Theodolite

 

3.1   Introduction and Uses of Theodolite:

 INTRODUCTION

 A theodolite is a precise instrument for measuring for horizontal angles, angles of elevation and depression i.e., vertical angle, bearing and azimuth of a line.

Theodolite is also used for prolongation of survey lines, finding difference in elevation and setting out engineering works requires higher precision  i.e. ranging the highway and railway curves, aligning tunnels, etc.

Uses of Theodolite

a)   To measure horizontal angle accurately.

b)   To measure vertical angle(zenithal angle) accurately.

c)    To decide true north by astronomical observation.

d)   To know the difference in elevation of two points.

e)   To measure the height of tower, building and depth of a valley

f)     To measure distance between two points.

g)   For the alignment fixing of tunnel, road, railway, bridge, canal, etc. on the ground.

3.2   Geometry of theodolite:

3.3   Classification of Theodolite

Based on the type of telescope used:

1. Non-Transit Theodolite

A theodolite is said to be a non- transit one when its telescope cannot be revolved through 180^o in a vertical plane about its trunnion axis. These types of theodolite are not used nowadays.

It can be revolved only to certain extent in vertical plane to measure angle of elevation and angle of depression.

Example are: Y theodolite and Everest theodolite

2. Transit theodolite

A theodolite is said to be a transit one when its telescope can be revolved through 180^o  in a vertical plane about its trunnion axis thus directing the telescope in exactly opposite direction.

Based in technology advancement:

1. Analog theodolite

Type of theodolite in which there are vernier scale and micrometer fitted to take horizontal and vertical angular observations are called analog theodolite.  It doesn’t have digital screen and doesn’t use battery.

It is comparatively tedious to use

2. Digital theodolite

Digital theodolite are the types of theodolite that uses electronic devices to measure the angles and displays the result in the screen.

It needs battery to work. It is comparatively quick and easy to use.

It is more precise instrument than analog.

3.4.   Fundamental planes and lines of theodolite

1.    The vertical axis, horizontal axis and the line of sight must meet at a point known as instrument center.

2.    The vertical axis must be perpendicular to the horizontal axis.

3.    The line of collimation must be perpendicular to horizontal axis.

4.    When the vertical axis is truly vertical, the plate bubble must occupy  the central position

5.    The horizontal graduated circle must be perpendicular to the vertical axis.

6.    When the line of sight is horizontal the altitude bubble must be at the center.

3.5 Working Principle of Theodolite

A theodolite works by combination of plumb bob, a spirit level and graduated circles to find vertical and horizontal angles in surveying. A plumb bob insures that the theodolite is placed exactly above the survey stations. The spirit level makes sure that the device is level to the horizontal. The graduated circles, one vertical and another horizontal allow users to survey for angles.

3.6 Temporary Adjustment of Theodolite

The adjustments which are required to be made at every instrument station before making observations are known as temporary adjustments.

Temporary adjustments of a theodolite includes following:

      i.          Setting up and Centering the theodolite over the station

    ii.          Leveling of the theodolite

iii.          Elimination of the parallax

 

 

1.  Setting up and Centering the theodolite over the station

Setting up a theodolite: -

•       The setting operation consists of fixing the theodolite with the tripod stand along with  approximate leveling and centering over the station.

•       For setting up the instrument, the tripod is placed over the station with its legs widely  spread so that the center of the tripod head lies above the station point and its head  approximately level (by eye estimation).

•       The instrument is then fixed with the tripod by  screwing through trivet. The height of the instrument should be such that observer can see  through telescope conveniently.

•       After this, a plumb bob is suspended from the bottom of  the instrument and it should be such that plumb bob should point near to the station mark.

Centering:-  

•       The operation involved in placing the vertical axis of the instrument exactly over the station  mark is known as centering.

•       First, the approximate centering of the instrument is done by moving the tripod legs radially or circumferentially as per need of the circumstances.

•       Finally, exact centering is done by using the shifting head of the instrument. During this, first  the screw-clamping ring of the shifting head is loosened and the upper plate of the shifting  head is slid over the lower one until the plumb bob is exactly over the station mark.

•       After  the exact centering, the screw clamping ring gets tightened.

 

2. Leveling:-

Leveling of an instrument is done to make the vertical axis of the instrument truly vertical.

Generally, there are three leveling screws and two plate levels are placed in instrument. Thus, leveling is being achieved by following procedures:

•      Step 1: Bring one of the level tube parallel to any two of the  foot screws, by rotating the upper part of the instrument.

•      Step 2: The bubble is brought to the center of the level tube by  rotating both the foot screws either inward or outward. The  bubble moves in the same direction as the left thumb

•      Step 3: The bubble of the other level tube is then brought to the  center of the level tube by rotating the third foot screw either  inward or outward

•      Step 4: Repeat Step 2 and step 3 in the same quadrant till both the bubble remain central

•       Step 5: By rotating the upper part of the instrument through  180°, the level tube is brought parallel to first two foot screws in reverse order

 

The bubble will remain in the center if the

Instrument is in permanent adjustment. 

Otherwise, repeat the whole process

starting from step1 to step5

 

 

 

 

3. Elimination of parallax

·      An apparent change in the position of the object caused by the change in the position of observer’s eye is known as parallax .

·      It is a condition arising when the image formed by the objective is not in plane of cross hairs.

·      Unless parallax is removed ,accurate bisection and sighting of objects become difficult. Parallax can be eliminated in two steps:

1.    Focusing of the eye-piece: - For clear and distinct vision of cross hair

2.    Focusing of the objective:- For clear and sharp image of an object.

 

 

 

 

 

 

 

 

3.7 Measurement of angles

3.7.1 Horizontal angles

a. Ordinary method/ Direct method

Procedure:

       i.           Perform temporary adjustment at station ‘O’ and put the instrument at face left position.

    ii.           Roughly target the telescope at station A with the help of gun sight and clamp the horizontal clamp screw.

  iii.           Use objective focus to clearly focus the station A and exactly bisect the station using tangential screw.

  iv.             Set zero horizontal reading at station A.

    v.           Release the clamp screw and similarly bisect the station B.

  vi.           Read the horizontal angle at station B.

vii.           Now change the face of the instrument and bisect the station A and note the horizontal reading.

viii.           Again bisect the station B and take the horizontal reading.

  ix.           <AOB _left = (Horizontal Reading at station B – Horizontal Reading at station A)_left

     x.           <AOB _right = (Horizontal Reading at station B – Horizontal Reading at station A)_right

 xi.     <AOB=

 

b. Repetition Method

This method is used for very accurate work. In this method same angle is added several times and the correct value of the angle is obtained by dividing the accumulated reading by the no. of repetitions.

The number of repetition made usually in this method is six, three with face left and three with the face right.

 

Procedure:

   i.           Perform temporary adjustment at station ‘O’ with face left position.

 ii.           Bisect the station A and set horizontal reading zero.

iii.           Bisect the station B and note the horizontal reading.

iv.           Press hold to hold the reading at the station B and then again bisect the station A.

 v.           Now release the hold at station A and again rotate the theodolite to bisect the station B.

vi.           Note the reading at station B and press hold button.

vii.           Repeat the above procedure n no. of times.

viii.         <AOB_left=

ix.           Set Horizontal Reading zero at station A and transite the face to right. Note the horizontal reading at station A. And repeat above procedure for face right condition also.

 x.         <AOB_right=

xi.      <AOB=

 

c. Reiteration Method

Reiteration is another precise and comparatively less tedious method of measuring the horizontal angles. It is generally preferred when several angles are to be measured at a particular station. This method consists in measuring the several angles successively, and finally closing the horizon at the starting point. The final reading of the vernier A should be the same as its initial reading. If not, the discrepancy is equally distributed among all the measured angles.

 

 

Procedure:

      i.          Perform the temporary adjustment at station O at face left position.

    ii.          Bisect the station A and set horizontal reading zero.

  iii.          Now bisect station B and note the horizontal reading.

  iv.          <AOB= Horizontal reading at B – Horizontal Reading at A

    v.          Bisect station C and note the horizontal reading.

  vi.          <BOC= Horizontal reading at C – Horizontal Reading at B

vii.          Bisect station D and note the horizontal reading.

viii.          <COD= Horizontal reading at D – Horizontal Reading at C

  ix.          Bisect station A and note the horizontal reading.

    x.          <DOA= Horizontal reading at A – Horizontal Reading at D

  xi.          Here, <AOB+<BOC+<COD+<DOA must be equal to 360^o and error = 360^o- (<AOB+<BOC+<COD+<DOA)

xii.          This error is equally distributed to all above angles

 

3.7.2   Vertical Angle and Zenithal Angles

Vertical angle:

Vertical angle is the angle in vertical plane made by line of sight with horizontal line.

It can be angle of elevation and angle of depression. When line of sight is inclined upward then the angle made by it with horizontal line is angle of elevation and when line of sight is inclined downward then the angle made by it with horizontal is angle of depression. The value of angle of elevation is always positive and the value of angle of depression is always negative.

Zenithal angle:

Zenithal angle is the angle in vertical plane made by line of sight with zenithal line.

Zenithal angle and vertical angle are complementary to each other meaning there sum is always 90^o.

i.e. vertical angle + zenithal angle = 90^o

V.A. + Z.A. = 90^o

Procedure for measurement of vertical angle:-

      I.          Perform temporary adjustment at the instrument station.

    II.          Roughly target the object using the gun sight and clamp the vertical and horizontal clamping screw.

 III.          Clearly focus the target using the objective focus.

 IV.          Use the vertical and horizontal tangential screw to exactly bisect the target.

   V.          Now note the reading of vertical angle.

 VI.          To calculate the zenithal angle, subtract the vertical angle from 90^o.

 

3.8. Layout the horizontal angles.

To layout the horizontal angle we need two fix points, one for setting the instrument and other for zero set.

Procedure:

1. Perform the temporary adjustment at the station A.

2. Bisect the station B and perform zero set.

3. With the help of working drawing find out the horizontal angle that needs to be layout on field. (Say 39^o40’50”)

4. Rotate the theodolite until the horizontal reading is around the 39^o.

5. Clamp the horizontal screw.

6. Use tangential screw to exactly make horizontal reading 39^o40’50”.

7. Sight from the telescope and range carefully using the ranging rod and mark the required point C using tape. Hence the point C is set such that <BAC= 39^o40’50”.

 

 

3.9. Errors in theodolite survey.

a. Instrumental error.

b. Natural error

c. Personal error

 

a. Instrumental Error

Instrumental error in theodolite may arise due to imperfections in the adjustment and construction of theodolite. Measurement of face left and face right safeguard from the instrumental error.

 

 

Examples of the instrument errors are as follows:

i. Imperfect adjustment a of the plate bubble.

If the plate bubbles are not adjusted properly the vertical axis of the instrument doesn’t remain vertical even if plate bubble remains at the center. Due to non-verticality the measurement of both the horizontal and vertical angle will be incorrect.

 ii. Line of collimination not being perpendicular to the trunnion axis.

If the line of collimination is not truly perpendicular to the trunnion axis the measurement of horizontal angle between two points which are at considerable difference in elevation will be incorrect.

iii. Horizontal axis not being perpendicular to the vertical axis.

If the horizontal axis isn’t perpendicular to vertical axis, the line of sight will move in an inclined plane. Thus the measured horizontal and vertical angle will be incorrect.   

iv. Imperfect adjustment of the vertical circle:

If the vertical circle do not read zero when the line of sight is horizontal the measured VA will be incorrect. This error can be eliminated by taking mean VA on both faces.

 

b. Natural Errors:

·      Strong wind producing vibration to the instrument

·      Unequal settlement of the tripod

·      The sun shining on the instrument

·      Poor visibility

·      Unequal expansion of the various parts of the instrument

·      Error due to refraction of light

·      Error due to curvature of earth, etc.

 

c. Personal error

·      Inaccurate centering

·      Inaccurate leveling

·      Improper use of tangential screw

·      Slip if the clamping screw is not properly tightened

·      Inaccurate bisection of the target

·      Non verticality of ranging rod

·      Inaccurate reading of data

·      Carelessness while booking the reading