## 3 Experimental Results and Analysis
### Spatial Distribution of Relative Cumulative Energy of BAD
Considering that the crack propagates along the bulge thickness direction and breaks through the bulge wall to produce fragments, taking the bulge wall thickness \(\delta_{b}\) at the fracture time as the fragment thickness (Figure 17), the fragment mass can be expressed as:  
\[\frac{E(<\beta)}{E_{0}}=-90.97\exp(-\beta/9.81)+103.72 \tag{3}\]0  
\[\frac{E(<\beta)}{E_{0}}=-90.97\exp(-\beta/9.81)+103.72 \tag{3}\]1 Schematic diagram of force and dispersion of BAD. where \(\rho_{t}\) is the material density of the target. Substitute Equations (4), (15) and (16) into Equation (13) to obtain the following:  
\[\frac{E(<\beta)}{E_{0}}=-90.97\exp(-\beta/9.81)+103.72 \tag{3}\]2  
It can be seen that, when the target material is determined, the friction coefficient \(\mu_{s}\) is a constant, the fragment scattering angle is affected by the residual EFP velocity \(v_{r}\) and the bulge fracture thickness \(\delta_{b}\). When the \(L/D\) of EFP is large, i.e., the residual velocity of EFP is high, the scattering angle is primarily affected by it. Conversely, when the residual velocity of EFP is low, the bulge fracture thickness \(\delta_{b}\) is the main factor affecting the scattering angle. Since the diameters of three EFPs differ greatly, the \(L/D\) actually affected the fragment dispersion characteristics through the EFP diameter. The specific kinetic energy of EFP decreases with increasing EFP diameter. Additionally, the residual EFP velocity decreases through the high-speed images, which further led to a certain degree of increase in the scattering angle of the fragment at the same position \(\theta\) (according to Equation (17)). The energy distribution of the fragments then shifted towards the large scattering angle region. When the resultant energy of a fragment is constant, the radial energy component increases and the radial scattering distance increases. As a result, the radial distribution of the striking area in Figures 8 and 9 was uniform. However, the bulge diameter become large when the EFP diameter was too large. Meanwhile, the bulge thickness becomes larger at the fracture time, then the dispersion angle of fragment at the same position gradually decreases. The energy distribution of the fragments then no longer moved towards the large scattering angle region. In addition, the fragment resultant velocity and resultant energy decreased due to a small axial penetration ability of EFP, i.e., the radial scattered energy components of the fragments were weakened. Hence, in Figures 8 and 9, the maximum radial scattering distance gradually decreased with the increase in the depth of the recovery plate. Therefore, there are obvious differences in the radial distribution of the striking area behind the target and the spatial energy distribution of BAD with different EFP \(L/D\)s.  
In summary, a larger \(L/D\) is not always better from the perspective of the damaging effect of the BAD. This is because, when EFP can penetrate the target, EFP diameter will have the most significant impact on the radial distribution of BAD. When the \(L/D\) is too small, the EFP penetration ability decreases and the energy of the BAD is small. Although an increase in the \(L/D\) can increase the penetration depth into armor and the BAD energy, a very large \(L/D\) will cause the spatial energy distribution of the fragments to become concentrated close to the residual projectile axis, thus reducing the degree of scattering and the radial distribution of the striking area. Therefore, in the damage assessment of EFPs and warhead structural design, a reasonable and moderate \(L/D\) can cause the spatial energy distribution of the BAD to shift towards the large scattering angle and a uniform radial distribution of the striking area while ensuring damage to the components behind the armor.