Aircraft Cost Model for Preliminary Design Synthesis

5th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 9-12 January 212, Nashville, Tennessee AIAA 212-686 Aircraft Cost Model for Preliminary Design Synthesis Tim Lammering, Katharina Franz, Kristof Risse, Ralf Hoernschemeyer and Eike Stumpf Institute of Aeronautics and Astronautics (ILR), RWTH Aachen University, 5262 Aachen, Germany A new methodology for assessment of cost and benefit in preliminary aircraft design is presented. The proposed model allows for estimating aircraft list price, unit costs, as well as non-recurring and recurring costs for development and production. Further, the targeted aircraft units during life cycle and for break-even are estimated. Focus is put on civil jet transport aircraft and on applicability of the proposed model in early preliminary design. Although the proposed model is tailored for early design, it shows the required sensitivities to important design parameters, so that design trade-offs can be assessed in terms of costs. The different cost items are derived from a combined top-down and bottom-up approach. The model is based on list price data of current transport aircraft in combination with semiempirical analyses that are published in literature. The proposed methodology is directly integrated into the ILR Preliminary Aircraft Design Suite for fast assessment of new aircraft concepts and was verified against current aircraft cost data. In the scope of this paper, sensitivity studies are presented to show the influences of different design parameters on costs. In a case study, the proposed model is applied to an existing aircraft program. In another case study, the proposed model is fully integrated into preliminary design synthesis and the resulting influence of costs on multi-disciplinary design optimization are discussed. ϕ 25,wing b C A/C C F CP D E i I A/C l LF L m payload,max MF W M T OW n engines N P V N RC Nomenclature Quarter chord sweep, deg Span, m Aircraft unit costs, 21-USD Communality factor Communality percentage Discount per unit sold, 21-USD Earnings per unit sold, 21-USD Relative interest rate per period required for production of one aircraft Investment costs, 21-USD Length, m Landing field length, m Maximum payload, kg Maximum fuel weight, kg Maximum take-off weight, kg Number of engines Net present value, 21-USD Non-recurring costs, 21-USD OW E Operating weight empty, kg P List price function, 21-USD P A/C Aircraft list price, 21-USD p A/C Monthly production rate, 1/month P engine Engine power (turboprop), kw P AX Passengers Q BE Aircraft units for break-even Q LC Aircraft units during life cycle R Range, NM R 2 Coefficient of determination RC Recurring costs per unit, 21-USD S Reference area, kg/m 2 SLST Sea level static thrust (jet), kn ST D Statistical standard deviation T OF L Take-off field length, m v Velocity, kts V M O Maximum operating speed, kts W C Component weight, kg Fuselage width, m w fuselage Researcher and PhD student, Institute of Aeronautics and Astronautics (ILR), RWTH Aachen University, Wuellnerstrasse 7, 5262 Aachen/Germany. Academic Counselor, Institute of Aeronautics and Astronautics (ILR), RWTH Aachen University, Wuellnerstrasse 7, 5262 Aachen/Germany. Chair of Aeronautics and Astronautics and head of institute, Institute of Aeronautics and Astronautics (ILR), RWTH Aachen University, Wuellnerstrasse 7, 5262 Aachen/Germany. 1 of 21 Copyright 212 by Insitute of Aeronautics and Astronautics, RWTH Aachen University. Published by the, Inc., with permission.

I. Introduction Commercial transport aircraft are value creating products. 1, 2 Hence, it is the main goal to design aircraft for maximum value rather than only for performance or comfort. Experience shows that a highperforming, absolutely state-of-the-art aircraft, like the Concorde was, does not turn out to be commercially successful. Instead, well balanced designs turn out to be the most successful ones. Measuring the actual product value, however, is not easy in preliminary design. Today, aircraft are assessed based on costs in 1, 3, 4 general, and on direct operating costs (DOC) in particular. Recently, focus is put more on assessment on overall life cycle costs (LCC). 5 9 Operating costs are to be minimized from the customer s perspective. The manufacture, however, measures product profitability typically in net present value (NPV). 1 A design that shows lowest operating costs does not necessarily lead to highest net present value. Hence, both parameters have to be assessed already in preliminary aircraft design synthesis. The design space is still wide in preliminary design. Many different design options are explored and assessed against each other. The design space is then narrowed by down-selection of the most promising concepts. Thus, for decision making, reliable models are already required in preliminary design. It is especially important that such models show sufficient sensitivity to the relevant design parameters, so that design trade-offs are mirrored in the results. Numerous research on cost estimation during preliminary aircraft design have been published in the past. This holds for single cost items like e.g. manufacturing costs, as well as for the overall life cycle costs. Comprehensive overviews of past research on this topic are given by Johnson, 11 Asiedu and Gu, 12 Eaglesham 13 or Thokala. 14 Existing cost models are either detailed cost accounting methods, 15 17 or use 6, 7, 18 21 simple semi-empirical cost functions. A drawback of detailed models is that they are generally not applicable in early design phases, due to still unknown input parameters. Simple empirical functions, on the other hand, do not show the required sensitivities to the relevant design parameters. Tirovolis and Serghides 22 published a reliable method for estimating aircraft list price from the most relevant design parameters during preliminary design. Their model, however, only determines aircraft list price and does not estimate other cost items. Many of the currently published studies focus on increasing accuracy of cost estimation in early design phase, the general idea is to combine semi-empirical methods with detailed cost accounting methods. For example, within the Implied Cost Evaluation System (ICES), a product data structure was developed by Scanlan et al., 23 which contains several examples of costs for design and manufacturing of components, with which quite accurate cost estimations can already be derived in an early design phase. Castagne et al. 24 have developed a generic model to estimate costs in aircraft design. Therein for different aircraft components, several cost items are defined by cost equations, which have to be derived from detailed regression analysis. Hence, an extensive data collection is required. Furthermore, current studies on this topic often consider approaches to overall cost-benefit analyses to determine the feasibility of design cases. Lee and Olds 25 have developed a conceptual design tool for launch vehicle design, which also includes prediction of key business indicators for business simulation. Markish 1, 26 sees the shareholder value, which is obtained by demand, price and costs of manufacturing as well as of taxes and interests, as the ultimate objective function from the perspective of the firm designing the aircraft. He has developed a framework wherein a cost model, a revenue model, as well as a performance model are linked to determine the net present value of an aircraft program under consideration of market uncertainties. Based on this work, Peoples and Willcox 27 have established an optimization framework, which besides technical parameters also includes financial parameters into the optimization process during conceptual aircraft design. The resulting designs can then be assessed against business risk due to technical and financial uncertainties. In the scope of this paper, a new approach towards estimating different cost items in preliminary aircraft design is presented. It includes estimates for aircraft list price, aircraft unit costs, as well as non-recurring (NRC) and recurring (RC) costs. Furthermore, it allows for assessing the business case by estimating the targeted units of aircraft that ought to be sold during life cycle, as well as the net present value of the specific aircraft program for given earnings. The proposed methodology is fully integrated into a framework for preliminary aircraft design synthesis, which allows for fast assessment of different designs and for multidisciplinary design optimization with different target functions. Sensitivity studies that are presented in the scope of this paper show the influences of different parameters on costs. The proposed model is also applied in case studies to an existing aircraft program, as well as to preliminary design synthesis and optimization. 2 of 21

II. Overall Methodology for Aircraft Design and Cost Modeling At the Institute of Aeronautics and Astronautics (ILR) of RWTH Aachen University a design methodology for multi-disciplinary preliminary aircraft design 28 33 was developed, in which the presented aircraft cost model is directly integrated for fast and reliable assessment of technology. A. ILR Preliminary Design Suite From a defined set of top-level requirements and design specifications, a sizing of the aircraft is derived in terms of a general arrangement, see figure 1. Analysis tools are then used to estimate mass and aerodynamic performance of the design. Based on the general arrangement and estimated performance characteristics, the design mission is simulated to derive the required total loaded fuel and to check for changes in maximum take-off weight (MTOW). The design loop is run until convergence is achieved. If started from a white sheet, the design synthesis generally takes less than 1 to 15 minutes depending on the computer speed. After convergence, the design is assessed based on different criteria such as fuel efficiency, costs, or emissions. Different scenarios as well as weighting functions can be applied in the assessment. Based on the assessment, a multi-disciplinary design optimization (MDO) is conducted in which a defined parameter space is investigated. The overall design synthesis has been implemented into a fully automated process: the ILR Preliminary Aircraft Design Suite (IPADS). Optimized designs can be generated with only a minimum of required user input and required preprocessing efforts. Multi-disciplinary optimization Initial Sizing Wing Sizing Engine Sizing Top-Level Req s Aircraft Sizing Fuselage Design Empenage Sizing Gear Sizing Specific Design & Analysis Aircraft Concept Design optional for design study Systems Stability & Control Structures Aircraft Performance Analysis Mass Estimation Performance Analysis Polar Estimation Aircraft Assessment Scenario & Weighting Functions Monetary Values Noise Emission Custom Criteria MTOW convergence B. Cost Modeling in IPADS: A Combined Top-Down and Bottom-Up Approach Figure 1. ILR Preliminary Aircraft Design Suite. For assessment of commercial transport aircraft, monetary values play an important role. Different items like aircraft list price (P A/C ), aircraft unit costs (C A/C ), recurring (RC) and non-recurring costs (NRC), direct operating costs (DOC) or life cycle costs (LCC) have to be considered for assessment of technology, see figure 2. The different cost items are not independent of each other but influence each other. One example are the DOC, which are directly influenced by aircraft list price via depreciation and insurance costs. As highlighted in figure 2, this paper concentrates on an aircraft cost model that allows for estimating aircraft list price, unit costs, as well as recurring and non-recurring costs within preliminary design synthesis. Models for estimating DOC and LCC are already integrated within IPADS but are not the focus of this paper. Before the different underlying models are described in greater detail, the overall methodology is described in the following paragraphs. The structural overview of the proposed methodology is illustrated in figure 3. 1. Schematics of the Proposed Methodology In a first step, aircraft list price is derived from aircraft design parameters with a top-down approach. Aircraft list price is defined as the selling price that a customer pays for the entire aircraft and it is derived from non-linear regression analyses of different relevant design parameters with the current list price of various commercial aircraft. According to equation 1, aircraft list price can be broken down into targeted aircraft unit costs (C A/C ), a margin for possible discounts (D) and earnings (E). Since tax is generally applied 3 of 21

Monetary values Aircraft list price Aircraft units costs Recurring costs Non-recurring costs DOC LCC Figure 2. Different monetary values for assessment of aircraft designs. Aircraft list price (P A/C ) Aircraft design synthesis Top-down... Aircraft unit costs (C A/C ) Recurring costs (RC) Earnings (E) Non-recurring costs (NRC) Component recurring costs Airframe Engine Systems Assembly Discount (D) Net present value (NPV) Investment (I) Units (Q LC ) Bottom-up... Figure 3. Structural overview of the proposed aircraft cost model. after the list price in the purchase of commercial aircraft, tax can be neglected in scope of the proposed model. Targeted aircraft unit costs can further be split into recurring (RC) and non-recurring costs (N RC), investment costs (I A/C ), where the two later are divided by the targeted units (Q LC ) of aircraft that are ought to be sold during product life cycle, see equation 2 and figure 3. Investment costs depend on the interest rates and the investment that was made during product life cycle. For the proposed model a simplified approach was chosen, which assumes constant interest rates (i) over the depreciation period. For constant production rates (p A/C ), the timeframe of product life cycle can be substituted by the quotient of targeted units and production rate. Investment costs can be calculated from equation 3. P A/C = C A/C + D + E (1) C A/C = RC A/C + NRC A/C + I A/C (2) Q LC Q LC [ ] I A/C = NRC A/C (1 + i) (Q LC/p A/C ) 1 (3) Hence, for a given P A/C, as well as for given discounts, earnings and investment costs, equation 2 combines three unknowns: RC A/C, NRC A/C, and Q LC. The targeted recurring costs per unit can then be derived from initial estimates for non-recurring costs and for initial targeted units of aircraft from the following equation: RC A/C = C A/C NRC A/C Q LC (1 + i) (Q LC/p A/C ) To derive the remaining unknown Q LC, Beltramo et al. 34 provide a model for estimating aircraft recurring costs from summation of recurring costs of the various components and of final assembly. The different component recurring costs are estimated from functions of component weights (W C,i ) and aircraft units, see equation 5. The component weights directly result from overall aircraft design synthesis and are required (4) 4 of 21

input of the proposed methodology. The required aircraft units can then iteratively be computed, so that accumulated component recurring costs match total targeted recurring costs per aircraft by equalizing results from equation5 and 4. RC A/C = n RC C,i = i=1 n f(q LC, W C,i ) (5) It has to be kept in mind that for the top-down approach a starting value for non-recurring costs is used to derive initial targeted recurring costs. For estimating non-recurring costs a model by Roskam 7 is proposed. Total aircraft non-recurring costs are estimated from component costs, required man month for development and applicable labor rates. The estimated component costs from the model by Beltramo et al. 34 are fed into the non-recurring costs model and a new estimate for non-recurring costs is derived. The models for recurring and non-recurring costs are then iteratively run until a convergence in costs and the targeted units is achieved, cf. figure 3. 2. Net Present Value and Estimating Break-Even i=1 The ILR cost model also allows for estimating the net present value as well as the break-even point of the aircraft development project. In cost-benefit analysis, the net present value is a reliable indicator for measuring the benefit for the company s stakeholders that is gained from a specific product. The net present value is defined by the required investments and the cash flow during product life cycle. 35 In the proposed model it is assumed that the required investments equal the non-recurring costs of the project. For constant interest rates, the net present value can be estimated from the following equation: total earnings + - revenue break-even earnings non-recurring costs recurring costs Q LC NP V = NRC + j=1 P A/C D RC A/C (1 + i) j/p A/C (6) Figure 4. sold units Dependency of the break-even point. As shown in figure 4, break-even is achieved when total program costs match total revenue. 36 For break-even the net present value also equals zero. 35 Thus, the required units for break-even can be calculated iteratively from equation 6, so that the net present value equals zero. III. Underlying Models In this section the underlying models for estimating the different cost items are described in more detail. Due to the impact of inflation, it is important to relate all prices and costs to the same reference year. In the proposed model, 21-USD are consistently used as reference. If prices or costs are given for a different reference year, the consumer price index (CPI) theory 37 is used for conversion to 21-USD. Only the aircraft list price model was newly derived by the authors. All other implemented models are taken from literature and were already validated by the different authors. An explicit validation is therefore only provided for the aircraft list price in the scope of this paper. However, the presented sensitivity studies as well as the case studies proofs plausibility in the obtained results of the proposed methodology. A. Aircraft List Price The aircraft list price is estimated from a semi-empirical model that was developed by the authors. The necessary data set was established by collecting technical as well as list price data of 11 aircraft. All aircraft that are included in the regression analysis are listed in table 1. The focus lies on commercial jet airliners. Nevertheless, regional (jets and turboprops) as well as business aircraft are also included; small general aviation aircraft are not considered. 5 of 21

The technical design and performance parameters mainly originate from publication by the Jane s Group 38, 39 and airport planning manuals (e.g. references 4, 41 ) that are published directly by the manufacturers. For information on aircraft list price, two primary sources Jane s Group 38, 39 and Lloyd s 42 were used that publish current selling prices of different aircraft models. Information provided by manufacturer s press releases (e.g. references 43 ) were also used as secondary sources if available. For most aircraft, a range of list prices is given rather than one specific price. This is due to differences in equipment and furnishing between aircraft models as well as due to differences in sales discounts for different customers. For the regression analysis, on which the proposed model is based, average list prices for each aircraft model have been used. Table 1. Aircraft used for regression analysis to determine aircraft list price. Airbus Boeing and McDonnellDouglas A3 B2-1 A33-2 77 757-2 DC-1-1 A3 B4-2 A33-2F 717-2 757-2F DC-1-3 A3 B4-6 A33-3 727-2 757-3 DC-1-4 A31-2 A34-2 737-3 767-2 MD-11 A31-3 A34-3 737-6 767-2ER MD-11F A318-1 A34-5 737-7 767-3 MD-8 81 A319-1 A34-6 737-8 767-3ER MD-8 82 A32-2 A38-8 737-9 777-2 MD-8 83 A321-1 747-1 777-2ER MD-8 87 A321-2 747-SP 777-2LR MD-8 9-3 747-2 777-3 747-4 787-3 747-4F 787-8 747-8 787-9 Bombardier Lockheed Embraer Dassault & ATR Others CRJ-2 L-111-1 ERJ 135 Dassault Falcon 5 Dornier 328-1 CRJ-7 L-111-2 ERJ 145 Dassault Falcon 9 Dornier 328 Jet CRJ-9 L-111-25 E-Jet 17 Dassault Falcon 2 Fokker 7 CRJ-1 L-111-5 E-Jet 19 Dassault Falcon 7X Fokker 1 Dash 8Q-2 ATR 42-3 Gulfstream V Dash 8Q-3 ATR 42-5 Gulfstream G4 Dash 8Q-4 ATR 72-5 Gulfstream G5 Global 5 ATR 72-6 Gulfstream G55 Global Express Gulfstream G65 Challenger 3 Sukhoi SSJ 1-95 Learjet 4 BAE 146-2 Learjet 45 Non-linear regressions between the aircraft list prices, and all technical design and performance parameters were conducted. Different regression functions were applied to the data and assessed by means of coefficient of determination (R 2 ), which gives direct measure for the correlation of each fit. For each parameter, the regression function that shows the highest R 2 is implemented within the list price model. From a large set of design and performance parameters only those were implemented that show fits with a R 2 greater than.85. A total of 27 design parameters were identified that show this close correlation with aircraft list price, see table 2. All of the identified parameters are already available within preliminary aircraft design synthesis in IPADS. Also the most important parameters for design trade-offs are covered, which lets the 6 of 21

Table 2. Technical parameter used for regression analysis. Weights & Payload Propulsion Geometry Wing Geometry Other Performance MT OW Type of Engine S ref S tail, S fin v initial climb OW E n engines b wing b tail, b fin v approach m payload,max SLST ϕ 25,wing l fuselage R max payload MF W P engine w fuselage R max fuel P AX l wheel track R ferry l wheel base T OF L LF L estimated aircraft list price show the required sensitivity for assessing design trade-offs. In figure 5, the obtained fits for two design parameters (MT OW and l fuselage ) are shown exemplarily. Aircraft list price, m. 21-$ 4 3 2 1 P MTOW =.59 MTOW.83 R 2 =.94 Jane s Lloyd s Others 1 2 3 4 5 6 MTOW, 1, kg (a) Maximum take-off weight Aircraft list price, m. 21-$ 4 3 2.43 P l,fuselage =.79 l fuselage + 7.4 R 2 =.9 2 1 Jane s Lloyd s Others 1 2 3 4 5 6 7 8 l fuselage, m (b) Fuselage length Figure 5. Exemplary data fits for estimating aircraft list price. From the regression analyses, 27 functions are obtained that all give a non-linear relation between a specific design parameter and aircraft list price. Overall aircraft list price is then estimated by summation of the single obtained price functions (P i ), which are weighted with the corresponding R 2, see equation 7. Weighting of the different price functions with the corresponding R 2 allows for reflecting the quality of correlation on the influence of the specific design parameter on overall aircraft list price. P A/C = n i=1 (R2 i P i) n i=1 R2 i = R2 MT OW P MT OW +... + RLF 2 L P LF L n i=1 R2 i (7) Table 3. Statistical deviation of aircraft list price. relative mean deviation P A/C 1.4 % ±16.8% maximum mean deviation P A/C max 25.3 % absolute mean deviation PA/C 8. % standard deviation STD 8.4 % The proposed aircraft list price model is directly validated against the collected price data, for which regression analyses were conducted. Figure 6 illustrates relative deviations of estimated list prices from prices given by both Jane s 39 and Lloyd s. 42 For the sake of clarity, only deviations for current Airbus and Boeing aircraft are plotted. For these aircraft, absolute maximum deviation lies well below 25 %, whereas absolute mean deviation is 6.8 %. Validation by means of all included aircraft results in an absolute mean deviation of 8 % and an absolute maximum deviation of 25.3 %. Statistical standard deviation (STD) is 8.4 % for the given dataset. Data is randomly scattered about the means and maximum deviations are within limits, so that statistical normal distribution can be assumed. Thus, a confidence inter- 7 of 21

vall with a certainty of 95 % that estimated values lie within it, is given by ±2 ST D. Statistical data of the validation are summarized in table 3. The aircraft list price model shows sufficient accuracy for application in preliminary design. Deviation, % 2 1-1 -2 717-2 737-3 Figure 6. 737-6 737-7 737-8 737-9 B. Non-Recurring Costs Deviation to Price given by Jane s Deviation to Price given by Lloyd s 747-4 757-2 757-3 767-2 767-2ER 767-3 767-3ER 767-4ER 777-2 777-2ER 777-2LR 777-3 A3B4-6 A31-3 A318-1 A319-1 A32-2 A321-1 A33-2 A33-3 A34-2 A34-3 A34-5 A34-6 A38-8 Relative deviations of estimated list prices for current Airbus and Boeing aircraft. For estimating non-recurring costs the semi-empirical model that is given by Roskam 7 has been selected. It is based on the first Development and Procurement Costs of Aircraft (DAPCA) model developed by the RAND Corporation. 44 Since the DAPCA model was developed on the basis of military aircraft data, it was assessed for application to commercial aircraft against two other semi-empirical models: the latest version of DAPCA IV 6 and the Aircraft Cost Estimation Methodology developed by Burns, 2 which both are also based on military aircraft. Non-recurring costs of twenty commercial aircraft, see table 7, were estimated with the different methods and compared against published non-recurring costs from literature. Manufacturer s press releases, e.g. published in Flight International 45 and Flug Revue, 46 were used; all cost data was converted to 21-USD. The comparison showed that best results were obtained with the Roskam model. Accuracy of the Roskam model has been improved further by the authors, by implementation of a communality factor (CF ) that considers cost reductions when using components from parent aircraft also for derivatives. Definition of the communality factor is based on a break down of non-recurring costs onto component-level that is shown in figure 8. It is representative for a typical commercial aircraft and originates from Markish. 1 Communality in landing gear is neglected due to the small impact of only 1 % in the proposed model. Communality factors can be chosen for all other components as user input. They are then multiplied with the given cost percentage and accumulated to the overall communality factor as shown in the following equation: CF =.37 CP fuselage +.2 CP wing +.26 CP systems +.9 CP empennage +.8 CP engines (8) For example, if an aircraft is a stretched derivative of an existing aircraft with new engines but no other changes: the CP of the fuselage is set to e.g. 8 %, the CP of the engine is set to zero and all other CPs are set to 1 %, which leads to an overall communality factor of 85 %. The non-recurring cost items, which are affected by communality, are then reduced by this percentage. From the considered cost items as shown in figure 9, only the production costs of flight test aircraft, except for tooling, are not reduced by communality. Each cost item that is shown in figure 9 is covered by a cost estimation relationship (CER), which allows for calculating non-recurring costs as function of different aircraft design parameters. The labor costs for the items: Airframe Engineering and Design, Manufacturing labor, Tooling and Quality Control are derived from the different labor rates and the required labor hours. The latter can be estimated by the given CERs which depend on aircraft characteristics like maximum operating speed or maximum take-off weight, as well as on process parameters like monthly rate of production or numbers of test aircraft that are produced. The costs for Development Support & Testing, Flight Test Operations, Test & Simulation Facilities and Manufacturing material are directly estimated by CERs, and are multiplied with the CPI for conversion to the actual year. 8 of 21

Figure 7. Aircraft used for examination of NRC-models. Boeing Airbus Bombardier Miscellaneous 737-8 A3 CRJ-2 Embraer 17 747-1 A318-1 CRJ-7 Embraer 19 747-8 A319-1 CRJ-1 Dornier 728 777-2 A32 Gulfstream G65 A33-2 Mitsubishi MRJ A34-6 Honda HA-42 A38-8 installed engines 8 % landing gear 1% systems 26 % wing 2 % fuselage 37 % tail 9 % Figure 8. Non-recurring cost break down by parts for commercial aircraft. 1 Since engines and avionics are treated as supplier parts, the component costs from the recurring cost model are fed into the corresponding CERs, cf. figure 3. Non-recurring costs (NRC) Airframe Engineering & Design Development Support & Testing Flight Test Airplanes Flight Test Operations Test & Simulation Facilities Engine & Avionics Manufacturing labor Manufacturing material Tooling Quality control Figure 9. Cost components of non-recurring costs. C. Recurring Costs In accordance to figure3, the implemented model for estimating recurring costs per unit still have to be described in more detail. The break down of overall aircraft recurring costs into component-level is desirable for assessment of technology and for evaluation of design trade offs. Models that allow such a break down onto component-level are rare for application in preliminary aircraft design synthesis. Often simple cost break downs that are based on a fixed percentage are used instead. Such models, however, do not show the required sensitivities for trade studies. One of these cost break downs was for example proposed by Markish. 1 In the herein presented methodology, a component cost model that was published by Beltramo et al. 34 is used. The model allows for estimating recurring costs for the following aircraft components: wing, fuselage, empennage, nacelles, landing gear, propulsion, systems, and final assembly. The costs for the systems group can be further broken down into system-level by following the ATA-1 classification. 47 Costs for the following systems are estimated by the implemented model: 9 of 21

operator items, environmental control system (ATA-21), power systems (ATA-24, ATA-29, ATA-36 and ATA-49), furnishing (ATA-25), flight controls (ATA-27), avionics (ATA-22, ATA-23, ATA-31 and ATA-34), and support systems (ATA-26, ATA-28, ATA-3, ATA-33, ATA-35 and ATA-38). Estimated component costs as well as system costs for a single-aisle aircraft are exemplarily shown in figure 1. A break down for airframe, propulsion and total system costs is shown in figure 1(a), whereas a further break down of the system costs into system-level is provided in figure 1(b). Assembly 2 % Systems 38 % Empennage 2 % Nacelles 5 % Wing 7 % Fuselage 11 % Gear 2 % Engines 15 % Avionics 39 % Support systems < 1 % Flight controls 1 % Operator items 2 % Furnishing 12 % ECS 5 % Power systems 14 % (a) Airframe, propulsion and systems (b) Systems group Figure 1. Component recurring costs break down for a single-aisle aircraft. As already briefly described in the previous section, the model by Beltramo et al. 34 estimates component recurring costs as function of component weight (W C,i ) and the targeted units (Q LC ), cf. equation 5. Component weights are derived beforehand within the overall aircraft design synthesis, cf. figure 1, and are strongly impacted by the relevant design parameters. In the proposed methodology, the model is used to iteratively determine the targeted number of aircraft that has to be sold during product life cycle, such that the targeted recurring costs match the ones that are obtained from equation 4 for a given list price, non-recurring costs as well as given earnings, discounts and investment costs. IV. Reference Aircraft for Sensitivity and Case Studies For the sensitivity and case studies that are presented in the scope of this paper, the authors choose to use a single-aisle aircraft in conventional configuration and with conventional technology. Its top-level requirements, as well as its design specifications were specified by Airbus Germany for academic purposes. 48 A. General Arrangement The aircraft is designed for 185 passengers in a typical two-class layout and for a maximum payload of 23 t. Its design range is specified to 4 NM with a design payload of 16.3 t. Since the design range is significantly longer than a typical mission during operations, an additional study mission is defined for assessment. The study mission has a range of 1 NM and is flown with maximum payload. The ILR Preliminary Aircraft Design Suite was used to design the reference aircraft for the top-level requirements. Minimum fuel burn was chosen as target function for design optimization, which resulted in a wing loading of 65 kg/m 2 and a thrust-to-weight ratio of.337, see figure 11. Key specifications as well as calculated performance characteristics of the design are summarized in table 4. The general arrangement of the derived reference aircraft is plotted in figure 12. 1 of 21

Fuel, % 2 15 1 5 52 54 56 58 6 62 64 66.33 Wing Loading, kg/m 2.34.35.36.37 Thrust Loading, --- Figure 11. Optimization of W/S and T/W for the reference aircraft. Figure 12. General arrangement of the reference aircraft. Table 4. Key specifications and performance characteristics of the reference aircraft. (a) Design Specifications. (b) Performance for design and study mission. Parameter Values Units MTOW 99,45 kg OWE 5,986 kg Wing loading 65 kg/m 2 Thrust loading.337 Cruise mach number.8 Maximum payload 23,33 kg Passengers 185 ULD devices 12 LD3-45W Parameter Mission Mission Units (design) (study) Take-off weight 99,45 85,56 kg Payload 16,78 23,33 kg Mission range 4, 1, NM Block time 9:2 2:41 hh:mm Block fuel 27,256 7,657 kg Total fuel 31,684 11,487 kg Reserve fuel 4,428 3,83 kg The level of technology of the propulsion system has significant influence on fuel efficiency. For design of the reference aircraft, a validated thermodynamic model of the CFM56-5C2 engine is used. Within the design synthesis, engine decks are slightly scaled by sea level static thrust to match the specific thrust requirements, which are derived from the required thrust to weight ratios of the design. The specific fuel consumption remains constant when scaling the engines slightly. B. Verification of the Reference Design For verification of the conventional reference design, a preliminary aircraft design that was published by Werner-Spatz 48 is used. He used similar top-level requirements and derived his design with the well documented and verified DLR PrADO 49 (Preliminary Aircraft Design and Optimization Program) tool. Deviations in typical overall aircraft design parameters between the two designs are shown in figure 13. It can be seen that similar top-level requirements have been used as input data and close agreement between the two designs are obtained. For all but one parameter, deviations are well below 5 %. A larger deviation can only be seen in the estimated required landing distance, which is highly sensitive to a semi-empirical breaking coefficient. Thus, it is likely caused by a different chosen breaking coefficient. For cost studies that are the scope of this paper, sufficient accuracy can be expected from the IPADS design methodology. C. Application of Cost Model to Reference Aircraft The results of the cost model when applied to the reference aircraft are summarized in table 5. As input targeted earnings of 3 %, an average discount of 7 % and interest rates of 5 % were assumed. Further, the reference aircraft is treated as entirely new white sheet design that features no commonalities to any 11 of 21

Deviation, % 5 4 3 2 1-1 -2-3 -4 % W/S results of design synthesis on overall aircraft-level input parameters for aircraft design synthesis % T/W % design range % design payload + 1.4% L/D cruise +.5% wing mass - 1.% fuselage mass + 3.4% engine mass +.8% OWE +.2% MTOW -.7% trip fuel + 2.7% take-off distance required - 16 % landing distance required -5 Figure 13. Comparison between DLR PrADO and ILR IPADS preliminary aircraft designs. parent aircraft. Compared to today s single-aisle aircraft, the estimated list price is approximately 2 % higher. This, however, seems realistic, since the reference aircraft features higher payload and higher range requirements then the A32 or 737 family, which again leads to e.g. higher design weights. The same is true for the estimated unit costs and the recurring costs per unit. Total non-recurring costs of 2.4 billion USD seem to be rather low when compared to other programs. However, this design does not consider any derivatives, which are common for aircraft families, but one single baseline design only. The same holds for the low targeted units during life cycle and for break-even. Other than for a technical assessment of a specific aircraft design, it is important to consider the entire aircraft family for a cost benefit analysis. In a case study, which follows later, the cost model is applied examplarily to the entire A32 family to show the benefits of the proposed model. Results show more realistic estimates regarding non-recurring costs and required units, other than for the single baseline aircraft. V. Sensitivities of the Proposed Model In the following section, the sensitivities of the proposed model towards selected parameters are discussed. The reference aircraft was used as baseline Table 5. Results of Cost Model for Reference Aircraft. for the presented sensitivity studies. The studies are Parameter Result Units structured into sensitivities of the model towards: Aircraft list price 9.2 m. 21-USD (A) program parameters, (B) aircraft design parameters, and (C) top-level aircraft requirements, and Aircraft unit costs 75.5 m. 21-USD are intended to show the main influences on the Non-recurring costs 2,428 m. 21-USD model. The aircraft is not re-sized for investigations Recurring costs 71.3 m. 21-USD of the sensitivities towards program parameters and Targeted units LC 713 aircraft design parameters, so that snowball effects from overall design synthesis do not impact the results. Units for break-even 224 The reference aircraft was only fully re-sized for capturing the sensitivities of the proposed model towards top-level aircraft requirements. Here, changes in top-level requirement first have to propagate through the entire design synthesis before an influence on the proposed model can be assessed. A. Program Parameters Program parameters are direct input for the proposed model, e.g. labor rates or targeted earnings, but they do not influence the aircraft design synthesis in any other way. The strongest sensitivities towards the program parameters are summarized in figure 14. Aircraft list price is determined only from overall aircraft design parameters, hence it shows no sensitivity towards the program parameters, cf. figure 14(a) - 14(d). 12 of 21

Results, % Results, % 25 2 15 1 5-5 -1-15 P A/C RC Q BE -2 NRC Q LC -25-25 -2-15 -1-5 5 1 15 2 25 Discount, % 25 2 15 1 5-5 -1-15 -2 (a) Sensitivities towards discount rates. -25-25 -2-15 -1-5 5 1 15 2 25 Labor Rates, % (c) Sensitivity towards labor rates. Results, % Results, % 25 2 15 1 5-5 -1-15 -2-25 -25-2 -15-1 -5 5 1 15 2 25 Earnings, % (b) Sensitivity towards earnings. 25 2 15 1 5-5 -1-15 -2-25 -25-2 -15-1 -5 5 1 15 2 25 Aircraft Communality, % (d) Sensitivity towards aircraft communality. Figure 14. Sensitivities of the cost model towards program parameters. The assumed discount rate mainly influences targeted units during life cycle and for break-even, see figure 14(a). For higher discounts, the margin for amortization of development and capital costs per unit becomes narrower, and thus more units have to be sold. The slight decrease in recurring cost is not directly caused by an increase in discount, but by the increase in targeted units. The more aircraft are produced, the lower are the production costs per unit. Sensitivities of the model are closely linear towards changes in discount rate. The model shows the same sensitivities towards changes in interest rate. The impact, however, is of a lower order since interest rates are usually also of a lower order then discount rates. Sensitivities towards changes in the targeted earnings are shown in figure 14(b). They also mainly influence the targeted units during life cycle and for break-even. The influence, however, is different for the two parameters. Whereas the targeted units during life cycle increase with higher earnings, the required units for break-even decrease. The increase in targeted units is caused by the fixed list price and the resulting lower acceptable unit costs. Recurring costs have to decrease, and thus more aircraft have to be produced. Break-even, however, is reached earlier for higher earnings, since the margin for amortization of program costs is higher as stated in equation 6. As shown in figure 14(c), labor rates have the strongest influence on the results. Non-recurring costs significantly increase with higher labor rates, recurring costs would have to increase accordingly. Since the proposed methodology assumes targeted recurring costs that are derived from equation 4, estimated recurring costs cannot increase as direct consequence of increased labor rates. Instead more targeted units are required for keeping recurring costs down despite higher labor costs. However, a non-linear increase also in recurring costs can be observed from figure 14(c). It is caused by changes in non-recurring costs and targeted units, 13 of 21

cf. equation 4. The impact of increased labor rates on targeted units and for break-even is high, due to the two discussed influences on non-recurring and recurring costs. Margins for cost amortization decrease for higher labor costs, and thus more aircraft have to be sold. Aircraft communality mainly influences the required non-recurring costs, see figure 14(d). For increased communality, the required non-recurring costs decrease. Simultaneously, less units have to be sold for breakeven and during the life cycle. Recurring costs are only slightly impacted by the decrease in targeted units. Communality is a useful factor for assessing entire aircraft families as it is later shown in the presented case study. B. Aircraft Design Parameters In a second step, sensitivities towards aircraft design parameters are discussed, see figure 15. Aircraft list price shows sensitivity to all parameters that are listed in table 2. Most of these parameters only influence aircraft list price and not the other cost items. For these parameters, the proposed model shows the same trends in its sensitivity. Thus, only one is exemplarily discussed here. It can be observed from figure 15(a) that the aircraft list price increases with increasing number of passengers. Since the aircraft list price is estimated from a total of 27 parameters, the sensitivity towards changes in one of them is of low order. Non-recurring costs are not influenced by a change in aircraft list price. For a higher list price and constant non-recurring costs, the acceptable recurring costs also increase, cf. equation 4. Thus, less units are required during life cycle and for break-even. Maximum operating speed (V M O) is only an input parameter for the non-recurring model. Thus, it only directly influences the estimated non-recurring costs but no other cost items as shown in figure 15(b). The non-recurring cost model by Roskam 7 uses the maximum operating speed as characteristic parameter for measuring the performance requirements of a design. Accordingly non-recurring costs increase with maximum operating speed. As discussed beforehand, more units are required for amortization if nonrecurring costs increase. Aircraft list price and non-recurring costs are not impacted by changes in component weights, see figure 15(c). In the model by Beltramo et al., 34 an increase in component weights would directly lead to an increase in estimated recurring costs for a fixed unit count. Since the acceptable recurring costs are determined from equation 4, they are only influenced slightly. Instead units that are required to keep the recurring costs down are increasing significantly as shown in figure 15(c). Both the sensitivities of units during life cycle and for break-even are non-linear, due to the exponential characteristic of equation 4. A change in maximum take-off weight directly impacts the estimated aircraft list price as well as the estimated non-recurring costs, see figure 15(d). The impact on list price is much higher than that shown in figure 15(a). Hence, propagation to recurring costs, as well as to required units during life cycle and for break-even is much stronger. These impacts, however, are superposed by the increase in non-recurring costs and its impact that was discussed beforehand for the example of changes in maximum operating speed. The influence of list price is much stronger, so that the required units decrease and the units for break-even almost stay constant. The sensitivity of both parameters is also non-linear. C. Top-Level Aircraft Requirements Finally, sensitivities towards changes in top-level aircraft requirements are discussed, see figure 16. Other than before, the reference aircraft is fully re-sized with IPADS according to the changes in top-level requirements before the cost model is applied. This allows for the changes in top-level requirements to propagate through the entire design synthesis. Hence, many aircraft design parameters are simultaneously influenced, and the trace back of single influences on the results of the proposed cost model is hardly possible. Both the increase in design payload and design range for example lead to a quasi inflation of the aircraft. Hence, masses (MTOW and component weights), dimensions or thrust requirements increase, whereas the performance (e.g. TOFL or LFL) degrades. The impact of changes in design payload and design range can be observed from figure 16. It is clearly non-linear and superposes the influence of changes in different design parameters. The presented sensitivity studies underline that the proposed model shows the required sensitivities towards important design parameters. Further, sensitivities are of correct order as well as of correct magnitude. Thus, merging of the single models into the proposed methodology seems reasonable. 14 of 21

Results, % Results, % 25 2 15 1 5-5 -1-15 P A/C RC Q BE -2 NRC Q LC -25-25 -2-15 -1-5 5 1 15 2 25 Passengers, % 5 4 3 2 1-1 -2-3 -4 (a) Sensitivities towards number of passengers. -5-25 -2-15 -1-5 5 1 15 2 25 Component Weights, % (c) Sensitivity towards component weights. Results, % Results, % 25 2 15 1 5-5 -1-15 -2-25 -25-2 -15-1 -5 5 1 15 2 25 VMO, % (b) Sensitivity towards maximum operating speed. 25 2 15 1 5-5 -1-15 -2-25 -25-2 -15-1 -5 5 1 15 2 25 MTOW, % (d) Sensitivity towards maximum take-off weight. Figure 15. Sensitivities of the cost model towards aircraft design parameter. Results, % 2 16 12 8 4-4 -8-12 P A/C RC Q BE -16 NRC Q LC -2-25 -2-15 -1-5 5 1 15 2 25 Design Payload, % (a) Sensitivities towards design payload. Results, % 2 16 12 8 4-4 -8-12 -16-2 -25-2 -15-1 -5 5 1 15 2 25 Design Range, % (b) Sensitivity towards design range. Figure 16. Sensitivities of the cost model towards top-level aircraft requirements. 15 of 21

VI. Case Studies In the following section, case studies are presented that show the application of the proposed model both to existing aircraft families as well as to overall design synthesis. A. Application to an Existing Aircraft Family In a first case study, the proposed cost model is applied to an existing aircraft family program for evaluation of costs and benefits. The authors choose to apply the model to the Airbus A32-family, since the single aircraft are well documented and verified in-house IPADS models are available. Results of the cost model for each aircraft are summarized in table 6. Close communality towards the A32 parent aircraft is assumed for the derivatives. No reliable data for verification of the cost items is available from literature. However, total non-recurring costs of 4.6 billion USD seem to be in the right order for a single-aisle program with a white sheet design baseline aircraft and three derivatives. For assumed earnings of 3 % the required units during life cycle result in 699 aircraft, break-even is achieved for 526 aircaft. Sparaco 5 states that at program start Airbus intended to sell only 6 aircraft of that family. Thus, the assumed earnings seem to be realistic for the given aircraft program. Today Airbus, however, has secured order of nearly 8, A32-family aircraft. Comparing the calculated net presented value for 6 aircraft with the one for 8, aircraft shows an increase in profitability of the program by a factor of 11. Table 6. Results of the Cost Model for the Airbus A32-family aircraft. Parameter A32-2 A318-1 A319-1 A321-2 Total family Units P A/C 67.7 63.4 64.6 74.4 m. 21-USD C A/C 65.7 61.5 62.6 72.2 m. 21-USD NRC A/C 1,96 771 792 1,5 4,598 m. 21-USD RC A/C 56.9 54.8 56.5 67.4 m. 21-USD Q LC 233 116 132 218 699 Q BE 188 91 99 148 526 Recently Airbus has officially launched the reengined NEO derivatives of its A319, A32 and A321 aircraft. Sparaco 5 states total non-recurring costs of approximately 1.5 billion USD for the NEO program, and Airbus 51 claims communality in airframe structure and systems of 95 % compared to todays A32-family aircraft. When neglecting small deviations in design parameters, such as changes in e.g. engine weight of the NEO aircraft, the proposed model can be used to assess profitability of the program. The same metrics as for the above discussed results were used to obtain the costs estimates that are listed in table 7. Further, a communality in airframe structure and systems of 95 % as well as entirely new engines were assumed. Estimated non-recurring costs of 1.56 billion USD match NPV, m. 21-USD 1 1 1 1 1 25 5 75 1 125 15 175 2 Units Figure 17. Estimated net present value for A32NEO program (logarithmic scale). those stated by Sparaco well. For targeted earnings of 3 % per aircraft, the program requires 28 aircraft for break-even. Targeted units during life cycle are estimated to approximately 45 aircraft. Already today Airbus has secured orders and commitments for nearly 1,2 NEO aircraft. 5 The estimated net present values of the program for different assumed units are shown in figure 17, which expressly underlines profitability of the program for Airbus. 16 of 21