## 4 Hybrid-Electric Aircraft Design Optimization
### Results of the Optimization  
Table 4 reports the main results related to the optimal BW and TW configurations; the last two columns report the percentage difference of \(m_{\beta\text{/}}\) with respect to the thermal TW benchmark described in Table 1.  
As expected from the output of the sensitivity analysis, the BW configurations show better performance in terms of block fuel consumption with respect to the TW; the discrepancy increases as the MTOW increases. Figure 18 shows the mass breakdown of the BW and TW optima; the increase of OEW for the TW is related to the higher mass of the TW lifting system, as discussed in Section 3.1.1. For these optimal solutions, the \(\Delta\)OEW ranges from 900 kg to 1660 kg between TW and BW. The reduction of block fuel depends also on two different aspects: the higher \(L/D\) and the better usage of the propulsion system, depicted in Figures 19 and 20, respectively. Figure 19 top reports a comparison between BW and TW of the energy required to accomplish the climb (left) and the cruise (right); it is observed that the BW exhibits a reduction in energy consumption of about 1.5% in the climb and 4% in cruise. This is also due to the highest \(L/D\) ratio of the BW configurations; indeed, as reported in Figure 19 bottom, the BW exhibits an \(L/D\) higher than the corresponding TWs, of about 2% in the climb and 4.5% in cruise. The overall energy saving allows for improving BW fuel reduction. Figure 20 shows that the BW powertrain utilization is better than the TW aircraft, as \(\eta_{pr}\) is 25% higher than the TW aircraft in cruise; this contributes to reducing the energy loss in the powertrain and reducing fuel consumption. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline  & & \multicolumn{6}{c}{**Design Variables**} & \multicolumn{6}{c}{**Constraint**} & \multicolumn{3}{c}{**Obj.**} \\ \cline{2-13}  & \multicolumn{3}{c}{(\(\text{W/gl/S}\) [kg\(\text{/m}^{2}\)] & \(\mathbf{H_{P}}\) & \(\Phi_{CL}^{ice}\) & \(\Phi_{CR}^{ice}\) & \(\Phi_{DE}^{ice}\) & \(\mathbf{\Omega}\) [kg] & \(\mathbf{m_{\beta\text{/}}}\) [kg] & \(\mathbf{\Delta\%\)\(m_{\beta\text{/}}}\) \\ \hline
**Tag** & **BW** & **TW** & **BW** & **TW** & **BW** & **TW** & **BW** & **TW** & **BW** & **TW** & **BW** & **TW** & **BW** & **TW** & **BW** & **TW** \\ \hline
23t & 320 & 325 & 0.38 & 0.27 & 0.23 & 0.33 & 0.35 & 0.33 & 0.17 & 0.22 & 22,976 & 22,962 & 705 & 907 & \(-\)39 & \(-\)21 \\
30t & 314 & 305 & 0.40 & 0.39 & 0.15 & 0.29 & 0.21 & 0.30 & 0.16 & 0.30 & 30,117 & 30,000 & 523 & 816 & \(-\)55 & \(-\)29 \\
40t & 311 & 325 & 0.59 & 0.45 & 0.19 & 0.11 & 0.13 & 0.20 & 0.15 & 0.13 & 40,132 & 39,913 & 320 & 631 & \(-\)72 & \(-\)45 \\
50t & 309 & 325 & 0.46 & 0.40 & 0.11 & 0.13 & 0.01 & 0.10 & 0.10 & 0.11 & 50,160 & 50,019 & 113 & 525 & \(-\)90 & \(-\)55 \\ \hline \end{tabular}
\end{table} 
Table 4: Data of hybrid-electric optimal configurations with BED = 500 Wh/kg. TW (second row) configurations; for each MTOW, the TW wingspan is higher than the BW one. As commented in Section 3.1.1, this is due to the fact that for TW, only the front wing generates the trim lift, whereas, for the BW configurations, the trim lift is split between two lifting surfaces. Accordingly, since non-dimensional parameters (i.e., the aspect ratio) are similar for the lifting surfaces of both architectures, the TW exhibits a higher wingspan to achieve the same lift. Table 5 resumes the comparison between BW and TW in terms of wingspan for each MTOW category; the BW airframe, in conjunction with the performance gains, offers an operative advantage when compared with the TW architecture. In particular:  
* If the hybrid-electric propulsion is exploited to cut block fuel as much as possible, hence increasing MTOW, the BW configuration is compatible with the aprons of category 'C'; this category is the most widespread in the airport infrastructure [66].