1. Elements of Design
This chapter discusses the elements common to all classes of highways and streets including
Sight Distance
Superelevation
Traveled Way Widening
Grades
Horizontal and Vertical Alignments

2. Sight Distance
A driver’s ability to see ahead is of the utmost importance in the safe and efficient operation of a vehicle on a highway.
Four aspects of sight distance are sight distances needed for stopping (all highways), passing sight distances (2-lane highways), decision sight distances (complex locations), and criteria for measuring these sight distances for use in design.
Stopping Sight Distance: 1) the distance traversed by the vehicle from the instant the driver sights an object necessitating a stop to the instant the brakes are applied and 2) the distance needed to stop the vehicle from the instant brake application begins.
The height of the driver’s eye is 1080 mm (3.5 ft) and the height of the object to be seen by the driver is 600 mm (2.0 ft).

3. More on Stopping Sight Distance

4. More on Stopping Sight Distance
SSD = 0.278Vt V2/a Grade zero
SSD = 0.278Vt + V2/ (254 (a/9.81)±G) Grade is G
Case 3
a = 3.4m/s2
-3.5%
+4%
One-Way
G = 3.5%
+2%
-3.5%
One or
Two-way
Flat
One-way or
Two way
G = 0.02 or
G = 0.035
G= 0
-3.5%
+4%
Two-Way
G = 4%
Case 2
Case 1
Case 4

5. Decision Sight Distance
Decision Sight Distance The distance needed for a driver to detect an expected or otherwise difficult-to-perceive information source or condition in a roadway environment that may be visually cluttered, recognize the condition or its potential threat, select an appropriate speed and path, and initiate and complete the maneuver safely and efficiently.
Placement Critical Locations such as land drops and tool plazas, where driver errors may be experienced in digesting complicated traffic information. The locations

6. More on Decision Sight Distance

7. More on Decision Sight Distance
DSD = 0.278Vt V2/a Avoidance Maneuvers A and B
Where a = 3.4 m/s2
DSD = Vt Avoidance Maneuvers C, D, and E
Two Examples

8. Passing Sight Distance for Two-Lane Highways

9. More on Passing Sight Distance
Assumptions:
The overtaken vehicle travels at uniform speed
The passing vehicle has reduced speed and trails the overtaken vehicle as it enters a passing section
When the passing section is reached, the passing driver needs a short period of time to perceive the clear passing section and to react to start his/her maneuver.
The passing vehicle accelerates during the maneuver and its average speed during the occupation of the left lane is 15 km/h higher than that of the overtaken vehicle.
When the passing vehicle returns to its lane, there is a suitable clearance length between it and an oncoming vehicle in the other lane

10. More on Passing Sight Distance
Exhibit 3-5 on Page 120 shows the elements of Safe Passing Sight Distance for Design of Two-Lane Two-Way Highways
d1 = 0.278ti(v-m+ati/2)
a – 2.25 – 2.41 km/h/s, m – 15 km/h
v and t see Exhibit 3-5.
d2 = 0.278Vt2
t2 see Exhibit 3-5.
d3 = see Exhibit 3-5
d4 = 2d2/3

11. More on Passing Sight Distance
Exhibit 3-6 on Page 124 shows the design value of Passing Sight Distance for Design of Two-Lane Two-Way Highways
Insert the Table here

12. More on Passing Sight Distance
Effect of Grade on Passing Sight Distance
Downgrade Passed and Passing Vehicles easy to speed up
Opposite vehicle slow down
Upgrade Passed and passing vehicles slow down
Opposite vehicle speed up.
Frequency and Length of Passing Sections
f(topography, design speed, cost and/or intersection spacing)
% time spent following and Average travel speed

13. Measuring Sight Distance
Designers should check if the available sight distance is greater than the minimum sight distance. The available sight distance is dependent on the height of the driver’s eye above the road surface, the specified object height above the road surface, and the height and lateral position of the sight obstructions within the driver’s line of sight.
Height of Driver’s Eye 1080 mm (3.5 ft) for passenger cars
2330 mm (7.6 ft) for trucks
Height of Object 600 mm (2.0 ft) for SSD
1080 mm (3.5 ft) for PSD
Sight Obstructions Crest vertical curves for tangent roadways
Physical features outside the traveled way

14. Procedures for Measuring Sight Distance
Exhibit 3-8 shows the methods for scaling sight distance on plans
Check on Horizontal Alignments
Step One At each station, identify potential obstructions outside the traveled way downward and upward (in two directions) and estimate available sight distance between the station and the ending point of the line of sight that is controlled by every obstruction.
Step Two Compare the available sight distance to the minimum sight distance
Question How to use computer (with a digital straightedge) to check the Sight Distance Requirements

15. Procedures for Measuring Sight Distance
Check on Vertical Alignments
Step One Each each vertical curve,
1) find the highest or lowest point
2) draw a tangent line from the point downward and upward
3) find the point where the offset of the tangent from the vertical curve is 1080 mm and get the station of the point
4) find the point where the offset of the tangent from the vertical curve is 600 mm and get the station of the point
5) Calculate the difference between the stations. The difference will be the available sight distance
Step Two Compare the available sight distance to the minimum sight distance
Question How to use computer (with a digital transparent strip) to check the Sight Distance Requirements

16. Horizontal Alignment Curve Design Controls
The design of roadway curves should be based on an appropriate relationship between design speed and curvature and on their joint relationships with superelevation and side friction.
Centripetal or lateral acceleration is balanced by side friction and superelevation in geometric design.
Lateral Acceleration = side friction + superelevation or
0.01e + f = V2/127R
Side friction varies from 0 to fmax depending on the speed of the vehicle
Superelevation rate or cross slope has its limit or emax that is controlled by
emax = f (weather, adjacent land use, frequency of slow- moving vehicles, construct ability)

17. Horizontal Alignment
A design agency normally sets up emax based on facility type. Caltrans has set up emax in its highway design manual.
With the emax is defined and pre-selected, designers can choose superelevation rate e which is less than emax. The sum of e and side friction (f) balances the lateral acceleration.
f = f(V, surface, and tire) Wet surface is the worse case
Several rates, rather than a single rate, of maximum superelevation should be recognized in establishing design controls for highway curves. A rate of 12% should not be exceeded. A rate of 4-6% is applicable for urban design. Superelevation may be omitted on low-speed urban streets.

18. Horizontal Alignment
Ball-bank indicator is a testing tool for determining comfortable f for drivers. The comfortable f is 0.21 for km/h
Electronic accelerometer is another testing tool used in determining advisory speeds for horizontal curves and ramps.
Testing results are shown in Exhibits 3-10 and 3-11.
Horizontal curves should not be designed directly on the basis of the maximum available side friction factor. Rather, the maximum side friction factor used in design should be that portion of the maximum available side friction that can be used with comfort and safety by vast majority of drivers.

19. Horizontal Alignment
Distribution of Superelevation (e) and side friction (f)
There are five methods for the distribution of e and f (see Exhibit 3-12)
Application
M 1 e and f to 1/R Highways with uniform speed flow
such as rural highways
M2 fmax first & e make up Urban streets with speeds not uniform
M3 emax first & f make up Negative friction for curves with flat radii
M4 emax first & f make up A solution to M3 but still with negative on average speed frictions problem
M5 curvilinear relation to A practical distribution for e over the range of 1/R curvature.

20. Horizontal Alignment Design Considerations
Design considerations in horizontal alignment involves the determination of maximum superelevation rates, minimum radius, and others
The minimum radius is the limiting value of curvature for a given design speed and is determined from the maximum rate of superelevation and the maximum side friction factor selected for design
Rmin = V2/(127(0.01emax+fmax)

21. Horizontal Alignment
F value for these facilities is shown in Exhibit The minimum radius for each of the five maximum superelevation rates (4%, 6%, 8%, 10%, 12%) is shown in Exhibit 3-14 for design of Rural Highways, Urban Freeways, and High-Speed Urban Streets.
Method 5 is recommended for use for these facilities. Method 5 assumes the f curve is shown in Exhibit 3-13 (dark solid line). The e value is the difference of the lateral acceleration rate and the f value for a certain speed.
Exhibits 3-16 to 3-25 show the tables and curves derived from the Method 5 procedure.
Very flat horizontal curves need no superelevation. Traffic entering a curve to the right has some superelevation provided by the normal cross slope. Traffic entering a flat curve to the left uses friction to sustain the lateral acceleration and counteract the negative superelevation due to the normal cross slope.

22. Horizontal Alignment
SE adjustment
SE needed
No SE needed R R’

23. Horizontal Alignment Transition Design Controls
Transition from a tangent to a curve or from a curve to a tangent has two parts: superelevation transition (transition in the roadway cross slope) and alignment transition (transition curves incorporated in the horizontal alignments)
Superelevation transition involves superelevation runoff and tangent run out.
Alignment transition is made of a spiral or compound transition curve. When no spiral curve is used, the transition is called “tangent-to-curve” transition.

24. Horizontal Alignment Tangent-to-curve transition New Policy
Superelevation Runoff
New Policy e%
Tangent
Run out 1’
125’ 2
Old Policy: Superelevation Runoff Length is at least the distance
traveled in 2.0 s at the design speed

25. Horizontal Alignment Tangent-to-curve transition Lr = (wn1)edbw/
Example 1: Assume a circular curve is designed on a two-lane two-way
undivided highway with design speed of 40 km/h.
The design e is 6%. Lr =?
Example 2: Assume a circular curve is design on a four-lane undivided
highway with design speed of 100km/h. The design e is 10%.
Lr = ?

26. Horizontal Alignment Minimum Length of Tangent Runout Lt = encLr/ed
Example 1: Assume a circular curve is designed on a two-lane two-way
undivided highway with design speed of 40 km/h.
The design e is 6%. Lt =?
Example 2: Assume a circular curve is design on a four-lane undivided
highway with design speed of 100km/h. The design e is 10%.
Lt = ?

27. Horizontal Alignment Distribution of Runoff on Tangent and Curve Lr
0% 100%
100% 0%
67% 33%
Lr Distribution
Design Portion of runoff located prior
Speed to the curve
No. of lanes rotated
20-70 km/h

28. Horizontal Alignment Spiral Curve Transitions
The Euler spiral, also known as the clothoid, is used in the design of spiral transition curves.
The radius varies from infinity at the tangent end of the spiral to the radius of the circular arc at the end that adjoins that circular arc.
L = V3/RC
Rmax see Exhibit 3-33 on Page 179
Given R, the minimum length of spiral is as follow
Lmin,s = (24PminR)0.5 where Pmin = 0.2
Lmin,s = V3/RC where C = 1.2 m/s3

29. Horizontal Alignment Spiral Curve Transitions
Given R, the maximum length of spiral is as follow
Lmin,s = (24PmaxR)0.5 where Pmax = 1.0
The desirable length of spiral is as follows:
The distance traveled in 2 s at the design speed of the roadway. Exhibit 3-34 on Page 181 shows the list of the desirable length at different design speed.
Length of superelevation runoff is the minimum length of spiral.
Length of Tangent Run Out:
Lt = encLr/ed

30. Horizontal Alignment Methods of Attaining Superelevation
Four methods are used to transition the pavement to a superelevated cross section.
Method 1 Revolve a traveled way about centerline
Method 2 Revolve a traveled way about the inside-edge profile
Method 3 Revolve a traveled way about the outside-edge profile
Method 4 Revolve a straight cross slope traveled way about the
outside-edge profile
Exhibit 3-37 shows these four methods on Page 185.

31. Horizontal Alignment Axis of Rotation with a Median
The inclusion of a median in the cross section influences the superelevation transition design of divided highways, streets and parkways
Case I The whole of the traveled way including the median is superelevated as a plane section
Medians: < 4m and e: moderate
Case II The median is held in a horizontal plane and the two traveled ways are rotated separately around the median edges. Median: m.
Case III The two traveled ways are treated separately for runoff with a resulting variable difference in elevations at the median edges. Median > 18 m

32. Horizontal Alignment Minimum Transition Grades
Criteria 1 Maintain minimum profile grade of 0.5 % through the transition section
Criteria 2 maintain minimum edge of pavement grade of % (0.5% for curbed streets) through the transition section
Example: An uncurbed transition section with  = 0.65%
Criteria 1 any grade but -0.5% - 0.5%
Criteria 2 any grade but –0.85% %
and 0.45% – 0.85%

33. Horizontal Alignment Turning Roadway Design
Turning Roadways consist of interchange ramps, roadways, or intersection curves for right turning vehicles. Turning roadway design does not apply to minimum edge-of-traveled-way design for turns at intersections
Turning roadways with V  70 km/h, compound curves OK
V > 70 km/h, compound curves not OK
When compound curves are considered,
2: 1 for the radius of the Intersections
large curve and smaller curve
1.75 : 1 Interchanges
The minimum arc length for the curve is given in Exhibit 3-38 on Page 192.

34. Horizontal Alignment Design for Low-Speed Urban Streets
Method 2 is often used for the design of horizontal curves on low-speed urban streets.
Exhibit 3-39 on Page 193 shows the design values of f that are applicable to low-speed urban streets (solid line)
Superelevation is impractical in many built-up areas. Very often superelevation is not considered in urban streets design
When superelevation is considered, Exhibit 3-41 should be used in selecting e given the minimum R or r given a pre-selected e.

35. Horizontal Alignment Design for Low-Speed Urban Streets
Maximum Comfortable Speed on Horizontal Curves is derived from the following formula (see Exhibit 3-40):
0.01 e + f max = V2/127R
Minimum Superelevation Runoff Length (when e is used in design)
L = 2.72fVd/C

36. Horizontal Alignment
Curvature of Turning Roadways and Curvature at Intersections
Minimum radius for turning speeds is controlled by the turning speed of the vehicle, normally 15 km/h.
Exhibit 3-43 shows the minimum radius given design speed for intersection curves.
Transitions and Compound Curves are often considered in design of turning roadways and urban streets.
When spirals are used for a transition section, the minimum length of the spiral is given in Exhibit 3-45 on Page 204.
Compound circular curves keep the radius ratio to be 1.5 : 1.

37. Horizontal Alignment Offtracking
Offtracking is the characteristics, common to all vehicles, although much more related to the large design vehicles, in which the rear wheels do not follow precisely the same path as the front wheels when the vehicle takes a horizontal curve or makes a turn.
W = Wc – Wn
Wc = N(U+C) + (N-1)Fa +Z
U = u+R – (R2-li2)0.5
Fa = R2+A(2L+A)0.5 –R
Z = 0.1(V/R0.5)
Example on Page 215.

38. Horizontal Alignment Sight Distance on Horizontal Curves
Stopping Sight Distance
Relationships among, R, M, and S is shown in Exhibit 3-58
The sight line is the line whose two ends have 1080 mm eye height and 600 mm object height and whose midpoint is 840 mm high.
Passing Sight Distance
The sigh line has its two ends with an eye height of mm, an object height of 1080 mm and a midpoint of mm.

39. Horizontal Alignment General Controls for Horizontal Alignment
Alignment should be as directional as practical but should be consistent with the topography and with preserving developed properties and community values
Rmin should be avoided for a given design speed. Use R > Rmin
Consistent alignment should be sought. Sharp curves should not be introduced at the ends of long tangent.
For small deflection angles, curves should be sufficiently long to avoid the appearance of a kink.
Sharp curvature should be avoided on long hill fills.
Compound curves should be cautiously considered.