The Art of the Helicopter John Watkinson - Karatunov.net

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2.17 The gyroscope Technical background 53 When bodies move in a straight line, all of the body is going at the same velocity and energy calculations are easy. However, when a body rotates, those parts furthest from the axis are going faster than those parts near the axis. The amount of rotational energy stored is a function of the distribution of mass with respect to the axis of rotation. This is measured by the moment of inertia (MoI). In a flywheel, as much mass as possible is concentrated at the outside of the rotor to give the greatest MoI. Angular momentum is the product of inertia and the rate of rotation about a given axis. Earlier in this chapter it was seen that a body may be accelerated by changing its speed or its direction. The same is true of a gyroscope. Changing rotational speed is acceleration but so also is changing the direction of the rotational axis. If the rotor is spinning rapidly it has a large momentum, and even a very small rate of movement of the rotational axis represents a large rate of change of momentum and so a large force is necessary. Put simply a gyroscope tends to resist disturbances to its axis in a manner disproportionate to its weight. That makes it attractive for aviation where weight is at a premium. The tendency to resist axis disturbance is called rigidity. Figure 2.33(a) shows a gyroscope suspended by the shaft in a pair of nested cages called gimbals. The axis of rotation is vertical and the gimbals allow turning in two Fig. 2.33 (a) A vertical axis gyro supported by nested rings called gimbals. (b) A couple applied to a gimbal is resisted by rigidity. The gyro axis turns with a 90 ◦ phase lag. This is called precession.
54 The Art of the Helicopter orthogonal (at 90 ◦ to one another) horizontal axes. If the base of the system is pitched and rolled, the rigidity of the gyroscope will be much greater than the friction in the gimbals and the result is that the gyroscope axis remains vertical so that its angular momentum stays the same. Figure 2.33(b) shows that a couple is being applied to the outer gimbal, which tries to twist it in the direction shown. The couple is transmitted through the bearings of the inner gimbal and to the rotor shaft. If a small element on the periphery of the flywheel is considered, this reacts in the same way as the blade in the previous section. As the flywheel is really a collection of such elements, all of which behave in the same way, it is clear that in response to a couple on the outer gimbal axis, the rotor responds by turning around the inner gimbal axis. The gyroscope rotor has a 90 ◦ phase lag just like a helicopter rotor. The outer gimbal will not turn because the applied couple is perfectly opposed by a reaction due to the rigidity of the gyro. The gyro can only generate the rigidity reaction by changing its angular momentum and to do this it must precess as the rotational speed cannot change. The rate of precession is proportional to the applied couple and inversely proportional to the angular momentum. 2.18 Piezo-electric and laser gyroscopes The mechanical gyroscope held sway for a long time but has recently been supplanted by two alternatives. A piezo-electric material is one that deflects when an electrical voltage is applied to it and which creates an electrical voltage when it is distorted. The quartz crystal in an electronic wristwatch works on the same principle. In the quartz watch the natural mechanical resonant frequency of the crystal forms the timing reference. Signals from sensing electrodes measure the deflection and are amplified and fed to drive electrodes that cause the crystal to resonate. By dividing down this highly stable frequency a count of seconds can be obtained. In the piezo-electric gyroscope a vibrating element is made to oscillate as shown in Figure 2.34(a). If the assembly then rotates, the Coriolis effect causes a component Fig. 2.34 (a) In the piezo-electric gyro there is a vibrating beam. Rotation about an axis along the beam causes the beam to twist as it tries to conserve momentum. This can be measured to sense the rotation. (b) In a laser gyro, light is sent in both directions around an optical path. If the system rotates, there will be a phase change between the two components of light.
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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
Page 18 and 19: Introduction to rotorcraft 3 Fig. 1
Page 24 and 25: Introduction to rotorcraft 9 for th
Page 26 and 27: Introduction to rotorcraft 11 Fig.
Page 28 and 29: (a) (b) (c) (d) Introduction to rot
Page 30 and 31: Fig. 1.18 The contra-rotating coaxi
Page 32 and 33: Fig. 1.20 The structure of a light
Page 34 and 35: Introduction to rotorcraft 19 wings
Page 36 and 37: Introduction to rotorcraft 21 a rot
Page 38 and 39: Technical background 23 Fig. 2.1 At
Page 40 and 41: Fig. 2.3 Effect of force on velocit
Page 42 and 43: C Force A E Resultant (a) Force B (
Page 44 and 45: (a) (b) Technical background 29 Fig
Page 46 and 47: Technical background 31 Fig. 2.11 A
Page 48 and 49: Technical background 33 Fig. 2.12 (
Page 50 and 51: Technical background 35 If the volu
Page 52 and 53: Fig. 2.16 The definition of a radia
Page 54 and 55: Technical background 39 force would
Page 56 and 57: Technical background 41 Figure 2.20
Page 58 and 59: Technical background 43 force where
Page 60 and 61: Technical background 45 the cosine
Page 62 and 63: Technical background 47 Fig. 2.28 F
Page 64 and 65: Technical background 49 Fig. 2.30 T
Page 66 and 67: Technical background 51 centripetal
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
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Introduction to helicopter dynamics
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4.1 Introduction 4 Rotors in practi
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(a) (b) Rotors in practice 119 Fig.
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Rotors in practice 121 Designers of
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Rotors in practice 123 opposite occ
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Rotors in practice 125 Fig. 4.6 (a)
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Rotors in practice 127 assembly tha
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Rotors in practice 129 Pitch change
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× T=c× D Rotors in practice 131 F
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Rotors in practice 133 In a real he
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Rotors in practice 135 Fig. 4.15 Va
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(a) (b) Rotors in practice 137 Fig.
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Rotors in practice 139 Fig. 4.18 Th
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Rotors in practice 141 swashplate a
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Fig. 4.23 A fixed-pitch tilting hea
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Rotors in practice 145 Fig. 4.25 Bl
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Rotors in practice 147 Fig. 4.27 Ef
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Rotors in practice 149 Fig. 4.29 (a
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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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