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Geometric Design

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Geometric Design

CEE 320Anne Goodchild

- 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.

Piilani Highway on Maui

Horizontal Alignment

Vertical Alignment

From Perteet Engineering

Vertical Alignment

- Objective:
- Determine elevation to ensure
- Proper drainage
- Acceptable level of safety

- Determine elevation to ensure
- Primary challenge
- Transition between two grades
- Vertical curves

Sag Vertical Curve

G1

G2

G2

G1

Crest Vertical Curve

- 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

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

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

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.

PVI

PVT

G1=2.0%

PVC: STA 100+00

EL 59 ft.

G2= -4.5%

- G1, G2 in percent
- L in feet

G1

x

PVT

PVC

Y

Ym

G2

PVI

Yf

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

SSD

PVI

Line of Sight

PVC

PVT

G2

G1

h2

h1

L

For SSD < L

For SSD > L

- 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

- Assuming L > SSD…

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

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

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

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

- Simplified Equations

For SSD < L

For SSD > L

- Assuming L > SSD…

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

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

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?

- 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.

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

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?

- 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.

SSD

PVI

Line of Sight

PVC

PVT

G2

G1

h2

h1

L

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

- Geometry of directional transition to ensure:
- Primary challenge
- Transition between two directions
- Horizontal curves

- Fundamentals
- Circular curves
- Superelevation

Δ

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

PI

T

Δ

E

M

L

Δ/2

PT

PC

R

R

Δ/2

Δ/2

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?

Rv

≈

Fc

α

Fcn

Fcp

α

e

W

1 ft

Wn

Ff

Wp

Ff

α

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

This is the minimum radius that provides

for safe vehicle operation

Rv because it is to the vehicle’s path

- 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

For Open Highways and Ramps

from the 2005 WSDOT Design Manual, M 22-01

For Low-Speed Urban Managed Access Highways

from the 2005 WSDOT Design Manual, M 22-01

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

emax = 8%

from the 2005 WSDOT Design Manual, M 22-01

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?

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

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

SSD (not L)

Ms

Obstruction

Rv

Δs

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.

FYI – NOT TESTABLE

from the 2001 Caltrans Highway Design Manual

FYI – NOT TESTABLE

No Spiral

Spiral

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

FYI – NOT TESTABLE

FYI – NOT TESTABLE

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

FYI – NOT TESTABLE

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