The Art of the Helicopter John Watkinson - Karatunov.net

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Technical background 51 centripetal force in the absence of acceleration, a new virtual force of equal magnitude but opposite direction has to be imagined to act. This is called the centrifugal force. In the real world centrifugal force does not exist, it is a mathematical convenience needed to allow an apparent state of equilibrium in a rotating frame of reference. In a fixed frame of reference, consider a turning rotor. Figure 2.31(b) shows that if one of the blades should move upwards, the centre of mass of the blade will move closer to the axis of rotation, reducing the moment of inertia. Conservation of momentum requires that the reduced moment of inertia be balanced by an increase in velocity. Consequently the blade will accelerate in the direction of rotation as it moves up. Naval gunners discovered a related effect which is that when a shell is fired a distance of several miles, the shell moves significantly with respect to the earth’s axis in a rotating frame of reference and so it will also experience conservation of momentum which takes it to the left or right of its intended target. These are examples of the Coriolis effect, named after the mathematician who derived the mechanics of rotating frames of reference. Figure 2.31(c) shows that when the frame of reference rotates at the same angular velocity as the component of interest, the rotation apparently disappears. However, the conservation of momentum effect is still occurring and the blade appears to accelerate with respect to the frame of reference. In order to account for this acceleration, a new virtual force is imagined to act. This is called the Coriolis force. In the real world the Coriolis force does not exist, like centrifugal force, it is a mathematical convenience needed to allow the use of a rotating frame of reference. The uninformed will often make reference to both centrifugal and Coriolis forces as though they really existed, usually as a result of reading an advanced textbook without understanding it. Such observations must be treated with suspicion. Centrifugal force and Coriolis force are the technical equivalent of the unicorn and the mermaid. They are in the imagination and the literature but they don’t exist. There is a further consequence of the use of a rotating frame of reference that affects vibration frequencies created in the rotor and transmitted to the hull. The frequencies generated in the rotor may have the rotational frequency of the rotor both added and subtracted. The phenomenon is known as heterodyning and was treated in section 2.11. 2.16 Rotating masses and precession The rotors of a helicopter at flight RPM contain a large amount of stored energy and this alters the way they respond to forces. In order to control the helicopter, the entire rotor has to be tilted in the direction the pilot wishes to go. This will not be achieved by applying a couple in that direction. Figure 2.32(a) shows that if one blade is considered, when a couple is applied to the rotor, as it rotates the couple will alternately try to move the blade up and down. In fact in a rotating frame of reference the blade experiences a sinusoidal forcing function at the rotational frequency of the rotor. The way in which the blade responds to this is non-intuitive. Figure 2.32(b) is drawn in a rotating frame of reference with respect to which the blade is stationary and it becomes correct to refer to centrifugal force. The figure shows that if it is assumed that the blade is displaced from its normal plane of rotation and released, there will be a component of centrifugal force trying to return the blade to the original plane. For small angles this force is proportional to the displacement, so the condition for SHM is met. The blade will oscillate like a pendulum about the normal plane at some natural frequency. This frequency can be calculated from the mass of the blade and the centrifugal force. It turns out that the frequency is nearly identical to the rotational frequency.
52 The Art of the Helicopter Fig. 2.32 (a) A couple applied in the plane of the rotor is experienced as an alternating force by each blade. (b) In rotating co-ordinates, centrifugal force tends to return a flapping blade to the flat position. The restoring force for small angle is proportional to the angle and so the blade performs SHM. As a result when an external couple tries to tilt the plane of a rotor, the sinusoidal force on each blade is driving the blade at its natural resonant frequency. Section 2.9 showed that at resonance the driving force is in phase with the velocity. This means (from Figure 2.22) that the displacement lags both the velocity and the force by 90 ◦ of rotation. Thus the rotor does not tilt in the direction of the applied couple, but on an axis thatis90 ◦ further around the rotor in the direction of rotation. This is a fundamental characteristic of gyroscopes and is called gyroscopic precession (invariably changed to procession by the ill-advised use of spelling checkers). This 90 ◦ lag in the response of a rotor to applied forces has a significant bearing both on the control of the helicopter and on how it responds to external forces. The controls have to be connected up at right angles to the intuitive way. As the blade tension is proportional to the square of RRPM (rotor revolutions per minute), when the rotors are turning slowly, the acceleration experienced by the blades due to rotation is small and the phase lag due to precession will be considerably reduced. The helicopter cannot fly at such low RRPM, but the effect may be noticed during rotor start or shutdown in a strong wind. When the pilot tries to minimize blade sailing by using the cyclic control, it will be found that the response is not as expected. Instead at low speeds the blades will respond with an advance with respect to the cyclic control. On a clockwise-from-the-top helicopter if the blades sail up on the right, the cyclic stick will have to be moved backwards.
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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
Page 16 and 17: 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 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
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(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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