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The Art of the Helicopter John Watkinson - Karatunov.net

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2.17 <strong>The</strong> gyroscope<br />

Technical background 53<br />

When bodies move in a straight line, all <strong>of</strong> <strong>the</strong> body is going at <strong>the</strong> same velocity and<br />

energy calculations are easy. However, when a body rotates, those parts fur<strong>the</strong>st from<br />

<strong>the</strong> axis are going faster than those parts near <strong>the</strong> axis. <strong>The</strong> amount <strong>of</strong> rotational energy<br />

stored is a function <strong>of</strong> <strong>the</strong> distribution <strong>of</strong> mass with respect to <strong>the</strong> axis <strong>of</strong> rotation. This<br />

is measured by <strong>the</strong> moment <strong>of</strong> inertia (MoI). In a flywheel, as much mass as possible<br />

is concentrated at <strong>the</strong> outside <strong>of</strong> <strong>the</strong> rotor to give <strong>the</strong> greatest MoI.<br />

Angular momentum is <strong>the</strong> product <strong>of</strong> inertia and <strong>the</strong> rate <strong>of</strong> rotation about a given<br />

axis. Earlier in this chapter it was seen that a body may be accelerated by changing<br />

its speed or its direction. <strong>The</strong> same is true <strong>of</strong> a gyroscope. Changing rotational speed<br />

is acceleration but so also is changing <strong>the</strong> direction <strong>of</strong> <strong>the</strong> rotational axis. If <strong>the</strong> rotor<br />

is spinning rapidly it has a large momentum, and even a very small rate <strong>of</strong> movement <strong>of</strong><br />

<strong>the</strong> rotational axis represents a large rate <strong>of</strong> change <strong>of</strong> momentum and so a large force<br />

is necessary. Put simply a gyroscope tends to resist disturbances to its axis in a manner<br />

disproportionate to its weight. That makes it attractive for aviation where weight is at<br />

a premium. <strong>The</strong> tendency to resist axis disturbance is called rigidity.<br />

Figure 2.33(a) shows a gyroscope suspended by <strong>the</strong> shaft in a pair <strong>of</strong> nested cages<br />

called gimbals. <strong>The</strong> axis <strong>of</strong> rotation is vertical and <strong>the</strong> gimbals allow turning in two<br />

Fig. 2.33 (a) A vertical axis gyro supported by nested rings called gimbals. (b) A couple applied to a gimbal is<br />

resisted by rigidity. <strong>The</strong> gyro axis turns with a 90 ◦ phase lag. This is called precession.

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