CE-421 Transportation Engineering Alignment Of Highways

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Transportation Engineering
(CE-421)
Alignment Of Highways

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Topics;
__Alignment Of Highways
__Grade Line
__Horizontal & Vertical Curves
(1) Super Elevation
(2) Transition Curve
(3) Curve Widening
 __Sight Distance Requirements

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 The alignment is the route of the road, defined as a series of horizontal
tangents and curves.

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 Grade Line: is a line or slope used as a longitudinal reference for a
railroad or highway. Inclinations with the horizontal of a road, railroad,
etc., usually expressed by stating the vertical rise or fall as a percentage
of the horizontal distance; slope. Main consideration while selecting
grade line are,
1. Amount of earth work
2. Natural Terrain
3. Minimum sight distance requirement
4. Flood water level
5. Maximum Level of ground water
 Profile grade line (PGL) - This is a single line, straight or curved, along
the length of the highway, sometimes but not always on the center of the
highway.

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 The alignment of a highway is composed of horizontal and
vertical elements
 The horizontal alignment:
 includes the straight (tangent) sections of the roadway
 circular curves that connect their change in direction
 The vertical alignment:
 includes straight (tangent) highway grades
 parabolic curves that connect these grades

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 Highway alignment is in reality a three-dimensional
problem
 Design & construction is difficult in 3-D so highway design
is typically treated as two 2-D problems: Horizontal
alignment, vertical alignment

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VerticalAlignment
HorizontalAlignment
Horizontal Alignment
 Corresponds to “X” and “Z”
Coordinates
 Plan view – Roughly
 Equivalent to perspective
view of an aerial photograph
of highway.
Vertical Alignment
 Corresponds to highway
length and “Y” coordinate.
 Presented in a profile view.
 Gives elevation of all points
measured along the of a
highway.

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• Instead of using the coordinates system, highway positioning and length are
defined as the distance usually measured along the center line of the
highway from a specified point (also called “Reduced Distance” or ‘RD’)
• The notation for stationing distance is such that a point on highway 4250 ft
(1295.3 m) from a specified origin (0+00 or 0+000) is said to be at station:
– 42+50 ft (42 stations and 50 feet)
– I + 295.300 meter( 1 station and 295.300 meters)

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 The horizontal alignment consists of tangents and curves
 The curves are usually segments of circles, which have radii
that will provide for a smooth flow of traffic
 The critical design feature of horizontal alignment:
 horizontal curve that transitions the roadway between
two straight (tangent) sections
 focus on the design of directional transition of the
roadway in a horizontal plan
 A key concern in the directional transition is the ability of
the vehicle to negotiate the horizontal curve

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 Horizontal alignment to accommodate the cornering capability
of a variety of vehicles (cars to combination trucks)
 The design of the horizontal alignment entails the
determination of:
 the minimum radius of the curve
 determination of the length of the curve
 Side friction factor
 Superelevation
 Adequate stopping sight distance

(1) Simple horizontal curve
Horizontal Curves - Types of Curves
o Horizontal Curves: curves used in horizontal planes to connect two
straight tangent sections
o Simple Curve: circular arc connecting two tangents

Horizontal Curves
 A properly designed transition curve provides a
natural, easy-to-follow path for drivers, such that
the lateral force increases and decreases
gradually as a vehicle enters and leaves a circular
curve.
 Transition curves minimize encroachment on
adjoining traffic lanes and tend to promote
uniformity in speed.
 A spiral transition curve simulates the natural
turning path of a vehicle.

(2) Compound curve
R1
R2
Horizontal Curves
o Compound Curve: a curve which is composed of two or more
circular arcs of different radii, with centers on the same side of the
alignment
o Compound curves are used to fit horizontal curves to very specific
alignment needs …..interchange ramps, intersection curves etc.
o Radii should not be very different- difficult for drivers to maintain
lane position during transition from one to another curve

o Spiral Curve: A curve with constantly changing radius
o a curve whose radius decreases uniformly from infinity at the
tangent to that of the curve it meets
o Motorist usually create their own transition path while moving from
tangent section to curve….spiral curves not often used
o Special case use: used to gradually introduce superelevation
Spiral curve
Horizontal Curves

R1
R2
R1
R2
(4) Reverse Curve
(a) With tangent (b) Without tangent
o Reverse Curve: Two circular arcs tangent to each other, with their
centers on opposite sides of the alignment
o Two consecutive curves that turn in opposite direction
o Not recommended- drivers may find it difficult to stay in their lane
as a result of sudden change in alignment
Horizontal Curves

o Easement Curves: curves used to lessen the effect of the sudden
change in curvature at the junction of either a tangent and a
curve, or of two curves.
Horizontal Curves

Properties of Circular Curves
Degree of Curvature
• Traditionally, the “steepness” of the curvature is defined by either the
radius (R) or the degree of curvature (D)
• In highway work we use the ARC definition
• Degree of curvature = angle subtended by an arc of length 100 feet
Horizontal Curves

Properties of Circular Curves
o Degree of curvature = angle subtended by an arc of length 100 feet
o By simple ratio: D/360 = 100/2*Pi*R
Therefore
R = 5730 / D
o D = Degree of curvature - degrees
o R = Radius of curvature - feet
Horizontal Curves

o Length of Curve:
The length of the curve derives directly from the
arc definition of degree of curvature
o A central angle equal to the degree of curvature
subtends an arc of 100 ft, while the actual central
angle (Δ) subtends the length of the curve (L).
o By simple ratio
D/100=Δ/L
L = 100 Δ / D
o Or (from R = 5730 / D, substitute for D = 5730/R)
o L = Δ R / 57.30
o (note: D is not Δ – the two are often confused )
Horizontal Curves

Horizontal Curves Fundamentals -Layout
R = Radius of Circular Curve (ft)
PC = Point of Curvature
(Beginning of Curve)
PT = Point of Tangency
(End of Curve)
PI = Point of Intersection
T = Tangent Length
(T = PI – PC)
L = Length of Curvature
(L = PT– PC)
M = Middle Ordinate
E = External Distance
L.C = Chord Length
Δ = Deflection Angle or
external angle

Useful Formulas…
o Tangent: T = R tan(Δ/2)
(Triangle143)
o Chord: L.C = 2R sin(Δ/2)
(Triangle 364)
o Mid Ordinate: M = R – R cos(Δ/2)
o External Distance: E = R sec(Δ/2) - R

Deflection angle of a 4º curve is 55º25’, PI at station
245+97.04. Find length of curve,T, and
station of PT.
D = 4º ,  = 55º25’ = 55.417º
R
D 
5729.58
R 
5729.58
1432.3ft.
4

Horizontal Curves – Example1
D = 4º
 = 55.417º
R = 1,432.4 ft
L = 2R
360
= 2(1,432.4 ft)(55.417º) = 1385.42ft
360

Horizontal Curves – Example1
D = 4º
 = 55.417º
R = 1,432.4 ft
L = 1385.42 ft
T = R tan  = 1,432.4 ft tan (55.417) = 752.29 ft
2 2

Horizontal Curves – Example
A horizontal curve is designed with a 2000-ft radius. The curve has a
tangent length of 400 ft. and the PI is at station 103 + 00. Determine
the stationing of PT
Formulas…
o Tangent: T = R tan(Δ/2)
(Triangle 143)
o Chord: L.C = 2R sin(Δ/2)
(Triangle 364)
o Mid Ordinate: M = R – R cos(Δ/2)
o External Distance: E = R sec(Δ/2) - R
Horizontal Curves – Example 2

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o The presence of horizontal curve imparts centrifugal force which is a
reactive force acting outward on a vehicle negotiating it
o Centrifugal force depends on speed and radius of the horizontal
curve and is counteracted to a certain extent by transverse friction
between the tyre and pavement surface
o On a curved road, this force tends to cause the vehicle to overrun or
to slide outward from the center of road curvature
o For proper design of the curve, an understanding of the forces
acting on a vehicle taking a horizontal curve is necessary.
o From the basic laws of physics ….centrifugal force is as:
Concept of Super-elevation

Super-elevation
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Forces acting on a vehicle on horizontal curve of radius R (m) at a speed of V m/sec^2
P = centrifugal force acting horizontally out-wards through the center of gravity
W = weight of the vehicle acting down-wards through the center of gravity, and
F = friction force between the wheels and the pavement, along the surface inward

Super-elevation
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• The exact expression for superelevation
• For small ϴ (ϴ < 4 degrees and f=0.15 (generally) )
o 1- f tan ϴ = 1 (f tan ϴ =0)
o tan ϴ = ϴ = e ……………..above expression can be written as
V 2
 0.01e f
gR
e = rate of roadway superelevation, percent (number of vertical feet of rise per 100 feet
of horizontal distance)
f = side friction factor
g = gravitational constant
V = vehicle speed
R = radius of curve measured to a vehicle’s center of gravity

Super-elevation
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e = rate of roadway superelevation, %
f = side friction (demand) factor
v = vehicle speed, m/s
g = gravitational constant, 9.81 m/s2
V = vehicle speed, Kmph
R = radius of curve measured to a
vehicle’s center of gravity, meter
e = rate of roadway superelevation, %
f = side friction (demand) factor
v = vehicle speed, ft/s
g = gravitational constant, 32.2 ft/s2
V = vehicle speed, mph
R = radius of curve measured to a
vehicle’s center of gravity, ft
• AASHTO expression for superelevation after
simplification

Superelevation Example -1
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A roadway is being designed for a speed of 70 mi/h. At one
horizontal curve, it is known that the superelevation is 8.0% and
the coefficient of side friction is 0.10. Determine the minimum
radius of curve (measured to the traveled path) that will provide
for safe vehicle operation

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Determine the proper superelevation rate for an urban highway with a
design speed of 50 mph and degree of curvature of 8 degrees
Super elevation Examples

A 1.0-km long racetrack is to be designed with turns 250 m in length
at each end. Determine the superelevation rate you would
recommend for a design speed of 130 km/h.
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Super elevation Examples

Maximum Super-elevation
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o The maximum rates of superelevation:
o Climate conditions: (i.e., frequency and amount of snow and ice)
o Terrain conditions (i.e., flat, rolling, or mountainous)
o Type of area (i.e., rural or urban)
o Frequency of very slow-moving vehicles whose operation might
be affected by high superelevation rates
o No single maximum superelevation rate is universally applicable
o Design consistency: Using only one maximum superelevation rate
within a region of similar climate and land use is desirable

Maximum Super-elevation
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o AASHTO recommendation:
o 4% and 12%
o Increments of 2%
o Maximum rates adopted vary from region to region
– 12% - maximum superelevation rate. Drivers feel uncomfortable
on sections with higher rates, and driver effort to maintain lateral
position is high when speeds are reduced on such curves
– Snow and Ice Conditions:
• 8% is generally used
• Ice on the road can reduce friction force and vehicle travelling
at less than the design speed on the excessively
superelevated curve slide inward off the curve due to
gravitational forces
– Urban areas: 4%-6%
– Low-speed urban streets or at intersections: may be eliminated

Minimum Super-elevation
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o It should be noted that on open highway sections, there is generally
a minimum superelevation maintained, even on straight sections
o This is to provide for cross drainage of water to the appropriate
roadside(s) where sewers or drainage ditches are present for
longitudinal drainage
o This minimum rate is usually in the range of 1.5% for high-type
surfaces and 2.0% for low-type surfaces.

Side-Friction Factor
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o With the wide variation in vehicle speeds on curves, there usually is
an unbalanced force whether the curve is superelevated or not.
o This force results in tire side thrust, which is counterbalanced by
friction between the tires and the pavement surface
o This frictional counterforce is developed by distortion of the contact
area of the tire
o The upper limit of the side friction factor is the point at which the
tire would begin to skid; this is known as the point of impending
skid
o Because highway curves are designed so vehicles can avoid skidding
with a margin of safety, the “f” values used in design should be
substantially less than the coefficient of friction at impending skid

Side-Friction Factor
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o Important factors affecting side friction factor at impending skid:
o speed of the vehicle (f decreases as speed increases (less
tire/pavement contact))
o the type and condition of the roadway surface
o type and condition of the vehicle tires
o Design values represent wet pavements and tires in reasonable but
not top condition
o Values also represent frictional forces that can be comfortably
achieved; they do not represent, for example, the maximum side
friction that is achieved the instant before skidding
o Design values for the coefficient of side friction (f) vary with speed
from 0.38 at 10 mph to 0.08 at 80 mph

OFFFF
Off Tracking
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Off tracking is the characteristic, common to all vehicles, although
much more pronounced with the larger design vehicles, in which the
rear wheels do not precisely follow the same path as the front wheels
when the vehicle traverses a horizontal curve or makes a turn.
 At slow speed, off track inward
 At higher speeds, the rear wheels may even track outside the
front wheels.

Curve Widening
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On horizontal curves , especially when they are not of very
large radius, it is a common practice to widen the pavement
slightly more than the normal width, the object of providing Extra
Widening of pavements on horizontal curves are due to the
following reasons....
(a) An automobile such as car, bus or truck has a rigid wheel base
and only the front wheels can be turned. When the vehicle
takes a turn to negotiate a horizontal curve, the rear wheels do
not follow the same path as that of the front wheels. This
phenomenon is called ‘off tracking’. The off tracking depends
on
(1) the length of the wheel base of the vehicle
(2) the turning angle or the radius of the horizontal curves.

Curve Widening
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(b) At more than design speed if super elevation and lateral
friction jointly cannot counteract the centrifugal force, full
outward slipping of rear wheels may occur and thus more width
of road is covered. This condition occurs at very high speeds.
(c) At start of the curves drivers have a tendency to follow outer
edge of the pavement to have better visibility and large radius
curved path. This also necessitates extra width of the road.
(d) Trailer units require even larger extra width at curves.

Curve Widening
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Analysis of extra widening on horizontal curves
The extra widening of pavement on horizontal curves is
divided into two parts
(i) Mechanical widening and
(ii) Psychological widening.
Here,
n =number of traffic lanes
l = length of wheel base of longest vehicle in m
R= radius of horizontal curves in m
The widening required to account for the off tracking due
to the rigidity of wheel base is called ‘Mechanical widening ‘.

Curve Widening
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(ii) Psychological widening :-
At horizontal curves driveres have a tendency to maintain a
greater clearance between the vehicles than on straight stretches of
road. Therefore an extra width of pavement is provided for
psychological reasons for greater manoeuvrability of steering at
higher speeds and to allow for the extra space requirements for the
overhangs of vehicles. Psychological widening is therefore
important in pavements with more than one lane. An empirical
formula has been recommended byt IRC for deciding the additional
psychological widening ‘Wps’ which is dependent on the design
speed, V of the vehicle and the radius. R of the curve. The
psychological widening is given by the formula:

Curve Widening
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Hence the total widening Werequired on a horizontal curve is
given by:
Here,
n =number of traffic lanes
l = length of wheel base of longest vehicle in m
R= radius of horizontal curves in m
V= design speed Kmph

Sight Distances
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Sight distance is the length of the road way
section visible to the road user.
A driver’s ability to see ahead is needed for safe and
efficient operation of a vehicle on a highway.
For example, on a railroad, trains are confined to a
fixed path, yet a block signal system and trained
operators are needed for safe operation.

Sight Distances
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The designer should provide sight distance of sufficient
length that drivers can control the operation of their
vehicles to avoid striking an unexpected object in the
traveled way.
Sight distance is the distance along a roadway throughout
which an object of specified height is continuously visible to
the driver.
This 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 sight
obstructions within the driver’s line of sight

Sight Distances
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Criteria For Sight Distances
Height of Driver’s Eye
For all sight distances calculations the height of the driver’s eye is
considered to be 1.08 m [3.50 ft.] above the road surface. This value is based on a
study (17) that found average vehicle heights have decreased to 1.30 m [4.25 ft.]
with a comparable decrease in average eye heights to 1.08 m [3.50 ft.].
For large trucks, the driver eye height ranges from 1.80 to 2.40 m [3.50
to 7.90 ft]. The recommended value of truck driver eye height for design is 2.33 m
[7.60ft] above the road surface.
Green Book (AASHTO,2011)
Height of Object
For stopping sight distance and decision sight distance calculations,
the height of object is considered to be 0.60 m [2.00 ft] above the
road surface. For passing sight distance calculations, the height of
object is considered to be 1.08 m [3.50 ft] above the road surface.
Green Book (AASHTO,2011)

Sight Distances
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Stopping Sight Distance (SSD)
It is the minimum required distance by a drive travelling at a
given speed to stop vehicle after seeing an object on
highway from a specific height.
 Two most important driver characteristics
 Visual and hearing perceptions
 Perception-Reaction Process

Sight Distances
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Perception-Reaction Process
 Perception
 Identification
 Emotion
 Reaction (volition)
PIEV or PRT
Used for Signal Design and Braking Distance

Sight Distances
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 Perception
 Sees or hears situation (sees deer)
 Identification
 Identify situation (realizes deer is in road)
 Emotion
 Decides on course of action (stop, change lanes, etc)
 Reaction (volition)
 Acts (time to start events in motion but not actually do
action)
Foot begins to hit brake, not actual deceleration

Sight Distances
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 PRT is important factor:
 Determination of braking distances
 Establishing minimum sight distance on highway
 Length of the yellow phase at a signalized intersection
 Typical Perception-Reaction time range - 0.5 to 7 seconds
 For stopping sight distance - AASHTO recommends 2.5 sec
PRT

Sight Distances
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Perception-Reaction Time Factors
 Environment (Urban vs. Rural, Night vs. Day, Wet vs. Dry)
 Driver Age
 Physical Condition
 Medical Conditions (Visual Acuity)
 Complexity Of Situation
 Expected v/s Unexpected
 Distractions

Sight Distances
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Perception-Reaction Process –Reaction Distance
 Stopping Sight Distance (SSD) - Length of the roadway ahead that is
visible to the driver or the distance along a roadway throughout which an
object of specified height is continuously visible to the driver.
 Composed of Two Parts
 Distance traveled during perception/reaction time
 Distance required to physically brake vehicle
 SSD = PRD + BD
 PRD = dr = 1.47(Vi)(t)
dr = Distance traveled during PRT(feet)
Vi = velocity (mph),
t = PRT= 2.5s (generally)

Sight Distances
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Effect Of Gravity On BD

Sight Distances
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 Use basic assumptions to determine SSD at 60 mph on
and a=11.2 ft/s
a) 0% grade, b) 3% grade
(a) G  0% b) 3% grade
2
Effect Of Gravity On BD

Sight Distances
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Passing Sight Distance (PSD)
 The passing sight distance is the minimum sight
distance required on a two-lane, two way
highway that will permit a driver to complete a
passing maneuver without colliding with an
opposing vehicle and without cutting off the
passed vehicle

Sight Distances
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Two Lane Highway

Sight Distances
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 d(1) = distance traversed during perception and reaction time and during the
initial acceleration to the point of encroachment on the rightlane
 d(2) = distance traveled while the passing vehicle occupies the rightlane

Sight Distances
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 d(3) = distance between the passing vehicle at the end of its maneuver and the
opposing vehicle
 d(4) = distance traversed by the opposing vehicle for two-thirds of the time the
passing vehicle occupies the right lane

Sight Distances
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Passing Sight Distance for Design of Two-Lane Highways

Sight Distances
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Decision Sight Distance
 Decision sight distance is the distance required for a
driver to:
 Detect an unexpected or otherwise difficult-to-perceive
information source or hazard in a roadway environment
 hazard may be visually cluttered
 recognize the hazard or its potential threat
 select an appropriate speed and path
 initiate and complete the required safety maneuver
safely and efficiently

Sight Distances
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Where to Provide…….?
 AASHTO recommends that decision sight distance be
provided
 At interchanges or intersection locations where
unusual or unexpected maneuvers are required;
 Changes in cross-section such as lane drops and
additions, toll plazas, and intense-demand areas
where there is a substantial ‘visual noise’ from
competing information (e.g. control devices,
advertising roadway elements)

Sight Distances
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 Avoidance Maneuvers A& B
 Avoidance Maneuvers C, D & E
MetricU.S.
Customary

Sight Distances
74

CE-421 Transportation Engineering Alignment Of Highways

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