Latitudes, Departures, and Closure

lat = L cos θ, dep = L sin θ, E = (\sum lat)^{2} + (\sum dep)^{2}

Azimuth from north: lat = L cos az, dep = L sin az (east +). Linear closure E over perimeter P is the precision 1:(P/E). Compass rule distributes corrections proportional to side length.

$l a t$: Northing change
$d e p$: Easting change
$E$: Linear misclosure

Step-by-step solved example

One course 100 m due N, next 100 m due E, close with 141.4 m SW? Ideal close?

lat/dep close the traverse loop; misclosure E.

1. Sums
Σlat=+100, Σdep=+100 so far. Need lat=−100, dep=−100.
2. Length
L=√(100²+100²)=141.4 m at azimuth 225° (S 45° W).

Answer: 141.4 m at S 45° W

10 practice questions

0/10 correct

1.A closed traverse of perfect data has

2.Precision 1:5000 means

3.Compass (Bowditch) correction to a side is proportional to

4.Course 80 m, az 30°: lat ≈

5.Due west departure is

6.If E=0.20 m and P=1000 m, ratio is

7.Transit rule weights by

8.Bearing N 90° E is

9.Missing one side (length+bearing) is solved from

10.sin and cos of azimuth need