# Check-Valve Design in Enhancing Aerodynamic Performance of Flapping Wings
## 1 Introduction  
Through the research of more than two decades, flapping wing micro air vehicles (FWMAVs) made recently great progress by the control of the tailless configuration. The \"Delfly Nimble\" [1] and the \"KU Beetle\" [2] are two successful examples that could perform hovering flight and some distinguished maneuvers. However, based on the flapping wing design improvement by the conventional wind tunnel testing, the forward flight and the level cruising of FWMAVs are still the most primary forms of flapping flight under investigation [3; 4; 5]. How to reduce the air drag and flight power during cruising, so as to achieve long-term flight endurance, are crucial to the development of FWMAVs [6; 7]. Observed from the downstroke and upstroke motions of a full flapping cycle, most of the researchers performed lift enhancement during the downstroke period. There are several ways for lift improvement; for instance, by increasing the wing foil thickness and the camber [8], by adding wing corrugation [9], by enlarging the stroke angle [10], using wing rotation mechanisms [11], using morphing wings [12; 13; 14], by changing thewing materials [15; 16; 17], or by adjusting the wing stiffness along the chord-wise/span-wise direction [18]. Not many studies have been performed for the enhancement of lift through mimicking feathers [19; 20; 21; 22; 23; 24; 25] in the upstroke. The adaptive flight control of Caltech's Micro-bat by using check valves [23], the Festo's BionicSwift using of aerodynamic feathers similar to overlapping shingles on the roof [26; 27], and the ventilated design [22] are the prominent research works in lift enhancement. Compared to the Caltech's Microbat, the wingspan and body mass of Festo's Bionic Swift and the ventilated design [22; 27] is much larger. Based on the more familiar understanding of the 20 cm-span FWMAVs [28; 29; 30], herein we would like to qualitatively address the validity of the lift enhancement mechanism in Figure 1.  
Figure 1a,b illustrate the closing and opening of the check-valve during the downstroke and upstroke, respectively. The valve-opening action can effectively reduce the magnitude of the negative lift since its pin-hole opening spoils both the completeness of the wing and smoothness of the air flow. On the other hand, it also shows that the closing of check-valve during the downstroke completely restores the wing contour. It ensures that the positive lift is similar to the plain membrane wing without valves. The expected lift waveforms are shown in Figure 1c,d. In Figure 1d, dash line is the reference line shown in order to compare the region where the magnitude of the negative lift of the closed check-valve is reduced to a solid line waveform of the open check-valve case. It is evident that the proper opening and closing of the check-valves can enhance the average lift during flapping. However, there are still open issues with reference to the design of check-valves for FWMAVs. The following are limitations in comparing to the existing study [23]. Problem (i): There seems to be no baseline for the size and number of four serpentine (S) arms of the check-valves. Number 4 is not a prime number; thus, resonance may be present in this design. Problem (ii): Other studies fail to describe the dynamic behavior of the check-valves. Therefore, it is difficult to justify the appropriateness of their design. Figure 1: Illustration of check-valve closing and opening on the wing surface: (**a**) Check-valve closing during downstroke; (**b**) check-valve opening during upstroke; (**c**) expected lift wave form without check-valves; (**d**) expected lift wave form with check-valves. Problem (iii): There are too many check-valves distributed at the leading and trailing edges of the flapping wing [31; 32]. They will induce many unpredictable issues. To eliminate these stumbling blocks, a modified design and corresponding experimental studies are conducted. In this work, the check-valve is designed by examining static and dynamic characteristics using finite element analysis (FEA).