# Railway Lines across the Alps: Analysis of Their Usage through a New Railway Link Cost Function
## 2 The Proposed Cost Function
### Monetary Cost
#### 2.1.3 Calculation of the Traction Cost  
As stated before, the electric traction cost, \(T\) (\(V_{A}\),\(i\),\(R_{C}\)) [\(\ell\)/km], has been determined from the power consumption, in kWh/km, multiplied by the cost of electricity, in \(\ell\)/kWh. The power consumption has been calculated basing on all resistances to motion. The resistances to motion considered in the calculation, as suggested in [PERSON] and Mantecchini [16], are the rolling resistance, the aerodynamic resistance, as well as the grade and curve resistances. In the calculation of these resistances, the speed in rank A, i.e., \(V_{A}\), has been used. As stated before, we have taken into account the acceleration and deceleration transitories, by considering the resistances to motion dependent on the speed in rank A, \(V_{A}\), instead of the average speed, \(V_{M}\). The resistances were determined according to the methodology proposed in [PERSON] [17], but the formulas for resistances, which were old, have been updated. The rolling resistance has been calculated according to [PERSON] [18] (p. 2). The air resistance has been calculated according to [PERSON] et al. [19] (p. 823). The grade resistance has been calculated  
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considering the slope of each line section in detail while the curve resistance has been calculated from the classic [PERSON] formula. The resistances to motion depend on the weight of the train (locomotive + wagons). An E189 locomotive (produced by Siemens) has been considered, which has a weight of 87 tons [20]. This type of locomotive is currently used, by the rail company 'Rail Traction Company', in the international freight transport across the Alpine Passes of Brenner and Tarvisio. It is widely used in Europe because it is a multi-tension locomotive. One of the most common flat wagons, for the transport of containers, is the Sgns, with an unladen weight of 17.5 t/wagon (source: Mercitalia Rail [21]). In order to determine the average number of wagons composing a train, and the average number of TEUs (or ITUs) loaded on each train, four main MTOs (Hupac, Mercitalia Intermodal, Kombiverkehr, and Lineas Intermodal) operating between Italy and northern Europe, have been interviewed. The calculation of the weight of the train is described in detail in [PERSON] et al. [22]. The towed weight has resulted equal to 1234 tons. The total weight of the train has resulted 1321 tons if only one locomotive is used, 1408 tons if two locomotives are used, 1495 tons in case of three locomotives. For the cost of electricity, the average prices, in \(\xi\)/kWh, applied to companies (companies in general, not railway companies in particular), in each European country, were taken into account. For example, in Italy the average price for electricity, in the first half of 2019, for companies, has been around 0.0952 \(\xi\)/KWh (source: Eurostat [23]). A different electricity price for each European country has been considered, taken from Eurostat [23]. 1.4 Maximum Towable Weight on a Railway Line Section and 'Lines with Special Operation Characteristics'  
There are two main constraints related to the maximum towable weight on a railway line:  
1. The maximum towable weight due to the resistance of train couplers. It depends on the geometrical characteristics of the rail line, in particular on the sum of the grade and curve resistances. The towed weight of the train considered in this study is 1234 tons. From RFI (Rete Ferroviaria Italiana, the Italian rail network manager) prescriptions (source: Prefazione Generale all'Orario di Servizio [24]), 20 N/kN is the maximum value for the sum of grade and curve resistances, due to the resistance of train couplers for a 1234 tons towable weight. Indeed, the Disposition n\({}^{\circ}\) 18 of 19 November 2015, published by RFI [25], has removed the limit about the maximum towable weight due to the resistance of train couplers, in order to satisfy the requirements of freight railway companies which aim at improving their productivity operating longer trains.