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## Vertical Alignment

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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 • 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 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 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 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 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.**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)**Coordination of Horizontal and Vertical Alignment**Source: FHWA, Chapter 5**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**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**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.**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? 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.**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.**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.**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???**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.**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.**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.**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.**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.**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 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.**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.**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**Equations**Curve/grade tradeoff**• a 3% grade causes a reduction in speed of 10 mph after 1400 feet**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.)**• 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 - 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 - 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)**• 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/**Assistant with Target Rod (2ft object height)**Observer with Sighting Rod (3.5 ft)**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**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**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)|**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 (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**• 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)**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 (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.**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**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**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**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 (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:**• Use lighting if need to use shorter L than headlight requirements • Sight distance at under crossings**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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