4. Examples

These examples are a continuation of those from the Latitudes and Departures chapter.

a. Traverse with Bearings

img15
Figure E-6
Bearing Traverse Example

 

Line Bearing Length (ft) Lat (ft) Dep (ft)
AB S 68°05'35"W 472.68 -176.357 -438.548
BC N 19°46'00"W 216.13 +203.395 -73.093
CD N 45°55'20"E 276.52 +192.357 +198.651
DA S 54°59'15"E 382.24 -219.312 +313.065
  sums: 1347.57 +0.083 +0.075
    Distance Lat err
too far N
Dep err
too far E

 

(1) Adjust the Lats and Deps

Setup Equation (E-3):

img24

 

Line AB

img25

Line BC

img26

Line CD

 img27

Line DA

 img28

Check the closure condition

  Adjusted
Line Lat (ft) Dep (ft)
AB -176.386 -438.574
BC +203.382 -73.105
CD +192.340 +198.635
DE -219.336 +313.044
sums: 0.000 0.000
  check check

 

A common mistake is to forget to negate Lat err and Dep err in the correction equations. If that happens, the closure condition will be twice what it originally was as the corrections were applied in the wrong direction.

(2) Compute adjusted lengths and directions

 Use Equations (E-5) and (E-6) along with Figure E-5 to compute the new length and direction for each line.

Line AB

Adj Lat = -176.386 <- South
Adj Dep = -438.574 <- West

img29

 img30

Because it's the SW quadrant, Brng =S 68°05'27.4" W.

Line BC

Adj Lat = +203.382 <- North
Adj Dep = -73.105 <- West

img31

img32

Because it's the NW quadrant, Brng = N 19°46'14.9" W

Line CD

Adj Lat = +192.340 <- North
Adj Dep = +198.635 <- East

img33

 img34

Because it's the NE quadrant, Brng = N 45°55'20.7" E

Line DA

Adj Lat = -219.336 <- South
Adj Dep = +313.044 <- East

img35

img36

Because it's the SE quadrant, Brng = S 54°58'58.0" E


(3) Adjustment summary

  Adjusted Adjusted
Line Lat (ft) Dep (ft) Length Bearing
AB -176.386 -438.574 472.715 S 68°05'27.4" W
BC +203.382 -73.105 216.122 N 19°46'14.9" W
CD +192.340 +198.635 276.479 N 45°55'20.7" E
DE -219.336 +313.044 382.237 S 54°58'58.0" E

 

b. Traverse with Azimuths

img16 
Figure E-7
Azimuth Traverse Example

 

Line Azimuth Length (ft) Lat (ft) Dep (ft)
ST 309°05'38" 347.00 +218.816 -269.311
TU 258°34'22" 364.55 -72.226 -357.324
UV 128°04'44" 472.74 -291.560 +372.123
VS 60°21'26" 292.94 +144.885 +254.602
  sums: 1477.23 -0.085 +0.090
    Distance Lat err
too far S
Dep err
too far E

 

(1) Adjust the Lats and Deps

Setup Equation (E-3):

img37

Line ST

img38

Line TU

img39

Line UV

img40

Line VS

img41

Check the closure condition

  Adjusted
Line Lat (ft) Dep (ft)
ST +218.836 -269.332
TU -72.205 -357.346
UV -291.533 +372.094
VS +144.902 +254.584
sums: 0.000 0.000
  check check

 

(2) Compute adjusted lengths and directions

Use Equations (E-5) and (E-6) along with Figure E-5 to compute the new length and direction for each line.

Line ST

Adj Lat = +218.836 <- North
Adj Dep = -269.332 <- West

img42

 img43

Because it's in the NW quadrant: Az = 360°00'00"+(-50°54'20.4") =309°05'39.6"

Line TU

Adj Lat = -72.205 <- South
Adj Dep = -357.346 <- West

img44

img45

Because it's in the SW quadrant: Az = 180°00'00"+(78°34'36.0") = 258°34'36.0"

Line UV

Adj Lat = -291.533 <- South
Adj Dep = +372.094 <- East

img47

img48

Because it's in the SE quadrant: Az = 180°00'00"+(-51°55'17.6") = 128°04'42.4"

Line VS

Adj Lat = +144.902 <- North
Adj Dep = +254.584 <- East

img49 

 img50

Because it's in the NE quadrant: Az = 60°21'09.7"

(3) Adjustment summary

  Adjusted Adjusted
Line Lat (ft) Dep (ft) Length (ft) Azimuth
ST +218.836 -269.332 347.029 309°05'39.6"
TU -72.205 -357.346 364.568 258°34'36.0"
UV -291.533 +372.094 472.700 128°04'42.4"
VS +144.902 +254.584 292.933 60°21'09.7"

 

c. Crossing Loop Traverse

As long as a traverse closes back on its beginning point, it can be adjusted the same as any other loop traverse.

img17 
Figure E-8
Crossing Loop Traverse Example

 

Line Azimuth Length (ft) Lat (ft) Dep (ft)
EF 133°02'45" 455.30 -310.780 +332.737
FG 24°33'35" 228.35 +207.691 +94.912
GH 241°05'15" 422.78 -204.403 -370.084
HE 349°25'20" 312.85 +307.534 -57.430
  sums: 1419.28 +0.042 +0.135
    Dist Lat err
too far N
Dep err
too far E

 

(1) Adjust and recompute each line.

Setup Equation (E-3):

img51

Line EF

img52

img53

img54

Because it's in the SE quadrant: Az = 180°00'00"+(-46°56'57.1") = 133°03'02.9"

Line FG

img55

img56

img57

Because it's in the NE quadrant: Az = 24°33'19.7"

Line GH

img58

img59

img61

Because it's in the SW quadrant: Az = 180°00'00"+(61°05'18.8") =241°05'18.8"

Line HE

img63

 img64a

img65

Because it's in the NW quadrant: Az = 360°00'00"+(-10°35'00.5") = 349°24'59.5"

(2) Adjustment summary

  Adjusted Adjusted
Line Lat (ft) Dep (ft) Length (ft) Azimuth
EF -310.794 +332.694 455.278 133°03'02.9"
FG +207.684 +94.890 228.335 24°33'19.7"
GH -204.416 -370.124 422.821 241°05'18.8"
HE +307.525 -57.460 312.847 349°24'59.5'
sums: -0.001 0.000
  check (rounding) check