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SHREE VENKATESHWARA HI – TECH

ENGINEERING COLLEGE

GOBI – 638 455

DEPARTMENT OF CIVIL ENGINEERING

MANUAL

CE 2259 – SURVEYING PRACTICAL II

ANNA UNIVERSITY CHENNAI – 600 025

(Regulation 2008)

II – Year IV – Semester

Prepared by

Mr.J.Saravanakumar, ME

Assistant professor / Civil

Staff HOD Principal



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TABLE OF CONTENTS

S.No. Name of the experimentPage

No.Marks Remark

1. Study of theodolite 2

2.Measurement of horizontal angles by reiteration

method10

3. Measurement of horizontal angle by repetition method 14

4. Measurement of vertical angles 18

5. Closed theodolite traverse - Measuring included angle 19

6. Heights and distances by single plane method 23

7. Heights and distances by Double plane method 25

8. Tangential system 27

9. Stadia system 33

10.Determination Of The Multiplying And Additive

Constant37

11. Setting out work- Foundation marking 42

12. Setting out of a simple curves by long chord method 44

13. Setting out of a curves by Rankine’s method 47

14.Determination of Azimuth of Survey line by

observation of sun50

15. Field work using Total Station 51

16. Measurements Of Distance And Co-Ordinates Of GivenPoints

54

17. Subtense bar method 57

Average of marks



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EX.NO:1

DATE:

STUDY OF THEODOLITE

AIM:

To study the component parts, temporary adjustment of a theodolite and reading

horizontal angle.

COMPONENT PARTS OF A THEODOLITE:

Levelling Head

Shifting Head

Lower Plate

Upper Plate

Plate Levels

Standard ( or a Frame)

Vernier Frame

Telescope Vertical Circle

Altitude Bubble

Screws

Tripod



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1. Levelling Head:

It is the lowermost part of a theodolite. It consists of two parallel horizontal plates

separated by three levelling screws.

The lower plate with a large threaded hole in its centre is called trivet or foot plate. It

provides a means to place the instrument on (tripod) stand and get it screwed. Its central

aperture provides a way for suspending a plumb bob.

The upper plate of the leveling head is called the tribrach . It contains a tapered bearing

at the centre. It has three arms each carrying a leveling screw. It provides a support for theupper part of the instrument.

The principal use of levelling head is to provide a means for levelling the instrument.

2. Shifting Head:

It consists of a pair of horizontal plates and an annular treaded ring. One of the plates is

placed below the lower plate but above the tribrach and the other below the tribrach. The

annular treaded ring is placed in between lower plate and the tribrach which is used to

tighten/untighten the whole of the instrument. The shifting head is used for exact centring of

the instrument after leveling has been completed.

3. Lower Plate:

It is a horizontal circular plate monolithically constructed with the outer spindle. A

scale is engraved at its beveled edge with divisions in degrees and minutes increasing in

clockwise direction. It provides the main scale reading of a horizontal angle and a means to

fix / unfix the whole of the instrument.

4. Upper Plate:

It is a horizontal circular plate monolithically constructed with the inner spindle. It

is fitted with two diametrically opposite vernier scales designated as A and B. Functions of

upper plates are to support a pair of magnifiers for the verniers, a pair of plate levels, a pair

of support frames for telescope and a means to fix / unfix the upper plate of the instrument

with its lower plate.

5. Plate Levels:

A pair of level tubes is placed at right angles on the upper plate. These are used to

make the vertical axis of the instrument truly vertical i.e., for leveling of the instrument.

6. Standard ( or a Frame):

Two standards resembling the letter a are attached on the upper plate. These

provide the bearings of the pivots of the telescope allowing it to rotate on its trunnion axis

in vertical plane. The vernier frame and arm of vertical circle clamp are also attached to it.

7. Vernier Frame:

Also called T -frame or index frame, consists of a vertical leg known as clipping arm

and a horizontal bar called the index arm engraved with verniers C and D at its ends. Each

of the verniers at C and D are having two scales which increase in opposite

directions.



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It is used as seat for altitude bubble and also provides vernier reading for vertical

angle measurement.

8. Telescope:

The telescope of a theodolite is identical in structure and uses, as in case of a dumpylevel. But, in theodolite, the telescope is mounted on a horizontal spindle called the

horizontal axis or the trunnion axis to rotate it also in vertical plane.

9. Vertical Circle:

The vertical circle is attached with the trunnion axis. It is engraved with a scale

reading vertical angle in degrees and minutes. The vertical circle is divided into four

quadrants each reading 0° to 90° with 0° - 0° either along vertical or in horizontal. It

provides the main scale reading for vertical angle.

10. Altitude Bubble:

A sensitive level tube placed on vernier frame is called altitude bubble. It is used to

make horizontal axis truly horizontal.

11. Screws:

A theodolite instrument has number of screws as its component parts. These are

classified into different types depending on their functions.

a) Levelling Screws

b) Clamp Screws

c) Tangent Screws

a) Levelling Screws:

These are present in the leveling head of a theodolite in between trivet and tribrach.

These work in threaded holes in the tribrach arms and their lower ends rest in recesses in

the trivet. These screws are used for leveling the instrument i.e., to make plate level axis

truly horizontal.



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b) Clamp Screws:

These are used to fix the parts of a theodolite with which these are attached.

i. Lowerplate Clamp Screw

ii. Upperplate Clamp Screw

iii. Vertical plate Clamp Screw

i. Lowerplate Clamp Screw:

The clamp screw attached to the lower plate of a theodolite is called lower plate

clamp screw. When it is tightened, the outer spindle gets fixed with the tribrach, and, thus,the lower plate gets fixed in position.

ii. Upperplate Clamp Screw:

The clamp screw attached with the upper plate of a theodolite is called upper plate

clamp screw. When it is tightened, the inner spindle gets fixed with the outer spindle and,

thus, the upper plate gets fixed in position.

The manipulation of the upper plate and lower plate clamp screws provide three

conditions:

When both the upper plate clamp screw and the lower plate clamp screw are

tightened, the instrument gets fully fixed.

When the upper plate clamp screw is tightened and the lower plate clamp

screw is opened, the instrument rotates on its outeraxis, There is no relative

motion between the two plate and the readings in the horizontal vernier

scales do not change.

When the lower plate clamp screw is tightened, and the upper plate is

opened, the instrument rotates on the inner axis with outer axis fixed. The

readings in the horizontal vernier scales change.

iii. Vertical plate Clamp Screw:

It is present on a frame fixed with standard and above the shaft of trunnion axis. It is

used to clamp the telescope in any plane and hence at any desired vertical angle.

c) Tangent Screws:

With each clamping screw, there is a tangent screw present in the instrument to

provide fine movement. The tangent screws work only after its clamping screws get

tightened. Thus when the upper clamp screw has been tightened, small movement of the

upper plate can be made by the upper tangent screw; when the lower clamp screw has

been tightened, small movement of the lower plate can be made by the lower tangent screw

and similarly for vertical clamp screw.

12. Tripod:

The theodolite is mounted on a strong tripod when being used in the field. The legs of thetripod are solid or framed. At the lower ends of the legs, pointed steel shoes are provided to get

them pushed into ground. The tripod head has male screws on which the trivet of the leveling

head is screwed.



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Adjustments of aTransit Theodolite:

The adjustments are mainly of two types. There are,

1) Permanent adjustments

2) Temporary adjustments

1) Permanent adjustments:

Adjustments made to establish fixed relations between the fundamental lines of a

theodolite are known as permanent adjustments. These adjustments once made remainpermanent for a long period.

2) Temporary adjustments:

Adjustments made at each setting of the instrument before taking observations are known

as temporary adjustments.Temporary Adjustments includes,

a) Setting up the level

b) Levelling up

c) Elimination of parallax

a) Setting up the level :

This operation includes fixing the instrument on the tripod and also approximate levelling

by leg adjustment.

b) Levelling up :

Accurate levelling is done with the help of foot screws and by using plate levels. The object

of levelling up the instrument is to make its vertical axis truly vertical.

c) Elimination of parallax:

If the image formed by the objective does not lie in the plane of the cross hairs, there will be

a shift in the image due to shift of the eye. Such displacement of image is termed as parallax.

Parallax is removed in two stages.

Focusing the eye for distinct vision of cross hairs.

Focusing the objective so that image is formed in the plane of cross hairs.

Reading the horizontal angles:

A horizontal angle is the angular measurement between two points. The angles are

measured in the horizontal plane. It can be expressed in this way also. A horizontal angle is the

angle formed by two intersecting vertical planes at their point of intersection.

The following is the procedure to read the vernier,

1) The main scale reading is taken to the zero of the vernier . ( Refer fig. in A-Vernier)



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3) Vernier scale readings are taken by this method.

a) Determine the least count of the vernier. ( 20seconds)

b) Note the main scale graduation beyond which the index lies. ( inVernier A & B ). This is

the approximate reading ( say 127° right & 232° left ) in vernier A.

c) Observe which division of the vernier coincides exactly with any divisions on the main

scale. ( i.e, 14’ right & 46’ left )

d) Multiply the number of the coinciding Vernier divisions by the least count. This is the

value of fractional part. Add this to the approximate reading taken to get the exactreading on the main scale. ( i.e,127°+ 14’ = 127°14’ right & 232°+ 46’ = 232°46’ left )

RESULT:

Temporary adjustment of a theodolite has been practiced and reading horizontal angles in

the vernier are also practiced.



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B

A

O

D

C



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Ex.No.2 DATE:

MEASUREMENT OF HORIZONTAL ANGLE BY THE METHOD OF REITERATION

AIM:

To measure the horizontal angles by the method of reiteration method.

APPARATUS REQUIRED:

1. Theodolite

2. Tripod

3. Four Ranging Rods

4. Arrows

PROCEDURE:

1. Set the instrument at O and do all temporary adjustments

2.

Keep vernier A to zero and bisect the ranging rod at A.3. Keep the lower clamp in tightened condition and loosen the upper clamp.

4. Swing the telescope towards right and bisect the ranging rod at B. Take vernier A and B

readings. The mean value of the vernier reading will give the angle AOB

5. Swing the telescope towards right and bisect the ranging rod at C and take vernier A

and B readings.

6. Swing the telescope towards right and bisect the ranging rod at D and take vernier A

and B readings.

7. Again turn the telescope clockwise and bisect the ranging rod at A and there by closing

the horizontal.

8. Change the face and keep the vernier at 0º.



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TABULATION:

Inst.

station

Station

bisected

Reading on

vernier Angle Mean angle CorrectionCorrected

angleRemarks

A B

° ' " ' "

O

A

Face left

B AOB

C BOC

D COD

A DOA

O

A

Face Right

B AOB

C BOC

D COD

A DOA

MODEL CALCULATION:



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9. Bisect the ranging rod at A keeping the lower clamp tightened. Swing the telescope in

the counter clock direction and bisect the ranging rod at D and note down the readings .

10. Rotating further anticlockwise bisect the ranging rods at C and B, note down the vernier

readings.

11. Finally bisect the ranging road at A and note down the readings. Now the readings must

be same as the initial reading otherwise error should be equally distributed between

the included angles.

RESULT:

The horizontal angles :

Angle AOB = ……………..

Angle BOC = …………….. Angle COD = ……………..

Angle DOA =……………….



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P Q

O



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Ex.No.3

DATE:

MEASUREMENT OF HORIZONTAL ANGLES BY REPETITION METHOD

AIM:

To measure the horizontal angle at a particular given instrument station by Repetition

method.

INSTRUMENTS REQUIRED:

1. Theodolite

2. Tripod

3. Two Ranging Rods

4. Arrows

PROCEDURE:

The method of repetition is used to measure the horizontal angle to a finer degree ofaccuracy than that obtainable with the least count of the vernier. By this method an angle is

measured two (or) more time by allowed the vernier to remain clamped each time at the end of

each measurement of the previous station. Thus an angle reading is mechanically repetitions. The

average horizontal angle is then obtained by dividing the final reading by number of repetitions.

To measure the angle of horizontal AOB, the following Procedure:

1. Set the instrument at station ‘O’ and level it with the help of alidade bubble and foot screw.

Set zero reading (or) vernierA note the reading at vernier B.

2. Loose the lower clamp and direct the telescope towards the point ‘P’ accurately by lowertangential screw.

3.

Then unclamp the upper clamp and turn the instrument clockwise about inner axistowards ‘Q’ accurately with the upper tangential axis.

4. Unclamped the lower clamp and turn the telescope and sight P. Again bisect ‘P’ accuratelyby using the lower tangential screw. It should be noted that the vernier reading will not be

changed in this operation. Since the upper plate is clamped to the lower.

5. Unclamp the upper clamp, turn the telescope clockwise and Sight ‘Q’ accurately by uppertangent screw.

6. Repeat the process until the angle i.e. for repeated no. of times say three times. The average

angle with face left will be equal to the final reading divided by number of repetition (3).



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TABULATION:

MODEL CALCULATION:

Inst.

station

Sight

to

Face Left Face Right

Average

Horizontal

angleNo. of

RepetitionReading on

vernier Mean angleReading on

vernier Mean angle

A B A B

° ' " ' " ° ' " ° ' " ' " ° ' " ° ' "

O

P

1Q

P

2Q

P

3Q



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RESULT:

The average horizontal angle POQ = ..................



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TABULATION:

MODEL CALCULATION:

From the triangle QPQ’

R.L of Q = R.L of B.M + Staff reading on BM + V

V= D tan

Inst.

station

Sight

to


Average

Vertical angle No. of

RepetitionReading on


vernier Mean angle

C D C D

° ' " ' " ° ' " ° ' " ' " ° ' " ° ' "

O

A

1

B

A

2

B

A

3

B



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Ex.No.4

DATE:

MEASUREMENT OF VERTICAL ANGLE

AIM:

To determine the vertical angle between the top and the bottom of the building and

also find the height of the building.

INSTRUMENT REQUIRED:

1. Theodolite

2. Tripod Stand

3. Chain (or) tape

4. Arrow

PROCEDURE:

1. The instrument fixed over the station and leveled with reference to the alidade

bubble.

2. The telescope clamping screw is loosened C & D verniers to set 0° exactly using

vertical tangent screw. .

3. Turn the telescope and bisect exactly to the staff on B.M. the height of the

instrument measured as “h”.

4. Loosen the telescope clamp screw and the telescope is moved in vertical direction

and object Q is bisected. For exact bisection use vertical circle tangent screw.

5. The vernier reading C and D are noted. The mean value of the vernier C and D gives

the vertical angle ““.

6.

Changing, the faces makes similar observations and mean of vertical angle (face left& face right) ““is noted.

7. The horizontal distance “D” between the base of the object and instrument station ismeasured using tape.

8. Then the height of the building is calculated by using the trigonometrically relations.

RESULT:

The height of the object, h+V = …………....

R.L of Q = …………….



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Ex.No.5

DATE:

CLOSED THEODOLITE TRAVERSE -

ME ASURING INCLUDED ANGLE

[BALANCING THE TR AVERSE BY GRAPHICAL METHOD]

AIM: To plot the closed theodolites traverse by measuring included angles and then the

error of closure is balanced by Graphical method.

APPARATUS REQUIRED:

1. Transit theodolite

2. Chain

3. Tape

4. Ranging rods

5. Arrows.

PROCEDURE:

1. Setup the Theodolite over the starting station "A"and do the temporary adjustments.

2. Orient the telescope towards the magnetic north and then determine the magnetic

bearing of the initial line AB (i.e., b)

3. Set the vernier A to 0º using lower clamp and tangent screw, take a back sight on

last station "E" using lower clamp and tangent screw (vernier "A" still reads zero).

4. Loosen the upper clamp turn the telescope clockwise and take a foresight on B,

clamp the upper clamp and bisect "B" use upper tangent screw for exact bisection.

Read both verniers the mean for the two verniers is the required included angle EAB

(θ1).5. Change the face, face left to face right and again measure angle EAB (θ1).

6. The average of the two included angles in steps 4 & 5 is the correct included angle

EAB(θ1).

7. Shift the instrument to second station "B" measure the included angle ABC (θ2) by

taking a back sight on "A” and a foresight on "C" as done in steps (3) & (4)8. Similarly measure included angles at C,D& E (i.e.,(θ3) (θ4) & (θ5)).

9. Measure the distances of traverse line in AB, BC, CD, DE & EA using tape or chain.

10. After the completion of field work, it becomes necessary to plot the same. The sum -

of the interior angles ((θ1) + (θ2) + (θ3) + (θ4) + (θ5)) should be equal to (2n - 4) 90°

where n is the number of sides.



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TABULATION:

I n s . S t a t i o n

Sight

to


Average

Horizontal

angleSide

Length “m” R e m a r k s

Reading on

vernierMean angle

Reading on

vernierMean angle

A B A B

° ' " ' " ° ' " ° ' " ' " ° ' " ° ' "

AE

B

B

A

C

CB

D

D

E

C

EA

D



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Balancing the traverse by Graphical method

1. Plot the traverseABCDE. If t he traverse is not closing with the st arting point 'A'.Then the

error of closure or closing error Aa’ occurs. Error of closure is t o be adjusted

proportionat ely in all stations to obtain an adjusted traverse. (Fig - a)

2. Draw a straight line aA-(Fig - b ) equal to the perimeter of the traverse a b c d e. Mark b,c,

d &e on the line to the same scale.

3. Draw a line a' A (Fig - b ) parallel' and equal to the closing errorAa' (Fig - a ). Draw a linejoining Aa (in Fig - b ).

4. Draw the lines bB, cC, dD, eE (I.e., These are the direction & magnitude of the corrections

to be carried out in the traverse from t he stations b, c, d, e ( Fig- b ) parallel to a' A (error

of closure).

5. Draw a line bBfrom station b ( Fig - a ) parallel and to the same magnitude of bB(Fig - b)

to locate the correct station B.

6. Similarly cC, dD, eE lines are drawn in the traverse to locate the correct location of

traverse stations CDE (Fig - a).

7. Now stations ABCDE are the correct location of t he t raverse.

8. Join the traverse stations to get a adjusted traverse ABCDE.

RESULT:

Thus the plot is adjusted (ABCDE) & plotted.



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TABULATION

CALCULATIONS:

D = d tan α2 - h / (tan α1 - tan α2)

V1 = D tan α1

V2 = (D+d) tan α2

R.L of given point = R.L of BM + h1+V1 (or) R.L of BM + h2+V2

I n s t . S t a t i o n

Sight

to


Average

Vertical angle

R e

m a r k s

Reading on

vernier

Mean angleReading on

vernier

Mean angle

C D C D

° ' " ' " ° ' " ° ' " ' " ° ' " ° ' "

P is higher than R

PQ

R

P is lower than R

PQ

R



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Ex.No.6

DATE:

HEIGHTS AND DISTANCES BY SINGLE PLANE METHOD

AIM:

To find the RL of an inaccessible point by single plane method.

APPARATUS REQUIRED:

1. Theodolite2. Ranging rod

3. Chain

PROCEDURE:

1. Keep the theodolite over a point O and all temporary adjustments. Set vernier C and

D to zero.

2. Bisect the staff at BM and take the Stadia reading

3. Rotate the theodolite in the vertical direction and bisect the point Q (the peak

point).

4. Note the readings on vernier C and D (α 1)

5. Transit the theodolite through 180° and mark the station 2 along the line of sight at

a distance of 20m from station 1.

6. Shift the theodolite over the station 2 and do the temporary adjustments.

7. Note the staff reading on the BM and rotate the theodolite and bisect the point Q

8. Note down the angles on vernier C and D (α2).

RESULT:

RL of the peak point Q =………………

Horizont al distance “D” = ………………



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TABULATION

CALCULATIONS:

I n s t . S t a t i o n

Sight

to


Average

Vertical angle

R e

m a r k s

Reading on

vernier

Mean angleReading on

vernier

Mean angle

C D C D

° ' " ' " ° ' " ° ' " ' " ° ' " ° ' "

P is higher than R

PQ

R

P is lower than R

PQ

R



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Ex.No.7

DATE:

HEIGHTS AND DISTANCES BY DOUBLE PLANE METHOD

AIM:

To find the RL of an inaccessible point by Double plane method.

APPARATUS REQUIRED:

1. Theodolite

2. Ranging rod

3. Chain

PROCEDURE:

1. Let A and B be the two instrument stations not in line with the object b.

2. α1 and α2 be the vertical angles observed from instrument stations A and

B respectively.

3. a and b the staff reading observed on the BM from the instrument stations

A and B respectively.4. θ1 and θ2 be the horizontal angle observed at the instrument stations A

and B respectively, between the object and the next instrument station.

5. d be the horizontal distance between the two instrument stations A and

B.

6. d1 and d2 be the horizontal distance between the object and the

instrument stations A and B respectively.

7. V1 and V2 be the vertical heights to the top of object P from the horizontal

line of collimation at the instruments A and B respectively.



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CALCULATION:

P’ be the base of the object P.

In ∆APB

Angle P’AB=θ1; Angle P’BA=θ2; AB=d

AP’=d1; BP’=d2

AP’B=180O – (Angle P’AB+ P’BA=θ2)

=180O –(θ1+θ2) =θ3

Using sine rule we can write

In above Equation expect d1 and d2 others are known

Having calculated the distance d1 and d2 vertical height V1 and V2 can be computed

considering the triangles PCD and PEF.

In ∆PCD

PD=V1 ; CD=AP’=d1

V1 =d1

RL of P=RL of BM + Staff reading on BM from A +V1

=RL of BM + a +V1

In ∆PEFPF=V2; EF=BP’=d2

V1 =d2

RL of P=RL of BM + Staff reading on BM from B +V2=RL of BM + b +V2

RESULT:

RL of the peak point P at A =……………

RL of the peak point P at B= ………………



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Ex.No.8

DATE:

TANGENTIAL TACHEOMETRY

AIM:

To find the Reduced level of a point Q and the distance between two given points P and

Q.

APPARATUS REQUIRED:

1. Theodolite

2. Levelling staff

PROCEDURE:

1. Setup the instrument at point ‘P’ and center the instrument. Level the instrument with

the help of foot screws and the bubble tubes.

2. Keep the staff at the Bench mark and note down the axial hair reading. Let it be ‘h’. 3. Direct the theodolite towards point Q. Keep the leveling staff at point ‘Q’. Mark the two

readings on the leveling staff such that the distance between the two readings is 1m andlet it be ‘S’.

4. Sight the top reading marked in the leveling staff and note down the vertical angle, with

reference to horizontal. Let it be ‘1’.

5. Similarly sight the bottom reading marked in the staff and note down the vertical angle

with reference to the horizontal and let it be ‘2’.

6. Calculate the distance ‘D’ and vertical distance‘V’ using the formula,

if 1 and 2 are angles of elevation,

D = S/ (tan 1- tan 2) and V = D tan 2

If α1 and α2 are angles of depression,

D = S/ (tan α2 – α1) and V = D tan α2

If one is angle of depression and the other is angle of elevation,

D = S/ (tanα1 + tanα2) and V = D tan α2

Reduced level of point Q = R.L of P + h + V – r.

Where,

r is the axial hair reading noted down at point ‘Q’.



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TABULATION:

Instrument

Station

Staff

station

Vertical

Angle θ

Staff Readings (m)Reduced Level of

B.M (m)

Middle

Inst.

station

Sight

to


Average

Vertical angle

R

e m a r k s

Reading on


vernier Mean angle

C D C D

° ' " ' " ° ' " ° ' " ' " ° ' " ° ' "

P Q



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CALCULATION:

Staff intercept = S = 2-1 = 1m

Vertical angle at 1m = α1 =

Vertical angle at 2m = α2 =

Horizontal distance D = S/ (tan α2 – α1)

Vertical distance V = D tan α2

Reduced level of point Q = R.L of P + h + V – r.

RESULT:

(i) Reduced level of point Q = ……………….

(ii) Distance between the two points P and Q =………



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CASE(i) : WHEN BOTH ANGLE VERTICAL

From Figure 24.1,

V = D tan q1

and V+s = D tan q2

Thus, s = D ( tan q2 - tan q1 )

Therefore R.L. of Q = (R.L. of P + h) + V – r -------------------- where, h is the height of the

instrument, r is the staff reading corresponding to lower vane.

http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-ROORKEE/SURVEYING/modules/module7/html/24-3.htm






33

CASE(ii) : WHEN BOTH VERTICAL ANGLES ARE DEPRESSION ANGLES



34

CASE(iii) : WHEN ONE OF THE VERTICAL ANGLES IS ELEVATION ANGLE

AND THE OTHER IS DEPRESSION ANGLE



35

Ex.No.9

DATE:

STADIA TACHEOMETRY

AIM:

To determine the Reduced level of point ‘P’, when the Reduced level of point ‘Q’ is given.

APPARATUS REQUIRED:

1. Theodolite,

2. Leveling staff.

PROCEDURE:

1. Set up the theodolite and center the instrument over point ‘P’ and make initial leveling

adjustments using the foot screws and bubble tube.

2. Keep the staff on the bench mark and note down the axial hair reading on the staff with

line of sight, horizontal, to determine the height of instrument.

3.

Direct the telescope to the point ‘Q’ and note down the staff readings and the verticalangle subtended by the line of sight with the horizontal.

4. Calculate the distance between the points ‘P’ and ‘Q’ by using the formula, D = KS

Cos2, Where D is the distance between the two points, S is the staff intercept at ‘Q’ and

is the vertical angle.

5. Reduced level of point ‘Q’ = R.L of Benchmark + Axial hair reading at BM+ V – r. Where V

is the vertical intercept at ‘Q’ and r is the axial hair reading at ‘Q’.



36

TABULATION:

Instrument

Station

Staff

station

Vertical

Angle θ

Staff Readings (m) Reduced

Level of

B.M (m)Top Middle Lower

Inst.

station

Sight

to


Average

Vertical angle

R e m

a r k s

Reading on


vernier Mean angle

C D C D° ' " ' " ° ' " ° ' " ' " ° ' " ° ' "



37

CALCULATION:

Observation from P to B.M:

The axial hair reading , h =

Observation from P to Q:

Staff intercept, S =

Axial hair reading = r =

Vertical angle, θ =

Horizontal distance = D = KS Cos2 θ

Vertical intercept, V = (KS Sin2θ)/2

R.L of height of instrument at P = R. L of Q – V + r

R.L of P = R. L of height of instrument at P – h

RESULT:

(i) Horizontal distance between the points P and Q =…………..

(ii) Reduced level of point P =…………….



38

Observation Table:

Instrument

Station

Staff

StationDistance

Vertical

Angle

Stadia hair Reading

Remarks

Top Center Bottom

A

D1

D2

D3

D4



39

Ex.No.10

DATE:

DETERMINATION OF THE MULTIPLYING AND ADDITIVE CONSTANT

AIM:

Determination of the Multiplying and additive constant of given Tachometer

APPARATUS:

1. Tachometer with tripod,

2. Tape

3. Leveling staff

4. Wooden pegs

5. Ranging rods

FORMULAE

When the line of sight is horizontal, then

D = KS + c

Where,

D = Horizontal distance between instrument station and staff station.

M = Multiplying constant of a tachometer

S = Staff intersect i.e. difference between top and bottom stadia hair reading.

When line of sight is inclined and staff vertical then:D = KS cos2 θ + c cosθ

Where,

D = Horizontal distance between instrument station and staff station.

K = Multiplying constant of a tachometer

S = Staff intersect i.e. difference between top and bottom stadia hair reading.

θ = The inclination of the line of collimation to the horizontal.



40

c = The additive constant of the tachometer

DETERMINATION OF CONSTANT K AND CThe values of the multiplying constant k and the additive constant C can be computed

by the following methods:

1st METHOD:

In this method ,the additive constant C=(f +d) is measured from the instruments while

the multiplying constant k is computed from field observations

1) Focus the instruments to a distant object and measure along the telescope the

distance between the objective and crosshair.

Since f1 is very large in this case ,f is approximately equal to f2 i.e , equal to the

distance of the diaphragm from the objective.

2) The distance d between the instrument axis and the objective is variable in case of

external focusing telescope, being greater for short sights and smaller for long sights. It should,

therefore, be measured for average sight. Thus, the additive constant (f +d) is known.

3) To calculate the multiplying constant k, measure a known distance and take the S1 on

the staff kept at that point , the line of sight being horizontal. Using equation

For the average value, staff intercepts, s2, s3 etc., can be measured corresponding

to distance d2, d3 etc., and mean value can be calculated.

2nd METHOD:

In this method, both the constants are determined by field observations as under:

1) Measure a line, about 200 m long on fairly level ground and drive pegs at some

intervals, say 50 meters.

2) Keep the staff on the pegs and observe the corresponding staff intercepts with

horizontal sight.

3) Knowing the values of d and s for different points, a number of simultaneousequations can be formed by substituting the values of d and s in equation (1.1). the

simultaneous solution of successive pairs of equations will give the values of k and c, and the

average of these can be found. If s1 is the staff intercept corresponding to distance D1 and s2

corresponding to D2, we have,



41

Subtracting (1) from (2) we get,

Substituting the values of k in (1) we get,

Thus, equations 3 and 4 give the values of K and C.

1) Tachometry: It is a branch of angular Surveying in which horizontal and vertical distance of

point are obtained by instrumental observation.2) Tachometer: It is a transit theodolite having a stadia telescope i.e. telescope fitted with

stadia diaphragm.

A leveling staff can be used for sighting purpose up to 100m distance.

PROCEDURE:

1) Select an instrument station A on a fairly leveled ground and fix a peg.

2) Do the temporary adjustment over A.

3) With vertical circle to the left of the observer and reading 00000’00” bisect staff

held at 10m, 20m,30m. from A along straight line.

4) Note down the staff reading against top and bottom stadia hair on staff held

at 10m, 20, 30m. from A.

5) In case of inclined line of sight the same procedure as stated above is followed step

by step with a vertical angle of 05000’00” in the vertical circle of the theodolite. In this

case, the vertical circle is held to the left of the observer and with the reading 05000’00”

in the circle the staff is bisected at 10m, 20m, and 30m from A along straight but

inclination line of collimation.

CALCULATION:

D = Ks + c

For three staff stations,

D1 = Ks1+c ------- (1)

D2 = Ks2+c ------- (2)

D3 = Ks3+c ------- (3)



42

As ; s1, s2, s3 can be known solving (1) &(2), (2) & (3) , (1) & (3) to get 3 values of m & c

,then average of three values is required answer.

D = Ks cos2 θ + c cosθ

For, three station the equations are;

D1 = Ks1 cos2 θ1 + C cosθ1 ------- (1)

D2 = Ks2 cos2 θ2 + C cosθ2------- (2)

D3 = Ks3 cos2 θ3 + C cosθ3------- (3)

As ; s1, s2, s3 can be known solving (1) &(2), (2) & (3) , (1) & (3) to get 3 valuesof K & C ,then average of three values is required answer.

RESULT:

A) For horizontal line of collimation; 1) The additive constant ‘c’ for a given tacheometer is found out to be ---------

2) The multiplying constant ‘m’ for a given tacheometer is found to be ---------

B) For inclination line of collimation;

1) The additive constant ‘c’ for a given tacheometer is found out to be ----------

2) The multiplying constant ‘k’ for a given tacheometer is found to be ---------



43



44

Ex.No.11

DATE:

SETTING OUT WORK – FOUNDATION MARKING

AIM:

To set out the centerlines for the Foundation walls of the buildings and mark the

lines for excavation.

APPARATUS REQUIRED:1. Tape or chain.

2. Cross staff.

3. Ranging rod.

4. Arrows.

5. String.

PROCEDURE:

1. Prepare a centre line sketch of the building (indicate the centre of cross walls also).

2. Remove any vegetation in the construction site.

3. Set out the baseline with reference to given any reference points.4. Mark the ends of the cent re line of the walls, point s A and B from the base line.

5. As the end marks A, B, C, et c. disturbed during excavat ion, stakes (or masonry pillars) are

fixed at L, M, N,etc., a little away (about 2 to 3 m) for end mark and tie a string accurat ely.

6. Mark the centre line for all other walls AD, BC, etc. by dropping perpendicular. For small

buildings the perpendiculars may be setout by using a chain or a tape by'3-4-5' method.

For aimportant and big building when sides are long a theodolite may be employed t o

accurat ely set out the perpendiculars and to range t he lines.

7. For every wall drive the pegs a lit t le away f or end mark and tie a string accurately.

8. Measure the diagonals and check with t heir corresponding calculated lengt hs.

9. Mark the width of foundation from t he centre line and fix up the corners 1,2,3,4,5, etc.,

pegs are driven at t hese corners, the chord is stretched and lime is spread along t hechords.

10. Now the trench plan being marked on the ground, excavation may be started.

RESULT:

The centerline and foundation mark to be excavated has been set out.



45

TABULATION:

S.L NO PEG INTERVAL CHAINAGE PEG

INTERVAL x (m)

ORDINATE DISTANCE

FROM THE MID POINT

OBSERVATION & CALCULATION:

Tangent length = R tan Δ/2

Mid ordinate OO = Ox = Sqrt ( R2 – X2) - Sqrt (R2 –(L/2)2)

Ox = Sqrt( R2 – X2) - Sqrt (R2 –(L/2)2)



46

Ex.No.12

DATE:

SETTING OUT CURVES BY LONG CHORD METHOD

AIM:

To set out a simple curve using Long Chord method.

APPARATUS REQUIRED:

1. Chain

2. Arrows

3. Ranging rods and

4. Cross Staff.

PROCEDURE:

1. Curves are generally used or highways and railways it is necessary to change the

direction of motion. A curve may be circular, parabolic or spherical.

2. To sets the curve by using offset from long chord method. First we must know the

radius of curvature and the deflection angle. Now tangential length is calculated byusing the formula.

3. Now keeping the theodolite levelled on tripod and keeping a point as a reference

deflection angle is marked on the ground.

4. Length of long chord is calculated by using the formula.

5. By chaining and ranging method, the length of long chord is marked on the ground.

6. The distance x1, x2…. Are measured from the mid of the long chord.

7. Ordinate distances which is calculated from the formula,

Ox = Sqrt( R2 – X2) - Sqrt (R2 –(L/2)2)

Are erected on the ground with the help of staff and tape.

8. Similarly for all the points the ordinates are measured joining them all will give a

smooth curve.



47

RESULT

Thus a simple curve of given radius has been set out by Long Chord method.



48

TABULATION:

Points Chainage Chord

length

Deflection

angle for

chord

Total

Deflection

angle

Angle to be

set

R e m a r k s

° ° " ' " ' " ' "

CALCULATIONS:

Length of the tangent AT1& AT2 = R tan φ/2

Length of long chord T1& T2 = 2R sin φ/2

Length of the curve L = πRφ/2

Deflection angle φ = 180º-Iº = 180º - 90º = 90º

Deflection angle for initial sub chord = (1718.9/R) x ln

Where, ln = length of sub chord

R = Radius of the curve

Φ = Deflection angle



49

Ex.No.13

DATE:

SETTING OUT A SIMPLE CURVE BY RANKINE’S METHOD

AIM:

To set out a simple curve of radius 60m and deflection angle of 60o by Rankine’s

tangential angle method.

APPARATUS REQUIRED:

1. Theodolite,

2. Ranging rods,

3. Chain and arrows.

PROCEDURE:

1. Setup the theodolite at the point of curve(T1) with both the plates clamped to zero.

Direct the theodolite to bisect the point of intersection (V).The line of sight is then in

the direction of the rear tangent.2. Fix the first deflection angle(1) in the horizontal circle and now the theodolite is

directed towards T1A.

3. Now, hold the zero end of the tape at T1 and hold an arrow at a distance of T1A (i.e.

the first chord length). Swing the tape around T1 till the arrow is bisected by the

cross hairs. Thus the first point ‘A’ is fixed.

4. Set the second deflection angle (2) in the horizontal circle and repeat the same

procedure, as done for the first deflection angle and fix the second point ‘B’.

5. And the same procedure are to be adopted for other deflection angles also and other

points on the curve are fixed.



50

RESULT:

Thus a simple curve of radius 60m and deflection angle, 60o has been set out by

Rankine’s method.



51

TABULATION:

CALCULATION

Inst.

At Sight toHorizontal angle

Mean angleVertical angle

Mean angle

A B C D

° ' " ' " ° ' " ° ' " ' " ° ' "

O



52

Ex.No.14

DATE:

DETERMINATION OF AZIMUTH OF THE LINE BY

EXTRAMERIDIAN OBSERVATION ON THE SUN

AIM:

Let OP be a line whose azimuth ( fore bearing) is to be determined by taking

extrameridian observation on the sun.

APPARATUS REQUIRED:

1) Theodolite

2) Ranging rod

PROCEDURE:

1. Set up the instrument at O, and make all temporary adjustment.

2. Keep the vernier A at 0º.

3. Sight the ranging rod P for bisecting the rod using lower tangent screw for

necessary.

4. Release the upper clamp and direct the telescope to the sun and note down linevertical angle , the sun first quadrant by upper tangential screw and Vertical

tangent screw.

5. Next being to image of the sun III quadrant the down, the time for vertical angle 2

.Note down the horizontal angle θ2also.

a) Indian standard time observation t n = t 1 + t 2 / 2.

b) Altitude of the sun of the time of observation, = 1 + 2 / 2

c) GMT of observation = t – 5 h 30 min

d) Declination of the sun of the GMT = sqrtSin (S-Z)x sin (S-C)

Sin (S-P) x sin S

S = (Z + C + P)/2

e) Average horizontal angle between OP and OS is θ = (θ1 + θ2)/2

f) Azimuth of line OP = True bearing of DA = θ -

PRINCIPLE AND SIGNIFICANCE:

The required altitude and the horizontal angles are those to the sun centre. Hence

the hairs should be set tangential to the two limbs simultaneously. The opposite limbs are

then observed by chaining the face.

RESULT:

The azimuth of line OP = ……………



53

Ex.No:15

DATE:

STUDY OF TOTAL STATION

AIM:

Study of total station, getting to know about the equipment

INTRODUCTION:

The Electronic Total Station is ultimate in surveying instruments.

It is a combination of digital t heodolite and EDMI (Electronic Distance Measuring Instrument)

that allows the user to measure distances and angles electronically, calculateCoordinates of

points and attach an electronic field book to collect and record the data.

The uses of the total station are:

1) Reduction of distances

2) Input of station coordinates and target point eccentricities

3) Determination of polar coordinates in the national system or local system4) Determination of check distances in a random combination

5) Determination of objects heights

6) Determination of point distances in relation to a definable line.

7) Setting out with continuous display of distances in and offset from the trial

point to point to be set .



54

ON-SITE SET-UP

a) Place Tripod firmly into the soil and raise legs to a comfortable height . The Telescope of

the Total Station should be approximately at eye height or slightly lower. Make

allowance for the instrument height once it is attached. Take into account that multiple

people "Will be using the Total Station through the day and adjust the station height to

the eye-height of the shortest group member. The Tripod cannot be moved during a

measurement session so get it right the first time.

b) Use leg height adjustments to visually level the top surface of the Tripod. Check with the

bull's-eye level of your Brunton compass.

c) Remove Tribrach (13) from instrument by rotating the black lever on the Tribrach

counterclockwise until freed from the Tripod. Mount the Tribrach on the Tripod with

large aluminum screw. Insure you do not strip the threads.

d) Verify that the three foot-screws (1) are in a neutral position (near center). This will

allow for the greatest range of adjustments.

e) Using the three foot-screws (1), level the Tribrach (13) using the bulls eye level on the

Tribrach.

f) Mount the Total Station to the Tribrach base (13) and secure by rotating latch

clockwise.

g) Turn on the Total Station

h) Press Menu

i)

Go to Level

j) Release the Horizontal Drive gross adjustment screw (9)

k) Rotate the Total Station so that the Eyepiece of the Telescope is between two of the

three foot-screws. Using only these two foot -screws, level the instrument as indicated

on the Total Station display. (off level and level images will be inserted)

l) Rotate the Total Station one third of a turn and repeat using the next pair of foot screws.

Repeat again for the third and final combination of two foot-screws. Then repeat all

three combinations in the same order until perfectly level.

m) Press the ESC key.

n) Measure and record the instrument height using the small Indentation on the right side

of the Total Station. Set the Prism Rod to match the instrument height .

o) Have one person walk out at least 10 meters due north, the farther the better. Using a

properly declinatedBrunton compass, shoot a bearing from the Prism rod to the total



55

Station. Adjust the Prism Rod position until the bearing is due south. Rotate the Total

Station and sight the Prism. The Total Station should now be facing due north. It is

critical during this step that the Prism rod is exactly vertical and that the cross-hair in

the Total Station Optical Sight is exactly in the center of the Prism.

p) Press the Menu key, go to set Horizontal. Set the Horizontal angle to zero and press

enter. Finally, press enter once again to return to the measurement screen.

q) The Total Station is now ready to take measurements.



56

EX.NO:16

DATE :

MEASUREMENTS OF DISTANCE AND CO-ORDINATES OF GIVEN POINTS

AIM:

To measure the distances and coordinate of the given points using the total station.

APPARATUS REQUIRED:

1. Total station with tripod

2. Prism with telescopic stand

PROCEDURE:

A X

INSTRUMENT AT A:

1. Consider the station where the instruments set is A .

2. Switch on the instruments.

3. Select option level/plummet.

4. A laser point will be sighted against station A.

5. Adjusting by legs focus the red light on the station Aby adjusting the f oot screws do the final

setting.

6. After setting press OK (F4).

7. Go to menu programme.

8. Select the surveying option.

a) Press F1 and set the job.

b) Press F2 and set the station.

c) Press F3 and set the orientation. The coordinates to be entered say 5000.00 Northing,

5000.00 Easting and 100.00 Height (RL). (Arbitrary bench mark of A )

d) Press F4 and start the work .



57

TABULATION:

STATION

NO

DISTANCE

‘m’

CO-ORDINATES

HEIGHT(R.L)

‘m’

REMARK

NORTHING ‘m’ EASTING ‘m’

1

2

3

4

5

6



58

INSTRUMENT AT X:

a. Place the prism rod at the given point X.

b. Sight the telescope to the prism viewing through focusing ring and adjust to sight .the

prism with the horizontal and vertical drives for fine adjust to align cross hair in to the

centre of the prism.

c. Press F1 (Distance) after sighting the given point X.

d. Now distance will be displayed in the screen. Eg. 80.474 m.

e. Press the button page, the coordinates, and the height of the station X,will be displayed

on the screen. Eg. East: 3839.974 m, North: 5057.665 m and height 101.933m.

f. Now press, the button REC to record the details as displayed in the Item (d) and (e)

g. Repeat the steps (a) to (f) and sight the other 5 given stations and record the distance ,

coordinate and height of the locations similarly.

RESULT:

The distances and coordinate are =………………



59

Ex.No.17

DATE:

SUBTENSE BAR METHOD

AIM:

To determine the distance between the two given points.

APPARATUS REQUIRED:

1. Subtense bar and

2. Theodolite.



60

PROCEDURE:

1. Setup the subtense bar at one of the given points. Level the instrument with the help of

the bubble tube and foot screws. Let the length of the subtense bar be‘s’. 2. Keep a telescope in between the two arms of the subtense bar and locate a line which is

perpendicular to the subtense bar.

3. Along the perpendicular line, set up the theodolite at the other given point.

4. Center the instrument over that point and do the initial levelling adjustments.

5. Direct the telescope towards the marking in any one arm of the subtense bar and set the

horizontal circle in the theodolite at 0-0.

6. Rotate the theodolite in the horizontal direction till the vertical cross hair coincides

with the marking in the other arm of the subtense bar.

7. Note down the horizontal angle in the horizontal circle of the theodolite. Let it be β.8. The distance between the two points can be calculated using the formula,

D = (s * 206265)/β if β is in seconds.

D = s/ (2* tan β/2) if β is in radians.



TABULATION:

Instrument StationSubtended angle (β)

In secondsDistance (m)

CALCULATION:

S =

=

D = (S * 206265)/β

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