9.1 INERTIAL SENSOR TECHNOLOGIES

A sampling of inertial sensor technologies used in inertial navigation is presented in Table 9.1. There are many more, but these will serve to illustrate the great diversity of technologies applied to inertial navigation. How these devices function will be explained briefly. A more thorough treatment of inertial sensor designs is given in [190].

The histories by Draper [47], Mackenzie [129], Mueller [144], and Wrigley [215] contain much more information on the history of inertial systems and sensor technologies and the individuals involved. See also Refs. 8, 63, 110, 168 and the cited references below for more historical and technical details.

9.1.1 Early Gyroscopes

9.1.1.1 Momentum Wheel Gyroscopes (MWGs) The earth itself is a giant momentum wheel gyroscope, the spin axis of which remains pointing at the pole

star Polaris. The toy top is essentially a MWG that is probably older than recorded history. These are devices with stored angular momentum, a vector quantity that tends to remain constant and pointing in a fixed inertial direction unless disturbed by torques.

Jean Bernard Léon Foucault (1819-1868) had used a momentum wheel gyroscope to measure the rotation of the earth in 1852, and it was he who coined the term "gyroscope" from the Greek words for "turn" (γυρος) and "view" (σκοπóς).

9.1.1.2 Gyrocompass Technology Gyroscope technology advanced significantly in the early 1900s, when gyrocompasses were developed to replace magnetic compasses, which would not work on iron ships (see Section 2.2.3.3). The first patent for a gyrocompass was issued to M. G. van den Bos in 1885, but the first known practical device was designed by Hermann Anschütz-Kaempfe¹ in 1903. It performed well in the laboratory but did not do well in sea trials- especially when the host ship was heading northeast-southwest or northwest-southeast in heavy seas. Anschütz-Kaempfe's cousin Maximilian Schuler analyzed its dynamics and determined that lateral accelerations due to rolling of the ship were the cause of the observed errors. Schuler also found that the gyrocompass suspension could be tuned to eliminate this error sensitivity [174]. This has come to be called Schuler tuning. It essentially tunes the pendulum period of the suspended mass to mimic a gravity pendulum with an effective arm length equal to the radius of curvature of the earth (called a Schuler pendulum). The period of this pendulum (called the Schuler period) equals the orbital period of a satellite at the same altitude (about 84.4 min at sea level).

Inertial navigators also experience oscillatory errors at the Schuler period, as described in Section 9.5.2.1.

9.1.1.3 Bearing Technologies The earliest gyroscopes used bearing technology from wheeled vehicles, industrial rotating machinery and clocks-including sleeve bearings, thrust bearings, jewel bearings and (later on) ball bearings. Bearing technologies developed explicitly for gyroscopes include the following:

¹When the American inventor Elmer Sperry attempted to patent his gyrocompass in Europe in 1914, he was sued by Anschütz-Kaempfe. Sperry hired the former Swiss patent examiner Albert Einstein as an expert witness, but Einstein s testimony tended to support the claims of Anschütz-Kaempfe, which prevailed.

Dry-tuned gyroscopes use flexible coupling between the momentum wheel and its shaft, as illustrated in Fig. 9.1, with spring constants "tuned" so that the momentum wheel is effectively decoupled from bearing torques at the wheel rotation rate. This is not so much a bearing technology as a momentum wheel isolation technology. The very popular AN/ASN-141 military INS (USAF Standard Navigator) used dry-tuned gyroscopes.

Gas bearing gyroscopes support the momentum wheel on a spherical bearing, as illustrated in Fig. 9.2, with a thin layer of gas between the moving parts. Once operating, this type of bearing has essentially no wear. It was used in the gyroscopes of the USAF Minuteman I-III ICBMs, which were operated for years without being turned off.

Electrostatic gyroscopes (ESGs) have spherical beryllium rotors suspended by electrostatic forces inside a spherical cavity lined with suspension electrodes, as illustrated in Fig. 9.3. The electrostatic gyroscope in the USAF B-52 INS in the 1980s used optical readouts from a pattern etched on the hollow rotor to determine the direction of the rotor spin axis. The Electrically Supported Gyro Navigation (ESGN) system in USN Trident-class submarines in the late twentieth century used a solid rotor with deliberate radial mass unbalance, and determined the direction of the rotor spin axis from the effect this has on the suspension servo signals. Neither of these

gyroscopes was torqued, except for induction torquing during spinup and spindown.

9.1.1.4 Gyroscope Performance Grades Gyroscopes used in inertial navigation are called "inertial grade," which generally refers to a range of sensor performance, depending on INS performance requirements. Table 9.2 lists some generally accepted performance grades used for gyroscopes, based on their intended applications but not necessarily including integrated GNSS/INS applications.

These are only rough order-of-magnitude ranges for the different error characteristics. Sensor requirements are determined largely by the application. For example, gyroscopes for gimbaled systems can generally use much smaller input ranges than can those for strapdown applications.