# 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
#### 3.1.5 The Tarvisio, Semmering and Tauern Lines  
As far as the Tarvisio line is concerned, it does not have particular problems as to the resistance of train couplers. The maximum sum of grade and curve resistances is 14.6 N/kN from Carnia to Tarvisio pass (west ramp) and 20 N/kN from Villach to Tarvisio pass (east ramp). This line is operated in double traction between Carnia and Villach, in both directions.  
As regards the Semmering line, the situation is the following. Between Villach and Klagenfurt (38 km) the line is flat. From Klagenfurt to Neumarkt im Steiermark (70 km), the line has a maximum sum of grade and curve resistances of 18 N/kN, while from Neumarkt im Steiermark to Bruck an Der Mur (99 km) the line is descending. In the opposite direction, from Bruck an Der Mur to Neumarkt im Steiermark (99 km), the line has a maximum sum of grade and curve resistances of 16 N/kN. From Bruck an Der Mur to Murzzuschlag (27 km), the line has a maximum sum of grade and curve resistances of 11 N/kN. From Murzzuschlag to the Semmering Pass (13 km), the line has a maximum sum of grade and curve resistances of 18 N/kN. From Gloggnitz to the Semmering Pass (27 km) the line has a maximum grade resistance of 22.5 N/kN but in particular a maximum curve resistance of 5.5 N/kN: some curves even have a radius of 150 m, and the maximum sum of grade and curve resistances is 28 N/kN.  
The line is operated in double traction from Villach to Gloggnitz; in the opposite direction, it is operated in triple traction from Gloggnitz to Murzzuschlag and double traction from Murzzuschlag to Villach [39]. The part of the line between Villach and Klagenfurt could be operated in single traction, but it is only 38 km long and it is preceded and followed by lines operated in double traction. As a result, also this line portion is operated in double traction.  
Although the Semmering line shows geometrical problems only for 40 km, an entire new line from Klagenfurt and Gloggnitz is under construction. This choice has been made also because the current Semmering line does not cross the important city of Graz. The new Semmering line will be composed of the following parts:  
* new Koralmbahn, between Klagenfurt and Graz;
* upgrading of the old line between Graz and Bruck an der Mur
* upgrading of the old line between Bruck an der Mur and Murzzuschlag
* Semmering base tunnel between Murzzuschlag and Gloggnitz.  
The new Semmering line will be entirely operated in single traction in both directions. The maximum sum of grade and curve resistance, in the direction Villach--Vienna, which will take place from Graz to Bruck an der Mur, is equal to 11 N/kN. In the direction Vienna--Villach, the maximum sum of grade and curve resistances is 9 N/kN, which will take place in the Koralmbahn east ramp.  
The Tauern Line connects Villach with Salzburg, but the steepest part is located between Spittal an der Drau (located on the south) and Schwarzach im Pongau (located on the north) in both directions;this line involves also the Tauern tunnel, 8.37 km long. The line has been highly improved recently, in order to reduce the curves, but the slopes have remained high and the maximum sum of grade and curve resistances is 27 N/kN in both directions. The line is operated in triple traction between Spittal an der Drau and Shwarzach im Pongau in both directions and in double traction in the rest of the line in both directions.