# Railway Lines across the Alps: Analysis of Their Usage through a New Railway Link Cost Function
## 2 The Proposed Cost Function
### Detailed Characteristics of the Alpine Railway Lines Taken into Account in This Study  
#### 3.1.1 Gotthard Line and Its Branches  
With regard to the Gotthard line, thanks to the opening of the new Gotthard Base tunnel, 57 km long, between Bodio on the south and Erstfeld on the north, the maximum sum of grade and curve resistances, which occurs in the south ramp, has been reduced from 27 to 13 N/kN [29; 30]. It must be underlined that 13 N/kN is not recorded in the Gotthard base tunnel, but in the line from Bellingona to Biasca. Because we took into account only one type of locomotive, the E189, for the whole network, and always the towed weight of 1234 tons, double traction has been considered from Bellingona to Biasca and single traction on the rest of the line. However, it can be noticed that with another type of locomotive, for example Siemens Vectron, it is possible to tow 1234 t with only one locomotive also between Bellingona to Biasca and this choice is more convenient economically. However, in our model, we considered only one locomotive and we chose the E189 because it is the most commonly used on the alpine lines. In a future extension of the work we will provide for different locomotive (with different costs), for the different railway lines. The Gotthard line branches out in three lines on the south side, and in two lines on the north side. The three branches on the south side are: the line across the Ceneri pass to Chiasso, a branch of the previous line crossing the Ceneri pass, then Mendrisio and after Varese to reach Busto Arsizio--Gallarate, the main Italian freight Intermodal Terminal [31], and the line across Luino. The line across Luino is not steep, nor tortuous, but it is composed of a single track; however, no improvement projects are currently planned on it. The Ceneri Pass north ramp (south direction) is operated in triple traction, as the sum of grade and curve resistances is 26 N/kN, while the Ceneri Pass south ramp (north direction) is operated in double traction: the sum of grade and curve resistances is 21 N/kN (source: interviews to the MTO Hupac). The Ceneri Base tunnel is under construction and it is expected to be operative in September 2020: it is 15.4 km long. In the 'project scenario', the line Chiasso-Bellinzona has a maximum sum of grade and curve resistances equal to 12 N/kN which occurs from Chiasso to the south entrance of the tunnel. Instead in the Bellingona--Chiasso direction, the line has a maximum sum of grade and curve resistances equal to 10 N/kN which occurs in the new Ceneri base tunnel [29; 30]. The two branches of the Gotthard line on the north side involve: the line across Rotkreuz, Lenzburg and Olten; the line across the Zimmerberg pass to Zurich. While the first branch does not show relevant slopes and is operated in single traction, the Zimmerberg branch is currently operated in double traction: thanks to the new Zimmerberg tunnel, also this branch will be operated in single traction, with a maximum sum of grade and curve resistances of 12 N/kN. In synthesis, taking into account the Gotthard line and all its branches, in the 'current scenario' it is operated: in the north direction, in single traction from Milan and from Varese to Lugano, in double traction from Lugano to Biasca, and again in double traction from Zug (at the beginning of current Zimmerberg line) to Zurich, while the rest of the line is operated in single traction; in the south direction, in double traction from Zurich to Zug (Zimmerberg), in triple traction from Bellinzona to Riviera/Bironico (on the south of the old Ceneri tunnel), grade 28%o, and the rest of the line is operated in single traction. In the 'project scenario', it has been considered: in the northern direction double traction from Bellinzona to Biasca and single traction in the rest of the line and on its branches; in the south direction single traction in the entire line.