## 4 Comparison with Test Data and Numerical Simulation Predictions
Figures 5 and 6 confirm the ability of the modified NNO BLE to predict the P/NP response of foam-filled dual wall systems more correctly, but now also at velocities as high as 30 km/s. In these figures, the P/NP datapoints are not always where they might be expected to be found with respect to their placement about the original NNO BLE. In Figure 5, e.g., most of the NP points are above the plot of the original NNO BLE (whereas they should be below it), and in Figure 6, most of the P datapoints are below it, whereas they should be above it. However, when the placements of the P/NP datapoints are compared against the plots of the modified NNO BLEs for these wall systems, we see that these points are now, for the most part, where they need to be. That is, the solid NP points in Figure 5 are now below the BLE curve, and in Figure 6, the hollow P points are now above it. It is important to note that the comparisons shown in Figures 2-6 are those where the modified BLE is plotted against the datapoints used in the development of the modifications given by Equations (1)-(6). It would be instructive, of course, to compare the predictions of the original and modified NNO BLEs against some P/NP data from tests using targets that were not part of the dataset that was used in the development of those modifications. These comparisons are shown in Figures 7 and 8 below. Figure 5: Comparison of Original and Modified NNO BLEs against P/NP data in [12] for Dual-Wall Systems with Aluminum Outer and Inner Walls. Figure 6: Comparison of Original and Modified NNO BLEs against P/NP data in [12] for Dual-Wall Systems with Non-Aluminum Outer and Inner Walls. In Figures 7 and 8 it is evident that the modified NNO BLE fared very well in predicting the P/NP response of the dual-wall systems and fillers under consideration. There was, of course, in each figure, one non-perforation datapoint that appeared on the side opposite to where it was expected. However, that kind of \"spillage\" is not at all surprising or unexpected (see, e.g., [15]). Table 5 below presents a top-level overview of the ability of the original and modified NNO BLEs to correctly predict the P/NP response of a foam-filled dual-wall system. As can be seen in this table, there is a marked reduction in the number of incorrect response predictions (and a corresponding increase in the number of correct predictions) of the modified NNO BLE as compared to the original NNO BLE formulation. That is, in approx. Figure 8: Comparison of Original and Modified NNO BLEs against P/NP data in [10,11] for Dual-Wall Systems with Non-Aluminum Walls and a Polymethacrylamide Filser. Figure 7: Comparison of Original and Modified NNO BLEs against P/NP data in [4,6] for Dual-Wall Systems with Aluminum Walls and a Polyurethane Filler. 37% of the impact tests, the original NNO BLE incorrectly predicted whether or not the inner wall would be perforated. This occurred in only approx. 17% of the tests when the modified NNO BLE was used. As a final comment, we recall that the original formulation of the NNO BLE has three sections: a downward curving low velocity section, and upward sloping intermediate section, and a second less steep downward sloping high velocity section. In an effort to reduce the complexity of the modifications, the same modification formulation was applied to all three sections of the dual-wall BLE. The less-than-hoped for improvements to the NNO BLE when the modifications presented herein in the low and intermediate velocity sections seen in Figures 2, 3, 7 and 8 indicate that perhaps in might be necessary to investigate the possibility that the different sections of the dual-wall BLE might each need its own modification factor. Similarly, the results in Figure 3 show that the predictions of the modified model at 0\({}^{\circ}\) are not as good as those at 30\({}^{\circ}\) as shown in Figures 5 and 6. The modification factor \(f_{3}\) as given by Eq 6 does have an impact obliquity term.