--- title: "Level book, RL of B 1180.750 m" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:level-book-dumpy-4m-staff-b-1180-750" source: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-dumpy-4m-staff-b-1180-750 site: BCT Engineering --- # Level book, RL of B 1180.750 m Surveying I · Chapter 5: Leveling - Asked in: 2075 Asoj, 6 marks - Video: [Rise and fall method in leveling](https://www.youtube.com/watch?v=HNiafKfY0cQ) — 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/level-book-dumpy-4m-staff-b-1180-750 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question The following consecutive readings were taken with a dumpy level and a 4 m staff on a continuously sloping ground on a straight line at a common interval of 30 m: 0.680 [?], 1.455, 1.855, 2.880, 2.800, 3.380, 1.055, 1.860, 2.265, 3.540, (B) 0.835, 0.945, 1.530 and 2.445. The RL of B was 1180.750 m. Rule out a page of a level field book and enter the above readings. Calculate the RLs of the points by the rise and fall method, and also the gradient of the line joining the first and last points. ## Short answer RLs of points 1 to 12: 1185.935, 1185.160, 1184.760, 1183.735, 1183.815, 1183.235, 1182.430, 1182.025, 1180.750, 1180.640, 1180.055, 1179.140 m. The line from first to last point falls at a gradient of 1 in 48.6 (about 1 in 49). ## Answer **Reading of the data.** The first reading is printed as 0.680 [?]; it is read as 0.680 m. The printed "(B)" stands against the change point where the 10th reading (FS 3.540) and the 11th reading (BS 0.835) are taken, so the point B (RL 1180.750 m) is this change point (CP2); the RLs of all the other points are found from it. If the 1180.750 m belonged to the first point instead, every RL below would change by the same constant and the gradient would be unchanged. The staff is 4 m, so the instrument was shifted after the readings 3.380 and 3.540 (6th and 10th readings). The set-ups are: - Set-up 1: BS 0.680; IS 1.455, 1.855, 2.880, 2.800; FS 3.380 on CP1. - Set-up 2: BS 1.055 on CP1; IS 1.860, 2.265; FS 3.540 on CP2 (point B). - Set-up 3: BS 0.835 on B; IS 0.945, 1.530; FS 2.445 on the last point. The 14 readings are on 12 points, 30 m apart. Taking B (9th point) as RL 1180.750 m, the HI of set-up 3 is $1180.750 + 0.835 = 1181.585$ m, and the other RLs follow by working back through the rises and falls. #### Level field book (rise and fall method) | Station | BS | IS | FS | Rise | Fall | RL (m) | |---|---|---|---|---|---|---| | 1 | 0.680 | | | | | 1185.935 | | 2 | | 1.455 | | | 0.775 | 1185.160 | | 3 | | 1.855 | | | 0.400 | 1184.760 | | 4 | | 2.880 | | | 1.025 | 1183.735 | | 5 | | 2.800 | | 0.080 | | 1183.815 | | 6 (CP1) | 1.055 | | 3.380 | | 0.580 | 1183.235 | | 7 | | 1.860 | | | 0.805 | 1182.430 | | 8 | | 2.265 | | | 0.405 | 1182.025 | | 9 (CP2) | 0.835 | | 3.540 | | 1.275 | 1180.750 | | 10 | | 0.945 | | | 0.110 | 1180.640 | | 11 | | 1.530 | | | 0.585 | 1180.055 | | 12 | | | 2.445 | | 0.915 | 1179.140 | #### Arithmetic check $\Sigma BS - \Sigma FS = 2.570 - (9.365) = -6.795$ ; $\Sigma \text{Rise} - \Sigma \text{Fall} = 0.080 - 6.875 = -6.795$ ; last RL $-$ first RL $= 1179.140 - 1185.935 = -6.795$ All three are equal, so the reduction is correct. #### Gradient of the line joining the first and last points Distance $= 11 \times 30 = 330$ m. $$ \text{Fall} = 1185.935 - 1179.140 = 6.795\ \text{m}, \qquad \text{Gradient} = \frac{6.795}{330} = \frac{1}{48.6}\ (\text{falling}) $$ **Answer:** RLs of the points 1 to 12 = 1185.935, 1185.160, 1184.760, 1183.735, 1183.815, 1183.235, 1182.430, 1182.025, 1180.750, 1180.640, 1180.055, 1179.140 m. The line from the first to the last point falls at a gradient of 1 in 48.6 (about 1 in 49). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Where is point B (RL 1180.750 m) taken, and what if it belonged to another point? A. At change point CP2; all RLs would shift by a constant and the gradient would be unchanged B. At the first point; the gradient would change C. At the last point; RLs unchanged D. At CP1; the gradient doubles Answer: A. A constant shift in RLs does not change the difference between first and last levels. (Key point: Where B is) 2. Why is the instrument shifted after 3.380 and 3.540? A. The staff is inverted B. The 4 m staff is nearly at its limit, so the next point cannot be read C. The gradient changes D. The readings are mistakes Answer: B. Readings approaching the 4 m length require a new set-up. (Key point: Set-ups) 3. With HI of set-up 3 = 1181.585 m, how are points before B found? A. By adding all BS to B B. By taking the HI as their RL C. By working back through rises and falls, and RL of B = 1180.750 m D. By repeating the gradient Answer: C. Starting from B's known RL, rise and fall values give RLs of the earlier points. (Key point: Working back) 4. RL of first = 1185.935, last = 1179.140 m, 12 points at 30 m. What is the gradient? A. Falling 6.795 m in 360 m, 1 in 53 B. Rising 6.795 m in 330 m, 1 in 48.6 C. Falling 6.795 m in 30 m, 1 in 4.4 D. Falling 6.795 m in 330 m, about 1 in 48.6 Answer: D. 12 points give 11 intervals x 30 = 330 m; 330/6.795 = 48.6. (Key point: Gradient) ## Close variants set in other exams - [Level book, 5 m staff, B at 1200.800](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-5m-staff-20m-points-a-b-c-d) — Surveying I, chapter 5, asked 2× ## Related in Surveying I - [Level book, staff readings at B and C (1251.250)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-1250-800-1251-250) — Surveying I, chapter 5, asked 3× - [Level book, staff readings at B and C (1251.000)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-1250-800-1251-000) — Surveying I, chapter 5, asked 3× - [Level book, RL of A 380.500, 3.945 on B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-4m-staff-30m-380-500-minus) — Surveying I, chapter 5, asked 3× - [Level book, RL of B 1380.500](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-4m-staff-b-1380-500) — Surveying I, chapter 5, asked 3× - [Level book, RL of A 380.500, 3.845 on B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-4m-staff-a-380-500-3-845) — Surveying I, chapter 5, asked 3× - [Level book, B and C, RL 50.250 base](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-50-800-51-000) — Surveying I, chapter 5, asked 3× ## Related in other subjects - [RL, distance, gradient P to Q, instrument RL 1325.750](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aanallatic-rl-distance-gradient-pq-1325) — Surveying II, chapter 2