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to vertical gusts, 190
to lateral cyclic pitch, 188
to longitudinal cyclic pitch, 183
Cyclic pitch:
helicopter response to, 183
Absorbers, see vibration
Actuator disc, 34, 37
Aeroelastic behaviour:
main rotor
blade weaving, 332
flap-lag instability, 335
pitch-flap flutter, 324
pitch-lag instability, 320
stall flutter, 329
tail rotor
flap-lag instability, 335
pitch-flap-lag instability, 341
pitch-flap (umbrella mode) instability,
334
Aerofoil characteristics:
in forward flight, 221–232
effect of Mach number, 222
oscillating at low incidence, 204–212
oscillating at high incidence, 225–232
Aeromechanical behaviour:
air resonance, 352
ground resonance, 342
Air resonance, 352
Angular momentum, 360
Attitude of helicopter:
lateral, 30
longitudinal, 28, 116
Autorotation, 132
Autostabilization, 175–179
Bell stabilising bar, 176
Bending of blades, 238–289
calculation of modes and frequencies, 242
finite-element method, 253
Galerkin method, 249
Lagrange’s equations, 243
Myklestad method, 251
372 Index
Cyclic pitch (continued)
lateral cyclic pitch to trim, 30
longitudinal cyclic pitch to trim, 28
Damping in pitch and roll, 139
Downwash velocity:
forward flight, 77
hovering flight, 39
Dynamic stability, 137–195
equations, 363
lateral, 166–175
longitudinal, 140–166
Eigenvalues and eigenvectors of flapping
blade, 241
Euler’s equations, 362
extended equations, 363
Feathering:
equation of motion, 10
torsional vibrations, 260
Figure of merit, 55
Flapping:
coefficients, 106
in terms of disc axes, 108
equation, 7
forward flight, 105
at high μ, 105
in hovering flight, 10
response to pitching and rolling, 15
Flutter, 324
stall, 329
Free wake model 74, 216
Fuselage drag, 130
variation with weight, 130
Goldstein circulation factors, 63
Goldstein–Lock theory, 59
Ground effect, 57
Ground resonance, 342
H-force:
definition, 27
forward flight, 98
Hingeless rotor:
basic features, 277
hub moment, 279
effect on stability, 165, 174, 189
Hovering flight:
actuator disc theory, 34
blade element theory, 46
figure of merit, 55
induced velocity in, 39
inflow angle, 52
optimum rotor, 54
performance in, 50
Induced power:
forward flight, 90
hovering flight, 40
Induced velocity:
flight and wind tunnel tests, 84
forward flight, 77
hovering flight, 39
vertical climb and descent, 43
Inflow angle:
forward flight, 95
vertical flight, 52
In-plane motion:
equation of motion for, 9
effect of drag hinge distance on, 9
geometric interpretation, 19
Lagging:
equation of motion, 9
motion due to flapping, 19
Lateral trim equations, 30
solution of, 125
Lift coefficient:
contours of, 228
in terms of thrust coefficient, 49
Longitudinal trim equations, 28, 116
solution of, 1, 117–123
stability, 140
Mangler and Squire induced velocity
distribution, 81
Manoeuvrability, 186
pull-up manoeuvre, 194
Multiblade summations, 365
Offset hinges:
effect on flapping frequency, 7
effect on lag frequency, 9
moment due to, 25
Optimum rotor, 54
figure of merit, 55
Index 373
Orthogonal property of normal modes, 267
Performance:
autorotation, 132
calculation of, 128
forward flight, 127–136
hovering flight, 51
Power calculations:
forward flight, 128
hovering flight, 51
induced power, 51
Prandtl wake theory, 60
Prescribed wake model, 69, 202
Response to vertical, gust, 190
Reverse flow area, 106
Rotating frame of reference:
angular momentum in, 360
Rotor:
axes systems, 26
forces and moments, 21
hinge system, 1
response to pitching and rolling, 15
Rotor wake, see vortex wake
Second order system, frequency response, 368
Solidity, definition, 48, 55
Stability characteristics:
forward flight, 163, 173
effect of hingeless rotor on, 165
hovering flight, 160, 173
effect of tailplane on, 164
Stability derivatives:
lateral, 168–172
longitudinal, 143–147
Stability equations, 363
lateral, 166–168
longitudinal, 140–143
Stall flutter, 329
Stall of oscillating aerofoil, 228
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Bramwell’s Helicopter Dynamics(183)
