## 2 Aerodynamic Load and Deformation Analysis of Multi-Stage Telescopic Wings  
As shown in Figure 1, to enable the aircraft to perform diverse flight profiles, such as long-duration cruising and high-speed penetration, while minimizing the occupation of internal space, this study proposes a high space-utilization multi-stage telescopic wing design. This design allows the telescopic wing to adapt to various flight mission profiles with almost no impact on the internal space of the aircraft. The lift-to-drag ratio of the telescopic wing changes by between 20% and 70% between the fully retracted and fully extended states. Consequently, the aerodynamic shape can be adjusted to suit different flight environments across varying speed regimes, significantly enhancing the wide-speed-range service performance of the aircraft.  
The geometric model of the multi-stage telescopic wing is shown in Figure 2. Figure 2a illustrates the motion mechanism, where the multi-stage telescopic wing adopts a lap joint configuration. In practical applications, the wing root is fixed to the aircraft structure to provide stable support, while the other end of the telescopic wing remains free. The first-stage and second-stage telescopic wings achieve rapid, synchronized, and repeatable extension and retraction under the actuation of a dual-screw-nut mechanism. This mechanism features a self-locking capability, allowing the telescopic wing to stop at any position, thereby enabling multiple configurations. The guide rail and slider provide directional constraints for the telescopic motion, while the second-stage wing extension is synchronized through a motor-driven screw mechanism.  
Figure 2b presents the key dimensional parameters of the multi-stage telescopic wing. The airfoil used in this study is a non-standard airfoil, defined through a 3D CAD model. The root chord length of the telescopic wing is 1495 mm, with a fixed-section wingspan of 150 mm, a first-stage telescopic wingspan of 140 mm, and a second-stage telescopic wingspan of 136 mm. The wall thickness of each wing section is 1.5 mm, while the wall thickness at the reinforced rib sections is designed to be 4 mm. The wing has a fixed sweep angle of 35\({}^{\circ}\) and a thickness-to-chord ratio of 5.62%. Additionally, the tip-to-root chord  
Figure 1: Telescoping wing aircraft.  
length ratio is 0.86. The total wingspan of the wing in its fully extended state is 410 mm, whereas in the fully retracted state, it is 160 mm.  
The aerodynamic forces, aerodynamic heating, vibrations, and noise loads encountered in a hypersonic flight environment are extremely severe. Consequently, the load-bearing and transmission structures of the multi-stage telescopic wing impose stringent requirements on the comprehensive performance of materials under high-temperature conditions. High-temperature alloys exhibit superior strength at elevated temperatures, among which GH4169 demonstrates excellent oxidation resistance, fatigue resistance, and corrosion resistance over a wide temperature range of \(-253\)\({}^{\circ}\)C to 700 \({}^{\circ}\)C. Notably, at temperatures not exceeding 650 \({}^{\circ}\)C, GH4169 possesses the highest strength among high-temperature alloys. Additionally, GH4169 offers excellent machinability, weldability, and long-term stability, enabling the fabrication of complex structural components. Therefore, GH4169 is selected as the primary material for the wing structure. The material has a density of 8240 kg/m\({}^{3}\), and its mechanical properties, including elastic modulus and thermal expansion coefficient, vary with temperature. Detailed material properties are presented in Table 1.  
Figure 2: Telescoping wing aircraft. (**a**) Schematic diagram of mechanism composition; (**b**) dimensional parameter model.