# Geometric Design by oddt1s8q

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```									              Geometric Design
Spring 2008
CEE 320

CEE 320
Anne Goodchild
Outline

1. Concepts
2. Vertical Alignment
a.   Fundamentals
b.   Crest Vertical Curves
c.   Sag Vertical Curves
d.   Examples
3. Horizontal Alignment
a. Fundamentals
b. Superelevation
4. Other Non-Testable Stuff
Spring 2008
CEE 320
Concepts

• 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.
Spring 2008
CEE 320

Piilani Highway on Maui
Stationing
Horizontal Alignment

Vertical Alignment
Spring 2008
CEE 320
From Perteet Engineering
Vertical Alignment
Spring 2008
CEE 320
Vertical Alignment

• Objective:
– Determine elevation to ensure
• Proper drainage
• Acceptable level of safety
• Primary challenge
– Vertical curves
Sag Vertical Curve
G1          G2
G1                 G2
Spring 2008

Crest Vertical Curve
CEE 320
Vertical Curve Fundamentals

• Parabolic function
– Constant rate of change of slope
– Implies equal curve tangents

y  ax  bx  c
2

• y is the roadway elevation x stations
(or feet) from the beginning of the curve
Spring 2008
CEE 320
Vertical Curve Fundamentals

PVI
G1             δ
PVC                             G2
PVT
L/2

L
x

y  ax  bx  c
2

Choose Either:
Spring 2008

• G1, G2 in decimal form, L in feet
CEE 320

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

Relationships                                • G1, G2 in percent, L in stations

At the PVC : x  0 and Y  c
dY
At the PVC : x  0 and                b  G1
dx

d 2Y        G2  G1     G2  G1
Anywhere :    2
 2a          a
dx             L          2L
PVI
G1         δ
PVC                         G2
PVT
L/2
Spring 2008
CEE 320

L
x
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

PVC: STA 100+00
EL 59 ft.
Spring 2008
CEE 320
PVI

PVT

PVC: STA 100+00
EL 59 ft.
•G1, G2 in percent
Other Properties                        •L in feet

G1           x

PVT
PVC

Y
Ym         G2

PVI                        Yf
A  G1  G2

A 2               AL              AL
Y      x         Ym             Yf 
200L                800             200
Spring 2008
CEE 320
Other Properties

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

L
K
A

high / low pt.  x  K G1
Spring 2008
CEE 320
Crest Vertical Curves
SSD

PVI
Line of Sight

PVC                             PVT          G2
G1

h2
h1

L
For SSD < L                                  For SSD > L

L
ASSD 
2

L  2SSD 

200 h1  h2         
2

                        
Spring 2008

2
100        2h1  2h2                                   A
CEE 320
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
ASSD 
2
L  2SSD 
2158
L
2158                                A
Spring 2008
CEE 320
Crest Vertical Curves

• Assuming L > SSD…

2
SSD
K
2158
Spring 2008
CEE 320
Design Controls for Crest Vertical Curves
Spring 2008
CEE 320

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
CEE 320
Spring 2008

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

PVC                                           PVT

h1                       PVI
h2=0

L
For SSD < L                                           For SSD > L

ASSD                                   200h1  SSD tan  
2
L                                L  2SSD 
200h1  S tan  
Spring 2008

A
CEE 320
Sag Vertical Curves

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

• Simplified Equations
For SSD < L                        For SSD > L

ASSD                          400  3.5SSD 
2
L                      L  2SSD                  
400  3.5SSD                            A       
Spring 2008
CEE 320
Sag Vertical Curves

• Assuming L > SSD…

2
SSD
K
400  3.5SSD
Spring 2008
CEE 320
Design Controls for Sag Vertical Curves
Spring 2008
CEE 320

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
CEE 320
Spring 2008

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?
Spring 2008
CEE 320
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?
Spring 2008
CEE 320
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?
Spring 2008
CEE 320
Horizontal
Alignment
Spring 2008
CEE 320
Horizontal Alignment

• Objective:
– Geometry of directional transition to ensure:
• Safety
• Comfort
• Primary challenge                       Δ
– Transition between two directions
– Horizontal curves
• Fundamentals
– Circular curves
– Superelevation
Spring 2008
CEE 320
Horizontal Curve Fundamentals
PI
T             Δ
E

T  R tan              L
M
2     PC                   Δ/2       PT

       100
L     R 
180       D        R                   R

 180               Δ/2 Δ/2
100     
D        18,000
Spring 2008

 R
CEE 320

R
Horizontal Curve Fundamentals
PI
T             Δ
E
M
L
PC                 Δ/2       PT

 1          
 cos  2  1
E  R            
                    R                   R

Δ/2 Δ/2
       
M  R1  cos 
Spring 2008

       2
CEE 320
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?
Spring 2008
CEE 320
Superelevation                    W p  F f  Fcp

Rv

≈
Fc

e
W                    1 ft

α

         WV 2        WV 2
W sin   f s W cos       sin   
 gR cos
Spring 2008


CEE 320

         gRv           v
Superelevation

         WV 2        WV 2
W sin   f s W cos 
              sin   
 gR cos
         gRv           v

V2
tan   f s      1  f s tan  
gRv
V2
e  fs      1  f s e
gRv

V2
Rv 
g  f s  e
Spring 2008
CEE 320
Selection of e and fs

• Practical limits on superelevation (e)
– Climate
– Constructability
• Side friction factor (fs) variations
– Vehicle speed
– Pavement texture
– Tire condition
Spring 2008
CEE 320
Side Friction Factor
Spring 2008
CEE 320

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
Spring 2008
CEE 320
WSDOT Design Side Friction Factors
For Open Highways and Ramps

from the 2005 WSDOT Design Manual, M 22-01
Spring 2008
CEE 320
WSDOT Design Side Friction Factors
For Low-Speed Urban Managed Access Highways

from the 2005 WSDOT Design Manual, M 22-01
Spring 2008
CEE 320
Design Superelevation Rates - AASHTO
Spring 2008
CEE 320

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
Design Superelevation Rates - WSDOT

emax = 8%
Spring 2008
CEE 320

from the 2005 WSDOT Design Manual, M 22-01
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?
Spring 2008
CEE 320
Stopping Sight Distance
SSD
          100 s
SSD      Rv  s 
180            D
180 SSD                         Ms
s 
Rv
        90SSD 
 R 
M s  Rv 1  cos
Obstruction

           v                   Rv

Rv    Rv  M s 
cos           
1
SSD           R        
Δs
Spring 2008

90               
CEE 320

v
FYI – NOT TESTABLE

Supplemental Stuff

• Cross section
• Superelevation Transition
– Runoff
– Tangent runout
• Spiral curves
• Extra width for curves
Spring 2008
CEE 320
FYI – NOT TESTABLE

Cross Section
Spring 2008
CEE 320
FYI – NOT TESTABLE

Superelevation Transition
Spring 2008
CEE 320

from the 2001 Caltrans Highway Design Manual
FYI – NOT TESTABLE

Superelevation Transition
Spring 2008
CEE 320

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001
CEE 320
Spring 2008

Superelevation Runoff/Runout
FYI – NOT TESTABLE

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
FYI – NOT TESTABLE

Superelevation Runoff - WSDOT
Spring 2008
CEE 320

from the 2005 WSDOT Design Manual, M 22-01
FYI – NOT TESTABLE

Spiral Curves

No Spiral

Spiral
Spring 2008
CEE 320

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
FYI – NOT TESTABLE

No Spiral
Spring 2008
CEE 320
FYI – NOT TESTABLE

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
Spring 2008
CEE 320
FYI – NOT TESTABLE

Desirable Spiral Lengths
Spring 2008
CEE 320

from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
FYI – NOT TESTABLE

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
Spring 2008
CEE 320
Primary References

• Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005).
Principles of Highway Engineering and Traffic Analysis, Third
Edition. Chapter 3

• American Association of State Highway and Transportation
Officials (AASHTO). (2001). A Policy on Geometric Design of
Highways and Streets, Fourth Edition. Washington, D.C.
Spring 2008
CEE 320

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