# Analysis of Carrier-Based Aircraft Catapult Launching Based on Variable Topology Dynamics
## 4 Calculation Results of the Variable Topology of Carrier-Based Aircraft  
Taking the catapult take-off of a carrier-based aircraft (Table 3) as an example, the dynamic response of the catapult of the modified aircraft is calculated by using the catapult dynamics model established in this paper.  
Figure 8 shows the component variation curve of the restraint reaction force in the axis direction of the restraining rod at the joint of the restraining rod and the antitorsion arm of the nose gear, during the catapulting of the aircraft. After the catapulting starts, the load of the restraining rod increases rapidly, and at 0.123 s, the curve appears at a breakpoint. The reason is that the restraint bar load reaches the design unlocking threshold (192.0 kN) at 0.123 s, which meets the restraint bar separation condition, then the system removes the restraint relationship between the restraining rod and the connection between the restraining rod component and the nose gear from the dynamic equation, and the subsequent calculation results no longer include the restraint reaction force at the joint of the restraining rod.  
Figure 8: Time versus restraint reaction force at the pin joint.  
Figure 7: Rigid body removal method from the dynamic equations.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Numerical Values** & **Parameters** & **Numerical Values** \\ \hline Take-off weight & 20,000 kg & Catapult heading overload & 2.5 \\ Engine thrust & 78.0 kN & Restraint bar load threshold & 192.0 kN \\ Catapult stroke & 90 m & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Catapult dynamics model parameters.  
Figure 9 shows the component variation curve of the restraining reaction force at the joint of the catapult rod and the catapult trolley, in the direction of the catapult rod axis. At 2.867 s, the load curve of the catapult rod has a breakpoint. The reason is that the catapult trolley reaches the end of the catapult stroke (92 m) at 2.867 s, and the catapult rod is separated from the catapult trolley. The system removes the catapult trolley rod and the connection constraint relationship between the catapult trolley and the nose gear catapult rod from the dynamic equation, and the subsequent calculation results no longer include the constraint reaction force at the connection of the catapult rod and the catapult trolley.  
Figure 10 shows the change curve of the projected component of the restraining reaction force at the connection between the rear strut of the nose gear and the strut during the catapulting of the carrier-based aircraft. At 0.123 s, due to the separation of the restraining rod and the front landing gear, the force transmission path of the front landing gear changes, and the catapult force is transmitted to the rear strut (Figure 2), causing the load of the rear strut to change from \(-0.5\) kN to 238.0 kN. At 2.867 s, due to the separation of the catapult rod and the catapult tackle, the catapult rod load disappears, and the load of the rear strut of the nose landing gear is reduced from 486.2 kN to \(-20.3\) kN.  
Figure 10: Time versus restrained reaction force at the catapult rod joint.  
Figure 9: Time versus restrained reaction force at the catapult rod joint.  
Figure 11 shows the pitch angle change during the catapulting of the carrier-based aircraft. The aircraft is always dragged obliquely downward by the ejection rod, which leads to the pitch down moment of the aircraft in the process of dragging and sliding. As shown in Figure 11, the pitch angle ranges from \(-1.61^{\circ}\) to \(-0.64^{\circ}\). After the separation of the ejection rod and the shuttle, the pitch angle increases rapidly from \(-0.93^{\circ}\) and reaches \(0.54^{\circ}\) when the aircraft rushes out of the deck, which is mainly caused by the sudden extension of the nose landing gear.