# Design and Verification of a Large-Scaled Flapping-Wing Aircraft Named \"Cloud Owl\"
## Materials and Methods
### Wing Design  
Flapping wings are the key component of flapping-wing aircraft. The lift and thrust of a flapping wing are intimately correlated with its shape, motion, and structural stiffness. The structural parameters, motion parameters, and dynamic parameters of flapping-wing vehicles are typically estimated by the bionic scaling rate [15]. The initial take-off weight of these vehicles is 1310 g, and the scale rate calculation is used to determine the overall parameters, which are fitted by the exponential function k \(\times\) mp, as shown in Table 3.  
The computation of the flapping amplitude, which can be done using the Strouhal number similarity principle, is not required by the scale law. To account for both thrust and propulsion efficiency, St is set at 0.3 [16]. The following formula yields the calculated flapping amplitude of 63.7\({}^{\circ}\). \[\varphi=2\arcsin(St\times V\div f\div b) \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Part** & **Materials** & **Density** & **Weight** & **Proportion of Cloud** & **Proportion of** \\  & & **(kg/m\({}^{3}\))** & **Estimation(g)** & **Owl’s Weight (\%)** & **Dove’s Weight (\%)** \\ \hline Fuselage & EPP & 30 & 40 & 3 & 7.1 \\ \hline Structure & 3K carbon fiber composite & 1500 & 80 & 6.1 & 14.3 \\ \hline Flapping wing & 3K carbon fiber composite & 1500 & 100 & 7.6 & 5 \\ \hline Tail & Laminates, KT board & 500,140 & 80 & 6.1 & 2.5 \\ \hline Flapping mechanism & 3K carbon fiber composite, & 1500,2810,150 & 200 & 15.3 & 17.9 \\ \hline Avionics & / & / & 110 & 8.4 & 15.7 \\ \hline Payload & / & / & 300 & 23 & 14.3 \\ \hline Battery & / & / & 400 & 30.5 & 23.2 \\ \hline Total weight & / & / & 1310 & 100 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of flapping-wing aircraft with large wingspan at home and abroad. Figure 3: Schematic of the Cloud Owl. The results of wind tunnel measurements show that, under the assumption that average angular velocities are similar [17], the aerodynamic properties of flapping wings are similar and independent of variations in flapping amplitude and frequency. The scale rate calculation results show that the flapping frequency is lower but the flapping amplitude is higher, which is counterproductive to increasing cruise speed. As a result, the flapping frequency and amplitude should be adjusted in accordance with the cycle's average angular velocity. The flapping amplitude was calculated to be 43.8\({}^{\circ}\), and the flapping frequency was changed to 5.5 Hz. The following formula, where A is the amplitude of the flapping, yields the mean periodic angular velocity. \[\overline{\omega}=\frac{1}{T}\int_{0}^{x}\left|\omega_{flap}\right|dt=2 Af \tag{2}\]  
The actual wing surface area Se is a dimensionless reference region that has more reference value because it has nothing to do with the law of flapping. These parameters are displayed in Figure 4.  
\[S_{e}=f\int_{0}^{\frac{1}{2}}S\cos(\varphi\sin(2\pi ft))dt \tag{3}\]  
F stands for the flapping frequency (Hz), S is the area of the wing (m\({}^{2}\)), \(\varphi\) is the flapping amplitude (\({}^{\circ}\)), and T is any point in the flapping period. Due to the fact that flapping-wing vehicles share some characteristics with both rotorcraft and fixed-wing aircraft, the following is the definition of the wing load of a flapping-wing aircraft:  
\[Q=\frac{W_{\rm TO}}{S_{n}}=\sqrt{\frac{W_{\rm TO}}{S_{e}}\times\frac{W_{\rm TO }}{S_{P}}} \tag{4}\]  
The equivalent wing area, Sn, in the formula, is equal to the square root of the product of Se of the effective wing area and S\({}_{\rm P}\) of the wing disk area. S\({}_{\rm P}\) is the disk area; S\({}_{\rm P}=2\pi\)b\({}^{2}\varphi/360\), where b is half of the wingspan. W\({}_{\rm TO}\)/S\({}_{\rm e}\) is known as normal wing load, and W\({}_{\rm TO}\)/S\({}_{\rm P}\) is referred to as tangential wing load. The term \"normal wing load\" has the same definition as \"wing load\" for fixed-wing aircraft.