The Art of the Helicopter John Watkinson - Karatunov.net

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Introduction to helicopter dynamics 103 Fig. 3.34 (a) A blade element encountering a vortex from an earlier blade will experience first an increase in angle of attack (a), then a reduction (b). The variations in angle of attack produce a pressure dipulse (c) rapid enough to be audible as blade slap. in the case of lateral (in-plane) directions the vibration frequencies beat or heterodyne with the rotor frequency to produce sum and difference frequencies. The concept of sidebands was discussed in section 2.11, but the result can be demonstrated graphically. It is possible conceptually to replace the blade generating in-plane vibrations due to modulation of its root pull with a device generating the same vibration. This consists of a pair of contra-rotating eccentrics called a Lanchester exciter shown in Figure 3.35(a) which produces linear sinusoidal vibration. Figure 3.35(b) shows that if the rotor blades vibrate radially at the second harmonic (two-per) this can be simulated by an exciter which makes two revolutions with respect to the blade in one rotor revolution. The result is that one of the eccentrics makes three revolutions with respect to the hull whilst the other makes only one. Thus a two-per in-plane blade vibration results in three-per and one-per at the hub in stationary co-ordinates. Third harmonic vibration produces four-per and two-per vibration in stationary co-ordinates and so on. The discussion so far has considered the action of individual blades. However, in practice the hub will vectorially sum all of the forces and moments acting on it. Vectorial summation must consider the phase of the contributions from each blade. Clearly the phase difference between the blades is given by 360 ◦ divided by the number of blades. The overall result must then also depend on the number of blades in the rotor. If the blades are identical, and experience the same forces as they turn, they will develop the same vibration, except that the phase will be different for each blade. If, however, one blade has different characteristics to the others, a one-per function may result. It is interesting to see how the number of blades affects the spectrum of vibration and how this effect is different for in-plane vibrations. Figure 3.36(a) depicts a two-bladed rotor and shows a graph of the fundamental flapping for each blade (one-per) and the second harmonic (two-per). Note that the two blades are 180 ◦ apart and so the one-per waveforms are in anti-phase and cancel. As one-per flapping is the result of tilting the disc this is no surprise and remains true for any number of blades. However, note that the second harmonic flapping of the two blades is in-phase and will therefore add.
104 The Art of the Helicopter (a) (b) Fig. 3.35 (a) A pair of contra-rotating eccentrics produces linear vibration. (b) If the mechanism of (a) is rotated, one of the eccentrics will turn faster and the other slower. Thus frequencies transmitted to the hull will be the vibration frequency plus or minus the rotor frequency. It will be clear that a two-bladed rotor is at a disadvantage because both blades will be in the lift trough simultaneously at 90 ◦ and 270 ◦ , and in a lift peak simultaneously at 0 ◦ and 180 ◦ . The result at high speed is a vertical vibration known as 2P hop. Figure 3.36(b) shows the situation for the third flapping harmonic. As the third harmonic flapping has one and a half cycles in the time between blade passings, it will be clear that the 3P components will be out of phase between the two blades. Following similar logic it should be clear that in a two-bladed rotor, only even vertical harmonics exist; the odd ones cancel. Figure 3.37 shows the case for a three-bladed rotor. At (a) it will be seen that the second flapping harmonic waveform of each blade is at 120 ◦ to that of the next. The sum of three sine waves at 120 ◦ is constant and so there can be no 2P hop in a three-bladed
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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
Page 68 and 69: 2.17 The gyroscope Technical backgr
Page 70 and 71: Technical background 55 of oscillat
Page 72 and 73: Technical background 57 the inertia
Page 74 and 75: Technical background 59 shut down a
Page 76 and 77: 3 Introduction to helicopter dynami
Page 78 and 79: Introduction to helicopter dynamics
Page 100 and 101: (a) (c) (b) Introduction to helicop
Page 104 and 105: (a) (b) (c) (d) Introduction to hel
Page 106 and 107: Fig. 3.23 Conditions for hover and
Page 110 and 111: (a) (b) Introduction to helicopter
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 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
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Rotors in practice 153 and lag damp
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Rotors in practice 155 disappears a
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(d) (e) (f) Rotors in practice 157
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Rotors in practice 159 hull and a v
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Rotors in practice 161 Fig. 4.35 (C
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Rotors in practice 163 Abrasion is
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Rotors in practice 165 There are so
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eing more visible to ground personn
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otates the rod in the screw thread.
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In the case of a rotor having offse
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The tail rotor designer is faced wi
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Fig. 5.5 A right-side wrong-directi
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centre of mass. The solution was to
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safe to start the rotors. However,
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Fig. 5.10 Tail plane locations: (a)
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Fig. 5.12 (a) A top-mounted fin is
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Fig. 5.14 (a) Main rotor lateral ro
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long. The cross-section of the duct
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drag. However, the slots are emitti
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6 Engines and transmissions The pow
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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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