# Mini Glider Design and Implementation with Wing-Folding Mechanism
## 3 Simulation and Analysis  
In this section, simulation studies are described for the glider whose design is completed according to the rules and theoretical calculations based on the developed mathematical model. According to the parameters that are determined by theoretical calculations, the dynamic behavior of the glider is repeated in the simulation environment. The analysis should be performed by using authentic equipment with their properties to see more realistic behaviour in the design model to further improve the glider design after simulation. The location of center of gravity, horizontal and vertical stabilizers' size estimation, determining \(\alpha\) to provide maximum lift, and so forth are obtained in the previous section. The simulation's aim is to compare parametric verification of the results with the theoretical calculations. Firstly, there are five different natural modes to determine stability of an aircraft which are related with two longitudinal and three lateral axes should be investigated. They are phugoid mode and short period mode for longitudinal and the spiral mode, the roll damping mode and the dutch roll mode for the lateral axis. Short period mode eigenvalues are \(s_{1,2}=-15.2\pm 5.7i\) and phugoid mode eigenvalues are \(s_{3,4}=-0.1\pm 0.2i\). All the roots are on the negative side of the Alpha axis. In this case, it represents that all the roots of the system are stable. For the roots with smaller values of the imaginary axis (beta), the damping ratio is lower. In such a case of phugoid oscillations, the change between kinetic energy (speed) and potential energy (height) is very slow, so that the glider can return to its horizontal flight position again. Phugoid mode response can be given in the form (Equation (36)) for \(\sigma=\zeta\omega_{n}\) and \(\omega=\omega_{n}\sqrt{1-\zeta^{2}}\),  
\[\lambda=\sigma+\omega i, \tag{36}\]  
where damping ratio is \(\zeta\) and natural frequency is \(\omega_{n}\). In the case of phugoid mode, the glider dynamic response according to the step input is \(\lambda=-0.0392+1.1644i\) and \(f=0.185\) Hz. Stability and control coefficients are determined and showed that the glider can fly steadily depending on the eigenvalues. In addition, to obtain aerodynamic behaviour of the system, XFLR5(r) is preferred since it has a more realistic approach through using VLM. To determine aerodynamic coefficients and efficiency, the range is selected from \(\alpha=-5^{\circ}\) to \(15^{\circ}\) and \(Re=5~{}\times~{}10^{4}\) to \(12.6~{}\times~{}10^{4}\) in Figure 5. In this figure, the pressure points on the glider's wing can be seen with an orange-red colour. The pressure coefficient \(c_{p}\) varies between 0.66-1.11, which determines stability and axial moments, and it is more likely to be on the leading edge. Lift coefficient \(C_{L}=0.66\), which is greater than \(C_{L,r}=0.4855\), which is mentioned in Section 2.1. Table 2 is found when the speed of glider is \(V_{glider}=12.07\) (m/s) and AoA\(=-3^{\circ}\). The pitching moment of the glider is determined as zero when AoA is selected as \(=-3^{\circ}\). \(C_{m}-\alpha\) graph shows that, mathematically, the design is stable if it has a negative gradient. Figure 4: The model is designed by 3D Solidworks® and is shown from an isometric view including equipment. The servo motor mechanism is used to separate the glider from the container autonomously at a height of 400 m. The servo motor rotates and releases the glider at certain pre-defined height, which is measured by GPS unit. Furthermore, it is crucial to determine the lift to drag \(C_{L}/C_{D}\) ratio since a higher \(C_{L}/C_{D}\) is typically one of the major goals in aircraft design. Here, \(C_{L}/C_{D}\) is calculated as 3.953. Accordingly, it has been observed that the glider can produce the lifting force greater than its own weight [30]. In Figure 6, lift to drag ratio with respect to AoA is presented. A Gaussian curve characteristic can be observed based on XLFR5 results, as expected.