Rolling Error of Gyrocompass Caused by Liquid Ballistic

Abstract

This paper discusses the rolling error of a gyro-compass having a liquid ballistic as a north seeking device.The purpose of this paper is to present a formula of rolling error which takes into consideration both of torque applied about the horizontal axis of the gyro, caused by the force directly applied to the tube by viscosity of the flowing liquid, and influence of movement of the gyro supporting device and other elements as a physical pendulum whose fulcrum is at the gimbal ring centre. In this paper, the formula is theoretically derived from the equation of motion of gimballed system as a physical pendulum, and also from the equation of motion of the liquid.
The formula obtained is more suitable for practical calculation than previous formula, especially for short period rollings common in small fishing ships when high viscosity oil is used.