## 4 Comparison with Test Data and Numerical Simulation Predictions  
The next series of plots shows comparisons between the predictions of the original NNO BLE and NNO BLE as modified according to Equations (1)-(4). Two types of plots were used for comparison for different configurations:  
* \(D_{\text{{proj}}}/D_{\text{{crit}}}\) vs. \(V_{\text{{inj}}}\)--When the ratio > 1, did the test result in an inner wall perforation for that particular impact velocity? Likewise, when the ratio < 1, did the test result in a non-perforation event? \begin{table}
\begin{tabular}{c c c c} \hline  & **A** & **B** & **C** \\ \hline \(MF_{0}\) & 3.0 & \(1.4\times 10^{3}\) & 45 \\ \hline \(f_{PD}\) & 2.4 \(\times\) 10\({}^{3}\) & 2.0 \(\times\) 10\({}^{9}\) & 163 \\ \hline \(f_{VP}\) & 100.0 & 3.4 \(\times\) 10\({}^{4}\) & 70 \\ \hline \end{tabular}
\end{table} 
Table 4: Parameter Values for Lower Projectile Density Function. * \(D_{crit}\) vs. \(V_{imp}\)--Are the tests with the inner wall perforations above the ballistic limit curse, and are those without inner wall perforation below the curve, as impact velocity is increased? In these plots, the original NNO BLE predictions of \(D_{crit}\) are calculated with the following parameter modifications as necessary:
* _Projectile Density_--density of actual projectile material
* _Outer Wall Thickness_--mass equivalent aluminum thickness (assuming an aluminum density of 2.71 gm/cm\({}^{3}\)) for original outer wall material and thickness and 50% of the foam stuffing
* _Outer Wall Density_--density of original aluminum outer wall material, or 2.71 gm/cm\({}^{3}\) if mass equivalent aluminum outer thickness is being used
* _Stand-off Distance or Spacing_--this is the thickness of the foam between the outer wall and the inner wall
* _Inner Wall Thickness_--mass equivalent aluminum thickness (assuming an aluminum density of 2.71 gm/cm\({}^{3}\)) for original inner wall material and thickness and 50% of the foam stuffing
* _Inner Wall Density_--density of original aluminum inner wall material, or 2.71 gm/cm\({}^{3}\) if mass equivalent aluminum bumper thickness is being used
* _Inner Wall Yield Strength_--actual yield strength for aluminum inner wall materials; ultimate tensile strength for non-aluminum inner wall materials Figures  
This change is a significant improvement in the ability of the (modified) NNO BLE to predict the P/NP response of foam-filled dual-wall systems with aluminum as well as composite material outer and inner walls (at least for impact velocities between 2 and 8 km/s). Of course, as can be seen in Figure 3, the modified NNO BLE, while significantly closer to the NP datapoints than the original NNO BLE, failed to end up above those points. So while an accuracy improvement is still evident for the modified NNO BLE over the original NNO BLE for foam-filled dual-wall systems with laminated rayon outer walls and cloth or fabric inner walls, there are still some response characteristics not entirely correctly captured by the modifications made to the original NNO BLE for this particular dual-wall configuration. In Figure 2, we also see that while all of the non-perforation datapoints are now below the modified NNO BLE, the perforation datapoint is not above it, as it should be. Of additional interest is that it appears to fall amidst a series of non-perforation datapoints, indicating that there might be something amiss with this test that resulted in a perforation. However, all of the datapoints in Figure 4 do appear to fall on the correct sides of the modified NNO BLE-the non-perforation datapoint is below it, and all of the perforation datapoints are above it. Figure 4: Comparison of Original and Modified NNO BLEs against P/NP data in [6] for Dual-Wall Systems with Aluminum Outer and Inner Walls. Figure 3: Comparison of Original and Modified NNO BLEs against P/NP data in [8] for Dual-Wall Systems with Rayon Outer and Inner Walls.