4. Examples
These examples are a continuation of those from the Latitudes and Departures chapter.
a. Traverse with Bearings
 |
| 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 Equations E-1 and E-2:
Now solve Equations E-3 and E-4 for each line:
Line AB
Line BC
Line CD
Line DA
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
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
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
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
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
 |
| 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 Equations E-1 and E-2:
Solve Equations E-3 and E-4 for each line:
Line ST
Line TU
Line UV
Line VS
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
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
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
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
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.
 |
| 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 Equations E-1 and E-2:
Solve Equations E-3 and E-4 for each line:
Line EF
Because it's in the SE quadrant: Az = 180°00'00"+(-46°56'57.1") = 133°03'02.9"
Line FG
Because it's in the NE quadrant: Az = 24°33'19.7"
Line GH
Because it's in the SW quadrant: Az = 180°00'00"+(61°05'18.8") =241°05'18.8"
Line HE
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 | |||