## 2 The Flying Wing Carrier-Launcher System
### Comparison of Ground and Air Launch Systems: Velocity Budgets Estimation  
The use of a flying wing as a carrier was motivated by a feasibility analysis based on the calculation and comparison of the velocity budgets, \(\Delta v\), necessary to place a satellite in low earth orbit (about 180-200 km); in this regard, Table 2 shows some reference data taken from [55]. The column \(\Delta v_{\mathbf{tot}}\) represents the velocities due to LEO orbital velocity added to the effects of gravity \(\Delta v_{\mathbf{grav}}\), atmospheric drag \(\Delta v_{\mathbf{drag}}\), and steering losses \(\Delta v_{\mathbf{steer}}\). The column \(\Delta v_{\mathbf{tot}}\) indicates the velocity budgets without the effect of the rotation of the earth \(\Delta v_{\mathbf{rot}}\), whose ta are reported in the last column of Table 2 for each launch system. The last column \(\Delta v_{\mathbf{prop}}\), which represents the propulsion velocity budget, is calculated by adding the total velocity budget and the velocity budget due to earth rotation,\((\Delta v_{\mathbf{tot}}+\Delta v_{\mathbf{rot}})\), and also contains the ascent velocity \(\Delta v_{s}\), that varies between 8.8 and 9.3 km/s [55]. The row Mean Values of Table 2 was added in this contest to estimate the velocities to be used in our conceptual analysis. Table 3 shows the data estimated for the proposed flying wing carrier-launcher system assuming, as a starting point, the mean value of \(\Delta v_{\mathbf{tot}}=9498\) m/s (Table 2). Because the engine of the launcher ignites at an altitude of about \(h=8.0\) km with an attitude angle \(\theta=45^{\circ}\), we assumed a reduction in the absolute values for gravity, drag, and steering losses of about the 20% of the mean values indicated in Table 2. Moreover, to be conservative, the assumed effect of earth rotation \(\Delta v_{\mathbf{rot}}=-100\) m/s is set small enough to account for launches at higher latitudes. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Launch** & \(v_{LEO}\) & \(\Delta v_{grav}\) & \(\Delta v_{\mathbf{drag}}\) & \(\Delta v_{\mathbf{star}}\) & \(\Delta v_{\mathbf{tot}}\) & \(\Delta v_{\mathbf{rot}}\) & \(\Delta v_{\mathbf{prop}}\) \\
**System** & **[m/s]** & **[m/s]** & **[m/s]** & **[m/s]** & **[m/s]** & **[m/s]** & **[m/s]** \\ \hline Ariane A-44L & 7802 & 1576 & 135 & 38 & 9551 & \(-\)413 & 9138 \\ Atlas I & 7946 & 1395 & 110 & 167 & 9618 & \(-\)375 & 9243 \\ Delta 7925 & 7842 & 1150 & 136 & 33 & 9161 & \(-\)347 & 8814 \\ Space Shuttle & 7794 & 1222 & 107 & 358 & 9481 & \(-\)395 & 9086 \\ Saturn V & 7798 & 1534 & 40 & 243 & 9615 & \(-\)348 & 9267 \\ Titan & 7896 & 1442 & 156 & 65 & 9559 & \(-\)352 & 9207 \\ IV/Centaur & & & & & & & \\ \hline Mean Values & 7846 & 1387 & 114 & 151 & 9498 & \(-\)372 & 9126 \\ \hline \end{tabular}
\end{table} 
Table 2: Velocity budgets for Ground Launch to Low-Earth Orbits for selected Launch Vehicles [55]. Figure 7: Boeing BACXX airfoil sketch (airfoil adopted in the present study) [54]. A major advantage of using an atmospheric carrier is due to the initial velocity of the launcher when its engine ignites, i.e., \(\Delta v_{\textit{carrier}}=-260\) m/s. As expected, the final estimated ascent velocity for the flying wing launch system is lower than the references collected in Table 2 for ground launch systems; namely \(\Delta v_{\textit{prop}}=8802\) m/s, with a reduction of about 320 m/s is obtained. Starting from the estimated velocity changes \(\Delta v_{\textit{prop}}=9126\) m/s for ground launch systems (Table 2) and \(\Delta v_{\textit{prop}}=8802\) m/s for the flying wing (Table 3), we calculated the mass of propellant \(M_{\textit{prop}}\) needed to reach the low earth orbit assuming a specific impulse of \(\mathbf{I_{\textit{sp}}}=400\) s and applying the well-known rocket equation of _Tsiolkovsky_ (where \(g_{0}\) is the standard gravity):  
\[M_{\textit{prop}}=M_{0}\Big{\{}1-e^{-[\Delta v_{\textit{prop}}/(L_{\textit{ prop}}g_{0})]}\Big{\}}, \tag{1}\]  
\(M_{0}\) is the launcher mass.