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Surveying Computations for Two Missing Bearings: Derivation of Formula

This surveying guide explores the derivation of formulas for determining two missing bearings in a triangulation setup. Learn how to calculate positions based on known distances and bearings, with a focus on the intersection of distances. The importance of direction in bearing calculations is highlighted, providing a comprehensive overview of the surveying process.

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Surveying Computations for Two Missing Bearings: Derivation of Formula

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  1. E4004 Surveying Computations A Two Missing Bearings

  2. Derivation of Formula • Consider line RS • If distances RP and PS are known the position of P is also known • The intersection of two distances S P R

  3. Derivation of Formula • But P could also lie on the other side of RS • There are always two solutions in a two missing bearing problem P S P’ R

  4. Derivation of Formula • From a surveying viewpoint • In the triangle RSP the bearing and distance RS will be known and the distances SP and PR will be provided D1 P S • The direction of the bearings are important D2 MB MD R

  5. Derivation of Formula • We have a triangle with three known sides • Each angle can be solved with the cosine rule D1 P S D2 MB MD R

  6. Derivation of Formula a B D1 P S C D2 MB c MD b R A

  7. Derivation of Formula a b B D1 P C S A C a D2 MB c MD b c R A B

  8. Derivation of Formula • The same formula apply for the second triangle • Again the bearing directions are important P S MB D1 MD P’ R D2

  9. Derivation of Formula • Angles R & S have been calculated RIGHT of line RS B1 P LEFT of line RS S S S B2 MB B1’ MD R P’ R R B2’

  10. Summary of Formula LEFT of line RS RIGHT of line RS B1 P S S S B2 MB B1’ MD R P’ R R B2’

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