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PROCEDURE,CALCULATION,ADVANTAGES AND DISADVANTAGES OF USING THEODOLITE
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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:
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:
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