Mapping the impact of fire station closures: methodology

This post sets out my methodology for modelling the potential closure of fire stations. The actual analysis will be included in my next post.

The Fire Brigade incident data includes a location for each incident mapped to a 100 metre square, based on Ordnance Survey Northings and Eastings. The FT data blog (which happens to be my favourite website) has mapped this squares to build a heat map of response times (unfortunately I haven't been able to look at it as my subscription is a corporate one and our version of IE can't handle it).

However, whilst the use of the OS National Grid for the location information means that I can't readily analyse the data using Google Fusion Tables (which uses information in degrees), it is very convenient for calculating distances, as the coordinates actually correspond to the distance in metres, north and east from somewhere south west of the Scilly Isles.

Once again, we have a project where I've been able to use somethings I learnt during my GCSEs: 1) Pythagoras' theorem and 2) any essay is better with clipart.

Taking these in reverse order, I was amazed how pyromaniacal Microsoft Office's library of clipart is; search for fire and you get a whole host of pictures of buildings on fire, fire fighters dealing with fire etc etc. I remember (though noone else does) when Microsoft's clipart library for jazzing up powerpoint involved a man balancing a pile of hats and a tall man bending over with a magnifying glass; now in the 21st century I can decorate my financial models with the Towering Inferno.

Now I've got that out of my system, back to Pythagoras (you know, the one about the square of the hypotenuse). Using an OS map, I worked out the National grid coordinates for each of the six fire stations in Tower Hamlets, plus the Shoreditch and Homerton stations. I chose Shoreditch and Homerton because of their location and that their appliances had been the first to attend in over 100 incidents in Tower Hamlets over the period 2009-12.

For each incident I calculated the distance of the incident to each of the stations, using pythagoras' theorem as shown below (nice clipart no?). Dividing the resulting distance by response time allows an estimation of the speed achieved by the responding appliance.

Now, this gives me linear distrance rather than the actual distance travelled. When I was doing some quality assurance work on this I noticed some very odd speeds in Shadwell- the incidents were only a few hundred metres away but the response time and speed were very odd. That was until it occured to me that the one-way system on Cable Street requires an appliance to travel away from the incident before turning back down The Highway.

Another problem with using linear distance is that it gives the shortest theoretical distance possible. However, as this is unlikely to always be achievable (unless fires are always on the same road as a fire station) the distance in the majority of cases will be underestimated and the speed over estimated. Because of this, I have also calculated what I am calling the 'perpendicular distance', which is the total distance you would need to travel if you set out north/south before the turning 90 degrees (eg perpendicular) to travel east/west. This gives a greater distance than the direct route and is an approximation for the maximum distance needed to be travelled without going in the wrong direction.

A little additional inaccuracy is further added by the fact that as noted, locations are identified by 100m squares, but fortunately this particular inaccuracy should even itself out.

So my spreadsheet now has 23,000 lines of data that include:

• the linear distance between 8 fire stations and incidents;
• the perpendicular distance between 8 fire stations and incidents; and for good measure...
• the average of the linear and perpendicular distance
• the distance (for each of the 3 measures) from an incident to the station that responded
• the distance (for each of the 3 measures) from an incident to the nearest station
• the distance (for each of the 3 measures) from an incident to the nearest station if Bow and Whitechapel fire stations were to close
• the effective speed achived based on the time to respond and the distance travelled.

At this point I think we're ready to do some analysis.