## 3 Experimental Results and Analysis
### Spatial Distribution of BAD in the Striking Area
The scattering angle of each fragment could be calculated based on \(R\) and the distance \(h\) between the recovery plate and the back of the steel target:  
\[\beta=\arctan(R/h)=\arctan(\frac{\sqrt{y^{2}+z^{2}}}{h}) \tag{1}\]  
Figure 5: Schematic diagram of three-dimensional coordinates of the striking position of BAD. The fragments collected in each recovery plate were numbered. For example, Figure 6 also shows the fragments embedded in this layer of witness plate. Additionally, the he numbers next to each fragment indicate the number of the fiber plate or foam plate and the position of the fragment, which correspond to the position on the recovery plate in Figure 6. Thus, the relation between the mass and spatial coordinates of the fragments could be established. According to the model proposed by [PERSON] [34], the BAD cloud is described from three aspects. The residual EFP, large fragments of the target plug in the last few layers of recovery plates, and the fragments in the large hole formed by the residual EFP were excluded; statistical analysis of the fragments scattered around the residual EFP was then performed. We accumulated the two tests data of EFP with the same \(L/D\) and obtained the spatial distribution map of the BAD damage area behind the target according to the relation between the mass and 3D coordinates of the fragments (Figure 7). The fragments are represented by spheres. The color of the spheres reflects the fragment mass. A color closer to red implies a larger fragment mass. Some fragments in certain holes were not retrievable. Thus, these fragments only have position information and do not have mass information; such fragments are represented by black spheres. Figure 7 shows the spatial striking area after the fragments penetrated the multi-layered recovery plate. The fragments were densely distributed immediately after the target, and the fragments then became sparsely distributed along the residual EFP trajectory. Hence, there was a densely distributed striking area. There were some small fragments in the first few layers of the recovery plate which did not reach the deeper layers. In general, the large-mass fragments had a large penetration depth, thus indicating large energy. The 3D distribution field is projected on the \(X\)Z plane as shown in Figure 8 to analyze the distribution of the fragment striking area. The scales of each coordinate axis in the graphs are kept consistent in order to reflect the actual striking position of the fragment. As can be seen from Figure 8, the fragment striking area distribution of the EFPs with a large \(L/D\) (\(L/D\) = 3.86) and small \(L/D\) (\(L/D\) = 1.66) were trapezoidal. The lateral scattering of the fragments became smaller and smaller with increasing distance behind the target. They then gradually converged to the vicinity of the ballistic line. The increase in the \(L/D\) led to an increase in the depth of the striking area. The fragment striking areas of the EFP with a medium \(L/D\) (\(L/D\) = 2.4) were distributed in a rectangle. With increasing distance behind the target, the lateral scattering of the fragments did not converge but remained fairly even, thus indicating that the striking area distribution of the fragments of the EFP with a moderate \(L/D\) was uniform in the range of 500-1100 mm behind the target. Figure 6: Radial scattering distance in the recovery plate and the corresponding collected fragments. Figure 8: Two-dimensional projection of the striking area on the \(X\)Z plane. (**a**) \(L/D=1.66\) (**b**) \(L/D=2.4\) (**c**) \(L/D=3.86\). Figure 7: Three-dimensional distribution of the striking area of BAD. (**a**) \(L/D=1.66\) (**b**) \(L/D=2.4\) (**c**) \(L/D=3.86\). The EFP material (copper) fragments and target material (steel) fragments were then separated for further research. Figure 8 shows that there are many fragments with a mass less than 0.1 g. Considering their small lethality, only the positions of fragments greater than 0.1 g were included in the subsequent analysis.