Friday, 11 September 2015

September's silly statistic

News item in the property pages today:

Letting agent Rentify has estimated that the 240-bedroom Buckingham Palace would come at a rental cost of £303,340 per month.  

Not, you may think, a round £300,000, but a splendid £3340 per month more. 

However, the estimate is not quite as crazy as it appears, just the way it has been expressed.  Rents for property are usually round sums, either per month or per week.  And this monthly rent is a nice round estimate of £70,000 per week - but someone felt that it would sound better as a monthly amount.  On the Rentify website, the figures are given per month, and you have to make the conversion yourself when some figure looks odd.

Moral - if a figure is an estimate with one set of units, don't change the units!

Wednesday, 2 September 2015

Car park layout - what is good, what is best?

The magazine of the Institute of Mathematics and its Applications (Mathematics Today, August 2015) has an interesting and amusing article about optimising the layout of car parking spaces in a car park.  Tina and I have found several car parks at supermarkets and motorway services where the layout of spaces strikes us as sub-optimal.  (Mind you, the way that drivers negotiate such car parks is also sub-optimal.) 

So, what does the article consider?  It focuses on those which are on one level, not multi-storey.  Most car parks have a rectangular pattern with corridors for cars, and parking spaces at right angles, creating a rectangular pattern.  What happens if you have the spaces at an angle, creating a herringbone pattern?  Or if alternate corridors have traffic moving in opposite directions, so you can have a diagonal pattern?  The corridors can be narrower, because cars do not need so much space to turn.  So, you can have more corridors.  But possibly fewer spaces per corridor.

This problem has been examined in more detail by mathematicians at Bristol University(report here)

In Mathematics Today, the problem is treated as an optimisation problem with the fixed parameters length of bay, width of bay and turning circle of car, and one decision - the angle of the bay.  The car park is assumed to be infinite (as some car parks appear to be).  Taking the fixed parameters of a Rolls Royce Phantom, the best angle is about 36 degrees - but the optimal solution is insensitive to small changes so one could suggest either 30 or 45 (easier to measure).

Car users are very conservative, so it is unlikely that many car park designers will change to increase the capacity of their creations in this way.  But there is scope for designers to think about the likely flow of vehicles to try and achieve designs which are efficient and work.

For a completely whimsical discussion about the possibilities of an irregular layout of markings on a car park, Ian Stewart's book "Another Fine Math You've Got Me Into" has a chapter (The Thermodynamics of Curlicues) where the author imagines someone laying out a car park following Dekking and Mendes-France curves.