10 TRAVERSE COMPUTATIONS
Asterisks indicate problems that have partial answers given in Appendix G.
10.1 In adjusting measured traverse angles, why aren’t adjustments made in proportion to the
angle sizes?
*10.2 The sum of seven interior angles of a closed-polygon traverse each read to the nearest
3
is
899 59 39 .
What is the misclosure, and what correction would be applied to each
angle in balancing them by method 1 of Section 10.2?
10.3 Similar to Problem 10.2, except the angles were read to the nearest 2″ and their sum was
10.4 Similar to Problem 10.2, except the angles were read to the nearest 1″ and their sum for
*10.5 Balance the angles in Problem 9.22. Compute the preliminary azimuths for each course.
Preliminary computations are in the solution of Problem 9.22. The misclosure was 14″.
(*)
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10.6 Balance the following interior angles (angles-to-the-right) of a five-sided closed
polygon traverse using method 1 of Section 10.2. If the azimuth of side AB is fixed at
218°59′30″ calculate the azimuths of the remaining sides. 𝐴 = 132°47′06″; 𝐵 =
108°46′18″; 𝐶 = 107°19′37″; 𝐷 = 81°50′36″; 𝐸 = 109°16′18″. (Note: line BC
bears NE.)
*10.7 Compute departures and latitudes, linear misclosure, and relative precision for the
traverse of Problem 10.6 if the lengths of the sides (in feet) are as follows: AB = 202.74;
BC = 283.87; CD = 498.37; DE = 320.33; and EA = 380.78. (Note: Assume units of feet
for all distances.)
Course
Length
Dep
Lat
AB
202.74
−127.565
−157.577
BC
283.87
151.42
−240.113
CD
498.37
481.592
128.224
DE
320.33
−125.5
294.722
EA
380.78
−379.946
−25.193
∑ = 1686.09
0.001
0.063
LEC = 0.063 ft; Relative precision = 1:26,800
10.8 Using the compass (Bowditch) rule, adjust the departures and latitudes of the traverse
in Problem 10.7. If the coordinates of station A are X = 20,000 ft and Y = 15,000 ft,
calculate (a) coordinates for the other stations, (b) adjusted lengths and azimuths of lines
BC and CD, and (c) the final adjusted angles at stations B and C.
Course
Dep
Lat
−127.566
−157.585
−240.123
481.592
128.206
294.71
−379.946
10.9 Balance the following interior angles-to-the-right for a polygon traverse to the nearest
1″ using method 1 of Section 10.2. Compute the azimuths assuming a fixed azimuth of
35°09′32″ for line AB. 𝐴 = 57°00′34″; 𝐵 = 88°24′40″; 𝐶 = 126°37′20″; 𝐷 =
46°03′46″; 𝐸 = 221°53′30″. (Note: Line BC bears NW.)
10.10 Determine departures and latitudes, linear misclosure, and relative precision for the
traverse of Problem 10.9 if lengths of the sides (in meters) are as follows: AB = 383.808;
10.11 Using the compass (Bowditch) rule adjust the departures and latitudes of the traverse in
Problem 10.10. If the coordinates of station A are X = 310,630.892 m and
121,311.411 m,Y
calculate (a) coordinates for the other stations and, from them, (b)
the lengths and bearings of lines BC and EA, and (c) the final adjusted angles at B and
D.
10.12 Same as Problem 10.9, except assume line AB has a fixed azimuth of 125°09′32″ and
line BC bears NE.
10.13 Using the lengths from Problem 10.10 and azimuths from Problem 10.12, calculate
departures and latitudes, linear misclosure, and relative precision of the traverse.
Course
Length
Dep
Lat
AB
383.846
313.8165
−221.0361
BC
360.256
199.2084
300.1673
CD
342.244
−115.9685
321.9973
DE
336.228
−148.7449
−301.5364
EA
267.550
−248.3276
−99.5810
∑ = 1690.124
−0.0162
0.0110
Linear misclosure = 0.0196; Relative precision = 1:86,300
10.14 Adjust the departures and latitudes of Problem 10.13 using the compass (Bowditch) rule,
and compute coordinates of all stations if the coordinates of station A are
243,605.596 mX
and
25,393.201 m.Y
Compute the length and azimuth of line
CD.
Course
Dep
Lat
Point
X
Y
AB
313.8202
−220.0386
A
243,605.596
25,393.201
BC
199.2118
300.1649
B
243,919.416
25,172.162
CD
−115.9652
321.9951
C
244,118.628
25,472.327
DE
−148.7417
−301.5386
D
244,002.663
25,794.322
EA
−248.3251
−99.5828
E
243,853.921
25,492.784
Course
Length
Azimuth
CD
342.241
340°11’37”
10.15 Compute and tabulate for the following closed-polygon traverse: (a) preliminary
bearings (b) unadjusted departures and latitudes (c) linear misclosure and (d) relative
precision. (Note: line BC bears NE.)
Course
Azimuth
Length (m)
Interior Angles
AB
75°14′47″
409.838
A = 12°25’31”
BC
360.225
B = 48°19’25”
CD
342.213
C = 126°37’24”
DE
337.191
D = 46°03’36”
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copyright laws as they currently exist. No portion of this material may be reproduced, in any form
or by any means, without permission in writing from the publisher.
EA
85.125
E = 306°34’19”
(a) Preliminary azimuths are listed below.
(b) Unadjusted latitudes and departures are listed below.
(c) 1.0024 m
(d) 1:1500
From WolfPack:
Station
Unadj. Ang.
Adj. Ang.
A
12°25’31.0″
12°25’28.0″
B
48°19’25.0″
48°19’22.0″
C
126°37’24.0″
126°37’21.0″
D
46°03’36.0″
46°03’33.0″
E
306°34’19.0″
306°34’16.0″
Angular
misclosure:
15″
Course
Length
Azimuth
Dep
Lat
AB
409.838
75°14’47”
396.326
104.371
BC
360.225
303°34’09”
−300.146
199.184
CD
342.213
250°11’30”
−321.965
−115.97
DE
337.191
116°15’03”
302.415
−149.14
EA
85.125
242°49’19”
−75.7265
−38.882
∑=1534.592
0.9033
−0.4345
*10.16 In Problem 10.15, if one side and/or angle is responsible for most of the error of closure,
which is it likely to be?
*10.17 Adjust the traverse of Problem 10.15 using the Compass Rule. If the coordinates in
meters of point A are 10,356.548 E and 98,761.391 N, determine the coordinates of all
other points. Find the length and bearing of line EA.
Course
Dep
Lat
Point
X
Y
AB
396.0843
104.4866
A
10,356.548
98,761.391
BC
−300.3583
199.2860
B
10,752.632
98,865.878
CD
−322.1662
−115.8705
C
10,452.274
99,065.164
DE
302.2168
−149.0447
D
10,130.108
98,949.293
EA
−75.7766
−38.8574
E
10,432.325
98,800.248
EA = 85.159 m; AzEA = 242°51’06”
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copyright laws as they currently exist. No portion of this material may be reproduced, in any form
or by any means, without permission in writing from the publisher.
Course
AB
BC
CD
DA
10.18
Bearing
N 22°36′40″ W
S60°39′24″W
S 38°46′10″E
N 88°22′58″ E
Length
314.02
264.49
213.50
217.69
10.19
Azimuth
252°36′35″
124°51′20″
50°41′28″
320°27′42″
Length
449.60
427.28
301.49
243.23
10.18 Solution from WolfPack
Unbalanced
Course Length Bearing Dep Lat
10.19 Solutions from WolfPack
Unbalanced
Course Length Azimuth Dep Lat
———————
Course Distance Azimuth
10.20 Compute the linear misclosure, relative precision, and adjusted lengths and azimuths for
the sides after the departures and latitudes are balanced by the compass rule in the
following closed-polygon traverse.
Length
Departure
Latitude
Course
(m)
(m)
(m)
AB
412.516
−216.2394
−351.2975
BC
513.185
+512.9654
+15.0112
CA
448.495
−296.7364
+336.2964
Linear Misclosure = 0.0145
Relative Precision: 1: 94,600
Course
Length
Dep
Lat
Adj Dep
Adj Lat
Length
Azimuth
AB
412.516
−216.2394
−351.2975
−216.236
−351.301
412.517
211°36‘49″
BC
513.185
+512.9654
+15.0112
+512.969
+15.008
513.189
88°19‘27”
CA
448.495
−296.7364
+336.2964
−296.733
+336.293
448.490
318°34‘34”
1374.196
−0.0145
0.0101
0.000
0.000
10.21 The following data apply to a closed link traverse [like that of Figure 9.1(b)]. Compute
preliminary azimuths, adjust them, and calculate departures and latitudes, misclosures in
departure and latitude, and traverse relative precision. Balance the departures and latitudes
using the compass rule, and calculate coordinates of points B, C, and D. Compute the final
lengths and azimuths of lines AB, BC, CD, and DE.
Station
Measured
Angle (to the
right)
Adjusted
Azimuth
Measured
Length (ft)
X (ft)
Y (ft)
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322°41’31”
A
267°19’13”
2,517,347.31
395,025.36
243.07
B
248°59’20”
258.93
C
110°29’24”
197.41
D
92°03’00”
2,517,910.07
395,184.30
321°32’20”
From WolfPack:
Unbalanced
Course Length Azimuth Dep Lat
AzMk1
AzMk2
10.22 Similar to Problem 10.21, except use the following data:
Station
Measured
Angle (to
right)
Adjusted
Azimuth
Measured
Length (m)
X (m)
Y (m)
314°09′23″
A
263°48′52″
194,325.090
25,353.988
957.957
B
263°45′24″
945.617
C
98°55′04″
857.724
D
110°21′40″
196,277.341
26,262.583
331°00′27″
AzMk2
From WolfPack:
Angle Summary
Station Unadj. Angle Adj. Angle
—————————————
1 263°48’52.0″ 263°48’53.0″
2 263°45’24.0″ 263°45’25.0″
3 98°55’04.0″ 98°55’05.0″
4 110°21’40.0″ 110°21’41.0″
Angular misclosure (sec): –4″
Unbalanced
Course Length Azimuth Dep Lat
————————————————————
1-2 957.957 37°58’16.0″ 589.3965 755.1777
2-3 945.617 121°43’41.0″ 804.2980 –497.2888
3-4 857.724 40°38’46.0″ 558.7086 650.7958
———- ——— ———
Sum = 2,761.298 1952.4032 908.6847
Misclosure in Departure = 1,952.4032 – 1,952.2510 = 0.1522
Misclosure in Latitude = 908.6847 – 908.5950 = 0.0897
Balanced Coordinates
Dep Lat Point X Y
————————————————————
589.3437 755.1466 1 194,325.090 25,353.988
804.2459 –497.3195 2 194,914.434 26,109.135
558.6613 650.7679 3 195,718.680 25,611.815
4 196,277.341 26,262.583
Linear misclosure = 0.1766
Relative Precision = 1 in 15,600
AzMk1
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*10.23 Algebraic sum of departures = 5.12 ft latitudes = −3.13 ft.
5354.54); D (4756.66, 5068.37).
Course
Length
Azimuth
AB
523.55
33°35’31”
BC
412.85
258°36’12”
CD
313.61
204°08’54”
DA
252.76
223°10’58”
10.26 Compute the lengths and azimuths of the sides of a closed-polygon traverse whose
corners have the following X and Y coordinates (in meters): A (8000.000, 5000.000); B
(2650.000, 4702.906); C (1752.028, 2015.453); D (1912.303, 1511.635).
Course
Length
Azimuth
AB
5358.24
266°49’18”
BC
2833.51
198°28’35”
CD
528.70
162°21’11”
DA
7016.32
231°40’28”
10.27 In searching for a record of the length and true bearing of a certain boundary line which
is straight between A and B, the following notes of an old random traverse were found
(survey by compass and Gunter’s chain, declination 4°45′W). Compute the true bearing
and length (in feet) of BA.
Course
A-1
1-2
2-3
3-B
Magnetic bearing
Due North
N 20°00′ E
Due East
S 46°30′ E
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Distance (ch)
11.90
35.80
24.14
12.72
Course
BA
Distance (ch)
58.60
Bearing
S55°51’50″W
Convert direction to true north and then compute departures and latitudes shown below.
Course
A-1
1-2
1-3
3-B
Total
Departure
0.985
14.988
24.057
8.470
48.501
Latitude
11.859
32.512
−1.999
−9.490
32.882
10.28 Describe how a blunder may be located in a traverse.
From Section 10.16: If a single blunder in a distance exists, the azimuth of the
misclosure line will closely approximate the azimuth of the course with the blunder. If
the blunder is in an angle, the perpendicular bisector of the misclosure line will come
close to bisecting the angle with the blunder.
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