## 3 Performance Comparison
### Block Fuel Comparison
#### 3.1.2 Lift-to-Drag Ratio  
In the following, a general comparison of the aerodynamic performance of BW and TW is provided, taking the lift-to-drag ratio \(L/D\) as the performance metric. The comparison in terms of \(L/D\) is shown in Figure 11 left, for each configuration designed in this sensitivity study, and in Figure 11 right in the form of the corresponding statistical analysis. The general outcome is that the BW configurations exhibit a higher \(L/D\) than the TW aircraft, while Figure 11 right highlights that the BW dataset achieved from the sensitivity analysis exhibits the median and the interquartile range median is 2.4% higher than the TW dataset, and the interquartile range is 1% lower.  
Improvements in \(L/D\) imply reductions of \(E_{\textit{fly}}\), and, consequently, reductions in block fuel. An analysis of the drag breakdown, in terms of induced and parasitic contributions (Figure 12), is discussed in the following to highlight the aerodynamic differences between the TW and BW configurations designed within the sensitivity analysis.  
Induced drag for the BW is generally higher than the TW (Figure 12a); this result seems counterintuitive since it is well-known the BW can minimize the induced drag. Nevertheless, it is worth noting that this result is achieved if the comparison is carried out assuming the same wingspan and lift, whereas comparing lifting systems with different wingspans results in different outcomes than that of the best wing system theory. To clarify this concept, we recall the definition of induced drag for BW (\(D_{ind}^{BW}\)) [31], which is given by Equation (10):  
\[D_{ind}^{BW}=\frac{L^{2}}{\pi q\left(b^{\textit{BW}}\right)^{2}}\bigg{(}\frac {1}{2}+\frac{v_{12}}{2}\bigg{)} \tag{10}\]  
Figure 11: \(L/D\) vs. MTOW chart (**left**) and related statistical analysis (**right**) of BW and TW.  
where \(q\) is the dynamic pressure, \(b^{BW}\) is the BW wingspan, and \(v_{12}\) is the parameter that quantifies the mutual interactions of the wings, defined as follows:  
\[v_{12}=\frac{1}{8}\text{log}\Bigg{(}1+\bigg{(}\frac{b^{BW}}{h_{w}}\bigg{)}^{2} \Bigg{)} \tag{11}\]  
where \(h_{w}\) is the vertical gap between the front and rear wing. The induced drag of a monoplane can be written as follows:  
\[D_{ind}^{TW}=\frac{L^{2}}{\pi q(b^{TW})^{2}} \tag{12}\]  
If the value of the MTOW is the same for both architectures, then the total trim lift is also the same. Exploiting Equations (10) and (12), it is possible to derive the following inequality which, if satisfied, establishes if BW's induced drag is higher than the TW one:  
\[\frac{1}{2}+\frac{v_{12}}{2}>\bigg{(}\frac{b^{BW}}{b^{TW}}\bigg{)}^{2} \tag{13}\]  
The statistical analysis of the term \(\bigg{(}\frac{b^{BW}}{b^{TW}}\bigg{)}^{2}\) for the configurations designed in this sensitivity analysis is reported in Figure 13; the term \(v_{12}\cong 0.41\) since the \(h_{w}\)/\(b\) ratio is 0.2 for each BW aircraft; accordingly, the first member of the inequality (13) is about 0.7, which is always higher than the term \(\bigg{(}\frac{b^{BW}}{b^{TW}}\bigg{)}^{2}\). Therefore, the BW induced drag is higher than the TW for the considered designs. It is worth noting that this result does not influence the Oswald factor, which remains higher in the case of the BW configuration.  
Nevertheless, the BW configurations show, on average, a higher cruise \(L/D\); this is due to the prevailing contribution of the BW wing parasitic drag reductions with respect to the TW (Figure 12b). Being the same fuselage shape, the combination of the main wing and tail wetted surfaces is always higher than those of the BW designed in this study case, as shown in Figure 14, and this contribution overcomes the induced drag penalization previously discussed. In this sensitivity study, however, the effect of \(L/D\) on block fuel reductions resulted in being much less important than that of the OEW reductions, which instead is predominant.  
Figure 12: Average values of induced (**a**) and parasitic drag (**b**) vs. MTOW for BW and TW.