Design of a Hybrid Wing-Body Aircraft to Maximize

Market Disruption

Alexander Donaldson∗ and Jonathan Gibbs ∗

Pritesh Mody∗

Massachusetts Institute of Technology, Cambridge, MA 02139

A method is developed for quantifying the possible market share disruption caused bythe entry of a new aircraft into the commercial air transportation market. Disruption is aphenomena in which a new product enters the market and rapidly captures market sharefrom existing products by introducing higher performance that satisfies customers needs.The quantified disruption potential was then used as the objective in the optimizationof a small, single-pilot class commercial passenger transport aircraft. This led to aircraftdesigns with disruptive performance is some aspects of design and competitive performancein others, which historical trends indicate is critical to long term market diffusion andsuccess. The configuration selected for study was the hybrid wing body aircraft due to thelarge opportunity space (albeit small disjointed feasible space) for multi-disciplinary designoptimization. Since the market analysis required for quantification of relative performanceof different aircraft is inherently non-smooth, heuristic optimization methods were selectedand the analysis was based on a single objective and multi-objective genetic algorithm.Optimization results for the short haul market considered, showed a bias for increasedcruise Mach past the high subsonic regime, high fuel efficiency and increased ranges toincrease the time spent in more efficient cruise but with limits on fuel volume as the smallaircraft scale. The optimal disruptive design for the short range market had a design rangeof 2000 nautical miles and maximized efficiency and cruise Mach to bound limit of 0.65.The design resulted in a high disruptive potential for capturing market share from slowerturboprop aircraft but lower potential for capturing larger, faster, jet powered aircraft.

I. Problem Formulation

The motivation for this work was to explore the feasibility of integrating a qualitative framework foraircraft market disruption into a quantitative multi-disciplinary aircraft design optimization framework.

A 10 passenger hybrid wing body airplane was used as a test case based on potential technological advantagesover conventional aircraft. The airplane was optimized within the framework to disrupt as many regionalaircraft markets as possible by achieving better technical performance than the competition. The marketsincluded 50 passenger turbo props and 50 passenger jets, 10 passenger pistons, 100 passenger turbopropsand 100 passenger jets.

The hybrid wing body (HWB) aircraft was selected for its potential performance improvements overconventional tube and wing aircraft. The configuration bridges the gap between the flying wing and conven-tional tube-and-wing aircraft by blending the wings and fuselage into a hybrid all lifting configuration. Theearliest predecessors of the concept include the Junkers G.38 that first flew in 1929. The concept continues tobe explored today for both commercial and military applications with focus of fuel efficiency, noise reductionand even stealth.

Current designs of research focus include Boeing’s Blended Wing Body (BWB) concept developed incollaboration with NASA . The original concept developed for a 800 passenger, 7000 n.m. design is describedby Leibeck1 and compared to conventional tube-and-wing aircraft. The centerbody housed a double deckcabin extended spanwise and used as wing bending structure to enable a long wingspan while loweringoperating empty weight by 12%. The total wetted area reduction for the all-lifting body along with wing

∗Graduate Research Assistant, Department of Aeronautics and Astronautics, AIAA Student Member.

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49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-1204

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

boundary layer ingestion (BLI) using embedded engines results in an overall 20% higher lift/drag. Theoverall concept was estimated to have 27% lower fuel burn and 15% lower take-off weight.

Another HWB design of interest, is the Silent Aircraft experimental (SAX-40) aircraft2,3 that resultedfrom the work of the Silent Aircraft Initiative (SAI) to reduce noise to inaudible levels out the airportboundary in typical urban areas. The HWB system was optimized in a MDO framework to achieve acalculated noise level of 62 dBA at the airport perimeter. Additionally, the innovative aerodynamic designand airframe boundary layer ingestion resulted in an estimated 25% fuel burn improvement compared toexisting commerical aircraft. The study highlighted the HWB concept ability to simultaneously reduce noiseand fuel burn through mutually beneficial multidisciplinary design interactions.

The fuel burn and noise focus was continued as part of NASA N+2 work. The analysis included studyof the SAX-40F,4 a cargo variant of the SAX-40 with double the payload weight and 20% greater range.The SAX-40F was further refined by Boeing to produce podded engine (N2A) and embedded engine (N2B)aircraft variants to address the N+2 programmatic goals.5

I.A. Disruption Model

The disruption model was formed by considering three categories of technical performance (speed, efficiency,and flexibility) of the design aircraft (damach, daefficiency, daflexability) and entry in to service date relative toa given competing aircraft (camach, caefficiency, caflexability) and defining a non-dimensional disruptive index(di) to indicate the disruptive nature of the design aircraft relative to each competitive aircraft in eachcategory. The cruise mach has historically been a significant driver in aircraft design and more recently thefuel efficiency (passenger miles per gallon) has also played a significant role. Flexibility is a measure of howeasy it is for an airline to add more flights (frequency) to a route for a fixed number of passengers. It isgiven by maximum number of passengers / design range. An aircraft carrying fewer passengers over a fixedrange can potentially serve the same market (number of passengers than what to fly a route) as an aircraftthat carries more passengers per flight over fewer flights per day. The disruptive coefficient was formed bysumming a disruptive index (di) for each category which is set based on two thresholds for each category,a poor performance threshold and a disruptive performance threshold: (drpoor, drdis) and the performancedifference between the competing aircraft and the design aircraft in the corresponding category.

The thresholds and the disruptive index function were based upon historical observations of the increasesand decreases in performance from disruptive aircraft, and the extent to which these changes in performanceresulted in captured market share from existing products. Several aircraft in the long range aircraft marketwere used for validation because that market is complicated less by substitute forms of transportation, wartime orders, and a large number of firms than the short range aircraft market. Some of the aircraft observedinclude the Lockheed Constellation, the Boeing 707, 747, 767, and 777, the BAE Concorde, the AirbusA300, A330, and A340. These aircraft presented increases in performance in some categories and decreasesin performance in others and depending on their performance and entry into service date, the resulting marketdiffusion was ether minimal, equal, or dominant (capturing the largest market share amongst competitors).The disruptive index function and the thresholds were adjusted to match the performance-market diffusionrelationship as much as possible.

The disruptive index function took the form of (−1/x3 + 1), where x was determined by taking scaleddifference between the performance of the design aircraft and the competing aircraft for a the given category:

x = 3/(drdis − drpoor) ∗ ((da/ca− drpoor)) + 1 (1)

When the aircraft achieves exactly satisfactory performance (equal to the poor performance threshold)X is given a value of 1. Below this threshold, x becomes negative and the disruptive index will also returna steep, negative gradient for x < 1 and asymptote to 1 as x → inf. At x = 4 (the disruptive threshold),the value of the function is .9844. The function asymptotes to one as x → ∞ in order to bound thepositive performance and keep the function differentiable and smooth. The poor performance and disruptiveperformance thresholds (dipoor and didis) are used to scale the relative performance between the designaircraft and the competing aircraft which a disruptive performance achieving a value of 4 and satisfactoryperformance achieving a value 1. The disruptive index is a smooth function, it is differentiable over its range.

If the design aircraft do not meet the poor performance threshold, the disruptive index function willreturn a negative value and a negative gradient. This behavior was meant to severely penalize aircraft thatare disruptive in one category but have unsatisfactory performance in other categories. An example of such

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an aircraft is the Concorde which had disruptive speed performance (over 100% faster) but unsatisfactoryefficiency (75% lower). The Concorde subsequently gained little market share, with only 20 aircraft built.However, other aircraft such as the Boeing 707 were disruptive in speed (75% faster) and had poorer efficiency(40% lower) but were still able to gain a dominant market share position. The poor performance thresholdwas used to differentiate the function behavior between these two types of market responses. The disruptivecoefficient was formed by summing the three disruptive performance indices. The index has values in therange of -500 to 3. The coefficient was then used to determine the amount of route revenue from thecompeting aircraft the design aircraft receives.

I.B. Market Model

Figure 1. Function describing the level ofdisruption cause by different relative per-formance levels

The available revenue was determined by examining the revenue gen-erating routes flown by the competing aircraft. Routes that the newaircraft was capable of flying were then selected from these routesby comparing the maximum takeoff field length of the originatingairport and the distance of the route with the takeoff field lengthand the range of the design aircraft. This part of the market modelresembles a step function and was not smooth because the revenuefor each route is added discretely, only when both the takeoff fieldlength and range requirements were met. When these requirementswere not met, the available revenue from that route returns 0. If theaircraft was disruptive (coefficient value close to 3), it would obtaina large proportion of the route revenue. If the aircraft offered onlysatisfactory performance (coefficient value of 0) it would not gainany market share. The revenue and route information was takenfrom the 2008 Department of Transportation B1B databases. Thedatabase does not differentiate a route based on whether it is a stopon the way to the final destination or if it is a non-stop route. The resulting revenue from each competingaircraft was then summed to form a total revenue for the design aircraft which was then divided by theavailable revenue to return a total market share number (−J). It should be noted that the disruptive coeffi-cient was not intended to predict market share, it is only an indication of the relative technical performancebetween the design aircraft and competing aircraft. Revenue and market share were used to weigh the im-portance of being disruptive with respect to one competing aircraft relative to another competing aircraft.It is also acknowledged, that actual market share is determined by many other operational and social factorsnot considered in this initial study.

I.C. Formal Problem Formulation

xle5

ale1

cho5

cho9

span Fixed Payload & Cabin

Operation: Mach Range Cruise Altitude

Wing Planform

Fixed Propulsion Configuration

Figure 2. Graphical representation of the de-sign variables and parameters used in this de-sign problem formulation

The objective of this design problem was to minimize J(x,p, c),where J is the negative market share number computed bythe market model. There were four non linear constraintsgi(x,p) <= 0: cruise angle of attack for passenger comfort,max takeoff weight to allow for a single pilot crew, static sta-bility margin to ensure no special control systems are needed,and a geometric twist limit to ensure manufacturability. Fuelvolume was an additional constraint, implemented has a hardrequirement for aircraft design closure. The max takeoff weightwas specified by the parameter p. There were 10 design vari-ables in the design vector x. These variables corresponded tothe mission performance (mach, desired range, altitude), andthe planform definition of the aircraft (leading edge location,twist and 3 wing locations, span, wing sweep, wing chord androot chord). Each design variable was bounded by a lower andupper bound in the vectors, xlb and xub. The competing air-craft are described in a vector c with three entries for each aircraft corresponding to the competing aircraft’sperformance in the three categories. The thresholds for each category are set independently inside of the

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disruption module.

min J(x,p, c)subject to gi(x,p) ≤ 0 i = 1, . . . , 4

xlb ≤ x ≤ xub

(2)

II. HWB Design Model

The design methodology used for the HWB design aircraft considered here is built upon the frameworkdeveloped during SAI and N+2 programs but adapted at the disciplinary model level for simplified analysisof business jet / regional transport class aircraft. Since system level validation is not possible due to thelack of data for aircraft in this configuration and size class, the disciplinary models are selected based on theempirical data, where available. This allows subsystem level performance to be bounded within the typicalperformance levels of existing systems while still allowing opportunity for exploitation of multidisciplinaryinteractions in the HWB design. The high level design methodology is illustrated in the N2 diagram shownin Figure 3, with modules arrangement to minimize feedback.

Figure 3. N2 diagram showing the feedback and feedforward of information in the HWB model

The analysis began with the specification of design variables and parameters, including the missiondefinition and airframe planform. The planform was then lofted into a 3D airframe to envelop the pre-configured cabin for the fixed payload case assessed. The aircraft weight was then estimated and usedalong with initial aerodynamic analysis to size the propulsion system for top of climb thrust requirements.Performance of the propulsion system was required to compute fuel burn. The cruise analysis also requiredadjustment of the wing twist to trim the aircraft at the start of cruise. The new fuel estimate feeds back to theinitial weight estimate and the design loop iterates until a converged statically stable design is achieved. Thiswas followed by off-design analysis that involves stall speed calculations for takeoff and approach analysis,as is required to assess performance relative to the market. The inability to trim the aircraft or individualdisciplinary models to run, resulted in a non-convergent design.

II.A. Structural Model

Structural design of the unconventional HWB continues to remain a challenge due to the lack of data andlimited understanding of sizing load cases. Secondary weights were estimated using empirical correlationsfor business jets from the same source, and are not expected to vary significantly from their tube and wingcounterparts. To use the existing body of data on aircraft structural sizing, the system was modeled as aflying wing with an embedded pressure vessel. The wing structure was expected to consist of a continuousaft spar and a forward spar that would be required to wrap around the forward cabin. Using the work ofKroo6 for Aluminum class aircraft, the wing weight is considered fully-stressed bending weight of the wingbox. It includes the effect of total wing load (at the ultimate load factor, Nult), span (b), average airfoilthickness (t/c), taper (l), sweep of the structural axis (Λ), gross wing area (Swg), takeoff weight (TOW),zero fuel weight (ZFW) and wing taper ratio (λ), all of which were estimated for the entire HWB airframe.

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Wwing = 4.22Swg + 1.642× 10−6 Nultb3√

TOW ZFW (1 + 2λ)(t/c)avg cos2 ΛSwg(1 + λ)

(3)

This model was validated based on actual data from 15 aluminum transport aircraft, and expected torepresent a conservative overestimate for a typically composite HWB airframe.

The pressure vessel was also sized using Kroo’s models with dependence on fuselage geometry: width B,height H, length L and surface area (Sfuse). The cabin was sized based on the payload assuming typicalinterior sizing rules in a single aisle configuration. The weight sizing is based on the dominant load betweenpressure and bending. The pressure loads are represented by the pressure index Ip = 1.5× 10−3PB, whereP is the maximum pressure differential (lb/sq.ft). The bending loads are represented using the limit loadfactor N , as Ib = 1.91× 10−4NWL/H2.

Pressure Dominated: Ifuse = Ip (4)Bending Dominated: Ifuse = (I2

p + I2b )/(2Ib) (5)

Wfuse = (1.051 + 0.102Ifuse)Sfuse (6)

II.B. Aerodynamics Model

The aerodynamic model used a modified version of the quasi-3D aerodynamic analysis methodology de-veloped and validated to assess SAX-402,3 and N2A/N2B4,5 airframes. The airframe lift distribution,induced drag and neutral point were computed for each lofted airframe (including twist and control sur-face deflection) using a vortex-lattice analysis performed using AVLa. Profile and viscous drag for theouter wing supercritical airfoil were computed offline with 2D viscous analysis using XFOILb at discretecruise Mach numbers of [0.1,0.2,0.3,0.4,0.5,0.6,0.6] and corresponding representative Reynolds numbers of[5e5,1e7,2e7,3e7,4e7,5e7,6e7]. The resulting drag polars were integrated as a lookup table of sectional dragas a function of sectional lift and Reynolds number, with sweep corrections. This 2-D approach is notapplicable for the centerbody due to the 3-D nature of the flow field. The centerbody profile and viscousdrag was computed using Hoerner correlations7 for bodies of revolution with lift coefficient dependence. Themethodology was assessed as part of the N+2 program and shown to be in good agreement with a BoeingCFD study using CFL3Dv6c for a test HWB operating at Mach 0.8 at 40000 ft altitude. Unlike the originalimplementation that captured transonic effects not applicable here, the current model included considera-tion for Reynolds/Mach scaling and is expected to be applicable for the flow regimes under consideration.However, fidelity of the centerbody correlations, may require additional validation at these smaller scales,where the centerbody is relative larger part of the overall aircraft.

II.C. Static Stability Model

The thick centerbody airfoil with leading edge carving for forward loading was designed during SAI to trimto aft lift from the centerbody airfoils and the airfoil stack was retained here. The twist distribution wasscaled from input reference parameters to trim aircraft pitching moments for longitudinal static stability andmeet static margin limits (> 5%). The pressure loading and moment computation was based on the AVLanalysis embedded in the aerodynamics model.

II.D. Propulsion Model

The propulsion architecture was restricted to dual aft podded turbofan engines. Engine performance wasbased on curvefits of current engines in the considered thrust class using Jane’s small engine database. Theengines were sized for top of climb thrust (FTOC) based on the drag input (L/D) from the aerodynamicsmodel and the flight path angle (γ). The equivalent sea-level static thrust (FSLS) was then obtained usingthe altitude (through density ρ).

FTOC = WTOC(D/L + sin γ) (7)FSLS = FTOC(ρSLS/ρTOC) (8)

aAthena Vortex Lattice, Drela, M., MIT, Cambridge, MA. http://raphael.mit.edu/avlbXFOIL, Drela, M., MIT, Cambridge, MA. http://raphael.mit.edu/xfoilcCFL3D Version 6, NASA Langley Research Center

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The maximum dry specific fuel consumption (SFCSLS) was intepolated from Jane’s data using the equiv-alent sea-level static thrust (FSLS). The cruise specific fuel consumption (SFCCBN) was then corrected forcruise Mach and altitude (through static temperature T ).

θ =TCBN

TSLS

(1 +

γ − 12

M2CBN

)(9)

SFCCBN = SFCSLS/√

θ (10)

The engine weight and fan diameter were also interpolated using the equivalent static thrust.

(a) SLS thrust to weight (b) SLS thrust to SFC

Figure 4. Small engine performance curve fits

III. Optimization Methodology

III.A. Characterization of the design space

In order to select an appropriate optimization algorithm, the shape of the solution-space of the objectivefunction had to be quantified. Several features of this non-linear problem lead to challenges in effectivelyexploring the solution space. First, the sensitivity of the system to satisfy the static stability constraintsfor different geometric parameters led to a small feasible design space and several infeasible designs. Thisfeasible space was also fragmented into islands of feasibility due to the complex interactions between theaerodynamic loading, weight distribution and the ability to achieve a twist distribution across the wingrequired to satisfy non-linear longitudinal stability constraints. The second challenge was the non-smoothnature of the solution space. The stability challenge also resulted in several non-convergent designs where thetwist distribution problem was ill-defined, resulting in geometrically degenerate planforms or designs outsidethe assessment capability of the individual disciplinary models. In these cases and cases with inadequate fuelvolume, no measure of the objective value was available. The objective function also had inherent steps dueto the nature of market value part of the objective. The ability of an aircraft to generate revenue at differentcombinations of range and takeoff performance is inherently discrete - a given market for air travel can onlybe capitalized if the required range between the origin and destination is met, there is also no benefit forexceeding that range requirement. These flat regions of the market response can be observed in figure 5.

III.B. Single Objective

The non-smooth nature of the objective space combined with the inability of the aerodynamic and stabilitymodel to provide any solution for several infeasible or non-convergent designs meant that use of a gradient-based optimization technique was not well matched for this problem. Even if the model could have beenadapted to improve the error handling for infeasible cases, the non-linear, non-contiguous nature of thefeasible space meant that multiple starting points would be required in order to investigate the multiple,isolated minima. For these reasons, a heuristic optimization method was chosen for this problem. InitiallySimulated Annealing (SA) was attempted because it allows the balance between energetic global search andrefined local search to be tuned using just two parameters (the initial system temperature, and the coolingschedule). An exponential cooling profile was used to maximize coverage of the design space during the

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0

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2000

20004000

60008000

1000012000

0

1

2

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7

x 109

Minimum Takeoff Field Length (ft)Range (n.m.)

Mar

ket V

alue

($)

Figure 5. U.S. domestic air transportation market for different range and takeoff performance values

initial random search phase. Constraints were included using a quadratic penalty function of the form:

P (x) = ρp

6∑j=1

(max [0, gj(x)])2 (11)

0 100 200 300 400 500 600 700−200

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Sys

tem

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rgy

SA convergence history

current configurationnew best configuration

Figure 6. Convergence history for one example simulatedannealing optimization run

This penalty function allowed information aboutthe degree of infeasibility to be captured by the op-timizer (for those cases where the model converged).In addition, the formulation converges to the exactsolution in the limit ρ →∞ and the quadratic formdoes not add large discontinuities to the objectivefunction for smaller values of ρ. Unfortunately bal-ancing the penalty parameter with the initial tem-perature and cooling schedule proved to be more dif-ficult than anticipated. For the several optimizationruns preformed, the optimizer spent the high-energytime exploring completely infeasible solutions (ob-jective function values > 0) (figure 6) and would cooltowards one of only a few feasible solutions that itfound, which yielded a great deal of variability be-tween runs.

Due to these issues the optimization method wasswitched from Simulated Annealing to an GeneticAlgorithm using the same external penalty method.The Genetic Algorithm while potentially computationally intensive required less tuning in order to reliablyhandle the large infeasible space and several non-convergent designs using population based optimization.The canonical GA without elitism is provably non-convergence but even with elitism the GA does notguarantee convergence. Binary encoding (with chromosome length B) was selected since it allows coarsediscretization of the solution space compared alternate higher cardinality or real valued encoding schemes.The population size N used in the algorithm was selected to be above the minimum required to make anypoint in the resulting subspace reachable with probability P (=99.99%), by crossover alone, as given byReeves:8

Nmin ≈ �1 + log(−B/ log P )/ log 2 (12)

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The actual population size used was selected to limit computational cost, while also controlling the numberof generations required for convergence with typical value of about 4-5 B. The population was initializedwith known feasible solutions supplemented with Latin Hypercube sampling to ensure uniform sampling ofthe individual design variables. Evolution of each generation was achieved using tournament selection assuggested by Spall,9 single point crossover and a uniform mutation rate of 0.0099 as suggested by Rudolph.10

III.C. Multi-Objective

In order to develop more insight into the solution found by the single objective optimization,a subsequentmulti-objective optimization was conducted. For this optimization the design problem was broken intoobjectives of Range, True Airspeed and Fuel efficiency (in passenger miles per gallon).

A normal boundary intersection (NBI) optimization method was attempted to see what results, if any,could be obtained for initial assessment. If it is able to converge onto a Pareto front an NBI method isable to capture the front with controlled and regular grid spacing and in substantially fewer iterations thanthe adaptive weighted sum (AWS) method. However it was known at the start of this experiment that thedesign space for the HWB optimization had islands of feasibility, and as such had confounded our previousattempts to use gradient-based techniques on the problem.

The NBI optimization failed in an irrecoverable manner. The first step of the NBI optimization is tofind three anchor points, which are the solution when the design is optimized for each objective individually(using a gradient-based method). This step proceeded correctly, with the optimizer being able to findthree distinct feasible maxima starting from the given initial point. The subsequent step in the algorithm,conducted further gradient based optimizations from starting point along the vectors connecting the anchorpoints. Unfortunately, it appears that much of the design space along the vectors connecting the anchor pointwas infeasible. This meant that the subsequent gradient based optimization from the intermediate pointstowards the Pareto front was initialized with an infeasible design vector. This initial infeasibility often leadsthe optimizer to fail to find any feasible design space. In the worst cases the aerodynamic analysis failed torun due to completely unrealistic planform geometries.

After these initial trials the NBI optimization was abandoned in favor of a heuristic method, morerobust to the large infeasible regions in the design space. Extending the single-objective implementation,the multi-objective extension of the genetic algorithm (MOGA) was used. Despite the MOGA robustnessto the general non-linear problem, the drawbacks of the approach include typically increased computationalburden for problems with no discrete variables and clustering of solutions due to crossover of neighboringsolutions. In practice, the computation burden was acceptable since the clustering issue was not observedin this case. Given more time it would be insightful to see if any of the other gradient-based multi-objectivealgorithms could produce results. AWS in particular might have more success given that the subsequentoptimization points may be initialized closer to the Pareto front.

IV. Optimization Results

IV.A. Single Objective

The single objective optimization yielded the optimal design vector shown in table 1 and figure 7. Onlythe Cruise Mach number design variable was found to be at either an upper or lower bound. The Machnumber was forced to the upper allowed value of 0.65, which reflects the market preference for faster vehicles.Mach .65 is slow to many current commercial aircraft but the market context for regional aircraft serviceshas many turbo prop aircraft with speeds in the Mach .5 to .6 range along with several faster jet poweredaircraft. In the subsonic model used in this analysis the cost of extra cruise speed is relatively small. Thetrue optimum cruise Mach number is likely to lie in the transonic regime (Mach 0̃.8-1) where the drag risewith increasing velocity becomes severely non-linear. The aerodynamic model used in this analysis cannotreliably model mach numbers larger than .7, so an upper bound of Mach 0.65 was used. The optimal rangeof 2000 n.m. reflected the tradeoff between designing an aircraft that can fly all routes in the continentalUnited States (range 3̃000 n.m.) and the inefficiency of operating climb/descent dominated short haul flightswhere significant demand exists. An aircraft operating at less than its design range is carrying the weight oflarger fuel tanks and the increased drag of a larger airframe to accommodate those larger tanks comparedto an aircraft optimized for a shorter range and therefore an efficiency penalty is paid in many markets fora longer (3000 n.m.) range aircraft.

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Table 1. Best design vector found by optimization with a genetic algorithm, and sensitivity of the solution calculatedusing finite differences

Design Variable J(i) Value ∂Ji/∂xi

Cruise Mach 0.65 -546Range (n.m.) 2000 -0.0022

Cruise Altitude (ft) 29000 -0.0018Span 0.81 6.16

Wing root position 23.1 -2.55Wing root chord 5.2 1.69

Leading edge sweep angle 58 -0.0728Twist0 (deg.) 0.27 4.81Twist1 (deg.) -0.37 1.14Twist2 (deg.) 0.91 -4.29

Figure 7. 3-view of the best HWB design found by the genetic algorithm

IV.B. Multi Objective

After computing the Pareto surface with respect to the range, true airspeed and efficiency, the market shareat each Pareto point was also computed and overlayed to evaluate the market response across the Paretosurface. As expected, the fastest, furthest flying, most efficient designs capture the most market share.Contrary to long range aircraft trends, the optimization shows a strong preference for increased range withthe efficiency dropping off rapidly for lower range values. This effect is largely due to the mission modelused in this analysis, the inefficient climb and fixed reserves portions of the mission require a fixed amountof time to complete and therefore represent a higher fraction of the total mission fuel burn at short ranges.It is expected that the range would reach a maximum value if a suitably large design space were consideredsince as the fuel weight fraction of the aircraft becomes large and eventually limiting. This effect can beseen in the Pareto front with the gradient of efficiency with respect to range becoming substantially smallerat high ranges. The true airspeed (effectively cruise altitude at the maximum Mach of 0.65) has a weakereffect on efficiency, however lower cruise altitudes (lower true airspeed) produce more efficient designs basedon altitude scaling effects on the engine thrust and sfc and trade-offs with the aerodynamic performance.

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Figure 8. Pareto front of range, true airspeed and fuel efficiency produced by the MOGA

V. Conclusion

The multi-disciplinary optimization of the hybrid wing body aircraft for disruption was feasible usingheuristic algorithms due to the inherently non-smooth nature the market. The non-linear constraints in theaerodynamic and stability model created islands of feasibility which made using gradient-based approachesdependent upon the feasibility of the starting points. Tuning of simulated annealing algorithms was alsovery challenging for this class of problem with a non-convergent design space. The population based geneticalgorithm was observed to be robust of the challenges encountered and used for final analysis. The optimaldisruptive design had a design range of 2000 nautical miles and maximized efficiency and cruise Mach tobound limit of 0.65. The results from these studies also agreed with Pareto optimal designs that came fromusing the multi-objective genetic algorithm with the market disruption framework removed. The currentanalysis bounds on the range and speed based on modeling limits did make it difficult to identify some ofthe tradeoffs with the hybrid wing body configuration. Though the analysis suggests strong preference forincreased Mach, the non-linear behavior of the trade space in the transonic regime is not captured. The lowerground speeds for some of the more disruptive designs were a result of cruising at higher altitudes basedon the trade-off between higher efficiency (higher altitudes) and faster true airspeed (lower altitudes) at themach limit imposed. The ranges obtained were limited by the available fuel volume as the small scale aircraftbeing considered with increased ranges favored to increase time spent in more efficient cruise compared toinefficient climb. The curvature of the Pareto front also shows diminishing returns with increased rangeleading up the long haul aircraft segment where the trend is typically reversed. The same results from thedisruption framework overlayed on the Pareto front added value by helping the designer understand thedifferent market repsonses to Pareto optimal designs with regard to several technical performance object.

References

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TM-2009-215680, NASA, 2009.6Kroo, I. and Shevell, R., “Aircraft design: Synthesis and analysis,” Desktop Aeronautics Inc., 2006.7S., H., Fluid-Dynamic Drag, Hoerner Fluid Dynamics, 1965.8Reeves, C. and Rowe, J., Genetic Algorithms - Principles and Perspectives: A Guide to GA Theory, Kluwer Academic,

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