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E4004 Surveying Computations A

E4004 Surveying Computations A. Circular Curves. Circular Curves - Chord. Let O be the centre of circular arc AC. Arc AC subtends an angle of D at O. Line AC is a chord. A. chord. C. O. Circular Curves - Sector. Area OACO is a sector. A. C. O. Circular Curves - Segment.

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E4004 Surveying Computations A

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  1. E4004 Surveying Computations A Circular Curves

  2. Circular Curves - Chord • Let O be the centre of circular arc AC • Arc AC subtends an angle of D at O • Line AC is a chord A chord C O

  3. Circular Curves - Sector • Area OACO is a sector A C O

  4. Circular Curves - Segment • Area ACA is a segment A C O

  5. Circular Curves • Let X bisect the chord AC such that • AX = XC • Angle AXO is 90° • AX cuts the curve AC at B B A X C O

  6. Circular Curves - Arc Length B A X C R R O

  7. Circular Curves - Area Circle B A X C O

  8. Circular Curves - Sector Area B A X C R R O

  9. Circular Curves - Sector Area B A X C R R O

  10. Circular Curves - Triangle Area B A X C R R O

  11. Circular Curves - Segment Area B A X C R R O

  12. Circular Curves - Chord Length • Consider triangle AXO B A X C R R O

  13. Circular Curves - Intersection Pt • Let AI have bearing B1 and IC have bearing B2 - note the bearing directions • Extend the tangents at A and C to intersect at I I B1 B2 B A X C • X and B lie on the line OI R R O

  14. Circular Curves - Tangent Length • Consider triangle AIO I B1 B2 B A X C R R O

  15. Circular Curves - Area OAICO • Again consider triangle AIO I B1 B2 B A X C R R O

  16. Circular Curves - Area Outer Segment • Consider Area AICBA - “Outer Segment” I B1 B2 B A X C R R O

  17. Circular Curves - Secant Distance BI I B1 B2 B A X C R R O

  18. Circular Curves - Deflection Angle & Subtended Angle Extend AI to D Consider the quadrilateral OAIC D Quadrilateral internal angles = 360° I B1 B2 B A Line AID is straight X C R R O

  19. Circular Curves - Deflection Angle & Subtended Angle Provided bearings are expressed in one direction D I B1 B2 B A X C R R O

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