# Scaled Experiment of the Detonation Control System for the High-Speed Penetration on Concrete
## 3 Parameter Analysis of the Deceleration
### Parameter Analysis of the Projectile
#### 3.2.2 The Diameter and Length of the Projectile  
Under the premise that the impact velocity of the projectile is unchanged, the increase in the projectile diameter and length will significantly increase the projectile mass, and then increase the kinetic energy of the projectile. From Equation (13), if the projectile diameter \(d\) is given, the caliber-radius-head (\(CRH\)) \(\varphi\) is the only parameter to represent the nose shape, and the body length \(L\) is an important parameter to represent the projectile mass. According to the structure of the ogive-nosed projectile (\(\varphi=3\)) in Figure 2, the FE models of nine projectiles are established, and their design variables are listed in Table 2. The models of the detonation control systems are also established at the tail of these nine projectile models, and their structures are consistent with the detonation control system in Figure 2. These different projectiles penetrate the concrete with the strength of 20 MPa, 30 MPa and 40 MPa at a speed of 300 m/s and the deceleration data of the detonation control system are obtained. The deceleration peak and time history of the FE simulations are sorted out, as shown in Figure 4.  
From the FE simulation results in Figure 4, the diameter and length of the projectile can significantly affect the deceleration. The larger the diameter and the length are, the lower the deceleration peak and the longer the time history is. According to the deceleration characteristics of the high-speed deep penetration, the part with the peak greater than 10,000 g on the deceleration peak surface is projected on the horizontal plane, and the part with duration greater than 4 ms on the time history surface is also projected on the horizontal plane, as shown in Figure 5. As shown in Figure 5a, when selecting a set of projectile length and diameter, the deceleration peak and time history of the detonation control system can be known intuitively when penetrating 40 MPa concrete. It should be noted that the length-to-diameter ratio of the projectile usually meets \(5\leq(\mathrm{L+b})/\mathrm{d}\leq 10\), so it is best to select the projectile length and diameter in the purple area. It is also possible to find the corresponding points in the figure after clarifying the assessment indicators of \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Variable** & **Value** \\ \hline d (mm) & 67, 77, 87 \\ \hline \((\mathrm{L+b})/\mathrm{d}\) & 6, 8, 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design variables and value ranges. Figure 4: FE simulation results of deceleration peak and time history of the detonation control system for projectiles with different diameters and lengths. the detonation control system (the deceleration peak and time history), so as to clarify the geometric size of the projectile in the scaled experiment. Figure 5b-d can be understood with the same idea. When the compressive strength of the concrete target is 40 MPa and 30 MPa, as shown in Figure 5a,b, the overlapping area between the deceleration peak and the time history is very large, which means that there are many groups of projectile diameters and lengths that can be selected to meet different high-speed deep penetration. Especially when the time history is longer than 7 ms, the deceleration peak can still be satisfied at the 10\({}^{4}\) orders of magnitude. When the compressive strength of the concrete target is 20 MPa, as shown in Figure 5c, the overlapping area becomes very small. When a long time history is needed, the deceleration peak will not be too high. In a word, when the solid projectile penetrates the concrete target, combined with Figure 5a-c, a suitable set of the diameter and the length can be selected for the scaled experiment to meet the needs of different deceleration peak and time history of the high-speed deep penetration. Compared with a solid projectile, the difference in a projectile with a cavity structure penetrating into the target is the different equivalent density.