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The Art of the Helicopter John Watkinson - Karatunov.net

The Art of the Helicopter John Watkinson - Karatunov.net

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104 <strong>The</strong> <strong>Art</strong> <strong>of</strong> <strong>the</strong> <strong>Helicopter</strong><br />

(a)<br />

(b)<br />

Fig. 3.35 (a) A pair <strong>of</strong> contra-rotating eccentrics produces linear vibration. (b) If <strong>the</strong> mechanism <strong>of</strong> (a) is rotated,<br />

one <strong>of</strong> <strong>the</strong> eccentrics will turn faster and <strong>the</strong> o<strong>the</strong>r slower. Thus frequencies transmitted to <strong>the</strong> hull will be <strong>the</strong><br />

vibration frequency plus or minus <strong>the</strong> rotor frequency.<br />

It will be clear that a two-bladed rotor is at a disadvantage because both blades will be<br />

in <strong>the</strong> lift trough simultaneously at 90 ◦ and 270 ◦ , and in a lift peak simultaneously at 0 ◦<br />

and 180 ◦ . <strong>The</strong> result at high speed is a vertical vibration known as 2P hop. Figure 3.36(b)<br />

shows <strong>the</strong> situation for <strong>the</strong> third flapping harmonic. As <strong>the</strong> third harmonic flapping<br />

has one and a half cycles in <strong>the</strong> time between blade passings, it will be clear that <strong>the</strong><br />

3P components will be out <strong>of</strong> phase between <strong>the</strong> two blades. Following similar logic it<br />

should be clear that in a two-bladed rotor, only even vertical harmonics exist; <strong>the</strong> odd<br />

ones cancel.<br />

Figure 3.37 shows <strong>the</strong> case for a three-bladed rotor. At (a) it will be seen that <strong>the</strong><br />

second flapping harmonic waveform <strong>of</strong> each blade is at 120 ◦ to that <strong>of</strong> <strong>the</strong> next. <strong>The</strong> sum<br />

<strong>of</strong> three sine waves at 120 ◦ is constant and so <strong>the</strong>re can be no 2P hop in a three-bladed

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