## 3 Sensitivity Analysis of Aerodynamic Characteristics
### Results of Sensitivity Analysis  
In this section, the global sensitivity analysis is conducted to assess the effect of design parameters on the aerodynamic characteristics of the projectile. The first step is to determine the input design parameters of the system and their distributions. The simulation and tests show that the main factors affecting the aerodynamic characteristics include the angle of attack of the vehicle, the incoming velocity, the position of the center of mass, the diameter of the projectile, the length, and so on [9]. In this study, the design parameters and their distributions are chosen, as shown in Table 4.  
A total of 50 groups of design sampling points are selected within the given design space, and the corresponding aerodynamic characteristics (lift coefficient, drag coefficient, pitch moment coefficient, and combined dynamic derivatives) are obtained through CFD simulations proposed in Section 2. Subsequently, the ARBF models for the lift coefficient, drag coefficient, pitch moment coefficient, and combined dynamic derivatives can be constructed. Based on the ARBF models, the Sobol method is employed to determine the first-order and the total sensitivity coefficients, as shown in Section 3.  
The first-order and total global sensitivities of the design parameters on the aerodynamic characteristics while the angle of attack is 10\({}^{\circ}\) are shown in Table 5 and Figure 7. Comparison of the two graphs in Figure 7 clearly shows that the centroid position has the greatest effect on the lift coefficient and drag coefficient, while the incoming velocity has the greatest effect on the pitch moment coefficient and combined dynamic derivatives, when the angle of attack is 10\({}^{\circ}\). The variation of the total sensitivity of the pitch moment coefficient with the different angles of attack are shown in Figure 8. From Figure 8, it can be seen that, at different angles of attack, the effect of the four design parameters on the pitch moment coefficient varies. In order to ensure the dynamic performance of the different angle of attack maneuvering, the influence of these four parameters should be fully and comprehensively considered in practical design.  
\begin{table}
\begin{tabular}{c c c} \hline
**Serial Number** & **Parameters** & **Value Range** \\ \hline P1 & Radius (m) & 0.05–0.2 \\ P2 & Length (m) & 0.48–0.68 \\ P3 & Centroid position (m) & 0.1–0.45 \\ P4 & Inlet flow field velocity (Ma) & 0.1–0.5 \\ \hline \end{tabular}
\end{table}
Table 4: Parameters for sensitivity analysis.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Parameters** & **P1/Radius** & **P2/Length** & \begin{tabular}{c} **P3/Centroid** \\ **Position** \\ \end{tabular} & \begin{tabular}{c} **P4/Inlet Flow** \\ **Field Velocity** \\ \end{tabular} \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} First-Order \\ Sensitivity \\ \end{tabular} } & Lift coefficient & 0.133 & 0.016 & 0.628 & 0.193 \\  & Drag coefficient & 0.208 & 0.147 & 0.538 & 0.071 \\  & Pitch moment coefficient & 0.050 & 0.132 & 0.017 & 0.772 \\  & Combined dynamic & 0.114 & 0.230 & 0.037 & 0.604 \\  & derivatives & & & & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Total Sensitivity \\ \end{tabular} } & Lift coefficient & 0.148 & 0.043 & 0.638 & 0.201 \\  & Drag coefficient & 0.229 & 0.175 & 0.549 & 0.084 \\ \cline{1-1}  & Pitch moment coefficient & 0.061 & 0.145 & 0.032 & 0.791 \\ \cline{1-1}  & Combined dynamic & & & & \\ \cline{1-1}  & derivatives & & & & \\ \hline \end{tabular}
\end{table}
Table 5: Sensitivity indices of different design parameters at the angle of attack at 10\({}^{\circ}\).