2.1. Overview of Aircraft Design Framework
The design methodology used in this work was implemented in an in-house tool named THEA-CODE (“
Tool for Hybrid-Electric Aircraft COnceptual DEsign”), specifically developed to deal with the design of hybrid-electric aircraft. In the following, a brief overview of the methodology is reported, whereas more details can be found in [
34,
35]. The design process, based on an iterative procedure on the convergence of the MTOW, is composed of a set of interconnected blocks, involving aerodynamic assessment, powertrain sizing, mission simulation, and weight evaluation. The aircraft polar drag curve s evaluated by properly computing induced drag and parasitic drag, as detailed in
Section 2.2. The installed power is calculated by means of the matching chart [
36,
37], which correlates the specific power
P/
W with the wing loading
W/
S, taking into account regulation constraints [
38]; for hybrid-electric powertrain, by using the matching chart, it is possible to assess the split of the installed power between the electric and the thermal chains, and the related degree of hybridization
HP can be defined according to Equation (1):
where
and
represent the installed power of thermal engine and electric motor, respectively. Consequently, the mission simulation s performed by considering the aircraft point mass equations of motion, taking into account taxi in/out, take-off, climb, cruise, descent, and diversion, to compute the block fuel and the battery mass needed to accomplish the design mission; specific in-depth focus on hybrid-electric mission simulation and performance analysis can be found in [
18]. In particular, the general power supply strategy adopted is the following: taxi in/out is accomplished by using only electric power; full thermal and electric power are provided in the take-off phase, whereas the supplied power is split between thermal and electric chain during climb, cruise, and descent according to a designer-specified strategy; and the diversion is accomplished by means of only the thermal power. Finally, the weight breakdown of the aircraft is obtained as described in
Section 2.3. Note that the THEA-CODE has not been designed to modify and/or optimize the aircraft geometry, instead, that is an input for the process. In fact, this particular (automatic) tool only allows for homothetically scaling the input geometry by using the wing loading
W/
S as a scaling factor, as sketched in
Figure 1.
The input geometry can be provided by another numerical tool, named AEROSTATE [
39,
40,
41], that allows for designing aircraft lifting systems to optimize lift-to-drag ratio
L/
D, fulfilling the constraints on longitudinal stability and trim. AEROSTATE, by means of an optimization procedure, whose details are discussed in [
40,
41], is based on the same aerodynamic solvers described in
Section 2.2 and handles all the geometrical parameters describing the lifting system to maximize
L/
D in a prescribed design point, i.e., the initial point of the cruise phase. The problem of longitudinal stability and trim is properly assessed within the AEROSTATE optimization by the introduction of a set of specific constraints; namely, the lifting system geometry is designed to fulfill a prescribed static margin of stability and to satisfy the pitch trim in cruise without elevator deflection. For the box-wing architecture, these constraints can be satisfied by properly acting on the longitudinal positioning of the two horizontal wings, as well as by managing their sweep angles and other geometrical variables, and, finally, by the proper aerodynamic load distribution between the front and rear wings, as detailed in [
41,
42]. The input geometry adopted as a reference in this work, both for the BW and the TW configuration, has been optimized by means of AEROSTATE, with the same objective function, constraints, and design space, to assess the performance comparison.
2.2. Aerodynamic Assessment
The aircraft’s polar drag is obtained by evaluating both induced and parasitic drag, where the induced drag is computed by means of a Vortex Lattice Method (VLM) solver, named Athena Vortex Lattice (AVL) [
43]. In fact, such a model allows for properly assessing the potential aerodynamic performance of any lifting system, making consistent the comparison between TW and BW. In this context,
Figure 2 shows an example of AVL modeling for both configurations studied in this work; for both configurations, the fuselage is replaced with a flat plate resembling its planform [
44]; this choice to model the fuselage is an outcome of the work presented in [
45], which investigated the accuracy of AVL fuselage modeling among the different possibilities, i.e., doublets distribution, flat plate, and fuselage elimination. The flat plate model resulted in being more accurate for aeromechanics predictions in the longitudinal plane.
On the other hand, the parasitic drag
is calculated according to the classical component build-up method [
46] for both airframes. In particular, the wing, tail, and fin drag are calculated according to Equation (2):
where
p is the air density,
V is the airspeed,
y is a generic spanwise station,
c is the chord distribution, and
is the airfoil drag coefficient evaluated by the classic tool XFOIL [
47]. Finally, fuselage and nacelle drag are calculated according to the semi-empirical method proposed in [
46].
2.3. Weight Breakdown Evaluation
The aircraft weight breakdown is expressed as in Equation (3):
where
g is the standard gravity. In particular, the structural mass of fuselage, fin, nacelle, and landing gear (
), the onboard systems mass (
), and the operating items mass (
) are calculated according to the semi-empirical relations collected in [
48], whereas payload mass
is evaluated by assuming 95 kg/passenger (including the baggage). The propulsion system mass
is evaluated as a function of the installed specific power obtained through the matching chart for both thermal and electrical power sources, and by using the literature data on their specific power density [
49,
50], while the fuel
and the battery mass
are two outputs of the numerical simulation. In particular, the term
does not include the structural wing mass
, which is evaluated by means of a specific structural model developed to estimate the mass of lifting system of both cantilever-wing and BW.
This is of paramount importance in this comparative work, as the two lifting architectures being compared have quite different structural configurations, and using models that are unable to detect such differences could lead to errors in the comparative evaluation. Therefore, it was decided to use physics-based structural mass prediction models starting from a finite element modeling (FEM) of the wings-fuselage assembly. Specifically, the developed structural model exploits metamodeling technique to estimate the structural mass of the lifting system, as this approach allows for obtaining high level of accuracy and low computational cost [
51,
52], which is an important feature in conceptual assessments; the developed procedure is widely described in [
53,
54], whereas a brief overview is proposed in the following. The metamodeling process mainly follows these steps:
(i) definition of the main design variables and their boundaries, hence identifying an
n-dimensional design space;
(ii) sampling of the design space by means of a specific technique (e.g., central composite or Latin hypercube) to identify a subset of configurations to be analyzed;
(iii) run of FEM simulations for each configuration belonging to the subset;
(iv) definition of an interpolative model (e.g., polynomial function or splines) and calculation of its unknown coefficients through fitting models (e.g., least square regression or best linear predictor); and
(v) the interpolative model represents a response surface able to predict the output of the physical problem. This procedure has been used to develop a FEM-based metamodel that allows for predicting the lifting system structural mass, without the need to conduct a FEM analysis for each assessed configuration during the conceptual design, hence providing a huge cut of the computation time. Regarding phase
(i), geometric and structural design variables defining the lifting system have been selected for both BW and TW, as sketched in
Figure 3; due to the different shapes of BW and TW, geometric design variables are different, whereas structural variables defining the wing box are fixed equally for the two architectures.
The FEM simulations to sample the design space have been carried out by means of the software ABAQUS (v 6.14) [
55,
56] to obtain relevant outputs, such as wing tip displacement (
u), maximum equivalent stress on forward (
σF) and rear (
σR) wing, and wing structural mass. The structural mesh consists of shell and beam elements; shell elements are used to model skins, ribs, and spar webs, whereas beam elements are utilized to model stringers and spar caps. The finite element mesh primarily focuses on the wing-box structure of the wings, excluding the fixed and movable parts of the leading and trailing edges, which are represented as point masses attached to the spar webs by means of surface-based constraint relationships. Only a stress-based static structural assessment has been performed, neglecting buckling and/or aeroelastic loads; specifically, the loading condition is evaluated according to Equation (4), referring to the cruise flight condition:
where
L is the lift distribution, extracted by AVL (a qualitative distribution is shown in
Figure 4), and
is the load factor fixed equal to 2.5. Battery and fuel weights have been introduced as distributed vertical load according to this assumed layout: for the BW, the two terms
and
are placed in the front (60%) and rear (40%) wing, whereas, for TW, the whole masses
and
have been placed in the main wing.
The metamodel provides (simplified) interpolated functions that relate the main structural figures of merit (i.e., the values of
u,
σF,
σR, and
) to the geometrical
x and structural
z design variables. These specific (simple) functions allow for setting an optimization problem useful for sizing the structure of the lifting system by minimizing the wing structural mass according to the problem described in Equation (5):
where
345 Mpa is the yielding stress of Al2024 and
1.5 is a safety factor. Once the geometry of the lifting system is determined, the optimization procedure can act on the structural variables to minimize the structural wing mass. The optimization problem is subject to the following constraints:
(i) the maximum equivalent Von Mises stress of both front and rear wing (
σF and
σR) must be lower than yielding stress of the material scaled by the safety factor; and
(ii) the maximum tip displacement
u must be lower than 12.5% of the half-wingspan. The optimization problem described in Equation (5) focuses on the minimization of the structural mass of the lifting system; however, non-structural mass has been considered as well in the FE model. The movable surfaces of secondary structures, namely the leading edge and trailing edge, are represented as point masses connected to the primary structures, specifically to the spar webs of the wingbox structure. The determination of these masses has been conducted following the methodology outlined in [
57]. Apart from considering the weight of primary and secondary aircraft structures, the finite element (FE) model also incorporates additional masses associated with systems, equipment, and other non-structural components; these miscellaneous masses have been assessed based on the guidelines presented in [
58].
2.4. Architectural Assumptions and Design Requirements
In this section, the main design choices on both the TW and BW airframe are described. First, the same fuselage is selected for both configurations and, in particular, both the fuselage shape and internal layout are designed to be similar to the reference regional aircraft ATR-42 [
59]. Hence, the TW configuration shows a high wing attached to the upper part of the fuselage, engines and propellers installed on the main wing, and a T-tail configuration for the horizontal and vertical tailplanes; see
Figure 5 left. The BW lifting system shows a front wing attached to the low part of the fuselage and a rear wing attached to the fin (see
Figure 5 right); engines and propellers are mounted below the rear wing, as the low front wing does not guarantee enough clearance between propellers and runway during ground operations. For both configurations, the main landing gear is in fuselage sponsons. The selected hybrid-electric powertrain architecture is the parallel one.
Regional hybrid-electric aircraft have been designed to fulfill the following top-level aircraft requirements, set to be comparable to reference ATR-42 [
59,
60]: a number of passengers equal to 40, a design range of 600 nm flown at Mach 0.4 and at an altitude of 6100 m, and a take-off and landing required field of 1100 m. To provide a benchmark for quantitative performance comparison assessments, a thermal-powered regional aircraft has also been designed according to the same TLARs and the same methodology proposed in
Section 2.1; this reference TW exhibits the features reported in
Table 1.