essential notes on: * theodolite surveying ......essential notes on: * theodolite surveying *...

ESSENTIAL NOTES ON:* Theodolite Surveying* Computation of Area* Setting out of works

By:Prof. H. A. Rathod

Civil Engineering DepartmentSNPIT & RC, UMRAKH

S. N. PATEL INSTITUTE OF TECHNOLOGY &

RESEARCH CENTRE, Umrakh(A Vidyabharti Trust Institution)

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THEODOLITE SURVEYING






Contents

• Definition & Introduction to SURVEYING

• Introduction to theodolite

• Uses / Purpose of theodolite

• Classification of theodolite

• Components / Description of theodolite with sketch

• Terminologies / Definition

• Setting up the theodolite (Temporary Adjustment)

• Measuring Horizontal Angle with theodolite

i. General Method

ii. Repetition Method

iii. Reiteration Method

• Measuring Vertical Angle with theodolite

• Measuring Deflection Angle with theodolite

• Measuring Direct Angle with theodolite

• Measuring Magnetic Bearing with theodolite

• Prolongation of line with theodolite

i. Fore sight method

ii. Back Sight Method, and

iii. Double reversing Method

• Errors in theodolite

i. Instrumental

ii. Personal, and

iii. Natural

• Theodolite Traversing

i. Fast Angle (OR Magnetic Bearing)

ii. Loose Needle Method

iii. Included Angle Method

iv. Direct Angle Method

v. Deflection Angle Method

• Closing Error

• Latitude & Departure

• Balancing the Traverse

i. Bowditch’s Rule

ii. Transit Rule

• Gale’s Traverse Table

• Omitted Measurements

THEODOLITE SURVEYING

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

SURVEYING

Surveying or land surveying is the technique, profession, andscience of determining the terrestrial or three-dimensionalposition of points and the distances and angles between them.

Examine and record the area and features of an area of land soas to construct a map, plan, or description.

The Theodolite is a most accurate surveyinginstrument mainly used for: (Uses of theodolite)

Measuring horizontal and vertical angles.

Locating points on a line.

Prolonging survey lines.

Finding difference of level.

Establishing grades.

Setting out curves.

Measure height & depths.

Measure distance.

Alignment of various civil works.

Measure slope. & etc.

CLASSIFICATION OF THEODOLITES

Theodolites may be classified as ;

A. Based on movement of telescope:

i) Transit Theodolite

ii) Non Transit Theodolite

• Transit Theodolite

• The telescope can be transitedi.e. revolved through acomplete revolution (180○)about its horizontal axis in thevertical plane.

• The position of theodolite canbe changed from face left toface right.

• Ranging of line can be done byback sighting.

• Deflection angles can bemeasured easily.

• These are widely used insurveying.

•Non-Transit type

• The telescope cannot betransited.

• The position of theodolite cannot be changed from face leftto face right.

• Ranging of line can not bedone by back sighting.

• Deflection angles can not bemeasured easily.

• These are now becomeobsolete.

Vernier Theodolite:

For reading the graduated circle if Vernier are used, the theodoliteis called as a Vernier Theodolite. It can measure an angle up-to 20”.This theodolites are commonly used.

Micrometer Theodolite:

If Micrometer is provided to read the graduated circle then it iscalled as a Micrometer Theodolite. It can measure an angle up-to1”.

Electronic Theodolite:

In Electronic Theodolite, the readings of angle is obtained in digitalform. When EDM instrument is attached with Electronic Theodoliteit becomes Total Station.

B. Based on arrangement to measure angles:

i) Vernier Theodolite

ii) Micrometer Theodolite

iii) Electronic Theodolite

SIZE OF THEODOLITE

A theodolite is designated by diameter of the graduatedcircle on the lower plate.

The common sizes are 8cm to 12 cm while 14 cm to 25 cminstrument are used for triangulation work.

Greater accuracy is achieved with larger theodolites as theyhave bigger graduated circle with larger divisions henceused where the survey works require high degree ofaccuracy.

TYPE OF THEODOLITE

TRANSIT VERNIER THEODOLITE

DESCRIPTION OF TRANSIT VERNIER THEODOLITE

Transit vernier theodolite essentially consist of thefollowing essential parts:

• Telescope

• Vertical circle

• A-Frame

• Levelling Head

• Two spindles OR Axes

• Lower Circular Plate

• Upper Plate

• Upper & Lower clamp screw

• Upper & Lower tangential screw

• Plumb –bob

• Tripod Stand

• Vernier Scale

• Shifting head

• Clip screw

• Level tubes OR Plate levels

• Altitude level tube

FUNDAMENTAL AXES OF THEODOLITE & THEIR RELATIONSHIP

FUNDAMENTAL AXES / LINES OF THEODOLITE :1. Vertical axis2. Horizontal axis OR trunion axis3. Line of collimation OR Line of sight4. Axis of plate level5. Axis of altitude level

THEIR RELATIONSHIPa. The axis of the plate level must lie in a plane perpendicular to the

vertical axis.b. The line of collimation must be perpendicular to the horizontal axis.

Vertical axis, Horizontal axis and Line of collimation must intersect at a point.

c. The Horizontal axis must be perpendicular to the Vertical axis.d. The Axis of altitude level must be parallel to the line of collimation.

TERMS USED IN TRANSIT VERNIER THEODOLITE

1. Centering: Centering means setting the theodolite exactly over aninstrument station so that its vertical axis lies immediately above thestation mark.

2. Transiting: Transiting is also known as plunging or reversing. It is theprocess of turning the telescope about its horizontal axis through1800 in the vertical plane.

3. Swinging the telescope: It means turning the telescope about itsvertical axis in the horizontal plane. A swing is called right or leftaccording as the telescope is rotated clockwise or counter clockwise.

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

5. Face Right: If the vertical circle of the instrument is on the right sideof the observer while taking a reading ,the position is called the faceright; and the observation taken on the horizontal or vertical circle inthis position, is known as the face right observation.

6. Changing Face: It is the operation of bringing the vertical circle to theright of the observer ,if originally it is to the left , and vice – versa.

7. Axis of the Level Tube / Bubble Line: It is a straight line tangential tothe longitudinal curve of the level tube at the center of the tube. Itis horizontal when the bubble is in the center.

8. Vertical Axis: It is the axis about which the telescope can be rotatedin the horizontal plane.

9. Horizontal Axis / Trunnion Axis: It is the axis about which thetelescope can be rotated in the vertical plane.

10. Line of Collimation (LOC) / Line Of Sight (LOS): It is an imaginaryline joining the intersection of the cross- hairs of the diaphragmto the optical center of the object- glass and its continuation.

11. Axis Of The Telescope: It is also known an imaginary line joiningthe optical center of the object- glass to the center of eye piece.

LINE OF COLLIMATION

DIAPHRAGM

TELESCOPE

AXIS OF THE TELESCOPE

TELESCOPE

OBJECT GLASS

.

ADJUSTMENT OF A THEODOLITE

The adjustments of a theodolite are of two kinds :-

1. Permanent Adjustments.

2. Temporary Adjustments.

1) Permanent adjustments: The permanent adjustments are madeto establish the relationship between the fundamental lines of thetheodolite and , once made , they last for a long time. They areessential for the accuracy of observations.

1) Permanent adjustments:

The permanent adjustments are made to establish the relationshipbetween the fundamental lines of the theodolite and , once made ,they last for a long time. They are essential for the accuracy ofobservations.

The permanent adjustments in case of a transit theodolites are :-

Adjustment of Horizontal Plate Levels. The axis of the plate levelsmust be perpendicular to the vertical axis.

Horizontal axis adjustment. The horizontal axis must beperpendicular to the vertical axis.

Collimation Adjustment. The line of collimation should coincidewith the axis of the telescope and the axis of the objective slideand should be at right angles to the horizontal axis.

Adjustment of Telescope Level or the Altitude Level Plate Levels.The axis of the telescope levels or the altitude level must beparallel to the line of collimation.

Vertical Circle Index Adjustment. The vertical circle vernier mustread zero when the line of collimation is horizontal.

2) Temporary Adjustment

The temporary adjustments are made at each set up of theinstrument before we start taking observations with theinstrument.

There are three temporary adjustments of a theodolite:-

i) Setting up and Centering

ii) Levelling

iii) Elimination of parallax

MEASUREMENT OF HORIZONTAL ANGLES:

There are three methods of measuring horizontal angles:-

i) Ordinary Method.

ii) Repetition Method.

iii) Reiteration Method.

1. Ordinary Method:To measure horizontal angle AOB:-

1. Set up the theodolite at station point O and levelit accurately.

2. Set the vernier A to the zero of the horizontalcircle. Tighten the upper clamp.

3. Loosen the lower clamp. Turn the instrument anddirect the telescope towards A to bisect itaccurately with the use of tangent screw. Afterbisecting accurately check the reading whichmust still read zero. Read the vernier B andrecord both the readings.

o

A B

HORIZONTAL ANGLE

AOB

4. Loosen the upper clamp and turn the telescope clockwise until line ofsight bisects point B on the right hand side. Then tighten the upperclamp and bisect it accurately by turning its tangent screw.

5. Read both vernier. The reading of the vernier A which was initially set atzero gives the value of the angle AOB directly and that of the othervernier B by deducting 1800 .The mean of the two vernier readings givesthe value of the required angle AOB.

6. Change the face of the instrument and repeat the whole process. Themean of the two vernier readings gives the second value of the angleAOB which should be approximately or exactly equal to the previousvalue.

7. The mean of the two values of the angle AOB ,one with face left and theother with face right, gives the required angle free from all instrumentalerrors.

This method is used for very accurate work. In thismethod, the same angle is added several timesmechanically and the correct value of the angle isobtained by dividing the accumulated reading bythe number of repetitions.

The number of repetitions made usually in thismethod is six, three with the face left and threewith the face right. In this way, angles can bemeasured to a finer degree of accuracy than thatobtainable with the least count of the vernier.

o

A B

HORIZONTAL ANGLE

AOB

2. Repetition Method:To measure horizontal angle AOB:-

To measure horizontal angle by repetitions:-

1) Set up the theodolite at starting point O and level it accurately.

2) Measure The horizontal angle AOB.

3) Loosen the lower clamp and turn the telescope clock – wise until theobject (A) is sighted again. Bisect B accurately by using the uppertangent screw. The vernier will now read the twice the value of theangle now.

4) Repeat the process until the angle is repeated the required number oftimes (usually 3). Read again both vernier . The final reading after nrepetitions should be approximately n X (angle). Divide the sum by thenumber of repetitions and the result thus obtained gives the correctvalue of the angle AOB.

5) Change the face of the instrument. Repeat exactly in the same mannerand find another value of the angle AOB. The average of two readingsgives the required precise value of the angle AOB.

3. Reiteration Method:

o

AB

Reiteration Method

C

D

This method is another precise andcomparatively less tedious method ofmeasuring the horizontal angles.

It is generally preferred when severalangles are to be measured at aparticular station.

This method consists in measuringseveral angles successively and finallyclosing the horizon at the starting point.The final reading of the vernier A shouldbe same as its initial reading. If not, thediscrepancy is equally distributedamong all the measured angles.

Procedure:

1) Suppose it is required to measure the angles AOB, BOC and COD. Thento measure these angles by repetition method :

2) Set up the instrument over station point O and level it accurately.

3) Direct the telescope towards point A which is known as referringobject. Bisect it accurately and check the reading of vernier as 0.Loosen the lower clamp and turn the telescope clockwise to sightpoint B exactly. Read the vernier again and the mean reading will givethe value of angle AOB.

4) Similarly bisect C & D successively.

5) Finally, close the horizon by sighting the object A again. The vernier Ashould now read zero degree. If it does not, note down the readingand find the total error in closing the horizon and distribute it equallyamong all the angles respectively.

6) Now change the face and repeat the whole procedure to obtain theindividual angle in anticlockwise direction.

7) Determine the final value of each angle by taking average of the valueobtained by face left and face right.

MEASUREMENT OF VERTICAL ANGLES:

A vertical angle is an angle between the inclined line of sight and thehorizontal line. It may be an angle of elevation or depressionaccording as the object is above or below the horizontal plane.

A

B

O O

A

B

A

B

OHORI. LINE

HORI.

LINE

β

HORI. LINE

VERTICAL ANGLEFig.a

Fig. b Fig. c

AOB= α+

βAOB= α - β

β

β

αα

α

To Measure the Vertical Angle of an object A at a station O:

1. Set up the theodolite at station point O and level it accurately withreference to the altitude bubble.

2. Set the zero of vertical vernier exactly to the zero of the vertical circleclamp and tangent screw.

3. Bring the bubble of the altitude level in the central position by using clipscrew. The line of sight is thus made horizontal and vernier still readszero.

4. Loosen the vertical circle clamp screw and direct the telescope towardsthe object A and sight it exactly by using the vertical circle tangent screw.

5. Read both vernier on the vertical circle. The mean of the two vernierreadings gives the value of the required angle.

6. Change the face of the instrument and repeat the process. The mean ofthe two vernier readings gives the second value of the required angle.

7. The average of the two values of the angles thus obtained, is therequired value of the angle free from instrumental errors.

READING MAGNETIC BEARING OF A LINE

N

A

B

Fig.

Magnetic

Bearing

of a Line

To find the bearing of a line AB as shown in fig. :

1. Set up the instrument over A and level it accurately.

2. Set the vernier to the zero of the horizontal circle.

3. Release the magnetic needle and loosen the lowerclamp.

4. Rotate the instrument till magnetic needle points toNorth.

5. Now clamp the lower clamp with the help of lowertangent screw. Bring the needle exactly against themark in order to bring it in magnetic meridian. Atthis stage the line of sight will also be in magneticmeridian.

6. Now loose the upper clamp and point the telescope towards B. With thehelp of upper tangent screw, bisect B accurately and read both thevernier. The mean of the two readings will be recorded as magneticbearing of line.

7. Change the face of the instrument for accurate magnetic bearing of theline and repeat.

8. The mean of the two values will give the correct bearing of the line AB.

PROLONGING A STRAIGHT LINE

There are three methods of prolonging a given line such as AB

(1) Fore sight method,

(2) Back Sight Method, and

(3) Double reversing Method

(1) Fore sight method:

As shown in the fig. below

A B C D Z

(2) Back Sight Method:


A B C D Z

C

’ D’

(3) Double reversing Method:


A B C D Z

C1

C2

D

1

D2

ERRORS IN THEODOLITE

A. INSTRUMENTAL

Imperfect level of plate level,

LOC not perpendicular to horizontal axis,

Horizontal axis not perpendicular to vertical axis,

LOC & axis of telescope not parallel,

Eccentricity of inner & outer axis,

Imperfect graduation,

Eccentricity of vernier.

B. PERSONAL

Errors in Manipulation

Inaccurate centering,

Inaccurate leveling,

Slip,

Wrong tangent screw.

Errors in Sighting & Reading

Inaccurate sighting,

Ranging rod is not vertical,

Parallax.

C. NATURAL

Unequal expansion due to temperature change,

Atmospheric refraction due to high temperature,

Strong winds,

Unequal settlement.

Theodolite TraversingIncluded Angle Method

In this method, the magnetic bearing of any line is measured withtheodolite. All the included angles are also measured. The bearing of allother lines are determined from the bearing of the initial line and includedangles.

If traversing is done in anti-clockwise direction, interior angles aremeasured. And if traversing is done in clockwise direction exterior anglesare measured.

The following procedure is adopted for traversing in anti-clockwisedirection.

1. Select survey stations P, Q, R.... and insert peg at each station in to theground.

2. Set up the instrument over the station P and level it.3. Orient the telescope in the magnetic meridian and determine the bearing

of the initial line PQ.4. Set the vernier A to zero using the upper clamp and tangent screws. Take a

back sight on station T. Loosen the upper plate. Turn the telescopeclockwise and take a foresight to station Q. The vernier reading will giveinterior angle TPQ.

5. Similarly set the theodolite on station Q, R, S... and measure includedangles PQR, QRS, RST.

6. Using measured included angles and the bearing of line PQ, find thebearings of the other lines.

7. Measure the length of survey lines PQ, QR, RS... one in front direction andthen in reverse direction.

8. Record the details of objects on each side of the survey lines by takingoffsets.

Closing Error Due to the errors in field measurements of angles and lengths, sometimes

the finishing point may not coincide with the starting point of a closedtraverse. The distance by which a traverse fails to close is known as closingerror OR error of closure.

Relative error of closure = Closing error (e) / Perimeter of traverse (p)

Latitude & Departure

-0.16 -0.55

Balancing the TraverseTransit Rule

Balancing the TraverseBowditch’s Rule / Compass Rule

Omitted MeasurementsI. Length / Bearing / Length & Bearing of a line omitted.

II. Length of one line & Bearing of adjacent line omitted.

III. Length of two adjacent line omitted.

IV. Bearing of two adjacent line omitted.

Case 2

AREA






4. Simpson’s One Third Rule

PLANIMETER

The essential parts of a planimeter are:

• Anchor: It is a heavy block with a fine anchor pin at its base. It is used toanchor the instrument at a desired point on the plan.

• Anchor arm: It is a bar with one end attached to anchor block and theother connected to an integrating unit. Its arm length is generally fixedbut some planimeter are provided with variable arms length also.

• Tracing arm: It is a bar carrying a tracer point at one end connected tothe integrating unit at the other end. The anchor arm and tracer armsare connected by a hinge. The length of this arm can be varied by meansof fixed screw and slow motion screw.

• Tracing point: This is a needle point connected to the end of tracer arm,which is to be moved over the out line of the area to be measured.

• Integrating unit: It consists of a hard steel roller and a disc. The axis ofroller coincides with the axis of tracer arm hence it rolls only at rightangles to the tracer arm. The roller carries a concentric drum which has100 divisions and is provided with a vernier to read tenth ofroller division. A suitable gear system moves a pointer on disc by onedivision for every one revolution of the roller. Since the disc is providedwith 10 such equal divisions, the reading on the integrating unit has fourdigits:

(i) Unit read on the disc(ii) Tenth and hundredth of a unit read on the roller(iii) Thousandth read on the vernier.

• Thus if reading on disc is 2, reading on roller is 42 and vernier reads 6,then the total reading F = 2.426

• Area = M (F – I + 10 N + C)

where,

M = A multiplying constantF = Final readingI = Initial reading.N = The number of completed revolutions of disc. Plus sign to be used if the zero mark of the dial passes index mark in clockwise direction and minus sign if it passes in anticlockwise direction.C = Constant of the instrument, which when multiplied with M, gives the area of zero circle.The constant C is added only when the anchor point is inside the area.

Multiplying constant M and C are normally written on the planimeter.

ZERO CIRCLE IN PLANIMETER

A=MC

SETTING OUT OF WORK






essential notes on: * theodolite surveying ......essential notes on: * theodolite surveying *...

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