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Fly levelling from BM RL 1291.610

Short answer

Using the height of instrument method with rise and fall check, the reduced levels are: TP1 = 1292.508 m, TP2 = 1293.166 m, TP3 = 1294.126 m, and the last point = 1294.996 m. The arithmetic check gives ΣBS − ΣFS = 3.386 m, matching the difference between last and first RL.

In running a fly level from a bench mark of RL 1291.610 m, the following readings were obtained. Back Sight: 2.543 (B.M.), 2.094, 1.916, 2.725. Fore Sight: 1.645, 1.436, 0.956, 1.855. Prepare a level book and compute reduced levels with necessary checks.

Method: a fly level uses only back sights and fore sights (no intermediate sights), each fore sight and the next back sight being on the same turning point. Height of instrument (HI) method is used with a check by rise and fall.

Taking BM = 1291.610 m, the readings are booked in four set-ups as below.

PointBSISFSHIRiseFallRL (m)RL by HI (m)
BM2.5431294.1531291.6101291.610
TP12.0941.6451294.6020.8981292.5081292.508
TP21.9161.4361295.0820.6581293.1661293.166
TP32.7250.9561296.8510.9601294.1261294.126
Last1.8550.8701294.9961294.996

HI at each row with BS = RL of that point + BS; RL of the next point = HI - FS.

Arithmetic checks

ΣBS−ΣFS=9.278−5.892=3.386ΣRise−ΣFall=3.386−0.000=3.386Last RL−first RL=1294.996−1291.610=3.386\begin{aligned} \Sigma BS - \Sigma FS &= 9.278 - 5.892 = 3.386\\ \Sigma \text{Rise} - \Sigma \text{Fall} &= 3.386 - 0.000 = 3.386\\ \text{Last RL} - \text{first RL} &= 1294.996 - 1291.610 = 3.386 \end{aligned}

All checks agree.

Answer: RLs of the turning points = 1292.508, 1293.166, 1294.126 m, and the last point = 1294.996 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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