Highway Engineering Code No. (CM 304) Lec. 7& 8

Horizontal Alignment

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

Factor Affecting the Design of Horizontal Curves The Design Speed of the road The Safe allowable Coefficient of Friction in the lateral direction Maximum Allowable Rate of Superelevation, and Permissible Centrifugal Ratio

Horizontal alignments with and without transition curves.

ELEMENTS OF A HORIZONTAL CURVE

Transition Curves Transition curves are used to connect tangents to circular curves.

tangent to spiral point (TS), spiral to curve point (SC), curve to spiral point (CS), spiral to tangent point (ST).

Length of Spiral Curve 1. According to rate of acceleration 2. According to spiral geometry (A = spiral curve parameter) 3. Minimum Length

α α F cp F cn WpWp WnWn FfFf FfFf α FcFc W 1 ft e ≈ RvRv Forces acting on a vehicle running on a horizontal Curve SUPERELEVATION

V (km/h) f Case 1: Side friction Only where f = coefficient of side friction V= design speed (km/h) R= radius of horizontal curve (m) Case 2: Superelevation Only where e = superelevation Speed is reduced to avoid sliding inward during wet or icy seasons. Case 3: Superelevation and Side friction For rural roads, e max = For urban roads, e max =

Side Friction Factor from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

Minimum Radius Tables

WSDOT Design Side Friction Factors from the 2005 WSDOT Design Manual, M For Open Highways and Ramps

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

Design Superelevation Rates - WSDOT from the 2005 WSDOT Design Manual, M e max = 8%

Superelevation Transition from the 2001 Caltrans Highway Design Manual

Superelevation Transition from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

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

Spiral Curves No Spiral Spiral from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

No Spiral

Stopping Sight Distance RvRv ΔsΔs Obstruction MsMs SSD