Solution: Coordinate Systems

Problem (4)

Horizontal ground measurements for a survey in Tippecanoe County, Indiana, are shown below. The horizontal angles have been balanced to eliminate angular misclosure.
Using included control point LB2204 Morenci, the measurements will ultimately be reduced to Indiana's West SPC zone.



Might the angular misclosure be affected if arc-to-chord corrections are applied to the angles when reducing them to grid?

Solution

Being on the west side of Indiana, the survey is west of the zone's central meridian.The projected traverse lines are concave easterly.

The corrected grid angle at a point is

For each line, the arc-to-chord correction is the same magnitude at both ends. Each correction is subtracted as a BS for one angle and added as a FS for another. The sum of the corrections, then, is zero.
Each angle changes by the difference between its BS and FS arc-to-chord corrections. While there might be slight differences, they will be less than 0.1 seconds so the angle total will still balance correctly within the measurement accurary.