FIGURE 3 Three cross sections of hindwing and the microstructure of the first groove on the leading edge. (a) The H. axyridis hindwing and sampling positions from P1 to P3; The microstructure of the first leading edge groove on P1 (b), P2 (c) and P3 (d). DS is dorsal side and VS is ventral side.

3.2 | Cl andCd analysis and interpretation

Figure 4 shows the changes of Cl andCd at different flapping frequency for the three CA models during one flapping cycle. In previous studies (Yang et al., 2015; Truong et al., 2013), the flapping frequency of the ladybird was usually set in the range between 55 Hz and 75 Hz. Here, the frequencies were set at 55 Hz, 65 Hz and 75 Hz. The graphs show first the downstroke and upstroke after that.
As shown in Figure 4 (a-c), theCl tends to rise in the first half of the downstroke and decrease in the second half, and then decreases further during the first half of the upstroke and rises again during the second half. The higher the frequency, the higher the lift coefficient. The results are related to the veins distribution of models (Figure 1b and 1c). Because the veins distribution decides the corrugated shape. A leading edge vortex (LEV) appears to be crucial for lift development during the downstroke, causing more air to be deflected downwards, hence producing more lift, as was also shown in Hawkmoth hovering flight (Yang et al., 2021). Simulations of Hawkmoth hovering show that about two thirds of the lift is associated with the LEV (Willmott et al., 1995). The average Cl and Cd are shown in Table 2. It shows that the average Cl of each model increases gradually with the increase of flapping frequency. The increment of AP1, AP2, and AP3 reached 33.99%, 13.61% and 67.35%, respectively.
From Figure 4(d-f), the change of Cd is shown during this flapping cycle. The first drag peak is caused mainly by the falling off of the LEV and the delayed stall phenomenon (Addo-Akoto et al., 2019). The second drag peak is caused mainly by the wake effect when the upstroke is about to end (Sujoy et al., 2012). The wake effect hardly changes with an increase in frequency, the second force peak is almost constant. As the frequency increases, the averageCd of these models increases first with frequency and then decreases at even higher frequency; the highest drag values were obtained at 65 Hz.