Theodolite Surveying * Computation of Area * Setting out of Works

Home , Surveying, Theodolite, Vernier scale

S. N. PATEL INSTITUTE OF TECHNOLOGY & RESEARCH CENTRE, Umrakh (A Vidyabharti Trust Institution)

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

By: Prof. H. A. Rathod Civil Engineering Department SNPIT & RC, UMRAKH

THEODOLITE SURVEYING

By: Prof. H. A. Rathod Civil Engineering Department SNPIT & RC, UMRAKH

| This work is licensed under the creative commons attribution-noncommercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to creative commons, PO box 1866, Mountain View, CA 94042, USA. 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 SURVEYING  Surveying or land surveying is the technique, profession, and science of determining the terrestrial or three-dimensional position of points and the distances and angles between them.  Examine and record the area and features of an area of land so as to construct a map, plan, or description.

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

The Theodolite is a most accurate surveying instrument 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 • Non-Transit type • The telescope can be transited • The telescope cannot be i.e. revolved through a transited. ○ complete revolution (180 ) • The position of theodolite can about its horizontal axis in the not be changed from face left vertical plane. to face right. • The position of theodolite can • Ranging of line can not be be changed from face left to done by back sighting. face right. • Deflection angles can not be • Ranging of line can be done by measured easily. back sighting. • These are now become • Deflection angles can be obsolete. measured easily. • These are widely used in surveying. B. Based on arrangement to measure angles: i) Vernier Theodolite ii) Micrometer Theodolite iii) Electronic Theodolite

 Vernier Theodolite: For reading the graduated circle if Vernier are used, the theodolite is 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 is called as a Micrometer Theodolite. It can measure an angle up-to 1”.  Electronic Theodolite: In Electronic Theodolite, the readings of angle is obtained in digital form. When EDM instrument is attached with Electronic Theodolite it becomes Total Station. SIZE OF THEODOLITE

. A theodolite is designated by diameter of the graduated circle on the lower plate. . The common sizes are 8cm to 12 cm while 14 cm to 25 cm instrument are used for triangulation work. . Greater accuracy is achieved with larger theodolites as they have bigger graduated circle with larger divisions hence used where the survey works require high degree of accuracy.

TYPE OF THEODOLITE TRANSIT VERNIER THEODOLITE

DESCRIPTION OF TRANSIT VERNIER THEODOLITE Transit vernier theodolite essentially consist of the following 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 axis 2. Horizontal axis OR trunion axis 3. Line of collimation OR Line of sight 4. Axis of plate level 5. Axis of altitude level

THEIR RELATIONSHIP a. 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 an instrument station so that its vertical axis lies immediately above the station mark. 2. Transiting: Transiting is also known as plunging or reversing. It is the process of turning the telescope about its horizontal axis through 1800 in the vertical plane. 3. Swinging the telescope: It means turning the telescope about its vertical axis in the horizontal plane. A swing is called right or left according as the telescope is rotated clockwise or counter clockwise. 4. Face Left: If the vertical circle of the instrument is on the left side of the observer while taking a reading ,the position is called the face left; and the observation taken on the horizontal or vertical circle in this position, is known as the face left observation. 5. Face Right: If the vertical circle of the instrument is on the right side of the observer while taking a reading ,the position is called the face right; and the observation taken on the horizontal or vertical circle in this position, is known as the face right observation. 6. Changing Face: It is the operation of bringing the vertical circle to the right of the observer ,if originally it is to the left , and vice – versa. 7. Axis of the Level Tube / Bubble Line: It is a straight line tangential to the longitudinal curve of the level tube at the center of the tube. It is horizontal when the bubble is in the center. 8. Vertical Axis: It is the axis about which the telescope can be rotated in the horizontal plane. 9. Horizontal Axis / Trunnion Axis: It is the axis about which the telescope can be rotated in the vertical plane. 10. Line of Collimation (LOC) / Line Of Sight (LOS): It is an imaginary line joining the intersection of the cross- hairs of the diaphragm to the optical center of the object- glass and its continuation.

DIAPHRAGM LINE OF COLLIMATION

TELESCOPE

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

OBJECT GLASS

AXIS OF THE TELESCOPE .

TELESCOPE

ADJUSTMENT OF A THEODOLITE

The adjustments of a theodolite are of two kinds :- 1. Permanent Adjustments. 2. Temporary Adjustments.

1) Permanent adjustments: The permanent adjustments are made to establish the relationship between the fundamental lines of the theodolite and , once made , they last for a long time. They are essential for the accuracy of observations. 1) Permanent adjustments: The permanent adjustments are made to establish the relationship between the fundamental lines of the theodolite and , once made , they last for a long time. They are essential for the accuracy of observations. The permanent adjustments in case of a transit theodolites are :- . Adjustment of Horizontal Plate Levels. The axis of the plate levels must be perpendicular to the vertical axis. . Horizontal axis adjustment. The horizontal axis must be perpendicular to the vertical axis. . Collimation Adjustment. The line of collimation should coincide with the axis of the telescope and the axis of the objective slide and should be at right angles to the horizontal axis. . Adjustment of Telescope Level or the Altitude Level Plate Levels. The axis of the telescope levels or the altitude level must be parallel to the line of collimation. . Vertical Circle Index Adjustment. The vertical circle vernier must read zero when the line of collimation is horizontal.

2) Temporary Adjustment The temporary adjustments are made at each set up of the instrument before we start taking observations with the instrument. There are three temporary adjustments of a theodolite:- i) 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:- A B 1. Set up the theodolite at station point O and level it accurately. 2. Set the vernier A to the zero of the horizontal circle. Tighten the upper clamp. 3. Loosen the lower clamp. Turn the instrument and direct the telescope towards A to bisect it accurately with the use of tangent screw. After o bisecting accurately check the reading which HORIZONTAL ANGLE must still read zero. Read the vernier B and AOB record both the readings. 4. Loosen the upper clamp and turn the telescope clockwise until line of sight bisects point B on the right hand side. Then tighten the upper clamp and bisect it accurately by turning its tangent screw. 5. Read both vernier. The reading of the vernier A which was initially set at zero gives the value of the angle AOB directly and that of the other vernier B by deducting 1800 .The mean of the two vernier readings gives the value of the required angle AOB. 6. Change the face of the instrument and repeat the whole process. The mean of the two vernier readings gives the second value of the angle AOB which should be approximately or exactly equal to the previous value. 7. The mean of the two values of the angle AOB ,one with face left and the other with face right, gives the required angle free from all instrumental errors. 2. Repetition Method: To measure horizontal angle AOB:-

. This method is used for very accurate work. In this A B method, the same angle is added several times mechanically and the correct value of the angle is obtained by dividing the accumulated reading by the number of repetitions. . The number of repetitions made usually in this method is six, three with the face left and three with the face right. In this way, angles can be o measured to a finer degree of accuracy than that obtainable with the least count of the vernier. 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 the object (A) is sighted again. Bisect B accurately by using the upper tangent screw. The vernier will now read the twice the value of the angle now. 4) Repeat the process until the angle is repeated the required number of times (usually 3). Read again both vernier . The final reading after n repetitions should be approximately n X (angle). Divide the sum by the number of repetitions and the result thus obtained gives the correct value of the angle AOB. 5) Change the face of the instrument. Repeat exactly in the same manner and find another value of the angle AOB. The average of two readings gives the required precise value of the angle AOB. 3. Reiteration Method: A . This method is another precise and B comparatively less tedious method of measuring the horizontal angles. . It is generally preferred when several angles are to be measured at a o particular station. D . This method consists in measuring several angles successively and finally closing the horizon at the starting point. The final reading of the vernier A should C be same as its initial reading. If not, the Reiteration Method discrepancy is equally distributed among all the measured angles. Procedure: 1) Suppose it is required to measure the angles AOB, BOC and COD. Then to 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 referring object. Bisect it accurately and check the reading of vernier as 0. Loosen the lower clamp and turn the telescope clockwise to sight point B exactly. Read the vernier again and the mean reading will give the value of angle AOB. 4) Similarly bisect C & D successively. 5) Finally, close the horizon by sighting the object A again. The vernier A should now read zero degree. If it does not, note down the reading and find the total error in closing the horizon and distribute it equally among all the angles respectively. 6) Now change the face and repeat the whole procedure to obtain the individual angle in anticlockwise direction. 7) Determine the final value of each angle by taking average of the value obtained by face left and face right. MEASUREMENT OF VERTICAL ANGLES: A vertical angle is an angle between the inclined line of sight and the horizontal line. It may be an angle of elevation or depression according as the object is above or below the horizontal plane. A A AOB= α+ β B α AOB= α - β α HORI. β HORI. LINE O O LINE O HORI. LINE β β Fig. b α Fig. c Fig.a B B VERTICAL ANGLE A  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 with reference to the altitude bubble. 2. Set the zero of vertical vernier exactly to the zero of the vertical circle clamp and tangent screw. 3. Bring the bubble of the altitude level in the central position by using clip screw. The line of sight is thus made horizontal and vernier still reads zero. 4. Loosen the vertical circle clamp screw and direct the telescope towards the 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 vernier readings gives the value of the required angle. 6. Change the face of the instrument and repeat the process. The mean of the two vernier readings gives the second value of the required angle. 7. The average of the two values of the angles thus obtained, is the required value of the angle free from instrumental errors. READING MAGNETIC BEARING OF A LINE

To find the bearing of a line AB as shown in fig. : N 1. Set up the instrument over A and level it accurately. B 2. Set the vernier to the zero of the horizontal circle. 3. Release the magnetic needle and loosen the lower clamp. A 4. Rotate the instrument till magnetic needle points to North.

5. Now clamp the lower clamp with the help of lower Fig. tangent screw. Bring the needle exactly against the Magnetic mark in order to bring it in magnetic meridian. At Bearing this stage the line of sight will also be in magnetic of a Line meridian. 6. Now loose the upper clamp and point the telescope towards B. With the help of upper tangent screw, bisect B accurately and read both the vernier. The mean of the two readings will be recorded as magnetic bearing of line. 7. Change the face of the instrument for accurate magnetic bearing of the line 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: As shown in the fig. below

A B C D Z

C ’ D’

(3) Double reversing Method: As shown in the fig. below

C1 D 1

A B C D Z

C2 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 Traversing Included Angle Method

. In this method, the magnetic bearing of any line is measured with theodolite. All the included angles are also measured. The bearing of all other lines are determined from the bearing of the initial line and included angles. . If traversing is done in anti-clockwise direction, interior angles are measured. And if traversing is done in clockwise direction exterior angles are measured. . The following procedure is adopted for traversing in anti-clockwise direction. 1. Select survey stations P, Q, R.... and insert peg at each station in to the ground. 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 telescope clockwise and take a foresight to station Q. The vernier reading will give interior angle TPQ. 5. Similarly set the theodolite on station Q, R, S... and measure included angles PQR, QRS, RST. 6. Using measured included angles and the bearing of line PQ, find the bearings of the other lines. 7. Measure the length of survey lines PQ, QR, RS... one in front direction and then in reverse direction. 8. Record the details of objects on each side of the survey lines by taking offsets. 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 closed traverse. The distance by which a traverse fails to close is known as closing error OR error of closure. . Relative error of closure = Closing error (e) / Perimeter of traverse (p) Latitude & Departure

-0.16 -0.55

Balancing the Traverse Transit Rule

Balancing the Traverse Bowditch’s Rule / Compass Rule

Omitted Measurements I. 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

S. N. PATEL INSTITUTE OF TECHNOLOGY & RESEARCH CENTRE, Umrakh (A Vidyabharti Trust Institution)

AREA

By: Prof. H. A. Rathod Civil Engineering Department SNPIT & RC, UMRAKH

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 to anchor the instrument at a desired point on the plan. • Anchor arm: It is a bar with one end attached to anchor block and the other connected to an integrating unit. Its arm length is generally fixed but some planimeter are provided with variable arms length also. • Tracing arm: It is a bar carrying a tracer point at one end connected to the integrating unit at the other end. The anchor arm and tracer arms are connected by a hinge. The length of this arm can be varied by means of 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 of roller coincides with the axis of tracer arm hence it rolls only at right angles to the tracer arm. The roller carries a concentric drum which has 100 divisions and is provided with a vernier to read tenth of roller division. A suitable gear system moves a pointer on disc by one division for every one revolution of the roller. Since the disc is provided with 10 such equal divisions, the reading on the integrating unit has four digits:

(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 constant F = Final reading I = 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=MC S. N. PATEL INSTITUTE OF TECHNOLOGY & RESEARCH CENTRE, Umrakh (A Vidyabharti Trust Institution)

SETTING OUT OF WORK

By: Prof. H. A. Rathod Civil Engineering Department SNPIT & RC, UMRAKH