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Flight Dynamics,Simulation, and ControlFor Rigid andFlexible Aircraf t

Boca Raton London New York

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Flight Dynamics,Simulation, and Control

Ranjan Vepa

For Rigid andFlexible Aircraf t

MATLAB is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This books use or discussion of MATLAB soft-ware or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB software.

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To my teachers, Hans Wagner, Horst Leipholz,

HoltAshley, Art Bryson and Geoff Hancock

vii

Contents

List of Acronyms ................................................................................................ xviiPreface ................................................................................................................... xixAuthor ................................................................................................................. xxiii

1 Introduction to Flight Vehicles ....................................................................11.1 Introduction ...........................................................................................11.2 Components of an Aeroplane ..............................................................1

1.2.1 Fuselage .....................................................................................11.2.2 Wings .........................................................................................21.2.3 Tail Surfaces or Empennage ...................................................21.2.4 Landing Gear ............................................................................3

1.3 Basic Principles of Flight ......................................................................31.3.1 Forces Acting on an Aeroplane ..............................................31.3.2 Drag and Its Reduction ...........................................................51.3.3 Aerodynamically Conforming Shapes: Streamlining ........61.3.4 Stability and Balance ...............................................................6

1.4 Flying Control Surfaces: Elevator, Ailerons and Rudder ................71.4.1 Flaps, High-Lift and Flow Control Devices ....................... 101.4.2 Introducing Boundary Layers .............................................. 121.4.3 Spoilers .................................................................................... 15

1.5 Pilots Controls: The Throttle, the Control Column andYoke,the Rudder Pedals and the Toe Brakes .......................... 16

1.6 Modes of Flight .................................................................................... 161.6.1 Static and In-Flight Stability Margins ................................. 18

1.7 Power Plant .......................................................................................... 191.7.1 Propeller-Driven Aircraft ..................................................... 191.7.2 Jet Propulsion ......................................................................... 19

1.8 Avionics, Instrumentation and Systems .......................................... 201.9 Geometry of Aerofoils and Wings .................................................... 21

1.9.1 Aerofoil Geometry ................................................................. 211.9.2 Chord Line .............................................................................. 211.9.3 Camber ....................................................................................221.9.4 Leading and Trailing Edges .................................................221.9.5 Specifying Aerofoils ..............................................................231.9.6 Equations Defining Mean Camber Line ............................. 241.9.7 Aerofoil Thickness Distributions ........................................ 241.9.8 Wing Geometry ...................................................................... 26

Chapter Highlights ........................................................................................30

viii Contents

Exercises ..........................................................................................................30Answers to Selected Exercises ..................................................................... 32References ....................................................................................................... 32

2 Basic Principles Governing Aerodynamic Flows ..................................332.1 Introduction .........................................................................................332.2 Continuity Principle ...........................................................................33

2.2.1 Streamlines and Stream Tubes ............................................342.3 Bernoullis Principle ............................................................................342.4 Laminar Flows and Boundary Layers .............................................342.5 Turbulent Flows ...................................................................................352.6 Aerodynamics of Aerofoils and Wings ...........................................35

2.6.1 Flow around an Aerofoil .......................................................362.6.2 Mach Number and Subsonic and Supersonic Flows ........36

2.7 Properties of Air in the Atmosphere ................................................382.7.1 Composition of the Atmosphere: The Troposphere,

Stratosphere, Mesosphere, Ionosphere and Exosphere ....382.7.2 Air Density ............................................................................. 392.7.3 Temperature ............................................................................ 392.7.4 Pressure ................................................................................... 392.7.5 Effects of Pressure and Temperature ..................................402.7.6 Viscosity ..................................................................................402.7.7 Bulk Modulus of Elasticity ................................................... 412.7.8 Temperature Variations with Altitude: The Lapse Rate ... 41

2.8 International Standard Atmosphere (from ESDU 77021, 1986) .... 412.9 Generation of Lift and Drag ..............................................................452.10 Aerodynamic Forces and Moments ................................................. 47

2.10.1 Aerodynamic Coefficients ....................................................502.10.2 Aerofoil Drag ..........................................................................532.10.3 Aircraft Lift Equation and Lift Curve Slope ......................542.10.4 Centre of Pressure .................................................................. 572.10.5 Aerodynamic Centre ............................................................. 572.10.6 Pitching Moment Equation ...................................................582.10.7 Elevator Hinge Moment Coefficient ....................................60

Chapter Highlights ........................................................................................ 61Exercises ..........................................................................................................63Answers to Selected Exercises .....................................................................65References .......................................................................................................66

3 Mechanics of Equilibrium Flight .............................................................. 673.1 Introduction ......................................................................................... 673.2 Speeds of Equilibrium Flight ............................................................ 713.3 Basic Aircraft Performance ................................................................ 73

3.3.1 Optimum Flight Speeds ........................................................ 733.4 Conditions for Minimum Drag ......................................................... 76

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3.5 Stability in the Vicinity of the Minimum Drag Speed ..................773.6 Range and Endurance Estimation ....................................................773.7 Trim ....................................................................................................... 793.8 Stability of Equilibrium Flight .......................................................... 823.9 Longitudinal Static Stability ..............................................................84

3.9.1 Neutral Point (Stick-Fixed) ....................................................853.9.2 Neutral Point (Stick-Free) ......................................................85

3.10 Manoeuvrability ..................................................................................863.10.1 Pull-Out Manoeuvre .............................................................863.10.2 Manoeuvre Margin: Stick-Fixed .......................................... 873.10.3 Manoeuvre Margin: Stick-Free ............................................ 89

3.11 Lateral Stability and Stability Criteria ............................................. 893.12 Experimental Determination of Aircraft Stability Margins ......... 913.13 Summary of Equilibrium- and Stability-Related Equations......... 92Chapter Highlights ........................................................................................ 95Exercises .......................................................................................................... 97Answers to Selected Exercises ................................................................... 101References ..................................................................................................... 102

4 Aircraft Non-Linear Dynamics: Equations of Motion ........................ 1034.1 Introduction ....................................................................................... 1034.2 Aircraft Dynamics ............................................................................ 1034.3 Aircraft Motion in a 2D Plane ......................................................... 1044.4 Moments of Inertia ............................................................................ 1094.5 Eulers Equations and the Dynamics of Rigid Bodies ................. 1114.6 Description of the Attitude or Orientation .................................... 1154.7 Aircraft Equations of Motion .......................................................... 1194.8 Motion-Induced Aerodynamic Forces and Moments .................. 1224.9 Non-Linear Dynamics of AircraftMotion

andtheStabilityAxes....................................................................... 1254.9.1 Equations of Motion in Wind Axis Coordinates,

VT, and ............................................................................. 1304.9.2 Reduced-Order Modelling: The Short Period

Approximations ................................................................... 1354.10 Trimmed Equations of Motion ........................................................ 137

4.10.1 Non-Linear Equations of Perturbed Motion .................... 1394.10.2 Linear Equations of Motion ................................................ 140

Chapter Highlights ...................................................................................... 141Exercises ........................................................................................................ 142References ..................................................................................................... 143

5 Small Perturbations and the Linearised, Decoupled Equations of Motion ...................................................................................................... 1455.1 Introduction ....................................................................................... 1455.2 Small Perturbations and Linearisations ........................................ 145

x Contents

5.3 Linearising the Aerodynamic Forces andMoments: Stability Derivative Concept ........................................................................... 148

5.4 Direct Formulation in the Stability Axis ....................................... 1525.5 Decoupled Equations of Motion ..................................................... 158

5.5.1 Case I: Motion in the Longitudinal Plane of Symmetry ...1585.5.2 Case II: Motion in the Lateral Direction,

Perpendicular to the Plane of Symmetry ......................... 1605.6 Decoupled Equations of Motion in terms of theStability

Axis Aerodynamic Derivatives ....................................................... 1615.7 Addition of Aerodynamic Controls and Throttle ........................ 1645.8 Non-Dimensional Longitudinal and Lateral Dynamics ............. 1735.9 Simplified State-Space Equations of Longitudinal

andLateral Dynamics ...................................................................... 1795.10 Simplified Concise Equations of Longitudinal and Lateral

Dynamics ........................................................................................... 181Chapter Highlights ...................................................................................... 182Exercises ........................................................................................................ 182Reference ....................................................................................................... 184

6 Longitudinal and Lateral Linear Stability and Control ..................... 1856.1 Introduction ....................................................................................... 1856.2 Dynamic and Static Stability ........................................................... 185

6.2.1 Longitudinal Stability Analysis ......................................... 1856.2.2 Lateral Dynamics and Stability ......................................... 196

6.3 Modal Description of Aircraft Dynamics and the Stability ofthe Modes ...................................................................................... 2016.3.1 SlowFast Partitioning of the Longitudinal

Dynamics .............................................................................. 2016.3.2 SlowFast Partitioning of the Lateral Dynamics ............. 2046.3.3 Summary of Longitudinal and Lateral Modal

Equations ............................................................................... 2136.3.3.1 Phugoid or Long Period ...................................... 2136.3.3.2 Short Period ........................................................... 2146.3.3.3 Third Oscillatory Mode ....................................... 2146.3.3.4 Roll Subsidence ..................................................... 2156.3.3.5 Dutch Roll .............................................................. 2156.3.3.6 Spiral ...................................................................... 215

6.4 Aircraft Lift and Drag Estimation .................................................. 2166.4.1 Fuselage Lift and Moment Coefficients ............................ 2196.4.2 WingTail Interference Effects ........................................... 2206.4.3 Estimating the Wings Maximum Lift Coefficient .......... 2206.4.4 Drag Estimation ................................................................... 221

6.5 Estimating the Longitudinal Aerodynamic Derivatives ............2256.6 Estimating the Lateral Aerodynamic Derivatives ........................ 232

6.6.1 Perturbation Analysis of Trimmed Flight ........................238

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6.6.2 Perturbation Analysis of Longitudinal Trimmed Flight ......................................................................................238

6.6.3 Perturbation Analysis of Lateral Trimmed Flight........... 2436.6.3.1 Control Settings for Steady Sideslip .................. 2436.6.3.2 Control Settings for Turn Coordination

andBanking .......................................................... 2456.6.4 Perturbations of Coupled Trimmed Flight.......................2506.6.5 Simplified Analysis of Complex Manoeuvres:

TheSidestep Manoeuvre ....................................................250Chapter Highlights ...................................................................................... 252Exercises ........................................................................................................255Answers to Selected Exercises ................................................................... 263References .....................................................................................................264

7 Aircraft Dynamic Response: Numerical Simulation andNon-Linear Phenomenon .................................................................. 2657.1 Introduction ....................................................................................... 2657.2 Longitudinal and Lateral Modal Equations.................................. 2657.3 Methods of Computing Aircraft Dynamic Response.................. 269

7.3.1 Laplace Transform Method ................................................ 2707.3.2 Aircraft Response Transfer Functions .............................. 2707.3.3 Direct Numerical Integration ............................................. 275

7.4 System Block Diagram Representation ..........................................2777.4.1 Numerical Simulation of Flight Using

MATLAB/Simulink .........................................................2837.5 Atmospheric Disturbance: Deterministic Disturbances .............2847.6 Principles of Random Atmospheric Disturbance Modelling ...... 291

7.6.1 White Noise: Power Spectrum and Autocorrelation ...... 2917.6.2 Linear Time-Invariant System with Stochastic

Process Input ........................................................................ 2937.7 Application to Atmospheric Turbulence Modelling .................... 2967.8 Aircraft Non-Linear Dynamic Response Phenomenon .............. 299

7.8.1 Aircraft Dynamic Non-Linearities and Their Analysis ....3027.8.2 High-Angle-of-Attack Dynamics and Its

Consequences .......................................................................3057.8.3 Post-Stall Behaviour.............................................................3067.8.4 Tumbling and Autorotation................................................ 3077.8.5 Lateral Dynamic Phenomenon .......................................... 3077.8.6 Flat Spin and Deep Spin .....................................................3087.8.7 Wing Drop, Wing Rock and Nose Slice ............................3097.8.8 Fully Coupled Motions: The Falling Leaf ........................3097.8.9 Regenerative Phenomenon ................................................. 311

Chapter Highlights ...................................................................................... 312Exercises ........................................................................................................ 312References .....................................................................................................330

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8 Aircraft Flight Control ..............................................................................3338.1 Automatic Flight Control Systems: An Introduction ...................3338.2 Functions of a Flight Control System .............................................3368.3 Integrated Flight Control System ....................................................347

8.3.1 Guidance System: Interfacing to the Automatic Flight Control System .......................................................... 352

8.3.2 Flight Management System ................................................3538.4 Flight Control System Design .........................................................354

8.4.1 Block Diagram Algebra ....................................................... 3578.4.2 Return Difference Equation ...............................................3608.4.3 Laplace Transform ............................................................... 3628.4.4 Stability of Uncontrolled and Controlled Systems ......... 3628.4.5 Rouths Tabular Method ......................................................3658.4.6 Frequency Response ............................................................3668.4.7 Bode Plots .............................................................................. 3698.4.8 Nyquist Plots ........................................................................ 3698.4.9 Stability in the Frequency Domain ................................... 3698.4.10 Stability Margins: The Gain and Phase Margins ............ 3708.4.11 Mapping Complex Functions and Nyquist Diagrams ... 3708.4.12 Time Domain: The State Variable Representation .......... 3718.4.13 Solution of the State Equations and the

Controllability Condition ................................................... 3738.4.14 State-Space and Transfer Function Equivalence ............. 3758.4.15 Transformations of State Variables .................................... 3768.4.16 Design of a Full-State Variable Feedback Control Law .... 3778.4.17 Root Locus Method ............................................................. 3798.4.18 Root Locus Principle ........................................................... 3818.4.19 Root Locus Sketching Procedure ...................................... 3818.4.20 Producing a Root Locus Using MATLAB ......................3858.4.21 Application of the Root Locus Method: Unity

Feedback with a PID Control Law .................................... 3878.5 Optimal Control of Flight Dynamics ............................................. 390

8.5.1 Compensating Full-State Feedback: Observers and Compensators ....................................................................... 391

8.5.2 Observers for Controller Implementation ........................ 3928.5.3 Observer Equations ............................................................. 3938.5.4 Special Cases: The Full- and First-Order Observers ....... 3938.5.5 Solving the Observer Equations ........................................ 3958.5.6 Luenberger Observer ........................................................... 3968.5.7 Optimisation Performance Criteria................................... 3968.5.8 Good Handling Domains of Modal Response

Parameters ............................................................................ 3978.5.9 CooperHarper Rating Scale .............................................400

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8.6 Application to the Design of Stability Augmentation Systems and Autopilots .................................................................... 4018.6.1 Design of a Pitch Attitude Autopilot Using PID

Feedback and the Root Locus Method ............................. 4018.6.2 Example of Pitch Attitude Autopilot Design for the

Lockheed F104 by the Root Locus Method ........................4058.6.3 Example of Pitch Attitude Autopilot Design,

Including a Stability Augmentation Inner Loop, bythe Root Locus Method .................................................405

8.6.4 Design of an Altitude Acquire-and-Hold Autopilot .......4088.6.5 Design of a Lateral Roll Attitude Autopilot ..................... 4168.6.6 Design of a Lateral Yaw Damper ....................................... 4198.6.7 Design of a Lateral Heading Autopilot ............................. 4218.6.8 Turn Coordination with Sideslip Suppression ................4238.6.9 Application of Optimal Control to Lateral Control

Augmentation Design .........................................................4258.7 Performance Assessment of a Command or Control

Augmentation System ......................................................................4288.8 Linear Perturbation Dynamics Flight Control Law Design

by Partial Dynamic Inversion .........................................................4298.8.1 Design Example of a Longitudinal Autopilot Based

on Partial Dynamic Inversion ............................................4348.9 Design of Controllers for Multi-Input Systems ............................ 437

8.9.1 Design Example of a Lateral Turn Coordination Using the Partial Inverse Dynamics Method .................. 437

8.9.2 Design Example of the Simultaneously Operating Auto-Throttle and Pitch Attitude Autopilot .................... 439

8.9.3 Two-Input Lateral Attitude Control Autopilot ................ 4418.10 Decoupling Control and Its Application: Longitudinal

andLateral Dynamics Decoupling Control ..................................4468.11 Full Aircraft Six-DOF Flight Controller Design by Dynamic

Inversion .............................................................................................4488.11.1 Control Law Synthesis ........................................................ 4598.11.2 Example of Linear Control Law Synthesis

byPartialDynamic Inversion: The Fully Propulsion-Controlled MD11 Aircraft ............................. 462

8.11.3 Example of Quasi-Non-Linear Control Law Synthesis by Partial Dynamic Inversion: The Fully Propulsion-Controlled MD11 Aircraft .............................464

8.11.4 Full Aircraft Orientation Control Law Design byDynamic Inversion .........................................................468

8.11.5 Aircraft Flight Control Synthesis in Wind Axes Coordinates, VT, and ..................................................... 471

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Chapter Highlights ...................................................................................... 474Exercises ........................................................................................................ 475Answers to Selected Exercises ...................................................................484References .....................................................................................................485

9 Piloted Simulation and Pilot Modelling ............................................... 4879.1 Introduction ....................................................................................... 4879.2 Piloted Flight Simulation .................................................................488

9.2.1 Full Moving-Base Simulation: The Stewart Platform ..... 4919.2.2 Kinematics of Motion Systems ........................................... 4929.2.3 Principles of Motion Control .............................................. 4939.2.4 Motion Cueing Concepts .................................................... 493

9.3 Principles of Human Pilot Physiological Modelling .................... 4979.3.1 Auricular and Ocular Sensors ........................................... 498

9.4 Human Physiological Control Mechanisms ................................. 5029.4.1 Crossover Model ..................................................................5049.4.2 NealSmith Criterion .......................................................... 5079.4.3 Pilot-Induced Oscillations ..................................................5089.4.4 PIO Categories ......................................................................5099.4.5 PIOs Classified under Small Perturbation Modes .......... 5109.4.6 Optimal Control Models ..................................................... 5109.4.7 Generic Human Pilot Modelling ....................................... 5119.4.8 PilotVehicle Simulation ..................................................... 515

9.5 Spatial Awareness ............................................................................. 5169.5.1 Visual Displays ..................................................................... 5179.5.2 Animation and Visual Cues ............................................... 5189.5.3 Visual Illusions ..................................................................... 520

Chapter Highlights ...................................................................................... 522Exercises ........................................................................................................ 522References ..................................................................................................... 528

10 Flight Dynamics of Elastic Aircraft ........................................................ 52910.1 Introduction ....................................................................................... 52910.2 Flight Dynamics of Flexible Aircraft.............................................. 52910.3 NewtonEuler Equations of a Rigid Aircraft ................................53010.4 Lagrangian Formulation .................................................................. 536

10.4.1 Generalised Coordinates and Holonomic Dynamic Systems .................................................................................. 537

10.4.2 Generalised Velocities ......................................................... 53710.4.3 Virtual Displacements and Virtual Work ........................ 53810.4.4 Principle of Virtual Work .................................................... 53910.4.5 EulerLagrange Equations .................................................54010.4.6 Potential Energy and the Dissipation Function ..............54310.4.7 EulerLagrange Equations of Motion

inQuasi-Coordinates ..........................................................545

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10.4.8 Transformation to Centre of Mass Coordinates ..........55010.4.9 Application of the Lagrangian Method to a Rigid

Aircraft ............................................................................... 55310.5 Vibration of Elastic Structures in a Fluid Medium .................... 559

10.5.1 Effects of Structural Flexibility in Aircraft Aeroelasticity ....................................................................563

10.5.2 Wing Divergence ..............................................................56310.5.3 Control Reversal ...............................................................56510.5.4 Wing Flutter ......................................................................56610.5.5 Aerofoil Flutter Analysis ................................................. 567

10.6 Unsteady Aerodynamics of an Aerofoil ...................................... 57510.7 EulerLagrange Formulation of Flexible Body Dynamics ........ 58210.8 Application to an Aircraft with a Flexible Wing Vibrating

in Bending and Torsion .................................................................. 59510.8.1 Longitudinal Small Perturbation Equations

withFlexibility .................................................................. 59510.8.2 Lateral Small Perturbation Equations with Flexibility ....... 599

10.9 Kinetic and Potential Energies of the Whole Elastic Aircraft... 60110.9.1 Kinetic Energy .................................................................. 60110.9.2 Simplifying the General Expression ..............................60410.9.3 Mean Axes .........................................................................60410.9.4 Kinetic Energy in terms of Modal Amplitudes ...........60510.9.5 Tisserand Frame ............................................................... 607

10.10 EulerLagrange Matrix Equations of a Flexible Body inQuasi-Coordinates ..................................................................... 611

10.11 Slender Elastic Aircraft................................................................... 61410.12 Aircraft with a Flexible Flat Body Component ........................... 618

10.12.1 Elastic Large Aspect Ratio Flying Wing Model............. 61810.12.2 Flexible Aircraft in Roll ................................................... 620

10.13 Estimating the Aerodynamic Derivatives: Modified Strip Analysis ............................................................................................ 622

Chapter Highlights ...................................................................................... 627Exercises ........................................................................................................ 627Answers to Selected Exercises ...................................................................648References .....................................................................................................649

Index .............................................................................................................. 651

xvii

List of Acronyms

AC Aerodynamic centreADF Automatic direction findingamc Aerodynamic mean chordAR Aspect ratioBDF Backward difference formulaCG Centre of gravityCH CooperHarper (rating)CM Centre of massCP Centre of pressureDME Distance measuring equipmentEFIS Electronic flight information systemEIS Electronic information systemEPR Engine pressure ratioFBW Fly by wireFCU Flight control unitFDAU Flight data acquisition unitFMGS Flight management and guidance systemGPS Global positioning systemHSI Horizontal situation indicatorHUD Head-up displaysIAS Indicated airspeedIFS In-flight simulationILS Instrument landing systemINS Inertial navigation systemNDF Numerical differentiation formulaNP Neutral pointPD Proportion derivativePID Proportional, integral, derivativePIO Pilot-induced oscillationpsfc Power-specific fuel consumptionRMI Radio magnetic indicatorSISO Single input, singe outputTCAS Traffic collision avoidance systemTR Trapezoidal ruleTsfc Thrust-specific fuel consumptionVHF Very high frequencyVOR VHF omni-range or vestibulo-ocular reflex

xix

Preface

In the last decade, we have seen a phenomenal increase in air travel to phenomenal levels. A plethora of low-cost airlines have made it possible for the common man to travel between continents at relatively reasonable fares. This has also led to the design of newer energy-efficient aircraft incorporat-ing the principles of feedback control. These aircraft have generally tended to be lighter and more flexible because of the use of composite structures and other smart materials. It therefore becomes important to consider the aircraft not as a rigid body, as has been done traditionally in the past, but as an inher-ently flexible body. Such considerations will require a revision of a number of traditional concepts, although many of them can be easily adapted to the flexible aircraft.

This book addresses the core issues involved in the dynamic modelling, simulation and control of a selection of aircraft. The principles of model-ling and control could be applied both to traditional rigid aircraft as well as more modern flexible aircraft. A primary feature of this book is that it brings together a range of diverse topics relevant to the understanding of flight dynamics, its regulation and control and the design of flight control systems and flight simulators.

This book will help the reader understand the methods of modelling both rigid and flexible aircraft for controller design application as well as gain a basic understanding of the processes involved in the design of control systems and regulators. It will also serve as a useful guide to study the simu-lation of flight dynamics for implementing monitoring systems based on the estimation of internal system variables from measurements of observable system variables.

The book brings together diverse topics in flight mechanics, aeroelasticity and automatic controls. It would be useful to designers of hybrid flight con-trol systems that involve advanced composite structurebased components in the wings, fuselage and control surfaces. The distinctive feature of this book is that it introduces case studies of practical control laws for several modern aircraft and deals with the use of non-linear model-based tech-niques and their applications to flight control.

Chapter 1 begins with an introduction and reviews the configuration of a typical aircraft and its components. Chapter 2 deals with the basic principles governing aerodynamic flows. Chapter 3 covers the mechanics of equilib-rium flight and describes static equilibrium, trimmed steady level flight, the analysis of the static stability of an aircraft, static margins stick-fixed and stick-free, modelling of control-surface hinge moments and the estimation of the elevator angle for trim. Basic concepts of stability based on disturbances to one parameter alone are discussed. The effects of a change in the angle of

xx Preface

attack on the pitching moment and its application to stability assessment are discussed. Also considered are steady flight at an angle to the horizontal and the definition of flight path, incidence and pitch angles and the heading, yaw and sideslip angles. The assessment of manoeuvrability and the application of margins required for a steady pull-out from a dive are also introduced.

Chapter 4 is dedicated to the development of the non-linear equations of motion of an aircraft, including simple two-dimensional dynamic models, and the development of the aircrafts equations of motion in three dimen-sions. The general Euler equations of rigid body and the definition and estimation of moments of inertia matrix are discussed. The definitions of motion-induced aerodynamic forces and moments and the need for vari-ous reference axes that are fixed in space, fixed to the body and fixed in the wind as well as the definition of stability axes are clearly explained. The non-linear dynamics of aircraft motion in the stability axes is derived both in terms of body axis degrees of freedom and wind axis variables. The concept of non-linear reduced order modelling is introduced, and the short period approximation is discussed. Finally, the trimmed equations of motion as well as the non-linear perturbation equations of motion are derived. The concept of linearisation is also introduced, and the linear equations of air-craft motion are briefly discussed. In Chapter 5, the small perturbation equa-tions of motion are described in detail, and the equations are expressed as two sets of decoupled equations representing the longitudinal and lateral dynamics. Chapter6 introduces the methodology of linear stability analysis and provides a modal description of aircraft dynamics. The application of small perturbation equations in determining the control setting angles for executing typical manoeuvres is also discussed in this chapter.

Chapter 7 covers the evaluation of aircraft dynamic response and the application of MATLAB/Simulink in determining the aircrafts response to typical control inputs. A basic introduction to aircraft non-linear dynamic phenomenon is also presented in this chapter. Chapter 8 deals with aircraft flight control, the design of control laws, stability augmentation, autopilots and the optimal design of feedback controllers. Chapter 9 describes flight simulators and the principles governing their design. Finally, Chapter 10 is dedicated to the flight dynamics of elastic aircraft, including the principles of aeroelasticity from an aircraft perspective.

I thank my colleagues and present and former students at the School of Engineering and Material Science, Queen Mary University of London, for their support in this endeavour.

I thank my wife Sudha for her love, understanding and patience. Her encouragement and support provided me the motivation to complete this project. I also thank our children Lullu, Satvi and Abhinav for their under-standing during the course of this project.

Ranjan VepaLondon, United Kingdom

xxiPreface

MATLAB is a registered trademark of The MathWorks, Inc. For product information, please contact:

The MathWorks, Inc.3 Apple Hill DriveNatick, MA 01760-2098 USATel: 508-647-7000Fax: 508-647-7001E-mail: [email protected]: www.mathworks.com

xxiii

Author

Dr. Ranjan Vepa earned his PhD in applied mechanics from Stanford University, Stanford, California, specialising in the area of aeroelasticity under the guidance of the late Prof. Holt Ashley. He currently serves as a lecturer in the School of Engineering and Material Science, Queen Mary University of London, where he has also been the programme director of the Avionics Programme since 2001. Prior to joining Queen Mary, he was with the NASA Langley Research Center, where he was awarded a National Research Council Fellowship and conducted research in the area of unsteady aerodynamic modelling for active control applications. Subsequently, he was with the Structures Division of the National Aeronautical Laboratory, Bengaluru, India, and the Indian Institute of Technology, Chennai, India.

Dr. Vepas research interests include the design of flight control systems and the aerodynamics of morphing wings and bodies with applications in smart structures, robotics and biomedical engineering and energy systems, including wind turbines. He is particularly interested in the dynamics and in the robust adaptive estimation and the control of linear and non-linear aerospace, energy and biological systems with uncertainties. The research in the area of the aerodynamics of morphing wings and bodies is dedicated to the study of aerodynamics and its control. This includes the use of smart structures and their applications to the control of aerospace vehicles, jet engines, robotics and biomedical systems. Other applications of this work are to wind turbine and compressor control, maximum power point track-ing, flow control over smart flaps and the control of biodynamic systems. Dr. Vepa currently conducts research on biomimetic morphing and aero-dynamic shape control and their applications, which include feedback con-trol of aerofoil section shape in subsonic and transonic flow for unmanned aerial vehicles (UAV), airship and turbomachine applications and integra-tion of computational aeroelasticity (CFD, computational fluid dynamics/CSD, computational structural dynamics) with deforming grids as well as their applications to active flow control. Of particular interest are the bound-ary layer instabilities in laminar flow arising due to various morphing-induced disturbances. Dr. Vepa has also been studying the optimal use and regulation of alternate power sources such as fuel cells in hybrid electric vehicle power trains, modelling of fuel cell degradation and health monitor-ing of aircraft structures and systems. With regard to structural health moni-toring and control, observer and Kalman filterbased crack detection filters are being designed and applied to crack detection and isolation in aeroelastic aircraft structures such as nacelles, casings, turbine rotors and rotor blades. Feedback control of crack propagation and compliance compensation in cracked vibrating structures is also being investigated. Another issue is the

xxiv Author

modelling of damage in laminated composite plates, non-linear flutter anal-ysis of their plates and their interaction with unsteady aerodynamics. These research studies are contributing to the holistic design of vision-guided autonomous UAVs, which are expected to be extensively used in the future.

Dr. Vepa is the author of three books: Biomimetic Robotics (Cambridge University Press, 2009), Dynamics of Smart Structures (Wiley, 2010) and Dynamic Modeling, Simulation and Control of Energy Generation (Springer, 2013). He is a member of the Royal Aeronautical Society, London; the Institution of Electrical and Electronic Engineers (IEEE), New York; a fellow of the Higher Education Academy; a member of the Royal Institute of Navigation, London; and a chartered engineer.

11Introduction to Flight Vehicles

1.1 Introduction

While aerodynamics is the study of flows past and over bodies, the principles of flight are governed by the dynamics and aerodynamics of flight vehicles. The focus of this chapter is on the general principles of flight and the pri-mary features of aircraft. Further details may be found in Anderson [1] and Shevell [2]. As the aerodynamics of bodies is greatly influenced by their external geometry, the aerodynamics of flight vehicles is entirely deter-mined by their external geometry. The external geometry is in turn com-pletely influenced by the entire complement of components external to the vehicle. The basic architecture of a typical aeroplane, the simplest of flight vehicles, is well known to any cursory observer of aeroplanes. It can be con-sidered to be the assemblage of a number of individual components. The principal external components are the fuselage, the left and right wings, the power plant pods or nacelles, the tail plane unit comprising of the horizontal and vertical stabilisers, the various control flaps and control surfaces and the landing gear. When the components are assembled or integrated together, a complete external picture of a typical aeroplane emerges. A typical planform or top-down view of an aeroplane is shown in Figure 1.1.

1.2 Components of an Aeroplane

The primary components of an aeroplane are the fuselage, the wing, the tail surfaces which are collectively referred to as the empennage, the power plant, the various control surfaces used to control the flight of the aeroplane and the landing gear.

1.2.1 Fuselage

The fuselage is the main body of any aeroplane, housing the crew and pas-sengers or the cargo or payload and the like.

2 Flight Dynamics, Simulation, and Control

1.2.2 Wings

The wings are the main lifting element of the aeroplane. They comprise of the wing leading and trailing edges, flaps and slats that are used to aug-ment the lift on the wing, ailerons to enable the aeroplane to bank while turning and spoilers that are capable of reducing the wing lift during land-ing and act as speed brakes. The high-lift devices controlled and oper-ated below the wing permit the wing to develop the necessary lift during take-off when a large passenger jet attains speeds of the order of 320km/h after accelerating down a runway of length 34km. The controls and drive mechanisms linking these devices are usually shrouded in canoe-shaped fairings attached to the underside of the wing. The wing essentially carries the entire aeroplane and all other associated systems. The wing is essen-tially a single aerodynamic element although it extends symmetrically on either side of the fuselage.

1.2.3 Tail Surfaces or Empennage

The tail surfaces are the basic elements that stabilise and control the aero-plane. Normally, both the vertical and horizontal tail surfaces have a fixed forward portion and a hinged rearward portion. The forward portion of the horizontal tail surface is known as the stabiliser, while the rearward hinged portion on the same surface is known as the elevator. On many long-haul air-liners, the horizontal stabiliser is an all movable unit. On the vertical tail, the fixed forward portion is known as the fin, while the hinged rearward portion is known as the rudder. Both on the rudder and on the elevator are additional hinged surfaces known as the trim tabs which are used to adjust the forces on

FIGURE 1.1Typical planform view of an aeroplane.


the pilots control column (which controls the movement of the elevator) and rudder pedals so that these are force free. Together, the entire horizontal and vertical tail surface assembly is known as the empennage.

1.2.4 Landing Gear

To enable an aeroplane to operate from land, aeroplanes are provided with landing gear comprising of wheels with types mounted on axles. Brakes are integral elements while the axles are attached via supporting struts and shock absorbers to the fuselage. To minimise drag during take-off and in steady flight, cowlings and retractable mechanisms are provided. The lat-ter permit the retraction of the entire landing gear to an enclosed housing within the fuselage once the aeroplane is airborne.

1.3 Basic Principles of Flight

1.3.1 Forces Acting on an Aeroplane

Consider the equilibrium of an aeroplane on the ground. Its weight may be regarded as acting vertically downwards through the aeroplanes centre of gravity (CG) and this is balanced by two sets of reactions acting vertically upwards, one at the points of contact of the main undercarriage and the ground surface and the other either at the nose wheel or tail skid depend-ing on the type of aeroplane. To maintain an aeroplane in vertical equilib-rium during flight, the vertical reactions at the main undercarriage and nose wheels must be replaced by equivalent upward forces: the lift components acting on the main wing and tail plane surface. In the days of the lighter than air balloons, which were axially symmetric about the CG axis, the reaction was a single lift force due to the buoyancy. This force was due to the differ-ence in the weight of the air displaced by the balloon and the gas contained within and acted in the vicinity of the CG. However, with the arrival of the airship, the forces were no longer acting in a single vertical line. Typically, a steady level flight is held in balance or equilibrium by a combination of forces (Figure 1.2a). The forces comprise

1. The lift on the aeroplane with the principal contributions being due to the wing and horizontal tail

2. The drag which consists of two main components the profile drag and the induced drag

3. The thrust produced by the power plants 4. The weight of the aeroplane


In addition to the equilibrium of forces, the forces on the tail plane contrib-ute principally towards rotational moments acting on the aeroplane. All the rotational moments acting on the aeroplane must cancel each other to ensure that the aeroplane is in rotational equilibrium. Rotational equilibrium is essential so the aeroplane can maintain steady orientation during a long and sustained flight. Thus, the attitude of the aeroplane must remain steady dur-ing extended periods of flight.

The principal phenomenon that is responsible for holding the aeroplane in flight is the wing lift which is caused as a result of the generation of a low-pressure or suction region over the top surface of the wing and high-pressure region below the lower surface of the wing (Figure 1.2b). The region of low pressure on the top surface of the wing is caused by the flow of air over the curved surface of the wing with a resultant increase in flow velocity and con-sequent decrease in pressure relative to the rest of the atmosphere. Similarly, the region of high pressure below the lower surface of the wing represents a region where the pressure is relatively greater than in the surrounding air. The result of these two complementary effects on the two surfaces of the

Relative windWinglift, LW

Induceddrag, Di

Proledrag, Dp Tail

lift, LT

rust, T

Weight, mg

Suction

Suction

PressurePressure

(a)

(b)

FIGURE 1.2(a) Forces acting on aeroplane in steady, level, equilibrium flight and (b) pressure distribution on a wing: front and side view of a typical wing section.


wing is the generation of lift. This generation is due to the fact that the two flows emerging from the upper and lower surfaces at the trailing edge of the wing result in a downwash or vortical flow. Thus, the wing experiences an upward and opposite reaction in the form of lift.

The lift is directly proportional to the air density and also a function of the airspeed; the higher the airspeed, the greater the lift generated by the wings. An increase in the wing surface area increases the lift in direct proportion. The wing camber and angle of attack are the other parameters that cause the lift to increase.

1.3.2 Drag and Its Reduction

As for the drag on the aeroplane, there are two distinct types of drag that act to retard the aeroplane when it is forward flight. The first is profile drag that is itself made up of two components, form drag and skin friction drag. The former is produced due to the finite shape of the aeroplane as the result of the streamlined flow around its body. Thus, the shape of the body is almost always optimally streamlined to reduce this component to minimum. The latter component is produced due to the viscous friction between the aero-planes skin and the airflow around the body. The airflow results in the for-mation of a thin boundary layer where the flow velocity reduces to zero as one gets closer to the skin of the aeroplane. This type of drag depends to a large extent on the thickness of the boundary layer that must be kept to a minimum to reduce the drag. These aforementioned two components that constitute the profile drag have one common feature: they both increase markedly as the speed of the aeroplane increases and the increase is directly proportional to the square of the airspeed.

The second type of drag experienced by an aeroplane is the induced drag. Due to the pressure difference between the top and bottom side of the wing surface, there is a spill over of air, particularly at the wing tips, from the bottom to the top. To a large extent, the induced drag is caused by a meeting of the airflow emerging from the upper and lower surfaces at the trailing edge, at a finite angle, resulting in the formation of vortices, set up due to the air spilling over. The vortices accumulate at the wing tips to produce a rotating flow of air, rotating in the direction of the wing root and resulting in a wing tip vortex. These wing tip vortices are the principal contributors to the induced drag which is caused by the energy dissipated in rotating the air. Due to the wing tip vortices being washed away at a faster rate at higher airspeeds, there is a decrease in the induced drag with the increase in the speed.

As a result of the different behaviours of the two types of drag as speed increases, there is a speed at which the drag is in fact a minimum. At this speed, the contributions to the total drag by the two types of drag are equal, and as a result, either an increase or decrease in the airspeed causes the drag to increase. Aeroplanes are generally flown at a cruise speed that is just above


the minimum drag speed as it is important to operate on the right side of the drag curve. Operating on the wrong side implies that a small reduction in the airspeed increases the drag substantially and unacceptably large increments of power are required to increase the aeroplanes speed. Operating on the wrong side is not acceptable and unsafe especially when the power plant is already being operated near its maximum power output.

Finally, the drag must be low and well below the thrust generated by the aeroplanes power plants or propulsive units to ensure that the aeroplane may be accelerated fast enough as may be desired during various phases of the flight.

1.3.3 Aerodynamically Conforming Shapes: Streamlining

There is a patent need to reduce the drag acting on an aeroplane. This is done by shaping the envelope of the various components in the flow or streamlin-ing. By appropriately shaping the envelope so that all directions tangential to it are parallel to the directions of the flow adjacent to it, the drag could be considerably minimised. In most cases, this is because air is able to smoothly pass over the body generating any eddies or turbulence. The generation of a turbulent wake behind the body could substantially increase the drag.

Streamlining is also necessary for the generation of lift. There are indeed three effects that contribute to wing lift: (1) the shape of the aerofoil or wing section is such that the velocity of the flow must necessarily be higher over the upper surface than below the lower surface; (2) the velocity of the flow field gives rise to a pressure differential or suction that is a principal contrib-utor to the wing lift; and (3) there is the effect of the downward inclination of the streamlines behind the aerofoil section, known as downwash, as well as the slight upward inclination of the flow in the vicinity of the leading edge or front of the aerofoil, known as the upwash. Together, the upwash and the downwash are responsible for producing a curved streamlined flow with a resulting inertia force acting outwards. This is a significant contributor to the lift acting on the wing section.

1.3.4 Stability and Balance

The weight distribution on an aeroplane also plays a critical role in ensuring a stable flight. By stability we mean the ability of the aeroplane to return to its equilibrium orientation when disturbed by an external effect of any kind. To ensure stability, it is essential that the CG of the aeroplane is sufficiently forward. Thus, it is particularly important to ensure not only that the weight is laterally balanced but also that the aeroplane is not too tail heavy.

Maintaining rotational balance is an important requirement in flight. Lift and weight generally do not act at the same point during a particular flight of an aeroplane. The centre of aerodynamic pressure can be expected to change continually depending on the selection of control surfaces deployed


during the different phases of the flight. Moreover, the weight distribution around the aeroplane is also changing due to variations in payloads and fuel consumption. Fuel can account for up to 30%45% of an aeroplanes weight, while in an airline, the total weight of the passengers and other payloads could weigh as much as 15%20% of the maximum take-off weight. Thus, ensuring stability is a difficult proposition. The problem is overcome by making the entire horizontal tail plane movable so it could be deployed as a stabilising surface. The tail plane generates lift and as a result of its long moment arm, it is adequate to restore the aeroplane to an equilibrium posi-tion when a disturbing force acts at the CG. The movable or variable position tail plane is used to rebalance the aeroplane and particularly to maintain equilibrium when there are changes in the aeroplanes weight and CG loca-tion. Thus, when the CG is aft of the centre of pressure (CP), the aeroplane is tail heavy and it is essential to stabilise the aeroplane. At this stage, the stabiliser is moved up to decrease the lift on the tail unit and hence rebalance the aeroplane. This process of balancing the aeroplane by movement of the stabiliser is known as trimming. On the smaller general aviation aeroplane, this function is performed by the trim tabs that are smaller movable control surfaces hinged to the rear of the elevator and rudder. Aeroplanes that are provided with trim tabs generally have fixed stabilisers. Some aeroplanes are provided with both an all moving horizontal tail plane, for automatic trim, and a full set of trim tabs for manual trimming. To be able to trim the aeroplane, the pilot must have a feel of the out of balance forces. A feel unit usually provides this feedback and the pilot usually feels the pressure of out of balance forces on the control column. When the aeroplane is trimmed, the control column is relieved of the out of balance feedback and is free of any forces acting on it. Thus, the aeroplane may be flown in a stable condition with hands off of the control column.

1.4 Flying Control Surfaces: Elevator, Ailerons and Rudder

To understand the fundamentals of the dynamics of heavier than an aero-plane, it is essential to first understand not only the basic principles of flight but also its control. The aeroplane in level flight at constant speed can be considered to be flying in equilibrium. The weight of the craft is completely balanced by the lift generated by the wings of the aeroplane. The thrust imparted to it by the engines is completely balanced by the drag. The lift is generated by the flow of air over the surface of the wing that is designed to have a special cross section. When the aeroplane loses speed, there is also a loss of lift that must be compensated, if the aeroplane is to fly at constant altitude. The aeroplane compensates the loss of lift by increasing its angle of attack that results in an increased lift. However, there is a limiting angle


(about 15) beyond which any further increase in the angle of attack only causes the aeroplane to lose lift due to flow separation over the upper surface of the wing as illustrated in Figure 1.3. Consequently, the aeroplane stalls and any further increase in the angle of attack or reduction in speed results in a dramatic loss of lift. The speed at which this condition of stalling occurs is the stalling speed that is always the same for a particular aeroplane.

The most dangerous moments in the flight of an aeroplane are during take-off and landing. At these stages in the flight, there is demand for maximum lift at low speeds. To generate additional lift during these low-speed stages of the flight, the aeroplane is provided with high-lift devices such as retractable flaps (the Fowler flaps) and movable slats in the leading edge region which can effectively increase the curvature of the wing section or aerofoil and thus generate the additional lift. After take-off, every effort is generally made to reduce the aeroplanes drag thereby increasing its flight speed. To do this, the landing gear is retracted and held within the belly of the aeroplane, so the shape of the aeroplane is apparently streamlined and the drag is minimised.

The flight of the aeroplane is controlled by means of the controllers within the cockpit of the aeroplane: the control column, the throttle levers, the rud-der pedals and the toe brakes. These controls allow a whole family of control surfaces to be controlled indirectly using intermediate, electro-hydraulically

(a) (b)

(c) (d)

FIGURE 1.3Flow separation and the onset of stall. (a) Flat plate aerofoil at 0 incidence, (b) flat plate aerofoil at 15 incidence, (c) aerofoil at 13 incidence and (d) aerofoil at 18 incidence. Trailing edge separation initiated.


operated mechanisms, known as power control units. Figure 1.4 shows the complete complement of controls on a typical aeroplane.

The control columns operate the elevator when moved fore and aft. When the elevator moves down, the additional lift generated on the tail plane forces the aeroplane to pitch nose downwards and vice versa. The elevators are hinged at the trailing edge of the horizontal stabiliser. The elevators are gen-erally operated by the power control units, but on most aeroplanes, there is the option of manual reversion, so the pilot could, when necessary, take con-trol and manually operate them. When operated by the power control units, there is need for some form of artificial feel. The artificial feel is provided by an actuator applying a force on the control column. The force is computed by the feel computer which receives its inputs from the pilot, the static pressure ports and the horizontal stabiliser setting.

The horizontal stabilisers function is to provide for longitudinal trim. This is accomplished by changing the incidence angle of the horizontal stabiliser. It may also be driven by an electro-hydraulic power control unit or manu-ally by cables. On some aeroplanes, increase in the airspeed causes the CP to move aft and the aerodynamic centre forwards causing the aeroplane to tuck. In this state, the natural phugoid mode of the aeroplane is absent and the aeroplane could come dangerously close to being unstable. To avoid this behaviour, the horizontal stabiliser is sometimes fitted with an automatic pitch-trim compensator. Horizontal stabilisers are generally set in motion by switches on the pilots control column. Trimming may be achieved either automatically or manually.

Spoilers EnginesUnderwing leadingedge aps/slats

Flaps

FinCanoe fairings

Stabiliser

Elevator

Rudder

Ailerons

FIGURE 1.4The complete complement of controls on a typical aeroplane.


When the control column is moved or rotated from left to right, the aile-rons at the far end of each of the two wings rotate in a differential manner, thereby generating a rolling moment. Thus, the aeroplane banks, the angle of bank being directly proportional to the differential moment of the ailerons. Roll may not only be initiated by the ailerons but also be controlled by them. On some aeroplanes, there are two ailerons on each wing. The outboard pair is usually locked in with the wing in high-speed flight while they may be proportionally controlled at low speeds. The outboard pair is not used when the flaps are deployed. Like the case of the elevator, it is often possible to revert to manual control and artificial feel is also provided. The artificial feel unit is usually a spring loaded roller cam mechanism which is responsible for providing a feedback force to the control column that is directly propor-tional to the roll actuator command input.

The rudder pedals operate the rudder that generates the necessary turning moment to turn the aeroplane. The rudder generally provides for the control of yaw (nose right or nose left). Some aeroplanes are provided with dual rudders, each of which is split into two separately actuated sec-tions. To protect the vertical tail from structural damage that may result from excessive rudder deflection, rudder travel is limited by incorporat-ing signal limiters in the rudder control circuits. The rudder control sys-tem also incorporates, most often, a yaw damper which receives inputs from a yaw rate gyro and provides additional signals to the rudder power control unit so as to move the aeroplane in the direction opposing the yaw motion and in proportion to the yaw rate. The yaw damper is not usually operational in the manual reversionary mode. An artificial feel unit similar to the one fitted to the ailerons is also fitted to the rudder. The toe brakes apply braking to the wheel assemblies on the respective sides while allowing for differential braking to supplement the rudder on the ground.

Various types of control tabs, balance tabs and differentially controlled balance panels are also used in aeroplane control. These devices are gener-ally used to balance the forces or moments acting on the control column in the respective directions. This is achieved without adversely affecting the control forces and moments generated by the main control surface and thus maintaining the control column in a force-free condition. Thus, the tabs can mechanically fly the elevator, aileron or rudder while effectively relieving the pilot of having to provide a command input to the control column. The pilot may then fly the aeroplane in the particular trimmed condition in a hands-free mode. These controlling movements are illustrated in Figures 1.5 through 1.7.

1.4.1 Flaps, High-Lift and Flow Control Devices

There are a plethora of high-lift devices that may be used to improve the lift characteristics of the aeroplanes primary lifting surfaces during


take-off or other phases of the flight. Broadly, all flow control devices fall into five primary categories:

1. Short chord/short span passive devices 2. Single multi-element/multi-surface variable camber or deployable

systems 3. Blown or suction systems 4. Inflatable systems including leading edge devices 5. Active/passive vortex and circulation control systems

Relative wind

Relative wind

(a)

(b)

FIGURE 1.5Operation of the elevator. (a) Elevator down results in aeroplane nose down and (b) elevator up results in aeroplane nose up.

FIGURE 1.6Operation of the aileron: up aileron forces wing down and down aileron forces wing up, result-ing in bank for turning left; aeroplane continues to turn left when ailerons are returned to the normal position.


High-lift devices are usually deployed to increase the lift force. However, there is also a substantial increase in the drag accompanying any increase in lift. During take-off, an increase in the lift is generally required to reduce the unstick speed and take-off run, while during landing, there is need to reduce the landing speed and to reduce the landing run. Thus, the increase in drag can be effectively optimised in reducing the take-off and landing runs. One of several short chord/short span passive devices is available to reduce the wing lift over sections of the wing surface to achieve flow control. Although there are several methods available to increase the wing lift, single control surfaces or multi-element/multi-surface variable camber or deploy-able systems are normally used on most aeroplanes. These generally offer almost negligible resistance when they are not deployed and their deploy-ment is completely controlled by the pilot.

Wing leading edge deflection, at high angles of attack, is essential to impede stall, thus enabling to attain higher angles of attack thus generating greater lift. Effectively, the leading edge deflection of the wing results in an increased curvature of the wing section. This is achieved by a combination of slats, slots and flaps (Figures 1.8 and 1.9).

1.4.2 Introducing Boundary Layers

The very thin layer of air in which the velocity is gradually increasing from zero to that of the airstream is called the boundary layer. Viscous friction plays an important part in its evolution and typically the boundary layer affects the streamline flow, which is outside it. The separation of the boundary layer from the surface of the wing can result in an extreme loss of lift. Boundary layer separation due to adverse pressure gradients on lifting surfaces due to high angles of attack or due to transonic shock effects is the primary cause for the flow separation followed by a loss of lift. Boundary layer separation also causes an increase in the drag. Thus, there is an increased demand for fuel and loss of performance. The unsteady flow associated with separation leads

FIGURE 1.7Operation of the rudder: moving the rudder to the left turns the aeroplane to the left and vice versa.


to a random loading on the wing that results in the so-called phenomenon of buffeting. There are several techniques used to control boundary layer sepa-ration and these are

1. Vanes 2. Flow control rails 3. Boundary layer blowing 4. Boundary layer suction 5. Vortex mixing 6. Passive control of boundary layer 7. Control of wing camber and thickness 8. Active control techniques

Openings in the vicinity of the leading edge wing surfaces allow the flow of air, with a higher energy, into the boundary layer of the upper surface to blow it off and inhibit the separation of airflow at that angle of attack.

(a)

(c)

(e)

(b)

(d)

(f)

FIGURE 1.8Typical complement of trailing edge high-lift flaps. (a) Plain hinged flap, (b) slotted flap, (c) double-slotted flap, (d) Wragg or external aerofoil flap, (e) split flap and (f) fowler flap (which is moved down to the rear).

FIGURE 1.9Handley page leading edge slat (which is pulled out into place by suction at high angles of attack).


Thus, as a consequence of these openings or slots, separation now occurs at a much higher angle of attack. Thus, the result is an increase in the effective lift coefficient. The slots in the vicinity of the leading edge wing surfaces are hydraulically opened only when the trailing edge laps are down and auto-matically closed when the flaps are up. Leading edge segments that move on tracks and extend from the wing leading edge to form slots are essentially movable slots. They are known as slats and produce the same effect as fixed slots. Slats are also hydraulically operated and the deployment and exten-sion of slats is usually synchronised with the deployment and extension of trailing edge flaps. The coordinated movement of slots, slats and trailing edge flaps is designed to effectively increase the camber of the wing and thus improve the wing characteristics at low flight speeds. Leading edge flaps, which can give the wing an additional droop when extended, may also be deployed to produce the same effect. The deployment of leading edge flaps, known also as Krueger flaps, is also automatically synchronised with the deployment of trailing edge flaps by an electrically signalled and hydraulically operated power control unit.

The deployment of trailing edge flaps is controlled by a flap handle that is located on the pilots control pedestal in the cockpit. Earlier forms of trailing edge flaps were usually split flaps although the use of plain flaps and exten-sion flaps (Fowler flaps) is now widespread. In one form, trailing edge flaps are usually deployed in a two-section configuration, which are designated as the inboard and outboard sections. Each of the inboard and outboard sections is independently signalled electrically and can be programmed to operate, symmetrically, in one of several coordinated schedules. In many of the older aeroplanes, the coordination of the inboard and outboard sections and the symmetric operation of the left and right wing flaps is achieved by mechanical torque tubes and cabling.

Wing lift may also be regulated by controlling the airflow over the wing. Typically, a narrow jet of air passing between the wing and trailing edge flaps blows off the boundary layer, thus providing for attached flow and consequently a higher lift coefficient. Theoretically, the most advantageous methods are the boundary layer blowing off and suction from the upper surface of the wing. Suction increases the rate flow, and consequently, there is an increase in the rarefaction close to the wing surface in the region ahead of the suction point. By contrast, the effect of blowing is an increase in the rarefaction close to the wing surface over the entire chord. With boundary layer blowing or suction, the wing drag decreases with increasing lift coef-ficient and consequently there is an increase in liftdrag ratio.

A jet flap is another means of increasing the lift force. It is essentially estab-lished by blowing air through a special slot in the trailing edge of the wing, at angle to the extended chord line. The jet flap extends the wing virtually as well as its camber and there is an increase in the total lift force acting on the wing. The magnitude of the pressure distribution in the vicinity of the trail-ing edge area is usually substantially greater than a wing without the jet flap.


A hybrid boundary layer suction system coupled with a jet flap is considered to be a promising high-lift generating system.

Inflatable wings are particularly suitable for compensating the aeroplanes wing section for the in-flight ice accretion process. Ice accretion is particu-larly a problem in the vicinity of the aeroplanes leading edge, and compen-sation is achieved by designing inflatable and deflatable wing leading edges. During the ice accretion period, an active controller is used to deflate the leading edge and thus compensate for the ice accretion.

A circulation control system employs rearward tangential blowing over a rounded or near-rounded trailing edge, to reinforce the boundary layer and delay the separation. Separation is delayed due to the flow remaining attached to the trailing edge due to the Coanda effect. The location of the separation point may be controlled by varying the blowing rate, thus affect-ing the wing lift. Generally in the case of flaps with circulation control, there is substantial increase in wing lift than in the case of conventional mechani-cal flaps. A similar approach is adopted in the wings with vortex control jets.

There are indeed several alternate methods of controlling and regulating wing lift. In the case of most high-speed jets, particularly those capable of flying faster than the speed of sound, wings are swept back to minimise drag. Yet it is well known that swept wings do not perform as well as straight wings at lower speeds. Thus, in the case of swing wing aircraft, the wings are movable and may be deployed as swept wings at high speeds with the ability to revert to a straight wing configuration at low speeds.

There are also some vertical take-off and landing aircraft where the aircrafts lift is controlled entirely by control jets. The jets nozzle can be mechanically swivelled and the jets exhaust directed accordingly, to alter the direction of the net thrust acting on the aeroplane. Fluidic jets, where the jets directional control is based on the so-called Coanda effect, have also been employed in some experimental programmes.

1.4.3 Spoilers

Spoilers, so called because they are employed to spoil the lift on the wing by disrupting the streamlined airflow around it, are usually deployed at the instant of landing to place the full weight of an aircraft on the wheels and prevent it from bouncing back into the air after a heavy landing. They are also deployed automatically on an abandoned take-off following the selection of reverse thrust, again to place the full weight of the aircraft on the wheels and to improve braking performance. In-flight spoilers are deployed as speed brakes to slow the aircraft rapidly and to greatly increase the rate of descent (Figure 1.10). They are also employed occasionally for enhanced roll control. Deploying the spoilers on one side of the aircraft disrupts the lift on that side and aids the aircraft in rolling.

Spoilers are normally actuated by electro-hydraulic power control units. On most civil aircraft, there are a number of spoilers and groups of these are


actuated by one of several hydraulic channels to provide for redundancy and fault tolerance. During operation they are designed to be adaptive; that is, the extension is generally much lower at higher speeds. Spoiler actuators are also designed to retract back to their unloaded position when hydraulic power to them is lost. In the case of flight spoilers, which are used to supplement the aileron in roll control, the spoiler inputs are generated by the ailerons move-ment and moderated by a spoiler mixer mechanism or a spoiler control law. Ground spoiler actuators are normally activated only while the aircraft are on the ground and are controlled so the entire weight of the aircraft acts on the landing gear just before touchdown.

1.5 Pilots Controls: The Throttle, the Control Column and Yoke, the Rudder Pedals and the Toe Brakes

A primary complement of the pilots control in the cockpit are the throttle levers to control the fuel delivered to the power plant, the control column which may be pulled back or pushed forwards to rotate an aeroplane or to flare the aeroplane during landing, the yoke which when turned banks the aeroplane to one side or the other, the rudder pedal that is used to change the direction of the aeroplanes flight path and toe brakes which allow for the differential braking of the wheels during landing.

1.6 Modes of Flight

Speed and power are intimately connected with changes in attitude or the change in the direction in which the nose is pointing relative to the direction of flight. Vertical changes in the direction of flight as well as the changes in

FIGURE 1.10Aircraft with spoilers deployed: spoilers function as lift dumpers or speed brakes.


attitude affect the forces acting on an aeroplane. Flight at constant velocity is called steady and we have already dealt with steady horizontal flight. The simplified force diagrams for steady flight other than horizontal are shown in Figure 1.11. These represent climbing, power gliding and gliding flight. In addition, there are also the cases of an aircraft, in steady spin, in a terminal velocity dive, climbing in a turn and gliding in a turn.


Proledrag, Dp

Induceddrag, Di

Taillift, LT

Weight, mg

rust, T


Proledrag, Dp

Induceddrag, Di

Taillift, LT

Weight, mgrust, T

Relative wind

Winglift, LW

Proledrag, Dp

Induceddrag, Di Tail

lift, LT

Weight, mg

(a)

(b)

(c)

FIGURE 1.11Modes of flight. (a) Climbing flight, (b) power gliding and (c) gliding.


We observe from Figure 1.11 that the direction of the airflow relative to the aeroplane is exactly opposite to the direction of motion of the aeroplane. The air itself is not moving and it only has velocity relative to the aeroplane. The direction of airflow is important as it determines the directions of the lift and drag.

Based on the figure, we may establish that the conditions for equilibrium flight may be obtained, as in the case of steady level flight, by resolving the forces in the directions of the lift and drag.

1.6.1 Static and In-Flight Stability Margins

The problem of stability has already been discussed. Yet the overall sta-bility of an aeroplane is particularly important and in large passenger aeroplane a good deal of stability is desirable. An important feature of these aeroplanes is the inherent stability in the three aeroplane attitudi-nal degrees of freedom of pitch, roll and yaw as well the static stability in equilibrium flight.

As already mentioned, the tail plane generates lift, and as a result of its long moment arm, it is adequate to restore the aeroplane to an equilibrium position when a disturbing force such as a gust of wind acts to displace the aeroplane from its equilibrium position. A measure of this characteristic is the distance of the aerodynamic centre, the location of the CP of all aerody-namic forces generated when the aeroplane pitches forwards or backwards from a position of equilibrium and the CG. This is known as the longitudinal static stability margin.

Stability in roll is achieved due to the dihedral construction; that is, each half of the wing is positioned at a small positive angle (410) to the horizontal. Thus, when the aeroplane rolls to one side, there is an increased lift on the corresponding side of the wing resulting in a restoring moment and the aeroplane returns to a state of equilibrium.

Stability in yawing motion is due to the tail fin. It plays the same role in yawing motion as the horizontal tail plane does in pitching motion. Similar to longitudinal static stability margins, one could define lateral static stabil-ity margins. The lateral or weathercock stability margin is essential to pro-vide the aeroplane with directional stability.

The aforementioned stability characteristics refer to the desirable static stability margins of an aeroplane. In addition, an aeroplane must possess certain dynamic stability characteristics; that is, although an aeroplane may return to state of equilibrium from a disturbed position, certain motion characteristics are essential during its return to equilibrium. These desirable motion features are observed when the aeroplane has acceptable dynamic stability margins that are equally important, if not more, than the static sta-bility margins.


1.7 Power Plant

Thus far, we have generated a thrust by drawing an arrow in the direction of thrust and indicated it by the letter T, but the production of thrust in real-ity is a different matter. A forward force can only be generated by pushing a quantity of air back, that is, by increasing the velocity of the relative air-flow. The thrust produced is directly proportional to this increase in the rela-tive air velocity. Thus, thrust is produced whenever energy is imparted to a stream of air. Without exception, all powered aircraft are propelled by one or more thrust-producing thermal engines that convert heat energy released by fuel combustion into mechanical power. Thrust-producing power plants used on board an aircraft may be typical supercharged piston engines driv-ing a propeller or one of a variety of jet engines. The former class of engines is used for the smaller purpose-built general aviation aeroplanes, while the latter class is used on most airliners. These power plants are mounted on the aeroplane in one of several ways such as on the wings inside specially built enclosures known as nacelles, on the tail plane, mounted on but external to the fuselage or integrated into the fuselage. As many as six of these power plant units may be used to propel a single aeroplane.

1.7.1 Propeller-Driven Aircraft

These aircraft are primarily driven by typical supercharged piston engines driving a propeller. The propeller itself is constructed just like a wing of constant chord and a very high span to chord ratio, a uniform twist in the spanwise direction. It acts like a screw winding its way through the air, and the velocity of air relative to each part of the blade will be directed like a screw thread. The blade is designed such that the aerofoil sections along the span are inclined at the appropriate angle attack to the net airflow, and con-sequently, the lift components at each section will combine constructively to produce the thrust in the direction of motion of the aircraft, while the drag components combine to form a resisting torque. When this total resist-ing torque is less than torque of the engine, the engine speed will continue to increase. Consequently, there is an increase in the resisting torque, and when this torque balances the engine torque, the equilibrium engine speed is attained. The equilibrium engine speed and the corresponding thrust determine the conditions of equilibrium flight.

1.7.2 Jet Propulsion

Jet propulsion is based on the production of thrust by means of the reaction of the force due to a rapid change in momentum of a jet of gas produced within the aircraft but directed rearwards. It is usually associated with gas


turbi

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