## 3 Two-Dimensional Flyer Projection
From the figure above (Figure 7), the general velocity profile bearing the three projection stages, and each velocity profile, is somewhat different depending on the width of the flyer (with constant (\(M/C\)). From this result, the following observations are made: (1) As the flyer width gets larger, the terminal velocity (or converging point velocity) of the flyer increases (Table 1 and Figures 8 and 9) and it approaches to the Gurney prediction. This observation is one of the reasons why the conventional Gurney model limits itself, and this originated from the one-dimensional assumption. When the flyer width increases, the rarefaction from the flyer edges needs to travel a long distance (or time) to the center, and this long duration causes a faster projection of the center segments due to the longer acceleration time in the center flyer segments; (2) The velocity converging time shows a very clear trend. As the width of the flyer becomes large, the converging point time and velocity (or terminal velocity) increases. See Figure 7 and Table 1 for comparison. This is somewhat related with the speed of rarefaction, or tension wave speed, in the flyer, and this may provide a clue to understand the material behavior under the strong detonation gas release. However, the converging point data shows somewhat large discrepancies depending on the width of the flyer, and this is believed to originate from the dynamic material behavior where the local speed of sound somewhat decreases as the flyer experiences more deformation. This is out of scope of this paper; (3) The comparison between the velocity converging point in the simulation and [PERSON]'s effective charge mass included calculation delivers an interesting result. When the width of the flyer is large, the two data points show somewhat good agreement (see the values in 50, 75 and 100 mm width flyers) (Figure 8, Table 1). However, when the width of the flyer decreases (see the values in 12, and 25 mm width flyers), the two data points show a large discrepancy. It is believed that this is due to how [PERSON]'s approach is constructed, which is based on the removal of the charge mass affected by the side rarefaction near the edge of the original configuration (Figure 1). This is to calculate the optimum (or effective) charge mass depending on the configuration. However, this approach may provide some discrepancy when the width is varied. For example, if (\(M/C\) is constant, the removed charge from the varied width of flyer/charge system should be the same, and the removed charge mass grows larger (comparatively) as the width of the flyer gets smaller (Figure 10). This creates a large discrepancy in flyers with smaller widths. In other words, when the charge width becomes large, the [PERSON]'s approach may lose its effectiveness because the removed charge  
Figure 10: [PERSON]’s side loss comparison between large and small width. The charge removed for the side loss is constant, and the effect (or velocity reduction) from the removed charge decreases as the flyer width gets larger. Figure 9: Flyer velocity variation depending on width in simulation. weight is always constant, and becomes relatively smaller. (4) As the width of the flyer gets larger, the simulation approach, [PERSON]'s approach, and the Gurney model show a good agreement regarding the flyer velocity (Figure 8). This is an important observation because it may deliver a range where all three approaches are under a reasonable agreement, and an analytical solution may exist. In addition, it was observed that when the (\(M/C\) value decreases, the discrepancy between [PERSON]'s, and the Gurney Model, reduces, which represents a general solution tendency for different approaches (Figure 8).