--- title: "Closed/open traverse, transit rule" subject: "Surveying II" chapter: 1 key: "semester_4/surveying_ii:closed-open-traverse-transit-rule" source: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-open-traverse-transit-rule site: BCT Engineering --- # Closed/open traverse, transit rule Surveying II · Chapter 1: Traversing - Asked in: 2068 Bhadra, 7 marks - Video: [Compass Rule and Transit Rule](https://www.youtube.com/watch?v=xMq0hBR8jvU) — Fech - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-open-traverse-transit-rule - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1 ## Question What are closed and open traverses? Explain transit rule for balancing the traverse. ## Short answer A closed traverse returns to its start or joins known stations; an open traverse ends without a closing check. Transit rule distributes latitude and departure errors in proportion to the absolute latitude and departure of each line: C_L = -sumLat x |lat|/sum|lat|, C_D = -sumDep x |dep|/sum|dep|. It suits traverses with precise angles and less precise lengths. ## Answer #### Closed and open traverses - **Closed traverse:** a traverse that ends where it began (a *closed loop*) or that starts and ends on stations of known position (a *closed link/connecting traverse*). It gives a mathematical check on the field work. - **Open traverse:** a traverse that starts at a known station and ends at a point of unknown position, so there is no closing check. It is used for roads, canals, pipelines and similar route surveys, and the angles and lengths must be checked by repeat measurement. #### Transit rule **Transit rule:** the total error in latitude (or departure) is distributed in proportion to the latitude (or departure) of each line, taken without sign. $$ C_L=-\Sigma L_{at}\times\frac{|\text{lat of line}|}{\Sigma|\text{lat}|},\qquad C_D=-\Sigma D_{ep}\times\frac{|\text{dep of line}|}{\Sigma|\text{dep}|} $$ It is used when angles are measured more precisely than lengths (for example with a precise theodolite and ordinary taping). The assumption is that the error in a line's latitude depends on the latitude itself, so a line running mainly north-south gets a large latitude correction and a small departure correction. It is used less often than Bowditch's rule because its corrections depend on the directions of the lines relative to the reference axes, so the result changes if the axes are rotated. #### Example For the traverse with the latitudes and departures below, $e_N=+0.26$ m, $\Sigma|\text{Lat}|=230.34$ and $e_E=-0.13$ m, $\Sigma|\text{Dep}|=398.33$. The correction to the latitude of AB is $-(+0.26)\times85.20/230.34=-0.096$ m. | Line | Lat | Dep | Corr. lat | Corr. dep | Adj. lat | Adj. dep | |---|---|---|---|---|---|---| | AB | +85.20 | +52.30 | -0.096 | +0.017 | +85.10 | +52.32 | | BC | +30.10 | +146.80 | -0.034 | +0.048 | +30.07 | +146.85 | | CD | -92.40 | -76.50 | -0.104 | +0.025 | -92.50 | -76.48 | | DA | -22.64 | -122.73 | -0.026 | +0.040 | -22.67 | -122.69 | The corrected latitudes and departures sum to zero. Note that the lines with larger latitudes or departures get the larger corrections. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is an open traverse weaker than a closed traverse? A. Its lines must be shorter B. It cannot be measured with a theodolite C. It always has larger angular errors D. It has no closing check, since it ends at an unknown point Answer: D. With no known end position, the field work cannot be verified mathematically, so measurements must be repeated. (Key point: Open traverse) 2. In the transit rule, the correction to the latitude of a line is proportional to: A. The length of the line B. The latitude of that line, taken without sign C. The departure of that line D. The bearing of the line Answer: B. The transit rule distributes the latitude error in proportion to |lat| of each line, and departure error in proportion to |dep|. (Key point: Transit rule statement) 3. The transit rule is suited when: A. Angles are measured more precisely than lengths B. Lengths are more precise than angles C. Angles and lengths are of equal precision D. A compass has been used for the angles Answer: A. Transit rule assumes angular measurement is better than linear, so the error lies in the lengths and scales with latitude/departure. (Key point: When to use transit rule) 4. With e_N = +0.26 m, sum|Lat| = 230.34 and AB latitude +85.20, the correction to AB latitude is about: A. +0.096 m B. -0.026 m C. -0.096 m D. -0.260 m Answer: C. C = -0.26 x 85.20 / 230.34 = -0.096 m; the sign is opposite to the error. (Key point: Transit rule calculation) ## Close variants set in other exams - [Closed/open traverse, Bowditch's rule](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-open-traverse-bowditch-rule) — Surveying II, chapter 1, asked 2× ## Related in Surveying II - [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× - [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 - [Field measurements in traversing, closed/open traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-field-measurements-closed-open) — Surveying II, chapter 1 - [Closed/open traverse, consecutive, independent coordinates](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-open-traverse-consecutive-independent) — Surveying II, chapter 1 - [Link traverse A to X, Y by transit method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-transit-a-x-y) — Surveying II, chapter 1 - [Balancing traverse, methods, independent coordinates](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abalancing-traverse-methods-independent-coordinates) — Surveying II, chapter 1 ## Related in other subjects - [Checking open traverse; Bowditch graphically](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-check-bowditch) — Surveying I, chapter 4 - [Open traverse ABCDEFG, deflection angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-deflection-angles-40-45) — Surveying I, chapter 4, asked 2× - [Open traverse ABCDEFGH, deflection angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-deflection-angles-81-45) — Surveying I, chapter 4, asked 2× - [Open loop versus closed loop control](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aopen-vs-closed-loop) — Embedded System, chapter 7, asked 6×