E4004 Survey Computations A
Bowditch Adjustment
Traverse Adjustment
• Bowditch Rule
– based on the assumption that angles
(bearings) are observed to the same degree of
precision that distances can be measured
Bowditch Rule from E0007
• Adjust the angular misclose
• calculate the misclose in position
• adjust according to the formula
CorrLat 
l
l
L
l  length of the current line
CorrDep 
l
l
D
L = latitude of the current line
D = departure of the current line
 l = sum of the traverse line lengths
Bowditch - New Method
•
•
•
•
Adjust the angular misclose
calculate the misclose in position
consider the diagram
AB’C’D’ is a traverse from A to D
C’
D’
B’
A
D
Bowditch - New Method
• But the traverse coordinates of D’ are not
the same as D
• the misclose at D is D’D
C’
D’
B’
A
D
Bowditch - New Method
• Let the traverse line lengths be 1, 2 and 3 as
shown
• The total length of traverse is 1+2+3=6
C’
2
3
D’
B’
A
1
D
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 D’D
C’
2
3
D’
B’
A
1
D
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’
2
3
D’
B’
A
1
D
Bowditch - New Method
• In this example the correction at D’ must be
1 2  3 6

of the total misclose
6
6
• Divide D’D into 6 parts
C’
2
B’
A
1
3
D’
6
Corr
6
D
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’
2
A
1
B’1 Corr
6
BAdj
3
D’
6
Corr
6
D
Bowditch - New Method
• The correction at C’ must be in the same
direction but for a length proportional to
(1+2)/6 of the total correction
C’
2
A
1
B’1 Corr
6
BAdj
3
3
Corr
6
CAdj
D’
6
Corr
6
D
Bowditch - New Method
• The adjusted bearings and distances would
form the lines as shown
C’
2
A
1
B’1 Corr
6
BAdj
3
3
Corr
6
CAdj
D’
6
Corr
6
D
Bowditch - New Method
• A close program can be used to calculate
the adjusted bearings and distances and
the adjusted coordinates
C’
2
A
1
B’1 Corr
6
BAdj
3
3
Corr
6
CAdj
D’
6
Corr
6
D
Bowditch - New Method
• Consider the triangle AB’B
• Once the correction (D’D) is known both
lines AB’ and B’B are known
• The line AB can be calculated by closure
C’
2
A
1
B’1 Corr
6
BAdj
3
3
Corr
6
CAdj
D’
6
Corr
6
D
Bowditch - New Method
• From Badj draw a line parallel to B’C’
• The bearing and distance BAdjC” are the
same as for B’C’
• The line C”Cadj is the correction relevant to
this line i.e. 2/6 Corr
C’
2
A
1
B’1 Corr
6
BAdj
3
C” 3
6
D’
Corr
CAdj
6
Corr
6
D
Bowditch - New Method
• Close the triangle BAdjC”Cadj and the
adjusted bearing and distance BAdjCAdj is
found
C’
2
A
1
B’1 Corr
6
BAdj
3
3
Corr
6
CAdj
D’
6
Corr
6
D
Bowditch - New Method
• Similarly, draw a line parallel to C’D’ from
CAdj
• The line D”Dadj is the correction relevant to
this line i.e. 3/6 Corr
C’
2
A
1
B’1 Corr
6
BAdj
3
C” 3
6
D’
Corr
CAdj
6
Corr
6
D”
D
Bowditch - New Method
• Close the triangle CAdjD”Dadj and the
adjusted bearing and distance CAdjDAdj is
found
C’
2
A
1
B’1 Corr
6
BAdj
3
3
Corr
6
CAdj
D’
6
Corr
6
D