## 3 Sensitivity Analysis of Aerodynamic Characteristics
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Grid Number** & **Number of Grids** & **Number of Nodes** & **Lift Coefficient \(\mathbf{C_{I}}\)** & **Drag Coefficient \(\mathbf{C_{d}}\)** \\ \hline
1 & 87,394 & 26,164 & 1.0999 & 1.3036 \\ \hline
2 & 93,118 & 27,175 & 1.0491 & 1.2873 \\ \hline
3 & 117,365 & 31,539 & 1.0288 & 1.2734 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Verification of grid independence of aerodynamic parameters at an angle of attack of 30\({}^{\circ}\). resulting in a slight decrease in the lift-to-drag ratio. Subsequently, when the angle of attack exceeds 60\({}^{\circ}\), the phenomenon of fluid separation is observed in the majority of areas on the leeward side of the model. At this point, the change in the angle of attack will not cause any significant impact on the pressure difference between the windward and leeward surfaces of the model, and the lift-to-drag ratio shows a declining trend. The evolution of the pitching moment coefficient in relation to the angle of attack is shown in Figure 6c. The absolute value of the pitching moment coefficient is relatively small. The pitching moment coefficient is positive at small angles of attack, indicating that the basic model is in a static unstable state at these angles of attack. The negative value of this coefficient within the calculated angle of attack variation indicates that the model is in a static stable state. Its absolute value firstly increases with the increase in the angle of attack but starts to fluctuate around the angle of attack near 60\({}^{\circ}\). The fluctuations observed in the pitching moment coefficient can be attributed to the gradual expansion of the separation zone on the leeward side of the front of the model towards the center and rear part. Figure 4: Velocity vector diagram and its streamline distribution diagram on the symmetry plane with different angles of attack. (**a**) The attack angles of 0\({}^{\circ}\); (**b**) The attack angles of 10\({}^{\circ}\); (**c**) The attack angles of 30\({}^{\circ}\); (**d**) The attack angles of 60\({}^{\circ}\); (**e**) The attack angles of 90\({}^{\circ}\). Figure 5: Velocity distribution of circumferential flow field with different angles of attack. (**a**) The attack angles of 0\({}^{\circ}\); (**b**) The attack angles of 10\({}^{\circ}\); (**c**) The attack angles of 30\({}^{\circ}\); (**d**) The attack angles of 60\({}^{\circ}\); (**e**)the attack angles of 90\({}^{\circ}\). Table 3 presents the results of the dynamic derivatives of the pitching motion for Inlet flow field velocity = 0.3 Ma and the initial angle of attraction \(\alpha_{0}=0^{\circ}\), \(10^{\circ}\), \(30^{\circ}\), \(60^{\circ}\), and \(90^{\circ}\). It can be seen that the pitching combined dynamic derivatives for each state are negative. This indicates that the pitching damping moments applied to the model during the forced vibration are always in the opposite direction of the rotational velocity. This inhibits the pitching rotation of the model, and the smaller the value of the pitching combined derivatives, the greater the inhibition of the rotation. The combined pitching derivative of the model fluctuates in a small range as the initial angle of attack increases. The maximum value is observed at an initial angle of attack of \(30^{\circ}\), which means that the model's dynamic stability is the worst at this point. Conversely, the minimum value is observed at an initial angle of attack of \(10^{\circ}\) and then \(90^{\circ}\), which indicates that the model's dynamic stability is the best at these points. Although there are some discrepancies in the calculated aerodynamic parameters of the cylindrical projectile model at large angles of attack, the magnitude of the discrepancy is within the acceptable range.