--- title: "Omitted measurement cases, traverse plotting" subject: "Surveying II" chapter: 1 key: "semester_4/surveying_ii:omitted-measurement-cases-plotting" source: https://www.bctengineer.com/q/semester_4/surveying_ii/omitted-measurement-cases-plotting site: BCT Engineering --- # Omitted measurement cases, traverse plotting Surveying II · Chapter 1: Traversing - Asked in: 2073 Magh, 6 marks - Video: [Omitted Measurements | Part 1 |](https://www.youtube.com/watch?v=NrqHNmTpqCM) — NDMU_Rolly Tambe - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/omitted-measurement-cases-plotting - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1 ## Question Explain different cases of omitted measurements in theodolite traversing. Explain plotting of traverse in grid sheet by co-ordinates method. ## Short answer Omitted measurements in a closed traverse are solved using ΣLat=0, ΣDep=0. Cases: missing length or bearing of one line, length and bearing of one line, lengths of two lines (sine rule), bearings of two lines (cosine rule), or one length and one bearing (SSA). Plotting by coordinates: compute station coordinates, draw grid, plot stations by (E,N), and join; errors don't accumulate. ## Answer #### Cases of omitted measurement The sum of latitudes and the sum of departures of a closed traverse are both zero. These two equations allow two unknowns (lengths or bearings) to be found. The known lines are combined into a single resultant with latitude $\Sigma L_{at}$ and departure $\Sigma D_{ep}$; the closing line is equal and opposite to it, with length $\sqrt{\Sigma L_{at}^2+\Sigma D_{ep}^2}$ and bearing given by $\tan\theta=(-\Sigma D_{ep})/(-\Sigma L_{at})$, with the quadrant taken from the signs. | Case | Unknown quantities | Method | |---|---|---| | 1 | Length **or** bearing of one line | Direct from $\Sigma L_{at}$, $\Sigma D_{ep}$ | | 2 | Length and bearing of one line | Closing line gives both directly | | 3 | Lengths of two lines | Sine rule in the closing triangle | | 4 | Bearings of two lines | Cosine rule in the closing triangle | | 5 | Length of one line and bearing of another | Solve the closing triangle (SSA, two solutions possible) | The affected lines may be adjacent or non-adjacent. If they are not adjacent, the known lines between them are shifted (a closed traverse still closes if the order of its lines is changed), which brings the unknown lines together so that the same triangle method applies. #### Plotting by the coordinates method (outline) 1. Compute the independent coordinates of all stations (from the adjusted latitudes and departures). 2. Choose a scale, draw a grid sheet and label the grid lines with northings and eastings. 3. Mark each station at its $(E,N)$ position measured from the grid lines, join the stations in order and check that the plotted lengths agree with the field lengths. 4. Plot details from the stations and complete the map with the title, scale and north arrow. Plotting by coordinates is preferred to protractor plotting because errors do not accumulate. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why can only two unknown quantities be found? A. Only two equations are available: SigmaLat = 0 and SigmaDep = 0 B. Only two bearings can be measured C. Triangles have only two sides D. Bowditch allows only two corrections Answer: A. Each closure equation solves one unknown. (Key point: Maximum unknowns) 2. Which rule is used when the lengths of two lines are missing? A. Cosine rule B. Sine rule in the closing triangle C. Transit rule D. Bowditch's rule Answer: B. Angles are known from bearings, so the sine rule gives the unknown lengths. (Key point: Both lengths missing) 3. When length of one line and bearing of another are missing, what can happen? A. No solution is ever possible B. The answer is always unique C. Two solutions are possible (SSA case) and the one that suits the sketch is chosen D. The traverse must always be re-measured Answer: C. Triangle with two sides and a non-included angle is ambiguous. (Key point: Length and bearing) 4. Why is plotting by coordinates preferred to protractor plotting? A. It needs no scale B. It avoids the need for computing C. It is faster than any other method D. Errors do not accumulate Answer: D. Each station is located directly from its coordinates. (Key point: Why coordinate plotting) ## 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 - [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 - [Field measurements in traversing, Bowditch rule](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-field-measurements-bowditch-rule) — 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 - [Omitted measurement, non-adjacent affected sides](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aomitted-measurement-nonadjacent-sides) — Surveying II, chapter 1, asked 4× ## 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 - [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