Surveying Capter-3: Surveying Instruments: Theodolite

Theodolite: It was invented by Roemer, a Danish astronomer in 1690. The instrument was used to observe the passage (transit) of stars across any portion of the celestial meridian. About a century later it was modified to suit the surveying requirements.

It is a most precise instrument designed for the measurement of horizontal and vertical angles and has wide applicability in surveying such as laying of horizontal angles, locating points on line, prolonging survey lines, establishing grades, etc.

Figure shows three assemblies of theodolite

Following three axis of theodolite should always be perfectly perpendicular to each other, and by considering this permanent adjustment of theodolite carried out.

1.       Vertical axis

2.       Horizontal axis

3.       Line of sight

Theodolite may be classified as:

1.       Transit theodolite

2.       Non-transit theodolite

Transit theodolite is one in which the line of sight can be reversed by revolving the telescope through 180◦ in the vertical plane.

Non-transit theodolite are either plain theodolites or Y-theodolite in which the telescope cannot be transited. The transit theodolite is mainly used and Y-theodolites have now become obsolete.

Purposes for which a theodolite can be used:

1.       Measuring the horizontal angles

2.       Measuring the vertical angles

3.       Measuring the deflection angles

4.       Measuring the magnetic bearings

5.       Finding the vertical height of an object

6.       Measuring the horizontal distance between two points

7.       Finding the difference of elevation between various points

8.       Ranging a line

Terms used in Theodolite surveying:

1.       Centering: it involves setting the theodolite such that its vertical axis passes through the station mark on the ground. It is done by means of a plumb line attached to a hook below the instrument, or by optical plummet, if available. (Optical plummet substitutes for a plumb bob when centering the instrument.)

2.       Levelling: The operation of levelling involves the plates being made horizontal with the aid of bubble tubes or plate levels attached to them.

3.       Transiting (or plunging or reversing): It is a process of turning the telescope over the horizontal axis through 180◦ in a vertical plane, making its upside down and pointing in the opposite direction.

4.       Face left (bubble up): if the vertical circle is to the left of the observer when sighting from the eyepiece end. The angle measured in this position is called a face left observation. The bubble tube attached to the instrument lie above it.

5.       Face right (bubble down): if the vertical circle is to the right of the observer when sighting from the eyepiece end. The angle measured in this position is called a face right observation. The bubble tube attached to the instrument lie below it.

6.       Changing face: it is the process of changing face from right to left. The face of theodolite is changed by transiting the telescope first and then turning it through 180◦.

7.       Right swing: it is made by turning the telescope to the right (or clockwise) in the horizontal plane. The reading on the horizontal circle then increases.

8.       Left swing: it is made by turning the telescope to the left (or anti clockwise) in the horizontal plane. The reading on the horizontal circle then decreases.

Figure: The essential components of a transit theodolite

Figure: The essential components of transit theodolite

Some important terms:

Vertical axis: It is the axis of rotation of telescope in horizontal plane.

Horizontal axis: It is the axis of rotation of telescope in vertical plane. It is also known as turnnion axis.

Ques. What are the permanent adjustment of theodolite?

Ans. A theodolite is said to be in permanent adjustment if the the following requirements are fulfilled:

1.       The plate level axis is perpendicular to vertical axis.

2.       The horizontal axis is perpendicular to vertical axis.

3.       The line of sight coincide with optical axis of the telescope.

4.       The axis of the altitude level is parallel to the line of sight.

5.       When the line of sight is horizontal vertical circle Vernier reads zero.

First four requirements are the requirements among five fundamental axis and the fifth one is about the vertical circle index.

Ques. What is the procedure to check the plate level axis is perpendicular to vertical axis?

Ans. Following procedure is adopted:

1.       Set up the theodolite on a firm ground and complete all temporary adjustment. See that the plate bubble is exactly in the centre when the telescope is parallel to the two screws.

2.       Revolve the telescope by 180◦,

3.       If the instrument is in adjustment, bubble remains in the centre, otherwise note down the number of divisions by which the bubble has moved out.

Oues. Define for vertical axis, bubble axis, collimation axis, horizontal axis?

Ans.  Vertical axis: It is the axis of rotation of telescope in horizontal plane.

Horizontal axis: It is the axis of rotation of telescope in vertical plane. It is also known as turnnion axis.

Collimation axis: it is a line joining the optical centres of objective lens and eyepiece.

Ques. What relationship exist among the above principal axes of theodolite??

Ans. Principal axises of theodolite are perfectly perpendicular to each other to maintain the permanent adjustment.

Ques. What are the fundamental lines of a transit?

Ans. Following are the fundamental lines of theodolite:

1.       Vertical axis

2.       Horizontal axis

3.       Line of sight or line of collimation

Ques. How is the principal of reversal applied while adjusting the axis of plate bubble of a theodolite??

Ans. The principle of reversal sates that if there is any error in a certain part of instrument, then it will be doubled by reversing i.e. by revolving the telescope through 180◦. Thus apparent error becomes twice the actual error on reversing.

Using the Principle of Reversal following steps can be adopted:

1.       Set up the theodolite on a firm ground and complete all temporary adjustment. See that the plate bubble is exactly in the centre when the telescope is parallel to the two screws.

2.       Revolve the telescope by 180◦,

3.       If the instrument is in adjustment, bubble remains in the centre, otherwise note down the number of divisions by which the bubble has moved out.

Ques. Under what situation can there be difference between the Vernier readings of horizontal circles of a theodolite? How will you eliminate the error in one or both of them?

Ans. Difference in Vernier readings can occur

1.       If the centre of graduated horizontal circle does not coincide with the centre of the Vernier plate. Reading against Vernier will be incorrect. This can be eliminated by taking average of two readings.

2.       If there is imperfect graduations of the horizontal circle. This can be minimized by taking mean of several readings distributed over different portions of the horizontal circle.

3.       If the zeroes of the Vernier are not at the end of the same diameter, this can be eliminated by taking mean of the two readings.                                                                                                                         

Ques. Bring out the difference in theodolite, if any, between the

a.       Horizontal axis and trunnion axis

b.      Line of collimation and line of sight.

Ans. Trunnion axis of a theodolite is the axis about which the telescope and vertical circle rotate. It is the line passing through the journals which fit into the bearings at the top of the standards. When this line is horizontal, it becomes the horizontal axis of the instrument.

Line of sight is any line passing through the eyepiece and the optical centre of the objective of telescope. Line of collimation is an imaginary particular line joining the intersection of the crosshair of the diaphragm and the optical centre of the objective. This line should be perpendicular to the horizontal axis and should also be truly horizontal when the reading on the vertical circle is zero and the bubble on the telescope or on the Vernier frame is at the centre of its run.

Ques. What is the basic difference between temporary and permanent adjustments of a theodolite?

Ans. Temporary adjustment are required to be made at each station before taking readings. Permanent adjustments which usually last for a long time etc. in proper relation to one another.

References:

Surveying, Volume 1 By Dr. B.C. Punmia, Ashok Kumar Jain, Ashok Kr. Jain, Arun Kr. Jain

Surveying And Levelling By Basak

Surveying, Volume 1 By Duggal

The Surveying Handbook By Russell Charles Brinker

Surveying and Levelling, Volume 1 By S. S. Bhavikatti

Textbook of Surveying By C Venkatramaiah