The Art of the Helicopter John Watkinson - Karatunov.net

54 The Art of the Helicopter
orthogonal (at 90 ◦ to one another) horizontal axes. If the base of the system is pitched
and rolled, the rigidity of the gyroscope will be much greater than the friction in the
gimbals and the result is that the gyroscope axis remains vertical so that its angular
momentum stays the same. Figure 2.33(b) shows that a couple is being applied to the
outer gimbal, which tries to twist it in the direction shown. The couple is transmitted
through the bearings of the inner gimbal and to the rotor shaft. If a small element
on the periphery of the flywheel is considered, this reacts in the same way as the blade
in the previous section. As the flywheel is really a collection of such elements, all of
which behave in the same way, it is clear that in response to a couple on the outer
gimbal axis, the rotor responds by turning around the inner gimbal axis.
The gyroscope rotor has a 90 ◦ phase lag just like a helicopter rotor. The outer gimbal
will not turn because the applied couple is perfectly opposed by a reaction due to the
rigidity of the gyro. The gyro can only generate the rigidity reaction by changing its
angular momentum and to do this it must precess as the rotational speed cannot change.
The rate of precession is proportional to the applied couple and inversely proportional
to the angular momentum.
2.18 Piezo-electric and laser gyroscopes
The mechanical gyroscope held sway for a long time but has recently been supplanted by
two alternatives. A piezo-electric material is one that deflects when an electrical voltage
is applied to it and which creates an electrical voltage when it is distorted. The quartz
crystal in an electronic wristwatch works on the same principle. In the quartz watch
the natural mechanical resonant frequency of the crystal forms the timing reference.
Signals from sensing electrodes measure the deflection and are amplified and fed to
drive electrodes that cause the crystal to resonate. By dividing down this highly stable
frequency a count of seconds can be obtained.
In the piezo-electric gyroscope a vibrating element is made to oscillate as shown in
Figure 2.34(a). If the assembly then rotates, the Coriolis effect causes a component
Fig. 2.34 (a) In the piezo-electric gyro there is a vibrating beam. Rotation about an axis along the beam causes
the beam to twist as it tries to conserve momentum. This can be measured to sense the rotation. (b) In a laser
gyro, light is sent in both directions around an optical path. If the system rotates, there will be a phase change
between the two components of light.