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The Art of the Helicopter John Watkinson - Karatunov.net

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

orthogonal (at 90 ◦ to one ano<strong>the</strong>r) horizontal axes. If <strong>the</strong> base <strong>of</strong> <strong>the</strong> system is pitched<br />

and rolled, <strong>the</strong> rigidity <strong>of</strong> <strong>the</strong> gyroscope will be much greater than <strong>the</strong> friction in <strong>the</strong><br />

gimbals and <strong>the</strong> result is that <strong>the</strong> gyroscope axis remains vertical so that its angular<br />

momentum stays <strong>the</strong> same. Figure 2.33(b) shows that a couple is being applied to <strong>the</strong><br />

outer gimbal, which tries to twist it in <strong>the</strong> direction shown. <strong>The</strong> couple is transmitted<br />

through <strong>the</strong> bearings <strong>of</strong> <strong>the</strong> inner gimbal and to <strong>the</strong> rotor shaft. If a small element<br />

on <strong>the</strong> periphery <strong>of</strong> <strong>the</strong> flywheel is considered, this reacts in <strong>the</strong> same way as <strong>the</strong> blade<br />

in <strong>the</strong> previous section. As <strong>the</strong> flywheel is really a collection <strong>of</strong> such elements, all <strong>of</strong><br />

which behave in <strong>the</strong> same way, it is clear that in response to a couple on <strong>the</strong> outer<br />

gimbal axis, <strong>the</strong> rotor responds by turning around <strong>the</strong> inner gimbal axis.<br />

<strong>The</strong> gyroscope rotor has a 90 ◦ phase lag just like a helicopter rotor. <strong>The</strong> outer gimbal<br />

will not turn because <strong>the</strong> applied couple is perfectly opposed by a reaction due to <strong>the</strong><br />

rigidity <strong>of</strong> <strong>the</strong> gyro. <strong>The</strong> gyro can only generate <strong>the</strong> rigidity reaction by changing its<br />

angular momentum and to do this it must precess as <strong>the</strong> rotational speed cannot change.<br />

<strong>The</strong> rate <strong>of</strong> precession is proportional to <strong>the</strong> applied couple and inversely proportional<br />

to <strong>the</strong> angular momentum.<br />

2.18 Piezo-electric and laser gyroscopes<br />

<strong>The</strong> mechanical gyroscope held sway for a long time but has recently been supplanted by<br />

two alternatives. A piezo-electric material is one that deflects when an electrical voltage<br />

is applied to it and which creates an electrical voltage when it is distorted. <strong>The</strong> quartz<br />

crystal in an electronic wristwatch works on <strong>the</strong> same principle. In <strong>the</strong> quartz watch<br />

<strong>the</strong> natural mechanical resonant frequency <strong>of</strong> <strong>the</strong> crystal forms <strong>the</strong> timing reference.<br />

Signals from sensing electrodes measure <strong>the</strong> deflection and are amplified and fed to<br />

drive electrodes that cause <strong>the</strong> crystal to resonate. By dividing down this highly stable<br />

frequency a count <strong>of</strong> seconds can be obtained.<br />

In <strong>the</strong> piezo-electric gyroscope a vibrating element is made to oscillate as shown in<br />

Figure 2.34(a). If <strong>the</strong> assembly <strong>the</strong>n rotates, <strong>the</strong> Coriolis effect causes a component<br />

Fig. 2.34 (a) In <strong>the</strong> piezo-electric gyro <strong>the</strong>re is a vibrating beam. Rotation about an axis along <strong>the</strong> beam causes<br />

<strong>the</strong> beam to twist as it tries to conserve momentum. This can be measured to sense <strong>the</strong> rotation. (b) In a laser<br />

gyro, light is sent in both directions around an optical path. If <strong>the</strong> system rotates, <strong>the</strong>re will be a phase change<br />

between <strong>the</strong> two components <strong>of</strong> light.

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