Mar 01, 2016
Higher Diploma in Civil Engineering | CON4381 Highway Engineering
Topic 1 Geometric Alignment and Design | Page 1-1
1
Geometric Design and Alignment
INTRODUCTION
Highway Engineering is the science and art of making the best use of available resources to provide
a safe, durable and aesthetic road network for the movement of goods and people. Geometric
design deals with the dimensioning of the elements of highways. Several principal elements
include sight distance, superelevation, grades, and other elements of geometric design.
On the other hand, the alignment consists of a variety of design elements that combine to
create a facility that serves traffic safely and efficiently. The alignment topic is particularly well
suited for demonstrating the effect of vehicle performance (specifically braking performance) and
vehicle dimensions (e.g. height of the drivers eye and headlight height) on the design of highways,
and is referred to vertical alignment and horizontal alignment.
Road Network Hierarchy
The aim of defining the road network hierarchy is to develop a pattern of routes, having regard to
the traffic volume and type of traffic, for providing basis for resource allocation required in the
inspections and the subsequent maintenance works. A good hierarchy should become the
foundation of a coherent, consistent and auditable maintenance strategy. The Transport Planning
and Design Manual divides the road network in the territory into three hierarchies, namely,
carriageways, footways and cycle tracks.
Carriageway Hierarchy
For adopting a coherent network classification, the carriageway classification follows the road types
specified in the Transport Planning and Design Manual, Volume 2 as shown in Table 1. For
defining the carriageway types, maintenance offices are recommended to refer to the Annual
Traffic Census published annually by the Transport Department (TD) or other relevant documents.
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Table 1 : Carriageway Hierarchy
Category No. Category Name Brief Description
EX Expressway Roads designated as Expressways under the Road
Traffic (Expressway) Regulations.
UT Trunk Road (Urban) Roads connecting the main centers of population.
High capacity roads with no frontage access or
development, pedestrians segregated, widely
spaced grade-separated junctions, and 24 hour
stopping restriction.
RT Trunk Road (Rural)
PD Primary Distributor Roads forming the major network of the urban
areas. Roads having high capacity junctions, though
may be at-grade, segregated pedestrian facilities
wherever possible and frontage access limited if
not entirely restricted, and 24 hour stopping
restrictions.
DD District Distributor Road linking Districts to the Primary Distributor
Roads. High capacity at-grade junctions, with peak
hour stopping restrictions and parking restrictions
throughout the day.
LD Local Distributor Roads within Districts linking developments to the
District Distributor Roads.
RR Rural Road Roads connecting the smaller centers of population
or popular recreation areas with major road
networks. Frontage access should be limited
wherever possible and junction design whilst not
necessarily grade separated should be of a high
capacity standard.
FR Feeder Road Roads connecting villages or more remote
settlements to Rural Roads.
Note : The road types and descriptions are reproduced from the Transport, Planning and Design
Manual (TPDM), Volume 2, Chapter 3, 2013.
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Footway Hierarchy
Footway inspections and maintenance should be dealt with according to the pedestrian usage
under available resources and may not necessarily relate to the importance and classification of the
adjoining carriageway. Two categories for footways as shown in Table 2 are recommended.
Table 2 : Footway Hierarchy
Category No. Category Name Brief Description
1 Footway within
Pedestrianisation Schemes
Footways within the pedestrianisation schemes
initiated by TD
2 Footway outside
Pedestrianisation Schemes
Other footways not classified under Category 1
Notes:
(1) A footway may consist of more than one footway section and each footway section should be assigned an
appropriate footway category.
(2) For the purpose of easy naming and location referencing, the start/end of those footway sections should take into
account the start/end of the associated carriageway if any so that any naming or location referencing to the
footway section could be made with reference to just one associated carriageway.
(3) In order to minimise the potential data maintenance effort of the footway sections, the recommended minimum
length of a footway section should be the lesser of 100m or the entire length of the footway between the
consecutive road junctions.
Cycle Tracks
The decision to provide separate facilities for cycles will generally be based on accident records and
levels of existing or predicted cycle flows. However other arguments not necessarily having any
factual support may also be used to influence the decision on the provision of cycle facilities. In
these latter cases care should be taken that in agreeing to such facilities, a reasonable level of
cycling activity can be guaranteed and that an overprovision of facilities is not made. Cycle tracks
provided but not used to any extent will quickly deteriorate and may be occupied by undesirable
activities. Such under-utilisation can also prejudice any future provision of cycle facilities.
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Cycling in the Territory at the present time is mainly recreational, although in the New Territories
some work journeys are made by cycle. However evidence on such journeys that are made is
sparse and therefore it is difficult to provide warrants for cycle tracks based on local experience and
reliance has to be put on information published abroad, which may or may not be entirely relevant
to local conditions.
The Application of Classifications for Highway Design
Only the carriageway hierarchy is considered in this module. In general, a road is firstly classified
by its type and function based on planning consideration. The width and number of lanes of the
road can then be chosen in accordance with the road classification and the projected traffic volume.
Finally, the geometric alignments of the road can be designed based on the design speed
determined from the classification and the cross-section of the road.
CLASSIFICATION OF ROADS
The classification of roads is to provide a logical basis for the planning, design and administration of
roads and road systems. It is based on the types of road and on the particular functions they are
intended to serve.
TYPES OF ROAD
A highway can be classified either as a Rural or an Urban road defined by its specific cross-section.
In general, a road with a rural cross-section will cost less to construct but usually require more land.
A road cross-section can have opposing traffic lanes either undivided (single) or divided (dual) road.
Figure 1 outlines the typical elements of different road types.
Elements of a Road Cross-section
Traffic Lanes. A traffic lane is the part of the road that is reserved for vehicular traffic. The
number of lanes will depend on the volume and the type of traffic ranging from one to twelve lanes
or more although two-lane roads are most predominant.
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Shoulders. A shoulder is that part of a rural road adjacent to the traffic lane that is primarily used
as a refuge area for parked vehicles. When its surface is constructed of the same pavement as the
traffic lane, it is called a hard shoulder. Where a grass surface is provided, it is called a verge.
Footway. A footway is the part of an urban road for pedestrian traffic. The width of a footway
will depend on the amount of pedestrians with a minimum width of 1.5m being standard. Footways
are usually separated from the traffic lanes with kerbs.
Kerbs and Channels. Kerbs are normally constructed along the edge of a traffic lane to delineate
the traffic lane from the rest of the element and in case of the existence of a footway, to provide a
barrier between the vehicular and pedestrian traffic. It is usually constructed with a channel for
the drainage of surface runoff.
Figure 1. Simplified road cross-sections: (a) 2-lane street, (b) urban motorway, (c) 2- or 3-lane rural highway, and (d) rural motorway [Reproduced from OFlaherty, C.A. (ed.), Transport Planning and Traffic Engineering, 1997, Figure 19.10]
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Central Reserve and Median. A central reserve or a median is essentially an element of a divided
roadway (dual road). Its main function is to separate two streams of opposing traffic to reduce the
risk of conflict. A median is used in urban area and is 1 to 5m wide. It is often delineated by
kerbs on both side and act as a refuge island for pedestrians crossing the road. Other function of a
median is to provide space for lighting, traffic signals, signs, landscaping and planting as well as to
accommodate level differences between pavements. In rural area, a central reserve is used and is
generally 10m or wider with a ditch in the middle for the drainage of the surface runoff.
The choice of types of cross-section will mainly be determined by the characteristics of the
environment the highway is situated. There are however occasions a combination of the two
types of cross-section will be used.
FUNCTIONS OF ROAD
The functions of a highway will determine the standards to be adopted both in design and in
operation. There are in general 4 main types of functions.
Primary Distributor. Roads of major significance catering for relatively high volume and/or long
distance travel. In rural areas they comprise the main intercity roads connecting the major
provincial cities to the large metropolitan centres. In urban areas, they comprise the high volume
routes serving the major transport corridors that link the larger activity centres. In general there is
no access to frontage, no parking and no stopping. Connections to other roads are mainly through
interchanges.
District Distributor. Roads cater for relatively high volume and on which through traffic
predominates. In rural areas, they comprise routes linking small towns. In urban areas they
comprise routes linking town centres, large residential districts and industrial estates. Their
function is to feed traffic from the primary distributors to these localities and have restricted access
to frontage with no parking or stopping either at all time or during peak periods.
Local Distributor. Roads connect the local road system to the primary and district distributor
system, and serve both through and local traffic with very minor restriction to frontage access,
stopping and parking.
Access Road. Roads predominantly cater for local short distance travel and access to abutting
property.
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Hong Kong Road Classification T.P.D.M. V.2 - Chapter 3 (2013)
Rural Road Types
Trunk Roads Roads connecting the main centres of population. High capacity roads with no
frontage access or development, pedestrians segregated, widely spaced grade-separated
junctions, and 24 hour stopping restrictions.
Rural Roads Roads connecting the smaller centres of population or popular recreation areas with
major road networks. Frontage access should be limited wherever possible and junction
design whilst not necessarily grade separated should be of a high capacity standard.
Feeder Roads Roads connecting villages or more remote settlements to Rural Roads.
Urban Road Types
Trunk Roads Roads connecting the main centres of population. High capacity roads, with no
frontage access or development, segregation of pedestrians, widely spaced grade
separated junctions, and 24 hour stopping restrictions.
Primary Distributor Roads forming the major network of the urban area. Roads having high
capacity junctions, though may be at-grade, segregated pedestrian facilities wherever
possible and frontage access limited if not entirely restricted, and 24 hour stopping
restrictions.
District Distributors Roads Linking Districts to the Primary Distributor Roads having high capacity
at-grade junctions, with peak hour stopping restrictions and parking restrictions
throughout the day.
Local Distributors Roads within Districts linking developments to the District Distributor Roads.
Expressway
Roads are designated as Expressways under the Road Traffic (Expressway) Regulations. An
expressway may be formed from a trunk road or a primary distributor road. Details of Expressway
standards are contained in Chapter 6 of this Volume.
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Road Network Showing Different Road Classifications
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Road Classification By Type Rural Urban Little frontage development Abundant frontage development Infrequent intersections Frequent intersections very often with traffic control Relatively low traffic volume Extremely high traffic volume Low pedestrian movement High pedestrian movement Mainly functioned as an intercity expressway Mainly functioned as an expressway through a city or as a
ring road around a city Part of the local road network in rural (small town, village) areas
Part of the local road network in urban (towns, city) areas
By Functions in accordance with Hong Kong Road Classification
Item Trunk Road Primary Distributor District Distributor Local Distributor Rural Roads Rural Feeder
Connecting Main centres of population
Major urban road network
Districts to Primary Distributor Roads
Developments to District Roads
Smaller centres of population to major road networks
Villages or more remote settlements to Rural Roads.
Traffic volume High High to medium Medium Medium to low High to medium Medium to low
Type & spacing of intersections
Interchange only, @ 1-2 km apart
High capacity intersections may be at grade
High capacity at grade intersections with traffic controls
At grade intersections, some with traffic controls
High capacity at grade junctions
At grade intersections
Restriction on:
Frontage access
No Stopping
No Parking
No access 24 hr 24 hr
Limited access 24 hr 24 hr
Restricted access @ Peak hours 24 hr
Direct access Some restriction Some restriction
Limited access 24 hr 24 hr
Direct access Some restriction Some restriction
Pedestrian segregation Yes Yes where possible No No
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Intersection
In the design of a highway network, intersection layout design is usually encountered. An intersection is a location in the network where two or more roads intersect. It is separated into at grade and grade separation intersections. At Grade Intersections An at grade intersection is formed when two or more roads intersection at the same level. They can be divided basically into eight forms. To reduce the amount of conflicts, an intersection can be channelized. Traffic flows can also be controlled by stop signs, give-away signs or traffic signals.
T Y
Scissors Cross
Staggered Staggered & Skewed
Multiway Rotary
Basic forms of at-grade intersections
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The design considerations of an at grade intersection should include the following factors: traffic
factors, physical factors, economic factors and human factors.
Grade Separation Intersection (Interchanges)
An interchange is used for reducing the conflicts of traffic crossing each other at grade by constructing
one road over or under another (i.e. grade separated). The two roads are then connected by slip
roads. At a fully developed interchange such as a clover type, all at-grade crossing conflicts are
eliminated, and all manoevours take place either by merging, diverging or weaving.
Trumpet Diamond
Roundabout Cloverleaf
There are many factors in determining the type of interchange to be used. Some of the common
factors are:
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1. Classification 2. Environmental consideration
3. Adjacent land use 4. Economics
5. Design speed 6. Safety
7. Traffic volumes 8. Topography
9. Composition of traffic 10. Right-of-way and property
11. Relationship to other features of the
highway system
The various geometric layout of an intersection can be considered by piecemeal extended highway
sections, which can be considered as a combination of both horizontal alignments and vertical
alignments. Safety is the important consideration in the design of any highway sections and
alignments, which is related to the traffic volume and vehicle speed and hence the sight distance.
In the following sections, these concepts and the governing design equations are introduced.
Volume and Speed
The functional classification of roads on its own is not sufficient for road design purposes and a
more detailed classification referring to the volume and the speed is also required. In general,
the volume of traffic will govern the width and the number of lanes of the road; and the alignment
of the road will be determined by the design speed (The definition and the measurement of
Volume and Speed are more specific for traffic engineering. For design purposes, it will be
sufficient to know the meaning of some of the more common terms).
Volume Traffic volume is the number of vehicles that pass a given point on the highway in a
given period of time. The traffic pattern for a particular stretch of road varies from hour to hour,
from day to day and from season to season. For design purposes, the following units of
measurement for different time periods are used:
AADT - Annual Average Daily Traffic is the daily traffic volume based on the total traffic throughout
the year divided by 365 days.
DHV - Design Hour Volume (Peak hour flow) is the hourly traffic volume usually based on actual
traffic count on site or by multiplying the AADT by an appropriate factor.
Speed Traffic speed is the rate of movement of traffic. There are four different types of speed
measurement.
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Running speed - is the average speed maintain over a given route while the vehicle is in motion.
Thus, in determining the running speed, the times along the route when the vehicle is
at rest are not taken into account in the calculation.
Journey speed - The average journey speed is the distance travelled divided by the total time taken
to complete the distance.
Spot speed - The instantaneous speed of a vehicle at a specific location which can be used for
traffic speed enforcement as well as for design purposes. On a stretch of road, the spot
speed varies depending on the drivers behaviour, the volume of traffic, the geometry
of the road and the number of junctions and other factors.
Percentile speed - is the speed at or below which the stated percent of vehicles in the traffic
stream travel on a section of highway. 85th-percentile speed means 85% of the traffic
travels at or below this speed and it is normally used as the design speed of a highway.
Sight Distance
Sight distance is defined as the length of carriage that the driver can see in both the horizontal and
vertical planes. Two types of sight distance are detailed: stopping sight distance and overtaking
distance.
Stopping Sight Distance
Stopping sight distance is the distance required by the driver of a vehicle travelling at the design
speed to perceive and react to an unexpected situation, and to brake to a stop before reaching a
stationary object on the road. These two components are measured between the driver's eye
and a small object on the road.
Stopping sight distance
Stopping sight distance
eye height object height
Road surface
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The stopping sight distance SSD equals to the sum of perception-reaction distance d1 and the
braking distance d2.
SSD metres = d +
= t v + 2
2
= 0.278 tV+ 2
254
where v is the speed in m/s
t is the perception-reaction time in seconds, and
f is the coefficient of longitudinal friction between the vehicle tyres and the road surfaces
V is the speed in km/h = 3.6v
Stopping Sight Distance on Grades
At any given speed, the braking distance increases on down-grades, and reduces on up-grades due
to the effect of gravity. If grade is allowed for, the equation for stopping sight distance becomes:
Down-grade Up-grade
d metres = 0.278 t V + 2
254[(
9.81)+]
where is the per cent grade in decimal; + for an upgrade and - for a downgrade and =
where is the rate of deceleration (ms-2).
Overtaking Sight Distance
Overtaking sight distance is the distance required for a driver of vehicle to safely overtake a slower
moving vehicle travelling in the same direction before meeting an oncoming vehicle. It is
measured between the driver's eye and an oncoming vehicle.
1 d2
s
Direction of travel
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Overtaking sight distance
The overtaking sight distance only applies to two or three lane roads and does not apply to dual
roads. There are four components required for safe overtaking.
The dimension d represents the distance travelled by a vehicle while its driver decides whether
or not it is safe to pass the vehicle in front. It is described as the hesitation distance equaling the
distance travelled at the design speed for about 3.5s.
The dimension d represents the passing distance travelled by the overtaking vehicle in carrying
out the actual passing manoeuvre. Thus it begins the instant the overtaking driver turns the
wheel and ends when the vehicle is returned to its own lane. Usually, the speed of the
overtaking vehicle is assumed to be about 10 mph (16 kph) higher than that of the vehicle being
overtaken.
The dimension d has been called the safety margin and is the distance between the overtaking
vehicle and the oncoming vehicle at the instant the overtaking vehicle has returned to its own lane.
It is based on the time gap and one value that has been suggested is 1.5s. This means that if the
combined relative speed is 160 km/h, then a safety margin of 67 m is available between the two
vehicles.
The dimension d represents the distance travelled by the opposing vehicle at the design speed
of the road while the actual overtaking manoeuvre is taking place. Conservatively, it should be
the distance travelled by Vehicle B during the time required for Vehicle A to travel over the
distance d + d . In practice, as Vehicle A can return freely to its own lane at any instance prior
to drawing alongside the overtaken vehicle, the hesitation time is not taken into account. Also,
the speed for Vehicle A tends to be higher than that of Vehicle B. Hence the distance d can be
taken as approximately equal to 2/3d2.
Further calculation, discussion and examples are provided in Chapter 7 Geometric Alignment and
Design in Rogers (2008).
1
2
3
4
1 2
4
d1 d2 d3 d4
Vehicle A Vehicle B Vehicle C
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Horizontal Alignment
Horizontal alignment deals with the design of the directional transition of the highway in a
horizontal plane. The horizontal alignment of a road usually consists of a series of straight lines
(tangents) and circular curves which are often joined to each other by transition curves.
Circular Curves
T.P. T.P.
T
P.I.
IO
RTangent Tangent
Circular curve
LC
T
R = radius of the circular curve
P.I. = point of intersection of two tangents
T.P. = tangent point, or the point at which the tangent and the circular curve join
I = intersection angle
T = tangent length
LC = length of circular curve
Some basic equations for circular curve are as follows:
T =R tanI
2 Lc = I R
Clear Zone and Lateral Offset Concept
As per the 2011 AASHTO Roadside Design Guide (AASHTO RDG), the clear zone concept was first
discussed in the early 1960s. A clear zone is the unobstructed, traversable area provided beyond
the edge of the through traveled way for the recovery of errant vehicles. The clear zone includes
shoulders, bike lanes and auxiliary lanes, except those auxiliary lanes that function like through
lanes. Many obstacles located within this clear zone distance were removed, relocated,
redesigned, or shielded by traffic barriers or crash cushions.
180
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For arterials and other non-controlled access facilities in an urban environment, however,
rights-of-way often are extremely limited and, in many cases, establishing a clear zone is not
practical. These urban environments are characterized by sidewalks beginning at the back of
curb, enclosed drainage, numerous fixed objects (ex: signs, utility poles, fire hydrants, etc.) and
frequent traffic stops. These environments typically have lower operating speeds and, in many
instances, on-street parking. In these environments, a lateral offset to vertical obstructions,
including breakaway devices, is needed to accommodate motorists operating on the highway.
This lateral offset to obstructions helps to:
Avoid adverse impacts on vehicle lane position and encroachments into opposing or adjacent
lanes.
Improve driveway and horizontal sight distances.
Reduce the travel lane encroachments from occasional parked and disabled vehicles.
Improve travel lane capacity
Minimize contact from vehicle-mounted intrusions, such as large mirrors, car doors, and the
overhang of turning trucks.
It is imperative that adequate sight distance be provided when designing the horizontal curves
within a highway layout. Restrictions in sight distance occur when obstructions exist as shown
below. These could be boundary walls or, in the case of a section of highway constructed in cut,
an earthen embankment.
The minimum offset clearance M required between the centreline of the highway and the
obstruction in question can be estimated in terms of the required sight distance SD and the radius
of curvature of the vehicles path as follows:
M = R [1 cos ( .
)]
where
M = minimum offset clearance = stopping sight distance = radius of curve
Full derivation can be found in
Chapter 7.5.3 Geometric Alignment
and Design in Rogers (2008).
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Transition Curves
The primary purpose of a transition curve is to enable vehicles moving at high speeds to make the
change from the tangent section to the curved section of a road in a safe and comfortable fashion.
Other purposes of transition curves are to provide a convenient means of introducing
superelevation and to improve the appearance of the road.
The essential requirement of any transition curve is that its radius of curvature should decrease
gradually from infinity at the tangent-spiral intersection (T.S.) to the radius of the circular curve at
the spiral-curve intersection (S.C.) where r*l = constant (Clothoid).
Basic Properties of the Clothoid Transition
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Basic properties of a circular curve with transition curves at both ends
R = radius of the circular curve in metres; I = intersection angle;
P.I. = point of intersection of the two tangents;
T.S. = tangent-spiral intersection; S.C. = spiral-curve intersection;
C.S. = curve-spiral intersection; S.T. = spiral-tangent intersection;
s = spiral angle; T = tangent length;
LT = length of transition curve from T.S. to S.C. and C.S. to S.T.;
L = length of circular curve from S.C. to C.S.;
l = distance to a point along the transition from T.S.;
r = radius of the curve at distance l from T.S.;
Some basic relationships for Clothoid transition curves are as follows:
=
2
4 =
3
402 =
1 0
= ( + ) tan
+ =
1 0( ) =
0.0 143
= 3
402 =
2
4
33 3
where q = rate of change of centripetal acceleration
A vehicle travelling along a transition curve from tangent to the end radius at a constant speed
experiences a centripetal acceleration which varies at a constant rate along the length of the
transition. The shorter the transition length, the quicker is the change in the acceleration. In order
to travel comfortably along the transition, it is necessary to limit the rate of change of centripetal
acceleration. The normal range used for the rate of change of centripetal acceleration is between
0.3 to 0.86 m/s3.
Widening on Horizontal Curves
Pavements need to be widened on some curves for two basic reasons, namely:
1. A vehicle travelling on a curve occupies greater road space than on a straight especially for
heavy goods vehicles.
2. Vehicles tend to wander more in a lane on a curve than on a straight.
c
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The amount of widening required depends on factors such as the radius of the curve, the width of
the traffic lane or lanes on the straight and the type of vehicle and its dimensions.
If you look for more details on widening on horizontal curves, you may check chapter 3.3.10 in A
Policy on Geometric Design of Highways and Streets 2011, 6th Edition published by the American
Association of State Highway and Transportation Officials.
Superelevation
Superelevation is the sloping of the surface across the full width of a roadway. When a vehicle
travels round a circular horizontal curve it is subjected to a radial force which tends to cause it to
slide outwards. The purpose of providing superelevation is to create a gravitational force and a
frictional force to counter balance this force in order to keep the vehicle on the circular path.
W v
R g
2
W v
R g
2
W v
R g
2
W v
R g
2
cos
sin
sin xF
W
W cos xF W sin
Radial forces
Gravitational & Frictional forces
Forces acting on a vehicle travelling round a circular curve
The notations in the preceding figure are:
W = weight of vehicles; R = radius of the curve in metres;
v = speed of the vehicle in m/s ; g = gravity constant in m/s ;
F = coefficient of sideways friction; E = superelevation in m/m = tan ;
2 2
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For equilibrium along the plane,
and this reduces to
or
In practice FE is negligible, so where is known as the centrifugal ratio.
For design purpose and noting , we have v2
and g = 9.81 m/s to get
+ =2
1 7
In Hong Kong, driving in wet condition during rain is considered more dangerous with reduced
friction between the tyres and the road surface. The coefficient of sideways friction F is
therefore ignored. At the same time, traffic will be travelling at a slower speed and the velocity is
assumed to be reduced by 67%. The equation for calculating the superelevation then becomes:
=(0. 7)2
1 7=
2
.
Minimum Radius
By adopting desirable maximum values for superelevation and for sideways friction, a set of values
for the minimum radius of horizontal curves at various design speeds can be calculated using the
above equations. In practice it is desirable, where practicable, to adopt larger radii than the
minimum values so that the sideways friction and/or superelevation are reduced below the
maximum values. At the same time, a check should be carried out to ensure that the minimum
stopping sight distance is provided. Otherwise, bigger radius should be used.
Development of Superelevation
Development of superelevation usually take place along the transition curve and is the sloping of
the road across its section from the normal crown section along the tangent to the superelevated
section at the beginning of the circular curve. At the end of the circular curve, the process is
Wv
RgF W
Wv
RgW
2 2
cos ( cos sin ) sin
v
RgF F
2
1( tan ) tan v
RgFE F E
2
1( )
v
RgE F
2 V
Rg
2
v V1000
3600
V 2
236.
2
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reversed until the road returns to normal crown section.
Normal crown section Superelevated section
Circular Curves With Transition
For a circular curve with a transition curve, the development of superelevation starts at the
Tangent Runout (T/RO). This is a point in the tangent section where the high side begins to
rotate upward from the normal crown section. The high side should become horizontal at the
beginning of the transition curve (T.S.). It continues to rotate upward until its crossfall is the
same as that of the low side at which point, both sides will rotate together until the superelevated
section is reached at the beginning of the circular curve (S.C.). The superelevated section will be
maintained throughout the circular curve before reversing the process to return to a normal crown
section at the Tangent Runout.
Development of superelevation for a left-hand circular curve with transition curves
T.S.
S.C. PII
-2.5%-2.5%-2.5%-2.5%+2.5%+2.5% 0%
+E%
-E%
Tangent
Runout
-2.5%
C.S.
+E%
-E%
S.T.
-2.5% 0%-2.5%-2.5%
TangentRunout Circular curve
+E%
-E%
Centreline of road
-2.5% -2.5%
Centreline of road
S.T. T/RO. S.C. C.S. T/RO.
High side
Low side
+E%
-2.5% -E% -2.5%
+2.5% +2.5%
Profile for superelevation with transition curves
Centre line
Higher Diploma in Civil Engineering | CON4381 Highway Engineering
Topic 1 Geometric Alignment and Design | Page 1-23
Plain Circular Curves Without Transition Curves
When superelevation is developed on a plain circular curve without transition curves, it is
desirable, wherever possible, for the length of the circular arc to be at least twice and preferably
four times the length required for superelevation development in order to give a satisfactory visual
appearance. Typically, approximately two thirds of the superelevation should be introduced on
the approach tangent and the remainder in the circular curve based on the mathematical
transition length.
T.P. T.P.
Plain circular curve
Tangent section Tangent section
2/3L
1/3L 1/3L
2/3L
Superelevated section
Normal crown
Normal crown
L = mathematical transition length
T/RO T/RO
Development of superelevation for a plain circular curve without transition curves
2/3L. 2/3L
T/RO. T.P. T.P. T/RO.
High side
Low side
+E%
-2.5% -E% -2.5%
+2.5% +2.5%
Profile for superelevation without transition curves
Centre line
1/3L 1/3L
Higher Diploma in Civil Engineering | CON4381 Highway Engineering
Topic 1 Geometric Alignment and Design | Page 1-24
Vertical Alignment
The vertical alignment of a road usually consists of a series of straight lines (grades) joined to each
other by vertical curves.
Vertical Curves
The purposes of vertical curves are to join grades to each other and to provide:
1. a safe and comfortable transition from one grade to the next;
2. adequate sight distance across the junction of two grades;
3. a satisfactory appearance.
Parabolic curve properties
PI
EVC
BVC
p
qe
LV/2
LV
ey
Y
LV /2x
where
BVC is the beginning of the vertical curve and EVC is the end of the vertical curve.
LV is the horizontal length of vertical curve.
p is the slope of the first grade in decimal and q is the slope of the second grade in decimal;
upgrades take positive values and downgrades take negative values
x is the horizontal distance of the point from BVC, y is the vertical height between the point
and the p-grade and Y is the vertical height between the point and BVC, where
{
=
=
2
The highest (or lowest) point on the curve only occurs when p-grade and q-grade are of opposite
signs which can be determined using
x
LV p
p q
and
y
LV p
p q
2
2
Higher Diploma in Civil Engineering | CON4381 Highway Engineering
Topic 1 Geometric Alignment and Design | Page 1-25
1. Crest or Summit Curves
Summit or crest curves are those curves between two tangents which either a positive grade is
followed by a negative grade, a positive grade is followed by a lesser positive grade or a negative
grade is followed by a steeper negative grade (i.e. the grade difference from left to right is
positive).
Sight distance (S) over a summit curve: (a) required sight distance is contained entirely within the
length of the vertical curve and (b) required sight distance is greater than the length of the vertical
curve
p q
PI
SLV
TP TP
e
e
Line of
sight
h1 h 2
1d 2d
TP TPLV
S
PI
p q
h2
Line of
sight
h1
h1h2/p /qLV/2
(a) S < LV (b) S > LV
=
{
| | 2
(1 +2)2 for <
(1 +2)
2
| |for >
2. Sag Vertical Curves
Sag curves are those curves between two tangents which either a negative grade is followed by a
positive grade, a negative grade is followed by a less negative grade, or a positive grade is followed
by a steeper positive grade. (i.e. the difference of grade change from left to right is negative.)
In addition to the appearance criteria, drainage should always be checked in sag curves to ensure
that adequate provision has been made for it. Further considerations in the design of sag vertical
curves are as follows :
a) Comfort Considerations on Sag Vertical Curves
Higher Diploma in Civil Engineering | CON4381 Highway Engineering
Topic 1 Geometric Alignment and Design | Page 1-26
If an occupant of a vehicle is subjected to a rapid change in vertical acceleration, discomfort will be experienced. Consequently, it is usual to place an upper limit on the vertical acceleration (normally 0.03g m/s2) that is developed on a vertical curve.
T .P .
T .P .
p
qLV
=2| |
1 .9 m, where a = vertical acceleration in m/s
2 and V = velocity in km/h.
b) Headlight sight distance
On a normal sag vertical curve, sight distance is not a problem during the day or at night provided
there is full roadway lighting. However, on unlit roads at night, the sight distance available may
be limited by headlight reach, and accordingly on the more important roads it is good practice to
provide headlight sight distance i.e. the distance that can be seen by the headlight beam should
be at least equal to the stopping sight distance for the relevant design speed. Typical
assumptions are indicated in the following figure, and in particular:
1. The height of headlight h is 0.6m.
2. The upward divergence of the light beam from the longitudinal axis of the vehicle
is 1.
T .P .
T .P .
p
qLV
h
S
Typical assumptions for calculation of headlight sight distance on sags
=
{
2| |
( + tan )
for <
( + tan )
| |for >
Higher Diploma in Civil Engineering | CON4381 Highway Engineering
Topic 1 Geometric Alignment and Design | Page 1-27
c) Vertical Obstructions
At sag vertical curves, overhead obstructions such as overpass structures, sign gantries and
overhanging trees may limit the available sight distance, particularly in those cases where it is
desired to provide greater than stopping sight distance. If these types of obstruction are likely to
be present, adequate checks should be carried out to ensure that the intended sight distance is in
fact available.
T.P.
T.P .
p
qLV
h
h
C
S
O verhead structure
Typical assumptions for calculation of vertical obstruction on sags
=
{
2| |
( 1+22
)
for <
( 1+2
2)
| |for >
where = vertical clearance to the critical edge of the structure in metres.
Use of K Values
Parabolic vertical curves are sometimes specified in terms of K values, where K is defined as the
length of vertical curve required for a 1 per cent change of grade. Thus:
LV = KA
LV = length of vertical curve in metres;
A = change of grade i.e. x100;
K = the K value appropriate to the design speed and to the particular sight distance
considerations.
Should you look for more details on the above criteria, you may help yourself by studying the
essential texts on the reference or read Garber and Hoel (2015).
p q
Higher Diploma in Civil Engineering | CON4381 Highway Engineering
Topic 1 Geometric Alignment and Design | Page 1-28
Desirable Requirements for Vertical Alignment
In addition to the specific design requirements for grades and vertical curves there are several
desirable requirements for vertical alignment that also should be satisfied to achieve safe and
consistent traffic operation:
1. A smooth grade line with gradual changes, consistent with the nature and importance of the road and with the topography is desirable. An alignment with short grades and numerous grade changes should be avoided although this type of grading is acceptable on relatively low volume local roads where it may result in significant cost savings.
2. Roller-coaster and hidden-dip alignments should be avoided.
3. Undulating grade lines involving significant lengths of momentum grades should be examined for their effect on traffic operation.
4. Broken-back grades (i.e. two vertical curves in the same direction separated by a short length of tangent grade) generally should be avoided, particularly in sags because of adverse appearance.
5. At intersections on moderate to steep grades, it may be desirable to reduce the grade through the intersection. This will considerably help vehicles performing turning movements and to reduce potential accidents.
6. On long gradients, it may be desirable in certain instances to have a steeper slope near the bottom of the hill and heighten the slope near the top, instead of using a uniform sustained grade that may only just below the maximum allowable.
7. Climbing lanes should be considered on roads carrying significant numbers of trucks on critical lengths of grades.
Co-ordination of Horizontal and Vertical Alignment
The horizontal and vertical alignment should be designed to complement each other to provide
improved safety and appearance.
Guidelines that relate specifically to safety considerations include the following:
1. The design speed of the road in both the horizontal and vertical directions should be of the same order.
2. Horizontal and vertical sight distances should be considered together. While each may be adequate when taken separately they may be deficient in combination.
3. Particularly on two-lane two-way roads the need to provide adequate overtaking opportunities may override considerations of co-ordination of alignment.
Higher Diploma in Civil Engineering | CON4381 Highway Engineering
Topic 1 Geometric Alignment and Design | Page 1-29
4. Sharp horizontal curves should not be obvious to a driver, particularly at night. This situation may be avoided if the horizontal curve leads the vertical curve. E.g. sharp horizontal curves should not be introduced near the top of a crest curve or the trough of a sag curve. On undivided roads, this requirement should be checked in both directions.
5. Provision of reverse horizontal curves in association with crest vertical curves is undesirable particularly if the horizontal curves are short, because the reverse curvature may not be obvious to the driver.
6. As far as practicable, crest vertical curves should be located away from intersections, road-rail level crossings and the like.
7. Adequate visibility should be provided at the transition between undivided and divided roads and on the approaches to intersections. In such situations if crest vertical curves cannot be avoided, they should be longer than the minimum requirement.
Guidelines that relate more specifically to appearance considerations include:
1. Desirably a horizontal curve should be longer than any associated vertical curve, and it should begin before the start of the vertical curve. In general, PIs of both curves should be near the same location.
2. A sag vertical curve should be located on the horizontal curve rather than on the adjacent tangent close to the start of the horizontal curve.
3. Short vertical curves on long horizontal curves should be avoided.
4. Rolling grades on isolated straights between curves should be avoided.
5. Short tangents between sag curves should be avoided.
6. Broken-back crest or sag curves should be avoided.
7. A disjointed effect occurs when the start of a horizontal curve is obscured by an intervening crest while the continuation of the road is visible in the distance.
8. A short sag curve on a straight is undesirable, whereas a long sag curve may provide a pleasing appearance.
REFERENCES
AASHTO. A Policy on Geometric Design of Highways and Streets 6th ed. American Association of State Highway and Transportation Officials, Washington, DC, 2011.
Garber, N.J. and Hoel, L.A. Traffic & Highway Engineering, 5th ed. Cengage Learning, 2015.
OFlaherty, C.A. (ed.) Transport Planning and Traffic Engineering. Elsevier Ltd., 1997.
Rogers, M. Highway Engineering, 2nd ed. Blackwell Publishing, 2008.
Transport Department. Transport Planning and Design Manual. HKSAR Government, December 2013.