## Thursday, December 20, 2007

### Within 50 km: correct sources

Thanks to the indications from a reader of the "Within 50 km" entry, we have now more authoritative sources regarding the commitments by the Spanish goverment on the evolution of the high-speed reailroad network. According to these sources, the plans are that

• (R1) all (continental) province capitals will be directly connected to the network,
• (R2) 90% of the population will live within 50 km of an AVE station

by 2020, and not 2010 as I incorrectly had assumed. In 2020 previsions are that the network length will reach 10,000 km, which is far more than the 2,230 km planned for 2010, and certainly more than enough to satisfy the coverage requirements stated above, as we see later. These figures are related to the so called Infrastructures and Transport Strategic Plan (PEIT) for the 2005-2020 period. The development of PEIT implies that the high-speed network will grow at the impresive rate of 777 km per year during 2010-2020. Whether this is feasible looks questionable to me, but the nature of my skepticism is not mathematical, so I leave it here.

Just for the fun of it, let us estimate the minimum network lengths needed to satisfy requirements R1 and R2. With respect to R1, we can use again the genetic program written for our previous entry on this issue, with only some changes to the initial parameters needed. After several hundred iterations we obtain an estimation for the minimum length of L1 = 3,870 km approximately. As for R2, we have, according to the National Statistics Institute (INE) data for the municipal register as of January 1st, 2006, that the Spanish population was 44,708,964. What is the minimum area the railroad network should cover so as to contain 90% of this population, i.e. 40,238,068 people? Francisco Ruiz provides an amazing resource at his website, a single Excel file including a comprehensive list of Spanish municipalities, along with their populations and areas, according to INE 2006 data: using this, we need only sort the (continental) municipalities by descending population density and look up the aggregated surface of the n first entries totalling up 40,238,068. This gives us an area A = 262,039 km2; repeating our original analysis with this value of A yields a minimum length L2 = 3,464 km. Anyway, this estimation is very imprecise as the analysis assumes the area to cover to be of compact shape, while in this case the shape is expected to be elongated along the Spanish coast with isolated dots over inland larger cities.

To satisfy both R1 and R2 we would need a minimum length between max{L1,L2} and L1 + L2, which in any case is well below 10,000 km.