WELCOME

DR.KHALED ALI

Highway Engineering Code No. (CM 304)

Lec. 7& 8

Horizontal Alignment

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).

R28V Ls

3

2A R Ls

m50 (min) Ls

Length of Spiral Curve

1. According to rate of acceleration

2. According to spiral geometry

(A = spiral curve parameter)3. Minimum Length

DR 1746

cpfp FFW α

α

Fcp

Fcn

Wp

Wn F f

F f

α

Fc

W 1 fte

≈Rv

Forces acting on a vehicle running on a horizontal Curve

SUPERELEVATION

V (km/h) 50 65 80 95 110f 0.16 0.15 0.14 0.13 0.12

Case 1: Side friction Only

RVf

127

2

wheref = coefficient of side frictionV= design speed (km/h)R= radius of horizontal curve (m)

Case 2: Superelevation Only

RV

RV

e228127

)75.0( 22

wheree = superelevationSpeed is reduced to avoid sliding inward during wet or icy seasons.

Case 3: Superelevation and Side friction

RVfe

127

2

For rural roads, emax = 0.10 - 0.12For urban roads, emax = 0.08 - 0.10

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

WSD

OT D

esig

n M

anua

l, M

22-

01

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 22-01

emax = 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

Rv

Δs

Obstruction

Ms

SSD

v

svv

RMRRSSD 1cos

90