# A Methodology Linking Tamping Processes and Railway Track Behaviour
## 2 Basics of Track Geometry
### Track Quality Indices  
The principal track geometry parameters are critical for safe railway operation, and the respective measurement signals must not exceed defined threshold levels (intermediate action level, IAL) at any point along the track [13]. However, while these geometry signals are appropriate for comparison with threshold values, they are less suited to describe the general track quality and observe its behaviour over a longer section. For this purpose, track quality indices (TQIs) have been established [14; 15; 16]. A track quality index considers all data points of a track geometry signal within a defined track segment (\"window\") and represents the average track condition of this segment by a single value. The most widely used index to describe the quality of a track is the standard deviation (\(SD\)) of the longitudinal level [16], calculated according to Equation (1) [17]:  
\[SD=\sqrt{\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2}}{N-1}} \tag{1}\]  
Track quality indices based on an individual track geometry parameter are typically used for maintenance planning; the selected parameter already indicates the required maintenance work (e.g., a poor standard deviation of the longitudinal level triggers levelling-lining-tamping) [5; 9]. Single-parameter indices can also be combined to create a holistic track quality index, representing the overall track geometry condition. A holistic TQI, however, is not appropriate to predict maintenance tasks, as it is impossible to identify the source of a quality issue, thus the required maintenance type cannot be derived from the aggregated quality figure. An overview of existing track quality indices can be found in [16].  
The magnitude of any track quality index at a certain cross section is severely affected by two calculation parameters: (i) the calculation type (discrete or moving) and (ii) the window length [16; 18]. (i) A discrete calculation delivers a continuous value for the entire considered window, i.e., the respective track segment. On the plus side, segments in need of maintenance can be easily identified. A downside is that the location of the segments (start and end point) has a strong effect on the results. For example, a severe isolated defect at the cut-off point between two segments affects both; if the segments are shifted by a small distance, the isolated defect will have a stronger influence on one segment while not affecting the other [18]. A moving calculation assigns the calculated track quality value of the current window to its centre point, before the window is shifted by one data break and the calculation is repeated. Thus, a moving TQI reflects the input signal better than a discrete TQI and is considered more suitable to represent the track quality [18]. (ii) The window length defines how many data points are included in the calculation of a TQI. Larger windows have a smoothing effect, while shorter windows emphasise local defects [16]. Typical window lengths are 200 m [17] and 100 m (applied at Austrian Federal Railways and Swiss Federal Railways, for example [19; 20]).  
Figure 2: Principal track geometry parameters according to EN 13848-1; red lines illustrate the deviation from the ideal geometry.