Rotary-Wing Aerodynamics

893 Pages·1984·33.18 MB·English

by  Stepniewski

ROTARY-WING AERODYNAMICS
Two Volumes Bound as One
VOLUME I:
BASIC THEORIES OF ROTOR AERODYNAMICS
(With Application to Helicopters)
by W. Z. STEPNIEWSKI
VOLUME II:
PERFORMANCE PREDICTION OF HELICOPTERS
by C. N. KEYS
Edited by W. Z. Stepniewski
Dover Publications, Inc., New York
This Dover edition, first published in 1984, is an unabridged, slightly corrected republication in one
volume of the work originally published in two volumes by the Science and Technical Information Office
of the National Aeronautics and Space Administration for the U.S. Army Air Mobility Research &
Development Laboratory of the Aviation Systems Command. Volume I, “Basic Theories of Rotor
Aerodynamics (With Application to Helicopters),” by W. Z. Stepniewski, was originally published in 1979.
Volume II, “Performance Prediction of Helicopters,” by C. N. Keys, originally published in 1979, is being
reprinted here from the 1981 edition revised and edited by W. Z. Stepniewski. The Volume II revision was
prepared by Boeing Vertol Company. Indexes have been added to the Dover edition at the end of each
volume. Wanda L. Metz was Associate Editor for this work.
Library of Congress Cataloging in Publication Data
Stepniewski, W. Z. (Wieslaw Zenon), 1909-
Rotary-wing aerodynamics.
“An unabridged, slightly corrected republication in one volume of the work originally published in two
volumes by the Science and Technical Information Office of the National Aeronautics and Space
Administration… in 1979. Volume II… is being reprinted here from the 1981 edition revised and edited by
W. Z. Stepniewski [for the U.S. Army Air Mobility Research and Development Laboratory]”–T. p. verso.
Includes bibliographical references and indexes.
Contents: Basic theories of rotor aerodynamics (with application to helicopters)–Performance prediction
of helicopters.
1. Helicopters–Aerodynamics. I. Keys, C. N. II. Title.
TL716.S76 1984 629.132'3 83-20528
ISBN-13: 978-0-48664647-3
ISBN-10: 0-486-64647-5
Manufactured in the United States by Courier Corporation
64647508
www.doverpublications.com
FOREWORD

In recent years, there has been an increasing volume of reports, articles,
papers, and lectures dealing with various aspects of rotary-wing aircraft
aerodynamics. To those who enter this domain, either as graduate students with
some background in general aerodynamics, or those transferring from other
fields of aeronautical or nonaeronautical engineering activities, this vast amount
of literature becomes a proverbial haystack of information; often with the result
of looking for a needle that isn’t there. But even those who are professionally
engaged in some aspects of rotary-wing technology may experience a need for a
reference text on basic rotor aerodynamics.
Through my experience both as an educator and practicing engineer
directly involved in various aspects of industrial aeronautics, it became doubly
apparent that there was a need for a textbook that would fulfill, if not all, at least
some of the above requirements.
With this goal in mind, the text entitled Rotary-Wing Aerodynamics was
written under contract from USAAMRDL/NASA Ames. On one hand, the
objective is to provide an understanding of the aerodynamic phenomena of the
rotor and on the other, to furnish tools for a quantitative evaluation of both rotor
performance and the helicopter as a whole.
Although the material deals primarily with the conventional helicopter and
its typical regimes of flight, it should also provide a comprehensive insight into
other fields of rotary-wing aircraft analysis as well.
In order to achieve this dual aim of understanding and quantitative
evaluation, various conceptual models will be developed. The models will reflect
physical aspects of the considered phenomena and, at the same time, permit
establishment of mathematical treatment. To more strongly emphasize this
duality of purpose, the adjective phystco-mathematical will often be used in
referring to these models.
It should be realized at this point that similar to other fields of engineering
analysis, conceptual models—no matter how complicated in detail—still
represent a simplified picture of physical reality. It is obvious, hence, that the
degree of sophistication of the physicomathematical models should be geared to
the purpose for which they are intended. When faced with the task of developing
such a model, one may be advised to first ask the following two questions: (1)
whether the introduction of new complexities truly contributes to a better
understanding of the physics of the considered phenomena and their qualitative
and quantitative evaluation, and (2) whether the possible accuracy of the data
inputs is sufficiently high to justify these additional complexities.
In this respect, one should determine whether a more complex model
would truly lead to a more accurate analysis of the investigated phenomena or
just, perhaps, that the procedure only looks more impressive while mathematical
manipulation would consume more time and money. Furthermore, it should be
realized that often in the more complex approach, neither intermediate steps nor
final results can be easily scrutinized.
With respect to rotary-wing aerodynamics in general, and performance
predictions in particular, one should realize that aerodynamic phenomena
associated with the various regimes of flight of an even idealized, completely
rigid rotor are very complicated. Furthermore, the level of complexity increases
due to the fact that in reality, every rotor is non-rigid because of the elasticity of
its components and/or built-in articulations. As a result, a continuous interaction
exists between aerodynamics and dynamics, thus introducing new potential
complexities to the task of predicting aerodynamic characteristics of the rotor.
Fortunately, even conceptually simple models often enable one to get either
accurate trends or acceptable approximate answers to many rotary-wing
performance problems.
By following the development of basic rotor theories-from the simple
momentum approach through the combined momentum and blade-element
theory, vortex theory, and finally, potential theory-the reader will be able to
observe the evolution of the physicomathematical model of the rotor from its
simplest form to more complex ones. It will also be shown that an understanding
or explanantion of the newly encountered phenomena may require modifications
and additions and sometimes, a completely new approach to the representation
of the actual rotor by its conceptual model. By the same token, a better feel is
developed with respect to the circumstances under which a simple approach may
still suffice. Finally, these simpler and more easily scrutinized methods may
serve as a means of checking the validity of the results obtained by potentially
accurate, but also more complicated ways which may be prone to computational
errors.
Presentation of the above-outlined theories, plus considerations of airfoils
suitable for rotary-wing aircraft constitutes the contents of Vol I. “Reduction to
practice” of the material presented in Vol I is demonstrated in Vol II, where
complete performance predictions are carried out for classical, winged, and
tandem configurations including such aspects as performance guarantees and
aircraft growth.
The existing need for a text conforming to the above outlined philosophy
was recognized by representatives of USAAMRDL and in particular, by Mr.
Paul Yaggy, then Director of USAAMRDL, and Dr. I. Statler, Director of Ames
Directorate whose support made possible the contract for the preparation of the
first two volumes.
To perform this task, a team was formed at Boeing Vertol consisting of the
undersigned as Editor-in-Chief and author of Vol I; Mr. C.N. Keys as the
principal author of Vol II; and Mrs. W. L. Metz as Associate Editor. The course
of the work was monitored by Mr. A. Morse and Dr. F.H. Schmitz of Ames
Directorate; while Mr. Tex Jones from USAAMRDL-Langley Directorate
provided his technical assistance and expertise by reviewing the material
contained in both volumes. Thanks are extended to the abovementioned as well
as the other representatives of USAAMRDL. Finally, my associates and I wish
to thank the management of Boeing Vertol; especially, Messrs. K. Grina, J.
Mallen, W. Walls, and E. Ratz for their support, understanding and patience.
There are, of course many more people from this country and abroad who
significantly contributed to the technical contents. Their individual contributions
are more specifically acknowledged in the prefaces of the individual volumes.
W. Z. Stepniewski
Ridley Park, Pa.
March 31, 1978
VOLUME I:
BASIC THEORIES OF ROTOR AERODYNAMICS
(With Application to Helicopters)
PREFACE

Volume I of the text entitled Rotary-Wing Aerodynamics is devoted in
principle to Basic Theories of Rotor Aerodynamics. However, the exposition of
the material is preceded by an introductory chapter wherein the concept of
rotary-wing aircraft in general is defined. This is followed by comparisons of the
energy effectiveness of helicopters with that of other static-thrust generators in
hover; as well as with various air and ground vehicles in forward translation.
While the most important aspects of rotor-blade dynamics and rotor control are
only briefly reviewed, they should still provide a sufficient understanding and
appreciation of the rotor dynamic phenomena related to aerodynamic
considerations.
The reader is introduced to the subject of rotary-wing aerodynamics in Ch
II by first examining the very simple physicomathematical model of the rotor
offered by the momentum theory. Here, it is shown that even this simple
conceptual model may prove quite useful in charting basic approaches to
helicopter performance predictions; thus providing some guidance to the
designer. However, the limitations of the momentum theory; i. e., its inability to
account for such phenomena as profile drag and lift characteristics of blade
profiles and geometry, necessitated the development of a more sophisticated
conceptual rotor model.
The combined biade-eiement and momentum theory presented in Ch III
represents a new approach which demonstrates that indeed, greater accuracy in
performance predictions is achieved, and this would also become a source of
more-detailed guidelines for helicopter design. Even with this improvement,
many questions regarding flow fields (both instantaneous and time averaged)
around the rotor still remain unanswered.
In the vortex theory discussed in Ch IV, a rotor blade is modeled by means
of a vortex filament(s) or vorticity surface; thus opening almost unlimited
possibilities for studying the time-average and instantaneous flow fields
generated by the rotor. Unfortunately, the price of this increased freedom was
computational complexity usually requiring the use of high-capacity computers.
It appears that some of the rotor aerodynamic problems amenable to the
treatment of the vortex theory may be attacked with a somewhat reduced
computational effort by using the approaches offered by the velocity and
acceleration potential theory. This subject is presented in Ch V which also
contains a brief outline of the application of potential methods to the
determination of flow fields around three-dimensional, nonrotating bodies.
Considerations of airfoil sections suitable for rotors, as presented in Ch
VI, completes the sequence on fundamentals of rotary-wing aerodynamics. This
material provides a basis for development of the methods for helicopter
performance predictions used in Vol II.
In order to create a complete series on Rotary-Wing Aerodynamics the
author anticipates a third volume devoted to the application of the basic theories
established in Vol I. This volume would include (1) selected problems of
helicopter flight mechanics (e.g., ground effect, flight maneuvers, performance
limitations, and autorotation); (2) establishment of a link between aerodynamics
and design optimization; and (3) development of techniques leading to
performance maximization of existing helicopters. In fairness to the aeronautical
engineers and designers who have been anxiously awaiting for the publication of
this series, the first two volumes are being released prior to the writing of the
proposed third volume.
Returning to the present volume, the reader’s attention is called to the fact
that both SI metric and English unit systems are used in parallel; thus expediting
an acquaintance with the metric approach for those who are not yet completely
familiar with this subject.
In conclusion, I wish to express my indebtedness to the following persons
who generously contributed to this volume: Professor A. Azuma of the
University of Tokyo, Japan for his review of the appendix to Ch IV; and to Drs.
R. Dat and J.J. Costes of ONERA, France for their valuable inputs and review of
Ch V.
W. Z. Stepniewski
NOTES ON METRIC SYSTEM

In order to assist the reader in making the transition from English units to
equivalent SI metric units of measure, some important aspects of the SI system
encountered in applied subsonic aerodynamics and rotary-wing mechanics of
flight are listed below and briefly reviewed.
The reader’s attention is called to the fact that as long as metric units are
input into relationships designated as SI, and no special conversion factors are
incorporated into the formulae, the obtained forces will be in newtons, pressures
in newtons per meter squared, work or energy in newton meters, and power in
newton meters per second. It should be noted however, that in many countries,
the kilogram of force (symbolized in this text as kG) is widely used for the
determination of weight (including that of aircraft), while such quantities as disc
and/or wing loadings are measured in kG/m2.
The popularity of the kilogram as a unit of force stems from the fact that
prior to the establishment of the newton as a unit of force, the kilogram was
generally accepted in engineering practice as well as in everday life. It was
defined as a force resulting from the acceleration of earth’s gravity acting on one
kilogram of mass. However, the earth’s g value varies with altitude over sea
level and geographic latitude. Consequently, the definition of the kilogram of
force as the weight of a kilogram of mass on the earth surface required additional
specifications of earth coordinates as to where the weight is measured. The
newton (kg m/s2) as a unit of force is more universal in the context of its not
being directly related to the gravity conditions encountered on this particular
planet.
It should also be mentioned that in addition to the direct use of the
kilogram of force in engineering practice, its indirect influence can be
consistently found when dealing with the metric horsepower defined as hp = 75
kG m/s. It should also be noted that the so-defined metric horsepower amounts to
0.9863 of its English counterpart defined as hp = 550 ft-lb/s.
One final note – The most important characteristics of air according to the
International Standard Atmosphere are given in the following table.
THE INTERNATIONAL STANDARD ATMOSPHERE