## 3 Results and Discussion
### The Trimmed Results by Two Methods Separately  
The forward-sweep is mainly generated by the forward-motion of the humerus, and since a model of the two-segment wing is not given in the literature, the forward-sweep cannot be accurately modeled. However, forward-sweep is an effective trimming method, whether in gliding mode or flapping mode [1; 2; 3]. The sweep angle mainly adjusts the center of gravity and aerodynamic center relative position. Although data on forward-sweep is not given in the literature [14], in order to consider as many factors affecting the trim as possible, here we set the forward-sweep angle as a variable.  
Figure 8 shows the trim process through adjusting the angle of attack and flapping frequency, while keeping the wash-out angle at \(-13\) degrees and neglecting the effect of forward-sweep. In other words, the forward-sweep angle is set to be zero. It can be seen from the figure that at the same flapping frequency, drag decreases first and then increases with the increase in the angle of attack, and the pitching moment increases with the increase in the angle of attack. Since the moment at zero lift is greater than zero, the growth slope of the moment to the angle of attack is negative, ensuring longitudinal static stability. As the frequency increases, the drag decreases, and so does the pitching moment, because the increase in thrust will increase the nose-down moment.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Lift** & **Drag** & **Pitching Moment** \\ \hline Average Force & 4.95 N & \(-0.043\) N & \(-0.28\) N\(\cdot\)m \\ \hline Average Coefficient & 0.97 & \(-0.0085\) & \(-0.056\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average aerodynamic coefficients (c.g = 0.5).  
Figure 7: The variation of the coefficients of lift, drag, and pitching moment within a flapping period (gray shadow represents the course of upstroke).  
Comparatively, Figure 9 gives the results of the trim process through adjusting the angle of attack and flapping frequency, while keeping the forward-sweep angle at 28 degrees. It can be seen that at the same flapping frequency, the drag decreases first and then increases with the increase in the angle of attack, and the pitching moment increases with the increase in the angle of attack. The growth slope of the moment to the angle of attack is positive, resulting in unstable characteristics in the longitudinal direction. This means the forward-sweep motion will bring an unstable factor to longitudinal stability. As the frequency increases, the pitching moment first decreased and then increases, which shows a process of trade-off between the nose-down moment, produced by added thrust, and head-up moment, generated by forward movement of the aerodynamic center.  
By changing the flapping frequency, the states of trim by wash-out and trim by forward-sweep, respectively, can be obtained. The trim results in Table 4 show that the angle of attack obtained by the wash-out method is smaller than that obtained by the forward-sweep method; the corresponding flapping frequency is larger, and the weight obtained is smaller, than that obtained by forward-sweep. The increase in flapping frequency will increase energy consumption, so the aerodynamic efficiency of the wash-out trim is far less than that of the forward-sweep. However, due to the slope of the pitching moment being negative, forward-sweep motion will bring an unstable characteristic to the longitudinal stability of a seagull.  
Figure 8: Trim process through adjusting the angle of attack and flapping frequency while keeping the wash-out angle at \(-13\) degrees.  
Figure 9: Trim process through adjusting the angle of attack and flapping frequency while keeping the forward-sweep angle at 28 degrees.