# A Morphing Deployable Mechanism for Re-Entry Capsule Aeroshell
## 2 Re-Entry Mission from LEO  
Mechanically deployed aeroshells can be deployed and retracted repeatably. Unlike rigid or inflatables decelerators, adaptive deployable concepts can provide controlled re-entry trajectories and enhanced flight maneuverability by integrating shape-morphing strategies into high temperature and flexible TPS. The sample return mission has three main challenges: 1. Withstanding high temperatures during re-entry; 2. Steering the Cubesat during re-entry in order to follow a predefined trajectory; 3. Enabling high precision landing after passing through the atmosphere. The aim of this paper is to propose an initial idea of a low ballistic coefficient planetary entry system that incorporates an innovative shape-changing mechanism that can be housed in the folded configuration inside a 12U Cubesat and then deployed with the intent of a re-entry and landing for payload recovery. By considering an ISS payload as an example, scientific data can be recovered for post flight inspections and experimentations, opening new possibilities of samples to return from space with minimal or no propulsion systems. As a very first approximation, a Newtonian approach is considered to estimate the spacecraft drag coefficient (CD) by simplifying its shape with a cone, as shown in Figure 2, by using the equation:  
\[C_{D}=\left(1-\sin^{4}\delta_{C}\right)\left(\frac{r_{n}}{r_{c}}\right)^{2}+2 \sin^{2}\delta_{C}[1-\left(\frac{r_{n}}{r_{c}}\right)^{2}\cos^{2}\delta_{C}] \tag{1}\]  
where \(\delta_{C}\) is the cone half angle, \(r_{c}\) is the cone base radius and \(r_{n}\) is the nose radius. A is the area of the frontal cross section, which is perpendicular to the motion direction. A nominal undeflected \"rigid\" surface is preliminary considered to compute drag and ballistic coefficients for various cone half angles, as shown in Table 1. We can calculate also the ballistic coefficient (BC) for a target mass of 24 kg of the spacecraft:  
\[\text{BC}=\frac{\text{m}}{\text{AC}_{D}} \tag{2}\]  
Figure 1: Preliminary SPLASH concept for 12U Cubesat Platform. To calculate the heating rate (\(\dot{q}\)) we can use the formulas suggested by [PERSON] [28]:  
\[\dot{q}=1.83\times 10^{-4}v^{3}\sqrt{\frac{\rho}{r_{cn}}} \tag{3}\]  
where \(v\) is the spacecraft velocity, \(r_{cn}\) is the curvature radius of the spacecraft nose, and \(\rho\) is the air density, which can be calculated according to the NRLMSIS atmosphere model. At 400 km, the density is about 2.42 \(\times\) 10\({}^{-12}\) kg/m\({}^{3}\), while at 120 km (reentry interface) the density is about 1.67 \(\times\) 10\({}^{-8}\) kg/m\({}^{3}\). The two heights represent the operational altitude of the satellite and the altitude defined as the reentry interface. The value of heating rate at the two altitudes can thus be estimated. In case of active deorbiting, a Hohmann transfer is assumed at this preliminary stage between the two orbits at 400 and 120 km, respectively, in red and in green in Figure 3. In both cases, the orbits are circular (\(e\) = 0) and equatorial (\(I\) = 0). Table 2 summarizes the values of the circular velocities on the two orbits and the apogee and perigee velocities of the transfer orbit, as well as the \(\Delta\)vs required for the two transfers. After the second \(\Delta\)v, the CubeSat begins to spiral toward the ground, due to the increase in drag as atmospheric density increases. \begin{table}
\begin{tabular}{c c c c c} \hline \(r_{n}\) (m) & 0.108 & 0.108 & 0.108 & 0.108 \\ \(r_{c}\) (m) & 0.305 & 0.35878 & 0.419 & 0.488 \\ m (kg) & 24 & 24 & 24 & 24 \\ A (m\({}^{2}\)) & 0.2923 & 0.40439 & 0.551 & 0.749 \\ \(\delta_{\rm C}\) (deg) & 15 & 30 & 45 & 60 \\ C\({}_{\rm D}\) & 0.243 & 0.551 & 1.017 & 1.503 \\ BC (kg/m\({}^{2}\)) & 337.779 & 107.716 & 42.882 & 21.306 \\ \hline \end{tabular}
\end{table} 
Table 1: Drag Coefficient (C\({}_{\rm D}\)) and Ballistic Coefficient (BC). Figure 2: Example SPLASH concept configurations.