## 5 Conclusions  
The present work illustrates a structural optimization procedure for the definition of a deployable wing connection system of a sub-orbital unmanned re-entry vehicle (USV3), class 2500 kg, equipped with a deployable wing housed within the fairing of the European VEGA-C launcher. The obtained results provide useful data for the preliminary design of the deployment system consisting of two hinges, which allow the wing deployment after it is placed in orbit, and, thus, allow a descent, a hypersonic flight, and a landing phase with greater control capabilities. The optimization process uses two pieces of commercial software (ModeFrontier and ANSYS) and, in particular, it exploits a fully parametric model generated by means of an APDL macro and a multi-objective genetic algorithm. The optimization process focuses on minimizing the bearing forces that are generated by the design loads, defined both by the launch phase (inertial loads) and by the hypersonic flight phase (aerodynamic loads). The results show how it is possible to significantly reduce the loads on the hinges by shifting these in strategic convenient positions. In particular, a set of optimum designs has been defined (hinge location) that is able to minimize the loads, both in the deployed and folded configuration. The hinges, obviously, have to be positioned within the root rib domain, and the optimization process has shown that the optimal position of the forward hinge (point C1) is between 100 and 400 mm w.r.t the leading edge of the root profile in the longitudinal direction. The afterward hinge (point C4) should be positioned between 750 and 962 mm (remember that the maximum dimension of the root rib is 1180 mm). Regarding the transversal position, for both hinges (point C2 and C5) the locking pins have to be positioned as low as possible, i.e., at 10 mm. The remaining two points C3 and C6 are automatically determined considering that the maximum wing rotation that is 55\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wing Configuration** & **Max Force [N]** & **Yield Bearing** & **SF** & **Min Bolt Diameter** & **Plate Thickness** \\  & & **[MPa]** & & **[mm]** & **[mm]** \\ \hline
**Deployed** & 23,878.6 & 1071.8 & 1.5 & 7.57 & 4.42 \\
**Folded** & 7449.1 & 1071.8 & 1.5 & 4.23 & 2.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Preliminary evaluation of the thickness of connecting plates. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wing Configuration** & **Max Force [N]** & **Yield Stress** & **SF** & **Shear Plane** & **Min Bolt Area** & **Min Bolt Diameter** \\  & **[N]** & **[MPa]** & **SF** & **[mm2]** & **[mm]** \\ \hline
**Deployed** & 23,878.6 & 398.3 & 1.5 & 2 & 44.96 & 7.57 \\
**Folded** & 7449.1 & 398.3 & 1.5 & 2 & 14.03 & 4.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Preliminary evaluation of the diameter of locking pins and bolts. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Wing Configuration** & **Max Force [N]** & **Yield Bearing** & **SF** & **Min Bolt Diameter** & **Plate Thickness** \\  & & **[MPa]** & & **[mm]** & **[mm]** \\ \hline
**Deployed** & 23,878.6 & 530.6 & 1.5 & 7.57 & 8.92 \\
**Folded** & 7449.1 & 530.6 & 1.5 & 4.23 & 4.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Preliminary evaluation of the retained lags thickness. The optimization process provides several configurations suitable to be used as the best design. Indeed, they are able to minimize both the diameter of the pins/bolts and the thickness of the surrounding and locking plates. This guarantees the fulfillment of a fundamental requirement, i.e., structural mass reduction. The final choice could be completed considering other functional requirements/constraints that will be discussed and introduced in a subsequent design phase, which will also include the detailed design of the deployment system. Conceptualization, F.D.C., R.S., R.F. and D.T. ; Data curation, R.S. and R.F. ; Formal analysis, F.D.C. ; Investigation, F.D.C. ; Methodology, F.D.C. and R.F.