Traversing
A traverse is a series of connected survey lines whose lengths and directions are measured, used to establish control points for mapping and construction. A closed traverse either returns to its starting point (loop traverse) or runs between two known points (link traverse); both allow the errors to be checked and distributed. An open traverse, ending at an unknown point, cannot be checked and should be avoided for control work.
Field work measures the angles at each station and the length of each line, today usually with a total station. The office work follows a fixed routine. First, check the angular misclosure against the theoretical sum and distribute it equally among the angles if within tolerance. Second, compute bearings of each line from the starting bearing and the adjusted angles. Third, compute latitudes (north components) and departures (east components) of each line. For a closed loop both sums should be zero; their actual values give the linear misclosure. Fourth, adjust by the Bowditch (compass) rule, which distributes corrections in proportion to line length, or the transit rule, which uses the sizes of the latitudes and departures.
Finally, coordinates of each station are found by adding the adjusted components. For large or precise networks, least squares adjustment replaces these rules and gives realistic accuracy estimates. Traverses are now often combined with GNSS control, which fixes a few points absolutely while the traverse provides dense local control.
Interior angles of a closed loop: Σ = (n − 2) × 180°Linear misclosure: e = √(ΣL² + ΣD²) (sums of latitudes and departures)Bowditch: correction to a line = − (error in Σ) × (line length / perimeter)Precision = e / perimeter
Problem. A closed traverse has a perimeter of 860 m and sums of latitudes +0.12 m and departures −0.09 m. A 210 m line has latitude +150.20 m and departure +146.95 m. Apply Bowditch.
- Misclosure e = √(0.12² + 0.09²) = 0.15 m; precision = 1 in 5 733.
- Latitude correction = −0.12 × 210 / 860 = −0.029 m; adjusted latitude = 150.171 m.
- Departure correction = +0.09 × 210 / 860 = +0.022 m; adjusted departure = 146.972 m.
Answer. Adjusted latitude 150.171 m, departure 146.972 m; precision about 1 in 5 700
Quick quiz
1Why avoid open traverses for control?
They cannot be checked for errors.
2What does the Bowditch rule distribute corrections by?
Line length relative to perimeter.
3Which method replaces Bowditch for precise networks?
Least squares adjustment.
References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- S. K. Duggal, Surveying (Vols 1 and 2), McGraw Hill Education (India), latest edition.
- B. C. Punmia, A. K. Jain, A. K. Jain, Surveying (Vols 1 to 3), Laxmi Publications, latest edition.
- C. D. Ghilani, P. R. Wolf, Elementary Surveying: An Introduction to Geomatics, Pearson, latest edition.
Free and official sources
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