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Driving Challenges revealed by new roundabout formulae


A new formula by mathematicians at the University of Surrey shows an ideal trajectory for a car tackling a typical UK roundabout… something esure’s new analysis shows is rarely achievable!

In the last three years, more than one in every dozen UK car accidents has occurred while motorists approach or drive around roundabouts – with a quarter involving collisions while drivers change lanes - according to new research by internet insurer, The annual bill is estimated at over £75m per year.’s report, Roundabout Trajectories and Intersections, researched by Dr Anne Skeldon of the Mathematics and Statistics Department at the University of Surrey reveals the complex formulae that underpin roundabout trajectories and manoeuvres. It casts light on why roundabouts can be so potentially hazardous by showing that the ‘textbook’ way of negotiating a roundabout becomes near impossible when a number of cars are using a multi-lane roundabout at a time.

The report describes the formula for the ‘ideal’ path that a driving school might recommend a driver follows to enter and negotiate a roundabout smoothly (above). However, further investigation shows that this formula becomes inadequate very quickly on a typical well-used roundabout.

Dr Anne Skeldon said: “A driving instructor may show a learner how to approach, enter and leave a roundabout smoothly, but plotting the paths of multiple cars on a multi-lane roundabout makes it clear just how difficult negotiating roundabouts can be. There will be numerous points where the paths of different cars intersect - each of which is a potential accident point. In real life, this adds up to danger.

“Cars can only follow textbook routes around a roundabout if there is a precise relationship between their times of entry and speeds. Unfortunately, with modern traffic this is rarely the case.

“The criss-crossing of paths on busy roundabouts turns the desired smooth passage into a much more complex manoeuvre – both mathematically and in terms of the driving skills required. Drivers must be prepared to use their mirrors, switch lanes, signal and brake very precisely to ensure a safe passage.” She added.

To test the research, also analysed drivers’ reports from 15,000 insurance claims where accidents had occurred on roundabouts. The results show that more than a quarter (25.3%) involved accidents during lane changes - although interestingly 20% occurred while one driver was stationary on - or in the entry lanes of – a roundabout.

Mike Pickard, Head of Risk and Underwriting at esure, said:

“Changing lanes on any road requires care. When you are doing this on a circular road with cars trying to enter, exit and manoeuvre accordingly it is easy to see why a roundabout becomes a recipe for problems.

“Roundabout accidents result in claims totalling over £75m each year, so we would urge people to be especially careful when using them, particularly in bad weather.”

Stuart Miller | alfa
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