# Traverse omitted measurements.pdf - TYPES OF OMITTED...

• 13

This preview shows page 1 - 4 out of 13 pages.

TYPES OF OMITTED MEASUREMENTS The omitted measurement in a theodolite traverse, may be classified in four general cases. I. ( a ) When length of one traverse leg is omitted. (b) When bearing of one traverse leg is omitted. (c) When length and bearing of one traverse leg are omitted. II. When length of one traverse leg and bearing of another ad- jacent leg are omitted. III. When lengths of two legs are omitted. IV. When bearings of two legs are omitted. In case I only one traverse leg is affected. In remaining cases two legs are affected, both of which may be either adjacent or may not be adjacent. Case I. Either Length or Bearing or both of one Traverse Leg are Omitted (Fig. 12.20). Let ABCDEFA be a closed traverse. Assume that either the length or bearing or both of the traverse leg FA is/are omitted from field measurements. Proceed as under: I. Calculate the algebraic sum of the latitudes from A to F . Let it be Σ L . II. Calculate the algebraic sum of the departures from A to F . Let it be Σ D . We know that for a closed traverse the algebraic sum of all latitudes and departures should each be equal to zero. If L and D are the latitude and the departure of the traverse leg FA , Then L ±Σ L = 0 Or latitude of FA = ±Σ L Similarly, Departure of FA = ±Σ D Knowing the latitude and departure of FA , (Fig. 12.21) its length and bearing may be calculated by equation (12.9) and (12.12) respectively. Case II. Length of one leg and bearing of an adjacent leg omitted (Fig. 12.22).
Let ABCDEF A be a closed traverse in which length of the leg EF and bearing of the leg FA are omitted. Construction. Join EA which becomes the closing line of the traverse ABCDEA. Now all quantities of traverse ABCDEA being known, the length and bearing of EA may be calculated as explained in case I. In Δ AEF the sides AE and AF are known. Angle FEA = bearing of EA bearing of EF = β Applying the sine formula, we get Also, knowing α, the bearing of AF can be calculated i.e. Bearing of AF = Bearing of AE + α. Case III. Length of two adjacent legs omitted (Fig. 12.23) Let ABCDEFA be a closed traverse in which lengths of both EF and FA are omitted. Construction. Join EA which becomes the closing line of traverse ABCDEA. The length and bearing of AE may now be calculated as explained in case I. In Δ AEF , Angle FEA = bearing of EA bearing of EF = β Angle FAE = bearing of AF bearing of AE = α Angle AFE = 180° − (α + β) = θ. Applying the sine formula, we get
Case IV. Bearings of two adjacent legs omitted (Fig. 12.24) Let ABCDEFA be a closed traverse in which bearings of