## 4 Validation of Optimization Results  
To validate and provide reference data for the optimized projectile aerodynamic layout performance, wind tunnel experiments and CFD simulations were conducted on the deterministic and robust optimization schemes. The wind tunnel experimental model was  
Figure 14: Divergent characteristics of design performance. (**a**) Max range versus _aero_factor_. (**b**) Lateral correction distance versus _aero_factor_. (**c**) Angle of attack versus _aero_factor_. designed in sections, and different aft fin components could be obtained by replacement. The test model parts and the experimental schlieren image are shown in Figures 15 and 16, respectively. To facilitate comparative analysis of the design schemes, the CFD simulation conditions were consistent with scheme 1 in Figure 5a. The comparison between the wind tunnel experimental drag coefficient \(C_{x(W)}\) and the CFD drag coefficient \(C_{x(CFD)}\) under different operating conditions for the design scheme is shown in Table 5. The pressure distribution on the fin surfaces of the original configuration and the optimized design at \(\delta=0^{\circ}\) and a Mach number of 0.6 is depicted in Figure 17a-c. The optimized design shows a decrease in the pressure values on the fin surface and a weakening of the surface shock wave intensity compared to the original design, as seen from Figure 17. This reduction is attributed to the decreased number of fins and the windward surface area, which effectively reduce the drag on the projectile. Furthermore, Figure 18 compares the curves of the fin surface roll moment coefficient (\(m_{xu}\)) and the roll damping moment coefficient (\(m_{zz}\)) obtained from CFD calculations. The optimized design exhibits a larger resultant moment vector in the roll direction due to an increase in the lead edge cart angle. The fin can angle is an important factor that affects the balance spin rate of the projectile, and therefore its flight characteristics and the correction efficiency of the trajectory. However, it is not the only determining factor. Figure 19 presents curve diagrams of the static moment coefficient (\(m_{z}\)) and the center of pressure (\(X_{p}\)) as a function of the Mach number, obtained from CFD simulations. The optimized design adjusts the fin installation position to move closer to the projectile's nose, which reduces the distance between the center of mass and the center of pressure, thereby decreasing the static stability and enhancing the trajectory correction capability. It should be noted that the static stability of a pulse correction projectile should not be excessively high, as it may adversely affect its trajectory correction performance, nor too low, as it may cause flight instability. Therefore, the fin installation position should be rationally arranged based on the overall design requirements during the design process. Figure 16: Experimental schlieren image. Figure 15: Test model parts. Figure 17: Pressure distribution on the empennages of different empennage models (\(\delta=0\)’). (**a**) Original design. (**b**) Deter DKM. (**c**) Robust SKM. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Configuration**} & \multicolumn{2}{c}{\(\mathbf{Ma=2,\delta=-4\)°}} & \multicolumn{2}{c}{\(\mathbf{Ma=2,\delta=0\)°}} & \multicolumn{2}{c}{\(\mathbf{Ma=2,\delta=2\)°}} \\ \cline{2-7}  & \(\mathbf{C_{x(W)}}\) & \(\mathbf{C_{x(CFD)}}\) & \(\mathbf{C_{x(W)}}\) & \(\mathbf{C_{x(CFD)}}\) & \(\mathbf{C_{x(W)}}\) & \(\mathbf{C_{x(CFD)}}\) \\ \hline Original design & 0.463 & 0.467 & 0.457 & 0.459 & 0.465 & 0.463 \\ Deter\_DKM & 0.412 & 0.415 & 0.391 & 0.394 & 0.434 & 0.430 \\ Robust\_SKM & 0.427 & 0.430 & 0.418 & 0.416 & 0.447 & 0.4421 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of drag coefficient based on DK model and SK model. Based on the aerodynamic parameters obtained from CFD, Figures 20 and 21 present the corresponding flight trajectories and angle of attack curves for the original configuration and the two optimized designs.