Use of theodolite

USE of THEODOLITE

  

 Introduction

The theodolite is a versatile instrument and is commonly used for the following tasks.

a)      Measurement of horizontal angles

b)      Measurement of vertical angles

c)      Setting out horizontal angles

d)      Ranging
                                                                                              

e)      Levelling

f)        Optical distance measurement

g)      Controlling verticality

 Measurement of horizontal angles

The reiteration method is a common method of observing horizontal angles.  The procedure is as follows:

a) Accurately center and level the theodolite over a ground mark

b)      Sight the left hand target (face left) with a small reading on the plate using the lower plate clamp and slow motion screw.  Do not touch the lower plate again

during this round of angles.  If several rounds of angles are to be observed, the initial plate setting is changed by about 90 each time.

c)      Sight on to the right hand target(s) using the upper plate clamp and slow motion screw, noting the reading each time.

d)      When the last target has been sighted, change face,  This is done by rotating the telescope vertically through 180 and the upper plate horizontally though

180 to sight back onto the last target.

e)      If face right re-observe all the targets.

f)      It is essential that the plate readings are checked for accuracy on completion of each round of angles.  Check that there is 180 difference between the

readings.  Any variation from the 180 difference is an indication of instrumental error and should be reasonably constant.  This will discover gross errors due to

misreading scales, using wrong slow motion screws, sighting wrong targets, etc. The targets can be re-sighted and the readings corrected before changing the

lower plate.

g)        Horizontal plate readings and reduced angles can be recorded in a standard field book.

Note the different initial plate settings for each round, the use of the remarks column and the summary of angles.

The operation of one second theodolites is practically the same as that outlined above.  The only difference occurs during the initial sighting of the left hand target.

Sight the target first and then set the required plate reading.

 Measurement of vertical angles

Vertical angles are useful in applying slope corrections to distance measurement and for determining reduced levels of inaccessible points.

The observing procedure is practically the same for all theodolites.

a)      Sight the target with the horizontal cross wire.

b)      Level the altitude bubble, unless the instrument has automatic vertical indexing in which case there may be a release button to press

c)      After adjusting the micrometer note the plate reading.

d)      Change face and repeat

The orientation of the vertical circle varies from one instrument to another and several examples are in Figure 4.6.  Study your theodolite carefully as it is

necessary to reduce vertical angles.
     Levelling

The theodolite could be used for leveling provided a number of precautions are taken.

a) The altitude bubble should be centred and the telescope locked with a vertical angle of exactly 00-00-00,

b) Read the staff.

a) Change face and repeat the above steps

b) The mean of the two staff readings will give a reasonable result over short distances.

Levelling by theodolite must never be regarded as an acceptable alternative to the surveyor’s level where accuracy is needed.

        Optical distance measurement



Horizontal distances can be measured using theodolite and leveling staff.  These distances can be accurate to 0.1 m and cannot be used where accuracy is

required.

4              Sight a vertically held leveling staff and read the staff where it is cut by the horizontal crosswire and the two stadia hairs.

5              Check the staff readings.  The difference between center and top readings should equal difference between centre and bottom readings.  Read the staff again if there is a disagreement.

6              Note the vertical angle after levelling the altitude bubble.

7              Compute the horizontal distance from

100 xsxcos2  vertical angle

where s= difference between top and bottom stadia readings
 Sources of error

(a) Instrumental errors

      The geometry of a theodolite comprises three axes directly related to ech other called vertical, trunnion and optical axes.

When the theodolite is in adjustment:

i)The vertical axis is vertical

ii)The trunnion axis is at right angles to the vertical axis

iii)The optical axis is at right angles to the trunnion axis.

iv)The zero line of the vertical circle is horizontal when the altitude bubble is level.

v)The crosshairs are vertical

vi)The optical plummet provides a vertical line of sight once the instruments is level

These sources of error can be detected by undertaking a series of standard tests (see paragraph 3.7).

Changing face will eliminate errors due to (ii), (iii), (iv)

Note: Changing face will not eliminate errors crept in while levelling  the instrument.

 
b)Manipulation errors

i)Parallax not properly eliminated

ii)Sighting wrong target, or part of target

ii)Using stadia hair in vertical angle measurement

iii)Incorrect use of upper and lower plate clamps and slow motion screws

iv)Poor centering of instrument over a ground mark

v)Targets not properly centred over ground marks

vi)Incorrectly set up tripod

c)Reading and booking errors

i)Incorrect reading of scales

ii)Incorrect booking of plate readings

iii)Arithmetic errors – there is no convenient arithmetic check.

iv)Check left and right face readings – is there the correct difference between them?

v)If several rounds of angles have been observed, look for the odd one out.

 Theodolite checks



There are six standard checks on a conventional theodolite and these should be done on a regular basis.

a)Plate bubble

    Simply leveling the theodolite and “freezing” the bubble will check for plate bubble error.  If the bubble “freezes” away from the central position, the theodolite is

still leveled.  Centralising the bubble by adjusting the bubble tube is not a necessary adjustment.

b) Verticality of crosshairs

With the instrument correctly leveled the vertical crosshair should be truly vertical.  To check this sight on to a well defined distant object and move the telescope

up and down.  The object should remain on the vertical crosshair throughout its entire length.

c) Horizontal collimatioin

This check determines whether the optical axis of the telescope is at right angles to the trunnion axis.  With the theodolite set up and leveled sight a well defined

mark, say 50 m away with the lower plate clamped.  Record the horizontal plate reading.  Change face and sight on to the mark again.  Record this plate reading.

The difference between the two readings should be 180 and any variation from 180 is twice the collimation error.  Collimatioin errors of 40 seconds or less are

acceptable for most site applications.  This error will be eliminated by observing on both faces of the instrument.

a)      Trunnion axis error

This check determines whether the trunnion (or horizontal) axis is at right angles to the vertical axis.  With the instrument set up and leveled, sight a high target

using the vertical crosshair (vertical angle approximately 40 – 50).  Depress the telescope and read a staff or other graduated scale laid horizontal under the target

and facing the theodolite.  Change face and repeat this operation.  If the two staffreadings re within 5 mm the trunnion axis error is within 5 mm the trunnion axis

error is within acceptable limits for mot site applications.

By observing on both faces of the instrument, this error will be eliminated. However, this is quite impractical if the theodolite is used for plumbing purposes.

e)Vertical collimation error

The zero line of the vertical circle should be horizontal when the altitude bubble is levelled or the automatic compensator is in operation.  The check follows the

procedure for measuring vertical angles (see paragraph 3.3).  The difference between the two reduced vertical angles is twice the vertical collimation error.

Collimation errors of 40 seconds or less are acceptable for mot site applications.  By observing on both faces o the instrument, this error will be eliminated.

(f) Optical plummet

Set up and level the theodolite.  Place on the ground a white card with a cross, drawn on it.  Position this card so that that the cross is exactly in the center of the

plummet graticule..  Tum the instrument through 180 and observe whether the cross remains in the center of the circle.
 Maintenance of equipment 



See paragraph 2.6 – Maintenance of levelling equipment.