A line of levels has been run from a benchmark of elevation +25.32 m and ends at another benchmark of elevation +25.35 m. The sum of back sights is 18.55 m and the sum of foresights is 18.58 m respectively. The closing error in the survey work is:
0.06 m
Understanding Closing Error in Leveling Surveys
In leveling surveys, the closing error is a measure of the inaccuracy found when a survey loop is completed or when the difference in elevation between two known points is compared using field observations.
The error arises from various sources like instrument inaccuracies, reading mistakes, and atmospheric conditions. It's crucial to calculate this error to assess the precision of the survey work.
Calculating the Closing Error
There are two main ways to determine the difference in elevation between the starting and ending points:
- Using Benchmark Elevations: This is the known, true difference.
Known Elevation Difference = (RL of Last Point) - (RL of First Point)
- Using Field Observations (BS and FS): This is the calculated difference based on the leveling readings.
Calculated Elevation Difference = (Sum of Backsights) - (Sum of Foresights)
$\text{Calculated Elevation Difference} = \Sigma \text{BS} - \Sigma \text{FS}$
Formula for Closing Error
The closing error is the difference between the known elevation difference and the calculated elevation difference from the field readings.
Closing Error = (Known Elevation Difference) - (Calculated Elevation Difference)
Closing Error = [(RL of Last Point) - (RL of First Point)] - [($\Sigma \text{BS}$) - ($\Sigma \text{FS}$)]
Applying the Values
Given:
- Elevation of the first benchmark (RL of First Point) = +25.32 m
- Elevation of the last benchmark (RL of Last Point) = +25.35 m
- Sum of Backsights ($\Sigma \text{BS}$) = 18.55 m
- Sum of Foresights ($\Sigma \text{FS}$) = 18.58 m
Step 1: Calculate the Known Elevation Difference
Known Elevation Difference = RL of Last Point - RL of First Point
Known Elevation Difference = +25.35 m - (+25.32 m)
Known Elevation Difference = +0.03 m
Step 2: Calculate the Elevation Difference from Field Observations
Calculated Elevation Difference = Sum of Backsights - Sum of Foresights
Calculated Elevation Difference = 18.55 m - 18.58 m
Calculated Elevation Difference = -0.03 m
Step 3: Calculate the Closing Error
Closing Error = Known Elevation Difference - Calculated Elevation Difference
Closing Error = (+0.03 m) - (-0.03 m)
Closing Error = +0.03 m + 0.03 m
Closing Error = +0.06 m
Conclusion
The closing error in the survey work is determined to be +0.06 m. This indicates a slight discrepancy between the expected elevation change and the one measured through the leveling process.
Important Questions from Levelling
The expression for sensitivity of the bubble tube (α) can be taken as, ______
Where n = No. of divisions, s = Net staff reading, D = Distance, R = Radius of curvature, l = Length of one division
A vertical line which is perpendicular to the level line is called:
In levelling between two points A and B on the opposite sides of a river, the level was first set up near A and the staff readings on A and B were 2.645 m and 2.30 m respectively. The level was then moved near B and set up; the respective staff readings then were 1.085 m and 1.665 m on A and B respectively. What is the true difference of level between A and B?
A level, when set up $20$ m from peg A and $70$ m from peg B, reads $0.750$ m on a staff held on A and $2.065$ m on a staff held on B, keeping the bubble at its centre while reading. If the reduced levels of A and B are $100.500$ m and $101.800$ m respectively, what is the collimation error per $100.0$ m?
In levelling back, sight is also called as ______.
