--- title: "Steps of closed traverse computation" subject: "Surveying II" chapter: 1 key: "semester_4/surveying_ii:closed-traverse-computation-steps" source: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-traverse-computation-steps site: BCT Engineering --- # Steps of closed traverse computation Surveying II · Chapter 1: Traversing - Asked in: 2079 Jestha, 4 marks - Video: [Surveying Traverse Computations in 10 Steps](https://www.youtube.com/watch?v=V3sJQ1SS7rw) — Federico Fernandez - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-traverse-computation-steps - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1 ## Question Explain different steps for close traverse computations in Theodolite traversing. ## Short answer Adjust interior angles to (2n-4)×90°, compute bearings, then latitudes and departures. Find linear misclosure e = √(ΣLat²+ΣDep²) and precision 1/N. If acceptable, balance by Bowditch's rule. Compute corrected lengths and bearings, then independent coordinates from a known station. Tabulate and plot by coordinates. ## Answer Computation of a closed theodolite traverse (closed loop) proceeds as follows. 1. **Angular check and adjustment:** the sum of interior angles must equal $(2n-4)\times90^\circ$. If the angular error is within the permissible limit, it is spread equally over the angles (or according to the weights of the stations). 2. **Bearings:** starting from the observed or assumed bearing of one line, find the bearings of the others from the adjusted angles. Check that the bearing of the first line is obtained again at the end. 3. **Latitudes and departures:** $\text{Lat}=L\cos\theta$, $\text{Dep}=L\sin\theta$ for each line. 4. **Linear misclosure and precision:** $$ e_N=\Sigma\text{Lat},\quad e_E=\Sigma\text{Dep},\quad e=\sqrt{e_N^2+e_E^2},\quad \frac{e}{\Sigma L}=\frac1N $$ Accept the traverse if the precision is within the required limit (e.g. 1 in 5000); otherwise repeat the field work. 5. **Balancing:** distribute $e_N$ and $e_E$ among the lines by Bowditch's rule (or the transit rule) to get corrected latitudes and departures, whose sums are zero. 6. **Final lengths and bearings:** from the corrected values, $L=\sqrt{\text{Lat}^2+\text{Dep}^2}$ and $\theta=\tan^{-1}(\text{Dep}/\text{Lat})$. 7. **Independent coordinates:** starting from the known coordinates of one station (or an assumed origin), add the corrected latitudes and departures in sequence, checking that the starting station is reproduced. 8. **Tabulate** all the above in a Gale's traverse table, then plot by coordinates. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the first check in computing a closed theodolite traverse? A. Sum of interior angles must equal (2n-4) x 90°, and the error is spread equally if within the limit B. Sum of latitudes must be zero C. The precision must be 1 in 5000 D. Coordinates of the start must be reproduced Answer: A. Angles are checked and adjusted first, before bearings are derived from them. (Key point: Angular check) 2. How is the linear misclosure and precision of a closed traverse computed? A. e = SigmaLat + SigmaDep and precision = e x total length B. e = SigmaLat/SigmaDep C. e = sqrt((SigmaLat)^2 + (SigmaDep)^2) and precision = e / total length D. e = sqrt(n) x least count Answer: C. The closing error is the resultant of the latitude and departure sums and is divided by the perimeter to give 1 in N. (Key point: Relative precision) 3. When is Bowditch's (or transit) balancing of latitudes and departures applied? A. Before computing latitudes and departures B. After the precision is found acceptable; otherwise the field work is repeated C. Before the angular check D. Instead of computing the closing error Answer: B. If the precision is below the required limit, the traverse is re-observed; only acceptable error is distributed. (Key point: Order of balancing) 4. How are independent coordinates verified? A. Coordinates are compared with the scale of the plot B. The sum of bearings must be 360° C. Adjusted angles are added to the coordinates D. Corrected latitudes and departures are added in sequence from a known station and the starting station must be reproduced Answer: D. Running round the loop with corrected values must return to the start coordinates. (Key point: Coordinate check) ## Related in Surveying II - [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 - [Principles and planning of theodolite traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atheodolite-traverse-principles-planning) — Surveying II, chapter 1 - [Traverse and traverse computation process](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-computation-process) — Surveying II, chapter 1 - [Closed/open traverse, transit rule](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-open-traverse-transit-rule) — Surveying II, chapter 1, asked 2× - [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× - [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 ## Related in other subjects - [Plotting theodolite traverse; repetition errors](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aplotting-theodolite-traverse-repetition-errors) — Surveying I, chapter 7 - [Theodolite traverse ABCDA with missing VCR (68°30′10″)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-traverse-abcda-hcr-vcr-68-30-10) — Surveying I, chapter 7 - [Theodolite traverse ABCDA, booking format with VCR](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atraverse-abcda-booking-format-vcr-120-14-20) — Surveying I, chapter 7 - [Corrected bearings of closed traverse PQRST](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-traverse-pqrst-correct-bearings) — Surveying I, chapter 4