# Development of a New Vertical Dynamic Model of a Rail Vehicle for the Analysis of Ride Comfort
## 3 Ride Comfort Evaluation  
Comfort, which is a part of well-being, is disturbed by various disturbances in the physiological and physical environment (movements, temperature, noise, seat characteristics, etc.) [14]. A recent study [24] on metro vehicle comfort investigated the issue in a more comprehensive way, by considering ride dynamics, thermal comfort, humidity and illuminance. They suggested that these factors should also be considered together with ride dynamics to increase the attractiveness of the railway system. For example, the EN 13129:2016 standard [25] sets comfort parameters for air conditioning in passenger compartments of railway vehicles, and it outlines conditions, performance values and measurement methods. The ride comfort in dynamical terms represents the comfort level of the passenger who is affected by the vibrations from any direction during the travel [26]. These vibrations are mainly determined by the direction, frequency and amplitude of the vibration.  
In this study, a widely used method for comfort evaluation was used: the method of the ISO 2631 standard. According to ISO 2631, a frequency range of 0.5-80 Hz must be considered [20]. Humans are most sensitive in the frequency range of 4-10 Hz, and this range is significant for comfort evaluation in the vertical direction [27]. ISO 2631 states that measurement data gathered from the floor in the middle of the car body can be used for ride comfort evaluation in rail vehicles.  
This evaluation method uses the frequency-weighted r.m.s (root mean square) accelerations, according to the following equation:  
\[a^{wrms}=\left[\frac{1}{T}\int\limits_{0}^{T}a_{w}^{2}(t)dt\right]^{0.5} \tag{5}\]  
where \(a^{wrms}\) is the root mean square of weighted accelerations, \(a_{w}(t)\) is the weighted acceleration as function of time and \(T\) is the duration of measurement in seconds. The weighting filter, according to ISO 2631, for vertical comfort evaluation is as follows:  
\[W_{k}(s)=\frac{(s+2\pi\cdot f_{3})}{s^{2}+\frac{2\pi\cdot f_{4}}{Q_{4}}\cdot s +(2\pi f_{4})^{2}}\cdot\frac{\left(s^{2}+\frac{2\pi\cdot f_{5}}{Q_{5}}\cdot s +(2\pi\cdot f_{5})^{2}\right)}{s^{2}+\frac{2\pi\cdot f_{6}}{Q_{6}}\cdot s+(2 \pi\cdot f_{6})^{2}}\cdot\frac{2\pi f_{4}^{2}}{f_{3}} \tag{6}\]  
where \(W_{k}(s)\) is the vertical comfort filter as a transfer function, and its variables, used in the function, are given in Table 2. The calculation scheme of this filter is embedded in the Vampire software.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Weighting** & \(f_{3}\) & \(f_{4}\) & \(f_{5}\) & \(f_{6}\) & \(Q_{4}\) & \(Q_{5}\) & \(Q_{6}\) \\ \hline \(W_{k}\) (ISO) & 12.50 & 12.50 & 2.37 & 3.35 & 0.63 & 0.91 & 0.91 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the vertical frequency weighting filters (\(f_{i}\)’s are in Hz).  
The values used in the transfer function are the frequency values, represented by \(f_{l}\), and the resonant quality factor values, represented by \(Q_{i}\). Together, they determine the frequency weighting process. The levels of the ride comfort according to ISO 2631 are given in Table 3.