1 Chapter 3: Elements of Design Horizontal Alignment (p.3-18 – 3-58) Be able to derive the minimum radius of a curvature formula Be able to tell a typical range of side friction values Be able to explain the five methods of distributing e and f Be able to tell which method is used for urban low speed streets and for other higher speed roadways Be able to extract a radius of a curve for a superelevation for a roadway given a maximum superelevation value (using the tables in the GB) Objectives:

Theoretical Considerations The basic formula that governs vehicle operation on a curve is: ef 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)

3 Minimum Radius of a Circular Curve The centrifugal force: F c = Wa c g This normal portion of the centrifugal force was omitted from the derivation.

4 Minimum Radius of a Circular Curve (cont) The centrifugal force: F c = Wa c g  Superelevation

General Considerations (cont) Note that these are side friction values. They are different from longitudinal friction values. Fig. 3-4 Fig. 3-5

6 Side 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

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

8 Distribution of e and f over a range of curves: 5 methods (p. 3-27) Fig. 3-7 Table 3-6

Design Considerations (p.3-29) Normal cross slope: on tangents. 1.5 to 2.0% cross slope are used. Sharpest curve without superelevation: an important part of superelevation design policy is a criterion for the maximum radius for which superelevation is needed, or conversely, the minimum radius for which a normal roadway cross section is appropriate.

10 Design Considerations (cont) Max & Min superelevation rates: affected by four factors (1) climate conditions, (2) terrain conditions, (3) type of area like rural or urban, and (4) frequency of very slow- moving vehicles. –Max e for open highways  about 10%, or sometimes 12% –If you have snow and ice problems  8% or less to minimize slipping across a highway when stopped or attempting to slowly gain momentum from a stopped position –In urban areas, may use a low max rate of e  4 to 6% –Superelevation may be omitted on low speed urban streets subjected to severe constraints –Greenbook uses e = 4, 6, 8, 10, 12% to develop easy-to-read tables and figures to distribute e and f.

11 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)

12 Table 3-7. Min Radius Using Limiting Values of e and f In recognition of safety considerations, use of e max = 4.0% should be limited to urban conditions. Side friction factors: See Fig 3.6. From 0.38 for 10 mph to 0.15 for 45 mph. Based on the maximum allowable side friction factors from Fig 3-6, Tab 3- 7 gives the minimum radius for each of the five maximum superelevation rates.

13 Effects of Grades (on Superelevation) (p.3-33) The side friction demand is greater on both downgrades (due to braking forces) and steep upgrades (due to the tractive forces). Some adjustment in superelevation rates should be considered for grades steeper than 5%. In the case of a divided highway, assume a slightly higher design speed for the downgrade. For upgrades, use the original design speed, i.e., there is no need to reduce the design speed for the upgrade (because vehicles tend to slow down) On two-lane and multilane undivided roadways, the adjustment for grade can be made by assuming a slightly higher design speed for the downgrade and apply it to the whole traveled way (both directions) Read this section in the text carefully.

Design for Low-Speed Urban Streets (p.3-52) Superelevation: Although superelevation is advantageous for traffic operations, various factors often combine to make its use impractical in low-speed urban areas. –wide pavement areas, –the need to meet the grade of adjacent property, –surface drainage considerations, – the desire to maintain low-speed operations, and –frequency of cross streets, alleys and driveways Therefore, horizontal curves on low-speed urban streets are frequently designed without superelevation, sustaining the lateral force solely with side friction. (adverse or negative superelevation for traffic traveling along curves to the left). - Method 2 in Exhibit 3-13 (Fig. 3-7) is used.

15 Design for Low-Speed Urban Streets (cont) Sharpest curve without superelevation –The -2.0% (or -1.5%) row in Tab 3-13b provides the minimum curve radii for which a normal crown 2.0% (or 1.5%) should be retained. –Sharper curves than listed should have no adverse cross slope and should be superelevated in accordance with Tab 3-13b. –Superelevation without having a plane slope when a superelevation of between 1.5% and 2.5% is required? Read the top statement of the first paragraph of p –On a curve sharp enough to need a superelevation rate in excess of 2.5%, a plane slope across the whole traveled way should be used Table 3-13b

16 Design for Low-Speed Urban Streets (cont) Fig Graphic presentation of Tab 3-13b. Fig. 3-14

Design for Rural Highways, Urban Freeways, and High-Speed Urban Streets (p3-33) Side friction factors –From 0.4 at 10 mph to 0.08 at 80 mph from Fig 3-6. Superelevation –Use Method 5 to distribute e and f for all curves with radii greater than the minimum radius of curvature.

18 Procedure for Development of Method 5 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

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

20 Design Superelevation Tables (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

21 Graphical Presentation of the Calculation (Based on Method 5) 2.8 Fig. 3-9