## 2 Conceptual Aircraft with Morphing Airfoil  
Taking into consideration the fact that the required lift of an aircraft is continuously decreasing due to the fuel consumption during flight, morphing airfoil is utilized in this paper to achieve all-stage high performance of a conceptual aircraft. Supposing the take-off weight of this conceptual aircraft is \(W_{0}\). The aircraft enters the first high-altitude high-speed cruise stage (the Mach number of airfoil is 0.734, and the required lift range is 0.96\(W_{0}\)\(\sim\)0.84\(W_{0}\)) after the climbing stage; when it arrives at the destination, it lowers the altitude to enter the low-altitude low-speed mission stage (the Mach number of airfoil is 0.3, and the required lift range is 0.835-0.775\(W_{0}\)); after this mission is completed, it climbs to high altitude and enters the second high-altitude high-speed cruise stage (the Mach number of airfoil is 0.734, the required lift range is 0.745-0.665\(W_{0}\)); finally, it returns to the airport. The freestream conditions under these different flight stages are shown in Table 1. In order to realize high lift characteristics during the take-off stage and high lift-to-drag ratio characteristics during high-speed cruise and low-speed mission stage, three types of morphing airfoils are designed: variable-camber airfoil, variable-chord airfoil, and the combination of both morphing styles. Investigations on the aerodynamic characteristics of these morphing airfoils will be conducted to obtain the proper type of morphing airfoil for each flight stage. RAE 2822 supercritical airfoil is regarded as the baseline airfoil (identified as BA in the following). The baseline airfoil's chord length is 1 m, and has the max thickness 12.11% at 37.9% chord. The simultaneous variable-camber and variable-chord airfoil (identified as VCaCh in the following) is obtained by translating the airfoil section after 70% chord length of the baseline airfoil by 5% chord length, and then deflecting the airfoil section from 90% chord length of the original airfoil to the trailing edge by a specified angle (upward deflection is negative and downward deflection is positive) when taking the thickness midpoint at 70% chord length of the baseline airfoil as the rotation axis. Finally, the airfoil section from 50% to 90% chord length is replaced by a smooth curve (in reality, this smooth curve is realized by flexible structure and flexible skin [8; 59; 60]); in a computational model, this smooth curve is realized by geometry software) so that a geometric model of variable camber and variable chord is obtained. The variable-camber airfoil (identified as VCa in the following) deflects the airfoil section from 90% chord length of the original airfoil to the trailing edge and the rotation axis is the same as VCaCh, then the airfoil section from 50% to 90% chord length is replaced by a smooth curve. The variable-chord airfoil (identified as VCh in the following) is obtained by translating the airfoil section after 70% chord length of the baseline airfoil by 5% chord length, then the airfoil section from 50% to 90% chord length is also replaced by a smooth curve. The above four airfoils are shown in Figure 1. In fact, there are mature implementation schemes to achieve the variable camber and variable chord mentioned above. For example, the ACTE technology uses compliant structures to make changes in wing trailing-edge shape with smoothly curved surfaces along the flow direction [32]. The variable chord can be realized by using the telescopic wing scheme, and the NextGen Company proposed the concept of sliding skin and conducted flight tests in which the chord length can be varied by up to 110% [61]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Flight Stage** & **Typical Altitude (m)** & **Mach Number** & **Reynolds Number** \\ \hline Take off & 0 & 0.2 & \(4.66\times 10^{6}\) \\ Lower speed mission & 3000 & 0.3 & \(5.29\times 10^{6}\) \\ High-speed cruise & 11200 & 0.734 & \(5.39\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table}