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A review of some recent geometric road
standards and their application to
developingcountries
by D Kosasih, R Robinson and J Snell
The tibraw
Transpoti and Road Research Laborato~
~Jepartment of Transpoti
cr;gl~pA~ Berks
Digest RR114 1987
A REVIEW OF SOME RECENT GEOMETRIC ROAD STANDARDS AND THEIR
APPLICATION TO DEVELOPING COUNTRIES
by
D Kosasih, R Robinson and J Snell
COMPARISON OF STANDARDS
Since 1980, Australia, Britain and the United States have all made major modifications to their
recommendations for geometric design standards for rural roads (NAASRA 1980, Department of
Transport 1981, AASHTO 1984). This report reviews the research that formed the basis of the
current standards under the headings of design speed, sight distance, horizontal and vertical
alignment, and cross-section.
The three standards are all based on the concept of design speed, but the application of this differs
considerably between the standards. The AASHTO method of determining design speed is based on a
qualitative assessment of traffic volume and terrain conditions. It has the objective of achieving
consistency of standards commensurate with the function of the road, and a balance between
construction and operating costs. NAASRA introduces the concept of ‘speed environment’ related to
terrain and range of horizontal curvature along an alignment. The design speed of individual
geometric elements is related to the speed environment and, on successive elements, should not differ
by more than 10 km/h. The British design speed standard is based on overall ‘alignment constraints’
and ‘roadside friction’ values. Relaxation of standards is allowed on cost grounds, but these still
provide acceptable levels of safety and operating conditions.
The key design chart for the NAASRA standard is shown in Figure 6 from the report and Figure 7
shows the key chart for the British TD 9/81 standard.
lm, I , , A ,1 1 r
-,
,20
1!0
“.r!z.”!a( curve ,s,!”! (m)
F,g. 6 NAASRA r.lalion$htps for minimum cutva rti.$
DEVELOPING COUNTRIES
,o~:o02,6810 1214161820
.l,,”me”! ..”s(,,,”, AC km(fi f., 0“., C/w,,, .66. 8/!0
,,”,,. Clw.,$ = ,2- “,s, (60 , 28/45
Fig, 7 TD9{81 Design chart
Standards that have traditionally been applied in developing countries are also
that traffic requirements, road safety and network considerations are different
discussed. It is noted
in developing countries
I
,,
and that, in order to develop local standards, it is convenient to define the objectives of road projects
in terms of three levels of development. These are:
Level 1: to provide access;
Level 2: to provide additional capacity;
Level 3: to increase operational efficiency.
For roads whose objective is to provide fundamental access (Level 1), absolute minimum standards
can be used to provide an engineered road. The choice of standards will be governed only by such
issues as traction requirements, turning circles and any requirement for the road to be ‘all weather’.
If the object of the project is to provide additional capacity for the road (Level 2), then decisions will
need to be taken on whether or not it should be paved and on what is an appropriate structural
strength. Road width will normally be governed only by the requirement that vehicles should be able
to pass each other. It may be appropriate to design a variable width road where the cross-section is
narrow on straights, but is increased on bends or where other restrictions on sight distance apply.
It is only when the objective of a road is to increase the operational efficiency of a route (Level 3)
that standards such as those developed by AASHTO, NAASRA or the UK Department of Transport
become relevant. It is not normally practicable to apply standards such as these to roads at Levels 1
or 2. Because the requirements of roads in developing countries are different to those in the
industrialised countries where these standards were developed, the three standards should only be
applied with caution in developing countries, even to Level 3 roads.
APPLICATION OF STANDARDS
Before American, Australian or British standards are applied to Level 3 roads in developing countries,
it is necessary to review the assumptions on which the standards have been based to determine where
they are appropriate for conditions found in individual countries. To assist with this task, this report
reviews the principal assumptions in the three standards to determine which aspects of each might be
appropriate in developing countries.
Guidance is thereby given on how to adapt standards from the industrialised countries for use until
such time as specific standards have been developed that are appropriate for use in developing
countries.
REFERENCES
AASHTO, 1984. A policy on geometric design of highways and streets. Washington DC: American
Association of State Highway and Transportation Officials.
DEPARTMENT OF TRANSPORT, 1981. Road layout and geometry: highway link design.
Departmental Standard TD 9/81. London: Department of Transport.
NAASRA, 1980. Interim guide to the geometric design of rural roads. Sydney: National Association
of Australian State’ Road Authorities.
The work described in this Digest forms part of the programme carried out by the Overseas Unit
(Unit Head: Mr J S Yerrell) of TRRL for the Overseas Development Administration, but the views
expressed are not necessarily those of the Administration.
If this information is insufficient for your needs a copy of the ful[ Research Report RR114, may be
obtained, free of charge, (pre-paid by the Overseas Development Administration) on written request
to the Technical Information and Library Services, Transport and Road Research Laboratory, Old
Wokingham Road, Cro wthorne, Berkshire, United Kingdom.
Crown Copyright. The views expressed in this Digest are not necessarily those of the Department of
Transport. Extracts from the text may be reproduced, except for commercial purposes, provided the
source is acknowledged.
TRANSPORT AND ROAD RESEARCH LABORATORY
Department of Transport
RESEARCH REPORT 114
A REVIEW OF SOME RECENT GEOMETRIC ROAD
STANDARDS AND THEIR APPLICATION TO
DEVELOPING COUNTRIES
by
D Kosasih
R Robinson
J Snell
Institut Teknologi Bandung, Indonesia
Overseas Unit, Transport and Road Research Laboratory
Department of Transportation and Highway Engineering,
University of Birmingham
The work described in this Report forms part of the programme carried out for
the Overseas Development Administration, but the views expressed are not
necessarily those of the Administration
Overseas Unit
Transport and Road Research Laboratory
Crowthorne, Berkshire
United Kingdom
1987
ISSN 0266-5247
CONTENTS
Abstract
1. Introduction
2. Design speed
2.1 Driver behaviour and expectation
2.2 AASHTO
2.3 NAASRA
2.3.1 Speed environment
2.3.2 Selection of speed
environment
2.3.3 Speeds on curves
2.3.4 Side friction factor
2.3.5 Curve design speed
2.4 TD9/81
I
2.4.1 Background to the standard
2.4.2 Determining the design speed
2.4.3 Relaxation of standards
2.5 Comments on design speed
3. Sight distance
3.1
3.2
3.3
3.4
3.5
Basic considerations
Stopping sight distance
3.2.1 Recommended values
3.2.2 Driver reaction time
3.2.3 Coefficient of longitudinal
friction
3.2.4 Effect of gradient
3.2.5 Effect of trucks
Passing sight distance
3.3.1 Critical factors
3.3.2 Recommended values
Eye and object heights
Comments on sight distance
Page
1
1
1
1
3
3
3
4
4
5
5
6
6
7
7
8
10
10
10
10
10
13
14
14
14
14
15
17
17
4. Horizontal alignment
4.1
4.2
4.3
4.4
4.5
4.6
Alignment, user costs and accidents
Vehicle movement on a circular
curve
Minimum curve radius
4.3.1 Fundamental relationship
4.3.2 AASHTO
4.3.3 TD9/81
4.3.4 NAASRA
Transition curves
4.4.1
4.4.2
4.4.3
4.4.4
Shortt’s method
Superelevation run-off
method
Rate of pavement rotation
method
Other considerations
Pavement widening on curves
Comments on horizontal alignment
5. Vertical alignment
5.1 Gradient
5.2 Vertical curves
5.3 Comments on vertical alignment
6. Cross-section
6.1
6.2
6.3
6.4
6.5
Road width
Shoulder width
Pavement crossfali
Shoulder crossfall
Comments on cross-section
7. Application of standards in developing
countries
7.1 Available standards
Page
18
18
19
21
21
22
22
22
23
24
24
25
25
26
26
27
27
29
30
32
32
32
33
33
34
34
34
7.2
7.3
7.4
Considerations for developing
countries
7.2.1 Level of development
7.2.2 Traffic requirements
7.2.3 Road safety
7.2.4 Network considerations
Development of local standards
Review of assumptions
7.4.1 Design speed
7.4.2 Sight distance
7,4.3 Horizontal alignment
7,4.4 Vertical alignment
7.4.5 Cross-section
8. Summary
9. Acknowledgements
10. References
Page
35
35
35
36
36
36
37
37
’37
37
38
38
38
38
39
@ CROWN COPYRIGHT 1987
Extracts from the text may be reproduced,
except for commercial purposes, provided the
source is acknowledged.
A REVIEW OF SOME RECENT GEOMETRIC ROAD
STANDARDS AND THEIR APPLICATION TO
DEVELOPING COUNTRIES
ABSTRACT
Since 1980, Australia, Britain and the United States
have all made major modifications to their
recommendations for geometric design standards for
rural roads. This report reviews the research that
formed the basis of the current standards under the
headings of design speed, sight distance, horizontal
and vertical alignment, and cross-section. Standards
that have traditionally been applied in developing
countries are also discussed.
It is noted that traffic requirements, road safety and
network considerations are different in developing
countries and that, in order to develop local
standards, it is convenient to define the objectives of
road projects in terms of three levels of development
of the road network. These are:
Level 1: to provide access;
Level 2: to provide additional capacity;
Level 3: to increase operational efficiency.
It is only when the objectives of the road are at Level
3 that standards such as those developed in
Australia, Britain and the United States are relevant
and the principal assumptions in these standards are
reviewed to assist in their adaptation to roads in
developing countries.
1 INTRODUCTION
Geometric design is the process whereby the layout
of the road in the terrain is designed to meet the
needs of the road users. The principal geometric
features are the horizontal alignment, vertical
alignment and road cross-section. The use of
geometric design standards fulfills three objectives.
Firstly, the standards ensure minimum levels of
safety and comfort for drivers by the provision of
adequate sight distances, coefficients of friction and
road space for vehicle manoeuvres; secondly, they
ensure that the road is designed economically; and,
thirdly, they ensure uniformity of the alignment. The
design standards adopted must take into account the
environmental conditions of the road, traffic
characteristics and driver behaviour. The
interdependence between these factors and the
geometric features is summarised in Table 1.
Since 1980, Australia, Britain and the United States
have all made major modifications to their
recommendations for geometric design standards for
rural roads. This report reviews the current standards
under the headings of design speed, sight distance,
horizontal and vertical alignment, and cross-section.
The Australian standards were published by
NAASRA (1980) as an interim guide, the British code
was produced as Departmental Standard TD 9/81
(Department of Transport 1981) with subsequent
background information (Department of Transport
19W) and amendments, and the American standards
were published as a policy document by AASHTO
(19M).
A study to develop appropriate geometric design
standards for use in developing countries is being
undertaken by the Overseas Unit of TRRL. As a first
step in this work, a comparison between the recent
American, Australian and British standards has been
carried out. This Report describes the findings of this
preliminary study and discusses the potential for
applying these industrialised country standards in
developing countries.
2 DESIGN SPEED
2.1 DRIVER BEHAVIOUR AND
EXPECTATION
In design guides, a design speed for a particular road
classification is usually selected according to the
terrain and traffic volume. To provide consistency of
the design elements, general controls for the
horizontal alignment, the vertical alignment and the
combination between them are given. It is also
recommended that the design speed chosen should
be consistent with the speed a driver is likely to
expect. It is this issue which causes difficulty when
applying the standards since, except for reference to
typical speed distributions of a general nature on
similar facilities already built, designers generally have
insufficient information available to them to take
account of the actual behaviour and speed
expectations of drivers on the different alignment
elements along a section of road.
Designing according to the design elements
permitted by a specified design speed does not
necessarily ensure alignment standards consistent
with driver behaviour. This is because drivers tend to
vary their speeds along the road especially when
negotiating different horizontal curves.
1
TABLE 1
Driver, vehicle and road characteristics in geometric design standards
Geometric design standard
Driver characteristics Vehicle characteristics Road characteristics
considered considered considered
Minimum safe stopping Perception – reaction time Layout of controls,
distance
Skid resistance of road
braking systems, tyre surface, design speed
condition, tread pattern
Minimum safe passing Judgement of gap Acceleration capability Design speed
distance availability and vehicle
capability
Driver eye height Physiology Dimensions —
Object height — Dimensions for passing —
Horizontal geometry
Superelevation (e”,X) Consistency of steering — Urban/rural environment,
effort on successive climatic conditions, open
curves highway lintersection,
degree of curvature
Coefficient of friction Comfort — Skid resistance of road
(fmax) surface, open highwayl
intersection
Radius (R~i”) — — Design speed, open
highway lintersection
Transition curves Behaviour on entering — Appearance of
curves, comfort carriageway edges, design
speed
Phasing Response to visual defects — Appearance, creation of
and hazards visual defects and
hazards, design speed
Vertical geometry
Crest curves
Sag curves
Gradients
Speeds during night-time
compared with day-time
comfort
Comfort
Behaviour on approach to
gradients
Headlight height,
proportion of stopping
distance illuminated by
headlights
Headlight height, beam
divergence, distance
illuminated by headlights
Passenger car and truck
performance,
powerlweight ratio of
design vehicle, dimensions
Drainage, appearance of
road, design speed
Drainage, appearance of
road, design speed
Crawler lanes provide
overtaking opportunity,
design speed
2
TABLE 1–continued
~ ‘rive;;:=‘ehic:;;::zristics Road characteristics
considered
Cross-section
Number of lanes
Lane width
Lateral clearance
Shoulder width
Median width
Crossfall
Vertical clearance
Comfort, ability to
manoeuvre in traffic
stream and maintain
desired speed
Sensitivity to restricted
width
Sense of restriction
Sense of restriction
Sense of well-being
—
Sense of restriction
2.2 AASHTO
AASHTO continues to use the conventional
definition of design speed: ‘the maximum safe speed
that can be maintained over a specified section of
highway when conditions are so favorable that the
design features of the highway govern’. Since the
standard caters for freeways, rural and urban arterial
roads, collector roads and streets, and local roads
and streets, a range of design speeds is used. Design
speeds recommended for local rural roads range from
20 to 50 mph whilst, for rural collectors, the range is
20 to 60 mph, both dependent on terrain and traffic
volume. Rural arterials should have design speeds of
50, 60 or 70 mph in mountainous, rolling or level
terrain respectively. For rural freeways the normal
design speed is 70 mph which may be reduced to 60
or 50 mph in difficult terrain, this being consistent
with driver expectancy.
AASHTO recommends that a design speed of
70 mph should be used on main roads to ensure an
adequate design in the future should the current
55 mph speed limit in US be removed.
In recommending the above values, the standard
makes the following points:
(i) Speed is governed by the traffic volume and
physical limitations of the road, not the
importance of the road.
Dimensions of design
vehicle
Dimensions of design
vehicle
Vehicle/barrier collision
—
Dimensions of design
vehicle
Urban/rural environment,
design speed
—
Nature of lateral
obstruction
Urban/rural environment,
type of facility
Type of facility, terrain,
urban/rural environment,
appearance of
carriageway edges
Drainage, type of facility
Future resurfacing
(ii)
(iii)
(iv)
2.3
Higher traffic volumes may justify higher
standards, since savings in operating costs can
offset the increased construction costs.
Design speed establishes minimum standards
for safe operation, but there should be no
restriction on the use of more generous designs
if they are justified economically.
A relevant consideration in selecting design
speeds is the average trip length. Standards
provided on long lengths of a highway for
longer trip lengths, should be as consistent as
possible throughout and provide a good
level-of-service.
NAASRA
2.3.1 Speed environment
To some extent, these standards are based on a field
study of speeds on curves. The study was directed
at investigating the relationship between vehicle
speeds and the geometric properties of horizontal
curves on two-lane rural roads (McLean and Chin
Lenn 1977, McLean 1978 a, b, c, 1979). In order to
take driver behaviour into consideration in the
standards, two different speeds were recognised;
namely speed environment and design speed. Speed
environment is the desired speed of the 85th
percentile driver and, as such, is the 85th percentile
3
speed on the longer straights or large radius curves
of a section of road where the speed is
unconstrained by traffic or alignment elements.
Design speed is defined as the 85th percentile speed
on a particular geometric element, which is used for
example to correlate curve radius, superelevation,
friction demand, etc. Design speed varies along the
road depending on the speed environment, the
ho~izontal curve radius and, to some extent, on the
gradients.
I
Select nominal
P
———
speedenvironment 1
I I
I I
n
I
I
DETERMINE
CHECK– Should be of
TRIAL
the same order unless
ALIGNMENT
very long straights occur
I
1 I
I
I
o
Predict 85th percentile
curve speeds
= curve design speeds
a
*
check consistency
and sight distance
c
Modify if
necessarv
nSatisfactory
alignment
I
I
NAASRA introduced an iterative process in the
geometric design as shown in the flow chart in
Figure 1. The most important part of this process is
the consistency checks which ensure that the design
speeds of successive geometric elements should not
differ by more than about 10 km/h. This agrees with
the recommendation by Leisch and Leisch (1977) that
the change should not be more than 10 mph
(15 km/h). On two way roads, consistency is
checked for travel in both directions.
2.3.2 Selection of speed environment
The speed at which a driver will choose to travel a
section of road is generally a compromise between
the maximum speed at which he would be prepared
to travel to reach his destination and the perceived
level of risk which is seen to increase with increased
speed. On straight open roads, road features will
present little risk and the choice of speed will be
determined largely by drivers preference and vehicle
capabilities. The presence of features which a driver
perceives as contributing to risk tends to restrict the
speed of travel chosen. Such restrictions might arise
from horizontal curvature, gradient, pavement width
and condition, and the volume and nature of other
traffic. Desired speeds of travel, and hence speed
environment, therefore, whilst being defined in terms
of unconstrained geometric elements, will be affected
by overall standards of geometry and the terrain
through which the road passes. Speed environments
recommended by NAASRA for single carriageway
roads are given in Table 2. These reflect the lower
speed environment values associated with more
difficult terrain resulting in higher values of bendiness
on sections of road.
TABLE 2
NAASRA speed environment value as a function of
overall geometric standards and terrain type for
single carriageway rural roads for use when geometry
is constrained.
Approximate
range of
horizontal curve
radii (metres)
Less than 75
75–300
150–500
Over 300–500
Over 600–700
Speed environment (km/h)
Terrain type
Flat I Undulating \ Hilly
75
90 85
100 95
115 110
120
Mountainous
70
* The more consideration given
to consistency at the trial
alignment stage, the fewer will
be the modifications required
later
Fig. 1 NAASRA alignment selection procedure
4
2.3.3 Speeds on curves
The NAASRA standards are based on the following
research results. From field observations, a good
correlation was found between curve speeds and
approach speeds of individual vehicles. Curve speed
is defined as the speed at the mid point of the curve,
whereas approach speed is the speed measured 100
to 400 metres before the entrv tangent point. In
general, the vehicles approaching at high speeds
showed a greater speed reduction on curves
compared to the vehicles approaching at low speeds.
There are at least two reasons for this. FirstIV, drivers
adopt much higher speeds on tangent sections than
the design speed; and secondlv, drivers are not
confident of negotiating curves at high speeds. A
tvpical relationship between curve and approach
speeds of individual cars is given in Figure 2 (McLean
1978 a).
/’
/
/ ●“/’
oL-~
o 60 80 100 120
VA = approach speed (km/h)
Fig. 2 TVpical relationship from Australia betvveen
curve speed and approach speed for cars
For curves with speed standards (as defined below)
greater than about 90 kmlh, the 85th percentile car
operating speeds on curves tended to be less than
the curve speed standards. For curves with lower
speed standards, the 85th percentile car operating
speeds tended to be in excess of the curve speed
standards. This is shown in Figure 3 (McLean
1978 a). The curve speed standard is defined as the
maximum speed (Vd) at which vehicles can negotiate
the curve without exceeding the earlier NAASRA
(1970) side friction factors according to:
e+f = Vd2
127R
where e = superelevation
f = side friction factor
vd = maximum (design) speed km/h
R = curve radius, metres.
Considering the findings above, for curve speed
standards less than 90 km/h, drivers tended to travel
at speeds which are much faster than the design
speed on the tangent sections and still above the
design speed on the curves. For curve speed
standards greater than 90 km/h, drivers might travel
at about the design speed on the tangent sections,
but they reduced their speeds below the design
speed when entering the curves. This suggested
that, for design speeds greater than 90 km/h, driver
behaviour tended to be more conservative relative to
the design assumptions. Hence the earlier NAASRA
curve standards were retained for design speeds in
excess of 90 km/h in order to provide a high level of
safetv and comfort for drivers.
2.3.4 Side friction factor
It could be deduced from Figure 3 that, for the 85th
percentile curve speeds less than about 90 km/h, the
corresponding side friction factors were in excess of
the values assumed previously for design purposes;
whereas for speeds higher than 90 kmlh, the side
friction factors were less than assumed for design, as
shown in Figure 4 (McLean 1978 a).
140
mc.-
% 80
k
n
0
Vc (85) = vd
L“”
8’
●
●
.*
●
*
●
/
/
I
$, I
0 L-- I 1 1 1 I I 1 1 I I
0 40 60 80 100 120 140
Curve speed standard (km/h) Vd
Fig. 3 Relationship between observed 85th percentile
curve speed and curve speed standard for cars
in Australia
The proposed design values for side friction factors
derived from Figure 4 are discussed in more detail in
Section 4.3
2.3.5 Curve design speed
The variation in observed 85th percentile speed on
curves was explained bv the following regression
equation:
V8S=53.8+ 0.464 VE–3.26C+0.0848C2
where VE5= 85th percentile curve speed km/h
VE = speed environment km/h
C = curvature (1000/radius, R) (metres)’1
5
However for curves of radius below 70 metres (C>
approximately 14), this equation was not a
satisfactory representation of the observed
relationship. An improved representation was
provided by using four separate linear regression
equations of speed on curvature for the data grouped
according to four speed environment ranges. These
four equations were then used as a basis to derive
the family of curves relating 85th percentile car
speeds to speed environment and curvature as
shown in Figure 5 (McLean 1978 b). This family of
.
.
. .
.
..
.
.
.*.
.**.
. .
:* :
.0 *:
●
●. . ●
.*. :
.AA5RA(1,~=~._
Side friction factor– . ~ .::
Speed design relationship n. “
. . .
o 20 40 60 80 100 120
85th percentile car speed (km/h)
Fig. 4 Relationship beween f85 and 85th percentile
speed used as basis for NAASRA design criteria
1
c
‘; 100
u
II
Design
speed
50
60.
70
80
90
100
110
120
130
curves can be combined with superelevation rates
and maximum side friction factors to give values of
85th percentile curve speed for specified speed
environments and curve radii shown in Figure 6.
2.4 TD9/81
2.4.1 Background to the standard
This standard is based on a speed-flow-geometry
study which led to the development of both speed
distribution curves and a relationship between mean
operating speed and geometric features. The concept
of desig~ speed is still used, but in a more flexible
way than previously.
120 ,V85=115– 3.94 c
-;F< ‘“’;;”a: ;6 ,
- ‘=~-o, c
70 69-0.715 C
b
60~
60-0,360 C
I
Desired speed (km/h)
~ o~
o 5 10 15 20 2
C = curvature = 1000/R (m-l)
Fig. 5 Relationships used for predicting curve speeds
in Australia
I 20
Max. side friction s uperelevation Q“ ~
coefficient (sealed
pavement)
0.35
0.33
0.31
0.26
0.18
0,12
0.12
0.11 A
0.11 A
1
110
-
-1 Speed environment, km/h
I
7/ v — 90
- ● #-
-- -80
#
Y- -
. Example:
—-70
---- —
Speed environment 100 km/h
Max. superelevation 0.08
~___ -
/
Curve design speed 84 km/h
-60 Min. radius 183m
y I 1 1 I I I I I I I 1 1 I 1 I I 1 I I I 1 1 1
--40 50 60 70 80 90 100 150 200 300 400 500 600 700
Horizontal curve radius (m)
Fig. 6 NAASRA relationships for minimum curve radius
Observations suggested that mean operating speed
was a function of traffic volume and geometric
features. In order to derive geometric design
standards, speeds of light vehicles at the nominal
traffic volume of 100 vehicles per hour were used.
These mean free operating speeds on dual and single
carriageways were expressed by the following
equations:
V~(D–wet)=103.4*– B + HF
10 4
VL(S– Wet) =73.6g+ l.l CW+VISi–5
-{
2+1
-}
-:-{%++} ‘w+’ Cw
where VL(D – wet) = mean free operating speed of
light vehicles on dual
carriageways in wet
conditions (km/h)
V~(S – wet) = mean free operating speed of
light vehicles on single
carriageways in wet
conditions (km/h)
I = number of intersections, laybys and non-residential
accesses (total for both sides)
per km
B = bendiness (degrees/km)
CW = carriageway width (metres)
VW = verge width (metres, including
metre strips)
VISI = harmonic mean visibility
HF = sum of the falls (metres/km)
HR = sum of the rises (metres/km)
H =total hilliness (HR + HF)
(metres/km)
NG = net gradient (HR – HF)
(metres/km)
These equations were rationalised to the following
single equation:
VL~(wet) = 110 – Ac – Lc
where VLW(wet) = mean free operating speed in
wet conditions.
Ac = alignment constraint (see 2.4.2)
Lc = layout constraint (see 2.4.2)
The effect of hilliness is excluded from initial
assessments of design speed and specific
adjustments can be applied during the detailed
design of the road.
In the standard, this equation is presented in the
form of a chart as shown in Figure 7. From the
speed distribution curves in Figure 8 (Kerman 1980),
it was found that the ratios 99th/85th, 85th/50th
percentile spee~s were approximately constant at the
value of about {2 for each road type. Nominal
design speeds were then arranged on the basis of
this ratio and the values of 120, 100, 85, 70, etc,
km/ h were adopted. Since the 85th percentile speed
is normally adopted as the design speed, an increase
or decrease of one design speed step means that the
design is based on the 99th or 50th percentile speed
respectively. For example, on a rural single
carriageway road with a nominal 85th percentile
design speed of 85 km/h, provision for 100 km/h
geometries would cater for the 99th percentile speed,
whilst provision for 70 km/h geometries would cater
for only the 50th percentile speed. Hence the
implication of raising or lowering design speed for a
particular geometric element is clear.
2.4.2 Determining the design speed
TD 9/81 adopts an iterative approach to design. The
first step is to design a trial alignment for an
assumed design speed. For this design the alignment
constraint (Ac) is determined from:
For dual carriageways: AC= 6.6 + B
10
For single carriageways: AC= 12 – VISI + 26
60 45
The layout constraint, Lc, is then determined from
Table 3.
Mean free operating speed, and hence design speed
(ie the 50th and 85th percentile speeds under wet
road conditions), are determined by entering these
values of AC and LC into Figure 7. There are two
categories A and B, for each design speed
representing upper and lower bands. Whilst
relaxation of standards for a given design speed is
permitted for both categories on individual elements
of the design, there are restrictions on the relaxations
in category A because of the lower values of
alignment and layout constraints and hence higher
85th percentile speeds.
The trial design speed and that determined from
Figure 7 are then compared to identify locations
where elements of the initial design may be relaxed
to achieve cost or environmental savings, or
conversely where the design should be upgraded to
match the calculated design speed.
The design speed is then used to determine the
design standards from Table 4, which shows
desirable and absolute minimum values for each
the main elements.
2.4.3 Relaxation of standards
of
● For dual 3 lane motorways; lower basespeedsare applicable
for dual 2 lane motoways and for dual 2 and 3 lane all
purposeroads.
Desirable minimum values generally cater for vehicles
at the 85th percentile speed at the normally accepted
high levels of safety and driver comfort, whilst
V5Q ~~~ ’85 wet
1 r
100
90
80
70
60
Layout constraint Lc km/h Design speed
J
120~
A
-_
120km/h
% -w
-~
100 —
\
\
100km/h
\
\
\
*
85 —
85km/h
straight roads or where 70 —
—— 70km/h
1 1 11 1 1 I I I I I
B
60 —
o 2 4 6 8 10 12 14 16 18 20
Alianment constraint AC.
kmlh for Dual Clwavs = 6.6 + BI1O
Single ClwaVs = 12 – VIS1/60 + 20145
Fig. 7 TD9/81 Design chart
E
30 50 70 90 110 130 150
V = Speed (km/h)
Fig. 8 Distributions of car journey speeds in UK
absolute minimum values for a particular design
speed are identical to desirable minimum values for
the next lower design speed step.
For the higher vehicle speeds, relaxation of standards
to absolute minimum levels can imply design levels of
safety and comfort below what has normally been
accepted for design in the past. However the
research leading to TD9/81 has shown that these
high design levels of safety can be lowered to a
limited extent without affecting accident rates.
Further departures below absolute minimum levels
may be allowed in exceptional circumstances. These
further departures require detailed consideration of
safety implications since, whilst they will not create
hazards, the margin between what is considered safe
and hazardous will, in these cases, be significant.
2.5 COMMENTS ON DESIGN SPEED
AASHTO recommends ranges of design speeds for
the different road classifications, depending mainly
on terrain and traffic volume, and that the standards
used should be consistent on long lengths of road.
Consideration should be given to the economic tradeoffs between the increased construction costs of
higher standards and the savings in operating costs
which result. Most of these savings in operating
costs will be savings in travel time from higher
speeds of travel.
In general, time and vehicle operating costs can be
represented by the following equation:
C=a+ (b+d) +c~
v
where C =
v=
a, b,c=
d=
unit operating cost per km
operating (travel) speed, km/h
coefficients of vehicle operating costs
coefficient representing the value of
time per vehicle
The above equation can be used to determine a
minimum operating cost speed and will give very
different values of this speed depending on whether
time is valued in the road appraisal. It would seem
logical to provide standards which encourage freeflow speeds in the vicinity of these minimum
operating cost speeds.
The new approaches in both NAASRA and TD 9/81
involve a check of initial designs against an overall
measure of speed to achieve consistency and reflect
8
TABLE 3
TD9/81 Layout constraint– Lc (km/h)
Road type S2 WS2 D2AP D3AP D2M D3M
dual dual dual dual
Carriageway width (excl. metre strips) 6m 7.3 m 10 m 7.3 m 11 m 7.3 m* 11 m*
Degree of access and junctions H M M L M L M L L L L
Standard verge width 29 26 23 21 19 17 10 9 6 4 0
1.5 m verge 1311281251231
0.5 m verge 33 30
Notes: L = Low access numbering 2 to 5 per km
M = Medium access numbering 6 to 8 per km
H = High access numbering 9 to 12 per km
*
= Hard shoulder is recommended
S2 = Two-lane single carriageway
WS2 = Two-lane wide single carriageway
D2AP = Two-lane all purpose dual carriageway
D3AP = Three-lane all purpose dual carriageway
D2M = Two-lane motorway dual carriageway
D3M = Three-lane motorway dual carriageway
TABLE 4
TD9/81 Design Standards
Design speed kmlh
STOPPING SIGHT DISTANCE m
Al Desirable Minimum
A2 Absolute Minimum
HORIZONTAL CURVATURE m
61 Minimum R * without elimination of Adverse
Camber and Transitions
62 Minimum R * with Superelevation of 2.5%
B3 Minimum R * with Superelevation of 3.5%
B4 Desirable Minimum R with Superelevation of 5%
B5 Absolute Minimum R with Superelevation of 7%
B6 Limiting Radius with Superelevation of 7V0 at
sites of special difficulty (Category B Design
Speeds only)
VERTICAL CURVATURE
Cl FOSD Overtaking Crest K Value
C2 Desirable Minimum * Crest K Value
C3 Absolute Minimum Crest K Value
C4 Absolute Minimum Sag K Value
OVERTAKING SIGHT DISTANCE
D1 Full Overtaking Sight Distance FOSD m
120
295
215
2880
2040
1440
1020
720
510
*
182
100
37
*
100
215
160
2040
1440
1020
720
510
360
* Not recommended for use in the design of single carriageways
400
100
55
26
580
85
160
120
1440
1020
720
510
360
255
285
55
30
20
490
70
120
90
1020
720
510
360
255
180
200
30
17
20
410
60
90
70
720
510
360
255
180
127
142
17
10
13
345
50
70
50
510
360
255
180
127
90
100
10
6.5
9
290
@lR
5
7.07
10
14.14
20
28.28
—
9
driver expectations along a section of road. This then
allows some variation in design speed or standards
for the individual elements to achieve cost effective
designs, at the same time taking into account
observed driver behaviour on the individual elements.
[n the NAASRA standards, speed consistency is
provided by the concept of a speed environment
related to the terrain and range of horizontal
curvature along the road. A family of relationships
has been developed between speed environment and
design speed for horizontal curves which, together
with the criterion that design speed on successive
elements should not differ by more than 10 km/h,
ensures overall consistency with regard to driver
expectations and safe efficient design of individual
elements.
Similarly, in TD 9/81, an overall design speed is
determined from the alignment and layout frictions
along a road and variation in provision of standards
on individual elements is allowed to a prescribed
extent. By developing a unique relationship between
design speed steps and speed distributions, and from
studies of accident rates within the margin that exists
between the traditional interpretations of safe and
unsafe design, relaxations of standards are now
possible which are acceptable in both safety and
level-of-service terms.
3 SIGHT
3.1 BASIC
DISTANCE
CONSIDERATIONS
The driver’s ability to see ahead contributes to safe
and efficient operation of the road. Ideally, geometric
design should ensure that at all times, any object on
the pavement surface is visible to the driver within
normal eye-sight distance. However, this is not
usually feasible because of topographical and other
constraints, so it is necessary to design roads on a
basis of lower, but safe, sight distances.
There are two principal sight distances which are of
particular interest in geometric design.
Stopping sight distance: If safety is to be built into
the road, then sufficient sight distance should be
available for drivers to stop their vehicles prior to
colliding with an unexpected object on the
pavement.
Passing sight distance: If operational efficiency is
to be built into the road, for higher traffic volumes,
then lengths of road with sufficient sight distance
may have to be provided for drivers to overtake
slower vehicles safely.
3,2 STOPPING SIGHT DISTANCE
3.2.1 Recommended values
Itis important that, on all engineered roads,
sufficient forward visibility is provided for safe
stopping on vertical and horizontal curves throughout
the length of the road. The derivation of stopping
sight distance is based on assumed values for total
driver reaction time and rate of deceleration, the
latter expressed in terms of the coefficient of
longitudinal friction.
D, = ——R,.V = $
3.6 2%.f
where Ds = stopping sight distance, metres
RT = total driver reaction time, seconds
V = design speed, kmlh
f = coefficient of longitudinal friction.
Tables 5, 6, and 7 show the minimum stopping sight
distances recommended by AASHTO, TD 9/81 and
NAASRA respectively.
The three standards employ different stopping sight
distances depending on the values of total driver
reaction time, coefficient of longitudinal friction and
vehicle speed assumed. These values are usually
determined from experimental studies related to
criteria such as safety, comfort and economics.
3.2.2 Driver reaction time
Driver reaction time consists of two components:
perception time and brake reaction time. Perception
time is the time required for the driver to perceive
the hazard ahead and come to the realisation that
the brake must be applied. This depends on the
distance to the hazard, the physical and mental
characteristics of the driver, atmospheric visibility,
types and condition of the road and colour, size and
shape of the hazard.
Brake reaction time is the time taken by the driver to
actuate the brake after the decision to brake. This
depends on the physical and mental characteristics of
the driver, the driver position and layout of the
vehicle controls.
Johansen (1977) made a detailed study of driver
reaction time. He defined total driver reaction time as
the time which elapses from the moment a signal is
perceived until the moment the driver initiates
preventative action. He described the psychological
and physiological processes involved as illustrated in
Figure 9. However, quantitatively, whilst it is
relatively easy to carry out controlled experiments
under alert laboratory conditions to measure driver
reaction time, the relationship between this time and
that which would obtain under non-alerted road
conditions, where the perception of hazards on the
road ahead is but one of a number of driver tasks, is
difficult to determine. Also, it is easier to observe
total reaction time rather than to measure separately
its component processes.
Most of the limited number of field studies have
shown that total driver reaction time varies from
about 0.5 to 1.7 seconds. At high speeds, the values
10
TABLE 5
Stopping sight distances recommended by
Design
Speed
(mph)
20
25
30
35
40
45
50
55
60
65
70
AASHTO
Assumed Brake Reaction
Speed for
Condition ~me
(mph) (see)
20–20 2.5
24–25 2.5
28–30 2.5
32–35 2.5
36–40 2.5
40–45 2.5
4–50 2.5
48-55 2.5
52–60 2.5
55–65 2.5
58–70 2.5
Driver eye height (feet)
Object height (feet)
Distance
(ft)
73.3– 73.3
88.0– 91.7
102.7–1 10.0
117.3 –128.3
132.0–146.7
146.7–165.0
161 .3–183.3
176.0–201.7
190.7 –220.0
201 .7–238.3
212.7–256.7
design
speed
(km/h)
50
60
70
85
100
120
Coefficient
of Friction
f
0.40
0.38
0.35
0.34
0.32
0.31
0.30
0.30
0.29
0.29
0.28
total driver
reaction time
(seconds)
2.0
2.0
2.0
2.0
2.0
2.0
driver eye height (metres)
object height (metres)
Stopping
Sight
Distance
for Design
(ft)
125–1 25
150–150
200–200
225-250
275–325
325–400
400–475
450–550
525–650
550–725
625–850
3.5
0.5
TABLE 6
Stopping sight distances recommended by TD 9/81
stopping sight distance
coefficient
of friction desirable min. * absolute mint
fwet (metres) (metres)
0.25 70 50
0.25 95 70
0.25 120 95
0.25 160 120
0.25 215 160
0.25 295 215
1.05–2,00 1.05–2.00
0.26–2.00 0.26–2.00
Notes:
* Based on 85th percentile speeds (design speeds)
tBased on 50th percentile speeds (one step down from the given design speeds) or based on a coefficient of
friction of 0.375
of this time are less than those at low speeds. This is
because fast drivers are usually more alert. It is also
expected that drivers will be more alert on roads in
difficult terrain and so the reaction time in this
situation is likely to be less than that in rolling or
level terrain. Johansen suggested a total driver
reaction time of about 0.5 seconds in situations
where drivers are keenly attentive and a time of 1.5
seconds for normal driving.
The AASHTO standard for total driver reaction time
is 2.5 seconds which represents the time used by
nearly all drivers under the majority of road
conditions. Total driver reaction time recommended
in TD 9/81 standards is 2.0 seconds which provides
a limited margin of safety over the field study figure.
NAASRA recommends total driver reaction time of
2.5 seconds as a standard value and 1.5 seconds as
an absolute minimum value. The latter value should
11
design
speed
(km/h)
50
60
70
80
90
100
110
120
TABLE 7
Stopping sight distances recommended by
NAASRA
driver eye height (m)
object height (m)
coefficient
of friction
fwe,
0.65
0.60
0.55
0.50
0.45
0.40
0.37
0.35
stopping sight distance (metres)
normal design
R,=2.5 sec
D,
50
65
85
105
140
170
210
250
(1)
1.15
0.20
1.4 Ds
70
90
120
150
200
240
290
350
(2)
1.15
0
constrained situations
R,=2 sec.
45
60
75
95
120
(3)
1.15
0.20
Rt=l.5 sec.
35
50
65
(4)
1.15
0.20
Notes:
(1) = Standard values for stopping sight distance
(2) = Values used in less constrained budget situations or in easier terrain
(3) = Adopted as manoeuvre sight distance
(4) = Absolute minimum values for stopping sight distance
Visible Psychological Physiological Psychological Physiological
signal process process process process
x v a b c d e f 9
Attention Sensation Perception Movement Initiation
and decision
Total driver reaction time
commonlv defined
I
Total driver reaction time
better defined I
x : Stimulus (signal, obstacle) visible (audible, etc) to a normal driver
V : Driver attention to the stimulus
a : Stimulation of the sense organ
b : Transmission of the sensation bv the senorv nerve and the
initiation of the brain processes
c : Identification of the obstacle
d : Interpretation of the obstacle
e : Decision-making to avoid the obstacle
f : Transmission of brain impulses bv the motor nerves
9 : Stimulation of the muscles and the initiation of movements
Fig. 9 Total driver reaction time
12
be used only if drivers are expected to be driving in
conditions which lead to alertness and the
carriageway is sufficiently wide to provide reasonable
space for evasive action.
NAASRA also recommends the use of ‘manoeuvre
site distance’ to achieve cost effective designs of
vertical curves in difficult situations. This distance
ensures that the driver can perceive a hazard on the
road ahead in sufficient time to take evasive action
through lateral manoeuvring, rather than stopping the
vehicle. Reasonable manoeuvre times from
observation vary from about 3 seconds at a
horizontal alignment design speed of 50 km/h to 5
seconds at 100 km/h. The resulting manoeuvre site
distances, which are shown in Table 8, are close to
values for stopping sight distances based on a driver
reaction time of 2.0 seconds.
TABLE 8
Manoeuvre sight distances recommended by
NAASRA
design speed
(km/h)
derived manoeuvre manoeuvre sight
time (seconds) distance (metres)
50
60
70
80
90
100
3.2
3.6
3.9
4.3
4.8
5.6
45
60
75
95
120
155
The NAASRA manoeuvre site distance can be
contrasted with the AASHTO ‘decision sight
distance’ which has been introduced to allow for
situations where the normal stopping sight distances
are inadequate. This may be appropriate in situations
when complex or instantaneous decisions,
unexpected or unusual manoeuvres are required, and
when information is difficult to perceive. Such
locations might be at interchanges, intersections,
changes in cross-section, or where drivers in heavy
traffic need to perceive information from a variety of
competing sources. The provision of the longer sight
distance at these critical locations will ensure that
drivers can safely
(a) detect and recognise these hazards or information
sources,
(b) decide and initiate an appropriate response and
(c) manoeuvre his vehicle accordingly.
Times for these components of decision sight
distances range from (a) 1.5 to 3.0 seconds. (b) 4.2
to 7.0 seconds. (c) 4.0 to 4.5 seconds, resulting in
decision sight distances ranging from 10.2 to 14.5
seconds depending on design speed. These distances
are at least twice the normal stopping sight
distances.
3.2.3 Coefficient of longitudinal friction
The determination of design values of longitudinal
friction (f) is complicated because of the many
factors involved. It is, however, known that f values
are a decreasing function of vehicle speed, except
under the most favorable road surface textures.
Coefficient of longitudinal friction is measured using
either the sideways-force machine (SCRIM) or the
portable skid pendulum. The main factors affecting
the friction between the tyres and the road surface
are:
(i)
(ii)
(iii)
(iv)
Road surface macrotexture: rough macrotexture
is required to maintain skidding resistance at
higher speeds.
Road surface microtexture: harsh microtextures
of surfacing materials are important to provide
good skid resistance as they will puncture and
disperse the thin film of water remaining after
removal of the bulk water by the macrotexture
and tyre tread.
Road surface condition: wet pavements are
assumed when deriving values for design
purposes.
Tyres: a good tread pattern provides escape
channels for bulk water and a radial ply
increases contact area; tyre stiffness is also a
factor.
If comfort for vehicle occupants is considered to be
the sole criterion, f values greater than about 0.5
should not be used as decelerations (f. g) of 0.5g
result in unrestrained passengers sliding from their
seats. In normal driving, such values of f would only
be generated in emergency braking. For design
purposes, it is important that no loss of control of
the vehicle occurs during stopping and lower f values
are therefore desirable.
The design values of f used by AASHTO, shown in
Table 5, are generally conservative since they include
most of the curves shown in Figure 10(b). The range
of speeds assumed for design in Table 5 are based
on average running speeds for low traffic volume
conditions (AASHO 1965) at the lower extreme, and
design speed at the higher extreme. This reflects
current observations that many drivers travel as fast
on wet pavements as on dry.
Constant f values were adopted in the TD 9/81
standards with a value of 0.25 for desirable minimum
and 0.375 for absolute minimum stopping sight
distances for the 85th percentile vehicle speed. The f
value of 0.25 is slightly less than the minimum target
value of pavement skidding resistance of 0.30 for
straight sections and large radius curves proposed by
TRRL (Salt and Szatkowski 1973) and shown in
Table 9, whilst the f value of 0.375 is considered
acceptable for retaining vehicle control in stopping
on wet normally textured surfaces.
13
0%
1o%
40%
60%
90%
100%
o 10 20 30 40 50 60
Speed of vehicle (mph)
(a) Skid resistanceof pavement
(basedonGermanvalues)
I
— Test data
--- Extrapolated I
II
o.a
O.J
0.6
0.5
0.4
0.3
0.2
Lo 30 40 50 60 JO
Fig. 10
14
Speed of vehicle (mph)
(b) Skid resistancefor varioustyre and
pavementrenditions
Variation in coefficient of friction with vehicle
speed in United States
NAASRA adopted relatively high f values as shown
in Table 7. These were based on the tests conducted
by the Australian Road Research Board (McLean
1978 c), ranging from 0.65 at 50 km/h design speed
down to 0.35 at 120 kmlh, due consideration having
been given to road surface polishing, the reduction in
wet skidding resistance with increasing speed, and
the need for vehicle control in stopping.
3.2.4 Effect of gradient
Shorter braking distances are required on uphill
grades and longer distances on downhill grades as
follows:
Braking distance = ~ metres
254(f~G)
where V = design speed, kmlh
f = coefficient of longitudinal friction
G = gradient, Yo, positive if uphill
negative if downhill
For two-lane roads, sight distances are longer on
many downgrades than on upgrades, so that the
above correction is provided automatically.
3.2.5 Effect of trucks
Trucks generally require longer distances to stop for
a given speed than cars, but this is offset by the
higher eye height of truck drivers and hence their
better visibility and earlier perception of potential
hazards. Truck speeds on crest curves are also
generally lower than the speeds of cars. No
adjustment of the stopping sight distance standards
is normally considered for trucks. However, where
there is a combination of steep downhill grade and
horizontal curvature, higher values than the minimum
standards should be used.
3.3 PASSING SIGHT DISTANCE
3.3.1 Critical factors
Factors affecting passing sight distance are the
judgement of overtaking drivers, the speed and size
of overtaken vehicles, the acceleration capabilities of
overtaking vehicles, and the speed of oncoming
vehicles. Driver judgement and behaviour are
important factors which vary considerably among
drivers. For design purposes, the passing sight
distance selected should be adequate for the majority
of drivers.
Passing sight distances are determined empirically
and are usually based on passenger car requirements.
On average, heavy commercial vehicles take about
four seconds longer than cars to complete the
overtaking manoeuvre. Nevertheless, it is unusual for
passing sight distance to be based on commercial
vehicle needs, except when the proportion of trucks
in the traffic stream is very high. Apart from the
TABLE 9
Minimum values* of side frictional coefficient (SFC) for different sites, proposed by TRRL
for roads in the United Kingdom
SITE
Al
(very difficult)
A2
(difficult)
B
(average)
c
(easy)
DEFINITION
(i) Approaches to traffic signals on
roads with a speed limit greater
than 40 mile/h (64 km/h)
(ii) Approaches to traffic signals,
pedestrian crossings and similar
hazards on main urban roads
(i)
(ii)
(iii)
(iv)
Approaches to major junctions on
roads carrying more than 250
commercial vehicles per-lane per
day
Roundabouts and their approaches
Bends with radius less than 150 m
on roads with a speed limit greater
than 40 mile/h (64 km/h)
Gradients of 5% or steeper, longer
than 100 m
Generally straight sections of and
large radius curves on:
(i) Motorways
(ii) Trunk and principal roads
(iii) Other roads carrying more than
250 commercial vehicles per lane
per day
(i) Generally straight sections of
lightly trafficked roads
(ii) Other roads where wet accidents
are unlikely to be a problem
SFC (at 50 km/h)
Risk Rating~
1
0.30
0.30
2
9.35
).35
3
0.40
0.40
4
0.45
0.45
0.45
5
).50
D.50
8
0.65
0.65
9
D.7C
10
).75
Notes:
*
= Minimum value is defined as the mean summer SFC (averaae of three readings taken during the months
May–September) in a year of normal weather conditions. -
t = Risk ratin9 is relative classification based on accident rates.
extra expense that this would involve, commercial
vehicle drivers have greater visibility ahead because
of their higher eye height and hence are able to
judge sooner and better whether a gap is suitable or
not for overtaking, thus partially offsetting any
additional overtaking length that might be required.
3.3.2 Recommended values
The minimum passing sight distances recommended
by AASHTO, TD 9/81 and NAASRA are given in
Tables 10, 11, 12 respectively.
The AASHTO standard is based on four components
of the overtaking manoeuvre:
(i)
(ii)
(iii)
(iv)
The distance travelled during perception and
reaction time (in judging the acceptability of an
overtaking opportunity) and, during the initial
acceleration, to the point of encroachment on
the centre line of the road.
The distance travelled while the passing vehicle
occupies the opposing lane.
The distance between the passing vehicle at
completion of the overtaking manoeuvre and an
oncoming vehicle.
The distance travelled by an oncoming vehicle
during the time from when the passing vehicle is
abreast of the overtaken vehicle to completion of
15
TABLE 10
Passing sight distances recommended by
the overtaking manoeuvre (approximately two
thirds of the time the passing vehicle occupies
the opposing lane).
To determine safe passing sight distances, AASHTO
assumes that the speed of the overtaken vehicle is
equal to the average running speed at intermediate
volumes of traffic where overtaking occurrences are
most likely. The speeds of the overtaking and
oncoming vehicles are considered to be 10 mph
(16 km/h) faster than that of the overtaken vehicle.
The TD 9/81 standard for passing sight distance (full
overtaking sight distance FOSD) was based on a
study carried out by the Transport and Road
Research Laboratory (Simpson and Kerman 1982),
the results of which are summarised in Figure 11.
This shows the distribution of overtaking durations
for a typical road at an approximate design speed of
85 km/h. It can be seen that the time taken for most
overtaking manoeuvres to be completed was
between 3 and 15 seconds, with 85 per cent of
drivers overtaking in less than 10 seconds. The 10
second value was therefore adopted for design
purposes. The standard assumes that the overtaking
vehicle starts to overtake at a speed two design
speed steps below the nominal design speed and
accelerates to the design speed over the duration of
the overtaking manoeuvre, whilst the oncoming
vehicle travels at the design speed.
In determining lengths of road available for safe
passing, TD 9/81 assumes that such lengths
terminate when only an equivalent ‘Abort Sight
Distance’ (equal to FOSD/2) is available. This
distance is that required for an overtaking driver to
complete a manoeuvre in the face of oncoming
vehicles from when it is abreast of the overtaken
AASHTO
Assumed Speeds
Passed Passing
Vehicle Vehicle
(mph) (mph)
20 30
26 36
34 44
41 51
47 57
50 60
54 64
Design
Speed
(mph)
20
30
40
50
60
65
70
Minimum Passing
Sight Distance (ft)
(Rounded)
800
1,100
1,500
1,800
2,100
2,300
2,500
driver eye height (feet)
object height (feet)
3.50
4.25
TABLE 11
Passing sight distances recommended by
TD 9/81
Design
Speed
kmfh
Overtaking Manoeuvre
Time
(seconds)
Minimum Passing
Sight Distance
(metres)
10.0
10.0
10.0
10.0
10.0
50 290
60
70
85
100
345
410
490
580
driver eye height (metres)
object height (metres)
1.05–2.00
1.05–2.00
vehicle.
TABLE 12
Passing sight distances recommended by NAASRA
Passing Sight Distance Continuation Distance
Design
Speed
(km/h)
Overtaken
Vehicle Speed
(km/h)
Time
gap
(see)
Sight
distance
(metres)
Time
gap
(see)
Sight
distance
(metres)
50
60
70
80
90
100
110
120
130
43
51
60
69
77
86
94
103
111
13.6
14.6
15.7
16.9
18.2
19.7
21.3
23.1
25.2
350
450
570
700
840
1010
1210
1430
1690
4.5
5.0
5.4
6.4
7.6
8.3
9.1
10.0
11.0
165
205
245
320
410
490
580
680
800
driver eye height (m)
object height (m)
1.15
1.15
1.15
1.15 —
16
100
80
60
40
20
0
——-- ———— ——-—- __
....... . ......
-—85%—————–
1“- 15%
T = Duration of overtaking manoeuvres (sees)
Fig. 11 Distribution of overtaking duration in
United Kingdom
Passing sight distances recommended by NAASRA
were based on studies carried out by Troutbeck
(1981 ), which used a gap-acceptance approach. The
passing manoeuvre was assumed to be in three
phases.
Phase 1 is the distance travelled from the point at
which the opposing lane is entered to when the
vehicle is alongside that being overtaken.
Phase 2 is the distance from the end of Phase 1 to
when the vehicle, still in the opposing lane, is clear
of that being overtaken.
Phase 3 is the distance from the end of Phase 2 to
the point at which the vehicle is entirely back in its
own lane.
The minimum distance which is adequate to
encourage a given proportion of drivers to
commence an overtaking manoeuvre is known as the
‘establishment sight distance’ and is the sum of
Phases 1 to 3. The sum of Phases 2 and 3 was
considered as the Continuation distance which would
enable an overtaking driver to either complete safely
or abort a manoeuvre already underway.
3.4 EYE AND OBJECT HEIGHTS
The, higher the driver eye height and object height,
the longer will be the sight distance available over a
vertical crest curve. On sag curves, obstructions can
occur where an overbridge crosses the alignment.
Msibility on horizontal curves depends on whether
the sight line falls outside the right-of-way limits, For
sight lines on horizontal curves within the right-ofway, eye and object heights are not generally
significant, except where cutting slopes, bridge
parapets, etc, obstruct the line of sight. Sight
distances outside the right-of-way are much more
dependent on eye and object heights. For example,
in determining the value of Alignment Constraint AC
(see para 2.4.2),TD 9/81 requires estimation of the
harmonic mean visibility between eye and object,
both with assumed heights of 1.05 m.
For geometric design purposes, driver eye and object
heights reflect conditions found in practice. Driver
eye height depends largely on vehicle characteristics
and to some extent on driver posture. It is generally
accepted that provision of visibility to the road
surface, ie an object height of zero, for a distance
equal to that required for safe stopping is not costeffective. Selection of a higher object height for
design is thus a compromise between possible
reduced safety and savings in construction costs.
Object heights must also be related to whether the
vehicle is stopping or passing.
Driver eye and object heights proposed by the three
standards are given in Tables 5, 6 and 7. The
AASHTO driver eye height of 3.50 ft reflects the
observed reduction that was taken place in the last
twenty-five years in average passenger car and driver
eye heights. The AASHTO object height for stopping
of 6“ is derived from economic considerations as
above. This height was the lowest which could be
considered a hazard and perceived by the driver as
requiring him to stop. The AASHTO object height for
passing of 4.25 ft represents the current average
passenger car height.
TD 9/81 proposes an envelope of clear visibility for
stopping involving driver eye heights between 1.05
and 2.00 m. The lower bound represents the height
exceeded by 95 per cent of driver heights in UK,
whilst the upper bound is a typical eye height for
heavy goods vehicle drivers. For object height, the
lower bound of the visibility envelope is 0.26 m, with
an upper bound of 2.00 m. For passing, an envelope
of clear visibility between points 1.05 and 2.00 m
above the road surface over the full passing sight
distance is required.
Studies of driver eye heights in Australia have
resulted in the NAASRA recommendation of 1.15 m
and 1.8 m for car and heavy vehicle driver eye
heights. NAASRA adopts an object of 0.2 m for
stopping under normal design, but allows an object
height of zero on the approaches to causeways and
floodways subject to flood water residues or
washouts. For passing, an object height of 1.15 m is
used.
3.5 COMMENTS ON SIGHT DISTANCE
Design standards for stopping sight distance are
largely dependent on assumed values of total driver
reaction time and longitudinal coefficient of friction.
There is consistency between the three standards in
choice of total driver reaction time, with normal
values in the range 2.0 to 2.5 seconds representing
most drivers and road conditions. However, it should
be recognised that a simple criterion is being used,
based on limited field studies, and which is assumed
17
to represent the whole population of drivers. The
NAASRA standards allow a lower reaction time of
1.5 seconds where drivers are alert but, whilst this
may be attractive in order to achieve construction
cost savings, further investigation is needed and a
more detailed specification of such situations would
be helpful.
Driver eye heights in the three standards are broadly
similar, all reflecting trends that have occurred in
vehicle design and, to some extent, driver position.
The concept of an envelope of clear visibility used in
TD 9/81 is useful in ensuring safe design for all
vehicle types using the road.
There is some variation between the three standards
in assumed design values of wet coefficient of
longitudinal friction. However, other important
factors to be considered are those related to
questions of vehicle maintenance (tyre and brake
condition) and whether the skid resistance of the
road surface is adequate to provide the likely required
deceleration, in addition to the need to maintain
vehicle control during stopping in wet conditions.
The studies for TD 9/81 have indicated increasing
accident rates with reducing sight distances,
particularly where the latter are sub-standard.
Nevertheless, the standard allows consideration of
departures from design values in difficult situations
on road sections without accesses or junctions.
The NAASRA manoeuvre site distance standard will
achieve cost effective designs in terms of
construction costs and would appear attractive for
low volume roads, given the assumed driver
behaviour of lateral manoeuvring instead of stopping.
The AASHTO decision sight distances provide more
generous standards where the decision and initiation
of appropriate reponses to perceived information is
more complex. Whilst this may be desirable in
identified locations, it has been introduced here as an
example of where the search for cost effective
standards based on studies of driver behaviour, and
the safety implications of altering standards, can
result in a recommendation for higher standards than
otherwise.
There are considerable differences in the three
standards for passing sight distance due to different
assumptions about the component distances of the
standard, different assumed speeds for the
manoeuvre and, to some extent, driver behaviour.
Nevertheless, the standards are based on studies of
driver overtaking behaviour in all three countries. An
additional important practical consideration would be
the siting of overtaking sections. If faster vehicles are
constrained to follow slower ones over a particular
subsection of road, then it is desirable to follow this
with an overtaking subsection. Otherwise, increased
driver frustration results and drivers will attempt to
overtake at increased risk on more dubious
overtaking alignments. The principle in TD 9/81 of
using sharper non-overtaking bends and longer
straights where overtaking is safe is a welcome move
in this regard, and moves away from the provision of
longer and larger radii curves in ‘flowing alignments’
where overtaking can only be carried out at risk.
18
Choice of object height is a compromise between
safety and savings in construction cost. The use of a
minimum object height for stopping of 0.26 m in
TD 9/81 has brought UK standards broadly in line
with those in US and Australia. Design object
heights must be related to the likely occurrence of
hazards on the pavement surface, which may be
related to the problems of routine maintenance of
roads.
4 HORIZONTAL ALIGNMENT
4.1 ALIGNMENT, USER COSTS AND
ACCIDENTS
Horizontal alignment usually consists of a series of
intersecting tangents and circular curves, with or
without transition curves. The alignment should be
designed to be as direct as possible in order to
reduce road user costs, but will be constrained by
topography in hilly terrain, land use, availability of
road materials and crossing points. The
environmental effects of roads and traffic have
become increasingly important considerations in
many developed countries, where the nonquantifiabie costs and benefits of road schemes in
addition to construction, operating and maintenance
costs are taken into account. Many of these
environmental effects are related to choice of
alignment.
The layout of the horizontal alignment significantly
affects the total cost of the road. Mean operating
speed is a decreasing function of overall horizontal
curvature, so that the road user costs of fuel and
time, which are functions of vehicle speed, will be
affected by the horizontal curvature. Construction
cost normally increases with increasing horizontal
radius, especially in hilly terrain.
The effects of horizontal curve radius on accident
rates have been studied in the United Kingdom
(Shrewsbury and Sumner 1980) and are shown in
Figure 12. This study showed that accident rates
increased with reducing horizontal curve radius, but
more rapidly below a value of about QO m. A more
comprehensive study was carried out earlier in the
United Kingdom (Road Research Laboratory 1965),
the results of which are summarised in Table 13. The
study showed that inconsistency of the horizontal
alignment of a road significantly increased accident
rates, which were affected not only by individual
curve radius and average horizontal curvature, but
also by the combination of the two. A sharp curve
radius on an otherwise straight alignment would
cause a higher accident rate than that on an
alignment with a high degree of bendiness.
‘1
I
1 1 1 1 1
0 200 400 600 aoo 1000 1200
Horizontal radius (m)
Fig. 12 Relationship between accident rate and curve
radius in United Kingdom
TABLE 13
UK non-intersection injury accidents on straights and
curves on a 9 metre roadway with different levels of
average curvature
Average
Curvature
(deg/km)
O–25
25–50
50–75
>75
Injury Accidents/10G veh-km
Curve Radius (m)
Straights
and Radius 610 to 305 to
>1520m 1520 610
0.7 0.7 0.6
0.6 0.6 0.6
0.4 0.3 0.6
0.2 0.3 0.6
4.2 VEHICLE MOVEMENT O
CIRCULAR CURVE
1
t <305 Total
5.3 0.8
0.9 0.6
1.0 0.5
0.7 0.4
1A
When a vehicle traverses a superelevated circular
curve, it is subject to a lateral force, acting in the
plane of the road surface, which is counteracted by
the component of the vehicle weight along the plane
of the road surface, and by side friction generated
between the tyres and road surface. This side friction
is equal to the coefficient of friction(f) between the
tyres and the road surface multiplied by the normal
reaction at the tyre/road contact areas; the latter, in
turn, is equal to the component of the vehicle weight
normal to the plane of the road surface. For the
small values of superelevation generally used on
highways, the following equation can be derived
from the above considerations:
~2
‘+ f=~27R
where e = superelevation
f = coeticient of side friction, (side friction
factor)
V = design speed, kmlh
R = curve radius, metres.
For design purposes, a constant design speed is
usually assumed and, for a given curve radius, the
required superelevation can be determined which
provides an acceptable level of coefficient of friction
and driver comfort. The relationships between design
speed, curve radius and superelevation recommended
by AASHTO, TD 9/81 and NAASRA are shown in
Figures 13, 14 and 6 respectively.
The relationship between superelevation and curve
radius for each design speed adopted by AASHTO
was based on a parabolic curve over the range of
curvatures from Do (zero degree of curve) to Dmax
(maximum degree of curve, or minimum radius). The
corresponding curves for side friction factors (f) are
smooth curvilinear relationships with f values
gradually increasing to the maximum design value at
D~,,. This relationship ensures that, on the different
horizontal curves along a section of road, for vehicles
at or above average running speed, some
consistency in the steering effort required to generate
the side friction on successive curves is achieved, ie
the driver always has to turn his wheel towards the
centre of curvature at these speeds.
The TD 9/81 standards are based on the following
relationship:
e =0.45 x V852= VS52
1~R 282R
where V85 is the normal design speed. This ensures
that a vehicle at the 99th percentile speed on a curve
of absolute minimum radius will experience a gross
lateral acceleration of not more than 0.22 g and a
nett lateral acceleration, to be balanced by friction,
of not more than 0.15 g. The equation also implies
that the ‘hands-off’ condition (nett lateral
acceleration = O) iq approximately the 15th percentile
speed. Hence consistency of steering effort on
successive-curves will be maintained for 85 per cent
of drivers.
The standard does not recommend the use of curves
whose radius is in band C in Figure 15. This avoids
sections of road with dubious overtaking conditions
for traffic in the left hand curve direction. It is
therefore a principle of the standard that design
should concentrate only on bands A and B for clear
overtaking sections, and band D for clear nonovertaking sections.
A low degree of curvature or large curve radius is
usually introduced on long straight sections by gently
deflecting the alignment approximately 4° to the left
and right alternatively .~,!tsfunction is to break the
19
monotony for drivers and to avoid glare from vehicle The NAAS RA standard does not specify a method
headlights or the setting sun. Drivers are also found for determining superelevation and side friction
to have difficulty in judging oncoming vehicle factors for the range of intermediate curve radii.
speeds, and hence overtaking opportunities, on long Figure 6 is in terms of maximum friction values and
straight sections. superelevation rates from which a minimum curve
\
R = Radius of curve (ft)
3
4
.10 f
V=80
.08
,06
.04
.02
0
0 5 10 15 20 25
D = Degree of curve
Fig. 13 Design superelevation rates for e ~ax = 0.10 recommended by AASHTO
0.04
0 200 400 600
Fig. 14
20
800 1000 1200 1400 1600 1800 2000
Radius (m)
Superelevation of curves recommended by TD9/81
TABLE 14
Maximum degree of curvature and minimum radius determined for limiting values of e and f by AASHTO
Design
Speed
(mph)
20
30
40
50
60
20
30
40
50
60
65
70
20
30
40
50
60
65
70
20
30
40
50
60
65
70
Maximum
e
.04
.04
.04
.04
.04
.06
.06
.06
.06
.06
.06
.06
.08
.08
.08
.08
.08
.08
.08
.10
.10
.10
.10
.10
.10
.10
Maximum
f
.17
.16
.15
.14
.12
.17
.16
.15
,14
.12
.11
.10
.17
.16
.15
.14
.12
.11
.10
.17
.16
.15
.14
.12
.11
.10
Total
(e+f)
.21
.20
.19
.18
.16
.23
.22
.21
.20
.18
.17
.16
.25
.24
.23
.22
.20
.19
.18
.27
.26
.25
.24
.22
.21
.20
Maximum
Degree of
Curve
44.97
19.04
10.17
6.17
3.81
49.25
20.94
11.24
6.85
4,28
3.45
2.80
53.54
22.84
12.31
7.54
4.76
3.85
3.15
57.82
24.75
13.38
8.22
5.23
4.26
3.50
Rounded
Maximum
Degree of
Curve
45.0
19.0
10.0
6.0
3.75
49.25
21.0
11.25
6.75
4.25
3.5
2.75
53.5
22.75
12.25
7.5
4.75
3.75
3.0
58.0
24.75
13.25
8.25
5.25
4.25
3.5
Minimum
Radius
(ft)
127
302
573
955
1,528
116
273
509
849
1,348
1,637
2,083
107
252
468
764
1,206
1,528
1,910
99
231
432
694
1,091
1,348
1,637
NOTE: In recognition of safety considerations, use of e~,~ = 0.04 should be limited to urban conditions
8160
5760
tl’1 4080 :X
Straight and nearlv
straight o/taking sections
(both directions)
+
Over~aking
section
+
I Radii NOT recommended
llo.o~
‘“w
Design speed (km/h)
Fig. 15 Horizontal cuwe designrecommendedby TD9/81
radius is determined for a given curve design speed
and speed environment. However the standard notes
that radii greater than minimum, together with
superelevation and friction less than maximum
values, are usually adopted; and that curves are
designed so that, over the range of speeds likely to
occur, drivers will be required to turn their steering
wheels towards the centre of curvature to generate
the necessarv side friction.
4.3 MINIMUM CURVE RADIUS
4.3.1 Fundamental relationship
For a given design speed, the minimum curve radius
can be calculated from the equation e + f = V21127. R
using maximum values of e and f.
A maximum e value of 0.10 has generally been
accepted for rural roads where ice and snow
problems do not occur. A superelevation rate of 0.12
is sometimes used in verv hilly terrain, but other
21
factors should also be taken into account, such as
the proportion of slow vehicles, the stability of high
laden commercial vehicles, appearance of the road
and the need to match levels at junctions and
entrances.
The minimum curve radii recommended by AASHTO,
TD 9/81 and NAASRA are given in Table 14, Table 4
and Figure 6 respectively.
Maximum f values depend on a number of factors
such as driver comfort, vehicle speed, types and
condition of the road surface, types and condition of
tyres and expected weather. Various studies have
shown a decrease in friction values for an increase in
vehicle speeds.
4.3.2 AASHTO
Maximum f values recommended by AASHTO are
based on comfort and safety criteria. The comfort
criterion was determined by limiting the residual
sideways force on the vehicle, which is related to the
side friction factor. The safety criterion was satisfied
by adopting smaller values than those observed from
various experimental studies, as shown in Figure 16,
varying from 0.17 at 20 mph to 0.10 at 70 mph,
0.22
0.2C
0,18
& 0.16
:
c
.-
,: 0,14
&
f
m
0.12
0.10
0.08
. . . . . HR8 lg40 Mover and Berry
—.. — MeVer 1949
● aea e.... Arizona
---— HRB 1936 Barnett
— HRB 1940 Stonex and Noble
—
..-.
.
Assumed for curve design
i I I 1 I
10 20 30 40 50 60 70
Speed (mph)
Fig. 16 AASHTO maximum safe side friction factors
4.3.3 TD 9/81
As mentioned in Section 4.2, TD 9/81 maximum
values of f were based on the need to limit gross
lateral acceleration to 0,22 g, a level established
some fifty years ago from safety and comfort
considerations. A study of driver discomfort due to
lateral forces on curves (Leeming 1944, Leeming and
Black 1950) confirmed this by suggesting that, when
maximum superelevation (e= 0.07) is allowed for, the
maximum design value of f should be 0.15. By
requiring the 99th percentile speed vehicle to
generate this f value on curves of absolute minimum
radius, the corresponding 85th percentile speed gross
lateral acceleration of 0.16 g on a curve of absolute
minimum radius will require an f value of about 0.09
to be generated. Desirable minimum values of radius
have been established using a limit on the gross
lateral acceleration at design speed of 0.11 g, ie half
the maximum value. Wth the same proportions of
gross lateral acceleration taken by superelevation
(45Yo) and by friction (55%), this results in a
desirable f value of about 0.06, and a desirable
maximum superelevation rate of 0.05 (5Yo).
Studies for TD 9/81 have shown that drivers use
speeds that are reduced more on curves of lower
radii compared with their approach speeds. However,
the resulting calculated values of gross lateral
acceleration that would be used by drivers on these
curves were greater than the maximum value of
0.22 g used for design, indicating that a relaxation of
standards below absolute minimum radius could be
considered at very difficult sites. In these cases,
values of limiting radius have been established with a
maximum superelevation rate of 0.07, requiring f
values of 0.15 to be generated by vehicles at design
speed.
4.3.4 NAASRA
The proposed NAASRA design values for side
friction factors were introduced in Section 2.3.4. The
curve in Figure 17 was derived from the following
considerations:
(i) For design speeds up to about 50 kmlh, the
curve recommended by Kummer and Meyer
(1967) was adopted. This curve was based on
the minimum recommended skid numbers for
American roads which were a function of mean
operating speed. Skid number can be regarded
as being approximately equal to the wet side
friction factor multiplied by 100. Although this
curve was not adjusted to the 85th percentile
speed (design speed), the curve was of more
than two standard deviations below the mean
side friction factors on horizontal curves
measured in Australia and was therefore
adopted as a lower bound estimate of the
minimum pavement friction likely to be
encountered and, as such, was regarded as the
upper limit for plausible design f values.
22
(ii) For design speeds between 50 and 90 km/h,
the data in Figure 4 was used to derive two sets
of points based on:
(a) the upper 85th percentile confidence band
of a linear regression on the data (Method
1, Figure 17) and
(b) grouping of the data in 10 km/h ranges to
form the cumulative distributions shown in
Figure 18 and then taking the 85th
percentile value of each curve. (Method 2,
Figure 17).
0.40
0.30
fg5
0.20
0,10
0
Derivation of
data points
● Method ‘1
O Method 2
A Method 3
\
● Kummer and Meyer
recommended minimum
pavement friction
“,
o
p
Proposed
A design values
o
A
\
●
\
A
\
~
●
P *.
NAASRA ‘?0 ‘o ● \
values A
.O
●
1 I I 1 I 1
0 20 40 60 80 100 120 140
85th percentile curve speed (km/h)
Fig. 17 Relationship between 85th percentile car side
friction factor and 85th percentile car speed
for Australia
A third set of points (Method 3) was calculated
for 85th percentile side friction factors from the
NAASRA 1973 curve speeds and side friction
factors using the relationship between curve
speed standards and 85th percentile curve
speeds shown in Figure 3.
From the three sets of points proposed design
values were derived using the best fitting curve
to the sets of points and giving a smooth
transition to the recommended values below
50 kmfh and above 90 kmlh.
(iii) For design speeds in excess of 90 km/h, the
values recommended bv NAASRA (1970) were
retained. These values were higher than those
utilised bv drivers, but were adopted to provide
a high level of safetv and comfort.
Observed operating
(/~’
speed grouping
0.1 0.2 0,3 0.4 0.5 0.6 0
Side friction factor
Fia. 18 Distribution of side friction factors computed
from observed car speeds grouped bv 85th
percentile speed for Australia
The NAASRA curvelspeed studv found that the
paths of vehicles transversing curves varied. On small
radius curves, drivers tended to utilise the available
lane width such that the vehicle path radius
increased and the f value utilised was below that
implied bv the assumed circular path. For longer,
large radius curves, however, drivers tended to
decrease the radius of the vehicle path, utilising an f
value greater than assumed. This study also
suggested that there were many drivers who were
prepared to tolerate a high degree of discomfort on
horizontal curves. In addition, the higher f values
utilised bv drivers could also be due to improvements
in road surfaces, tvres and vehicle performance since
the earlier studies were carried out. Compared with
the AASHTO standards, the NAASRA maximum
values for f are higher, particularly for the lower
design speeds, ranging from 0.35 at 50 km/h to 0.11
at 130 km/h.
4.4 TRANSITION CURVES
Transition curves are inserted between tangents and
circular curves, or between circular curves of
substantially different radius for the following
reasons:
(i)
(ii)
(iii)
(iv)
to provide a gradual increase or decrease in the
radial acceleration when a vehicle enters or
leaves a circular curve.
to provide a length over which the
superelevation can be applied.
to facilitate pavement widening on curves.
to improve the appearance of the road by
avoiding sharp discontinuities in alignment at
the beginning and end of circular curves.
23
The type of transition curve which is normallv used
in practice is the euler spiral, or clothoid. This spiral
is defined bv the degree of curvature at anv point on
the spiral being directly proportional to the distance
along the spiral. There are several methods of
determining the length of transition curves.
4.4.1 Shortt’s method
This method was derived for the gradual increase in
radial acceleration on railway curves. The equation
used is
L= = VB13.63 C R
where LS = length of transition curve, metres
U = design speed, krnlh
R = circular curve radius, metres
C = rate of increase of radial acceleration,
metres/second3
TD 9/81 adopts this equation to derive lengths of
transition curves. It was recommended that the value
of C should not normally exceed 0.3 m/secB
although, in difficult cases, it could be increased up
to 0.6 m/sec3.
A modified equation could also be used which takes
account of the superelevation (e) on modern
highways. This leads to much shorter lengths of
transition:
This equation implies that, for a driver at the ‘handsOff speed for a particular curve radius and
superelevation, then L,= O, which is theoretically
correct.
Leeming (1944) observed that there was no
theoretical justification for any particular length of
transition curve, since driver comfort in negotiating
superelevated curves was dependent on the value of
lateral acceleration itself and not on its rate of
increase, the latter being the basis for the above
equations.
AASHTO suggests that roads do not need the same
degree of precision in computing length of transition
curve using either of the above equations. A more
practical control was adopted known as the
‘superelevation run-off method.
4.4.2 Superelevation run-off method
Superelevation run-off is defined as the length of
road required to achieve the change in superelevation
from a normal cross section on a tangent to the fullv
superelevated cross section required on the circular
curve, or vice versa. This length is determined such
that the slope of the pavement edges (ie the edge of
pavement profiles) over the transitional length
compared with the centreline slope or profile should
not exceed a maximum value. These maximum
relative gradients are usuallv established from
considerations of appearance of the road. The values
recommended by AASHTO are given in Table 15.
Superelevation run-off is directly proportional to the
total superelevation, which is the product of the lane
width and the summation of the normal crossfall and
superelevation
L. =
and L, =
where L~ =
L, =
b=
m=
e“ =
e=
rate:
~ (e+e”)
superelevation run-off, metres
length of spiral, metres
lane width, metres
relative gradient
normal crossfall of pavement
superelevation of the curve
Table 16 shows the values recommended bv
NAASRA to obtain a smooth visual appearance.
TD 9/81 stipulates that the edge of carriageway
profile gradients should not differ bv more than 1 per
cent with respect to the line of rotation to ensure
satisfactory appearance.
TABLE 15
Relative gradients between pavement edge
and centre-line for two-lane roads
recommended by AASHTO
design speed maximum relative grade
(mph) (%)
20
30
40
50
60
65
70
0.75
0.67
0.58
0.50
0.45
0.41
0.40
TABLE 16
Relative gradients between pavement edge
and centre-line for two-lane roads
recommended by NAASRA
design speed maximum relative grade
(km/h) (Ye)
40 or under 0.90
60 0.60
80 0.50
100 or over 0.40
24
4.4.3 Rate of pavement rotation method
This method adopted by the NAASRA standards was
based on driver comfort as well as road appearance
criteria. The rate of pavement rotation (n) is defined
as the change in crossfall divided by the time taken
to travel along the length of superelevation transition
at a given design speed. NAASRA recommends that
the rate of pavement rotation should not exceed
0.025 radians per second of travel time for design
speeds greater than 80 km/h, and 0.035 radians per
second of travel time for design speeds up to
70 kmlh.
Thus
L,=fi
3.6 n
and L.= L,+*
3.6 n
where V = design speed, kmlh
4.4.4 Other considerations
The superelevation run-off method in Section 4.4.2
can result, in some instances, in unacceptably short
transition lengths, particularly for low superelevation
rates and with higher design speeds. AAS HTO
therefore recommends minimum lengths, regardless
of superelevation, ranging from 100 ft to 200 ft for
design speeds of 30 and 70 mph respectively. These
distances are approximately those travelled in two
seconds at the design speed.
The TD 9/81 standard recommends that, on sharp
curves, the length of transition should be limited
such that the shift (p) of the circular curve is not
greater than one metre
L,2
iep= — <1 metre
24 R
UK practice has traditionally preferred transition
curves which consume an angle of at least 3° for
aesthetic reasons. Thus, a minimum length of
transition curve is given by: L,= R/9.
NAASRA recomends that, for appearance purposes,
length of transitions should be sufficient to provide a
shift of between 0.25 and 0.5 metres. If the shift
would otherwise be less than 0,25 metres, the
transition may be omitted.
The AASHTO standards allow the transition to be
omitted if the required superelevation is less than
about 3 per cent, which would give shifts broadly
consistent with the NAASRA recommendations. On
Elementsof pavementwidening DesignVehicle
U (FT)
(1) U=wc–wn
(2) WC= N(U+C)+(N-l)FA+Z
N = Number of lanes
w = Widening for pavement On curve, ft
Wc = Width of pavement On curve, ft
(4) FA=J R2+A(2L+A)– R
(5)z=v/~
o 0.2 0.4
FA (FT)
o 1.0 2.0
Z (FT)
Wn = Width of pavement on tangent, ft
U = Track width of vehicle (out-to-out tyres), ft
C = Lateral clearance per vehicle; assumed 2,2.5 &
3ft for Wn of 20, 22& 24ft, respectively
FA = Width of front overhang, ft
z = Extra width allowance for difficulty of driving
on curves, ft
# = Track width on tangent (out-toaut) 8.5ft
R = Radius on centreline of 2-lane pavement, ft
L = Wheelbase
A = Front overhang
V = Design speed of highway, mph
Fig. 19 Derivation of AASHTO criteria for widening on curves
25
such curves, a vehicle can follow a transitional path
within its own lane without the provision of a
transition curve. In addition, the effects of such
curves on appearance is negligible.
4.5 PAVEMENT WIDENING ON
CURVES
On horizontal curves, vehicle path width is larger
since the rear wheels track inside the front wheels. In
addition, there is a tendency for drivers to shy away
from the edge of the carriageway as they traverse a
curve. Therefore, pavements are sometimes widened
on curves to provide a safe clearance between
opposing vehicles.
The amount of widening required depends on
curve radius,
basic lane width on straight sections,
vehicle dimensions, and
required safe clearance (empirical value).
An empirical derivation for pavement widening on
curves was developed by AASHTO and is
reproduced in Figure 19. For practical reasons, and
because of the empirical nature of the extra width
derivation, it is recommended that design values for
widening should be multiples of one half-foot and the
minimum value should be two feet. Table 17 gives
the values recommended by AASHTO assuming a
rigid chassis design vehicle.
Neither the NAASRA nor TD 9/81 standard relate
widening specifically to design speed, unlike the
AASHTO standard. These standards for widening are
shown in Tables 18 and 19.
4.6 COMMENTS ON HORIZONTAL
ALIGNMENT
For the detailed design of horizontal curves, both
safety and driver behaviour considerations have been
important in establishing standards. Lower curve
standards do give the designer more flexibility in
difficult areas and can help reduce construction and
land-take costs, but the safety and driver implications
should also be considered in these cases.
TABLE 17
AASHTO calculated and design values for pavement widening on open highway curves
with two-lane pavements, one-way or two-way.
Widening, in feet, for 2-lane pavements on cuves for width of pavement on tangent of:
24 feet 22 feet 20 feet
Degree
of Design speed, mph Design speed, mph Design speed, mph
curve 30 40 50 60 70 80 30 40 50 60 70 30 ~ 50 60
1 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.5 0.5 1.0 1.0 1.5 1.5 1.5 2.O
2 0.0 0.0 0.0 0.5 0.5 0.5 1.0 1.0 lo 1.5 1.5 20 2.O 2.O 2.5
3 0.0 0.0 0.5 0.5 1.0 1.0 1.0 1.0 1.5 1.5 2.O 2.O 2.O 2.5 2.5
4 0.0 0.5 0.5 1.0 1.0 1.0 1.5 1.5 2.0 2.0 2.0 2.5 2.5 3.0
5 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.5 2.5 3.0 3.0
6 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.5 2.5 3.0 3,0 3.5
7 0.5 1.0 1.5 1.5 2.0 2.5 2.5 3.0 3.5
8 1.0 1.0 1.5 2.0 2.0 2.5 3.0 3.0 3.5
9 1.0 1.5 2.0 2.0 2.5 3.0 3.0 3.5 4.0
10–11 1.0 1.5 2.0 2.5 3.0 3.5
12–14.5 1.5 2.0 2.5 3.0 3.5 4.0
15–18 2.0 3.0 4.0
19–21 2.5 3.5 4.5
22-25 3.0 4,0 5.0
26–26.5 3.5 4.5 5.5
NOTE:
Values less than 2.0 may be disregarded.
3-lane pavements: multiply above values by 1.5.
4-lane pavements: multiply above values by 2.
Where semitrailers are significant, increase tabular values of widening by 0.5 for curves of 10 to 16 degrees, and
by 1.0 for curves 17 degrees and sharper.
26
TABLE 18
NAASRA recommended values for curve widening
for two-lane pavements based on a rigid design truck
total amount of widening (metres)
curve where normal width of traffic lane is
radius
(m) 6.0 m 6.5 m 7.0 m 7.5 m
<50 2.0 1.5 1.5 1.0
50–100 1.5 1.0 1.0 0.5
100–250 1.0 1.0 0.5
250–750 1.0 0.5
>750 0.5
Detailed studies of speeds and friction factors on
bends for the NAASRA standards have led to the
adoption of side friction factors for design much
more related to driver behaviour than previously.
The recommendation in TD 9/81 standards that
horizontal radii should be chosen to provide clear
overtaking and non-overtaking sections avoids curves
giving dubious overtaking conditions. This principle
would appear to have wider application provided
appropriate pavement markings are used and adhered
to by drivers. The use of gentle deflections of
alignment on otherwise long straights is also
desirable.
TABLE 19
TD 9/81 recommended values for curve widening
k
pavement widening (metres) on
curve radius
(metres) <150 0.6 (7.9) 1.2 (7.9)
150–300 — 1.0 (7.3)
300–400 — 0.6 (7.3)
Note: Figures in brackets are the maximum allowable
carriageway widths including widening.
Current economic assessment procedures for
alternative alignments do not take the radius of
individual horizontal curves into account in
determining mean operating speeds and hence fuel
and time costs. Mean operating speeds are related to
overall horizontal curvature (bendiness).
The need to determine side friction factors, and
hence minimum curve radius for design standards,
means that studies of these aspects of driver
behaviour on curves need to be carried out, as has
been the case in all three countries.
Those studies for TD 9/81 standards have been
concerned with accident rates and the relationship
between approach speed and curve speed. The
procedures outlined in Section 2 to determine design
speed, together with a limited allowable relaxation of
horizontal curve standards below desirable minimum,
should ensure that some measure of consistency,
and hence safety, is achieved in choice of horizontal
curves in designs. Consistency of steering effort on
successive curves of an alignment should also help to
improve safety. The method of determining
superelevation rates on curve radii above the
minimum values ensures that the majority of drivers
will have to turn their steering wheels towards the
centre of the curve to generate the required friction
to maintain equilibrium.
The use of transition curves on all but the largest
radius curves is general practice in the three
countries. Elsewhere, for large radius curves, the
question arises as to whether shifts of vehicle paths
within a lane are desirable.
Whilst there is some variation between the three
countries in the methods used to determine transition
curve length, perhaps the NAASRA rate of pavement
rotation has most appeal as it takes into account
driver comfort and quality of ride as well as the
appearance of the road.
All three standards stipulate amounts of pavement
widening on curves for basic narrow road widths and
sharp curve radii. The AASHTO empirical derivation
of pavement widening values is the most explicit and
is a good example of how such standards can be
determined from studies incorporating appropriate
design vehicles and driver behaviour.
5 VERTICAL ALIGNMENT
5.1 GRADIENT
In current geometric design standards, maximum
gradients are determined according to road class or
design speed, terrain, and vehicle performance.
A chart was produced in the TD 9/81 standards to
show the relationship between road user costs and
gradients, and this is shown in Figure 20. It can be
seen that the road user costs increase rapidly with
increasing gradient. This chart allows the designer to
carry out cost benefit analysis for individual gradients
and particularly to investigate the economic
implications of steep gradients. The standard user
costs are for both single carriageways with climbing
lanes, and dual carriageways. The disbenefits of
steep gradients on single carriageways with
insufficient traffic to justify a climbing line are
insignificant and a minimum construction/
environmental cost solution is recommended in these
cases.
27
USER COST
~~~~y~ ~OtalUUCx(l+~)]+~l.33 tilli0”xL]
Single
Clways ~Otal”UCx~+~)]+~l.42 milli0nXL]
Where L = Length of section in km
H = % HGVS
230
0 2 4 6 8
Gradient (per cent)
Relationship between user cost and gradient
from TD9/81
The AASHTO standard noted that passenger cars
can readily negotiate gradients as steep as 4 or 5 per
cent without appreciable loss in speed, except for
cars with low power-to-weight ratios. The effect of
gradients on truck speeds is much more pronounced
and the maximum gradient that can be negotiated
depends on the power-to-weight ratio. For the
purpose of deriving geometric design standards,
AASHTO described the terrain as follows:
Level terrain: That condition where sight distances,
as governed by both horizontal and vertical
restrictions, are generally long or could be made so
without construction difficulty or major expense.
Rolling terrain: That condition where the natural
slopes consistently rise above and fall below the
road gradeline and where occasional steep slopes
offer some restrictions to normal road alignment.
Mountainous terrain: That condition where
longitudinal and transverse changes in the elevation
of the ground with respect to a road are abrupt
and where the road bed is obtained by frequent
benching or side hill excavation.
Tables 20 and 21 give the maximum gradients
recommended by the AASHTO and NAASRA
standards.
TABLE 20
Maximum gradients recommended by AASHTO
(a) Local roads and streets
Type of
terrain
~
Level 87765
Rolling 11 10 9 8 6
Mountainous 16 14 12 10 –
(b) Rural collectors
Design speed (mph)
Type of
terrain 20 30 40 50 60 70
Level 777654
Rolling 1098765
Mountainous 12 10 10 9 8 6
(c) Rural arterials
Design speed (mph)
Type of
terrain 50 60 70
Level 433
Rolling 544
Mountainous 765
TABLE 21
General maximum gradients*
recommended by NAASRA
I
maximum grade (per cent)
Design I terrain
speed‘~
(km/h) I flat I rolling I mountainous
Notes: *
t
Values closer to the lower figures would be
aimed for on primary highways
Grades over 10 per cent should be used
with caution
28 .
The length of steep gradient can also be limited to
maintain the quality of service of the road. AASHTO
produced a chart to determine, for a given
percentage and length of gradient, various speed
reductions that would occur. This chart is shown in
Figure 21 and is derived from consideration of the
petiormance of a typical heavy truck of 300 pounds
per horse power. It was recommended that the
maximum, or critical, length of gradient which
causes a speed reduction of not more than 10 mph is
used in the design. A longer length of gradient could
be used if a climbing lane is provided on the
upgrade. On existing roads, Figure 21 can be used to
determine where a climbing lane should start for
various assumed reductions in the speed of trucks
due to the gradient.
9
a
7
:
~ 6
&
a 5
%m 4
&
:3
2
1
I 1 I 1
0 500 1000 1500 2000 2500
Length of grade (ft)
Fig. 21 AASHTO critical lengths of gradient for design
(assumed typical heavy truck of 3001 b/hp,
entering speed = 55mph)
5.2 VERTICAL CURVES
Vertical curves are required to provide a smooth
transition between consecutive gradients. For both
crest and sag curves, the minimum length required
may be fixed by sight distance or driver comfort
cirteria. An absolute minimum length of vertical
curve is usually stipulated to avoid poor appearance
of the road when very short curves are used with
shallow approach gradients.
The most common type of vertical curve used in
practice is the simple parabola which gives a
constant rate of change of curvature, and hence
visibility, along its length. It is relatively easy to
calculate this manually, the form being:
{}
G.L ~ 2
‘== L
where y = vertical distance from the tangent to
the curve, metres
x = horizontal distance from the start of
the vertical curve
G = algebraic difference in gradients, per
cent
L = length of vertical curve, metres.
Minimum required lengths of crest curves are
normally designed to provide sufficient sight distance
during daylight conditions. Longer lengths would be
needed to meet the same visibility requirements at
night on unlit roads. Even on a level road, low-beam
(meeting) headlight illumination may not show up
small objects at the design stopping sight distances.
However, higher objects and vehicle tail lights will be
illuminated at the required stopping sight distances
on crest curves, and it is felt that, since drivers are
likely to be more alert at night, these longer lengths
of curve are not justified.
Working on the parabolic properties of vertical curves
it can be shown that for crest curves:
For S