinematic equation 998.5.3 A moment equation 1008.5.4 A force equation 1038.6 Customs and Conventions 1058.6.1 Omission of Δ 1058.6.2 Dimensional derivatives 1058.6.3 Added mass 1058.7 The Linear Equations 1068.7.1 Linear equations 1068.7.2 Matrix forms of the linear equations 1089 Solutions to the Linear Equations 1139.1 Scalar Equations 1139.2 Matrix Equations 1149.3 Initial Condition Response 1159.3.1 Modal analysis 1159.4 Mode Sensitivity and Approximations 1209.4.1 Mode sensitivity 1209.4.2 Approximations 1239.5 Forced Response 1249.5.1 Transfer functions 1249.5.2 Steady-state response 12510 Aircraft Flight Dynamics 12710.1 Example: Longitudinal Dynamics 12710.1.1 System matrices 12710.1.2 State transition matrix and eigenvalues 12710.1.3 Eigenvector analysis 12910.1.4 Longitudinal mode sensitivity and approximations 13210.1.5 Forced response 13710.2 Example: Lateral–Directional Dynamics 14010.2.1 System matrices 14010.2.2 State transition matrix and eigenvalues 14010.2.3 Eigenvector analysis 14210.2.4 Lateral–directional mode sensitivity and approximations 14410.2.5 Forced response 14811 Flying Qualities 15111.1 General 15111.1.1 Method 15211.1.2 Specifications and standards 15511.2 MIL-F-8785C Requirements 15611.2.1 General 15611.2.2 Longitudinal flying qualities 15711.2.3 Lateral–directional flying qualitities 15812 Automatic Flight Control 16912.1 Simple Feedback Systems 17012.1.1 First-order systems 17012.1.2 Second-order systems 17212.1.3 A general representation 17712.2 Example Feedback Control Applications 17812.2.1 Roll mode 17812.2.2 Short-period mode 18412.2.3 Phugoid 18812.2.4 Coupled roll–spiral oscillation 19813 Trends in Automatic Flight Control 20913.1 Overview 20913.2 Dynamic Inversion 21013.2.1 The controlled equations 21213.2.2 The kinematic equations 21513.2.3 The complementary equations 22113.3 Control Allocation 22413.3.1 Background 22413.3.2 Problem statement 22513.3.3 Optimality 23113.3.4 Sub-optimal solutions 23213.3.5 Optimal solutions 23513.3.6 Near-optimal solutions 241Problems 243References 244A Example Aircraft 247Reference 253B Linearization 255B.1 Derivation of Frequently Used Derivatives 255B.2 Non-dimensionalization of the Rolling Moment Equation 257B.3 Body Axis Z-Force and Thrust Derivatives 258B.4 Non-dimensionalization of the Z-Force Equation 260C Derivation of Euler Parameters 263D Fedeeva's Algorithm 269Reference 272E MATLAB Commands Used in the Text 273E.1 Using MATLAB 273E.2 Eigenvalues and Eigenvectors 274E.3 State-Space Representation 274E.4 Transfer Function Representation 275E.5 Root Locus 277E.6 MATLAB® Functions (m-files) 277E.6.1 Example aircraft 278E.6.2 Mode sensitivity matrix 278E.6.3 Cut-and-try root locus gains 278E.7 Miscellaneous Applications and Notes 280E.7.1 Matrices 280E.7.2 Commands used to create Figures 10.2 and 10.3 281Index 283