theodolite notes

Surveying II 10CV44

SURVEYING – II

Sub Code : 10 CV 44

Sub Code : 10 CV 44 IA Marks : 25
Exam Hours : 03
No. of Lecture Hours/Week: 04 Exam Marks : 100

Total No. of Lecture Hours : 52

PART – A

UNIT 1:
THEODOLITE SURVEY
Thedolite and types, Fundamental axes and parts of a transit theodolite, Uses of theodolite,
Temperary adjustments of a transit thedolite, Measurement of horizontal angles – Method of
repetitions and reiterations, Measurements of vertical angles, Prolonging a straight line by a
theodolite in adjustment and theodolite not in adjustment.

6 Hours

UNIT 2:
PERMANENT ADJUSTMENT OF DUMPY LEVEL AND TRANSIT THEODOLITE
Interrelationship between fundamental axes for instrument to be in adjustment and step by step
procedure of obtaining permanent adjustments.

7 Hours

UNIT 3:
TRIGONOMETRIC LEVELING
Determination of elevation of objects when the base is accessible and inaccessible by single
plane and double plane method, Distance and difference in elevation between two inaccessible
objects by double plane method. Salient features of Total Station, Advantages of Total Station
over conventional instruments, Application of Total Station.

8 Hours

UNIT 4:
TACHEOMETRY
Basic principle, Types of tacheometric survey, Tacheometric equation for horizontal line of sight
and inclined line of sight in fixed hair method, Anallactic lens in external focusing telescopes,
Reducing the constants in internal focusing telescope, Moving hair method and tangential
method, Subtance bar, Beaman stadia arc.

7 Hours

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Surveying II 10CV44

PART – B

UNIT 5:
CURVE SETTING (Simple curves)
Curves – Necessity – Types, Simple curves, Elements, Designation of curves, Setting out simple
curves by linear methods, Setting out curves by Rankines deflection angle method.
6 Hours

UNIT 6:
CURVE SETTING (Compound and Reverse curves)
Compound curves, Elements, Design of compound curves, Setting out of compound curves,
Reverse curve between two parallel straights (Equal radius and unequal radius).
6 Hours

UNIT 7:
CURVE SETTING (Transition and Vertical curves)
Transition curves, Characteristics, Length of Transition curve, Setting out cubic Parabola and
Bernoulli‟s Lemniscates, Vertical curves – Types – Simple numerical problems.
6 Hours

UNIT 8:
AREAS AND VOLUMES
Calculation of area from cross staff surveying, Calculation of area of a closed traverse by
coordinates method, Planimeter – principle of working and use of planimeter to measure areas,
digital planimter, Computations of volumes by trapezoidal and prismoidal rule, Capacity
contours
6 Hours

TEXT BOOKS:
1. Surveying II by Punmia
2. Surveying & Levelling by Duggal
3. Surveying & Levelling by Subramanyam

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Surveying II 10CV44

Table of Contents

Unit 1 - THEODOLITE SURVEY (05 – 15)

1. Introduction
2. Thedolite and types
3. Fundamental axes and parts of a transit theodolite
4. Uses of theodolite
5. Temperary adjustments of a transit thedolite
6. Measurement of horizontal angles – Method of repetitions and reiterations
7. Measurements of vertical angles
8. Prolonging a straight line by a theodolite in adjustment and theodolite not in adjustment

Unit 2 - PERMANENT ADJUSTMENT OF DUMPY LEVEL AND TRANSIT

THEODOLITE (16 – 27)

1. Interrelationship between fundamental axes for instrument to be in adjustment and step
by step procedure of obtaining permanent adjustments

Unit 3 - TRIGONOMETRIC LEVELING (28 – 37)

1. Determination of elevation of objects when the base is accessible and inaccessible by
single plane double plane method.

2. Distance and difference in elevation between two inaccessible objects by double plane
method.

3. Salient features of Total Station, Advantages of Total Station over conventional
instruments, Application of Total Station.

Unit 4 – TACHEOMETRY (38 – 58)

1. Basic principle
2. Types of tacheometric survey
3. Tacheometric equation for horizontal line of sight and inclined line of sight in fixed hair

method
4. Anallactic lens in external focusing telescopes
5. Reducing the constants in internal focusing telescope
6. Moving hair method and tangential method
7. Subtance bar
8. Beaman stadia arc.

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Unit 5 - CURVE SETTING (Simple curves) (59 – 73)
(75 – 81)
1. Curves – Necessity – Types
2. Simple curves
3. Elements
4. Designation of curves
5. Setting out simple curves by linear methods
6. Setting out curves by Rankines deflection angle method.

Unit 6 – CURVE SETTING (Compound and Reverse curves)

1. Compound curves
2. Elements
3. Design of compound curves
4. Setting out of compound curves
5. Reverse curve between two parallel straights
(Equal radius and unequal radius)

Unit 7 - CURVE SETTING (Transition and Vertical curves) (82 – 86)

1. Transition curves (87– 105)
2. Characteristics
3. Length of Transition curve
4. Setting out cubic Parabola and Bernoulli‟s Lemniscates
5. Vertical curves – Types – Simple numerical problems.

Unit 8 - AREAS AND VOLUMES

1. Calculation of area from cross staff surveying
2. Calculation of area of a closed traverse by coordinates method.
3. Planimeter – principle of working and use of planimeter to measure areas, digital

planimter
4. Computations of volumes by trapezoidal and prismoidal rule
5. Capacity contours

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Unit 1 – THEODOLITE SURVEY

Contents

1. Introduction
2. Axis of theodolite
3. Technical terms

Centering

Transiting / Plunging

Face

Face left

Face right

Swing

4. Temporary Adjustments

Fixing & Centering

Levelling

Elimination of Parallax

5. Measurement of Angles
6. Horizontal angle measurement

Method of repetition

Method of Reiteration

7. Vertical angle measurements
8. Prolonging a Line

When theodolite is in adjustment

When the theodolite is not in adjustment (Poor adjustment)

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Unit 1 - Theodolite Survey

Introduction

Theodolite is an angle measuring instrument used in surveying both vertical and horizontal
angles is measured using the theodolite.

Theodolite are an important and accurate instruments which are used in prolonging a line laying
of pipelines and road networks in locating the foundation points finding out differences in
heights e.t.c

A theodolite basically consists of

a. Telescope: Helps in bisecting the far of objects. It‟s an integral part of the theodolite.

b. Vertical circle: Has a vertical scale useful in vertical angle measurements circular
graduated are attached to the traction a in of telescope.

c. Horizontal plate: They support the telescope vertical circle and A. frame. They have
horizontal scale which helps in horizontal angle measurements.

d. Head and foot plate: These are the support plates on which the horizontal plate is made to
rest between head and foot plate, there are 3 foot screws which help in leveling the
instruments.

Axis of Theodolite:

Following are the major axes present in theodolite:

1. Horizontal/ trunion axis: It is an axis parsing though the centre of vertical circle and A.
frame. Telescope is supported and rotated about this axis in the vertical place.

2. Vertical axis: It‟s an axis passing through the centre of the level plates. Instrument is
rotated about this axis in the horizontal place.\

3. Axis of collimation: It is an axis passing through the centre of cross hair of the eyepiece
of the and the objective. This should run along the centre of the telescope tube.

4. Axis of plate level: It is an axis passing tangentially to the bubble of the spirit tube of the
horizontal plate, when the instrument is leveled.

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Fig: Transit Vernier Theodolite Page 7
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Surveying II 10CV44

Technical Terms

Centering: It‟s a process of placing the instrument over the identified point on the ground when
the instrument is centered the vertical axis should pass through the ground point about which the
instrument is centered.

Transiting/Plunging: It‟s a process of rotating the telescope about horizontal axis along the
vertical plane through 1800.

Face: It is a condition that tells informs the side or position of the vertical circle to the observer

Face left: If the vertical circle is to the left of the observer it is called face left observation

Face right: It‟s a condition when the vertical circle is to the light of the observer

Swing: It is a direction of rotation of the instrument about vertical axis in the horizontal plane

When the instrument is rotated in the clockwise direction it is called right swing. When the
instrument is rotated in the anticlockwise direction it is called left swing.

Temporary Adjustment:

Before the instrument is put to field usage certain adjustments one to be carried out so that the
instrument is ready.

Fixing & Centering: It is an adjustment in which the instrument is attached to the tripod stand
and then placed exactly over the identified ground point.

Levelling: It is a stage of adjustment in which the instrument in made level w.r.t the mean
ground at the station.

1. The 3 foot screens are brought to the certain of their run

2. By adjusting the legs the head plate is made horizontal by eye judgment

3. The plate level is brought parallel to any of the two foot screens and the corresponding
foot screens are turned inwards or outwards simultaneously till the bubble is in the center
of the run

4. Plate level is turned perpendicular to its earlier position and the 3rd foot screen is turned
inwards or outwards till the bubble comes to the centre.

5. The steps 3 & 4 are repeated till the bubble is at the centre for any direction

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Elimination of Parallax: It is an adjustment in which the image of the bisected object is made to
fall on the plane of cross hair.

It is done through the following steps:

1. Looking through the eyepiece lye piece is turned clockwise or anticlockwise till the
cross hairs are seen dark.

2. Telescope is turned to a far off object and looking through the eye piece the focusing
screen is turned till the clean image of the object is seen.

Measurement of Angles:

Angle is a deviation between 2 objects measured with reference to a point and expressed in
degrees minutes and seconds. Using theodolite both horizontal and vertical angles can be
measured.

Horizontal angles are measured and observed w.r.t horizontal plate scale Horizontal plate scale in
marked from zero to 360o. It consists of main scale and vermin scale.

Vernier scale is attached to upper plate and its movement is controlled by upper clamp screw
(U C S)

Main scale is attached to lower plate and its movement is controlled through lower clamp screw
(LCS)

The value of each big division in a main scale is 1 which is divided into 3 parts there by value of
each small division is 200

In version scale each big division is 1 and is divided into 3 parts there by the smallest division =

20‟‟ (20second). There 20‟‟ is the LC (least count) of theodolite.

General procedure for Angular Measurements

1. Both UCS & LCS are released Upper & lower plates are turned mutually till O of the
version co-insides with O (Zero) of the main scale.

2. The clamp screws are locked and lower tangential screw is used for accurate matching.

3. Releasing LCS instrument is turned towards the reference point P till accurate bisection is
made now the reading in the scale will be 00 0‟ 0”.

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4. Releasing UCS the second object (Q) is bisected accurately and UCS is clamped.

5. The reading on the scale A & B is observed and entered .

In scale A complete reading is noted down
i.e. M.S – 1770 20‟

V.S - 9‟ 40”
1770 29‟ 40”

In scale B only minutes and seconds are observed
i.e, M.S -20‟

10‟ 40”
30‟ 40‟‟

The true angle PRQ in the mean of scale A and scale B.

Horizontal angle measurement

Horizontal angles are measured in 2 method
A) Method of repetition:
It is a method in which the angle between 2 points on objects in measured repeatedly
for n no. of times, in different formats the actual angle in each format will be.

The method is adopted
i) When there are few objects between which angle is required
ii) Very accurate value of the angle is required.

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Tabulation Scale B Mean ,, No. of repetition
, ,, 0, 0 1
Object Bisected Face:- 00 00 00 2
26 40 42 26 30 3
Scale A 26 40 84 48
0 , ,, 48 20
P 0 00 48 20 126 21 40
Q 42 25 20 21 0
P 42 25 20
Q 84 48 40
P 84 48 40
Q 126 22 20

PR

Q

Procedure:

1. Instrument is fixed and centered at R ( the reference point)

2. Releasing UCS and LCS the horizontal plate reading is made 00 0‟ 0‟‟ the clamp screws
are tightened.

3. Releasing UCS the telescope is turned to Q and UCS is clamped.

4. With Upper tangential screw bisection of point is made.

5. The reading of scale A and scale B are interred in the corresponding column of the tabular
column.

This completes 1st repetition.

6. Releasing LCS the telescope in turned back to of „P‟ LCS is clamped after bisection with
this the same reading which was at Q now will be at P.

7. The above procedure listed in step 3 and 4 is repeated to the required No. of repetitions

The accurate angle PRQ will be equal to the final reading/No.of repetitions

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B) Method of Reiteration:-

Object Bisected Face:- Scale B Mean Horizontal angle
, ,, 0 , ,, 0 , ,,
P Scale A 00 000
Q 0 , ,, 26 40 42 26 00 135018‟ 30‟‟-42026‟00‟
R 0 00 18 20 135 18 30 307057‟50‟‟-135018‟30‟‟
42 25 20
135 18 40 57 40 307 57 50

S 307 58 0

The method is adopted when
(i) There are lot of objects b/w which we need the horizontal angle
(ii) When objects are spread all around the reference pt.
(iii) When it is necessary to check the adjustment or accuracy of the instrument.

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Procedure:

1. Instrument is fixed and centered at the reference point or about the reference point „O‟ all
the temporary adjustments am ode Releasing UCS and LCS horizontal scale reading is
made to read o.0‟0‟‟ and stoutly pt in bisected UCS + LCS a locked.

2. Releasing UCS each and every object is bisected in sequence and champed after every
bisection.

3. Scale A and scale B readings for each object bisections is observed and entered in the
tabular column.

4. The angle b/w any 2 objects is obtained by subtracted the reading observed at the 1st
object from reading observed at the next object.

5. Finally after the last point bisection the telescope should to be brought back to the startle
point to check 0.0‟0‟‟.

Vertical angle measurements

The deviation of objects in the vertical plane will give the vertical angle. Vertical angles are
measured with respect to horizontal LOS which is taken as the reference

When the bisected objects are above the line of sight (los), vertical angle is called Angle
of elevation.

When the bisected object is below the los vertical angle is called Angle of depression

Vertical angles are measured with the help of scale C and scale D which are on the vertical
circle or vertical plate. The marking are 00 to 900 an either side of 0 marking

In vertical circle main scale is attached to the telescope and hence it is movable.

The vernier is attached to the vertical plate and is fixed.

General Procedure:

1. Instrument is adjusted for temporary adjustment. But the leveling is done w.r.t the attitude
bubble only

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2. Releasing the vertical clamp screw (VCS) telescope is turned till 0 of the main scale is in
line with 0 of the version and it is clamped.

3. Releasing the VCS, telescope is turned above or below the horizontal line of sight (los)
depending on the position of the object.

4. UCS in clamped and accurate bisection is made using vertical tangential screw.

5. The obtained ladings on the scale C & D are observed and entered in tabular Colum.
6. Angle of elevation are marked with +ve sign and angle of depression are signed a negative

sign
Eg: + 180 25‟ 30‟‟

- 400 30‟ 20‟‟

Prolonging a Line:

Prolonging a line is an important supplementary work carried out by theodolite.

a) When theodolite is in adjustment:

This procedure helps in continuing a line during base line measurement in laying
out pipe line or roadway, setting out curves e.t.c the work is accurate and is faster.

Procedure:

1. Let AB be the line to be prolonged

2. Instrument is placed at pt B with all temporary adjustments

3. Releasing the UCS and LCS telescope is turned about the vertical axis till the peg or

arrow at pt A is bisected then the plate ensues i.e (UCS & LCS) are clamped.

4. Telescope is plunged there by line of sight shifts after B in line with AB.

5. Telescope is now rotated to bisect the tip of the ranging rod at a convenient distance.

This gives point C.

6. Now again the instrument is shifted to point C and the procedure in step 3 & 4 us

repeated to get further pints D,E,F etc and hence the line is prolonged.

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b) When the theodolite is not in adjustment (Poor adjustment)

This method is adopted when the instrument is not in adjustment.

Procedure:

1. Let AB be the line which is to be continued on prolonged.

2. Instrument is centered about point B with all temporary adjustments.

3. The arrow kept at A is bisected and the horizontal plate is clamped

4. Telescope is transited and a pt C on other side of B is bisected. Releasing the

horizontal plate, pt „A‟ is again bisected by swinging the telescope and the horizontal
plate is clamped

5. Transiting the telescope to bisect the earlier pt C, when we don‟t get C we bisect

another point C‟‟ in the same line (Now instrument is said to be not in adjustment.

6. Distance C‟ C‟‟ is measured pt. C is obtained by measuring distance C‟C or C‟‟ C =

C‟C‟‟/2

7. Instrument is now shifted to point „C‟ which is in line with AB and the above

procedure from step 2 to 5 is repeated.

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Surveying II 10CV44

Unit 2 - PERMANENT ADJUSTMENT OF DUMPY LEVEL AND
TRANSIT THEODOLITE

Contents
1. Introduction
2. Fundamental Axes of Theodolite
3. Permanent adjustments
4. Adjusting the Plate Level
5. Adjusting the line of collimation
6. Adjusting vertical cross hair
7. Adjusting the horizontal axis (Spire Test)
8. Adjustment of Altitude bubble
9. Adjustments of Dumpy Level

Collimation axis perpendicular to axis of bubble tube
Axis of bubble tube perpendicular to vertical axis
Vertical axis perpendicular to horizontal cross hair

10. Errors in Theodolite survey

Instrumental errors
Personal errors
Natural errors

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Unit 2 -
Permanent Adjustments of Theodolite & Dumpy Level

Introduction:

Permanent adjustments are those which are carried out during or while manufacturing the
instrument.

These adjustments are done so as to maintain the proper relationship between the various
fundamental axes of an instrument. Unlike temporary adjustments. These are to be carried out at
regular intervals periodically like once in a month a once in a year etc

Fundamental Axes of Theodolite:

Following are the basic fundamental axes in a theodolite

1. Vertical axis

2. Horizontal axis

3. Axis of collimation

4. Axis of plate bubble/ level

5. Axis of Altitude bubble /level

Following are the desired relationship b/w the various axes for the proper functioning of
theodolite.

1. Plate level axis must be perpendicular to vertical axis: If this relation does not exist
vertical axis will not be truly vertical and hence we get error in centering of the
instrument which gives a very wrong observed value.

2. Horizontal axis must be perpendicular to vertical axis: This is essential to get accurate
horizontal angle measurements in any face.

3. Horizontal axis shall be perpendicular to axis of collimation (AOC): This is important
while prolonging a line or to eliminate the index error in the vertical circle.

4. Altitude bubble shall be parallel to axis of collimation (AOC): This relationship will
reduce the index error in the vertical forms as well as in getting concurrent values in
different face readings.

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Permanent adjustments:

Adjusting plate level axis:
Aim: To get the plate level axis to be perpendicular to vertical axis
Necessity: To get proper and concurrent staff readings in different face readings.

To get the exact centering during angle measurements.
Procedure:

1. Instrument is set with all temporary adjustments on a fairly level grand
2. A level staff kept approximately at a distance of 10m is bisected
3. The level staff reading as well as the vertical circle reading in observed

Telescope is transited and then releasing the horizontal plate, theodolite is notated
back toward the staff
4. With the same vertical circle reading staff reading in observed.
5. It is the same reading as that of the first, instrument is in adjustment if not
adjustment has to be carried out.

Adjusting the Plate Level
1. The plate level is leveled with two foot screws and it is turned by 900 and is leveled again

using 3rd foot screw.

2. The plate level is brought back to initial position deviation of the bubble tube from the

center is observed.

3. Half the deviation is corrected using the foot screws and the other half deviation is

corrected by turning the screw of the bubble tube (Clip screw & nearer to altitude
bubble))

4. The steps 1 to 3 is repeated till the bubble is in the center for all directions.

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Adjusting the line of collimation (A.O.C must be perpendicular to HA + VA)

Aim: To make A.O.C or LOC pass through optical axis (axis joining centre of eye piece )

By doing this axis of collimation will be perpendicular to both vertical axis and horizontal axis

Necessity: If A.O.C coincides with optical axis, the face left and face right readings do not differ.
This helps in getting accurate horizontal vertical angle as well as in prolonging a line.

AOC may not coincide with optical axis if either horizontal cross main is moved up or down
or vertical cross hair might have moved left on right from their respective positions.

Corrections / Adjustments

Looking through the telescope in the last position the horizontal cross hair is moved using
capstans screw on the telescope. Horizontal cross hair is moved till the mean of the two readings
in bisected.

Testing and adjusting vertical cross hair

(i) Instrument is set at a convenient point O with all temporary adjustments such that we
have about 10m of level ground on either side

(ii) Pt. A on one side of the instrument is bisected with horizontal plates clamped

(iii) Telescope is transited to get point B on the other side

(iv) Releasing the horizontal plate telescope is rotated and point A is bisected again

(v) Transiting the telescope with change of face we try to bisect point B
(vi) If B is bisected instrument is said to be in adjustment or else another Pt „C‟ is

established in line with B now the instrument needs to be adjusted

Connection or Adjustment
i. A point „D‟ on the ground is marked such that distance CD in 1/4th of CB

ii. Looking through telescope the trunion screw in the vertical A-frame is tuned till pt
„D‟ is bisected & connection

iii. The testing is repeated again till the same point is bisected

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Adjusting the horizontal axis (Spire Test):

Aim: Horizontal axis perpendicular to V.A

Necessity: If the horizontal axis is not prospered to V.A when the telescope is transited we do not
get the vertical plane but it will be scant thus during prolonging a line or while transferring
foundation points we do not get the designed straightness.

Testing:

1. Instrument is established nears to high rised object like transmission town or multistoried
building with all temporary adjustments.

2. Top of the object is bisected and horizontal plate is clamped. Telescope is rotated down to
get a point on the ground mares to the station pt.(B)

3. Telescope is made to transit & the instrument swing back to bisect B again

4. Clamping the horizontal plate telescope is lifted up to bisect earlier point A if bisected
instrument is said to be another pt.C is noted and in adjustment if not corrections has to
be applied.

Rectification or Adjustments:

1) Looking through the telescope in the last stage trunion screw of the vertical frame is
released and the telescope is physically adjusted till the midpoint of AC is bisected.

2) The tasting procedure is repeated again with the corrections applied at the end of tartly
till point A is bisected. When telescope is transited in the different face.\

Adjustment of Altitude bubble:

Aim: To make A.O.C llle TO Altitude bubble. When the altitude bubble in leveled the axis
passing through that should be parallel to the axis of collimation the right should be truly
property vertical axis.

If this relation does not exist there will be error in measurement of vertical angles

Necessity: To get proper vertical angle we need the altitude bubble axis to be parallel to axis of
collimation.

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Testing:

1. Instrument is established at a convenient point on a level grand with all temporary
adjustments.

2. Instrument is leveled with respect to the foot screws.

3. Altitude bubble is leveled with a help of clip screw of the altitude bubble

4. Reading on a staff kept at about 100m is observed

5. Instrument is rotated about vertical axis and transited back , altitude bubble is checked
again and leveled if required

6. Reading on the staff is observed. If it is the same reading instrument is said to be in
adjustment if not correction has to be made.

Correction or Adjustments
1. The mean value of the two staff reading s is bisected by vertical tangential screw.
2. Releasing the capstan screw of the vertical plate venires is moved to coincide with O of
the main scale.

3. Testing is repeated to check the correctness.

ADJUSTMENTS OF DUMPY LEVEL Page 21

Fundamental axis / line
Collimation axis / axis of line of sight
Vertical axis
Axis of bubble tube

Desired relation
i. Collimation axis perpendicular to axis of bubble tube
ii. Axis of bubble tube perpendicular to vertical axis
iii. Vertical axis perpendicular to horizontal cross hair

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Surveying II 10CV44

Relation:
Dumpy level is again a precise instrument which helps in finding out the elevation for heights of
different points these levels are useful in calculation the volume of earthwork, or in
understanding the profile of the ground. Hence the permanent adjustments need to be properly.

This can be maintained by keeping the desired relations between various axes in place
Following are the fundamental axes in dumpy level:
Collimation axis / axis of line of sight
Vertical axis
Axis of bubble tube

These fundamental axis should be in a desired relations among themselves they are
1. Collimation axis parallel to axis of bubble tube:
2. Axis of bubble tube should be perpendicular to vertical axis
3. Horizontal cross hair should be in a plane perpendicular to vertical axis

Collimation axis parallel to Axis of bubble tube:

Aim: Collimation axis should be parallel to axis of bubble tube

Necessity: Only if axis of collimation is parallel to axis of bubble once the instrument is leveled
we get horizontal line of sight through telescope this is an important aspect as the entire principle
of leveling depends on horizontal line of sight.

Testing: Two peg tests adopted to rectify the collimation axis

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1. Two level staffs are kept at 100m apart on a level ground say at A & B

2. Dumpy level to be tested in placed closed to staff A and reading on staff B is taken as ha
& hb. The difference in elevation between A and B is having which is partially correct \

3. Instrument is shifted and placed very close to staff B, such that telescope is in contact
with level staff

4. The staff readings on B and A are taken as ha‟ and hb‟, the true difference between A and
B is obtained as ha‟ ~ hb‟ which is partially correct.

5. The actual difference in elevation between A and B is calculated as
(ha ~ hb) + (ha‟ ~ hb‟)

2

6. If the difference in elevation obtained when instrument is at P is equal to difference in
elevation when the instrument in at Q instrument is said to be in adjustment. If not
correction has to be applied.

Correction/Adjustments

1) With the calculated the difference in elevation the correct staff reading at B is calculated
as Reading at A correct difference in elevation = Reading at B

2) Releasing the capstans screw on the today of the telescope and looking through the eye
piece diaphragm is moved till the calculated ready on staff B is bisected keeping
instrument at B.

Vertical axis perpendicular to bubble tube axis

Aim: To make the bubble tube axis truly perpendicular to the vertical axis

Necessity: If the bubble tube axis is perpendicular to vertical axis the true verticality of the
instrument in maintained.

Or else the telescope will not given the horizontal line of sight

Testing:

1) Instrument is placed on a level ground and is leveled in 2 positions of telescope

2) When the telescope is in the second position above the third foot screw telescope is
rotated through 1800.

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3) If the bubble in still in the center the instrument is said to be in adjustment, If not
rectification has to be done.

Rectification:

1) The no. of divisions by which bubble has moved is observed

2) Bubble is brought back by half the distance with the help of foot screw.

3) Remaining half the distance is rectified by releasing of adjusting the clip screw of the
bubble tube.

Horizontal cross hair should be in a plane perpendicular to vertical axis

Aim: To make horizontal cross hair perpendicular to vertical axis of the instrument.

Necessity: If the relation do not exists while finding out same RL points we will not be getting
the same RL but points having higher or lower RL points Also while calculating volume of earth
work in longitudinal retinoic we end up in calculating wrong values.

Testing:

1. Instrument is set on a level ground with all temporary adjustments.

2. A sharp object is bisected at one end of the telescope (Right of the view or left of the
view)

3. Observing through the eyepiece telescope is turned slowly so that object comes to the
other side of the view.

4. If image of the object moves along the H.A., the instrument is said to be in adjustment; if
not corrections has to be made.

Rectification:

1. Releasing the capstan screw of the telescope the objective is turned so that the horizontal
cross hair in approximately horizontal.

2. Testing is again repeated to check the adjustment.

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Surveying II 10CV44

Errors in Theodolite survey

Following the sources that cause error in theodolite survey.
Instrumental errors
Personal errors
Natural errors

1) Instrumental errors: This is due to imperfect adjustment of the instrument structural
defects in the instrument and imperfections due to wear Errors due to imperfect
adjustment

i. Plate level axis not being perpendicular to ventricle axis

Due to this imperfectness, the vertical axis of the instrument will not be truly
vertical and in the centering of the instrument, we get error due to which wrong
reading will be observed.

ii. Horizontal axis not being perpendicular to vertical axis

Due to this, accurate horizontal angle measurement cannot be achieved and the
vertical plane will be slant when the telescope is transacted and hence do not get
desired straightness.

iii. Horizontal axis not being perpendicular to axis of collimation:

Due to this error there will be index error in the vertical circle & prolonging a line
will not be easy and also if AOC is perpendicular to both HA+Va,

We get correct and accurate horizontal & vertical angles.

iv. Error due to AOC not being parallel to Altitude bubble.

If this error occurs there will be error in vertical angle measurement.

v. Error due to imperfect graduations index error

Sometimes there will be error in readings etched i.e adulations between the
graduations due to this error can be eliminated by taking the mean of the several
readings distributed over different portions of the graduated circle.

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vi. Error due to eccentricity of vernier:

Due to this the difference between the two vernier readings will not be 1800 but
there will be a constant difference of other than 1800

2) Personal errors:
a. Error in manipulation
b. Errors in sighting & reading

a. Error in manipulation

i. Inaccurate centering: If the vertical axis of the instrument is not exactly over the
station mark the observed angles will either be greater smaller

ii. Inaccurate leveling: This is due to non-adjustment of plate levels. Due to this
error, we do not get correct reading when observing difference in elevation.

iii. Slip: The error is due to the improper clamping of LCS or shifting head is loose
on if the instrument is not finely tightened on tripod head. Due to this error we get
incorrect observations.

iv. Error due to wrong manipulation of tangent screw

Using lower tangent screw for foresight and using upon tangent screw for back
sight, which is incorrect.

b. Error is sighting & Reading

i. Inaccurate bisection of points observed : The observed angles will be incorrect if
the station mark is not bisected accurately

ii. Parallax error: Accurate bisection is not possible, due to parallax. It can eliminate
by focusing the eyepiece & objective.

iii. Mistakes in setting the venire taking the reading and wrong booking of the
readings.

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Surveying II 10CV44

c. Natural errors:
i. Unequal atmospheric reflection due to high temperature.
ii. Unequal expansion of parts of telescope and circles due to temperature changes.
iii. Unequal settlement of tripod.
iv. Wind producing vibrations

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Surveying II 10CV44

Unit 3 - TRIGONOMETRIC LEVELING

Contents

i. To determine the height / elevation of the object

When the base of the object is accessible
When the base of the object is “Inaccessible” (single plane method)

ii. To determine the height of an object when the base is inaccessible
(Double plane method)

Dept of Civil Engineering, SJBIT Page 28

Surveying II 10CV44
Unit 3 – Trigonometric Levelling

Trigonometrical relations

Along with theodolite we use trigonometrical relations

To fill levels/height of objects

This survey is also called is Indirect leveling

Here, the height or elevations of objects which are must above the line of sight are calculated.

The vertical angle to the top of the object and the distance between instrument and base of
the object is collected in the field. These data‟s are substituted in trigonometrical relations like
sine, cosine, tan e.t.c. to get the required height of the object.

To determine the height / elevation of the object.

A. When the base of the object is accessible

Data collected:

θ0 – Vertical angle to the top of object Horizontal distance between inst. St and base of the
object – D mt.

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Calculation:

Elevation of top of lower= HI(P)+h

In triangle ABC,
tan θ = BC / AC = h / D
h = D tan θ
And HIP = BM + BS

This is a condition where, base of the object whose height is required in accessible.

Following procedure is adopted to determine the height of the object.

Procedure:

1. Theodolite is set at a convenient position with all temporary adjustments so that the
object is visible.

2. The top of the object is bisected and the vertical angle is observed
3. The horizontal distance between the inst. St and base of the object is measured accurately.
4. With the telescope in horizontal position, staff reading on a Bm is observed (by taking

BS)
5. The collected data are used to determine the elevation of the tower or object as shown in

calculations

B. When the base of the object is “Inaccessible” (single plane method)
i. When the perpendicular inst. Is at a lower level than 2nd inst. St
Data collected:
Instrument at A
O1 – Vertical angle to top of object/tower
S1 – Staff reading on BM

Inst. At B Page 30
O2 – Vertical angle to top of object/tower

Dept of Civil Engineering, SJBIT

Surveying II 10CV44

S2 – staff reading on BM
b – Horizontal distance between st A and st B

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Surveying II 10CV44

Calculation:

RL of tower or height of tower = HIA + h1
h1 = D tan θ1 ----------- (1)
h2 = (b + D) tan θ2 ---------- (2)
(2) – (1)
D = [S + b tan θ2] / [tan θ1 - tan θ2]

This is a condition when the object whose height is required will be in a thick forest on mid of a
pond and we cannot reach the base of the object. In such case, we take the help of the data
collected from 2 inst. Stations and calculate the height of the object.

Procedure
1. Let Q be the top of the lower whose height of is required

2. Instrument is set at a convenient point with all temporary adjustments.
3. Bisecting the tip, the vertical angle to the object and staff reading on the BM is observed

as Q1 and S1 respectively.
4. When the top of the object is bisected horizontal plates are clamped

5. Telescope is transited and a ground point B for the second instrument station is bisected.
6. Instrument is shifted and centered over B.

7. With all temporary adjustments vertical angle Q2 to the top of the object and staff reading
with telescope horizontal on BM as S2 are observed.

8. These data‟s are utilized to find the height of the object as shown in the calculations.

Data Collected: Page 32
Inst. At „A‟ : Q1 – vertical angle to top of the lower h1-ht of top of tower above LOS.
Inst At „B‟ : Q2 – vertical angle to top of lower h2 – ht of top of lower above LOS

b- Distance between 1st and 2nd inst

Dept of Civil Engineering, SJBIT

Surveying II 10CV44

Calculation:
h1 = D tan θ1
h2 = (D + b) tan θ2
But h1- h2 S1- S2 = S

(D + b) tan θ2 – D tan θ1 = h1- h2 =S
D (tan θ2- tan θ1) + b tan θ2 = S
D = (S – b tan θ2) / (tan θ2 – tan θ1)

Substituting D is h1 we get
H1 = (S – b tan θ2) tan θ1 / (tan θ2 – tan θ1)
R.L of top of tower = S1 + BM + h1

(Procedure same as previous)

To determine the height of an object when the base is inaccessible (Double plane method)
When the object is much more above 4m.

Calculation:
RLp = BM + S1 + h1
In ∆le SPQ, tan θ1 = h1 / D
h1 = D tan θ1
In ∆le ABC , by sine rule, we have
D = [d sin α2] / [sin (180 – (α1 + α2))]

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Surveying II 10CV44

Data collected:
At instrument station A, θ1 is the vertical angle to the top of the tower or object.
α = horizontal angle measured between the line joining the object and first. Station to the 2nd
station

S1 = Staff reading to staff held on BM.
D = distance from 1st st. to 2nd st.

At instrument station b
θ2 is the vertical angle to the top of the tower
α2 is the horizontal angle measured between instrument and 2nd station to the 1st station.
The method is adopted when 2nd station cannot be established in line with 1st station & object.

Procedure:

1. Theodolite is established at a convenient pt.
2. Horizontal scale is made to read 00 0‟ 0‟‟ and the instrument is turned by releasing only

LCS. Top of the tower is bisected to take the vertical angle O

3. Releasing UCS instrument is turned to the left or to the right, ground pt B in bisected as
the 2nd st.

4. Instrument is shifted and centered about B with all temporary adjustments.

5. Vertical angle to the top the horizontal angle to first station is observed

The distance between first and second instrument st. is measured as d.

PROBLEMS

1) In order to find the elevation of top of signal (Q) observations were made from 2 stations C &
D in line with the signal and 80m apart the vertical angles observed to the top of the signal from
A and B are 30045‟ and 16010‟ respectively the staff reading on the BM of RL 178.450 is 2850 &
3.580,, observed from stations respectively what is the RL of top and bottom of the signal if the
height of the signal is 5m above its base.

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Surveying II 10CV44

Data : θ 1 = 30045‟ Page 35
θ 2 = 16010‟
B = 80m
SC = 2.850m
SD= 3.580m

Solution we have to find
RLQ = HIC + h1
But h1 = Dtan θ 1
Here D = S+btan θ 2 / tan θ 1 - tan θ 2
Here S = SC – SD = 3.580 – 2650 = 0.730
B = 80m
D = 78.420

Substitute D is equation 1 we get,
h1 = 78.420tan30045‟

= 46.650m

h1 = 46.650m
RLQ = (178.450+2850)+46.650

= 227.950
RLQ = 227.950m
RL of top of signal = 227.950m

Dept of Civil Engineering, SJBIT

Surveying II 10CV44

Now,
RL of bottom of signal = 227.950 – 5

= 222.95m

2)To find the elevation of top of a hill, a flag staff 3m height was erected with its top as P

observations were made from2 stations A +B 50m apart. The vertical angle observed from A and
B to the top of the flag staff is 11040‟ and 12050‟ rasp the horizontal angle at „A‟ between flag
staff and B is 55030‟ and that at B between flag staff 7 A is 60015‟ If height of 105 at A is

346.150m find the elevation of top of the hill.

Data: flag staff height = 3m Page 36
B = 50m
θ 1 = 110 40‟
θ 2 = 120 50‟

HI of inst = 346.150m
Solution: To find RL of top of hill

= HI +h1 – 3.0m
But h1 = D tan θ
From
∆le ABC, By applying sin rule we get,
h1 = 9.95m
To find the elevation of top of the will
= HI + h1 -3.0
= 346.150+9.95 – 3
353.120m
RL of top of hill = 353.120m

Dept of Civil Engineering, SJBIT

Surveying II 10CV44

3) Determine the elevation of top Q of a signal on a hill whole observation were made from 2
stations A + B 60m apart and in the same vertical plane as Q a is at a higher level B also
determine the horizontal distance between A &Q

Inst. st Vertical angle to Q Staff reading on RL of BM
A 180 30‟
B 220 40‟ BM

2.815 105.00

1.865

Data : b = 60m Page 37
θ1 = 18030‟
θ 2 = 12040‟
SA = 2.815
SB=1865
RL of BM = 10500

To find RL of Q = RL of BM +h1
h1 = Dtan θ1
But D = S – btan θ 2 / tan θ 2 - tan θ 1
Here S = SA – SB = 0.95m
b = 60m

D = 114.12m
h1 = 38.18m
RL of Q = 143.18m

Dept of Civil Engineering, SJBIT

Surveying II 10CV44

Unit 4 – TACHEOMETRY

Contents
1. Introduction
2. Principle of tachometric surveying
3. Systems of Tacheometers / Methods of tacheometers

Stadia method
Non-stadia method

4. Tacheometric equation for inclined line of sight
5. Tacheometric equation for distance and elevation
6. Non – Stadia Method of Tacheometric Sureying

Tangential method
Sub-tense bar method

7. Beamen stadia arc / stadia circle

Dept of Civil Engineering, SJBIT Page 38

Surveying II 10CV44

Unit 4 – Tacheometric Surveying

Introduction

Also called as indirect leveling to find the height of object / RL of object only with one
instrument station RL is found & θ is calculated. Compared to previous measuring methods this
is very fast. Tachometric surveying is a type of surveying in which we determine the height or
elevation of the objects similar to leveling work.

In this method, the horizontal distance to the object base is not measured but calculated
from the observed data. Hence the method is fast easy and convenient. Thus the method is
suitable to find out the elevation sin hilly areas, river valley, rough terrain where the distance to
the object from the instrument cannot be measured.

As all the calculations depends only on observed data. The method may not be accurate.
The staff man should be able to reach the point whose elevation is required. In tachometric
surveying and instrument called tachometer is adopted this is nothing but normal venire
theodolite fitted with stadia haired.

Stadia hairs are the additional cross hairs placed one above & one below the regular
horizontal cross hair.

Following are the different arrangements of stadia hairs.

Dept of Civil Engineering, SJBIT Page 39

Surveying II 10CV44

Principle of tacheometric surveying:- Tachometric equation with usual notation.

Let us take and internal focusing telescope to obtain tachometric equation.

As in the fig.F is a focal point M is a midpoint and O is a vertical axis pt for the
telescope.

Proof: Let AB be the two pts bisected on a level staff.

The distance between AB is S its inverted image is seen on the diaphragm as ab the

distance between ab will be i(stadia internal) i.e., (Distance between top and bottom stadia hair)
from the ∆le AMB & AMI

AB / ab = u / v -------------- (1)

Here u & v are the conjugate distances and f is the focal length distance, d is the distance
between vertical axis & midpoint.

The lens formula can be used i.e

1/f = 1/u + 1/v

Multiplying uf on both sides

u = f + uf / v

u = (AB / ab) v

Substituting values

u = f + (s/i)f

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Surveying II 10CV44

Where AB = s, ab = i
But D = Horizontal distance to the object is from the vertical axis of the inst.
D = u+d
Substring the value of U from (2) we get.
D = (f/i) s + (f + d)
Here f, i, d are constants for a given instrument.
D = Ks + C
K = is the multiplication constant
C = additive const.
The values of K and C are constant for a given instrument.
And no two instruments will have same constants K and C hence this constant has to be
determined for a given instrument before a survey or starts working with that instrument.

Determination of constants k and C

Tachometric constants K and C are determined in the field with the following procedure.

1. Instrument is set at a convenient point on a level ground withal temporary adjustments.

2. Horizontal plate of the instrument is clamped and along the plane ground points are
marked at regular intervals from the instrument ground point.

3. Staff is held at all the marked points say A,B,C …. And the corresponding staff intercept
(Upper hair heading lower hair reading) say SA, SB, SC,…….are determined.

4. Knowing the distance to each staff point form the instrument the constant K & C are
determined as shown in the calculations

We have,

D1= K SA+C

D2= K SB+C

Dept of Civil Engineering, SJBIT Page 41

Surveying II 10CV44

D3= K Sc+C

Solving above e equations
Equation2 – equation 1 gives
D2- D1 = (KSB+C) - (KSA+C)

= KSB - KSA
D2- D1 = K(SB – SA)
K1 = D2 – D1 / SB – SA
K2 =D2 – D1 / SC - SA
K3 = D3 – D2 / SC - SB

True value of K = (K1 + K2 + K3) / 3
In the same way values are substituted in corresponding equations to get value of C1, C2, C3
True value of C is obtained by taking the average
C = (C1 + C2 + C3) / 3

Systems of Tacheometers / Methods of tacheometers.
Tachometric surveying can be carried out in 2 different methods on systems

a. Stadia method
b. Non-stadia method

1. Stadia method:

It‟s a system or method in which the stadia hairs are used to calculate the required data.
This method can be done in 2 ways,

a. Fixed hair method: Here the distance between top and bottom stadia hairs which in called
as stadia interval is fixed in the instrument

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Surveying II 10CV44

The staff readings corresponding to these top and bottom hairs are taken and the staff
intercept is calculated.

Thus as the staff moves away from the instrument, staff intercept is more and as the
staff comes closed staff intercept is less therefore stadia interval is constant and the staff
intercept.

b. Movable hair method: In movable hair method the distance between stadia hairs stadia
interval can be varied here, the staff intercept in kept const for this staff intercept targets
are fixed on the level staff.

Whenever the staff reading is to be taken looking through the telescope the stadia hairs
are moved, so that they coincide to the targets on the staff

It is difficult to measure accurately the stadia interval Thus; in majesty of the practical
work movable hair method is not adopted and only fixed hair method is preferred.

Tacheometric equation for inclined line of sight:

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Surveying II 10CV44

L = Inclined distance to pt. „P‟

D = Horizontal distance

O = Vertical angle to mid cross hair
S = AB, S1 = A1B1

R = distance between microns hair to bottom of level staff

V = distance between horizontal Los to mid cross hair reads.

When the object are above the line of sight to get the staff intercept the telescope will be moved
up and the LOS will be inclined and hence the regular tachometric equation D = KSW +C1 can‟t

be adopted.

Let P be the point whose elevation is required where staff is held vertically as shown in the fig.

O is the vertical angel A and B are top and bottom cross hair readings for inclined line of sight

Staff is tilted so that it is perpendicular to line of sight and A1B1 are top and bottom cross
hair readings

In ∆le AA1C

O is very small hence A1C A

cos θ = A1C / AC

Dept of Civil Engineering, SJBIT Page 44

Surveying II 10CV44

AC = AB / 2 Page 45
2A1C = AB cos θ
2A1C =A1B1 (C is midpoint of A1B1)
A1B1 = AB cos
But A1B1 = S1 & AB = S
S1 = S cos θ
Here L is the inclined distance which can be set as
L = KS1 +C
Substitute for S1, we get
L = K(S cos θ )+C
But D the horizontal distance is L cosθ
D = Lcos θ
D = (K(S cos θ )+ C) cos θ
D = Ks cos2 θ + C cos θ
Here
Sin θ = V/L
V = L sin θ
Put L value from 2
We get
V = (K(S cos θ )+C) sin θ
= KS cos θ sin θ + Csin θ

Elevation of point „P‟ i.e RLp
RLp = HI of station + (v-r)
RLp = HI + (v-r)

Dept of Civil Engineering, SJBIT

Surveying II 10CV44

If the telescope is fitted with the Anallactic lens, then the additive constant C=(f+d) in totally
eliminated or is equal to zero.

The equation reduced to
D = KScos 2 θ
V = KS sin2θ / 2

When the line of sight is inclined (downwards)

When the line of sight is inclined downwards as in the fig. the distance and elevation of
equation will be same.
D = KScos2 θ
V = KS sin2θ / 2
At point „D‟ = HIp – v – r .

Tacheometric equation for distance and elevation (when the staff is held normal to the line
of sight)

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Surveying II 10CV44

a. When the LOS is normal upwards
When the staff is held normal the staff intercept „S‟ will be normal to the inclined
distance along the inclined line of sight.
Therefore we can write
L = KS+C
But D = the horizontal distance between the inst. & object
D = P1D1
D = P1C1 + C1D1
From the figures
In ∆le PCC1 = cos θ x P1C1 / L
P1C1 = Lcos θ
& C1D1 = r sin θ
In ∆le CC1D1
sin θ = C1D1/ r
Substitutes the value of L (1) from we get
D = (KScos θ) +rsin θ
or
D = KS cos θ + Ccos θ +rsin θ
For telescope with analectic lens
And, we know that.
V = Lsin θ
(KS+C) sin θ
V = KSsin θ +C sin θ
For telescope with anallactic lens
Elevation of Pt D = HI +V – r cos θ

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Surveying II 10CV44

b. When the line of sight is normal but downwards
Here,
D = P1C1 + C1D1
= Lcos θ - rsin θ
D = (KS+C) cos θ - rsin θ
V = Lsin θ
= (KS+C)sin θ
Depression/elevation of pt „D‟
RLp = HI – V - rcos θ

Non – Stadia Method of Tacheometric Surveying

It‟s a method of tachometric surveying in which, the help of stadia hairs is not taken into
consideration some times, during tachometric surveying, the stadia hairs night fade away then,
Non stadia method will be of help
Following are the 2 methods in Non-stadia method of tachometric surveying

1. Tangential method
2. Sub-tense bar method.

1. Tangential method: It is a tachometric surveying in which the vertical angles to the two
targets fixed on the level staff are taken then using the trigonometrically relation, the
required distance f the object and elevation of the object is calculated.
Hence the angles to the tangent can be above or below the line of sight depending on this
condition following are the 3 conditions in tangential methods.

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Surveying II 10CV44

Both angles are angles of elevation (i.e, above LOS)

1. Here 2 targets are fixed at specified distance called „S‟ on the level staff
2. Level staff is held at the point whose elevation & distance in required
3. Theodolite is established at a convenient pt with all temporary adjustments.
4. Vertical angles 1 f2 to top and bottom targets are observed.
5. The distance elevation are obtained as in the calculation.

In ∆le PC1 A Page 49
tan θ 1 = AC1 / PC1 = V/D
V = Dtan θ1 ------------------- (1)
In ∆le PC1 B
tan θ 2 = Dtan θ2
V - S= Dtan θ 2 --------------- (2)
Equation 1 – equation 2
V-V+S= Dtan θ 1 – Dtan θ 2

Dept of Civil Engineering, SJBIT

Surveying II 10CV44

S= D (tan θ 1 – tan θ 2) Page 50
V = Dtan θ 1
V = S tan θ1 / tan θ1 – tan θ2
RLC = Elevation of pt.C = HI +V- S - r

Both the angles are angles of depression.
Calculations:

In ∆le PC1A = tan θ 1 = V/D V Dtan θ 1
In ∆le PC1B1 = tan θ 2 = V+S/D V+S= Dtan θ 2
Equation 2 – 1
V + S - V = Dtan θ 2 - Dtan θ 1

S = D (tan θ 2 - Dtan θ 1)
D = S / tan θ 2 - tan θ 1
And elevation of pt „C‟= HI –V – S – r

One angle is angle of elevation and the other is angle of depression
Calculation:
In ∆le PEA = tan θ 1 = V/D V = D tan θ 1
In ∆le PEB = tan θ 2 = S-V/D S-V= D tan θ 2

Equation 2 – 1
V + S - V = = D (tan θ 1 – D tan θ 2)

D = Stan θ1 - tan θ2
And elevation of pt „C‟
= HI +V – S – r

Dept of Civil Engineering, SJBIT