Single-line tram is optimal solution for city

An NUI Galway mathematician has found that a single-line tramway is the optimal solution to help Galway city solve its traffic congestion problem.

A new study carried out by Dr Michael Mc Gettrick at the School of Mathematics, Statistics and Applied Mathematics at NUI Galway, shows that it is more feasible to construct a one line tram in Galway City than in other similarly sized cities.

The study, which was recently published in the International Journal of Public Transport, is based on the “shape” of the city, which for Galway is close to rectangular.

It stretches east-west about 15km (from say Oranmore to Barna ), but north-south only 5km, along Galway Bay. In a smaller model, it could be said to stretch 12km east-west and 4km north-south, but the shape is the same, a rectangle that is three times as wide as it is high.

This is in contrast to the shape of many cities worldwide, that have radial shape — growing from the centre equally in every direction to make a circle. The study shows that in rectangular cities, the average distance travelled between any two points in the city is greater than in the radial case.

This is one of the factors that increases feasibility: If a person has to make a short trip, which is more likely in the circular city, then he/she are less inclined to take a tram.

For a rectangular city, it is very efficient to build a single tram line through the centre of the rectangle, going parallel to the longer sides (for Galway, east-west ). In the case of Galway, this could be of length between 12km and 15km.

To compare this with an equally sized Irish city, for example Limerick city, which is much more circular, an equal length of tram (say 15km ) would have to correspond to two tram lines meeting in the centre (each line seven or eight kilometres ).

There are obvious major disadvantages to having two such lines, for example any trip involving changing trams increases substantially the travel time, and further these trips are in many cases far from direct. An unfortunate consequence is that many people turn to other travel means, such as single-occupier cars.

Best route

The study describes in broad terms the best route to be taken by a one-line tram, based on population density. It does not give fine grain detail, as this would have to be decided by other local factors such as geography, roads, buildings, rivers etc. The conclusions give leeway for a transport engineer to move the tram up to 500 metres to either side of the suggested route.

The route proposed (see picture ) links the areas of maximum population density in the city. For this route, about 48,000 people live within five minutes walk (500 metres ) of the tram line, the distance proposed in other transport research articles as the maximum distance most people will walk to access public transport.

In the research a single “Infeasibility Factor” is calculated for rectangular cities, compared to circular ones, and it is shown that this infeasibility factor is smaller in the rectangular case. For any departure point and any destination in the city, the analysis compares making the journey using the tram with the “direct line” journey made without using the tram (driving, walking, cycling, etc, ).

In the former case, the trip has three components: (1 ) Get to the nearest tram stop; (2 ) travel along the tram line to the nearest station to your destination, and (3 ) get from that station to your actual destination. Infeasible trips are then classified as those for which parts (1 ) and (2 ) are already greater than the direct line distance: In these cases there could be no benefit in using the tram.

It turns out that it is quite simple to calculate the feasibility (and infeasibility ) of Irish cities because, by and large, they do not have a huge variation in population density.

This is mainly because of the lack of genuinely high-rise apartments, which are common in many cities in other countries. From the study we can approximate to a large extent the population distribution as being reasonably uniform over the city area.

The research examines mathematical aspects of feasibility, but does not claim to present an overall analysis of other aspects that may be important (environmental, sociological, political, financial, etc )

The detailed report is available at


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