--- title: "Closed loop/link traverse, misclosure balancing" subject: "Surveying II" chapter: 1 key: "semester_4/surveying_ii:closed-loop-link-traverse-angular-misclosure" source: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-loop-link-traverse-angular-misclosure site: BCT Engineering --- # Closed loop/link traverse, misclosure balancing Surveying II · Chapter 1: Traversing - Asked in: 2071 Bhadra, 6 marks - Video: [How to correct angular Misclosure in traverse (closed loop)](https://www.youtube.com/watch?v=-DUmFgynmEE) — Mining Rabbi - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-loop-link-traverse-angular-misclosure - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1 ## Question Define closed loop and closed link traverse. Also explain angular misclosure balancing process in linked traverse. ## Short answer Closed loop: starts and ends at the same point; checks: sum interior angles = (2n-4)×90°, ΣLat=0, ΣDep=0. Closed link: starts and ends at known stations with known reference bearings. Angular misclosure in link: compute bearings through traverse; misclosure = computed last bearing – known bearing. If within limit, apply equal correction –misclosure/n cumulatively to each bearing. ## Answer #### Closed loop and closed link traverse - **Closed loop traverse:** the traverse starts and ends at the same station and forms a polygon. Checks: sum of interior angles $=(2n-4)\times 90^\circ$, and $\Sigma\text{Lat}=0$, $\Sigma\text{Dep}=0$. - **Closed link (connecting) traverse:** the traverse starts at one known station and ends at another known station, both with known coordinates, and with known reference bearings at the two ends. Checks: the computed bearing of the last line must equal its known value, and the computed coordinates of the last station must equal the known ones. #### Balancing angular misclosure in a link traverse A link traverse starts and ends on stations of known coordinates, and the bearings of the first and last reference lines are known. The angular misclosure is therefore found by carrying the bearing through the traverse. 1. Starting from the known bearing of the first reference line, compute the bearing of every line from the observed angles. For clockwise angles, bearing of a line $=$ bearing of previous line $+180^\circ+$ angle; for anticlockwise angles, bearing of previous line $+180^\circ-$ angle (adding or subtracting $360^\circ$ as needed). 2. The computed bearing of the last reference line is compared with its known bearing: $$ \text{Angular misclosure}=\text{computed bearing}-\text{known bearing} $$ 3. If it is within the allowable limit (for example $\pm k\sqrt{n}$, $n$ = number of angles), distribute it equally, the correction per angle being $-\text{misclosure}/n$. The first bearing receives one correction, the second two, and so on, so the last bearing receives $n$ times the correction and then equals the known value. After the angles are balanced, the lengths are balanced through the linear misclosure of coordinates. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What defines a closed link (connecting) traverse? A. It starts and ends at the same station B. It starts and ends on known stations, with known reference bearings at both ends C. It has no closing check D. It consists only of deflection angles Answer: B. A link traverse begins and ends at stations of known coordinates, with known reference bearings, so it can be checked. (Key point: Closed link traverse definition) 2. Which checks apply to a closed loop traverse? A. Sum of interior angles = (2n-4) x 90° and ΣLat = ΣDep = 0 B. Computed bearing of the last line equals its known value only C. Sum of exterior angles = 180° D. No checks exist Answer: A. A closed loop returns to its start, so both the angle sum and the latitude/departure sums give checks. (Key point: Closed loop check) 3. How is the angular misclosure found in a link traverse? A. Computed bearing of the last reference line minus its known bearing, after carrying the bearing through all lines B. Sum of angles minus 360° C. Difference in lengths of first and last lines D. Sum of latitudes Answer: A. The known first bearing is carried through the observed angles, and the result is compared with the known final bearing. (Key point: Angular misclosure in a link traverse) 4. With n angles and misclosure e, how is the correction applied? A. Each angle gets -e/n, the k-th bearing receives k times this, and the last bearing equals the known value B. Only the last angle is corrected C. All bearings get the same total correction D. Each angle gets -e Answer: A. Equal distribution -e/n per angle accumulates along the bearings, so the last bearing receives n x (-e/n) = -e. (Key point: Distribution of correction) ## Related in Surveying II - [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 - [Closed loop/link traverse, grid plotting](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-plotting-grid) — Surveying II, chapter 1 - [Balancing linked traverse, transit rule](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alinked-traverse-misclosure-transit-rule) — Surveying II, chapter 1, asked 2× - [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× - [Link traverse B to M, coordinates X and Y](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-bowditch-x-y-between) — Surveying II, chapter 1 - [Link traverse Gale's table M2 to M8](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-gale-m2-m8) — Surveying II, chapter 1 ## Related in other subjects - [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 - [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 - [Corrected bearings, closed link traverse T1-T2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-t1-t2-corrected-bearings) — Surveying I, chapter 4