--- title: "Two peg: closing error and precision of level" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:two-peg-cd-50m-e-mid-f-5m" source: https://www.bctengineer.com/q/semester_3/surveying_i/two-peg-cd-50m-e-mid-f-5m site: BCT Engineering --- # Two peg: closing error and precision of level Surveying I · Chapter 5: Leveling - Asked in: 2078 Kartik, 6 marks - Video: [Surveying 3 - Two peg test OTEN Building & Construction](https://www.youtube.com/watch?v=ij-yIAvChhk) — OTENBuildingCourses - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/two-peg-cd-50m-e-mid-f-5m - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question During permanent adjustment of level by two peg method the following observations were made on staffs C and D held vertically 50 m apart on fairly level ground. Instrument at E, mid of CD: staff reading at C = 1.455 and staff reading on D = 1.860. Instrument at F such that CF = 5 m and DF = 45 m: staff reading on C = 1.500 and staff reading on D = 1.925. Find the magnitude and direction of closing error and precision of the instrument. What is the reading in C and D with respect to the horizontal line of sight? ## Short answer Closing error +0.020 m in 40 m, precision 1:2000, line inclined upward. Correct staff readings: C = 1.4975 m, D = 1.9025 m. ## Answer **Data:** C and D are 50 m apart. Instrument at E (mid-point): C = 1.455 m, D = 1.860 m. Instrument at F with CF = 5 m and DF = 45 m: C = 1.500 m, D = 1.925 m. #### Step 1: True difference of level (instrument at the mid-point) With equal sight lengths the collimation error cancels, so $$ \text{True difference (D} - \text{C)} = 1.860 - 1.455 = 0.405\ \text{m}\ (\text{D is lower than C}) $$ #### Step 2: Apparent difference from the second setup $$ \text{Apparent difference (D} - \text{C)} = 1.925 - 1.500 = 0.425\ \text{m} $$ #### Step 3: Error and collimation precision The reading error of a staff is proportional to its distance from the instrument. In the second setup the distances are C = 5 m (near) and D = 45 m (far), so the difference of sight lengths is 40 m. $$ e = \text{apparent} - \text{true} = 0.425 - 0.405 = +0.020\ \text{m} $$ $$ \text{Error per metre of sight} = \frac{0.020}{40} = 0.0005\ \text{m/m}, \qquad \text{collimation precision} = \frac{1}{2000} $$ This is 50 mm per 100 m of sight, which is more than the usual permissible limit of about 10 mm per 100 m (1 in 10,000) for ordinary levelling, so the instrument needs adjustment. The error is positive: the far staff D reads too much, and the error grows with distance, so the line of collimation is **inclined upward**. #### Step 4: Correct readings for a horizontal line of sight (second setup) Error in the reading on C $= 0.0005 \times 5 = +0.0025$ m; error in the reading on D $= 0.0005 \times 45 = +0.0225$ m. $$ C = 1.500 - 0.0025 = 1.4975\ \text{m}, \qquad D = 1.925 - 0.0225 = 1.9025\ \text{m} $$ Check: D $-$ C $= 1.9025 - 1.4975 = 0.405$ m, equal to the true difference. **Answer:** the closing (collimation) error is 0.020 m in 40 m, that is 0.0005 m per metre or 1 in 2000 (25 mm over a 50 m sight); the line of collimation is inclined **upward**. The precision of the instrument is 1 in 2000, which is poor, so it needs adjustment. With respect to a horizontal line of sight the readings are **C = 1.4975 m and D = 1.9025 m** (the readings 1.500 and 1.925 less the errors 0.0025 and 0.0225). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. True difference (C - D) at the mid-point is: A. -0.405 m B. -0.425 m C. +0.405 m D. -0.020 m Answer: A. 1.455 - 1.860 = -0.405 m. (Key point: True difference) 2. The error e = (-0.425) - (-0.405) is: A. -0.020 m over 45 m B. -0.020 m over 40 m C. -0.830 m D. +0.020 m over 50 m Answer: B. The sight difference is 45 - 5 = 40 m. (Key point: Error) 3. Precision is: A. 1 in 4000 B. 1 in 200 C. 1 in 2000, poor D. 1 in 20000 Answer: C. 0.020/40 = 0.0005 = 1/2000. (Key point: Precision) 4. Corrected C and D are: A. 1.5025 and 1.9475 B. 1.455 and 1.860 C. 1.480 and 1.900 D. 1.4975 and 1.9025 Answer: D. Subtract 0.0005 x 5 = 0.0025 and 0.0005 x 45 = 0.0225. (Key point: Corrected readings) ## Related in Surveying I - [Two peg test and permanent adjustment](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-test-procedure) — Surveying I, chapter 5, asked 4× - [Two peg test: collimation inclined up or down](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-dumpy-cd-df-120m) — Surveying I, chapter 5 - [Two peg, AB = 60 m, near A](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-ab-60m-near-a-6m-inside) — Surveying I, chapter 5 - [Collimation error with level mid-way and near B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-60m-staff-1-855-1-625) — Surveying I, chapter 5 - [Factors of closing error; graphical adjustment](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosing-error-factors-graphical) — Surveying I, chapter 4 - [Two peg test, AB 100 m, Q 10 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-ab-100m-q-10m-inside) — Surveying I, chapter 5 ## Related in other subjects - [Anallatic tacheometer distance CD and gradient](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aanallatic-staff-cd-gradient-abcd) — Surveying II, chapter 2 - [Length and bearing of CD from stations A, B](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atacheometer-length-bearing-cd-from-a) — Surveying II, chapter 2 - [Fault level: two 50 MVA generators, 50% reduction](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Afault-two-50mva-50-percent) — Power Plant Equipment, chapter 4 - [Fault level: two 25 MVA generators, 50% reduction](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Afault-two-25mva-50-percent) — Power Plant Equipment, chapter 4