## 4 Results and Discussion
### Effects of the Pump Tube Pressure  
For any particular gun with a fixed geometry, the operating parameters or loading condition that can be adjusted to achieve the desired velocity include the initial gas conditions in the pump tube, the piston mass, the rupture pressure of diaphragm II, and the projectile mass. However, it is desirable to minimize the maximum base pressures to obtain the most uniform base pressure history and maintain gas reservoir pressures that are within the strength capabilities of the gun. Generally, the initial pressure of the pump tube and detonation tube is the easiest parameter to adjust.  
The influence of the initial pump tube pressure on the gas gun was investigated; the operating conditions for Case 4 are listed in Table 2. Figure 13 shows the piston and projectile speed as a function of the pump tube pressure. Since the pump tube pressure tends to limit the acceleration of the piston, the piston speed decreases as the pump tube pressure increases at different detonation pressures. However, the pump tube pressure has little influence on the maximum piston speed, and the detonation pressure is the dominant influence. The projectile velocity has an optimal value at different pump tube pressures. For example, at a detonation pressure of 3.0 MPa, the maximum projectile speed occurs at a pressure of 0.4 MPa. The projectile base pressure in the launch tube is presented in Figure 14. When the initial pump tube pressure is lower than 0.4 MPa, the projectile has a relatively high base pressure of more than 130 MPa, indicating high acceleration in the early stages. However, the density decreases rapidly due to the lower initial pressure after the projectile has traveled about 2 m in the launch tube, leading to a significant decrease in the base pressure of the projectile. When the initial pump tube pressure is higher than 0.4 MPa, the peaks of the pressure of the projectile are much lower, and the curves are smooth due to stable acceleration. For the other different detonation pressures, the maximum projectile speed occurs at different initial pump tube pressure. At a detonation pressure of 1.5 MPa, an optimal projectile speed is not observed at the pump tube pressure range of 0.2 to 1.2 MPa.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & & **4** & **5** \\ \hline \multirow{2}{*}{Detonation tube} & Mixing molar ratio, H\({}_{2}\):O\({}_{2}\) & 3:1 & \\  & Pressure (MPa) & 1.5, 2.0, 3.0, 5.0 & 5.0 \\ \hline \multirow{3}{*}{Pump tube} & Gas & H\({}_{2}\) & \\  & Pressure (MPa) & 0.2, 0.4, 0.6, 0.8, 1, 1.2 & 0.6 \\ \cline{1-1}  & Piston mass (kg) & 10 & 12.5 \\ \cline{1-1}  & Rupture pressure (MPa) & 45 & 150 \\ \hline Launch tube & Projectile mass (g) & 19 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Operating conditions in the simulation of Case 4 and Case 5.  
Figure 13: Simulated results at different detonation pressures. (**a**) maximum piston speed versus the initial pump pressure; (**b**) muzzle projectile speed versus the initial pump pressure.  
We estimated the maximum capabilities of the gaseous detonation-driven two-stage light-gas gun. We increased the rupture pressure of diaphragm II to 150 MPa and maintained the maximum piston velocity at less than 900 m/s to protect the high-pressure section of the barrel. An appropriate set of calculation parameters was chosen (Case 5). The projectile velocity and base pressure are shown in Figure 15. The projectile muzzle velocity is more than 7100 m/s, and the maximum base pressure is close to 250 MPa, which is lower than the strength of the metal. Therefore, if we further optimize the launch parameters, the muzzle velocity of the projectile with a mass of less than 20 g can reach 6-8 km/s.