CENG431: Traffic Engineering

Chapter 27: Geometric Design of

Roadways
 Roadway Geometry
• Three elements: Horizontal alignment, Vertical
alignment, and Cross-sectional elements
 Primarily affect traffic flow
 All standard practices in geometric highway design are
specified by the American Association of State Highway
and Transportation Officials (AASHTO) in the current
version of A Policy on Geometric Design of Highways
and Streets.
 The latest edition was published in 2018 (7th edition)
 Often referred to as the “Green Book,” due to the
predominant color of its cover.
 Horizontal Alignment
• Plan view
• Includes tangent sections and the horizontal
curves and other transition elements that join
them
• Generally initiated by laying out a set of
tangents on topographical and development
maps of the service area
 Horizontal Design Considerations
• Forecast demand volumes, with known or Demand
projected origin-destination patterns
• Patterns of development
• Topography Engineering

• Natural barriers
• Subsurface conditions
• Drainage patterns
• Economic considerations
• Environmental considerations Critical

• Social considerations
 Vertical Alignment
• Profile view
• Straight grades are connected by vertical curves
• Grade: Longitudinal slope, expressed as ““feet of
rise or fall” per “longitudinal foot” of roadway
length, either as decimal or percentage
• Attempts are made to conform to the
topography, wherever possible, to reduce the
need for costly excavations and landfills as well as
to maintain aesthetics
• Usually follow from the horizontal route layout
and specific horizontal design but may cause
changes in it, to minimize problems
 Design Criteria of Vertical Curves
• Provision of adequate sight distance at all
points along the profile
• Provision of adequate drainage
• Maintenance of comfortable operations
• Maintenance of reasonable aesthetics
 Cross-Section Elements
• Cut across the plane of the highway
• Includes features such as; such elements as lane widths,
superelevation (cross-slope), medians, shoulders,
drainage, embankments (or cut sections)
• Cross-sections are generally designed every 100 feet along
the facility length and at any other locations that form a
transition or change in the cross-sectional characteristics
 Surveying and Stationing
• All elements of highways are staked out at
every 100ft, also referred to as a “station”
• Notation: xxx+yy
– Values of xxx indicate the number of hundreds of
feet of the location from the origin point.
– The yy values indicate intermediate distances of
less than 100 ft
– Examples: 0+00,100+00,200+00
– 1200 + 52, which signifies a location 1,252 ft
 Horizontal Curves
• All horizontal curves are circular, formed by an arc with
a constant radius.
• Compound horizontal curves may be formed by
consecutive horizontal curves with different radii.
• On high-speed, high-type facilities, a horizontal curve
and a tangent (straight) segment are often joined by a
spiral transition curve, which is a curve with a varying
radius that starts at ∞, and ends at the radius of the
circular curve.
• The severity of a circular horizontal curve is measured
by the radius or by the degree of curvature, which is a
related measure.
 Degree of Curve
• 2πR/360 = 100/D
• D=5729.58/R
• A circular curve with a
radius of 2,000 ft has a
degree of curvature of:
• D=5,729.58/2,000 =
2.915o
 Characteristics of Circular Horizontal
Curves
• P.I.=point of intersection; point at which the
two extended tangent lines meet,
• P.C.=point of curvature; the point at which
the circular horizontal curve begins,
• P.T.=point of tangency; the point at which the
circular horizontal curve ends,
• T=tangent length; length from the P.C. to the
P.I. and from the P.I. to the P.T., ft.,
• E=external distance from point 5 to the P.I. in
Figure, ft.,
• M=middle ordinate distance from point 5 to
point 6 in Figure, ft.,
• LC=length of the long chord, from the P.C. to
the P.T., ft.,
• Δ=angle of the curve, sometimes referred to
as the angle of deflection, degrees, and
• R=radius of the circular curve, ft.
• L = Length of circular curve, ft
Key Values for Circular Horizontal
Curves
 Example
• Two tangent lines meet at Station 3200+15. The
radius of curvature is 1,200 ft, and the angle of
deflection is 14°. Find the length of the curve (L),
the stations for the P.C. and P.T., and all other
relevant characteristics of the curve (LC, M, E).
 Superelevation for Horizontal Curves
• to assist drivers in resisting
the effects of centripetal
force.
• Superelevation is quantified
as a decimal or percentage,
computed as follows:
• e=(total rise in pavement
from edge to edge)/(width
of pavement)

𝑆2 R=radius of curvature, ft,S=speed of the

𝑅= vehicle, mi/h,e=rate of superelevation
15(𝑒 + 𝑓) expressed as a decimal ), and f=coefficient
of side friction.
 Ranges for Superelevation
• Between 4% and 12%
• vary from region to region based upon factors such as climate,
terrain, development density, and frequency of slow-moving
vehicles
• Practical considerations:
– Drivers feel uncomfortable on sections with higher rates, and driver
effort to maintain lateral position is high when speeds are reduced on
such curves.
– Where snow and ice are prevalent, a maximum value of 8% is
generally used. Many agencies use this as an upper limit regardless,
due to the effect of rain or mud on highways.
– In urban areas, where speeds may be reduced frequently due to
congestion, maximum rates of 4% to 6% are often used.
– On low-speed urban streets or at intersections, superelevation may be
eliminated.
 Side Friction

• Represent wet pavements and tires in

reasonable but not top condition.
 Example
• Consider a roadway with a design speed of 60
mi/h, for which a maximum superelevation
rate of 0.06 has been selected. What are the
minimum radius of curvature and/or
maximum degree of curve that can be
included on this facility?
 Example (Contd.)
• For the highway described above, what
superelevation rate would be used for a curve
with a radius of 1,500 ft?
 Achieving Superelevation
• Tangent Runoff: The outside lane of the curve must have a
transition from the normal drainage superelevation to a
level or flat condition. The length of this transition is called
the tangent runoff (Lt).
• Superelevation Runoff: the outside lane of the curve must
be rotated (with other lanes) to the full superelevation rate
of the horizontal curve. The length of this transition is
called the superelevation runoff (Lr).
 Rotation for Superelevation
• For most undivided highways, rotation is around the
centerline of the roadway, although it can also be
accomplished around the inside or outside edge.
• For divided highways, each directional roadway is separately
rotated, usually around the inside or outside edge.
 Lr
• W=lane width of one lane of traffic, in feet
• e = design superelevation rate
d

• Δ = maximum relative gradient, in percent, representing the

rate of transition of the cross slope of the pavement
• n1 = number of lanes rotated (1 for a two-lane highway rotated
about the centerline, 2 for a four-lane highway rotated about
the centerline, etc.)
• b = adjustment factor for the number of lanes rotated, (1 for 1
w

lane rotated, 0.75 for 2 lanes, 0.67 for 3 lanes)

 Example
• Consider the example of a four-lane highway,
with a superelevation rate of 0.04 achieved by
rotating two 12 ft lanes around the centerline.
The design speed of the highway is 60 mi/h.
What is the appropriate minimum length of
superelevation runoff?
 Lt
• Lt = eNC/ed x Lr
• If, in the previous example, the normal drainage cross-
slope was 0.01, then the length of the tangent runoff
would be:
• Lt=40 ft
• Total transition length = 160 + 40 = 200ft
• To provide the most comfortable operation, from 60%
to 80% of the total runoff is achieved on the tangent
section.
• The large majority of agencies use value of 67% of total
runoff on the tangent
 Spiral Transition Curves
• It is difficult for drivers to travel immediately from a
tangent section to a circular curve with a constant
radius.
• A spiral transition curve begins with a tangent (degree
of curve, D=0) and gradually and uniformly increases
the degree of curvature (decreases the radius) until the
intended circular degree of curve is reached.
• Construction is difficult and construction cost is
generally higher than simple circular curve.
• Hence, they are recommended for high-volume
situations where degree of curvature exceeds 3°.
 Benefits of Spiral Curve
• Provides an easy path for drivers to follow:
Centrifugal and centripetal forces are increased
gradually.
• Provides a desirable arrangement for
superelevation runoff
• Provides a desirable arrangement for pavement
widening on curves (to accommodate off-tracking
of commercial vehicles)
• Enhances highway appearance
Geometry of Spiral Curve
 Recommended Values of Spiral Curve

• One approach is to make the length of the spiral equal to the sum of the
(Lt) and (Lr).
• Another approach is to make the length of the spiral equal to (Lr) alone.
• If the desired length is < the minimum value, use the minimum spiral
length.
• If the desired length is > the maximum value, use the maximum spiral
length.
 Example
• A 4° curve is to be designed on a highway with
two 12 ft lanes and a design speed of 60 mi/h. A
maximum superelevation rate of 0.06 has been
established, and the appropriate sidefriction
factor for 60 mi/h is found from Table 27.2 as
0.120. The normal drainage cross-slope on the
tangent is 0.01. Spiral transition curves are to be
used. Determine the length of the spiral and the
appropriate stations for the T.S., S.C., C.S., and
S.T. The angle of deflection for the original
tangents is 38°, and the P.I. is at station 1,100+62.
The segment has a two lane cross-section.
 Sight Distance on Horizontal Curves
• Fundamental design criteria:
a minimum sight distance
equal to the safe stopping
distance must be provided
at every point along the
roadway.
• On horizontal curves, sight
distance is limited by
roadside objects that block
drivers’ line of sight by
roadside objects such as
buildings, trees, and natural
barriers disrupt motorists’
sight lines.
 Sight Distance on Horizontal Curves
• Sight distance is measured
along the arc of the roadway,
using the centerline of the
inside travel lane.
• The middle ordinate, M, is
the distance from the
centerline of the inside lane
to the nearest roadside sight
blockage.
• AASHTO refers to it as the
“horizontal sight line offset
(HSO).”
 Sight Distance on Horizontal Curves
• M=R [1−Cos (Δ/2)]
• L=ds=100 (Δ/D); Δ=ds(D/100)
• M=R [1−Cos(dsxD/200)]
• M=5,729.28/D [1−Cos(ds D/200)], or
• M=R [1−Cos(28.65 ds/R)]
• ds=1.47 S t+S2/[30(0.348±G)]
 Example
• A 6° curve (measured at the centerline of the
inside lane) is being designed for a highway
with a design speed of 70 mi/h. The grade is
level, and driver reaction time will be taken as
2.5 seconds, the AASHTO standard for
highway braking reaction. What is the closest
any roadside object may be placed to the
centerline of the inside lane of the roadway?
 Compound Horizontal Curves
• Use of compound curves should be limited
to cases in which physical conditions
require it.
• The larger radii should not be more than
1.5 times the smaller or the degrees of
curvature should not differ by more than
5°.
• Whenever two consecutive curves in the
same direction are separated by a short
tangent (≤200 ft) they should be combined
in a compound curve.
• Its a series of simple horizontal curves
subject to the same criteria as isolated
horizontal curves.
• AASHTO relaxes some of these criteria for
compound curves on ramps.
 Reverse Horizontal Curves
• Should always be separated by a tangent of at
least 200 ft.
• Use of spiral transition curves is a significant
assist to drivers negotiating reverse curves.
 Vertical Alignment of Highways
• Vertical curves are in the shape of a parabola.
• This provides for a natural transition from a
tangent to a curved section – no need to
provide transition curves
• Grades: 4% grade of 2,000 ft involves a vertical
rise of 2000×4/100=80 ft
• Upgrade = +ve, Downgrade = -ve
 Effect of Trucks
• For trucks with weight to horsepower ratio
200lb, entering at 70mph

The crawl speed is that constant

speed that the truck can maintain for
any length of grade (of the given
steepness).
 Critical Length
• For grades entered at 70 mi/h, the critical
length is generally defined as the length at
which the speed of trucks is 15 mi/h less than
their speed upon entering the grade.
• When trucks enter an upgrade from slower
speed, a speed reduction of 10 mi/h may be
used
 Example
• A rural freeway in rolling terrain has a design
speed of 60 mi/h. What is the longest and
steepest grade that should be included on the
facility?
 Geometric
Characteristics of
Vertical Curves

• Two types of vertical

curves: Crest and Sag
• For crest vertical
curves, the entry
tangent grade is
greater than the exit
tangent grade. While
traveling along a
crest vertical curve,
the grade is
constantly declining.
• For sag vertical
curves, the opposite
is true
 Terms
• VPI=vertical point of intersection
• VPC=vertical point of curvature, VPT=vertical point of tangent
• Length, and all stationing, on a vertical curve is measured in the
plan view, (i.e., along a level axis).
• A=|G2−G1|, the algebraic change in grade, %
• Equation of Parabola: y=ax2+bx+c
• y=Yx=the elevation of the roadway at a point “x” from the VPC, ft,
• x=distance from the VPC, ft, and
• c=Yo=elevation of the VPC, which occurs where x=0, ft.
• slope of the curve at any point x; dy/dx=2ax+b
• When x=0, the slope is equal to the entry grade, G1
• Dy/dx=G1/100=2a(0)+b, b=G1/100
 Terms
• the second derivative of the equation is equal to the
rate of change in slope along the grade
• d2y/dx2=2a=(G2−G1)/(100L), a=(G2−G1)/(200L)
• Yx=(G2−G1)/(200L)x2+(G1/100)x+Yo
• The location of the high point (on a crest vertical curve)
or the low point (on a sag vertical curve) is at a point
where the slope (or first derivative) is equal to “zero”
• dYx/dx=0=(G2−G1)/(100L) x+G1/100x
• xhigh, low=−G1L/(G2−G1)
• If both grades are negative (downgrades), the low
point on the curve is the VPT and the high point is the
VPC. If both grades are positive (upgrades), the low
point on the curve is the VPC and the high point is the
VPT.
 Example
• A vertical curve of 600 ft connects a +4%
grade to a −2% grade. The elevation of the
VPC is 1,250 ft. Find the elevation of the VPI,
the high point on the curve, and the VPT.
 Sight Distance on Vertical Curves
• On vertical curves, sight distance is measured
from an assumed eye height of 3.5 ft and an
object height of 2.0 ft.
 Sight Distance on Vertical Curves
• For crest vertical curves, the daylight sight line
controls minimum length of vertical curves
• For sag vertical curves, the sight distance is
limited by the headlamp range during
nighttime driving conditions
 Example
• What is the minimum length of vertical curve
that must be provided to connect a +5% grade
with a +2% grade on a highway with a design
speed of 60 mi/h? Driver reaction time is the
AASHTO standard of 2.5 s for simple highway
stopping reactions.
Cross-Sectional Elements of Highways
• The cross-section view of a highway is a 90° cut across the
facility from roadside to roadside
• The cross-section includes the following features:
• Travel lanes
• Shoulders
• Side slopes
• Curbs
• Medians and median barriers
• Guardrails
• Drainage channels
 General design practice is to specify the cross-section at
each station and at intermediate points where a change in
the cross-sectional design occurs.
 Travel Lanes and Pavement
• Paved travel lanes provide the space that moving vehicles occupy during
normal operations.
• The standard width of a travel lane is 12 ft (metric standard is 3.6 m).
• The minimum recommended lane width is 9 ft.
• Lanes wider than 12 ft are sometimes provided on curves to account for
the off-tracking of the rear wheels of large trucks.
• Narrow lanes will have a negative impact on the capacity of the roadway
and on operations.
• 9-ft lanes are acceptable only on low-volume, low-speed rural or
residential roadways, and 10 ft lanes are acceptable only on low-speed
facilities.
• All pavements have a cross-slope that is provided
a. to provide adequate drainage and
b. to provide superelevation on curves.
 Travel Lanes and Pavement
• For high-type pavements, normal drainage cross-slopes range from 1.5%
to 2.0%.
• On low-type pavements, the range of drainage cross-slopes is between 2%
and 6%.
• A pavement can be drained to both sides of the roadway or to one side
depending upon the position of drainage ditches or culverts and pipes.
• In some cases, water drained to the roadside is simply absorbed into the
earth if soil is adequate to handle maximum expected water loads.
• Where more than one lane is drained to one side of the roadway, each
successive lane should have a cross-slope that is 0.5% steeper.
• On superelevated sections, cross-slopes are usually sufficient for drainage
purposes, and a slope differential between adjacent lanes is not needed.
• Superelevated sections, must drain to the inside of the horizontal curve.
 Shoulder
• “A shoulder is the portion of the roadway contiguous with the traveled way
that accommodates stopped vehicles, emergency use, and lateral support
of sub-base, base, and surface courses (of the roadway structure)”
• The shoulder width ranges from 2 ft to 12 ft.
• Most shoulders are “stabilized”
• This can range from a fully paved shoulder to shoulders stabilized with
penetration or stone surfaces or simply grass over compacted earth.
• It is critical that the joint between the traveled way and the shoulder be
well maintained.
• Shoulders are generally considered necessary on rural highways serving a
significant mobility function, on all freeways, and on some types of urban
highways.
• A minimum width of 10 ft is generally used, as this provides for stopped
vehicles to be about 2 ft clear of the traveled way.
• The narrowest 2 ft shoulders should be used only for the lowest
classifications of highways.
 Functions of Shoulder
• Providing a refuge for stalled or temporarily stopped vehicles
• Providing a buffer for accident recovery
• Contributing to driving ease and driver confidence
• Increasing sight distance on horizontal curves
• Improving capacity and operations on most highways
• Provision of space for maintenance operations and equipment
• Provision of space for snow removal and storage
• Provision of lateral clearance for signs, guardrails, and other
roadside objects
• Improved drainage on a traveled way
• Provision of structural support for the roadbed
Recommended Cross-slope for
Shoulders
 Side-Slopes for Cuts and
Embankments
• In urban areas, sufficient right-of-way is generally not available to
provide for natural side-slopes, and retaining walls are frequently
used.
• Where natural side-slopes are provided, the following limitations
must be considered:
 A 3:1 side-slope is the maximum for safe operation of maintenance
and mowing equipment.
 A 4:1 side-slope is the maximum desirable for accident safety.
 Barriers should be used to prevent vehicles from entering a side-
slope area with a steeper slope.
 A 2:1 side-slope is the maximum on which grass can be grown, and
only then in good climates.
 A 6:1 side-slope is the maximum that is structurally stable for where
sandy soils are predominate.
 Recommended Side-slopes

*Avoid where soils are subject to erosion

 Guardrail
• “Guardrail” is intended to prevent vehicles from entering a dangerous area of the
roadside (cross-slope steeper than 4:1) or median during an accident or intended
action.
• Roadside guardrail is provided to prevent vehicles from colliding with roadside
objects such as trees, culverts, lighting standards, sign posts, and so on.
• Once a vehicle hits a section of guardrail, the physical design also guides the
vehicle into a safer trajectory, usually in the direction of traffic flow.
• Median guardrail is primarily provided to prevent vehicles from encroaching into
the opposing lane(s) of traffic. It also prevents vehicles from colliding with median
objects.
• If the median is 20 ft or wider and if there are no dangerous objects in the median,
guardrail is usually not provided, and the median is not curbed.
• Wide medians can effectively serve as accident recovery areas for encroaching
drivers.
• Narrower medians generally require some type of barrier, as the potential for
encroaching vehicles significant.
Types of Guardrail
 Guardrails
• The major differences in the various designs are the flexibility of
guardrail upon impact and the strength of the barrier in preventing
a vehicle from crossing through the barrier.
• Example 1: The box-beam design is quite flexible. Upon collision,
several posts of the box-beam will give way, allowing the beam to
flex as much as 10 to 12 ft. The colliding vehicle is gently
straightened and guided back toward the travel lane over a length
of the guardrail. Obviously, this type of guardrail is not useful in
narrow medians, as it could well deflect into the opposing traffic
lanes.
• Example 2: Concrete median or roadside barrier. These blocks are
almost immovable, and it is virtually impossible to crash through
them. Thus, they are used in narrow roadway medians (particularly
on urban freeways). On collision with such a barrier, the vehicle is
straightened out almost immediately, and the friction of the vehicle
against the barrier brings it to a stop.
 Guardrails
• A vehicle colliding with a blunt end of a guardrail
section is in extreme danger. Thus, most W-beam
and box-beam guardrails are bent away from the
traveled way, with their ends buried in the
roadside.
• Even with this done, vehicles can hit the buried end
and “ramp up” the guardrail with one or more
wheels.
• Various impact attenuating devices can also be
used to protect the ends of such barriers.
• Concrete barriers have sloped ends, but are usually
protected by impact attenuating devices, such as
sand or water barrels or mechanical attenuators.
• Connection of guardrail to bridge railings and
abutments is also important.
• Where guardrails meet bridge railings or
abutments, they are anchored onto the railing or
abutment itself to ensure that encroaching vehicles
are guided away from the object.