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  • Writer's pictureMichal J A Paszkiewicz

Are road speed limits based on safety?

Rules, once established, can often gain a life of their own. People seem to feel the need to support or nourish, even if the original purpose of them is forgotten. The postmodern approach to such rules is to just drop them entirely and make up entirely new sets of rules, until hopefully one day we will rediscover why the rules were made in such a way and put them back in place. Perhaps some of them will be changed for the better. A better approach than this is to thoroughly investigate the rules, and to understand their historical purpose. We need to know whether the reasons had merit, and whether those reasons are still applicable. Further to this, there needs to be an understanding of the effects of changing these rules, some of which may be second order and difficult to reverse.


One of my friends recently told me that they had been caught by a speed camera and made to go through the National Speed Awareness Course, an alternative to having points put on your driving licence and potentially losing it. He attended the course, but found the course leaders unable to answer any basic questions regarding the reasoning for the choices of National Speed Limits. What was the reasoning behind the choice of our National Speed Limits? Why do other countries have higher, or no speed limits? Surely one could drive more dangerously while going slowly by swerving than while going fast? Who is the arbiter of what constitutes reckless driving?


These are all great questions that are worth addressing. I would like to address all of these over time, but this article will be limited to a light investigation into the relationship between National Speed Limits and road safety.


Why do other countries have higher, or no speed limits?


My hypotheses, based on my memory of a chapter of Lily Elefteriadou's An Introduction to Traffic Flow Theory (which contained an explanation for Urban planners on how to calculate an appropriate speed limit for a road) were that countries with higher speed limits either:

  1. Had good road conditions that allowed higher road speeds to be reached (e.g. better road surfacing, straighter roads, wider lanes, good signage, better driver behaviour).

  2. Had a higher tolerance for risk and were more interested in faster journeys than in the difference in safety this accounted for.

Using data from the EU commission for European nations can help us to see if there is anything like a simple relationship between road deaths and National Speed Limits. Plotting road deaths against the National Speed limit on motorways gives almost no correlation. We can see that the spread is wide and unclear. When I attempted to plot a trend line the best I could find gave me an R² value of 0.20. This means that 80% of the variance in the data can not be explained by this trend line, and it's a pretty poor result.

A graph showing the average number of road deaths per million inhabitants per year against the motorway national speed limits of European countries. There is very little correlation between these datasets and therefore Motorway National Speed limits cannot be the main cause of Road Deaths.

For many it will be surprising that there is little correlation, since people are often inclined to think of the fastest speeds, which occur on motorways, as some of the most dangerous. Danger or risk is not so easy to quantify though.


The simplest method is to use data from past accidents and try to create values of risk for particular circumstances based on this. However, there are many variables involved in what makes a road safe for a driver, and even more variables for a group of drivers. The data from past accidents often doesn't contain information on all the variables or situations. To expand the dataset, it is possible to extrapolate from this data by building computer simulations of driver behaviour based on general driving datasets and then put various situations into the simulations. We can then arrive at some value of risk, but it's hard to then translate this value into something that people can understand or feel to be a risk.


Risk or danger of road accidents is usually split into different categories. There is a particular risk of accident, but there is also a risk of severity of an accident. Road transport experts consider the accident risk to increase with the square of speed. The number of severe injuries increases with the cube of the speed, and the number of fatal accidents is proportional to the power of 4 of vehicle speed. Why then do we not see such a clear correlation with Europe's Motorway National Speed Limits?


Perhaps most road deaths be linked to roads that are not motorways? We can run the same comparison of deaths against Expressway speed limits. This time a line of best fit shows a far closer correlation. The R² value is now about 0.53 and out of the realm of low correlation (<0.4).

A scatter graph of Average road deaths per million inhabitants against the Expressway National Speed Limits of European countries. There is some correlation between the data showing an increase of deaths as the Expressway National Speed Limit increases.

47% of the variance of the data is still not explained by this simple trend line. By looking at the graph above we can see that the data more or less has a shape that inclines seemingly with the line. However, the data is still widely spread out, rather than holding tightly to the line. This is usually due to other variables being involved.


Perhaps this could be explained if most fatal accidents were occurring on Expressways rather than Motorways, and then Motorways could account for some smaller amount of deaths. It could also be due to different driver behaviour in different countries.


A comparison between Australian rural (motorways and country lanes) and urban (expressway and arterial) road risk research shows that there is in fact a considerable difference in accident risk between them when speeding is involved. In both cases, speeding relative to the average traffic speed increases risk exponentially. However, the exponentiation of crash risk in urban roads is substantially higher and quickly dwarfs that of the rural roads. The EU commission included this comparison in their road safety report, but omitted the data above a difference of 20km/h, probably because it would become difficult to notice that the rural speeding risk is also increasing exponentially.


Graph showing the exponential increase of risk of crashing as a driver speeds more above the average traffic speed. Urban roads show a much faster exponentiation than rural roads, meaning that speeding in Urban roads is substantially riskier.

Studies on road traffic almost always propose a decrease in speed limits. With risk increasing either with polynomial or exponential growth, a small decrease in speed always makes huge changes in statistics and seems worthwhile. The above graph suggests that stricter measures on speeding on urban roads should decrease crash risk more than on rural roads. Speeding by 10km/h on rural roads would still double your risk and going 20km/h over the average would increase your risk almost 6 times, but such speeding on urban roads would be relatively far riskier.


This study of Australian rural and urban roads may be a bit misleading for UK readers - in the UK, rural roads usually refers to country lanes that are often set with the national speed limit of 60mph. 10 times as many people die on UK country lanes than on motorways. This furthers our evidence that motorway limits have less effect on deaths than other roads, but it poops all over the idea of using a combination of Motorways and Country lanes in the UK as a meaningful grouping.


The Department of Transport has made this clear for us: Motorways are the safest roads. This is due to the fact that there are fewer collisions in total. An actual collision at these high speeds means a much higher likelihood of death, but the collisions are so infrequent that deaths are lower than on other roads.


Why are collisions on motorways less frequent than on other roads? There are numerous reasons for this - straighter roads, fewer obstructions, wider lanes, a feeling of risk that drivers may compensate for, segregated traffic, better maintenance, better lighting, and fewer crossings.


So let us have a look again at the various countries and see how we can compare how the design of motorways in Europe vary.


A good place to start would be to look at how bendy roads are. A very bendy road will have a maximum speed past which cars can no longer make the turns safely. But the curvature of roads can also mean drivers don't see as far ahead. So this could be a good way to start comparing different roads across Europe and their relation to maximum speed limits.


There are a variety of metrics that can be used to measure how bendy a line is. For example, curvature can be measured for example by dividing up a line into segments and seeing which radius of a circle would best approximate each segment. I will opt with a different metric - sinuosity. Sinuosity is simply the length of a line divided by the shortest distance between the start point and the end point. A straight line would give a value of 1, and a bendy road will have a higher value.


We can download UK roads that are at national speed limit using Overpass-Turbo - a tool for mining OpenStreetMap data. We can set the window to include the area of the UK and then the following query gets us all the roads in the UK with the maximum speed limit:

[out:json];
(
  way[highway=trunk][maxspeed = "70 mph"]({{bbox}});
);
out body;
>;
out skel qt;

We hit run and then download the dataset. The data can be nicely dragged into QGIS (a free and open source mapping tool) where we can start playing with the data. We can display it, and we can perform various geographical calculations with ease.


A map of roads with a maximum speed limit of 70mph.

QGIS turns out to make this investigation a lot easier, by having a formula for sinuosity built into its system. We can add a new field to all of our road datasets using this formula:


sinuosity($geometry)

I repeated this process for the other European countries. We can now plot European maximum speed limits against the average sinuosity of the roads that are at that limit:


The correlation again isn't too strong with quite a wide spread of data. However, there seems to be some form of downwards trend where countries with more sinuous roads seem to have lower maximum speed limits, starting with Poland at the top left with the highest enforced speed limit and some of the straightest motorways.


This data may of course be heavily affected by the fact that regions of motorways that suddenly become more bendy may have a lower speed limit than the national one. But both this possibility and some existence of a trend would both indicate that nations are to some extent accounting for curvature in setting road speed limits.


The variance around the trend line could be interpreted as the risk tolerance - with the most risk tolerant countries above the line, and the most risk averse below the line. The UK finds itself highly risk averse in comparison to the other European countries, despite its fairly average road sinuosity.


What is perhaps interesting is that the trend line becomes considerably steeper when we consider the 95th percentile sinuosity of national-speed limit roads, as opposed to their average sinuosity. This means that 95% of each country's roads are less sinuous than this value. But seeing somewhat of a relation between road limits and the sinuosity of most roads perhaps inspires a bit more confidence than the relationship with the average, which can be skewed by exceptional values.


Is there a similar relationship between sinuosity and road speeds in general in a country? A short look through England's primary road data shows that this generally isn't the case... In fact, the median and upper quartile sinuosity both increase with road speed up to 60mph and then has a sudden drop on 70mph roads. The mean decreases between 50mph and 60mph roads and then has a sharper drop for 70mph roads.



But why? Well, the curvature of the road is probably not the main reasoning for selecting road speeds under 50mph. These are more likely based on whether they are going into a village, whether there is a school or other facility nearby, approaches to intersections, and whether there have been past accidents in the area. 70mph roads are heavily reviewed and have speed limits lowered, giving the sharp drop. Similarly the mean sinuosity on 60mph dropping from that of 50mph roads suggests that these roads are often reviewed.


But the high value for the 60mph median and upper quartile is due to the multitude of country lanes that have been simply left at 60mph, with no authority having any method of enforcing limits there, and no interest from locals for changing these limits. These roads can be considerably bendy - I haven't shown the multitude of outliers in this chart, as it was hard to see the data structure at all otherwise.


So we have a bit of a mix of an answer - yes, transport authorities limit road speeds to try to ensure safety, but not on all roads. In the UK the 60mph country roads in particular shouldn't be trusted to provide a safe speed at all times. But as for UK motorways - we are one of the most risk averse European countries in setting our motorway national speed limit. The UK (and particularly England) has one of the highest population densities in Europe. This fact together with the high GDP per capita can lead to a good reasoning as to why we should have risk averse policies for motorways. Any issues resulting from a crash on a motorway likely has a bigger effect on others than in the less dense countries, and a higher total cost in damages when losses due to delays are included. Perhaps we are entering the realm of speculation now, but this will have to do until we also review the historical decisions made in this regard.



 


Michal is a Software Developer with over a decade of experience, the majority of which he has worked on complex Transport systems. When he isn't working, he spends more time learning about Transport than is healthy for him.


If you learnt anything here, or enjoyed reading this analysis, please support Michal by buying his new book - The Perfect Transport: and the science of why you can't have it.


Some of his other writing and interactive content on Transport can also be found on his blog.

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