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inimitable qualities and characteristics.
Long sections of the book are analytical, starting from fundamental principles, and
do not change significantly in the course of time; however, we have tried to eradicate
errors, printer’s and otherwise, and improve explanations where considered necessary.
There are also many sections that are largely descriptive, and, over the space of 25
years since the first edition, these had tended to become out of date, both in terms of
the state-of-the-art and supporting references; thus, these have been updated.
Opportunities, too, have been taken to expand the treatment of, and to include additional
information in, the vibrational dynamics area, with both the additional and updated
content introduced, hopefully, in such a way as to be compatible with Bram’s style.
Another change which has taken place in the past quarter century is the now
greater familiarity of the users of books such as this one with matrices and vectors.
Hence, Chapter 1 of the first edition, which was aimed at introducing and explaining
the necessary associated matrix and vector operations, has disappeared from the
second edition. Also, some rather fundamental fluid dynamics that also appeared in
this chapter was considered unnecessary in view of the material being readily available
in undergraduate textbooks. What remained from the original Chapter 1 that was
thought still necessary now appears in the Appendix. Readers familiar with the first
edition will notice the inclusion of a notation list in the present edition. This became
an essential item in re-editing the book, because there were many instances in the
first edition of repeated symbols for different parameters, and different symbols for
the same parameters, due to the fact that the much of the material in the original book
was based on various technical papers published at different times. As far as has been
possible, the notation has now been made consistent throughout all chapters; this has
resulted in some of the least used symbols being changed.
Apart from the removal of the elementary material in the original Chapter 1, the
overall structure of the book has not changed to any great degree. The order of the
chapters is as before, although there has been some re-titling and compression of two
chapters into one. Some of the sections in the last three chapters have been rearranged
to provide a more natural development.
Since publication of the first edition, there have appeared in the market-place
several excellent scientific textbooks on rotorcraft which cover some of the content
of Bram’s book to a far greater depth and degree of specialisation, and also other
texts which are aimed at a broad coverage but at a lower academic level. However,
the comprehensive nature of the subject matter dealt with in this volume should
continue to appeal to those helicopter engineers who require a reasonably in-depth
and authoritative text covering a wide range of topics.
Sherborne David Balmford
Kew George Done
2001
viii Preface to the second edition
Preface to the first edition
In spite of the large numbers of helicopters now flying, and the fact that helicopters
form an important part of the air strength of the world’s armed services, the study of
helicopter dynamics and aerodynamics has always occupied a lowly place in aeronautical
instruction; in fact, it is probably true to say that in most aeronautical universities in
Great Britain and the United States the helicopter is almost, if not entirely, absent
from the curriculum. This neglect is also seen in the dearth of textbooks on the
subject; it is fifteen years since the last textbook in English was published, and over
twenty years have passed since the first appearance of Gessow and Myer’s excellent
introductory text Aerodynamics of the Helicopter, which has not so far been revised.
The object of the present volume is to give an up-to-date account of the more
important branches of the dynamics and aerodynamics of the helicopter. It is hoped
that it will be useful to both undergraduate and postgraduate students of aeronautics
and also to workers in industry and the research establishments. In these days of fast
computers it is a temptation to consign a problem to arithmetical computer calculation
straightaway. While this is unavoidable in many complicated problems, such as the
calculation of induced velocity, the important physical understanding is thereby often
lost. Fortunately, most problems of the helicopter can be discussed adequately without
becoming too involved mathematically, and it is usually possible to arrive at relatively
simple formulae which are not only useful in preliminary design but which also
　
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