# Development of Energy-Based Impact Formula--Part I: Penetration Depth
## 4 Verification of Developed Impact Formula
### Critical Impact Mechanism  
Table 3 shows energy portions for each experiment, where the deformed energy of a projectile accounted for 0.1-7.4% of kinetic energy. The elastic penetrated energy of a concrete panel accounted for 0-3.8% of kinetic energy. The overall deformed energy of a concrete panel accounted for 0-2.7% of kinetic energy. The average sum of spalling-resistant energy and tunneling-resistant energy accounted for 97.9% of kinetic energy, which was the largest proportion in all experiments. The sum of the spalling-resistant and tunneling-resistant energies was overwhelming, while the other energies were small. In other words, \(E_{\text{DP}}\), \(E_{EP}\), and \(E_{SD}\) can be ignored in the impact mechanism, with \(E_{K}\) being applied only to \(E_{SP}\) and \(E_{T}\). That is, Equations (120) and (127) can be modified to Equations (128) and (129), respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & \(E_{\text{DP}}\)/\(E_{K}\) (\%) & \(E_{\text{EP}}\)/\(E_{K}\) (\%) & \(E_{\text{SD}}\)/\(E_{K}\) (\%) & \((E_{\text{SP}}\)/\(E_{T}\))/\(E_{K}\) (\%) \\ \hline [PERSON] and [PERSON] [59] & 0.07 (0.06–0.08) & 0.24 (0.2–0.28) & 0.04 (0.02–0.06) & 99.7 (99.6–99.7) \\ [PERSON] et al. [57] & 0.3 (0.1–0.5) & 0.7(0.5–1.2) & 0.1 & 98.9 (98.1–99.4) \\ [PERSON] et al. [58] & 1.86 (1–4.2) & 0.2 (0.1–0.5) & 0.1 (0.1–0.3) & 97.8 (95.1–98.8) \\ [PERSON] et al. [54] & 0.9 (0.7–1.7) & 0.2 (0.1–0.4) & 0.1 (0–0.1) & 98.8 (97.9–99.2) \\ [PERSON] et al. [56] & 3.3 (0.1–7.4) & 0.5 (0.3–0.9) & 0.2 (0.1–0.3) & 95.9 (91.4–98.7) \\ [PERSON] et al. [53] & 1.6 (0.6–4.8) & 0.2 (0.1–0.5) & 0.2 (0.1–0.5) & 98 (94.8–99.2) \\ [PERSON] et al. [55] & 1 (0.9–1.3) & 0.1 (0.1–0.1) & 0.1 (0.0–0.1) & 98.8 (98.5–9.0) \\ [PERSON] et al. [52] & 1 (0.8–1.4) & 0.1 & 0.1 (0.0–0.2) & 98.8 (98.4–99.0) \\ [PERSON] et al. [24] & 0.8 (0.4–1.3) & 0.2 (0.1–0.3) & 0.3 (0.1–0.6) & 98.7 (98.0–99.2) \\ [PERSON] [60] (first test) & 0.2 & 0.4 (0.2–0.8) & 0 & 99.3 (98.9–99.6) \\ [PERSON] [60] (second test) & 1.2 (0.2–4.6) & 1.9 (0.4–3.8) & 0.1 (0–0.3) & 96.8 (92.2–99.2) \\ [PERSON] [60] (third test) & 2.4 (1.9–3.1) & 1.1 (0.5–2.1) & 0.4 (0.2–2.7) & 96 (94–97.1) \\ Total & 1.1 (0.1–7.4) & 0.9 (0–3.8) & 0.1 (0–2.7) & 97.9 (91.4–99.6) \\ \hline \hline \end{tabular} Note: \(E_{K}\) is the kinetic energy (N-mm); \(E_{DP}\) is the deformed energy of a projectile (N-mm); \(E_{EP}\) is the elastic penetrated energy of a concrete panel (N-mm); \(E_{SD}\) is the overall deformed energy of a concrete panel (N-mm); \(E_{SP}\) is the spalling-resistant energy (N-mm); and \(E_{T}\) is the tunneling-resistant energy (N-mm).  
\end{table} 
Table 3: Energy portion. Table 3 shows the energy portions for each experiment, where the deformed energy of a projectile accounts for 0.1-7.4% of the kinetic energy. The elastic penetrated energy of a concrete panel accounts for 0-3.8% of the kinetic energy. The overall deformed energy of a concrete panel accounts for 0-2.7% of the kinetic energy. The average sum of spalling- and tunneling-resistant energies accounts for 97.9% of the kinetic energy, which is the largest proportion in all experiments. The sum of the spalling- and tunneling-resistant energies is overwhelming, while that of the other energies is small. In other words, \(E_{DP}\), \(E_{EP}\), and \(E_{SD}\) can be ignored in the impact mechanism, with \(E_{K}\) being applied only to \(E_{SP}\) and \(E_{T}\). That is, Equations (120) and (127) can be modified to Equations (128) and (129), respectively. Figure 11 compares the average tested-to-predicted penetration depth ratios obtained using the detailed formula and the simplified formula. The overall average of the detailed formula decreases by 0.01, from 1.00 to 0.99, but can still be considered equal. The standard deviation for both the detailed and simplified formulae is 0.23. Thus, no significant difference is observed between the detailed formula and simplified formula.