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

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Horizontal alignment

Horizontal Alignment


Horizontal alignment1
Horizontal Alignment

  • Objective:

    • Geometry of directional transition to ensure:

      • Safety

      • Comfort

  • Primary challenge

    • Transition between two directions

  • Fundamentals

    • Circular curves

    • Superelevation or banking

Δ


Vehicle cornering
Vehicle Cornering

Centripetal force parallel to the roadway

Fc

Fcn

Fcp

W

Wn

Ff

Side frictional force

Wp

Ff

Weight parallel to the roadway


Vehicle cornering1
Vehicle Cornering

Fc

α

Fcn

Fcp

α

W

Wn

Ff

Wp

Ff

α

Vehicle weight and centripetal force normal to roadway


Vehicle cornering2
Vehicle Cornering

Rv

Fc

α

Fcn

Fcp

α

W

Wn

Ff

Wp

Ff

α


Horizontal curve fundamentals
Horizontal Curve Fundamentals

PI

L

PT

PC

R

R

Curve is a circle, not a parabola


Superelevation
Superelevation

  • Banking

  • number of vertical feet of rise per 100 ft of horizontal distance

  • e = 100tan

α


Superelevation1
Superelevation

Divide both sides by Wcos(α)


Superelevation2

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)

Superelevation


Selection of e and f s
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.



Wsdot design side friction factors
WSDOT Design Side Friction Factors

For Open Highways and Ramps

from the 2005 WSDOT Design Manual, M 22-01


Design superelevation rates aashto
Design Superelevation Rates - AASHTO

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


Design superelevation rates wsdot
Design Superelevation Rates - WSDOT

emax = 8%

from the 2005 WSDOT Design Manual, M 22-01


Example 5
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?


Example 51
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


Horizontal curve fundamentals1
Horizontal Curve Fundamentals

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2


Horizontal curve fundamentals2
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

Δ/2

PT

PC

R

R

Δ/2

Δ/2


Horizontal curve fundamentals3
Horizontal Curve Fundamentals

PI

Tangent length (ft)

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Length of curve (ft)

Δ/2

Δ/2


Horizontal curve fundamentals4
Horizontal Curve Fundamentals

PI

External distance (ft)

T

Δ

E

M

L

Δ/2

PT

PC

Middle ordinate (ft)

R

R

Δ/2

Δ/2


Example 4
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?

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
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


Stopping sight distance1
Stopping Sight Distance

SSD (not L)

Ms

Obstruction

Rv

Δs


Example 6
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)

Ms=20.01 ft

degrees


Superelevation transition
Superelevation Transition

from the 2001 Caltrans Highway Design Manual


Spiral curves
Spiral Curves

No Spiral

Spiral

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


Spiral curves1
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



Spiral curves2
Spiral Curves

  • 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
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


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