# Development of Energy-Based Impact Formula--Part I: Penetration Depth
## 4 Verification of Developed Impact Formula
### Penetration Depth Assessment
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Tests** & \begin{tabular}{c} **Data** \\ **(ea)** \\ \end{tabular} & \
\begin{tabular}{c} **Proposed** \\ **Formula** \\ \end{tabular} &
\begin{tabular}{c} **Modified** \\ **NDRC** \\ \end{tabular} & **ACE** & **Halar** & **Hughes** & **UKAEA** & **UMIST** & **Li-Chen** \\ \hline [PERSON] and [PERSON] [59] & 7 & 0.76 & 0.62 & 0.56 & 0.57 & 0.6 & 0.64 & 0.69 & 1.78 \\ [PERSON] et al. [57] & 24 & 0.97 & 1.09 & 1.09 & 1.4 & 1.01 & 1.36 & 3.17 & 0.84 \\ [PERSON] et al. [58] & 16 & 1.23 & 0.77 & 0.91 & 0.8 & 0.58 & 0.8 & 1.12 & 1.27 \\ [PERSON] et al. [54] & 7 & 1.03 & 1.85 & 1.5 & 2.01 & 1.87 & 1.88 & 1.87 & 0.48 \\ [PERSON] et al. [56] & 33 & 0.86 & 1.13 & 1.35 & 1.31 & 0.78 & 1.16 & 1.88 & 1.04 \\ [PERSON] et al. [53] & 15 & 0.88 & 1.62 & 1.34 & 1.89 & 1.63 & 1.64 & 1.67 & 0.58 \\ [PERSON] et al. [55] & 18 & 1.35 & 1.59 & 1.55 & 1.81 & 1.41 & 1.53 & 1.65 & 0.91 \\ [PERSON] et al. [52] & 18 & 1.06 & 1.29 & 1.27 & 1.54 & 1.19 & 1.3 & 1.33 & 1.06 \\ [PERSON] et al. [24] & 17 & 0.88 & 1.27 & 1.18 & 1.57 & 1.13 & 1.28 & 1.27 & 1.08 \\ [PERSON] [60] (first test) & 86 & 0.95 & 0.68 & 0.71 & 0.63 & 0.55 & 0.76 & 1.5 & 1.69 \\ [PERSON] [60] (second test) & 149 & 1.06 & 0.65 & 0.59 & 1.22 & 0.53 & 1.12 & 2.32 & 1.47 \\ [PERSON] [60] (third test) & 12 & 0.76 & 0.42 & 0.31 & 1.7 & 0.29 & 1.59 & 2.69 & 2.31 \\ Total & 402 & 1 & 0.87 & 0.85 & 1.2 & 0.74 & 1.13 & 1.97 & 1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average ratio of tested to predicted penetration. The proposed impact formula predicts the average value well as 1.0. However, the test results of [PERSON] and [PERSON] [59] were predicted to be 0.76 and those of [PERSON] et al. [55] were predicted to be 1.35. The proposed formula is closer to 1 than other formulae, which means that it is better. However, the test specimens used by [PERSON] and [PERSON] [59] and [PERSON] et al. [55] were, respectively, seven and eighteen. If there were more test specimens, the average predicted value might to be closer to 1. Other experimental results are predominantly close to 1. The modified NDRC formula overestimates the penetration depth as a whole (Figure 10b). The experimental results obtained with small diameter-to-thickness values are particularly underestimated. The ACE formula also overestimates the penetration depth as a whole, and this trend is similar to that of the modified NDRC (Figure 10c). The Haldar and [PERSON] formulae are very similar and the trend of the tested-to-predicted penetration depth ratio is similar up to the first test results obtained by [PERSON] [60] (Figure 10d,e). For the second and third experiments, conducted by [PERSON] [60], the Haldar formula is predicted to be 1.2 and above. However, the Hughes formula overestimates, as in the first test, and has a trend similar to those of the modified NDRC and ACE formulae. The Haldar formula looks better considering the overall average tested-to-predicted penetration depth ratio, but the Hughes formula predicts consistently for each test, and thus, appears to be a better formula. The UKAEA formula shows a similar trend to that exhibited by the Haldar formula, predicting better results for these test programs (Figure 10f). UMIST underestimates the predicted penetration depth as a whole, and the data points in Figure 10g are scattered widely; thus, there is no other inconsistency in the experiments. The tested-to-predicted penetration depth ratio obtained using [PERSON]'s formula is close to 1.36 (Figure 10h), which slightly underestimates the penetration depth.