Question

Observations, using an electronic theodolite were taken in the field for 5 sided polygon traverse, ABCDE. These observations are tabulated below. The coordinates of station A are 1000.000m E, 1000.000 m N. Orienting bearing of leg AB is 73°00’00”. Leg BC is in S.E quadrant.
Using these data determine the adjusted coordinates of B, C, D and E applying Bowditch’s rule.

Horizontal distance (m) Horizontal Angle (included) Line Length (m) Station Angle AB 51.766 A 101°03’18” BC 26.947 B 101°41’48” CD 37.070 C 102°22’02” DE 35.292 D 115°57’20” EA 19.192 E 118°55’28”


(i) Visualise the problem and sketch.   
(ii) Find the sum of the observed angles (measured) against the sum of the inclusive angles (internal or external, depending on the traverse direction) of the polygon, and find if there is any angular misclosure.   
(iii) If there is any misclosure, distribute it equally among the stations and calculate the corrected horizontal angles.   
(iv) Find the bearing (WCB) of the first leg of the polygon using the given relevant information.   

(v) Once you have found the WCB of the first leg, then calculate the WCB of the successive legs, using;
Bearing of a line (or Leg) = SUM of Bearing of the Previous line + included angle at the given station + 180° if SUM < 180° - 180° if SUM is between 180° & 540° - 540° if SUM > 540° (vi) Using these bearings then calculate the changes in Easting and Northing for each line using,


(vii) Get the algebraic sum of ∆Ε & ∆Ν to find the Easting error eE and the Northing error eN. Using them calculate the linear misclosure e = √ (eE2
+ eN2).   


(viii) To distribute the error using Bowditch method, Calculate Correction to Eastings, δE, (for a given leg XY) using



Calculate Correction to Eastings, δΝ, (for a given leg XY) using
δN XY = [ eN / SD ] x D XY   

D = sum of lengths of all legs DXY = Length of the given leg XY   

(ix) Using these corrections, re-calculate the corrected ∆Ε & ∆Ν.   

(x) Using the corrected ∆Ε & ∆Ν, and starting from the first station (whose coordinates are already known), calculate the coordinates (Eastings and Northings) of each successive station.   

Answer 1