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Vertical AlignmentSee: http://www.fhwa.dot.gov/environment/flex/ch05.htm
(Chapter 5 from FHWA’s Flexibility in Highway Design)
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed. P. 284
Coordination of Vertical and Horizontal Alignment Curvature and grade should be in proper
balance Avoid
Excessive curvature to achieve flat grades
Excessive grades to achieve flat curvature
Vertical curvature should be coordinated with horizontal
Sharp horizontal curvature should not be introduced at or near the top of a pronounced crest vertical curve Drivers may not perceive change in
horizontal alignment esp. at night
Image source: http://www.webs1.uidaho.edu/niatt_labmanual/Chapters/geometricdesign/theoryandconcepts/DescendingGrades.htm
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
Coordination of Vertical and Horizontal Alignment
Sharp horizontal curvature should not be introduced near bottom of steep grade near the low point of a pronounced sag vertical curve Horizontal curves appear distorted Vehicle speeds (esp. trucks) are highest at the
bottom of a sag vertical curve Can result in erratic motion
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
Coordination of Vertical and Horizontal Alignment
On two-lane roads when passing is allowed, need to consider provision of passing lanes Difficult to accommodate with certain
arrangements of horizontal and vertical curvature
need long tangent sections to assure sufficient passing sight distance
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
Coordination of Vertical and Horizontal Alignment
At intersections where sight distance needs to be accommodated, both horizontal and vertical curves should be as flat as practical
In residential areas, alignment should minimize nuisance to neighborhood Depressed highways are less visible Depressed highways produce less noise Horizontal alignments can increase the buffer zone
between roadway and cluster of homes
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
Coordination of Vertical and Horizontal Alignment
When possible alignment should enhance scenic views of the natural and manmade environment Highway should lead into not away from
outstanding views Fall towards features of interest at low elevation Rise towards features best seen from below or
in silhouette against the sky
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•Coordination of horizontal and vertical alignment should begin with preliminary design•Easier to make adjustments at this stage•Designer should study long, continuous stretches of
Coordination of Horizontal and Vertical Alignment
highway in both plan and profile and visualize the whole in three dimensions (FHWA, Chapter 5)
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Coordination of Horizontal and Vertical Alignment
Source: FHWA, Chapter 5
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Coordination of Horizontal and Vertical Alignment
Source: FHWA, Chapter 5
Should be consistent with the topography
Preserve developed properties along the road
Incorporate community valuesFollow natural contours of the land
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Good Coordination of Horizontal and Vertical Alignment
Source: FHWA, Chapter 5
Does not affect aesthetic, scenic, historic, and cultural resources along the way
Enhances attractive scenic views Rivers Rock formations Parks Historic sites Outstanding buildings
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
There are 2 problems with this alignment. What are they?
There are 2 problems with this alignment.
What are they?
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
Maybe we want this if we are trying to slow people down???
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
21
Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
22
Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
A
B
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Vertical Alignment
Equations
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Curve/grade tradeoff
a 3% grade causes a reduction in speed of 10 mph after 1400 feet
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Vertical Alignment - General1. Parabolic shape
2. VPI, VPC, VPT, +/- grade, L
3. Types of crest and
sag curves – see
Exhibit 3-73 p. 269
Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Vertical Alignment – General (Cont.)
4. Crest – stopping, or passing sight distance controls
5. Sag – headlight/SSD distance, comfort, drainage and appearance control
6. Green Book vertical curves defined by K = L/A = length of vertical curve/difference in grades (in percent) = length to change one percent in grade
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Vertical Alignment - GeneralParabolic shape as applied to vertical curves
y = ax2 + bx + c
Where:
y = roadway elevation at distance x
x = distance from beginnning of vertical curve
a, b = coefficients that define shape
c = elevation of PVC
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Vertical Alignment - GeneralParabolic shape as applied to vertical curves
a = G2 – G1
L
b = G1
Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Vertical Curve AASHTO Controls (Crest)
1. Based on stopping sight distance
2. Minimum length must provide sight distance S
3. Two situations (Crest, assumes 3.5 and 2.0 ft. heights)
Source: Transportation Engineering On-line Lab Manual, http://www.its.uidaho.edu/niatt_labmanual/
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Assistant with Target Rod (2ft object height)
Observer with Sighting Rod (3.5 ft)
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Vertical Curve AASHTO Controls (Crest)
Note: for passing site distance, use 2800 instead of 2158
Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Example: Assume SSD < L,
Design speed is 60 mph
G1 = 3% and G2 = -1%,
what is L?
SSD = 525 feet
Lmin = |(-3 - 1)| (525 ft)2 = 510.9 ft
2158
S > L, so try other equation
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Example: Next try SSD > L,
Design speed is 60 mph
G1 = 3% and G2 = -1%,
what is L?
SSD = 525 feet
Lmin = 2 (525’) – 2158’ = 510.5’
S > L, so equation works
|(-3 - 1)|
37
Can also use
K = L / A
Where
K = length of curve per percent algebraic difference in intersecting grade
Charts from Green Book
38From Green book
39From Green book
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Vertical Curve AASHTO Controls (Crest)
Since you do not at first know L, try one of these equations and compare to requirement, or use L = KA (see tables and graphs in Green Book for a given A and design speed)
Note min. L(ft) = 3V(mph) – Why?
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Sag Vertical Curves
Sight distance is governed by nighttime conditions Distance of curve illuminated by headlights
need to be considered
Driver comfortDrainageGeneral appearance
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Vertical Curve AASHTO Controls (Sag) Headlight Illumination sight distance with S < L
S < L
L = AS2
S > L
L = 2S – (400 + 3.5S)
AHeadlight Illumination sight distance with S > L
Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
400 + (3.5 * S)
43
Vertical Curve AASHTO Controls (Sag) For driver comfort use:
L = AV2
46.5
(limits g force to 1 fps/s)
To consider general appearance use:
L = 100 A
Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Ed.
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Sag Vertical Curve: Example
A sag vertical curve is to be designed to join a –3% to a +3% grade. Design speed is 40 mph. What is L?
Skipping steps: SSD = 313.67 feet S > L
Determine whether S<L or S>L
L = 2(313.67 ft) – (400 + 2.5 x 313.67) = 377.70 ft
[3 – (-3)]
313.67 < 377.70, so condition does not apply
45
Sag Vertical Curve: Example
A sag vertical curve is to be designed to join a –3% to a +3% grade. Design speed is 40 mph. What is L?
Skipping steps: SSD = 313.67 feet
L = 6 x (313.67 ft)2 = 394.12 ft
400 + 3.5 x 313.67 ft
313.67 < 394.12, so condition applies
46
Sag Vertical Curve: Example
A sag vertical curve is to be designed to join a –3% to a +3% grade. Design speed is 40 mph. What is L?
Skipping steps: SSD = 313.67 feet
Testing for comfort:
L = AV2 = (6 x [40 mph]2) = 206.5 feet 46.5 46.5
47
Sag Vertical Curve: Example
A sag vertical curve is to be designed to join a –3% to a +3% grade. Design speed is 40 mph. What is L?
Skipping steps: SSD = 313.67 feet
Testing for appearance:
L = 100A = (100 x 6) = 600 feet
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Vertical Curve AASHTO Controls (Sag)
For curb drainage, want minimum of 0.3 percent grade within 50’ of low point = need Kmax = 167 (US units)
For appearance on high-type roads, use minimum design speed of 50 mph (K = 100)
As in crest, use minimum L = 3V
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Other important issues:
Use lighting if need to use shorter L than headlight requirements
Sight distance at under crossings
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Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = 2184.0 ft. Station at PVI is 345+ 60.00, elevation at PVI = 250 feet. Find elevations and station for PVC and PVT.
L/2 = 1092.0 ft
Station at PVC = [345 + 60.00] - [10 + 92.00] = 334 + 68.00
Distance to PVC: 0.03 x (2184/2) = 32.76 feet
ElevationPVC = 250 – 32.76 = 217.24 feet
Station at PVT = [345 + 60.00] + [10 + 92.00] = 357 + 52.00
Distance (vertical) to PVT = 0.04 x (2184/2) = 43.68 feet
Elevation PVT = 250 – 43.68 = 206.32 feet
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Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = 2184.0 ft. Station at PVI is 345+ 60.00, elevation at PVI = 250 feet. Station at PVC is 334 + 68.00, Elevation at PVC: 217.24 feet.
Calculate points along the vertical curve.
X = distance from PVC
Y = Ax2
200 L
Elevationtangent = elevation at PVC + distance x grade
Elevationcurve = Elevationtangent - Y
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Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = 2184.0 ft. Station at PVI is 345+ 60.00, elevation at PVI = 250 feet. Find elevation on the curve at a point 400 feet from PVC.
Y = A x 2 = 6 x (400 ft)2 = 4.40 feet
200L 200 (2814)
Elevation at tangent = 217.24 + (400 x 0.03) = 229.24
Elevation on curve = 229.24 – 4.40 feet = 224.84
53Source: Iowa DOT Design Manual
54
Source: Iowa DOT Design Manual
55Source: Iowa DOT Design Manual
Note: L is measured from here to here
Not here
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