# Technology Identification, Evaluation, Selection, and Optimization of a HALE Solar Aircraft
## 2 HALE Solar Aircraft Concepts
### Aerodynamic Analysis  
HALE solar incrafts that have been developed so far have average cruising speeds of 15-30 m/s and perform missions in low Reynolds number range. The DAEs airfoil has an excellent max lift coefficient, lift to drag ratio, and large thickness ratio in low Reynolds number range. Moreover, the HALE solar aircraft wing characteristic of being less sensitive to airfoil surface accuracy makes it easier to produce by applying solar panels. For these reasons, DAE-11 was selected as the airfoil of the main wing in this study. With respect to the DAE-11 airfoil, 2-dimensional aerodynamic data were produced using XFLR5 [14] and, based on these data, the lift and drag coefficients of a finite wing (3 dimensional) were calculated. The lift coefficient (\(C_{L}\)) can be calculated from Equation (2):  
\[q=\frac{1}{2}\rho V^{2} \tag{1}\]  
\[C_{L}=\frac{W}{S}\frac{1}{q} \tag{2}\]  
where \(\rho\) is density, \(V\) is flight speed, \(W\) is the total weight of the aircraft, \(S\) is the wing area, and \(q\) is the dynamic pressure. Drag coefficient (\(C_{D}\)), as in Equation (3), is divided into induced drag and parasite drag. The parasite drag is composed of form drag and skin friction drag [16]. Equation (3) can be expressed as a quadratic approximation of the lift coefficient (\(C_{L}\)) like Equation (4) [1]. In Equation (4), \(K_{1}\) is the coefficient of drag-due-to lift and \(K_{2}\) is assumed to be 15% of \(K_{1}\). \[C_{D}=C_{D,induced}+C_{D,form}+C_{D,skin} \tag{3}\]  
\[C_{D}=K_{1}C_{L}^{2}+K_{2}C_{L}+C_{D,skin} \tag{4}\]  
where \(K\) is the coefficient of drag-due-to lift and \(K_{1}\) can be expressed as Equation (5) [1]. \[K_{1}=\frac{1}{\pi ARe} \tag{5}\]  
Induced drag (\(C_{D,induced}\)) increases in proportional to the square of the lift coefficient, as in Equation (6) [17]. \[C_{D,induced}=\frac{C_{L}^{2}}{\pi ARe} \tag{6}\]  
where \(e\) is the Oswald span coefficient and generally varies according to the wing aspect ratio [18]. \[e= \begin{cases}0.9&AR\leq 20\\ 1.2-0.015 AR&AR>20\end{cases}  \tag{7}\]  
Form drag (\(C_{D,\,form}\)) changes depending on the characteristics of the configuration, such as aircraft cross-section size. In this study, \(K_{2}\) is assumed to be 15% of \(K_{1}\); this is a typical value for a glider aircraft with large wings and small fuselage area [17]. \[K_{2}=0.15\frac{1}{\pi ARe} \tag{8}\]  
\[C_{D,form}=0.15\frac{C_{L}}{\pi ARe} \tag{9}\]  
Skin friction drag (\(C_{D,skin}\)) is generated by skin friction between aircraft wing surface and air. Air viscosity is the cause. This is a critical factor of low-speed aircraft [19]. \[C_{D,skin}=\sum_{i=1}^{4}FF_{i}C_{fi}\frac{S_{wet,i}}{S_{ref,i}} \tag{10}\]  
where \(i\) denotes fuselage, main wing, horizontal wing, and vertical wing respectively, \(FF\) is form factor, \(C_{f}\) is skin friction factor, \(S_{wet}\) is wetted area, and \(S_{ref}\) is reference area. \(FF\), for [PERSON]'s streamlined body, was employed as in Equations (11) and (12) [20]. \[FF_{\mathit{fuselage,i}}=1+\frac{1.5}{\left(f\right)^{1.5}}+\frac{7}{\left(f\right) ^{3}}(i\,=\,1) \tag{11}\]  
\[FF_{\mathit{wing,i}}=1+2\Big{(}\frac{t}{c}\Big{)}_{i}+60\Big{(}\frac{t}{c}\Big{)} _{i}^{4}\left(i\,=\,2,\,3,\,4\right) \tag{12}\]  
where \(f\) means the fineness ratio of the fuselage and \(t\)/\(c\) is the ratio of the chord length (\(c\)) to maximum thickness (\(t\)) of airfoil. Table 2 shows the aerodynamic characteristic values calculated with respect to form using OpenVSP program. C\({}_{f}\) is the skin friction factor and varies according to the fluid flow (laminar flow, turbulent flow), as in Equation (13). In this study, the laminar flow was assumed in the low Reynolds area [16]. \[\mathrm{C}_{f,i}=\left\{ \begin{array}{ll}\frac{1.328}{\sqrt{\mathrm{R}c}}& \left(Laminar\right)\\ \frac{0.074}{\sqrt{\mathrm{R}c^{0.2}}}&\left(Turbulent\right)\end{array} \right. \tag{13}\]  
XFLR5 was utilized in this study; aerodynamic analysis was implemented for each main wing and tail wing.