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### Contents

Concepts

Vertical Alignment

Fundamentals

Crest Vertical Curves

Sag Vertical Curves

Examples

Horizontal Alignment

Fundamentals

Superelevation

Alignment is a 3D problem broken down into two 2D problems

Horizontal Alignment (plan view)

Vertical Alignment (profile view)

Stationing

Along horizontal alignment

IntroductionPiilani Highway on Maui

Introduction

From Perteet Engineering

Geometric Design Elements

- Sight Distances
- Superelevation
- Horizontal Alignment
- Vertical Alignment

Sag Vertical Curve

G1

G2

G2

G1

Crest Vertical Curve

Vertical Alignment- Objective:
- Determine elevation to ensure
- Proper drainage
- Acceptable level of safety
- Primary challenge
- Transition between two grades
- Vertical curves

Vertical Curve Fundamentals

- Parabolic function
- Constant rate of change of slope
- Implies equal curve tangents
- y is the roadway elevation x stations (or feet) from the beginning of the curve

Vertical Curve Fundamentals

PVI

G1

δ

PVC

G2

PVT

L/2

L

x

- Choose Either:
- G1, G2 in decimal form, L in feet
- G1, G2 in percent, L in stations

Relationships

- Choose Either:
- G1, G2 in decimal form, L in feet
- G1, G2 in percent, L in stations

Example

A 400 ft. equal tangent crest vertical curve has a PVC station of 100+00 at 59 ft. elevation. The initial grade is 2.0 percent and the final grade is -4.5 percent. Determine the elevation and stationing of PVI, PVT, and the high point of the curve.

PVI

PVT

G1=2.0%

G2= - 4.5%

PVC: STA 100+00

EL 59 ft.

Other Properties

- K-Value (defines vertical curvature)
- The number of horizontal feet needed for a 1% change in slope

For SSD < L

For SSD > L

Crest Vertical Curves- Assumptions for design
- h1 = driver’s eye height = 3.5 ft.
- h2 = tail light height = 2.0 ft.
- Simplified Equations

- Assuming L > SSD…

Design Controls for Crest Vertical Curves

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

Design Controls for Crest Vertical Curves

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

Sag Vertical Curves

Light Beam Distance (SSD)

G1

headlight beam (diverging from LOS by β degrees)

G2

PVT

PVC

h1

PVI

h2=0

L

For SSD < L

For SSD > L

For SSD < L

For SSD > L

Sag Vertical Curves- Assuming L > SSD…

- Assumptions for design
- h1 = headlight height = 2.0 ft.
- β = 1 degree
- Simplified Equations

Design Controls for Sag Vertical Curves

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

Design Controls for Sag Vertical Curves

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

Horizontal Alignment

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

Δ

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

Side Friction Factor

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

WSDOT Design Side Friction Factors

For Open Highways and Ramps

from the 2005 WSDOT Design Manual, M 22-01

WSDOT Design Side Friction Factors

For Low-Speed Urban Managed Access Highways

from the 2005 WSDOT Design Manual, M 22-01

Design Superelevation Rates - AASHTO

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

Circular Curve Geometrics

- PC = Point of Curvature
- PT = Point of Tangency
- PI = Point of Intercept
- 100/D = L/Δ, so,
- L = 100 (Δ /D) where:
- L = arc length(measured in Stations (1 Sta = 100 ft)
- Δ = internal angle (deflection angle)
- D = 5729.58/R
- M = middle ordinate m=R [1 – cos(Δ /2) ]

M - is maximum distance from curve to long chord

Circular Curve Geometrics

Degree of curvature: D = central angle which subtends an arc of 100 feet

D=5729.58/R where R – radius of curve

For R=1000 ft. D = 5.73 degrees

Maximum degree of curve/min radius:

Dmax = 85,660 (e + f)/V2 or

Rmin = V2/[15 (e + f)]

Horizontal Sight Distance

1) Sight line is a chord of the circular curve

2) Applicable Minimum Stopping Sight Distance (MSSD) measured along centerline of inside lane

Criterion: no obstruction

within middle ordinate

Assume:

driver eye height = 3.5 ft

object height = 2.0 ft.

Note: results in line of sight obstruction height at middle ordinate of 2.75 ft

Horizontal Alignment

- Basic controlling expression:

e + f = V2/15R

- Example:
- A horizontal curve has the following characteristics: Δ = 45˚, L = 1200 ft, e = 0.06 ft/ft. What coefficient of side friction would be required by a vehicle traveling at 70 mph?

Circular Curve Geometrics

- PC = Point of Curvature
- PT = Point of Tangency
- PI = Point of Intercept
- 100/D = L/Δ, so,
- L = 100 (Δ /D) where:
- L = arc length(measured in Stations (1 Sta = 100 ft)
- Δ = internal angle (deflection angle)
- D = 5729.58/R
- M = middle ordinate m=R [1 – cos(Δ /2) ]

M - is maximum distance from curve to long chord

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

- Involve complex geometry
- Require more surveying
- Are somewhat empirical
- If used, superelevation transition should occur entirely within spiral

Desirable Spiral Lengths

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

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