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Section 5: Vertical Alignment

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Overview

The two basic elements of vertical alignment are Grades and Vertical Curves.

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Grades

The effects of rate and length of grade are more pronounced on the operating characteristics of trucks than on passenger cars and thus may introduce undesirable speed differentials between the vehicle types. The term “critical length of grade” is used to indicate the maximum length of a specified ascending gradient upon which a loaded truck can operate without an unreasonable reduction in speed (commonly 10 mph [15 km/h]). Figure 2-3 shows the relationship of percent upgrade, length of grade, and truck speed reduction. Where critical length of grade is exceeded for two-lane highways, climbing lanes should be considered as discussed in the Transportation Research Board’s Highway Capacity Manual.

Critical Lengths of Grade for Design. Click here to
see a PDF of the image. (click in image to see full-size image) Anchor: #i1034284grtop

Figure 2-3. Critical Lengths of Grade for Design. Click here to see a PDF of the image.

NOTE: Online users can view the metric version of this figure in PDF format.

Table 2-11 summarizes the maximum grade controls in terms of design speed. Generally, maximum design grade should be used infrequently rather than as a value to be used in most cases. However, for certain cases such as urban freeways, a maximum value may be applied in blanket fashion on interchange and grade separated approaches.

Anchor: #i1589012Table 2-11: Maximum Grades

 

Functional Classification

Type of Terrain

15

20

25

30

35

40

45

50

55

60

65

70

75

80

Urban and Suburban:

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Local1

All

<15

<15

<15

<15

<15

<15

<15

--

--

--

--

--

--

--

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Collector

Level

9

9

9

9

9

9

8

7

7

6

--

--

--

--

-

Rolling

12

12

12

11

10

10

9

8

8

7

--

--

--

--

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Arterial

Level

--

--

--

8

7

7

6

6

5

5

--

--

--

--

-

Rolling

--

--

--

9

8

8

7

7

6

6

--

--

--

--

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Freeway

Level

--

--

--

--

--

--

--

4

4

3

3

3

3

3

-

Rolling

--

--

--

--

--

--

--

5

5

4

4

4

4

4

Rural:

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Local

Level

9

8

7

7

7

7

7

6

6

5

--

--

--

--

-

Rolling

12

11

11

10

10

10

9

8

7

6

--

--

--

--

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Collector

Level

-

7

7

7

7

7

7

6

6

5

--

--

--

--

-

Rolling

-

10

10

9

9

8

8

7

7

6

--

--

--

--

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Arterial

Level

--

--

--

--

--

5

5

4

4

3

3

3

3

3

-

Rolling

--

--

--

--

--

6

6

5

5

4

4

4

4

4

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Freeway

Level

--

--

--

--

--

--

--

4

4

3

3

3

3

3

-

Rolling

--

--

--

--

--

--

--

5

5

4

4

4

4

4

1 8% maximum in commercial areas on local streets, desirably less than 5%. Flatter gradients should be used where practical.



Flat or level grades on uncurbed pavements are satisfactory when the pavement is adequately crowned to drain the surface water laterally. When side ditches are required, the grade should seldom be less than 0.5 percent for unpaved ditches and 0.25 percent for lined channels. With curbed pavements, desirable minimum grades of 0.35 percent should be provided to facilitate surface drainage. Joint analyses of rainfall frequency and duration, the longitudinal grade, cross slope, curb inlet type and spacing of inlets or discharge points usually is required so that the width of water on the pavement surface during likely storms does not unduly interfere with traffic. Criteria for water ponding for various functionally classified roadways are contained in the Hydraulic Design Manual.

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Vertical Curves

Vertical curves provide gradual changes between tangents of different grades. The simple parabola shown in Figure 2-4 is used in the highway profile design of vertical curves.

 Vertical Curve. Click here to
see a PDF of the image. (click in image to see full-size image) Anchor: #i1044241grtop

Figure 2-4. Vertical Curve. Click here to see a PDF of the image.

NOTE: Online users can view the metric version of this figure in PDF format.

For vertical curve discussion purposes, the following parameters are defined:

L = length of vertical curve;

S = sight distance for crest vertical curves or headlight beam distance for sag vertical curves;

A = algebraic difference in grades, percent;

K = length of vertical curve per percent change in A (also known as the design control)

Crest Vertical Curves. The minimum lengths of crest vertical curves for different values of A to provide the stopping sight distances for each design speed are shown in Figure 2-5. The solid lines give the minimum vertical curve lengths on the basis of rounded values of K. These lengths represent minimum values based on design speed and longer curves are desired wherever practical.

A dashed curve crossing the solid lines indicates where S = L. Note that to the right of the S = L line, the value of K is a simple and convenient expression of the design control. For each design speed this single value is a positive number that is indicative of the rate of vertical curvature. The design control in terms of K covers all combinations of A and L for any one design speed; thus A and L need not be indicated separately in a tabulation of the design values. The selection of design curves is facilitated because the length of curve is equal to K times the algebraic difference in grades in percent, L = KA. Conversely, the checking of curve design is simplified by comparing all curves with the design value for K.

Where S is greater than L, the values plot as a curve (as shown by the dashed curve extension for 45 mph [70 km/h]. Also, for small values of A, the vertical curve lengths are zero because the sight line passes over the apex. Since this relationship does not represent desirable design practice except in limited conditions (see discussion on Grade Change Without Vertical Curves), a minimum length of vertical curve is shown. Attention should be given where there are successive vertical curves.

These minimum length of vertical curves (both crest and sag) are expressed as approximately three times the design speed in miles per hour (Lmin = 3 V) or 0.6 times the design speed in kilometers per hour (Lmin = 0.6 V). However, these minimum lengths are not considered a design control (i.e., a design exception would not be required for these minimum length values as long as the minimum K value for the relevant design speed is met).

There is a level point on a vertical curve which can affect drainage; particularly on curbed facilities. Typically, there is no difficulty with drainage on highways if the curve is sharp enough so that a minimum grade of 0.30 percent is reached at a point about 50 ft [15 m] from the crest or sag. This corresponds to a K value of 167 ft [51 m] per percent change in grade which is plotted in Figures 2-5 and 2-6 as the drainage threshold. All combinations above or to the left of this line satisfy the drainage criterion. The combinations below and to the right of this line involve flatter vertical curves. Special attention is needed in these cases to ensure proper pavement drainage. It is not intended that these values be considered a design maximum, but merely a value beyond which drainage should be more carefully designed.

Sag Vertical Curves. At least four different criteria for establishing the lengths of sag vertical curves are recognized to some extent. These are (1) headlight sight distance, (2) passenger comfort, (3) drainage control, and (4) general appearance.

Generally, a sag vertical curve should be long enough that the light beam distance is nearly the same as the stopping sight distance. Accordingly, it is appropriate to use stopping sight distances for different design speeds to establish sag vertical curve lengths. The resulting sag vertical curves for the recommended stopping sight distances for each design speed are shown in Figure 2-6 with the solid lines representing the rounded K values. As with crest vertical curves, these lengths are minimum values based on design speed and longer curves are desired wherever practical. For sag vertical curves, drainage criteria and minimum curve lengths are established similarly to crest vertical curves.

(US). Design Controls for Crest Vertical
Curves. Click here to see a PDF of
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Figure 2-5. (US). Design Controls for Crest Vertical Curves. Click here to see a PDF of the image.

NOTE: Online users can view the metric version of this figure in PDF format.

(US). Design Controls for Sag Vertical
Curves. Click here to see a PDF of
the image. (click in image to see full-size image) Anchor: #i1044247grtop

Figure 2-6. (US). Design Controls for Sag Vertical Curves. Click here to see a PDF of the image.

NOTE: Online users can view the metric version of this figure in PDF format.

Because cost and energy conservation considerations are factors in operating continuous lighting systems, headlight sight distance should be generally used in the design of sag vertical curves. Comfort control criteria is about 50 percent of the sag vertical curve lengths required by headlight distance and should be reserved for special use. Instances where the comfort control criteria may be appropriately used include ramp profiles where safety lighting is provided and for economical reasons in cases where an existing element, such as a structure not ready for replacement, controls the vertical profile. Comfort control criteria should be used sparingly on continuously lighted facilities since local, outside agencies often maintain and operate these systems and operations could be curtailed in the event of energy shortages.

Care should be exercised in sag vertical curve design to insure that overhead sight obstructions such as structures for overpassing roadways, overhead sign bridges, tree crowns, etc., do not reduce stopping sight distance below the appropriate minimum value.

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Grade Change Without Vertical Curves

Designing a sag or crest vertical point of intersection without a vertical curve is generally acceptable where the grade difference (A) is:

  • 1.0 percent or less for design speeds equal to or less than 45 mph [70 km/h]
  • 0.5 percent or less for design speeds greater than 45 mph [70 km/h].

    When a grade change without vertical curve is specified, the construction process typically results in a short vertical curve being built (i.e., the actual point of intersection is “smoothed” in the field). Conditions where grade changes without vertical curves are not recommended include:

  • Bridges (including bridge ends)
  • Direct-traffic culverts
  • Other locations requiring carefully detailed grades.
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Combination of Vertical and Horizontal Alignment

Due to the near permanent nature of roadway alignment once constructed, it is important that the proper alignment be selected consistent with design speed, existing and future roadside development, subsurface conditions, topography, etc. The following factors are general considerations in obtaining a proper combination of horizontal and vertical alignment:

  • The design speed of both vertical and horizontal alignment should be compatible with longer vertical curves and flatter horizontal curves than dictated by minimum values. Design speed should be compatible with topography with the roadway fitting the terrain where feasible.
  • Alignment should be as flat as possible near intersections where sight distance is important.
  • For rural divided facilities, independent mainlane profiles are often more aesthetic and economical. Where used on non-controlled access facilities with narrow medians, care should be exercised in the location of median openings to minimize crossover grades and insure adequate sight distance for vehicles stopped therein.
  • When designing independent vertical and horizontal profiles on divided facilities, considerations should be given to the impact these profiles may have on future widening into the median.
  • For two-lane rural highways and Super 2 Highways the need for safe passing sections at frequent intervals should be carefully considered in developing horizontal and vertical alignments.
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