mine surveying-gyro-theodolite

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Surveys

as

accurate as those done by

conventional m etho ds are completed more

quickly b y the use of a new ty pe of north

seeking gyro attachm ent for theo dolites .

Gyro ttachment For Theodolites

Simplifies

Surveying Procedures

0

R E L L E N S M A N N and E. P. PFLEIDER

n th e May 1959 issue of E the authors re-

mines and in applied geophysics to determine mag-

ported on the gyrotheodolite as used for deter - netic declinations.

mining azimuths in surface and underground work.

Further research has led to the development of

a new typ e of gyro instrum ent, 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 stand ard 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 par ts of the world,

however, they have been adopted as the stand ard

surveying instrument by mining engineers.

In addition to underground work, the gyrotheo-

dolite has been used in geodetic surveys, surface

Theory and Principle

free gyro is a symmetrically constructed

rotor which is able to turn about all three

axes and whose center points of gravi ty and rota-

tion coincide. In the case of a north-seeking gyro

there is

no such coincidence between the centers

of gravi ty and rotation because a heavy mass of

lead is placed a t the bottom of t he gyro-contain-

ing ball. The distance between the center of gravity

and the center of rota tion is known as th e meta-

centric height.

The most interesting phenomenon in gyro-appli-

cation is precession (Fig .

1 .

If we apply a force

K

on the end of a non-spinning gyro, the end

of t he axis moves downward, while in the case of

a spinning gyro the axis turns perpendicular in

thehorizontal plane according to the force parallel-

OTTO

RELLENSMANN is Professor Emeritus Clausthal Mining

ogram 1-2-3. The horizontal velocity vector 1-2

Academy Clausthal-Zellerfe ld West Germany. Co-author EU-

depends on the magnitude of the angularvelocity

GEN E P. PFLEIDER SME member is Professor of M ine ral Engi-

f

the spinning gyro, while the horizontal velocity

neering School of Min eral and Metallurgica l Engineering Univer-

sity of Minnesota Minneapolis Minn.

vector 2-3 depends on the magnitude of K . There-

7 2 - M I N I N G E N GI NE E RI N G M A R C H

1968

SOCIETY OF


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Fig. I-By apply ing a force K to a spinning gyro a moue-

ment perpendicular to results and is equal to the 1 3

uector.

fore, 1-3 is the resultant vector that causes the

end of the axis to move perpendicu lar to

K

If the ear th 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 t he 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 th e inerti a 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 th e form of weakly damped,

simple harmonic motion.

The oscillations around true north, as effected

by the earth's rotation, ar e summarized as follows:

There is no change in the direction of plumbline

on the North Pole but there is a change of 15

Fig. 2-By arranging it

s

a suspended

pendulous gyro the gyro-instrument

be-

comes north seeking. The phenomenorl

of precession illustrated hm e form9

the

basis

fo r the operation of the gyro

attach men t for theodolites .

per hr on the equator. At other latitudes the change

after one hour is 15 x cos lati tude 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 lati tude amounts to:

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

where

C11

I moment of inertia of gyro, gm cma

angu lar velocity of gyro, radians per sec

n angular velocity of ear th, radians per sec

latitude of observation

Y

angle of precession fro m north, degrees

The swing time, T, of t he oscillations is given

by the following equaton:

where

m = mass of pendulum, gm

a metacen tric height, cm

g acceleration of gravity , cm per secZ

The form of oscillations of the gyro-axis is ellip-

tical, 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 tha t would not have the

disadvantage of preceding instruments, namely, ex-

treme sensitivity to outside disturbances such as vi-

bration (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 leadmass 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 contacts opposite each other. By means

of a Wheatstone bridge it is possible to give the

envelope-sphere the same direction, which is ob-

M IN IN G ENGINEERS

M A R C H 1968 M I N I N G E N G IN E E R IN G 7 3


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a gyro

gyro sphere

c

envelope sphere

d electri cal contacts for

off-take of direction

a

divided circle

f alidade

Fig. 3 A cross section of the first Clausth al mer idia n in

dicator illustrates the basic constr~cctionof the g yro atta ch

ment .

tained by peaks of an electrical tone signal, as

that indicated for the gyro-sphere. The envelope-

sphere can be rotated around its vertical axis and

has a plate on top for mounting the theodolite.

Optical read ing of direction by an

auto-collima-

tion telescope, and introduction of band-suspension

were important subsequent refinements.

Through the work of McLelland and Rellens-

mann, an instrument called the Gyrotheodolite KT-

1

(McLelland) was developed, and has been suc-

cessfully used in several areas.I3 Subsequent modi-

fication, 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 clamp

b lower band clamp

c Index

d mast

e gy r o

v-mark

l racer poml

magnnl~er

forced cenler lng

k

locknng

Fig. 4 This sectional vie w of the gyro attachm ent indicates

the mir ror ~ ys temby whic h the wing ampli tu des of the

gyro axis are obserced. Inset shows V mark ima ge.

a theodolite. The basic fea tures of this instrum ent

are presented in Table 1.

Gyro Theodolite Unit

The normal theodolite is modified with a bridge

mounted on the telescope standards and the range

of t he horizontal tangent screws is increased. Three

centering pins in the bridge insure that the gyro

will always have the same position in relation to

th e line of sight of the telescope.

Since the tele-

scope 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 th e earth's spin-

ning motion, takes up a slightly damped oscillation

symmetrical to the meridian plane. A gyro mark,

forming part of t he optical system connected to

the gyro mechanism, allows observations of t he

oscillations in relation to a reading index attached

to the ins trument. By observing a series of oscilla-

tion turning points and reading the theodolite hori-

zontal circle each time, or by timing the transit

through a line of sight previously oriented approxi-

mately 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 t he observation.

Measuring Procedure

The methods of operating th e gyro theodolite

(Rellensmann System) are described in detail by

Schwendener4 and in the ma nuals prepared by the

manufacturers of th e instrument. A brief descrip-

tion of the procedures, howe ver, will assist in un-

derstanding the simple techniques involved.

The telescope is preoriented towards the north

by a so-called quick method , and subsequently

oriented precisely, eithe r by the trans it method,

or the reversal point method described below.

The uick ethod

As the time of an oscillation period remains con-

stant within a large area, and as that time can be

calculated in advance for each geographical lati-

tude, it is possible to obtain an approximate orien-

tation in a few minutes with the aid of a stopwatch

fitted with an independently controlled trailing

second hand.

The Transit ethod

The alidade is clamped with the telescope in

the approximate orientation obtained by the Quick

Method described above. With the stopwatch, the

transit of th e gyro mark through the center of the

index (Fig, 4) is timed and, in addition, the ampli-

tud e of the oscillation is read on an auxilia ry 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 propor-

tional factor can be determined either empirically

74-M ININ G ENGINEERING MA RCH 1968

SOCIETY O


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Table I. Basic Features of Fennel TK 3

Band Suspended Gyro Attachmen t and

Wild T 16 Theodolite

POWER:

A synchrynous motor, 3 ph, 115 v

Powe r source-two 12 v batteries in series with transistorized

convertor at 400

CDS

stabilized either s tuning fork or ouartz

crystal

Consumption-0.3 A h (ampere hr) fo r 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

THEODOLITE:

Erect image, fixed foc us magnification o f 28 diam and 16 mm

aperture.

Spirit level sensitivity-30 in. per 2 mm

TOTAL WEIGHT: 18 k g (4 0 1b)

or by calculation. Depending on the desired accu-

racy, the circle reading for the tru e north is derived

from three or more transits through the center of

th e 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 th e

gyro reaches the reversal point, it appears to stand

still and in this position the horizontal circle is

read. Depending on the desired accuracy, tru e no rth

is determined by observing three or more turning

points and th e 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 (in-

cluding runnin g up time) are as follows:

Quick Method

23 ' of arc in about min.

Trans it Method and Reversal Po int Method

230 of arc in about 20 min.

This final adaptat ion of the gyro attachmen t to

the theodolite helped introduce this instrument

for numerous tasks in geodesy, mine surveying,

geophysical work and military applications.

Gyro Surveys in Underground Mi nin g

In many cases orientation work in mines can

be done more accurately and economically with

Arnplltude

horlzontel clrcle readlng for

reve rsal left (west1 or rlght (east1

of rnerldlan plane

Schuler mean

z , lntermedlate mean

2,-total mean

lndlcatlng relerence

bearlng

corresponding

to

true nonn

+ i l , + I . I + l .

2

2

11, t 1 . 1 1 .

2

-

Z

Fig. 5 The Schuler Mean is calculated by the equations

shown here. The points are the reuersal points obseroed

in the V sh aped index of the gyro attachment.

MINING ENGINEERS

the application of a north-seeking gyro. In tran s-

ferring a bearing from the surface to the under-

ground 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 t he underground line. If the differences be-

tween the values on surface and underground range

within a certain limit, the transfer work is con-

sidered satisfactory.

Gyro Theodolite in Surface Mini ng and Geodesy

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

ar e 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 gyro-

method 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 dis-

tances 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 triangu-

lation points are necessary for resection with th e

gyro-theodolite, whereas three points must be

known when using the transit alone, thus simpli-

fying calculations.

Gyro Application in Applie d 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-

pass 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 repo rted on such work,

carried out on a large scale within northwest re-

gion in Germany. They state that this declination

method is a very valuable aid in geomagnetics

to solve geologiotectonic problems. i

References

G. B. Lauf: The Gyrotheod olite and its Application in the Min-

ing Industry of South Africa. Journal of the South

Af ~i ca n nstitute

of Mining and Metallurgy, 1963, pp. 349-386.

a A. Falter: The Gyrotheodolite and its Value in Modern Survey-

ing Practice. The Canadian Mining and Metallurgical B ulletin, 1964,

PP. 413-420.

3

0 Rellensmann: Recent Application of the Gyrotheodolite in

Tunneling-Work in Underground-Workings and in Applied Geo-

physics. Mining Research, Pergamon Press, pp. 283-288.

LH. R. Schwendener: Methods and Practical Experience in the

Determination of True North with a T heodolite Gyro Attachment.

English translation of article in German published in Allgemeine

Ve7messungs-Nauchrichten 4 (April 1966).

M. Torricos: Results of ~eciinations:~easurementsn the North-

wes t Harzregion. Dissertation Mining Unive rsity Clausthal, 1965.

M A R C H

1968

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mine surveying-gyro-theodolite

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