# Research on the Flight Performance of Biomimetic Moth Based on Flapping Function Control
## 3 Calculation and Simulation
### Simulation of the Impact of Key Parameters on the Performance of Flapping-Wing Aircraft
#### 3.2.4 Impact of Mid-Position Angle of Flapping Function on Lift  
As can be seen from the lift calculation formula, under the same flapping amplitude and flapping frequency conditions, the greater the absolute value of the mid-position angle, the smaller the lift generated. However, the change of mid-position angle may cause a change in the angle of attack, thereby changing the lift coefficient and then affecting the aerodynamic performance. To qualitatively explore the impact of mid-position angle on aerodynamic performance, five groups of flapping functions are designed, simulated, and calculated. The control parameters of the right-wing flapping function are shown in Table 6, and the left-wing flapping function is opposite to the right wing. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Flapping Motion with a 3 Hz** & **Flapping Motion with a 4 Hz** & **Flapping Motion with a 5 Hz** \\  & **Flapping Frequency** & **Flapping Frequency** & **Flapping Frequency** \\ \hline \(\phi_{max}\) & 2\(\pi\)/9 & 2\(\pi\)/9 & 2\(\pi\)/9 \\ \(T_{1}\) & 0.198 & 0.15 & 0.12 \\ \(T_{2}\) & 0.132 & 0.1 & 0.08 \\ \(\phi_{1}\) & \(\pi\)/2 & \(\pi\)/2 & \(\pi\)/2 \\ \(\phi_{2}\) & 0 & 0 & 0 \\ \(\phi_{0}\) & \(\pi\)/18 & \(\pi\)/18 & \(\pi\)/18 \\ \(T\) & 0.33 & 0.25 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Control parameters of flapping motion with different flapping frequencies. Figure 7: The impact of flapping frequency on lift. The simulation time is set to 1 s, including four flapping cycles. The simulation data is imported into the software Origin, and the lift curves of the five flapping motions over time are drawn, as shown in Figure 8. It can be seen that the mid-position angle of flapping motion has an unremarkable impact on aerodynamic performance. The average lift within a period is calculated (0.25 s-0.5 s). The average lift generated by the flapping motion with a mid-position angle of \(-10^{\circ}\) within a period is about 0.609 N. The average lift of the flapping motion with a mid-position angle of \(-5^{\circ}\) is about 0.653 N. The average lift of the flapping motion with a mid-position angle of \(0^{\circ}\) is about 0.715 N. The average lift of the flapping motion with a mid-position angle of \(5^{\circ}\) is about 0.741 N, and the average lift of the flapping motion with a mid-position angle of \(10^{\circ}\) is about 0.782 N. Therefore, it can be concluded that increasing the mid-position angle can slightly improve the aerodynamic performance. This is slightly different from the results of mathematical modeling analysis. The difference between the results of simulation calculation analysis and mathematical modeling analysis is that the former shows that the larger the mid-position angle, the greater the average lift, while the latter shows that the larger the absolute value of the mid-position angle, the smaller the average lift. The similarity is that the change of mid-position angle has an insignificant impact on the average lift. It is speculated that this is because the impact of the mid-position angle on the angle of attack is ignored when mathematical modeling is carried out, resulting in an imperfect calculation model. In the lift calculation formula for flapping-wing motion, \(C_{Ld}\) and \(C_{Lu}\) are periodically varying, and the mid-position angle may affect this variation. However, to simplify the calculation, in the computational model, we set both as constants. This may be the reason for the  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameter** & **Mid-Position** & **Mid-Position** & **Mid-Position** & **Mid-Position** & **Mid-Position** \\
**Angle of \(-10^{\circ}\)** & **Angle of \(-5^{\circ}\)** & **Angle of \(0^{\circ}\)** & **Angle of \(5^{\circ}\)** & **Angle of \(10^{\circ}\)** \\ \hline \(\phi_{max}\) & \(2\pi/9\) & \(2\pi/9\) & \(2\pi/9\) & \(2\pi/9\) & \(2\pi/9\) \\ \(T_{1}\) & \(0.15\) & \(0.15\) & \(0.15\)  
difference between the conclusions of the computational model and the simulation results.