1. Vertical Alignment
See: (Chapter 5 from FHWA’s Flexibility in Highway Design)

2. 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:
Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed. P. 284

3. 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, th Ed.

4. 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, th Ed.

5. 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, th Ed.

6. 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, th Ed.

7. 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)

8. Coordination of Horizontal and Vertical Alignment
Source: FHWA, Chapter 5

9. 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

10. 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

11. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

12. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

13. 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, th Ed.

14. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

15. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

16. 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, th Ed.
Maybe we want this if we are trying to slow people down???

17. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

18. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

19. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

20. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th 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, th 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, th Ed.

23. 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, th Ed.

24. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

25. Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.

26. Vertical Alignment
Equations

27. Curve/grade tradeoff
a 3% grade causes a reduction in speed of 10 mph after 1400 feet

28. 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, th Ed.

29. 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

30. 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

31. 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, th Ed.

32. 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,

33. Assistant with Target Rod (2ft object height)
Observer with Sighting Rod (3.5 ft)

34. 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, th Ed.
Note: for passing site distance, use 2800 instead of 2158

35. 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 = ft
2158
S > L, so try other equation

36. |(-3 - 1)| 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’ = ’
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

38. From Green book

39. From Green book

40. 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?

41. 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

42. Vertical Curve AASHTO Controls (Sag)
Headlight Illumination sight distance with S < L
S < L
L = AS2
S > L
L = 2S – ( S) 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, th 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, th Ed.

44. 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 = feet S > L
Determine whether S<L or S>L
L = 2( ft) – ( x ) = ft
[3 – (-3)]
< , 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 = feet
L = x ( ft)2 = ft
x ft
< , 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 = feet
Testing for comfort:
L = AV2 = (6 x [40 mph]2) = feet

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 = feet
Testing for appearance:
L = 100A = (100 x 6) = 600 feet

48. 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

49. Other important issues:
Use lighting if need to use shorter L than headlight requirements
Sight distance at under crossings

50. Example: A crest vertical curve joins a +3% and –4% grade
Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = ft. Station at PVI is , elevation at PVI = 250 feet. Find elevations and station for PVC and PVT.
L/2 = ft
Station at PVC = [ ] - [ ] =
Distance to PVC: 0.03 x (2184/2) = feet
ElevationPVC = 250 – = feet
Station at PVT = [ ] + [ ] =
Distance (vertical) to PVT = 0.04 x (2184/2) = feet
Elevation PVT = 250 – = feet

51. Example: A crest vertical curve joins a +3% and –4% grade
Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = ft. Station at PVI is , elevation at PVI = 250 feet. Station at PVC is , Elevation at PVC: 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

52. Example: A crest vertical curve joins a +3% and –4% grade
Example: A crest vertical curve joins a +3% and –4% grade. Design speed is 75 mph. Length = ft. Station at PVI is , 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 (2814)
Elevation at tangent = (400 x 0.03) =
Elevation on curve = – 4.40 feet =

53. Source: Iowa DOT Design Manual

54. Source: Iowa DOT Design Manual

55. Note: L is measured from here to here
Not here
Source: Iowa DOT Design Manual