--- title: "Plotting theodolite traverse; repetition errors" subject: "Surveying I" chapter: 7 key: "semester_3/surveying_i:plotting-theodolite-traverse-repetition-errors" source: https://www.bctengineer.com/q/semester_3/surveying_i/plotting-theodolite-traverse-repetition-errors site: BCT Engineering --- # Plotting theodolite traverse; repetition errors Surveying I · Chapter 7: Transit and Theodolite - Asked in: 2078 Bhadra, 4 marks - Video: [THEODOLITE TRAVERSE | PLOTTING A TRAVERSE SURVEY | LATITUDE & DEPARTURE](https://www.youtube.com/watch?v=DVwKssP3fH0) — BIG C - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/plotting-theodolite-traverse-repetition-errors - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-7 ## Question What are the methods used to plot the theodolite traverse? State what errors are eliminated by the repetition method. ## Short answer Traguverse plotting uses the polar (angle-and-distance) or coordinate (latitudes and departures) method; the latter avoids accumulating errors. The repetition method reduces reading, graduation, eccentricity, and bisection errors, and cancels collimation and trunnion errors when both faces are used, but not centering or levelling errors. ## Answer #### Methods of plotting a theodolite traverse 1. **Angle and distance (polar) method:** the stations are plotted one after another from the measured angles and lengths, using a protractor (or the tangent or chord method for greater accuracy) and a scale. It is easy, but errors accumulate because each angle is plotted from the previous line. 2. **Coordinate method:** the latitudes and departures of all the lines are computed and adjusted (for example by Bowditch's rule), and the total (independent) coordinates of every station are found from a chosen origin. The stations are then plotted from their coordinates, so errors do not accumulate. This is the more accurate method and is used for large traverses. In the *tangent method*, each angle is laid off using its tangent (offset = base length × tan of the angle), which is more accurate than using a protractor. #### Errors eliminated by the repetition method - **Reading errors** (least count error): the angle is added several times, so the error of a single reading is divided by the number of repetitions. - **Errors due to imperfect graduation** of the horizontal circle, since different parts of the circle are used. - **Error of eccentricity** of the verniers and centres (when both verniers are read and averaged). - The errors removed by changing face (line of collimation and trunnion axis errors), when the repetitions are made on both faces. - **Errors of inaccurate bisection** of the signals, which are reduced to some extent because the target is bisected many times and the errors tend to compensate. It does *not* remove errors due to bad centering, or due to the vertical axis not being truly vertical (imperfect levelling). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the coordinate method of plotting more accurate than the polar method? A. It uses a protractor for each angle B. Stations are plotted from coordinates, so error does not accumulate C. It needs no computation D. It ignores closing error Answer: B. Each station is plotted from a common origin by its total coordinates, so errors do not accumulate as in angle-and-distance plotting. (Key point: Coordinate method advantage) 2. Which rule is used to adjust latitudes and departures before finding coordinates? A. Simpson's rule B. Bowditch's rule C. Trapezoidal rule D. Tangent rule Answer: B. Bowditch's rule distributes the closing error among latitudes and departures. (Key point: Adjustment before coordinate plotting) 3. Which error is NOT eliminated by the repetition method? A. Reading error B. Imperfect graduation C. Error of bisection (sighting) D. Eccentricity with both verniers read Answer: C. Repetition does not remove centring, sighting or levelling errors. (Key point: Errors removed by repetition) ## Related in Surveying I - [Errors eliminated by face observation](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aface-observation-errors-and-temporary-adjustment) — Surveying I, chapter 7 - [Face observation errors; optical theodolite](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aface-observation-errors-optical-theodolite) — Surveying I, chapter 7, asked 2× - [Levelling methods; errors eliminated by balancing](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprinciple-methods-leveling-balancing-sight) — Surveying I, chapter 5, asked 2× - [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 - [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 ## Related in other subjects - [Omitted measurement cases, traverse plotting](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aomitted-measurement-cases-plotting) — Surveying II, chapter 1 - [Plotting coordinated traverse on grid paper](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-plotting-grid-paper) — Surveying II, chapter 1, asked 2× - [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 - [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