Traverse Computation 1) Calculation of starting and closing bearings; 2) Calculation of angular misclosure by comparing the sum of the observed bearings with the closing bearings. 3) If angular misclosure is acceptable, distribute it throughout the traverse in equal amounts to each angle. 4) Reduction of slope distance to horizontal distance;

Traverse Computation (con’t) 5) Calculation of the changes in coordinates (N, E) of each traverse line. 6) Assessing the coordinate misclosure. 7) Balancing the traverse by distributing the coordinate misclosure throughout the traverse lines. 8) Computation of the final coordinates of each point relative to the starting station, using the balanced values of N, E per line.

Adjustment of Traverse discrepancies between eastings and northings must be adjusted before calculating the final coordinates. Adjustment methods: Compass Rule Least Squares Adjustment Chak’s Rule Bowditch Rule Bowditch Rule is most commonly used.

Adjustment by Bowditch Rule devised by Nathaniel Bowditch in 1807. Ei, Ni = coordinate corrections E, N = coordinate misclosure (constant) Li = sum of the lengths of the traverse (constant) Li = horizontal length of the ith traverse leg.

Example: Closed Traverse Computation Measurements of traverse ABCDE are given in Table 1. Given that the co-ordinates of A are 782.820mE, 460.901mN; and co-ordinates of E are 740.270mE, 84.679mN. The WCB of XA is 123-17-08 and WCB of EY is 282-03-00.

Example: Closed Traverse Computation (con’t) a) Determine the angular, easting, northing and linear misclosure of the traverse. b) Calculate and tabulate the adjusted co-ordinates for B, C and D using Bowditch Rule.

Example: Closed Traverse Computation (con’t) 1) There is no need to calculate the starting and ending bearings as they are given. 2) Calculate the angular misclosure and angular correction using: F’ = I + sum of angles - (n x 180)

Example: Closed Traverse Computation (con’t) F’ = I + sum of angles - (n x 180) sum of angles = (260-31-18) + (123-50-42) + (233-00-06) + (158-22-48) + (283-00-18) = (1058-45-12) I = 123-17-08; (n x 180) = 900 F’ = (123-17-08) + (1058-45-12) - 900 = 282-02-20 angular misc. = (282-02-20) - (282-03-00) = -40” As there are five angles, each will be added by the following factor of (40”/5) = 8”.

Example: Closed Traverse Computation (con’t) Angular correction: AX 303-17-08 A 260-31-18 (+8”) 563-48-34 360-00-00 A to B 203-48-34 180-00-00 B to A 23-48-34  B 123-50-42(+8”) B to C 147-39-24 180-00-00 C to B 327-39-24  C 233-00-06(+8”) 560-39-38 360-00-00 C to D 200-39-38

Example: Closed Traverse Computation (con’t) C to D 200-39-38 180-00-00 D to C 20-39-38  D 158-22-48(+8”) D to E 179-02-34 E to D 359-02-34  E 283-00-18(+8”) 642-03-00 360-00-00 E to Y 282-03-00 (checks)

Example: Closed Traverse Computation (con’t) Set up table and fill in bearings, distances, starting and ending bearings. Calculate the total traversed distance.

Example: Closed Traverse Computation (con’t) For each leg, calculate N [Dist * cos(Brg)] & E [Dist * sin(Brg)]. Sum N and E. Compare results with diff. between start and end coords.

Example: Closed Traverse Computation (con’t) Compute the error in eastings , northings and linear misclosure error in Eastings = - 42.610 - (-42.550) = -0.060m error in Northings = -376.237 - (-376.222) = - 0.015m Linear misclosure = (((-0.060)2 + (-0.015)2)0.5) / 406.437 = 0.062 / 406.437 = 1 / 6555

Example: Closed Traverse Computation (con’t) Using Bowditch Rule, calculate correction for each N & E. ((partial dist./total dist.) * (error in N or E)

Example: Closed Traverse Computation (con’t) Final coordinates of station = coords. of previous station + partial coords () + corr.

Detection of Gross Errors Gross errors might still occur despite taking all the required precautions during observations. Erroneous observation must be re-measured in the field to provide satisfactory check on the work. Such error can sometimes be found by examination of the calculations.

Location of a Gross Angular Error (Method 1) By plotting or calculating the traverse from each end. Station which has the same coordinates in each case will be the one at which angular error occurred.

Location of a Gross Angular Error (Method 2) By plotting the incorrect traverse and the correct position of the closing station. Join B and B’, and bisect this line at right-angle. This line will intersect the point at which the angular error occurred. (isosceles triangle)

Location of a Gross Taping Error By comparing the bearing of the closing error with the bearings of the individual traverse legs. Gross error = roughly the same bearing. will not be possible to find the exact position, if there is more than one gross error exists.

References 1. Bannister, A., Raymond, S and R. Baker. (1998), Surveying, 7th edn, Longman - ELBS. 2. Schofield W. (1994), Engineering Surveying, 4th edn, Butterworth - Heinemann. 3. Wilson, R.J.P. (1983), Land Surveying, 3rd edn, MacDonald & Evans. 4. Uren, J. and Price, W.F. (1983), Surveying for Engineers, ELBS. 5. Tang, P. K. and Yeung, A. K. W. (1987), Site Surveying III, HKPolyU.

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