If you are working in the field of civil engineering, understanding sources of error in theodolite work | theodolite | surveying is absolutely essential. In this comprehensive guide, we will walk you through everything you need to know about this topic, from the basic concepts to practical applications on the construction site.
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
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
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
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
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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Conclusion
We hope this guide on sources of error in theodolite work | theodolite | surveying has given you a clear and practical understanding of the topic. Whether you are a student preparing for exams or a working professional on the construction site, this knowledge will serve you well. If you found this article helpful, do share it with your fellow engineers and bookmark our site for more such in-depth civil engineering resources.
❓ Frequently Asked Questions (FAQ)
Why is surveying important in construction?
Surveying is critical in construction because it helps establish accurate measurements, positions, and levels on the ground. Without proper surveying, structures could be misaligned, leading to costly errors and structural issues.
What are the most common surveying instruments?
The most commonly used surveying instruments include the auto level, theodolite, total station, GPS equipment, chain, tape measure, and ranging rods. The choice of instrument depends on the type and precision of the survey required.