1. Horizontal Alignment

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

3. Vehicle Cornering Fc Fcn Fcp W Wn Ff Wp Ff
Centripetal force parallel to the roadway Fc
Fcn
Fcp W Wn Ff
Side frictional force Wp Ff
Weight parallel to the roadway

4. Vehicle Cornering Fc α Fcn Fcp α W Wn Ff Wp Ff α
Vehicle weight and centripetal force normal to roadway

5. Vehicle Cornering Rv ≈ Fc α
Fcn
Fcp α W Wn Ff Wp Ff α

6. Horizontal Curve FundamentalsPI L PC PT R R
Curve is a circle, not a parabola

7. Superelevation Banking
number of vertical feet of rise per 100 ft of horizontal distance
e = 100tan α

8. Superelevation
Divide both sides by Wcos(α)

9. Superelevation Minimum radius that provides for safe vehicle operation
Given vehicle speed, coefficient of side friction, gravity, and superelevation
Rv because it is to the vehicle’s path (as opposed to edge of roadway)

10. 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
Maximum side friction factor is the point at which tires begin to skid.
Design values are chosen below maximum.

11. Minimum Radius Tables

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

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

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

15. 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?

16. 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

17. Horizontal Curve FundamentalsPI T Δ E M L PC
Δ/2 PT R R
Δ/2
Δ/2

18. Horizontal Curve Fundamentals
Degree of curvature:
Angle subtended by a 100 foot arc along the horizontal curve
A function of circle radius
Larger D with smaller R
Expressed in degrees PI T Δ E M L PC
Δ/2 PT R R
Δ/2
Δ/2

19. Horizontal Curve Fundamentals
Tangent length (ft) PI T Δ E M L PC
Δ/2 PT R R
Length of curve (ft)
Δ/2
Δ/2

20. Horizontal Curve Fundamentals
External distance (ft) PI T Δ E M L PC
Δ/2 PT
Middle ordinate (ft) R R
Δ/2
Δ/2

21. Example 4 T = Rtan(delta/2). Delta = 29.86 degrees
A horizontal curve is designed with a 1500 ft. radius. The tangent length is 400 ft. and the PT station is What is the PC station?
T = Rtan(delta/2). Delta = degrees
D = /R, D = 3.82 degrees
L = 100(delta)/D = 100(29.86)/3.82 = 781 ft.
PC = PT – L = 2000 – 781 = 1219 = 12+19

22. 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

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

24. Example 6 degrees SSD=566 ft (table 3.1) Ms=20.01 ft
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.
SSD=566 ft (table 3.1) Ms=20.01 ft
degrees

25. Superelevation Transition
from the 2001 Caltrans Highway Design Manual

26. Spiral Curves No Spiral Spiral
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

27. Spiral Curves Ease driver into the curve
Think of how the steering wheel works, it’s a change from zero angle to the angle of the turn in a finite amount of time
This can result in lane wander
Often make lanes bigger in turns to accommodate for this

28. No Spiral
I-90 past North Bend looking east

29. Spiral Curves WSDOT no longer uses spiral curves
Involve complex geometry
Require more surveying
If used, superelevation transition should occur entirely within spiral

30. Operating vs. Design Speed
85th Percentile Speed vs. Inferred Design Speed for 138 Rural Two-Lane Highway Horizontal Curves
85th Percentile Speed vs. Inferred Design Speed for Rural Two-Lane Highway Limited Sight Distance Crest Vertical Curves