4. Example

a. Data

The traverse shown below will be adjusted by all three methods.

Line Azimuth Length (ft) Lat (ft) Dep (ft)
AB 30°00'00" 365.79 +316.783 +182.895
BC 325°33'52" 354.52 +292.395 -200.474
CD 219°03'25" 645.84 -501.508 -406.939
DA 104°12'35" 437.64 -107.428 +424.250
  sums: 1083.79 +0.242 -0.268

The traverse misclosure is purposely large so adjustment differences are more easily seen.

For each adjustment

  • Constants are computed
  • Computations are shown for the first line
  • Adjusted latitudes and departures are shown in a table along with adjusted lengths and directions

b. Compass Rule

Set up the adjustment constants using Equations K-3 and K-4.

Adjust the latitude and longitude of each line using Equations K-5 and K-6. Computations for line AB are:

Fully adjusted traverse

Line ALat (ft) ADep (ft) Azimuth Length (ft)
AB +316.734 +182.949 30°00'40" 365.775
BC +292.347 -200.421 325°34'02" 354.451
CD -501.594 -406.843 219°02'44" 645.847
DA -107.487 +424.315 104°12'54" 437.717
 sums: 0.000 0.000    

c. Transit Rule

Set up the adjustment constants using Equations K-7 and K-8.

Adjust the latitude and longitude of each line using Equations K-9 and K-10. Computations for line BC are:

Fully adjusted traverse

Line ALat (ft) ADep (ft) Azimuth Length (ft)
AB +316.720 +182.935 30°00'37" 365.756
BC +292.337 -200.429 325°33'54" 354.447
CD -501.607 -406.849 219°02'43" 645.861
DA -107.450 +424.343 104°12'34" 437.736
sums: 0.000 0.000    

d. Crandall Method

 Set up the adjustment constants using Equations X-11 and -12.

 Adjust the latitude and longitude of each line using Equations X-13 and -14. Computations for line AB are:

 Fully adjusted traverse

Line ALat (ft) ADep (ft) Azimuth Length (ft)
AB +316.783 +182.895 30°00'00" 365.752
BC +292.395 -200.474 325°33'52" 354.341
CD -501.508 -406.939 219°03'25" 645.855
DA -107.488 +424.250 104°12'35" 437.842
 sums: 0.000 0.000    

e. Comparison of adjusted values

(1) Distances
Line Original Compass Transit Crandall
AB 365.79 365.756 365.756 365.752
BC 354.52 354.447 354.447 354.341
CD 645.84 645.861 645.861 645.855
DA 437.64 437.736 437.736 437.842
 (2) Interior angles
Point Original Compass Transit Crandall
A 105°47'25" 105°47'46" 105°48'03" 105°47'25"
B 115°33'52" 115°33'21" 115°33'17" 115°33'52"
C 73°29'33" 73°28'42" 73°28'49" 73°29'33"
D 65°09'10" 65°10'11" 65°09'51" 65°09'10"

 

The Crandall Method puts all the corrections into distances so angles do not change from their original values. Because the Compass and Transit Rules modify the angles, they both also change the initial azimuth from 30°00'00"; the starting azimuth is unaffected with the Crandall Method.

If the initial direction must be held, then the direction of each line in the Compass and Transit Method adjustments should be rotated by a constant. The constant is the difference between the initial and adjusted directions of the first line. Even though rotating each line the same amount changes the latitudes and departures, traverse closure is not affected.