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A study of accident rates on rural roads
in developing
by
G. D. Jacobs
countries
TRANSPORT and ROAD
RESEARCH LABORATORY
Depatiment of the Environment
TRRL LABORATORY REPORT 732
A STUDY OF ACCIDENT RATES ON RURAL ROADS
IN DEVELOPING COUNTRIES
by
G D Jacobs
Any views expressed in the Repoti are not necessarily
those of the Depatiment of the Environment.
Overseas Unit
Transpoti and Road Research Laboratory
Crowthorne, Berkshire
1976
lSSN 0305 – 1293
CONTENTS
Abstract
1. Introduction
2. Data collection
2.1 Kenya data
2.1.1 Geometric design parameters
2.2 Jamaica data
2.2.1 Geometric design parameters
3. Analysis procedure
4. Results
4.1 The relationships between accident rate and vehicle flow
4.2 The results of the simple regression analysis
4.3 Multiple regression analysis
4.4 Comparison of the Kenya and Jamaica results with those from other countries
5. Conclusions
6. Acknowledgements
7. References
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@ CROWN COPYRIGHT1976
Extracts fmm the text maybe reproduced, except for
commercial purposes, provided the source is acknowledged
A STUDY OF ACCIDENT RATES ON RURAL ROADS
IN DEVELOPING COUNTRIES
ABSTRACT
The purpose of the study described in this report was to investigate
relationships between personal injury accident rates on rural roads in
Kenya and Jamaica and factors such as vehicle flow and road geometry.
Regression analysis was used to derive equations which can be
used to estimate changes in accident rates following improvements to
the geometric design of the road.
The accident rate per ktiometre per annum was found to be significantly related to the vehicle flow whist the rate per million vehiclekdometres was found to be significantly related to the physical characteristics of the road tested, such as junctions per kilometre, surface
irregularity and road width.
Comparisons were made with similar relationships derived in a
number of developed countries; the accident rates in Kenya and
Jamaica were found to be consistently greater for similar values of
vehicle flow and geometric design.
1. INTRODUCTION
Studies of road accidents in developing countries have indicated that accident rates tend to be particularly
high on rural roads’,’. An analysis of road accidents involving personal injury in Kenya’, showed that singlevehicle accidents were particularly prevalent on rural roads, being almost 50 per cent of the total number of
accidents occurring. In this situation it is probable that design features of the road are a significant factor.
Even in Great Britain where the standard of road construction is high compared with most developing
countries, the road layout, surface or furniture was found to be a contributory factor in ahost 30 per mnt
of dl accidents occurring on mainly rural roads within a defined study area: Work carried out in Oxfordshir$ in 1937 (when vehicle flows were probably in the order of those in some developing countries at
present) concluded that 75 per cent of the accidents would not have occurred had the road conformed to
the (then) current Ministry of Transport Memorandum 575 on the Layout and Construction of Roads.
1
In order to study the relationships between personal injury accident rates and geometric design of the
road, data have been collected from Kenya and Jamaica. The primary objective of the investigation was to
attempt to correlate tie number of accidents per million vehicle-kflometres on a length of road with the
design characteristics of the road Iin order to obtain information which would be of use in formulating
principles for the design of safer roads in developing countries. However, relationships derived in this
investigation need to be verified by studies on roads in other countries. In particular it is hoped that the
relationships derived here and in other countries wuld eventually be incorporated into the Road Transport
Investment Model’ developed by the Overseas Unit. This Model attempts to minimise the total transport
cost of a given project by devising the optimum standard of road construction and design.
2. DATA COLLECTION
In order to correlate accident rates with road design it is necessary to have, for each section of road, the
precise location of each personal injury accident taking place over a given period of time, an accurate
measurement of traffic flow throughout the year and measurement of factors such as road width, horizontal and vertical curvature, surface irregularity etc. There were very few developing countries where such
data were avtiable but it proved possible, by using data from various research studies, to obtain the
required information for Kenya and Jamaica.
2.1 Kenya data
During 1974 a visit was made to Kenya by the author to collect information on dl personal injury
accidents taking place in 1972. In 1975, fo~owing co~aboration with the Kenya Ministry of Works, detafls
of all injury accidents taking place in 1973 on the Nairobi:Mombasa Road (see Figure 1) were obtained.
With this extra road accident data and with accurate traffic flow data avadable, it was decided to use this
road for detaded study.
The Road Transport Investment Model’, designed by the Overseas Unit to finimise total transportation costs on a given road project, was based on data collected in Kenya over the period 1969-1974.
Test sections were set up throughout Kenya, particularly on the Nairobi-Mombasa Road, and the traffic
flow and geometric design data collected durtig that period have been used for this investigation of road
accident rates. The road in question was divided into various sections (see Figure 1) with the following
information avadable for each road length:
1)
2)
3)
4)
5)
6)
7)
8)
personal injury accidents occurring in 1972 and 1973
the length of each section
the average annual dady traffic flow
the average road width (metres)
the number of junctions (per kilometre)
the average horizontal curvature (degrees per km)
the average vertical curvature (metres per km)
surface irregularity (millimet res per km).
From 1) and 2) personal injury accidents per ktiometre per annum were obtained, and from 1),2)
and 3) accidents per million vehicle-kdometres were obtained.
2.1.1 Geometric design parameters The road width was the width of the surfaced section of the road
excluding the gravel shoulders.
The vertical curvature of a road can be described most easily by its ‘average gradient’ or its total
2
vert icd ‘rise and fall’. Neither measure is fu~y satisfacto~ but rise ,and fd was preferred. A method of
measuring it from a specially designed and instrumented moving vehicle was developed for the study in
Kenya. The development of this technique allowed a high degree of accuracy to be obtained even on roads
with irregular surfaces.
Horizontal curvature is simply the ‘bendiness’ of a road. A particular bend can be defined either
by the radius of curvature measured in metres or by the degree of curvature, defined as the angle in degrees
between the straight wctions of road which are joined by the curve. Mthought the latter definition does
not dtiferentiate between bends of different radii, it is the most suitable for evaluating the overall effect of
a wries of bends on accident rates because it is additive and easier to measure. In developed countries where
simdar studies have been carried oute”, the accident rate has frequently been correlated with the exist ing
radius of curvature. On busy roads where numerous accidents occur and where high levels of vehicle flow
exist, this is probably the most convenient dimension to use.
Surface irregdarity is sometimes ca~ed the ‘riding qutity’ of the road. A method of measuring
surface irregularity was developed from the principles of the ‘bump integrator’* in which the vertical
movements of the axle of a sin~e-wheel trader are summed over a test section by an integrating clutch.
Though necessarily arbitrary, the system that was developed provided an index of the irregularity which
was useful for comparing the surface renditions of the test sections.
The parameters obtained for the sections of road used in the analysis are given in Table 1.
2.2 Jamaica data
In 1962 a team was sent by the Laborato~ to arry out urban and rural research work in Jamaica.
During this period an unpublished report was produced’” which gave detads of accident rates and ‘black
spots’ on rural ‘A’ and ‘B’ roads on the island. The accident rates (per million vehicle-mfies) were calculated
for almost the entire ‘A’ road network on the island (see Figure 2) and have been used in this present
report after converting the rates into metric units. A detafled investigation was dso carried out on the
deficiencies of the rural road network in Jamaica”, with detafled inventories being made of the existing
rural road system. For each section of rural ‘A’ road the foflowing parameters were obtained:
1) average width (feet)
2) profde and gradients (per cent)
3) average vertical curvature (ft/mile)
4) average horizontal curvature (degrees/mile)
5) average surface irregularity (in/rode)
6) average sight distance (ft)
7) the number of junctions (per mile)
2.2.1 Geometric design parameters Average road width was obtained by taking five measurements at
equrd intervals every mile.
The vertical curvature was obtatied by measuring the elevation at every crest and hollow and
accurately measuring the distances in between. Thus, as in Kenya, the ‘rise and fall’ per unit length of road
was obtained. The gradient was obtained by using an Abney level mounted in a survey car and modified to
read grade directly.
As in Kenya, the horizontal curvature was measured in terms of degree of curvature or ‘bend iness’ per
unit length of road, but in this case was obtained by taking measurements from 1 : 12,500 scale land
vahrat ion maps.
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The average surface irregularity (see above) for each section of road was obtained by using a towed
bump integrator where, as described above, the vertical movement of a wheel relative to its mounting was
measured, thus providing a measure of the unevenness of the road surface.
The average sight distance of each section was obtained by measuring how far ahead a driver could see
an obstruction on the road. Measurement’s were made by putting down markers at 100 ft intervals along the
road and, at each marker, counting how many markers could be seen on the road ahead. Twelve-inch high
rubber cones were used as markers. This method has the advantage of simplicity and speed. The average
sight distance was calculated from the total of the numbers of cones counted in the section and the number
of observations made within the section.
The parameters obtained for the sections of road used in this analysis are given in Table 2.
3. ANALYSIS PROCEDURE
Regression analysis was used to establish and quantify relationships between one dependent variable and
one or more independent variables. (The first variable, which is the quantity under study, is known as the
dependent variable and the others are defined as the independent variables.)
In this investigation four dependent variables were studied separately.
1) personal injury accidents per kilometre per annum Kenya
2) personal injury accidents per kdometre per annum Jamaica
3) personal injury accidents per million vehicle-kdometres Kenya
4) personal injury accidents per million vehicle-kfiometres Jamaica.
The choice of independent variables implied that they were ‘sensibly’ related to the dependent
variable. In this study, a further condition in choosing independent variables was that they should be simple
to define and, for an engineer working in the field, reasonably easy to measure.
As a preliminary investigation of which variables were most closely correlated with accident rate,
simple regressions of accident rate on each of the road features individually, were performed. Equations
derived were of the form:
y=atblxl
where
y = independent variable
x, = dependent variable
a = regression constant
bl = regression coefficient
However because many of the road design features are inter-related simple regression analysis may
give a misleading impression of the relationships that they have with accident rate. Multiple regression, in
which the accident rate is expressed as a function of several ‘independent’ variables simultaneously, is likely
to be a better guide.
Equations derived were then of the form:
y=a+blxlt b2x2tb3x3 . . . .. b”xn
where y, xl, X2, Xn, bl, b2, bn were as above.
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For these estimates to be acceptable it was necessary to test the hypothesis that the value computed
for each regression coefficient was unlikely to have arisen by chance. To check this, the standard error of
each regression coefficient was computed and tested for significance; variables with non-significant coefficients were el~nated from the analysis.
The computer program used was part of a statistical package and had an automatic prowdure for
eliminating non-significant variables and for testing such variables with other combinations and replacing
them where necessary. This technique is known as ‘stepwise’ regression analysis.
Data obtained on rural roads in Kenya and Jamaica were analysed separately.
4. RESULTS
From the analysis, equations were derived which related accidents per kilometre per annum to vehicle flow
and accidents per tillion vehicle-kdometres to the geometric parameters. Table 3 gives the maximum,
minimum and means of the parameters obtained on the rural roads studied. The standard deviation, which
measures the variance about the mean, is dso given.
4.1 The relationships between accident rate and vehicle flow
The number of injury-accidents per kdometre of road per annum occurring on rural roads in Kenya
and Jamaica were regressed against the vehicle flow per hour occurring on each test section of road
(averaged over a 12-hour 7am – 7pm period). In both cases the accident rate was found to be related to the
vehicle flow (with results being stat isticdly significant at the 5 per cent level). The equations derived were
as follows:
For Kenya y= O.l16t 0.0091x
For Jamaica y= 0.158t 0.0126x
where y = persoml injury accidents per km per annum
x = average vehicle flow/hour.
Figure 3 Wustrates how the accident rate in both countries increases with. increasing flow. (Figure 3
dso shows a relationship derived for a number of developed countries; this is discussed later). It can be seen
from Fig 3 that, for a similar rate of vehicle flow, Jamaica has a higher accident rate than Kenya.
In order to investigate relationships between geometric design and accident rates, the number of
accidents per kilometre of road per annum were divided by the vehicle flow per annum on each section of
road, to obtain the number of personal-injury accidents per million vehicle-kilomet res. In this way the
relationship between vehicle flow and the accident rate is taken into account.
4.2 The results of the simple regression analysis
The results of the simple regression analysis are given in Table 4. The ‘t’ value is the ratio of the
regression coefficient to the standard error and was used to test whether the relationship was statistica~y
significant (ie were unlikely to have occurred by chance). The tables indimte the relationships which were
found to be significant at the 5 or 10 per cent level. (Note: 5 per cent is the level usually accepted in
statistical analysis, ie there is only a. 5 per cent probabdity that the relationship could have occurred by
chance. Bearing in mind the many factors affecting accident rates, a relationship found significant at the
10 per cent level in this study could be considered satisfactory). The correlation coefficient r is also given.
The value r2 provides a measure of the proportion of variabdity in y that is accounted for by variabdity in
the appropriate x value. Thus, for example in Kenya, junctions per kdometre was found to be the most
significant independent variable. The r2value of 0.49 indicates that 49 per cent of the variation in
accident rate is ‘explained’ by variation in the number of junctions per kdometre alone.
In both countries the most significant parameter of those considered in this study was found to be
the number of junctions per kflometre. The correlation between the junctions and the accident rate was
greater on the Nairobi-Mombasa road, Kenya, than in Jamaica but as can be seen from Figure 4, the ranges
were quite different in the two countries. In Kenya where there were never more than two junctions per
kilometre an addition of one junction per kilometre was associated with an increase in the accident rate of
over one accident per million vehicle-kilometres. In Jamaica, where there were often as many as eight
junctions per kilometre, an increase of three junctions per kilometre would increase the accident rate by
one accident per million vehicle-kilometres.
On the Jamaican ‘A’ roads, road width was dso a very significant factor, the wider the road the lower
the accident rate (see Figure 5). On the Nairobi-Mombasa road, there was very little variation in the road
width and the small amount of variation (see Table 3) has not provided a significant relationship with
accident rate.
In both countries the surface irregularity was related to the accident rate: the rougher the road the
higher the number of accidents per mfllion vehicle-kilometres. In Jamaica the relationship was statistically
significant at the 5 per cent level whflst in Kenya it was significant at the 10 per cent level. (Again, in
Jamaica, the range was greater than in Kenya). The effect of surface irregularity was very similar in both
countries; an improvement in roughness of 2000 millimetres per kilometre was associated with a reduction
in the accident rate of 0.8 accidents per million vehicle-kflometres per annum.
In Kenya the horizontal curvature was found to be significantly related to the accident rate, a
decrease of 35 degrees per kilometre reducing the accident rate by one accident per million vehiclekilometres. In Jamaica neither horizontal curvature nor sight distance was found to be a significant
factor. This is a somewhat surprising result since the range of horizontal curvature is much greater in
Jamaica than in Kenya.
4.3 Multiple regression analysis
The results obtained in the previous section show how various features of the road considered
separately were related to the accident rate. In order to determine how the combined factors are associated
with the accident rate, multiple regression analyses as described in Section 3 were carried out.
Parameters were given the following not ation
y=
‘1 =
X2 =
x=3
X4 =
‘5 =
‘6 =
accident rate per million vehicle-kilometres
road width (metres)
vertical curvature (m/km)
horizontal curvature (deg/km)
surface irregulatiry (mm/km)
junctions per kilometre
sight distance (metres)
The regression equation of factors related to the accident rate (significant at the 5 per cent level) in
Kenya was as follows:
y = 1.45 + 1.02X5 t 0.017X3
(Note: The independent variables in this equation and those below are listed in order of significance;
thus, in Kenya, junctions per kilometre was found to be the variable which had greatest ‘effect’ on the
accident rate).
Other parameters were not significant at the 5 per cent level but were at the 10 per cent level.
Although 5 per cent is the level normafly accepted in statistical analysis, in this case, taking into account
the limitations of the data, the 10 per cent level might be considered acceptable. The equation for Kenya
then becomes
y = 1.09 t 0.031x3 + 0.62x5 t 0.0003x4 t 0.062x2
The ‘effects’ of surface irregularity and verticrd curvature are considerably less than those of junctions
per kdometre and horizontrd curvature. Nevertheless they are worth including, particularly surface
irregularity where, for example, the improvement under consideration is the upgrading of a gravel road to a
bituminous-surfaced road and the change in riding quality maybe considerable.
The multiple regression equation for Jamaica (with parameters significant at the 5 per cent level) was
as follows
y = 5.77- 0.755x1 t 0.275x5
In this equation, road width was the variable most closely associated with the accident rate. In
section 4.2 it was seen that, in Jamaica, the accident rate was related separately to road width, junctions
per kilometre and surface irregularity (all at the 5 per cent level). In the multiple regression analysis
however, it was found that surface irregularity was not significmt (even at the 10 per cent level). The
reason for this is that surface irregularity and road width were themselves related, the correlation between
the two variables being significant at the 5 per cent level. The most significant factor (road width) enters
the equation first and since this is closely related to surface irregularity, it aslo ‘explains’ most of the
variation associated with surface irregularity, which was therefore found to be non-significant.
4.4 Comparison of the Kenya and Jamaica resulfi with those from other countries
In January 1973 Silyanov published the results of a comparison of accident rates on roads of
different countries”. This work has enabled a comparison to be made between the relationships derived
in Kenya and Jamaica with those obtained on rural roads in developed countries.
Silyanov examined the relationships between accidents per kilometre of road per annum and traffic
flow derived by workers in Russia’3, Sweden” and Austrdia’5 and, grouping the results from the different
countries together, found that the relationship between accidents and vehicle flow could be expressed by
the formula:
y= 0.256 t 0.000408N t 1.36 (10-7)N2
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