Theodolite Traversing Mr. Vedprakash Maralapalle, Asst. Professor Department: B.E. Civil Engineering Subject: Surveying – I Semester: III eCourseware@AIKTC Teaching Aids Service by KRRC Information Section

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

USES OF THEODOLITE Measuring horizontal and vertical angles Locating points on a line Prolonging survey lines Finding difference of level Setting out grades Ranging curves Tachometric Survey Magnetic bearing (W.C.B.) measurement

DEFINITION Centring: The process of setting about the theodolite exactly over the station mark is known as centring. Transiting: The process of turning the telescope about its horizontal axis in a vertical plane through 180ᵒ is termed as transiting. 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. 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

Changing face: It is an operation of bringing the face of the telescope form left to right and vice versa. Swinging the telescope: It is the process of turning the telescope in horizontal plane. Line of collimation: It is an imaginary line passing through the intersection of the cross hairs at the diaphragm and the optical centre of the object glass and its continuation.

Parts of theodolite

TEMPORARY ADJUSTMENT OF THEODOLITE Such adjustments involve the following steps Setting up Centring Levelling up Focusing the eye-piece Focussing the object glass Elimination of parallax

MEASURING HORIZONTAL ANGLE Set up the theodolite at station point O and level it accurately. Set the vernier A to the zero of the horizontal circle. Tighten the upper clamp. Loosen the lower clamp. Turn the instrument and direct the telescope towards A to bisect it accurately with the use of tangent screw. After bisecting accurately check the reading which must still read zero. Read the vernier B and record both the readings. 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.

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. Change the face of the instrument and repeat the whole process. 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.

There are two methods of measuring horizontal angles. Repetition method Reiteration method This method is used for very accurate work. In this 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 no. of repetitions. The No. 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 measured to a finer degree of accuracy than that obtainable with the least count of the vernier.

- Set up the theodolite at starting point O and level it accurately. Vernier A is set to 0° and vernier B to 180° The upper clamp is fix and lower one loosen . By turning the telescope ranging rod at A is bisected. With the help of lower clamp screw and lower tangent screw. Here initial reading on vernier A is 0° The upper clamp is loosen and telescope is turn clockwise to ranging rod at B. the upper clamped is clamped. Suppose the reading on vernier A is 30°. The lower clamped is loosen and the telescope turned anticlockwise to exactly bisect the ranging rod at A. here the initial reading is 30° for second observation.

The lower clamp is tightened the upper one is loosened and the telescope is turned clockwise to exactly bisect the ranging rod at B let the reading on vernier A is 60° The initial reading for third observation is set to 60° <AOB is again measured . Let the final reading on the vernier A is 90° which is the accumulated angle 90°/3 = 30° The face of the instrument is changed and previous procedure is followed. The mean of the two observation gives the actual angle <AOB

Reiteration method This method is comparatively less tedious method of measuring the horizontal angles. It is generally preferred when several angles are to be measured at one particular station. 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 be same as its initial reading.

Theodolite is perfectly centered over O and levelled properly in the usual manner . Vernier A is set to 0° and vernier B to 180° the upper clamped is fixed and lower is loosened. The ranging rod at A is perfectly bisected. Now the lower clamp is tighten. The upper clamped is loosened and the ranging rod or object at B is bisected properly by turning the telescope clockwise. The reading on the both vernier are taken. < AOB is noted. Similarly the object C is bisected properly and the reading on the vernier are noted <BOC is recorded.

Now the horizon is closed i. e. the last angle < COA is measured Now the horizon is closed i.e. the last angle < COA is measured. The position of the leading vernier is noted. The leading vernier should show the initial reading on which it was set. If does not the amount of discrepancy is noted . If it is small The error is distributed among the angles. If the discrepancy large, the observation should be taken again.

MEASURING VERTICAL ANGLE Set up the theodolite at station point O and level it accurately. Set the zero of vertical vernier exactly to the zero of the vertical circle. At this position the line of collimation is exactly horizontal. To measure angle of elevation the telescope is raised slowly to bisect the point A accurately . The reading on the both vernier are noted and the angle of elevation recorded.

The face of the instrument is changed and point A is again bisected The face of the instrument is changed and point A is again bisected. The reading on the vernier are noted. The mean of the angels of the observed is assume to be the correct angle of elevation. To measure the angle of depression the telescope is lowered slowly and the point B is bisected. The reading on the vernier is noted for the two observations . The mean angle of observation is taken to be correct angle of depression.

Closing Error In closed traverse the algebraic sum of latitude & Departure must be equal to zero. But due to the error in field measurement of angles and length , 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 knows as closing error.

Balancing of traverse In case of traverse the algebraic sum of latitude & departure must be equal to zero. In other words the sum of northing must be equal to zero in ideal condition. But the actual practice some closing error is always found to exist while computing the latitude and departure of the traverse stations. Total error in latitude and departure are determined. These error are then distributed among the traverse station.

Bowditch rule:- Correction to latitude of any side = length of that side / perimeter of traverse X total error in latitude. Correction to departure of any side = length of that side / perimeter of traverse X total error in departure. Transit rule: Correction of latitude of any side = latitude of that side / arithmetical sum of all latitudes X total error in latitude. Correction to departure of any side = Departure of that side / arithmetical sum of all Departure X total error in departure

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

References Surveying and Levelling: Vol-I and II: Kanetkar and Kulkarni, Pune Vidyarthi Griha, Pune. Surveying and Levelling: N N Basak, Tata McGraw Hill, New Delhi. Surveying: R. Agor, Khanna Publishers. Surveying: Vol-I: Dr K.R. Arora, Standard Book House. http://nptel.iitm.ac.in/courses-contents/IIT Kanpur and IIT Madras. http://www.slideshare.net www.scribd.com Google images.

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