Category HELICOPTER FLIGHT DYNAMICS

The underlying premise of this book is that flight dynamics and control is a central discipline, at the heart of aeronautics, linking the aerodynamic and structural sciences with the applied technologies of systems and avionics and, above all, with the pilot. Flight dynamics engineers need to have breadth and depth in their domain of interest, and often hold a special responsibility in design and research departments. It is asserted that more than any other aerospace discipline, flight dynamics offers a viewpoint on, and is connected to, the key rotorcraft attributes and technologies – from the detailed fluid dynamics associated with the interaction of the main rotor wake with the empen­nage, to the servo-aeroelastic couplings between the rotor and control system, through to the evaluation of enhanced safety, operational advantage and mission effectiveness of good flying qualities. It is further asserted that the multidisciplinary nature of ro­torcraft flight dynamics places it in a unique position to hold the key to concurrency in requirements capture and design, i. e., the ability to optimize under the influence of multiple constraints. In the author’s view, the role of the practising flight dynamics engineer is therefore an important one and there is a need for guidebooks and practi­tioner’s manuals to the subject to assist in the development of the required skills and knowledge. This book is an attempt at such a manual, and it discusses flight dynamics under two main headings – simulation modelling and flying qualities. The importance of good simulation fidelity and robust flying qualities criteria in the requirements cap­ture and design phases of a new project cannot be overstated, and this theme will be expanded upon later in this chapter and throughout the book. Together, these attributes underpin confidence in decision making during the high-risk early design phase and are directed towards the twin goals of achieving super-safe flying qualities and getting designs right, first time. These goals have motivated much of the research conducted in government research laboratories, industry and universities for several decades.

In this short general Introduction, the aim is to give the reader a qualitative appreciation of the two main subjects – simulation modelling and flying qualities. The topics that come within the scope of flight dynamics are also addressed briefly, but are not covered in the book for various reasons. Finally, a brief ‘roadmap’ to the seven technical chapters is presented.

In this preface, I want to communicate three things. First, I would like to share with the reader my motivation for taking on this project. Second, I want to try to identify my intended audience and, third, I want to record some special acknowledgements to colleagues who have helped me.

When I decided to pursue a career as an aeronautical engineer, my motivation stemmed from an aesthetic delight in flight and things that flew, combined with an uncanny interest in tackling, and sometimes solving, difficult technical problems. Both held a mystery for me and together, unbeknown to me at the time, helped me to ‘escape’ the Welsh mining community in which I had been sculptured, on to the roads of learning and earning. Long before that, in the late 1940s, when I was taking my first gasps of Welsh air, the Royal Aircraft Establishment (RAE) had been conducting the first research flight trials to understand helicopter stability and control. It should be remembered that at that time, practical helicopters had been around for less than a decade. From reading the technical reports and talking with engineers who worked in those days, I have an image of an exciting and productive era, with test and theory continuously wrestling to provide first-time answers to the many puzzles of helicopter flight dynamics.

Although there have been quiet periods since then, the RAE sustained its heli­copter research programme through the 1950s, 1960s and 1970s and by the time I took charge of the activities at Bedford in the mid-1980s, it had established itself at the leading edge of research into rotor aerodynamics and helicopter flight dynamics. My own helicopter journey began in the Research Department at Westland Helicopters in the early 1970s. At that time, Westland were engaged with the flight testing of the prototype Lynx, a helicopter full of innovation for a 1960s design. This was also an exciting era, when the foundations of my understanding of helicopter flight dynamics were laid down. Working with a small and enthusiastic group of research engineers, the mysteries began to unfold, but at times it felt as if the more I learned, the less I understood. I do not want to use the word enthusiastic lightly in this context; a great number of helicopter engineers that I have known have a degree of enthusiasm that goes way beyond the call of duty, so to speak, and I do believe that this is a spe­cial characteristic of people in this relatively small community. While it is inevitable that our endeavours are fuelled by the needs of others – the ubiquitous customer, for example – enthusiasm for the helicopter and all of the attendant technologies is a powerful and dynamic force. In writing this book I have tried to share some of my enthusiasm and knowledge of helicopter flight dynamics with as large an audience as possible, and that was probably sufficient personal motivation to undertake the task. This motivation is augmented by a feeling that my own experience in theory and test has given me insight into, and a somewhat unique way of looking at, the

subject of flight dynamics that I hope will appeal to the reader in search of under­standing.

There are, however, more pragmatic reasons for writing this book. While fixed – wing flight dynamics, stability and control have been covered from a number of per­spectives in more than a dozen treatise over the years, there has never been a helicopter textbook dedicated to the subject; so there is, at least, a perceived gap in the available literature, and, perhaps more importantly, the time is ripe to fill that gap. The last 10-20 years has seen a significant amount of research in flight simulation and flying qualities for helicopters, much of which has appeared in the open literature but is scattered in scores of individual references. This book attempts to capture the essence of this work from the author’s perspective, as a practitioner involved in the DRA (RAE) research in national and international programmes. It has been a busy and productive period, indeed it is still continuing, and I hope that this book conveys the impression of a living and mature subject, to which many contributions are yet to be made.

The book is written mainly for practising flight dynamics engineers. In some organizations, such a person may be described as a flying qualities engineer, a flight simulation engineer or even a flight controls engineer, but my personal view is that these titles reflect subdisciplines within the larger field of flight dynamics. Key activities of the flight dynamics engineer are simulation modelling, flying qualities and flight control. Simulation brings the engineer into a special and intimate relationship with the system he or she is modelling and the helicopter is a classic example. The present era appears to be characterized by fast-disappearing computational constraints on our ability to model and simulate the complex aeroelastic interactions involved in helicopter flight. Keeping step with these advances, the flight dynamics engineer must, at the same time, preserve an understanding of the link between cause and effect. After all, the very objectives of modelling and simulation are to gain an understanding of the effects of various design features and insight into the sensitivity of flight behaviour to changes in configuration and flight condition. In the modelling task, the flight dynamics engineer will need to address all the underlying assumptions, and test them against experimental data, in a way that provides as complete a calibration as possible. The flight dynamics engineer will also have a good understanding of flying qualities and the piloting task, and he or she will appreciate the importance of the external and internal influences on these qualities and the need for mission-oriented criteria. Good flying qualities underpin safe flight, and this book attempts to make the essence of the theoretical developments and test database, assembled over the period from the early 1980s through to the present time, accessible to practising engineers. Flight testing is an important part of flight dynamics, supporting both simulation validation and the development of flying qualities criteria. In this book I have attempted to provide the tools for building and analysing simulation models of helicopter flight, and to present an up-to-date treatment of flying qualities criteria and flight test techniques.

While this is primarily a specialist’s book, it is also written for those with empathy for the broader vision, within which flight dynamics plays its part. It is hoped that the book, or parts of the book, will appeal to test pilots and flight test engineers and offer something useful to engineers without aeronautical backgrounds, or those who have specialized in the aerodynamic or controls disciplines and wish to gain a broader perspective of the functionality of the total aircraft. In writing Chapters 2, 6 and 7, I have tried to avoid a dependence on ‘difficult’ mathematics. Chapters 3, 4 and 5, on the other hand, require a reasonable grasp of analytical and vectorial mechanics as

would, for example, be taught in the more extensive engineering courses at first and higher degree levels. With regard to education programmes, I have had in mind that different parts of the book could well form the subject of one or two term courses at graduate or even advanced undergraduate level. I would strongly recommend Chapter 2 to all who have embarked on a learning programme with this book. Taught well, I have always believed that flight dynamics is inspirational and, hence, a motivating subject at university level, dealing with whole aircraft and the way they fly, and, at the same time, the integration of the parts that make the whole. I have personally gained much from the subject and perhaps this book also serves as an attempt to return my own personal understandings into the well of knowledge.

In the sense that this book is an offering, it also reflects the great deal of gratitude I feel towards many colleagues over the years, who have helped to make the business enjoyable, challenging and stimulating for me. I have been fortunate to be part of several endeavours, both nationally and internationally, that have achieved significant progress, compared with the sometimes more limited progress possible by individuals working on their own. International collaboration has always held a special interest for me and I am grateful to AGARD, Garteur, TTCP and other, less formal, ties with European and North American agencies, for providing the auspices for collaboration. Once again, this book is full of the fruits of these activities. I genuinely believe that helicopters of the future will perform better, be safer and be easier to fly because of the efforts of the various research groups working together in the field of flight dynamics, feeding the results into the acquisition processes in the form of the requirements specifications, and into the manufacturing process, through improved tools and technologies.

In the preparation of this book several colleagues have given me specific support which I would like to acknowledge. For assistance in the generation and presentation of key results I would like to acknowledge the Rotorcraft Group at DRA Bedford. But my gratitude to the Bedford team goes far beyond the specific support activities, and I resist identifying individual contributions for that reason. As a team we have pushed forward in many directions over the last 10 years, sometimes at the exciting but lonely leading edge, at other times filling in the gaps left by others pushing forward with greater pace and urgency. I want to record that this book very much reflects these team efforts, as indicated by the many cited references. I was anxious to have the book reviewed in a critical light before signing it off for publication, and my thanks go to colleagues and friends Ronald Milne, Ronald DuVal, Alan Simpson, Ian Simons and David Key for being kind enough to read individual chapters and for providing me with important critical reviews. A special thanks to Roy Bradley for reviewing the book in its entirety and for offering many valuable ideas which have been implemented to make the book better.

I first had the serious idea of writing this book about 4 years ago. I was familiar with the Blackwell Science series and I liked their productions, so I approached them first. From the beginning, my publisher at Blackwell’s, Julia Burden, was helpful and encouraging. Later, during the preparation, the support from Julia and her team was sustained and all negotiations have been both positive and constructive; I would like to express my gratitude for this important contribution. I would like also to acknowledge the vital support of my employer, the Defence Research Agency, for allowing me to use material from my research activities at RAE and DRA over the past 18 years. My particular thanks to my boss, Peter England, Manager, Flight Dynamics and Simulation Department at DRA Bedford, who has been continually supportive with a positive

attitude that has freed me from any feelings of conflict of interest. Acknowledgements for DRA material used and figures or quotes from other sources are included elsewhere in this book. The figures in this book were produced by two artists, those in Chapter 2 by Peter Wells and the rest by Mark Straker. Both worked from often very rough drafts and have, I believe, done an excellent job – thank you both.

All these people have helped me along the road in a variety of different ways, as I have tried to indicate, but I am fully accountable for what is written in this book. I am responsible for the variations in style and ‘colour’, inevitable and perhaps even desirable in a book of this scope and size. There have been moments when I have been guided by some kind of inspiration and others where I have had to be more concerned with making sure the mathematics was correct. I have done my best in this second area and apologise in advance for the inevitable errors that will have crept in. My final thanks go to you, the reader, for at least starting the journey through this work. I hope that you enjoy the learning and I wish you good fortune with the application of your own ideas, some of which may germinate as a result of reading this book. It might help to know that this book will continue to be my guide to flight dynamics and I will be looking for ways in which the presentation can be improved.

Gareth D. Padfield Sharnbrook, England

In the preface to the first edition of my book I talked about flight dynamics as a ‘ living and mature subject, to which many contributions are yet to be made’; I believe this statement is still true and every new generation of engineers has something new to add to the store of knowledge. During the 10 years since its publication, the disciplines of flight dynamics and handling/flying qualities engineering have matured into a systems approach to the design and development of those functions and technologies required to support the piloting task. At the same time, as pilot-centred operational attributes, flying qualities are recognised as the product of a continual tension between perfor­mance and safety. These two descriptions and the interplay between them highlight the importance of the subject to continuing helicopter development. The most obvious contributors to flying qualities are the air vehicle dynamics – the stability and control characteristics – and these aspects were treated in some depth in the first edition. Fly­ing qualities are much more, however, and this has also been emphasized. They are a product of the four elements: the aircraft, the pilot, the task and the environment, and it is this broader, holistic view of the subject which is both a technical discipline and an operational attribute, which emphasizes the importance to flight safety and operational effectiveness. I have tried to draw out this emphasis in the new material presented in Chapter 8, Degraded Flying Qualities, which constitutes the bulk of the new content in this second edition.

During the preparation of the first edition, ADS-33C was being used extensively in a range of military aircraft programmes. The handling qualities (HQs) criteria repre­sented key performance drivers for the RAH-66 Comanche, and although this aircraft programme would eventually be cancelled, Industry and the surrounding helicopter ‘community’ would learn about the technology required to deliver Level 1 HQs across a range of operational requirements. The last decade has seen ADS-33 applied to aircraft such as NH-90 and the UK’s attack helicopter, and also to new operations including maritime rotorcraft and helicopters carrying external loads, and used as a design guide for civil tilt rotor aircraft. It is now common at annual European and American Helicopter Fora to hear presentations on new applications of ADS-33 or ex­tensions to its theoretical basis. The Standard has also been refined over this period and currently exists in the ADS-33E-PRF (performance) version, emphasizing its status as a performance requirement. A brief resume of developments is added to Chapter 6.

Significant advances have also been made on the modelling and simulation front, and it is very satisfying to see the considerable pace at which the modelling of complex helicopter aerodynamics is moving. It surely will not be very long before the results of accurate physical flow modelling will be fully embodied into efficient, whole aircraft design codes and real-time simulation. A combination of high-quality computer tools for comprehensive synthesis and analysis and robust design criteria pave the way for

massive reductions in timescales and costs for design, development and certification. The modelling and simulation material in Chapters 3, 4 and 5 is largely unchanged in this second edition. This is simply a result of the author needing to put limits on what is achievable within the timescale available.

In August 1999, I left government ‘service’ to join The University of Liverpool with a mandate to lead the aerospace activity, both on the research and the learning and teaching (L&T) axes. I was confident that my 30 years of experience would enable me to transition fairly naturally into academia on the research axis. I had very little experience on the L&T side however, but have developed undergraduate modules in rotorcraft flight, aircraft performance and flight handling qualities. I confirm the old adage – to learn something properly, you need to teach it – and it has been very satisfying to ‘plough’ some of my experience back into the formative ‘soil’ of future careers.

As with the first edition, while this work is a consolidation of my knowledge and understanding, much has been drawn from the efforts and results of others, and not only is acknowledging this fact appropriate but it also feels satisfying to record these thanks, particularly to the very special and highly motivated group of individuals in the Flight Science and Technology Research Group at the University of Liverpool. This group has formed and grown organically, as any university research group might, over the period since 2000 and, hopefully, will continue to develop capabilities and contribute to the universal pool of knowledge and understanding. Those, in academe, who have had the pleasure and privilege to ‘lead’ a group of young post-graduate students and post-doctoral researchers will perhaps understand the sense in which I derive satisfaction from witnessing the development of independent researchers, and adding my mite to the process. Thanks to Ben Lawrence and Binoy Manimala who have become experts in FLIGHTLAB and other computational flight dynamics analyses and helped me in numerous ways, but particularly related to investigating the effects of trailing wake vortices on helicopters. Neil Cameron derived the results presented in Chapter 8 on the effects of control system failures on the handing qualities of tilt rotor aircraft. Gary Clark worked closely with me to produce the results in Chapter 8, relating to terrain following flight in degraded visibility. Immeasurable gratitude to Mark White, the simulation laboratory manager in FS&T, who has worked with me on most of the research projects initiated over the last 5 years. The support of Advanced Rotorcraft Technology, particularly Ronald Du Val and Chengian Ho, with various FLIGHTLAB issues and the development of the HELIFLIGHT simulator has been huge and is gratefully acknowledged.

Those involved in flight dynamics and handling qualities research will understand the significant contribution that test pilots make to the subject, and at Liverpool we have been very fortunate indeed to have the sustained and consistently excellent support from a number of ex-military test pilots, and this is the place to acknowledge their contribution to my developing knowledge captured in this book. Sincere thanks to Andy Berryman, Nigel Talbot, Martin Mayer and Steve Cheyne; they should hopefully know how important I consider their contributions to be.

Thanks to Roger Hoh and colleagues at Hoh Aeronautics, whose continuous commitment to handling qualities excellence has been inspirational to me. Roger has also made contributions to the research activities in FS&T particularly related to the development of handling criteria in degraded conditions and the attendant design of displays for flight in degraded visual environments. The whole subject of visual per­ception in flight control has been illuminated to me through close collaboration with David Lee, Professor of Perception in Action at The University of Edinburgh. David’s

contributions to my understanding of the role of optical flow and optical tau in the control of motion has been significant and is gratefully acknowledged.

Over the last 10 years I have received paper and electronic communications from colleagues and readers of the first edition worldwide who have been complementary and have politely identified various errors or misprints, which have been corrected. These communications have been rather too numerous to identify and mention individually here but it is hoped that a collective thanks will be appreciated.

Mark Straker produced the figures in the form they appear in this book to his usual very high standard; thanks again Mark for your creative support.

Finally, grateful thanks to Julia Burden at Blackwell Publishing who has been unrelenting in her encouragement, dare I say persistence, with me to produce material for this second edition. Any Head of a fairly large academic department (at Liverpool I am currently Head of Engineering with 900 students and 250 staff) will know what a challenging and rather absorbing business it can be, especially when one takes it on to direct and increase the pace of change. So, I was reluctant to commit to this second edition until I felt that I had sufficient new research completed to ‘justify’ a new edition; the reader will now find a consolidation of much of that new work in the new Chap­ter 8. Only the authors who have worked under the pressures of a tight schedule, whilst at the same time having a busy day job, will know how and where I found the time.

So this book is offered to both a new and old readership, who might also find some light-hearted relief in a ‘refreshed’ version of my poem, or sky-song as I call it, Helicopter Blues, which can also be sung in a 12-bar blues arrangement (normally in Emaj but in Am if you’re feeling cool)

I got the helicopter blues They’re going round in my head I got the helicopter blues They’re still going round in my head

brother please tell me what to do about these helicopter blues

My engine she’s failing Gotta reduce my torque My engine she keeps failing Gotta pull back on my power

seems like I’m autorotating from all these helicopter blues

My tail rotor ain’t working Ain’t got no place to go My tail rotor she ain’t working Ain’t got no place to turn These helicopter blues brother They’re driving me insane

My humms are a humming

Feel all fatigued, used and abused

My humms are humming

I’m worn out from all this aerofoil toil

If I don’t get some maintenance

sister I’ve had it with all these helicopter blues

My gearbox is whining Must need more lubrication

I said I can’t stand this whining

please ease my pain with boiling oil

If I don’t get that stuff right now

I’m gonna lock up with those helicopter blues

Dark blue or light

The blues got a strong hold on me

It really don’t matter which it is

The blues got no respect for me

Well, if only I could change to green

Maybe I could shake off these helicopter blues

I’ve designed a new helicopter It’ll be free of the blues

I’ve used special techniques and powerful computers I’m sure I know what I’m doing

now I gotta find someone to help me chase away these helicopter blues

I went to see Boeing

Said I got this new blues-free design

I went up to see Boeing, told them my story and it sounded fine But they said why blue’s our favourite colour Besides which, you’re European

So I took my design to Eurocopter I should have thought of them first If I’d only gone to Eurocopter I wouldn’t be standing here dying of thirst

They said ‘ces la vie mon frere’ you can’t make a sans bleu helicoptre

I went to see Sikorsky

I thought – They’ll fix the blues

They sent for Nick Lappos

To fix the helicopter blues

Nick said don’t be such a baby Gareth

(besides, I don’t work here anymore)

Just enjoy those helicopter blues

I’ll go see Ray Prouty

People say, Ray – he ain’t got no blues

Please help me Ray – how much more aerodynamics do I need – I’ll clean your shoes Ray said, wake up and smell the coffee fella Learn how to hide those helicopter blues

I’ve learned to live with them now I’m talking about the helicopter blues Even got to enjoy them Those sweet, soothing helicopter blues

I’m as weary as hell but please don’t take away my helicopter blues

Gareth D. Padfield Caldy, England

The cover photograph is reproduced with permission from AgustaWestland.

The following people and organizations are gratefully acknowledged for granting per­mission for the use of copyright material.

TheUKMoD and Defence Research Agency for Figs 2.31, 2.43, 2.44, 2.50, 3.15, 3.28, 3.29, 3.35, 3.37, 3.38, 5.7-5.9, 5.28-5.31, 5.34, 6.7, 6.8, 6.9, 6.10, 6.18, 6.19, 6.35, 6.36, 6.38, 6.39, 6.47-6.52, 6.59, 7.10-7.24, 7.38, 7.44, 7.45 and 7.46.* The US Army for Figs 6.15, 6.17, 6.20, 6.25, 6.30, 6.33, 6.40-6.45, 6.56, 6.61, 6.64, 6.65, 6.70 and 7.28 and Table 7.4. The American Helicopter Society (AHS) for Figs 3.16 and 7.5 (with the US Army). Bob Heffley for Figs 6.6 and 6.11. Cambridge University Press for the quote from Duncan’s book at the beginning of Chapter 3. Chengjian He and the AHS for Fig. 5.27. Chris Blanken, the US Army and the AHS for Figs 7.29 and 7.30. Courtland Bivens, the AHS and the US Army for Fig. 6.63. David Key and the Royal Aeronautical Society for Figs 6.3 and 6.31. David Key for the quote at the beginning of Chapter 7. DLR Braunschweig for Figs 6.21, 6.23 (with RAeSoc), 6.32, 6.37, 6.58 (with the AHS), 6.68 (with the US Army) and 7.4 (with AGARD). Eurocopter Deutschland for Figs 6.46 and 6.66. Ian Cheeseman andMoD for Figs 3.28 and 3.29. Jeff Schroeder and the AHS for Figs 7.32-7.36. Jeremy Howitt and the DRA for Figs 7.39, 7.40 and 7.41. Knute Hanson and the Royal Aeronautical Society for Fig. 6.69. Lt Cdr Sandy Ellin and the DRA for Figs 2.7, 3.44 and 3.45. Mark Tischler and AGARD for Figs 5.25, 5.26, 6.34 and 6.57. McDonnell Douglas Helicopters, AGARD and the US Army for Fig. 6.71. NASA for Figs 4.12 and 6.2. Institute for Aerospace Research, Ottawa, for Figs 6.54 and 7.7 (with the AHS). Pat Curtiss for Figs 3.46, 3.47 and 5.4. Roger Hoh for Figs 6.24, 6.26 (with the AHS), 6.29 (with the RAeSoc) and 7.27 (with the AHS). Sikorsky Aircraft, the US Army and the AHS for Fig. 6.72. Stewart Houston and the DRA for Figs 5.10-5.13. Tom Beddoes for Fig. 3.42. Jan Drees for Fig. 2.8. AGARD for selected text from References 6.72 and 7.25. Westland Helicopters for granting permission to use configuration data and flight test data for the Lynx helicopter. Eurocopter Deutschland for granting permission to use configuration data and flight test data for the Bo105 helicopter. Eurocopter France for granting permission to use configuration data and flight test data for the SA330 Puma helicopter.

In this second edition, once again the author has drawn from the vast store of knowledge and understanding gained and documented by others and the following people and organizations are gratefully acknowledged for the use of copyright material.

Philippe Rollet and Eurocopter for the use of Table 8.9. John Perrone at the University of Waikato for Figs 8.4, 8.6 and 8.11. James Cutting at Cornell University andMIT Press for Figs 8.7,8.8 and the basis of Fig 8.10. NASA for Fig. 8.14. David Lee for Figs 8.18 and 8.19. The US Army Aviation Engineering Directorate for the use of Table 6.6 andFigs 6.74,6.75 and 6.77 and general reference to ADS33. AgustaWestland

Helicopters for the use of the photographs of the EH101 at the start of Chapter 8 and also on the book cover. Roger Hoh and the American Helicopter Society for Fig. 8.2. The American Helicopter Society for a variety of the author’s own figures published in Ref 8.31, 8.33 and 8.55. The Institution of Mechanical Engineers for Fig. 8.45 from the author’s own paper. The Royal Aeronautical Society for the use of the author’s own figures from Ref 8.53. J. Weakly and the American Helicopter Society for Fig. 8.43. Franklin Harris for Fig. 8.62.

*© British Crown Copyright 1995/DRA; reproduced with the permission of the Controller of Her Britannic Majesty’s Stationery Office.

Notation

main rotor blade lift curve slope (l/rad) constant acceleration of the т guide tail rotor blade lift curve slope (l/rad) coefficients of characteristic (eigenvalue) equation acceleration of P relative to fixed earth (components ax, ay, az) (m/s2, ft/s2) acceleration vector of P relative to G (m/s2, ft/s2) acceleration components of a blade element in rotating blade axes system (m/s2, ft/s2) peak normal acceleration (m/s2, ft/s2) rotor blade chord (m, ft) constant т motion local drag force per unit span acting on blade element (N/m, lbf/ft) flap hinge offset (m, ft) lag hinge offset (m, ft) forcing function vector coefficients in blade flapping equation in-plane and out-of-plane aerodynamic loads on rotor blade at radial station rb acceleration due to gravity (m/s2, ft/s2) lateral cyclic stick-blade angle gearing constants longitudinal cyclic stick-blade angle gearing constants collective lever-lateral cyclic blade angle gearing constants pedal/collective lever-tail rotor control run gearing constant nonlinear trim functions collective lever-longitudinal cyclic blade angle gearing constants pedal-tail rotor collective blade angle gearing constant tail rotor gearing height above ground (m(ft)) eye-height height (m, ft), height rate (m/s, ft/s) height of fin centre of pressure above fuselage reference point along negative z-axis (m, ft) height of main rotor hub above fuselage reference point (m, ft) height of tail rotor hub above fuselage reference point (m, ft) unit vectors along x-, y – and z-axes т coupling constant inertia coupling parameters

ao

ag aoT an—l, an—2 , • •

a P

a P/g axbt ayb, azb

azpk c c d (f, rb) eR R f(t) fe (f), Mf) fy(rb), fz (rb) g glc0, glcl gls0, glsl gcc0> gccl gcT0

gsc0> gscl gT0, gTl

gT

h, h

hfn

hR hT i, j,k к kl, к2, кз