The Author

The wonder of flight, and things that flew, led Gareth Padfield to study aeronautical engineering at the University of London, and later learning to fly both aeroplanes and helicopters. His career has been spent in the aviation industry, government research and in academia and has involved all aspects of flight dynamics - flight testing, modelling and simulation, flying qualities and flight control. He has held senior management and leadership roles in Government service (Chief Rotorcraft Scientist) and Academia (Head of School of Engineering) and has always endeavoured to keep his technical skills active as a practitioner.

Gareth's current role is Emeritus Professor of Aerospace Engineering at The University of Liverpool where he supports staff and students in their endeavours. He also operates a consultancy company, Flight Stability and Control, undertaking a variety of specialist projects for the aviation industry, and delivering short courses in Europe, the USA and the Far East.

Gareth Padfield is a Chartered Engineer, a Fellow of the Royal Academy of Engineering and the Royal Aeronautical Society. He is an honorary member of the American Helicopter Society's Modelling and Simulation and Handling Qualities Technical Committees and he has served on the UK's Defence Scientific Advisory Council.

While Helicopter Flight Dynamics is primarily for practising engineers, his 'other' book, So You Want to be an Engineer, (ISBN: 978-0-9929017-2-1) is primarily for students and early practitioners; it is available as a pdf on [...].

Gareth is also a musician and songwriter, recognising the close connection between creativity in engineering and creativity in music; both require a mix of disciplined and free thinking that, in the right combination, can work wonders and unmask mysteries.

Series Preface xv

Preface to Third Edition xvii

Preface to Second Edition xix

Preface to First Edition xxiii

Acknowledgements xxvii

Notation xxix

List of Abbreviations xxxix

Chapter 1 Introduction

1.1 Simulation Modelling 2

1.2 Flying Qualities 3

1.3 Missing Topics 4

1.4 Simple Guide to the Book 5

Chapter 2 Helicopter and Tiltrotor Flight Dynamics - An Introductory Tour

2.1 Introduction 8

2.2 Four Reference Points 9

2.2.1 The Mission and Piloting Tasks 9

2.2.2 The Operational Environment 12

2.2.3 The Vehicle Configuration, Dynamics, and Flight Envelope 13

2.2.4 The Pilot and Pilot-Vehicle Interface 19

2.2.5 Résumé of the Four Reference Points 20

2.3 Modelling Helicopter/Tiltrotor Flight Dynamics 21

2.3.1 The Problem Domain 21

2.3.2 Multiple Interacting Subsystems 22

2.3.3 Trim, Stability, and Response 24

2.3.4 The Flapping Rotor in a Vacuum 25

2.3.5 The Flapping Rotor in Air - Aerodynamic Damping 28

2.3.6 Flapping Derivatives 31

2.3.7 The Fundamental 90¿ Phase Shift 31

2.3.8 Hub Moments and Rotor/Fuselage Coupling 32

2.3.9 Linearization in General 35

2.3.10 Stability and Control Résumé 36

2.3.11 The Static Stability Derivative Mw 37

2.3.12 Rotor Thrust, Inflow, Zw, and Vertical Gust Response in Hover 39

2.3.13 Gust Response in Forward Flight 41

2.3.14 Vector-Differential Form of Equations of Motion 42

2.3.15 Validation 45

2.3.16 Inverse Simulation 48

2.3.17 Modelling Review 49

2.4 Flying Qualities 50

2.4.1 Pilot Opinion 50

2.4.2 Quantifying Quality Objectively 51

2.4.3 Frequency and Amplitude - Exposing the Natural Dimensions 52

2.4.4 Stability - Early Surprises Compared with Aeroplanes 53

2.4.5 Pilot-in-the-Loop Control; Attacking a Manoeuvre 56

2.4.6 Bandwidth - A Parameter for All Seasons? 57

2.4.7 Flying a Mission Task Element 59

2.4.8 The Cliff Edge and Carefree Handling 60

2.4.9 Agility Factor 60

2.4.10 Pilot's Workload 61

2.4.11 Inceptors and Displays 63

2.4.12 Operational Benefits of Flying Qualities 63

2.4.13 Flying Qualities Review 65

2.5 Design for Flying Qualities; Stability and Control Augmentation 66

2.5.1 Impurity of Primary Response 67

2.5.2 Strong Cross-Couplings 67

2.5.3 Response Degradation at Flight Envelope Limits 67

2.5.4 Poor Stability 68

2.5.5 The Rotor as a Control Filter 68

2.5.6 Artificial Stability 69

2.6 Tiltrotor Flight Dynamics 71

2.7 Chapter Review 71

Chapter 3 Modelling Helicopter Flight Dynamics: Building a Simulation Model

3.1 Introduction and Scope 74

3.2 The Formulation of Helicopter Forces and Moments in Level 1 Modelling 78

3.2.1 Main Rotor 79

3.2.2 The Tail Rotor 120

3.2.3 Fuselage and Empennage 122

3.2.4 Powerplant and Rotor Governor 127

3.2.5 Flight Control System 129

3.3 Integrated Equations of Motion of the Helicopter 134

3.4 Beyond Level 1 Modelling 136

3.4.1 Rotor Aerodynamics and Dynamics 137

3.4.2 Interactional Aerodynamics 143

3.5 Chapter 3 Epilogue 147

Appendix 3A Frames of Reference and Coordinate Transformations 153

3A.1 The Inertial Motion of the Aircraft 153

3A.2 The Orientation Problem - Angular Coordinates of the Aircraft 156

3A.3 Components of Gravitational Acceleration along the Aircraft Axes 158

3A.4 The Rotor System - Kinematics of a Blade Element 158

3A.5 Rotor Reference Planes - Hub, Tip Path, and No-Feathering 161

Chapter 4 Modelling Helicopter Flight Dynamics: Trim and Stability Analysis

4.1 Introduction and Scope 164

4.2 Trim Analysis 168

4.2.1 The General Trim Problem 170

4.2.2 Longitudinal Partial Trim 171

4.2.3 Lateral/Directional Partial Trim 176

4.2.4 Rotorspeed/Torque Partial Trim 178

4.2.5 Balance of Forces and Moments 178

4.2.6 Control Angles to Support the Forces and Moments 179

4.3 Stability Analysis 181

4.3.1 Linearization 183

4.3.2 The Derivatives 187

4.3.3 The Natural Modes of Motion 205

Appendix 4A The Analysis of Linear Dynamic Systems (with Special Reference to 6-Dof Helicopter Flight) 218

Appendix 4B The Three Case Helicopters: Lynx, Bo105 and Puma 227

4B.1 Aircraft Configuration Parameters 227

The RAE (DRA) Research Lynx, ZD559 227

The DLR Research Bo105, S123 229

The RAE (DRA) Research Puma, XW241 231

Fuselage Aerodynamic Characteristics 233

Lynx 233

Bo105 233

Puma 233

Empennage Aerodynamic Characteristics 234

Lynx 234

Bo105 234

Puma 234

4B.2 Stability and Control Derivatives 234

4B.3 Tables of Stability and Control Derivatives and System Eigenvalues 242

Appendix 4C The Trim Orientation Problem 258

Chapter 5 Modelling Helicopter Flight Dynamics: Stability Under Constraint and Response Analysis

5.1 Introduction and Scope 262

5.2 Stability Under Constraint 263

5.2.1 Attitude Constraint 264

5.2.2 Flight Path Constraint 275

5.3 Analysis of Response to Controls 283

5.3.1 General 283

5.3.2 Heave Response to Collective Control Inputs 284

5.3.3 Pitch and Roll Response to Cyclic Pitch Control Inputs 291

5.3.4 Yaw/Roll Response to Pedal Control Inputs 301

5.4 Response to Atmospheric Disturbances 309

Appendix 5A Speed Stability Below Minimum Power; A Forgotten Problem? 315

Chapter 6 Flying Qualities: Objective Assessment and Criteria Development

6.1 General Introduction to Flying Qualities 334

6.2 Introduction and Scope: The Objective Measurement of Quality 338

6.3 Roll Axis Response Criteria 341

6.3.1 Task Margin and Manoeuvre Quickness 341

6.3.2 Moderate to Large Amplitude/Low to Moderate Frequency: Quickness and Control Power 347

6.3.3 Small Amplitude/Moderate to High Frequency: Bandwidth 353

6.3.4 Small Amplitude/Low to Moderate Frequency: Dynamic Stability 371

6.3.5 Trim and Quasi-Static Stability 372

6.4 Pitch Axis Response Criteria 374

6.4.1 Moderate to Large Amplitude/Low to Moderate Frequency: Quickness and Control Power 374

6.4.2 Small Amplitude/Moderate to High Frequency: Bandwidth 377

6.4.3 Small Amplitude/Low to Moderate Frequency: Dynamic Stability 378

6.4.4 Trim and Quasi-Static Stability 381

6.5 Heave Axis Response Criteria 385

6.5.1 Criteria for Hover and Low-Speed Flight 388

6.5.2 Criteria for Torque and Rotorspeed During Vertical Axis Manoeuvres 391

6.5.3 Heave Response Criteria in Forward Flight 392

6.5.4 Heave Response Characteristics in Steep Descent 393

6.6 Yaw Axis Response Criteria 395

6.6.1 Moderate to Large Amplitude/Low to Moderate Frequency: Quickness and Control Power 396

6.6.2 Small Amplitude/Moderate to High Frequency: Bandwidth 398

6.6.3 Small Amplitude/Low to Moderate Frequency: Dynamic Stability 398

6.6.4 Trim and Quasi-Static Stability 401

6.7 Cross-Coupling Criteria 402

6.7.1 Pitch-to-Roll and Roll-to-Pitch Couplings 402

6.7.2 Collective to Yaw Coupling 404

6.7.3 Sideslip to Pitch and Roll Coupling 405

6.8 Multi-Axis Response Criteria and Novel-Response Types 406

6.8.1 Multi-Axis Response Criteria 406

6.8.2 Novel Response Types 407

6.9 Objective Criteria Revisited 410

Chapter 7 Flying Qualities: Subjective Assessment and Other Topics

7.1 Introduction and Scope 418

7.2 The Subjective Assessment of Flying Quality 419

7.2.1 Pilot Handling Qualities Ratings - HQRs 420

7.2.2 Conducting a Handling Qualities Experiment 425

7.3 Special Flying Qualities 438

7.3.1 Agility 438

7.3.2 The Integration of Controls and Displays for Flight in Degraded Visual Environments 445

7.3.3 Carefree Flying Qualities 455

7.4 Pilot's Controllers 462

7.5 The Contribution of Flying Qualities to Operational Effectiveness and the Safety of Flight 464

Chapter 8 Flying Qualities: Forms of Degradation

8.1 Introduction and Scope 470

8.2 Flight in Degraded Visual Environments 472

8.2.1 Recapping the Usable Cue Environment 472

8.2.2 Visual Perception in Flight Control - Optical Flow and Motion Parallax 475

8.2.3 Time to Contact; Optical Tau, ¿ 483

8.2.4 ¿ Control in the Deceleration-to-Stop Manoeuvre 486

8.2.5 Tau-Coupling - A Paradigm for Safety in Action 487

8.2.6 Terrain-Following Flight in Degraded Visibility 494

8.2.7 What Now for Tau? 507

8.3 Handling Qualities Degradation through Flight System Failures 511

8.3.1 Methodology for Quantifying Flying Qualities Following Flight Function Failures 512

8.3.2 Loss of Control Function 514

8.3.3 Malfunction of Control - Hard-Over Failures 517

8.3.4 Degradation of Control Function - Actuator Rate Limiting 522

8.4 Encounters with Atmospheric Disturbances 524

8.4.1 Helicopter Response to Aircraft Vortex Wakes 525

8.4.2 Severity of Transient Response 538

8.5 Chapter Review 542

Appendix 8A HELIFLIGHT, HELIFLIGHT-R, and FLIGHTLAB at the University of Liverpool 545

8A.1 FLIGHTLAB 545

8A.2 Immersive Cockpit Environment 547

8A.3 HELIFLIGHT-R 551

Chapter 9 Flying Qualities: The Story of an Idea

9.1 Introduction and Scope 554

9.2 Historical Context of Rotorcraft Flying Qualities 557

9.2.1 The Early Years; Some Highlights from...