Leveling Errors: Causes and Correction Techniques
Some causes that can produce errors in leveling:
1. Imperfect Leveling (Systematic Error)
The instrument must be properly calibrated. This condition affects the optical axis parallel to the line of sight of the level. This produces a systematic error. If the optical axis is tilted, the error is proportional to the distance at which readings are taken.
To mitigate this:
- Check the instrument’s condition before leveling. If it is uncalibrated, correct it.
- Ensure that the distances are the same backwards and forwards, so that the error tends to compensate.
2. Parallax
When taking readings, ensure the telescope is properly focused so the image is clear. Uncertainty in the reading occurs if the image is not sharp. If you move your eye, the horizontal wire will appear in different positions.
To fix this error:
- Adjust the eyepiece to focus the crosshairs sharply.
- Make sure the target image is also sharply focused.
3. Curvature of the Earth
This error can occur when the distances from the instrument to the staff are large (over 100m). However, if you ensure that the distances back and forth are the same, the error is eliminated. In practice, readings are rarely taken at more than 100 meters, so this type of error is often negligible (unless using a very precise level).
4. Atmospheric Refraction
This error occurs when there are high temperatures, causing heat waves. Reading very close to the ground can produce a serious indeterminacy in reading due to a lack of clarity in the images. Its effect can be reduced by shortening the distance until the staff is clearly visible.
5. Temperature Variation
The sun’s rays falling on the instrument produce uneven heating, which causes temporary irregular expansion of the instrument. This error is usually negligible and considered an accidental mistake.
6. Leveling Staff with Non-Standard Length
This is a systematic error that varies directly with the level difference. The error can be eliminated by comparing the staff with a standard length and applying the necessary corrections.
If the staff should have a length L but has (L + e), the corrected level difference H is given as: H = H (1 + e / L)
7. Leveling Staff Not Held Vertically
This produces readings higher than the real value. The error can be eliminated if:
- Using a staff with spherical levels.
- Tilting the staff for the lowest reading (as it passes the vertical).
8. Unclear Change Points
This refers to turning points that are not well-defined. The staff must have a good foothold:
- The fulcrum should not sink.
- The staff must be rotated to ensure that the reading is the same from both back and forward sights.
9. Sinking Tripod
Always take care to secure the tripod legs on the ground so it does not move or sink, thereby avoiding the level becoming uneven. This type of error occurs frequently in sandy or soft ground.
10. Poor Bubble Centering
This error is detected in levels that use a bubble. The bubble should be centered every time one takes a reading. This error tends to vary with distance from the eye; a greater distance means a greater error.
11. Readings on the Staff
This produces an accidental error of a magnitude that depends on the instrument used, weather conditions, length of the visual, and the observer.