The Art of the Helicopter John Watkinson - Karatunov.net

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Introduction to helicopter dynamics 73 Fig. 3.10 The blade reaction is usefully resolved into components both in and orthogonal to the tip path plane. These allow the rotor thrust and torque to be derived. In the presence of inflow, the angle of attack is the amount by which the pitch angle exceeds the angle of the relative airflow. just changes the collective pitch and the system computes the engine power for itself. Correlators will be described in Chapter 6. 3.9 The rotor as an actuator Without considering constructional details, it is possible to conceive of an ideal hovering rotor as an actuator disc that somehow accelerates air downwards over a circular region and develops thrust from the reaction. In this case the operation of an ideal rotor can be analysed theoretically from the change of momentum of the air passing through. The concept of an ideal rotor is useful because it can act as a benchmark with which to compare real designs. Clearly the performance of the ideal rotor can only be approached, but never exceeded. Figure 3.11(a) shows the actuator concept which makes some simplifying assumptions. One of these is that the air is somehow constrained to flow only within the tapering column shown, known as a stream tube, and doesn’t mix with the surrounding air. The mass of air passing any horizontal plane in the column per unit time must be constant. The actuator causes a pressure difference to exist across itself. This pressure must be given by the thrust divided by the disc area. A further assumption is that this pressure is uniform. The pressure difference across the actuator can only be sustained locally. Figure 3.11(b) shows that at a distance, the pressure must be the same as static pressure. To allow the pressure difference across the actuator, the pressure must have a falling gradient along the streamlines except at the actuator itself. Bernouilli’s theorem can be used to predict what happens along a stream tube. Bernouilli’s theorem is simply another example of conservation of energy. Air has a static pressure and a dynamic pressure due to its motion. Bernouilli’s theorem states that the sum of the two, known as the head, remains constant. As a result when static pressure falls, the dynamic pressure must increase to compensate. As the density doesn’t change significantly, the velocity must increase. Clearly Bernouilli’s theorem does not hold across the actuator, as energy is put into the air there. Except for the pressure step at the actuator, the air in the stream tube experiences a falling pressure gradient which causes the stream to accelerate and contract. This is the phenomenon of wake contraction seen in propellers and rotors. Thus the velocity with
74 The Art of the Helicopter Fig. 3.11 (a) In actuator theory, air passes along a stream tube which is intersected by the actuator. (b) In order to allow a step pressure difference across the rotor, pressure must fall both approaching and leaving. Note the wake contraction to about 0.7 of the rotor diameter. which air arrives at the actuator is higher than it is some distance before the actuator. This difference is the induced velocity. The induced velocity is important because it determines the velocity the rotor sees which has a large bearing on the RAFand the power needed. It should not be confused with the final velocity which is higher still. In the case of an actuator that is climbing vertically, the rotor thrust is given by the rate of change of momentum of the air passing through the disc. The power needed must be the product of the thrust and the velocity, where the velocity is the rate of climb plus the induced velocity. This power must be equal to the difference in the kinetic energy well above and well below the disc. Clearly this assumption implies that only the induced drag is being considered. Actuator theory cannot account for profile drag and assumes it to be zero. The increased velocity applied to the downwash is twice the induced velocity at the disc. In a stationary hover, the total velocity is the induced velocity alone and the downstream velocity will be twice this. In practice the contraction has completed by about one diameter below the rotor. At this point, as the velocity has doubled, the cross-sectional area must have halved in order to have constant mass flow and so the downwash diameter will be about 0.7 of the rotor diameter. In Figure 3.11, uniform inflow over the disc is assumed. In other words the induced velocity and the pressure are the same all over. This is the most efficient condition. It is easy to show that any other condition requires more power. For a given total thrust, if one area of the disc has greater induced velocity and thrust, another area must have less induced velocity and thrust. The thrust is proportional to the momentum change, which is in turn proportional to the induced velocity, whereas the kinetic energy imparted is
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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
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 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
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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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