# Effect of Wing Corrugation on the Aerodynamic Efficiency of Two-Dimensional Flapping Wings
## 1 Introduction  
For several decades, the characteristics of the corrugations found in insect wings have attracted considerable interest, because of their promising application to the design of micro air vehicles (MAVs). The contribution of the corrugation to wing stiffness is relatively well studied, and it has been concluded that wing corrugation contributes to spanwise bending stiffness with low mass, preventing wing fracture while allowing wing twist and wing camber formation [1]. These advantages of the corrugated wing are considered to be applicable to the wings of insect-like flapping-wing micro air vehicles (FW-MAVs) [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. For FW-MAVs using the reciprocating motion of flapping wings, significant energy loss occurs during the acceleration and deceleration phases at the stroke reversals of the wings, due to inertial force. Therefore, for higher energy efficiency, the wing mass should be as light as possible. Meanwhile, the wing stiffness must be high enough to maintain the wing shape during flapping motion so that it can meet the desired aerodynamic performance requirement. Another aspect of the wing corrugation that requires further investigation is the effect of wing corrugation on aerodynamic performance. Many experiments and numerical investigations have beencarried out to identify the aerodynamic benefits of the corrugated wing. Their conclusions have differed. Some claimed that the wing corrugation was helpful for enhancing the aerodynamic performance of the wing [13; 14; 15; 16], while others reported that the effect of wing corrugation on aerodynamic performance was insignificant [17; 18; 19]. [PERSON] [16] tested a corrugated wing and another wing whose outer contour followed the envelope of the corrugated wing for different Reynolds numbers and aspect ratios [16]. He found that the ratios between the quasi-lift coefficients and quasi-drag coefficients of the two wings with an aspect ratio of 1.12 were quite similar for different Reynolds numbers of (450 and 900). However, the ratio of the corrugated wing was higher than that of the envelope wing with an aspect ratio of 0.53. [PERSON] et al. [13] conducted wind-tunnel and free-flight tests for various wings. In the comparison of a thin flat plate and corrugated wing at the Reynolds number of around (1.1 to 1.5) \(\times\) 10\({}^{4}\) at an angle of attack (AoA) in the range of (\(-6\) to 20)\({}^{\circ}\), they showed that the nose-down wing corrugation contributes to an increase in the lift coefficient (C\({}_{\text{L}}\)) and gliding ratio (C\({}_{\text{L}}\)/C\({}_{\text{D}}\)). However, the result in the case of nose-up corrugation was obviously altered, and the lift coefficient and gliding ratio were significantly diminished, compared to those of a non-corrugated wing. Therefore, they claimed that the configuration of the leading edge plays an important role in aerodynamic performance, and the nose-down wing corrugation at the leading edge performs better than the nose-up wing corrugation. [PERSON] [14] performed experiments on various corrugated sectional profiles, following the cross-section of a dragonfly forewing at different locations, to examine the effect of the wing's corrugation on the aerodynamic performance at an AoA in the range of (\(-25\) to 40)\({}^{\circ}\). Her results showed that aerodynamic performance in terms of lift coefficient and gliding ratio was slightly improved for the corrugated wing compared to that of the flat plate airfoils at the Reynolds number of (7880 and 10,000). However, due to the similar results of two corrugated wings, in which the orientations of the leading edges were in opposite directions, she concluded that the orientation of the leading edge did not affect the aerodynamic efficiency. This conclusion was in contrast to the finding by [PERSON] et al. [13]. [PERSON]'s experiment was verified by [PERSON] et al. [15], using two-dimensional numerical analysis with the same wing profiles. [PERSON] et al.