--- title: "Closing error and graphical adjustment" subject: "Surveying I" chapter: 4 key: "semester_3/surveying_i:closing-error-graphical-adjustment" source: https://www.bctengineer.com/q/semester_3/surveying_i/closing-error-graphical-adjustment site: BCT Engineering --- # Closing error and graphical adjustment Surveying I · Chapter 4: The Compass - Asked in: 2075 Chaitra, 4 marks; 2079 Bhadra, 1+3 marks; 2078 Bhadra, 4 marks; 2074 Chaitra, 4 marks; 2073 Shrawan, 4 marks; 2076 Chaitra, 2+2 marks; 2076 Asoj, 4 marks; 2070 Chaitra (old course), 6 marks; 2068 Baisakh, 8 marks; 2067 Asar, 3+4 marks; 2063 Baisakh, 6 marks; 2059 Chaitra, 10 marks; 2057 Chaitra, 6 marks (asked 13 times) - Video: [Closing error and it's adjustment by Bowditch's graphical method | Closing error in compass survey](https://www.youtube.com/watch?v=O-jM8KR8_CM) — EngineeringMantra - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/closing-error-graphical-adjustment - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4 ## Question What is closing error (misclosure) in a compass traverse? Explain how it is adjusted graphically (Bowditch method) with neat sketches. ## Answer **Closing error (misclosure)** is the gap by which a closed traverse fails to close when it is plotted from the observed bearings and lengths. Starting at A, the plotted end falls at A′ instead of A; the distance A′A is the closing error. It arises from errors in the measured angles/bearings, errors in the measured lengths, local attraction, and plotting errors. The accuracy is judged by the relative error of closure: $\dfrac{\text{closing error}}{\text{perimeter}}$ (acceptable for compass work if about 1/300 or smaller). #### Graphical adjustment by Bowditch's rule Bowditch's rule says that the correction to each station is proportional to the length of traverse up to that station, so that the whole closing error is removed at the last station. It can be applied without calculation: 1. Plot the traverse A-B-C-D-E-A′; the closing error is A′A. 2. Draw a straight base line AA′ equal to the perimeter and mark b, c, d, e at distances AB, AB+BC, AB+BC+CD, ... (in any scale). 3. At the end A′ erect a perpendicular A′X equal to the closing error (to the plan scale) and join A to X. 4. The vertical ordinates bb′, cc′, dd′, ee′ drawn from the base to the line AX are the corrections for stations B, C, D, E. They increase uniformly, and the last ordinate equals the full error. 5. On the plan, from each of B, C, D, E draw a line parallel to the closing line A′A and mark off the corresponding correction towards A. Join the new points in order to get the adjusted closed traverse. ```text X . | . | . e' | . d' | | . c' | | | . b' | | | | A -----b-----c-----d-----e-----------A' (base = perimeter, marks at cumulative distances; A'X = closing error, drawn at right angles) ``` The method is satisfactory only when the error is small (about 1/300 of the perimeter); a larger error means a mistake in the field, and the survey should be repeated. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The closing error of a traverse is: A. The sum of all interior angles B. The perimeter C. The distance A'A by which the plotted end fails to meet the start D. The difference between bearings Answer: C. A' is where the plotted traverse ends. (Key point: Closing error) 2. The accuracy is judged by: A. Closing error x perimeter B. Perimeter / closing error squared C. Sum of angles D. Closing error / perimeter Answer: D. Acceptable for compass work about 1/300 or smaller. (Key point: Relative error) 3. Under Bowditch's rule the correction to a station is: A. Proportional to the length of traverse up to that station B. Equal at every station C. Largest at the first station D. Proportional to the square of angles Answer: A. Corrections increase uniformly to the full error at the last station. (Key point: Bowditch's rule) 4. In the graphical adjustment, the perpendicular at A' has length equal to: A. The perimeter B. The closing error C. The longest side D. The first side Answer: B. Ordinates to line AX give corrections. (Key point: Graphical construction) ## Related in Surveying I - [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 - [Closing error; plotting methods in compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosing-error-plotting-methods) — Surveying I, chapter 4 - [Checking open traverse; Bowditch graphically](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-check-bowditch) — Surveying I, chapter 4 - [Angular misclosure, link traverse ABCDEFG](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-initial-154-50-last-335-30) — Surveying I, chapter 4 - [Link traverse PABCQ: permissible misclosure](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-pabcq-permissible-misclosure) — Surveying I, chapter 4 - [Angle misclosure, closed link traverse AT1-ET2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-at1-et2) — Surveying I, chapter 4 ## Related in other subjects - [Closed loop/link traverse, misclosure terms](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-misclosure) — Surveying II, chapter 1 - [Bowditch balancing of link traverse XABCY](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abowditch-link-traverse-xabcy) — Surveying II, chapter 1, asked 2× - [Bowditch link traverse XABCY (X 1162.510 N)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abowditch-link-traverse-xabcy-1162) — Surveying II, chapter 1, asked 2× - [Bowditch link traverse XABCY (X 1877.51 N)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abowditch-link-traverse-xabcy-1877) — Surveying II, chapter 1