SURVEYING USING THEODOLITE, Essays (university) of Survey Sampling Techniques

PROCEDURE,CALCULATION,ADVANTAGES AND DISADVANTAGES OF USING THEODOLITE

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2019/2020

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Measurement of Direction using Theodolite
The different ways by which the direction of a line is depicted in surveyig are computed either
from horizontal angles or from vertical angles or both. Thus, primary elements of observation
during surveying are the horizontal angles and the vertical angles . These quantities can be
observed directly in the field using theodolite.
Measurement of Horizontal Angle (Figure 22.1)
To represent the direction of a line, the horizontal angle of the line from a reference line is to be
measured. The steps required to be adopted are as follows:
1. Two points one on each of the lines, say P and Q, are to be marked.
2. A transit theodolite is to be set at the point of intersection of the lines, say at O. Initially,
the instrument is in the face left condition and its temporary adjustment is to be done
over the point O.
3. Both the lower and upper plate main screws are to released and get the vernier A set to
0° (or 360°) mark on the main scale. After clamping the upper main screw, index of
vernier A is to be brought exactly to the zero of the main scale using the upper plate
tangent screw.
4. At this stage the reading of the vernier B should be 180°.
5. Swing the telescope in the horizontal plane and point it to the left station, say P. Tighten
the lower plate clamp screw, and bisect the signal at P exactly using the lower plate
tangent screw. Record the readings in the form of Table 22.1.
6. Loosen the upper plate main screw and turn the telescope the signal at Q is sighted.
Tighten the upper clamp screw and bisect the ranging pole at Q exactly using the upper
plate tangent screw.
7. Read both the verniers A and B and record the readings. The reading of the vernier A is
the angle POQ. The vernier B gives the value of angle POQ after deducting from it 180°.
The mean of two values of the angles obtained from the verniers A and B is the required
angle P'O'Q'.
8. Change the face of the instrument to the face right by transiting the telescope and
swinging it by 180°.
9. Repeat steps 3 to 8 and determine another value of the angle P'O'Q'.
10. The mean of the face left and face right observations is the final required angle P'O'Q'
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Measurement of Direction using Theodolite The different ways by which the direction of a line is depicted in surveyig are computed either from horizontal angles or from vertical angles or both. Thus, primary elements of observation during surveying are the horizontal angles and the vertical angles. These quantities can be observed directly in the field using theodolite. Measurement of Horizontal Angle (Figure 22.1) To represent the direction of a line, the horizontal angle of the line from a reference line is to be measured. The steps required to be adopted are as follows:

  1. Two points one on each of the lines, say P and Q, are to be marked.
  2. A transit theodolite is to be set at the point of intersection of the lines, say at O. Initially, the instrument is in the face left condition and its temporary adjustment is to be done over the point O.
  3. Both the lower and upper plate main screws are to released and get the vernier A set to 0° (or 360°) mark on the main scale. After clamping the upper main screw, index of vernier A is to be brought exactly to the zero of the main scale using the upper plate tangent screw.
  4. At this stage the reading of the vernier B should be 180°.
  5. Swing the telescope in the horizontal plane and point it to the left station, say P. Tighten the lower plate clamp screw, and bisect the signal at P exactly using the lower plate tangent screw. Record the readings in the form of Table 22.1.
  6. Loosen the upper plate main screw and turn the telescope the signal at Q is sighted. Tighten the upper clamp screw and bisect the ranging pole at Q exactly using the upper plate tangent screw.
  7. Read both the verniers A and B and record the readings. The reading of the vernier A is the angle POQ. The vernier B gives the value of angle POQ after deducting from it 180°. The mean of two values of the angles obtained from the verniers A and B is the required angle P'O'Q'.
  8. Change the face of the instrument to the face right by transiting the telescope and swinging it by 180°.
  9. Repeat steps 3 to 8 and determine another value of the angle P'O'Q'.
  10. The mean of the face left and face right observations is the final required angle P'O'Q'

Method of Reiteration Method of reiteration for measurement of horizontal angle is usually adopted in case several angles of well distributed points/ objects are to be measured from the same instrument station with high precision. In this method, angles are measured successively starting from a point termed as initial station (Figure 22.2). The angle between the terminating station and the initial station is the last observation during a set of measurement of horizontal angle by method of reiteration. This process of measuring the angles at an instrument station round the point is to obtain a check on their sum being equal to 360° and is called closing the horizon. When the horizon is closed, the final reading of the vernier should be the same as its initial reading if there is no discrepancy. Figure 22.2 shows a instrument station O where the angles POQ, QOR and ROS have to be measured by method of reiteration. The steps involved in the measurement of the horizontal angles by method of reiteration are as follows:

A vertical angle is the angle between the inclined line of sight and the horizontal plane through the trunnion axis of the instrument. Prior to the measurement of vertical angle, instrument is required to be leveled with reference to the altitude level. Figure 22.3 shows vertical angles. The procedure for measuring a vertical angle is as follows:

  1. The temporary adjustment of the instrument is to be done on the station.
  2. Then, leveling of theodolite is to be done using altitude level (the operations involved are same as leveling using plate level).
  3. Loosen the vertical circle clamp, and direct the telescope towards the object whose vertical angle is required to be measured. Clamp the vertical circle, and bisect the point by turning the vertical tangent screw.
  4. Read and record the scale with vernier C and D in Table 22.
  5. Change the face of the instrument and read the vertical angle again.

Instrumental Error Errors due to imperfections and/or non-adjustment of instrument are all systematic, and these can either be eliminated or reduced to a negligible amount by adopting appropriate methods. The instrumental errors involved in theodolite surveying are  Error due to imperfect adjustment of the plate level in Horizontal angles  Error in Vertical angles due to imperfect adjustment of the plate level  Error due to line of Collimation not being perpendicular to horizontal axis  Error due to Horizontal axis not being perpendicular to the Vertical axis  Other Instrumental Errors Error in Horizontal angles (due to Imperfect adjustment of the plate level) When the bubbles of plate levels are not in adjustment, the vertical axis is inclined, and hence measured angles are not truly horizontal angles. The larger the vertical angle, greater is the error in direction. Thus, errors in horizontal angles due to non adjustment of plate levels or of horizontal axis become large as the inclination of the sights increases. Error in Vertical angles (due to Imperfect adjustment of the plate level) These errors vary with the direction in which the instrument is pointed. With the fixed vertical vernier they are eliminated by observing (for each sighting) the index error of the corresponding observed vertical angle. Error due to line of Collimation not being perpendicular to the Horizontal axis With the line of sight out of adjustment by a given amount, the effect of the error depends on the vertical angle to the point sighted. For all ordinary cases, the error (E) in direction of an inclined sight is given by E = e sec q (approx.) (Figure 22.4) where e is the error in direction for a horizontal sight, where q is the observed vertical angle. The maximum error in horizontal angles due to non adjustment of the line of sight is introduced when the telescope is plunged between backsight and foresight readings and

usually appears in the measurement of a deflection angle. Error due to Horizontal axis not being perpendicular to the Vertical axis The error in horizontal direction of a line due to horizontal axis not being perpendicular to the vertical axis is given by q = e' tan a (approx.) (Figure 22.5) Where q is the angular error in direction, e' is the angular amount of non- adjustment of horizontal axis with the vertical axis; a is the observed vertical angle.

 Error in ranging pole location or Staff Station  Error in Focusing (parallax) Error in setting up of the Instrument The effect of not setting up exactly over the station produces an error in measurement of all angles measured at the station. The amount of the error varies with the direction of pointing and inversely with the length of sight. Error in centring of the Instrument The error from this source is small when the sights are nearly level, but may be large for steeply inclined sights. Errors in setting and reading the Vernier The effect of this error depends on the least count of the vernier and on the legibility of scale and vernier lines. Error in ranging pole location or Staff Station The effect of this error depends on the verticality of the range pole /staff and the height of the point of observation on the pole/staff. This is likely to be a source of rather large error on ordinary surveys. For short sights the plumb line should be employed instead of the range pole Error in Focusing (parallax) The error due to imperfect focusing is always present to a greater or less degree, but with reasonable care it can be reduced to a negligible quantity Error due to Natural Causes The error due to natural causes are not large enough to affect appreciably the measurements of ordinary precision except settlement of the tripod stand/leg.

 Error due to settlement of the tripod stand / leg  Error due to atmospheric condition Error due to settlement of the tripod stand / leg Settlement is usually accompanied by an angular movement about the vertical axis as well as linear movements both vertically and horizontally. When horizontal angles are being measured, usually a larger error is produced by the angular displacement of the circle between backsight and corresponding foresight than by the movement of the transit laterally from the point over which it is set Error due to Atmospheric Condition Errors due to adverse atmospheric conditions such as temperature, wind, refraction etc. can usually be rendered negligible by choosing appropriate times for observing. Large variations in temperature during surveying causes unequal expansion of parts of the instrument and error in observed values. Unreasonable wind during surveying produces vibration of the transit and thus making it difficult to plumb correctly. Refraction effects the reading of observation. Elimination of Errors Errors due to instrumental imperfections and/or nonadjustment are all systematic, and without exception they can be either eliminated or reduced to a negligible amount. This can be achieved by obtaining the mean of two values one observed before and the other after a reversal of the horizontal plate by plunging the telescope and rotating it about the vertical axis. Further, the error in either horizontal or vertical angle due to inclination of the vertical axis can be eliminated, so far as its systematic character is concerned, by leveling the plate bubbles again in addition to the reversal of the plate. However, for precise work the usual practice would be to make the vertical axis truly vertical by means of the telescope level, and then to proceed in the ordinary manner. The personal errors are random and hence cannot be eliminated. They form a large part of the resultant error in transit and theodolite work. Of the personal errors, those due to inaccuracies in reading and setting the vernier or reading and setting of the optical micrometer and to not sighting exactly on the point are likely to be of greater magnitude. Natural errors are generally random, but under certain conditions systematic errors may arise from natural causes. On surveys of very high precision, special attempt is made to establish a procedure which will as nearly as possible eliminate natural systematic errors