11

Chapter 3: Elements of DesignChapter 3: Elements of DesignHorizontal Alignment (p.3-18 – 3-58)Horizontal Alignment (p.3-18 – 3-58)

Be able to derive the minimum radius of a curvature Be able to derive the minimum radius of a curvature formulaformulaBe able to tell a typical range of side friction valuesBe able to tell a typical range of side friction valuesBe able to explain the five methods of distributing e Be able to explain the five methods of distributing e and fand fBe able to tell which method is used for urban low Be able to tell which method is used for urban low speed streets and for other higher speed roadwaysspeed streets and for other higher speed roadwaysBe able to extract a radius of a curve for a Be able to extract a radius of a curve for a superelevation for a roadway given a maximum superelevation for a roadway given a maximum superelevation value (using the tables in the GB)superelevation value (using the tables in the GB)

Objectives:

22

3.3.1 Theoretical Considerations3.3.1 Theoretical Considerations

The basic formula that governs The basic formula that governs vehicle operation on a curve is:vehicle operation on a curve is:

1-0.01ef in equation 3-6 is so small 0.01ef is usually omitted as you see in equation 3-7. This reflects the centripetal force acting normal to the roadway surface. In the derivation in the next few pages this term was omitted because the effect of 0.01ef is very small.

(3-6)

(3-7)

33

Minimum Radius of a Circular CurveMinimum Radius of a Circular Curve

The centrifugal force: Fc =Wac

g

This normal portion of the centrifugal force was omitted from the derivation.

44

Minimum Radius of a Circular Curve (cont)Minimum Radius of a Circular Curve (cont)

The centrifugal force: Fc =Wac

g

Superelevation

55

3.3.2 General Considerations (cont)3.3.2 General Considerations (cont)

Note that these are side friction values. They are different from longitudinal friction values.

Fig. 3-4

Fig. 3-5

66

Side friction assumed for designSide friction assumed for design

Note that the longitudinal friction values for SSD:

f = a/g

where a is deceleration rate and g is gravity.

Fig. 3-6

77

Distribution of e and f over a range of Distribution of e and f over a range of curves: 5 methods (p.3-26) curves: 5 methods (p.3-26)

88

Distribution of e Distribution of e and f over a and f over a

range of curves: range of curves: 5 methods5 methods(p. 3-27)(p. 3-27)

Fig. 3-7

Table 3-6

99

3.3.3 Design Considerations (p.3-29)3.3.3 Design Considerations (p.3-29)

Normal cross slope: on tangents. 1.5 to Normal cross slope: on tangents. 1.5 to 2.0% cross slope are used.2.0% cross slope are used.Sharpest curve without superelevation: an Sharpest curve without superelevation: an important part of superelevation design important part of superelevation design policy is a criterion for the maximum radius policy is a criterion for the maximum radius for which superelevation is needed, or for which superelevation is needed, or conversely, the minimum radius for which conversely, the minimum radius for which a normal roadway cross section is a normal roadway cross section is appropriate.appropriate.

1010

Design Considerations (cont)Design Considerations (cont)

Max & Min superelevation rates: affected by four factors Max & Min superelevation rates: affected by four factors (1) climate conditions, (2) terrain conditions, (3) type of (1) climate conditions, (2) terrain conditions, (3) type of area like rural or urban, and (4) frequency of very slow-area like rural or urban, and (4) frequency of very slow-moving vehicles.moving vehicles.– Max e for open highways Max e for open highways about 10%, or sometimes 12% about 10%, or sometimes 12%– If you have snow and ice problems If you have snow and ice problems 8% or less to minimize 8% or less to minimize

slipping across a highway when stopped or attempting to slowly slipping across a highway when stopped or attempting to slowly gain momentum from a stopped positiongain momentum from a stopped position

– In urban areas, may use a low max rate of e In urban areas, may use a low max rate of e 4 to 6% 4 to 6%– Superelevation may be omitted on low speed urban streets Superelevation may be omitted on low speed urban streets

subjected to severe constraintssubjected to severe constraints– Greenbook uses e = 4, 6, 8, 10, 12% to develop easy-to-read Greenbook uses e = 4, 6, 8, 10, 12% to develop easy-to-read

tables and figures to distribute e and f.tables and figures to distribute e and f.

1111

Minimum Radius (p.3-31)Minimum Radius (p.3-31)

The minimum radius is a significant value in alignment design. It is also an important control value for determination of superelevation rates for flatter curves

For multi-lane highways, the radius used to design horizontal curves should be measured to the inside edge of the innermost travel lane, particularly for wide roadways with sharp horizontal curvature.

For two-lane roadways, the difference between the roadway centerline and the center of gravity used in the horizontal curve equations is minor. Therefore, the curve radius for a two-lane roadway may be measured to the centerline of the roadway.

(3-6)

1212

Table 3-7. Min Table 3-7. Min Radius Using Radius Using

Limiting Values Limiting Values of of ee and and f f

In recognition of safety considerations, use of emax = 4.0% should be limited to urban conditions.

Side friction factors: See Side friction factors: See Fig 3.6. From 0.38 for 10 Fig 3.6. From 0.38 for 10 mph to 0.15 for 45 mph. mph to 0.15 for 45 mph. Based on the maximum Based on the maximum allowable side friction allowable side friction factors from Fig 3-6, Tab 3-factors from Fig 3-6, Tab 3-7 gives the minimum radius 7 gives the minimum radius for each of the five for each of the five maximum superelevation maximum superelevation rates.rates.

1313

Effects of Grades (on Superelevation) Effects of Grades (on Superelevation) (p.3-33)(p.3-33)

The side friction demand is greater on both downgrades The side friction demand is greater on both downgrades (due to braking forces) and steep upgrades (due to the (due to braking forces) and steep upgrades (due to the tractive forces). Some adjustment in superelevation rates tractive forces). Some adjustment in superelevation rates should be considered for grades steeper than 5%.should be considered for grades steeper than 5%.In the case of a divided highway, assume a slightly In the case of a divided highway, assume a slightly higher design speed for the downgrade. For upgrades, higher design speed for the downgrade. For upgrades, use the original design speed, i.e., there is no need to use the original design speed, i.e., there is no need to reduce the design speed for the upgrade (because reduce the design speed for the upgrade (because vehicles tend to slow down)vehicles tend to slow down)On two-lane and multilane undivided roadways, the On two-lane and multilane undivided roadways, the adjustment for grade can be made by assuming a adjustment for grade can be made by assuming a slightly higher design speed for the downgrade and slightly higher design speed for the downgrade and apply it to the whole traveled way (both directions)apply it to the whole traveled way (both directions)

Read this section in the text carefully.

1414

3.3.6 Design for Low-Speed Urban 3.3.6 Design for Low-Speed Urban Streets (p.3-52)Streets (p.3-52)

SuperelevationSuperelevation: Although superelevation is advantageous : Although superelevation is advantageous for traffic operations, various factors often combine to for traffic operations, various factors often combine to make its use impractical in low-speed urban areas.make its use impractical in low-speed urban areas.– wide pavement areas,wide pavement areas,– the need to meet the grade of adjacent property,the need to meet the grade of adjacent property,– surface drainage considerations,surface drainage considerations,– the desire to maintain low-speed operations, andthe desire to maintain low-speed operations, and– frequency of cross streets, alleys and drivewaysfrequency of cross streets, alleys and driveways

Therefore, horizontal curves on low-speed urban streets are Therefore, horizontal curves on low-speed urban streets are frequently designed without superelevation, sustaining the lateral frequently designed without superelevation, sustaining the lateral force solely with side friction. (adverse or negative superelevation force solely with side friction. (adverse or negative superelevation for traffic traveling along curves to the left). - for traffic traveling along curves to the left). - Method 2Method 2 in Exhibit in Exhibit 3-13 (Fig. 3-7) is used.3-13 (Fig. 3-7) is used.

1515

Design for Low-Speed Urban Streets (cont)Design for Low-Speed Urban Streets (cont)Sharpest curve without Sharpest curve without superelevationsuperelevation– The -2.0% (or -1.5%) row in The -2.0% (or -1.5%) row in

Tab 3-13b provides the Tab 3-13b provides the minimum curve radii for which minimum curve radii for which a normal crown 2.0% (or 1.5%) a normal crown 2.0% (or 1.5%) should be retained.should be retained.

– Sharper curves than listed Sharper curves than listed should have no adverse cross should have no adverse cross slope and should be slope and should be superelevated in accordance superelevated in accordance with Tab 3-13b.with Tab 3-13b.

– Superelevation without having Superelevation without having a plane slope when a a plane slope when a superelevation of between superelevation of between 1.5% and 2.5% is required? 1.5% and 2.5% is required? Read the top statement of the Read the top statement of the first paragraph of p.3-57.first paragraph of p.3-57.

– On a curve sharp enough to On a curve sharp enough to need a superelevation rate in need a superelevation rate in excess of 2.5%, a plane slope excess of 2.5%, a plane slope across the whole traveled way across the whole traveled way should be usedshould be used

Table 3-13b

1616

Design for Low-Speed Urban Streets (cont)Design for Low-Speed Urban Streets (cont)

Fig 3-14. Graphic presentation of Tab 3-13b.Fig 3-14. Graphic presentation of Tab 3-13b.

Fig. 3-14

1717

3.3.4 Design for Rural Highways, Urban 3.3.4 Design for Rural Highways, Urban Freeways, and High-Speed Urban Streets Freeways, and High-Speed Urban Streets

(p3-33)(p3-33)

Side friction factorsSide friction factors– From 0.4 at 10 mph to 0.08 at 80 mph from From 0.4 at 10 mph to 0.08 at 80 mph from

Fig 3-6.Fig 3-6.

SuperelevationSuperelevation– Use Use Method 5Method 5 to distribute e and f for all to distribute e and f for all

curves with radii greater than the minimum curves with radii greater than the minimum radius of curvature.radius of curvature.

1818

Procedure for Development of Method 5 Procedure for Development of Method 5 Superelevation Distribution (p.3-34)Superelevation Distribution (p.3-34)

The f distribution curves for the various speeds are first determined. Subtracting these computed f values from the computed value of e/100 + f at the design speed, the finalized e distribution is thus obtained.

Fig. 3-8

1919

Procedure for Development of Method 5 Procedure for Development of Method 5 Superelevation Distribution, Example (p.3-42).Superelevation Distribution, Example (p.3-42).

2020

Design Superelevation Tables Design Superelevation Tables (p.3-44)(p.3-44)

Practice: Suppose Vd = 60 mph, and you can provide R = 4000 ft. What kind of e and f combination you would use to follow Method 5?

Table 3-8

2121

Graphical Presentation of the CalculationGraphical Presentation of the Calculation

(Based on Method 5)

2.8

Fig. 3-9