---
title: "Closed/open traverse, consecutive, independent coordinates"
subject: "Surveying II"
chapter: 1
key: "semester_4/surveying_ii:closed-open-traverse-consecutive-independent"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/closed-open-traverse-consecutive-independent
site: BCT Engineering
---

# Closed/open traverse, consecutive, independent coordinates

Surveying II · Chapter 1: Traversing

- Asked in: 2069 Bhadra, 8 marks
- Video: [Traverse Surveying: Consecutive Co-ordinates](https://www.youtube.com/watch?v=7bEDwcdrGXw) — Concepta 71
- 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-consecutive-independent
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1

## Question

What are closed and open traverse? Explain consecutive and independent co-ordinates with examples.

## Short answer

A closed traverse ends at its start or at known stations and can be checked; an open traverse ends at an unknown point. Consecutive coordinates are latitudes and departures measured from the preceding station, while independent coordinates are total northings and eastings from one common origin, obtained by summing consecutive values.

## Answer

#### Closed and open traverse
- **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.

#### Consecutive and independent coordinates
**Consecutive (dependent) coordinates:** the latitude and departure of a line, i.e. the coordinates of its end point measured from the preceding station taken as origin. Example: line AB with $L=100$ m and bearing $60^\circ$ gives $\Delta N=100\cos 60^\circ=+50$ m and $\Delta E=100\sin 60^\circ=+86.6$ m from A.

**Independent (total) coordinates:** the northing and easting of a station measured from one common origin (the reference station or a national grid). They are the algebraic sum of consecutive coordinates from the origin. Example: if A is $(1000,\,1000)$, then B is $(1050,\,1086.6)$, and C is B plus the consecutive coordinates of BC.

Independent coordinates are used for plotting because all stations refer to one origin, so plotting errors do not accumulate.

#### Worked example
Take A = (1000.00 N, 1000.00 E) and the consecutive coordinates (latitude, departure) of the lines:

| Line | Consecutive lat | Consecutive dep | Station | Independent N | Independent E |
|---|---|---|---|---|---|
| AB | +85.20 | +52.30 | B | 1085.20 | 1052.30 |
| BC | +30.10 | +146.80 | C | 1115.30 | 1199.10 |
| CD | -92.40 | -76.50 | D | 1022.90 | 1122.60 |

Each independent coordinate is the sum of A's coordinates and all consecutive coordinates up to that station. For example $N_C=1000+85.20+30.10=1115.30$ m.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which description fits an open traverse?
   A. It starts and ends on the same station and closes mathematically
   B. It starts at a known station and ends at a point of unknown position, so there is no closing check
   C. It starts and ends on two stations of known position
   D. It is run only with a compass and never with a theodolite
   Answer: B. An open traverse ends at an unknown point, so no closure check exists; angles and lengths must be verified by repeat measurement. (Key point: Open traverse)

2. Which of these is a closed traverse?
   A. A road survey ending at a new, unfixed point
   B. A pipeline route with no known end station
   C. A link traverse starting and ending on stations of known position
   D. A canal survey checked only by repeat chaining
   Answer: C. A closed traverse is either a closed loop or a closed link between known stations; both give a mathematical check. (Key point: Closed traverse types)

3. Line AB has L = 100 m and bearing 60°. What are its consecutive coordinates (latitude, departure)?
   A. +86.6 m, +50 m
   B. +50 m, +86.6 m
   C. +100 m, +60 m
   D. +50 m, +50 m
   Answer: B. Latitude = 100 cos60° = +50 m and departure = 100 sin60° = +86.6 m, measured from the preceding station A. (Key point: Consecutive coordinates)

4. Why are independent coordinates preferred for plotting?
   A. They are measured from the previous station, so errors cancel
   B. They need no origin
   C. All stations refer to one common origin, so plotting errors do not accumulate
   D. They are always smaller numbers
   Answer: C. Independent coordinates are the algebraic sum of consecutive coordinates from a single origin, so each station is plotted independently. (Key point: Independent coordinates)

## Related in Surveying II

- [Consecutive, independent coordinates, plotting](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aconsecutive-independent-coordinates-plotting) — 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
- [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×
- [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 traverse ABCDA missing data, C(1200, 2000)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcda-c-1200-2000) — 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
- [Area of traverse by DMD and coordinates (N/S/E/W)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aarea-closed-traverse-nswe-108) — Surveying I, chapter 9
- [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×