Opinion: here's what geometry has to say about where to build the most efficient tram and light rail lines in Irish cities

One of the solutions to climate change is to have fewer people driving cars, and one way to do that is to provide an efficient public transport system. In Irish cities, this is done by Dublin Bus, LUAS, DART and smaller city services in Cork, Limerick and Galway.

But is this public transport system efficient? Is it effective? "No" I hear commuters cry. So how do we make it better? Higher speed, more stops (these last two may be contradictory aims to many), more frequency, more coverage, cheaper,....the list goes on.

However, what if some cities lend themselves to a more efficient and better designed public tram network because of their shape? This is where mathematics - geometry to be exact - has something to say. Cities have unique shapes, often because of natural features such as the sea, mountains or a lake. While most cities are probably in some sense circular, many are not. You may live in a city that resembles more a square, or a triangle. Then, there's rectangles, pentagons, parallelograms, hexagons, trapezoids... If you look at the shape of Dublin, it looks like a pizza with a substantial slice taken out of it for Dublin Bay. By contrast, Galway looks like a long rectangle.

From RTÉ Radio 1's Morning Ireland, TCD economist Ronan Lyons on how Dublin renters are paying 15% more to live by Luas or DART lines

Limerick and Galway cities have similar populations though their shapes are very different (Limerick is pretty circular). If you start building a tram in Limerick in the shape of a straight line through the centre, the city proper stops about 5km out of the centre so you would build one 10km line, and start on a second line through the centre.

If you build such a line in Galway, one line running through the centre of the rectangular city can extend 8km (or maybe further if you include Oranmore and Bearna) before reaching "countryside". Here, there are some obvious advantages because of the shape. More people will live closer to such a line in a rectangular city, and travelling on a single line to get from A to B increases efficiency, as opposed to having to change trams once or twice, with associated delays.

A single tram line fits the rectangular shape of Galway city with one or two small twists and turns and serves about 48,000 people living within 0.5km of the line. Red corresponds to the highest population area, then yellow, green, grey and blue, which has the lowest population.

In cities of equal size in terms of population and size, it's easier to build an efficient tram network where there is a longer perimeter, whether that be a squashed parallelogram or triangle, or a narrow rectangle or elipse. On the other hand, it's hardest to build an efficient system in a circular city, which has a minimum perimeter for its area.

Researchers at NUI Galway have shown that the efficiency for a single line tram through the centre of a square city can be as high as 67%. Here, the efficiency is calculated as the percentage of all trips between any two points for which it is feasible to (possibly) use the tram. For example, in the map above, it would not be feasible to go in Galway from G6 to E6, or to H8 by tram, but it would be feasible to go from G6 to F14 by tram.

The views expressed here are those of the author and do not represent or reflect the views of RTÉ