Mine Surveying-gyro-theodolite 5n6o1m

Surveys as accurate as those done by conventional methods are completed more quickly by the use of a new type of northseeking gyro attachment for theodolites.

Gyro Attachment For Theodolites Simplifies Surveying Procedures 0 . RELLENSMANN and E. P. PFLEIDER

n the May 1959 issue of 8 E the authors reported on the gyrotheodolite as used for determining azimuths in surface and underground work. Further research has led to the development of a new type of gyro instrument, the band-suspended gyro attachment, which is essentially an upset gyro attached to the top of a theodolite. The new gyro attachment is light enough to be mounted on any angle-measuring instrument if the design of the telescope standard permits. Gyrotheodolite units have been used to transfer meridian lines underground in the Coeur d'Alene mining district, although they have not ,been used extensively in the U.S. In other parts of the world, however, they have been adopted as the standard surveying instrument by mining engineers. In addition to underground work, the gyrotheodolite has been used in geodetic surveys, surface

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mines and in applied geophysics to determine magnetic declinations.

OTTO RELLENSMANN is Professor Emeritus, Clausthal Mining Academy, Clausthal-Zellerfeld, West . Co-author EUGENE P. PFLEIDER, SME member, is Professor of Mineral Engineering, School of Mineral and Metallurgical Engineering, University of Minnesota Minneapolis, Minn.

A free gyro is a symmetrically constructed rotor which is able to turn about all three axes and whose center points of gravity and rotation coincide. In the case of a north-seeking gyro there is no such coincidence between the centers of gravity and rotation because a heavy mass of lead is placed at the bottom of the gyro-containing ball. The distance between the center of gravity and the center of rotation is known as the metacentric height. The most interesting phenomenon in gyro-application is precession (Fig. 1). If we apply a force K on the end of a non-spinning gyro, the end of the axis moves downward, while in the case of a spinning gyro the axis turns perpendicular in thehorizontal plane according to the force parallelogram 1-2-3. The horizontal velocity vector 1-2 depends on the magnitude of the angularvelocity Of the spinning gyro, while the horizontal velocity vector 2-3 depends on the magnitude of K. There-

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ENGINEERING, M A R C H 1968

Theory and Principle

SOCIETY OF

per hr on the equator. At other latitudes the change after one hour is 15" x cos latitude so that a north-seeking gyro is only applicable in latitudes between the equator and 80". The meridian direction moment, R (gm cm' x sec") , at latitude Q amounts to: where

R=I.w.n.cos+-sins

C11

I = moment of inertia o = angular velocity of

of gyro, gm cma gyro, radians per sec n = angular velocity of earth, radians per sec 4 = latitude of observation = angle of precession from north, degrees (Y

The swing time, T, of the oscillations is given by the following equaton: Fig. I-By applying a force K to a spinning gyro, a mouement perpendicular to K results and is equal to the 1-3 uector.

where fore, 1-3 is the resultant vector that causes the end of the axis to move perpendicular to K. If the earth is considered to be a very big gyro that turns around its axis once every 24 hours, and on this big gyro we are operating our small gyro-instrument, the problem of making this small gyro-instrument north-seeking consists of arranging it as a suspended pendulous gyro (Fig. 2 ) . With the earth rotating from west to east, the axis of the spinning gyro is directed in an east-west direction (position I ) . When the plumbline has changed 15 degrees, the gyro-axis tends to keep the same position as in I (shown in position 11) because of its inertia. But the precession due to the gravity force F compels the gyro-axis to turn to a north-south orientation, which is shown in position 111. If the inertia of the system is great enough, the axis of the gyro-wheel will overshoot the meridian, and therefore cause the axis to precess in the opposite direction. According to the laws of dynamics, it can be easily proved that these oscillations are in the form of weakly damped, simple harmonic motion. The oscillations around true north, as effected by the earth's rotation, are summarized as follows: There is no change in the direction of plumbline on the North Pole but there is a change of 15"

m = mass of pendulum, gm a = metacentric height, cm g = acceleration of gravity, cm per secZ The form of oscillations of the gyro-axis is elliptical, with the major axis being in the horizontal plane, the minor axis in the vertical plane and a ratio between the two axes of about 30: 1. For the north determination only five or seven east and west reversal points are observed and then, by use of the Schuler-mean, the north position is calculated.

Historical Development In April 1947, Rellensmann began consrtuction of a meridian-indicator that would not have the disadvantage of preceding instruments, namely, extreme sensitivity to outside disturbances such as vibration (Fig. 3 ) . The gyro a, which has an angular momentum of approximately 50 x 10' gm cm" per sec is installed in a sphere b, which carries a heavy leass on its lower side in order to decrease swing time. The gyro-sphere is surrounded by an envelope-sphere c, and both spheres have electrical s opposite each other. By means of a Wheatstone bridge it is possible to give the envelope-sphere the same direction, which is ob-

Fig. 2-By arranging it as a suspended pendulous gyro, the gyro-instrument becomes north seeking. The phenomenorl of precession, illustrated hme, form9 the basis for the operation of the gyro attachment for theodolites.

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M A R C H 1968, M I N I N G ENGINEERING-73

a theodolite. The basic features of this instrument are presented in Table 1.

a

gyro

b

gyro sphere

c

envelope sphere

d

electrical s for

Gyro-Theodolite Unit

off-take of direction a

divided circle

f

alidade

Fig. 3-A cross-section of the first Clausthal meridian indicator illustrates the basic constr~cctionof the gyro-attachment.

tained by peaks of an electrical tone signal, as that indicated for the gyro-sphere. The envelopesphere can be rotated around its vertical axis and has a plate on top for mounting the theodolite. Optical reading of direction by an auto-collimation telescope, and introduction of band-suspension were important subsequent refinements. Through the work of McLelland and Rellensmann, an instrument called the Gyrotheodolite KT1 (McLelland) was developed, and has been successfully used in several areas.I3 Subsequent modification, termed the "Rellensmann System," has led to a new instrument design characterized by having a small upset gyro attached to the top of a

upper band c l a m p

b

lower band c l a m p

c

Index

d

mast

e

gyro

I

v-mark

g

lracer poml

h

magnnl~er

I

forced cenlerlng

k

locknng

Fig. 4-This sectional view of the gyro attachment indicates the mirror ~ y s t e m b y which the wing-amplitudes of the gyro axis are obserced. Inset shows V-mark image. 74-MINING

ENGINEERING, MARCH 1968

The normal theodolite is modified with a bridge mounted on the telescope standards and the range of the horizontal tangent screws is increased. Three centering pins in the bridge insure that the gyro will always have the same position in relation to the line of sight of the telescope. Since the telescope can still be transited below the bridge, the instrument is not prevented from carrying out its normal duties. The north-seeking gyro system (Fig. 4) hangs on a thin suspension tape with the result that the spin axis of the gyro is kept in the horizontal plane and, under the influence of the earth's spinning motion, takes up a slightly damped oscillation symmetrical to the meridian plane. A gyro mark, forming part of the optical system connected to the gyro mechanism, allows observations of the oscillations in relation to a reading index attached to the instrument. By observing a series of oscillation turning points and reading the theodolite horizontal circle each time, or by timing the transit through a line of sight previously oriented approximately in the north direction, the geographic or true north direction is obtained by the gyro. The two measuring methods commonly used are simple and make complicated calculations unnecessary so that the final determination is completed by the end of the observation.

Measuring Procedure The methods of operating the gyro theodolite (Rellensmann System) are described in detail by Schwendener4 and in the manuals prepared by the manufacturers of the instrument. A brief description of the procedures, however, will assist in understanding the simple techniques involved. The telescope is preoriented towards the north by a so-called "quick method", and subsequently oriented precisely, either by the "transit method," or the "reversal point method" described below.

The Quick Method As the time of an oscillation period remains constant within a large area, and as that time can be calculated in advance for each geographical latitude, it is possible to obtain an approximate orientation in a few minutes with the aid of a stopwatch fitted with an independently controlled trailing second hand. The Transit Method The alidade is clamped with the telescope in the approximate orientation obtained by the Quick Method described above. With the stopwatch, the transit of the gyro mark through the center of the index (Fig, 4) is timed and, in addition, the amplitude of the oscillation is read on an auxiliary scale. Corrections are then applied to the approximate orientation, proportional to the amplitude and also to the time difference in oscillation periods to the left and right of the index center. The proportional factor can be determined either empirically SOCIETY OF

Table I. Basic Features of Fennel TK-3 Band-Suspended Gyro Attachment and Wild T-16 Theodolite POWER: A synchrynous motor, 3 ph, 115 v Power source-two 12 v batteries in series with transistorized convertor at 400 CDS stabilized either bs tuning - fork or ouartz crystal Consumption-0.3 A h (ampere hr) for a 30 min setup. GYRO ATTACHMENT: Inertia-0.18 x 103 gr cma Impulse-1.8 x 160 gr cma per sec Half period-4 min at 50' latitude

Gyro Theodolite in Surface Mining and Geodesy

THEODOLITE: Erect image, fixed focus magnification of 28 diam and 16 mm aperture. Spirit level sensitivity-30 in. per 2 mm TOTAL WEIGHT: 18 k g (40 1b)

or by calculation. Depending on the desired accuracy, the circle reading for the true north is derived from three or more transits through the center of the index.

The Reversal Point Method The oscillating gyro mark is followed by means of a continuous turning of the tangent screw, which keeps it in the center of the V-shaped index. As the gyro reaches the reversal point, it appears to stand still and in this position the horizontal circle is read. Depending on the desired accuracy, true north is determined by observing three or more turning points and the mean of the oscillation is computed according to Schuler's Mean (Fig. 5). The mean square error or standard deviation of a true north orientation and the time required (including running up time) are as follows: Quick Method 2 3 ' of arc in about 7 min. Transit Method and Reversal Point Method 230" of arc in about 20 min. This final adaptation of the gyro attachment to the theodolite helped introduce this instrument for numerous tasks in geodesy, mine surveying, geophysical work and military applications.

Gyro Surveys in Underground Mining In many cases orientation work in mines can be done more accurately and economically with Arnplltude

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- horlzontel clrcle readlng for reversal left (west1 or rlght (east1 of rnerldlan plane

Schuler mean z , lntermedlate mean 2,-total mean lndlcatlng relerence bearlng corresponding to true nonn

-

+il,+I.I+l.

21

2

$11, t 1 . 1 + 1 . 2

-

Z*

Fig. 5--The Schuler Mean is calculated b y the equations shown here. The points I are the reuersal points obseroed in the V-shaped index of the gyro-attachment. M I N I N G ENGINEERS

the application of a north-seeking gyro. In transferring a bearing from the surface to the underground workings of a mine, usually one gyroscopic determination of azimuth is made at each end of the surface line and also one determination at each end of the underground line. If the differences between the values on surface and underground range within a certain limit, the transfer work is considered satisfactory. Determining the true meridian is an important task for the surveyor and usually has been done by observing the bearing of the pole-star at its greatest elongation. Observations on the pole-star are less conveniently made than those on the sun, but the calculations are simpler and accuracy is much greater. It is faster and more economical to solve this task by using a gyro-attachment, and the accuracy is high enough for all geodetic purposes. The gyromethod is particularly advantageous as it may be used at all times and under all conditions, and the whole procedure is rapid, involving virtually no calculations. It is not necessary to carry out observations at each point of a long traverse when measuring distances and determining bearings because only every second point need be occupied. Also the location of new points by resection can be easily perfected by using the gyro-attachment. Only two triangulation points are necessary for resection with the gyro-theodolite, whereas three points must be known when using the transit alone, thus simplifying calculations.

Gyro Application in Applied Geophysics In applied geophysics the gyro-attachment is used to determine magnetic declinations, i.e. the angle between true and magnetic north, which can be done with an accuracy of 1'. To determine this angle, magnetic north is observed with a com and true north with the gyro-attachment. Using this method, and choosing a distance between observation points of one mile, precise isogonic charts can be drawn. This is much more accurate than conventional isogonic charts, as they use ten mile intervals between observations. In addition, useful information can be obtained concerning the disturbing magnetic layers within the earth's crust. Torricos6 and Horst have reported on such work, carried out on a large scale within northwest region in . They state that this declination method is a very valuable aid in geomagnetics to solve geologiotectonic problems. i5E

References 1 G. B. Lauf: The Gyrotheodolite and its Application in the Mining Industry of South Africa. Journal of the South A f ~ i c a nInstitute of Mining and Metallurgy, 1963, pp. 349-386. a A. Falter: The Gyrotheodolite and its Value in Modern Surveying Practice. The Canadian Mining and Metallurgical Bulletin, 1964, PP. 413-420. 3 0. Rellensmann: Recent Application of the Gyrotheodolite in Tunneling-Work in Underground-Workings and in Applied Geophysics. Mining Research, Pergamon Press, pp. 283-288. LH. R. Schwendener: Methods and Practical Experience in the Determination of True North with a Theodolite Gyro Attachment. English translation of article in German published in Allgemeine Ve7messungs-Nauchrichten, 4 (April 1966). in the NorthM. Torricos: Results of ~eciinations:~easurements west Harzregion. Dissertation Mining University Clausthal, 1965.

M A R C H 1968, M I N I N G ENGINEERING-75