Levelling Computation – RL by Height of Instrument Method with Given BS and FS A back sight of 2.685 m is taken on a benchmark of RL 500.000 m. A fore sight of 1.345 m is then taken on a point. Compute the reduced level (RL) of the point.
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A502.685 m
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B501.345 m
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C501.340 m
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D504.030 m
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E502.585 m
Answer
Correct Answer: 501.340 m
Explanation
Introduction / Context:The Height of Instrument (HI) method in levelling computes RLs by first establishing the instrument height above a known benchmark and then subtracting staff readings at other points. It is fast and reliable when BS and FS are correctly identified and the level is properly adjusted.
Given Data / Assumptions:
- Benchmark RL = 500.000 m.
- Back sight (BS) on BM = 2.685 m.
- Fore sight (FS) on point = 1.345 m.
- Instrument is correctly levelled; no collimation error.
Concept / Approach:
Using HI method: HI = RL_BM + BS. Then RL_point = HI − FS. Careful sign discipline (add BS, subtract FS) avoids frequent mistakes. Units remain in metres throughout.
Step-by-Step Solution:
Compute instrument height: HI = 500.000 + 2.685 = 502.685 m.Compute point RL: RL = 502.685 − 1.345 = 501.340 m.Report RL to three decimal places as in standard levelling records.Therefore, RL of the point = 501.340 m.Verification / Alternative check:
Perform the standard arithmetic check after a full run: ΣBS − ΣFS should equal RL_last − RL_first. With one setup, 2.685 − 1.345 = 1.340 which matches 501.340 − 500.000 = 1.340.
Why Other Options Are Wrong:
502.685 m is HI, not the point RL; 501.345 m is a rounding/typo; 504.030 m is impossible; 502.585 m incorrectly subtracts 0.100 m.
Common Pitfalls:
Subtracting BS instead of adding; mixing IS with FS; transposing digits when copying field-book entries.
Final Answer:
501.340 m