E 4004 Survey Computations A Bowditch Adjustment Traverse

E 4004 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 E 0007 • 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

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 A 1 3 D’ B’ 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 A 1 3 D’ B’ 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 A 1 3 D’ B’ D

Bowditch - New Method • In this example the correction at D’ must be of the total misclose • Divide D’D into 6 parts C’ 2 A 1 3 D’ B’ 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 3 D’ B’ BAdj 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’ 3 2 A 1 D’ B’ BAdj CAdj D

Bowditch - New Method • The adjusted bearings and distances would form the lines as shown C’ 3 2 A 1 D’ B’ BAdj CAdj D

Bowditch - New Method • A close program can be used to calculate the adjusted bearings and distances and the adjusted coordinates C’ 3 2 A 1 D’ B’ BAdj CAdj 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’ 3 2 A 1 D’ B’ BAdj CAdj D

Bowditch - New Method • From Badj draw a line parallel to B’C’ • The bearing and distance BAdj. C” 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’ BAdj 3 C” D’ CAdj D

Bowditch - New Method • Close the triangle BAdj. C”Cadj and the adjusted bearing and distance BAdj. CAdj is found C’ 3 2 A 1 D’ B’ BAdj CAdj 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’ BAdj 3 C” CAdj D’ D” D

Bowditch - New Method • Close the triangle CAdj. D”Dadj and the adjusted bearing and distance CAdj. DAdj is found C’ 3 2 A 1 D’ B’ BAdj CAdj D