3. Traverse Closure; Adjustment

a. Similarities; Differences

Latitudes and departures are computed same as those for a loop traverse:

img38

Eqn (H-1)

Where the two differ is in how their closure is determined and adjustments made.

On a loop traverse, the closure condition is:

img40

Eqn (H-2)

 

But because a link traverse does not close back on itself, that condition does not apply. Instead, we need to know the location, relative or absolute, of the traverse's end points.

If we know the relative location, Figure H--12,

img2

Figure H-12
Relative Positions of Endpoints Are Known

 

the closure condition is

img41

Eqn (H-3)

 

If we have coordinates of the endpoints, Figure H-13,

img4

Figure H-13
Endpoint Coordinates are Known

 

the closure condition is

img42

Eqn (H-4)

 

The latitude and departure errors would be a result of how well the closure condition was met. Linear closure and precision would be determined just as for a loop traverse.

 

b. Example

Given the link traverse in Figure H-14 with adjusted directions and known end point coordinates:

img43

Figure H-14
Adjust Angles on a Crossing Traverse

 

(1) Compute latitudes and departures

img44

img45

img46

 

Line Direction Length Lat Dep
QR S 56°23'38"E 398.75' -220.700' +332.104'
RS S 75°17'42"W 422.89' -107.347' -409.038
ST N 43°05'47"E 604.49' +441.402' +413.004'
  sums: 1426.13' +113.355' +336.070

 

(2) Compute closure and precision

From the coordinates

img47

The closure and precision are

img48

img49

(3) Adjusting by the Compass Rule

img50

img51

img52

img53

img54

 

Line Direction Length Lat Dep Adj Lat Adj Dep
QR S 56°23'38"E 398.75' -220.700' +332.104' -220.715' +332.124'
RS S 75°17'42"W 422.89' -107.347' -409.038 -107.363' -409.017'
ST N 43°05'47"E 604.49' +441.402' +413.004' +441.379' +413.034'
  sums: 1426.13' +113.355' +336.070 +113.301' +336.141'
          check check

 

Adjusted lengths and directions would be computed the same as for a loop traverse, as would coordinates.