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
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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-
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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
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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
M IN IN G ENGINEERING 75
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