# Mini Glider Design and Implementation with Wing-Folding Mechanism
## 2 Mathematical Model
### Wing Design  
The glider is designed in accordance with the rules that are given by [15]. The glider's longitudinal length and wingspan of folding position are limited by the fixed container size. For this reason, the dimensions of folding and deploying configurations are important criteria to be considered firstly. Depending on these, the weight of the glider, the position of the center of gravity, the appropriate dimensions of the glider's body and wing, and the material to be used, etc. will be determined. Pre-designed model and container including the materials and dimensions are shown in Figure 2. In this figure, dimensions of the glider are shown in the folded condition. Body and wing dimension, the position of center of gravity can also be seen. Generally, the center of gravity is adjusted to correspond to the mean aerodynamic chord (MAC) of 25% with reference to the leading edge. This position affects the performance of the glider's pitching stability when it is positioned ahead or behind. The most forward position that can be selected depends on the lift force capacity that the horizontal stabilizer can apply downwards. This force must match the pitching moment generated by the wings of the glider. Therefore, it is preferable to adjust 1/3 to the leading edge (Figure 2A,B). In the folded case of the glider, the dimensions of the container to be placed in and the material to be  
Figure 1: Glider is launched from point A and after following the trajectory B, it is separated from capsule at point C, which is 600 m above the ground. The glider has to be separated autonomously at 400 m altitude at point D and the collected data during glide have to be observed by a ground station at point F. Point E shows the data communication between a glider and the ground station. produced are included (Figure 2C). Since the weight and strength are important criteria, it has been preferred to use Kevlar in the container body. Properties of both configuration of the glider can be also seen in Table 1.  
In order to determine the dynamic behaviour of the glider during descent, the required lift coefficient \(C_{L,r}\) must be calculated according to the maximum pre-designed glider's established mass. In addition, the lift force of the glider should be observed under glide condition together with the drag coefficient, \(C_{D}\), that is acting on it. Lift and drag forces acting on the glider during descent will be determined by calculating these coefficients. According to pre-designed model, the mass of the container and glider, by using Kevlar material, are calculated to be 248 g and 252 g, respectively. When the glider performs a hovering movement around a helical orbit, the profile drag coefficient, \(C_{D,0}\), is used to determine the calculating maximum glide speed, \(V_{max}\) (m/s). Then, aerodynamics coefficients can be determined by using angle of attack (AoA) where the range is selected from \(\alpha=-9.5^{\circ}\) to \(9.5^{\circ}\). In this range, (\(C_{L}/C_{D}\)-\(\alpha\)) represents the lift coefficient \(C_{L}\) as a variable of the AoA angle, which is selected from \(2^{\circ}\) to \(6^{\circ}\) to have maximum \(C_{L}\). In addition, similar stability effects can be seen in pitching moment-AoA, (\(C_{M}\)-\(\alpha\)), for the same range of \(\alpha\). By using a (\(C_{L}\)-\(\alpha\)) graph, having a more stable and reliable flight can be observed when \(\alpha=5.5^{\circ}\) is selected. Minimum profile drag, \(C_{D,0}=0.07\) and aspect ratio(AR), \(AR=9.466\) are determined at the same \(\alpha\). To determine necessary initial parameters, which need to be calculated to determine the glider dynamic behavior, Equations (1)-(5) can be used  
\[V_{t}=\sqrt{\frac{2W}{\rho\pi C_{D}R^{2}\cos^{2}(\frac{r\pi}{2R})}}, \tag{1}\]  
\[V_{max}=\sqrt{\frac{2W}{\rho S}\sqrt{\frac{K}{C_{D,0}}}}, \tag{2}\]  
\[C_{L}=\frac{2L}{\rho SV^{2}}, \tag{3}\]