SOURCES OF ERROR IN THEODOLITE WORK | THEODOLITE | SURVEYING | LCETED

SOURCES OF ERROR IN THEODOLITE WORK

The sources of error in the theodolite work may be broadly divided into three categories:

a. Instrumental errors

b. Personal errors

c. Natural errors

INSTRUMENTAL ERRORS

The theodolites are very delicate and sophisticated surveying instruments.

In spite of the best efforts during manufacturing, perfect adjustment of the fundamental axes of the theodolite may not be possible. Instrumental errors may be further subdivided as discussed below:

Error due to imperfect adjustment of the plate level

If the plate bubbles are not adjusted properly, the vertical axis of the instrument does not remain vertical even if the plate bubbles are at the centre of their run. Non-verticality of the vertical axis introduces errors in the measurements of both the horizontal and vertical angles. This error can be eliminated only by levelling the instrument carefully, with the help of the altitude or telescope bubble before starting the observations.

Error due to line of collimation not being perpendicular to the trunnion axis

If the line of collimation of the telescope is not truly perpendicular to the trunnion axis, it generates a cone when it is rotated about the horizontal axis. This introduces errors in horizontal angles measured between stations at different elevations. This error may be eliminated from the measured angle by taking the average of the two values of the horizontal angles measured on both faces.

 

Error due to the horizontal axis not being perpendicular to the vertical axis

If the horizontal axis is not perpendicular to the vertical axis, the line of collimation does not revolve in the vertical plane, when the telescope is raised or lowered. Due to this imperfect adjustment, errors are introduced in both the horizontal and vertical angles. The magnitude of the error depends on:

• The angle between the horizontal axis and the vertical axis.

• The vertical angle of the station sighted.

• Elevations of the stations sighted. It is considerable if the stations sighted are at different elevations.

For elimination of the error, observations must be made on both faces. This is because the average of the two values of the horizontal angle observed on both faces is equal to the correct value of the angle.

 

Error due to non-parallelism of the axis of the telescope level and line of collimation

If the axis of the telescope level is not parallel to the line of collimation, an error is introduced in the vertical angle, because the zero line of the vertical verniers do not represent the true line of reference. The error can be eliminated by taking the mean of the two observed values of the angle, one with the telescope normal and the other with the telescope inverted.

 

Error due to eccentricity of inner and outer vertical axes

If the centre of the graduated circle plate does not coincide with the centre of the vernier plate, the angle recorded by either of the verniers is incorrect. To eliminate the error due to this source, observe both the verniers and take the mean value.

 

Error due to eccentricity of verniers

If the line joining the zeros of the horizontal plate verniers do not pass through the centre of the vernier plate, an error in the measured horizontal angles is introduced. The error may be eliminated by taking the mean of the two values by reading both the verniers.

 

PERSONAL ERRORS

This includes the following two categories of errors:

i. Errors of manipulation

ii. Errors of sighting and reading

 

Errors of manipulation

This includes errors as explained below:

Inaccurate centring: If the centre of the theodolite does not coincide with the ground station mark, the horizontal angles measured will be in error, known as a centring error. The magnitude of the error depends upon the distance between the theodolite centre and the ground station mark, the direction and distance of the station sighted, etc.

It may be noted that the error due to centring cannot be eliminated unless accurate centring is done. Also, the error due to defective centring varies inversely as the length of sights.

Error due to inadequate levelling: Inaccurate levelling introduces a serious error in the horizontal angles when the stations sighted are at considerable height differences. This error is similar to the error due to the non-adjustment of the plate levels. If the stations sighted are at the same level, the error is small. For elimination of the error, accurate levelling should be done with the help of an altitude bubble or telescope bubble which is generally more sensitive.

 

Error due to manipulation of the wrong tangent screw: An inexperienced surveyor generally commits mistakes of using the wrong tangent screws. It must be noted that manipulation of the upper tangent screw changes the graduated circle reading whereas manipulation of the lower tangent screw swings the theodolite without changing the readings.

Errors due to sighting and reading

These errors may arise due to the following reasons:

Inaccurate bisection of signals: If the signal erected at the station sighted is not clearly visible, due to vegetative cover or intervening ground, the observer may bisect the signal wrongly. This introduces an error whose magnitude varies inversely with the length of sights. It may be eliminated by sighting the signal clearly and always at its lowest portion.

Non-verticality of signals: If the signal is not truly vertical, an error is introduced. This error is inversely proportional to the length of sight. This error may be eliminated by erecting the signal truly vertical and also bisecting its lowest portion.

Error due to parallax: If the objective and eyepiece are not properly focused before bisecting the station mark, this error is introduced. The error may be eliminated by properly focusing the eyepiece and objective before bisecting the station mark.

 

NATURAL ERRORS

The errors included in this category are the errors occurring due to higher temperature, strong wind, blazing hot sun and unequal settlement of the tripod.

The sources of error in the theodolite work may be broadly divided into three categories:

a. Instrumental errors

b. Personal errors

c. Natural errors

INSTRUMENTAL ERRORS

The theodolites are very delicate and sophisticated surveying instruments.

In spite of the best efforts during manufacturing, perfect adjustment of the fundamental axes of the theodolite may not be possible. Instrumental errors may be further subdivided as discussed below:

Error due to imperfect adjustment of the plate level

If the plate bubbles are not adjusted properly, the vertical axis of the instrument does not remain vertical even if the plate bubbles are at the centre of their run. Non-verticality of the vertical axis introduces errors in the measurements of both the horizontal and vertical angles. This error can be eliminated only by levelling the instrument carefully, with the help of the altitude or telescope bubble before starting the observations.

Error due to line of collimation not being perpendicular to the trunnion axis

If the line of collimation of the telescope is not truly perpendicular to the trunnion axis, it generates a cone when it is rotated about the horizontal axis. This introduces errors in horizontal angles measured between stations at different elevations. This error may be eliminated from the measured angle by taking the average of the two values of the horizontal angles measured on both faces.

 

Error due to the horizontal axis not being perpendicular to the vertical axis

If the horizontal axis is not perpendicular to the vertical axis, the line of collimation does not revolve in the vertical plane, when the telescope is raised or lowered. Due to this imperfect adjustment, errors are introduced in both the horizontal and vertical angles. The magnitude of the error depends on:

• The angle between the horizontal axis and the vertical axis.

• The vertical angle of the station sighted.

• Elevations of the stations sighted. It is considerable if the stations sighted are at different elevations.

For elimination of the error, observations must be made on both faces. This is because the average of the two values of the horizontal angle observed on both faces is equal to the correct value of the angle.

 

Error due to non-parallelism of the axis of the telescope level and line of collimation

If the axis of the telescope level is not parallel to the line of collimation, an error is introduced in the vertical angle, because the zero line of the vertical verniers do not represent the true line of reference. The error can be eliminated by taking the mean of the two observed values of the angle, one with the telescope normal and the other with the telescope inverted.

 

Error due to eccentricity of inner and outer vertical axes

If the centre of the graduated circle plate does not coincide with the centre of the vernier plate, the angle recorded by either of the verniers is incorrect. To eliminate the error due to this source, observe both the verniers and take the mean value.

 

Error due to eccentricity of verniers

If the line joining the zeros of the horizontal plate verniers do not pass through the centre of the vernier plate, an error in the measured horizontal angles is introduced. The error may be eliminated by taking the mean of the two values by reading both the verniers.

 

PERSONAL ERRORS

This includes the following two categories of errors:

i. Errors of manipulation

ii. Errors of sighting and reading

 

Errors of manipulation

This includes errors as explained below:

Inaccurate entering: If the centre of the theodolite does not coincide with the ground station mark, the horizontal angles measured will be in error, known as a centring error. The magnitude of the error depends upon the distance between the theodolite centre and the ground station mark, the direction and distance of the station sighted, etc.

It may be noted that the error due to centring cannot be eliminated unless accurate centring is done. Also, the error due to defective centring varies inversely as the length of sights.

Error due to inadequate levelling: Inaccurate levelling introduces a serious error in the horizontal angles when the stations sighted are at considerable height differences. This error is similar to the error due to the non-adjustment of the plate levels. If the stations sighted are at the same level, the error is small. For elimination of the error, accurate levelling should be done with the help of an altitude bubble or telescope bubble which is generally more sensitive.

 

Error due to manipulation of the wrong tangent screw: An inexperienced surveyor generally commits mistakes of using the wrong tangent screws. It must be noted that manipulation of the upper tangent screw changes the graduated circle reading whereas manipulation of the lower tangent screw swings the theodolite without changing the readings.

Errors due to sighting and reading

These errors may arise due to the following reasons:

Inaccurate bisection of signals: If the signal erected at the station sighted is not clearly visible, due to vegetative cover or intervening ground, the observer may bisect the signal wrongly. This introduces an error whose magnitude varies inversely with the length of sights. It may be eliminated by sighting the signal clearly and always at its lowest portion.

Non-verticality of signals: If the signal is not truly vertical, an error is introduced. This error is inversely proportional to the length of sight. This error may be eliminated by erecting the signal truly vertical and also bisecting its lowest portion.

Error due to parallax: If the objective and eyepiece are not properly focused before bisecting the station mark, this error is introduced. The error may be eliminated by properly focusing the eyepiece and objective before bisecting the station mark.

 

NATURAL ERRORS

The errors included in this category are the errors occurring due to higher temperature, strong wind, blazing hot sun and unequal settlement of the tripod.

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