## 5 Discussion and Conclusions  
A series of simulations and field tests reveal the unique characteristics of the flyer projection velocity driven by an explosive detonation. The flyer projection speed varies depending on the flyer width. An analytical analysis for this occurrence is out of the scope of this report because the only focus of this paper is on the observation of such an occurrence. Certainly, the rarefaction intrusion during the projection can be a reason for this occurrence as is suggested in a previous publication [6,7] and shown in numerical simulations in the sections above. More detailed and accurate investigation would be available with the use of more sophisticated equipment like multi-points Photon Doppler Velocimetry (PDV) system to measure the velocity profile of the flyer during projection. The difference in the projection velocity originates from the rarefaction (or release wave) beginning from the edge of the flyer and intruding to the center of the flyer, which reduces the projection velocity. The conventional Gurney approach lacks this aspect due to the fact that it is based on simple, one-dimensional analysis. Conventional analytical tools have delivered a great deal of improvement, but also reveal some limitations by the one-dimensional assumption. The most important outcome from this observation is the understanding of the velocity profile on varied flyer widths. The properties \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Thickness of** & **Thickness of** & **M/C * & **Width of** & **Terminal** & **Gurney Model** \\  & **Charge (mm)** & **Flyer (mm)** & **Flyer (mm)** & **Velocity * (m/s)** & **(m/s)** \\ \hline \multirow{3}{*}{Field Test} & 12 & 1.6 & 0.82 & 24 & 1624 & 1703 \\  & 12 & 1.6 & 0.82 & 37 & 1980 & 1703 \\  & 26 & 1.6 & 0.38 *** & 50 & 2219 & 2292 \\ \hline \hline \end{tabular}  
* Symmetric sandwich with side cladding added; ** Symmetric sandwich configuration; *** This configuration is different than M/C = 0.82, and it is not included in the analysis.  
\end{table} 
Table 2: Flyer velocity comparison of field test. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Thickness of** & **Thickness of** & **M/C * & **Width of** & **Terminal** \\  & **Charge (mm)** & **Flyer (mm)** & **Flyer (mm)** & **Velocity * (m/s)** \\ \hline \multirow{3}{*}{Analytical} & 20 & 10 & 2.72 * & 25 & \(\sim\)220 ** \\  & 20 & 10 & 2.72 & 50 & \(\sim\)350 ** \\ \cline{1-1}  & 20 & 10 & 2.72 & 100 & \(\sim\)530 ** \\ \hline \hline \end{tabular}  
* Type of charge: EL506A, density: 1.48 g/cm\({}^{3}\), Flyer: Steel, density 8.05 g/cm\({}^{3}\), Symmetric sandwich configuration [6]; ** These values are from the graph in the publication [6] and this is an approximated value.  
\end{table} 
Table 3: Flyer velocity comparison from Chanteret [6]. of the detonation gas during acceleration is the key information to study the flyer behavior because the explosively-driven flyer is significantly affected by the detonation gas. Finally, because any realistic flyers will have finite dimensions, this effect cannot be neglected, and a more detailed investigation should continue to advance the conventional theoretical approaches. [PERSON] leads the research project and technical/theoretical approaches, and [PERSON] contributes the completion of the detailed subtasks and technical analysis. This research was partially funded by Office of Naval Research, grant number: N00014-17-1-2181, and the APC was funded by New Mexico Tech, Socorro, NM, USA. The authors declare no conflicted of interest. The series of simulations in this paper is based on the similar size (but not identical) of flyers that have tested in the field. This is to identify the possible variations of projection speed depending the varied M/C ratios as reference points. The flyers are 2 mm thick and varied width in Lagrange cells, and 5 cells per 2 mm in linear length, totaling \(30\times 5\) cells in the 12 mm width flyer and \(63\times 5\) cells in the 25 mm width flyer.