THE GYROSCOPE The gyroscope consists of a perfectly balanced wheel, which is arranged to spin symmetrically at high speed about an axis. By suspending the mass of the wheel, or rotor, in a precisely designed gimbal arrangement, the unit is free to move in two planes, each perpendicular to each other as well as to the plane of spin. This grants the gyroscope freedom to move in three dimensions.

Fig. 1 The free gyroscope.

A gyroscope, where the freedom of movement is not restricted in any way, is referred to as a free gyroscope. But there exists gyroscopes where the freedom of movement is somewhat restricted, such as the constrained and the spring restrained gyros.

PHYSICAL PROPERTIES The behaviour of a free gyroscope can be derived from two physical properties, gyroscopic inertia and precession.

OBSERVATION METHODS Since the gyro oscillates about the meridian plane one has to measure the size or swing periods of these oscillations to be able to determine True North. Two methods have been developed for this: the Transit Method and the Reversal Point Method. Modern gyros have automated this methods, and all one has to do is to focus the theodolite telescope to target and press START. However, the theory of the methods used for the GAK 1 still applies for the modern instruments. Another parameter, which at least needs to be checked for every surveying campaign, is the adaptation constant, i.e. the angle between the centre of the gyro oscillation and the ascertained position N of the alidade, which is correlated to the line of sight of the theodolite telescope. MEASURING METHODS FOR GAK 1 TRANSIT METHOD It refers to the gyro directional methods that Fixed gyro theodolite approve department, observation index line after points cross zero line of the time and board the biggest swing value The instrument must be approximately orientated toward True North. Then the time intervals between at least three successive transits of the moving gyro mark through the middle of the scale are measured, and the amplitude of the gyro oscillation is read on the scale at the turning points.

Fig. 2 Transit-Method The angular correction that must be applied to the provisional orientation is proportional to the amplitude and to the difference in the times taken to make the half swings to the east and west of the middle of the scale. By measuring in two different directions N one may calculate the proportional factor c using:

c =

N ' 1 N '2

.

(2-1)

t 1 a 1 t 2 a2 Thereby True North can be calculated using:

N = N'+N

(2-2)

where: N = c a t

a = amplitude of gyro oscillation observed on instrument display

REVERSAL POINT METHOD It refers to the gyro orientation method that tracking the theodolite with gyro swinging index line, read to arrive Two reversal point degrees plate reading. Using the horizontal slow motion drive screw of the theodolite in order to follow-up, the moving mark is kept as sharply as possible in the middle of the scale. When a reversal point is reached, the horizontal circle of the theodolite is read.

Fig. 3 Reversal point MethodAn experience gained in the study of the gyro is that one should strive after having smooth, pendulous movement with a starting amplitude not higher than

10 units in the gyro amplitude scale. There is a radical decrease in accuracy when these conditions have not been fulfilled. The problem is that in order to achieve this, one has to start measuring with the gyro quite closely in line with the meridian plane. It is therefore recommended to pre-orient the gyro with, for example, a few readings using the reversal point method and then start over.