What a traverse is
A traverse is a chain of survey lines: horizontal angles between the lines are measured with a theodolite or total station, and horizontal distances with a tape or EDM. From these measurements and the known data (coordinates and an initial bearing) the coordinates of every station are computed. Traverses provide horizontal control for topographic surveys, setting out and cadastral work.
- A closed traverse starts and ends at the same station and forms a polygon. The check is the polygon angle sum and the return to the start.
- A link (open) traverse runs between two control points A and B with known coordinates and two known bearings. The check is arriving at B and at the closing bearing.
Angular misclosure
For a closed traverse with n stations the theoretical sum of interior angles is 180°·(n − 2), of exterior angles 180°·(n + 2). For a link traverse with right-hand angles Σβ = α start − α end + 180°·n, with left-hand angles Σβ = α end − α start + 180°·n.
The misclosure fβ = Σβ meas − Σβ theor is compared with the tolerance, for a 30″ theodolite ±1′·√n, and distributed equally over the angles with the opposite sign.
Bearings and quadrants
The next bearing: with right-hand angles α(i+1) = α(i) + 180° − β, with left-hand angles α(i+1) = α(i) − 180° + β, reduced to 0…360°.
| Bearing α | Quadrant bearing r | Sign ΔX | Sign ΔY |
|---|---|---|---|
| 0°…90° | NE: r = α | + | + |
| 90°…180° | SE: r = 180° − α | − | + |
| 180°…270° | SW: r = α − 180° | − | − |
| 270°…360° | NW: r = 360° − α | + | − |
Increments and linear misclosure
Increments (latitudes and departures): ΔX = d·cos α, ΔY = d·sin α. In a closed traverse their sums should be zero, in a link traverse equal to the coordinate differences of B and A. The misclosures fx, fy give the linear misclosure f = √(fx² + fy²) and the relative precision f / P = 1 : N (P is the traverse length); 1 : 2000 is a common tolerance. Corrections are proportional to side lengths (Bowditch, compass rule): vx = −fx·d / P, vy = −fy·d / P.
Example
A closed five-station traverse, right-hand angles 107°29′, 112°05′, 92°09′, 119°16′, 109°02′, sides 159.31, 181.60, 165.84, 152.12, 152.95 m, bearing 1–2 = 32°19′, X1 = Y1 = 5000.00 m. Σβ = 540°01′, theoretical 540°00′, fβ = +1′ (tolerance ±2.2′), −12″ to each angle; fx = +0.05 m, fy = −0.04 m, f = 0.064 m, relative 1 : 12 600 — accepted. Press “Example” to see the full sheet.
How to use
- Choose the traverse type and whether right- or left-hand angles were measured.
- Enter the initial bearing and coordinates; if only control point coordinates are known, use the inverse problem.
- Fill in or paste the table of angles and sides. The link under the result keeps all the data.