--- title: "Closed loop level book, F BS blank" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:closed-loop-level-book-missing-a-295-909" source: https://www.bctengineer.com/q/semester_3/surveying_i/closed-loop-level-book-missing-a-295-909 site: BCT Engineering --- # Closed loop level book, F BS blank Surveying I ยท Chapter 5: Leveling - Asked in: 2070 Chaitra (old course), 10 marks - Video: [Rise and fall method in leveling](https://www.youtube.com/watch?v=HNiafKfY0cQ) โ€” Engr Suliman Khan - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/closed-loop-level-book-missing-a-295-909 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question A levelling operation is carried out in a closed loop. Fill all the missing data of a levelling field book and do the arithmetic check also. | Stations | BS | IS | FS | Rise | Fall | RLs (m) | |---|---|---|---|---|---|---| | A | ? | | | | | ? | | B | | 2.572 | | | 0.319 | 295.909 | | C | ? | | 1.987 | ? | | ? | | D | | 0.918 | | | 0.236 | ? | | E | ? | | ? | 1.433 | | ? | | F | | | 2.115 | ? | | 298.848 | | G | | 1.750 | | | ? | ? | | H | ? | | 2.057 | | ? | ? | | A | | | 1.456 | | 1.847 | ? | ## Short answer Missing readings: BS A=2.253, C=0.682, E=3.272, F=1.284, H=-0.391 m; FS E=-0.515 m. RLs: A 296.228, C 296.494, D 296.258, E 297.691, G 298.382, H 298.075, closing A 296.228 m. The loop closes with zero error. ## Answer **Method (rise and fall).** A fall at a station means its staff reading is larger than the previous reading on the same set-up; a rise means it is smaller. The same relations are used backwards to find the missing readings. 1. **A:** B has IS 2.572 and a fall of 0.319, so the reading at A (BS) = 2.572 - 0.319 = 2.253 m. RL of A = RL of B + fall = 295.909 + 0.319 = 296.228 m. 2. **C:** FS 1.987 is smaller than 2.572, so rise = 2.572 - 1.987 = 0.585 m, RL of C = 295.909 + 0.585 = 296.494 m. 3. **C (BS) and D:** D has IS 0.918 and fall 0.236 on the same set-up as the BS at C, so BS at C = 0.918 - 0.236 = 0.682 m. RL of D = 296.494 - 0.236 = 296.258 m. 4. **E:** rise 1.433 from D, so RL of E = 296.258 + 1.433 = 297.691 m and FS at E = 0.918 - 1.433 = -0.515 m. The negative reading means the staff was held *inverted* (touching a roof or beam), and the reading is booked with a minus sign. 5. **E (BS):** RL of F = 298.848, so the rise E to F = 298.848 - 297.691 = 1.157 m, and BS at E = 1.157 + 2.115 = 3.272 m. 6. **F, G and H:** the loop must close on A, so the last RL of A must be 296.228 m. The last fall to A is 1.847, hence RL of H = 296.228 + 1.847 = 298.075 m. The IS at G (1.750) and FS at H (2.057) are on the same set-up, so fall G to H = 2.057 - 1.750 = 0.307 m, giving RL of G = 298.075 + 0.307 = 298.382 m. Fall F to G = 298.848 - 298.382 = 0.466 m, so the reading at F (BS) = 1.750 - 0.466 = **1.284** m. 7. **H (BS):** the last FS at A is 1.456 with fall 1.847, so the BS at H = 1.456 - 1.847 = -0.391 m (again an inverted staff reading). #### Completed field book | Station | BS | IS | FS | Rise | Fall | RL (m) | |---|---|---|---|---|---|---| | A | **2.253** | | | | | **296.228** | | B | | 2.572 | | | 0.319 | 295.909 | | C | **0.682** | | 1.987 | **0.585** | | **296.494** | | D | | 0.918 | | | 0.236 | **296.258** | | E | **3.272** | | **-0.515** | 1.433 | | **297.691** | | F | **1.284** | | 2.115 | **1.157** | | 298.848 | | G | | 1.750 | | | **0.466** | **298.382** | | H | **-0.391** | | 2.057 | | **0.307** | **298.075** | | A | | | 1.456 | | 1.847 | **296.228** | #### Arithmetic check $$ \begin{aligned} \Sigma BS &= 2.253+0.682+3.272+1.284-0.391 = 7.100\\ \Sigma FS &= 1.987-0.515+2.115+2.057+1.456 = 7.100\\ \Sigma \text{Rise} &= 0.585+1.433+1.157 = 3.175\\ \Sigma \text{Fall} &= 0.319+0.236+0.466+0.307+1.847 = 3.175 \end{aligned} $$ $\Sigma BS - \Sigma FS = 0.000$, $\Sigma \text{Rise} - \Sigma \text{Fall} = 0.000$ and last RL - first RL = 296.228 - 296.228 = 0.000. All are zero, so the arithmetic is correct and the loop closes. **Answer:** missing readings BS: A 2.253, C 0.682, E 3.272, F 1.284, H -0.391 m; FS at E = -0.515 m. RLs: A 296.228, C 296.494, D 296.258, E 297.691, G 298.382, H 298.075, A (closing) 296.228 m. *Note on reading:* two readings (E FS and H BS) come out negative, so the staff was inverted at those points. F BS is blank in this copy; it is found from the closure of the loop. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. On the same set-up, B has IS 2.572 and a fall of 0.319 from A. What is the staff reading (BS) at A? A. 2.891 B. 2.253 C. 2.572 D. 0.319 Answer: B. A fall means the later reading is larger, so reading at A = 2.572 - 0.319 = 2.253 m. (Key point: Fall means larger reading) 2. The FS at C is 1.987, smaller than the previous reading 2.572 at B. What is the RL of C? A. 296.494 m B. 297.894 m C. 296.228 m D. 295.324 m Answer: A. Smaller reading means a rise: 2.572 - 1.987 = 0.585 m, so RL of C = 295.909 + 0.585 = 296.494 m. (Key point: Rise and RL of C) 3. Why does the FS at E come out as -0.515 m? A. The level was out of adjustment B. The staff was held upside down only by mistake and the reading is discarded C. A fall was added instead of a rise D. The staff was held inverted, touching a roof or beam, and booked with a minus sign Answer: D. A negative reading means the staff was inverted against an overhead point; it is booked with a minus sign. (Key point: Inverted staff) 4. How is the RL of H found in this closed loop? A. It cannot be found without more data B. From the closure: the last RL of A must equal the first (296.228), so RL of H = 296.228 + 1.847 = 298.075 m C. By adding the BS of H to the RL of A D. By taking the average of RL of G and RL of A Answer: B. A closed loop returns to the starting RL, so working back through the last fall of 1.847 gives H. (Key point: Loop closure condition) ## Related in Surveying I - [Closed loop level book, F BS 1.372](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-loop-level-book-missing-f-bs-1-372) โ€” Surveying I, chapter 5 - [Level book with missing data, RL 1249.260](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-missing-data-ba-1249-260) โ€” Surveying I, chapter 5