## 4 Ride Comfort Assessment Methods  
### Mean Comfort Method  
The mean comfort method was initially presented in UIC 513R leaflet [25], then in the standard of railway applications EN 12299 [26]. The UIC 513R leaflet is a guide to assess the mean comfort in the railway vehicles. The standard EN 12299 completes the UIC 513R leaflet by considering the effects from discrete events and running on connection curves upon the instantaneous comfort.  
The quantification of the mean comfort to vibrations is made with ride comfort index (\(N_{MV}\)) and with a conventional scale linking the values of this index and the comfort sensation (see Table 2).  
The ride comfort index is calculated with the general relation [25; 26]  
\[N_{MV}=6\cdot\sqrt{\big{(}a_{X95}^{Wad}\big{)}^{2}+\big{(}a_{Y95}^{Wad}\big{)}^ {2}+\big{(}a_{Z95}^{Wab}\big{)}^{2}} \tag{20}\]  
where \(a_{X}\), \(a_{Y}\) and \(a_{Z}\) is the root mean square of the longitudinal, lateral and vertical carbody acceleration, 95 refers to the quantile of order 95%, and _Wad_, _Wab_ represent the weighting filters of the longitudinal, lateral, respectively vertical acceleration.  
According to ref. [26] and depending on application, the following partial comfort indexes can be used: \(N_{MVX}\)--for ride comfort at longitudinal vibration, \(N_{MVY}\)--for ride comfort at lateral vibration and \(N_{MVV}\)--for ride comfort at vertical vibration. In this standard, there is no distinction regarding the conventional comfort scale (see Table 2) for \(N_{MV}\) or \(N_{MVX}\), respectively \(N_{MVY}\) and \(N_{MVZ}\). In other words, the comfort scale is general for the ride comfort index and any partial ride comfort index.  
To evaluate the vertical ride comfort, the partial comfort index is used, through the general relation [26]  
\[N_{MVZ}=6a_{Z95}^{W_{ab}} \tag{21}\]  
where \(W_{ab}\) = \(W_{a}\cdot W_{b}\) stands for the weighting filter of the vertical acceleration.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Ride Comfort Index \(N_{MV}\)** & **Significance** \\ \hline \(N_{MV}\) < 1 & Very good comfort \\ \(1\leq N_{MV}\) < 2 & Good comfort \\ \(2\leq N_{MV}\) < 4 & Acceptable comfort \\ \(4\leq N_{MV}\) < 5 & Poor comfort \\ \(N_{MV}\geq 5\) & Very poor comfort \\ \hline \hline \end{tabular}
\end{table}
Table 2: The significance of the ride comfort index \(N_{MV}\).  
The filter \(W_{a}\) is a passband filter with the following frequency weighting function  
\[H_{a}(s)=\frac{s^{2}(2\pi f_{2})^{2}}{\left[s^{2}+\frac{2\pi f_{1}}{Q_{1}}s+(2 \pi f_{1})^{2}\right]\left[s^{2}+\frac{2\pi f_{2}}{Q_{1}}s+(2\pi f_{2})^{2} \right]}, \tag{22}\]  
where \(s=\mathrm{i}\omega\) (with \(\mathrm{i}^{2}=-1\)),\(f_{1}=0.4\) Hz,\(f_{2}=100\) Hz and \(Q_{1}=0.71\).  
The filter \(W_{b}\) takes into account the high human sensitivity to the vertical vibrations and has the frequency weighting function in the form of  
\[H_{b}(s)=\frac{(s+2\pi f_{3})\cdot\left[s^{2}+\frac{2\pi f_{5}}{Q_{3}}s+(2\pi f _{5})^{2}\right]2\pi Kf_{4}^{2}f_{6}^{2}}{\left[s^{2}+\frac{2\pi f_{4}}{Q_{2}} s+(2\pi f_{4})^{2}\right]\left[s^{2}+\frac{2\pi f_{6}}{Q_{4}}s+(2\pi f_{6})^{2} \right]f_{3}f_{5}^{2}}, \tag{23}\]  
where \(f_{3}=16\) Hz,\(f_{4}=16\) Hz,\(f_{5}=2.5\) Hz,\(f_{6}=4\) Hz, \(Q_{2}=0.63\), \(Q_{4}=0.8\) and \(K=0.4\).  
Figure 2 shows the frequency weighting functions of the two weighting filters, whereas the Figure 3 showcases the frequency weighting function \(H_{ab}=H_{a}H_{b}\) of the filter \(W_{ab}\). The latter shows that the mean comfort takes into account the higher sensitivity of the human body to vertical vibrations within the frequency interval of 4 Hz and 16 Hz [28].