The Art of the Helicopter John Watkinson - Karatunov.net

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Rotors in practice 147 Fig. 4.27 Effects of dragging blade motion. (a) A sudden application of drive torque may result in all three blades dragging in the same phase. (b) When the dragging of each blade is at 120 ◦ phase to the next, the hub moves in a circle. (c) If the phase relationship of (b) is changed, the direction of whirling is reversed. (d) Where two blades drag in anti-phase and one blade is stationary, the hub is driven in a line. Note that all of these examples are in rotating co-ordinates. In the absence of preventive measures, if a resonant frequency in the hull is the same as that of a whirling frequency, one of two things can happen. Either the hull will act as a vibration absorber as was described in section 3.27, and the whirling will be opposed, or the rocking will become increasingly violent until the machine either comes apart or turns on its side. The phenomenon was first observed when a taxiing autogyro struck a rock with a wheel and literally disintegrated. Needless to say this Jekyll and Hyde behaviour in seemingly similar circumstances means that the mechanism involved must be extremely subtle. Whilst the results of ground resonance are painfully obvious, the mechanism causing it is not obvious at all. Until a mathematical basis for the phenomenon was found, designers proceeded empirically. For example, Frank Piasecki obtained an improvement on his first machine by filling the tyres with cork. It was concluded early that ground resonance is purely a mechanical phenomenon and that aerodynamic forces are not significant. There are some parallels with whirling phenomena observed in other disciplines such as steam turbines.
148 The Art of the Helicopter The first full mathematical treatment of ground resonance was due to Robert Coleman and Arnold Feingold who were working at NACA (the forerunner of NASA). The mathematics turned out to be so complicated that the authors had to present their results in the form of charts intended to be practically useful without the reader needing to have advanced mathematical skills. Using these charts, designers were able to tame ground resonance, but this is not the same thing as understanding it. In order to understand ground resonance it is necessary to consider the geometry of whirling. Initially this will be considered for the case of the rotor alone. The rotor is assumed to be isolated, and turning without translating. There is no external force on an isolated system so, according to Newton’s laws, the overall centre of mass of the rotor cannot move. If the centre of mass of the hub is whirling, this must mean that the blades together must have an effective centre of mass that is whirling in the opposite direction. Figure 4.28, which is in rotating co-ordinates, shows the orbits of various points on a blade and hub in a forwards whirling system. There will be a null point on the blade between the drag hinge and the blade CM that is oscillating radially but not tangentially. Note that the motion for a backwards whirling system can be seen by reversing all of the circles and ellipses. In whirling, the KE of the hub is constantly changing because the circular motion requires a constant change of velocity. It follows that the kinetic energy of the blades must also be changing constantly. The blade KE variation is due to motion of the blade CM plus that due to in-plane rotation of the moment of inertia of the blade about the null point. Essentially whirling is a continuous interplay of blade and hub energy and in the absence of friction at the hinges and any aerodynamic effect it could continue indefinitely. Figure 4.29 is in stationary co-ordinates. Figure 4.29(a) shows an articulated rotor turning anticlockwise and whirling forwards whereas (b) shows the same rotor which is still turning anticlockwise but which is whirling backwards. Let these rotors be fitted to a helicopter having a rocking hull resonance. In both cases the figure shows the blade at Fig. 4.28 In an isolated whirling rotor, the overall kinetic energy must remain constant. Consequently there must be an energy interchange between the blades and the hub. If the hub is whirling in one direction, the blade CMs must be whirling in the opposite direction. The loci of several points in the whirling system are shown.
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The Art of the Helicopter
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The Art of the Helicopter John Watk
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Contents Preface xi Acknowledgement
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4.12 Feathering 134 4.13 Pitch cont
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8.5 Power management 326 8.6 Flying
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xii Preface reader to make sense of
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1 Introduction to rotorcraft 1.1 Ap
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Introduction to rotorcraft 3 Fig. 1
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Introduction to rotorcraft 9 for th
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Introduction to rotorcraft 11 Fig.
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(a) (b) (c) (d) Introduction to rot
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Fig. 1.18 The contra-rotating coaxi
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Fig. 1.20 The structure of a light
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Introduction to rotorcraft 19 wings
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Introduction to rotorcraft 21 a rot
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Technical background 23 Fig. 2.1 At
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Fig. 2.3 Effect of force on velocit
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C Force A E Resultant (a) Force B (
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(a) (b) Technical background 29 Fig
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Technical background 31 Fig. 2.11 A
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Technical background 33 Fig. 2.12 (
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Technical background 35 If the volu
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Fig. 2.16 The definition of a radia
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Technical background 39 force would
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Technical background 41 Figure 2.20
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Technical background 43 force where
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Technical background 45 the cosine
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Technical background 47 Fig. 2.28 F
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Technical background 49 Fig. 2.30 T
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Technical background 51 centripetal
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2.17 The gyroscope Technical backgr
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Technical background 55 of oscillat
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Technical background 57 the inertia
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Technical background 59 shut down a
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3 Introduction to helicopter dynami
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Introduction to helicopter dynamics
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(a) (c) (b) Introduction to helicop
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(a) (b) (c) (d) Introduction to hel
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Fig. 3.23 Conditions for hover and
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(a) (b) Introduction to helicopter
Page 112 and 113: Introduction to helicopter dynamics
Page 116 and 117: (a) (b) Introduction to helicopter
Page 132 and 133: 4.1 Introduction 4 Rotors in practi
Page 134 and 135: (a) (b) Rotors in practice 119 Fig.
Page 136 and 137: Rotors in practice 121 Designers of
Page 138 and 139: Rotors in practice 123 opposite occ
Page 140 and 141: Rotors in practice 125 Fig. 4.6 (a)
Page 142 and 143: Rotors in practice 127 assembly tha
Page 144 and 145: Rotors in practice 129 Pitch change
Page 146 and 147: × T=c× D Rotors in practice 131 F
Page 148 and 149: Rotors in practice 133 In a real he
Page 150 and 151: Rotors in practice 135 Fig. 4.15 Va
Page 152 and 153: (a) (b) Rotors in practice 137 Fig.
Page 154 and 155: Rotors in practice 139 Fig. 4.18 Th
Page 156 and 157: Rotors in practice 141 swashplate a
Page 158 and 159: Fig. 4.23 A fixed-pitch tilting hea
Page 160 and 161: Rotors in practice 145 Fig. 4.25 Bl
Page 164 and 165: Rotors in practice 149 Fig. 4.29 (a
Page 166 and 167: Rotors in practice 151 concerned ar
Page 168 and 169: Rotors in practice 153 and lag damp
Page 170 and 171: Rotors in practice 155 disappears a
Page 172 and 173: (d) (e) (f) Rotors in practice 157
Page 174 and 175: Rotors in practice 159 hull and a v
Page 176 and 177: Rotors in practice 161 Fig. 4.35 (C
Page 178 and 179: Rotors in practice 163 Abrasion is
Page 180 and 181: Rotors in practice 165 There are so
Page 182 and 183: eing more visible to ground personn
Page 184 and 185: otates the rod in the screw thread.
Page 186 and 187: In the case of a rotor having offse
Page 188 and 189: The tail rotor designer is faced wi
Page 190 and 191: Fig. 5.5 A right-side wrong-directi
Page 192 and 193: centre of mass. The solution was to
Page 194 and 195: safe to start the rotors. However,
Page 196 and 197: Fig. 5.10 Tail plane locations: (a)
Page 198 and 199: Fig. 5.12 (a) A top-mounted fin is
Page 200 and 201: Fig. 5.14 (a) Main rotor lateral ro
Page 202 and 203: long. The cross-section of the duct
Page 204 and 205: drag. However, the slots are emitti
Page 206 and 207: 6 Engines and transmissions The pow
Page 208 and 209: Engines and transmissions 193 the D
Page 210 and 211: (a) (b) Engines and transmissions 1
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(a) (b) (c) Engines and transmissio
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Fig. 6.5 A typical horizontally opp
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Engines and transmissions 201 the v
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Engines and transmissions 203 The c
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6.9 The oil system Engines and tran
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Engines and transmissions 207 (non-
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(a) (b) Engines and transmissions 2
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Engines and transmissions 211 a hot
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Engines and transmissions 213 Fig.
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Engines and transmissions 215 In wa
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Engines and transmissions 217 is a
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Engines and transmissions 221 own t
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Fig. 6.16 The complex fuel system o
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Engines and transmissions 233 and c
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Engines and transmissions 237 Sensi
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Engines and transmissions 243 the A
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Fig. 6.37 Displays which may be see
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Engines and transmissions 251 slipr
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Engines and transmissions 253 a fau
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Engines and transmissions 255 resul
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Engines and transmissions 257 The p
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Fig. 7.1 (a) A minimal control loop
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Fig. 7.2 (a) When attitude conditio
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fixed point in the hover despite ex
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(a) (b) Fig. 7.4 (a) The earth beha
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7.4 Compass errors A magnetic compa
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In most cases the machine will have
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Fig. 7.7 The remote indicator for a
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is set by the use of a control knob
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Fig. 7.11 The VSI (vertical speed i
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Fig. 7.13 A chaser system which all
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e modified if the gyro is in a movi
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must be in steady flight when the D
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arranged on opposite sides of the p
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Fig. 7.19 The turn indicator is spr
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7.17 Airflow-sensing devices The he
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Fig. 7.24 Using RADAR signals. At (
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Fig. 7.27 Transducers used in signa
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Fig. 7.28 In PCM or digital signall
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(a) Fig. 7.30 Using slicing and rec
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Fig. 7.33 The false codes created i
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Fig. 7.35 In a pure binary system,
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Fig. 7.38 Producing two’s complem
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Fig. 7.40 A power-assisted hydrauli
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Fig. 7.42 An electro-hydraulic valv
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path axis and the flybar axis diver
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and autostabilization, it also prov
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Fig. 7.47 The Lockheed gyrobar syst
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Fig. 7.49 In the Lockheed AMCS, the
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Fig. 7.50 With the autopilot diseng
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or without the AFCS. Systems of thi
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Thus if a VOR receiver detected a 9
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7.29 Fault tolerance In feedback sy
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8 Helicopter performance 8.1 Introd
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Helicopter performance 325 column i
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Helicopter performance 327 Fig. 8.1
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Helicopter performance 329 to skid
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(a) (b) Helicopter performance 331
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Helicopter performance 333 Fig. 8.7
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8.7 Climbingand descending Helicopt
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Helicopter performance 337 In the c
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Helicopter performance 339 of its c
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8.10 Stability Helicopter performan
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Fig. 8.13 The origin of pitchup ins
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Helicopter performance 345 moment f
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9 Other types of rotorcraft Althoug
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Other types of rotorcraft 349 De la
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Other types of rotorcraft 351 Fig.
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Other types of rotorcraft 353 incre
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Other types of rotorcraft 355 and c
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Fig. 9.7 The Bell-Boeing Osprey til
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(a) (b) Other types of rotorcraft 3
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Other types of rotorcraft 365 a low
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Other types of rotorcraft 367 the y
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Other types of rotorcraft 371 the r
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Other types of rotorcraft 373 For e
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Acceleration: and force, 22-5 and v
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Convertiplane, 11-12, 355-8 Bell-Bo
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tanks, 219-20 turbine engines, 237-
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Lockheed flybar system, 309-13 AMCS
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centrifugal stiffening, 71, 100 and
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tail/main rotor interaction, 173 te
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