# Vertical Gyroscope

## Vertical Gyroscope

(also called an artificial horizon), a gyroscopic device for determining the direction of the true vertical or of the plane of the horizon, as well as of the angles of inclination of the object with respect to this plane. The simplest nongyroscopic device of this type is a physical pendulum (plumb). However, it is not usable for a moving object, since it will not position itself along the true vertical upon rotational or accelerated translational motion of the object (it will also deviate somewhat from the vertical during a uniform translational motion because of the earth’s rotation). In addition, rolling may generate induced oscillations of the pendulum with large amplitudes. The vertical gyroscope is to a large extent free of these disadvantages and therefore is widely used in aircraft, ships, and other moving objects.

The simplest vertical gyroscope is a free astatic gyroscope, whose axis tends to preserve its orientation in space. With respect to the rotating earth, however, this axis will change its orientation in time. Therefore, without corrective devices, such an instrument may serve only as a short-term indicator of direction (particularly of the vertical). Instruments of this type, called artificial horizons and roll stabilizers, are used in ballistic missiles for determining their deviation with respect to the vertical and horizontal planes (angles of pitch, yaw, and bank). Various correction systems are used for maintaining the axis of an astatic gyroscope in a vertical position for long periods of time.

A vertical pendulous gyroscope (Figure 1) is a free astatic gyroscope in which the correction system consists of the pendulum correctors, which record the angles of deviation of the gyroscope’s axis from the vertical of the locus, and the moment transducers, which apply to the gyroscope the corresponding correcting moments, causing the precession of the gyroscope’s axis toward the vertical of the locus. The potentiometers are used to determine the angles of inclination of the object with respect to the plane of the horizon. The error of vertical gyroscopes of this type, which is determined by the deviation of the axis from the vertical of the locus, may vary from a fraction of a degree to minutes of arc. In precision vertical gyroscopes, corrections for the earth’s rotation and for the object’s own motion are introduced to increase accuracy.

Figure 1. Schematic diagram of a vertical pendulous gyroscope: (1) rotor, (2) and (3) inner and outer gimbal rings, (4) and (5) correcting pendulums, (6) and (7) moment transducers, (8) and (9) potentiometers

Vertical pendulous gyroscopes are used for determining the roll and pitch angles of ships and the bank and pitch angles of aircraft. This type of vertical gyroscope is used in the automatic stabilization systems of various moving objects, in roll stabilizers for ships, and for the stabilization of aircraft, as well as for determining the curvature of boreholes and mine shafts.

Another type of vertical gyroscope, which does not require a correction system, is the gyropendulum—a gyroscope with three degrees of freedom, whose center of gravity G is located on the rotor axis at some distance l from the support point O (Figure 2). Upon deviation of the axis Oz of the gyroscope from the vertical , the axis Oz starts to precess about under the influence of the force of gravity P, circumscribing a cone whose vertex is at point O. Since the angular momentum H of the gyroscope is very large, the precession period

T = 2πH/lP

(where l = OG) is also large, which renders the instrument virtually immune to oscillations of the object. The preces-sional oscillations of the Oz axis in a real instrument are damped by a special device, and the Oz axis of the gyroscope assumes a position close to the vertical. However, for the instrument to have the required precision during accelerated motion (maneuvering) of the object, the period T must satisfy the condition of M. Schuler (it must be equal to the period of oscillation of a mathematical pendulum whose length is equal to the earth’s radius)—that is, it must be 84.4 min—which has not yet been achieved in practice. In the existing designs, T is usually about 10-20 min, and therefore vertical gyroscopes of this type are subject to considerable errors when the object maneuvers. Gyropendulums are used in sextants for stabilizing their optical systems with respect to the plane of the horizon and in some ship stabilization systems, which are used mainly at constant speeds and steady courses.

Figure 2. Schematic diagram of a gyropendulum: (1) chamber and rotor, (2) outer gimbal ring

An inertial vertical gyroscope is an instrument that permits the determination of the vertical with a high degree of accuracy during accelerated motion of the object on which it is mounted (see Figure 3). In addition to gyroscopes, this device contains accelerometers and computers (integrators), which simulate a pendulum with Schuler’s period.

Figure 3. Schematic diagram of an inertial vertical gyroscope: (1) chamber and rotor, (2) outer gimbal ring, (3) and (4) accelerometers, (5) and (6) integrators, (7) and (8) moment transducers

The inertial vertical gyroscope consists of a free astatic gyroscope with accelerometers mounted on its chamber (in real designs, the accelerometer is mounted on a gyro-stabilized platform). The apparent accelerations ax and au of the object along the horizontal axes Ox and Oy are determined by the accelerometers; the values are fed into the integrators, and the resulting output signals (velocities vE and vN along the axes Ox and Oy) are fed into the moment transducers, which apply correction moments to the gyroscope. These correction moments generate the precession of the gyroscope axis Oz toward the vertical. With a proper selection of the coefficient of the proportionality between the integrator signal and the magnitude of the correction moment, the period of precession becomes equal to the Schuler period. Because of this, the device is highly accurate during maneuvering of the object, and the corresponding errors do not exceed several minutes of arc. Inertial vertical gyroscopes are widely used in inertial navigation systems on ships and aircraft.

A. IU. ISHLINSKII and S. S. RIVKIN

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