## 1 Introduction
This research [3; 4; 5] begins with the side rarefaction near the edge of the flyer, indicating the flyer velocity variation depending on the width of the flyer, and it provides a significant improvement of the projection of the flat flyer. After [PERSON]'s and other similar approaches, and closer to the topic of this effort, [PERSON] proposed an analytical calculation of the flyer velocity variation depending on the width of the flyer [6]. His research specifically describes the rarefaction intrusion to the center of the flyer, and it causes the variation of flyer projection velocity during the detonation gas expansion. This analytical approach is added into the conventional Gurney equation with the use of Gurney velocity \(\sqrt{2E}\), and it is compared to the simulation and provided a favorable result (Figure 2). Note that the flyer projection velocity varies depending on the flyer width, and this trend is compared to 2D hydrocode simulation results. In this research, [PERSON] mainly used a symmetrical sandwich configuration, and it reveals the flyer velocity variation depending on the width of the flyer [6]. However, this research is built based on the assumption that the rarefaction intrusion from the edge would be the same in the difference configuration (i.e., open-face and symmetric sandwich), and the unknown factor of \(\sqrt{2E}\) (Gurney velocity) is obtained by the use of another set of hydrocode and it may carry some of the minor issues of the Gurney equation. Figure 1: [PERSON]’s effective charge mass and Gurney model (open face sandwich configuration). More recently, [PERSON] proposed an analytical calculation of the flyer acceleration profile under the influence of the side rarefaction based on the detonation gas isentrope, and [PERSON]'s law of motion [7]. In this approach, the Gurney equation is not applied in a way that would deliver more insight of the projection behavior. Due to the complexity of the given subject during the detonation along with the projection, [PERSON] proposed a new term of pressure release ratio \(\eta\), behind the flyer to predict the pressure/acceleration profile and the deformation profile shown by Equation (2) and Figure 3  
\[\overline{P}_{tn}{}^{*}=\overline{P}_{m-1}{}^{*}(\eta)^{\gamma} \tag{2}\]  
where, \(\overline{P}_{tn}{}^{*}\) is the rarefaction pressure behind the flyer at time \(t_{n}\), and \(\gamma\) is the specific heat ratio. The spirit of this approach is similar with [PERSON]'s work, but the description of the rarefaction intrusion and the specific velocity profile for each location on the flyer are greatly emphasized to predict the arc deformation of the flyer. This approach limits its applicability because the time range of investigation is at the immediate stage after detonation (around 3 \(\upmu\)s), and assumes the flyer is under a strong hydrodynamic regime. However, it delivers a way to predict the flyer projection velocity and acceleration profile in addition to the arc deformation. Because this approach is built on top of the side rarefaction, the width of the flyer affects the result as well. In this context herein, a general characteristic of the typical metallic flat flyer projection behavior driven by an explosive's detonation is investigated utilizing a series of hydrocode simulation, conventional analytical tools, including the Gurney model and [PERSON]'s approach, and a series of field tests. This paper focuses on the observation and description of the two-dimensional effect of the flyer configuration (i.e., flyer width) to understand and review the limitation and applicability  
Figure 3: Flyer projection and pressure profile behind the flyer [7]. Figure 2: Flyer velocity variation depending on the width of flyer [6]. of the conventional methods, while also exploring a more advanced approach to obtain an accurate estimation of the flyer projection behavior.