E4004 Survey Computations A

1
E4004 Survey Computations A

• Bowditch Adjustment

2
Traverse Adjustment

• Bowditch Rule
• based on the assumption that angles (bearings)
  are observed to the same degree of precision that
  distances can be measured

3
Bowditch Rule from E0007

• Adjust the angular misclose
• calculate the misclose in position
• adjust according to the formula

length of the current line
latitude of the current line
departure of the current line
sum of the traverse line lengths
4
Bowditch - New Method

• Adjust the angular misclose
• calculate the misclose in position
• consider the diagram
• ABCD is a traverse from A to D

C
D
B
A
D
5
Bowditch - New Method

• But the traverse coordinates of D are not the
  same as D
• the misclose at D is DD

C
D
B
A
D
6
Bowditch - New Method

• Let the traverse line lengths be 1, 2 and 3 as
  shown

• The total length of traverse is 1236

C
3
D
2
B
1
A
D
7
Bowditch - New Method

• In order to adjust the traverse such that D and
  D are coincident D would have to be corrected by
  a Brg and Dist equal to DD

C
3
D
2
B
1
A
D
8
Bowditch - New Method

• according to Bowditch the correction at each
  intermediate point is proportional to the length
  of each separate traverse line over the total
  traverse length times the misclose

C
3
D
2
B
1
A
D
9
Bowditch - New Method

• In this example the correction at D must be

of the total misclose

• Divide DD into 6 parts

C
3
D
2
B
1
A
D
10
Bowditch - New Method

• The correction at B must be in the same
  direction but for a length proportional to 1/6 of
  the total correction

C
3
D
2
B
1
A
BAdj
D
11
Bowditch - New Method

• The correction at C must be in the same
  direction but for a length proportional to
  (12)/6 of the total correction

C
3
D
2
B
1
CAdj
A
BAdj
D
12
Bowditch - New Method

• The adjusted bearings and distances would form
  the lines as shown

C
3
D
2
B
1
CAdj
A
BAdj
D
13
Bowditch - New Method

• A close program can be used to calculate the
  adjusted bearings and distances and the adjusted
  coordinates

C
3
D
2
B
1
CAdj
A
BAdj
D
14
Bowditch - New Method

• Consider the triangle ABB

• Once the correction (DD) is known both lines AB
  and BB are known

• The line AB can be calculated by closure

C
3
D
2
B
1
CAdj
A
BAdj
D
15
Bowditch - New Method

• From Badj draw a line parallel to BC

• The bearing and distance BAdjC are the same as
  for BC

• The line CCadj is the correction relevant to
  this line i.e. 2/6 Corr

C
3
D
2
C
B
1
CAdj
A
BAdj
D
16
Bowditch - New Method

• Close the triangle BAdjCCadj and the adjusted
  bearing and distance BAdjCAdj is found

C
3
D
2
B
1
CAdj
A
BAdj
D
17
Bowditch - New Method

• Similarly, draw a line parallel to CD from CAdj

• The line DDadj is the correction relevant to
  this line i.e. 3/6 Corr

C
3
D
2
C
B
1
CAdj
A
BAdj
D
D
18
Bowditch - New Method

• Close the triangle CAdjDDadj and the adjusted
  bearing and distance CAdjDAdj is found

C
3
D
2
B
1
CAdj
A
BAdj
D