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TRL511 is one of a series of reports from the Transport Research Laboratory. It was commissioned by the Department for Transport, Local Government and the Regions (DTLR) and published in 2002. Its title is “The relationship between speed and accidents on rural single-carriageway roads”. The executive summary (pages 1 and 2) sets the scene, with reference to the previous work by the TRL on the relation between the rate at which drivers choose to travel and the likelihood of their being involved in an accident. This previous work includes the EURO model, a speed-accident relationship derived for European rural single-carriageway roads, which was developed with EU funding (the MASTER project) and described more fully in another report (TRL421, “The effect of drivers’ speed on the frequency of road accidents”, published in 2000). This report is therefore an extension of TRL421, but refers to English roads only. It was extended by adding more sites to the MASTER database, to include C and unclassified roads and to give a wider geographical spread. In total 100 new sites were added to the 74 sites in the original study. Site selection was with respect to location and road class. The aim was to include about one third each of A, B, and C or unclassified roads, evenly distributed across the DTLR regions, with equal numbers characterised as straight/bendy, flat/hilly, and with high/low numbers of minor junctions. Sites including major junctions (requiring vehicles to give way) were not included. Table 1 gives the distribution of sites by region and by road class. Pages 3 and 4 describe the data collected and the methods of collection: speed and flow data (automatic equipment), site characteristic and geometric data (drive-through video recordings noting junctions, accesses, bends, lighting, road studs, kerbing, lanes, markings, land use, visibility, verge width and type, roadside type, together with road distances and widths and hilliness). Accident data came from the STATS19 national database. Summary data are presented on pages 6-8, with several tables. Table 2 gives traffic flow by road class. Accidents are given by road class in table 3, and by region in table 4. Non-junction accidents are related to road class in table 5, and single-vehicle accidents in table 6. Summary data for speed, flow and accident frequency are in table 7. So far so good. It is with the next sections that readers of this report may have difficulty, as it passes from the data collection account to the mathematical methods employed to analyse that data. The point is first made that taking all the data together gives a plot of accident frequency against speed with a negative slope, a somewhat surprising finding. A similar finding was indeed reported in the models in TRL421; however, it was shown that the number of pedestrian crossings was also a factor contributing to the accident rate, and correction for this factor changed the shape of the model. It was therefore appropriate to classify the roads further in this study. The mathematical methods used for the classification are named and discussed. Non-mathematical readers may feel that this is all witchcraft, and that the authors should be burned. I can do nothing for that, save remind folk that we accept difficult mathematics without question in many other aspects of daily life, from the provision of telephone and television services through to the design of the aircraft in which you fly on holiday. Slightly mathematical readers may recall solving pairs of simultaneous equations, with the encouragement that if 10 equations are given, it is possible to solve for 10 variables. The principles in the development of these models are the same, even if the simultaneous equations are of a different order of complexity. It really is possible to identify important and unimportant variables in devising a classification of the quality of a road. The 18 variables which were considered are named in appendix B (page 22) as annual average daily traffic, accident rate per 100 million vehicle kilometres, access density (accesses and laybys), bends, bus stops/bays, changes in centre markings, minor junctions, road markings, order/direction/information signs, separate turning lanes, rise and fall, mean traffic speed, 85th percentile speed, %age with hedge on roadside, %age with overhanging trees, %age with wide verge, %age with good forward visibility, road width. Section 5 (Classification of road links into groups, pages 9-12) gives the results of principal components analysis of these 18 variables. [A link is not specifically defined in this text, but appears to be a stretch of road between two junctions. There may therefore be several links, of varying quality, at a single site.] Component 1 was a useful measure, scoring high for roads which are relatively wide, with a high traffic speed and low accident rate, low bend density and good visibility. The road sections studied were divided into 4 groups by this measure. Table 8 shows that the annual average daily traffic was much the same in all groups (somewhat less in the low-quality road group 1, hilly, with a high bend density and low traffic speed). A second selection process, using discriminant analysis, was used to define the 6 of the 18 variables which best distinguished the groups. These were mean speed, accident rate, junction density, bend density, access density and hilliness (table 9). Table 10 plots the statistics of these discriminating variables. It is also worth noting that road class (A, B, C/unclassified) was only weakly correlated with the quality of the 4 groups derived above (table 11). Table 12 gives the percentages of accidents in each accident category by road group. Section 6 (Accident modelling, pages 12-15) models at 2 levels. In essence these models are equations relating the accident frequency to other variables and parameters. Thus the level 1 model relates accident frequency to the length of the link, the traffic flow, the mean speed and a constant which is a property of the road group. The power parameter for length is 1 (doubling the length should double the number of accidents, not a surprise). The power for traffic flow is 0.73, so doubling the flow should increase the accident frequency by 65%. The power for mean speed is 2.48, implying that a 10% increase in mean speed will result in a 27% increase in accident frequency. The figure of 2.48 is not too different from the 2.25 of the urban road model in TRL421, which included another speed parameter. The level 2 models are extensions of the level 1 model to include sharp bend density and crossroad density. The added predictions are that on a one-kilometre stretch of road an additional sharp bend would be expected to increase the accident frequency by 13%, while each additional crossroad junction would be expected to increase it by about 33%. Other speed parameters (standard deviation, coefficient of variation, percentage exceeding 60 mph, mean speed of those exceeding 60 mph) were not found to be useful components of the model, though the coefficient of variation, a measure of the spread of speeds, was useful in the urban model in TRL421. Road width, found in other studies to influence accident rate, did not find its own place in these models, as it was highly correlated with traffic flow. Section 7 (pages 15-18) is devoted to the practical implications of the models. Figure 2 shows a clear speed-accident relationship for each road group for the level 2 model. Figure 3 gives graphical predictions of accident savings from speed reductions for 4 separate models, English rural KSI, English rural all accidents, the EURO model and the urban model. Section 8 (pages 18-20) provides a summary and discussion. The point is made that the models developed explained a high proportion of the variability in the accident data. The effects of the key variables were found to be “strong, plausible and stable”. The main results are worth quoting at some length:
The discussion makes several points. Despite the results presented for rural roads, speed management policies applied to urban roads are still likely to produce the greatest benefits. It is possible that the effects of speed on accidents at rural major junctions (which were not directly investigated in this study) may also be large. Rural roads need to be redefined by a new hierarchy. Appropriate speeds for each road in this hierarchy need to be established, and the means of achieving those speeds need to be identified. A policy for setting appropriate speed limits needs to be defined. Appendix A is a little gem illustrating how easy it is to get confused by data when the underlying variables are not fully explored. Four lines with a positive slope are generated by linear equations, data are distributed around these lines with a random function, and the resulting data are then plotted as a single lump on a graph. The regression equation of this data has a negative slope with a highly significant correlation coefficient. The moral, which is what the body of this paper has adopted as a procedure, is to understand all the variables affecting your data before plotting it. Appendix B discusses the variables used to classify the road groups. Appendix C contains model equations, effect sizes and data ranges within which the models work. Appendix D discusses the allocation of link sections to road groups.
You might like some of my other jottings. Click here.
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