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### Geometric Design

CEE 320Anne Goodchild

Outline

- Concepts
- Vertical Alignment
- Fundamentals
- Crest Vertical Curves
- Sag Vertical Curves
- Examples
- Horizontal Alignment
- Fundamentals
- Superelevation
- Other Non-Testable Stuff

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

Horizontal Alignment (plan view)

Vertical Alignment (profile view)

Stationing

Along horizontal alignment

12+00 = 1,200 ft.

ConceptsPiilani Highway on Maui

Vertical Alignment

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

Sag Vertical Curve

G1

G2

G2

G1

Crest Vertical Curve

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

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

Crest Vertical Curves

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

For SSD < L

For SSD > L

Crest Vertical Curves

- Assuming L > SSD…

Design Controls for Crest Vertical Curves

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

Design Controls for Crest Vertical Curves

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

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

Sag Vertical Curves

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

For SSD < L

For SSD > L

Sag Vertical Curves

- Assuming L > SSD…

Design Controls for Sag Vertical Curves

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

Design Controls for Sag Vertical Curves

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

Example 1

A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long sag vertical curve. The entering grade is -2.4 percent and the exiting grade is 4.0 percent. A tree has fallen across the road at approximately the PVT. Assuming the driver cannot see the tree until it is lit by her headlights, is it reasonable to expect the driver to be able to stop before hitting the tree?

Sag Vertical Curve

- Assume S<L, try both, but this is most often the case
- Equation specific to sag curve which accommodates headlight beam
- L and S in horizontal plane and comparable (150 and 146 ft)
- Required SSD = 196.53 ft assumes 0 grade
- Text problem versus design problem.

Sag Vertical Curves

Light Beam Distance (S)

G1

diverging from horizontal plane of vehicle by β degrees

G2

PVT

PVC

h1

PVI

h2=0

L

Daytime sight distance unrestricted

Example 2

Similar to Example 1 but for a crest curve.

A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long crest vertical curve. The entering grade is 3.0 percent and the exiting grade is -3.4 percent. A tree has fallen across the road at approximately the PVT. Is it reasonable to expect the driver to be able to stop before hitting the tree?

Crest Vertical Curve

- Assume S<L, try both, but this is most often the case
- Equation specific to crest curve which accommodates sight over hill
- L and S in horizontal plane and comparable (150 and 243 ft)
- Required SSD = 196.53 ft assumes 0 grade
- Text problem versus design problem.

Example 3

A roadway is being designed using a 45 mph design speed. One section of the roadway must go up and over a small hill with an entering grade of 3.2 percent and an exiting grade of -2.0 percent. How long must the vertical curve be?

Horizontal Alignment

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

Δ

Horizontal Curve Fundamentals

D = degree of curvature (angle subtended by a 100’ arc)

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2

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 are the PI and PT stations?

e = number of vertical feet of rise per 100 ft of horizontal distance = 100tan

SuperelevationThis is the minimum radius that provides

for safe vehicle operation

Rv because it is to the vehicle’s path

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

Design values of fs are chosen somewhat below this maximum value so there is a margin of safety

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

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 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

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

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.

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

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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