## 2 Materials and Methods
### Summary of the Aircraft Design Procedure  
As anticipated in Section 1, this work extends and completes the one recently presented in [29], so that the design and performance analysis methodologies are only briefly mentioned here for the sake of brevity. The interested reader may refer to [29] and the other related authors' references [30; 31; 32] for a more in-depth examination of the methodological aspects. The design of the hybrid-electric aircraft, both in TW and BW configuration, was conducted using different conceptual design software, which was developed in house to deal with this specific scenario.  
In particular, the design of the lifting surfaces planform was carried out by means of an optimization procedure that handles the variables defining the wings geometry to maximize the lift-to-drag ratio, while typical constraints on trim and stability are satisfied. Such that procedure is implemented in the AEROSTATE code, which is described in detail in [31; 32]. The overall aircraft design, on the other hand, which involves the multidisciplinary iteration of propulsive (specific to hybrid-electric architectures), structural, aerodynamic, and weight aspects, is integrated in the conceptual design platform named THEA-CODE, which is described in detail in [30]. In such a software, the aerodynamics of the lifting systems is evaluated by means of the proper interaction of the AVL [33] and XPOIL [34] codes, while the drag contributions of the other components (e.g., fuselage and nacelic) are evaluated by means of established (classical) textbook methods [35]. Given the architectural differences between BW and TW, the structural sizing of the lifting surfaces is carried out by means of FEM-based surrogate models, as described in [36]. The weight of the fuselage, nacelles, systems, furnishings, and components required to operate the aircraft are estimated using the procedures given in [37]. The hybrid-electric powertrain is sized according to the requirements of the matching chart [38; 39], in which the distribution of installed power between the thermal and electric chains is defined by the hybridization factor \(H_{p}\), which is considered a design variable. The other design variables that THEA-CODE can handle are the wing loading \(W/S\) and the power fractions supplied by the thermal engine \(\Phi^{l}\) (in relation to the total installed thermal power) during the climb (\(\Phi^{l}_{CL}\)), cruise (\(\Phi^{l}_{CR}\)), and descent (\(\Phi^{l}_{DE}\)) phases. In particular, the design variables can be varied by the designer in the case of sensitivity analysis (see Section 3) or can be managed by an optimizer to minimize a given FoM, such as the block fuel (see Section 4). For further details on the methodology, the interested reader may refer to [10; 29; 30].  
In this work, the aircraft analyzed are the same as those sized and discussed in [29]. In particular, the design requirements that were used for the sizing are: design range equal to 600 nm, number of passengers equal to 40, flight altitude equal to 6100 m, cruise Mach equal to 0.4, and required runway length equal to 1100 m. In this context, Figure 3 shows two generic regional hybrid-electric BW and TW configurations, representative of the main architectural choices made in terms of arrangement of the lifting surfaces, positioning of the engines, and shape of the fuselage. The hybrid-electric powertrain selected is of a parallel architecture, and the forecasts used for the technological development of electric machines and batteries refer to the 2035 scenario. In this context, according to [17], the electric motor specific power is 13 kW/kg and its efficiency is 0.96, the battery gravimetric energy density is 500 Wh/kg (at pack level) and its efficiency is 0.96, the inverter shows specific power of 19 kW/kg with an efficiency of 0.98, and finally the wires/cables have a linear specific power of 352 kWm/kg with an efficiency of 0.99.