## 4 Discussion
### Effect of Vertical Track Irregularities on Train Body Accelerations
train body are between 63.9 and 83.3 m, and the critical wavelengths corresponding to the bouncing mode of the train body are between 91.3 and 119.0 m.  
In sum, it is appropriate to manage the track geometry with a 30-m chord for absolute track-geometrical errors of wavelengths of up to approximately 70 m. However, if the wavelength is longer (i.e., in cases of longer bridge spans), the longer chord length should be considered, because the dominant wavelength of the track-geometrical errors might, depending on the train speed, come close to the critical wavelength bands related to the natural frequency of the vehicle suspension. Figure 16 plots the FFT results of vertical track irregularities converted according to temperature in the test run. As could easily be predicted, the highest amplitude was observed at 70 m, which corresponds to the center arch span of the bridge, 45 and 60 m, which correspond to spans slightly smaller or larger than the span of the side arch (55 m), and 180 m, which corresponds to the entire length of the bridge. In summer, the peaks appeared at 70 m and 180 m. In winter, however, the amplitude, at around 70 m, was decreased, but was greatly increased beyond 180 m. This was due to the fact that, in winter, the temperature in the daytime increases relative to nighttime and the amplitude of the track-geometrical errors near 70 m decreases. This is one of the reasons why the acceleration of the train body was smaller in winter than in summer. Figure 17 plots the FFT results for the vehicle vertical accelerations in the wavelength domain. As can be seen, the peak vertical accelerations of the train body were observed in the vicinity of 40 to 50 and 60 to 70 m, which coincided with the dominant wavelengths of the track-geometrical errors in both summer and winter. As mentioned above, because the most dominant wavelengths of the track-geometrical errors are not superposed on the critical wavelengths for the train body vibration, the train body accelerations were not significant, and did not exceed the limits for ride comfort. However, if the train speed decreases, the critical wavelengths corresponding to the natural frequencies of the \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{3}{c}{**Natural Frequencies (Hz)**} & \multicolumn{3}{c}{**Critical Wavelength (m) Corresponding to Natural Frequencies at Train Speed of V (dm/h)**} \\ \cline{2-10}  & \multirow{2}{*}{**Train Body**} & \multirow{2}{*}{**Bogie**} & \multicolumn{3}{c}{**Train Body**} & \multicolumn{3}{c}{**Bogie**} \\ \cline{3-10}  & & & **V = 230** & **V = 250** & **V = 270** & **V = 300** & **V = 230** & **V = 250** & **V = 270** & **V = 300** \\ \hline Bouncing & 0.7 & 6.9 & 91.3 & 99.2 & 107.1 & 119.0 & 9.3 & 10.1 & 10.9 & 12.1 \\ \hline Pitching & 1.0 & 9.3 & 63.9 & 69.4 & 75.0 & 83.3 & 6.9 & 7.5 & 8.1 & 9.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Natural frequencies of train suspension system and corresponding critical wavelengths. Figure 16: FFT amplitude of vertical track irregularities in wavelength domain. vehicle suspension come close to 70 m, the dominant wavelength of the geometrical errors. According to Table 5, the critical wavelength for the pitching-mode resonance of the train body is 69.4 m at the train speed of 250 km/h. Therefore, at 250 km/h, the train body acceleration will be the largest. Figure 18 plots the train acceleration versus the unit track irregularity for the 30-m chord at different train speeds. There is no measurement data for 250 km/h, but Figure 18 shows that the train acceleration per unit track irregularity when the train travels at speeds of 230 and 270 km/h is slightly larger than that at 300 km/h.