# Dynamic Analysis and Seat Selection of Bus Driving Comfort under Different Road Conditions
## 4 Mechanical Responses of Bus in Driving under the Coupling Effect of Speed and Uneven Road Surface
### Road Condition I  
The sketch of road conditions for the bus is shown in Figure 3. The front wheel drives into the uneven road section, but the rear wheel is still in the flat road section. The bus travel distance is \(0\leq x\leq(b+c)\). The net displacement of the front and rear wheels of the bus at this point is presented in Figure 8. When the speed is relatively high, the maximum net displacement be reached quicker. This means that the net displacement of the bus is smaller when the bus speed is slower. Thus, a greater bus speed will generate bigger net displacement. Therefore, a bus running at low speed has smaller displacement and higher  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**GPS Time** & **Longitude [\({}^{\circ}\)]** & **Latitude [\({}^{\circ}\)]** & **GPS Speed [m/s]** & **\(a_{lat}\) [m/s\({}^{2}\)]** & **\(a_{long}\) [m/s\({}^{2}\)]** \\ \hline
10:33:55 & 9.10102 & 39.241895 & 4.01 & \(-\)0.7346 & \(-\)0.4840 \\
10:33:56 & 9.101006667 & 39.24188333 & 4.50 & \(-\)1.0937 & 0.5383 \\
10:33:57 & 9.10098333 & 39.24178783 & 5.06 & 0.9893 & \(-\)0.2925 \\
10:33:58 & 9.100963333 & 39.24165 & 5.61 & 0.7977 & \(-\)0.1417 \\
10:33:59 & 9.100926667 & 39.24165 & 6.08 & \(-\)0.1169 & 0.1289 \\
10:34:00 & 9.10092 & 39.24158667 & 6.43 & \(-\)0.7346 & 0.1193 \\
10:34:01 & 9.10095 & 39.241525 & 6.68 & 0.1896 & \(-\)0.4098 \\ \hline \hline \end{tabular} Note: \(a_{lat}\) means the acceleration component in latitude and \(a_{long}\) means the acceleration component in longitude.  
\end{table}
Table 2: Location-at-time raw data sample gathered by the app Torque on Tue Jul 2018 [43].  
Figure 7: Net displacement (**a**) and vertical acceleration (**b**) of front and rear wheels \(2 ns\leq x\leq 2 ns+(b+c)\) (\(n\in N^{\prime}\)).  
passenger comfort. Figure 9 shows the acceleration change of the bus at different speeds. The acceleration also shows that when the bus speed is low, it takes longer to reach the maximum net acceleration of the vehicle, which means that the acceleration changes less at low speed, and the passenger comfort is higher.  
Figure 8: Net displacement of front and rear wheels \(0\leq x\leq(b+c)\): (**a**) \(v=4\) m/s; (**b**) \(6\) m/s; (**c**) \(8\) m/s; (**d**) \(10\) m/s.  
Figure 9: Net vertical acceleration of front and rear wheels at different speeds \(0\leq x\leq(b+c)\).  
Figure 10 shows the displacement of the bus in the middle section. It clearly shows that there is only one wave peak in (a), one and a half wave peaks in (b), and two wave peaks in (c), but the results are not obvious, while there are two wave peaks in (d). This means that faster speed will generate a higher frequency of large displacement. Figure 10c has obvious fluctuations, which are different from the other three figures. This mainly reflects the large displacement in a short time. This may be because the bus resonates with the ground when \(v=8\) m/s, resulting in the continuous large displacement of the whole bus.  
The change in acceleration still shows that the comfort of the bus will be further reduced when the speed is fast. The change in \(v=8\) m/s is the most dramatic. At this time, the resonance situation does occur when the bus passes through the section \((b+c)\)\(\leq x\leq 2 ns\) (\(n\in N^{\bullet}\)), the comfort of passengers is the worst, and the overall displacement of the bus is the largest. Table 4 records the maximum net displacement and acceleration corresponding to different speeds during the whole bus driving in _road condition II_. The overall acceleration changes uniformly and the displacement changes slightly when the bus passes through this section. When the bus speed is \(8\) m/s, both net displacement and net acceleration reach a maximum value of a sharp increase. This indicates that the resonance phenomenon between the bus and the road occurs at this time, and the passenger comfort is the lowest.