--- title: "Level book TBM1-TBM2 with (-)1.685 reading" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:level-book-tbm1-tbm2-with-minus-1-685" source: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-tbm1-tbm2-with-minus-1-685 site: BCT Engineering --- # Level book TBM1-TBM2 with (-)1.685 reading Surveying I · Chapter 5: Leveling - Asked in: 2075 Chaitra, 6 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-tbm1-tbm2-with-minus-1-685 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question The following readings were taken during a levelling work from TBM1 to TBM2: 2.191, 2.505, 2.325, 1.496, 3.019, 2.513, (-)1.685, 2.811, 1.752, 3.824 m. The level instrument was changed after the 4th and 8th readings. Enter the above readings in a level field book format and compute RLs of all the points and adjust the RLs if error arises. RLs of TBM1 and TBM2 are 1449.870 and 1448.710 m respectively. ## Short answer Using rise and fall method, the computed RL of TBM2 is 1448.701 m against known 1448.710 m, giving a closing error of -0.009 m. Adjusted RLs: TBM1 1449.870, point 2 1449.557, point 3 1449.739, CP1 1450.569, point 6 1451.076, point 7 1455.275, CP2 1450.781, TBM2 1448.710 m. ## Answer **Entering the readings.** The level was changed after the 4th and 8th readings, so there are three set-ups: - Set-up 1: BS 2.191 on TBM1; IS 2.505, 2.325; FS 1.496 on CP1 (4th reading). - Set-up 2: BS 3.019 on CP1; IS 2.513 and $-1.685$; FS 2.811 on CP2 (8th reading). - Set-up 3: BS 1.752 on CP2; FS 3.824 on TBM2. The reading $-1.685$ m is taken with the staff held inverted (for example against a ceiling or beam): the point is 1.685 m **above** the line of sight, so it is entered with a negative sign and the usual rule RL $=$ HI $-$ reading still applies. RL of TBM1 $= 1449.870$ m; RL of TBM2 (known) $= 1448.710$ m. #### Level field book (rise and fall method) | Station | BS | IS | FS | Rise | Fall | RL (m) | |---|---|---|---|---|---|---| | TBM1 | 2.191 | | | | | 1449.870 | | 2 | | 2.505 | | | 0.314 | 1449.556 | | 3 | | 2.325 | | 0.180 | | 1449.736 | | CP1 | 3.019 | | 1.496 | 0.829 | | 1450.565 | | 6 | | 2.513 | | 0.506 | | 1451.071 | | 7 | | -1.685 | | 4.198 | | 1455.269 | | CP2 | 1.752 | | 2.811 | | 4.496 | 1450.773 | | TBM2 | | | 3.824 | | 2.072 | 1448.701 | #### Arithmetic check $\Sigma BS - \Sigma FS = 6.962 - (8.131) = -1.169$ ; $\Sigma \text{Rise} - \Sigma \text{Fall} = 5.713 - 6.882 = -1.169$ ; last RL $-$ first RL $= 1448.701 - 1449.870 = -1.169$ All three are equal, so the reduction is correct. #### Adjustment of misclosure Computed RL of the last point = 1448.701 m; known RL = 1448.710 m. $$ \text{Closing error} = 1448.701 - 1448.710 = -0.009\ \text{m} $$ The correction at a point is $-(-0.009) \times n / 7$, where $n$ is the number of intervals from TBM1. The distances between the points are not given, so the 8 staff points are taken at equal spacing (the 'Interval no.' column counts the intervals from TBM1, 0 to 7). | Station | Interval no. | Correction (m) | Adjusted RL (m) | |---|---|---|---| | TBM1 | 0 | +0.0000 | 1449.870 | | 2 | 1 | +0.0013 | 1449.557 | | 3 | 2 | +0.0026 | 1449.739 | | CP1 | 3 | +0.0039 | 1450.569 | | 6 | 4 | +0.0051 | 1451.076 | | 7 | 5 | +0.0064 | 1455.275 | | CP2 | 6 | +0.0077 | 1450.781 | | TBM2 | 7 | +0.0090 | 1448.710 | **Answer:** the computed RL of TBM2 is 1448.701 m against the known 1448.710 m, so the closing error is -0.009 m. Adjusted RLs: TBM1 1449.870, point 2 1449.557, point 3 1449.739, CP1 1450.569, point 6 1451.076, point 7 1455.275, CP2 1450.781, TBM2 1448.710 m. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The reading -1.685 m is taken with the staff inverted. What does this mean for the point? A. It is 1.685 m above the line of sight; RL = HI + 1.685 B. It is 1.685 m below the line of sight C. It is a change point D. It should be rejected Answer: A. Negative reading means the point is above the line of sight, and RL = HI - reading still applies. (Key point: Inverted staff) 2. The level is changed after the 4th and 8th readings. Which readings are FS and BS at the first change? A. 4th is BS and 5th is FS B. 4th (1.496) is FS on CP1 and 5th (3.019) is BS on CP1 C. Both on different points D. 4th is IS and 5th is IS Answer: B. At a change point the old set-up takes the FS and the new one the BS on the same point. (Key point: Set-ups) 3. Computed RL of TBM2 = 1448.701 m, known = 1448.710 m. What is the closing error? A. +0.009 m, computed is too high B. -1.169 m C. -0.009 m, computed is too low D. 0.000 m Answer: C. Closing error = computed - known = 1448.701 - 1448.710 = -0.009 m. (Key point: Closing error) 4. How is the misclosure distributed? A. Subtracted equally at each point B. Added entirely to TBM2 only C. Subtracted in proportion to distance D. Added in proportion to distance (+0.009 x d/7), giving +0.0090 m at TBM2 Answer: D. The closing error is negative, so a positive correction proportional to the distance is applied, ending at the known 1448.710 m. (Key point: Correction) ## Close variants set in other exams - [Level book TBM1 to TBM2 (4th, 7th)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-tbm1-tbm2-1449-870) — Surveying I, chapter 5, asked 4× ## Related in Surveying I - [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, 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, 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