# Parametric and Statistical Study of the Wing Geometry of 75 Species of Odonata
## 4 Discussion  
Comparing average results, one can say that the dimension of the maximum chord is around 25% of the wing semi-span in the species measured. However, its location is closer to the body for the HW, which is 37% of the wing semi-span. Furthermore, the location of the maximum chord can be significantly different for different species. The minimum span location belongs to the HW of the _Libellutiade_ family by a fraction of 0.1 of semi-span length. Among our dataset, the maximum chord is placed at approximately 79% of the FW semi-span. Figure 15 presents an illustrative example of the observed design criteria, regarding the minimum and maximum margins of the maximum chord and its location relative to the wing dimension (hatch-line areas). The hatch areas are the representative \begin{table}
\begin{tabular}{c c} \hline
**Wing Geometry Parameter** & \(\mathbf{R^{2}}\) \\ \hline C\({}_{\text{max}}\) FW = 0.219 \(\times\) (b/2) & 0.86 \\ C\({}_{\text{max}}\) HW = 0.276 \(\times\) (b/2) & 0.70 \\ C\({}_{\text{max},\text{L}}\) FW = 0.58 \(\times\) (b/2) & 0.62 \\ C\({}_{\text{max},\text{L}}\) HW = 0.37 \(\times\) (b/2) & 0.27 \\ C\({}_{\text{mean}}\) FW = 0.16 \(\times\) (b/2) & 0.73 \\ C\({}_{\text{mean}}\) HW = 0.20 \(\times\) (b/2) & 0.63 \\ b FW/HW = 1 & - \\ C\({}_{\text{nodus,L}}\) FW = 0.489 \(\times\) (b/2) & 0.78 \\ C\({}_{\text{nodus,L}}\) HW = 0.404 \(\times\) (b/2) & 0.91 \\ C\({}_{\text{pterostigma,L}}\) FW = 0.811 \(\times\) (b/2) & 0.95 \\ C\({}_{\text{pterostigma,L}}\) HW = 0.756 \(\times\) (b/2) & 0.91 \\ \hline \end{tabular}
\end{table} 
Table 1: Essential wing geometrical parameters exported from the graphs. \begin{table}
\begin{tabular}{c c} \hline
**Nondependent Parameters (R2 > 0.7)** & **Dependent Parameters (R2 < 0.7)** \\ \hline C\({}_{\text{max}}\) & C\({}_{\text{max},\text{L}}\) \\ C\({}_{\text{mean}}\) FW & Pterostigma size \\ C\({}_{\text{nodus}}\) & C\({}_{\text{mean}}\) HW \\ C\({}_{\text{nodus,L}}\) & - \\ L\({}_{\text{pterostigma}}\) & - \\ \hline \end{tabular}
\end{table} 
Table 2: List of family-dependent and nondependent geometric parameters of the dragonfly wing. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **Forewing** & & & **Hindwing** & \\ \hline  & Min. & Ave. & Max. & Min. & Ave. & Max. \\
2 \(\times\) C\({}_{\text{max}}\)/b & 0.17 & 0.22 & 0.32 & 0.17 & 0.27 & 0.40 \\
2 \(\times\) C\({}_{\text{max}}\) /b & 0.33 & 0.59 & 0.79 & 0.10 & 0.37 & 0.74 \\
2 \(\times\) C\({}_{\text{mean}}\)/b & 0.10 & 0.16 & 0.23 & 0.10 & 0.20 & 0.30 \\
2 \(\times\) C\({}_{\text{nodus}}\)/b & 0.06 & 0.20 & 0.25 & 0.06 & 0.247 & 0.34 \\ AR & 8.74 & 12.68 & 19.30 & 6.77 & 10.37 & 19.20 \\ \hline \end{tabular}
\end{table} 
Table 3: Maximum, minimum, and average ratio for FW and HW. of the estimation range for both max chord and its location. In other words, the length of the hatch areas is representative of the range of the location of the max chord, which can vary from 0.33 to 0.8 of the semi-span length. On the other hand, the width of the hatch areas is representative of the max chord length, which can vary between 0.17 and 0.32 of the semi-span length. This graph can be extended for the other parameters, such as pterostigma and nodus, to provide a general mapping algorithm for the preliminary design of a flapping wing drone aircraft. Another parameter shown in Table 3 is the aspect ratio (AR), which is generally defined as the ratio of full span to mean chord [41]. According to these data, the average AR is 12.68 and 10.37 for FW and HW, respectively. Pterostigma is the other significant factor for designing the bio-inspired wing. Possessing a favorable aerodynamic function, the pterostigma is located in close proximity to the tip of the wing as a dark, thickened membrane structure [14]. The pterostigma changes the center of mass of the wing at the leading edge, which leads to more stability in flapping flight [42].