--- title: "Closed loop/link traverse, misclosure terms" subject: "Surveying II" chapter: 1 key: "semester_4/surveying_ii:closed-loop-link-traverse-misclosure" source: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-loop-link-traverse-misclosure site: BCT Engineering --- # Closed loop/link traverse, misclosure terms Surveying II · Chapter 1: Traversing - Asked in: 2078 Chaitra, 1+1+3 marks - Video: [Theodolite Traversing](https://www.youtube.com/watch?v=foK4sYnnifs) — The Engineering Surveyor - 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-misclosure - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1 ## Question Define closed loop and closed link traverse. Explain the terms angular misclosure and relative closing error briefly. How is angular misclosure balanced in linked traverse? ## Short answer A closed loop traverse returns to the start, checking interior angle sum and ΣLat=0, ΣDep=0. A closed link traverse runs between known stations, checking computed vs known bearing and coordinates. Angular misclosure is the discrepancy from theoretical sum or known bearing. Relative closing error is √(ΣLat²+ΣDep²)/ΣL = 1/N. In a link traverse, misclosure from carrying bearings is divided equally per angle, applied cumulatively. ## 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. #### Angular misclosure The difference between the sum of the observed interior angles and the theoretical value $(2n-4)\times90^\circ$ in a closed loop (or between the computed and known bearing of the last line in a link traverse). #### Relative closing error The linear error of closure divided by the total length of the traverse: $$ \frac{e}{\Sigma L}=\frac{\sqrt{(\Sigma\text{Lat})^2+(\Sigma\text{Dep})^2}}{\Sigma L}=\frac{1}{N} $$ It is expressed as 1 in $N$ and compared with the specified precision. #### 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 loop traverse? A. It starts and ends at the same station, forming a polygon, with interior angle sum (2n-4) x 90° B. It starts and ends at different known stations C. It has no angle checks D. It is always a triangle Answer: A. A loop returns to its starting point, so both angle sum and SigmaLat = SigmaDep = 0 give checks. (Key point: Closed loop traverse) 2. What checks apply to a closed link (connecting) traverse? A. Sum of interior angles must be (2n-4) x 90° B. SigmaLat and SigmaDep must be zero C. Computed bearing of the last line and computed coordinates of the last station must equal their known values D. No checks are possible Answer: C. It runs between two known stations with known reference bearings, so those known values act as the checks. (Key point: Closed link traverse) 3. What is the relative closing error? A. Angular misclosure divided by the number of angles B. Linear closing error divided by the total traverse length, expressed as 1 in N C. Perimeter divided by closing error, expressed in degrees D. SigmaLat divided by SigmaDep Answer: B. e/SigmaL = sqrt((SigmaLat)^2+(SigmaDep)^2)/SigmaL = 1/N. (Key point: Relative closing error) 4. How is angular misclosure balanced in a link traverse? A. Proportional to line lengths B. The whole error is put on the last angle C. Proportional to the latitudes of the lines D. Equally, -misclosure/n per angle, with the k-th bearing getting k times the correction Answer: D. Cumulative equal corrections make the last computed bearing equal to its known value. (Key point: Balancing in link traverse) ## Related in Surveying II - [Closed loop/link traverse, misclosure balancing](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-angular-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× - [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 ## 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 - [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 - [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