Traverse adjustment: A systematic approach Ashish Kumar Kediya 1, Vivek Shankar2 1
Department of Mining Engineering, Indian School of Mines, Dhanbad-826004
2
Department of Mining Engineering, Indian School of Mines, Dhanbad-826004
Abstract: Traversing is basically associated with measuring the angles/bearings and distances between set of points on the field using surveying instruments. However this manual approach towards computation work is vulnerable to errors owing to a list of reasons. The present paper attempts toward providing with a more coherent approach for eliminating these errors through logical adjustments. In this regard several adjustment methods have been prescribed and their authenticity totally depends upon the closeness to the actual figure. Keywords: traverse, mistakes, systematic errors, accidental errors, normal probability curve, bowditch/transit method. I.
INTRODUCTION
Traversing is a method of establishing control points. It includes positioning of survey stations along a line or path of travel, and then using the previously surveyed/observed stations as a platform for surveying the next station. Traversing has got a hand to play in geodetics, civil engineering, tunneling, surveying engineering and is not aloof from particularly mining engineering, where it is used for preparation of mine plans, water drainage plans, mine layouts etc. it has got an upper hand over triangulation and trilateration in terms of accuracy. It also requires less reconnaissance and organization. It does not even require a great deal of linear and angular measurements to be taken rather only a few observations at each station. II.
TYPES OF TRAVERSES AND CLOSING ERROR
Traverses are of 3 kinds. 1. Open traverses. 2. Closed traverses. 3. Linked traverses.
Open traverse
Open or free traverse consists of a series of linked traverse lines which do not terminate at the starting point itself and thus abstaining from giving a polygonal structure. It is utilized in plotting a strip of land which can then be used to plan a route in road construction0.
FIG.1. AN OPEN TRAVERSE
Close or polygonal or loop traverse is a series of linked traverse lines where the terminal points closes at the starting point thus forming a polygon. It is useful into marking the boundaries of mines, lakes, ponds, etc. construction and civil engineers utilize this practice for preliminary surveys designated area.
FIG.2. A CLOSED TRAVERSE
Linked traverse It is a traverse in which an open traverse is linked to a closed traverse or vice versa.
FIG.3. A LINKED TRAVERSE
Closi ng errors
However most of the times a closed traverse FIG.4. CLOSING ERROR actually does not close it does not imply that it is an open traverse. It is due to a gap left behind called the closing error or linear misclosure arising out of miscalculations or errors in
linear and angular measurements. III.
ERRORS AND THEIR SOURCES
Errors of measurements are of three kinds. 1. Mistakes. 2. Systematic errors. 3. Accidental errors.
Mistakes Mistakes are errors arising out of inattention, inexperience, carelessness and poor judgment or confusion in the mind of the observer. If a mistake is undetected it can produce a serious effect on the final result. However there is no technical law that it follows and so in case of occurrence of mistakes it has to be dealt with distributing techniques. Systematic errors It is an error that under same conditions will always be of same size and sign. It follows some definite mathematical or physical law and a correction can be determined or applied. Such errors are of constant character and are regarded as positive or negative according as they make the result too great or too small. Their effect is cumulative and very serious too they arise generally due to errors in the instrument itself or their improper alignment. Accidental errors These are errors which are totally beyond the ability of the observer to control. They tend sometimes in one direction and sometime in the other. These errors differ in between the true value of the quantity and the determination that is free from mistakes
and systematic errors. They follow the law of chance and hence must be dealt with mathematical laws of probability. IV.
Theory of adjustment
For adjustment of closed traverses we follow approaches that bring the error (closing error/error in area/error in perimeter) as close as possible to zero. The errors have been classified according to the methods of adjustments.
FIG.5. CLASSIFICATION OF ERRORS
Adjusting systematic errors As we know that systematic errors follow certain mathematical law their adjustment is possible by simple algebraic approaches. 1. Errors in distance measurements
Distance measuring instruments (chain, tape, optical/laser instruments) are quite prone to errors and can give a biased distance reading. These may occur because of – •
The zero error of the scale
•
Improper length of chain.
•
Improper/unreadable markings on the tape.
•
Optical/laser errors.
•
Parallax errors.
•
Errors due to temp./sag/ pull/slope etc.
These tend to produce error in distance measurement which is either fixed or varies proportionately with the length measured.
Zero errors, improper length of chains or parallax produces a fixed error. While the rest produce an error which increases proportionately with the distance measured. Whether fixed or variable the error can be found out by direct measurement of a known distance in the field. a) Fixed errors
Supposing the fixed error to be ε. the coordinates of each point of the traverse can be calculated using a mathematical approach. The calculations have been made for a three point traverse but the result has been generalized.
FIG.6. DISTANCE ERROR
Calculating the deviation along x-axis for point (X2,Y2) i.e. δx2 δx2= [comp. of line a-B along x-axis-comp. of line ab along x-axis] Assuming slope= tanθ2 to be the slope of the line a-b Length of line a-b is d2. δx2=(d2+ε)cosθ2-d2cosθ2 Or δx2=εcosθ2 x2 =X2- εcosθ2____________(1) Similarly
y2=Y2-εsinθ2______________(2) Proceeding with the same approach, δx3=[comp of line a-B along x-axis+comp of line B-C along x-axis]-[comp. of line a-b along x-axis+comp.of line b-c along x-axis] δx3= [d2+ε]cosθ2+[d3+ε]cosθ3-d2cosθ2-d3cosθ3 δx3= ε[cosθ2+cosθ3] x3=X3-ε[cosθ2+cosθ3]__________(3) Similarly y3=Y3-ε[sinθ2+sinθ3]__________(4) From __(1),(2)(3),(4). We can infer that the true coordinates of a traverse starting at benchmark (x 1,y1) is ]
] b) Variable errors
Supposing the variable error to be εi=k.di Where k is the const. of proportionality and can be found in the field by measuring a known distance. Following a similar approach as for fixed errors, ]
]
2. Error in angle measurements.
Errors in angle measurements are rare and generally very small in magnitude but these errors can produce drastic effects so they must be adjusted. Unlike the errors in distance measurements, these errors are fixed and do not vary with the magnitude of the angle to be measured.
FIG.7. ANGULAR ERROR
δx2=d2cos[θ2-δ]-d2cosθ2 Or δx2= d2[2.sin(δ/2)sin(θ2-δ/2)] As δ is very small in comparison to the slope angle θ2 Therefore, θ2-δ/2=θ2 And sinδ/2=δ/2 So, δx2= δ.d2.sinθ2 x2=X2-δ.d2.sinθ2 δx3= X3-x3 δx3=X2+d3cos(θ3-δ)-x2-d3cosθ3 Therefore x3=X3-δ[d2.sinθ2+d3.sinθ3] Similarly for y3=Y3+δ[d2.cosθ2+d3.cosθ3]
Generalizing, ]
]
3. Error in both angle and distance measurement
If it is found that by independent measurements of known angles and distances that there is an error in both angle and distance readings. The above mentioned procedures can be applied to correct the readings but as the errors are mutually interdependent and not exclusive (error in angle depends upon length which again contains an error and vice-versa). Hence the order in which the corrections are applied becomes of utmost importance. An error analyses has shown that adjusting the distance error first followed by the angular error produces an overall minimal error. Hence the coordinates should be calculated by first adjusting the distance errors.
Adjustment of accidental errors and mistakes The law that accidental errors follow can be depicted by the normal curve.
FIG.8. NORMAL PROBABILITY CURVE
It shows that smaller the magnitude of error (positive or negative) greater is the frequency of its occurrence. It also shows that the possibility of any error of very large magnitude to occur is very low. Similarly the mistakes follow no mathematical law and hence they are adjusted by techniques of distribution. The approximate methods that are followed to distribute these errors are:
1. Graphical method 2. Bowditch method 3. Transit method
The graphical method This method distribute the errors in such a way that the first point after the initial point has least correction while the last point has the maximum correction applied to it which is equal to the closing error. For a five point traverse ABCDE which does not close as A and A’ do not coincide.
FIG.9. CLOSING ERROR
We draw a line ABCDEA’ with the lengths AB, BC, CD, DE and EA’ representing the actual lengths of the traverse sides (a proper scale may be used).
FIG. 10.
Th en we transfer the closing error (keeping the direction and the magnitude same) over the line.
FIG.11.
We then join the points A and A and also draw lines parallel to closing error AA’ as BB’, CC’, DD’ and EE’. These line segments represent the errors respectively at stations B, C, D and E.
FIG.12.
We can transfer these errors now to the traverse (keeping the magnitude and direction fixed) and we get the adjusted traverse.
FIG.13. ADJUSTED TRAVERSE
The adjustment should be such that the newly formed lines should not intersect their respective counterparts (for example C’D’ must not intersect CD). The bowditch method It distributes the total error in such a way that the longest side of the traverse gets the maximum correction while the shortest side the least. (Correction in latitude/departure of any station)= (Total error in latitudes/departures)*(length of that side)
(Perimeter of the traverse)
The Transit method This method goes one step ahead and distributes the error in latitudes/departures in such a way that the side having the maximum latitudes/departures gets the maximum error correction. (Correction in latitude/departure of any station)= (Total error in latitudes/departures)*(latitude/departure of that side)
(Arithmetic sum of latitudes/departures)
V.
COMPARISION OF METHODS-A CASE SUDY
In this section we try to compare the various methods for adjusting a traverse using a traverse of Indian School of Mines campus. The basic notion of comparison is that the correct and incorrect traverses were taken and the incorrect traverse was adjusted using the methods: 1. Adjusting the systematic error first then applying bowditch distribution. 2. Adjusting the systematic error first then applying transit distribution. 3.
Directly applying bowditch distribution.
4. Directly applying transit distribution.
The criteria for comparison of these methods were taken to be: 1. Closeness in area with the correct traverse. 2. Closeness in perimeter with the correct traverse. 3. Deviation of centroid with that of the correct traverse. 4. Rotation of the traverse from the correct traverse.
CORRECT AND INCORRECT TRAVERSES
APPLYING BOWDITCH DISTRIBUTION
CORRECTING SYSTEMATIC DISTANCE ERROR
APPLYING TRANSIT DISTRIBUTION
CORRECTING SYSTEMATIC ANGULAR ERROR
CORRECTED TRAVERSE USING BOWDITCH DISTRIBUTION ONLY.
TRAVERSE CORRECTED OF SYSTEMATIC ERRORS
APPLYING TRANSIT DISTRIBUTION
APPLYING BOWDITCH DISTRIBUTION
CORRECTED TRAVERSE BY SYSTEMATIC ADJUSTMENT AND BOWDITCH DISTRIBUTION.
TRAVERSE STATION NO. 14.
CORRECTED TRAVERSE USING TRANSIT DISTRIBUTION ONLY.
CORRECTED TRAVERSE BY SYSTEMATIC ADJUSTMENT AND TRANSIT DISTRIBUTION.
CORRECT
FIG.14. PROCEDURE OF COMPARISON
NORTHING(m)
EASTING(m)
2000.000
4000.000
1.
2000.4230
3956.5140
2.
1879.0044
3895.6140
3.
1875.3754
3829.0440
4.
1702.8590
3848.9580
5.
1642.0350
3897.9650
6.
1761.5130
3977.0220
7.
1701.9923
4023.8090
8.
1691.6320
4173.0900
9.
1698.1211
4128.4425
10.
1829.9910
4128.9940
REMARKS BENCH MARK
11.
1854.3040
4178.0940
12.
1911.0783
4182.8080
13.
2014.3300
4166.6270
INCORRECT TRAVERSE STATION NO.
NORTHING(m)
EASTING(m)
14.
2000.000
4000.000
1’.
2005.2885
3962.3698
2’.
1875.4952
3893.3574
3’.
1807.3430
3813.1804
4’.
1727.8280
3836.4824
5’.
1661.9085
3879.2910
ε6’.
1785.3406
3953.4564
7’.
1716.2767
3995.7787
8’.
1694.3047
4045.1284
9’.
1695.9277
4138.1142
10’.
1830.7988
4104.4870
11’.
1850.9570
4157.0009
12’.
1897.2778
4122.0957
13’.
1999.9498
4095.5428
14’.
1995.5524
3969.6195
LINE
COSθ
REMARKS BENCH MARK
SINθ
LENGTH
14-1’
0.1391
-0.9902
38
1’-2’.
-0.8829
-0.4694
147
2’-3’.
-0.6360
-0.7716
104
3’-4’.
-0.9612
0.2756
84.8
4’-5’.
-0.8386
0.5446
78.6
5’-6’.
0.8571
0.5150
144
6’-7’.
-0.8526
0.5225
81
7’-8’.
-0.4067
0.9135
54.02
8’-9’.
0.0174
0.9998
93
9’-10’.
0.9703
-0.2419
139
10’-11’.
0.3583
0.9335
56.25
11’-12’.
0.7986
-0.6018
58
12’-13’.
0.9681
-0.2503
106.05
13’-14’.
-0.0349
-0.9994
126
CORRECTING DISTANCE ERROR NCORRECT=NINCORRECT – ε[
]
ECORRECT=EINCORRECT – ε[
]
ε= -1.0 m STATION NO.
NORTHING (m)
EASTING (m)
14
2000.0000
4000.0000
1’
2005.4276
3961.3796
2’
1874.7514
3891.8978
3’
1805.9632
3810.9492
4’
1725.4870
3834.5268
5’
1658.7289
3877.8800
6’
1873.0181
3952.5604
7’
1713.1016
3995.4052
8’
1690.7229
4045.6684
9’
1692.3633
4139.6540
10’
1828.2047
4105.7849
11’
1848.7212
4159.2323
12’
1895.8406
4123.7252
13’
1999.4807
4096.9221
14’
1995.0484
3969.9994
CORRECTING ANGULAR ERROR NCORRECT=NINCORRECT –δ [
]
ECORRECT=EINCORRECT + δ [
]
δ=2o=0.0349c STATION NO.
NORTHING (m)
EASTING (m)
14
2000.0000
4000.0000
1’
2006.7753
3961.5689
2’
1878.5237
3887.5267
3’
1812.5630
3804.2475
4’
1731.2615
3824.9469
5’
1662.9905
3865.9704
6’
1784.6735
3944.9881
7’
1713.2618
3985.3930
8’
1689.1290
4034.8752
9’
1687.4894
4128.9179
10’
1824.5127
4099.7897
11’
1843.1841
4153.9530
12’
1891.5226
4120.0903
13’
1996.0979
4096.9041
14’
1996.0952
3969.8267
APPLYING BOWDITCH DISTRIBUTION TO TRAVERSE CORRECTED FOR SYSTEMATIC ERRORS LINE
LENGTH( m)
LAT.(m)
DIP.(m)
CORR. IN LAT. (m)
CORR. CORREC TED IN LAT.(m) DIP. (m)
CORREC TED DIP(m)
14-1’
39
6.7753
38.4311
0.1150
0.8889
6.8903
-37.5422
1’-2’.
148
128.251 6
74.0422
0.4366
3.3735
-127.8150
-70.6687
2’-3’.
105
65.9607
83.2792
0.3097
2.3933
-65.6510
-80.8859
3’-4’.
85.8
81.3015
20.6994
0.2531
1.9557
-81.0484
22.6551
4’-5’.
79.6
68.2710
41.0235
0.2348
1.8144
-68.0362
42.8379
5’-6’.
145
121.683 0
79.0177
0.4277
3.3051
122.0657
82.3228
6’-7’.
82
71.4117
40.4049
0.2419
1.8691
-71.1698
42.2740
7’-8’.
55.02
24.1328
49.4822
0.1624
1.2541
-23.9704
50.7363
8’-9’.
94
-1.6396
94.0427
0.2773
2.1426
-1.3623
96.1853
9’10’.
140
137.022 3
29.1282
0.4130
3.1911
137.4363
-25.9371
10’11’.
57.25
18.6714
54.1633
0.1688
1.3049
18.8402
55.4682
11’12’.
59
48.3385
33.8627
0.1740
1.3448
48.5125
-32.5179
12’13’.
107.05
104.575 3
23.1862
0.3158
2.4401
104.8911
-20.4671
13’14’.
127
-0.0027
127.077 4
0.3746
2.8948
0.3719
-124.1826
1323.72
-3.9051
-30.1733
CORRECTED TRAVERSE AFTER SYSTEMATIC ADJUSTMENT $ BOWDITCH DISTRIBUTION
STATION NO.
NORTHING(m)
EASTING(m)
14
2000.0000
4000.0000
1’
2006.8903
3962.4578
2’
1879.0753
3891.7891
3’
1813.4243
3810.9032
4’
1732.3759
3833.5583
5’
1664.3397
3876.3962
6’
1786.4054
3958.7190
7’
1715.2356
4000.9930
8’
1691.2652
4051.7293
9’
1689.9029
4147.9146
10’
1827.3392
4121.9775
11’
1846.1794
4177.4457
12’
1894.6919
4144.9278
13’
1999.5830
4124.1817
14’
1999.9549
3999.9991
APPLYING TRANSIT DISTRIBUTION TO TRAVERSE CORRECTED FOR SYSTEMATIC ERRORS LIN E
LENGTH( m)
LAT.(m)
DIP.(m)
CORR. IN LAT. (m)
CORR .
CORREC TED
CORREC TED
IN
LAT.(m)
DIP(m)
DIP. (m) 141’
39
6.7753
38.4311
0.0301
1.4718
6.8054
-36.9593
1’2’.
148
128.251
74.0422
0.5703
2.8356
-127.6183
-71.2066
6 2’3’.
105
65.9607
83.2792
0.2933
3.1894
-65.6674
-80.0898
3’4’.
85.8
81.3015
20.6994
0.3615
0.7927
-80.9400
21.4921
4’5’.
79.6
68.2710
41.0235
0.3036
1.5711
-67.9674
42.5946
5’6’.
145
121.683 0
79.0177
0.5411
3.0262
122.2241
82.0439
6’7’.
82
71.4117
40.4049
0.3175
1.5474
-71.0942
41.9523
7’8’.
55.02
24.1328
49.4822
0.1073
1.8950
-24.0255
51.3772
8’9’.
94
-1.6396
94.0427
0.0073
3.6016
-1.6323
97.6443
9’10’.
140
137.022 3
29.1282
0.6093
1.1155
137.6326
-28.0127
10’11’.
57.25
18.6714
54.1633
0.0830
2.0743
18.7544
56.2376
11’12’.
59
48.3385
33.8627
0.2149
1.2968
48.4634
-32.5659
12’13’.
107.05
104.575 3
23.1862
0.4650
0.8879
105.0403
-22.2983
13’14’.
127
-0.0027
127.077 4
0.00001 2
4.8668
-0.002688
-122.2102
1323.72
878.0437 787.8407
CORRECTED TRAVERSE AFTER SYSTEMATIC ADJUSTMENT $ TRANSIT DISTRIBUTION STATION NO.
NORTHING(m)
EASTING(m)
14
2000.0000
4000.0000
1’
2006.8054
3963.0407
2’
1879.1241
3891.8341
3’
1813.4567
3811.7443
4’
1732.5167
3833.2364
5’
1664.5493
3875.8310
6’
1786.7734
3857.8749
7’
1715.6792
3999.8272
8’
1691.6537
4051.2044
9’
1690.0214
4148.8487
10’
1827.6540
4120.8360
11’
1846.4084
4177.0736
12’
1894.8718
4144.5077
13’
1999.9121
4122.2094
14’
1999.9094
3999.9992
APPLYING BOWDITCH DISTRIBUTION DIRECTLY TO INCORRECT TRAVERSE LINE
LENGTH( m)
LAT.(m)
DIP.(m)
CORR. IN LAT. (m)
CORR. CORREC TED IN LAT.(m) DIP. (m)
CORREC TED DIP(m)
14-1’
38
5.2885
37.6302
0.1770
0.8673
5.4155
-36.7629
1’-2’.
147
129.793 3
69.0124
0.5012
3.4225
-129.2921
-65.5899
2’-3’.
104
68.1522
80.1770
0.3535
2.4145
-67.7987
-77.7625
3’-4’.
84.8
-
23.3020
0.2876
1.9644
-79.2274
25.2664
79.5150 4’-5’.
78.6
65.9195
42.8086
0.2664
1.8190
-65.6531
44.6276
5’-6’.
144
123.432 1
74.1654
0.4909
3.3521
123.9320
77.5175
6’-7’.
81
69.0645
42.3223
0.2763
1.8753
-68.7882
44.1976
7’-8’.
54.02
21.9720
49.3497
0.1820
1.2428
-21.7900
50.5925
8’-9’.
93
1.6230
92.9858
0.3158
2.1566
1.9388
95.1424
9’10’.
139
134.871 1
33.6272
0.4737
3.2349
135.3448
-30.3923
10’11’.
56.25
20.1582
52.5202
0.1896
1.2951
20.3478
53.8153
11’12’.
58
46.3208
34.9053
0.1956
1.3361
46.5164
-33.5692
12’13’.
106.05
102.672
26.5528
0.3606
2.4625
103.0326
-24.0903
13’14’.
126
-4.3974
125.323 3
0.4291
2.9302
-3.9383
-122.9931
1309.72
-4.4482
-30.3742
CORRECTED TRAVERSE AFTER APPLYING BOWDITCH DISTRIBUTION DIRECTLY STATION NO.
NORTHING(m)
EASTING(m)
14
2000.0000
4000.0000
1’
2005.4155
3963.2371
2’
1876.1234
3897.6472
3’
1808.3247
3819.8847
4’
1729.0973
3845.1511
5’
1663.4442
3889.7787
6’
1787.3672
3967.2962
7’
1718.5790
4011.4938
8’
1696.7890
4062.0863
9’
1698.7278
4157.2287
10’
1834.0726
4126.8364
11’
1854.4204
4180.6517
12’
1900.9368
4147.0825
13’
2003.9694
4122.9922
14’
2000.0011
3999.9991
APPLYING TRANSIT DISTRIBUTION DIRECTLY TO INCORRECT TRAVERSE LINE
LENGTH( m)
LAT.(m)
DIP.(m)
CORR. IN LAT. (m)
CORR. CORREC TED IN LAT.(m) DIP. (m)
CORREC TED DIP(m)
14-1’
38
5.2885
37.6302
0.0269
1.4555
5.3154
-36.1747
1’-2’.
147
129.793 3
69.0124
0.6612
2.6693
-129.1321
-66.3431
2’-3’.
104
68.1522
80.1770
0.3471
3.1011
-67.8051
-77.0759
3’-4’.
84.8
79.5150
23.3020
0.4050
0.9013
-79.1100
24.2033
4’-5’.
78.6
65.9195
42.8086
0.3358
1.6558
-65.5837
44.4644
5’-6’.
144
123.432
74.1654
0.6287
2.8686
124.0608
77.0340
1 6’-7’.
81
69.0645
42.3223
0.3518
1.6369
-68.7127
43.9592
7’-8’.
54.02
21.9720
49.3497
0.1119
1.9088
-21.8601
51.2585
8’-9’.
93
1.6230
92.9858
0.0082
3.5966
1.6312
96.5824
9’10’.
139
134.871 1
33.6272
0.6870
1.3006
135.5581
-32.3266
10’11’.
56.25
20.1582
52.5202
0.1026
2.0314
20.2608
54.5516
11’12’.
58
46.3208
34.9053
0.2359
1.3501
46.5567
-33.5552
12’13’.
106.05
102.672
26.5528
0.5230
1.0270
103.1950
-25.5258
13’14’.
126
-4.3974
125.323 3
0.0224
4.8706
-4.3750
-121.0527
1309.72
873.1796
785.2822
CORRECTED TRAVERSE AFTER APPLYING TRANSIT DISTRIBUTION DIRECTLY STATION NO.
NORTHING(m)
EASTING(m)
14
2000.0000
4000.0000
1’
2005.3154
3963.8253
2’
1876.1833
3897.4822
3’
1808.3782
3820.4063
4’
1729.2682
3844.6096
5’
1663.6845
3889.0740
6’
1787.7453
3966.1080
7’
1719.0326
4010.0672
8’
1697.1725
4061.3257
9’
1698.8037
4157.9081
10’
1834.3618
4125.5815
11’
1854.6226
4180.1331
12’
1901.1793
4146.5779
13’
2004.3743
4121.0521
14’
1999.9993
3999.9994
STATEMENT OF COMPARISION
VI.
AREA (A)=1/2[
i
.Ei+1 – Ni+1.Ei]
CENTROID (CN)=1/6A.[
i
CENTROID (CE)=1/6A.[
i
METHOD OF CORRECTION
DEVIATION IN AREA FROM CORRECT TRAVERSE (m2)
.Ei+1 – Ni+1.Ei).(Ni+Ni+1)]
.Ei+1 – Ni+1.Ei).(Ei+Ei+1)]
DEVIATION IN PERIMETER FROM CORRECT TRAVERSE (m)
DEVIATION OF CENTROID FROM THAT OF CORRECT TRAVERSE (m)
AVG. ROTATION FROM CORRECT TRAVERSE (DEGREES.)
SYSTEMATIC ADJUSTMENT FOLLOWED BY
13717.8998
100.6603
4.8729
-3.1031
14016.6363
100.7313
4.8695
-3.1550
15498.0834
115.3682
5.0572
-5.1047
15764.3624
115.2164
5.1312
-5.1517
BOWDITCH DISTRIBUTIO N SYSTEMATIC ADJUSTMENT FOLLOWED BY TRANSIT DISTRIBUTIO N DIRECT BOWDITCH DISTRIBUTIO N DIRECT TRANSIT DISTRIBUTIO N
VII.
CONCLUSION
The prime objective of traverse adjustment is to approach as close as possible to the original field traverse. However, this could be done through careful prospection of the instruments and minimizing human carelessness. In case of occurrence of any error, different methods could be followed depending upon the source of error. If mistakes and accidental errors dominate, a probable approach would be adopting any of the distributing methods. However, in case of occurrence of all three errors, the systematic errors should first be negated through the proposed set of rules and then the remaining errors must be combated in former way.
