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enable a physical interpretation of the dynamic and aerodynamic phenomena to be
obtained. The intention throughout this book, therefore, has been to try to arrive at
useful mathematical results and ‘working formulae’ and at the same time to emphasize
the physical understanding of the problem.
The first chapter summarizes some essential mechanics, mathematics, and
aerodynamics which find application in later parts of the book. Apart from some
recent research into the aerodynamics of the hovering rotor, discussed in Chapter 3,
the next six chapters are really based on the pioneer work of Glauert and Lock of the
1920s and its developments up to the 1950s. In these chapters only simple assumptions
about the dynamics and aerodynamics are made, yet they enable many important
results to be obtained for the calculation of induced velocity, rotor forces and moments,
performance, and the static and dynamic stability and control in both hovering and
forward flight.
Chapter 8 considers the complicated problem of the calculation of the induced
velocity and the rotor blade forces when the vortex wakes from the individual blades
are taken into account. Simple analytical results are possible in only a few special
cases and usually resort has to be made to digital computation. Aerofoil characteristics
under conditions of high incidence and high Mach number for steady and unsteady
conditions are also discussed.
Chapter 9 considers the motion of the flexible blade (regarded up to this point as
a rigid beam) and discusses methods of calculating the mode shapes and frequencies
for flapwise, lagwise, and torsional displacements for both hinged and hingeless
blades.
The last three chapters consider helicopter vibration and the problems of aeroelastic
coupling between the modes of vibration of the blade and between those of the blade
and fuselage.
I should like to thank two of my colleagues: Dr M. M. Freestone for kindly
reading parts of the manuscript and making many valuable suggestions, and Dr R. F.
Williams for allowing me to quote his method for the calculation of the mode shapes
and frequencies of a rotor blade.
A.R.S.B.
South Croydon, 1975
x Preface to the first edition
Acknowledgements
The authors would like to thank the persons and organisations listed below for
permission to reproduce material for some of the figures in this book. Many such
figures appeared in the first edition, and do so also in the second, the relevant
acknowledgements being to: American Helicopter Society for Figs 3.25 to 3.32, 6.40,
6.47, 6.48, and 9.16; American Institute for Aeronautics and Astronautics for Figs
6.50, 6.51, and 6.52; Her Majesty’s Stationery Office for Figs 3.6, 3.9, 4.7, 4.9, 4.10,
and 6.11; A. J. Landgrebe for Figs 2.24 and 2.33; National Aeronautics and Space
Administration for Figs 3.10, 3.11, 6.41, and 9.12; R.A. Piziali for Figs 6.24 and
6.25; Royal Aeronautical Society for Figs 4.15, 4.20, 6.19, 6.21, and 6.22; Royal
Aircraft Establishment (now Defence Evaluation and Research Agency) for Figs 3.8,
6.31, 6.32, 6.33, 6.40, 6.42, 6.46, 7.3, 7.28, 8.30, and 8.31.
For figures that have appeared for the first time in the second edition,
acknowledgements are also due to: GKN Westland Helicopters Ltd. for Figs 1.5(a),
1.5(b), 1.6(a), and 1.6(b), 6.37, 6.38, 7.28, 8.3 to 8.9, 8.12 to 8.18, 8.20 to 8.32, 9.13,
9.17 and 9.23; Stephen Fiddes for Fig. 2.37; Gordon Leishman of the University of
Maryland for Figs 6.28 and 6.30; Jean-Jacques Philippe of ONERA for Figs 6.34,
6.35, and 6.36. In a few cases, the figure is an adaptation of the original.
We are also indebted to several other friends and colleagues for contributions
provided in many other ways, ranging from discussions on content and provision of
photographic and other material, through to highlighting errors, typographical and
otherwise, arising in the first edition. These are Dave Gibbings and Ian Simons,
formerly of GKN Westland Helicopters, Gordon Leishman of the University of Maryland
and Gareth Padfield of the University of Liverpool.
Notation
A Rotor disc area
A Blade aspect ratio = R/c
A, B Constants in solution for blade torsion mode
A, B, C Moments of inertia of helicopter in roll, pitch and yaw,
or of blade in pitch, flap and lag
A, B, C, D, E, F, G Coefficients in general polynomial equation
A′, B′, C′ Moments of inertia of teetering rotor with built-in pitch
and coning
Aij, Bij ijth generalised inertia and stiffness coefficients
An nth coefficient in periodic or finite series
Aj Blade pitch jth input weighting (active vibration control)
A1, B1 Lateral and longitudinal cyclic pitch
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