## 2 The Flying Wing Carrier-Launcher System
### Description of Geometry and Mass Properties of the Carrier-Launcher System  
Since our research is preliminary, and with the aim of verifying the effectiveness of the use of control surfaces for wing stabilization in each phase of a flight, the airfoil adopted in the present study does not have a reflected trailing edge; in fact, the selected airfoil is BACXXX, depicted in Figure 7 [54]. Table 6 reports the data of the configuration, and, in accordance with [26; 27], the estimated mass and weight of the components of the carrier-launcher system. Thanks to a trade-off study, a wingspan of about 54.0 m has been selected to obtain increases in the lift-to-drag ratio without severe penalizations of the wing weight. We obtain an empty weight of 488.4 kN and a wing loading of 3,940 N/m\({}^{2}\) for the complete configuration at take-off, considering a total mass of about 122,000 kg and a reference surface of about 304 m\({}^{2}\). These values agree with historical data, as can be seen from the previous graphs (Figures 1-5). \begin{table}
\begin{tabular}{c c c} \hline
**Launcher Mass** & **Structural Mass** & **Mass of Systems** \\ \(M_{0}\) [kg] & **3.0\%\(\times M_{0}\) [kg]** & **3.0\%\(\times M_{0}\) [kg]** \\ \hline
10,000 & 300 & 300 \\ \hline \end{tabular}
\end{table} 
Table 4: Hypothesis about launcher’s mass budgets. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Launch** & \(\Delta v_{\textit{tot}}\) & \(\Delta v_{\textit{grav}}\) & \(\Delta v_{\textit{dmg}}\) & \(\Delta v_{\textit{steer}}\) & \(\Delta v_{\textit{rot}}\) & \(\Delta v_{\textit{carrier}}\) & \(\Delta v_{\textit{prop}}\) \\
**System** & **[m/s]** & **[m/s]** & **[m/s]** & **[m/s]** & **[m/s]** & **[m/s]** & **[m/s]** \\ \hline Flying Wing & 9498 & \(-284.27\) & \(-22.23\) & \(-29.38\) & \(-100\) & \(-260\) & 8802 \\ \hline \end{tabular}
\end{table} 
Table 3: Velocity budgets for Air Launch to Low-Earth Orbits for the Flying Wing. \begin{table}
\begin{tabular}{c c c c} \hline
**Launch System** & \(\Delta v_{\textit{prop}}\) & **Propellant Mass** & **Payload Mass** \\  & **[m/s]** & **[m/s]** & **[**\(M_{\textit{prop}}\) [kg]** & \(M_{\textit{payload}}\) [kg]** \\ \hline Ground Launch to Orbit & 9126 & 9023 & 377 \\ Air Launch to Orbit (FW) & 8802 & 8939 & 461 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of propellant and payload masses of GLTO and ALTO (Flying Wing). Winglets have been added at the tip of the wing to increase the lift-to-drag ratio. Figure 8 shows the CAD model of our conceptual flying wing configuration, and Figure 9 shows a plan sketch of the flying wing with its main dimensions, and with the selected layout of the control surfaces of the configuration [30]. The control surfaces consist of a pair of tip ailerons, a pair of centre double-acting flaps, and a pair of double-acting elevators; all the control devices are of single-surface type. The chord dimensions chords of the control surfaces are reported in Figure 10, whereas Figure 11 shows the dimensions of the winglet added to the flying wing tips with a c \begin{table}
\begin{tabular}{c c c} \hline
**Geometry Parameter** & **Component** & **Mass/Weight** \\ \hline Surface Area [m\({}^{2}\)] & 304.00 & Structure [kg] & 23,535 \\ Root chord [m] & 10.60 & Engines [kg] & 18,300 \\ Kink chord [m] & 5.70 & Landing gears [kg] & 3660 \\ Tip chord [m] & 3.77 & On-board systems [kg] & 3520 \\ Kink section position [m] & 7.00 & Control surfaces [kg] & 495 \\ Half wingspan [m] & 27.09 & Batteries [kg] & 200 \\ Aspect Ratio & 9.64 & APU [kg] & 80 \\ Angle of Sweep at L.E. [deg] & 35.00 & Fuel [kg] & 62,190 \\ Max t/c [\%] & 11.30 & Launcher (payload) [kg] & 10,000 \\ Dihedral angle [deg] & 7.00 & Carrier’s Structural Mass [kg] & 49,790 \\ Winglet cant angle [deg] & 35.00 & Carrier’s Take-Off Mass [kg] & 121,980 \\  & & Empty Weight [kN] & 488 \\  & & Max Take-Off Weight (MTOW) [kN] & 1196 \\  & & Wing loading [kN/m\({}^{2}\)] & 3.936 \\ \hline \end{tabular}
\end{table} 
Table 6: Geometric data and Mass/Weight data of the carrier-launcher system configuration.