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Helicopter Flight Dynamics: Including a Treatment of Tiltrotor Aircraft, 3rd Edition

Helicopter Flight Dynamics: Including a Treatment of Tiltrotor Aircraft, 3rd Edition

Gareth D. Padfield CEng, PhD, FRAeS

ISBN: 978-1-119-40107-0

Oct 2018

840 pages


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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.

Preface to first edition xiii

Preface to second edition xvii

Preface to third edition

Copyright acknowledgements xxi

Notation xxiii

List of abbreviations xxxiii

Chapter 1 Introduction

1.1 Simulation modelling 1

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 9

2.2 Four reference points 10

2.2.1 The mission and piloting tasks 11

2.2.2 The operational environment 14

2.2.3 The vehicle configuration, dynamics and flight envelope 15

Rotor controls 15

Two distinct flight regimes 17

Rotor stall boundaries 20

2.2.4 The pilot and pilot–vehicle interface 22

2.2.5 Résumé of the four reference points 24

2.3 Modelling helicopter flight dynamics 25

The problem domain 25

Multiple interacting subsystems 26

Trim, stability and response 28

The flapping rotor in vacuo 30

The flapping rotor in air – aerodynamic damping 33

Flapping derivatives 36

The fundamental 90° phase shift 36

Hub moments and rotor/fuselage coupling 38

Linearization in general 41

Stability and control résumé 42

The static stability derivative Mw 43

Rotor thrust, inflow, Zw and vertical gust response in hover 46

Gust response in forward flight 48

Vector-differential form of equations of motion 50

Validation 52

Inverse simulation 57

Modelling review 58

2.4 Flying qualities 59

Pilot opinion 60

Quantifying quality objectively 61

Frequency and amplitude – exposing the natural dimensions 62

Stability – early surprises compared with aeroplanes 63

Pilot-in-the-loop control; attacking a manoeuvre 66

Bandwidth – a parameter for all seasons? 67

Flying a mission task element 70

The cliff edge and carefree handling 71

Agility factor 72

Pilot’s workload 73

Inceptors and displays 75

Operational benefits of flying qualities 75

Flying qualities review 77

2.5 Design for flying qualities; stability and control augmentation 78

Impurity of primary response 79

Strong cross-couplings 79

Response degradation at flight envelope limits 80

Poor stability 80

The rotor as a control filter 81

Artificial stability 81

2.6 Tiltrotor flight dynamics

2.7 Chapter review 84

Chapter 3 Modelling helicopter flight dynamics: building a simulation model

3.1 Introduction and scope 87

3.2 The formulation of helicopter forces and moments in level 1 modelling 91

3.2.1 Main rotor 93

Blade flapping dynamics – introduction 93

The centre-spring equivalent rotor 96

Multi-blade coordinates 102

Rotor forces and moments 108

Rotor torque 114

Rotor inflow 115

Momentum theory for axial flight 116

Momentum theory in forward flight 119

Local-differential momentum theory and dynamic inflow 125

Rotor flapping–further considerations of the centre-spring approximation 128

Rotor in-plane motion – lead–lag 135

Rotor blade pitch 138

Ground effect on inflow and induced power 139

3.2.2 The tail rotor 142

3.2.3 Fuselage and empennage 146

The fuselage aerodynamic forces and moments 146

The empennage aerodynamic forces and moments 149

3.2.4 Powerplant and rotor governor 152

3.2.5 Flight control system 154

Pitch and roll control 154

Yaw control 158

Heave control 158

3.3 Integrated equations of motion of the helicopter 159

3.4 Beyond level 1 modelling 162

3.4.1 Rotor aerodynamics and dynamics 163

Rotor aerodynamics 163

Modelling section lift, drag and pitching moment 164

Modelling local incidence 167

Rotor dynamics 168

3.4.2 Interactional aerodynamics 171

3.5 Chapter 3 epilogue

Appendix 3A Frames of reference and coordinate transformations 175

3A.1 The inertial motion of the aircraft 175

3A.2 The orientation problem – angular coordinates of the aircraft 180

3A.3 Components of gravitational acceleration along the aircraft axes 181

3A.4 The rotor system – kinematics of a blade element 182

3A.5 Rotor reference planes – hub, tip path and no-feathering 184

Chapter 4 Modelling helicopter flight dynamics: trim and stability analysis

4.1 Introduction and scope 187

4.2 Trim analysis 192

4.2.1 The general trim problem 194

4.2.2 Longitudinal partial trim 196

4.2.3 Lateral/directional partial trim 201

4.2.4 Rotorspeed/torque partial trim 203

4.2.5 Balance of forces and moments 204

4.2.6 Control angles to support the forces and moments 204

4.3 Stability analysis 208

4.3.1 Linearization 209

4.3.2 The derivatives 214

The translational velocity derivatives 215

The angular velocity derivatives 224

The control derivatives 231

The effects of non-uniform rotor inflow on damping and control derivatives 234

Some reflections on derivatives 235

4.3.3 The natural modes of motion 236

The longitudinal modes 241

The lateral/directional modes 247

Comparison with flight 250

Appendix 4A The analysis of linear dynamic systems (with special reference to 6 DoF helicopter flight) 252

Appendix 4B The three case helicopters: Lynx, Bo105 and Puma 261

4B.1 Aircraft configuration parameters 261

The RAE (DRA) research Lynx, ZD559 261

The DLR research Bo105, S123 261

The RAE (DRA) research Puma, SA330 263

Fuselage aerodynamic characteristics 264

Empennage aerodynamic characteristics 268

4B.2 Stability and control derivatives 269

4B.3 Tables of stability and control derivatives and system eigenvalues 277

Appendix 4C The trim orientation problem 293

Chapter 5 Modelling helicopter flight dynamics: stability under constraint and response analysis

5.1 Introduction and scope 297

5.2 Stability under constraint 298

5.2.1 Attitude constraint 299

5.2.2 Flight-path constraint 306

Longitudinal motion 306

Lateral motion 310

5.3 Analysis of response to controls 315

5.3.1 General 315

5.3.2 Heave response to collective control inputs 317

Response to collective in hover 317

Response to collective in forward flight 323

5.3.3 Pitch and roll response to cyclic pitch control inputs 325

Response to step inputs in hover – general features 325

Effects of rotor dynamics 327

Step responses in hover – effect of key rotor parameters 327

Response variations with forward speed 330

Stability versus agility – contribution of the horizontal tailplane 331

Comparison with flight 332

5.3.4 Yaw/roll response to pedal control inputs 338

5.4 Response to atmospheric disturbances 344

Modelling atmospheric disturbances 346

Modelling helicopter response 348

Ride qualities 350

Appendix 5A Speed stability below minimum power; a forgotten problem?

Chapter 6 Flying qualities: objective assessment and criteria development

6.1 General introduction to flying qualities 355

6.2 Introduction and scope: the objective measurement of quality 360

6.3 Roll axis response criteria 364

6.3.1 Task margin and manoeuvre quickness 364

6.3.2 Moderate to large amplitude/low to moderate frequency: quickness and control power 371

6.3.3 Small amplitude/moderate to high frequency: bandwidth 378

Early efforts in the time domain 378

Bandwidth 381

Phase delay 386

Bandwidth/phase delay boundaries 387

Civil applications 389

The measurement of bandwidth 391

Estimating ωbw and τp 397

Control sensitivity 399

6.3.4 Small amplitude/low to moderate frequency: dynamic stability 401

6.3.5 Trim and quasi-static stability 402

6.4 Pitch axis response criteria 404

6.4.1 Moderate to large amplitude/low to moderate frequency: quickness and control power 404

6.4.2 Small amplitude/moderate to high frequency: bandwidth 408

6.4.3 Small amplitude/low to moderate frequency: dynamic stability 410

6.4.4 Trim and quasi-static stability 413

6.5 Heave axis response criteria 417

6.5.1 Criteria for hover and low speed flight 420

6.5.2 Criteria for torque and rotorspeed during vertical axis manoeuvres 424

6.5.3 Heave response criteria in forward flight 424

6.5.4 Heave response characteristics in steep descent 427

6.6 Yaw axis response criteria 429

6.6.1 Moderate to large amplitude/low to moderate frequency: quickness and control power 430

6.6.2 Small amplitude/moderate to high frequency: bandwidth 433

6.6.3 Small amplitude/low to moderate frequency: dynamic stability 433

6.6.4 Trim and quasi-static stability 436

6.7 Cross-coupling criteria 437

6.7.1 Pitch-to-roll and roll-to-pitch couplings 437

6.7.2 Collective to pitch coupling 440

6.7.3 Collective to yaw coupling 440

6.7.4 Sideslip to pitch and roll coupling 440

6.8 Multi-axis response criteria and novel-response types 442

6.8.1 Multi-axis response criteria 442

6.8.2 Novel response types 444

6.9 Objective criteria revisited 447

Chapter 7 Flying qualities: subjective assessment and other topics

7.1 Introduction and scope 455

7.2 The subjective assessment of flying quality 456

7.2.1 Pilot handling qualities ratings – HQRs 457

7.2.2 Conducting a handling qualities experiment 464

Designing a mission task element 464

Evaluating roll axis handling characteristics 466

7.3 Special flying qualities 478

7.3.1 Agility 478

Agility as a military attribute 478

The agility factor 481

Relating agility to handling qualities parameters 484

7.3.2 The integration of controls and displays for flight in degraded visual environments 487

Flight in DVE 487

Pilotage functions 488

Flying in DVE 489

The usable cue environment 490

UCE augmentation with overlaid symbology 496

7.3.3 Carefree flying qualities 500

7.4 Pilot’s controllers 508

7.5 The contribution of flying qualities to operational effectiveness and the safety of flight 511

Chapter 8 Flying qualities: forms of degradation

8.1 Introduction and scope 517

8.2 Flight in degraded visual environments 519

8.2.1 Recapping the usable cue environment 520

8.2.2 Visual perception in flight control – optical flow and motion parallax 523

8.2.3 Time to contact; optical tau, τ 532

8.2.4 τ control in the deceleration-to-stop manoeuvre 536

8.2.5 Tau-coupling – a paradigm for safety in action 538

8.2.6 Terrain-following flight in degraded visibility 545

τ on the rising curve 548

8.2.7 What now for tau?

8.3 Handling qualities degradation through flight system failures 559

8.3.1 Methodology for quantifying flying qualities following flight function failures 562

8.3.2 Loss of control function 564

Tail rotor failures 564

8.3.3 Malfunction of control – hard-over failures 568

8.3.4 Degradation of control function – actuator rate limiting 574

8.4 Encounters with atmospheric disturbances 576

8.4.1 Helicopter response to aircraft vortex wakes 578

The wake vortex 578

Hazard severity criteria 579

Analysis of encounters – attitude response 587

Analysis of encounters – vertical response 588

8.4.2 Severity of transient response 593

8.5 Chapter Review 597

Appendix 8A HELIFLIGHT, HELIFLIGHT-R and FLIGHTLAB at the University of Liverpool 599


Immersive cockpit environment 602


Chapter 9 Flying Qualities: the story of an idea

9.1 Introduction and Scope

9.2 Historical Context of Rotorcraft Flying Qualities

9.2.1 The Early Years; Some Highlights from the 1940s−50s

9.2.2 The Middle Years – Some Highlights from the 1960s−70s

9.3 Handling Qualities as a Performance Metric – the Development of ADS-33

9.3.1 The Evolution of a Design Standard – the Importance of Process

9.3.2 Some Critical Innovations in ADS-33

9.4 The UK MoD Approach

9.5 Roll Control; a driver for rotor design

9.6 Helicopter Agility

9.7 ADS-33 Tailoring and Applications

9.8 Handling Qualities as a Safety Net; The Pilot as a System Component

9.9 The Future Challenges for Rotorcraft Handling Qualities Engineering

Chapter 10 Tiltrotor Aircraft: modelling and flying qualities

10.1 Introduction and scope

10.2 Modelling and simulation of tiltrotor flight dynamics

10.2.1 Building a simulation model

Multi-Body Dynamic Modelling

Axes Systems

Gimbal rotors

FXV-15 model components and data

Interactional aerodynamics in low speed flight

Vortex Ring State and the consequences for tilt rotor aircraft

10.2.2 Trim, linearization and stability

10.2.3 Response analysis

10.3 The flying qualities of tiltrotor aircraft

10.3.1 General

10.3.2 Developing tiltrotor mission task elements

10.3.3 Flying qualities of tiltrotors; clues from the eigenvalues

10.3.4 Agility and closed-loop stability of tiltrotors

Lateral-directional agility and closed-loop stability

Longitudinal pitch-heave agility and closed-loop stability

10.3.5 Flying qualities during the conversion

10.3.6 Improving tiltrotor flying qualities with stability and control augmentation

Rate stabilisation

V-22 power management and control

Unification of Flying Qualities

Flying qualities of large civil tiltrotor aircraft

10.4 Load alleviation vs flying qualities for tiltrotor aircraft

10.4.1 Drawing on the V-22 experience

10.4.2 Load alleviation for the European civil tiltrotor

Modelling for the structural load alleviation ‘problem’ - oscillatory yoke (chordwise) bending moments

Control laws for structural load alleviation

10.5 Chapter Epilogue; Tempus Fugit for Tiltrotors

Appendix 10A FLIGHTLAB axes systems and gimbal flapping dynamics

10A.1 FLIGHTLAB axes systems

10A.2 Gimbal flapping dynamics

Appendix 10B The XV-15 Tiltrotor

10B.1 Aircraft configuration parameters

10B.2 XV-15 control ranges and gearings

10B.3 XV-15 3-view

Appendix 10C The FXV-15 stability and control derivatives

10C.1 Graphical forms

10C.2 FXV-15 stability and control derivative and eigenvalue tables

10C.2.1 Helicopter mode

10C.2.2 Conversion mode

10C.2.3 Airplane mode

Appendix 10D Proprotor gimbal dynamics in airplane mode

Appendix 10E Tiltrotor Directional instability through constrained roll motion; an elusive, paradoxical dynamic

10E.1 Background and the effective directional stability

10E.2 Application to tiltrotors