1. Geometric Design CEE 320Anne Goodchild

2. Outline • Concepts • Vertical Alignment • Fundamentals • Crest Vertical Curves • Sag Vertical Curves • Examples • Horizontal Alignment • Fundamentals • Superelevation • Other Non-Testable Stuff

3. Alignment is a 3D problem broken down into two 2D problems Horizontal Alignment (plan view) Vertical Alignment (profile view) Stationing Along horizontal alignment 12+00 = 1,200 ft. Concepts Piilani Highway on Maui

4. Stationing Horizontal Alignment Vertical Alignment

5. From Perteet Engineering

6. Vertical Alignment

7. Vertical Alignment • Objective: • Determine elevation to ensure • Proper drainage • Acceptable level of safety • Primary challenge • Transition between two grades • Vertical curves Sag Vertical Curve G1 G2 G2 G1 Crest Vertical Curve

8. Vertical Curve Fundamentals • Parabolic function • Constant rate of change of slope • Implies equal curve tangents • y is the roadway elevation x stations (or feet) from the beginning of the curve

9. Vertical Curve Fundamentals PVI G1 δ PVC G2 PVT L/2 L x • Choose Either: • G1, G2 in decimal form, L in feet • G1, G2 in percent, L in stations

10. Choose Either: • G1, G2 in decimal form, L in feet • G1, G2 in percent, L in stations Relationships

11. Example A 400 ft. equal tangent crest vertical curve has a PVC station of 100+00 at 59 ft. elevation. The initial grade is 2.0 percent and the final grade is -4.5 percent. Determine the elevation and stationing of PVI, PVT, and the high point of the curve. PVI PVT G1=2.0% G2= - 4.5% PVC: STA 100+00 EL 59 ft.

12. PVI PVT G1=2.0% PVC: STA 100+00 EL 59 ft. G2= -4.5%

13. G1, G2 in percent • L in feet Other Properties G1 x PVT PVC Y Ym G2 PVI Yf

14. Other Properties • K-Value (defines vertical curvature) • The number of horizontal feet needed for a 1% change in slope

15. Crest Vertical Curves SSD PVI Line of Sight PVC PVT G2 G1 h2 h1 L For SSD < L For SSD > L

16. Crest Vertical Curves • Assumptions for design • h1 = driver’s eye height = 3.5 ft. • h2 = tail light height = 2.0 ft. • Simplified Equations For SSD < L For SSD > L

17. Crest Vertical Curves • Assuming L > SSD…

18. Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

19. Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

20. Sag Vertical Curves Light Beam Distance (SSD) G1 headlight beam (diverging from LOS by β degrees) G2 PVT PVC h1 PVI h2=0 L For SSD < L For SSD > L

21. Sag Vertical Curves • Assumptions for design • h1 = headlight height = 2.0 ft. • β = 1 degree • Simplified Equations For SSD < L For SSD > L

22. Sag Vertical Curves • Assuming L > SSD…

23. Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

24. Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

25. Example 1 A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long sag vertical curve. The entering grade is -2.4 percent and the exiting grade is 4.0 percent. A tree has fallen across the road at approximately the PVT. Assuming the driver cannot see the tree until it is lit by her headlights, is it reasonable to expect the driver to be able to stop before hitting the tree?

26. Sag Vertical Curve • Assume S<L, try both, but this is most often the case • Equation specific to sag curve which accommodates headlight beam • L and S in horizontal plane and comparable (150 and 146 ft) • Required SSD = 196.53 ft assumes 0 grade • Text problem versus design problem.

27. Sag Vertical Curves Light Beam Distance (S) G1 diverging from horizontal plane of vehicle by β degrees G2 PVT PVC h1 PVI h2=0 L Daytime sight distance unrestricted

28. Example 2 Similar to Example 1 but for a crest curve. A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long crest vertical curve. The entering grade is 3.0 percent and the exiting grade is -3.4 percent. A tree has fallen across the road at approximately the PVT. Is it reasonable to expect the driver to be able to stop before hitting the tree?

29. Crest Vertical Curve • Assume S<L, try both, but this is most often the case • Equation specific to crest curve which accommodates sight over hill • L and S in horizontal plane and comparable (150 and 243 ft) • Required SSD = 196.53 ft assumes 0 grade • Text problem versus design problem.

30. Crest Vertical Curves SSD PVI Line of Sight PVC PVT G2 G1 h2 h1 L

31. Example 3 A roadway is being designed using a 45 mph design speed. One section of the roadway must go up and over a small hill with an entering grade of 3.2 percent and an exiting grade of -2.0 percent. How long must the vertical curve be?

32. Horizontal Alignment

33. Horizontal Alignment • Objective: • Geometry of directional transition to ensure: • Safety • Comfort • Primary challenge • Transition between two directions • Horizontal curves • Fundamentals • Circular curves • Superelevation Δ

34. Horizontal Curve Fundamentals D = degree of curvature (angle subtended by a 100’ arc) PI T Δ E M L Δ/2 PT PC R R Δ/2 Δ/2

35. Horizontal Curve Fundamentals PI T Δ E M L Δ/2 PT PC R R Δ/2 Δ/2

36. Example 4 A horizontal curve is designed with a 1500 ft. radius. The tangent length is 400 ft. and the PT station is 20+00. What are the PI and PT stations?

37. Superelevation Rv ≈ Fc α Fcn Fcp α e W 1 ft Wn Ff Wp Ff α

38. e = number of vertical feet of rise per 100 ft of horizontal distance = 100tan Superelevation This is the minimum radius that provides for safe vehicle operation Rv because it is to the vehicle’s path

39. Selection of e and fs • Practical limits on superelevation (e) • Climate • Constructability • Adjacent land use • Side friction factor (fs) variations • Vehicle speed • Pavement texture • Tire condition Design values of fs are chosen somewhat below this maximum value so there is a margin of safety

40. Minimum Radius Tables

41. WSDOT Design Side Friction Factors For Open Highways and Ramps from the 2005 WSDOT Design Manual, M 22-01

42. WSDOT Design Side Friction Factors For Low-Speed Urban Managed Access Highways from the 2005 WSDOT Design Manual, M 22-01

43. Design Superelevation Rates - AASHTO from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

44. Design Superelevation Rates - WSDOT emax = 8% from the 2005 WSDOT Design Manual, M 22-01

45. Example 5 A section of SR 522 is being designed as a high-speed divided highway. The design speed is 70 mph. Using WSDOT standards, what is the minimum curve radius (as measured to the traveled vehicle path) for safe vehicle operation?

46. Example 5 A section of SR 522 is being designed as a high-speed divided highway. The design speed is 70 mph. Using WSDOT standards, what is the minimum curve radius (as measured to the traveled vehicle path) for safe vehicle operation? For the minimum curve radius we want the maximum superelevation. WSDOT max e = 0.10 For 70 mph, WSDOT f = 0.10

47. Stopping Sight Distance SSD (not L) • Looking around a curve • Measured along horizontal curve from the center of the traveled lane • Need to clear back to Ms (the middle of a line that has same arc length as SSD) Ms Obstruction Rv Δs Assumes curve exceeds required SSD

48. Stopping Sight Distance SSD (not L) Ms Obstruction Rv Δs

49. Example 6 A horizontal curve with a radius to the vehicle’s path of 2000 ft and a 60 mph design speed. Determine the distance that must be cleared from the inside edge of the inside lane to provide sufficient stopping sight distance.

50. FYI – NOT TESTABLE Superelevation Transition from the 2001 Caltrans Highway Design Manual