## 2 Definition of Explosive Yield  
TNT equivalent model is to convert the explosive materials into equivalent TNT according to the equal energy, and then the explosive law of TNT is applied to predict the effect of liquid propellant explosion [30]. It is widely used in the field of explosive characteristics of liquid propellant [31]. Given that the mass of liquid propellant \(M_{0}\) and explosive yield \(Y\), the TNT \(M_{T}\) can be calculated by Equation (1).  
\[M_{T}=Y\cdot M_{0} \tag{1}\]  
where, \(M_{T}\) represents mass equivalent to TNT, kg. \(Y\) is explosive yield, dimensionless. \(M_{0}\) is mass of liquid propellant, kg.  
The object of this paper is a two-stage rocket with four boosters, whose propellant quality of each stage is shown in Table 1. It is very difficult to obtain an accurate explosive yield theoretically under different explosion modes, because the chemical reaction mechanism of liquid propellant is different from that of solid explosive, and is affected by various factors such as the type, mass, detonation time of the propellant, falling speed, and ground property, etc. Through statistical analysis of test data [2; 3; 4], the explosive yield of liquid propellant is estimated. This method has certain authority and has been widely used abroad. Explosive yield estimation is mainly calculated by two methods, that is,the table-lookup-method and chart-reading-method. Therefore, explosive yield under the two methods is calculated respectively and it is finally determined according to the minimum principle [32].  
The table-lookup-method is to obtain the explosive yield by reading Table 2, on the basis of determining the propellant type and the explosion mode. While as for the chart-reading-method, explosive power can be obtained from Figure 1 according to propellant mass, and the final explosive yield is obtained by multiplying the specific coefficients corresponding to different propellants in Table 2. The explosive yields are shown in Table 1.  
Combined explosive yields and combined explosive center coordinates are acquired by Equation (2) and (3). The height of the combined explosive center is 21.968 m. Given the height of the launch pad, the height of the true explosive center is 30.668 m.  
\[y_{\rm zh}=\sum m_{i}y_{i}/\sum m_{i} \tag{2}\]  
where, \(y_{\rm zh}\) is the combined explosive yield, \(y_{i}\) is the explosive yield of stage \(i\), \(m_{i}\) is total propellant mass of stage \(i\), whose unit is kg.  
\[x_{z}=\sum m_{i}x_{i}/\sum m_{i} \tag{3}\]  
where, \(x_{i}\) is the distance between the middle of tanks of stage \(i\) and the explosive center, whose unit is m.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Propellant Combination**} & \multicolumn{2}{c}{**Explosion Mode**} & \multirow{2}{*}{**Mix**} & \multirow{2}{*}{**Specific Coefficient**} \\ \cline{2-2} \cline{5-6}  & & & & & \\ \hline LOX/LH\({}_{2}\) & 60\% & 60\% & 1:5 & 370\% \\ \hline LOX/RP-1 & Within 226.7995t is 20\% plus 10\% & 10\% & 1:1.25 & 125\% \\ N\({}_{2}\)O\({}_{4}\)/UDMH & 10\% & 5\% & 1:2 & 240\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Explosive yields and specific coefficients of different liquid propellant combinations under different explosion modes.  
Figure 1: The curve between the explosive yields and the mass of propellant.