How can maths help us design the perfect car park?

A car park in Singapore. Image: Getty.

There can be few things as frustrating as being stuck in a car park for four hours on a scorching Sunday afternoon; yet this was the unhappy fate of shoppers at a new multi-storey grid car park at an IKEA store in Reading, UK.

The delays were caused by a few factors, including a particularly busy adjacent road, the popularity of the store’s opening weekend and the convergence of vehicles on a single exit ramp. Despite the retailer’s major £4m investment in constructing good access routes, the infrastructure simply could not cope with the volume of traffic leaving the car park.

As well as prompting a full-scale investigation by IKEA, such chaos invites us to consider how further gridlock can be prevented. Fortunately, mathematics can provide some basic guiding principles, as we consider how to design the perfect car park.

A numbers game

First, we need to decide how many parking spaces there should be. This is a perennial problem, to which there is no prescriptive answer. Too many spaces are costly and look ugly, while too few spaces result in distraught and dissatisfied customers. Yet some relatively simple maths can help us avoid the worst congestion.

Suppose that daily peak demand averages, say, m cars. We can get a sense of how much the number of cars is likely to vary from the average using standard deviation – let’s call this value s. If s is small, it means that the daily peak demand is quite consistent. If s is larger, it means that there’s a bit more variation; perhaps attendance spikes on Sundays, or over long weekends, or during sale periods.

Once we know these values, we can use the normal distribution to evaluate the probability that a car park with a given number of spaces will overflow. For example, if m=750 and s=100, then a car park with 800 spaces will overflow on 31 per cent of days, whereas a car park with 1,000 spaces will overflow on only 1 per cent of days. Greater accuracy can be achieved by modifying this simple model to focus on the more extreme events.

While avoiding excess capacity is an important consideration for some organisations, such as airlines, it’s better for car parks to err on the side of generosity. While some travellers might be willing to catch later flights in return for compensation, drivers are likely to find the prospect of being redirected to a multi-storey car park two blocks away somewhat less appealing.

The perfect angle

It’s also better to err on the side of generosity when it comes to the size of individual parking bays: my own modestly sized vehicle is pitted with craters caused by other doors banging into my side panels.

Bays should leave ample space around the cars to enable pedestrian access and to allow for the axle tracks of turning circles, so that vehicles can enter and exit smartly without cutting the corners of adjacent bays. This can also be achieved with sufficiently wide access lanes, so that cars are parallel to the lines when entering their bays.

Now consider the layout of parking spaces. Assuming that the building has a rectangular plan, there are some simple rules that ensure a convenient and dense population of bays. Rather than having access lanes around the perimeter of each storey, moving the lanes inwards allows us to place bays around the edges and increases the number of spaces.

Use your space well. Image: The Conversation.

Dead ends are undesirable, as they require drivers to reverse against the flow of traffic, so ramps should be located to avoid these. One-way flow systems throughout the car park also helps to avoid congestion and confusion, while allowing access lanes to be narrower than for a two-way flow of traffic.

A diagonal layout of car parking spaces offers significant advantages over a rectangular layout. Imagine proceeding along an access lane and finding an empty bay. With a rectangular layout you need to change your direction of travel by 90 degrees, which requires a substantial lane width to accommodate your turning circle.

But for a diagonal layout, the bays on both sides are inclined towards you. These require less course adjustment and the access lane can be narrower, so we can fit more parking bays into the same space. For a large car park, a 45 degree bay angle leads to an efficiency saving of 23 per cent. You also need to change your direction of travel much less, so manoeuvring is easier and safer when later reversing out of the bay.

The perfect parking lot

Clearly, there should be at least as many exits as there are entrances. Ramps should be not so steep that they are dangerous for drivers who queue or stall on them. Nor must they be too flat, or they will occupy too much precious space. Other factors are important, including the car wheelbase, ramp length and curvature, and possible transitional ramps.

Isaac Newton’s second law of motion – which tells us that that the rate of an object’s acceleration depends on the mass of the object, and the magnitude of the force which acts upon it – together with a simple vector diagram, help to balance the car’s weight with the slope’s normal and frictional forces, to determine acceptable limits for the gradient. One in ten is a generally accepted maximum slope, with lesser gradients often preferred.

A helix form car park in Newcastle city centre. Image: Trevor Littlewood/Wikimedia Commons.

If one were to design a new car park from scratch, one of the best of all systems is epitomised by the helical car park design. With one entrance, simple traffic flow and one exit, it is safe for pedestrians and uses the available space efficiently. Crucially, it is also reasonably pretty. Perhaps IKEA should ditch its grid design, and give the helix a whirl.The Conversation

David Percy is professor of mathematics at the University of Salford.

This article was originally published on The Conversation. Read the original article.


Covid-19 is highlighting cities' unequal access to green space

In the UK, Londoners are most likely to rely on their local park for green space, and have the best access to parks. (Leon Neal/Getty Images)

As coronavirus lockdowns ease, people are flooding back to parks – but not everyone has easy access to green space in their city.

Statistics from Google show that park attendance in countries across the globe has shot up as people have been allowed to move around their cities again.

This is especially true in urban areas, where densely populated neighbourhoods limit the size of private green space – meaning residents have to go to the park to get in touch with nature. Readers from England can use our interactive tool below to find out how much green space people have access to in their area, and how it compares to the rest of the country.


Prime Minister Boris Johnson’s announcement Monday that people are allowed to mingle in parks and gardens with groups of up to six people was partially following what people were doing already.

Data from mobile phones show people have been returning to parks across the UK, and also across Europe, as weather improves and lockdown eases.

People have been returning to parks across the world

Stay-at-home requirements were eased in Italy on 4 May, which led to a flood of people returning to parks.

France eased restrictions on 1 May, and the UK eased up slightly on 13 May, allowing people to sit down in public places so long as they remain socially distanced.

Other countries have seen park attendance rise without major easing of lockdown – including Canada, Spain, and the US (although states there have individual rules and some have eased restrictions).

In some countries, people never really stopped going to parks.

Authorities in the Netherlands and Germany were not as strict as other countries about their citizens visiting local parks during lockdown, while Sweden has famously been avoiding placing many restrictions on people’s daily lives.

There is a growing body of evidence to suggest that access to green space has major benefits for public health.

A recent study by researchers at the University of Exeter found that spending time in the garden is linked to similar benefits for health and wellbeing as living in wealthy areas.

People with access to a private garden also had higher psychological wellbeing, and those with an outdoor space such as a yard were more likely to meet physical activity guidelines than those without access to outdoor space. 

Separate UK research has found that living with a regular view of a green space provides health benefits worth £300 per person per year.

Access is not shared equally, however, which has important implications for equality under lockdown, and the spread of disease.

Statistics from the UK show that one in eight households has no garden, making access to parks more important.

There is a geographic inequality here. Londoners, who have the least access to private gardens, are most likely to rely on their local park for green space, and have the best access to parks. 

However the high population in the capital means that on the whole, green space per person is lower – an issue for people living in densely populated cities everywhere.

There is also an occupational inequality.

Those on low pay – including in what are statistically classed as “semi-skilled” and “unskilled” manual occupations, casual workers and those who are unemployed – are almost three times as likely as those in managerial, administrative, professional occupations to be without a garden, meaning they rely more heavily on their local park.

Britain’s parks and fields are also at significant risk of development, according to new research by the Fields in Trust charity, which shows the number of people living further than a 10-minute walk from a public park rising by 5% over the next five years. That loss of green spaces is likely to impact disadvantaged communities the most, the researchers say.

This is borne out by looking at the parts of the country that have private gardens.

The least deprived areas have the largest gardens

Though the relationship is not crystal clear, it shows at the top end: Those living in the least deprived areas have the largest private green space.

Although the risk of catching coronavirus is lower outdoors, spending time in parks among other people is undoubtedly more risky when it comes to transmitting or catching the virus than spending time in your own outdoor space. 

Access to green space is therefore another example – along with the ability to work from home and death rates – of how the burden of the pandemic has not been equally shouldered by all.

Michael Goodier is a data reporter at New Statesman Media Group, and Josh Rayman is a graphics and data visualisation developer at New Statesman Media Group.