Errors eliminated in method of repetition , Measurement of Deflection angle , Measurement of vertical angle , Prolonging a straight line , Sources of error in theodolite
Theodolite surveying
2nd portion
Errors eliminated in method of repetition
The method of repetition eliminates different types of errors.
1) The errors due to eccentricity of verniers and centers get eliminated as readings from both the verniers are taken.
2) The errors due to inaccurate graduation get eliminated.
3) The errors due to lack in adjustment of line of collimation and horizontal axis of the instrument get eliminated.
4) Errors due to inaccurate bisection of the object, ecentricity centering etc are eliminated partially.
Measurement of Deflection angle:
The deflection angle is the angle by which a line is deflected from its original direction. In other words it is the angle which, a survey line makes with the extension of the preceding line. The deflection may be towards the right or the left, depending upon whether the angle measured in the clockwise or anticlockwise direction from the extension of the preceding line . Deflection angles are measured for designing horizontal curves in railway, highway etc.
Measurement of vertical angle:
The vertical angle is the one between the horizontal line (line of collimation) and the inclined line of sight. When it is above horizontal line it is known as the angle of elevation. When it is below horizontal line it is known as angle of depression.
Measurement of magnetic bearing:
(1) To determine the magnetic bearing of line AB, set and level the theodolite at A.
(2) Use the upper tangent screw to release the upper plate and swing the instrument to set the reading on vernier A to read zero. Clamp the upper plate and the circle coincide exactly.
(3) Release the lower plate and the magnetic needle of the compass. Swing the instrument so that the magnetic needle is nearly at the centre line of its run, with the north end of the needle pointing to the zero of the graduations on the compass. Tighten the lower clamp.
(4) The line of sight of the instrument is in the direction of the magnetic meridian at A. Release the upper clamp and swing the instrument to bisect the signal at Q.
(5) Read both the verniers. The average of the two readings gives the magnetic bearing of the line AB.
• Prolonging a straight line:
Let PQ be the line given. It is desired to prolong the line to another point T in line with it and establish intermediate points R and S. There are many ways to do it. The following methods are common
Direct method:
a) Set up and level the theodolite at P. Swing the instrument and bisect the signal at Q.
b) Establish a point along the line of sign at R. Shift the instrument to Q. Sight the signal marked at R. Establish a third point at Salong the line of sight.
(c) Shift the instrument and set it up at R. Sight the station mark at S. Establish another station along the line of sight.
(d) Continue the process unite the point T is reached.
Back Sighting:
(a) Set up and level the theodolite at Q. Swing the instrument to take a back sight on P.clamp both the motions and transit the telescope.
(b) Set a point R along the line of sight. Shift the instrument to R. Similarly take a back sight at the station mark at Q.
(C) Shift the instrument to S and repeat the procedure till the point T is reached.
Double Sighting:
(a) Set up the theodolite at Q. Take a backsight on P.
(b) Take a backsight on P.
(c) Point R’ was established with the left face and point R “is established with the right face. Take the midpoint of R' and R” and mark the point R.
(d) Shifting the instrument to R and repeat the process of double sighting to establish other points till the point T is reached.
. Sources of error in theodolite:
(A) Instrumental Errors
(1) Non – adjustment of plate bubble.
(2) Line of collimation not being perpendicular to horizontal axis.
(3) Horizontal axis not being perpendicular to vertical axis.
(4) Line of collimation not being parallel to axis of telescope.
(5) Ecentricity of inner and outer axes.
(6) Graduations not being uniform.
(7) Verniers being eccentric.
(B) Personal errors:
Centering, leveling may not done properly. Clamp screws are not fixed, ranging rod may not be bisected accurately. Verniers may not be set in proper place.
(C) Natural errors:
(1) High temperature causes error due to irregular refraction.
(2) High wind cause vibration in the instrument.
Permanent adjustment of theodolite:
The permanent adjustment of theodolites are made to establish fixed relationship between the instrument's fundamental lines. The fundamental lines of axis of a transit theodolite include the following
- vertical axis
- Axis of plate levels
- Axis of telescope
- Line of collimation
- Horizontal axis
- Axis of altitude bubble
- The horizontal axis must be perpendicular to the vertical axis
- The vertical circle must read zero when the line of collimation is horizontal.
- The axis of altitude level must be parallel to the line of collimation.
- The line of collimation or line of sight should coincide with axis of telescope.
- The line of sight should also be perpendicular to the horizontal axis at its intersection with the vertical axis.
- The optical axis, the axis of the objective slide, and the line of sight should coincide.
- The axis of plate level must be perpendicular to vertical axis.
Traversing can be done by many methods measuring bearing of line measuring the included angles, deflection angles or exterior angles the traverse with the distances measured using basic instruments of survey.
Included angle method:
In closed traverse, traversing can be done anticlockwise or clockwise. In this process bearing of initial line is taken. After that the included angles interior) of the traverse are measured.
in this method the instrument is set up at A and centred and leveled properly. The vernier A and B is set at 'O' and 30° respectively. Fixing the upper clamp the telescope is oriented along the north line. Then the magnetic bearing of AB is measured. Then vernier A is set at 'O' and the upper clamp is fixed again. Then lower clamp is loosened and ranging rod at E is bisected. Now the clamp is tightened and upper one is opened. By turning the telescope clockwise the rod at B is bisected. ZA is obtained. Changing the face Za is obtained once more. The mean of these give the correct value of ZA. Similarly the remaining angles are measured. At last the arithmetical cheek is applied following this formula of sum of interior angles (2n-4) * 90°. :
Locating details with the theodolite
In most survey, it is necessary to locate the details such as building, railway lines, canal other landmarks along with the survey. A transit with the steel tape is used to locate details.
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