--- title: "Methods of reducing levels" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:methods-of-reducing-levels" source: https://www.bctengineer.com/q/semester_3/surveying_i/methods-of-reducing-levels site: BCT Engineering --- # Methods of reducing levels Surveying I · Chapter 5: Leveling - Asked in: 2063 Baisakh, 6 marks; 2058 Chaitra, 6 marks; 2062 Poush, 6 marks (asked 3 times) - 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/methods-of-reducing-levels - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question What are the methods of reducing levels (height of instrument and rise and fall methods)? Explain briefly with arithmetic checks. ## Short answer Height of instrument method: HI = RL + BS, RL = HI - staff reading; check ΣBS - ΣFS = last RL - first RL. Rise and fall method: rise/fall from consecutive readings; check ΣBS - ΣFS = ΣRise - ΣFall = last RL - first RL. HI is faster; rise and fall checks all readings. ## Answer Reduction of levels is the calculation of the reduced level (RL) of each point from the staff readings entered in the level book. Two methods are used. #### 1. Height of instrument (HI) or height of collimation method - HI (the RL of the line of collimation) = RL of the BM + BS. - RL of any point = HI $-$ staff reading (IS or FS) on it. - At a change point, the new HI = RL of the CP + new BS. $$ \text{HI} = \text{RL} + \text{BS}, \qquad \text{RL} = \text{HI} - \text{IS or FS} $$ **Arithmetic check:** $\Sigma BS - \Sigma FS = \text{last RL} - \text{first RL}$. It is quicker and suitable when many intermediate sights are taken (profile and cross-section levelling), but the intermediate sights are not checked. #### 2. Rise and fall method - The difference between consecutive staff readings gives a rise or a fall. - If the second reading is less than the first, it is a **rise**: rise $=$ previous reading $-$ present reading, and RL $=$ previous RL $+$ rise. - If it is greater, it is a **fall**, and RL $=$ previous RL $-$ fall. **Arithmetic check:** $$ \Sigma BS - \Sigma FS = \Sigma \text{Rise} - \Sigma \text{Fall} = \text{last RL} - \text{first RL} $$ It checks every reading (including the intermediate sights), but takes more time. It is preferred for precise work, such as fly levelling and check levelling. | Point | HI method | Rise and fall method | |---|---|---| | Speed | Faster | Slower | | Check | Only BS/FS | All sights | | Suitable for | Many intermediate sights | Few intermediate sights | **Example (HI):** BM RL 100.000, BS 1.500 gives HI 101.500; FS 0.800 on point P gives RL 100.700. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the height of instrument method, how is the RL of an intermediate point found? A. RL = HI − staff reading B. RL = HI + staff reading C. RL = previous RL + rise D. RL = BS − FS Answer: A. HI = RL + BS, and the RL of any point is HI minus the staff reading on it. (Key point: HI method formula) 2. What is the arithmetic check in the HI method? A. ΣBS − ΣFS = last RL − first RL B. ΣIS = ΣFS C. ΣRise = ΣFall D. ΣBS = ΣFS Answer: A. Only BS and FS are included; intermediate sights are not checked. (Key point: Arithmetic check HI) 3. In the rise and fall method, if the next reading is less than the previous one, what is it? A. A rise, and RL = previous RL + rise B. A fall, and RL = previous RL − fall C. A rise, and RL = previous RL − rise D. A change point Answer: A. A smaller reading means the point is higher, so it is a rise added to the previous RL. (Key point: Rise and fall rule) 4. Which statement is correct? A. HI is slower but checks every sight B. Rise and fall checks all sights including IS but is slower C. HI checks all intermediate sights D. Rise and fall is best for many intermediate sights Answer: B. Rise and fall checks every reading but takes longer; HI is faster and suited to many intermediate sights. (Key point: Method comparison) ## Related in Surveying I - [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 - [Closed loop level book, F BS blank](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-loop-level-book-missing-a-295-909) — Surveying I, chapter 5 - [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× - [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) — 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, RL of B 1180.750 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-dumpy-4m-staff-b-1180-750) — Surveying I, chapter 5, asked 2× ## Related in other subjects - [Rise and fall of current in RC circuit](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Arc-circuit-charge-discharge-current) — Engineering Physics, chapter 8 - [Capillary rise exceeding tube height](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Acapillary-rise-exceeds-tube-height) — Fluid Mechanics, chapter 1 - [Maximum obstruction height without upstream rise](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aobstruction-max-height-no-upstream-rise) — Hydraulics, chapter 7 - [Canal fall design, Q 12, drop 1.5 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acanal-fall-design-q12-drop15) — Irrigation and Drainage Engineering, chapter 7