# A Physics-Based Multidisciplinary Approach for the Preliminary Design and Performance Analysis of a Medium Range Aircraft with Box-Wing Architecture

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## Abstract

**:**

## 1. Introduction

- The transport of a larger number of passengers compared to the present aircraft operating on medium routes, by exploiting the increased lifting capacity of the box-wing system, and using a new fuselage design, in order to increase the number of travellers without increasing the number of flights;
- The exploitation of the increased lifting capacity of the box-wing to design an aircraft with the same overall dimensions, in particular of wingspan, of present aircraft operating on short/medium routes, while improving the passenger capability, in order to avoid the increase in required apron space; namely, this requires the design of a box-wing with wingspan limited to the standard related to short-to-medium-route aircraft, i.e., maximum 36 m (ICAO Aerodrome Code C), to be compliant with the airport infrastructure (aprons, taxiways), but at the same time, to transport a larger payload;
- The exploitation of the box-wing architecture designed according to the “Best Wing System” theory to maximise the aerodynamic efficiency; indeed, a properly designed box-wing aircraft allows one to theoretically minimise the induced drag, by exhibiting Oswald factor efficiencies larger than 1 [45], as well as to increase the lifting capability (i.e., to trim a larger weight), and thus to reduce the fuel consumption per passenger–kilometre compared to conventional aircraft.

## 2. Design Methodology Description

#### 2.1. Conceptual Design Initialisation

_{Di}, the parasite drag coefficient, C

_{D0}, and the wave drag coefficient, C

_{Dwave}, of the aircraft (Equation (1)).

_{L}represents the wing lift coefficient, AR is the related aspect ratio, and e is the Oswald factor. As the considered configuration is a box-wing designed according to the Prandtl’s theory on the best wing system [44], the Oswald factor, e, used in this phase is fixed equal to 1.46 [52]. Since the aircraft geometry does not exist at this initialisation stage, some reference parameters must be set reasonably, as indicated in the reference literature. This is the case for the Oswald factor, as, although it depends on the wings’ height to span ratio, h/b [44], it is set as equal to the theoretical maximum value for a box lifting system [52]. This does not represent a misalignment, since in the following design phases (Section 2.2) the Oswald factor is calculated for each configuration considered (taking into account its geometrical and lift distribution characteristics) by means of the VLM aerodynamic solver.

_{D0}, is evaluated by the equivalent skin friction model described in [53]; namely, the C

_{D0}

_{tot}of the aircraft is the sum of each aircraft component, C

_{D0}

^{comp}, evaluated by means of the formula of Equation (5).

_{fe}is the equivalent skin friction coefficient, equal to 0.0030 for civil transport aircraft from the approximation reported in [53]; the same reference presents a simplified way to estimate the components’ wetted surface, S

_{wet}

^{comp}, both in the case of a wing component (i.e., lifting surfaces, vertical tip-wing, tail, fin, Equation (7)) and cylindrical components (i.e., fuselage, nacelle, Equation (8)):

_{exposed}is the planform area of the wing exposed to the flow, $(t\mathit{/}c)$ is the wing thickness-to-chord ratio, and d

^{cyl}and l

^{cyl}are the diameter and the length, respectively, of the considered cylinder. For aircraft cruising in transonic flight, the wave drag coefficient, C

_{Dwave}, is fixed as constant and equal to 0.002, according to the Boeing definition of transonic drag rise reported in [53].

_{pay}, the fuel weight, W

_{fuel}, and the operating empty weight, W

_{oe}(Equation (9)):

_{fuel}, is evaluated by using the well-known Breguet formula [55], and the operating empty weight, W

_{oe}, is estimated by the statistic interpolation of historical trends proposed in [53].

#### 2.2. Optimisation Driven Preliminary Design

- Objective function

- Set of inequality constraints

- Design space

**x**); the design variables

**x**, limited by lower and upper boundaries (

**lb**and

**ub**, respectively), are reported in Figure 4.

- Vertical trim

- Longitudinal static stability

- Pitch trim

- Max local lift coefficient

- Wing loading constraints

- Taper ratio

- Relative wings position

_{M}is the pitching moment coefficient; ${c}_{l}\left(y\right)$ is the spanwise distribution of local lift coefficient and ${\widehat{{c}_{l}}}_{\mathit{TH}}$ is the related threshold value; ${(L}_{\mathit{wing}}{\mathit{/}S}_{\mathit{wing}})$ is the i-th lifting surface wing loading;${\lambda}_{j}$ is the j-th wing bay taper ratio; x

_{LE tip}is the longitudinal position of the wing tip leading edge; c

_{tip}is the wing tip chord; ε is a tolerance. Several details about the optimisation procedure and algorithms implemented in the AEROSTATE tool are described in [58,59,60]. This tool evaluates the lift-to-drag ratio at the reference design point by estimating the overall drag, as reported in Equation (1); nevertheless, in this case, the geometry of the lifting system is known, as it is computed at each iteration of the optimisation process, so the parasite drag coefficient of the wing components, ${C}_{D0}{}^{\mathit{Wing}}$ (i.e., front/rear wing, vertical tip-wing, fin), is computed by integrating spanwise the airfoil drag contribution, as expressed in Equation (20):

_{Dfoil}= f(Re, M, C

_{Lfoil}) is calculated by Xfoil [61] and is provided as input to the procedure, S

_{ref}is the wing reference surface, and c(y) is the spanwise chord distribution. The C

_{D0}

^{Fus}is computed by means of the component build-up method described in [53]; in particular:

_{f}, the form factor, FF, and the interference factor, Q, are reported in [53]. Concerning the lift induced drag, once the design weight is defined as an input, the optimiser uses a Vortex Lattice Solver to evaluate the vertical trim condition (Equation (13)), and so extracting the aircraft C

_{L trim}and C

_{Di}values. The solver used is the Vortex-Lattice-based AVL [62], and a typical representation of a box-wing configuration within this solver is reported in Figure 5.

^{Wings}represents the weight of the lifting system, W

^{Fus}is the fuselage weight, W

^{Eng}is the engine weight, W

^{Sys}represents the weight of the on-board systems, and W

^{Oper}represents the weight of the aircraft operating items. As the geometry of each configuration designed in this phase is known, single contributions can be estimated by means of slightly more accurate methods than those used in the initialisation phase; in particular, the wing weight and the systems and operating weights are estimated by means of the method proposed in [63], and the fuselage weight and the engine weight are evaluated by means of the methodology used in [64]. During the optimisation, these estimations are also useful to evaluate the centre of gravity position, and so to evaluate the constraints concerning the pitch trim and the longitudinal stability.

#### Transonic Aerodynamic Assessment: Level 1 and ½

#### 2.3. High-Fidelity Performance Assessment

#### 2.3.1. Aerodynamic Performance

#### 2.3.2. Structural Design and Mass Estimation

_{z}= 2.5, W = MTOW); qualitatively, two constraints are imposed into the sizing procedure: (1) the wing-tip deflection, intended as the maximum deflection occurring in one of the main wings, should be such that large displacements are avoided; (2) the structure must support the limit load (given as a combination of aerodynamic and gravity loads) within the elastic field, so the equivalent Von Mises stress in both wings is constrained to be lower than the yielding stress of the material (divided by a safety factor) [81]. The aerodynamic loads, such as the spanwise lift distribution on the lifting surfaces, are provided as inputs from the AVL code. The wing structural sizing process is integrated into an optimisation procedure; the objective function is the structural mass of the lifting systems, W

^{wing structure}(Equation (23)); the constraints are those related to structural stiffness, expressed as a maximum limitation on wings’ tip displacement, ${\delta}_{i}^{\mathit{tip}}$ (Equation (24)), and structural strength, expressed as maximum limitation on the equivalent stress, ${\sigma}_{i}^{\mathit{eq}}$ (Equation (25)), for the i-th wing; the design variable is the vector

**t**of the thicknesses of the k-th structural component of the i-th wing ${t}_{\mathit{ik}}$ (Equation (26)).

- Objective function

- Stiffness constraint

- Strength constraint

- Design variables

- Design space

#### 2.3.3. Mission Simulation

_{D}= f(C

_{L}, M), derived by the CFD simulations results); the initial mass breakdown, depending on the payload and on the initial fuel mass; the flight programme for each mission segment; the main performance of the propulsion system, namely the thrust specific fuel consumption, TSFC. The simulation models used for each mission stage are briefly described in the following:

- The taxing fuel consumption is extrapolated by the data reported in [84]. The take-off phase was simulated by integrating the equation of motion of the aircraft in the longitudinal plane, also considering its pitch dynamics; the take-off simulation and analysis procedure used in this work is widely described in [85];
- The climb phase was simulated by integrating the equation of motion of the aircraft considered as a point mass in the longitudinal plane:

_{cruise}”. According to this programme: (1) the aircraft flies at IAS equal to 250 kt until it reaches an altitude of 10,000 ft; (2) the aircraft accelerates in an almost level flight until the IAS is 300 kt, and then flies at this speed until the crossover altitude (the crossover is defined as the altitude where the current Mach reaches the target cruise Mach); (3) the aircraft flies at a constant Mach number until it reaches the cruise altitude. During the climb, the aircraft changes its altitude, so its TAS increases as depicted in Figure 18 (left); an example of the aircraft climb trajectory is depicted in Figure 18 (right).

- The cruise phase was simulated by integrating the equations of steady and level flights for the aircraft point mass model (Equations (33)–(35)); a constant altitude ($\dot{z}$) = 0 and constant speed ($\dot{x}$= V = constant) flight programme was considered; the simulation, taking aircraft aerodynamic performance and cruise length into account, provided stepped cruise programmes if it resulted in performance gains.

- The descent starts at the cruise altitude and ends at an altitude of 1500 ft; the equations of motion are obtained for the climb, and in the same manner, the flight programme for the descent is made by segments at constant IAS or Mach number [85]; the reference selected programme is “M
_{cruise}/300 kt/250 kt”, namely: (1) the aircraft flies at a constant Mach number from the cruise altitude to the crossover altitude; (2) the aircraft flies at IAS = 300 kt from the crossover altitude to an altitude of 10,000 ft; (3) the aircraft decelerates in an almost level flight until the IAS is 250 kt, and then flies at this IAS until an altitude of 1500 ft is reached. - Concerning diversion and loiter, analogous considerations about climb, cruise and descent were implemented.

## 3. Results of the Design Process

#### 3.1. Input Data

#### 3.2. Conceptual Design and Reference Layout Selection

_{rear}/(L/S)

_{front}reported in Table 5: this value is in agreement with what is reported in [58]: the parameter (L/S)

_{rear}/(L/S)

_{front}is the key lever to provide the maximum aerodynamic efficiency for box-wing aircraft compatibly with the constraints of static longitudinal stability and pitch trim; the result is also in agreement with what is described in [101], i.e., it provides the maximum performance in terms of C

_{Lmax}in clean conditions (unflapped) for box-wing lifting systems.

#### 3.3. Mission Performance Analysis

_{D}-C

_{L}polar curve is reported, together with the breakdown of the C

_{D}contribution of each aircraft component; Figure 24 (right) reports the viscous pressure breakdown of the polar curve.

#### 3.4. Box-Wing Performance Comparison with Respect to the Conventional Benchmark

_{oe}) reported on the aerodynamic efficiency curves for both the configurations; the dashed curves represent the result corrected with the additional drag of fins and nacelles calculated by the approximate method [53].

#### 3.5. Box-Wing Operating Performance

#### 3.6. Discussion of the Performance Comparison between the Box-Wing and the Conventional Competitor

- The PARSIFAL PrandtlPlane has a larger pax-range envelope with respect to the CeRAS CSR-01 monoplane; in particular, at the harmonic point, the PrandtlPlane presents +66% more passengers and +19% longer range. Both the aircraft are compliant with the ICAO Aerodrome Reference Code “C” constraint (max wingspan equal to 36 m);
- The PARSIFAL PrandtlPlane can transport the same maximum number of passengers of the CeRAS CSR-01 (186 pax in high density) for about 9350 km, 95% more than the reference aircraft.
- The PARSIFAL PrandtlPlane exhibits a gain in terms of mission fuel per pax km in the relevant area of the pax-range diagram, up to the harmonic range of the CeRAS CSR-01; considering the harmonic ranges, the PrandtlPlane needs 19% less fuel per passenger–kilometre; the reduction in fuel per passenger is relevant, from −13% up to −22%, in the whole operating space considered; this also reflects the aircraft environmental performance: the introduction of the PrandtlPlane configuration allows a reduction in pollutant and greenhouse gas emissions per passenger, as widely discussed in [99,103];

- The diagram in Figure 36 shows the contour maps of the percentage difference of the fuel consumption per passenger–kilometre for the two aircraft, both for the zone inside the CeRAS CSR-01 envelope and outside this limit, up to the CeRAS CSR-01 ferry range. It is clear that direct comparisons (i.e., with the same cabin load factor and range) can only be made within the limits of the CeRAS envelope; beyond this limit, the PARSIFAL PrandtlPlane can fly longer distances with the same cabin load factor, or have higher cabin load factors for the same range, with respect to the CeRAS competitor. In this area, the comparison in terms of fuel burnt per passenger–kilometre cannot be made considering the same range and cabin load factor for the two aircraft; thus, the values obtained for PARSIFAL are compared with those relevant to the best performance of CeRAS, i.e., the missions at the border of the envelope (maximum cabin load factor for each considered range). As a result, the comparisons are carried out considering a same range for the two aircraft, but with different cabin load factors. In this zone of the diagram, the higher fuel efficiency of the PARSIFAL PrandtlPlane is combined with the capability to fly with higher cabin load factors for the considered ranges, and therefore the reduction in fuel consumption per passenger–kilometre increases very sensitively as the range increases, as shown in Figure 36.

- In the area of the cabin load factor range diagram beyond the ferry range of the CeRAS CSR-01 configuration, it is not possible to make comparisons in terms of fuel consumption. This region is highlighted in amaranth in the diagram of Figure 37. The PARSIFAL PrandtlPlane, with the same constraints on maximum wingspan of the reference monoplane competitor, is able to fly longer routes with a number of passengers comparable to the CeRAS CSR-01, thus offering an additional advantage in terms of operational flexibility.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

APU | Auxiliar Power Unit |

AR | Aspect Ratio |

AVL | Athena Vortex Lattice |

CAD | Computer Aided Design |

CeRAS | Central Reference Aircraft Data System |

CFD | Computational Fluid Dynamics |

CSR | CeRAS Short Range |

FEM | Finite Element Method |

IAS | Indicated Air Speed |

ICAO | International Civil Aviation Organization |

LF | Load Factor (passenger cabin) |

MTOW | Maximum Take-Off Weight |

PrP | PrandtlPlane |

RANS | Reynolds Averaged Navier–Stokes equations |

SSM | Static Stability Margin |

TLARs | Top Level Aircraft Requirements |

TSFC | Thrust Specific Fuel Consumption |

VLM | Vortex Lattice Method |

## Symbols

b | Wingspan | m |

c | Chord | m |

C_{D} | Drag coefficient | |

C_{D0} | Parasite drag coefficient | |

C_{Di} | Induced drag coefficient | |

C_{Dwave} | Wave drag coefficient | |

C_{D foil} | Airfoil drag coefficient | |

C_{D tot} | Total drag coefficient | |

C_{f} | Friction coefficient | |

C_{fe} | Equivalent skin friction coefficient | |

C_{L} | Lift coefficient | |

C_{l} | Section lift coefficient | |

C_{M} | Pitch moment coefficient | |

d | Diameter | m |

D | Drag | N |

e | Oswald factor | |

E | Aerodynamic efficiency (Lift to Drag ratio) | |

FF | Form factor | |

g | Inequality constraint | |

g | Gravity acceleration | m/s^{2} |

h | Altitude | m |

h/b | Wings height to span ratio | |

k | Polar drag coefficient | |

k_{tip} | Stiffness constraint factor | |

k_{SF} | Strength constraint safety factor | |

l | Length | m |

L | Lift | N |

lb | Lower boundary | |

L/S | Lifting surface wing loading | kg/m^{2} |

M | Mach number | |

n_{z} | Vertical load factor | |

Q | Interference factor | |

S_{exposed} | Planform area of the wing exposed to the flow | m^{2} |

S_{ref} | Reference surface | m^{2} |

S_{wet} | Wetted surface | m^{2} |

t | Vector of thicknesses of structural wingbox components | mm |

t/c | Thickness to chord ratio | |

T | Thrust | N |

ub | Upper boundary | |

V | Speed | m/s |

W | Weight | kg |

W_{des} | Design weight | kg |

W_{oe} | Operating empty weight | kg |

x | Design variables vector | |

x | Aircraft longitudinal position | m |

x_{LE} | Longitudinal leading edge coordinate | m |

y | Spanwise coordinate | m |

z | Aircraft vertical position | m |

α | Angle of attack | deg |

γ | Trajectory slope | deg |

δ_{tip} | Wing tip displacement | mm |

ε | Tolerance | |

θ | Section twist | deg |

λ | Taper ratio | |

Λ | Sweep angle | deg |

σ_{eq} | Equivalent stress | MPa |

Other subscripts: | ||

comp | Component | |

cruise | Cruise | |

cyl | Cylinder | |

eng | Engine | |

front | Front wing | |

fus | Fuselage | |

fuel | Fuel | |

max | Maximum | |

min | Minimum | |

oper | Operating items | |

pay | Payload | |

rear | Rear wing | |

root | Root section | |

sys | On board systems | |

TH | Threshold | |

tip | Tip section | |

trim | Trim condition | |

vertical | Vertical tail | |

wing | Wing |

## References

- Lee, D.S.; Fahey, D.W.; Forster, P.M.; Newton, P.J.; Wit, R.C.; Lim, L.; Owen, B.; Sausen, R. Aviation and global climate change in the 21st century. Atmos. Environ.
**2009**, 43, 3520–3537. [Google Scholar] [CrossRef] [Green Version] - Lee, D.S.; Pitari, G.; Frewe, V.; Gierens, K.; Penner, J.E.; Petzold, A.; Prather, M.J.; Schumann, U.; Bais, A.; Berntsen, T.; et al. Transport impacts on atmosphere and climate: Aviation. Atmos. Environ.
**2010**, 44, 4678–4734. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dessens, O.; Köhler, M.O.; Rogers, H.L.; Jones, R.L.; Pyle, J.A. Aviation and climate change. Transp. Policy
**2014**, 34, 14–20. [Google Scholar] [CrossRef] [Green Version] - Wuebbles, D. Evaluating the impacts of aviation on climate change. Eos Trans. Am. Geophy. Union
**2007**, 88, 157–160. [Google Scholar] [CrossRef] - Brasseur, G.P.; Gupta, M. Impact of aviation on climate. Am. Meteorol. Soc.
**2016**, 97, 561–583. [Google Scholar] [CrossRef] [Green Version] - Eurocontrol. European Aviation in 2040, Challenges of Growth, Annex 2, Adapting Aviation to a Changing Climate. 2018. Available online: https://perma.cc/842G-4A3R (accessed on 18 July 2021).
- Eurocontrol. European Aviation in 2040, Challenges of Growth, Annex 1, Flight Forecast to 2040. 2018. Available online: https://perma.cc/YW6Y-JU7J (accessed on 18 July 2021).
- PARSIFAL Project Consortium. Report on Socio Economic Scenarios and Expectations. PARSIFAL Project Deliverables, D 1.1. 2017. Available online: https://perma.cc/JYL5-K9ST (accessed on 18 July 2021).
- Airbus. Cities, Airports & Aircraft—2019–2038. Global Market Outlook. 2019. Available online: https://perma.cc/WSW3-7JK5 (accessed on 18 July 2021).
- Boeing. Commercial Market Outlook—2019–2038. 2019. Available online: https://perma.cc/WQ53-7WEB (accessed on 18 July 2021).
- Eurocontrol. European Aviation in 2040, Challenges of Growth. 2018. Available online: https://perma.cc/2A2J-B7PW (accessed on 18 July 2021).
- Schäfer, A.W.; Barrett, S.R.; Doyme, K.; Dray, L.M.; Gnadt, A.R.; Self, R.; O’Sullivan, A.; Synodinos, A.P.; Torija, A.J. Technological, economic and environmental prospects of all-electric aircraft. Nat. Energy
**2019**, 4, 160–166. [Google Scholar] [CrossRef] [Green Version] - Hoelzen, J.; Yaolong, L.; Bensmann, B.; Winnefiled, C.; Elham, A.; Fiedrichs, J.; Hanke-Rauschenbach, R. Conceptual design of operation strategies for hybrid electric aircraft. Energies
**2018**, 11, 217. [Google Scholar] [CrossRef] [Green Version] - Pornet, C.; Isikveren, A.T. Conceptual design of hybrid-electric transport aircraft. Prog. Aerosp. Sci.
**2015**, 79, 114–135. [Google Scholar] [CrossRef] - Palaia, G.; Zanetti, D.; Abu Salem, K.; Cipolla, V.; Binante, V. THEA-CODE: A design tool for the conceptual design of hybrid-electric aircraft with conventional or unconventional airframe configurations. Mech. Ind.
**2021**, 22, 19. [Google Scholar] [CrossRef] - Friedrich, C.; Robertson, P.A. Hybrid-electric propulsion for aircraft. J. Aircr.
**2015**, 52, 176–189. [Google Scholar] [CrossRef] - Brelje, B.J.; Martins, J.R. Electric, hybrid, and turboelectric fixed-wing aircraft: A review of concepts, models, and design approaches. Prog. Aerosp. Sci.
**2019**, 104, 1–9. [Google Scholar] [CrossRef] - Khandelwal, B.; Karakurt, A.; Sekaran, P.R.; Sethi, V.; Singh, R. Hydrogen powered aircraft: The future of air transport. Prog. Aerosp. Sci.
**2013**, 60, 45–59. [Google Scholar] [CrossRef] - Baroutaji, A.; Wilberforce, T.; Ramadan, M.; Olabi, A.G. Comprehensive investigation on hydrogen and fuel cell technology in the aviation and aerospace sectors. Renew. Sustain. Energy Rev.
**2019**, 106, 31–40. [Google Scholar] [CrossRef] [Green Version] - Nojoumi, H.; Dincer, I.; Naterer, G.F. Greenhouse gas emissions assessment of hydrogen and kerosene-fueled aircraft propulsion. Int. J. Hydrogen Energy
**2019**, 34, 1363–1369. [Google Scholar] [CrossRef] - Ng, W.; Datta, A. Hydrogen fuel cells and batteries for electric-vertical takeoff and landing aircraft. J. Aircr.
**2019**, 56, 1765–1782. [Google Scholar] [CrossRef] - Azami, M.H.; Savill, M. Comparative study of alternative biofuels on aircraft engine performance. Inst. Mech. Eng. Part G J.Aerosp. Eng.
**2017**, 231, 1509–1521. [Google Scholar] [CrossRef] [Green Version] - Moore, R.H.; Thornhill, L.; Weinzierl, B.; Sauer, D.; D’Ascoli, E.; Kim, J.; Lichtenstern, M.; Scheibe, M.; Beaton, B.; Beyersdorf, A.; et al. Biofuel blending reduces particle emissions from aircraft engines at cruise conditions. Nature
**2017**, 543, 411–415. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mazlan, N.M.; Savill, M.; Kipouros, T. Effects of biofuels properties on aircraft engine performance. Aircr. Eng. Aerosp. Technol.
**2015**, 87, 437–442. [Google Scholar] [CrossRef] [Green Version] - Liem, R.P.; Martins, J.R.; Kenway, G.K. Expected drag minimization for aerodynamic design optimization based on aircraft operational data. Aerosp. Sci. Technol.
**2017**, 63, 344–362. [Google Scholar] [CrossRef] - Zhu, J.H.; Zhang, W.H.; Xia, L. Topology optimization in aircraft and aerospace structures design. Arch. Comput. Methods Eng.
**2015**, 23, 595–622. [Google Scholar] [CrossRef] - Lei, R.; Bai, J.; Xu, D. Aerodynamic optimization of civil aircraft with wing-mounted engine jet based on adjoint method. Aerosp. Sci. Technol.
**2019**, 93, 105285. [Google Scholar] [CrossRef] - Gu, X.; Ciampa, P.D.; Jepsen, J.; Nagel, B. High fidelity aerodynamic optimization in distributed overall aircraft design. In Proceedings of the AIAA Aviation Forum, 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Washington, DC, USA, 13–17 June 2016. [Google Scholar] [CrossRef]
- Lange, R.H. Review of unconventional aircraft design concepts. J. Aircr.
**1988**, 25, 385–392. [Google Scholar] [CrossRef] - Schmitt, D. Challenges for unconventional transport aircraft configurations. Air Space Eur.
**2001**, 3, 67–72. [Google Scholar] [CrossRef] - Iwanizki, M.; Wöhler, S.; Fröhler, B.; Zill, T.; Méheut, M.; Defoort, S.; Carini, M.; Gauvrit-Ledogar, J.; Liaboeuf, R.; Tremolet, A.; et al. Conceptual Design Studies of Unconventional Configurations. 3AF Aerospace Europe Conference 2020, Bordeaux. 2020. Available online: https://hal.archives-ouvertes.fr/hal-02907205 (accessed on 18 July 2021).
- Bijewitz, J.; Seitz, A.; Isikveren, A.T.; Hornung, M. Multi-disciplinary design investigation of propulsive fuselage aircraft concepts. Aircr. Eng. Aerosp. Technol.
**2016**, 88, 257–267. [Google Scholar] [CrossRef] - Defoort, S.; Méheut, M.; Paluch, B.; Liaboeuf, R.; Murray, R.; Mincu, D.C.; David, J.M. Conceptual design of disruptive aircraft configurations based on High-Fidelity OAD process. In Proceedings of the AIAA Aviation Forum, 2018 Aviation Technology, Integration, and Operations Conference, Atlanta, GA, USA, 25–29 June 2018. [Google Scholar] [CrossRef]
- Werner-Westphal, C.; Heinze, W.; Horst, P. Multidisciplinary integrated preliminary design applied to unconventional aircraft configurations. J. Aircr.
**2008**, 45, 581–590. [Google Scholar] [CrossRef] - Liebeck, R.H. Design of the blended wing body subsonic transport. J. Aircr.
**2004**, 41, 10–25. [Google Scholar] [CrossRef] [Green Version] - Qin, N.; Vavalle, A.; Le Moigne, A.; Laban, M.; Hackett, K.; Weinerfelt, P. Aerodynamic considerations of blended wing body aircraft. Prog. Aerosp. Sci.
**2004**, 40, 21–343. [Google Scholar] [CrossRef] - Okonkwo, P.; Smith, H. Review of evolving trends in blended wing body aircraft design. Prog. Aerosp. Sci.
**2016**, 82, 1–23. [Google Scholar] [CrossRef] - Cavallaro, R.; Demasi, L. Challenges, ideas, and innovations of joined-wing configurations: A concept from the past, an opportunity for the future. Prog. Aerosp. Sci.
**2016**, 87, 1–93. [Google Scholar] [CrossRef] - Wolkovitch, J. The joined wing: An overview. J. Aircr.
**1986**, 23, 161–178. [Google Scholar] [CrossRef] - Frediani, A.; Cipolla, V.; Rizzo, E. The Prandtl plane configuration: Overview on possible applications to civil aviation. In Variational Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design; Springer Optimization and Its Applications; Springer: Boston, MA, USA, 2012; Volume 66. [Google Scholar] [CrossRef]
- Frediani, A.; Rizzo, E.; Bottoni, C.; Scanu, J.; Iezzi, G. A 250 Passenger Prandtl plane transport aircraft preliminary design. Aerotecnica Missili Spazio
**2005**, 84. Available online: http://hdl.handle.net/11568/99885 (accessed on 18 July 2021). - Frediani, A. The Prandtl Wing. VKI, Lecture Series: Innovative Configurations and Advanced Concepts for Future Civil Transport Aircraft. 2005. Available online: https://perma.cc/XU6F-8YLG (accessed on 18 July 2021).
- Frediani, A.; Cipolla, V.; Oliviero, F. Design of a prototype of light amphibious Prandtl Plane. In Proceedings of the AIAA SciTech Forum, 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimmee, FL, USA, 5−9 January 2015. [Google Scholar] [CrossRef]
- Prandtl, L.; Induced Drag of Multiplanes. NACA TN-182. 1924. Available online: https://ntrs.nasa.gov/citations/19930080964 (accessed on 18 July 2021).
- Frediani, A.; Montanari, G. Best wing system: An exact solution of the Prandtl’s problem. In Variational Analysis and Aerospace Engineering; Springer Optimization and Its Applications; Springer: New York, NY, USA, 2009; Volume 33. [Google Scholar] [CrossRef]
- Demasi, L.; Dipace, A.; Monegato, G.; Cavallaro, R. Invariant formulation for the minimum induced drag conditions of nonplanar wing systems. AIAA J.
**2014**, 52. [Google Scholar] [CrossRef] [Green Version] - PARSIFAL Project. Available online: https://perma.cc/5ULW-HCP4 (accessed on 18 July 2021).
- Abu Salem, K.; Binante, V.; Cipolla, V.; Maganzi, M. PARSIFAL project: A breakthrough innovation in air transport. Aerotecnica Missili Spazio
**2018**, 97. [Google Scholar] [CrossRef] [Green Version] - Abu Salem, K. Studio Sulla Configurazione Aerodinamica di Velivoli Civili di Tipo PrandtlPlane di Piccole e Medie Dimensioni. M.Sc. Thesis, University of Pisa, Italy, 2016. Available online: https://etd.adm.unipi.it/theses/available/etd-06222016-110207/ (accessed on 18 July 2021).
- Bishop, K. Assessment of the Ability of Existing Airport Gate Infrastructure to Accommodate Transport Category Aircraft with Increased Wingspan for Improved Fuel Efficiency. M.Sc. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, Boston, MA, USA, 2012. Available online: http://hdl.handle.net/1721.1/76095 (accessed on 18 July 2021).
- European Commission. Mobility for Growth—Breakthrough Innovation. Funding Action for Research and Innovation. 2015. Available online: https://ec.europa.eu/inea/en/news-events/newsroom/new-transport-projects-selected-horizon-2020-funding (accessed on 18 July 2021).
- McMasters, J.; Paisley, D.; Hubert, R.; Kroo, I.; Bofah, K.; Sullivan, J.; Drela, M. Advanced configurations for very large subsonic Transport Airplanes. NASA CR 198351. 1996. Available online: https://ntrs.nasa.gov/citations/19970003675 (accessed on 18 July 2021).
- Raymer, D.P. Aircraft Design: A Conceptual Approach; AIAA Education Series: Washington, DC, USA, 1992; ISBN 0-930403-51-7. [Google Scholar]
- Association of European Airlines. Short-Medium Range Aircraft AEA Requirements. Report G(T); AEA: Bonn, Germany, 1989. [Google Scholar]
- Casarosa, C. Meccanica del Volo; Pisa University Press: Pisa, Italy, 2013; ISBN 978-8867410163. [Google Scholar]
- Rizzo, E. Optimization Methods Applied to the Preliminary Design of Innovative Non Conventional Aircraft Configurations. Ph.D. Thesis, University of Pisa, Pisa, Italy, 2009. Available online: https://etd.adm.unipi.it/t/etd-05122010-103814/ (accessed on 18 July 2021).
- Cappelli, L.; Costa, G.; Cipolla, V.; Frediani, A.; Oliviero, F.; Rizzo, E. Aerodynamic optimization of a large PrandtlPlane configuration. Aerotecnica Missili Spazio
**2016**, 95, 163–175. [Google Scholar] [CrossRef] [Green Version] - Abu Salem, K.; Palaia, G.; Cipolla, V.; Binante, V.; Zanetti, D.; Chiarelli, M. Tools and methodologies for box-wing aircraft conceptual aerodynamic design and aeromechanic analysis. Mech. Ind.
**2021**, 22, 1–19. [Google Scholar] [CrossRef] - Rizzo, E.; Frediani, A. Application of optimisation algorithms to aircraft aerodynamics. In Variational Analysis and Aerospace Engineering; Springer Optimization and Its Applications: New York, NY, USA, 2009. [Google Scholar] [CrossRef]
- Addis, B.; Locatelli, M.; Schoen, F. Local optima smoothing for global optimization. Optim. Methods Softw.
**2005**, 20, 417–437. [Google Scholar] [CrossRef] [Green Version] - Drela, M.; Youngren, H. XFOIL 6.9 User Primer. Online Software Manual. 2001. Available online: https://perma.cc/7AGE-C3XU (accessed on 18 July 2021).
- Drela, M.; Youngren, H. AVL 3.36 User Primer. Online Software Manual. 2017. Available online: https://perma.cc/R35R-W29F (accessed on 18 July 2021).
- Beltramo, M.; Trapp, D.; Kimoto, B.; Marsh, D. Parametric Study of Transport Aircraft Systems Cost and Weight. Report NASA CR151970. 1977. Available online: https://ntrs.nasa.gov/citations/19770019162 (accessed on 18 July 2021).
- Wells, D.; Horvath, B.; McCullers, L. The Flight Optimization System Weights Estimation Method. NASA/TM–2017–219627, Volume I; 2017. Available online: https://ntrs.nasa.gov/citations/20170005851 (accessed on 18 July 2021).
- Frediani, A.; Cipolla, V.; Abu Salem, K.; Binante, V.; Picchi Scardaoni, M. Conceptual design of PrandtlPlane civil transport aircraft. Inst. Mech. Eng. Part G J. Aerosp. Eng.
**2019**, 234, 1675–1687. [Google Scholar] [CrossRef] [Green Version] - Mason, W.H. Analytic models for technology integration in aircraft design. AIAA Aircr. Des. Syst. Op. Conf. Dayton
**1990**, 90, 3262-CP. [Google Scholar] [CrossRef] - Cipolla, V.; Frediani, A.; Abu Salem, K.; Binante, V.; Rizzo, E.; Maganzi, M. Preliminary transonic CFD analyses of a PrandtlPlane transport aircraft. Transp. Res. Procedia
**2018**, 29, 82–91. [Google Scholar] [CrossRef] - ANSYS, Ansys Fluent—Fluid Simulation Software. Available online: https://perma.cc/L56W-V8FZ (accessed on 18 July 2021).
- Fazalzadeh, S.; Scholz, D.; Mazidi, A.; Friswell, M. Flutter characteristics of typical wing sections of a box wing aircraft configuration. In Proceedings of the 3AF AEGATS Proceedings 2018, Toulouse, France, 23−25 October 2018. [Google Scholar] [CrossRef]
- Divoux, N.; Frediani, A. The lifting system of a PrandtlPlane, Part 2: Preliminary study on flutter characteristics. In Variational Analysis and Aerospace Engineering; Springer Optimization and Its Applications: Boston, MA, USA, 2012. [Google Scholar] [CrossRef]
- Cavallaro, R.; Bombardieri, R.; Silvani, S.; Demasi, L.; Bernardini, G. Aeroelasticity of the PrandtlPlane: Body freedom flutter, freeplay, and limit cycle oscillation. In Variational Analysis and Aerospace Engineering: Mathematical Challenges for the Aerospace of the Future; Springer Optimization and Its Applications: New York, NY, USA, 2016. [Google Scholar] [CrossRef]
- Bombardieri, R.; Cavallaro, R.; Demasi, L. A historical perspective on the aeroelasticity of box Wings and PrandtlPlane with new findings. In Proceedings of the AIAA SciTech Forum, 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, San Diego, CA, USA, 4−8 January 2016. [Google Scholar] [CrossRef]
- PARSIFAL Project Consortium. Aeroelastic Analysis of the Baseline PrandtlPlane. PARSIFAL Project Deliverables, D5.2. 2020. Available online: https://perma.cc/JYL5-K9ST (accessed on 18 July 2021).
- Abu Salem, K. Development of Design Tools and Methods for Box-Wing Airplanes and Application of the PrandtlPlane Concept to a Short-Medium Range Aircraft. Ph.D. Thesis, University of Pisa, Pisa, Italy, 2021. Available online: https://etd.adm.unipi.it/ (accessed on 18 July 2021).
- Picchi Scardaoni, M.; Binante, V.; Cipolla, V. WAGNER: A new code for parametrical structural study of fuselages of civil transport aircraft. Aerotecnica Missili Spazio
**2017**, 96, 136–147. [Google Scholar] [CrossRef] [Green Version] - 3DS Dassault Systems Simulia, ABAQUS Unified FEA. Available online: https://perma.cc/X8L3-JGSV (accessed on 18 July 2021).
- Fuchte, J. Enhancement of Aircraft Cabin Design Guidelines with Special Consideration of Aircraft Turnaround and Short Range Operations. Ph.D. Dissertation, DLR-Forschungsbericht, Hamburg, Germany, 2014. Available online: https://perma.cc/YT3N-99VV (accessed on 18 July 2021).
- Fuchte, J.; Nagel, B.; Gollnick, V. Weight and fuel saving potential through changed cabin and fuselage design. In Proceedings of the AIAA Aviation Forum, Aviation Technology, Integration, and Operations Conference, Los Angeles, California, USA, 12−14 August 2013. [Google Scholar] [CrossRef] [Green Version]
- PARSIFAL Project Consortium. Structural Analysis of the Baseline PrandtlPlane. PARSIFAL Project Deliverables, D5.1. 2020. Available online: https://perma.cc/JYL5-K9ST (accessed on 18 July 2021).
- Picchi Scardaoni, M.; Montemurro, M.; Panettieri, E. PrandtlPlane wing-box least-weight design: A multi-scale optimisation approach. Aerosp. Sci. Technol.
**2020**, 106, 106156. [Google Scholar] [CrossRef] - Cipolla, V.; Abu Salem, K.; Palaia, G.; Binante, V.; Zanetti, D. A DoE-based approach for the implementation of structural surrogate models in the early stage design of box-wing aircraft. Aerosp. Sci. Technol.
**2021**, 117, 106968. [Google Scholar] [CrossRef] - Torenbeek, E. Development and Application of a Comprehensive, Design-Sensitive Weight Prediction Method for Wing Structures of Transport Category Aircraft. Delft University of Technology, Faculty of Aerospace Engineering, Report LR-693. 1992. Available online: http://resolver.tudelft.nl/uuid:b45a61fe-317a-4201-82f0-dfae51ceb687 (accessed on 18 July 2021).
- Filippone, A. Advanced Aircraft Flight Performance; Cambridge University Press: Cambridge, United Kingdom, 2012. [Google Scholar] [CrossRef]
- Khadilkar, H.; Balakrishnan, H. Estimation of aircraft taxi fuel burn using flight data recorder archives. Transp. Res. Part D
**2012**, 17, 532–537. [Google Scholar] [CrossRef] - Abu Salem, K.; Palaia, G.; Bianchi, M.; Zanetti, D.; Cipolla, V.; Binante, V. Preliminary take-off analysis and simulation of PrandtlPlane commercial aircraft. Aerotecnica Missili Spazio
**2020**, 99, 203–216. [Google Scholar] [CrossRef] - Airbus. Getting to Grips with Aircraft Performance; Airbus SAS: Leiden, The Netherlands, 2002; Available online: https://perma.cc/FQ9P-FET4 (accessed on 18 July 2021).
- Cipolla, V.; Frediani, A.; Abu Salem, K.; Picchi Scardaoni, M.; Nuti, A.; Binante, V. Conceptual design of a box-wing aircraft for the air transport of the future. In Proceedings of the AIAA Aviation Forum, 2018 Aviation Technology, Integration, and Operations Conference, Atlanta, GA, USA, 25−29 June 2018. [Google Scholar] [CrossRef]
- Cipolla, V.; Abu Salem, K.; Picchi Scardaoni, M.; Binante, V. Preliminary design and performance analysis of a box-wing transport aircraft. In Proceedings of the AIAA SciTech 2020 Forum, Orlando, FL, USA, 6−10 January 2020. [Google Scholar] [CrossRef]
- Carini, M.; Méheut, M.; Kanellopoulos, S.; Cipolla, V.; Abu Salem, K. Aerodynamic analysis and optimization of a boxwing architecture for commercial airplanes. In Proceedings of the AIAA SciTech 2020 Forum, Orlando, FL, USA, 6−10 January 2020. [Google Scholar] [CrossRef]
- PARSIFAL Project Consortium. Requirements for the Adoption of the PrandtlPlane as a Mean of Transport. PARSIFAL Project Deliverables, D 2.1. 2017. Available online: https://perma.cc/BD3L-895C (accessed on 18 July 2021). (public).
- International Civil Aviation Organization. Aerodromes: Volume I—Aerodrome Design and Operations. International Standards and Recommended Practices; ICAO Annex 14: Montréal, QC, Canada, 2009. [Google Scholar]
- CeRAS—Central Reference Aircraft System. Available online: https://ceras.ilr.rwth-aachen.de/ (accessed on 18 July 2021).
- Risse, K.; Schäfer, K.; Schültke, F.; Stumpf, E. Central reference aircraft data system (CeRAS) for research community. CEAS Aeronaut. J.
**2016**, 7, 121–133. [Google Scholar] [CrossRef] - Airbus, Aircraft characteristics—Airport and Maintenance Planning, Airbus SAS. 2014. Available online: https://perma.cc/XM64-GZMT (accessed on 18 July 2021).
- Picchi Scardaoni, M.; Frediani, A. General closed-form solution of piecewise circular frames of aircraft. AIAA J.
**2019**, 57, 1338–1342. [Google Scholar] [CrossRef] - Bottoni, C.; Scanu, J. Preliminary Design of a 250 Passenger PrandtlPlane Aircraft. M.Sc. Thesis, University of Pisa, Pisa, Italy, 2004. Available online: https://etd.adm.unipi.it/theses/available/etd-09072004-140314/ (accessed on 18 July 2021).
- Schiktanz, D.; Scholz, D. Box wing fundamentals—An aircraft design perspective. In Proceedings of the DGLR: Deutscher Luft und Raumfahrtkongress 2011, Bremen, Germany, 27–29 September 2011; pp. 601–615, ISBN 978-3-932182-74-X. Document ID: 241353. Available online: https://perma.cc/2Q7R-WFAF (accessed on 18 July 2021).
- Picchi Scardaoni, M.; Magnacca, F.; Massai, A.; Cipolla, V. Aircraft turnaround time estimation in early design phases: Simulation tools development and application to the case of box-wing architecture. J. Air Transp. Manag.
**2021**, 96, 102122. [Google Scholar] [CrossRef] - PARSIFAL Project Consortium. Report on Operational and Economic Assessment. PARSIFAL Project Deliverables, D 1.2. 2020. Available online: https://perma.cc/U3QF-JQL7 (accessed on 18 July 2021). (public).
- Cipolla, V.; Abu Salem, K.; Bachi, F. Preliminary stability analysis methods for PrandtlPlane aircraft in subsonic conditions. Aircr. Eng. Aerosp. Technol.
**2018**, 91, 525–537. [Google Scholar] [CrossRef] [Green Version] - Cipolla, V.; Abu Salem, K.; Palaia, G.; Binante, V.; Zanetti, D. A semi-empirical VLM-based method for the prediction of maximum lift coefficient of box-wing aircraft. J. Aerosp. Eng.
**2021**. under review. [Google Scholar] - Arkell, D. Moving toward the Middle, Frontiers Magazine: Boeing. 2003. Available online: https://perma.cc/EK8C-B7RP (accessed on 18 July 2021).
- Tasca, A.L.; Cipolla, V.; Abu Salem, K.; Puccini, M. Innovative box-wing aircraft: Emissions and climate change. Sustainability
**2021**, 13, 3282. [Google Scholar] [CrossRef]

**Figure 2.**Multi-level aircraft design and analysis diagram (abbreviations used: VLM = Vortex Lattice Method, FEM = Finite Element Model, CFD = Computational Fluid Dynamics).

**Figure 8.**Local transonic critical issues (

**left**); box-wing without transonic issues (

**right**). Mach contours referring to freestream M

_{∞}= 0.79.

**Figure 12.**Typical Finite Element mesh of a PrP configuration (aircraft half-model) with some structural details.

**Figure 14.**FE mesh of half a fuselage and example of contour plots of stress and deformation induced by ultimate pressurisation and gravity load with ${n}_{z}=+2.5$ (deformed scale factor: 20).

**Figure 15.**Secondary structures of the box-wing lifting system and aerodynamic forces (aircraft half-model).

**Figure 16.**Example of deformed shape of the PrP configuration and Von Mises stress on both wings (aircraft half-model).

**Figure 21.**Cabin layout comparison between the PARSIFAL solution and a conventional single-aisle aircraft.

**Figure 24.**Details of the aerodynamic performance for PrandtlPlane in cruise condition; lift-to-drag curves (left), C

_{D}breakdown -aircraft components- (centre), C

_{D}breakdown -viscous/pressure- (right).

**Figure 35.**Comparison between the cabin load factor range diagrams (PARSIFAL PrandtlPlane vs. CeRAS CSR-01) and fuel consumption per pax km.

**Figure 36.**Overview of the comparison (PARSIFAL PrandtlPlane vs. CeRAS CSR-01) of the fuel per passenger–kilometre and cabin load factor range diagrams, up to the CeRAS ferry range.

**Figure 37.**Overview of the comparison (PARSIFAL PrandtlPlane vs. CeRAS CSR-01) of the fuel per passenger–kilometre and cabin load factor range diagrams, beyond the CeRAS ferry range.

Challenge | Possible Solution |
---|---|

To meet the large air traffic demand increase expected in the coming years, in particularly for short/medium routes [7] *. | To design an aircraft with an increased cabin capacity compared to the present aircraft operating on short/medium routes. |

To avoid airport saturation problems, already relevant today [11]. | To limit the size and overall dimensions of the aircraft. |

To reduce the environmental impact of the aircraft [2], thus minimising fuel consumption per passenger. | To increase the aerodynamic efficiency as much as possible and/or to adopt new types of propulsion (i.e., electric or hydrogen). |

Front wing loading, L_{front}/S_{front} | <600 kg/m^{2} |

Rear wing loading, L_{rear}/S_{rear} | <600 kg/m^{2} |

Front wing sweep angle, Λ_{front} | >35° |

Rear wing sweep angle, Λ_{rear} | free |

Cruise Mach | <0.79 |

Front wing tip twist angle, θ_{front}^{tip} | <−1° |

Rear wing root twist angle, θ_{rear}^{root} | <+1° |

Spanwise local lift coefficient, c_{l}(y) | <0.7 |

Max n° of passengers | 310 |

Design range | 5000 km |

Cruise Mach | 0.79 |

Initial Cruise Altitude | 11,000 m |

Max Wingspan | 36 m |

Ref. wing area | 122.4 (+32.2 *) m^{2} |

Design range | 5000 km |

Max n° pax | 186 |

Wingspan | 34.1 m |

Fuselage length | 37.5 m |

Cruise altitude | 11,000 m |

Cruise Mach | 0.79 |

@ Design Point | |
---|---|

M | 0.79 |

h_{in} | 11,000 m |

L/D | 21.62 |

C_{L} | 0.4473 |

C_{D} | 0.02068 |

(L/S)_{front} | 604 kg/m^{2} |

(L/S)_{rear} | 477 kg/m^{2} |

(L/S)_{rear}/(L/S)_{front} | 0.789 |

SSM | 0.10 |

Component | Mass (kg) |
---|---|

Front Wing | 7166 |

Rear Wing | 6614 |

Vertical Tip-Wing | 460 |

Fuselage | 11,230 |

Vertical Tail Plane | 1026 |

Number of passengers | 308 |

Mission range | 5722 km |

Mission time | 415 min |

Mission fuel | 21,844 kg |

Total fuel | 26,937 kg |

Mission fuel per pax/km | 0.01239 kg/km pax |

CeRAS CSR-01 | PrandtlPlane | |
---|---|---|

W_{oe} (kg) | 42,054 | 68,866 |

W_{oe}/MTOW | 54.7% | 55.0% |

W_{fuel} (kg) | 17,100 | 27,000 |

W_{fuel}/MTOW | 22.3% | 21.6% |

W_{pay} (kg) | 17,670 | 29,260 |

W_{pay}/MTOW | 23.0% | 23.4% |

MTOW (kg) | 76,824 | 12,5126 |

CeRAS CSR-01 | PrandtlPlane | |
---|---|---|

Number of passengers | 186 | 308 |

Mission range | 4790 km | 4790 km |

Mission fuel | 13,670 kg | 18,108 kg |

Mission fuel per pax/km | 0.01537 kg/km pax | 0.01227 kg/km pax |

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**MDPI and ACS Style**

Abu Salem, K.; Cipolla, V.; Palaia, G.; Binante, V.; Zanetti, D.
A Physics-Based Multidisciplinary Approach for the Preliminary Design and Performance Analysis of a Medium Range Aircraft with Box-Wing Architecture. *Aerospace* **2021**, *8*, 292.
https://doi.org/10.3390/aerospace8100292

**AMA Style**

Abu Salem K, Cipolla V, Palaia G, Binante V, Zanetti D.
A Physics-Based Multidisciplinary Approach for the Preliminary Design and Performance Analysis of a Medium Range Aircraft with Box-Wing Architecture. *Aerospace*. 2021; 8(10):292.
https://doi.org/10.3390/aerospace8100292

**Chicago/Turabian Style**

Abu Salem, Karim, Vittorio Cipolla, Giuseppe Palaia, Vincenzo Binante, and Davide Zanetti.
2021. "A Physics-Based Multidisciplinary Approach for the Preliminary Design and Performance Analysis of a Medium Range Aircraft with Box-Wing Architecture" *Aerospace* 8, no. 10: 292.
https://doi.org/10.3390/aerospace8100292