Closing the Loop: A 12-Station Traverse with a Failing Linear Misclosure
You are checking a 12-station closed traverse run for a proposed 1.2 km access road in Gampaha District. The total traverse length is 1,860 m. The field sheet records a clockwise angular misclosure of +52″ after distributing nothing; the coordinate misclosure is ΔE = +0.19 m and ΔN = -0.11 m. The project specification requires angular misclosure ≤ 20″√n and linear misclosure ≤ 1:10,000. The instrument was a 2″ total station, and distances were measured in two faces with a prism constant checked at the start. One leg, from Station 4 to Station 5, is only 8.5 m long and was observed with a steep vertical angle; the backsight at Station 4 was partly obstructed by a wall. The field party proposes applying Bowditch (compass) rule and submitting the coordinates, arguing that the linear misclosure is 'only 22 cm'. A junior surveyor suggests deleting the short leg and re-computing the closure. The client needs coordinates for earthwork quantities and a boundary check against an adjacent lot. You have the raw angles, distances, and station sketch.
1. Does the traverse meet the project specification? Show the checks.
Read the worked answer
For n = 12, the allowable angular misclosure is 20″√12 = 69.3″. The observed angular misclosure is 52″, so the angular check passes.
The linear misclosure is √(0.19² + 0.11²) = √(0.0361 + 0.0121) = √0.0482 = 0.2195 m. The relative misclosure is 0.2195 / 1,860 = 1 / 8,474. The specification requires 1:10,000, which allows 1,860 / 10,000 = 0.186 m. The observed 0.220 m fails the linear specification by about 0.034 m.
So the traverse is not acceptable as submitted for the boundary check. It may be adequate for some earthwork purposes after adjustment, but it should not be used to fix a boundary without further work.
2. How should you isolate the source of the misclosure, and is Bowditch adjustment appropriate?
Read the worked answer
Do not start by adjusting. First inspect the angle at Station 4, where the backsight was partly obstructed, and reobserve the short 8.5 m leg. A short leg with a steep vertical angle is sensitive to centring, pointing and prism setup errors, and a small angular error there can produce a disproportionate linear misclosure. Check the prism constant, EDM scale, temperature and pressure, and the control coordinates. Compare independent check measurements between stations.
Bowditch is not the best choice here. It distributes misclosure in proportion to leg length and assumes random error, so it will not correct a blunder and will distort a short leg. A least-squares adjustment with realistic weights for angles and distances is more defensible, and it provides residuals that help locate the bad observation. Deleting the short leg is not acceptable: it changes the network geometry and hides the problem.
3. If the suspect observations cannot be repeated, what coordinates may be issued?
Read the worked answer
Issue provisional coordinates only, clearly labelled as such, and only for uses that can tolerate the uncertainty, such as preliminary earthwork quantities. Do not issue them as boundary control. State the misclosure, the failed specification, the suspect station and the adjustment method used.
For the boundary check, use independent control or a reobserved connection to the adjacent lot. If a final product is required, reobserve the weak angle and short leg, then adjust by least squares and confirm that the closure passes. Document the decision so that the client and later users understand why the coordinates are provisional.