## 3 Analysis
### Energy Dissipation Analysis  
According to Equations (6)-(10), the incident energy, reflective energy, transmitted energy, dissipative energy, and energy dissipation rate of hard coal specimens at different impact velocities are calculated. The results are summarized in Table 4.  
Table 3 shows that both incident energy and reflected energy levels increase with the acceleration of bullet impact velocity. According to the propagation law of stress wave, a stress wave will be reflected through the contact surface of two materials. There is a great \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen No.**} & **Impact Velocity** & **Incident Energy** & **Reflective Energy** & **Transmitted Energy** & **Dissipative Energy** & **Energy Dissipation** \\  & **/(m\(\cdot\)s\({}^{-1}\))** & **/J** & **/J** & **/J** & **/J** & **Rate** \\ \hline
1 & 2.675 & 177.26 & 135.29 & 13.01 & 28.96 & 0.163 \\
2 & 3.275 & 257.16 & 194.17 & 23.88 & 39.11 & 0.152 \\
3 & 3.574 & 326.88 & 236.68 & 26.21 & 63.99 & 0.196 \\
4 & 4.024 & 405.53 & 302.53 & 29.21 & 73.79 & 0.182 \\
5 & 4.804 & 523.21 & 419.62 & 23.12 & 80.47 & 0.154 \\
6 & 4.819 & 558.42 & 452.61 & 22.51 & 83.3 & 0.149 \\
7 & 5.011 & 610.69 & 492.13 & 21.76 & 96.8 & 0.159 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Energy calculation results of coal rocks under dynamic impact. Figure 9: Relationship of CDI and impact velocity. difference in wave impedance between rod and coal specimens, and while most of the energy will be lost in the form of reflected waves, part of the energy will pass through the specimen to the transmission rod. The rest of the energy is absorbed, which is manifested in the macroscopic form of the extension and expansion of cracks and the fracture and breakage of the specimen. The dissipated energy also increases with the acceleration of bullet impact velocity. This is because the increase in external impact load increases the crack propagation length under the load. In this process, the energy absorption effect increases, and the dissipated energy is increased accordingly. According to the calculation results in Table 3, the variation curves of incident energy, reflective energy, and transmitted energy under impact loads are obtained. In Figure 10, both incident energy and reflected energy increase linearly, but the increase in the reflected energy is smaller than that of the incident energy. The transmitted energy is relatively small, and the overall trend increases first and then decreases. This is because when bullet impact velocity is small, the energy that is carried by the incident wave will cause the cracks and defects in the hard coal specimen to expand and penetrate until the specimen is broken. The loaded energy also increases with the increase in the bullet impact velocity. Under high-energy impact, the crack and defect extension time in the hard coal specimen is extremely short, and the specimen is instantaneously penetrated, so the transmitted energy is reduced compared with the previous section. Figures 11 and 12 show the relationship between dissipative energy and the energy dissipation rate with bullet impact velocity. In Figure 11, the dissipative energy of the fracture of specimen increases linearly. The increase in bullet impact velocity increases the energy absorption effect of the coal specimen, as well as the energy consumption of the crack development of the specimen. Additionally, the energy consumption of the fracture of the specimen increases. Figure 10: The relationship of incident, reflective, and transmitted energy with impact velocity. When the bullet's impact velocity increases, the incident energy and dissipated energy both increase. Therefore, the energy dissipation rate \(N\) can be used to represent the strength of energy dissipation of a hard coal specimen under impact load. Figure 12 shows variation in the energy dissipation rate with the bullet impact velocity.