## 4 Simulation Results and Discussion
### Insights into the Influence of Ball Bearing Size  
Figure 11 shows the velocity histories for 27.16 g charge mass, 30 mm charge diameter (aspect ratio of 0.8) detonations with different sized ball bearings. As might be expected, the peak velocities of the heavier ball bearings were lower (27% drop for the 8 mm bearing, 38% drop for the 10 mm bearing, both compared to the peak of the 5 mm ball bearing). Considering that the ball bearing mass increased fourfold for the 8 mm bearing and eightfold for the 10 mm bearing, these velocities decreases are smaller than might be expected. Figure 12 shows a graph of peak ball bearing velocity versus the ratio of charge mass to ball bearing mass; here, it is evident from the current work and our previous simulation results [17] that there are other factors of importance other than mass ratio, such as charge shape. It is also notable in Figure 11 that the biggest decrease in the peak velocity caused by the reflected pressure interactions occurred for the 5 mm ball bearing (20%), with only a 9% drop for the heaviest 10 mm bearing. The decrease in velocity due to the bearing interaction with the reflected blast pressure from the witness plate is influenced by the charge mass/ball bearing mass ratio and the aspect ratio of the charge. This is shown in Figure 13, where it is evident that the 30 mm diameter charges exhibited greater sensitivity to charge mass increases than the 18 mm diameter charge detonations. The percentage decreases were greater for the 30 mm charges, ranging from 10% to 20%, compared with 5% to 10% for the 18 mm charges. Figure 11: Simulated velocity–time histories for 27.16 g charge mass (30 mm charge diameter), detonations with different sized ball bearings. Figure 12: Graph of maximum ball bearing velocity versus charge mass/ball bearing mass ratio. These observations concerning peak velocity and the sharp drop in velocity can be explained by considering the pressure distribution following detonation, its interaction with the ball bearing, and the implications for the later reflected pressure interactions. Our previous work [8] showed that explosive charges with aspect ratios below a critical value were more efficient at transferring momentum to 5 mm diameter ball bearings. The aspect ratio of 0.8 was one of the best for transferring momentum because the shape of the pressure front reaching the 5 mm ball bearing meant that there was a slightly higher pressure behind the ball bearing located at the radial centre than the pressure at the radial edges of the charge. Figure 14 shows the simulated pressure contour plots from the 27.16 g detonation with a 10 mm ball bearing. The detonation front propagating through the explosive charge length was curved (Figure 14a), with its peak pressure at the radial centre, well-aligned with the bearing location (Figure 14b). This explains the efficient momentum transfer to the bearings that occurred between 2 us and 6 us, according to Figure 5b, as the pressure accumulation behind the ball bearing accelerated the bearing and caused a compressive hydrostatic pressure wave within the bearing itself. Figure 14c shows the pressure distribution within the explosive charge after 2.99 us. While the pressure interacting with the bearing was still high, the maximum pressures were observed on the charge face away from the radial centre, with the detonation wave moving past the ball bearing in the other sections of the charge. This interrupted detonation front is responsible for the pressure wave that moves ahead of the ball bearing. The diameter of the ball bearing determines how much of the detonation front interacts with the ball bearing (imparting momentum to it) and how much moves past, contributing directly to the blast pressure moving ahead of the bearing. Thus, heavier ball bearings with larger charge diameters require more momentum to import high peak velocities, but they also interact with a larger portion of the explosive charge because of their higher surface area.