# Power Modeling and Experiment Study of Large Flapping-Wing Flying Robot during Forward Flight
## 3 Results  
First, the forces in the x-axis direction in Figure 8 were measured in the wind tunnel using an experimental prototype with or without wings. The purpose of this experiment was to measure the drags acting only on the wings or only on the fuselage, then to further calculate the parasitic drag and profile drag coefficients. In the wind tunnel, the FWAV with wings was first mounted in the experimental platform and the drag D1 was measured at different wind speeds using the six-dimensional force sensor. Note that the wings were kept fully expanded and static during the experiment. Secondly, the wings were removed and only the fuselage was kept; the drag D2 on the fuselage was measured in the same way. The drag D3 acting only on the wings can be calculated as D3 = D1 \(-\) D2. Using Equations (17) and (19), we can calculate cd1 and cd2 obtained from the experiment. The results are shown in Table 2.  
Wind tunnel experiments on the wing #1 prototype with a wingspan of 1.8 m and the wing #2 prototype with a wingspan of 1.6 m were done in this study. Except for the wing to be analyzed, all components in the experiments were the same, including the power unit, fuselage skeleton, etc. The initial twist angle \(\gamma_{0}\) of a single wing segment was assumed to be 5\({}^{\circ}\), with a maximum twist angle \(\gamma_{\text{max}}\) of 15\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Physical Meaning** & **Wing \#1** & **Wing \#2** \\ \hline \(b\) & wing span (m) & 1.8 & 1.6 \\ \(S\) & wing area (m\({}^{2}\)) & 0.52 & 0.42 \\ \(c\) & average chord length (m) & 0.29 & 0.29 \\ \(AR\) & aspect ratio & 6.18 & 5.57 \\ \(R1\) & radius of wing tip (m) & 0.3 & 0.27 \\ \(m_{wing}\) & mass of wings (g) & 170.6 & 148.5 \\ \(m\) & mass of FWAV (g) & 537 & 515 \\ \hline \end{tabular}
\end{table} 
Table 1: Detailed parameter table of wing #1 and wing #2. It should be noted that due to the presence of noise, the experimental data were processed with low-pass filtering with a cutoff frequency of 50 Hz. Lift and thrust are very important for the flight of a flapping-wing vehicle. A graph of the lift (vertical direction) and thrust (horizontal direction) measured by experiment in the proposed model is in Figure 8a. As shown in Figure 8a, the lift results measured by model and experiment of wing #1 at angle of attack of 15\({}^{\circ}\), flapping frequency of 3.5 Hz, and wind speed of 5 m/s are compared. The trend of lift with time calculated by the model is basically the same as the experimental results, but the peak value of the model is slightly larger than the experimental results. The power comparison between the model and the experiment for wing #1 is illustrated in Figure 8b. Because aerodynamic power is cubically related to velocity, the model data can be seen clearly in two peaks in one flapping cycle, which is also corroborated in the experimental data. To better show the model and experimental results, the average power comparison between the model and experimental results under each condition and the difference percentage between the model and experimental results are plotted. As shown in Figure 9, with a wind speed of 5 m/s, the experimental data of wing #1 agrees well with the model calculations. At a given wind speed, when the flapping frequency rises, the velocity produced by wing flapping rises as well, and the closer to the wingtip, the greater the \(v_{\varphi}\), which leads to an increase in the sum velocity of the wing relative to the air, thus increasing the power. The angular velocity of the wings, on the other hand, increases as the flapping frequency increases, increasing the inertial power required for wing flapping.