## 3 The Carrier-Launcher System Performance: Preliminary Analyses and Results
### Aerodynamic and Aeromechanical Analyses of the Carrier-Launcher System  
In the present conceptual study, the aerodynamic and aeromechanical performance (in terms of stability characteristics) of the flying wing carrier-launcher system were performed by means of the Athena Vortex Lattice (AVL) software [31]; this is a vortex-lattice solver, which adopts linearized potential aerodynamic theory, discretizing the lifting surfaces with panels. This code allows us to evaluate aerodynamic performance, stability characteristics, and trim conditions. The geometric data of the wing and the geometry of the airfoil (Figure 7) were properly modelled and introduced in AVL; Figure 12 shows a sketch of the model of the flying wing implemented in AVL. Figure 11: Lateral view with dimensions of the winglet added to the flying wing tips [30]. Figure 12: (**a**) AVL model of the flying wing: isometric view, (**b**) AVL model of the flying wing: front view [30]. Figure 10: Dimensions of the chords of the flying wing control surfaces [30] (// not applicable). For the flying wing carrier-launcher system, during the transfer flight, the cruise flight condition corresponds to an altitude \(h=10,000\) m (air density \(\rho=0.41271\) kg/m\({}^{3}\)) with a cruise speed \(U=239.60\) m/s. The local sound speed is \(c=299.5\) m/s and the cruise Mach number is \(M=0.8\) (ISO standard). Referring to the MTOW in a conservative way when considering cruising, the estimated lift \(C_{L\_cwise}\) coefficient in a cruise flight is  
\[C_{L\_cwise}=2\;MTOW/\left(\rho SU^{2}\right)=0.33, \tag{2}\]  
and the drag coefficient is shown by  
\[C_{D\_cwise}=C_{D0\_carrier-launcher}+C_{L\_cwise}^{2}/(\pi\;AR\;e), \tag{3}\]  
where the value of the Oswald coefficient, \(e=0.9075\), has been estimated by applying the model described in [28]. The drag coefficient at zero lift has been calculated starting from the analysis performed with the use of AVL; thus, for the flying wing, \(C_{D0\_carrier}=0.013\). To take into account the effect of the launcher, we assumed a 20% increase in the carrier-launcher zero-lift drag coefficient (a pure translation in the polar curve). \[C_{D0\_carrier-launcher}=1.20\times 0.013=0.0156. \tag{4}\]  
Moreover, for a stable and trimmed flight condition (i.e., pitching moment equal to zero), we must rotate upward the central flap surfaces of an angle of approximately \(\delta=21.08\) deg; in the equilibrium condition, the trim angle of attack is \(\alpha_{w}=5.75\) deg. This latter control maneuver produces, due to the induced drag, an increase in the drag coefficient of about \(C_{D\_cwise\_ind}=0.0156\), as estimated by AVL code, so we may assume the finale value of the cruise drag coefficient as (adding up all the terms):  
\[C_{D\_cwise}=C_{D0\_carrier-launcher}+C_{D\_cwise\_ind}=0.0156+0.0156=0.0312. \tag{5}\]  
In a cruise flight condition, the estimated lift-to-drag ratio (or lift-to-drag ratio L/D) of the system is  
\[L/D=C_{L\_cwise}/C_{D\_cwise}=0.33/0.0312=10.58. \tag{6}\]  
As mentioned above, with the code AVL, it is possible to perform preliminary aeromechanical analyses and stability assessments; specifically, the cruise static stability margin (SM), i.e., the distance between the centre of gravity of the system and the neutral point divided by the mean aerodynamic chord (MAC), can be estimated in different flight conditions. AVL is indeed able to calculate the longitudinal position of the aircraft neutral point; then, by inserting the mass distribution of the model and the related longitudinal position of the centre of gravity, the SM is computed (Figure 13). The MAC of the considered flying wing is equal to 7.73 m. Assuming the origin of the longitudinal \(x\) coordinates at the vertex of the wing's leading edge (nose of the wing), the stability margin is computed by means of Equation (7):  
\[SM_{cwise}=\left(x_{np}-x_{cg}\right)/MAC=\left(9.60-7.64\right)/7.73=0.25, \tag{7}\]  
Figure 13: Stability Margin definition [30].