Preface... xv Preface to the second edition... xvii Preface to the first edition... xix Acknowledgements... xxi Nomenclature...

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2 Contents Preface... xv Preface to the second edition... xvii Preface to the first edition... xix Acknowledgements... xxi Nomenclature... xxiii CHAPTER 1 Introduction Overview Flying and handling qualities General considerations Basic control-response relationships Mathematical models Stability and control Stability and control augmentation Aircraft equations of motion Aerodynamics Small perturbations Computers Analytical computers Flight control computers Computer software tools Summary References Sources CHAPTER 2 Systems of Axes and Notation Earth axes Aircraft body fixed axes Generalised body axes Aerodynamic, wind, or stability axes Perturbation variables Angular relationships in symmetric flight Choice of axes Euler angles and aircraft attitude Axes transformations Linear quantities transformation Angular velocities transformation v

3 vi Contents 2.5 Aircraft reference geometry Wing area Mean aerodynamic chord Standard mean chord Aspect ratio Location of centre of gravity Tail moment arm and tail volume ratio Fin moment arm and fin volume ratio Controls notation Aerodynamic controls Engine control Aerodynamic reference centres References Problems CHAPTER 3 Static Equilibrium and Trim Trim equilibrium Preliminary considerations Conditions for stability Degree of longitudinal stability Variation in stability The pitching moment equation Simple development of the pitching moment equation Elevator angle to trim Condition for longitudinal static stability Longitudinal static stability Controls-fixed stability Controls-free stability Summary of longitudinal static stability Lateral-directional static stability Lateral static stability Directional static stability Calculation of aircraft trim condition Defining the trim condition Elevator angle to trim Controls-fixed static stability AeroTrim : A Mathcad trim program References Sources Problems CHAPTER 4 The Equations of Motion The equations of motion for a rigid symmetric aircraft The components of inertial acceleration... 73

4 Contents vii The generalised force equations The generalised moment equations Perturbation forces and moments The linearised equations of motion Gravitational terms Aerodynamic terms Aerodynamic control terms Power terms The equations of motion for small perturbations The decoupled equations of motion The longitudinal equations of motion The lateral-directional equations of motion Alternative forms of the equations of motion The dimensionless equations of motion The equations of motion in state space form The equations of motion in American normalised form References Problems CHAPTER 5 The Solution of the Equations of Motion Methods of solution Cramer s rule Aircraft response transfer functions The longitudinal response transfer functions The lateral-directional response transfer functions Response to controls Acceleration response transfer functions The state-space method The transfer function matrix The longitudinal transfer function matrix The lateral-directional transfer function matrix Response in terms of state description State-space model augmentation Height response transfer function Incidence and sideslip response transfer functions Flight path angle response transfer function Addition of engine dynamics References Problems CHAPTER 6 Longitudinal Dynamics Response to controls The characteristic equation

5 viii Contents 6.2 The dynamic stability modes The short-period pitching oscillation The phugoid Reduced-order models The short-period mode approximation The phugoid mode approximation Frequency response The Bode diagram Interpretation of the Bode diagram Flying and handling qualities Mode excitation References Problems CHAPTER 7 Lateral-Directional Dynamics Response to controls The characteristic equation The dynamic stability modes The roll subsidence mode The spiral mode The dutch roll mode Reduced order models The roll mode approximation The spiral mode approximation The dutch roll mode approximation Frequency response Flying and handling qualities Mode excitation References Problems CHAPTER 8 Manoeuvrability Introduction Manoeuvring flight Stability Aircraft handling The steady symmetric manoeuvre The steady pull-up manoeuvre The pitching moment equation Longitudinal manoeuvre stability Controls-fixed stability Normal acceleration response to elevator Controls-free stability Elevator deflection and stick force

6 Contents ix 8.5 Aircraft dynamics and manoeuvrability Aircraft with stability augmentation Stick force Stick force per g References CHAPTER 9 Stability Introduction A definition of stability Non-linear systems Static and dynamic stability Control The characteristic equation The Routh-Hurwitz stability criterion Special cases The stability quartic Interpretation of conditional instability Interpretation of the coefficient E Graphical interpretation of stability Root mapping on the s-plane References Problems CHAPTER 10 Flying and Handling Qualities Introduction Stability Short term dynamic models Controlled motion and motion cues The longitudinal reduced order model The thumb print criterion Incidence lag Flying qualities requirements Aircraft role Aircraft classification Flight phase Levels of flying qualities Flight envelopes Pilot opinion rating Longitudinal flying qualities requirements Longitudinal static stability Longitudinal dynamic stability Longitudinal manoeuvrability Control anticipation parameter

7 x Contents 10.8 Lateral-directional flying qualities requirements Steady lateral-directional control Lateral-directional dynamic stability Lateral-directional manoeuvrability and response Flying qualities requirements on the s-plane Longitudinal modes Lateral-directional modes References Problems CHAPTER 11 Command and Stability Augmentation Introduction The control law Safety Stability augmentation system architecture Scope Augmentation system design Closed-loop system analysis The root locus plot Longitudinal stability augmentation Lateral-directional stability augmentation The pole placement method Command augmentation Command path filter design The frequency response of a phase compensation filter Introduction of a command path filter to the system state model References Problems CHAPTER 12 Aerodynamic Modelling Introduction Quasi-static derivatives Derivative estimation Calculation Wind tunnel measurement Flight test measurement The effects of compressibility Some useful definitions Aerodynamic models Subsonic lift, drag, and pitching moment Supersonic lift, drag, and pitching moment Summary Limitations of aerodynamic modelling References

8 Contents xi CHAPTER 13 Aerodynamic Stability and Control Derivatives Introduction Longitudinal aerodynamic stability derivatives Preliminary considerations Aerodynamic force and moment components Force derivatives due to velocity perturbations Moment derivatives due to velocity perturbations Derivatives due to a pitch velocity perturbation Derivatives due to acceleration perturbations Lateral-directional aerodynamic stability derivatives Preliminary considerations Derivatives due to sideslip Derivatives due to rate of roll Derivatives due to rate of yaw Aerodynamic control derivatives Derivatives due to elevator Derivatives due to aileron Derivatives due to rudder North American derivative coefficient notation The longitudinal aerodynamic derivative coefficients The lateral-directional aerodynamic derivative coefficients Comments References Problems CHAPTER 14 Flight in a Non-steady Atmosphere The influence of atmospheric disturbances on flying qualities Methods of evaluation Atmospheric disturbances Steady wind Wind shear Discrete gusts Continuous turbulence Extension of the linear aircraft equations of motion Disturbed body incidence and sideslip The longitudinal equations of motion The lateral-directional equations of motion The equations of motion for aircraft with stability augmentation Turbulence modelling The von Kármán model The Dryden model Comparison of the von Kármán and Dryden models Turbulence scale length Turbulence intensity

9 xii Contents 14.6 Discrete gusts The 1-cosine gust Determination of maximum gust velocity and horizontal length Aircraft response to gusts and turbulence Variance, power spectral density, and white noise Spatial and temporal equivalence Synthetic turbulence Aircraft response to gusts Aircraft response to turbulence References CHAPTER 15 Coursework Studies Introduction Working the assignments Reporting Assignment 1: Stability augmentation of the North American X-15 hypersonic research aeroplane The aircraft model The solution tasks Assignment 2: The stability and control characteristics of a civil transport aeroplane with relaxed longitudinal static stability The aircraft model The governing trim equations Basic aircraft stability and control analysis Relaxing the stability of the aircraft Relaxed stability aircraft stability and control analysis Evaluation of results Postscript Assignment 3: Lateral-directional handling qualities design for the Lockheed F-104 Starfighter aircraft The aircraft model Lateral-directional autostabiliser structure Basic aircraft stability and control analysis Augmenting the stability of the aircraft Inclusion of the washout filter in the model Designing the aileron-rudder interlink gain Assignment 4: Analysis of the effects of Mach number on the longitudinal stability and control characteristics of the LTV A7-A Corsair aircraft The aircraft model The assignment tasks

10 Contents xiii 15.6 Assignment 5: The design of a longitudinal primary flight control system for an advanced-technology UAV The aircraft model The design requirements The assignment tasks References Appendices 1 AeroTrim: A Symmetric Trim Calculator for Subsonic Flight Conditions Definitions of Aerodynamic Stability and Control Derivatives Aircraft Response Transfer Functions Referred to Aircraft Body Axes Units, Conversions, and Constants A Very Short Table of Laplace Transforms The Dynamics of a Linear Second Order System North American Aerodynamic Derivative Notation Approximate Expressions for the Dimensionless Aerodynamic Stability and Control Derivatives Transformation of Aerodynamic Stability Derivatives from a Body Axes Reference to a Wind Axes Reference Transformation of the Moments and Products of Inertia from a Body Axes Reference to a Wind Axes Reference The Root Locus Plot Index