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Traverse Closure and Precision

E = (\sum Lat)^{2} + (\sum Dep)^{2} precision = 1 : \frac{P}{E}

Linear error of closure E is the hypotenuse of the latitude and departure misclosures. Precision (relative accuracy) is 1:(P/E) where P is the traverse perimeter. Compass (Bowditch) rule distributes corrections proportional to course length; transit rule uses |Lat| and |Dep|.

E

Linear error of closure

\sum Lat

Latitude misclosure

\sum Dep

Departure misclosure

P

Perimeter (sum of course lengths)

Step-by-step solved example

ΣLat = +0.12 ft, ΣDep = −0.16 ft, perimeter P = 2000 ft. Find E and precision.

Error of closure from Σlat, Σdep. Precision = 1:(P/E).

1. Closure
E = √(0.12² + 0.16²) = √0.0400 = 0.20 ft.
$E = 0.20 ft$
2. Precision
P/E = 2000/0.20 = 10 000 → precision 1:10 000.
$1 : 10000$

Answer: E = 0.20 ft, precision = 1:10 000

10 practice questions

0/10 correct

1.ΣLat = 0.30 m, ΣDep = 0.40 m. E =

2.Precision is reported as 1:n where n =

3.P = 5000 ft, E = 2.5 ft. Precision is

4.Bowditch correction to a course’s latitude is

5.A closed-loop traverse should have ΣLat and ΣDep theoretically equal to

6.If E = 0, the computed coordinates of the end point

7.Relative accuracy 1:5000 with P = 2.50 km means E is

8.Angular misclosure of an n-sided closed loop is

9.Transit rule (vs Bowditch) distributes Lat correction proportional to

10.ΣLat = −0.08, ΣDep = +0.06, P = 1000 (same units). Precision nearest