Errors in theodolite surveying can be categorized into three main groups:
i. Instrument errors.
ii. Personal errors.
iii. Natural errors.
i. Instrumental Errors
Theodolites are highly sensitive and complex surveying instruments. Despite meticulous efforts in manufacturing and calibration, achieving absolute perfection in the alignment of their fundamental axes is challenging. These unavoidable discrepancies, even after rigorous adjustments, are referred to as residual errors. Residual errors stem from slight misalignments or imperfections in the instrument’s components that cannot be completely eliminated during the production or adjustment processes. As a result, these minor errors can impact the precision of measurements during surveying activities. Instrumental errors can be categorized into several types, as described below:
1. Error due to Imperfect Adjustment of the Plate Level
If the plate level bubbles are not accurately adjusted, the vertical axis of the theodolite may not remain perfectly vertical, even when the bubbles appear centered. This misalignment causes the vertical axis to deviate from its true vertical position, introducing errors in both horizontal and vertical angle measurements. Specifically, when the vertical axis is not perfectly aligned, the horizontal plate becomes slightly inclined, meaning it is no longer in a true horizontal plane. This error becomes particularly significant when measuring horizontal angles between stations that are at notably different elevations.
Elimination of the Error
To correct this error, the instrument must be carefully leveled before taking any measurements . This can be achieved by properly adjusting the altitude or telescope bubble to ensure the theodolite is perfectly horizontal before starting observations.
2. Error Due to Line of Collimation Not Being Perpendicular to the Trunnion Axis
When the line of collimation of a theodolite’s telescope is not perfectly perpendicular to the trunnion axis, a notable error is introduced. As the telescope is rotated about the horizontal axis, the misalignment causes the line of sight to generate a conical surface rather than a straight line. When this conical surface intersects the vertical plane containing the station being observed, the resulting trace is hyperbolic. This imperfect adjustment introduces errors, particularly in the horizontal angle measurements between stations that are situated at different elevations.
Elimination of the Error
To eliminate this error, the horizontal angle should be measured on both the left and right faces of the theodolite. By averaging the two readings, the error due to the misalignment of the collimation line can be effectively cancelled out.
Note:
- The error becomes negligible if the vertical angles of both stations are equal, or if both stations are located on the same horizontal plane.
- Vertical angles are minimally affected by this error, so it can generally be ignored in routine observations.
3. Error Due to Horizontal Axis Not Being Perpendicular to the Vertical Axis
When the horizontal axis of a theodolite is not perpendicular to the vertical axis, the line of collimation does not rotate in a true vertical plane when the telescope is raised or lowered. This misalignment introduces errors in both horizontal and vertical angle measurements. The magnitude of the error depends on several factors:
- The angle of deviation between the horizontal and vertical axes.
- The vertical angle of the station being sighted.
- The relative elevations of the stations. This error becomes more significant when the stations are at different elevations.
Elimination of the Error
To eliminate this error, horizontal angles should be measured on both the left and right faces of the theodolite. The correct value is obtained by averaging the two readings, thereby compensating for the misalignment between the horizontal and vertical axes.
Note:
- The error is zero if the stations being measured are at the same elevation.
- This type of error is generally more significant than errors due to the non-perpendicularity of the line of collimation.
4. Error Due to Non-Parallelism of the Telescope Level Axis and Line of Collimation
If the axis of the telescope level is not parallel to the line of collimation, it results in an error in the vertical angle measurement. This is because the zero reading on the vertical verniers no longer represents the true line of reference, leading to inaccurate results.
Elimination of the Error
To eliminate this error, the angle should be observed twice: once with the telescope in its normal position and again with the telescope inverted. The mean of these two readings provides an accurate measurement, compensating for the misalignment.
5. Error Due to Eccentricity of Inner and Outer Vertical Axes
If the centers of the graduated circle plate and the vernier plate do not coincide, an error is introduced in the recorded angle. This misalignment causes the angle recorded by either vernier to be incorrect, as the instrument reads an angle that does not reflect the true measurement between two points.
Elimination of the Error
To eliminate this error, the readings from both verniers should be taken and averaged. The mean value provides the correct angle, compensating for the eccentricity between the inner and outer vertical axes.
6. Error Due to Eccentricity of Verniers
If the line connecting the zeros of the horizontal plate verniers does not pass through the center of the vernier plate, an error in the measured horizontal angle occurs. This misalignment affects the accuracy of the angle reading. The eccentricity of the verniers can be detected by comparing the readings of both verniers at different points on the graduated circle.
Elimination of the Error
To eliminate this error, read the horizontal angle using both verniers and calculate the average of the two values. This method compensates for any eccentricity and provides an accurate angle measurement.
7. Error Due to Unequal Graduations
If the graduations on the lower plate of the theodolite are not uniform, it can result in inconsistencies in the measured horizontal angles. This means that angles measured at different points on the graduated circle may appear to vary, even when they should be the same.
Elimination of the Error
To minimize this error, the horizontal angle should be measured using different starting points (zeros) on the graduated circle. The average of these measurements will provide a more accurate result, compensating for any discrepancies caused by unequal graduations.
ii. Personal errors
Personal errors can be divided into two main categories:
- Errors in manipulation
- Errors in sighting and reading
1. Errors in Manipulation
These errors occur due to improper handling of equipment and include the following:
(a) Inaccurate Centering
Inaccurate centering happens when the center of the theodolite is not exactly aligned with the ground station mark. This misalignment affects the accuracy of horizontal angle measurements, resulting in what is known as centering error. The size of the error is determined by:
- The distance between the center of the theodolite and the ground station mark.
- The direction and distance to the station being sighted.
Note:
- The error due to inaccurate centering cannot be eliminated unless proper centering is achieved.
- This error decreases as the sight distance increases.
- As a general guide, a one-centimeter centering error over a sight distance of 34.4 meters can cause an angular error of approximately one minute of arc in the measured angle.
(b) Error Due to Inaccurate Levelling
Inaccurate levelling can significantly affect the accuracy of horizontal angle measurements, especially when there is a considerable height difference between the stations being sighted. This type of error is similar to that caused by improper adjustment of the plate levels. However, if the stations being sighted are at the same elevation, the impact of the error is minimal.
Elimination of the Error
To avoid this error, it’s crucial to perform precise levelling. This can be achieved using the altitude bubble or the telescope bubble, which are generally more sensitive and help in ensuring accurate levelling.
(c) Error Due to Manipulation of the Wrong Tangent Screw
Inexperienced surveyors often make the mistake of using the wrong tangent screw. It’s important to remember:
- The upper tangent screw is used to adjust the graduated circle, affecting the reading.
- The lower tangent screw is used to rotate the theodolite without changing the reading.
Elimination of the Error
To avoid this error, careful attention must be given to the correct use of tangent screws:
- Use the lower tangent screw for taking back sights.
- Use the upper tangent screw for taking fore sights.
Note:
- If the upper tangent screw is mistakenly used for back sights, the error can be identified by checking the vernier reading before taking a fore sight.
- However, if the lower tangent screw is incorrectly used for a fore sight, this mistake is harder to detect.
2. Errors Due to Sighting and Reading
These errors can occur from various sources, including:
(a) Inaccurate Bisection of Signals
If the signal or target at the station being sighted is not clearly visible—due to obstacles like vegetation or uneven ground—the observer may incorrectly bisect the signal. This leads to an error that is similar to inaccurate centering, with the magnitude of the error decreasing as the sight distance increases.
Elimination of the Error
To minimize this error, ensure the signal is clearly visible and always aim at its lowest visible portion for a more accurate bisection.
(b) Non-Verticality of Signals
If a signal is not properly aligned in a vertical position, it introduces an error. This error is inversely proportional to the length of the sight. The relationship can be expressed as:
Where α represents the angular error caused by the non-vertical signal.
Elimination of the Error
To avoid this error, the signal must be erected in a perfectly vertical position. Additionally, always bisect the lowest visible part of the signal to ensure accurate measurements.
(c) Error Due to Parallax
Parallax error occurs when the objective and eyepiece of the theodolite are not properly focused before bisecting the station mark. This misalignment can lead to inaccurate readings.
Elimination of the Error
To eliminate parallax error, ensure that both the eyepiece and the objective are correctly focused prior to bisecting the station mark. This will help achieve more accurate measurements.
iii. Errors Due to Natural Causes
Errors in surveying can also arise from various natural factors, including:
- High Temperature: Elevated temperatures can cause equipment components to expand, leading to inaccuracies in measurements.
- Strong Winds: Wind can sway the theodolite or cause vibrations, affecting the stability of readings.
- Scorching Sun: Intense sunlight can create heat distortions, which may lead to visual inaccuracies when sighting.
- Unequal Settlement of the Tripod: If the tripod is not set up evenly, it can introduce errors in angle measurements.
