Category Principles of Helicopter Aerodynamics Second Edition

Producing Thrust

In its simplest terms, the thrust on the helicopter rotor is generated by the aerody­namic lift forces created on the spinning blades. To turn the rotor, power from an engine must be transmitted to the rotor shaft. It is the relatively low amount of power required to lift the machine compared to other vertical take off and landing (VTOL) aircraft that makes the helicopter unique. Efficient hovering flight with low power requirements comes about by accelerating a large mass of air at a relatively low velocity; hence we have the large diameter rotors that are one obvious characteristic of helicopters. In addition, the helicopter must be able to fly forward, climb, cruise at speed, and then descend and come back into a hover for landing. This demanding flight capability comes at a price, including mechanical and aerodynamic complexity and higher power requirements than for a fixed-wing aircraft of the same gross weight. All of these factors influence the design, acquisition, and operational costs of the helicopter. It is clear that much has been accomplished over the last sixty years in improving the capabilities and efficiency of the helicopter, but one must wonder what would really be possible with future helicopters if these complex aerodynamics could be fully understood and controlled to harness its maximum efficiency!

Besides generating all of the vertical lift, the rotor is also the primary source of control and propulsion for the helicopter, whereas these functions are separated on a fixed-wing aircraft. For forward flight, the rotor-disk plane must be tilted so that the rotor-thrust vector is inclined forward to provide a propulsive component to overcome both rotor and airframe drag. The orientation of the rotor disk to the airflow also provides the forces and moments to control the attitude and position of the helicopter. The pilot controls the magnitude and direction of the rotor thrust vector by changing the blade pitch angles (using collective and cyclic pitch inputs through the controls), which changes the blade lift and the distribution of lift forces over the rotor disk. By incorporating articulation into the rotor design through the use of mechanical flapping and lead-lag hinges that are situated near the root of each blade, the rotor disk can be tilted in any direction in response to these blade pitch inputs. However, the mechanical complexity of the rotor hub required to allow for articulation and pitch control leads to high design and maintenance costs. As the helicopter begins to move into forward flight, the blades on the side of the rotor disk that advance into the relative wind will experience a higher dynamic pressure and lift than the blades on the retreating side of the disk, and as a result asymmetric aerodynamic forces and moments will be

produced on the rotor. Articulation helps allow the blades to naturally flap and lag so as to help balance out these asymmetric aerodynamic effects. With the inherently asymmetric airflow environment and the flapping and pitching blades, the aerodynamics of the rotor become relatively complicated and lead to unsteady forces. These forces are transmitted from the rotor to the airframe and are a source of vibrations, resulting in not only crew and passenger discomfort, but also considerably reduced airframe component lives and higher maintenance costs. However, with a thorough knowledge of the aerodynamics and careful design, all these adverse factors can be minimized or overcome to produce a highly reliable and versatile aircraft.

Introduction: A History of Helicopter Flight

The idea of a vehicle that could lift itself vertically from the ground and hover motionless in the air was probably bom at the same time that man first dreamed of flying.

Igor Ivanovitch Sikorsky (1955)

LI Rising Vertically

Aerodynamics is the science of all flight. The role of aerodynamics in the engi­neering analysis and design of rotating-wing vertical lift aircraft, such as the helicopter, is the primary subject of this book. A helicopter can be defined as any flying machine using rotating wings (i. e., rotors) to provide lift, propulsion, and control forces. The rotor pro­duces a lift force equal to the weight of the helicopter and because the generation of this lift force does not require any forward flight speed, the helicopter can rise vertically from the ground and hover. A simpler definition, therefore, is that a helicopter is an aircraft using a rotor (or rotors) that can hover – see Hafner (1954). Tilting the orientation of the rotor disk(s) provides the forces and moments to control the helicopter in flight. Tilting the rotor disk fore and aft provides pitch control, and tilting it left and right gives roll control. If a single main lifting rotor is used, then a sideward thrusting tail rotor provides anti-torque and directional (yaw) control. If the rotor disk is tilted progressively forward, the rotor provides a propulsive force, accelerating the helicopter into forward flight.

Although the helicopter has been described as an “ungainly, aerodynamic maverick” [Carlson (2002)], the modem helicopter is indeed a machine of considerable engineering sophistication and refinement (Fig. 1.1) and plays a unique role in modern aviation provided by no other aircraft. It is truly a unique form of aircraft and a mastery of modem aeronautical engineering. The helicopter can take off, fly forward or backward, climb and descend, and move in almost any direction at the whim of the pilot. This is the form of tme flight that inspired humankind literally hundreds of years before the helicopter became a reality. Igor Sikorsky’s vision of a rotating-wing aircraft that could “lift itself vertically” and safely perform all these desirable flight maneuvers under full control of a pilot was ultimately only to be achieved in the mid-1930s, some thirty years after fixed-wing aircraft (airplanes) were flying successfully. In the last seventy years, the helicopter has matured from a cumbersome, vibrating contraption that could barely lift its own weight, into a modem and efficient aircraft that has become an indispensable part of modem life. Its modem civilian roles are almost limitless and encompass sea and land rescue, police surveillance, oil rig servicing, homeland defense, and other important missions. Without question, helicopters are an essential part of any modem military.

Rotating-wing aircraft are far more complicated than they might first appear. Aerody – namically, the airflow through the helicopter rotor is extremely difficult to define and even after many years of intense study it still defies a fully adequate description. The ability to define and predict the rotor aerodynamics, however, is key to the prediction of the perfor­mance of the helicopter as a whole. Mechanically, the helicopter is complicated as well. The long slender rotor blades twist and bend, flap up and down, and lead and lag about

Introduction: A History of Helicopter Flight

Figure 1.1 Modem helicopters have matured into sophisticated machines with extra­ordinary capability, which fulfill many civilian and military aviation roles. Agusta-Westland EH-Industries EH-101. (Photo by permission of Agusta-Westland.)


Подпись: o-i—і—і—і—і—і—■—і—і—і—і—і—і—і—г ч—■—>—'—г—' 1700 1750 1800 1850 1900 Figure 1.2 Until the middle of the nineteenth century, more attempts had been made to build rotating-wing aircraft than airplanes. Data source: Hafner (1954) and adapted from Harris (1994).

hinges that attach them to the rotor shaft. The need to control the aerodynamic forces on the rotor requires that the pitch of each blade be changed individually as the blades rotate about the shaft. Despite the relatively high aerodynamic and mechanical complexity of the rotor system and the helicopter as a whole, there are still many parallels in their devel­opment when compared to fixed-wing aircraft. However, the longer and more tumultuous

Year of first flight

Introduction: A History of Helicopter Flight Introduction: A History of Helicopter Flight

Figure 1.3 Types of helicopter, (a) Single main rotor/tail rotor (conventional) configura­tion. (b) Tandem rotors, (c) Coaxial rotors, (d) Side-by-side rotors, (e) Intermeshing rotors.

gestation period of the helicopter is clearly attributable to the greater depth of scientific and aeronautical knowledge that was required before all the various technical problems could be understood and overcome. Along with the need to understand the basic aerodynamics of vertical flight and improve upon the aerodynamic efficiency of the helicopter, technical barriers included the need to develop suitable high power-to-weight ratio engines and high strength-to-weight ratio materials for the rotor blades, hub, fuselage, and transmission.

Compared to airplanes – the development of which can be clearly traced to Liiientnai in Germany, Pilcher in Britain, Langley in the United States, and the first controlled flight of a piloted powered aircraft by the Wright Brothers in 1903 – the origins of successful helicopter flight are less clear. It may seem surprising that until the middle of the nineteenth century there had been more attempts to build helicopters than fixed-wing aircraft (see Fig. 1.2). Yet the early preference of helicopters over airplanes is perhaps not so surprising given the rapid adoption of the marine propeller during the same time period. Therefore it would seem that the preferred means of vertical-rising locomotion through a fluid would be a propeller of some type. Yet, other than making short hops off the ground, none of these early machines were successful in demonstrating sustained, fully controlled vertical and hovering flight.

Many problems plagued the early attempts at powered vertical flight with rotating wings. This included the relatively poor understanding of rotating-wing aeromechanics[1] to allow for efficient rotors, the lack of suitable engines, counteracting torque reaction from the shaft driven rotor(s), and providing the machine with enough stability and control. Many of the early machines were of the coaxial or side-by-side (lateral) rotor configuration – see Fig. 1.3. Contrarotating rotors – one rotor above the other on a concentric shaft – automatically balance torque reaction on the airframe, despite the greater mechanical complexity involved in gearing and controlling the two rotors. Side-by-side rotors, especially if the shafts were inclined inwards,, gave the early machines somewhat better lateral stability, but again there was a greater level of mechanical complexity associated with this type of design. The intermeshing rotor design has outward tilted contrarotating shafts. The simplest idea of using a single rotor with a sideward thrusting tail rotor to compensate for torque reaction was not used until much later in the initial development of the helicopter.


This book is the product of an opportunity afforded to me by the University of Maryland. The research and writing of the first edition of this book was unique experience and has lea to many lessons. It was gratifying to see how well the first edition was received, with feedback being received from the four comers of the world. The first edition took the best part of 2,500 desk hours, mainly during evenings and weekends and spread over three years. In this regard, I am forever grateful to my wife, Alice Marie Leishman, for her love and understanding, and for providing me continuous support where writing, proofreading, drawing figures, and plotting graphs meant many long nights and all too short weekends. Preparing this second edition required about 1,300 desk hours, spread over about eighteen months, but ultimately even with the benefit of experience and hindsight, it proved to be no lesser a task than the first edition.

Special acknowledgment is due to a great many people, both on and off the University of Maryland campus. I am most grateful for the council of my colleagues at the University of Maryland, Professors Alfred Gessow (now deceased), Inderjit Chopra, Roberto Celi, James Baeder, Christopher Cadou, and Dr. Vengalattore Nagaraj. Professor Gessow had read substantial parts of the first edition and offered many useful suggestions for improve­ment. Before he passed away in May of 2002, Alfred Gessow and I had many significant discussions about the autogiro and the role it played in the fundamental development of the helicopter, from the point of view of both engineering theory and practice. Chapter 12 in this second edition reflects the spirit of our discussions, and I dedicate this chapter to his memory. A1 Gessow’s knowledge and first-hand experience working at NACA Langley during the 1940s and 1950s in the technical development of early helicopters was also invaluable to me. Professors Inderjit Chopra and Roberto Celi provided good suggestions for Chapter 4 and kindly allowed me to use some of their own course material on blade motion and rotor trim. Professor James Baeder read Chapter 8 on unsteady aerodynamics and Chapter 14 on computational methods for helicopter applications, and I am grateful to him and his students for their willingness to help me with figure preparation. Dr. Chris Cadou read the revised parts of Chapter 1, and I enjoyed our engaging conversations on early engine development and the history of aircraft technology in general. Dr. Nagaraj read the revised Chapters 5 and 6 and offered more good suggestions on helicopter design issues.

I am particularly grateful to Dr. Richard Brown of Imperial College at the University of London who is responsible for a substantial part of the writing in Chapter 14 of the second edition. This chapter on computational methods proved to be one of the most satisfying to write, although it took the longest amount of time out of the four new chapters with numerous iterations required to finally define the appropriate content. Dr. Brown also provided useful feedback for improvement on the other three new chapters.

I am indebted to my graduate students at the University of Maryland, both past and current, who have both directly and indirectly contributed to the content of both the first and second editions of this book. The current members of my research group, namely Shreyas Ananthan, Sandeep Gupta, Arun Jose, Robin Preator, and Manikandan Ramasamy,

enthusiastically read many parts of the second edition and offered useful advice and con­structive criticism from a student’s perspective. Many of the students in my classes proof­read drafts of revised chapters, and I am particularly grateful to the group of Moble Benedict, Brandon Bush, Mamta Jangid, Nitin Gupta, Vinit Gupta, Vinod Lakshminarayan, and Eric Schroeder for their careful reading and checking of equations. Sandeep Gupta did much to help me refine the material in Chapter 13 on wind turbines. Yik-Loon Lee and Karthikeyan Duraisamy spent time with me explaining the intricacies of ad vanced computational meth­ods and grid generation techniques, and I appreciate them lending me some of the results from their own research for Chapter 14 in the second edition of this book. I am grateful to Dr. Mahendra Bhagwat (now at US Army/NASA Ames) for running the prescribed – and free-vortex wake solutions and for allowing me to adapt his analysis of the tip vortex aging problem in Chapter 10. Dr. Preston Martin (also now at US Army/NASA Ames) took several of the rotor wake visualization images for Chapter 10 and did much to help me find references and other material on airfoils and airfoil design for Chapter 7. Jacob Park (now at Bell Helicopter Textron) ran several of the rotor wake calculations, sifted through lots of experimental results on rotor wakes, and organized the data for a good number of the figures in Chapter 10. Gregory Pugliese read many of the draft chapters for the first edition, made endless trips to the library to hunt down reports, cross checked more than several hundred references, and helped me turn more than a few of my many crude sketches into professional looking figures. Other former students who have directly or indirectly contributed material used in this book include Dr. Ashish Bagai (Sikorsky), Dr. Peter Bi (US Navy NSWC), Dr. Gilbert Crouse (Da Vinci Technologies), Dr. Berend van der Wall (DLR), Mark Daghir (Boeing), Erwin Moederesheim, Joe Tyler, Alan Coyne (Sikorsky), Col. Keith Robinson (US Army), Greg Pugliese, and Dan Griffiths (Sikorsky). A special thanks to Dr. Ashish Bagai and Dr. Mahendra Bhagwat for their generosity in allowing me to adapt some of their results and graphics for Chapter 10. Dr. Peter Bi provided me with good feedback on the new content included in Chapter 11.

Off the university campus there are a great many people and colleagues who provided advice during the writing of both the first and second editions. I remain indebted to the reviewers of my original book proposal, who were able to make good suggestions on what should be included and what should be left out, particularly Prof. Edward Smith and Dr. Andrew Lemnios. The draft second edition saw many more critical eyes, and I was humbled by the care and thoroughness that each reviewer took over their respective chapters. All of their comments were duly taken into account and they led to a better book as a result. Many other people made suggestions on the originally published text or recommended topics for the second edition. Some colleagues read draft copies of the new chapters, while still others sent me hard-to-find reports, computer files of experimental data, figures, photographs, or other information that was used or adapted for the book. In particular, I appreciate the contributions of Douglas Baldwin, Tom Beddoes, Dr. John Berry, Dr. Bill Bousman, Dr. Richard Brown, Marshall Buhl, Tim Candsdale, Dr. Mark Chaffin, Prof. Muguru Chandrasekhara, Dr. Bruce Chamov, Dr. Colin Coleman, Roger Connor, Shawn Coyle, Prof. George Done, Lee-Jay Fingersh, Prof. Peretz Friedmann, Susan Gorton, Dr. Richard Green, David Groen, Jay Groen, Robert Hansford, Franklin Harris, Jennifer Henderson, Michael Hirschberg, Dr. Stuart Houston, Dr. Wayne Johnson, Markus Krekel, Andrew Line, James Mayfield, Dr. Kenneth McAlister, Dr. Patrick Moriarty, Dr. Khanh Nguyen, James Mayfield, Dr. Reinert Muller, Prof. Gareth Padfield, John Perry, Prof. Ganesh Rajagopalan, Dr. Rex Rivolo, Dr. Scott Schreck, Prof. Michael Sellig, Sergei Sikorsky, Dr. Roger Strawn, Prof. Edward Smith, Dr. James Tangier, Dr. Chee Tung, Dr. Hal Youngren, Dr. Daniel Wachspress, and Dr. David Wood. A great number of people, too numerous to mention, sent me letters or e-mail about the first edition giving me comments for improvement, pointing out remaining typographical errors, or suggesting areas for further clarification. Instructors who have used the book and the solutions manual for their classes gave me excellent feedback, which was duly taken into consideration. As they will see in this second edition of the book, most of their suggestions were enthusiastically incorporated and their critiques are most gratefully acknowledged.

Thanks are due to the helicopter companies, who were kind enough to send me pho­tographs of their various helicopters or give me permission to publish those that I found in publicity materials and on their web sites. In particular, I acknowledge Madelyn Bush and Jack Satterfield of Boeing Helicopters, Kevin Hale of Bell Helicopter Textron, David Long of Kaman Aircraft Corporation, Eurocopter, and the Public Affairs Department at GKN Westland (now Agusta-Westland). Other photographs were obtained from NASA, the National Renewable Energy Laboratory, Sandia National Laboratories, and the photo archive at Patuxent Naval Air Station. I am also grateful to the staff of the National Air and Space Museum for giving permission to publish some of the historical photographs included in Chapter 1 and to Brian Riddle of the Royal Aeronautical Society in London for finding some early published papers and reports on autogiros and helicopters.

I want to express my sincere gratitude to the staff at Cambridge University Press for their help and support during the writing and publication process of both the first and second editions of this book. Florence Padgett was the editor for the first edition, and my thanks extend also to Ellen Carlin for her help with the various editing and production issues. Peter Gordon was the editor for the second edition, and I am grateful for his enthusiastic support and encouragement throughout. Finally, my thanks again to the staff at TechBooks for their help in the production of the second edition of this book.

Principles of Helicopter Aerodynamics Second Edition

The helicopter is truly a unique form of aircraft and a mastery of modern aeronau­tical engineering that fulfills a variety of civilian and military roles. The usefulness of the helicopter lies in its unique ability to take off and land vertically on almost any terrain, to hover stationary relative to the ground, and to fly forward, backward, or sideways. These unique flying characteristics, however, come at a price, including complex aerodynamic problems, significant vibrations, high levels of noise, and relatively large power requirements compared to a fixed-wing aircraft of the same weight.

This book, written by an internationally recognized teacher and researcher in the field, provides a thorough, modern treatment of the aerodynamic principles of helicopters and other rotating-wing vertical lift aircraft such as tilt-rotors and autogiros. The first part of the text begins with a unique technical history of he­licopter flight and then covers basic methods of rotor aerodynamic analysis and related issues associated with the performance of the helicopter and its aerody­namic design. The second part is devoted to more advanced topics in helicopter aerodynamics, including airfoil flows, unsteady aerodynamics, dynamic stall, ro­tor wakes and rotor-airframe aerodynamic interactions. The third part of the book contains chapters on autogiros and advanced methods of helicopter aerodynamic analysis. A companion chapter on the aerodynamics of wind turbines recognizes both the commonalities and differences with the aerodynamic problems found on helicopters. Every chapter is extensively illustrated and concludes with a compre­hensive bibliography and a set of homework problems.

Advanced undergraduate and graduate students, as well as practicing engineers and researchers, will welcome this thorough and up-to-date text on the principles of helicopter and rotating-wing aerodynamics.

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Dr. J. Gordon Leishman is the Minta Martin Chair of Engineering and Professor of Aerospace

The reader will see many changes to this second and much enlarged edition of Principles of Helicopter Aerodynamics. However, the goal in writing the book remains the same, to give a reasonably adequate description of background theory and present an up-to-date treatment of the subject of helicopter aerodynamics, or at least as up to date as it can be. With the life span of a modem engineering textbook being measured in a few years, it seemed appropriate to regularly update the book with both revised and new material that, in part, reflect both current areas of topical interest as well as areas of ongoing fundamental research. The revised text will continue to appeal both to those learning the field anew and to those who are practicing engineers. The text requires some familiarity with basic aerodynamics and mathematical concepts, although no prior background in rotating-wing aerodynamics is assumed. Both new and updated questions at the end of each chapter will satisfy instructors who have used the first edition of the book in the classroom and have found the solutions manual useful in their teaching.

Work on revising the first edition and compiling the second edition started early in 2003, although planning, gathering materials, and writing started well before then. The new material was finally defined late in 2003 and some of it was taught in my “Helicopter Aerodynamics П” class during the spring of 2004. In this second edition I have taken the opportunity to thoroughly revise the original text for content and clarity, as well as to finally weed out the remaining evasive typographical errors that made it into the third printing of the first edition. Any errors that do remain are entirely of my own doing. Many revisions to the text have been made based on my own rereading during the last five years, as well as on the feedback and suggestions received from many readers, a lot of them students. In the first instance, I have put back some important parts of the original manuscript that were edited out of the first published edition. This by itself has provided much better detail and continuity between sections and chapters, as well as giving a fresh new look to the book. A few original sections have been deemed duplicative or redundant with the addition of the new chapters and so have been edited out completely. Other parts of the text have been moved to the new chapters. Most of the original figures have been revised or updated, or have been reordered in a more logical sequence.

The introductory chapter on the development of the helicopter has been completely revised. I have taken the opportunity to thoroughly check historical events, dates, and other details, which are often conflicting between different publications. Tracing original documents back over ninety years in some cases has proved challenging, but I have been helped in this task by many willing individuals. I am particularly grateful to Roger Connor of the National Air and Space Museum for sharing his extensive knowledge of helicopters and VTOL aircraft. I have also added new material to this chapter that has strengthened the description of the technological advances needed for vertical flight. The addition of new material on engines has helped put the development of the helicopter into a better perspective when compared to the development of other aircraft. Chapters 2 and 3 describe the fundamental aerodynamic characteristics of helicopter rotors, and these two chapters have seen the fewest changes in the second edition. Even here, however, several additions

have been made to better introduce the fundamentals of helicopter flight and to provide an essential primer for the more advanced materials contained in the subsequent chapters of the book. Chapter 4 on rotating blade motion has seen the addition of sections on teetering and semi-rigid rotors to complement the discussion on the articulated form of rotor. A discussion of pitch-flap coupling and an introductory section on ground resonance helps round out the revised chapter. Finally, the discussion on the methods of solving for rotor trim has expanded to complete this chapter. Chapter 5 is on helicopter performance. Initially I focused on a better description of the international standard atmosphere and why it is used in performance work. The addition of a section on compressibility losses on the rotor operating at higher forward speeds helps better explain the impact of this deleterious effect on helicopter performance. A new section on engines and the issues of specific fuel consumption connect better to a revised section on flight range and endurance. There is also a new section on maximum altitude (ceiling) performance. Performance issues in rapidly descending flight have received some recent attention and this seems to be a topic that is very poorly understood from a fundamental standpoint. To this end, revised and expanded sections on autorotational flight and the vortex ring state should help cover the field. Finally, a section on maneuvering flight performance helps round out Chapter 5.

The first part of the book concludes with Chapter 6, which addresses helicopter aerody­namic design issues. This chapter has seen an expanded consideration of airframe download and other performance penalties. A new section on the use of wind tunnel testing in the evaluation of rotor air loads and helicopter performance helps put the difficulties of accurate flight performance estimation into proper perspective. The issues of maneuvering flight are considered again through a discussion of precessional stall effects, both on the main rotor and the tail rotor. Four new sections have been added to Chapter 6. The first is on “smart” rotor systems, which may be one approach whereby the performance of the helicopter could be significantly improved. It remains to be seen, however, if the practical issues in building and certifying a cost-competitive smart rotor system can be overcome. Second, the ideas of a human-powered helicopter are introduced. This is a problem that continues to interest generation after generation of students, although, as the discussion shows, the physiological limits of humans severely limit the possibilities of ever achieving successful human-powered vertical flight. Nevertheless, it remains a problem that will continue to hold great fascination and it is worthy of consideration from both an aerodynamics and a vehicle design perspective. Third, there is a new section on micro air vehicles (MAVs). The flight of MAVs involves low Reynolds number issues for which there is little existing knowledge of their aerodynamics, and so they require special considerations in their performance es­timation. Fourth, a brief section on performance degradation issues associated with rotor and airframe icing completes this chapter.

The second part of the book starts in Chapter 7 with a revised discussion on airfoil sections used for helicopter applications. The chapter is enhanced by a more thorough and up-to-date discussion on advanced airfoil design. The addition of a section on circulation controlled airfoils reflects renewed interest in this concept for alternative rotorcraft concepts. A short section on very low Reynolds number airfoil characteristics complements the discussion on MAVs found in Chapter 6. Finally, a section on the aerodynamic degradation of helicopter rotor airfoils from ballistic damage completes this chapter. Chapter 8 is a fairly large chapter on unsteady aerodynamics, and the existing material has seen several changes. A new sec­tion on the unsteady aerodynamics of airfoils with trailing edge flaps recognizes their use on modem rotors for vibration and noise reduction and perhaps as a primary means of rotor control by replacing the swashplate. The addition of a new section on rotor aeroacoustics in this chapter helps make the connection between unsteady aerodynamic forces and the

often obtrusive noise that seems to plague the modem helicopter. This section also pro­vides a primer for students and aerodynamicists learning the field of acoustics anew, as well as lending a bridge to practicing acousticians who need greater than superficial knowl­edge about helicopter related acoustic problems. Chapter 10 on rotor wakes has seen the addition of new material throughout. This includes a fresh discussion on tip vortex mod­eling, including the effects of turbulence within the vortex core. The understanding of helicopters in maneuvering flight has received much recent attention by the technical com­munity, so a section on time-accurate wake modeling seemed a natural addition to the book.

Chapters 11 through 14 are all new chapters. Chapter 11 is on rotor-airframe interactional aerodynamics that contains material left over from the draft of the first edition. Because the helicopter as a system must function properly and predictably throughout its operational flight envelope, an understanding of component-interaction aerodynamics is essential to the successful design of the modem helicopter. Several sections on this topic from the original text have now been parsed out and integrated with the new material that forms this chapter. Chapter 12 describes the technological development of autogiros and gyroplanes, and recognizes the fundamental role that the autogiro played in the development of the helicopter. This chapter also contains the essential aerodynamic theory of the autogiro. The need for this chapter also reflects a renaissance of interest in the commercialization of a modem gyroplane, for which new engineers must be suitably knowledgeable.

Chapter 13 is on the aerodynamics of wind turbines. It may seem surprising to some to find a chapter on wind turbines in a book on helicopters, but the aerodynamics of wind turbines have many similarities to the aerodynamics of helicopters, yet also with important differences. There are so relatively few books on wind turbines and those describing the aerodynamics are frequently out of print. Environmental concerns about global warming and the storage of waste from nuclear power plants has seen an increased emphasis on the use of wind energy, which is likely to see much more rapid and expansive use in years to come. The performance of wind turbines can be analyzed by many of the same methods used for helicopters, and the cross fertilization of expertise in the two areas will hopefully help foster a new understanding of both fields.

Finally, Chapter 14 explains the basis of modem computational methods for rotor and helicopter analysis, and these are put into context with the capabilities classical methods and modem engineering approaches. Dr. Richard Brown of Imperial College at the University of London contributed heavily the writing of this chapter. To some, the development of the field of computational fluid dynamics (CFD) by itself is held out to be the “Holy Grail” for the helicopter aerodynamicist. But this is a very misleading perspective because CFD does not, by itself, hold the answer to all of the various problems found on helicopters. The answer lies more in the successful integration of advanced forms of aerodynamic analysis into other disciplines of analysis. It is also unwise for other approaches to be abandoned in the shorter term while CFD matures to an accepted level of capability, given that this could still be decades off, despite more optimistic claims. These CFD models require continuous and careful validation, both against more complete solutions and/or analytical results and against detailed experimental measurements. This is one reason why wind tunnel testing of helicopters and subsystems will continue to be essential to better understand and predict the capabilities of the helicopter in response to specific aerodynamic phenomena. The future offers many opportunities for new research focused toward the development of more innovative computational models with greater predictive capabilities for helicopter applications. Only then can the problems that limit the performance and capabilities of the helicopter be understood and mitigated.

This book is a college-level analytical and applied level exposition of the aero­dynamic principles of helicopters and other rotating-wing vertical lift aircraft. It is written for students who have no background m rotatmg-wmg aerodynamics but have had at least two semesters of basic aerodynamics at the undergraduate level and possibly one course at graduate level. The material covered has grown mainly out of two graduate-level courses in “Helicopter Aerodynamics” that I have taught at the University of Maryland since 1988.1 have also taught a somewhat more general senior-level undergraduate course in “Helicopter Theory” about every other year, which is centered around the first half of this book. These courses have been offered as part of the formal curriculum in the Center for Rotorcraft Education and Research, which was originally founded in 1982, partly through the efforts of Professor Alfred Gessow. It is now nearly fifty years since Alfred Gessow and Gary Myers’ well-known book The Aerodynamics of the Helicopter was first published. I am pleased to record in the preface to this book that in his status as Professor Emeritus, Alfred Gessow continues to be active in activities at the University of Maryland and also within government and professional organizations. As a testimony to his life-long dedication to education and research in helicopter technology, the Rotorcraft Center at the University of Maryland has been recently named in his honor.

In the institutions where formal courses in helicopter technology have been taught, either at the undergraduate or graduate level, my experience is that they have been well received and very popular with the students. What is often most attractive to students is the highly multidisciplinary nature of helicopter engineering problems. Therefore, an introductory course in helicopters provides a good capstone to the aerospace engineering curriculum. Another factor for most students who have taken a helicopter course is the realization that so much more remains to be learned about fundamental aerodynamics, especially as it applies to rotating-wing aircraft. This is reflected in the experience levels in predicting the aerodynamics and overall behavior of helicopters before their first flight, which are less than desirable. Consequently, it is fair to say that the various aerodynamic problems associated with helicopters and other new forms of rotary-wing aircraft probably provide the scientists and engineers of the future with some of the most outstanding research challenges to be found in the field of theoretical and applied aerodynamics.

Serious work on this book project started about three years ago and was motivated pri­marily by my students. It has grown out of a relatively informal collection of classroom notes and research papers and an overwhelming need to synthesize both older and newer information on the subject of helicopter aerodynamics into one coherent volume. With the ever increasing content of new research material on helicopters and the increasing pro­portion of recent research material being included in the course, especially in the second semester, the development of a formal textbook was really a logical step. Even since 1980, when Wayne Johnson’s excellent book Helicopter Theory was published, progress in un­derstanding helicopter aerodynamics and other related fields has been remarkable. A glance at the content of recent proceedings of the Annual Forum of the American Helicopter So­ciety or the European Rotorcraft Forum shows the scope and depth of new work being


conducted today, which continues despite tightly controlled budgets. This has been fueled, in part, by the great advances in computer technology, which has fostered ambitious new analytical and numerical approaches to solving helicopter technology problems. Some of these approaches now come under the banner of computational fluid dynamics (CFD) us­ing numerical solutions to the Euler and Navier-Stokes equations. While these techniques are not yet mature, CFD methods have begun to provide new insight into the complicated aerodynamic problems associated with helicopters that were previously intractable with existing mathematical methods or were limited by available experimental techniques. As these new numerical methods continue to mature and become better validated, the first decade of the twenty-first century will see an increasing use of CFD tools in the design of new and improved helicopters. The past twenty years has also marked a revolution in the experimental studies of helicopter aerodynamics, where advances in flow diagnostic and other instrumentation has allowed measurements on rotors to be made with a fidelity that was considered impossible just a few years ago. The complex nature of the problems found on helicopters means that both experiment and theory must continue to go hand in hand to forge a better understanding of the whole. This will result in the development of new rotating-wing aircraft with better performance, lower vibration, better reliability and main­tainability, and with lower direct and operational costs. The modem spirit of international cooperation in research and development makes the years ahead in the twenty-first century very exciting.

As I have already mentioned, a significant part of the content of this book has been focused toward students at the graduate level who are learning the principles of helicopter aerodynamics and are exploring the tools available to approach the vigorous, multidisci­plinary research and development of the modem helicopter. In planning the content of this book, I have organized the material in two main parts. The first part will be appropriate for a one-semester course in helicopter aerodynamics for senior undergraduate and first-year graduate students. This material essentially represents a thorough introduction to fundamen­tal helicopter problems, basic methods of rotor analysis, issues associated with helicopter performance, and conceptual design issues. I have attempted to follow the spirit of Gessow & Myers’s book, where theory is supported throughout by liberal references to experimen­tal observations and measurements. In this regard, rediscovering the less well-known early NACA and RAE technical literature on the subject of helicopter aerodynamics proved to be one of the most satisfying aspects of writing this book. The rapid progress made in un­derstanding the problems of the helicopter during the period between 1930 and 1950, and the ingenuity shown in both the experimental and analytical work, are quite remarkable.

The second part of the book gives a more advanced treatment of more detailed aspects of helicopter aerodynamics, again with emphasis on physical concepts and basic methods of analysis. This part will appeal more to those students who plan to conduct research in helicopter aerodynamics and related fields or who are already practicing engineers in industry and government laboratories. However, I do hope that practicing engineers will relish in the opportunity to revisit the first part of the book to review the basics and also to review the inherent assumptions and limitations of the fundamental concepts and methods. These are so often taken for granted, but they form the backbone of many modem forms of helicopter analysis. Because I have always found a need to bring “industrial practice” into the classroom, I have tried to incorporate engineering practice as well as some of my own industrial experience into the second part of the book. For this, I thank my former colleagues at Westland Helicopters for sharing their knowledge with me.

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Like most textbooks, the final product has turned out to be not exactly what was originally planned. Along the way, topics have been added, parts of the text rearranged, and some other

topics deleted. Also, in light of the reviews of the preliminary manuscript, new figures have been added, many were modified, and others deleted. While more than 400 figures were originally prepared, less than 275 finally made it to the finished book. In the interests of space and publication costs, two chapters have been left out completely. These were “Interactional Aerodynamics” and “Advanced Computational Aerodynamic Techniques.” Both topics are referred to, albeit briefly, throughout the book, but to include them would have made the final size of the book prohibitively long. There have also been such rapid recent advances in these areas in the past few years that they are best left for a second edition. The list of key references for each chapter is extensive but by no means complete, and the reader is encouraged to follow through with the references contained in each publication,

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proven homework and examination questions. Solutions have been provided in a companion instructors’ solution manual.

Chapter 1 introduces the helicopter through its technical history. This chapter grew out of my personal research into the Berliner helicopter experiments that were conducted during the early 1920s at the College Park Airport, which is close to the University of Maryland. Whereas in the technical development of fixed-wing aircraft it is possible to point to several key historical events, it becomes quickly apparent that things are much less clear in the development of the helicopter. There are already many authoritative publications that detail the historical development of the helicopter, so I have tried to approach the discussion on more of a technical theme and to put the background and difficulties in understanding the aerodynamics of vertical flight into broader perspective. This introduction is followed in Chapter 2 by an analysis of hovering and axial flight using the Rankine-Froude momentum theory. The basic momentum theory concept was extended to forward flight by Glauert and others from the RAE at Farnborough, inspired not by the helicopter, but by the success of ClCrVo. S Autogiro. It IS shown that Іїіаїіу Oi the important рСГіОПїІаПСб and ОрСГаиОПаї СііаГ – acteristics of the helicopter can be deduced from Glauert’s extension of the basic momentum theory. The blade element and combined blade-element momentum theory is discussed in Chapter 3. These ideas were developed in the 1940s and provide the foundation for a more modem treatment of the aerodynamics of rotors. On the basis of certain assumptions, im­portant information on blade design, such as optimum or ideal shapes for the blade planform and blade twist, can be deduced from the combined blade element momentum theory. Be­cause helicopter blades have articulation, in that they can flap and lag about hinges located near the root of each blade, it is not possible to understand the behavior of the helicopter solely from an aerodynamics perspective. Therefore, in Chapter 4 a discussion of rigid blade motion leads naturally into an understanding of the issues associated with rotor response to the changing aerodynamic loads and also to rotor control. Also introduced here are the ideas of rotor trim; that is, the pilot’s control inputs required to enable equilibrium flight of the helicopter. Chapter 5 gives an introduction to helicopter performance and operational issues such as climbing and descending flight, including the autorotative state and flight

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associated with the conceptual aerodynamic design of helicopters, including the main rotor, the fuselage and empennage, and the tail rotor. Although it might have been more appro­priate to place this chapter at the end of the book, it provides a good bridge between the fundamentals and results to many problems that are still more of a research nature for which experimental research is incomplete and predictive capabilities are not yet mature.

Chapter 7 starts the second part of the book with an important practical review of basic airfoil aerodynamics, including boundary layer and viscous aerodynamics, and the role of compressibility. This is followed by applications of these concepts to understanding some

of the special requirements and characteristics of rotor airfoils. Again, liberal reference to experimental measurements makes the present treatment relatively unique amongst text­books on helicopters. Chapters 8 and 9 comprise a comprehensive discussion on unsteady aerodynamics, with emphasis on the relevance to helicopter problems. Classical techniques of unsteady aerodynamics, including Theodorsen’s theory and Loewy’s theory, the indicial response method, and dynamic inflow, are reviewed in Chapter 8. Extensions of some of these methods to the compressible flow problems found on helicopters are described, with validation with experimental measurements where possible. Indicial methods are treated in some detail because they form the foundation for many modern methods of helicopter analysis and are not covered in any previous helicopter text. Chapter 9 discusses the prob­lem of dynamic stall, which is known to be a barrier to attaining high speed forward flight with a conventional helicopter. Engineering methods of dynamic stall prediction are also reviewed, along with some examples of the general predictive capability to be found with these models. The physical nature of helicopter rotor wakes, both in hovering and forward flight, are discussed in Chapter 10. Nearly all of what we know about rotor wakes comes from empirical observations, and this has led to the development of well-validated math­ematical models of the rotor wake using vortex techniques. Chapter 10 concludes with a brief discussion on interactional aerodynamics. Although many the problems of rotor aero­dynamics can be studied by considering the rotor in isolation to the fuselage, tail rotor and empennage, aerodynamic interactions between the components lead to many problems that are not yet fully understood.

A word about systems of units is in order. In the preparation of this book, I have found it necessary to use both the British (Imperial) and metric (SI) systems. Any preference for one over the other is done simply for the sake of convenience, and I think there is really little reason to change units for the sake of standardization in the text. As aerospace engineers, and particularly helicopter engineers, we are used to working with both systems and even with mixed units in the same breath, and so most readers will have no problems with this approach. For the foreseeable future, students will have to learn to become fully conversant in both systems. Where I have felt it would be helpful, units in both systems are stated. For convenience, a table of conversion factors is also included in the appendix.

Having said all this and made my excuses, I hope this edition of the book will be judged, especially by the practicing engineer, on what it contains and not on what else could po­tentially have been included. Like everything in aviation, the final product is always a compromise and is always under a continuous state of revision, development, and improve­ment. As a final comment, it seems appropriate to quote Igor Sikorsky who has said: “At that time [1908] aeronautics was neither an industry nor even a science… it was an art, 1 might say, a passion. Indeed at that time it was a miracle.” As we stand now at the turn of the new millennium, I’m sure that if he was alive Igor Sikorsky would have agreed that the past century has indeed seen many miracles, both in aeronautics and in helicopter technology. The new century will almost certainly see more.