- 2065 Shrawan · 9 marks
Fly levelling with inverted staff, BM 1290.500
Short answer
The inverted first BS (−1.650) is added to BM RL 1290.500 to get HI. Reducing levels yields CP4 RL 1288.345 m. With last HI 1290.780 m and a fall of 0.2 m per 20 m, the RLs of the four pegs are 1288.145, 1287.945, 1287.745, and 1287.545 m.
During a fly levelling operation, the following observations were made: BS: (-)1.650, 2.155, 1.405, 2.655, 2.435 m; FS: 2.455, 1.305, 0.555, 2.405 m. The first backsight was taken on a BM of RL 1290.500 m with inverted staff. From the last backsight, it is required to set four pegs each at a distance of 20 m on a falling gradient of 1 in 100. Calculate the RL (reduced levels) of these four pegs.
Method: HI = RL of the point on which the back sight is taken + back sight reading. An inverted staff reading (on a ceiling or beam above the point) is booked with a minus sign, so the instrument is lower than the point: HI = RL + (-1.650).
| Station | BS | FS | HI (m) | RL (m) |
|---|---|---|---|---|
| BM | -1.650 (inverted) | 1288.850 | 1290.500 | |
| CP1 | 2.155 | 2.455 | 1288.550 | 1286.395 |
| CP2 | 1.405 | 1.305 | 1288.650 | 1287.245 |
| CP3 | 2.655 | 0.555 | 1290.750 | 1288.095 |
| CP4 | 2.435 | 2.405 | 1290.780 | 1288.345 |
Station RLs by HI method: RL = HI - FS. For example, CP1 = 1288.850 - 2.455 = 1286.395 m.
Check
The last back sight (2.435) belongs to the next set-up, so it is left out of the check:
Last RL - first RL = 1288.345 - 1290.500 = -2.155 m. The two agree.
Setting out four pegs on a falling gradient 1 in 100
The last back sight (2.435 m) is on the last change point, CP4, whose RL is 1288.345 m. The HI of the last set-up is 1288.345 + 2.435 = 1290.780 m. A gradient of 1 in 100 falling means a fall of 1 m per 100 m, i.e. 0.2 m per 20 m peg.
| Peg | Distance from CP4 | RL = 1288.345 - fall (m) | Staff reading = HI - RL (m) |
|---|---|---|---|
| P1 | 20 m | 1288.145 | 2.635 |
| P2 | 40 m | 1287.945 | 2.835 |
| P3 | 60 m | 1287.745 | 3.035 |
| P4 | 80 m | 1287.545 | 3.235 |
Answer: RLs of the four pegs = 1288.145, 1287.945, 1287.745, 1287.545 m (staff readings 2.635, 2.835, 3.035, 3.235 m).
✓ Answer checked by Claude Opus 5.5 (high effort)
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