The Art of the Helicopter John Watkinson - Karatunov.net

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Rotors in practice 145 Fig. 4.25 Blade dragging is characterized by Southwell’s coefficients which describe the static and centrifugal components of the restoring force. (a) In the articulated rotor, there is no static stiffness. The dragging frequency is a fraction of the rotor frequency. (b) In the hingeless rotor there is static stiffness so there is a finite resonant frequency even at zero RRPM. As RRPM increases, centrifugal stiffening dominates and the frequency becomes asymptotic to what it would have been for a hinged blade with the same mass distribution. frequency becomes asymptotic to what it would have been with no structural stiffness. As a result the dragging frequency is no longer proportional to RRPM. It should be appreciated that in the above discussion and in Figures 4.24 and 4.25 the dragging frequency is with respect to the turning rotor, not with respect to stationary co-ordinates. Frequencies experienced at the hull will be in stationary co-ordinates and will be different from the frequency discussed here. 4.17 Ground resonance Given the flexible nature of rotors, it is possible for the centres of mass of the blades to get ‘out-of-pattern’ as shown in Figure 4.26. This is the term describing the condition where the blades are not evenly spaced around the disc. This may be due to an external influence such as the impact of a run-on landing or starting the rotor on a slope. It may also be self-excited. Section 4.16 considered the resonant dragging motion of a single blade, whereas in practice it is necessary to consider the phase relationship from blade to blade. Figure 4.27 shows some possibilities for a three-bladed rotor. Rotors with more blades will also behave in the same way except that there are more phases of blade motion. Twobladed rotors have different characteristics, but because such rotors seldom employ dragging hinges these differences will not be enlarged here. It must be stressed that throughout Figure 4.27 the diagrams are in rotating co-ordinates so that the rotor appears to be stopped. Figure 4.27(a) shows the case where, for example, a sudden increase in drive torque has caused all of the blades to drag back by the same amount. They will all resonate in the same phase and the result is that the CM of the rotor is undisturbed. Figure 4.27(b) shows the case where there is a120 ◦ phase difference between the motion of each blade. Now the centre of the rotor hub is moving in a circle. The motion may be visualized by considering the operation of a three-cylinder radial engine.
146 The Art of the Helicopter Fig. 4.26 Out-of-pattern blades shift the CM of the rotor and whirl the top of the mast. Figure 4.27(c) shows the same situation except that the phase relationship is −120 ◦ . The hub is still moving in a circle, but in the opposite direction. There is a strong analogy here with the three-phase electric motor that can be reversed by changing any two connections. This circular motion is known as whirling and it may be forward, in the same direction as the rotor, or backward, in the opposite sense to rotor direction. Figure 4.27(d) shows the case where one blade is not dragging, but the other two are dragging at 180 ◦ . Now the hub motion is linear. If the effects of Figure 4.27 are considered in a non-rotating frame of reference, (a) will have no effect. Effect (b) causes circular whirling at a frequency which is the sum of the rotor frequency and the dragging resonant frequency, whereas (c) will result in circular whirling at a frequency which is given by the rotor frequency minus the dragging frequency. The whirling frequency seen by the hull has been modified by the addition of the rotor frequency. If the whirling experienced by the hull is in the same direction as the rotor turns, it is said to be progressive. If it is in the opposite sense it is said to be regressive. The whirling orbit is reminiscent of some types of food mixer. A mild form of such an orbit is usually experienced during rotor starting with an articulated rotor and is called ‘padding’ by pilots. In a real helicopter these whirling forces are applied to the top of the mast. The CM of the hull is well below the rotor head, and the result is a combination of pitching and lateral rocking. The moment of inertia of a helicopter about the pitching axis is quite high owing to the long tail boom, but there is less inertia about the roll axis, so generally lateral movement will dominate. The hull will not be infinitely stiff and may also be supported on a sprung undercarriage, and so it will have natural resonant frequencies of rocking.
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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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Page 110 and 111: (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 162 and 163: Rotors in practice 147 Fig. 4.27 Ef
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
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(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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