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Vertical Alignment. See: http://www.fhwa.dot.gov/environment/flex/ch05.htm (Chapter 5 from FHWA’s Flexibility in Highway Design). Coordination of Vertical and Horizontal Alignment. Curvature and grade should be in proper balance Avoid Excessive curvature to achieve flat grades

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vertical alignment

Vertical Alignment

See: http://www.fhwa.dot.gov/environment/flex/ch05.htm (Chapter 5 from FHWA’s Flexibility in Highway Design)

coordination of vertical and horizontal alignment
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

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 alignment1
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

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 alignment2
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

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 alignment3
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

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 alignment4
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

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.

slide7

Coordination of Horizontal and 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 (FHWA, Chapter 5)

slide9

Coordination of Horizontal and Vertical Alignment

  • Should be consistent with the topography
  • Preserve developed properties along the road
  • Incorporate community values
  • Follow natural contours of the land

Source: FHWA, Chapter 5

slide10

Good Coordination of Horizontal and Vertical Alignment

  • Does not affect aesthetic, scenic, historic, and cultural resources along the way
  • Enhances attractive scenic views
    • Rivers
    • Rock formations
    • Parks
    • Historic sites
    • Outstanding buildings

Source: FHWA, Chapter 5

slide11

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.

slide12

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.

slide13

There are 2 problems with this alignment. What are they?

There are 2 problems with this alignment.

What are they?

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.

slide14

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.

slide15

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.

slide16

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???

slide17

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.

slide18

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.

slide19

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.

slide20

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.

slide21

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.

slide22

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.

slide23

A

B

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.

slide24

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.

slide25

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.

curve grade tradeoff
Curve/grade tradeoff
  • a 3% grade causes a reduction in speed of 10 mph after 1400 feet
vertical alignment general
Vertical Alignment - General
  • Parabolic shape
  • VPI, VPC, VPT, +/- grade, L
  • 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.

vertical alignment general cont
Vertical Alignment – General (Cont.)
  • 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
vertical alignment general1
Vertical Alignment - General

Parabolic 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

vertical alignment general2
Vertical Alignment - General

Parabolic 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.

vertical curve aashto controls crest
Vertical Curve AASHTO Controls (Crest)
  • Based on stopping sight distance
  • Minimum length must provide sight distance S
  • 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/

slide33

Assistant with Target Rod (2ft object height)

Observer with Sighting Rod (3.5 ft)

vertical curve aashto controls crest1
Vertical Curve AASHTO Controls (Crest)

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.

Note: for passing site distance, use 2800 instead of 2158

slide35

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

slide36

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)|

slide37
Can also use

K = L / A

Where

K = length of curve per percent algebraic difference in intersecting grade

Charts from Green Book

vertical curve aashto controls crest2
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?

sag vertical curves
Sag Vertical Curves
  • Sight distance is governed by nighttime conditions
    • Distance of curve illuminated by headlights need to be considered
  • Driver comfort
  • Drainage
  • General appearance
vertical curve aashto controls sag
Vertical Curve AASHTO Controls (Sag)

Headlight Illumination sight distance with S < L

S < L

L = AS2

S > L

L = 2S – (400 + 3.5S)

A

Headlight 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)

vertical curve aashto controls sag1
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.

slide44

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

slide45

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

slide46

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

slide47

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

vertical curve aashto controls sag2
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
other important issues
Other important issues:
  • Use lighting if need to use shorter L than headlight requirements
  • Sight distance at under crossings
slide50

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

slide51

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

slide52

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

slide55

Note: L is measured from here to here

Not here

Source: Iowa DOT Design Manual