Proof of Concept 1: MCDA in Aircraft Design
5.1 Definition of the Decision Making Problem
The design of an A320-like commercial airliner is implemented as a proof of concept with the air-craft conceptual design tool VAMPzero (Virtual Airair-craft Multidisciplinary Analysis and Design Processes) [19]. VAMPzero is developed at German Aerospace Center (DLR e.V.) and licensed under the Apache 2.0 license. The design has 150 passenger, twin engine with 3200 km range.
The simplified mission profile is illustrated in Figure 5.2.
Warmup, taxi out
Payload = 150 passenger + 5000 kg cargo
Figure 5.2: The Simplified Aircraft Mission Profile
The optimization framework shown in Figure 5.1 focuses on the assessment of added values of incorporating MCDA techniques in aircraft conceptual design process. Thus, in order to keep the design process transparent, the complexity of the design problem is limited. Five design variables are considered in this study: wing thickness-to-chord ratio, wing aspect ratio, wing reference area, cruise Mach number, and fuselage diameter. The baseline, minimum, and maximum values for the five design variables are listed in Table 5.1.
5.1 Definition of the Decision Making Problem
Table 5.1: The Baseline and Ranges of Design Variables
Thickness-to- Aspect Reference Cruise Fuselage chord ratio ratio area (m2) Mach number diameter (m)
Baseline 0.13 9.396 122.4 0.78 4
Minimum values 0.1 8 80 0.7 3.8
Maximum values 0.2 12 140 0.84 4.2
5.1.1 Identification of Design Criteria
The design criteria of interest are categorized into four groups: cost-based, weight-based, operation-based, and comfort-based. The four groups are described as follows.
Cost-based criteria
• DOC: DOC calculates all the direct operating costs per block hour, including fuel cost, maintenance cost, depreciation cost, crew cost, and miscellaneous cost.
• Fuel cost: Fuel cost calculates the mission fuel costs per block hour, as shown in Equa-tion 5.1. Fuel price is set to 0.85 Dollars per kilogram.
• Aircraft price: An estimation of aircraft price based on OEM, is shown in Equa-tion 5.2 [62]. The exchange rate from Dollar to Euro is set to 0.73.
Weight-based criteria
• OEM: Operating Empty Mass (OEM) calculates the operating empty mass from the components, including fuselage, wing, engine, landing gear, horizontal tail plane, vertical tail plane, and pylon, and operator’s items mass.
• Fuel mass: Fuel mass calculates the fuel needed for the complete mission via the sum of all mission segment fuel masses, including take-off, climb, cruise, descent, and reserve.
• TOM: Take-off Mass (TOM) is the sum of OEM, fuel mass, and payload.
Operation-based criteria
• Annual utilization: Annual utilization defines the number of flight hours relative to the number of possible flight hours, with the assumption that the aircraft is grounded for a quarter of an hour. Its formula is shown in Equation 5.3 [54].
• Block time: Block time calculates the time from engineson to enginesoff for the design mission [62]. Utilization/(block time) ratio provides the number of flight, as shown in Equation 5.4.
Comfort-based criteria
• Passenger density: Passenger density is defined by the number of passenger seats divided by cabin base area, where cabin base area is calculated by the product of fuselage diameter and cabin length. Its mathematical formula is shown in Equation 5.5.
Fuel Cost = (Fuel mass×Fuel price
Block time )(Exchange rate) (5.1)
Aircraft Price = (0.8109(OEM
1000) + 6.3722)(Exchange rate)(Inflation rate)106 (5.2) Annual Utilization = 4198
1 +Block time0.75
(5.3) Utilization/(Block time) = 4198
0.75 + Block time (5.4)
Passenger Density = Number of passenger seats
Fuselage diameter×Cabin length (5.5)
Selection of appropriate design criteria is critical to the determination of an optimal design.
Some recommendations were provided in [101]: the design criterion should represent a non-trivial and calculable indication of the worth of the concept, it should be significantly affected by the design variables and constraints, it should have clear meaning to designers and customers, and it needs clear rationale for methods and factors used for blending if it is blended.
In our case, the question is: Which design criteria are more appropriate to be fed into the MCDA method? In order to better answer this question, parametric studies of design criteria are conducted first, followed by the determination of which design criteria would be further fed into the MCDA method.
5.1.2 Parametric Studies of Design Criteria
The parametric study for cruise Mach number is illustrated in Figure 5.3. The increase of cruise Mach number has a higher fuel consumption for a given mission range and more fuel needs to be carried with the aircraft. Due to the increased aircraft weight, the aircraft price is also increased. Besides, the wave drag of the aircraft increases dramatically with cruise Mach number. Furthermore, it can be seen from Figure 5.3 that there are optimal points for cruise Mach number concerning the minimization of OEM, fuel mass, aircraft price, and TOM, respectively. Utilization/(block time), DOC, and fuel cost increase with cruise Mach number.
Cruise Mach number has no influence on passenger density. It is also important to point out that there does exist optimal cruise Mach number regarding the minimization of total DOC (Euro) instead of DOC per block hour.
5.1 Definition of the Decision Making Problem
Figure 5.3: Parametric Study of Cruise Mach Number versus OEM, Fuel Mass, Utilization/(Block time), Passenger Density, DOC, Aircraft Price, Fuel Cost, and TOM
Parametric studies for wing thickness-to-chord ratio, aspect ratio, reference area, and fuselage diameter are presented in Figure B.1, Figure B.2, Figure B.3, and Figure B.4 in Appendix B, respectively. The increase of thickness-to-chord ratio reduces the wing weight and more fuel volume can be obtained. However, with the increase of thickness-to-chord ratio, the wave drag of the aircraft is also increased, especially at high speed. It can be observed that there are optimal settings of thickness-to-chord ratio with regard to the minimization of OEM, aircraft price, DOC, and TOM. With the increase of thickness-to-chord ratio, fuel mass and fuel cost increase significantly. Thickness-to-chord ratio has no influence on utilization/(block time) and passenger density.
The increase of wing aspect ratio can reduce the induced drag of the wing and thus the overall drag of the aircraft will be reduced. Thus, less fuel is required to fly a given mission range. However, the increase of wing aspect ratio also leads to a heavier wing weight. It can be seen from Figure B.2 that there is one optimum of aspect ratio regarding the minimization of DOC. Besides, OEM, aircraft price, and TOM increase with aspect ratio, while fuel mass and fuel cost decrease. Aspect ratio has no influence on utilization/(block time) and passenger density.
A larger wing reference area has a small drag coefficient, thus, less fuel is required to fly a given mission. However, the increase of reference area leads to a larger wing and hence a heavier aircraft. Figure B.3 shows that there are optimum points for reference area to minimize DOC and TOM. OEM and aircraft price increase with reference area, while fuel mass and fuel cost decrease. Reference area has no impact on utilization/(block time) and passenger density.
The increase of fuselage diameter can increase the cabin volume, but the fuselage weight is increased. The overall drag of fuselage is also increased when the wetted area of fuselage is increased. Moreover, Figure B.4 shows that OEM, fuel mass, DOC, aircraft price, fuel cost, and TOM all increase with fuselage diameter, while passenger density decreases. Fuselage diameter has no influence on utilization/(block time).
Another observation obtained from parametric studies is that all design variables under investigation are continuous, and design criteria with respect to the design variables in the conceptual aircraft design tool (VAMPzero) are rather smooth. This observation can help to choose the optimization routine for the proposed framework in Section 5.3.
Determination of Evaluation Criteria
The common practice of using DOC as objective function in the optimization is not appropriate in this study, considering that DOC has high correlation with all other design criteria. Besides, aircraft price is highly correlated to OEM, and fuel cost is calculated by fuel mass and block time. Payload is fixed in this case, and TOM is merely determined by OEM and fuel mass.