# Impact of Environmental Factors on Passenger Ride Comfort
## 4 Methodology
### Vibration Comfort  
The impact of mechanical vibrations in vehicles is undoubtedly one of the most studied key factors that affect passenger comfort. Depending on the frequency and amplitude of vibrations, as well as the duration of exposure to them, the effect of vibrations on humans may vary. The sensation of vibrational comfort also depends on where the vibrations are applied and their direction [31]. Most of the commonly used standards for assessing the impact of vibrations on humans in vehicles involve the determination of a comfort index based on measured/simulated values of vibration accelerations, usually averaged using frequency weights reflecting the perception of vibration stimuli by various parts of the human body. Each of these indices is then related to a comfort scale with several levels. One of the first methods of this type was the Wz index (Wertunsziffer) developed by [PERSON] [9], which was widely used in rail transport regulations. Nowadays, a frequently used standard for assessing ride comfort is EN 12299:2009 [32]. However, this document only applies to rail vehicles. A standard that is applicable to many modes of transport and is globally recognised is ISO 2631-1:1997 [33]. Although this document was originally released almost three decades ago, it is still valid and regularly revised. The last revision of the standard was approved in 2021 [34]. A summary of relevant vibration comfort indicators is given in Table 2.  
For the assessment of vibration comfort, the proposed method adopts the recommendations of the ISO 2631-1 standard. The authors chose to use this standard because of its versatility and lack of restriction on the type of means of transport. The quoted document allows for the assessment of ride comfort on the basis of a weighted method. This method is based on the measurement of vibration accelerations propagating in three directions (\(x\), \(y\), \(z\)), which are defined in the standard depending on the position of the human body. The measured accelerations are used to determine the RMS values of vibration accelerations in one-third octave bands with frequencies in the range from 0.8 to 80 Hz. This range corresponds to humans' sensitivity to mechanical vibrations. On the basis of the calculated values of the effective vibration accelerations, the weighted RMS values should be calculated separately for the \(x\), \(y\), and \(z\) directions according to the formula  
\[a_{w,\eta}=\sqrt{\sum_{i=1}^{n}\left[W_{i}(f)\cdot a_{i,\eta}(f)\right]^{2}}, (\eta=x,y,z), \tag{2}\]  
where \(W_{i}\) is the weighting function in the \(i\)-th one-third octave band defined in the standard for the specific position (standing or seated) and the direction of vibration (\(\eta=x\), \(y\), \(z\) \begin{table}
\begin{tabular}{c c c} \hline
**Standard** & **Comfort Index** & **Comfort Scale** \\ \hline [PERSON]’s index & Wz & Seven levels of the descriptive scale \\ EN 12299:2009 & NMV & Five levels of the descriptive scale \\ ISO 2631-1:1997 & a\({}_{w}\) & Six levels of the descriptive scale \\ \hline \end{tabular}
\end{table} 
Table 2: Vibration comfort indicators used to assess transport means. respectively), and \(a_{i,n}\) is the RMS value of the vibration accelerations in the \(i\)-th one-third octave band for the respective subsequent vibration direction. From the weighted RMS values of vibration accelerations \(a_{w,x}\), \(a_{w,y}\), and \(a_{w,z}\), a synthetic ride comfort index is determined according to the relation  
\[a_{w}=\sqrt{k_{x}^{2}\cdot a_{w,x}^{2}+k_{y}^{2}\cdot a_{w,y}^{2}+k_{z}^{2}\cdot a _{w,z}^{2}} \tag{3}\]  
where \(k_{x}\), \(k_{y}\), and \(k_{z}\) are the correction factors specified in the standard. For a seated passenger, the standard sets the values of all correction factors equal to 1. In the proposed method of assessing ride comfort that takes into account a wider range of environmental factors, the recommendations of ISO 2631-1:1997 are only used to determine a vibration comfort index.