WHEN MOST people arrive in a full car park, they see a parking problem. When David Percy arrives in a full car park, he sees a geometry problem and, he says, most car parks have been offering the wrong answer.
Percy, a Salford University professor, has shown that the conventional car park, with its rows of rectangular boxes marked out by white paint, is an inefficient use of space. He found instead that with just minor tweaks you can improve capacity by more than 20%. You simply use the same white paint to draw lines at an angle.
The inspiration for his research came from a sprucing-up of his university car park. The standard rectangular lines were painted over and “this traditional conformity set me thinking”, he wrote in Mathematics Today.
What if the bays were at 45 degrees instead, angled towards the flow of traffic? While some car parks use this system, most do not. But does it have advantages? Might it give him more reliable access to departmental meetings?
Key to understanding his calculations is that the area required for a parking space is not only the rectangle it occupies but also the area a car needs to move into that rectangle. If you place the parking bay at 90 degrees to the traffic flow, that turning circle is greater than if the bay is angled.
“Instead of rectangular parking bays, I figured if they are diagonal you might save space and fit more cars into a car park,” he said.
His hunch was right. Because less room is required for turning, he found a car park that fitted 500 cars in the rectangular scheme could take 619 with judiciously angled white lines.
“For a 45 degree bay angle it was a 23% saving,” he said. “For 36 degrees it was 24%, but the difference is marginal and it is easier to draw lines at 45 degrees.” However, the system only works in large car parks — in smaller ones the wasted space at the edges from angled bays may negate the savings.
The system only works in large car parks — in smaller ones the wasted space at the edges may negate the savings in the lanes
How should the angled bays fit together, though, assuming you have two rows so cars can park back to back? Some car parks use tessellated herringbone pattern. Percy is against this.
“It is generally impractical for larger car parks because traffic cannot flow in opposite directions along adjacent aisles unless vehicles nose into some bays and reverse into others, which is a recipe for disaster,” he wrote. His preferred solution is to have bays slanted along the same axis, as if a row of rectangular bays had been twisted slightly.
Since he made the proposals, the professor said that some people have suggested the bays could also be angled in precisely the opposite way, allowing people to reverse in rather than go in forward.
While this proposal is identical in terms of geometry, he concedes that mathematics might have its limits and he should defer to his psychologist colleagues instead. “I think if you had to go in front of the bay then reverse in, it would be difficult to stop people sneaking in first and stealing your space,” he said.
Tom Whipple, Science Editor
This article first appeared in The Times