Types of Errors in Levelling- Instrumental, Natural and personal errors
The main types of errors in levelling arise due to three principal sources, they are instrumental errors, natural errors and personal errors.
1.Instrumental Errors in levelling
a. Error due to imperfect adjustment
The essential adjustment of a level is that the line of sight shall be parallel to the axis of the bubble line. If the instrument is not in this adjustment, the line of sight will either be inclined upwards or downwards when the bubble is centred and the rod readings will be incorrect. The error in the road reading will be proportional to the distance and can be eliminated by balancing the backsight and foresight distances. The error is likely to be cumulative, particularly in going up or down a steep hill, where all backsights are longer or shorter than all foresight unless care is taken to run a zigzag line.
b. Error due to sluggish Bubble
If the bubble is sluggish, it will come to rest in the wrong position, even though it may creep back to the correct position while the sight is being taken. Such a bubble is a constant source of annoyance and delay.
c. Error in the movement of the objective slide
In the case of external focusing instruments. if the objective slide slightly is worn our, it may not move in a truly horizontal direction. In the short sights, the objective slide is moved out nearly its entire length and the error is, therefore, more. Due to this reason, extremely short sights are to be avoided.
d. Rod not of Standard length
Incorrect lengths of divisions on a rod cause errors similar to those resulting from the incorrect marking on a tape. The error is systematic and is directly proportional to the difference in elevation.If the rod is too short, the correction is added to measured difference in elevation, if the rod is too short the correction is subtracted.
2.Natural Errors in levelling
a. Earth Curvature
The effect of curvature is to increase the rod readings. When the distances are small the error is negligible, but for greater distances when the back and foresight are not balanced, a systematic error of considerable magnitude is produced.
This effect makes actual level rod readings too large by:
where D is the sight distance in thousands of feet.
Due to refraction, the ray of light bends downwards in the form of the curve with its concavity towards the earth surface, thus decreasing the staff readings. Since the atmosphere refraction often changes rapidly and greatly in short distances, it is impossible to eliminate entirely the effect of refraction even though the backsight and foresight distances are balanced
The formula for computing the combined effect of curvature and refraction is:
C + R = 0.021K2
Where C = correction for curvature
R = correction for refraction
K = sighting distance in thousands of feet
C. Variation in temperature
The effect of variation in temperature on the adjustment of the instrument is not of much consequence in levelling of ordinary precision, but it may produce an appreciable error in precise work. The adjustment of the instrument is temporarily disturbed by unequal heating and consequent warping and distortion.
d. Settlement of tripod in the natural turning point
If the tripod settles in the interval that elapses between taking a backsight and the following foresight, the observed foresight will be too small and the elevation of the turning point will be too great. Similarly, if the turning point settles in the interval that elapses between taking a foresight and the following backsight in the next set up.
a. Mistakes in Manipulation
This includes mistakes in setting up the level, imperfect focussing of eye-piece and of objective, errors in centring the bubble and failure to watch it after each sight, and errors due to resting hands on tripods or telescope. In the long sights, the error due to the bubble not being centred at the time of sighting is more important.
b. Rod handling
If the rod is not in plumb, the reading taken will be too great. The error varies directly with the magnitude of the rod reading and directly as the square of the inclination. In running a line of levels uphill, backsight readings are likely to be increased more than foresight from this source and the elevation of a benchmark on the top will be too great.
c. Errors in sighting
The error is caused when it is difficult to tell when the crosshair coincides with the centre of the target in target rod and to determine the exact reading which the cross=hair appears to cover in the case of the self-reading rod.
d. Mistakes in reading the rod
- Reading Upwards, instead of downwards
- Reading downwards instead of upwards when the staff is inverted.
- Reading against stadia hair.
These are the common errors in levelling.