# Improvement of Boeing Bump Method Considering Aircraft Vibration Superposition Effect
## 3 Simulation of Aircraft Dynamic Response
### Verification of Virtual Prototype Models  
The FAA has used a B737-800 driving simulator to conduct research into airport runway roughness at the Mike Monronney Aeronautical Center in Oklahoma City, OK [18]. The FAA presents the simulation results in terms of the weighted root mean square of the vertical acceleration of the aircraft cockpit on eight existing runways. These results were obtained from both the driving simulator as well as from the FAA's computer program, ProFAA, which the FAA uses to compute pavement profile roughness [19]. In this paper, the driving simulator test results are used to verify the reliability of the virtual prototype compared to ProFAA. The longitudinal profiles of the eight runways were imported into ADAMS/Aircraft. Using the newly built B737-800 model, simulations were performed at the same speed (100 knots) as used in FAA B737-800 driving simulator and ProFAA. We were then able to calculate the weighted root mean square of the vertical acceleration of the cockpit from the ADAMS/Aircraft simulation. Table 3 and Figure 4 present comparisons of the simulation results obtained using ProFAA, the B737-800 simulator, and ADAMS/Aircraft software. Our simulation results obtained from ADAMS/Aircraft are closer to the driving simulator results than to the ProFAA results, and the overall trend of our results also is more consistent with the driving simulator data than with the ProFAA data. With regard to the average difference from the reference driving simulator results, the ProFAA results reached 64% whereas the difference for the ADAMS/Aircraft results was only 14 %. Therefore, using ADAMS/Aircraft for aircraft simulations is more reliable than using ProFAA.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Weighted Root Mean Square of Vertical Acceleration of**} \\ \cline{3-5}
**Runway No.** & **Airport** & \multicolumn{3}{c}{**Coockpit (m/s\({}^{2}\))**} \\ \cline{3-5}  & & **ProFAA** & **B737-800 Simulator** & **ADAMS/Aircraft** \\ \hline
47 & MSY & 0.25 & 0.15 & 0.15 \\
51 & ORD & 0.23 & 0.17 & 0.12 \\
54 & EWR & 0.37 & 0.2 & 0.21 \\
57 & ACY & 0.29 & 0.2 & 0.17 \\
63 & MDT & 0.39 & 0.22 & 0.19 \\
68 & ACY & 0.31 & 0.19 & 0.18 \\
70 & Trinidad & 0.64 & 0.32 & 0.4 \\
75 & RUS & 0.63 & 0.42 & 0.5 \\ Average difference from & & & & \\ simulator & & 64\% & 0\% & 14\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of results for three simulation methods [18].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{2}{c}{**\(40\times 16-16\) 26**} & \multicolumn{2}{c}{tire radius /inch} & 40 \\ \cline{3-5}  & front wheel & mass/kg & 255 & tire width /inch & 16 \\ \cline{3-5}  & front wheel & lxx, lyy/kg:m2 & 44,998 & aspect ratio & 0.75 \\ \cline{3-5}  & & lzz/kg:m2 & 77,416 & tire pressure /MPa & 1.29 \\ \cline{3-5} wheel & & 50 \(\times\)2 0 \(-\) 22 34 PR & tire radius /inch & 20 \\ \cline{3-5}  & main wheel & mass/kg & 392 & tire width /inch & 22 \\ \cline{3-5}  & & l\({}_{x}x\), \({}_{y}y\)/kg:m2 & 45,757 & aspect ratio & 0.7 \\ \cline{3-5}  & & l\({}_{z}z\)/kg:m2 & 78,721 & tire pressure /MPa & 1.57 \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._Figure 5 presents the simulation results for the five aircraft models with the same taxiing speed on the same runways (as used in the FAA's research). As shown, the root mean square of the vertical acceleration of the aircraft cockpit tends to decrease with the increase in the size of the aircraft.