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Vertical Curve Design in Transportation Engineering

Understand definitions, geometry, and design considerations of vertical curves for roadways. Learn about PVC, PVI, grades, curve length, and sight distance. Practice calculating curve equations and ensuring safe visibility.

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Vertical Curve Design in Transportation Engineering

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  1. CE 3500 Transportation Engineering Vertical curve design March 23, 2011

  2. ANNOUNCEMENTS

  3. Group assignment due Friday!

  4. REVIEW

  5. VERTICAL CURVE DEFINITIONS

  6. 11+00 13+00 15+00 17+00 10+00 12+00 14+00 16+00 Roadway locations are usually marked in stations (100s of feet)

  7. The vertical alignment consists of straight segments joined by vertical curves.

  8. The first curve is a crest curve. The second is a sag curve. (What’s the difference?)

  9. Let’s zoom in on the first curve.

  10. 10+00 11+00 12+00 10+57 Point of vertical curvature (PVC)

  11. 10+00 11+00 12+00 10+57 12+43 Point of vertical tangency (PVT) PVC

  12. 10+57 12+43 186 ft Curve length L PVT PVC

  13. Initial slope G1 Final slope G2 L PVT PVC

  14. Grades are expressed as a percent. (So a 3% uphill would mean G = +3) G2= -5 G1= +3 L PVT PVC

  15. A is the difference between the final and initial grades A = G2 – G1 G2= -5 G1= +3 L PVT PVC

  16. Point of vertical intersection (PVI) A = –8 G2= -5 G1= +3 L PVT PVC

  17. VERTICAL CURVE GEOMETRY

  18. The shape of a vertical curve is usually parabolic. Why? PVI A = –8 G2= -5 G1= +3 L PVT PVC

  19. Elevation y dy/dx d2y/dx2 PVT PVC

  20. Elevation y • For convenience, let x = 0 at PVC PVC PVT We can then write the equation for the curve: What are a, b, and c?

  21. Elevation y • For convenience, let x = 0 at PVC PVC PVT

  22. VERTICAL CURVE DESIGN

  23. Usually, the start and end grades are given. The main thing to choose is the curve length L. What happens if L is too short? too long?

  24. PVC PVT The curve has to be gentle enough to make sure the visibility exceeds the stopping sight distance.

  25. PVC PVT For a crest curve, assume driver is 3.5 ft above the road, and height of object is 2 ft.

  26. PVC PVT Case I: SSD is less than the curve length.

  27. PVC PVT Case II: SSD is greater than the curve length.

  28. PVC PVT May need to use trial and error to pick the right formula. (Bonus question on next homework: show that this recipe is well-defined, continuous, and differentiable.)

  29. Is sight distance still relevant for sag curves?

  30. If curve is too short, at night headlights may not reach all the way to the stopping sight distance.

  31. Assuming driver is 3.5 ft from the ground and upper beam of headlights is at an angle 1 degree above the direction of travel, we find....

  32. Case I: SSD is less than the curve length.

  33. Case II: SSD is greater than the curve length.

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