# Ground Simulation Tests in Two-Dimensional Dynamic Acceleration Environment
## 3 Simulation of Impact Overload Environment
### Impact Process of Air Cannon  
The structure of the adopted air cannon is shown in Figure 2. The air cannon consists of a back-pressure chamber, a high-pressure chamber, a quick-opening chamber, a control valve, a piston, and a piston rod. Initially, the pressure in the quick-opening chamber is higher than the pressure in the high-pressure chamber. Thus, the high-pressure chamber is sealed by the piston, and the piston rod remains stationary. When the control valve is opened, the pressure in the quick-opening chamber drops sharply, and the piston moves to the right quickly. Under this circumstance, the high-pressure chamber is opened, the high pressure gas drives the piston rod to move to the left, thus the air cannon is fired. The resultant force \(\mathrm{F_{P}}\) on the piston rod and arm and the thrust \(F_{\mathrm{Arm}}\) on the arm are expressed as follows:  
\[\left\{ \begin{array}{l}F_{\mathrm{P}}=s_{1}\cdot P_{1}-s_{2}\cdot P_{2}\\ F_{\mathrm{Arm}}{=(F_{\mathrm{P}}-\mathrm{m}_{P}A_{1})\cos\theta}\\ x=Ltg\theta\\ \ddot{\theta}=A_{2}\\ \ddot{\mathrm{x}}=A_{1}\end{array} \right. \tag{1}\]  
where \(s_{1}=0.02\) m\({}^{2}\), which is the area of the piston; \(s_{2}=0.0188\) m\({}^{2}\), which is the area of the piston minus the area of the piston rod; \(P_{1}\) denotes the air pressure in the high-pressure chamber during the launch; \(P_{2}\) denotes the air pressure in the back pressure chamber during the launch; A\({}_{1}\) is the acceleration of the piston rod in the propulsion process; \(\theta\) is the rotation angle of the arm in the propulsion process; m\({}_{\mathrm{P}}\) = 44.7 kg, which is the equivalent load of the piston rod; \(L\) is the distance between the propulsion point and the axis of the arm; x is the displacement of the piston rod; and \(A_{2}\) is the tangential acceleration of the arm during the propulsion process. The motion of the piston pushed by the air is assumed to follow an adiabatic expansion process of an ideal gas. The equation for the state of the gas is described below. \[P_{1}V_{1}=\frac{M}{\mu_{g}}RT \tag{2}\]  
where \(V_{1}\) denotes the volume of the high-pressure chamber during the launch, \(M\) indicates the mass of the air, \(\mu_{g}\) stands for the molar mass of the air, \(R\) is the gas constant, and \(T\) is the air temperature. Based on the polytropic relationship of the gas in the high-pressure chamber during the compression and expansion process [15], the polytropic index of the air during the charging and  
Figure 2: Schematic diagram of air cannon structure. discharging processes of the pneumatic system are set to 1.2. Thus, the pressures of the high-pressure chamber and the back-pressure chamber are expressed as follows:  
\[\left\{ \begin{array}{l}P_{1}=P_{10}(\frac{V_{10}}{V_{10}+x_{1}})^{1.2}\\ P_{2}=P_{20}(\frac{V_{20}}{V_{20}-x_{2}})^{1.2}\end{array} \right. \tag{3}\]  
where \(P_{10}\) is the initial pressure of the high-pressure chamber at the time of launch, \(V_{10}\) = 0.0972 m\({}^{3}\), which is the initial volume of the high-pressure chamber, \(P_{20}\) is the initial pressure of the back-pressure chamber at the time of launch, and \(V_{20}\) = 0.02827 m\({}^{3}\), which is the initial volume of the back-pressure chamber. Substituting Equation (3) into Equation (1) yields  
\[\left\{ \begin{array}{l}F_{\mathrm{P}}=s_{1}\cdot p_{10}(\frac{V_{10}}{V_{10 }+x_{1}})^{1.2}-s_{2}\cdot p_{20}(\frac{V_{20}}{V_{20}-x_{2}})^{1.2}\\ F_{\mathrm{Arm}}=m_{\mathrm{Arm}}A_{2}\end{array} \right., \tag{4}\]  
where \(m_{\mathrm{Arm}}\) = 45.7 kg, which is the effective load of the arm at the impact point, including the equivalent mass of the arm, the unit being tested, and the vector distributer. As shown in Equation (4), the acceleration of the arm during the impact is determined by the initial air pressures and volumes of the back-pressure and high-pressure chambers, the areas of the piston and piston rod, the displacement of the piston rod while it is propelled, the propulsion location, and the effective loads of the arm and piston.