Transportation Engineering
Course Code –CE-422
Contact Hours -3+3
Dr Hassan Mujtaba
Roadway Alignment
• An ideal, most desirable and economical road
is one that follows the existing natural
alignment of the country.
• Certain design aspects has to be maintained
which may prevent the designer from
following this undulating surface without
making considerable adjustments in both the
vertical and horizontal directions.
2
Roadway Alignment
• The designer must produce an alignment in
which conditions are consistent and uniform to
help reduce problems related to driver
expectancy.
• Sudden changes in alignment should be
connected with long sweeping curves, and
short sharp curves should not be interspersed
with long curves of small curvature.
3
Roadway Alignment
• The ideal highway location is one with
consistent alignment, where both vertical grade
and horizontal curvature receive consideration
and are configured to satisfy limiting design
criteria.
• The optimal final alignment will be that in
which the best balance between grade and
curvature is achieved.
4
Terrain
• Terrain has considerable influence on the final
choice of alignment. Generally, the
topography of the surrounding area is fitted
into one of three classifications:
– Level
– Rolling
– Mountainous
5
Level Terrain
• In level country, the alignment is in general
limited by considerations other than grade, that
is, cost of right-of-way, land use, waterways
requiring expensive bridging, existing cross
roads, railroads, canals, power lines and sub-
grade conditions or the availability of suitable
borrow material.
6
Rolling Terrain
• In rolling country, grade and curvature must be
carefully considered and to a certain extent
balanced.
• Depths of cut and heights of fill, drainage
structures, and number of bridges will depend
on whether the route follows the ridges, the
valleys or cross drainage alignment.
7
Mountainous Terrain
• In mountainous country, grades provide the
greatest problem, and, in general, the
horizontal alignment or curvature is controlled
by maximum grade criteria.
8
Horizontal Alignment
• Horizontal alignment consists of a series of straight
sections of highway joined by suitable curves. It is
necessary to establish the proper relation between
design speed and curvature as well as relationship
with super-elevation and side friction.
• Horizontal curves are designated by their radius or by
the degree of the curve.
• The degree of a curve is the central angle subtended
by an arc of 100 ft measured along the center of the
road.
9
SUPER-
ELEVATION
Raising the outer edge
with respect to the
inner edge is SUPER
ELEVATION
10
Superelevation
• A vehicle is forced radially outward by
centrifugal force when it moves in a circular
path.
• The vehicle weight component creates friction
between the road surface and tires to
counterbalance the centrifugal force.
• In addition, the superelevated section of a
highway offsets the tendency of the vehicle to
slide outward. 11
Superelevation
12
Force Diagram for Superelevation
R- Radius
n- speed
w- weight of
vehicle
N1& N2 -
normal forces
F1& F2 - lateral
forces/ friction
forces
13
Force Diagram for superelevation
μ- coefficient of friction between tires and
roadway
- angle of pavement cross slope
e = tan = superelevation rate = cross slope of
the road way
14
Derivation of Superelevation equation
For Highway F1 and F2
are friction forces
F1 N 1 and
F2 N 2
Summing forces parallel to roadway
15
Derivation of Superelevation equation
Defining a factor f, side
friction factor so that
F
f fNF
N
Summing forces normal to roadway
16
Derivation of Superelevation equation
The equation can be rewritten as
Dividing by Wcos q leads to
17
Derivation of Superelevation equation
tan q is the cross-slope of the roadway, which is
same as super-elevation rate e and can be
written as
or
The term ef is small and may be omitted so the
equation reduces to
or
18
Derivation of Superelevation equation
A commonly used equation is
V is in km/hr and
R in m
Alternatively
or
19
Superelevation Equation (FPS System)
Where V is in miles/h, and R is V2
in feet R
15 (e f )
• Studies show that the co-efficient of friction (µ)
between new tires and wet concrete pavements ranges
from about 0.5 at 20 mph (30 Km/h) to approximately
0.35 at 60 mph (100 Km/h).
• For normal, wet, concrete pavement and smooth tires,
the value is about 0.35 at 45 mph (70 Km/h).
However, curve design cannot be based entirely on
available co-efficient of friction (µ). Side friction
factor (f) is used in the design of curves.
20
Side Friction Factor f
• Values of f recommended by AASHTO are
conservative relative to actual friction between the
tires and road surface.
• Maximum rates of superelevation are limited by the
need to prevent
– slow moving vehicles from sliding to the inside of
the curve.
– to keep the parking lanes relatively level in urban
area
– to keep the difference in slope between roadway
and any street or driveways that intersect within
reasonable limits. 21
Side Friction Factor f (AASHTO)
22
Minimum Radius of Curve (AASHTO)
Minimum
23
Minimum Radius
for Limiting
values of e and f
(AASHTO)
24
Superelevation
• Several factors dictate the maximum rates of
superelevation: climate conditions, terrain, location
(urban or rural), and frequency of very slow-moving
vehicles. No single maximum superelevation rate is
universally applicable.
• AASHTO recommends maximum superelevation rate
of 12% for rural roadways, 8% for rural roadway for
which snow or ice is present and 6% or 4% for urban
streets.
• To facilitate cross-drainage, a commonly used
superelevation rate is 0.12.
25
Relation between e and f
• A variety of methods are practiced in balancing e and
f. One such method uses superelevation at speeds
lower than the design speed.
• Average running speed, which is estimated as 80 to
100 percent of design speed, provides superelevation
design where all lateral acceleration is sustained by
superelevation of curves.
• For flatter curve more rate of superelevation has to be
provided to counteract lateral acceleration.
26
Relation between e and f (cont’d)
• Maximum superelevation is reached near the middle
of the curve.
• At average running speed, no side friction is needed
up to this curvature, and side friction increases
rapidly and in direct proportion for sharper curves.
• Considerable side friction is available for higher
speeds.
• An alternate method for sustaining centripetal
acceleration on curves is to maintain super-elevation
and side friction inversely proportional to the radius
of the curve. 27
Minimum Radius
• The minimum radius is a 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 (limiting value
of f is used).
• Use of sharper curvature for the given design speed
would require superelevation beyond the limit
considered practicable or for operation with tire
friction and lateral acceleration beyond what is
considered comfortable by many drivers.
28
Minimum Radius (cont’d)
• Although based on a threshold of driver comfort,
rather than safety, the minimum radius of curvature is
a significant value in alignment design.
• The minimum radius of curvature is also an important
control value for determination of superelevation
rates for flatter curves.
• The minimum radius of curvature, Rmin can be
calculated directly from the simplified curve formula
for a given Side Friction Factor.
29
Problem-1
• A roadway is designed for a speed of 120 km/hr. At
one horizontal curve, it is known that the
superelevation is 8.0% and side friction factor is 0.09.
Determine the minimum radius of the curve
(measured to the traveled path) that will provide safe
vehicle operating.
30
Problem-2
• What is the minimum radius of curvature allowable
for a roadway with a 100 km/hr design speed,
assuming allowable super elevation rate is 0.12.
Compare this with the minimum curve radius
recommended by AASHTO.
• What is the actual maximum super elevation rate
allowable under AASHTO recommended standards
for a 100 km/hr design speed, if the value of f is the
maximum allowed by AASHTO for this speed.
31
Problem-3
• Determine a proper superelevation rate for a low
volume, gravel surface road with a design speed of 50
mph and a degree of curvature of 8 degrees.
Comment on the proposed super elevation.
32
Comments on Super Elevation for Problem
3
• To facilitate drainage, a commonly used super
elevation of 0.12 is recommended. However,
recommending super elevation of this magnitude can
lead to higher speed and associated problems of
rutting and displacement of gravels. Thus, 0.09 may
be a reasonable value.
33
Problem-4
• Calculate the super elevation rates for a roadway with
a design speed of 100 km/hr that has a wide range of
curve radii; i.e R= 1750, 875, 585, 440, 350 and 295
m. These values corresponds to degrees of curve, D =
1, 2, 3, 4, 5 and 6. Use maximum super elevation rate
= 0.10. Compare the results obtained from figure.
• Assuming f is 0.12.
34
35
Solution Problem-4
Recommended Design
Radius
Computed Superelevation, e Superelevation, e (From
(m)
Figure)
1750 -0.075 0.032
875 -0.030 0.06
585 0.015 0.078
440 0.059 0.095
350 0.105 Exceeds e max
295 0.147 Exceeds e max
36
Solution Problem-4
• For the sharpest two curves, the combination of
maximum super elevation rate and maximum side
friction factor is insufficient to sustain the centrifugal
force. These two curves are very sharp for the given
design speed. Hence unsuitable for stated conditions.
• On the other hand, negative values of super elevation
indicate that all the centrifugal force could be offset
without exceeding the side friction factor of 0.12
even with zero super elevation. However, AASHTO
recommends a slight but positive super elevation for
the flattest two curves.
37
Attainment of Superelevation
• Superelevation transitions involve modification of the
roadway cross-section from normal crown to full
superelevation, at which point the entire roadway
width has a cross-slope of e.
• The manner in which this transition is accomplished
is expressed by a superelevation diagram, which is a
graph of superelevation (cross-slope) versus distance
measured in stations.
• As an alternative, the diagram may show the
difference in elevation between the profile grade and
the edge versus distance. 38
Attainment of Superelevation
39
Superelevation Transition
• Figure is an example
of superelevation
diagram, showing
the transition from
normal crown with 2
percent cross-slopes
to 6 percent
superelevation for a
roadway with a
spiral transition
curve.
40
Superelevation Transition
• Figure on next slide is the alternative form of the
diagram, assuming a two-lane highway with 3.6 m
lanes.
• Figure “c” on next slide presents an interpretation of
the superelevation diagram, showing the appearance
of the cross section at intervals through the transition.
41
Superelevation Transition
• Figure “b” on next slide is the alternative form of the
diagram, assuming a two-lane highway with 3.6 m
lanes.
42
Superelevation Transition
43
Superelevation Runoff
• As shown in Figure “a”, the superelevation transition
is normally linear; that is, the rate of rotation of the
cross section is constant with respect to distance
through the transition.
• The distance marked L, which runs from the point at
which the outside half of the roadway (that is, the half
on the outside of the curve) is at zero cross-slope to
the full superelevation (or from the tangent -to-spiral
point TS to the spiral-to-curve point SC), is called
superelevation runoff
44
Tangent Runoff
• The distance from the point at which the
outside half of the roadway first begins to
rotate to the TS is referred to as tangent runoff.
45
Superelevation Transition
• The superelevation transition section consists of the
superelevation runoff and tangent runoff sections.
• Superelevation runoff section consists of the length of
roadway needed to accomplish a change in outside-
lane cross slope from zero (flat) to full
superelevation, or vice versa.
• Tangent runoff section consists of the length of
roadway needed to accomplish a change in outside-
lane cross slope from the normal cross slope rate to
zero (flat), or vice versa.
46
Superelevation Transition
• For reasons of safety and comfort, the pavement
rotation in the superelevation transition section
should be effected over a length that is sufficient to
make such rotation imperceptible to drivers. To be
pleasing in appearance, the pavement edges should
not appear distorted to the driver.
47
Determination of Length of Superelevation Runoff
• The length of the superelevation runoff L is
determined by either vehicle dynamics or appearance
criteria.
• More commonly, superelevation transition lengths for
highways are based on appearance or comfort criteria.
One such criterion is a rule that the difference in
longitudinal slope (grade) between the centerline and
edge of traveled way of a two-lane highway should
not exceed 1/200.
48
Determination of Length of Superelevation Runoff
• Figure on next slide illustrates the application
of this rule. L is measured from the TS to the
SC, as in the superelevation diagram.
• At the TS, the difference in elevation between
the centerline and edge is zero.
• At the SC, it is the superelevation rate e times
the distance D from the centerline to the edge.
49
Determination of Length of Superelevation Runoff
• Thus, the difference in grade
between the centerline and the
edge is
Since the criterion that the
difference in grade not exceed
1/200 implies that
De 1
50
L 200
Superelevation Transition
L is given by
L 200 De
L is normally rounded up to some convenient
length, such as a multiple of 20 m.
51
Example
• A two lane highway goes from 2% normal crown
to 6% superelevation. Sketch Superelevation
diagram for the following data:
Superelevation, e = 6%
Width of two lanes, B = 7 m (two lane)
Cross slopes = 2%
52
Solution
• Super elevation runoff= L= 200 De
• L= 200*3.5*.06 =42 m
• Take L = 60 m for multiples of 20
• Elevation difference between C/L and edge at TS = 0
• Elevation difference between C/L and edge at SC
= De = (width of lane x e) = 3.5 x 0.06
= 0.21 m = 210 mm
53
Superelevati
on Diagram
54
Superelevation Transition
• The transition from a tangent, normal crown section
to a curved superelevation section must be
accomplished without any appreciable reduction in
speed and in such a manner as to ensure safety and
comfort to the occupants of the traveling vehicle.
• In order to effect this change, the normal crown road
section will have to be tilted or banked as a whole to
provide superelevation cross section required for a
given design speed.
55
Attainment of Superelevation
• This attainment of superelevation is accomplished by
the following methods
– Rotate about the centerline of the pavement
– Rotate about the inner edge of the pavement
– Rotation about the outside edge of the pavement
56
Rotation about centerline Axis
• The effect of this rotation is to lower the inside edge
of pavement and, at the same time, to raise the
outside edge without changing the centerline grade.
Rotation about the centerline is most widely used
because the change in elevation of edge of the
pavement is made with less distortion than other
methods.
• However, for flat grades too much sag is created in
the ditch grades by this method.
57
Rotation about centerline Axis
• Used for highways with narrow medians and
moderate superelevation rates. Since large difference
in elevation can occur between extreme pavement
edges if median is wide.
58
Rotation about inner edge of the pavement
• Rotate about the inner edge of the pavement as an
axis so that the inner edge retains its normal grade but
the centerline grade is varied, or rotation may be
likewise about the outside edge.
• Half of the required change in cross slope is made by
raising center line profile with respect to inner edge
and other half by raising out side pavement edge with
respect to to the actual center line profile.
59
Rotation about inner edge of the pavement
• On grades below 2 percent, rotation about the inside
edge is preferred.
• Used for pavements with median width 30 ft. or less.
60
Rotation about outside edge of the pavement
• Same geometry as rotation about the inner
edge of the pavement except that the elevation
change is accomplished below the outside
edge profile instead of about the inside edge
profile.
• Used for pavements with median width 40 ft.
or greater.
61
Rotation about outside edge of the pavement
62
Rotation about outside edge of the pavement
• Revolves the traveled way about the outside
edge profile.
• In this case, section is not crowned.
• This method is often used for two-lane one
way road where the axis of rotation coincides
with the edge of the road adjacent to the
highway median.
63
Rotation about outside edge of the pavement
64
Axis of Rotation for undivided highways
General Consideration for Attainment of Superelevation
• Regardless of which method is utilized, care should
be exercised to provide for drainage in ditch sections
and adjacent gutters all along the length in
superelevated areas.
• The roadway on full SE sections should be a uniform
inclined section perpendicular to the direction of
travel.
• When a crowned surface is rotated to the desired SE,
the change from a crowned section to a uniformly
inclined section would be accomplished gradually at
a consistent rate along a length measured along the66
centerline.
