CEE 320 Fall 2008 Horizontal Alignment Horizontal Alignment

CEE 320 Fall 2008 Horizontal Alignment

Horizontal Alignment • Objective: – Geometry of directional transition to ensure: • Safety • Comfort • Primary challenge – Transition between two directions • Fundamentals CEE 320 Fall 2008 – Circular curves – Superelevation or banking Δ

Vehicle Cornering Centripetal force parallel to the roadway Fc F cn F cp W Wn Ff Side frictional force Ff Wp CEE 320 Fall 2008 Weight parallel to the roadway

Vehicle Cornering Fc α F cn F cp α W Ff Wn Ff Wp CEE 320 Fall 2008 α Vehicle weight and centripetal force normal to roadway

Vehicle Cornering ≈ Rv Fc α F cn F cp α W Ff CEE 320 Fall 2008 α Wn Wp Ff

Horizontal Curve Fundamentals PI PC L PT CEE 320 Fall 2008 R R Curve is a circle, not a parabola

Superelevation • Banking • number of vertical feet of rise per 100 ft of horizontal distance • e = 100 tan CEE 320 Fall 2008 α

CEE 320 Fall 2008 Superelevation Divide both sides by Wcos(α)

Superelevation CEE 320 Fall 2008 • 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)

Selection of e and fs • Practical limits on superelevation (e) – Climate – Constructability – Adjacent land use • Side friction factor (fs) variations – – CEE 320 Fall 2008 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.

CEE 320 Fall 2008 Minimum Radius Tables

WSDOT Design Side Friction Factors from the 2005 WSDOT Design Manual, M 22 -01 CEE 320 Fall 2008 For Open Highways and Ramps

CEE 320 Fall 2008 Design Superelevation Rates - AASHTO from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

Design Superelevation Rates - WSDOT CEE 320 Fall 2008 emax = 8% from the 2005 WSDOT Design Manual, M 22 -01

Example 5 CEE 320 Fall 2008 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?

Example 5 CEE 320 Fall 2008 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

Horizontal Curve Fundamentals PI T Δ E M PC L Δ/2 R R Δ/2 CEE 320 Fall 2008 PT

Horizontal Curve Fundamentals Degree of curvature: Angle subtended by a 100 foot arc along the horizontal curve PI T E A function of circle radius M Larger D with smaller R Expressed in degrees Δ PC L Δ/2 R R Δ/2 CEE 320 Fall 2008 PT

Horizontal Curve Fundamentals PI Tangent length (ft) T Δ E M PC Length of curve (ft) L Δ/2 R R Δ/2 CEE 320 Fall 2008 PT

Horizontal Curve Fundamentals External distance (ft) PI T Δ E M PC Middle ordinate (ft) L Δ/2 R R Δ/2 CEE 320 Fall 2008 PT

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 is the PC station? CEE 320 Fall 2008 T = Rtan(delta/2). Delta = 29. 86 degrees D = 5729. 6/R, D = 3. 82 degrees L = 100(delta)/D = 100(29. 86)/3. 82 = 781 ft. PC = PT – L = 2000 – 781 = 1219 = 12+19

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 CEE 320 Fall 2008 Δs Assumes curve exceeds required SSD

Stopping Sight Distance SSD (not L) Ms Obstruction Rv CEE 320 Fall 2008 Δs

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. SSD=566 ft (table 3. 1) CEE 320 Fall 2008 Ms=20. 01 ft degrees

CEE 320 Fall 2008 Superelevation Transition from the 2001 Caltrans Highway Design Manual

Spiral Curves No Spiral CEE 320 Fall 2008 Spiral from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

Spiral Curves CEE 320 Fall 2008 • 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

CEE 320 Fall 2008 No Spiral

Spiral Curves CEE 320 Fall 2008 • • WSDOT no longer uses spiral curves Involve complex geometry Require more surveying If used, superelevation transition should occur entirely within spiral

Operating vs. Design Speed 85 th Percentile Speed vs. Inferred Design Speed for 138 Rural Two-Lane Highway Horizontal Curves CEE 320 Fall 2008 85 th Percentile Speed vs. Inferred Design Speed for Rural Two-Lane Highway Limited Sight Distance Crest Vertical Curves