--- title: "Fly levelling for road pegs, BM 3010 m" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:fly-level-road-pegs-3010m" source: https://www.bctengineer.com/q/semester_3/surveying_i/fly-level-road-pegs-3010m site: BCT Engineering --- # Fly levelling for road pegs, BM 3010 m Surveying I · Chapter 5: Leveling - Asked in: 2079 Bhadra, 6 marks - Video: [PROBLEM ON FLY LEVELLING || DIPLOMA || B.TECH || CIVIL ENGINEERING || SURVEYING](https://www.youtube.com/watch?v=atebN2EuTp4) — Civil stuff by waheed TSPSC CIVIL ENGINEERING - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/fly-level-road-pegs-3010m - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question During the construction of a road, 5 pegs are to be set out at the centre lines of the road. For this purpose, fly level is run from a benchmark of RL 3010 m and the following readings were obtained: Backsight: (-)1.234, 2.594, 1.327, 2.869; Foresight: 0.456, 1.123, 0.499. From the last position of the instrument, first 5 pegs at 30 m intervals are to be set out on a uniform rising gradient of 1 in 80. Enter the readings on a level field book and work out the staff readings on the top of the pegs. If the last peg is to be established to have a RL of 3012.476 m, find the correct RLs of each station. ## Short answer After fly levelling from BM 3010.000 m, RL of CP3 is 3010.609 m and HI at last set-up is 3013.478 m. Correct RLs of pegs 1–5 set out on a rising 1 in 80 gradient: 3010.976, 3011.351, 3011.726, 3012.101, 3012.476 m; staff readings: 2.502, 2.127, 1.752, 1.377, 1.002 m. ## Answer **Reading the problem.** The fly levelling starts at a BM of RL 3010 m. There are four BS and three FS readings, so the instrument was set up four times; the fourth set-up (BS 2.869 m on the last change point CP3) is the last position, from which the five pegs are set out. The first BS ($-1.234$ m) is negative: the staff was held inverted. #### Level field book (rise and fall method) | Station | BS | FS | Rise | Fall | RL (m) | HI (m) | |---|---|---|---|---|---|---| | BM | -1.234 | | | | 3010.000 | 3008.766 | | CP1 | 2.594 | 0.456 | | 1.690 | 3008.310 | 3010.904 | | CP2 | 1.327 | 1.123 | 1.471 | | 3009.781 | 3011.108 | | CP3 | 2.869 | 0.499 | 0.828 | | 3010.609 | 3013.478 | Check: $\Sigma BS - \Sigma FS$ for the three complete set-ups $= (-1.234+2.594+1.327) - (0.456+1.123+0.499) = 2.687 - 2.078 = 0.609$ m $=$ RL of CP3 $-$ RL of BM $= 3010.609 - 3010.000 = 0.609$ m. HI of the last set-up $= 3010.609 + 2.869 = 3013.478$ m. #### Setting out the pegs on a rising gradient of 1 in 80 Rise per 30 m peg interval $= 30/80 = 0.375$ m. Staff reading at a peg $=$ HI $-$ RL of the peg. Taking peg 1 at the RL of the last change point (so the last peg is at 3012.109 m): | Peg | Distance (m) | RL (m) | Staff reading (m) | |---|---|---|---| | 1 | 0 | 3010.609 | 2.869 | | 2 | 30 | 3010.984 | 2.494 | | 3 | 60 | 3011.359 | 2.119 | | 4 | 90 | 3011.734 | 1.744 | | 5 | 120 | 3012.109 | 1.369 | #### Correct RLs when the last peg must be at 3012.476 m The last peg is to be established at RL 3012.476 m, which is 0.367 m higher than 3012.109 m. Keeping the same gradient (1 in 80), the RLs of all pegs are therefore raised by 0.367 m: the first peg is $3012.476 - 4 \times 0.375 = 3010.976$ m. | Peg | Distance (m) | Correct RL (m) | Staff reading (m) | |---|---|---|---| | 1 | 0 | 3010.976 | 2.502 | | 2 | 30 | 3011.351 | 2.127 | | 3 | 60 | 3011.726 | 1.752 | | 4 | 90 | 3012.101 | 1.377 | | 5 | 120 | 3012.476 | 1.002 | **Answer:** RLs of the stations: BM 3010.000, CP1 3008.310, CP2 3009.781, CP3 3010.609 m; HI at the last set-up = 3013.478 m. Correct RLs of pegs 1 to 5 = 3010.976, 3011.351, 3011.726, 3012.101, 3012.476 m; staff readings on the pegs = 2.502, 2.127, 1.752, 1.377, 1.002 m. *Assumption:* peg 1 is the first peg of the gradient line and the pegs are 30 m apart from peg 1 to peg 5 (120 m). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. There are four BS and three FS readings. What does this show? A. Four set-ups; the last BS is on CP3 and pegs are set out from the last set-up B. Seven set-ups C. Three set-ups, with BM in the last D. Four set-ups, with the last BS taken on a peg Answer: A. Each set-up has a BS and an FS except the last one, where only the BS is taken before setting out. (Key point: Set-ups) 2. RL of CP3 = 3010.609 m and BS = 2.869 m. What is the HI? A. 3007.740 m B. 3013.478 m C. 3010.609 m D. 3012.109 m Answer: B. HI = RL + BS = 3010.609 + 2.869 = 3013.478 m. (Key point: HI of last set-up) 3. On a rise of 1 in 80 with pegs 30 m apart, how is the staff reading at each peg found? A. Rise per peg = 80/30 = 2.67 m; reading = HI + RL B. Rise per peg = 0.375 m; readings increase by 0.375 per peg C. Rise per peg = 30/80 = 0.375 m; staff reading = HI - peg RL, decreasing by 0.375 m per peg D. Reading = RL of peg - HI Answer: C. On a rising gradient the peg RL increases, so HI - RL, the staff reading, decreases by 0.375 m per peg. (Key point: Gradient setting out) 4. Peg 5 must be at 3012.476 m. What is the first peg RL and the staff reading at peg 5? A. Peg 1 = 3010.609 m; reading = 1.369 m B. Peg 1 = 3011.343 m; reading = 1.002 m C. Peg 1 = 3010.976 m; reading = 2.502 m D. Peg 1 = 3010.976 m; staff reading at peg 5 = 1.002 m Answer: D. Peg 1 = 3012.476 - 4 x 0.375 = 3010.976 m; reading at peg 5 = 3013.478 - 3012.476 = 1.002 m. (Key point: Correct RLs) ## Related in Surveying I - [Fly levelling, BM 1470 m; set 4 pegs](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Afly-level-set-4-pegs-1470-rising-1-in-200) — Surveying I, chapter 5 - [Fly levelling, BM 1280 m; falling gradient](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Afly-level-set-4-pegs-1280-falling-1-in-200) — Surveying I, chapter 5 - [Fly levelling with inverted staff, BM 1290.500](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Afly-level-inverted-staff-1290-500) — Surveying I, chapter 5 - [Fly levelling from BM RL 1291.610](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Afly-level-bm-1291-610) — Surveying I, chapter 5 - [Level book: profile levelling readings](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprofile-leveling-readings-3rd-7th-9th) — Surveying I, chapter 5 - [Level book, benchmark RL 100.00 at 3rd reading](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-instrument-shifted-after-3rd-6th) — Surveying I, chapter 5