--- title: "Level book and longitudinal section, RL 525.50" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:level-book-chainage-200m-rl-525-50" source: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-chainage-200m-rl-525-50 site: BCT Engineering --- # Level book and longitudinal section, RL 525.50 Surveying I · Chapter 5: Leveling - Asked in: 2062 Poush, 10 marks - 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-chainage-200m-rl-525-50 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question The following consecutive readings were taken with a level at intervals of 20 m. The chainage and R.L. of the first point are 200 m and 525.50 m respectively. 0.515, 1.720, 2.50, 3.455, 1.30, 2.460, 2.950, 3.650, 0.855, 2.430, 3.105 The instrument was shifted after the fourth and eighth readings. Find the RL of all points and draw the longitudinal section (in suitable proportions). ## Short answer After shifting the instrument after the 4th and 8th readings, RLs at 20 m intervals from chainage 200 m are: 525.500, 524.295, 523.515, 522.560, 521.400, 520.910, 520.210, 518.635, and 517.960 m. The ground falls continuously at an average grade of about 1 in 21.2. ## Answer **Assumptions:** the 4th and 8th readings (3.455 and 3.650) are foresights on change points, and the next readings (1.30 and 0.855) are backsights on the same points after the instrument is shifted. So 11 readings give 9 points at 20 m spacing, chainage 200 m to 360 m. | Point | Chainage | BS | IS | FS | HI | Rise | Fall | RL (m) | |---|---|---|---|---|---|---|---|---| | 1 | 200 | 0.515 | | | 526.015 | | | 525.500 | | 2 | 220 | | 1.720 | | | | 1.205 | 524.295 | | 3 | 240 | | 2.500 | | | | 0.780 | 523.515 | | 4 | 260 | 1.300 | | 3.455 | 523.860 | | 0.955 | 522.560 | | 5 | 280 | | 2.460 | | | | 1.160 | 521.400 | | 6 | 300 | | 2.950 | | | | 0.490 | 520.910 | | 7 | 320 | 0.855 | | 3.650 | 521.065 | | 0.700 | 520.210 | | 8 | 340 | | 2.430 | | | | 1.575 | 518.635 | | 9 | 360 | | | 3.105 | | | 0.675 | 517.960 | HI is shown on the row where a new set-up starts. RL = previous RL + rise - fall. #### Arithmetic checks $$ \begin{aligned} \Sigma BS - \Sigma FS &= 2.670 - 10.210 = -7.540 \text{ m}\\ \Sigma \text{Rise} - \Sigma \text{Fall} &= 0.000 - 7.540 = -7.540 \text{ m}\\ \text{Last RL} - \text{First RL} &= 517.960 - 525.500 = -7.540 \text{ m} \end{aligned} $$ All three are equal, so the arithmetic is correct. #### Longitudinal section Plot chainage on the horizontal scale (say 1 cm = 20 m) and RL on the vertical scale (say 1 cm = 1 m, exaggerated for clarity); join the points by a straight line (ground profile). A text sketch of the profile is shown below (each column is one point, `*` marks the RL). ```text 525.50|* 524.81| 524.13| * 523.44| * 522.76| * 522.07| 521.39| * 520.70| * 520.02| * 519.33| 518.65| * 517.96| * +--------------------------------------------- 200 220 240 260 280 300 320 340 360 ``` The ground falls continuously from 525.500 m at chainage 200 m to 517.960 m at chainage 360 m, an average fall of 7.540 m in 160 m (about 1 in 21.2). **Answer:** RLs at chainage 200, 220, ..., 360 m = 525.500, 524.295, 523.515, 522.560, 521.400, 520.910, 520.210, 518.635, 517.960 m. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The instrument is shifted after the 4th and 8th readings. How many points result from 11 readings? A. 11 B. 8 C. 10 D. 9 Answer: D. Two readings (1.30 and 0.855) are BS repeated on the same change points, so 11 - 2 = 9 points. (Key point: Change points) 2. RL of point 1 is 525.500 and the readings are 0.515 and 1.720. RL of point 2? A. 524.295 m B. 524.780 m C. 526.705 m D. 526.220 m Answer: A. Fall = 1.720 - 0.515 = 1.205, so RL = 524.295 m. (Key point: Fall at point 2) 3. What equal value comes out of the checks? A. -10.210 m B. +7.540 m C. -7.540 m D. 0.000 m Answer: C. Sum BS - sum FS = 2.670 - 10.210 = -7.540 = last RL - first RL = 517.960 - 525.500. (Key point: Arithmetic check) 4. How is a longitudinal section plotted? A. Both on the same scale always B. RL horizontally, chainage vertically C. Only BS readings are plotted D. Chainage horizontally, RL vertically, usually with exaggerated vertical scale Answer: D. Chainage is on the horizontal axis and RL on the vertical axis, with the vertical scale larger to show relief. 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