# Improvement of Boeing Bump Method Considering Aircraft Vibration Superposition Effect
## 5 Results and Discussion
### Analysis of Superposition Effect  
When two successive bump wavelengths with the same shape and amplitude are present on the runway profile, taxiing simulation tests are carried out at the most unfavorable speed for the aircraft's vibration response. We set bumps with 10-mm amplitude and 3-60m wavelengths. Figure 9 presents comparisons of the maximum values of the MGDLC and PSA after the superposition of two bumps and a single bump. When the wavelength of two successive bumps is the sensitive wavelength of the aircraft at that speed, the frequency of the continuous excitation is close to the natural frequency of the aircraft's buffer system. Therefore, the dynamic responses of the aircraft reach their peak due to the superposition of resonation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Aircraft Type** & **B737-800** & **B757-200** & **B787-8** & **B777-300 ER** & **B747-400** \\ \hline For dynamic load & 80 & 100 & 120 & 120 & 120 \\ coefficient & & & & & \\ For vertical & & & & & \\ acceleration & 260 & 328 & 330 & 348 & 350 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Most unfavorable speeds for five types of aircraft (km/h).  
Figure 9: _Cont_.  
The bump wavelength is set to the aircraft's sensitive wavelength, which indicates that the frequency of the continuous excitation is the natural frequency of the aircraft. Table 8 shows the peak dynamic responses of the five types of aircraft under two identical successive bumps compared to their responses under a single bump. The increases in the peak dynamic responses (NGDLC and PSA) at the front of the aircraft after superposition are greater than the increases in those responses (MGDLC and CGA) at the center of the aircrafts. This trend becomes increasingly more distinct with the diminishing size of the aircraft type.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{MGDLC} & \multicolumn{2}{c}{NGDLC} \\ \cline{2-5} aircraft types & peak responses after superposition (m/s\({}^{2}\)) & increased percentage compared to under single bump & peak responses after superposition & increased percentage compared to under single bump \\ \hline B737-800 & 1.031 & 3.1\% & 1.080 & 6.1\% \\ \hline B757-200 & 1.017 & 2.2\% & 1.046 & 4.4\% \\ \hline B787-8 & 1.004 & 2.2\% & 1.023 & 4.1\% \\ \hline B777-300 ER & 0.986 & 2.0\% & 0.998 & 3.3\% \\ \hline B747-400 & 0.973 & 1.4\% & 0.984 & 2.5\% \\ \hline \multicolumn{5}{c}{CGA} & \multicolumn{2}{c}{PSA} \\ \cline{2-5} aircraft types & peak responses after superposition (m/s\({}^{2}\)) & increased percentage compared to under single bump & peak responses after superposition (m/s\({}^{2}\)) & increased percentage compared to under single bump \\ \hline B737-800 & 0.55 & 25.9\% & 0.65 & 48.5\% \\ \hline B757-200 & 0.45 & 22.4\% & 0.62 & 45.5\% \\ \hline B787-8 & 0.44 & 16.7\% & 0.51 & 41.6\% \\ \hline B777-300 ER & 0.38 & 14.3\% & 0.44 & 36.2\% \\ \hline \hline \end{tabular}
\end{table}
Table 8: Peak responses and increases following superposition of two successive bumps.  
Figure 9: Maximum values of MGDLC and PSA after superposition (compared with single bump).