## 4 Discussion
The frequency \(f_{h}\) of this movement is described by the Klingel equation, as summarized by [PERSON] and [PERSON] [26]:  
\[f_{h}=\frac{v}{2\pi}\cdot\sqrt{\frac{\delta}{e\cdot r}} \tag{6}\]  
The speed \(v\) of the train, the half track width \(e\), the radius \(r\) of the wheel as well as the equivalent conicity \(\delta\) influence the frequency \(f_{h}\). Since, in this study, a measurement on a meter gauge track was analyzed, a higher hunting motion frequency could be assumed compared with the 1435 mm standard gauge. The method for determining the velocity from the phase shift of the sensor signals to each other provides reliable values for selected segments. An advantage of this approach is that it does not require synchronization with measurement values from other sources, such as the velocity values recorded on-board the train. The sensor data are pre-filtered with a high pass filter. The short-wave components in the signal are especially suitable for determining the phase shift. Features such as local peaks in the signals can be successfully overlapped. Since four sensors in the setup measured the longitudinal profile, it was possible to calculate six different phase shifts and consequently six velocity values. No significant advantages could be determined in the comparison between small and larger sensor distances. The velocity value applied for the evaluation was calculated from the mean value of the six determined individual values. The segment length set for the evaluation of the acoustic roughness determines the averaging of the acoustic roughness over the length. This length should not be chosen over several kilometers, as the rail surface condition within several kilometers can already deviate significantly. For measurements of the entire rail network, a standard length must therefore be defined for the evaluations to ensure comparability between the measurement results. Since the velocity is averaged for a selected data segment, distortions in the spectrum are to be expected here, since the velocity over a long segment deviates from the average value. The deviations shown in Figure 4 are small due to the choice of a straight rail segment and the evaluation of a short part of 240.5 m, but they could vary more for other parts of the route. [PERSON] et al. [27] already demonstrated this distortion effect on the PSD (power spectral density) for measurements of axle-box accelerations. According to the EN 15610 [20] standard, the longitudinal profile must be measured on three laterally displaced lines as long as the width of the running surface exceeds a value of 20 mm. If the width is less than 20 mm, it is only necessary to measure on one line in the middle of the running surface. It must therefore be investigated if a positioning system is sufficient or whether, alternatively, three identical systems must be used to measure the profile on three different laterally offset lines. In this study, the reference was recorded on a straight rail section. The influence of curves has not been investigated. Depending on the mounting position, curves can lead to a diagonal position of the measurement setup, which means that not all sensors measure at the same lateral position.