The Art of the Helicopter John Watkinson - Karatunov.net

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Technical background 45 the cosine components will be in anti-phase and will cancel. Thus all real frequencies actually contain equal amounts of positive and negative frequencies. These cannot be distinguished unless a modulation process takes place. Figure 2.25(b) shows that when two signals of frequency ±ω1 and ±ω2, are multiplied together, the result is that the rotations of each must be added. The result is four frequencies, ±(ω1 +ω2) and ±(ω1 − ω2), one of which is the sum of the input frequencies and one of which is the difference between them. These are called sidebands. Sidebands are found extensively in avionics, where the deliberate use of the process is called heterodyning. In a communications radio the carrier frequency is multiplied or ‘modulated’ by the audio speech signal, called the baseband signal, and the result is a pair of sidebands above and below the carrier. The rotation of the helicopter rotor has a certain frequency. Any vibration due to periodic motion affecting the movement of the blades within the rotor plane may have a characteristic frequency with respect to the rotor. When referred to the hull of the helicopter, the frequency of the vibration may have been heterodyned by the rotor frequency and the frequencies experienced in the hull may then be the frequencies of the sidebands. This will be considered in Chapters 3 and 4. In a voice radio system, the carrier frequency is much higher than the frequencies in the speech, whereas in other systems this may not be the case. In digital systems, continuous signals are represented by periodic measurements, or samples, and sidebands are found above and below the frequency of the sampling clock Fs. Figure 2.26(a) shows the spectrum of a sampling clock which contains harmonics because it is a pulse train not a sinusoid. Figure 2.26(b) shows that the sidebands of the sampling frequency can be rejected using a low-pass filter which allows through only the original baseband signal. The sampled representation of the signal is returned to a continuous waveform. This is exactly what happens in a Compact Disc player. As the baseband frequency rises, the lower sideband frequency must fall. However, this can only continue until the base bandwidth is half the sampling rate. This is known as the Nyquist frequency and it represents the highest baseband frequency at which the original signal can be recovered by a low-pass filter. Fig. 2.26 (a) Spectrum of sampling pulses. (b) Spectrum of samples. (c) Aliasing due to sideband overlap.
46 The Art of the Helicopter Fig. 2.27 In (a) the sampling is adequate to reconstruct the original signal. In (b) the sampling rate is inadequate, and reconstruction produces the wrong waveform (dashed). Aliasing has taken place. Figure 2.26(c) shows what happens if the base bandwidth increases beyond the Nyquist frequency. The lower sideband now overlaps the baseband signal. As a result, the output frequency appears to fall as the input frequency rises. This is the phenomenon of aliasing. Figure 2.27 shows aliasing in the time domain. The waveform carried in the envelope of the samples is not the original, but has a lower frequency. There is an interesting result when the two frequencies are identical. The lower sideband frequency becomes zero. This forms the basis of Fourier analysis seen in the next section. It is also exactly what happens when a stroboscope is used, perhaps to check the tracking of a helicopter rotor. The frequency of the flashing light (the sampling rate) is adjusted until it is the same as the rotational frequency of the object to be studied. The lower sideband frequency becomes zero and the object appears stationary. The upper sideband frequency is usually visible as flicker. Small variations in the frequency of the strobe light above and below the rotational frequency will cause the rotating object to turn slowly forwards or backwards. The forward rotation is due to the lower sideband having a low frequency. However, when the strobe frequency is above the rotational frequency, the lower sideband frequency becomes negative, hence the illusion of reversed rotation. On a spectrum analyser, the negative frequency would fold about zero Hz to become a positive frequency. This folding phenomenon is particularly important to an understanding of ground resonance that will be considered in Chapter 4. 2.14 Fourier analysis Fourier was a French mathematician who discovered that all periodic or repetitive phenomena, however complex, could be described as the sum of a number of sinusoidal phenomena. As the rotation of a helicopter rotor is periodic, then Fourier analysis is a useful tool to study rotor motion. It was shown above that the sine wave is the waveform of a single frequency. Musically such a waveform would be called a pure tone or fundamental and the frequency would determine the pitch. If musical instruments only produced pure tones they would be hard to tell apart. They sound different partly because of the presence of harmonics. Harmonics are frequencies given by multiplying the frequency of the fundamental by a series of whole numbers. Figure 2.28 shows the waveforms of such harmonics. The final waveform is the sum of all of the harmonics. The relative amplitude of the different harmonics determines the tonality or timbre of an instrument. What Fourier did was to show how to measure the amplitude of each harmonic in any periodic waveform. The mathematical process that does this is called a transform. Reversing the process
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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
Page 10: 8.5 Power management 326 8.6 Flying
Page 13 and 14: 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 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
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(a) (b) Introduction to helicopter
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Introduction to helicopter dynamics
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(a) (b) Introduction to helicopter
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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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