*2.3.1 Track characteristics: Radii and speed classes*

Based on the differences between alignment of track sections, a classification of radii and speeds was done. For the TDM 5 radii classes (R) were defined. These 5 radii classes correspond to those used in the Standard Elements [1]. Further, defining different radii classes comprises not only the law of superelevation of the outer rail in curved tracks, but also the wear of this outer rail.

The fifth radius class (R5) represents track sections that show a radius of more than 1000 m. These sections are classified as straight track sections. Radius class R5 is again divided into eight speed classes (S1 to S8). For each radius and speed class one reference speed is allocated with which the vehicle parameters are calculated. The reference speeds of radius class R1 to R4 each represent the rounded median value of the line speeds of the Austrian core network. The reference speed of 60 kmph of radius class R1 thus indicates that on the Austrian main lines in curves with radii less than 250 m a median speed of 60 kmph is driven. The calculation of the reference radii is done analogously. **Table 2** lists the radius and speed classes with their reference radius and speed.

In the Austrian network vehicles used in freight traffic are always treated with a maximum speed of 100 kmph, in the model 90 kmph is therefore assumed as a


*Speed and radii classification.*

reference speed for freight traffic. This speed limitation applies to both freight wagons and also freight locomotives. For speed classes S3 to S8 of radius class R5 (straight tracks) and radius class R4, the reference speed is applied in the model, as the reference speed exceeds 90 kmph in these classes. The speed classes S2 to S8 are thus identical and further lead to equal calculated parameters for freight rolling stock. For universal locomotives, it therefore makes sense to differentiate according to type of traffic (passenger or freight traffic).

Additionally, it should be mentioned here that the reference speed is a reference value that is based on the maximum permissible speed of track sections due to their track alignment (STrack). If the maximum permissible speed of the vehicle/train (Smax, Veh) exceeds the speed due to track alignment (Smax,Veh > STrack), in the calculation of the vehicle parameters (Section 2.3.2), the reference speed (STrack) of **Table 2** is applied. This also applies analogously vice versa, as shown in Eq. (11).

$$\mathbf{S} = \min[\mathbf{S}\_{\text{max}, \text{Veh}}, \mathbf{S}\_{\text{Track}}] \tag{11}$$

S—relevant speed (kmph); Smax,Veh—maximum permissible speed due to rolling stock (kmph); STrack—maximum permissible speed due to track alignment (kmph).

Using the minimum of both speeds Smax,Veh and STrack reflects the operational reality. Regarding the speed the determined damage that is speed dependent (D1, D2, D5, D6 and D7) is thus also close to reality.

#### *2.3.2 Rolling stock parameters*

The TDM and its damage terms described in Section 2.2 are based on the following four parameters:


The parameters P1 and P2 stand for the dynamic vertical force, while Y describes the lateral force that occurs in a track curve on the outer wheel of a bogie in the leading wheelset. The traction power value (TPV) indicates the physical power per wheel due to traction. The fourth physical input parameter for the deterioration formula is Tγ that stands for the friction work due to longitudinal and lateral slip. The following sections include a discussion of the four vehicle parameters in more details.
