Highway Engineering 1

1. Highway Geometric Design
Analysis and Design of Superelevation

2. • WHAT IS SUPERELEVATION IN HIGHWAY ENGINEERING?
Superelevation is the transverse slope provided to counteract the effect
of centrifugal force and reduce the tendency of vehicle to overturn and
to skid laterally outwards by raising the pavement outer edge with
respect to inner edge. superelevation is represented by “ e ”.
Superelevation or cant or banking is the transverse slope provided at
horizontal curve to counteract the centrifugal force, by raising the outer
edge of the pavement with respect to the inner edge, throughout the
length of the horizontal curve.

3. • When vehicles approaching a horizontal curve, there will be force resulted
centripetal acceleration trying to push this vehicle outside the curve.
• This force is normally balanced by the force resulted from the friction
between vehicles’ tires and road surface.
• At high speeds and/ or low radius, the frictional force is not generally
sufficient to balance the centrifugal force.
• For this reason, the carriageway should be super-elevated to increase the
resistance as shown below.

4. Superelevation

6. Carriage way showing superelevation

7. • Objective of providing super elevations:
i. To counteract the effect of centrifugal force acting on the moving
vehicle to pull the same outward on a horizontal curve.
ii. To help a fast moving vehicle to negotiate a curved path without
overturning and skidding.
iii. To ensure safety of the fast moving vehicle.
iv. To prevent damaging effect on the road surface due to improper
distribution of load.

8. Figure: Superelevation

11. Superelevation in Highway Engineering

12. • Analysis of superelevation
Let us say Design speed = V m/s Radius = R m

13. • Various forces acting on the vehicle:

15. Where;
• e = rate of superelevation in %
• f = lateral friction factor = 0.15
• V = velocity of vehicle in m/s
• g = acceleration due to gravity = 9.81𝑚/𝑠2
• R = radius of circular curve in meters.

16. In order to find out how much this raising should be, the following analysis may
be done as presented
Figure below shows: Vehicle on curves, acting forces

18. W sin 𝜃 + w cos 𝜃. f = P cos 𝜃
Dividing above EQUATION by w. cos 𝜃, we get

20. • Limits for minimum superelevation
• Minimum superelevation = camber or cross slope Camber: Slope provide in
the transverse direction to drain off rain water quickly is known as Camber
or Cross slope. This will also prevents slipping and skidding of vehicles.

21. Design Of Superelevation
• There are four steps involved in the design of superelevation. And
they are;
•
Step 1:

22. • Step 1:
Calculate the superelevation necessary for 75% design speed and
assume No lateral friction is developed
If e value is less than 𝑒𝑚𝑎𝑥 = 0.07,
provide calculated e value.
Otherwise proceed to next step

23. • Step 2:
• When 𝑒𝑐𝑎𝑙 > 𝑒𝑚𝑎𝑥,
Provide e = 𝑒𝑚𝑎𝑥 = 0.07 in this step and go to next step.

24. • Step 3:
• From the above step we have the value of e. so, check for lateral friction
factor is applied in this step for the known value of e.
If 𝑓𝑐𝑎𝑙 < 𝑓𝑚𝑎𝑥 (0.15), then e = 0.07 is safe.
But if 𝑓𝑐𝑎𝑙 > 0.15.
Then restrict the values to f = 0.15, e = 0.07
And go to last step.

25. • Step 4:
• In this step we will find out the value of restricted speed. Let V = Va
If 𝑉
𝑎 > V, then e = 0.07, f = 0.15 if
𝑉
𝑎 < V, then also e = 0.07, f = 0.15
but,
speed restriction board is provided
which consists the value of 𝑉
𝑎 As
shown in the figure.

29. HORIZONTAL ALIGNMENT
• DEFINITION AND TYPES OF HORIZONTAL CURVES
• Horizontal alignment is one of the most important features of a highway
design. Its proper design can result in high performance regarding speed,
safety, efficiency, and comfort.
• In addition, it may result in the saving of economy and increase the highway
capacity.

30. • The design of horizontal alignments requires the understanding of design
speed and horizontal curves.
• Horizontal alignment includes of a road comprise a series of straight lines
known as tangents with the provision of curves to change direction. It
also includes the design of superelevation, extra widening, set back
distance, transition curve design, etc.

31. • Typically horizontal curves consist of a circular curve with a constant
radius.
• For faster design speeds circular curves are joined to the tangents using
transition curves which have varying radii.
• These curves improve the occupant safety and comfort by providing a
gradual increase of the sideways force felt by the vehicle due to the
introduction of the curve.
• A circular curve may also be accompanied by the introduction of
superelevation.
• This is were the road is tilted into the curve to reduce the likelihood of
vehicles running off the road at the curve.

33. • PC is the Point of Curvature. This is the point where the straight tangent
ends and the curve starts.
• IP is the point of intersection between the 2 tangent lines. It can be used
to help setting out of the road curve on site.
• PT is the Point of Tangency. This is the point where the curve ends and the
second straight starts.
• R is the radius of the curve determined as detailed below.
• Δ is the deflection angle.

34. Horizontal Curve
• Horizontal curves are provided in each and every point of intersection
of two straight alignments of highways in order to change the
direction.
• The direction change should be gradual to ensure safety and comfort
to the passengers.
• The necessity of curve arises due to the following reasons:

35. • Topography of the terrain
• Restrictions imposed by property
• Providing access to certain locality
• Restrictions by some unavoidable reasons of land
• Restrictions by certain religious, monumental or some other structures
• Making use of existing right of way
• Minimizing earthwork quantity
• Preservation of existing amenities
• Maintaining consistency with the topographical features of the terrain.

36. • The application of horizontal curves enhances comfort to the
passengers by avoiding the sudden change in direction and reduces
mental strain by travelling monotonously along the straight route.
• In addition, it makes the driver more alert while travelling along the
curved path which helps to reduce road accidents.
• This also plays an important role in speed control and compels the
driver to maintain the speed of vehicle within a reasonable limit.

37. Types Of Curves
• The simplest type of highway curve is the circular curve. It is a curve
used in highway having the constant radius.
i. Simple circular curves: It consists of a single arc connecting two
straight lines.
ii. Reverse circular curves: It consists of two or more arcs of one or
different circles turning in two opposite directions that join at the
common tangent point.
iii. Compound circular curves: It consists of series of simple circular
curves of one or different radius that turns in the same direction
and meet at the common tangent point.

38. Fundamental Horizontal Curve Properties
Aside from momentum, when a vehicle makes a turn, two forces are
acting upon it;
- The first is gravity, which pulls the vehicle toward the ground.
- The second is centrifugal force, for which its opposite, centripetal
acceleration is required to keep the vehicle on a curved path.
- For any given velocity, the centripetal force needs to be greater for a
tighter turn (one with a smaller radius) than a broader one (one with
a larger radius).
- On a level surface, side friction 𝑓𝑠 serves as a countering force to the
centrifugal force, but it generally provides very little resistance/force.
Thus, a vehicle has to make a very wide circle in order to make a
turn on the level.

39. • Given that road designs usually are limited by very narrow design areas,
wide turns are generally discouraged.
• To deal with this issue, designers of horizontal curves incorporate roads that
are tilted at a slight angle.
• This tilt is defined as superelevation, or e, which is the amount of rise seen
on an angled cross-section of a road given a certain run, otherwise known as
slope.
• The presence of superelevation on a curve allows some of the centripetal
force to be countered by the ground, thus allowing the turn to be executed
at a faster rate than would be allowed on a flat surface.

40. • Superelevation also plays another important role by aiding in drainage
during precipitation events, as water runs off the road rather than
collecting on it.
• Generally, superelevation is limited to being less than 14 percent, as
engineers need to account for stopped vehicles on the curve, where
centripetal force is not present.
• The allowable radius R
• for a horizontal curve can then be determined by knowing the intended
design velocity V
• , the coefficient of friction, and the allowed superelevation on the curve.

41. • The allowable radius R for a horizontal curve can then be determined by
knowing the intended design velocity V, the coefficient of friction, and the
allowed superelevation on the curve.
With this radius, practitioners can determine the degree of curve to see if it
falls within acceptable standards.

42. • How to Calculate the Degree of a Curve

43. • The ratio between the degree of curvature (D) and 360 is the same as
the ratio between 100 feet of arc and the circumference (C) of a circle
having the same radius. That may be expressed as follows:
Da = Degree of curve [angle subtended by a 30.5-m (100 ft) arc along
the horizontal curve

44. 1
Superelevation or Banking of Road: -
When a vehicle travels in a circular path or curved path, it is subjected to an outward force which
makes a vehicle to overturn and skid due to Centrifugal force. To overcome this force and for safe
travel of a vehicle, the outer edge of the road is raised above the inner edge. This is known as
superelevation or banking of road.
Superelevation/Banking of road reduces the effect of centrifugal force on the running wheels. If
superelevation is not provided with the entire centripetal force is produced by the friction
between the vehicle’s tires and the roadway, thus results in reducing the speed of a vehicle.
Advantages of providing Super elevation: -
i. Super elevation is provided to achieve the higher speed of vehicles.
ii. It increases the stability of fast-moving vehicles when they pass through a horizontal
curve, and it also decreases the stresses on the foundation.
iii. In the absence of super elevation on the road along curves, potholes are likely to occur at
the outer edge of the road.
iv. The max value of Super Elevation is 1 in 15.

45. 2
Derivation of Super Elevation:
As per the figure, the below forces are acting on a car
In order to find out the angle of elevation (Super Elevation) the “tan” formula is used;
From above fig, tan 𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒
Therefore, tan 𝜃 =
𝐸
𝐵
The below forces are acting on the vehicle as mentioned in figure:
Weight of the vehicle = W kg (↓);
Centripetal force = P (→);
Frictional forces = F1 & F2 (←);
You can check out the below figure more idea.
Hence, P. Cosθ = W. Sinθ + F1 + F2
Where, F = fR
P. Cosθ = W. Sin θ + fR1 + fR2
= W. Sin θ + f (R1 + R2)
= W. Sin θ + f (P Sin θ + W Cos θ)

46. 3
P. Cos θ - f. P Sin θ = W. Sin θ + f. W Cos θ
Divide with “W. Cos θ”;
(𝑷. 𝐜𝐨𝐬 𝜽 − 𝒇. 𝑷. 𝐬𝐢𝐧 𝜽)
𝑾. 𝐜𝐨𝐬 𝜽
=
(𝑾. 𝐬𝐢𝐧 𝜽 + 𝒇. 𝑾. 𝐜𝐨𝐬 𝜽)
𝑾. 𝐜𝐨𝐬 𝜽
𝑷
𝑾
−
𝒇. 𝑷
𝑾
𝐭𝐚𝐧 𝜽 = 𝐭𝐚𝐧 𝜽 + 𝒇
𝑷
𝑾
{𝟏 − 𝒇. 𝐭𝐚𝐧 𝜽} = 𝐭𝐚𝐧 𝜽 + 𝒇
𝑷
𝑾
=
(𝐭𝐚𝐧 𝜽 + 𝒇)
(𝟏 − 𝒇. 𝒕𝒂𝒏𝜽)
𝑷
𝑾
= 𝒆 + 𝒇
But,
𝑷
𝑾
=
𝑽𝟐
𝒈𝑹
Therefore, e + f =
𝑽𝟐
𝒈𝑹
Where,
e = rate of Super elevation in %
V = velocity of vehicle in m/s
f = lateral friction factor = 0.15
g = acceleration due to gravity = 9.81 m/s2
R = radius of circular curve in meters.
If velocity is in KMPH then; e + f = V2/ 127R
Super Elevation formula: -