The Art of the Helicopter John Watkinson - Karatunov.net

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Rotors in practice 121 Designers often try to trim the machine so that in cruise the action of the tail plane opposes couples due to drag on the hull in order to align the shaft axis with the tip path axis because this minimizes the amount of flapping and hence the amount of wear and vibration. However, this will often be compromised because of variations in the longitudinal position of the CM. In tandem helicopters it is easier to align the tip path axis with the shaft axis. During a roll manoeuvre the tip path axis and the shaft axis must diverge in order to roll the hull. An observer turning with the tip path axis would see the feathering action changing the pitch of a given blade sinusoidally about the collective pitch setting at one cycle per revolution but as he is turning in the tip path plane he would not see any flapping (except for harmonics). In the steady hover no dragging would be observed, but in forward flight dragging would be seen due to the increased drag on the advancing blade compared with that on the retreating blade. 4.3.3 The control axis There exists a third axis, not parallel to the disc axis in translational flight, about which no blade feathering takes place. This is called the control axis, and it is the hardest one to visualize. An observer turning with the control axis in forward flight would note that the pitch of the blades was constant, but that the blades flapped up at the advancing side of the nose of the machine and down at the retreating side of the tail. A given blade would appear to drag back when advancing, and then forward when retreating. The dragging would appear much greater than in the case of the observer on the disc axis. As Figure 4.3(b) shows, in the special case of a two-bladed rotor, if the pitch control rods stay parallel to the mast and are at 90◦ to the blades, the swashplate also rotates on the control axis. The blade stays parallel to the swashplate and so cannot feather with respect to it. In the general case the control axis and the swashplate axes are not the same as will be seen in section 4.13. There is an exact equivalence between the degree of flapping seen by an observer on the control axis and the degree of feathering seen by an observer on the tip path axis. Figure 4.3(c) shows that when the control and tip path axes differ by θ ◦ , if the blades reach a peak feathering angle of θ ◦ with respect to the tip path axis, they will flap to a peak deflection of θ ◦ with respect to the control axis. The reason for the difference between the tip path axis and the control axis should now be clear. In the hover, there would be no permanent difference as the blades follow the cyclic stick. However, in translational flight, the blades encounter highly asymmetrical conditions that pull the tip path axis away from the control axis. In order to fly straight and level, the pilot has to find a position for the cyclic stick in which the asymmetrical conditions on the blades are precisely opposed by cyclic input so that the rotor disc attitude is no longer affected by the asymmetry. For example, if at a certain airspeed the advancing/retreating effect would result in three degrees of flapback, the application of three degrees of forward cyclic will put the rotor disc back in the attitude it would have had in the absence of flapback. As the shaft axis and the tip path axes can be non-parallel, clearly some joints or bearings are necessary or something must be designed to flex. The flapping and lagging bearings in an articulated head approximate to a constant velocity joint between the shaft axis and the tip path axis. The spherical bearing in the centre of the swashplate and the feathering bearings in the rotor head allow the control axis to be different from the shaft axis. The motion of the blades can be studied with respect to any one of the above axes. Each has its own merits. The use of the control axis is instructive when studying the
122 The Art of the Helicopter helicopter in detail. For hingeless rotors use of the shaft axis has some advantages but the tip path axis excels when discussing articulated and teetering heads because it is easier to visualize what is taking place and the direction of the resultant rotor thrust is clear. It is best used for flying training because it is most tangible to pilots. In practice it is useful to be able to switch conceptually from one axis to another to obtain a proper understanding. The control axis was naturally used in the study of the autogyro and as the theory of the helicopter was in many ways derived from work done on the autogyro much early helicopter analysis also uses the control axis, including the classic work by Gessow and Myers. 1 Although the authors make it perfectly clear that the control axis is being used as a reference, not every reader understands what that means and there is scope for misunderstanding if the axes become confused. One example is the occurrence of numerous explanations that are seen claiming that flapping hinges prevent asymmetry of lift in translational flight in gyroplanes and helicopters. This is complete nonsense and comes about because the tip path and control axes have been confused. The blades can flap with respect to the control axis without any flapping hinges or flexibility at all simply because the control axis is not parallel to the tip path axis. It is important to appreciate that all of these axes are hypothetical and the rotor doesn’t care how we choose to observe it. Thus whatever axis is used for analysis the result must always be consistent with the result of an analysis on another axis. To give an example, as the blade pitch appears constant to an observer on the control axis, no force is necessary to make the blades perform cyclic pitch changes other than to overcome friction in the feathering bearings. If the same analysis is carried out on the tip path axis, the blades appear to be oscillating along the feathering axis. The effect shown in Figure 3.8 produces a restoring action tending to return the blades to flat pitch. This causes the blades to have a torsional resonant frequency. It can be shown that this is the same as the rotational frequency of the rotor. As a result the feathering blades are in torsional resonance and so no force is required to operate them other than to overcome friction. This is consistent with the analysis on the control axis. If harmonic pitch control is used, then strictly there is no axis about which the blades do not feather. However, the control axis could be redefined as the axis about which there is no first harmonic feathering. In other words only the higher harmonics of feathering would be seen with respect to the control axis. This is a reasonable approach because the tip path plane is not really a plane because of flapping harmonics and yet the concept is still useful. Interestingly with the correct application of harmonic pitch control the feathering will see more harmonics so that the tip path may see fewer. 4.4 Flapping Flapping is the movement of the blade CM along the shaft axis. It was shown in section 2.14 that the fundamental resonant frequency of the flapping blade is almost the same as the rotational frequency. With a zero-offset rotor the frequencies are identical and this results in a 90 ◦ phase lag in the rotor. When flapping hinge offset is used, the resonant flapping frequency rises slightly because the blades become a little shorter without the diameter changing and the result is that the phase lag of the rotor becomes a little less than 90 ◦ . This is compensated for in the design of the controls. Flapping is self-damping because of the effect it has on relative airflow. When a blade flaps down, its vertical velocity adds vectorially to the airflow to increase the angle of attack, providing more lift to oppose the flapping. When a blade flaps up, the
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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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Page 86 and 87: Introduction to helicopter dynamics
Page 100 and 101: (a) (c) (b) Introduction to helicop
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Page 106 and 107: Fig. 3.23 Conditions for hover and
Page 110 and 111: (a) (b) Introduction to helicopter
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Page 132 and 133: 4.1 Introduction 4 Rotors in practi
Page 134 and 135: (a) (b) Rotors in practice 119 Fig.
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
Page 168 and 169: Rotors in practice 153 and lag damp
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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
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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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