## 3 Sensitivity Analysis of Aerodynamic Characteristics
As all numerical simulations are conducted in the instantaneous solver mode, all the parameters in the flow field depicted in the figures are time-averaged over the computational time period. In particular, the velocity field is displayed on the symmetry plane of the projectile in Figure 4. The velocity distribution of the circumferential flow is displayed on the front, middle, and tail sections of the model in Figure 5. Since the dynamic derivative calculation is set according to the forced vibration of \(\pm 1^{\circ}\), it can be observed in the figures that the fluid separation phenomenon begins to appear in the front and middle part of the model when the initial angle of attack is 0\({}^{\circ}\). Upon increasing the initial angle of attack to 10\({}^{\circ}\), the fluid separation phenomenon has already appeared in the head, middle, and tail sections of the model. A pronounced asymmetric counter-rotating vortex is evident in the middle of the model in the streamline diagram. This pair of counter-rotating vortices has not yet fully detached from the wall under the angle of attack, and the flow field is essentially symmetrical with respect to the mid-vertical plane of the model. As the initial angle of attack continues to increase to 30\({}^{\circ}\), counter-rotating vortices also begin to appear in the head and tail of the model. Meanwhile, the counter-rotating vortex pairs on the leeward side at the center of the model gradually detach themselves from the wall, exhibiting an asymmetric phenomenon. When the angle of attack increases to 60\({}^{\circ}\), the fluid on the leeward side of the model is completely separated, the vortex on the leeward side of the model head also exhibits an asymmetric phenomenon, and the vortex structures in the middle and rear parts of the model all show an alternating shedding phenomenon. As the angle of attack increases to 90\({}^{\circ}\), the alternating vortex shedding phenomenon is observed on all of the model leeward surfaces. Additionally, a wide range of vortex shedding phenomena is observed in the middle of the model leeward surfaces, which even affects the formation of asymmetric vortices in the rear. These series of changes demonstrate that with the increase in the angle of attack, the counter-rotating vortex pairs on the leeward side of the model gradually detach from the wall at the tail of the model, resulting in an asymmetric structure due to the mutual extrusion of the two vortices. The aerodynamic coefficients in the pitch plane with different initial angles of attack are given in Figure 6. The results in Figure 6 are the time-averaged values obtained after a certain time of steady computation. Figure 6a illustrates that the lift coefficient of the model initially increases with the increasing angle of attack, reaching a maximum at 60\({}^{\circ}\). Thereafter, the lift coefficient starts to decrease with further increases in the angle of attack. This is due to the fact that, as the angle of attack increases, the normal force on the model gradually increases. The lift force is mainly composed of the component of the normal force perpendicular to the direction of the incoming velocity. In the range of angles of attack from 0\({}^{\circ}\) to 60\({}^{\circ}\), the increase in both the normal force and the angle of attack is favorable to the increase in this component. However, when the angle of attack is greater than 60\({}^{\circ}\), the increase in the angle of attack is not favorable to the increase in this component. Figure 6b illustrates that the lift-to-drag ratio increases with the increase in the angle of attack from 0\({}^{\circ}\) to 30\({}^{\circ}\). However, when the angle of attack is larger than 30\({}^{\circ}\), the resistance of the basic model still shows an increasing trend, but the increase in the lift force becomes smaller,