Theodolite survey

THEODOLITE:
INTRODUCTION
Mr. Momin Umarfarook H.
( B.E Civil , M.E Structure)

INTRODUCTION
 Theodolite is used to measure the horizontal and
vertical angles.
 Theodolite is more precise than magnetic compass.
 Magnetic compass measures the angle up to as
accuracy of 30’. However a vernier theodolite
measures the angles up to and accuracy of 10’’, 20”.
 There are variety of theodolite vernier, optic,
electronic etc.

 So far we have been measuring horizontal angles by
using a Compass with respect to meridian, which is
less accurate and also it is not possible to measure
vertical angles with a Compass.
 So when the objects are at a considerable
distance or situated at a considerable elevation or
depression ,it becomes necessary to measure
horizontal and vertical angles more precisely. So
these measurements are taken by an instrument
known as a theodolite.

THEODOLITE SURVEYING
The system of surveying in which the angles are
measured with the help of a theodolite, is called
Theodolite surveying.

HISTORY
 Early history:
People have been measuring angles for construction purposes for
many centuries. Egyptians used groma, an early version of a
theodolite, to help build the pyramids. Furthermore, there are also
records that indicate that the Romans used tools such as dioptra
(circular plate that marked angles), for similar purposes. In 1571,
Leonard Digges came up with a device which more closely
resembled an early theodolite and called it theodolitus. It was a
divided circle and square with a compass in the center, according to
"Brief History of Turning Angles" at noaa.gov, but it lacked a
telescope (found in modern versions).

HISTORY
 Modern History:
The telescope mounted on top of the measuring device came into
being by the mid 1700s. The device also had a horizontal circle with
a vertical semi-circle. Early theodolites were woks of art; they were
hand made out of brass and the angles were scribed by hand. They
did, however, have a significant margin for error because they were
only as accurate as the individual who scribed the angles. This is
important because an error of one second translated into an error of
one foot, at a distance of 40 miles.

HISTORY
 Later history:
In 1773, Jesse Ramsden invented a mechanical dividing engine that
allowed for higher accuracy and production of theodolites. This, in
turn, resulted in an increase of theodolite availability and placed
England at the front of the theodolite production industry.
Theodolites came to the United States in 1815, on the request of
Thomas Jefferson. He wanted Ferdinand Hassler, the appointed
Superintendent of the Survey of the Coast, to survey America.
Theodolites remained pretty much unchanged until the 1950s when
electronic distance measurements were adopted.

THEODOLITE
The Theodolite is a most accurate surveying
instrument mainly used for :
• Measuring horizontal and vertical angles.
• Locating points on a line.
• Prolonging survey lines.
• Finding difference of level.
• Setting out grades
• Ranging curves
• Tacheometric Survey

VERNIER THEODOLITE
 Vernier theodolite is
also known and
transit.
 A transit theodolite is
one in which the
telescope can be
rotated in a vertical
plane.
Alidade assembly
Horizontal circle
assembly
Levelling head assembly
Line of Sight
Traverse/horizontal axis
Vertical circle rigidly fixed to
the telescope
Vertical axis
Three assemblies of Theodolite

 Main parts of a theodolite
 Levelling head (7): Levelling
head is used to attach the
instrument to tripod and attach
the plumb bob along the vertical
axis of the instrument.

MAIN PARTS-2
 Lower plate/circle plate (18): an annular
horizontal plate with the graduations
provided all around, from 0 to 360°, in a
clockwise direction. The graduations are in
degree divided in to 3 parts so that each
division equals to 20 min.
 Horizontal angles are measured with this
plate.
 The size of the theodolite is defined by the
diameter of horizontal circle.
 Upper plate (17): Horizontal plate of
smaller diameter provided with two verniers.
on diametrically opposite parts of its
circumference. These verniers are designated
as A and B. They are used to read fractions
of the horizontal circle plate graduations.
The verniers are graduated in 20 min and
each minute is divided in 3 to 5 parts making
least count 20” or 10”.

MAIN PARTS-3
 Clamps and tangent screws (15, 19):
 There are two clamps and associated
tangent screws with the plate. These screws
facilitate the motion of the instruments in
horizontal plane.
 Lower clamp screw locks or releases the
lower plate. When this screw is unlocked
both upper and lower plates move together.
The associated lower tangent screw allows
small motion of the plate in locked position.
 The upper clamp screw locks or releases the
upper vernier plate. When this clamp is
released the lower plate does not move but
the upper vernier plate moves with the
instrument. This causes the change in the
reading. The upper tangent screw allows
the fine adjustment.

MAIN PARTS-4
 Plate level (5):
 Spirit level with the bubble and
graduation on glass cover.
 A single level or two levels fixed in
perpendicular direction may be
provided.
 The spirit level can be adjusted with
the foot screw (21) of the levelling
head (7).
 Telescope (10): The essential parts of the
telescopes are eye-piece, diaphragm with
cross hairs, object lens and arrangements
to focus the telescope.

MAIN PARTS-5
 Vertical circle (1): circular plate
supported on horizontal axis of the
instrument between the A-frames.
Vertical circle has graduation 0-90 in
four quadrants. Vertical circle moves
with the telescope when it is rotated
in the vertical plane.
 Vertical circle clamp and tangent
screw (11): Clamping the vertical
circle restrict the movement of
telescope in vertical plane.
 Altitude level (2): A highly sensitive
bubble is used for levelling
particularly when taking the vertical
angle observations.

Reading a
theodolite
Vernier scale graduation

TERMS USED IN MANIPULATING A TRANSIT VERNIER THEODOLITE.
1.Centering : Centering means setting the
theodolite exactly over an instrument- station
so that its vertical axis lies immediately above
the station- mark. It can be done by means of
plumb bob suspended from a small hook
attached to the vertical axis of the theodolite.
The centre shifting
arrangement if provided with the instrument
helps in easy and rapid performance of the
centring.

TERMS USED IN MANIPULATING A
TRANSIT VERNIER THEODOLITE.
2. Transiting :
Transiting is also known as plunging or
reversing. It is the process of turning the
telescope about its horizontal axis through 1800
in the vertical plane thus bringing it upside
down and making it point , exactly in opposite
direction.

3. Swinging the telescope
It means turning the telescope about its
vertical axis in the horizontal plane.
A swing is called right or left according as the
telescope is rotated clockwise or counter
clockwise.

4. Face Left
If the vertical circle of the instrument is on
the left side of the observer while taking a
reading ,the position is called the face left and
the observation taken on the horizontal or
vertical circle in this position, is known as the
face left observation

5. Face Right
If the vertical circle of the
instrument is on the right side of the
observer while taking a reading ,the
position is called the face right and
the observation taken on the
horizontal or vertical circle in this
position, is known as the face right
observation.

6. Changing Face
It is the operation of bringing the vertical
circle to the right of the observer ,if
originally it is to the left , and vice – versa.
It is done in two steps; Firstly revolve the
telescope through 1800
in a vertical plane and
then rotate it through 1800
in the horizontal
plane i.e first transit the telescope and then
swing it through 1800
.

7. Line of Collimation
LINE OF
COLLIMATION
DIAPHRAGM
TELESCOPE
It is also known as the line of sight .It is an
imaginary line joining the intersection of the
cross- hairs of the diaphragm to the optical
centre of the object- glass and its continuation.

8. Axis of the telescope
AXIS OF THE TELESCOPE
TELESCOPE
It is also known an imaginary line joining the
optical centre of the object- glass to the centre
of eye piece.
OBJECT GLASS
.

9. Axis of the Level Tube
It is also called the bubble line.
It is a straight line tangential to the longitudinal
curve of the level tube at the centre of the tube.
It is horizontal when the bubble is in the centre.

10. Vertical Axis
It is the axis about which the telescope
can be rotated in the horizontal plane.
11. Horizontal Axis
It is the axis about which the telescope
can be rotated in the vertical plane.
It is also called the trunion axis.

ADJUSTMENT OF A THEODOLITE
The adjustments of a theodolite are of two kinds :-
1. Permanent Adjustments.
2. Temporary Adjustments.
1) Permanent adjustments: The permanent
adjustments are made to establish the relationship
between the fundamental lines of the theodolite and ,
once made , they last for a long time. They are
essential for the accuracy of observations.

1. Permanent adjustments: The permanent
adjustments in case of a transit theodolites are :-
i) Adjustment of Horizontal Plate Levels. The axis
of the plate levels must be perpendicular to the
vertical axis.
ii) Collimation Adjustment. The line of collimation
should coincide with the axis of the telescope
and the axis of the objective slide and should be
at right angles to the horizontal axis.
iii) Horizontal axis adjustment. The horizontal axis
must be perpendicular to the vertical axis.

1. Permanent adjustments (contd.):
iv) Adjustment of Telescope Level or the Altitude
Level Plate Levels. The axis of the telescope levels
or the altitude level must be parallel to the line of
collimation.
v) Vertical Circle Index Adjustment. The vertical
circle vernier must read zero when the line of
collimation is horizontal.

2. Temporary Adjustment
The temporary adjustments are made at each set
up of the instrument before we start taking
observations with the instrument. There are three
temporary adjustments of a theodolite:-
i) Centering.
ii) Levelling.
iii) Focussing.

Measurement of horizontal angle
 Measurement of Angle ABC
 The instrument is set over B.
 The lower clamp is kept fixed and upper clamp is
loosened.
 Turn the telescope clockwise set vernier A to 0° and
vernier B to approximately 180°.
 Upper clamp is tightened and using the upper tangent
screw the vernier A and B are exactly set to 0° and
180°.
 Upper clamp is tightly fixed, lower one is loosened and
telescope is directed towards A and bisect the ranging
rod at A.
 Tightened the lower clamp and turn the lower tangent
screw to perfectly bisect ranging rod at A.
 Loose the upper clamp and turn the telescope clockwise
to bisect the ranging rod at C tightened the upper clamp
and do the fine adjustment with upper tangent screw.
 The reading on vernier A and B are noted. Vernier A
gives the angle directly and vernier B gives the reading
by subtracting the initial reading (180°) from final

 Read these two method
 Repetition method
 Reiteration method

 Measurements of
 Deflection angle
 magnetic bearing
A
B
C
P
A
B
N
θ
θ

PROLONGING A STRAIGHT A LINE
There are two methods of prolonging a given line such as AB
(1) Fore sight method ,and (2) Back Sight Method
Fig.
(1)Fore Sight Method. As shown in the fig. below
A B C D Z
i) Set up the theodolite at A and level it accurately .Bisect the
point b correctly. Establish a point C in the line beyond B
approximately by looking over the top of the telescope and
accurately by sighting through the telescope.
ii) Shift the instrument to B ,take a fore sight on C and establish
a point D in line beyond C.
iii) Repeat the process until the last point Z is reached.

(2) Back Sight Method. As shown in the fig. below
A B C D Z
i) Set up the instrument at B and level it accurately .
ii) Take a back sight on A.
iii) Tighten the upper and lower clamps, transit the
telescope and establish a point C in the line beyond B.
iv) Shift the theodolite to C ,back sight on B transit the
telescope and establish a point D in line beyond C.
Repeat the process until the last point ( Z) is
established.
C’
D’

(2) Back Sight Method.(contd.) As shown in the fig. below
A B C D Z
Now if the instrument is in adjustment, the points
A,B,C,D and Z will be in one line, which is straight but if
it is not in adjustment i.e. line of collimation is not
perpendicular to the horizontal axis ,then C’, D’ and Z’
will not be in a straight line.
C’
D’

 Read assignment (N. N. Basak, S. K. Duggal)
 Ranging and extending a line
 Method of traversing
 Included angle method
 Deflection angle method
 Fast angle (or magnetic bearing method)

Computation of latitude and departure
 Latitude of a line is the distances measured
parallel to the north south of the North-South
direction
 Departure of the line is the distance measured
parallel to the east-west direction

Computing latitude and departure

Sources of errors in theodolite
 Instrumental errors
 Non adjustment of plate bubble
 Line of collimation not being perpendicular to
horizontal axis
 Horizontal axis not being perpendicular to vertical
axis
 Line of collimation not being parallel to axis of
telescope
 Eccentricity of inner and outer axes
 Graduation not being uniform
 Verniers being eccentric

 . Personal errors
 Natural errors
 High temperature causes error due to irregular refraction.
 High winds cause vibration in the instrument, and this may
lead to wrong readings on verniers
 Closing error

Balancing of traverse
 Bowditch’s rule:
 Total error is distributed in proportion to the lengths of the
traverse legs.

PROBLEM
 Calculate the latitudes, departures and closing
error for the following traverse conducted at
allahabad. Adjust also the traverse using
Bowditch’s rule.
Line Length WCB
AB 89.31 45⁰ 10’
BC 219.76 72⁰ 05’
CD 151.18 161⁰ 52’
DE 159.10 228⁰ 43’
EA 232.26 300⁰ 42’

Theodolite survey

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