# Parametric and Statistical Study of the Wing Geometry of 75 Species of Odonata
## 1 Introduction  
There are various structural and aerodynamic demands related to the ecological niche of each species of Odonata that have influenced the characteristics of their wings through natural selection. An understanding of the aerodynamic performance of wings may inform considerations of metabolism, ecology, and evolutionary processes. Unlike many insects, Odonata wings have comparatively high aspect ratios [1], modest wing beat frequencies (30-40 Hz) [2; 3; 4], limited stroke angles (30\({}^{\circ}\)-60\({}^{\circ}\)) [5; 6], and are used in gliding flight modes [7]. Some steady-state aerodynamic parameters are worth considering under these circumstances [8; 9]. Odonata are categorized into the suborders _Epiprocta_ (dragonflies) and _Zygoptera_ (damselflies) [10]. The nodus size has been identified as an important parameter in the structure of a dragonfly wing, as illustrated in Figure 1b. The nodus is the point where the camber of the leading edge spar inverts [11], which is believed to provide strength and flexibility in flight [12]. [PERSON] et al. studied the dynamics of the nodus and wing in gliding flight [13]. According to their experimental visualization analysis,the nodus is an essential structural element of the wing, providing flexibility to the wing under aerodynamic loads [13]. The scanning electron microscopy (SEM) visualization and tensile testing have shown that the location of the nodus is critical during flight, due to high tensile stresses [14]. It also provides the wings with shock-absorbing capability that may help in dealing with any externally imposed torsion or bending stress [11]. During the flight, the wings undergo passive twist that is largely dependent on the position of the nodus [15]. The nodus is located at the leading edge at the interface of the second main vein and the leading edge of the wing where the orientation of the leading edge changes [16; 17], which is about 50% of wingspan from the root [18; 19]. The other prominent structure is the pterostigma. It is often found in the outer part of the span at the leading edge of Odonata wings, and is created by a blood-sinus during emergence [15] (Figure 1). Pterostigma probably plays a major role in the flight stability of Odonata. The concentrated mass of the pterostigma is believed to have a counteracting role during undesired twisting of the wing in the airflow [20]. As shown in Figure 1, the definition of chord lines for Odonata is different compared to commercial aircraft. For Odonata, chord lines are defined to have an angle \(\alpha\) to the reference body line, where \(\alpha\) is the angle between a perpendicular line to the reference body line and the perpendicular line to the chord. However, for aircraft, chord lines are defined parallel to a fuselage [21]. Odonata appear to have a characteristic arrangement of wings and overall planform common to all species, but with parameter variations. The purpose of our study was to explore how non-dimensional parameters might vary between species and scales of dragonflies for the next generation of the bio-inspired micro air vehicle. Our collection of 75 solid models of Odonata wings was measured to extract descriptive wing parameters. The main parameters of Odonata wings include forewing (FW) and hindwing (HW) span, minimum and maximum chord length, and location (these parameters play an important role to an optimum for the lift distribution over the wing) [22], nodus location and length, pterostigma size, and distance from the nodus. These parameters together describe the key features of an Odonata wing that are relevant to flight performance. Span and chord measurements have a significant role [23] in establishing the basic performance characteristics of fixed-wing aircraft, and are likely to be equally important to understanding the aerodynamic performance of Odonata. This paper presents the essential geometrical parameters of Odonata wings and explores the trends apparent in the dataset.