Scream if you want to go slower!

Why driving more slowly can get everybody to where they are going more quickly.


In a recent diatribe against slower driving speeds, the Daily Mail recently announced The Slow Death of driving”[i]. And the prime minister Rishi Sunak has just announced[ii] plans to restrict the ability of councils to impose “anti-motorist policies” such as 20mph speed limits.

So is driving more slowly really "anti-motorist"?

Well that, as they say, is “a complicated question”.

Let us consider a car driving along a single traffic lane (perhaps a lane on a motorway or one side of a single carriageway road) between two points A and B that are 1km apart:

Obviously, the faster the car drives, the shorter the journey time will be:

Graph 1: Journey times

Though it is interesting to note that this is not a simple linear relationship and faster speeds provide diminishing returns. In round numbers (my underlying calculations are all in metres per second) at 30mph, the journey will take 70 seconds; at 20mph, this will increase to 110 seconds. Going from 60mph to 70 mph only cuts the journey time by 5 seconds.

Now let us consider a more realistic scenario where the lane in question is saturated with cars:



Each car will have to drive so that there is a safe gap between it and the car in front. In the calculations below I have used the stopping distance to define this gap – allowing for the worst-case scenario where the car in front comes to a sudden and complete and unexpected halt (perhaps crashing into the back of a stationary lorry in fog) – but the same principles would still hold if I used figures that were more reflective of the less-safe gaps that average drivers actually maintain.

Graph 2: Stopping distances


The length of the safe gap increases in a non-linear and quite dramatic fashion. It doubles from about 12m at 20mph to about 24m at 30mph.

By calculating the time each car takes, at the relevant speed, to drive the distances represented by these gaps (plus its own car length), we can calculate the throughput of cars (e.g. the number of cars passing point B in one minute) along the lane of traffic for different traffic speeds when the lane is fully saturated with traffic:

Graph 3: Throughput


At 20mph there is a throughput of about 34 cars per minute. At 30 mph, this drops to 30 cars per minute and, apparently paradoxically (though not really paradoxically if you understand what is going on), the faster the speed at which the cars go between A and B thereafter, the fewer cars will get from A to B in a given time.

Of course, for the individual driver in the situation presented thus far, Graph 1 above still holds. The faster he or she is allowed to drive, the quicker his or her journey from A to B will be. Why should that driver care about throughput?

The problem is that there are often more cars trying to make the journey (from A to B in our example) than the throughput for a given speed can cope with. If the cars are going at 30mph and there are hundreds of cars (rather than 30 cars) trying to make the journey between A and B during the same minute, a queue will form and most of the cars will come to a complete stop. Waiting in stationary traffic can dramatically increase journey times - especially if you are at the back of the queuing traffic.

At times when we became stuck in an endless queue of stationary traffic, my late father would ask rhetorically (and, obviously, jokingly) “Why doesn’t whoever is at the front simply drive off?”. Let us imagine just such a situation:



The car at the front of the queue drives off and accelerates to whatever the speed limit is on this road, and the next in line does the same as soon as it is safe to do so.

Assuming everyone sets off promptly and accelerates promptly up to the speed limit and then maintains that speed, the limiting factor in how quickly the queue of cars can dissipate is the throughput. (If, on the other hand, a car takes too long to set off, it might never catch up with the car in front before it hits the speed limit. Such behaviour would make the figures for throughput and waiting times worse than calculated below.)

The car at the head of the queue obviously has zero waiting time. The tenth car in the queue has to wait for 16 seconds before setting off if the moving cars are going at 20mph; 18 seconds if the moving cars are going at 30mph. At a speed limit of 70mph, the waiting time goes up to 28 seconds:

Graph 4: Waiting times for 10th queuing car for different speed limits


The waiting times for the 100th car in the queue are, respectively, 177 seconds, 197 seconds, and 301 seconds at 20mph, 30mph, and 70mph:

Graph 5: Waiting times for 100th queuing car for different speed limits

If the queue gets up to a 1000 cars (that is about 5km long and I have certainly been in queues as long as that) waiting times for the last car in the queue goes up to 30 minutes, 33 minutes, and 51 minutes at 20mph, 30mph, and 70mph,


The main argument in favour of 20mph speed limits in built-up areas is road safety. The calculations presented above are, therefore, only of partial relevance to this particular debate. Moreover, most of those calculations are based on what happens when the roads are fully saturated with traffic. This is encountered often enough, but will vary in different locations and at different times of day.

Nonetheless, the point has been established that, given the simplifying assumptions detailed below in Methodology, lower speed limits will, in certain circumstances, keep traffic moving and get more cars along the road in a given time than higher driving speeds would. These kinds of considerations are the basis of variable speed reductions on smart motorways, which keep traffic flowing in situations where it would grind to a complete halt if everyone tried to drive at 70mph.

Far from being a way to persecute motorists, the enforcement of slower driving often improves life for car drivers and their passengers, while killing fewer pedestrians, cyclists, and animals in the process.



Graph 1 simply uses the equation for time, distance, and velocity[iii] [t=s/v] to calculate the Y-axis values.

Graph 2 adds thinking distance to braking distance to provide stopping distance. Thinking distance is assumed to be 0.7 seconds in line with the Highway Code estimate[iv]. Braking distance is calculated using the equation for distance, final velocity [which is 0 after braking], initial velocity, and acceleration [s=(v2-u2)/2a]. Acceleration is calculated using the formula for acceleration, force and mass [a=F/m] and assumes a braking force of 7 Newtons per kg of car – an assumption that provides braking distance broadly in line with those given in the Highway Code[v].

Graph 3 divides 60 seconds by the time to travel the stopping distance at the relevant speed plus the time to travel a car length at the relevant speed. The time to travel the stopping distance and the time to travel a car length are calculated using t=s/v and an average car-length is assumed to be 4m in line with the Highway Code assumption[v].

Graphs 4 and 5 divide the queue position minus 1 by the throughput per second.

All the calculations are based on average cars, and no attempt has been made to factor in larger vehicles like busses and lorries. There has also been no attempt to take account of overtaking or changing lanes – as might happen on a motorway or dual carriageway.

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