Wharf Control Traverse That Fails the Specification
You are the survey manager for a wharf deck extension in Kingston Harbour. Your six-station control traverse runs 380 m around the site and closes with misclosure 0.075 m (0.048 m east, 0.057 m north). The specification requires horizontal control to close at least 1:10,000. Observations were made with a 1-second total station and a prism constant of -30 mm; the instrument was calibrated six months ago. Distances were not corrected for temperature or pressure, and the day was 34 degrees C with a pressure of 1010 hPa. Two stations are on the wharf edge where passing forklifts cause vibration. The steel tape used to check a 30 m bay gives 30.012 m, while the total station gives 30.006 m. Pile caps are due to be set out from the traverse tomorrow. The client asks whether the traverse is acceptable and whether Bowditch adjustment can be used.
1. Compute the linear misclosure and relative precision, and assess the traverse against the specification.
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Linear misclosure = square root of (0.048 squared + 0.057 squared) = square root of (0.002304 + 0.003249) = square root of 0.005553 = 0.0745 m. Relative precision = 380 / 0.0745 = approximately 5,100, so about 1:5,100. The specification requires 1:10,000, so the traverse fails by roughly a factor of two. The 30 m bay check gives a difference of 0.006 m between tape and total station, about 1:5,000, which is not conclusive but is consistent with a possible distance problem. Relative precision alone is not a complete acceptance test: I would also compute angular misclosure, station residuals, and the geometry of the traverse. A traverse that fails the closure specification should not be used as the sole control for pile-cap setting out.
2. Identify the likely error sources and explain what checks or re-observation you would carry out before adjusting anything.
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Likely sources include a prism constant applied with the wrong sign or not applied at all over several legs; missing temperature and pressure corrections, which produce a systematic scale error; centering and instrument-height errors; vibration from forklifts causing poor pointings; weak control coordinates; and ordinary angular error. A 34 degrees C temperature with no correction can contribute tens of parts per million, which over 380 m is only about 0.015 m, so it may not explain the whole closure but it is still systematic. I would first check the prism constant and EDM settings, then reduce distances with temperature and pressure, reobserve angles on two faces, and repeat the traverse with forced centering if possible. I would compute angular closure and station residuals, and compare repeated measurements. A least-squares adjustment with realistic standard deviations will show whether the error behaves randomly or systematically. Bowditch is not appropriate if a systematic EDM or prism error is present, because it would smear that error across the traverse rather than remove it.
3. After re-observation, what adjustment and setting-out procedure would you recommend, and can Bowditch be used?
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If re-observation after correcting the identified errors meets 1:10,000 and the angular closure is acceptable, the traverse can be adjusted. For a small control traverse with random errors, Bowditch or the compass rule is defensible. For a wharf with tight tolerances and a suspected systematic error, a least-squares adjustment is preferable because it uses the actual observation geometry and weights and gives residuals that can be examined. Before setting pile caps, establish independent check points and set out one cap, then verify it by a different method, such as a total station from another control station or an offset from a verified baseline. Do not set all caps from a single adjusted traverse without redundancy. Report the final coordinates, adjustment method, residuals, and achieved accuracy, and state clearly that the original 1:5,100 traverse was not used.