## 5 Conclusions  
Through the penetration test of tungsten alloy spherical fragments into wood targets and the construction of wood parameters in finite element analysis, we achieved a preliminary understanding of the calculation of residual velocity of fragments penetrating wood. By analyzing the relationship between the initial parameters of fragments, residual velocity, stand density and average diameter of trees in the forest, the Poncelet formula was used to obtain the calculation formula of residual velocity, and a calculation model for fragment track length was proposed. The main conclusions of this paper are as follows:  
1. Based on the Poncelet formula, it is feasible to calculate the residual velocity of the spherical fragment penetrating the wood target, which is verified by the comparison with the experiment.
2. Based on the forest parameters such as stand density, tree diameter, and fragment flying angle, a simple calculation model of penetration path length is obtained, which has good applicability when the flying angle is small and the stand density is large.
3. The residual velocity increases with the increase in the number of spacer targets on the fragment penetration trajectory, and it changes most obviously when the number of layers is seven. The wood target is less affected by the boundary effect. When the thickness d outside the penetration trajectory decreases continuously, the influence of the wood boundary effect on the residual velocity is relatively stable, and the maximum difference is 2.67%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Fragment** & **Number of** & **Simulation** & **Difference** \\  & **Diameter/mm** & **Spacer Layers** & **Residual** & **Ratio/\%(Compared** \\  & & & **Speed/(m\(\cdot\)s\({}^{-1}\))** & **with 1)** \\ \hline
1 & 10 & 1 & 112.6 & 0 \\
2 & 10 & 3 & 109.5 & \(-\)2.75 \\
3 & 10 & 5 & 110.7 & \(-\)1.69 \\
4 & 10 & 7 & 124.0 & 10.12 \\
5 & 10 & 9 & 129.2 & 14.74 \\
6 & 10 & 11 & 139.5 & 23.89 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Effect of the number of spacer layers on the residual speed.  
**Author Contributions:** Conceptualization, [PERSON] and J.Y. ([PERSON]); Methodology, Z.W.; Software, Z.W.; Validation, Z.W.; Investigation, [PERSON], [PERSON] ([PERSON]), [PERSON] and [PERSON]. ([PERSON]); Experiment, [PERSON] and X.L.; Data curation, [PERSON] and J.Y. ([PERSON]); Writing--original draft preparation, [PERSON]; Writing--review and editing, [PERSON] ([PERSON]); Supervision, [PERSON] and J.Y. ([PERSON]); Project administration, [PERSON] All authors have read and agreed to the published version of the manuscript.  
**Funding:** The authors would like to acknowledge the financial support from the 2021 Basic Research Pro-gram of Shanxi Province (Free Exploration), grant number 20210302123207.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to programming privacy in structural design.  
**Conflicts of Interest:** The authors declare no conflict of interest.