Traverse Misclosure and Adjustment
A closed-loop traverse is run around a parcel. The traverse has 6 sides with the following measured interior angles: 120°00'00", 115°30'00", 125°15'00", 118°45'00", 122°30'00", and 118°30'00". The distances are: 100.000 m, 150.000 m, 200.000 m, 120.000 m, 180.000 m, and 130.000 m. The azimuth of the first side is 45°00'00". The coordinates of the starting point are (1000.000, 2000.000). The surveyor computes the traverse and finds a linear misclosure of 0.050 m. The allowable misclosure for the project is 0.03 m. The surveyor proposes to adjust the traverse using the compass rule. What is the angular misclosure? Should the surveyor adjust the angles before applying the compass rule? What is the precision of the traverse?
1. Calculate the angular misclosure and determine if it is within acceptable limits for a 6-sided traverse.
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Sum of interior angles for a 6-sided polygon = (6-2)*180 = 720°00'00". Sum of measured angles: 120°00'00" + 115°30'00" = 235°30'00"; +125°15'00" = 360°45'00"; +118°45'00" = 479°30'00"; +122°30'00" = 602°00'00"; +118°30'00" = 720°30'00". The sum is 720°30'00", which is 0°30'00" (30 minutes) too high. Angular misclosure = +0°30'00". For a 6-sided traverse, the allowable angular misclosure depends on the instrument and project specifications. Typically, for a 5" instrument, the allowable angular misclosure might be 5" * sqrt(n) = 5" * sqrt(6) ≈ 12.2". Here, 30 minutes is 1800 seconds, which is far beyond any reasonable tolerance. Therefore, the angular misclosure is unacceptable. The surveyor must re-observe the angles before proceeding.
2. Explain the proper procedure for adjusting the traverse and computing the final coordinates.
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The surveyor should not apply the compass rule until the angular misclosure is resolved. The angular misclosure is excessive (30 minutes), indicating a gross error in angle measurement. The surveyor should re-measure the angles, possibly checking for mistakes such as transposing digits or misreading the instrument. After re-measuring, if the angular misclosure is within tolerance, the angles should be adjusted equally (or according to weights) to sum to the theoretical value. Then, using the adjusted azimuths and measured distances, compute the linear misclosure. If the linear misclosure is within the allowable 0.03 m, apply the compass rule: distribute the misclosure in northing and easting proportional to the side lengths. Compute final coordinates. The precision of the traverse is the ratio of the linear misclosure to the total traverse length. Total length = 100+150+200+120+180+130 = 880 m. Linear misclosure = 0.050 m. Precision = 880/0.050 = 17600, or 1:17600. This is less precise than the allowable (which would be 880/0.03 = 29333, or 1:29333). So the traverse does not meet the project precision requirement. The surveyor must improve the traverse by re-measuring distances or angles, or using better equipment.