Closure and precision
Add up the north–south components (latitudes) and east–west components (departures) of every course. On a perfect loop both sums are zero. What's left over is the misclosure in northing and easting, and the linear misclosure is the hypotenuse of those two.
The precision ratio is the total length of the traverse divided by the linear misclosure, written as 1 : something. Bigger is better. A 1,600-foot loop that misses by 0.04 ft closes at about 1 : 40,000.
The compass rule
The compass rule assumes errors build up in proportion to distance. Each course gets a share of the misclosure equal to its share of the total length:
correction to latitude = −(misclosure in N) × course length ÷ total length
correction to departure = −(misclosure in E) × course length ÷ total length
Long courses take more of the correction and short ones less. The last point lands exactly on the start.
A worked example
A four-sided loop starting at N 5000.000, E 5000.000:
| Course | Azimuth | Distance | Corr. N | Corr. E | Adjusted N, E |
|---|---|---|---|---|---|
| 1→2 | 034°59'38" | 413.14 | −0.009 | −0.006 | 5338.441, 5236.925 |
| 2→3 | 119°08'10" | 386.67 | −0.008 | −0.006 | 5150.169, 5574.662 |
| 3→4 | 215°16'30" | 440.47 | −0.009 | −0.007 | 4790.564, 5320.283 |
| 4→1 | 303°10'57" | 382.68 | −0.008 | −0.006 | 5000.000, 5000.000 |
Total length is 1,622.96 ft. The unadjusted loop misses by +0.034 N and +0.025 E, a linear misclosure of 0.042 ft, so the precision is about 1 : 38,000. The corrections add up to exactly the misclosure with the sign flipped, and the loop closes. (Values are rounded for display.)
Doing it in ChainLink
Tap the traverse points in order on the plot, ending on your closing shot, the separate re-observation of the starting point, and tap Done. You'll see total distance, closure error in N and E, and the precision ratio.
Apply the Bowditch adjustment and the traverse points move by their proportional corrections. Sideshots move with the station they were shot from, so topo stays tied to the adjusted traverse. Undo restores everything. Because the adjustment rewrites coordinates, export a CSV first.
Questions
What is a good precision ratio for a traverse?
It depends on the work and on your state's minimum technical standards, which set the required closure for boundary surveys. Ratios of 1:10,000 and better are common targets, and control traverses are held to tighter values. Check the standard that applies to your job.
What is the difference between the compass rule and the transit rule?
The compass rule distributes the misclosure in proportion to each course's length. The transit rule distributes it in proportion to the size of each course's latitude and departure. ChainLink uses the compass rule. A least squares adjustment is the rigorous method and is not built in.
Does the adjustment fix angular error?
The compass rule distributes the linear misclosure that remains. It does not check or balance the angles first, so look at your angular closure on its own if your procedures call for it.