Helicopter Flight Dynamics

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 researchgate.net. 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 xvPreface to Third Edition xviiPreface to Second Edition xixPreface to First Edition xxiiiAcknowledgements xxviiNotation xxixList of Abbreviations xxxixChapter 1 Introduction1.1 Simulation Modelling 21.2 Flying Qualities 31.3 Missing Topics 41.4 Simple Guide to the Book 5Chapter 2 Helicopter and Tiltrotor Flight Dynamics – An Introductory Tour2.1 Introduction 82.2 Four Reference Points 92.2.1 The Mission and Piloting Tasks 92.2.2 The Operational Environment 122.2.3 The Vehicle Configuration, Dynamics, and Flight Envelope 132.2.4 The Pilot and Pilot–Vehicle Interface 192.2.5 Résumé of the Four Reference Points 202.3 Modelling Helicopter/Tiltrotor Flight Dynamics 212.3.1 The Problem Domain 212.3.2 Multiple Interacting Subsystems 222.3.3 Trim, Stability, and Response 242.3.4 The Flapping Rotor in a Vacuum 252.3.5 The Flapping Rotor in Air – Aerodynamic Damping 282.3.6 Flapping Derivatives 312.3.7 The Fundamental 90∘ Phase Shift 312.3.8 Hub Moments and Rotor/Fuselage Coupling 322.3.9 Linearization in General 352.3.10 Stability and Control Résumé 362.3.11 The Static Stability Derivative Mw 372.3.12 Rotor Thrust, Inflow, Zw, and Vertical Gust Response in Hover 392.3.13 Gust Response in Forward Flight 412.3.14 Vector-Differential Form of Equations of Motion 422.3.15 Validation 452.3.16 Inverse Simulation 482.3.17 Modelling Review 492.4 Flying Qualities 502.4.1 Pilot Opinion 502.4.2 Quantifying Quality Objectively 512.4.3 Frequency and Amplitude – Exposing the Natural Dimensions 522.4.4 Stability – Early Surprises Compared with Aeroplanes 532.4.5 Pilot-in-the-Loop Control; Attacking a Manoeuvre 562.4.6 Bandwidth – A Parameter for All Seasons? 572.4.7 Flying a Mission Task Element 592.4.8 The Cliff Edge and Carefree Handling 602.4.9 Agility Factor 602.4.10 Pilot’s Workload 612.4.11 Inceptors and Displays 632.4.12 Operational Benefits of Flying Qualities 632.4.13 Flying Qualities Review 652.5 Design for Flying Qualities; Stability and Control Augmentation 662.5.1 Impurity of Primary Response 672.5.2 Strong Cross-Couplings 672.5.3 Response Degradation at Flight Envelope Limits 672.5.4 Poor Stability 682.5.5 The Rotor as a Control Filter 682.5.6 Artificial Stability 692.6 Tiltrotor Flight Dynamics 712.7 Chapter Review 71Chapter 3 Modelling Helicopter Flight Dynamics: Building a Simulation Model3.1 Introduction and Scope 743.2 The Formulation of Helicopter Forces and Moments in Level 1 Modelling 783.2.1 Main Rotor 793.2.2 The Tail Rotor 1203.2.3 Fuselage and Empennage 1223.2.4 Powerplant and Rotor Governor 1273.2.5 Flight Control System 1293.3 Integrated Equations of Motion of the Helicopter 1343.4 Beyond Level 1 Modelling 1363.4.1 Rotor Aerodynamics and Dynamics 1373.4.2 Interactional Aerodynamics 1433.5 Chapter 3 Epilogue 147Appendix 3A Frames of Reference and Coordinate Transformations 1533A.1 The Inertial Motion of the Aircraft 1533A.2 The Orientation Problem – Angular Coordinates of the Aircraft 1563A.3 Components of Gravitational Acceleration along the Aircraft Axes 1583A.4 The Rotor System – Kinematics of a Blade Element 1583A.5 Rotor Reference Planes – Hub, Tip Path, and No-Feathering 161Chapter 4 Modelling Helicopter Flight Dynamics: Trim and Stability Analysis4.1 Introduction and Scope 1644.2 Trim Analysis 1684.2.1 The General Trim Problem 1704.2.2 Longitudinal Partial Trim 1714.2.3 Lateral/Directional Partial Trim 1764.2.4 Rotorspeed/Torque Partial Trim 1784.2.5 Balance of Forces and Moments 1784.2.6 Control Angles to Support the Forces and Moments 1794.3 Stability Analysis 1814.3.1 Linearization 1834.3.2 The Derivatives 1874.3.3 The Natural Modes of Motion 205Appendix 4A The Analysis of Linear Dynamic Systems (with Special Reference to 6-Dof Helicopter Flight) 218Appendix 4B The Three Case Helicopters: Lynx, Bo105 and Puma 2274B.1 Aircraft Configuration Parameters 227The RAE (DRA) Research Lynx, ZD559 227The DLR Research Bo105, S123 229The RAE (DRA) Research Puma, XW241 231Fuselage Aerodynamic Characteristics 233Lynx 233Bo105 233Puma 233Empennage Aerodynamic Characteristics 234Lynx 234Bo105 234Puma 2344B.2 Stability and Control Derivatives 2344B.3 Tables of Stability and Control Derivatives and System Eigenvalues 242Appendix 4C The Trim Orientation Problem 258Chapter 5 Modelling Helicopter Flight Dynamics: Stability Under Constraint and Response Analysis5.1 Introduction and Scope 2625.2 Stability Under Constraint 2635.2.1 Attitude Constraint 2645.2.2 Flight Path Constraint 2755.3 Analysis of Response to Controls 2835.3.1 General 2835.3.2 Heave Response to Collective Control Inputs 2845.3.3 Pitch and Roll Response to Cyclic Pitch Control Inputs 2915.3.4 Yaw/Roll Response to Pedal Control Inputs 3015.4 Response to Atmospheric Disturbances 309Appendix 5A Speed Stability Below Minimum Power; A Forgotten Problem? 315Chapter 6 Flying Qualities: Objective Assessment and Criteria Development6.1 General Introduction to Flying Qualities 3346.2 Introduction and Scope: The Objective Measurement of Quality 3386.3 Roll Axis Response Criteria 3416.3.1 Task Margin and Manoeuvre Quickness 3416.3.2 Moderate to Large Amplitude/Low to Moderate Frequency: Quickness and Control Power 3476.3.3 Small Amplitude/Moderate to High Frequency: Bandwidth 3536.3.4 Small Amplitude/Low to Moderate Frequency: Dynamic Stability 3716.3.5 Trim and Quasi-Static Stability 3726.4 Pitch Axis Response Criteria 3746.4.1 Moderate to Large Amplitude/Low to Moderate Frequency: Quickness and Control Power 3746.4.2 Small Amplitude/Moderate to High Frequency: Bandwidth 3776.4.3 Small Amplitude/Low to Moderate Frequency: Dynamic Stability 3786.4.4 Trim and Quasi-Static Stability 3816.5 Heave Axis Response Criteria 3856.5.1 Criteria for Hover and Low-Speed Flight 3886.5.2 Criteria for Torque and Rotorspeed During Vertical Axis Manoeuvres 3916.5.3 Heave Response Criteria in Forward Flight 3926.5.4 Heave Response Characteristics in Steep Descent 3936.6 Yaw Axis Response Criteria 3956.6.1 Moderate to Large Amplitude/Low to Moderate Frequency: Quickness and Control Power 3966.6.2 Small Amplitude/Moderate to High Frequency: Bandwidth 3986.6.3 Small Amplitude/Low to Moderate Frequency: Dynamic Stability 3986.6.4 Trim and Quasi-Static Stability 4016.7 Cross-Coupling Criteria 4026.7.1 Pitch-to-Roll and Roll-to-Pitch Couplings 4026.7.2 Collective to Yaw Coupling 4046.7.3 Sideslip to Pitch and Roll Coupling 4056.8 Multi-Axis Response Criteria and Novel-Response Types 4066.8.1 Multi-Axis Response Criteria 4066.8.2 Novel Response Types 4076.9 Objective Criteria Revisited 410Chapter 7 Flying Qualities: Subjective Assessment and Other Topics7.1 Introduction and Scope 4187.2 The Subjective Assessment of Flying Quality 4197.2.1 Pilot Handling Qualities Ratings – HQRs 4207.2.2 Conducting a Handling Qualities Experiment 4257.3 Special Flying Qualities 4387.3.1 Agility 4387.3.2 The Integration of Controls and Displays for Flight in Degraded Visual Environments 4457.3.3 Carefree Flying Qualities 4557.4 Pilot’s Controllers 4627.5 The Contribution of Flying Qualities to Operational Effectiveness and the Safety of Flight 464Chapter 8 Flying Qualities: Forms of Degradation8.1 Introduction and Scope 4708.2 Flight in Degraded Visual Environments 4728.2.1 Recapping the Usable Cue Environment 4728.2.2 Visual Perception in Flight Control – Optical Flow and Motion Parallax 4758.2.3 Time to Contact; Optical Tau, 𝜏 4838.2.4 𝜏 Control in the Deceleration-to-Stop Manoeuvre 4868.2.5 Tau-Coupling – A Paradigm for Safety in Action 4878.2.6 Terrain-Following Flight in Degraded Visibility 4948.2.7 What Now for Tau? 5078.3 Handling Qualities Degradation through Flight System Failures 5118.3.1 Methodology for Quantifying Flying Qualities Following Flight Function Failures 5128.3.2 Loss of Control Function 5148.3.3 Malfunction of Control – Hard-Over Failures 5178.3.4 Degradation of Control Function – Actuator Rate Limiting 5228.4 Encounters with Atmospheric Disturbances 5248.4.1 Helicopter Response to Aircraft Vortex Wakes 5258.4.2 Severity of Transient Response 5388.5 Chapter Review 542Appendix 8A HELIFLIGHT, HELIFLIGHT-R, and FLIGHTLAB at the University of Liverpool 5458A.1 FLIGHTLAB 5458A.2 Immersive Cockpit Environment 5478A.3 HELIFLIGHT-R 551Chapter 9 Flying Qualities: The Story of an Idea9.1 Introduction and Scope 5549.2 Historical Context of Rotorcraft Flying Qualities 5579.2.1 The Early Years; Some Highlights from the 1940s–1950s 5579.2.2 The Middle Years – Some Highlights from the 1960s–1970s 5649.3 Handling Qualities as a Performance Metric – The Development of ADS-33 5779.3.1 The Evolution of a Design Standard – The Importance of Process 5789.3.2 Some Critical Innovations in ADS-33 5799.4 The UK MoD Approach 5799.5 Roll Control; A Driver for Rotor Design 5809.6 Helicopter Agility 5839.6.1 ADS-33 Tailoring and Applications 5859.6.2 Handling Qualities as a Safety Net; The Pilot as a System Component 5879.7 The Future Challenges for Rotorcraft Handling Qualities Engineering 593Chapter 10 Tiltrotor Aircraft: Modelling and Flying Qualities10.1 Introduction and Scope 59810.2 Modelling and Simulation of Tiltrotor Aircraft Flight Dynamics 60410.2.1 Building a Simulation Model 60510.2.2 Interactional Aerodynamics in Low-Speed Flight 62010.2.3 Vortex Ring State and the Consequences for Tiltrotor Aircraft 62110.2.4 Trim, Linearisation, and Stability 62610.2.5 Response Analysis 63210.3 The Flying Qualities of Tiltrotor Aircraft 63510.3.1 General 63510.3.2 Developing Tiltrotor Mission Task Elements 63810.3.3 Flying Qualities of Tiltrotors; Clues from the Eigenvalues 64410.3.4 Agility and Closed-Loop Stability of Tiltrotors 65210.3.5 Flying Qualities during the Conversion 67010.3.6 Improving Tiltrotor Flying Qualities with Stability and Control Augmentation 67310.4 Load Alleviation versus Flying Qualities for Tiltrotor Aircraft 68610.4.1 Drawing on the V-22 Experience 68610.4.2 Load Alleviation for the European Civil Tiltrotor 68810.5 Chapter Epilogue; Tempus Fugit for Tiltrotors 698Appendix 10A Flightlab Axes Systems and Gimbal Flapping Dynamics 70010A.1 FLIGHTLAB Axes Systems 70010A.2 Gimbal Flapping Dynamics 703Appendix 10B The XV-15 Tiltrotor 705Aircraft Configuration Parameters 705XV-15 3-view 707XV-15 Control Ranges and Gearings 707Appendix 10C The FXV-15 Stability and Control Derivatives 71010C.1 Graphical Forms 71010C.2 FXV-15 Stability and Control Derivative and Eigenvalue Tables 725Helicopter Mode (Matrices Shown with and without (nointf) Aerodynamic Interactions) 725Conversion Mode 733Airplane Mode 737Appendix 10D Proprotor Gimbal Dynamics in Airplane Mode 742Appendix 10E Tiltrotor Directional Instability Through Constrained Roll Motion: An Elusive, Paradoxical Dynamic 74610E.1 Background and the Effective Directional Stability 74610E.2 Application to Tiltrotors 747References 753Index 789