1. Horizontal and vertical alignment
Introduction
Roadways must respect the existing and developed environment through which they pass while balancing the needs for safety and cost effectiveness.
Therefore, roadways are not always flat and straight – they possess vertical and horizontal curves in their alignments to circumvent or be compatible with existing constraints.
Alignment constraints typically include topographical variation, natural resource areas, property ownership, land use, cost, and environment.
Introduction of curvilinear alignments is necessary when the designer encounters these constraints

2. HORIZONTAL ALIGNMENT
Horizontal alignment is an important feature in road design which enhances smooth driving, comfort and safety for motorists.
Inappropriate alignment may:
Cause accidents – motorists are not able to maneuver their vehicles properly, or are not aware of the need to change speed
Reduce capacity – motorists will travel at low speeds, hence reducing capacity

3. Factor should be considered in designing effective and efficient road geometry
Horizontal curve
Compatibility between existing and proposed condition
Topographic/terrain variations
Vehicle characteristics
Driver limitations
Design speed
Lines of sight
Roadway cross section
Radius of curve
Tangent-to-curve transition
Profile
Drainage considerations
Cost
Vertical curves
Compatibility with existing grades and elevations on adjacent land and approaching roads and driveways/entrances adjacent to the new alignment
Design speed
Sight distance
Vertical clearances
Length of grade
Entrance considerations associated with acceleration and deceleration
Horizontal alignment
Drainage considerations
Cost

4. Horizontal alignment is applied when direction change involving two straight roads (road tangents) is required.
Road tangent 2
Horizontal Curve
Road tangent 1
Note:
The changes in direction along a highway are basically accounted for by curves consisting of portions of a circle.
Its principal characteristic is measured by the RADIUS or by a related quality referred to as the DEGREE of curve.

5. Types of Horizontal Curvature
Simple curves
Has constant circular
The most frequently used because of their simplicity for design, layout and construction

6. Types of Horizontal Curvature
Reverse Curves
consists of two simple curves joined together, but curving in opposite directions.
For safety reasons, the use of this curve should be avoided when possible. As with broken back curves, drivers do not expect to encounter this arrangement on typical highway geometry

7. Types of Horizontal Curvature
Compound Curves
a series of two or more simple curves with deflections in the same direction immediately adjacent to each other.
Compound curves are used to transition into and from a simple curve and to avoid some control or obstacle which cannot be relocated

8. Types of Horizontal Curvature
Broken-back curves
Two curves joined by short straight
Not desirable
Short straight should be a maximum of 0.6V where
V in km/hr ie about two seconds of travel – enable maintenance of super elevation
Normally try to keep straight longer – 4V

9. ELEMENTS OF HORIZONTAL CURVES
CIRCULAR CURVE
Each point will be identified by xyz coordinates.
(Sta._____ and Sta.______.)
May also referred as Chainage .

10. ELEMENTS OF HORIZONTAL CURVES
Description Δ
DELTA (Central Angle). The value of the central angle is equal to the I angle R
RADIUS. The radius of the circle of which the curve is an arc, or segment. The radius is always perpendicular to back and forward tangents. PI
POINT OF INTERSECTION. The point of intersection is the theoretical location where the two tangents meet. PT
POINT OF TANGENCY. The point of tangency is the point on the forward tangent where the curve ends. It is sometimes designated as EC (end of curve) or CT (curve to tangent). PC
POINT OF CURVATURE. The point of curvature is the point on the back tangent where the circular curve begins. It is sometimes designated as BC (beginning of curve) or TC (tangent to curve) L
LENGTH OF CURVE. The length of curve is the distance from the PC to the PT, measured along the curve. T
TANGENT. The length of tangent is the distance along the tangents from the PI to the PC or the PT. These distances are equal on a simple curve. C
LONG CHORD. The long chord is the straight-line distance from the PC to the PT. Other types of chords are designated as follows: E
EXTERNAL DISTANCE. The external distance (also called the external secant) is the distance from the PI to the midpoint of the curve. The external distance bisects the interior angle at the PI. January M
MIDDLE ORDINATE. The middle ordinate is the distance from the midpoint of the curve to the midpoint of the long chord. The extension of the middle ordinate bisects the central angle.

11. DEGREE OF CURVATURE - refresh
Curvature may be expressed by simply stating the length of the radius of the curve
For highway and railway work, however, curvature is expressed by the degree of curve
Two definitions are used for the degree of curve.
Degree of Curve (Arc Definition)
Degree of Curve (Chord Definition)

12. Degree of Curve (Arc Definition)
REFRESH…
States that the degree of curve is the central angle formed by two radii that extend from the center of a circle to the ends of an arc measuring 100 feet long (or 100 meters long if you are using metric units).
Therefore, if you take a sharp curve, mark off a portion so that the distance along the arc is exactly 100 feet, and determine that the central angle is 12°, then you have a curve for which the degree of curvature is 12°; it is referred to as a 12° curve

13. Degree of Curve (Chord Definition)
REFRESH…
This definition states that the degree of curve is the central angle formed by two radii drawn from the center of the circle to the ends of a chord 100 feet (or 100 meters) long.
If you take a flat curve, mark a 100-foot chord, and determine the central angle to be 0°30’, then you have a 30-minute curve (chord definition)
For a 10 curve (chord definition), D = 1; therefore R =5, feet, or meters, depending upon the system of units you are using.

14. Use trigonometric function
REFRESH…
Use trigonometric function

15. REFRESH…

16. MINIMUM CURVE RADIUS
R = curve radius (m)
V = speed (km/h)
e = superelevation (%)
f = side friction factor (the value can be found in AASHTO green book)
Derivation of the formula:

17. Note :
You have learned this in geomatic survey subject

18. The desired minimum curve radius proposed by JKR for roads:
JKR proposes a maximum superelevation (e) of 6% for urban roads and 10% or rural roads. (note : e = 6.0% is the maximum rate used in the commonwealth of Massachusetts)
The desired minimum curve radius proposed by JKR for roads:
The desired minimum curve radius proposed by LLM for highways:
Design Speed (km/h)
Minimum Radius (m)
e = 6%
e = 10%
120
710
570
100
465
375 80
280
230 60
150
125 50 85 40 30 35 20 15
Design Speed (km/h)
140
120
100 80
Minimum Radius (m)
1000
650
450
240

19. Side friction factor (f)
Design speed
Side friction factor (f) 30
0.17 40 50
0.16 60
0.15 70
0.14 80 90
0.13
100
Note : the side friction factor (f) represents the contribution of the roadway-tyre interface to counterbalance the centrifugal force of vehicle traversing the curve

20. Example:
A roadway is being designed for a speed of 120 km/h. At one horizontal curve, it is known that the superelevation value is 8% and the side friction factor is Determine the minimum radius of curve (measured to the traveled path) that will provide safe vehicle operation.

21. We know that a Circumference = 2R
Example 1:
A horizontal curve is designed with a 700-meter radius. The curve has a tangent of 130 m and the point of intersection (PI) is at station Determine the stationing of point of tangency (PT).
PI ( )
T = R tan /2
130 = 700 tan /2
/2 = 10.52
 = 21.04
We know that a Circumference = 2R
Therefore, L = R/180 = ( )(700)/180 = m
Given the tangent is 130 m,
Stationing point of curvature (PC) = ( ) – (1 + 30) =
Horizontal curve stationing is measured along the curve,
Stationing PT = ( ) + ( ) =
T = 130 m PT PC L
R = 700 m 

22. Example 2:

23. TRANSITION CURVE (SPIRAL)
The transition curve is also known as the spiral.
The spiral is one of the alignment components. It is used to allow for a transitional path from tangent to circular curve, and from circular curve to tangent, or from one curve to another which has substantially different radii.
The spiral provides ease in operation and comfort, allowing for easy-to-follow natural superelevated transitional paths and promotes uniformity in speed and increased safety.
The use of a spiral may also enhance highway aesthetics.
The use of spiral curves generally is limited to areas of rough terrain where curves often approach the maximum degree of curvature for the particular design speed. (For more information on spirals, see the current AASHTO publication A Policy on Geometric Design of Highways and Streets.)
Circular curve
Spiral
Spiral CS SC
Tangent ST TS
Tangent

24. DESIGN OF CIRCULAR
CURVE
AND
TRANSITION CURVE
REFRESH…

25. REFRESH…
DESIGN OF CIRCULAR
CURVE
AND
TRANSITION CURVE

26. REFRESH…
DESIGN OF CIRCULAR
CURVE
AND
TRANSITION CURVE

27. Horizontal curve - Superelevation
Introducing superelevation permits a vehicle to travel through a curve more safely and at a higher speed than would be possible with a normal crown section.
The rate of superelevation generally increases with speed and sharper curvature.
Superelevation is the rotation of the roadway cross section in such a manner as to overcome part of the centrifugal force that acts on a vehicle traversing a curve.
The purpose of employing superelevation of the roadway cross section is to counterbalance the centrifugal force, or outward pull, of a vehicle traversing a horizontal curve.
Side friction developed between the tires and the road surface also counterbalances the outward pull of the vehicle.
A combination of these two concepts allows a vehicle to negotiate curves safely at higher speeds than would otherwise be possible.

28. Horizontal curve - Superelevation
Superelevation may not desirable for:
Low speed roadway to help limit excessive speeds
Urban setting to limit impacts to abutting uses or drainage system and utilities.
When considering pedestrian or bicycle accomodations along the roadway segment
Designer must consider the trade-offs of introducing superelevation in roadway’s design

29. Superelevation on a horizontally aligned road

30. Superelevation

31. Desired Superelevation and Transition Curve Length for two-lane roads
(Source: JKR)

32. SUPERELEVATION TRANSITION

33. Advantages Good for drainage Good for aesthetics
SUPERELEVATION TRANSITION
Advantages
Good for drainage
Good for aesthetics

34. 0% 2.5% 2.5% 2.5% e% 0% 2.5% e% SUPERELEVATION TRANSITION Consist of :
Superelevation tangent runout
Superelevation runoff
Tangent runout is the length of highway needed to change the normal cross section to the cross section with the adverse crown removed. 0%
2.5%
2.5%
2.5%
Superelevation runoff is the length of highway needed to change the adverse crown removed to the cross section with full superelevation. e% 0%
2.5% e%

35. Superelevation Runoff and Tangent Runout
Simplified figure
Superelevation Runoff and Tangent Runout
Fully superelevated cross section (superelevation runoff)
Cross section with the adverse crown removed (tangent runout)
Normal cross section

36. ATTAINMENT OF SUPERELEVATION
Transition from tangent to superelevation
Must be done gradually without appreciable reduction in speed or safety, and
with comfort
Change in pavement slopes must be consistent over a distance
Methods:
The length over which superelevation is developed should be adequate to provide
safe and comfortable riding quality and give good appearance
Criteria used to determine minimum lengths:
Rotate pavement about centerline
Rotate about inner edge of the pavement
Rotate about outer edge of the pavement
Rate of rotation of the pavement
Relative grade of the pavement edges with respect to longitudinal grade

37. ROTATION OF PAVEMENT

38. Superelevation Diagram
Normal Crown
Tangent Runout
Superelevation Runoff
Full Superelevation
Superelevation Runoff
Tangent Runout
Normal Crown
Outer edge SC CS
Inner edge ST TS
Road Cross section
+2.5%
+e%
+e%
+2.5% 0% 0%
-2.5%
-2.5%
-2.5%
-2.5%
-2.5%
-e%
-2.5%
-2.5%
-e%
-2.5%
Normal Crown
Adverse Crown Removed
Remove Crown
Superelevation Diagram
+e%
+2.5%
Outer edge 0%
-2.5%
Inner edge
-e%

39. SUPERELEVATION PROFILE
Outside edge of
traveled way
Inside edge of
traveled way

41. Calculate the chainage TP1
Quiz
Calculate the chainage TP1