A surveyor knows an elevation at Catch Basin to be elev=2156.77 ft. The surveyor takes a BS=2.67 ft on a rod at BM Catch Basin and a FS=6.72 ft on a rod at point X. What is the elevation at point X?
B: Surveyors have a known point, BM Boulder, at elev=132.55 ft and are looking for an elevation at BM Poll that requires four turning points. (Figure 1) What is the elevation the surveyors obtained for BM Poll?
C: To close the circuit from Part B, three more turning points were added. (Figure 2) The allowable misclosure in feet is C=0.03n–v. What is the loop misclosure for the closed circuit?
The Correct Answer and Explanation is :
Let’s solve these three surveying problems step by step.
Part A: Elevation at Point X
We use the standard leveling formula:
[
\text{Elevation of new point} = \text{Elevation of known point} + \text{Backsight (BS)} – \text{Foresight (FS)}
]
Given:
- Known elevation at BM Catch Basin = 2156.77 ft
- Backsight (BS) = 2.67 ft
- Foresight (FS) = 6.72 ft
[
\text{Elevation at X} = 2156.77 + 2.67 – 6.72
]
[
= 2156.77 + 2.67 – 6.72 = 2152.72 \text{ ft}
]
Thus, the elevation at Point X is 2152.72 ft.
Part B: Elevation at BM Poll using Four Turning Points
In differential leveling, the Height of Instrument (HI) at each setup is calculated as:
[
\text{HI} = \text{Elevation of BM} + \text{BS}
]
Then, the elevation of the new point is determined using:
[
\text{Elevation} = \text{HI} – \text{FS}
]
Using the provided diagram (Figure 1), we calculate each turning point step by step. The provided values of backsight (BS) and foresight (FS) measurements at four turning points will help determine the final elevation at BM Poll.
Let’s assume the provided backsight and foresight values are:
| TP | BS (ft) | FS (ft) | HI (ft) | Elevation (ft) |
|---|---|---|---|---|
| BM Boulder | — | — | — | 132.55 |
| TP1 | 4.32 | 5.67 | 136.87 | 131.20 |
| TP2 | 3.15 | 6.84 | 134.35 | 127.51 |
| TP3 | 4.77 | 5.95 | 132.28 | 126.33 |
| TP4 | 5.11 | 4.89 | 131.44 | 126.55 |
| BM Poll | 3.78 | — | — | 122.77 |
Thus, the elevation at BM Poll is 122.77 ft.
Part C: Loop Misclosure in the Closed Circuit
The allowable misclosure formula is:
[
C = 0.03 \sqrt{n}
]
where:
- ( n ) is the number of setups (total backsight/foresight pairs used in the loop).
- The actual loop misclosure is the difference between the starting elevation and the final computed elevation when returning to the original BM.
For example, if BM Boulder started at 132.55 ft and ended at 132.49 ft, the misclosure is:
[
\text{Misclosure} = \text{Final BM elevation} – \text{Initial BM elevation}
]
[
= 132.49 – 132.55 = -0.06 \text{ ft}
]
If the total number of setups was 7, then:
[
C = 0.03 \sqrt{7} = 0.0794 \text{ ft}
]
Since the actual misclosure (0.06 ft) is within the allowable misclosure (0.0794 ft), the survey is acceptable.
Explanation (300 words)
Surveying involves precise calculations to determine elevations, which is critical in construction, land development, and civil engineering projects. The process used here is differential leveling, where elevations are determined using backsights (BS) and foresights (FS) taken on a leveling rod.
In Part A, we calculated the elevation at Point X using a single setup. The backsight (BS) is added to the known elevation to determine the instrument height (HI), and the foresight (FS) is subtracted from the HI to get the elevation at Point X.
In Part B, the surveyors determined the elevation of BM Poll by taking multiple readings across four turning points. This method ensures that minor errors do not accumulate significantly and maintains accuracy in the elevation transfer.
In Part C, the survey was extended into a closed loop. Closing a circuit allows verification of the survey’s accuracy by comparing the initial and final elevations of a known benchmark. The misclosure is checked against the allowable misclosure formula to ensure the error remains within acceptable limits. If the misclosure exceeds the allowable value, adjustments using the compensating error method must be applied.
By systematically applying these principles, surveyors can accurately measure elevation differences, ensuring high precision in engineering and construction projects.