1 vertical alignment ce 453 lecture 20 sources: a policy on geometric design of highways and streets...
TRANSCRIPT
1
Vertical AlignmentVertical Alignment
CE 453 Lecture 20
Sources: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, 2001 4th Edition, and FHWA’s Flexibility in Highway Design
2
Coordination of Vertical and Coordination of Vertical and Horizontal AlignmentHorizontal 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
3
Coordination of Vertical and Coordination of Vertical and Horizontal AlignmentHorizontal 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
4
Coordination of Vertical and Coordination of Vertical and Horizontal AlignmentHorizontal 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
5
Coordination of Vertical and Coordination of Vertical and Horizontal AlignmentHorizontal 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
6
Coordination of Vertical and Coordination of Vertical and Horizontal AlignmentHorizontal 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
7
Coordination of Horizontal Coordination of Horizontal and Vertical Alignmentand Vertical Alignment
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 highway in both plan and profile and visualize the whole in three dimensions
8
Coordination of Horizontal Coordination of Horizontal and Vertical Alignmentand Vertical Alignment
9
Should be consistent with the topography
Preserve developed properties along the road
Incorporate community valuesFollow natural contours of the land
Coordination of Horizontal Coordination of Horizontal and Vertical Alignmentand Vertical Alignment
10
Good Coordination of Good Coordination of Horizontal and Vertical Horizontal and Vertical
AlignmentAlignment Does not affect aesthetic, scenic, historic, and cultural resources along the way
Enhances attractive scenic views– Rivers– Rock formations– Parks– Historic sites– Outstanding buildings
13
16
Vertical CurvesVertical Curves
Connect roadway grades (tangents)
Grade (rise over run) – 10% grade increases 10’ vertically for
every 100’ horizontal
17
Vertical CurvesVertical Curves
Ascending grade:– Frequency of
collisions increases significantly when vehicles traveling more than 10 mph below the average traffic speed are present in the traffic stream
18
ExampleExample If a highway with
traffic normally running at 65 mph has an inclined section with a 3% grade, what is the maximum length of grade that can be used before the speed of the larger vehicles is reduced to 55 mph?
20
Climbing lanesClimbing lanes
When flatter grades cannot be accommodated, consider climbing lane when all 3 of the following criteria are met (AASHTO):– Upgrade traffic flow rate in excess of 200 vehicles
per hour.– Upgrade truck flow rate in excess of 20 vehicles per
hour.– One of the following conditions exists:
A 15 km/h or greater speed reduction is expected for a typical heavy truck.
Level-of-service E or F exists on the grade. A reduction of two or more levels of service is experienced
when moving from the approach segment to the grade.
21
Descending GradesDescending Grades
Problem is increased speeds and loss of control for heavy trucks
Runaway vehicle ramps are often designed and included at critical locations along the grade
Ramps placed before each turn that cannot be negotiated at runaway speeds
Ramps should also be placed along straight stretches of roadway, wherever unreasonable speeds might be obtained
Ramps located on the right side of the road when possible
22
Maximum GradesMaximum Grades
Passenger vehicles can easily negotiate 4 to 5% grade without appreciable loss in speed
Upgrades: trucks average 7% decrease in speed
Downgrades: trucks average speed increase 5%
23
Vertical CurvesVertical Curves Parabolic shape VPI, VPC, VPT, +/- grade, L Types of crest and sag curves
24
Vertical CurvesVertical Curves Crest – stopping, or passing sight
distance controls Sag – headlight/SSD distance, comfort,
drainage and appearance control 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
25
Parabola y = ax2 + bx + cWhere:
y = roadway elevation at distance x x = distance from beginning of
vertical curve a = G2 – G1 L b = G1 c = elevation of PVC
Vertical Curve EquationsVertical Curve Equations
26
Vertical Curve AASHTO Controls Vertical Curve AASHTO Controls
(Crest)(Crest) Minimum length must provide
stopping sight distance S Two situations (both assume h1=3.5’
and h2=2.0’)
Source: Transportation Engineering On-line Lab Manual, http://www.its.uidaho.edu/niatt_labmanual/
28
Vertical Curve AASHTO Controls Vertical Curve AASHTO Controls (Crest)(Crest)
Note: for passing sight distance, use 2800 instead of 2158
29
Example: Try SSD > L,
Design speed is 60 mph
G1 = 3% and G2 = -1%,
what is L?
(Assume grade = 0% for SSD)
SSD = 570feet ( see: Table 3.4 of text)
Lmin = 2 (570’) – 2158’ = 600.5’
|(-1-3)|
S < L, so it doesn’t match condition
30
Example: Assume SSD < L,
Design speed is 60 mph
G1 = 3% and G2 = -1%,
what is L?
Assuming average grade = 0%
SSD = 570 feet - ( Table 3.4 of text)
Lmin = |(-3 - 1)| (570 ft)2 = 602 ft
2158
SSD < L, equation matches condition
31
Evaluation of example:
The AASHTO SSD distance equations provided the same design length from either equation in this special case. (600 compared to 602 - this is not typical)
Garber and Hoel recommend using the most critical grade of - 1% for SSD computation.– Resulting SSD would be: d = 573 ft– Resulting minimum curve: L = 608 ft
Difference between 602 and 608 is too small to worry about
32
Text example : g1 = + 3% g2 = -3%
Design speed of 60 mph
If SSD = 570’ (AASHTO – no grade consideration)
Resulting minimum curve: L = 903 ft (S < L)
Consider grade per Garber and Hoel (p 693-694)
SSD, using - 3% grade, 598’
Resulting minimum curve L = 994 ft
33
Assessment of grade Assessment of grade adjustmentadjustment
If sight distance is less than curve length, the driver will be on an upgrade a greater portion of the distance than on a down grade
(for eye ht = 3.5’ and object ht = 2.0 ft, 68% of the distance between eye and object will be on + grade.)
For crest vertical curve, selecting a curve length based on down grade SSD may produce an overly conservative design length.
34
AASHTO design tablesAASHTO design tables
Vertical curve length can also be found in design tables
L = K *AWhere
K = length of curve per percent algebraic difference in intersecting grade
Charts from Green Book
37
Vertical Curve AASHTO Controls Vertical Curve AASHTO Controls (Crest)(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)
38
Chart vs computedChart vs computed
From chart V = 60 mph K = 151 ft / %
change
For g1 = 3 g2 = - 1
A = |g2 – g1| = |-1 – 3| = 4
L = ( K * A) = 151 * 4 = 604
39
Sag Vertical CurvesSag Vertical Curves
Sight distance is governed by night- time conditions– Distance on curve illuminated by
headlights need to be consideredDriver comfortDrainageGeneral appearance
40
Vertical Curve AASHTO Controls Vertical Curve AASHTO Controls
(Sag)(Sag) Headlight Illumination sight distance
S < L: L = AS2
400 + (3.5 * S)
S > L: L = 2S – (400 + 3.5S) A
41
Vertical Curve AASHTO Controls Vertical Curve AASHTO Controls
(Sag)(Sag)
For driver comfort use: L > AV2
46.5 (limits g force to 1 fps/s)
To consider general appearance use:
L > 100 A
42
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
43
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)2 = 394.12 ft
400 + 3.5 x 313.67
313.67 < 394.12, so condition applies
44
Sag Vertical Curve: ExampleA 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
Testing for appearance:
L = 100A = (100 x 6) = 600 feet
45
Vertical Curve AASHTO Controls Vertical Curve AASHTO Controls (Sag)(Sag)
For curb drainage, want min. of 0.3 percent grade within 50’ of low point = need Kmax = 167 (US units)
For appearance on high-type roads, use min design speed of 50 mph (K = 100)
As in crest, use min L = 3V
46
Other important issues:Other important issues:
Use lighting if need to use shorter L than headlight requirements
Sight distance at under crossings
48
Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = 2184.0 ft. Station at VPI is 345+ 60.00, elevation at VPI = 250 feet. Find elevations and station for VPC (BVC) and VPT (EVC).
L/2 = 1092.0 ft
Station at VPC = [345 + 60.00] - [10 + 92.00] = 334 + 68.00
Vertical Diff VPI to VPC: -0.03 x (2184/2) = - 32.76 feet
ElevationVPC = 250 – 32.76 = 217.24 feet
Station at VPT = [345 + 60.00] + [10 + 92.00] = 357 + 52.00
Vertical Diff VPI to VPT = -0.04 x (2184/2) = - 43.68 feet
Elevation VPT = 250 – 43.68 = 206.32 feet
49
Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = 2184.0 ft. Station at VPI is 345+ 60.00, elevation at VPI = 250 feet. Station at VPC (BVC) is 334 + 60.00, Elevation at VPC: 217.24 feet.
Calculate points along the vertical curve.
X = distance from VPC
Y = Ax2
200 L
Elevationtangent = elevation at VPC + distance x grade
Elevationcurve = Elevationtangent - Y
50
Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = 2184.0 ft. Station at VPI is 345+ 60.00, elevation at VPI = 250 feet. Find elevation on the curve at a point 400 feet from VPC.
Y = A x 2 = - 7 x (400 ft)2 = - 2.56 feet
200L 200 (2814)
Elevation at tangent = 206.32 + (400 x 0.03) = 218.32
Elevation on curve = 218.32 – 2.56 feet = 226.68’