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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

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E4004 survey computations a l.jpg

E4004 Survey Computations A

Bowditch Adjustment


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Traverse Adjustment

  • Bowditch Rule

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


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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


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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


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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


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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’

3

D’

2

B’

1

A

D


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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’

3

D’

2

B’

1

A

D


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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


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Bowditch - New Method

  • In this example the correction at D’ must be

of the total misclose

  • Divide D’D into 6 parts

C’

3

D’

2

B’

1

A

D


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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


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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’

3

D’

2

B’

1

CAdj

A

BAdj

D


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Bowditch - New Method

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

C’

3

D’

2

B’

1

CAdj

A

BAdj

D


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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


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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’

3

D’

2

B’

1

CAdj

A

BAdj

D


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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’

3

D’

2

C”

B’

1

CAdj

A

BAdj

D


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Bowditch - New Method

  • Close the triangle BAdjC”Cadj and the adjusted bearing and distance BAdjCAdj is found

C’

3

D’

2

B’

1

CAdj

A

BAdj

D


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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’

3

D’

2

C”

B’

1

CAdj

A

BAdj

D”

D


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Bowditch - New Method

  • Close the triangle CAdjD”Dadj and the adjusted bearing and distance CAdjDAdj is found

C’

3

D’

2

B’

1

CAdj

A

BAdj

D


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