topic1. geometric design and alignment

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.



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.



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.



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.



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]



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.



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.



Road Network Showing Different Road Classifications



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



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



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:



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.



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



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



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



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



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).



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



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



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



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



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



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



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



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



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 >



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



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.



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.

topic1. geometric design and alignment

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