The Optimal Size of a Resonant Vibrating Beam Gyroscope

The level of thermal noise in a resonant vibrating beam gyroscope is lower, the longer the beam. A limitation on the length of the beam arises from the consideration that the beam acts as a mechanical bandpass filter transmitting the signal being measured (the instantaneous rate of rotation) from the drive axis to the sense axis. A longer beam vibrates at a lower frequency and has a narrower resonance. The length that is acceptable depends on the bandwidth of the time variation of angular rate, which in turn, depends on the nature and mission of the vehicle that uses the gyroscope for inertial navigation. High rates of maneuvering indicate millimeter scale gyroscopes that are realized as micro-electro-mechanical devices. In the case of General Aviation, considerations of noise, as well as cost, favor a centimeter scale device.