## 3 Simulation Results and Analysis
### The Influence of Inter-Stage Distance on the Selection of Current Direction  
Based on the previous analysis, it can be preliminarily concluded that different inter-stage distances will affect the coupling relationship between the drive coils and the armature, thereby affecting the electromagnetic force exerted on the armature during the launching process. Inter-stage coupling causes the electromotive force on the drive coil to alternate from positive to negative. When the induced electromotive force and the capacitor voltage are connected in reverse series, the total voltage of the drive coil discharge circuit decreases, which is not conducive to the acceleration of the armature. When connected in the forward series, due to the presence of the freewheel diode, a circuit current will be \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Configuration** & **The nth-Stage Coil** & **The (n - 1)th-Stage Coil** & **The (n + 1)th-Stage Coil** \\ \hline \multirow{3}{*}{PN} & Acceleration section & \multirow{3}{*}{Braking force} & Acceleration force \\  & & & (ignored) \\ \cline{1-1}  & & Acceleration section & (ignored) \\ \hline \multirow{3}{*}{PP} & Acceleration section & Acceleration force & — \\ \cline{1-1}  & & \multicolumn{1}{c}{Braking force} & — \\ \cline{1-1}  & & (ignored) & — \\ \hline \hline \end{tabular}
\end{table} 
Table 4: In both configurations, the armature experiences the forces exerted by the previous and next drive coils during the two stages of the launch process. Figure 13: Mechanism analysis schematic diagram. formed, and some energy will be dissipated as heat on the discharge circuit resistance of the drive coil, leading to a decrease in system transmission efficiency. Therefore, the smaller the inter-stage distance of the drive coils, the tighter the coupling with the armature, and the more significant the influence of the induced current on the armature. In this case, the armature velocity of the PP configuration is better than that of the PN configuration. As the inter-stage distance of the drive coils increases, the armature velocity of the PP configuration gradually decreases, while the armature velocity of the PN configuration gradually increases, eventually surpassing the armature velocity of the PP configuration. The simulation results are consistent with the theoretical analysis. By giving a certain linear increment to the inter-stage distance of the drive coils, simulations are conducted on the launching devices with different inter-stage distances. The selection of specific inter-stage distances in our study is based on a combination of practical considerations and the need to explore a range of distances that are commonly encountered in electromagnetic launch systems. The chosen distances were intended to provide a comprehensive understanding of how variations in inter-stage distance impact system performance. The triggering time of the excitation current for each drive coil is optimized using the method mentioned earlier, and the optimal exit velocity of each device is obtained. Table 5 lists the simulation data of the optimal armature exit velocity obtained after acceleration by the drive coils of PP and PN configurations at different inter-stage distances, where N represents the number of acceleration stages. Analyzing the data in Table 5 reveals that in the coil launch device with a PP configuration, the optimal exit velocity gradually decreases as the distance between driving coil stages increases. In contrast, in the coil launch device with a PN configuration, the optimal exit velocity increases as the distance between driving coil stages increases. Furthermore, among the existing data on driving coil stage distances, the optimal exit velocity of the armature for PP configuration is superior to PN configuration within the 2.5 mm-7.5 mm stage distances, while for PN configuration, the 10 mm-22.5 mm range is superior to PP configuration. Figure 14 is obtained through curve fitting of the existing data.