# Design of a Variable-Stiffness Compliant Skin for a Morphing Leading Edge
## 2 Definition of Optimal Aerodynamic Profile  
The Chinese Aeronautical Establishment (CAE) has initiated a National Research Project titled \"Variable Camber Wing Technology (VCAN)\" for the next generation of long-range civil aircraft [25]. In the VCAN program, a morphing wing with adaptive leading and trailing edge is anticipated to be used in a long-haul business jet with a cruise Mach number of 0.87 [20]. It comprises a low-mounted backswept wing with a high aspect ratio, two aft-fuselage mounted engines, and a T-tail (Figure 1). The overall length is 33 m, and the wingspan is 33.5 m including the winglets. The aircraft targets a range of 11,000-13,000 km with a cruise altitude of 43,000 feet [25]. Before a structural design process, the first thing is to define the geometry input and geometry output. For a transport aircraft, the most common flight condition is the cruising case. It is reasonable to define the optimal aerodynamic surface in the cruising case as the initial profile, which will produce an easier actuation system and decrease the needed power, as the system can hold the cruising profile through a simple mechanical self-locking device in practical engineering. Inversely, the optimal aerodynamic surface in the takeoff or landing case is not the common case, but it is the most deflected one, which means the needed actuating power is the highest. Thus, the surface is defined as the target profile. Figure 1: Artist impression of the long-haul business jet concept with cruise Mach number of 0.87 [25]. In the project, the optimal initial aerodynamic profile is provided by [PERSON] et al., specifically in [26; 27], and has been verified by a CAE-AVM wind tunnel test conducted in the DNWHST, a continuous closed-circle pressurized transonic wind tunnel. The basic profile for the wing design is NPU-SP6, which is a 13% thick supercritical airfoil [28]. Both inverse method [27] and numerical optimization [29] are applied to the wing design. The free-form deformation (FFD) approach is used for wing optimization. The CFD-estimated maximum lift to drag ratio L/D reaches 20 in cruise condition [30]. During the optimization, a CAE in-house code AVICFD-Y [31] is employed for the flow analysis and aerodynamic performance estimation. It is a Reynolds-averaged Navier-Stokes (RANS) solver based on multi-block structured mesh capable of large-scale flow analysis on parallel computer clusters. Typical grid sizes of 20-40 million nodes and the shear stress transport (SST) turbulence model are used, while other turbulence models and codes are also applied for comparison in design stage. During the optimization for the target profile, the optimal initial profile obtained previously is utilized as the basic profile. The design variables are the leading edge radius and deflection angle, and the optimization objective is to maximize the lift coefficient. As there are only two design variables, a simple engineering parameter analysis method is used to determine the optimal target profile empirically. The variation range of the leading edge radius is set as 12, 14, 15, 16, and 18 mm, and the deflection angle is set to 20, 25, 30, 35, and 40\({}^{\circ}\). Figure 2 presents the different leading edge profiles in the deflection angles of 20, 25, 30, 35, and 40\({}^{\circ}\) with a leading edge radius of 14 mm. Figure 3 shows the corresponding curves of the lift coefficient versus deflection angle. It can be seen that as the deflection angle increases, the maximum lift coefficient increases nonlinearly and reaches around 3.5. Once the deflection angle increases beyond 25\({}^{\circ}\), the maximum lift coefficient increases at a slower rate. However, the circumferential length of the profiles in Figure 2 varies, which means the subsequent compliant skin needs to be extended or shortened during the deflection process. This is impossible for conventional metal or composite material in the aviation industry. Therefore, an additional constraint of a constant length should be included in the analysis process.