The Book The behaviour of helicopters and tiltrotor aircraft is so complex that understanding the physical mechanisms at work in trim, stability and response, and thus the prediction of Flying Qualities, requires a framework of analytical and numerical modelling and simulation. Good Flying Qualities are vital for ensuring that mission performance is achievable with safety and, in the first and second editions of Helicopter Flight Dynamics, a comprehensive treatment of design criteria was presented, relating to both normal and degraded Flying Qualities. Fully embracing the consequences of Degraded Flying Qualities during the design phase will contribute positively to safety. In this third edition, two new Chapters are included. Chapter 9 takes the reader on a journey from the origins of the story of Flying Qualities, tracing key contributions to the developing maturity and to the current position. Chapter 10 provides a comprehensive treatment of the Flight Dynamics of tiltrotor aircraft; informed by research activities and the limited data on operational aircraft. Many of the unique behavioural characteristics of tiltrotors are revealed for the first time in this book.  The accurate prediction and assessment of Flying Qualities draws on the modelling and simulation discipline on the one hand and testing practice on the other. Checking predictions in flight requires clearly defined mission tasks, derived from realistic performance requirements. High fidelity simulations also form the basis for the design of stability and control augmentation systems, essential for conferring Level 1 Flying Qualities. The integrated description of flight dynamic modelling, simulation and flying qualities of rotorcraft forms the subject of this book, which will be of interest to engineers practising and honing their skills in research laboratories, academia and manufacturing industries, test pilots and flight test engineers, and as a reference for graduate and postgraduate students in aerospace engineering.

Table of Contents:
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, 𝜏 483 8.2.4 𝜏 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 the 1940s–1950s 557 9.2.2 The Middle Years – Some Highlights from the 1960s–1970s 564 9.3 Handling Qualities as a Performance Metric – The Development of ADS-33 577 9.3.1 The Evolution of a Design Standard – The Importance of Process 578 9.3.2 Some Critical Innovations in ADS-33 579 9.4 The UK MoD Approach 579 9.5 Roll Control; A Driver for Rotor Design 580 9.6 Helicopter Agility 583 9.6.1 ADS-33 Tailoring and Applications 585 9.6.2 Handling Qualities as a Safety Net; The Pilot as a System Component 587 9.7 The Future Challenges for Rotorcraft Handling Qualities Engineering 593 Chapter 10 Tiltrotor Aircraft: Modelling and Flying Qualities 10.1 Introduction and Scope 598 10.2 Modelling and Simulation of Tiltrotor Aircraft Flight Dynamics 604 10.2.1 Building a Simulation Model 605 10.2.2 Interactional Aerodynamics in Low-Speed Flight 620 10.2.3 Vortex Ring State and the Consequences for Tiltrotor Aircraft 621 10.2.4 Trim, Linearisation, and Stability 626 10.2.5 Response Analysis 632 10.3 The Flying Qualities of Tiltrotor Aircraft 635 10.3.1 General 635 10.3.2 Developing Tiltrotor Mission Task Elements 638 10.3.3 Flying Qualities of Tiltrotors; Clues from the Eigenvalues 644 10.3.4 Agility and Closed-Loop Stability of Tiltrotors 652 10.3.5 Flying Qualities during the Conversion 670 10.3.6 Improving Tiltrotor Flying Qualities with Stability and Control Augmentation 673 10.4 Load Alleviation versus Flying Qualities for Tiltrotor Aircraft 686 10.4.1 Drawing on the V-22 Experience 686 10.4.2 Load Alleviation for the European Civil Tiltrotor 688 10.5 Chapter Epilogue; Tempus Fugit for Tiltrotors 698 Appendix 10A Flightlab Axes Systems and Gimbal Flapping Dynamics 700 10A.1 FLIGHTLAB Axes Systems 700 10A.2 Gimbal Flapping Dynamics 703 Appendix 10B The XV-15 Tiltrotor 705 Aircraft Configuration Parameters 705 XV-15 3-view 707 XV-15 Control Ranges and Gearings 707 Appendix 10C The FXV-15 Stability and Control Derivatives 710 10C.1 Graphical Forms 710 10C.2 FXV-15 Stability and Control Derivative and Eigenvalue Tables 725 Helicopter Mode (Matrices Shown with and without (nointf) Aerodynamic Interactions) 725 Conversion Mode 733 Airplane Mode 737 Appendix 10D Proprotor Gimbal Dynamics in Airplane Mode 742 Appendix 10E Tiltrotor Directional Instability Through Constrained Roll Motion: An Elusive, Paradoxical Dynamic 746 10E.1 Background and the Effective Directional Stability 746 10E.2 Application to Tiltrotors 747 References 753 Index 789