Feasibility of Electrified Propulsion for Ultra-Efficient Commercial Aircraft Final Report

4 Modeling Approach

This section describes the analysis and optimization approach used to assess aircraft performance for different missions and propulsion architectures. The details of the subsystem models are provided in Appendix A. Extensions of the trade space analysis, to higher fidelity models for electric components and aircraft conceptual design, are discussed in Section 6.

4.1 Air Vehicle Design Trade Space Model A modular approach is taken to aircraft sizing and performance, as indicated schematically in Fig. 4.1, which shows the various subsystem models and the connections between them. The input variables to the configuration performance model are fuselage geometry, payload, range, and cruise speed – which define the overall mission – and energy source, propulsor load electrification and amount of BLI – which define the propulsion architecture.

Propulsive power Propulsor mass flow Propulsion Aero-Propulsive Energy electrification, f Airframe drag buildup S Propulsor electrification, f Amount of BLI System Model Performance Model L Fuel flow Battery power draw Lift-to-drag ratio Propulsion system mass Payload Fuselage geometry Aero-Structure Mission Range Wing loading Sizing Model Integration Airframe mass Cruise Speed Figure 4.1: Modular approach to electrified aircraft performance trade space analysis .

4.1.1 Mission Integration The overall vehicle fuel and battery energy consumption are found using an augmented Breguet range equation analysis for the general hybrid case with both fuel and battery energy storage. The fuel con- sumption is assessed assuming the fuel flow rate is proportional to the vehicle mass as fuel is consumed (e.g., for constant lift-to-drag ratio and thrust-specific fuel consumption). Under this assumption, the total mass of the vehicle is,   ˙ m fuel m ( t ) = m exp − t , (4.1) TO m where m is the takeoff mass at time t = 0. Integrating Eqn. (4.1) over a mission of range R at velocity TO V yields an expression for the total fuel consumption.

  m R ˙ m fuel fuel = exp − 1 (4.2) m − m V m TO fuel The electrical energy consumption is determined assuming the battery discharge rate is also proportional to vehicle mass (i.e., f is constant). The total battery energy consumption, E , is found using a similar S batt integration of Eqn. (4.1) over the mission.

   ˙ ( E / m ) R ˙ m batt fuel E = m 1 − exp − . (4.3) batt TO ( ˙ m / m ) V m fuel N ASA/CR—2019-220382 17 For a given mission, PSEC is proportional to the sum of the fuel and battery energy, which can be related to their masses through the battery specific energy and fuel heating value, E = E + E (4.4) total batt fuel = m BSE + m h . (4.5) batt fuel fuel Each configuration examined is sized for a single design point, with a takeoff mass, m , including TO empty airframe and propulsion system masses described below, battery and fuel energy storage mass, and a specified payload, m = m + m + m + m + m . (4.6) TO airframe prop batt fuel payload 4.1.2 Aero-Structure Performance and Sizing The airframe mass is estimated based on approximate sizing methods [ 15 ] for fuselage, wing, and tail areas, based on specified fuselage dimensions. The wing is sized for a specified wing loading, ( W / S ) , m TO S = , (4.7) wing ( W / S ) and the horizontal and vertical tail are sized as a function of the fuselage and wing size using tail volume coefficients.

The aircraft aerodynamic efficiency, characterized by the lift-to-drag ratio, L / D , is estimated as a function of the wing aspect ratio and ratio of wing area to total airframe wetted area, √ √ S L √ wing = K AR . (4.8) ( L / D ) D S wet The maximum aspect ratio for a given span is seen to always give the best performance; the performance can be calculated from a specified maximum span, b , and the wing area from Equation (4.7), max b max AR = . (4.9) S wing The wing sizing and performance formulation described in Equations (4.7)-(4.9) captures trades involving airframe weight and aerodynamic efficiency that are important in the sizing and overall per- formance of electric vehicles. For battery-powered systems, the increase in energy-to-power conversion efficiency over conventional gas turbine systems trades against the weight of the low energy-density energy storage and reduced vehicle aerodynamic efficiency. This is illustrated conceptually in Fig. 4.2.

The figure shows notional aero-structure sizing for equivalent vehicles with conventional and all-electric propulsion architectures. The all-electric vehicle weighs more than the conventional vehicle for the same mission, and for constant span and wing loading, this leads to decreased aspect ratio and lift-to-drag ratio.

4.1.3 Aero-Propulsive Performance The vehicle mass and aerodynamic performance are related to the propulsion system power require- ments using the power balance method [ 2 ] , which allows treatment of BLI using the unpowered air- frame performance. An integral form of the general power balance equation [ 8 ] is used to relate the N ASA/CR—2019-220382 18

Conventional All-Electric

Figure 4.2: Notional conventional and all-electric vehicle planform shapes, illustrating the effect of takeoff weight on wing and tail sizing .

propulsor mass flow and jet velocity to the unpowered airframe drag as a function of a specified bound- ary layer ingestion fraction, f , and ratio of profile drag to total drag for the unpowered airframe, BLI ′ ′ ( D / D ) , p ′ D m p TO ˙ m ( V − V ) = 1 − f . (4.10) jet ∞ BLI ′ L / D D The propulsion system power requirement, as characterized by the mechanical flow power, P , is equal K to the increase in mechanical energy imparted to the flow by the propulsor. It is calculated as a function of the propulsor mass flow, ˙ m , jet velocity, V , and the ingested dissipation in cases with BLI, jet m TO 2 2 P = ˙ m ( V − V ) + f f V , (4.11) K BLI surf ∞ jet ∞ 2 ( L / D ) where f is the fraction of the airframe dissipation occurring in the fuselage boundary layer (approx- surf imately 0.9 for attached turbulent boundary layers). Equations (4.10) and (4.11) are evaluated on a per-propulsor basis (see Appendix A) to determine the power requirements in distributed and partial turbo- or hybrid-electric architectures.

4.1.4 Geometry Constraints for BLI Configurations Constraints must also be included in the model to capture the aerodynamic trades of BLI. For example, a fan performing full fuselage BLI must be at least as large as the boundary layer. These constraints create an important trade in optimal fan size between BLI, and drag and weight. There are multiple ways to integrate propulsors to achieve BLI. Here, a ducted array of propulsors at the trailing edge performs wing BLI, a tail cone thruster performs full fuselage BLI, and two embedded fans perform partial fuselage BLI.

N ASA/CR—2019-220382 19 Wing BLI is subject to boundary layer height and spanwise geometry constraints. The fan diameter is set to be as large as the wing boundary layer thickness: 6 / 7 d ≥ δ = K c (4.12) fan wing δ 1 / 7 4 where K is 0.05 m .

δ The array of N fans must also extend along enough of the span to capture the specified wing BLI fan fraction, f : wing N d fan fan = f = 2 f (4.13) wing BLI,elec b − d fuselage For full fuselage BLI, the model requires a fan area greater than or equal to the estimated area of the Δ fuselage boundary layer, Δ . The fans are assumed to have a hub-to-tip ratio of 0.3, and = 4.9. The ∗ Θ ∗ boundary layer’s kinetic energy area, Θ , is related to its kinetic energy defect which can be expressed as a function of aerodynamic and BLI parameters described in Appendix A.

  ′ D f f surf BLI,fuselage d Δ p fan A = π ≥ Δ = (4.14) fan ∗ 1 2 Θ ρ V ∞ The partial fuselage BLI configurations are based on 40% fuselage BLI via embedded aft fuselage fans, as is the case for the D8. At relevant fan diameters, the boundary layer height is readily captured but the necessary breadth may not be. Optimization without boundary layer constraints mostly led to fan diameters that satisfied the following constraint: N d ≥ 0.5 d (4.15) fan fan fuselage The inequality 4.15 was not applied as a model constraint and was rather referenced as a guideline.

Section 5.1 discusses the treatment of a point design which did not meet this guideline. The drag and weight of nacelles of propulsors in an array were reduced by a factor of from the individually-podded π model described in Appendix A. This applies to wing BLI and embedded fuselage BLI propulsors.

4.1.5 Propulsion System Performance and Sizing Figure 4.3 shows a generalized propulsion system model, which can parametrically represent the range of conventional, turbo-electric, hybrid-electric, and all-electric configurations of interest. The inputs re- quired are the source and load electrification factors defined in Section 2.1, f and f , and the number S L of turboshaft or turbofan cores and motor-powered propulsors. A power balance between the compo- nents is used to relate propulsor flow power (Equation (4.11)) to the fuel flow and battery discharge rate required by the mission integration model.

The electrical components are characterized by technology-dependent power-densities and efficien- cies, as in Table 3.1. The turboshaft core and ducted fan propulsor performance are similarly character- ized in terms of specified thermal and adiabatic efficiency. Their sizing is based on a power-law scaling with mass flow (less than cube-square was found to agree better with available engine data), 1.2 m = K ˙ m , (4.16) fan fan fan 1.2 m = K ˙ m . (4.17) core core core (4.18) Estimate based on flat plate turbulent boundary layer.

5 ∗ From cubic spline boundary layer profile with wall slip velocity such that H = 1.75, a representative value for turbulent attached flow [ 2 ] .

N ASA/CR—2019-220382 20 Turboshaft Turbine-powered propulsor Motor/ × N e.fan Generator . . .

TMS Shaft power Rectifier/ Electric power Inverter Heat flow Inverter Battery Motor-powered propulsors Figure 4.3: Electrified propulsion system .

The core mass flow is calculated from the core specific power, P , sp P core m = . (4.19) core P sp Details of the propulsion system power balance and specified scaling parameters are provided in Ap- pendix A.

4.2 Geometric Programming The present aircraft configuration design model is formulated as a signomial program (SP), which can be solved using existing geometric programming methods. A geometric program (GP) is a non-linear optimization problem of the form, minimize g ( x ) , subject to f ( x ) = 1, i = 1, . . . , m , (4.20) i g ( x ) ≤ 1, j = 1, . . . , n j where the objective ( g ) and constraints ( f and g ) are formed from monomials and posynomials : 0 i j a a 1 2 a n f ( x ) = c x x . . . x , (4.21) 1 2 n K ∑ a a a 1, k 2, k n , k g ( x ) = c x x . . . x , (4.22) k n 1 2 k = 1 where c > 0 are positive constant parameters and x > 0 are positive design variables raised to real constant powers, a ∈  . In log-space, GPs are convex optimization problems, which means they can be solved without an initial guess for the optimal value of the design variables, and with a guarantee of either global optimality or proof of infeasibility, using fast and robust “off-the-shelf” solvers. Further, the sensitivities of the objective function, g , to the constant design parameters, c , are calculated as part of the solution, providing insight into the impact of design requirements, constraints, and assumptions on performance.

N ASA/CR—2019-220382 21 If the constant coefficients, c , in Equation (4.22) are allowed to be negative, g ( x ) becomes a sig- nomial , and the resulting SP can be solved via sequential solutions of GP approximations. Even more permissive signomial equality constraints can be treated using trust region methods. The benefit of allowing SPs is that it enables modeling of a broader range of functions encountered in engineering design; any analytic function can effectively be modeled by a signomial Taylor series approximation.

The drawback of SPs is that the guarantee of global optimality is lost, and appropriate initial guesses for variables in the signomial constraints are sometimes necessary to converge on a solution. Most functional relationships encountered in engineering design can be cast as GP or SP constraints, i.e., as relationships between products of design variables raised to constant powers. In many cases, depending on the objective function, the impact of signomial equalities can be adequately modeled as GP inequality constraints that are always active; when this is not possible, addition of a small number of well-formed signomial constraints can still yield a robust SP model.

The model described here is implemented in GPkit [ 16 ] , an open source Python package for creat- ing, manipulating, and solving GP and SP models. GPkit leverages Python’s object-oriented framework to enable modular development of multi-disciplinary models from constituent component models with varying levels of fidelity. Another practical benefit in formulating the configuration model as an opti- mization problem is that the existing solution algorithms provide an iteration procedure for solving the entire system of equations. In other words, the optimization framework eliminates the need for “in- puts” and “outputs” for each of the subsystem modules, allowing simultaneous solution of the system of non-linear constraints.

4.3 Baseline Missions To span the space of aircraft sizes and missions, four baseline missions were defined for initial assessment with different electrified architectures. Table 4.1 lists the specified design payload, range, cruise speed, and altitude, and Figure 4.4 shows the nominal sizing and configurations. Additional details of mission- specific design parameters, e.g., fuselage dimensions and wing loading, are provided in Appendix A.

The results in Section 5 consider optimized electrified propulsion architectures for each of the baseline missions with different technology assumptions and the sensitivity of performance to variations in both payload and range.

4.4 Trade Space Exploration 4.4.1 Propulsion System Configurations In addition to aircraft mission and technology level, attributes of the propulsion system must be specified in order to define an aircraft design and evaluate its performance (i.e. its PSEC). Many attributes are treated as optimizable parameters within the GP framework (e.g., gas generator size, electric component size, battery capacity, propulsor size, electric propulsor count, and BLI fraction). However, some aircraft Table 4.1: Baseline missions Mission Payload Range Cruise Speed Cruise Altitude (passengers) (nmi) (ft) Thin Haul 20 500 150 knots 20,000 Regional 80 1,500 Mach 0.785 35,000 Medium Haul 180 3,000 Mach 0.785 35,000 Long Haul 350 6,000 Mach 0.840 35,000 N ASA/CR—2019-220382 22 Thin Haul Regional Long Haul Medium Haul Figure 4.4: Notional vehicle sizing for baseline missions with conventional propulsion .

attributes are discrete and must be specified a priori (e.g., propulsion system architecture, gas generator count, propulsor integration, and BLI and battery presence).

This motivates the concept of a configuration, which constitutes the minimum set of decisions needed to assess aircraft performance. A configuration (i) consolidates the discrete attributes of a propulsion system and (ii) samples a subset of the trade space by converging to the best-performing point within the range of optimizable attributes. Trade space exploration consists of selecting config- urations, evaluating their performance, and compiling the best-performing outputs. Figure 4.5 shows sample configuration sketches that illustrate the discrete attributes of two configurations.

4.4.2 Exploration Rationale To summarize the considered trade space, a conceptual two-dimensional test matrix is developed. One dimension of the matrix describes the baseline missions (thin haul, regional, etc.) and the other gives architecture classifications (conventional, turbo-electric, and all-electric). Any given “cell” in the ma- (a) (b) Figure 4.5: Sample configuration sketches and component legend for (a) B737-like conven- tional aircraft with under wing turbofans, (b) STARC-ABL-like turbo-electric aircraft with under wing turbofans and generators powering a BLI tail cone thruster.

N ASA/CR—2019-220382 23 trix may represent many configurations. The intent is to populate the cells with point designs that correspond to best-performing configurations.

Since electrification allows for more varied configurations, the architecture classifications capture parts of the trade space of different sizes. The conventional baseline classification represents the contin- uation of contemporary aircraft design and contains only one configuration. The advanced conventional case allows for novel non-electric configurations with the assumption that non-electric configurations preclude substantial propulsion distribution. This space includes more than one configuration, but the D8 conceptual design was identified as a representative configuration. This decision was also based on a performance comparison between partial fuselage BLI and tail cone fuselage BLI.

The electrified architecture classifications reflect the wider trade space: wing and fuselage BLI are possible, electric fan size and count may vary, batteries may be included, turbo-electrics may have turbofans (partial turbo-electric) or turbogenerators (full turbo-electric), and so on. Figure 4.6 presents a set of configurations assembled from combinations of architectures and attributes; these configurations will be considered in determining the best performing configuration.

These configurations are not exhaustive and there are assumptions and constraints that stem from limitations in the current model’s implementation. Specifically: • Only tube-and-wing airframes are considered.

• All mechanical fans in a design are the same size.

• All electrical fans in a design are the same size.

• Only ducted fans are considered.

• Distributing propulsion on the wing implies wing BLI via a ducted array of fans at the trailing edge. Propulsors fully embedded in the wing without BLI are not considered.

• Fuselage BLI is achieved via a tail cone thruster (full), or two embedded fans (partial).

• Fuel-burning configurations have two cores.

N ASA/CR—2019-220382 24 (a) Turbo-electrics * (i) (ii) (iii) Full turbo-electric n n (iv) (v) (vi) Partial turbo-electric n n (vii) (viii) *all turbo-electrics may also utilize a battery (not represented) n n n n (b) All-electrics (ix) (x) (xi) n n Figure 4.6: Electrified configurations considered in trade space assessment (see legend in Figure 4.5).

N ASA/CR—2019-220382 25

5 Trade Space Analysis

5.1 Propulsion Configuration Studies 5.1.1 Configuration Selection The analysis described above combined the configurations that were identified with the baseline mis- sions, and identified the best performers in terms of PSEC. For turbo-electrics, configuration (iii) per- formed best for the thin-haul mission and configuration (viii) did so for all other missions. Within the all-electrics, configuration (xi) performed best for all missions. Table 5.1 describes the architecture classifications and the best-performing configuration within each one.

In the case of a configuration (viii) aircraft flying a thin-haul mission, the mechanical fan diameters optimized to zero. This violated inequality 4.15. Since fuselage BLI was treated as a discrete choice, the trade in fan size and BLI benefit was not captured. To exclude the non-physical result of BLI with zero- diameter fans, full turbo-electric designs were selected as the best-performing over partial turbo-electric for thin-haul missions.

5.1.2 Performance with Optimistic 2035 Technology Level Figure 5.1 presents the minimum PSEC attained by optimized designs for each mission and architecture.

The percentage reductions in PSEC relative to the conventional baseline are noted above the bars for other architectures.

Comparing the minimum-PSEC design from the selected configurations between architectures shows Table 5.1: Summary of architecture classifications (columns of test matrix) Architecture classification Description Best-performing configuration Conventional (Baseline) Turbofans only Two podded turbofans BLI turbofans, no distribution Two embedded turbofans, 40% fuselage BLI.

Advanced Conventional Turbofans or turbo-generators Thin-haul: fully turbo-electric with wing BLI Turbo-electric powering electrical fans Larger classes: Partial turbo-electric with wing BLI BLI and electrical distribution Two turbofans with generators, 40% fuselage BLI Battery-powered electrical fans All-electric Fully turbo-electric with wing BLI BLI and distribution Figure 5.1: Productivity-Specific Energy Consumption (PSEC) versus mission and architec- ture; design range.

N ASA/CR—2019-220382 27 a hierarchy of performance. Advanced conventional (non-electric partial fuselage BLI) and turbo- electric demonstrate a PSEC reduction benefit of approximately equal magnitude, 12-27%. The all- electric designs are not feasible at any scale because the required battery mass is larger than the airframe parameters can support.

Although all-electric is non-competitive for the design missions, reducing the mission range so the all-electric aircraft designs close allows an assessment of the architecture. Figure 5.2 presents the min- imum PSEC for each combination of architecture and mission, where each mission is the maximum range at which the all-electric architecture closes.

Electrification on batteries alone decreases PSEC by 15% for a reduced thin haul mission compared to conventional aircraft, but offers no benefit for the other missions. Advanced and turbo-electric aircraft maintain performance improvements, though the benefit decreases with reduced mission length. Both trends are the result of the logarithmic nature of fuel-burning range. Specifically, conventional aircraft get lighter throughout the mission, requiring less power. Battery-powered flight does not share this advantage. All else equal, shorter ranges reduce the benefits of losing mass in flight and increasing overall efficiency, as seen in the decreased performance of advanced and turbo-electric architectures relative to design missions.

As context for the subsequent discussions, it is important to note that, as might be expected, the accuracy of the results depend on the fidelity of the physical models used. Some of the models, for ex- ample that used for the aero-structural sizing, are rudimentary and not meant to represent performance predictions of specific vehicle designs over large ranges of parameters. The results should therefore be viewed as a comparison of propulsion architectures within a given mission class , where the consistency of the modeling assumptions allows an appropriate comparison. Even with these limitations, however, the electrification trends are consistent across a wide range of missions; this, in turn, suggests the results are broadly applicable. Further, the framework can be extended to include higher-fidelity models, as described in Section 6.2, to allow more accurate assessment of specific configurations if desired.

5.1.3 Performance with Conservative 2035 Technology Level Reducing the technology level parameters to conservative 2035 values markedly reduces the space of beneficial electric designs. All electrics remain infeasible. Turbo-electric architecture still reduces the baseline PSEC but offers no benefit over advanced conventional due to the greater mass penalty from motors and power electronics. Partial turbo-electric designs optimize to f = 0 (i.e. the advanced L conventional architecture). The benefit of the full turbo-electric thin-haul design decreases to 19% from Figure 5.2: Productivity-Specific Energy Consumption (PSEC) versus mission and architec- ture; range reduced to make all-electric architecture feasible.

N ASA/CR—2019-220382 28 24%, offering 2% less energy benefit than the corresponding advanced conventional design. Advanced and baseline conventional aircraft are unaffected by the decreased electric technology level.

5.1.4 Minimum Battery Technology Level Increasing the battery technology level allows the all-electric designs to close at increased range. Fig- ure 5.3 lists the minimum BSE for an all-electric to close for design missions. At a minimum, the required BSEs are 60% greater than the optimistic 2035 value; batteries alone are unlikely to power aircraft at current design missions.

5.1.5 Features of Efficient Electrified Aircraft The best-performing electrified aircraft have highly-distributed propulsion and BLI, as reflected in propul- sor arrays with many ( > 250) small ( < 12 inch) fans. Table 5.2 summarizes the main propulsion system parameters for these best-performers, indicating the high degree of distribution. Partial turbo-electric designs minimize PSEC for regional missions and longer, while full turbo-electrics do so for thin haul missions. The PSEC benefit stems from two synergistic effects of distribution: (i) the mass scaling, which favors smaller propulsors, and (ii) the aero-propulsive performance improvement from BLI. The configurations with distributed propulsion are also aided by the reduction in nacelle mass and drag from propulsor arrays.

The reported optimized designs bound the benefits found in the study. However, practical consider- ations may preclude full wing BLI and hundreds of fans. Limiting the fan count results in smaller PSEC reductions, as in Figure 5.4, which compares a 24-fan thin-haul turbo-electric design with the conven- tional baseline. For a turbo-electric thin-haul aircraft, the PSEC reduction shrinks from 25% to 13%.

This is an improvement over the conventional baseline, but it is less than the conventional advanced configuration, which reduced PSEC by 21%.

5.1.6 Trends and Main Trade of Distributed Propulsion The propulsor scaling laws imply that decreases in size result in less weight per unit mass flow. The highly-distributed systems, however, have heavier, electrified propulsion components. Figure 5.5 il- lustrates the system level performance trends as an advanced conventional concept is electrified with the addition of wing BLI. The quantities shown are overall performance (PSEC), aero-propulsive perfor- mance (propulsive efficiency and effective lift-to-drag ratio), and propulsion system mass all as functions of the fraction of electrical distribution on the wing.

Figure 5.3: Minimum BSE required to close all-electric architecture at design missions.

N ASA/CR—2019-220382 29 Table 5.2: Propulsion system parameters for minimum PSEC point designs Mechanical Fans Electrical Fans Mission f f S L N d (in) f N d (in) f fan BLI,m fan BLI,e Thin-haul 0 1 2 − 0 254 4.5 0.5 (20 pax, 500 nmi) Regional 0 0.55 2 31 0.2 248 3.8 0.5 (80 pax, 1500 nmi) Medium-haul 0 0.48 2 45 0.2 308 4.1 0.5 (180 pax, 3000 nmi) Long-haul 0 0.43 2 86 0.2 296 7.3 0.5 (350 pax, 6000 nmi) Turbo-Electric Thin-Haul Transport Concept Conventional Baseline PSEC = 5.77 kJ/kg-km ( -13% ) PSEC = 6.59 kJ/kg-km Gross takeoff weight = 4530 kg Gross takeoff weight = 4490 kg Payload = 1950 kg Payload = 1950 kg Range = 500 nmi Range = 500 nmi Cruise speed = 150 kt Cruise speed = 150 kt Number of fans = 24 Number of engines = 2 Fan diameter = 10.0 in Fan diameter = 30.9 in Motor power = 1.80 kW Core power = 256 kW Propulsion system mass = 421 kg Propulsion system mass = 363 kg Fuel mass = 242 kg Fuel mass = 277 kg Figure 5.4: Moderately-distributed fully turbo-electric concept for thin haul mission com- pared to conventional baseline; fan count specified prior to optimization.

The propulsion system mass increases as electrical equipment is added due to the growing electric components. There is a shrinking propulsor mass, which decreases by 44% from full distribution, f = wing 0 to 1. The distribution-enabled BLI improves the propulsive efficiency, η , by 2 percentage points and p the effective lift-to-drag ratio, C / C by 30%. The aero-propulsive effects have a larger effect than L Φ , AC the added mass, netting a benefit in fuel burn.

This trade of weight and efficiency is sensitive to the considered parameter space. As discussed in Section 5.1.4, lower electric technology level decreases the PSEC benefit such that the turbo-electric configuration underperforms relative to the advanced conventional architecture. There are analogous engineering constraints that can limit the benefit of distributed BLI. For example, imposing a minimum fan size may reduce and even negate the aero-propulsive BLI benefits. Figure 5.6 demonstrates how a N ASA/CR—2019-220382 30 3.650 3.625 Productivity Specific Energy, 3.600 Consumption, PSEC [ kJ / kg-km ] 3.575 3.550 0.880 0.875 0.870 Propulsive Efficiency, η p 0.865 0.860 Effective lift-to-drag ratio, C / C L Φ ,AC Propulsion system mass, m [ kg ] prop 0.0 0.2 0.4 0.6 0.8 1.0 N d fan,e fan,e Wing BLI fraction, f = 2 f = wing BLI,e b − d fuse Figure 5.5: Medium haul advanced conventional aircraft is electrified via wing BLI propul- sors (partial turbo-electric); system parameters as a function of electric distribution.

minimum fan size constraint reverses the trend of fuel burn benefit with greater BLI. The figure shows, as the wing BLI fraction increases, fans shrink until they reach the specified minimum size (6 inches).

For f ≥ 0.52, the marginal benefit of distributing decreases, resulting in a shallower fan count slope.

wing The marginal benefit becomes negative at f = 0.7 and PSEC increases with further distribution.

wing This behavior highlights boundary layer height considerations for BLI since these constraints often drive electric fan size (Section 4.1.4).

N ASA/CR—2019-220382 31 5.60 5.55 Productivity Specific Energy, Consumption, PSEC [ kJ / kg-km ] 5.50 5.45 5.40 Number of electric fans, N fan,e 8.0 7.5 Electric fan diameter, d [ in ] fan,e 7.0 6.5 6.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 N d fan,e fan,e Wing BLI fraction, f = 2 f = wing BLI,e b − d fuse Figure 5.6: Performance and fan parameters of full turbo-electric, thin-haul design as a function of distribution, with minimum fan size constraint ( d ≥ 6 in.).

fan, e 5.1.7 Propulsion Configurations Summary Turbo-electric architectures offer the lowest PSEC across all design missions via fully turbo-electric con- figuration (iii) for thin haul missions and partial turbo-electric configuration (viii) for all other missions.

The advanced conventional architecture decreases PSEC by similar amounts. An all-electric architec- ture cannot fly any of the design missions due to the battery weight. Reduced mission length allow the all-electric designs to close, but only offer PSEC reduction benefit for the thin-haul mission. Since the all-electric architecture is non-competitive with turbo-electric or advanced conventional architectures outside of highly-reduced ranges, Section 5.2 discusses battery-powered flight in this corner of the trade space.

5.2 Mission Studies An objective of the current work was to determine the relation between mission (defined here as a combination of payload and range) and electrified aircraft performance. Two important questions to be answered were: (i) for what missions are electrified aircraft feasible, and (ii) for what missions might electrified aircraft provide a reduction in PSEC relative to an equivalent conventional aircraft?

In this section the results of a mission-related trade space analysis is presented. It should be noted N ASA/CR—2019-220382 32 that the aircraft considered take advantage of highly distributed architectures which facilitate high levels of boundary layer ingestion (BLI). The number of fans and fraction BLI used in this section is believed to be in line with determining the best possible performance that can be achieved by electrified aircraft, although these numbers of fans are not necessarily desirable from a practical standpoint.

5.2.1 Thin-Haul: All-electric Figure 5.7 shows PSEC and takeoff mass data for an all-electric thin-haul aircraft as a function of range, for the optimistic 2035 technology assumptions described in Section 3.

For this case, the range of the aircraft had to be reduced to 300 nmi for the design to be feasible.

Over the ranges shown in Fig. 5.7 there is a reduction in PSEC for all the levels of BLI. The maximum reduction in PSEC is achieved at a range of about 100 nmi, although this is a flat minimum and a reduction on the order of 50% is predicted for ranges between 50 and 200 nmi with 50% BLI and only slightly less with no BLI. For this aircraft class, increasing BLI also increases the feasible range of the aircraft; the maximum feasible range goes from 240 nmi (no BLI) to 300 nmi (50% BLI).

Figure 5.7 also shows that the aircraft weight increases rapidly with range due to the battery weight becoming a larger fraction of the total weight. As an example, at the range of maximum PSEC reduction (100 nmi) the all-electric aircraft is 10% heavier than the conventional aircraft sized for the same range and at the maximum feasible range (300 nmi) it is 45% heavier. This increase is slightly diminished with BLI.

For the conservative 2035 technology assumptions, this aircraft is only feasible up to 60 nmi with 50% BLI, and is thus not shown.

Figure 5.7: PSEC and takeoff mass versus range for all-electric thin-haul aircraft; BSE = 900 W · h / kg, [ P / m ] = 16 kW / kg, [ P / m ] = 19 kW / kg, f = 1, f = 1; N = 146, mot conv S L fan E d = 0.12 m.

fan E N ASA/CR—2019-220382 33 5.2.2 Thin-Haul: Turbo-electric Figure 5.8 shows PSEC and takeoff mass as a function of range for a fully turbo-electric thin-haul aircraft for the optimistic 2035 technology assumptions.

It was shown in Section 4.4.2 that the fully turbo-electric architecture ( f = 1) gives the lowest PSEC L for the thin-haul and was thus used for the current analysis. Figure 5.8 shows that over the entire range considered this architecture results in a reduction in PSEC of about 25% when 50% BLI is employed and about half of that with no BLI. The turbo-electric architecture also slightly reduces the takeoff mass compared to the conventional, even without the benefit of BLI.

With the conservative 2035 technology assumptions, a reduction in PSEC is only obtained if BLI is used and there is no change in takeoff mass.

5.2.3 Thin-Haul: Hybrid-electric For the results in this section, the source electrification factor f was optimized for minimum PSEC. The S load electrification was fixed at f = 1, meaning that all flow power is provided by electrically powered L fans.

The result of sweeping over range while optimizing f is shown in Figure 5.9. When 0 < f < 1 S S the configuration is a hybrid-electric and the energy required to produce propulsive power comes from both fuel and batteries. Such a design could be instantiated by using a fuel-powered turbo-generator to supply some electric power to the propulsive fans, with the remaining fraction supplied by a battery.

Figure 5.9 shows a summary of thin-haul aircraft behavior. For low ranges, all-electric architecture ( f = 1) results in the lowest PSEC, but for the higher ranges the all-electric is no feasible, and turbo- S electric architecture ( f = 0) has better PSEC performance. Over a small intermediate range, hybrid- S electric architecture with an energy split between fuel and batteries is optimal. The effect of BLI is to improve the all-electric and hybrid-electric performance, shifting the transition region to the right.

Figure 5.8: PSEC and takeoff mass versus range for turbo-electric thin-haul aircraft; [ P / m ] = 16 kW / kg, [ P / m ] = 19 kW / kg, f = 0, f = 1; N = 254, d = mot conv S L fan fan E E 0.071 m.

N ASA/CR—2019-220382 34 Figure 5.9: PSEC and source electrification factor f versus range for thin-haul aircraft; S [ P / m ] = 16 kW / kg, [ P / m ] = 19 kW / kg, f = 1; N = 254, d = 0.071 m.

mot conv L fan fan E E For the conservative 2035 technology assumptions the all-electric design is infeasible for ranges greater than 60 nmi and a hybrid-electric investigation is therefore not shown for those assumptions.

5.2.4 Thin-Haul: Payload sensitivity Another mission-related parameter is payload weight. The sensitivity of PSEC to variations in payload weight was assessed for design payload of 14, 17, and 20 passengers. Figure 5.10 shows the results for all-electric and turbo-electric architectures.

For the all-electric, PSEC is insensitive to the number of passengers over most of the range, except at the highest ranges where some benefit is achieved by carrying fewer passengers. This insensitivity to payload can be explained as follows. By reducing the number of passengers the aircraft weight and energy requirement is reduced, but the reduction in payload has a negative effect on PSEC and these two effects nearly balance. At higher ranges where a large fraction of the aircraft weight is battery weight, the reduction in energy required outweighs the reduction in productivity leading to a slight reduction in PSEC.

For the turbo-electric case the PSEC is insensitive to the number of passengers over the entire range considered, with the same trend observed for the conservative 2035 technology assumptions.

5.2.5 All-electric: All classes The trends observed for the larger aircraft classes are similar to the thin-haul aircraft and will thus not be shown in the same level of detail.

The relative PSEC benefit compared to the baseline conventional aircraft is shown for all-electric aircraft for all classes with the optimistic 2035 assumptions in Fig. 5.11. The all-electric aircraft only provide a substantial PSEC reduction at low ranges. The PSEC benefit for medium- and long-haul aircraft are very nearly equal even though these aircraft differ considerably in size. For ranges higher than those for the minimum PSEC, battery and thus aircraft weight grows so fast that the efficiency benefits of all-electric architectures are negated and the PSEC benefit drops rapidly.

N ASA/CR—2019-220382 35 , , Figure 5.10: PSEC versus range for all-electric and turbo-electric thin-haul aircraft with various payloads; BSE = 900 W · h / kg, [ P / m ] = 16 kW / kg, [ P / m ] = 19 kW / kg, mot conv f = 0.5; all-electric with N = 146, d = 0.122 m; turbo-electric with f = 1, BLI fan fan L E E E N = 254, d = 0.071 m.

fan fan E E For the conservative 2035 technology assumptions, even with 50% BLI, all-electric architecture is only feasible for very low ranges: 60 nmi for thin-haul, 130 nmi for regional and 200 nmi for medium- and long-haul. For these technology assumptions, none of the larger classes lead to a PSEC benefit over the ranges for which they are feasible.

5.2.6 Turbo-electric: All classes Figure 5.12 shows the PSEC benefit as a function of range for turbo-electric aircraft for all classes with the optimistic 2035 assumptions. The thin-haul is a fully turbo-electric, but the larger classes are partial turbo-electric with approximately 50% of the flow power coming from a conventional turbofan ( f ≈ L 0.5), as was found optimal in Section 4.4.2. A PSEC benefit of up to 25% is found for the thin-haul, 13% for the regional class, 15% for the medium-haul and 27% for the long-haul aircraft. All architectures provide a PSEC benefit over the ranges considered and the PSEC benefit increases with aircraft design range.

For the conservative 2035 technology assumptions, the PSEC benefit is reduced approximately 2%, shifting all the curves in Fig. 5.12 downwards.

5.2.7 Hybrid-electric: All classes Figure 5.13 shows the optimal load electrification factor, f , and the PSEC reduction, relative to a S conventional aircraft sized for the same mission, as a function of range for all classes considered. For all N ASA/CR—2019-220382 36 Figure 5.11: Relative PSEC benefit for all-electric aircraft for all classes; BSE = 900 W · h / kg, [ P / m ] = 16 kW / kg, [ P / m ] = 19 kW / kg, f = 0.5; f = 1, f = 1; thin-haul mot conv BLI S L E with f = 0; N = 146, d = 0.122 m; regional with f = 0.2; N = 98, BLI fan fan BLI fan M E E M E d = 0.246 m; medium-haul with f = 0.2; N = 94, d = 0.343 m; long-haul fan BLI fan fan E M E E with f = 0.2; N = 118, d = 0.464 m.

BLI fan fan M E E classes the load electrification factor is set to f = 1, meaning all flow power is provided by electrically L powered fans.

The transition from all-electric to turbo-electric occurs in the same manner, but at higher ranges, for the larger classes as for the thin-haul. Reducing f from unity has the benefit of extending the feasible S range of aircraft to higher ranges than all-electric architecture can achieve.

As f transitions from one to zero the PSEC benefit reduces and levels off at about 8% for the larger S classes and 22% for thin-haul. This effect occurs because PSEC is much less sensitive to range for turbo-electrics than for all-electrics.

Parallel hybrid-electric architectures were found to provide a PSEC reduction similar to series hybrid architectures for a given mission.

All-electrics are only feasible for ranges less than 60 nmi with the conservative 2035 technology assumptions, and they were therefore not considered for the hybrid-electric study.

5.2.8 Mission Trade-Space Analysis Summary All-electric aircraft are only feasible for ranges shorter than those for existing commercial aircraft. The maximum feasible range with optimistic 2035 battery and electrical machine technology assumptions are 300 nmi for thin-haul, 700 nmi for regional jet, 930 nmi for medium-haul and 940 nmi for long- haul aircraft. With the conservative 2035 technology assumptions, the feasible ranges are reduced even further to 60 nmi for thin-haul, 130 nmi for regional, and 200 nmi for medium- and long-haul.

For turbo-electric configurations, there are reductions in PSEC relative to conventional for all classes and ranges considered, both with optimistic 2035 and conservative 2035 technology assumptions. The magnitude of the benefit is much less sensitive to range than that of all-electric architectures. Addi- tionally, the benefit increases with range for all classes with partial turbo-electric architectures. This N ASA/CR—2019-220382 37 Figure 5.12: Relative PSEC benefit for turbo-electric aircraft for all classes; [ P / m ] = mot 16 kW / kg, [ P / m ] = 19 kW / kg, f = 0.5; thin-haul with f = 1, f = 0; N = conv BLI L BLI fan E M E 254, d = 0.071 m; regional with f = 0.55, f = 0.2; N = 248, d = 0.097 m; fan L BLI fan fan E M E E medium-haul with f = 0.48, f = 0.2; N = 308, d = 0.104 m; long-haul with L BLI fan fan M E E f = 0.43, f = 0.2; N = 298, d = 0.185 m.

L BLI fan fan M E E insensitivity to range might have advantages if off-design and fleet-wide considerations are taken into account, since different aircraft in a fleet will likely fly different ranges. Turbo-electric architectures appear to be the best choice for electrified propulsion for missions similar to those of conventional commercial aircraft.

The range-extending property of a turbo-generator added to an all-electric configuration, i.e., a hybrid-electric architecture, allows the efficiencies of aircraft with high source-electrification to be achieved at larger ranges than an all-electric architecture. Hybrid architecture provides no benefit at larger ranges because the efficiency benefits of the battery trades against the low energy density of bat- teries (relative to hydrocarbon fuel), and turbo-electric architectures are optimal for ranges not much larger than the maximum feasible all-electric range. There is thus a narrow intermediate band of short ranges at which hybrid-electric provides a PSEC benefit. Both series and parallel architectures provide approximately the same benefits compared to conventional propulsion.

5.3 Electric Component Technology Studies In this section, we examine the effect of technology level on the feasibility and performance of electri- fied aircraft, to quantify the benefits as technology improves. All-electric aircraft have been shown to be feasible only at reduced ranges for all sizes; to illustrate the effects of electrified propulsion for all ar- chitectures, we assess the performance of a reduced-range thin-haul aircraft as a function of technology parameters.

The baseline conventional aircraft, which carries 20 passengers over a range of 100 nmi, is assumed to be powered by two mechanically driven fans without BLI ( f = 0, f = 0, and f = 0). The S L BLI M all-electric aircraft ( f = 1 and f = 1) flies the same mission. It is assumed that electrification enables S L distributed propulsion (DP) and boundary layer ingestion (BLI). Battery effects (BSE and BSP) and N ASA/CR—2019-220382 38 Figure 5.13: Relative PSEC benefit for hybrid-electric aircraft for all classes; [ P / m ] = mot 16 kW / kg, [ P / m ] = 19 kW / kg, f = 0.5; f = 1; thin-haul with f = 0; N = conv BLI L BLI fan E M E 254, d = 0.071 m; regional with f = 0.2; N = 248, d = 0.097 m; medium- fan BLI fan fan E M E E haul with f = 0.2; N = 308, d = 0.104 m; long-haul with f = 0.2; N = BLI fan fan BLI fan M E E M E 298, d = 0.185 m.

fan E other component effects (specific powers of motors and converters) are considered separately. When one set of parameters is varied, the other technology parameters are set at the optimistic 2035 values from Section 3.4.

5.3.1 Effects of Battery Technology For a reduced-range 100 nmi mission, the all-electric aircraft is not feasible at current and conservative 2035 battery technology. Figure 5.14 shows the effect of increasing BSE (and with it, BSP) on PSEC.

The conventional aircraft has a constant PSEC as BSE varies because it carries no batteries. In terms of configuration, the closest all-electric aircraft has two electric fans and no BLI. When the BSE is under 350 W · h / kg, this all-electric aircraft is infeasible. Between 350–400 W · h / kg, the all-electric aircraft becomes feasible, but it requires more energy than the conventional aircraft. As BSE increases further, the battery mass to carry the mission energy decreases, leading to a sharp drop in the PSEC. For the optimistic 2035 battery technology assumptions, the all-electric aircraft consumes about 37% less energy than the conventional aircraft. At higher BSE values, the PSEC curve flattens out, due to the battery mass becoming a smaller fraction of the aircraft takeoff mass, and further increases in BSE provide diminishing benefits in energy consumption.

The all-electric aircraft becomes more beneficial with a greater number of smaller-diameter fans.

With distributed propulsion, the all-electric aircraft with more fans becomes feasible at lower BSE values.

It also provides a larger PSEC reduction at a given BSE value. For the optimistic 2035 battery technology assumptions, the 20-fan all-electric aircraft provides a PSEC benefit of about 40% over the conventional.

As with increasing BSE, however, increasing DP has diminishing returns: going from 20 fans to 100 fans provides less benefits than going from two to 20.

Figure 5.15 shows the range of propulsor configurations available for the all-electric aircraft by N ASA/CR—2019-220382 39   Conventional, 2 fans, no BLI    2 fans 2 0    All-electric , no BLI    Current Tech Optimistic 2035 Conservative 2035                  Figure 5.14: Effect of battery technology on PSEC with DP for 100 nmi all-electric thin-haul aircraft; [ P / m ] = 16 kW / kg, [ P / m ] = 19 kW / kg, f = 1, f = 1.

mot conv S L varying the number of fans and BLI. At optimistic 2035 battery technology, the all-electric aircraft with 2 fans and no BLI consumes less energy than the conventional baseline. When the design space is opened up to include massive distribution of fans and BLI, the benefits are twofold: (i) the aircraft becomes feasible at smaller BSE values, and (ii) it offers even greater PSEC reduction at a given BSE value. It can also be seen that all-electric aircraft are feasible at reduced ranges within the predicted BSE numbers.

Further, they provide a PSEC benefit over conventional aircraft, and this benefit increases with DP and BLI.

5.3.2 Effects of Component Specific Power Figure 5.16 shows the effects of increasing component (motors and inverter) specific powers on PSEC.

All-electric aircraft are feasible and beneficial over conventional aircraft even with current technology (although BSE and BSP are still set to optimistic 2035 values). Again, the conventional aircraft has a constant PSEC as component specific powers improve, since it does not carry any converters or motors.

For the all-electric aircraft, PSEC improves as specific powers increase. Even with 2 electric fans, current technology already provides a benefit of about 25% over conventional. At conservative and optimistic 2035 values, this benefit increases to 28% and 30% respectively.

With DP enabled, the all-electric aircraft provides even greater PSEC benefits, however, with dimin- ishing returns. Going from 2 fans to 20 provides a PSEC benefit of about 3%, whereas going from 20 fans to 100 fans only provides a 2% further improvement for conservative 2035 numbers.

Figure 5.17 also shows the effect of DP and BLI on PSEC. At conservative 2035 values, an all-electric aircraft with 2 fans and no BLI offers a PSEC reduction of about 42% over conventional, which increases to 48% with 100 fans and 50% BLI. Little benefit is obtained for values higher than 8 kW / kg since the components’ mass make up an increasingly smaller fraction of the aircraft takeoff mass. The flattened PSEC curve also suggests that the metric is less sensitive to component specific powers than it is to N ASA/CR—2019-220382 40   Conventional, 2 fans, no BLI      All-electric , 2 fans, no BLI   All-electric , 100 fans, 50% BLI   Current Tech Optimistic 2035 Conservative 2035                  Figure 5.15: Effect of battery technology on PSEC with DP and BLI for 100 nmi all-electric thin-haul aircraft; [ P / m ] = 16 kW / kg, [ P / m ] = 19 kW / kg, f = 1, f = 1.

mot conv S L   C onventional, 2 fans, no BLI     2 fans  20 All-electric , no BLI     Optimistic 2035 Conservative 2035 Current Tech            Figure 5.16: Effect of component specific powers on PSEC with DP for 100 nmi all-electric thin-haul aircraft; BSE = 900 W · h / kg, f = 1, f = 1.

S L battery technology, This indicates that the obstacles for a feasible all-electric aircraft lie with battery technology, rather than with motors and converters.

N ASA/CR—2019-220382 41   C onventional, 2 fans, no BLI     All-electric , 2 fans, no BLI   All-electric , 100 fans, 50% BLI    Optimistic 2035 Current Tech Conservative 2035            Figure 5.17: Effect of component specific powers on PSEC with DP and BLI for 100 nmi all-electric thin-haul aircraft; BSE = 900 W · h / kg, f = 1, f = 1.

S L Following this conclusion, a turbo-electric architecture (no batteries) could be feasible even with current technology. Figure 5.18 demonstrates this, here for a larger medium-haul aircraft designed to carry 180 passengers over 3000 nmi. The conventional aircraft has two mechanically driven fans with no BLI and a PSEC of about 4.2 kJ / kg · km. The turbo-electric aircraft has 308 electrically distributed fans, ingesting 20% of the total boundary layer over the fuselage and 50% over the wing.

Even with current technology, the turbo-electric aircraft has a PSEC benefit of 7% over the conven- tional. This advantage increases to 16% with conservative 2035 technology and to 19% with optimistic 2035 technology. Thus, while all-electric aircraft may be infeasible for longer missions, turbo-electrics are feasible for longer missions. This was demonstrated here for the medium-haul, but was found to be true for all classes.

5.3.3 Technology Analysis Summary For the different mission profiles, analysis of technology levels shows that currently, batteries have specific energy and power too low to enable all-electric propulsion for all missions. Motor and converter specific powers are high enough to allow turbo-electric aircraft. However, these aircraft have little to no benefit over the corresponding conventional aircraft. Benefits are seen by adding distributed propulsion (DP) and boundary layer ingestion (BLI) enabled by electrification. At conservative 2035 technology levels, battery technology is still too low to render all-electric aircraft feasible. BSE and BSP must increase significantly for all-electric aircraft, even for the smallest class and shortest missions. However, conservative 2035 technology more than adequate to enable turbo-electric aircraft across all missions, providing PSEC benefits over the conventional cases. With optimistic 2035 technology, the results for turbo-electric aircraft stand with greater PSEC reduction, and battery technology also improves enough to enable hybrid- and all-electric thin-haul aircraft, albeit at lower ranges.

Looking at the results from another angle, optimistic 2035 technology allows for all-electric thin- N ASA/CR—2019-220382 42      Conventional, 2 fans, no BLI   Turboelectric     Conservative 2035 Optimistic Current Tech            Figure 5.18: Effect of improving component specific powers on PSEC for a medium-haul aircraft; turbo-electric: f = 0.48, f = 0.2, N = 2, d = 1.14 m, f = 0.5, L BLI fan fan BLI M M M E N = 308, d = 0.104 m.

fan fan E E haul aircraft at a reduced range of 100 nmi with an energy consumption benefit over the conventional case. The design mission of 500 nmi, however, requires a BSE 1.6 times higher than the optimistic 2035 numbers. For a design regional mission (80 passengers, 1500 nmi), the BSE would have to be twice the optimistic prediction for 2035. For all-electric aircraft, specific energy is more important than specific power, so battery technology needs to improve substantially before commercial missions with such aircraft are possible.

If the battery is not in consideration, as with turbo-electric aircraft, design thin-haul, regional, and medium-haul missions are feasible with energy benefit within conservative 2035 specific powers. Over- all, improvements in electrical component technology make electrified aircraft feasible, and enable lower energy consumption than the current conventional aircraft.

5.4 Limiting Cases 5.4.1 Wake Propulsion Ideal As seen in the power balance framework, airframe parameters and propulsion system parameters deter- mine the aero-propulsive performance of an aircraft with or without BLI [ 2, 8 ] . Specifically, the power ′ coefficient, P / ( D V ) , is determined by the fraction of boundary layer ingested, f , the ratio of non- K ∞ BLI ′ ′ BLI profile drag to total non-BLI drag, D / D , the fraction of non-BLI viscous dissipation occurring before p ′ ingestion, f , and a propulsor mass flow parameter, ˙ mV / D . The power coefficient is the mechanical surf ∞ power delivered to the flow non-dimensionalized by the non-BLI drag power. The power savings coef- ficient, PSC, is the percentage reduction in flow power for a given BLI airframe relative to the non-BLI flow power.

− P P K ,non − BLI K ,BLI PSC = (5.1) P K ,non − BLI N ASA/CR—2019-220382 43 Table 5.3 identifies the power balance parameters for representative aircraft derived from TASOPT models [ 17 ] . These values inform the parameter space in Figures 5.19 and 5.20, which show trends in power coefficient and PSC from full BLI, respectively. The power parameters are plotted as functions ′ of mass flow parameter with vertical lines indicating ˙ mV / D for the identified aircraft. The figures ∞ consider multiple values of profile drag fraction and f is 0.9.

surf The figures show lower power coefficients for full BLI cases relative to non-BLI cases, resulting in PSCs greater than 15% for the plotted range of parameters. PSC increases with profile drag fraction because BLI produces benefit from axial wake defects; as more of the total drag is induced drag, BLI accomplishes less power reduction. In the ideal wake case, there is no induced drag and the propulsive streams return the wake to free stream conditions, resulting in the minimum power coefficient with full BLI. With increasing mass flows, propulsor jet velocity decreases and propulsive efficiency increases.

This performance improvement affects non-BLI cases more than full-BLI cases, resulting in a decrease ′ ′ in PSC with greater mass flow parameter. An aircraft with representative profile drag fraction ( D / D = p ′ 0.65) and a high mass flow parameter ( ˙ mV / D = 3) can reduce flight power by 18% with full BLI.

∞ Practical considerations may limit the amount of achievable BLI. Partial BLI offers appreciable benefit nonetheless. The change in BLI benefit with f is given by Figure 5.21 for the aircraft described in B LI Table 5.3.

Table 5.3: BLI parameter values for relevant aircraft from TASOPT models ′ D ˙ m V p ∞ Aircraft f ′ ′ surf D D Boeing 737-800 (CFM56) 1.36 0.66 0.84 Boeing 777-300ER 2.14 0.63 0.84 D8.2b (non-BLI) 1.42 0.65 0.87 D ' / D' = 0.5 p D ' / D' = 0.65 p 1.8 D ' / D' = 1 p B737-800 B777-300ER 1.6 D8.2b (non-BLI) 1.4 1.2 Ideal Wake Case 0.8 0.5 1 1.5 2 2.5 3 Figure 5.19: Power coefficient variation with BLI parameters as in Table 5.3. Mass flow parameter values given for reference aircraft.

N ASA/CR—2019-220382 44 0.6 D ' / D' = 0.5 Ideal Wake Case p D ' / D' = 0.65 p 0.5 D ' / D' = 1 p B737-800 B777-300ER 0.4 D8.2b (non-BLI) 0.3 0.2 0.1 0.5 1 1.5 2 2.5 3 Figure 5.20: Power saving coefficient variation with BLI parameters as in Table 5.3. Mass flow parameter values given for reference aircraft .

The estimated flow power savings can be translated to reduction in fuel weight via a modified Breguet range equation:         − 1 h P L W fuel K i Range = η ln (5.2) th ′ ′ g D V D W ∞ f Figure 5.22 shows fuel weight reduction as a function of BLI fraction for relevant aircraft parameters (Table 5.3) assuming the other factors, such as empty airframe weight, are constant. For full BLI, fuel weight is reduced by up to 30%.

The relative benefit increases when considering fuel burn due to the logarithmic nature of the range equation – less fuel is needed to carry a lighter plane. It should be emphasized, however, that the analysis neglects the impact of alternate (e.g., distributed, electrified) propulsion system configurations on airframe weight and performance. The significant propulsion system changes needed to achieve a high f motivate the higher-fidelity model with which the trade space study was conducted.

BLI 5.4.2 Battery Specific Energy In Section 5.3.3, it was noted that the feasibility and efficiencies of electrified aircraft improves with improvements in technology parameters. Analyses were done based on different predicted technology levels. This section approaches the matter a little differently – how would electrified aircraft perform with the “best of the best” technology numbers? In other words, if the battery is considered, there is a drop in its specific energy and specific power at the aircraft system level compared to the theoretical values. How would the aircraft performance change if the theoretical numbers were used?

For novel lithium-ion chemistries, the lithium-air battery has the highest theoretical specific energy of 3500 W · h / kg. In the literature, values as high as 11,000 W · h / kg are quoted; however, those numbers N ASA/CR—2019-220382 45 0.35 0.3 0.25 0.2 0.15 0.1 Airframe B737-800 0.05 B777-300ER D8.2b (non-BLI) 0 0.2 0.4 0.6 0.8 1 Figure 5.21: Power savings coefficient variation with extent of BLI for reference aircraft at fixed mass flow parameter.

Airframe + Range B737-800 -5 B777-300ER D8.2b (non-BLI) -10 -15 -20 -25 Fuel Weight Reduction [%] -30 -35 0 0.2 0.4 0.6 0.8 1 Figure 5.22: Relative fuel weight reduction from ideal BLI for extant aircraft configurations and missions.

N ASA/CR—2019-220382 46 are misleading as they only take into account the mass of lithium in the reaction. The other reactant, oxygen, is drawn by the battery from its environment and accumulates, adding to the battery mass as it discharges. When the mass of the oxygen is accounted for, the lower 3500 W · h / kg value is obtained.

Using this value, scaling the battery specific power appropriately, and keeping all other parameters at the optimistic 2035 level, each class of all-electric aircraft was flown on its design mission and the result- ing productivity-specific energy consumption (PSEC) was compared with the respective conventional aircraft, as shown in Table 5.4.

As can be seen, where the aircraft is feasible, the results show a substantial reduction in the specific energy consumption over the smaller mission. The energy benefit decreases as the mission grows in payload and range. At the Li-ion theoretical BSE of 3500 W · h / kg, the specific energy is still smaller compared to that of hydrocarbon fuel, so as more energy is required on-board, the less the benefit. On the other hand, even this high BSE is not enough to facilitate all-electric aircraft for long haul missions.

For those missions, the design will have to be turbo-electric or hybrid-electric even for the highest possible BSE values.

5.4.3 Electrical Component Power Density In section 5.3.3, it was noted that the electrified designs were a lot more sensitive to battery specific energy (BSE) than to component specific powers. To remove the effects of BSE, only turbo-electric designs were considered in this section, in order to isolate the effects of drastically improving specific powers. In section 5.3.2, it was also observed that the PSEC curves flattened out for increasing specific powers, leading to PSEC benefits with diminishing returns. This section compares the conventional aircraft for each mission with the respective turbo-electric aircraft for the same mission, but with the component specific powers set to 100 kW / kg. The results are shown in Table 5.5.

Across all missions, the high component specific powers enable a reduction in the on-board energy consumed. The PSEC benefits are higher for thin haul and long haul compared to regional and medium haul missions. The varying level of benefits can be attributed to the different baseline turbo-electric designs used in each case, as discussed in section 5.1. In the absence of a minimum fan diameter con- straint in the optimizer, the results when the number of electric fans was allowed to float led to a large number (thousands) of very very small (less than micrometer-scale) fans, which was deemed impracti- cal. However, improving component specific powers for turbo-electric designs results in smaller PSEC benefits compared to improving BSE for all-electric designs, so this drastic improvement in component specific powers is unlikely to yield substantial PSEC benefits over the optimistic 2035 predictions.

Table 5.4: Comparison of all-electric with limiting BSE vs conventional Mission Conventional PSEC [ kJ / kg · km ] All-electric PSEC [ kJ / kg · km ] Percent benefit Thin haul 6.593 2.816 57.3% Regional 5.764 3.080 46.6% Medium haul 4.147 2.713 34.6% Long haul 8.247 – – Table 5.5: Comparison of turbo-electric with limiting specific power vs conventional Mission Conventional PSEC [ kJ / kg · km ] Turbo-electric PSEC [ kJ / kg · km ] Percent benefit Thin haul 6.593 4.860 26.3% Regional 5.764 4.898 15.0% Medium haul 4.147 3.467 16.4% Long haul 8.247 5.757 30.2% N ASA/CR—2019-220382 47

6 Conceptual Design Framework Extensions

6.1 Detailed Electric Component Design Model This section presents electric component models that incorporate additional information (e.g., maxi- mum operating voltage and current) for estimation of their specific power and efficiency. These higher- fidelity models could be substituted into the analyses that have been described, which used specified efficiency and specific power, to explore the electric propulsion system design space in more depth.

6.1.1 Cable Model The cable model captures the impact of operating the propulsion system at different voltage and current levels. From Appendix B, the efficiency of the cable is, P P load load η = = . (6.1) P P + I R source load For a fixed load power, the efficiency can be increased by either decreasing the resistance of the cable or decreasing the current (i.e., increasing the source voltage).

The cable resistance is,  R = ρ , (6.2) A c where ρ is the cable resistivity,  its length, and A its conductor cross-sectional area. The resistivity is c fixed by the choice of conductor material, and the length of the cable is fixed by the aircraft configuration, thus the remaining degree of freedom to change the cable resistance is the conductor area; the efficiency of the cable can be improved by increasing A . However, the mass of the cable is directly proportional c to A , and there is a trade-off between cable specific power and efficiency. Figure 6.1 shows this trade- c off for a cable using the material parameters from Appendix B; increasing the conductor area yields diminishing marginal benefits in efficiency. A 6 meter cable that delivers 250 kW of power to the load at 270 Vdc was assumed, values which may be representative of a real aircraft power cable.

Figure 6.1: The conductor area presents a trade-off between cable mass and resistance (i.e., efficiency).

N ASA/CR—2019-220382 49 The efficiency of the cable can also be improved by decreasing the current. However, the necessarily larger source voltage increases the dielectric thickness of the cable, which increases its mass. Figure 6.2 shows a similar trade-off between mass and efficiency for a 250 kW cable as that in Fig. 6.1, at different voltage levels. An increase in voltage results in a lighter cable, but there is a diminishing marginal benefit. This is relevant to aircraft power systems which are traditionally limited to low voltages due to electric breakdown concerns.

6.1.2 Electrical Machine Model A survey on motor power-to-mass ratios shown in Fig. 6.3 shows that power-to-mass ratio is not constant across rated power [ 18 ] .

Generally, the power-to-mass ratio improves at lower power levels, but even then spans a wide range. This variation depends on a variety of factors, such as cost, materials, cooling technology, and rotor integrity (burst limit). To capture these effects and better understand these trade-offs, a more Figure 6.2: Increasing voltage improves the cable efficiency but gives diminishing marginal benefit.

Figure 6.3: Survey of power-to-mass ratios versus rated power for a variety of motors [ 18 ] .

N ASA/CR—2019-220382 50 detailed, GPkit-compatible electrical machine model was developed as documented in Appendix B.

Data from existing electrical machines for vehicular applications was used to assess the fidelity of the model. First, the dimensions and material properties from the MIT Cheetah Motor [ 19 ] , shown in Fig. 6.4, were substituted into the analytic expressions captured in Appendix B. This motor uses Neodymium magnets and Hiperco-50 steel. The angular speed and hence power level of this motor were not specified, so torque and masses only were checked, as in Tab. 6.1.

Second, an MIT outer rotor, electric automobile motor [ 20 ] was used for verification. This motor was designed with chromate plated NdFeB magnets and 29 Gage M-19 steel. The power level and angular speed were also not specified, so only torque and mass were compared, as in Tab. 6.2. The constituent masses (e.g., the magnet mass) differ by larger percentages, which may be explained from the motor design considering additional details such as slot skewing [ 20 ] .

The motor model can be used to explore trade-offs between design parameters. Fig. 6.5 shows the trade-off between specific power and ohmic heating losses from optimizing the motor geometry while varying the current density for a motor designed for 25 kW, 2000 rpm, and 200 m / s tip speed.

Reference [ 21 ] shows that the trade-off between specific power and efficiency is due to the armature reaction of the machine. For a machine with saturated teeth operating at the theoretical shear stress limit, the theoretical efficiency due to ohmic heating losses is given by [ 21 ] ρ J η = 1 − 2 2 (6.3) B U sat where J is the slot current density, B is the saturation flux density in the magnet material, and U is sat the tip speed.

Figure 6.4: Photo showing the layout of the MIT Cheetah Motor [ 19 ] .

Table 6.1: Gen-2 Cheetah Robot Inner Rotor Parameter Predicted Measured [ 19 ] % Difference Mass 1.05 kg 1.07 kg 1.9% Torque 42 Nm 42.36 Nm 0.85% N ASA/CR—2019-220382 51 Table 6.2: Electric Automobile Outer Rotor Parameter Predicted Measured [ 20 ] % Difference Mass 24.5 kg 25.1 kg 2.4% Magnets 1.88 kg 1.7 kg 10.7% Rotor Back-Iron 5.87 kg 5.9 kg 0.5% Stator Teeth 5.57 kg 6.6 kg -15.6% Stator Back-Iron 4.80 kg 4.8 kg 0% Conductors 6.36 kg 6.1 kg 4.3% Torque 457.1 Nm 450 Nm 1.6% Figure 6.5: A Pareto frontier of the motor specific power and efficiency (left) and the Ohmic heating loss compared to the theoretical limit from Ref. [ 21 ] (right).

Figure 6.5 shows that the model captures this trend. An increase in current density results in greater Ohmic heating losses, but also a lighter motor because the conductor size can be decreased. This result was generated by optimizing the motor model to minimize mass while varying the maximum allowable slot current density. The motor load power, angular speed, and tip speed were held constant at 25 kW, 2000 rpm, and 200 m / s, respectively. If this model was incorporated into an aircraft configuration and mission, these parameters could also be variables optimized to minimize the vehicle-level objective.

6.2 Aircraft Conceptual Design Model This section presents the results of a signomial programming (SP) airframe conceptual design model, applied to the NASA STARC-ABL turbo-electric aircraft configuration [ 22,23 ] . The mission performance, propulsion system, and aero-propulsive performance models described in Section 4 are used, but the aero-structure model has been replaced with higher-fidelity sizing and performance models for the airframe components listed in Table 6.3. The objective was to extend the trade space exploration tool to a fidelity suitable for conceptual design of a commercial aircraft while retaining the benefits of the GP optimization approach. The details of the component models are provided in Appendix C.

6.2.1 Comparison with Existing Aircraft Data Figure 6.6 shows an assessment of estimated aircraft empty mass for a range of commercial transports currently in production. Inputs to this sizing-only model are wing, fuselage, and tail dimensions, max N ASA/CR—2019-220382 52 Table 6.3: Airframe and propulsion sub-system component models Sub-system Components Sizing Model Performance Model Airframe Fuselage Torenbeek [ 24 ] Schaufele drag fit [ 25 ] Wing Raymer [ 15 ] Oswald efficiency, airfoil polar fits Vertical tail Torenbeek TASOPT drag model [ 26 ] Horizontal tail Torenbeek TASOPT drag model Nacelle TASOPT weight buildup TASOPT drag model Non-propulsive systems TASOPT weight buildup Propulsion Gas generator core corrected flow cube-squared specified thermal efficiency Ducted fan corrected flow cube-squared specified efficiency Electric generator specified power density specified efficiency Power electronics specified power density specified efficiency Electric motor specified power density specified efficiency Thermal management specified mass per heat flow Airbus A380 1000 lb) × Boeing 747-8 Boeing 777-200 Airbus A350-900 Airbus A330-200 Boeing 787-8 Boeing 767-300ER Airbus A320-200, A320neo Boeing 737-800, 737 MAX Predicted operating empty mass ( Embraer E190 Embraer E175 0 100 200 300 400 500 600 700 Actual operating empty mass ( × 1000 lb) Figure 6.6: Predicted vs actual operating empty weight for range of commercial transport aircraft .

payload and max takeoff mass, propulsion system mass, and fan diameter, all of which were obtained from aircraft and engine Type Certificate Data Sheets and Airport Planning Manuals. The model is a GP with 45 design variables, which solves in approximately 0.1 seconds on a personal computer. The model matches empty mass to within 4% of design data for aircraft from regional to super-jumbo scale.

The mass of the Boeing 787 and Airbus A350 are well-predicted without accounting in any way for the primarily composite construction of the airframe, suggesting mass reduction factors [ 15, 24 ] used to estimate composite fuselage structural mass may be optimistic.

Figure 6.7 shows the empty mass buildup compared with the Boeing SUGAR Free and Refined SUGAR single aisle concepts [ 13 ] . The model shows excellent agreement with the data, capturing component component masses to within 20%, and matching overall empty weight to within 3% for both designs. For the Refined SUGAR model, component mass reduction factors of 8%–16% were ap- plied, consistent with the N + 3 advanced composite technology assumptions; combined with reduced fuel mass due to improved efficiency, this results in a 14% reduction in empty mass relative to the N ASA/CR—2019-220382 53 Operational Items Systems + Equipment 1000 lb) × Propulsion 40 Nacelle + Pylon Mass ( Landing Gear Fuselage Empennage Wing Boeing SUGAR Free design GP SUGAR Free model Boeing Refined SUGAR design GP Refined SUGAR model Figure 6.7: Comparison of SUGAR aircraft concept empty weight buildup; published de- .

sign [ 13 ] vs current model; baseline and N + 3 technology assumptions baseline technology SUGAR Free. In the next section, the Refined SUGAR model is used as a baseline for comparison of the STARC-ABL configuration, consistent with the N + 3 time frame assumed for the original design [ 22, 23 ] .

6.2.2 Conventional Tube-and-Wing Baseline Performance To calibrate and assess the configuration performance model and to provide a baseline for comparison with the STARC-ABL configuration, we have developed a model for the Refined SUGAR concept. Ta- ble 6.4 lists the model inputs and provides a comparison of the published sizing and performance with the model estimates. The gas generator specific power and thermal efficiency were selected to yield agreement in engine bypass ratio and thrust-specific fuel consumption, as described in the previous section. The inclusion of a reserve range fraction of 15% results in less than 1% error in predicted max- imum takeoff mass. The resulting model matches the sizing and performance parameters in the range equation – empty mass, max takeoff mass, fuel consumption, and lift-drag ratio – to within 0.5%. The mission fuel burn is underpredicted by 3%. The largest discrepancies are the propulsion system mass and tail moment arms, indicating potential room for improvement in the ducted fan, gas generator, and tail sizing descriptions.

6.2.3 STARC-ABL Configuration Performance Table 6.5 lists the design variables for the baseline Refined SUGAR model and an equivalent STARC-ABL configuration. Payload mass, range, cruise altitude and Mach number, wing span, fuselage dimensions, tail moment arms, and wing loading were held constant to provide a fair comparison of the concepts (i.e., N ASA/CR—2019-220382 54 Table 6.4: Comparison of conventional tube-and-wing baseline configuration model with Boeing Refined SUGAR sizing and performance Refined Baseline Parameter SUGAR [ 13 ] Configuration Inputs Payload mass [ lb ] 46,000 Range (max payload, + 15% reserve) [ nmi ] 1450 Cruise altitude [ ft ] 37,000 Cruise Mach number 0.74 Wing reference area [ ft ] 1358 Wing span [ ft ] 118 Wing taper ratio 0.16 Wing sweep [ deg ] 20.1 Horizontal tail area [ ft ] 268 Horizontal tail aspect ratio 6.24 Vertical tail area [ ft ] 213 Vertical tail aspect ratio 1.94 Fuselage length [ ft ] 125 Fuselage diameter [ ft ] 12.7 Fan diameter [ in ] 70 Outputs Propulsion system mass [ lb ] 9027 8124 (-10%) Operating empty mass [ lb ] 77,042 77,030 (-0.02%) Max takeoff mass [ lb ] 136,412 135,900 (-0.4%) Wing loading [ lb / ft ] 100 100 (–) Horizontal tail moment arm [ ft ] 60.7 53.0 (-13%) Vertical tail moment arm [ ft ] 56.3 50.8 (-10%) Lift-to-drag ratio 20.9 20.9 (–) Thrust-specific fuel consumption [ 1 / hr ] 0.528 0.529 ( + 0.2%) Mission fuel mass [ lb ] 13,370 12,910 (-3%) both aircraft can be assumed to meet similar constraints such as balanced field length requirements).

The STARC-ABL propulsion systems fan diameters and electric motor power were specified, consistent with the most recent STARC-ABL design revision [ 23 ] . Performance calculations yield a 5.4% increase in fuel required for the mission being considered (max range at max payload).

Examination of the optimized design variables shows that the specified STARC-ABL propulsion sys- tem trades reduced specific fuel consumption for increased mass and drag. The reduced under wing fan diameter yields a 8% reduction in turbofan mass, but the total propulsion system mass is 38% higher than the baseline turbofan, in large part due to the tail cone fan mass. The re-sized distributed propul- sion system results in a 23% increase in total nacelle mass and a 28% increase in total nacelle drag. In total, the empty mass is 7% higher and the lift-drag ratio is 2% lower than the Refined SUGAR baseline.

On the other hand, the increased losses in the electric distribution system and the mixing of the under wing jet (which has a lower propulsive efficiency than the conventional baseline) are more than offset by propulsive power savings of BLI, yielding a net decrease in thrust-specific fuel consumption of 1.5%.

6.2.4 Sensitivity of Performance to Model Parameters As described in Section 4.2, a benefit of the GP optimization approach is that parameter sensitivities of the objective function are provided as part of the solution. Figure 6.8 shows the 30 parameters with the largest sensitivities in our STARC-ABL model, grouped into parameters related to mission, propulsion system, and airframe. The values are the magnitudes of the Lagrange multipliers for each parameter, which indicate the relative change in the objective function that would result for a given relative change N ASA/CR—2019-220382 55 Table 6.5: Comparison of baseline and STARC-ABL configuration sizing and performance Baseline STARC-ABL Parameter Configuration Configuration Max takeoff mass [ lb ] 135,900 141,800 ( + 4.3%) Operating empty mass [ lb ] 76,940 82,210 ( + 6.8%) Under wing nacelle mass ( × 2) [ lb ] 2212 1573 (-29%) Tail cone nacelle mass [ lb ] – 2311 Total propulsion system mass [ lb ] 8124 11,190 ( + 38%) Under wing fan diameter [ in ] 70 57 (-19%) Turbofan mass ( × 2) [ lb ] 4062 3755 (-7.6%) Generator mass ( × 2) [ lb ] – 238 Rectifier mass ( × 2) [ lb ] – 183 Cable mass [ lb ] – 451 Circuit protection mass [ lb ] – 226 Inverter mass [ lb ] – 357 Thermal management system mass [ lb ] – 110 Motor mass [ lb ] – 438 Tail cone fan diameter [ in ] – 77 Tail cone fan mass [ lb ] – 1261 Wing area [ ft ] 1358 1417 ( + 4.3%) Wing aspect ratio 10.3 9.8 (-4.9%) ′ Airframe lift-drag ratio ( L / D ) 20.9 20.4 (-2.4%) ′ Effective TSFC ( ˙ m g / D ) [ 1 / hr ] 0.529 0.521 (-1.5%) fuel Mission fuel mass [ lb ] 12,910 13,610 ( + 5.4%) in the parameter in question, including the effect of re-optimization. Red bars indicate positive sensitiv- ities, for which an increase in the parameter results in an (undesired) increase in the objective function; conversely, blue bars indicate negative sensitivities, where an increase in the parameter decreases the objective function. Sensitivities are local, i.e., they only indicate the direct effect of small changes in parameters, so that larger changes have a nonlinear impact on the objective function. Further, the sensitivities will change with a change in design parameter; for example, in the case of the optimized propulsion system presented in the next section, the sensitivities to fan diameter go to zero as they are optimized.

In many cases, the sensitivities indicate well-understood impact of design parameters or level of technology on overall performance. For example, the large sensitivities of fuel burn to payload mass, range, thermal efficiency, and fan efficiency show the direct effect of those parameters on the range equation. The largest sensitivity, which is to maximum wing span, is because higher aspect ratios and lift-drag ratios can be achieved with larger span. A majority of the smaller sensitivities shown are constant factors that directly impact component mass or drag. In some cases, sensitivities can point to an issue with the model. For example, the large sensitivity to cruise altitude an artifact of the fan sizing model, which assumes a fixed altitude, and thus does not capture the correct trend with free stream stagnation conditions. Another parameter of this type is the tail cone fan efficiency, which is assumed constant, but could be degraded due to inlet distortion; in this case the sensitivity provides useful information about how such changes in efficiency would impact overall performance.

The sensitivities to number of under wing engines and both fan diameters suggest design choices to improve overall configuration performance. The former is the benefit of distributed propulsion; more small propulsors yield better performance than fewer large ones, assuming the nacelle, fan, and core sizing and performance models are appropriate at smaller scale. The latter indicates the specified fan sizes, and thus the design fan pressure ratios, are not optimal for minimum fuel burn.

N ASA/CR—2019-220382 56 payload mass range cruise altitude gas generator thermal efficiency underwing fan efficiency number of underwing engines tailcone fan efficiency underwing nacelle velocity tailcone nacelle velocity tailcone fan diameter gas generator specific power gas generator scaling factor tailcone nacelle  / d max wing span fuselage diameter wing span efficiency fuselage length wing excrescence drag factor wing loading vertical tail thickness-to-chord ratio fuselage mass scaling factor wing mass scaling factor fuselage excrescence drag factor fuselage surface dissipation fraction ultimate load factor equipment mass per payload mass fuselage floor scaling factor equipment mass per max takeoff mass horizontal tail mass scaling factor operational item mass per payload mass 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Relative parameter sensitivity Figure 6.8: Sensitivities of baseline STARC-ABL configuration fuel burn to constant design parameters .

6.2.5 Propulsion System Optimization A second STARC-ABL configuration model with optimized fan diameters and electric motor power was also considered to determine the minimum fuel burn for a fixed airframe. To provide a fair comparison, the Refined SUGAR fan diameter was also optimized, with the results shown in Table 6.6. The baseline tube-wing configuration is seen to be near-optimal, with optimization increasing the fan diameter from N ASA/CR—2019-220382 57 70 to 73 inches, yielding a 10 lb (0.1%) decrease in mission fuel. Optimization of the STARC-ABL configuration, on the other hand, leads to a quite different propulsion system than the specified design, with under wing fan diameters approaching that of the tube-wing design, and the electric motor power reduced by 72%. This results in a 5% improvement in performance over the initial design, but the optimized STARC-ABL configuration consumes 0.5% more fuel than the optimized baseline tube-wing configuration.

The limited fidelity of the propulsion system models (to which the fuel burn benefit has been shown to be sensitive) and the limited scope of the design study do not allow us to draw any firm conclusions concerning the benefit of the STARC-ABL configuration. It is also worth mentioning that the present analysis assumes a mission and conventional configuration baseline based on the Refined SUGAR con- cept [ 13 ] , with different design parameters – cruise Mach number and design range – than that of the initial STARC-ABL studies [ 22, 23 ] . For the current assumptions, the results suggest the STARC-ABL concept is near the “break-even” point, with little or no benefit in performance over a advanced tech- nology baseline with conventional turbofan propulsion. The sensitivity and optimization analyses also show the importance of system-level optimization for new configurations, where system performance trades of conventional designs do not apply, and typical design choices based on engineering judgment may not provide the best performance.

Table 6.6: Comparison of conventional tube-and-wing and STARC-ABL configuration sizing and performance with and without propulsion system optimization Baseline Optimized Baseline Optimized Tube-Wing prop. sys. STARC-ABL prop. sys.

Under wing fan diameter [ in ] 70 73 ( + 4.3%) 57 68 ( + 19%) Tail cone fan diameter [ in ] – – 77 29 (-62%) Tail cone motor power [ hp ] – – 3500 972 (-72%) Total propulsion system mass [ lb ] 8124 8401 ( + 3.4%) 11,190 9231 (-18%) ′ Effective TSFC ( ˙ m g / D ) [ 1 / hr ] 0.529 0.522 (-1.3%) 0.521 0.522 ( + 0.3%) fuel ′ Effective lift-drag ratio ( L / D ) 20.9 20.8 (-0.5%) 20.4 20.8 ( + 2.0%) Operating empty mass [ lb ] 77,030 77,780 ( + 1.0%) 82,210 78,490 (-4.5%) Max takeoff mass [ lb ] 135,900 136,700 ( + 0.6%) 141,800 137,400 (-3.1%) Mission fuel mass [ lb ] 12,910 12,900 (-0.1%) 13,610 12,960 (-4.8%) To approximate the effect of the smaller tail cone fan on the amount of BLI, f is assumed to scale linearly with fan BLI f diameter, with a value of unity at the initial design diameter of 77 inches.

The fact that the STARC-ABL doesn’t simply optimize to the conventional configuration is an artifact of the cable model, which is effectively a fixed weight associated with the electric distribution system, regardless of size, combined with the slight BLI benefit that can be achieved if it is used.

N ASA/CR—2019-220382 58

7 Aspects Not Addressed and Questions for Future Research

The scope of the current program meant that there were a number of relevant aspects that we could not address. First, the analysis carried out was quasi-steady and aimed at the cruise condition; It did not include off-design performance and examination of electrical and mechanical dynamical systems in terms of stability and control of aircraft, propulsion operability, and electric power distribution. We also did not consider other (i.e., more than direct propulsive efficiency or weight) possible benefits from distributed propulsion and boundary layer ingestion.

The next steps involve the trajectory from trade-space analysis to the research needed to enable concept and design. At a high level, these questions are: • How do we create an efficient distributed propulsion system?

• How do we create high levels of boundary layer ingestion efficiently?

• If either of the above is accomplished electrically, what are the challenges of the electrical distri- bution network?

Questions such as the above can be asked at a fundamental level, but their resolution casts a light up the TRL ladder. They call for basic analysis and computation, coupled with targeted experiments to design the technology paths. They also call for close integration of different fields of expertise to address, as a team, a challenge that cuts across disciplines.

The next level of attack should involve the development of integrated sub-systems and demon- stration of performance to increase TRL of enabling technologies. For airframe-propulsion integration, these are distributed propulsion (DP) for ultra-low fan pressure ratio (ULFPR), boundary layer ingestion (BLI), lift augmentation, and flight control. For the propulsor module, these are electro-mechanically in- tegrated fan and motor sub-systems including aero-thermal integration of fan flow and thermal manage- ment system. For the electrified propulsion system, the configuration of the architecture (turboelectric, hybrid, partial, etc.) serves as an enabling concept across system-level trades.

Technical challenges associated with these system attributes include • Ultra-integrated electrified vehicle concept design and performance estimation – Develop and use new multi-disciplinary design tools to define and analyze commercial aircraft concepts that lever- age increased integration of vehicle subsystems and electrified propulsion system architectures to reduce noise, emissions, and fuel / energy consumption with operating costs favorable compared with conventional designs.

• High specific power electrical machines, drives, transformers, and protection equipment – Introduce ultra-efficient electrical components to reduce total electro-mechanical energy conversion and transmission losses and develop high-fidelity multi-physics models for system integration.

• Thermal management of electrified propulsion systems and components – Integrate of thermal man- agement into early stage conceptual design of electric power distribution system for optimal allo- cation of losses and weight across different components.

• Electric vehicle system dynamics – Develop analytical methodologies to describe design and off- design performance including examination of electrical and mechanical dynamical systems in terms of stability and control of aircraft, propulsion operability, and electric power distribution.

This implies assessment of interactions between systems with different characteristic dynamic time scales. A preliminary analysis of this type was developed under the current effort, and is documented in a separate report [ 28 ] .

• Airframe-integrated distributed propulsion for improved aerodynamics – Leverage flexibility of electric- drive distributed propulsion to enable ultra-low fan pressure ratios, boundary layer ingestion, and N ASA/CR—2019-220382 59 flow control to improve propulsive efficiency, reduce effective drag, and reduce wing, tail, trim, and control surface area and weight.

• Compact, efficient electric propulsor module design – Integrate the aerodynamic, mechanical, electri- cal, and thermal design optimization of electrically-powered propulsors to enhance overall specific power, efficiency, disturbance rejection, operability, noise, and off-design performance.

N ASA/CR—2019-220382 60

Appendix A

Trade Space Analysis Models

This section describes the details of the mission integration, aero-structure sizing, aero-propulsive performance, and electric propulsion system architecture models that make up the trade space analysis.

Each model consists of a set of governing equations that can be formed as GP or SP constraints, a list of design variables to be optimized, and a list of constant parameters defining the mission and technology assumptions.

A.1 Mission Integration The aircraft zero fuel mass is the sum of the airframe empty mass, propulsion mass (defined in later sections), battery mass (defined below), and a specified payload mass; the takeoff mass is the sum of the zero fuel mass and the mission fuel mass.

m = m + m + m + m (A1) ZF airframe prop batt payload m = m + m (A2) TO ZF fuel The mission fuel mass is defined using a form of the Breguet Range Equation, assuming the fuel mass flow is proportional to the mass of the vehicle (i.e., constant lift-to-drag ratio and thrust-specific fuel consumption). For all-electric architectures, the fuel mass is zero; for hybrid-electric architectures, the required fuel flow is reduced by power supplied by the battery, but the expression for total fuel consumption is unchanged. To make the expression GP , the exponential function is represented with a truncated Taylor series expansion, with N = 4 terms seen to be more than sufficient to provide accurate results.

    ˙ m R fuel m = m exp − 1 (A3) fuel ZF m V TO   N ∑ i 1 ˙ m R fuel ≈ m (A4) ZF i ! m V TO i = 1 The total battery energy required is defined similarly assuming the battery power is proportional to to the mass of the vehicle. For conventional architectures, the battery mass is zero; for all-electric architectures, the battery power consumption is constant, simplifying the analysis.

   ˙ E ˙ m R batt fuel E ≥ 1 − exp − (A5) tot ( ˙ m / m ) m V fuel TO TO   N i ∑ 1 ˙ m R fuel i ! m V ˙ TO E i = 1 batt ≈ (A6)   N ∑ i ( ˙ m / m ) fuel TO 1 ˙ m R fuel i ! m V TO i = 0 (A7) N ASA/CR—2019-220382 61 The battery mass related to both minimum energy requirement and the maximum battery power through the BSE and BSP , from which the battery efficiency is also determined, using a simple voltage- resistance circuit model.

E tot m = (A8) batt BSE P max m = (A9) batt BSP P ≤ P (A10) batt max P batt 4 η ( 1 − η ) = (A11) batt batt P max ˙ E batt ˙ E = (A12) batt η batt Tables A1 and A2 list the design variables to be optimized and constant parameters related to the vehicle sizing and mission energy consumption.

Table A1: Mission integration design variables Quantity Dimension Description E Wh total battery energy capacity tot ˙ E W battery discharge rate batt m kg empty airframe mass; no propulsion system airframe m kg battery mass batt m kg mission fuel mass fuel m kg propulsion system mass prop m kg aircraft takeoff mass TO m kg aircraft zero fuel mass ZF ˙ m kg cruise fuel consumption (at takeoff mass) fuel P W max battery power max η - battery efficiency batt Table A2: Mission integration constant parameters Quantity Value Dimension Description A1 BSE 175 / 250 / 900 Wh / kg battery specific energy BSP 520 / 745 / 2700 W / kg battery specific power A2 m 20 / 80 / 180 / 350 × 215 lb payload mass payload R 500 / 1500 / 3000 / 6000 nmi range V 77 / 233 / 233 / 249 m / s cruise velocity A1 Values for current state of the art, conservative 2035, and optimistic 2035 technology assumptions, respectively, defined in Section 3.

A2 Values for thin haul, regional, medium haul, and long haul, respectively.

N ASA/CR—2019-220382 62 A.2 Aero-Structure Sizing The airframe empty mass is modeled using scaling based on approximate sizing of the wing, tail, and fuselage surface areas. The wing is sized based on an assumed wing loading for each vehicle class, the tails are sized using fixed tail volume coefficients, and the fuselage is sized based on specified cabin dimensions.

m TO S = (A13) wing W / S bS wing S = c (A14) HT HT  AR fuse bS wing S = c (A15) VT VT  fuse S = π d  (A16) fuse fuse fuse The mass of each component is determined using approximate correlation-based methods suggested by Raymer [ 15 ] , with constants modified to better fit recent conceptual design data obtained using TASOPT [ 17 ] .

S wing m = K (A17) wing wing b m = K S (A18) HT HT HT m = K S (A19) VT VT VT m = K S (A20) fuse fuse fuse m = K m (A21) gear gear TO m = K m (A22) misc misc TO m = m + m + m + m + m + m (A23) airframe wing HT VT fuse gear misc The airframe aerodynamic performance, characterized by the lift-to-drag ratio, is estimated based on the above vehicle surface areas and the wing aspect ratio, which is constrained by a specified max span, using a correlation suggested by Raymer [ 15 ] .

S = 2 ( S + S + S ) + S (A24) wet wing HT VT fuse b ≤ b (A25) max b AR = (A26) S wing √ √ K AR S L √ wing ( L / D ) = (A27) D 2 S wet Tables A3 and A4 list the design variables to be optimized and constant parameters related to the airframe sizing and aerodynamic efficiency.

N ASA/CR—2019-220382 63 Table A3: Aero-structure sizing design variables Quantity Dimension Description AR - wing aspect ratio A3 b ft wing span c ft average wing chord L / D - airframe lift-to-drag ratio m lb fuselage mass fuse m lb landing gear mass gear m lb horizontal tail mass H T m lb miscellaneous mass misc m lb vertical tail mass V T m lb wing mass wing S ft fuselage wetted area fuse S ft horizontal tail area HT S ft vertical tail area VT S ft airframe wetted area wet S ft wing area wing Table A4: Aero-structure sizing constant parameters Quantity Value Dimension Description A4 c 0.9 / 1.47 - horizontal tail volume coefficient HT c 0.08 / 0.113 - vertical tail volume coefficient VT K 1.40 / 7.02 lb / ft fuselage scaling factor fuse K 0.057 / 0.053 - landing gear scaling factor gear Kgear K 2 / 5.47 lb / ft horizontal tail scaling factor HT K 9.53 / 15.2 - lift-to-drag ratio scaling factor ( L / D ) K 0.1 / 0.01 - miscellaneous mass scaling factor misc Kmisc K 2 / 6.50 lb / ft vertical tail scaling factor VT K 0.61 / 1.12 lb / ft wing scaling factor wing A5 b 65 / 90 / 118 / 200 ft max wing span max d 6 / 11 / 12.5 / 20 ft fuselage diameter fuse  52 / 105 / 130 / 242 ft fuselage length fuse W / S 30 / 100 / 130 / 140 lb / ft A3 Imperial units are used here to remain consistent with the suggested scaling coefficients [ 15 ] . GPkit has a built-in package to handle unit conversions, allowing specification of SI units everywhere else.

A4 Values for thin haul and all other vehicle sizes, respectively.

A5 Values for thin haul, regional, medium haul, and long haul, respectively.

N ASA/CR—2019-220382 64 A.3 Aero-Propulsive Performance The aero-propulsive power requirements are defined using the one-dimensional version of the power balance method [ 2 ] described by Hall et al for BLI configurations [ 8 ] . The unpowered airframe drag is determined from takeoff mass and lift-to-drag ratio. The profile drag, related to the potential amount of boundary layer ingestion that can be achieved, is assumed to be a fixed fraction of the unpowered airframe drag. Nacelle drag contributions, scaled with total mass flow of all propulsors, is also included in the overall vehicle drag buildup.

m g TO ′ D = (A28) L / D D p ′ D = D (A29) p D 0.7 D = r ˙ m (A30) nace,e nace e 0.7 D = r ˙ m (A31) nace,m nace m ′ ′ D = D + D + D (A32) nace,e nace,m tot (A33) The power balance equation relates the propulsor mass flows, jet velocities, and amount of BLI to the total vehicle drag.

′ ˙ m ( V − V ) + ˙ m ( V − V ) = D − ( f + f ) D (A34) e j , e ∞ m j , m ∞ BLI,e BLI,m p tot f + f ≤ 1 (A35) BLI,e BLI,m The mechanical flow power in each propulsive stream can then be determined as a function of the ingested profile dissipation and propuslor jet energy.

  P = ˙ m ( V − V ) 2 V + ( V − V ) + f f V D (A36) K , m m j , m ∞ ∞ j , m ∞ BLI,m surf ∞ p   P = ˙ m ( V − V ) 2 V + ( V − V ) + f f V D (A37) K , e m j , e ∞ ∞ j , e ∞ BLI,e surf ∞ p Tables A5 and A6 list the design variables to be optimized and constant parameters related to the aero-propulsive performance.

Table A5: Aero-propulsive performance design variables Quantity Dimension Description ′ D N unpowered airframe drag D N motor-driven propulsor nacelle drag nace,e D N turbine-driven propulsor nacelle drag nace,m ′ D N total (airframe + nacelle) drag tot D N airframe profile drag p ˙ m kg / s total motor-driven propulsor mass flow e ˙ m kg / s total turbine-driven propulsor mass flow m P W total motor-driven propulsor mechanical flow power K , e P W total turbine-driven propulsor mechanical flow power K , m ( V − V ) m / s motor-driven propulsor jet velocity excess j , e ∞ ( V − V ) m / s turbine-driven propulsor jet velocity excess j , m ∞ N ASA/CR—2019-220382 65 Table A6: Aero-propulsive performance constant parameters Quantity Value Dimension Description D / D 0.5 - profile drag fraction p A6 f [ 0,1 ] - motor-driven propulsor BLI fraction BLI,e f [ 0,1 ] - turbine-driven propulsor BLI fraction BLI,m f 0.9 - airframe surface dissipation fraction surf A7 0.7 r 51.9 / 33.0 kg / (kg / s) nacelle drag scaling factor nace A.4 Electrified Propulsion System Architecture Model A parametric description the general electrified propulsion system architecture shown in Fig. 4.3 allows the propulsion system sizing and performance to be modeled strictly as a function of propulsor powers and mass flows. Specification of the source and load electrification factors is sufficient to constrain the type of architecture (e.g., conventional, all-electric, turbo-electric, series or parallel hybrid-electric).

P batt f = (A38) S P + P batt core P K , e f = (A39) L P + P K , e K , m The propulsion system model consists of gas generator cores, ducted fans, electric motors, electric motors, rectifiers, inverters, batteries, and a thermal management system. The masses of the mechanical and electrical components are sized based on the power of each component using the scaling parameters listed in Tab. A8.

P core ˙ m = (A40) core P sp 1.2 m = K ˙ m (A41) core core core   − 1 P m = P (A42) gen / mot gen / mot m gen / mot   − 1 P m = P (A43) rect / inv rect / inv m rect / inv   1.2 ˙ m m m = K (A44) m.fan fan N cores ˙ m m m = K (A45) m.nace nace N cores   − 1 P m = P (A46) inv inv m inv   − 1 P m = P (A47) mot mot m mot   1.2 ˙ m e m = K (A48) e.fan fan N e.fan A6 BLI fraction is treated as a constant in the current model formulation; see Section 5.1.6 for discussion of performance trends with variation in f .

BLI A7 Values for individual podded nacelles and arrays of distributed propulsors, respectively.

N ASA/CR—2019-220382 66 ˙ m e m = K (A49) e.nace nace N e.fan   − 1 P m = Q (A50) TMS m TMS m = N ( m + m + m + m + m ) prop cores core gen / mot rect / inv m.fan m.nace + N ( m + m + m + m ) + m (A51) e.fan inv mot e.fan e.nace TMS The heat rejected from the electrical components, which ultimately sizes the thermal management system, is determined based on the power of each component and the efficiencies listed in Tab. A8.

Q = P ( 1 − η ) (A52) batt batt batt Q = P ( 1 − η ) (A53) gen / mot gen / mot gen / mot Q = P ( 1 − η ) (A54) inv inv inv Q = P ( 1 − η ) (A55) mot mot mot Q = P ( 1 − η ) (A56) rect / inv rect / inv rect / inv Q = Q + Q + Q + Q + Q (A57) batt gen / mot inv mot rect / inv A mechanical and electrical system-level power balance relates the propulsor mechanical flow pow- ers to the fuel consumption and battery power. It is assumed the efficiencies of all electric machines and all power electronics are equal.

η = η = η (A58) gen / mot mot EM η = η = η (A59) inv / rect rect PE Under these assumptions, the propulsion system can be considered a series architecture if the following inequality holds, f ( 1 − f ) > η η f ( 1 − f ) , (A60) L S PE EM S L otherwise the propulsion system may be considered a parallel architecture. Turbo-electric architectures may be considered a subset of series architectures, and conventional and all-electric architectures may be treated as either, where zero power in the mechanical and electric propulsors, respectively, yields the same power balance for both architectures.

A.4.1 Series Architecture Power Balance For series architectures, power is taken off the gas generator shaft by an electric generator and dis- tributed to the electric propulsor system.

N P = ˙ m h η (A61) cores core fuel fuel th P = P − P (A62) gen / mot core m.fan P = N P η (A63) K , m cores m.fan fan P = P − Q (A64) rect / inv gen / mot gen / mot N P = N ( P − Q ) + P (A65) e.fan inv cores rect / inv rect / inv batt P = P − Q (A66) mot inv inv P = P − Q (A67) e.fan mot mot P = N P η (A68) K , e e.fan e.fan fan N ASA/CR—2019-220382 67 A.4.2 Parallel Architecture Power Balance For parallel architectures, battery power is added to the gas generator shaft through an electric motor.

N P = ˙ m h η (A69) cores core fuel fuel th P = P + P (A70) m.fan core gen / mot P = N P η (A71) K , m cores m.fan fan P = P − Q (A72) gen / mot rect / inv rect / inv P = N P + N P (A73) batt cores rect / inv e.fan inv P = P − Q (A74) mot inv inv P = P − Q (A75) e.fan mot mot P = N P η (A76) K , e e.fan e.fan fan Tables A7 and A8 list the design variables to be optimized and constant parameters related to the propulsion system sizing and performance.

N ASA/CR—2019-220382 68 Table A7: Electrified propulsion system architecture design variables Quantity Dimension Description m kg electric fan mass e.fan m kg electric fan nacelle mass e.nace m kg gas generator core mass core m kg generator / motor mass gen / mot m kg inverter mass inv m kg mechanical fan mass m.fan m kg mechanical fan nacelle mass m.nace m kg motor mass mot m kg rectifier / inverter mass rect / inv m kg thermal management system mass TMS ˙ m kg / s core mass flow core ˙ m kg / s fuel flow rate fuel A8 N - number of electric fans e.fan N - number of gas generator cores cores P W battery power batt P W gas generator core power core P W electric fan shaft power e.fan P W generator / motor power gen / mot P W inverter power inv P W mechanical fan shaft power m.fan P W motor power mot P W rectifier / inverter power rect / inv Q W total thermal dissipation Q W battery thermal dissipation batt Q W generator / motor thermal dissipation gen Q W inverter thermal dissipation inv Q W motor thermal dissipation mot Q W rectifier / inverter thermal dissipation rect / inv A8 Optimization of the propulsion configuration as in Section 5.1 can be carried out treating the number of fans and gas generators as continuous variables. Optimal designs can then be assessed by rounding to the integer values that yield the best performance.

N ASA/CR—2019-220382 69 Table A8: Electrified propulsion system architecture constant parameters Quantity Value Dimension Description f [ 0,1 ] - load electrification factor L f [ 0,1 ] - source electrification factor S h 43 MJ / kg fuel heating value fuel 1.2 K 45.6 kg / (kg / s) core mass scaling factor core 1.2 K 1.30 kg / (kg / s) fan mass scaling factor fan K 4.56 kg / (kg / s) nacelle scaling factor nace P 400 kJ / kg core specific power sp ( P / m ) 8 hp / lb thermal management system specific power TMS η 0.9 - fan efficiency fan η 0.5 - core thermal efficiency th A9 ( P / m ) 2 / 9 / 16 W / kg generator / motor specific power gen / mot ( P / m ) 2.2 / 9 / 19 W / kg inverter specific power inv ( P / m ) 2 / 9 / 16 W / kg motor specific power mot ( P / m ) 2.2 / 9 / 19 W / kg rectifier / inverter specific power rect / inv η 0.95 / 0.98 / 0.99 - generator / motor efficiency gen / mot η 0.95 / 0.98 / 0.99 - inverter efficiency inv η 0.95 / 0.98 / 0.99 - rectifier / inverter efficiency rect / inv η 0.95 / 0.98 / 0.99 - motor efficiency mot A9 Values for current state of the art, conservative 2035, and optimistic 2035 technology assumptions, respectively, defined in Section 3.

N ASA/CR—2019-220382 70

Appendix B

Detailed Electric Component Models

This section describes the detailed electric component models used in the analysis in Section 6.1.

Table B1 lists the components, and the following subsections present the model formulations and the variables, parameters, and constraints used in their GPKit implementation.

B.1 Cable Model The cable model consists of a single cylindrical conductor with an outer insulation layer. The insulation of the cable must be sufficiently thick to prevent dielectric breakdown, and the conductor is sized based on acceptable voltage drop and hence cable ohmic heating losses. It is assumed that the cable conductor consists of stranded (Litz) wire for mitigating the skin and proximity effects - loss mechanisms that arise from time-varying signals. These losses are not modeled, but the impact of Litz wire on the mass and resistance of the cable is captured via a packing factor. This level of detail captures trade-offs in delivering propulsion power at specific voltage and current levels.

B.1.1 Cable Sizing The cable has an inner radius a and outer radius b as in Fig. B1. The conductor Litz wire has a packing factor k which represents the percent of the conductor area occupied by the conductive material. The pf Table B1: Electric component models Component Sizing Model Performance Model Cable voltage-current sizing resistor circuit Electrical Machine voltage-current and torque-speed sizing single-phase equivalent circuit Figure B1: Cable geometry .

N ASA/CR—2019-220382 71 conductor area, A , is c A = π a k (B1) c pf and the dielectric area, A is di   2 2 A = π b − a di (B2) = π ( b + a ) t di where t = b − a is the thickness of the dielectric. Assuming the cable has a length  , its mass is di m = A  d + A  d (B3) c c di di where d and d are the densities of the conductor and insulation, respectively.

c di Dielectric breakdown occurs when the electric field in the cable insulation exceeds E , a dielec- max tric material property. Assuming the insulator thickness is small compared to the conductor radius, a parallel-plate approximation is used for the electric field generated from the voltage difference between the conductor and cable exterior. The maximum electric field strength is V max E = (B4) max t di where V is the maximum voltage in the cable relative to ground.

max The conductor has a uniform cross-section, with resistance,  R = ρ . (B5) A c The maximum cable power is, P = V I . (B6) max max max The variables used in this formulation are given in Table B2. The cable model is general in that different conductor and insulator materials can be used to examine material property trade-offs. The constant parameters used during the studies in Section 6.1 are given in Table B3. The conductor pa- rameters correspond to an aluminum alloy, and the dielectric to polyimide tapes. The packing factor is derived assuming a hexagonal packing shape.

Table B2: Cable sizing design variables Quantity Dimension Description A m conductor area c A m dielectric area di a m inner insulation radius b m outer insulation radius I A max current max  m cable length m kg dielectric mass di m kg conductor mass c m kg total cable mass P W maximum cable power max R Ω cable resistance t m dielectric thickness di V V max cable voltage max N ASA/CR—2019-220382 72 Table B3: Cable sizing constant parameters Quantity Value Dimension Description d 2.83e6 kg / m conductor volumetric mass density c d 1.70e6 kg / m dielectric volumetric mass density di E 1.00e7 V / m dielectric max field strength max k 0.91 - Litz wire packing factor pf ρ 2.65e-8 Ω m conductor resistivity B.1.2 Cable Performance The cable performance is described by its resistance and terminal voltages, as in Fig. B2. From Kirchoff’s Figure B2: Cable appears as a resistor when connected to other components voltage law, V + IR = V . (B7) load cable source The ohmic heating losses are, Q = I R , (B8) and the load and source powers are, P = I V , (B9) load load P = I V . (B10) source source The cable efficiency is, P P load load η = = 1 − . (B11) P P + I R source load Equation (B11) illustrates that, for a fixed load power, a low current or low resistance tend to maximize the cable efficiency. Table B4 lists the variables used for cable performance.

Table B4: Cable performance design variables Quantity Dimension Description η - efficiency I A RMS current P W load power load P W source power source Q W Ohmic losses V V load voltage load V V source voltage source N ASA/CR—2019-220382 73 B.2 Electrical Machine Model In Section 6.1, the electrical machine is a permanent magnet synchronous machine. The magnets are mounted radially on the rotor and the windings are in slots on the stator. It is assumed to have three phases and three slots per pole. The machine can either have the rotor interior to (inner rotor) or exterior to (outer rotor) the stator. Both generator and motor models were developed.

For a fixed geometry, the maximum machine output power is limited by electrical loading (ther- mal and breakdown issues), magnetic saturation, tip speed limitations, and electrical frequency / core loss considerations. The following sections describe the analysis used to capture these fundamental limitations.

B.2.1 Electrical Machine Sizing This section details the sizing of an inner rotor electrical machine. The same approach was used for the outer rotor geometry available in the GPKit code, but for brevity is not included here. Figure. B3 shows a flattened cross-section of the inner rotor machine and the corresponding geometric variable definitions.

The total motor mass consists of the stator back iron mass, m , stator teeth mass, m , windings sbi teeth mass, m , magnets mass, m , and rotor back iron mass, m . For an axial motor length  , p pole wind magnet rbi pairs, and steel, magnet, and winding densities ( d , d , and d , respectively), the motor mass steel magnet wind m is motor   2 2 m = π R − R  d sbi stator 6 5 m = A  d teeth teeth stator m = k A (  + 2 L ) d wind pf wind et wind   (B12) 2 2 m = π R − R  d magnet magnet 3 2   2 2 m = π R − R  d rbi rotor 2 1 m = m + m + m + m + m motor sbi teeth wind magnet rbi .

Figure B3: Cutout of inner rotor geometry showing dimensions N ASA/CR—2019-220382 74 where L is the winding end turn length, and et A = 6 pT W , teeth t t   (B13) 2 2 A + A = π R − R .

teeth wind 5 4 Several of the sizing variables are shown in Fig. B3.

The end turns of the motor, L , are modeled assuming a triangular pattern [ 20 ] . The length of these et end turns is π λ L = R , (B14) et 4 2 p 1 − λ where λ is the slot fraction A wind λ = . (B15) A + A wind teeth The resistance of one slot of windings, R , is slot  + 2 L et R = ρ . (B16) slot k A pf slot The total resistance of all three phases, R , is tot R = 6 pR , (B17) tot slot and the per phase resistance is R = R . (B18) ph tot The slot area limits the number of windings, N , and area of the windings, A , that can be used.

slot Specifically, A wind A = , (B19) slot 6 p where 6 pN A wire A = . (B20) wind k pf The minimum number of windings is two. Increasing the number of windings decreases the size of the wire for a fixed winding area. The maximum winding is given by η A cond wind A = ≥ A , (B21) wire wire,min 6 pN where A is typically the area of a 20 AWG wire.

wire,min A summary of the sizing variables is shown in Table B5. For the studies in this report, the motor is assumed to use Neodymium magnets and Alnico 50 steel. Table B6 gives their sizing parameters.

B.2.2 Electrical Machine Performance The electrical machine performance model relates the input voltage and current to the output torque and angular speed. The torque is ˜ τ = ( 4 p ) B N I  R (B22) gap rms 3 The associated magnetic shear stress is τ σ = (B23) 2 π R  N ASA/CR—2019-220382 75 Table B5: Electrical machine sizing design variables Quantity Dimension Description A m single slot area slot A m stator teeth area teeth A m single wire area wire A m total winding area wind  m axial length λ - slot fraction L m end turn length et m kg rotor back iron mass rbi m kg magnet mass magnet m kg stator back iron mass sbi m kg teeth mass teeth m kg axial windings mass mainwindings m kg end windings mass endwindings m kg total PM machine mass N - number of winding turns p - number of pole pairs R V / A phase resistance ph R V / A slot resistance slot R V / A total resistance tot R m rotor back iron inner radius R m rotor back iron outer radius R m magnet outer radius R m teeth inner radius R m stator back iron inner radius R m stator back iron outer radius T m magnet thickness m T m rotor back iron thickness r T m stator back iron thickness s T m stator tooth thickness t U V max tip speed max W m magnet width m W m tooth width t The shear stress is limited by saturation in the teeth [ 21 ] . The magnetic flux in the tooth is the magnitude of the vector sum of the flux due to the magnets and the flux due to the armature reaction, √   √ ˜ √ B gap + ( μ J T ) = B ≤ B (B24) 0 slot t teeth sat λ where 4 pN I rms J = (B25) slot ( 1 − λ ) π R T 4 t The airgap flux can be found from line integral of the H-field around the contour in Figure B4.

2 H T + 2 H g + ( 2 T + W + W ) H = 0. (B26) m m gap t out in steel N ASA/CR—2019-220382 76 Table B6: Electrical machine sizing constant parameters Quantity Value Dimension Description A 0.518 mm minimum wire area wire,min B 2.4 N / m / A saturation flux sat d 8930 kg / m density of conductor cond d 8200 kg / m density of stator stator d 8200 kg / m density of rotor rotor d 7501 kg / m density of magnet magnet k 0.35 - packing factor of conductor pf g 400e-6 m airgap thickness M 8.6e5 A / m magnetization constant ρ 1.67e-8 Vm / A resistivity μ 4 π e-7 Vs / A / m vacuum permittivity μ 120 4 π e-7 Vs / A / m steel saturation permittivity sat Figure B4: Ampere law contour for airgap flux estimation .

Substituting in Eqn. (B26) B gap H = − M (B27) m μ B gap H = (B28) gap μ B steel H = (B29) steel μ s B is found as gap μ M T 2 T + W + W 0 m t out in B = − μ H , (B30) gap 0 steel T + g 2 T + 2 g m m N ASA/CR—2019-220382 77 where π ( R + R ) 1 2 W = , (B31) in 6 p π ( R + R ) 5 6 W = . (B32) out 6 p The airgap size and pole count must be sufficiently small for the magnet flux to pass across the airgap to the stator teeth rather than leak from magnet-to-magnet. To capture this effect, the magnet-to-magnet leakage flux can be modeled as a circular-arc [ 27 ] . From this assumption, the flux that passes across the gap while accounting for leakage, ˜ B , is gap   4 g p ˜ B = B 1 − . (B33) gap gap π R The angular speed and voltage are related via a power balance between ohmic heating, eddy current, and hysteresis losses.

P = τω − Q − Q − Q . (B34) in ohmic eddy hysteresis Assuming the motor is controlled such that two phases are active at any given time, the ohmic losses are Q = I ( 2 R ) . (B35) ohmic wind The electrical machine model is completed by characterizing the eddy and hysteresis losses:     2 2 2 2 Q = m k f B + m k f B , (B36) eddy sbi e teeth e sbi teeth     α α Q = m k f B + m k f B , (B37) hyst sbi h teeth e sbi teeth where k and k are eddy current and hysteresis loss coefficients for a particular material, respectively, e h f is electrical frequency, B is the stator back-iron flux density, B is the stator teeth flux density, sbi teeth and α is an exponential fit coefficient.

N ASA/CR—2019-220382 78 Table B7: Electrical machine performance design variables Quantity Dimension Description B N / m / A gap flux gap ˜ B N / m / A derated gap flux gap B N / m / A rotor back iron flux rotor B N / m / A stator back iron flux stator B N / m / A teeth flux teeth η - efficiency f Hz electrical frequency I A rms current rms J A / mm slot current density slot J A / mm wire current density wire P W load power load P W source power source Q W Ohmic losses ohmic Q W core losses core τ Nm torque μ Vs / A / m rotor back iron permittivity r μ Vs / A / m stator back iron permittivity s μ Vs / A / m teeth permittivity t V V rms voltage rms ω rad / s angular speed Table B8: Electrical machine constant parameters Quantity Value Dimension Description k 32.183e-6 W / lb / Hz eddy current loss coefficient e k 10.664e-3 W / lb / Hz hysteresis loss coefficient h N ASA/CR—2019-220382 79

Appendix C

Aircraft Conceptual Design Model

This section describes the details of airframe component sizing and performance models used in the aircraft conceptual design analysis presented in Section 6.2.

C.1 Free Stream State Model Free stream conditions fluid conditions are calculated as a function of altitude using an SP atmosphere model. All calculations were carried out for an altitude of of 37,000 ft, and the variables required for the airframe drag buildup, listed in Tab. C1, can be assumed constant, with the model formulation providing sensitivity of the vehicle performance to the input constant altitude.

Table C1: Flight state variables Quantity Value Dimension Description V 423 kt cruise free stream velocity ∞ − 5 ν 4.02 × 10 kg / m / s free stream kinematic viscosity ∞ ρ 0.3511 kg / m free stream density ∞ C.2 Fuselage Model C.2.1 Fuselage Sizing The fuselage mass is calculated using the buildup of Torenbeek [ 24 ] , which includes contributions pro- portional to fuselage shell and floor structural weight and a scaling factor to account for composite weight saving.

S = π d  (C1) wet fuse fuse   2 0.5 m g = f C d (  +  ) + Ω N d  (C2) fuse comp shell fuse ref fl fuse fuse fuse z A fuselage body form factor, used in the fuselage performance model below, is defined as a function of the fuselage fineness ratio.

 fuse FR = (C3) d fuse − 0.255 K = 1.4509 · FR (C4) Tables C2 and C3 list the variables to be optimized and constant parameters related to the fuselage sizing.

C1 Values for conventional and composite fuselage design, respectively.

N ASA/CR—2019-220382 81 Table C2: Fuselage sizing design variables Quantity Dimension Description d ft fuselage maximum diameter fuse FR - fuselage fineness ratio K - fuselage body form factor  ft fuselage length fuse m lb fuselage mass fuse N - ultimate load factor z S ft wing reference area ref S ft fuselage wetted area wet Table C3: Fuselage sizing constant parameters Quantity Value Dimension Description C 60 N / m fuselage shell density shell C1 f 1.0 / 0.9 - composite mass scaling factor comp  1.5 m reference length ref Ω 160 N / m non-shell mass scaling factor fl C.2.2 Fuselage Performance The fuselage profile drag is modeled using a Reynolds number scaling of turbulent skin friction and the form factor scaling of Schaufele [ 25 ] .

V  ∞ fuse Re = (C5)  ν ∞ 0.74 C = (C6) f 0.2 Re  KS wet C = C (C7) D ,fuse f p S ref D = ρ V S f C (C8) p ,fuse ∞ ref excr,fuse D ,fuse ∞ p D = D (C9) fuse p ,fuse Tables C4 and C5 list the variables to be optimized and constant parameters related to the fuselage performance.

Table C4: Fuselage performance design variables Quantity Dimension Description C - fuselage profile drag coefficient D ,fuse p C - skin friction coefficient f D lbf fuselage profile drag p ,fuse D lbf fuselage total drag fuse Re - fuselage length-reference Reynolds number  N ASA/CR—2019-220382 82 Table C5: Fuselage performance constant parameters Quantity Value Dimension Description f 1.00 - fuselage excrescence drag factor excr,fuse C.3 Wing Model C.3.1 Wing Sizing The wing mass is modeled as function of maximum lift, wing area, aspect ratio, thickness-to-chord ratio, taper ratio, sweep, and approximate control surface area using the statistical correlation of Raymer [ 15 ] .

S = 0.5 S (C10) CSW ref b AR = (C11) S ref   0.557 0.649 0.5 − 0.4 0.1 − 0.1 0.1 m g = f F L S AR ( t / c ) ( λ + 1 ) ( cos Λ ) S (C12) wing comp w max root CSW ref b ≥ b (C13) max Tables C6 and C7 list the variables to be optimized and constant parameters related to wing sizing.

Table C6: Wing sizing design variables Quantity Dimension Description AR - wing aspect ratio b ft wing span b ft max wing span max c ft mean aerodynamic chord cos Λ - cosine of wing sweep angle L lbf max wing lift max m lb wing mass wing S ft control surface area CSW S ft wing reference area ref λ + 1 - taper ratio plus one Table C7: Wing sizing constant parameters Quantity Value Dimension Description 0.443 2 0.749 F 0.00612 lbf / (ft ) wing mass factor w C2 f - 1.0 / 0.875 composite mass scaling factor comp ( t / c ) 0.127 - airfoil thickness ratio root C2 Values for conventional and composite wing design, respectively.

N ASA/CR—2019-220382 83 C.3.2 Wing Performance The wing induced drag is calculated based on the wing lift coefficient using the typical span loading efficient relation.

L = ρ V S C (C14) wing ∞ ref L , w ∞ C ≤ C (C15) L , w L ,max L ≤ L (C16) wing max C L , w C = (C17) D , w i π e AR D = ρ V S C (C18) i , w ∞ ref D , w ∞ i The wing profile drag is calculated as a function of wing lift, Reynolds number, Mach number, sweep, and thickness-to-drag ratio using a GP fit of TASOPT wing profile drag data [ 17 ] .

V c ∞ Re = (C19) c ν ∞   − 0.550434 Re c 1.29151 3.03609 1.77743 1.6515 C = 1.61418 ( t / c ) ( M cos Λ ) C D , w ∞ root L , w p   − 0.389048 Re c 0.784123 − 0.340157 0.950763 + 0.0466407 ( t / c ) ( M cos Λ ) C ∞ root L , w   − 0.218621 Re c 3.94654 19.2524 1.15233 + 190.811 ( t / c ) ( M cos Λ ) C (C20) ∞ root L , w   1.18147 Re c − 12 − 1.75664 0.10563 − 1.44114 + 2.82283 ( 10 ) ( t / c ) ( M cos Λ ) C ∞ root L , w D = ρ V S f C (C21) p , w ∞ ref excr,wing D , w ∞ p D = D + D (C22) wing p , w i , w Tables C8 and C9 list the variables to be optimized and constant parameters related to wing perfor- mance.

Table C8: Wing performance design variables Quantity Dimension Description C - wing induced drag coefficient D , w i C - wing profile drag coefficient D , w p C - wing lift coefficient L , w D lbf wing induced drag i , w D lbf wing profile drag p , w D lbf wing total drag wing L lbf wing total lift force wing Re - chord-referenced Reynolds number c N ASA/CR—2019-220382 84 Table C9: Wing performance constant parameters Quantity Value Dimension Description C 1.85 - max clean wing lift coefficient L ,max e 0.9 - wing Oswald efficiency f 1.00 - wing excrescence drag factor excr,wing C.4 Horizontal Tail Model C.4.1 Horizontal Tail Sizing The horizontal tail mass is calculated using the approximate tail area sizing and mass scaling described by Torenbeek [ 24 ] .

S  AR = 2 S  + 0.2 ( S c + 2 d  )( A + 2 ) f (C23) h h h h ref fuse w comp fuse S h c = (C24) h b h b h A = (C25) h S h m g = f [ F S ] (C26) v comp h h Tables C10 and C11 list the variables to be optimized and constant parameters related to horizontal tail sizing.

Table C10: Horizontal tail sizing design variables Quantity Dimension Description A - horizontal tail aspect ratio h b ft horizontal tail span h c ft horizontal tail mean aerodynamic chord h  ft horizontal tail moment arm h m lb horizontal tail mass h S ft horizontal tail area h Table C11: Horizontal tail sizing constant parameters Quantity Value Dimension Description F 250 N / m horizontal tail mass factor h C3 f - 1.0 / 0.855 composite mass scaling factor comp ( t / c ) 0.10 - airfoil thickness ratio root C3 Values for conventional and composite tail design, respectively.

N ASA/CR—2019-220382 85 C.4.2 Horizontal Tail Performance The horizontal tail drag is calculated as a function of Reynolds number, Mach number and tail thickness- to-chord ratio using a GP fit of TASOPT wing profile drag data [ 17 ] .

V c ∞ Re = (C27) c ν ∞   − 0.0021665 Re 0.119392 − 2 c 0.104391 − 0.0177484 C = 6.9696 × 10 ( 100 ( t / c ) ) M root D , h ∞ p   − 0.0017356 Re c − 0.164667 − 0.0233832 + 0.273439 ( 100 ( t / c ) ) M root ∞   − 0.186771 Re c 1.52706 3.89794 + 0.0001504 ( 100 ( t / c ) ) M (C28) root ∞   − 0.00170564 Re c − 0.175197 0.0242146 + 0.27215 ( 100 ( t / c ) ) M root ∞   − 0.00195720 Re c 0.22082 − 0.0439115 + 0.0608952 ( 100 ( t / c ) ) M root ∞ 1 2 D = ρ V S C f (C29) p , h ∞ h D , h excr, h 2 ∞ p D = D (C30) h p , h Tables C12 and C13 list the variables to be optimized and constant parameters related to horizontal tail performance.

Table C12: Horizontal tail performance design variables Quantity Dimension Description C - horizontal tail profile drag coefficient D , h p D lbf horizontal tail drag h D lbf horizontal tail profile drag p , h Re - chord-referenced Reynolds number c Table C13: Horizontal tail performance constant parameters Quantity Value Dimension Description f 1.0 - horizontal tail excrescence drag factor excr, h N ASA/CR—2019-220382 86 C.5 Vertical Tail Model C.5.1 Vertical Tail Sizing The vertical tail mass is calculated using the approximate tail area sizing and mass scaling described by Torenbeek [ 24 ] .

  S  = 0.03 S b + 10 d  (C31) v v ref fuse fuse S v c = (C32) v b v b v A = (C33) v S v m g = f [ F S ] (C34) v comp v v Tables C14 and C15 list the variables to be optimized and constant parameters related to vertical tail sizing.

Table C14: Vertical tail sizing design variables Quantity Dimension Description A - vertical tail aspect ratio v b ft vertical tail span v c ft vertical tail mean aerodynamic chord v  ft vertical tail moment arm v m lb vertical tail mass v S ft vertical tail area v Table C15: Vertical tail sizing constant parameters Quantity Value Dimension Description F 250 N / m vertical tail weight factor v C4 f - 1.0 / 0.855 composite mass scaling factor comp ( t / c ) 0.11 - airfoil thickness ratio root C4 Values for conventional and composite tail design, respectively.

N ASA/CR—2019-220382 87 C.5.2 Vertical Tail Performance The vertical tail drag is calculated as a function of Reynolds number and tail thickness-to-chord ratio using a GP fit of TASOPT wing profile drag data [ 17 ] .

V c ∞ v Re = (C35) c ν ∞   − 0.494 Re c 0.125 0.0017 0.0075 4 3.54 C = 0.19Re ( t / c ) + 1.83 × 10 ( t / c ) D , v c root root p     0.00165 0.00168 Re Re c c 0.0082 0.00168 + 0.118 ( t / c ) + 0.198 ( t / c ) (C36) root root 1000 1000 1 2 D = ρ V S C f (C37) p , v ∞ v D , v excr, v ∞ p D = D (C38) v p , v Tables C16 and C17 list the variables to be optimized and constant parameters related to vertical tail performance.

Table C16: Vertical tail performance design variables Quantity Dimension Description C - vertical tail profile drag coefficient D , v p D lbf vertical tail drag v D lbf vertical tail profile drag p , v Re - chord-reference Reynolds number c Table C17: Vertical tail performance constant parameters Quantity Value Dimension Description f 1.0 - vertical tail excrescence drag factor excr, v C.6 Nacelle Model C.6.1 Nacelle Sizing The TASOPT nacelle sizing model [ 17 ] is GP and is implemented directly.

1 2 S = N r π d (C39) nace e S nace fan A = 0.4 S (C40) inlet nace A = 0.2 S (C41) fan cowl nace A = 0.4 S (C42) exh nace d = d (C43) LPC fan A = 3 π d (C44) core cowl LPC m = f ( ρ S ) (C45) nace comp A nace nace m = ( m + m ) f (C46) pylon nace py,ref pylon m = m + m (C47) nace pylon  = 0.15 r d (C48) nace S fan nace N ASA/CR—2019-220382 88 Tables C18 and C19 list the variables to be optimized and constant parameters related to nacelle sizing.

Table C18: Nacelle sizing design parameters Quantity Dimension Description A ft core cowl area core cowl A ft exhaust area exhaust A ft fan cowl area fan cowl A ft inlet area inlet d in fan diameter fan d in LPC diameter LPC  ft nacelle length nace m lb nacelle + pylon mass m lb nacelle mass nace m lb pylon mass pylon m lb pylon reference mass py,ref S ft nacelle wetted area nace Table C19: Nacelle sizing constant parameters Quantity Value Dimension Description C5 f 1.0 / 0.925 - composite mass scaling factor comp f 0.1 - pylon mass fraction pylon C6 N 2 / 1 - number of engines e r 16.0 - nacelle wetted-to-flow area ratio S nace ρ 4.15 lb / ft nacelle weight per wetted area A nace C.6.2 Nacelle performance The TASOPT nacelle drag model [ 17 ] is GP and is implemented directly.

V  ∞ nace Re = (C49) nace ν inf 0.074 C = (C50) f ,turb 0.2 Re nace C = f C (C51) f ,nace excr,nace f ,turb V = 1.2 r V (C52) n LE V ∞ nac      V V n n LE LE r 3 = 0.25 + r + r (C53) V V nace V surf nace V V ∞ ∞ 1 2 D = ρ V S r C (C54) nace ∞ nace V f ,nace 2 ∞ surf Tables C20 and C21 list the variables to be optimized and constant parameters related to nacelle performance.

C5 Values for conventional and composite nacelle design, respectively.

C6 Values for under wing turbofan-generator and tail cone thruster nacelles, respectively.

N ASA/CR—2019-220382 89 Table C20: Nacelle performance design variables Quantity Dimension Description D lbf nacelle drag nace C - nacelle skin friction coefficient f ,nace C - turbulent skin friction coefficient f ,turb Re - nacelle Reynolds number nace r - surface velocity ratio cubed V surf V m / s V n LE n LE Table C21: Nacelle performance constant parameters Quantity Value Dimension Description f 1.0 - nacelle excrescence drag factor excr,nace r 1.0 - nacelle velocity ratio V nace C.7 Landing Gear Sizing Model The landing gear mass is assumed to be proportional to vehicle max takeoff mass, m , decomposed MTO into contributions from the nose and main gear.

m = f m (C55) main LG,main MTO m = f m (C56) nose LG,nose MTO m = m + m (C57) gear main nose Tables C22 and C23 list the variables to be optimized and constant parameters related to landing gear sizing.

Table C22: Landing gear sizing design variables Quantity Dimension Description m lb total landing gear mass gear m lb main gear mass main m lb nose gear mass nose Table C23: Landing gear sizing constant parameters Quantity Value Dimension Description f 0.03 - main gear mass fraction LG,main f 0.007 - nose gear mass fraction LG,nose C.8 Systems and Equipment Sizing Model The systems and equipment mass is assumed to consist of a fixed mass and components proportional to max takeoff mass and payload mass.

m = f m + f m + m (C58) equip equip,mTO MTO equip,pay payload fix N ASA/CR—2019-220382 90 Tables C24 and C25 list the design variables to be optimized and constant parameters related to systems and equipment sizing.

Table C24: Systems and equipment sizing design variables Quantity Dimension Description m lb systems and equipment mass equip Table C25: Systems and equipment sizing constant parameters Quantity Value Dimension Description f 0.0557 - equipment MTOW scaling equip,mTO f 0.221 - equipment payload scaling equip,pay m 2500 lb fixed mass fix C.9 Operational Items Sizing Model The operational item mass is assumed to consist of a fixed mass and a component proportional to payload mass.

m = f m + m (C59) items items,pay payload fix Tables C26 and C27 list the design variables to be optimized and constant parameters related to operational items sizing.

Table C26: Operational items sizing design variables Quantity Dimension Description m lb operational items mass items Table C27: Systems and equipment sizing constant parameters Quantity Value Dimension Description f 0.15 - equipment payload scaling items,pay m 440 lb fixed mass fix N ASA/CR—2019-220382 91

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