1. Chapter 3: Elements of Design 3. 3. 8 Transition Design Controls (p
Objectives:
Be able to discuss two considerations for the design of transition sections
Be able to determine the length of superelevation runoff
Be able to use relative gradient correctly to achieve full superelevation
Know how to determine the length of tangent runout
Know typical method to lay down superelevation runoff
Know when to select one of the four methods to attain superelevation
Please note we skip p.3-68 – 3-74 but with Civil 3D adding a spiral is very simple.

2. General considerations (p.3-59)
Two considerations for the design of transition sections:
Transitions in the roadway cross slope (superelevation transition)
Possible transition curves incorporated in the horizontal alignment (alignment transition)

3. 1. Superelevation Transition (p.3-59)
Superelevation transition = superelevation runoff + tangent runout
Superelevation runoff: Length of roadway needed to accomplish a change in outside-lane cross slope from zero (flat or adverse crown) to full superelevation, or vice versa.
Tangent runout: Length of roadway needed to accomplish a change in outside-lane cross slope from the normal cross slope rate to zero (adverse crown), or vice versa.

4. 2. Alignment Transition (tangent-to-curve or Tangent-Spiral-curve)
A spiral or compound transition curve may be used to introduce the main circular curve in a natural manner.
An alignment transition introduces the lateral acceleration associated with the curve in a gentle manner.
Transition is smooth but there is no definitive evidence that transition curves are essential to the safe operation of the roadway and, as a result, they are not used by many agencies.
Many use a tangent-to-curve transition. (A typical arrangement in the US. In Japan, for instance, most of the alignment transitions are designed with spiral curves.)
Tangent-to-curve
Tangent-to-spiral-to curve

5. Typical Alignment Transition (p.3-59)
In one widely used empirical expression, the runoff length is determined as a function of the slope of the outside edge of the traveled way relative to the centerline profile.  Called “relative gradient”
Table Maximum Relative Gradients
Table 3-15
Can you picture this concept?
Fig. 3-16

6. Tangent-to-Curve Transition (p.3-60)
Min. length of superelevation runoff: The relative gradient must not exceeds the values in Table  Range: .78% for 15 mph design speed to 0.35 for 80 mph design speed (see Table 3-15).
Use Eq to determine the length of superelevation runoff.
(3-23)

7. Adjustment for Multilane Highways, bw
To avoid excessive lengths for multi-lanes, minimum superelevation runoff lengths be adjusted downward, e.g. 4-lane highways. Do not multiply by 2, but use Table 3-16.
Table 3-16

8. 2. one side (2-lanes) of a multi-lane highway
Table 3-17b
Design speed affects the value of relative gradient (how so?). 1 & 2 in Table 3-17b are: 1. two-lane two-way rotated along the centerline
2. one side (2-lanes) of a multi-lane highway

9. Min. Length of Tangent Runout (p.3-66)
The length of tangent runout is determined by the amount of adverse cross slope to be removed and the rate at which it is removed.
To effect a smooth edge of pavement profile, the rate of removal should equal the relative gradient used to define the superelevation runoff length.
The tangent runout lengths for a 2.0% normal crown determined with Eq are listed in Table 3-17b in the 2.0% row. (Because eNC = ed, Lt = Lr for 2.0%)
(3-24)

10. Location with respect to end of curve: Alignment transition (p.3-66~)
Where do we place the superelevation runoff?
Observations indicate that a spiral path results from a driver’s natural steering behavior during curve entry or exit. This natural spiral usually begins on the tangent and ends beyond the beginning of the circular curve (PC).
Most agencies use 2/3 on the tangent and 1/3 on the curve. However, research showed larger values on the tangent are preferred. The values in Table 3-18 are desired.
But use of a single value in the range of 0.6 to 0.9 for all speeds and rotated widths is considered acceptable. The values in Table 3-18 are desirable where possible.
Table 3-18 PC
Fig. 3-16

11. Examples
Photos from the Public Roads website (FHWA)

12. Method of Attaining Superelevation (p.3-76)
Four methods
Revolving a traveled way with normal cross slopes about the centerline profile
Revolving a traveled way with normal cross slopes about the inside-edge profile
Revolving a traveled way with normal cross slopes about the outside-edge profile
Revolving a straight cross-slope traveled way about the outside-edge profile (turning roadways or one direction of a divided highway)
No general recommendation for the adoption of any particular axis of rotation can be made. To obtain the most pleasing and functional results, each superelevation transition section should be considered individually.

13. Method A (p.3-77)
Fig. 3-16
Most popular. One-half of the change in elevation is made at each edge. Less distortion at the edges.

14. Method B
Fig. 3-16
One-half of the change in elevation is made by raising the actual centerline profile with respect to the inside-edge profile and the other half by raising the outside-edge profile an equal amount with respect to the actual centerline profile.

15. Method C
Fig. 3-16
This method is similar to Method B except that the elevation change is accomplished below the outside-edge profile instead of above the inside-edge profile.

16. Method D
Fig. 3-16
This method is often used for two-lane one-way roadways where the axis of rotation coincides with the edge of the traveled way adjacent to the highway median.

17. Sample problem Given: Design speed: 70 mph Superelevation: 6%
2-lane 2-way highway
Lane width = 12 ft
Cross slope = 1.5%
From Table 3-17b the length of superelevation runoff is 180 ft. Now what is the length of tangent runout and the station of beginning and ending of superelevation runoff and tangent runout when the station of PC is STA ?
Rise at the outer edge is: 12ft x 0.06 = 0.72ft
Relative gradient is: 0.72ft / 180ft = 0.004=0.4%
Tangent runout is: (12ft x 0.015)/0.004 = 45 ft
or Lt = 0.015/0.06 x 180 = 45 ft)
45ft
180ft
45ft
PC: STA
About 30% of superelevation runoff is in the curve (see Slide #10) = 180*0.3 = About 54 ft in the curve.
About 70% is in the tangent = 126 ft.
STA 98+79
STA 99+69
(See Slide #10 or Tab 3-18 for percent splits.)
STA 101+4
STA 99+24

18. Axis of Rotation (p.3-80) Case I
In the design of divided highways, streets, and parkways, the inclusion of a median in the cross section influences the superelevation transition design. The most appropriate location for this axis depends on the width of the median and its cross section.
Case I
The whole of the traveled way, including the median, is superelevated
Limited to narrow medians up to 15 ft or less.
The length of runoff should be based on the total rotated width (including the median).
However, because narrow medians have very little effect on the runoff length, median widths of up to 10 ft may be ignored when determining the runoff length. (A)

19. Axis of Rotation (cont)
Case II
The median is held in a horizontal plane and the two traveled ways are rotated separately around the median edges.
Most appropriate for medians with widths between 15 to 60 ft.
Superelevation can be attained using any of the methods B, C, or D, with profile reference being the same for both traveled ways.
Case III
The two traveled ways are separately treated for runoff with a resultant variable difference in elevation at the median edges.
Can be used with wide medians 60 ft or more
With a wide median, it is possible to design the profiles and superelevation transition separately for the two roadways.
Accordingly, superelevation can be attained by the method otherwise considered appropriate (A, B, C, or D).