Multidisciplinary Design Optimization of a Transonic Commercial Transport with a Strut-Braced Wing

Transcription

1 Multidisciplinary Design Optimization of a Transonic Commercial Transport with a Strut-Braced Wing F. H. Gern, J. F. Gundlach, A. Ko, A. Naghshineh-Pour, E. Sulaeman, P. -A. Tetrault, B. Grossman, R. K. Kapania, W. H. Mason and J. A. Schetz Virginia Polytechnic Institute and State Univ. R. T. Haftka University of Florida 1999 World Aviation Conference October 19-21, 1999 San Francisco, CA SAE International 400 Commonwealth Drive Warrendale, PA U.S.A. American Institute of Aeronautics and Astronautics 370 L Enfant Promenade, S.W. Washington, D.C For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics or SAE International

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3 Multidisciplinary Design Optimization of a Transonic Commercial Transport with a Strut-Braced Wing F. H. Gern, J. F. Gundlach, A. Ko, A. Naghshineh-Pour, E. Sulaeman, P. -A. Tetrault, B. Grossman, R. K. Kapania, W. H. Mason and J. A. Schetz Virginia Polytechnic Institute and State Univ. Copyright 1999 by SAE International and the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. R. T. Haftka University of Florida ABSTRACT This paper details the multidisciplinary design optimization (MDO) of a strut-braced wing aircraft and its benefits relative to the cantilever wing configuration. The multidisciplinary design team is subdivided into aerodynamics, structures, aeroelasticity and synthesis of the various disciplines. The aerodynamic analysis consists of simple models for induced drag, wave drag, parasite drag and interference drag. The interference drag model is based on detailed computational fluid dynamics (CFD) analyses of various wing-strut intersection flows. The wing structural weight is partially calculated using a newly developed wing bending material weight routine that accounts for the special nature of strut-braced wings. The remaining components of the aircraft weight are calculated using a combination of NASA s Flight Optimization System (FLOPS) and Lockheed Martin Aeronautical System formulas. The strut-braced wing and cantilever wing configurations are optimized using Design Optimization Tools (DOT). Offline NASTRAN aerolasticity analysis preliminary results indicate that the flutter speed is higher than the design requirement. wing, to name only a few. This study exclusively compares the strut-braced wing concept (SBW) to the cantilever wing configuration. Favorable interactions between structures, aerodynamics and propulsion give the SBW potential for higher aerodynamic efficiency and lower weight than a cantilever wing (Fig. 2). The strut provides bending load alleviation for the wing, allowing the wing thickness to be reduced for a given wing load. Reduced wing thickness decreases transonic wave drag and parasite drag. This favorable drag reduction allows the wing to unsweep for increased regions of natural laminar flow and promotes further wing structural weight savings. Decreased overall weight, along with increased aerodynamic efficiency permits engine size reduction. INTRODUCTION Very few recent transonic transport aircraft designs divert from a low cantilever wing with either wing or fuselage mounted engines. Within that arrangement, few visual dissimilarities allow one to discern the various models (Fig. 1). It is unlikely that large strides in performance will be possible without a significant departure in vehicle configuration. Numerous alternative configuration concepts have been introduced over the years to challenge the cantilever wing design paradigm. These include the joined wing, blended-wing-body, twin-fuselage and the strut-braced Figure 1. Conventional Cantilever Configuration This strong synergism yields significant increases in performance over the cantilever wing. A Multidisciplinary Design Optimization (MDO) approach is necessary to fully exploit the interdependencies of various design disciplines. Several SBW design studies have been performed in the past ([1]-[6]), though not with a full MDO approach until quite recently ([7]-[9]). 1

4 This study was funded by NASA Langley with Lockheed Martin Aeronautical Systems (LMAS) as an industrial partner. The primary role of the LMAS interactions was to add practical industry experience to the vehicle study. This was achieved by calibrating the Virginia Tech MDO code to the LMAS MDO code for 1995 and 2010 technology level cantilever wing transports. LMAS also reviewed aspects of the Virginia Tech design methods specific to the strut-braced wing [9]. One of the authors worked on location at LMAS to upgrade, calibrate and validate the Virginia Tech MDO code before proceeding with optimizations of cantilever and strut-braced wing aircraft. Several SBW concepts have been investigated within this project. Design studies cover wingtip engines, underwing engines, and fuselage-mounted engines with a T- tail. However, emphasis of this paper is placed on the structural aspects of the optimization procedure for fuselage-mounted engine SBW configurations (Fig. 2). Since differences in T-tail fuselage-mounted and under-wing engine cantilever designs are small, this study uses cantilever optima with wing mounted engines, to make direct comparisons with the SBW. Table 1. Optimization constraints 1. Aircraft Zero Fuel Weight Convergence 2. Range Calculated > Reference Range 3. Initial Cruise Rate of Climb > 500 ft/min 4. Cruise Section C Lmax < Fuel Weight < Fuel Capacity 6. C N Available > C N Required 7. Wing Tip Deflection < Max. Wing Tip Deflection at Taxi Bump Condition 8. Wing Weight Convergence 9. Max. Body and Contents Weight Convergence 10. Second Segment Climb Gradient > 2.4% 11. Balanced Field Length < 11,000 ft 12. Approach Velocity < 140 kts. 13. Missed Approach Climb Gradient > 2.1% 14. Landing Distance < 11,000 ft 15. Econ. Mission Range Calculated > 4000 nmi 16. Econ. Mission Section C Lmax < Thrust at Altitude > Drag at Altitude Figure 2. SBW with Fuselage-Mounted Engines. DESIGN OPTIMIZATION GENERAL ASPECTS The Virginia Tech Truss-Braced Wing (TBW) code models aerodynamics, structures, weights, performance, and stability and control of both cantilever and strut-braced wing configurations. Design Optimization Tools (DOT) software by Vanderplatts R&D [10] optimizes the vehicles with the method of feasible directions. Between 15 and 22 design variables are used in a typical optimization. These include several geometric variables such as wing span, chords, thickness to chord ratios, strut geometry and engine location, plus additional variables including engine maximum thrust and average cruising altitude. As many as 17 inequality constraints may be used (Table 1). There are two side constraints to bound each design variable. Each design variable is scaled to have a value between 0 and 1 at the lower and upper limits, respectively. Take-off gross-weight, economic mission take-off gross weight, and fuel weight are important examples for possible objective functions that can be minimized. The MDO code architecture is configured in a modular way such that the analysis consists of subroutines representing various design disciplines. The primary analysis modules include: aerodynamics, wing bending material weight, total aircraft weight, stability and control, propulsion, flight performance and field performance (Fig. 3). Numerous differences between the analysis details of cantilever and SBW configurations are present in the design code, as is necessary for such dissimilar vehicles. The primary difference is in the analysis of the wing bending material weight, as discussed in the structures section. The strut has parasite drag and interference drag at its intersections with fuselage and wing. Some geometry differences are justified, such as setting the minimum root chord for the cantilever wing to 52 feet to make room for wing-mounted landing gear and kick spar. The SBW, without need for double taper, has the chord linearly interpolated from root to tip. The SBW has a high wing and fuselage mounted gear. It is important to note that, even though the external geometry of the fuselage for all cases is identical, the fuselage weights will generally be different. 2

5 Updated Design Variables Baseline Design Initial Design Variables Geometry Definition Induced Drag Friction and Form Drag Propulsion SFC Structural Optimization/ Weight Weight Aerodynamics L/D Wave Drag Interference Drag Field Performance Range Performance Offline CFD Analysis Stability and Control Objective Function, Constraints Optimizer Figure 3. Description of the MDO Process MISSION PROFILE The primary mission of interest is a 325-passenger, 7500 nautical mile range, Mach 0.85 transport with a 500 nautical mile fuel reserve (Fig. 4). Range effects on take-off gross weight and required fuel weight are investigated. A minimum fuel design is also considered. Several technology groups distinguish the 1995 and 2010 technology level aircraft. A 1995 technology aircraft represents an all-metallic benchmark similar to the Boeing 777. The other aerodynamics grouping includes the effects of riblets on the fuselage and nacelles, supercritical airfoils, active load management for induced drag reduction and all moving control surfaces. Systems technologies include integrated modular flight controls, fly-bylight and power-by-light, simple high-lift devices, and advanced flight management systems. Airframe technologies represent weight savings from composite wing and tails and integrally stiffened fuselage skins. The propulsion technology is reflected in reduced specific fuel consumption. Figure 4. Climb 11,000 ft T/O Field Length Mission Profile Mach 0.85 Cruise 140 Knot Approach Speed Mach Nmi Range 11,000 ft 500 Nmi Reserve LDG Field Length AERODYNAMICS Numerous iterations of both the Virginia Tech TBW code and Lockheed s version of NASA s Flight Optimization System (FLOPS) [16] were made so that drag polars produced by each code are consistent at reference design conditions. The drag components considered in the Virginia Tech TBW code are parasite, induced, interference and wave drag. Unless specified otherwise, the drag model is identical to previous Virginia Tech SBW studies [8]. A detailed description of the drag calculations can be found in [11]. Parasite Drag To calculate the parasite drag, form factors are applied to the equivalent flat plate skin friction drag of all exposed surfaces on the aircraft. The amounts of laminar flow on the wing and tails are estimated by interpolating Reynolds number vs. sweep data for F-14 and 757 glove experiments. Fuselage, nacelles, and pylon transition locations are estimated by an input transition Reynolds number. Laminar and turbulent flat-plate skin friction form factors are calculated with LMAS formulas in the Virginia Tech MDO tool. LMAS form factors for wing, tails, fuselage, and nacelles are applied to the skin friction drag to obtain the parasite drag. Induced Drag The induced drag module uses a discrete vortex method to calculate the induced drag in the Trefftz plane [8]. Given an arbitrary, non-coplanar wing/ truss configuration, it provides the optimum load distribution corresponding to the minimum induced drag. This load distribution is passed to the wing sizing subroutine. An additional lift-dependent parasite drag component was added to correlate with LMAS drag polars at offdesign conditions. Wave Drag The wave drag is approximated with the Korn equation, modified to include sweep using simple sweep theory [7], [8]. This model estimates the drag divergence Mach number as a function of airfoil technology factor, thickness to chord ratio, section lift coefficient, and sweep angle. The airfoil technology factor was selected by Lockheed to agree with the LMAS wave drag. Finally, the wave drag coefficient of a wing strip is calculated from the critical 3

6 Mach number. The total wave drag is found by integrating the wave drag of the strips along the wing. Interference Drag The benefits of a strut-braced wing configuration are accompanied by a potential interference drag penalty at the junction of the strut with the fuselage and the wing. The interference drag between the wing-fuselage and strut-fuselage intersections are estimated using Hoerner equations based on subsonic wind tunnel tests [12]. The drag of wing-strut junctions can be important in transonic flow because of the presence of shock waves and separated flow regions. In order to alleviate the problem associated with a sharp wing-strut angle, the strut employed here is given the shape of an arch and intersects the wing perpendicularly. Analyses for an arch radius ranging from 1 ft to 4 ft were performed with Computational Fluid Dynamics (CFD) tools. Unstructured grids were obtained with the advancing-front methodology implemented in the code VGRIDns [13], [ 14]. The Euler equations were solved using the CFD code USM3D [14], [15] at the cruise Mach number of A very convenient way to extract the interference drag penalty from a CFD calculation consists in subtracting the drag of the wing alone from the drag of the strutbraced wing design obtained with CFD. The resulting number is a DC D penalty associated with the presence of the strut. As the arch radius is increased, the drag penalty decreases almost exponentially. From these results, a curve fit is produced and used in the present analysis to account for the drag of the wing-strut junction. The drag polars output from the Virginia Tech MDO tool and LMAS modified FLOPS agree within 1% on average for cantilever wing designs. STRUCTURES Due to the unconventional nature of the proposed concept, commonly available weight calculation models for transport aircraft (such as the NASA Langley developed FLOPS) are not accurate enough. A special bending weight calculation procedure was thus developed, taking into account the influence of the strut upon the structural wing design. In addition to the strut design, a vertical strut offset was considered as to achieve a significant reduction in wing/strut interference drag. Load Cases To determine the bending material weight of the strut-braced wing, two maneuver load conditions (2.5g maneuver, -1.0g pushover) and a taxi bump (-2.0g) are considered to be design critical. For the -1.0g pushover and for the -2.0g taxi bump, the strut is not active and the wing acts like a cantilever beam. Since the strut is not supporting the wing in these cases, very high deflections of the wing are expected for the -2.0g taxi bump. As a result, an optimization procedure is implemented to distribute the bending material to prevent wing ground strikes. To maximize the beneficial influence of the strut upon the wing structure, strut force and spanwise position of the wing-strut intersection are optimized by the MDO code for the 2.5g maneuver load case. In order to attain acceptable aerodynamic characteristics of the strut, an airfoil cross section is considered. The strut is designed the way that it will not carry aerodynamic forces during the cruise condition. Structural Assumptions Preliminary studies have shown buckling of the strut under the 1.0g load condition to be the critical structural design requirement in the single-strut configuration, resulting in high strut weights [8]. To address this issue, an innovative design strategy employs a telescoping sleeve mechanism to allow the strut to be inactive during negative g maneuvers and active during positive g maneuvers. Thus, under the 1.0g case, the wing acts like a cantilever beam and for the positive g maneuvers, the wing is a strut-braced beam. Even more wing weight reduction can be obtained by optimizing the strut force and wing-strut junction location. On a typical optimum single-strut design, this means that the strut would first engage in tension at some positive load factor. This can be achieved by assuming a slack in the wing-strut mechanism. The optimum strut force at 2.5g is different from the strut force that would be obtained at 2.5g if the strut were engaged for all positive values of the load factor. Therefore, the slack load factor is defined as the load factor at which the strut engages for the first time. It is important to have the slack load factor always positive, otherwise the strut would be preloaded at the jig shape to achieve the optimum strut force. Double Plate Model For calculating the wing-bending weight of single strut configurations, a piecewise linear beam model, representing the wing structure as an idealized double plate model, was used (Fig. 5). Figure 5. t C b Double plate model for bending weight calculation This model is made of upper and lower skin panels, which are assumed to carry the bending moment. The double-plate model offers the possibility to extract the material thickness distribution by a closed-form equation. The cross-sectional moment of inertia of the wing-box can be expressed as: t( y) c I( y) = b d ( y) d 2 ( y) 2 (1) 4

7 where t(y) is the wing skin thickness c b (y) is the wingbox chord, and d(y) is the wing airfoil thickness. To obtain the bending material weight, the corresponding bending stress in the wing is calculated from: M ( y) d( y) σ max = 2I ( y) (2) where σ max denotes the maximum stress, M(y) is the bending moment of the wing, and I(y) denotes the crosssectional moment of inertia. If the wing is designed according to the fully-stressed criterion, the allowable stress σ all can be substituted into Eq. (2) for σ max. Substituting I(y) into equation (2), the wing panel thickness can be specified as: M ( y) t( y) = c ( y) d( y)σ b all (3) This skin thickness is modified by the results obtained from the tip displacement constraint optimization. The bending material weight of the half-wing therefore is: b s W wb = 2 b s / 2 0 t( y) c ( y) ρdy where is the structural span with. Vertical Strut Offset To reduce the wing/strut interference drag, a vertical offset between strut and wing is implemented. The vertical offset member is designed for a combined bending/tension loading. In this context, the horizontal component of the strut force is of special concern (Fig.6). Since this horizontal force results in a considerable bending load on the offset piece, its weight increases dramatically with increasing strut force and offset length. As a result, it is imperative to employ MDO tools to obtain optimum values for vertical offset, strut force, and spanwise wing/strut breakpoint. By this way, it is possible to trade off the two contrary design requirements: (i) a reduced offset length to reduce strut loading, (ii) an increased offset length to reduce the wing/strut interference drag. After a complete design optimization with the vertical strut offset as an active design variable, the influence of the offset weight on the total strut weight becomes comparably small. For the wing bending weight and especially for the TOGW it is almost immaterial. b b s = b cos Λ (4) Figure 6. Vertical strut offset and applied loads Figure 7 depicts the bending moment distributions on the wing for the design critical load cases of the fuselage mounted engine SBW design. Due to the vertical strut offset, an additional bending moment is induced into the wing at the wing/strut breakpoint, leading to a discontinuity in the bending moment distribution. Since the strut is inactive in compression, the bending moment distributions for the -1.0g pushover as well as for the 2.0g taxi bump do not exhibit this discontinuity. Bending Moment (Ft-Lb) 2.5E E E E E E E E+07 Figure 7. AEROELASTICITY Wing Lower Surface Wing Neutral Axis Structural Strut Offset Aerodynamic Strut Offset Horizontal Strut Force Vertical Strut Force 0.0E E+06 Wing Half Span (Ft) 2.5G Maneuver -1.0G Pushover -2.0G Taxi Bump Bending moment distributions for the design critical load cases of the fuselage mounted engine SBW Hexagonal Wing-Box Model Although the double plate model renders very accurate estimates for the wing bending material weight, it is not suitable for calculation of the wing-box torsional stiffness. Nevertheless, torsional stiffness becomes essential when calculating wing twist and flexible wing spanload, as well as for the incorporation of aeroelastic constraints and design variables into the MDO optimization. 5

8 Therefore, a hexagonal wing-box model provided by LMAS was implemented into the code (Fig. 8). In contrast to the double plate model, the hexagonal wing-box allows computation of bending and torsional stiffness with a high degree of accuracy. Based upon Lockheed Martin s experience in wing sizing, the wing-box geometry varies in the spanwise direction with optimized area and thickness ratios for spar webs, spar caps, stringers, and skins. Furthermore, minimum gauges and maximum stress cutoffs can be accurately applied. z/c Figure 8. Altitude (10 3 ft) Figure 9. L M x/c N g m Aerodynamic Center Hexagonal Wing-Bo Shear Center (Elastic Axis) Airfoil Center of Gravity Hexagonal wing-box and applied sectional forces and moments 1.15 Vd Flight Envelope Isolated Wing, full fuel Wing-Strut, full fuel Wing-Strut, zero fuel Isolated Wing, zero fuel Flutter Speed (fps) Flutter boundary vs. altitude for different flight conditions of the fuselage mounted strutbraced wing configuration Computational Aeroelasticity Beyond rendering accurate quantities for bending and torsional stiffness, the hexagonal wing-box is suitable to create input data and realistic sizing for detailed finite element analyses. Currently, the panel thickness distributions from the double plate model are used to create a hexagonal wing-box according to the spanwise variation of the respective cross sectional data. To obtain the spanwise distribution of the moments of inertia, the overall cross sectional area of stringers, spar caps, and skins are matched with the respective cross sections of the double plate model. With this data, a detailed finite element model of the structural wing-box is computed and analyzed using NASTRAN. It consists of 630 grid points, 1239 rod elements, and 3232 plate elements. The structural material is an equivalent isotropic composite model same as the one used in wing-bending weight calculations. The fuel load is distributed into 47 mass elements. For unsteady aerodynamics, the Doublet Lattice method with compressibility correction for subsonic flight is employed. Aerodynamic loads are simulated using 300 box elements. To calculate the flutter speed, 10 structural vibration modes are considered. In this model, no strut structure is included. Figure 9 illustrates the flutter boundary obtained using the PK method in terms of the true air speed. At each altitude, flutter is related to the fundamental wing bending and torsional modes. However, at 30,000 ft flight level, flutter occurs due to coupling of the yawing mode with the first torsional mode. The results should be corrected using a more accurate transonic unsteady aerodynamics modeling to simulate the transonic dip effect. Also, aeroelastic constraints must be included into the optimization. WEIGHTS The aircraft weight is calculated by incorporating several different methods. The majority of the weights equations come from NASA Langley s Flight Optimization System (FLOPS) [16]. Many of the FLOPS equations were replaced with those suggested by LMAS. The LMAS and original FLOPS methods do not have the option to analyze the strut-braced wing with the desired fidelity. Therefore, the bending material weight from the FLOPS equations is replaced by the bending material weight obtained from the piecewise linear wing load models described above [17]. The wing bending weight is calculated using the panel thickness results or hexagonal wing-box cross sections from the piecewise linear beam model for the different load cases (Fig. 10). The overall panel thickness distribution of the wing is obtained by considering the highest value of the panel thickness or cross section at each spanwise position (envelope). To account for sudden changes in the material distribution, an additional 1% weight penalty is applied. 6

9 Before linking the wing weight module to the MDO code, it has been validated using the wing. The results obtained from the double plate model as well as the hexagonal wing-box show good agreement with the actual and with the results obtained from FLOPS [16] and Torenbeek [18]. Panel thickness in tip constraint 2g taxi bump -1g maneuver 2.5g maneuver Wing half span ft Figure 10. Panel thickness distributions for the different load cases (fuselage mounted engine configuration) The total weights for the different components (strut, offset, wing) are obtained using the FLOPS equations. Here, the wing bending material and strut tension weights are being multiplied by a technology factor to account for the weight reduction achieved by the employment of composite materials by the year After computation of the load carrying weights, a 10% non-optimum factor is applied to account for manufacturing constraints. The total wing weight is calculated using the FLOPS equations with the overall load carrying weight, i.e. wing, strut, and offset. The total weights of the different components are determined according to the ratio of their contributions to the load carrying weight. LMAS provided a weight estimate for the telescoping sleeve mechanism based on landing gear component data. Weights calculated in the Virginia Tech transport optimization code are identical to FLOPS with the exception of nacelle, thrust reverser, passenger service, landing gear, wing, fuselage and tail weights. The above weights are now calculated from proprietary LMAS formulas. Weight technology factors are applied to major structural components and systems to reflect weight savings due to advances in technology levels from composite materials, advanced electronics and other technologies described above. Some aircraft weights are implicit functions, and internal iteration loops are typically required for convergence. However, utilizing the optimizer to converge the zero fuel weight of the aircraft showed to be more efficient by providing smoother gradients. DOT also selects the fuel weight so that the range constraint is not violated. Other weights such as the maximum body and contents weight and wing weight converge efficiently with the lagging variable method [10]. STABILITY AND CONTROL The horizontal and vertical tail areas are first calculated with a tail volume coefficient sizing method. The tail volume coefficients were determined based on Lockheed statistical data. A vertical tail sizing routine was developed to account for the one engine inoperative condition [8], [17]. The engine-out constraint is met by constraining the maximum available yawing moment coefficient to be greater than the required yawing moment coefficient. As specified by FAR requirements, the aircraft must be capable of maintaining straight flight at 1.2 times the stalling speed with the operable engine at its maximum available thrust. The lateral force of the vertical tail provides most of the yawing moment required to maintain straight flight after an engine failure [11]. The maximum available yawing moment coefficient is obtained at an equilibrium flight condition with a given bank angle and a given maximum rudder deflection. FAR limits the maximum bank angle to 5, and some sideslip angle is allowed. The stability and control derivatives are calculated using empirical methods of DATCOM as modified by Grasmeyer [8], [20]. In order to allow a 5 aileron deflection margin for maneuvering, the calculated deflection must be less than The calculated available yawing moment coefficient is constrained in the optimization problem to be greater than the required yawing moment coefficient. If the yawing moment constraint is violated, a vertical tail area scaling factor is applied by the optimizer. PROPULSION A GE-90 class high-bypass ratio turbofan engine is used for this design study. An engine deck was obtained from LMAS, and appropriate curves for specific fuel consumption and maximum thrust as a function of altitude and Mach number were found through regression analysis. The general forms of the equations are identical to those found in Mattingly [21] for highbypass ratio turbofan engines, but the coefficients and exponents are modified. The engine size is determined by the maximum thrust required to meet several constraints. These constraints are thrust at average cruise altitude, available rate of climb at initial cruise altitude, balanced field length, second segment climb gradient, and missed approach climb gradient. The dimensions of the engine nacelles vary as the square root of required thrust, and the engine weight is assumed to be linearly proportional to the engine thrust. The specific fuel consumption model is independent of engine scale. A specific fuel consumption technology factor is applied to reflect advances in engine technology. 7

10 Table 2. Parametric properties of aircraft designs for minimum take-off gross weight (TOGW) Cantilever SBW Wing Span (ft) S w (ft 2 ) AR Root t/c 14.50% 14.28% Tip t/c 7.80% 6.15% Wing Λ 1/4 (deg) Strut Λ 1/4 (deg) 20.1 η Strut 68.9% η Engine 37.0% Max Thrust (lbs) Cruise Altitude (ft) L/D Wing Wt. (lbs) Bending Matl (lbs) Fuel Wt. (lbs) TOGW (lbs) % TOGW Improv. 8.1% % Fuel Improv. 13.6% % Thrust Reduction 20.7% Section C l Limit ACTIVE ACTIVE 2nd Segment Climb ACTIVE ACTIVE Balanced Field ACTIVE Length Engine Out ACTIVE PERFORMANCE The range is calculated by the Breguet range equation [11]. The L/D ratio, flight velocity, and specific fuel consumption are determined for the average cruising altitude and Mach number. The initial weight is 95.6% of the take-off gross weight to account for fuel burned during climb to the initial cruise altitude. A reserve range of 500 nautical miles allows for emergency airport re-routing, extra loiter time while waiting for landing clearance at the end of a maximum range mission and strong headwinds. Figure 11. Minimum TOGW Designs Fuselage-Engine SBW Cantilever Wing Table 3. Minimum Fuel Optimum Designs Cantilever SBW Wing Span (ft) S w (ft^2) AR Root t/c 13.06% 12.37% Tip t/c 5.31E % Wing Λ 1/4 (deg) Strut Λ 1/4 (deg) 21.2 η Strut 66.6% Max Thrust (lbs) Cruise Altitude (ft) L/D Wing Wt. (lbs) Bending Matl (lbs) Fuel Wt. (lbs) TOGW (lbs) % TOGW Improvement 8.1% % Fuel Improvement 15.0% Section C l Limit ACTIVE ACTIVE 2nd Segment Climb ACTIVE Balanced Field Length ACTIVE Take-off and landing performance utilizes methods found in Roskam and Lan [22]. The field performance subroutine calculates the second segment climb gradient, balanced field length, missed approach climb gradient, and the landing distance. All calculations are done for hot day conditions at sea level. Sample drag polars for the aircraft at take-off and landing were provided by LMAS [11]. Trends are the same for both SBW and cantilever configurations. The actual drag polars use correction factors based on total aircraft wetted area and wing aspect ratio. The second segment climb gradient is the ratio of rate of climb to the forward velocity at full throttle while one engine is inoperative and the gear is retracted. Roskam and Lan methods are also used to determine the landing distance [22]. Three legs are defined: the air distance from clearing the 50-foot object to the point of wheel touchdown including the flare distance, the free roll distance between touch-down and application of brakes, and finally, the distance covered while braking. The lift coefficient on landing approach is the minimum C L associated with either V=1.3V stall or the C L to meet the tail scrape requirement. The drag coefficient is calculated with gear down. The missed approach climb gradient is calculated in the same way as the second segment climb gradient with a few exceptions. First, the weight of the aircraft at landing is assumed to be 73% of the take-off gross weight as specified by LMAS. Second, all engines are operational. Third, a landing drag polar distinct from the take-off drag polar is used. In the present study, the FAR minimum missed approach climb gradient constraint is never violated. 8

11 OPTIMIZATION RESULTS MIMIMUM TAKE-OFF GROSS WEIGHT Table 2 shows the parametric results for TOGW minimization and Fig. 11 gives an impression of the geometric differences of the investigated aircraft designs. Note that the cantilever wing has a trailing edge break to permit landing gear stowage. A comparison of the cantilever and SBW designs shows that in general, the SBW aircraft have less wing area, higher aspect ratio and a reduced wing sweep compared to their cantilever counterparts. MINIMUM FUEL CONSUMPTION Fuel burn is likely to be an increasingly important factor in aircraft design from two perspectives. First, as the Earth s petroleum resources are depleted, the cost of aviation fuel will rise. Any reduction in fuel demand will be welcome if the fuel price becomes a larger part of transport life cycle cost. Second, strict emissions regulations stemming from environmental concerns will limit the amount of pollutant discharge permitted by an aircraft. Beyond engine design, reducing the overall amount of fuel consumed for a given flight profile by improved configuration design will also reduce the total amount of emissions. Table 3 shows the minimum fuel weight results. MINIMUM TOGW VS. MINIMUM FUEL CONSUMPTION For minimum TOGW and minimum fuel cases, the SBW is superior for the selected objective functions. While the SBW has an 8.1% decrease in TOGW, the savings in fuel consumption are even more impressive. A SBW has a 13.6% lower fuel burn than a cantilever configuration when optimized for minimum TOGW, and a 15% lower fuel weight when both are optimized for minimum fuel weight. The minimum-fuel-sbw has a higher wingspan to increase the L/D and fly at higher altitudes. The minimum-fuel-sbw TOGW is 8.1% lower than an equivalent cantilever design, and 3.6% higher than a minimum- TOGW-SBW. The SBW L/D increases from 25.4 to 29.1 going from the minimum-togw to the minimum-fuel case, and from 21.7 to 26.1 for the cantilever configuration. This improved aerodynamic efficiency is achieved by increasing the wing span, and comes at a cost in structural weight. Airport noise pollution can limit the types of aircraft permitted to use certain urban airfields and impose operational restrictions on those that do. Minimizing engine size can also be expected to reduce the noise generated if the engine is of similar design. Minimum TOGW SBW engine thrust is reduced by 20.7% over the equivalent cantilever design, probably reducing airport noise pollution by a similar amount. Take-Off Gross Weight (lbs.) Take-Off Gross Weight vs. Range Range Figure 12. Effect of range on take-off gross weight Fuel Weight (lbs) Conventional SBW Fuel Weight vs. Range Conventional SBW Range Figure 13. Effect of range on fuel weight RANGE EFFECTS The SBW becomes increasingly desirable as the design range increases. Figures 12 and 13 show the effects of range on TOGW and fuel weight. The TOGW reduction relative to the cantilever configuration steadily improves from 5.3% at a 4,000 nautical mile range up to 10.9% at 12,000 nautical miles. The fuel weight savings fluctuates within about 11-16%, generally improving with increasing design range. These results are for minimum TOGW designs, however greater fuel burn improvements are expected for SBW aircraft optimized for minimum fuel weight. Maximum fuel weight is set at 400,000 pounds. At 12,000 nautical miles an aircraft can reach any destination on Earth. The SBW maximum range is 13,099 nautical miles at the maximum fuel weight, whereas the cantilever configuration can only reach 11,998 nautical miles, or the SBW has 8.4% greater maximum range. Therefore, the SBW can either have a reduced fuel weight for a given range or an increased range for a given fuel weight relative to the cantilever configuration. 9

12 CONCLUSIONS Virginia Tech transport studies have shown the potential of the SBW over the traditional cantilever configuration. After much added realism by a major airframe manufacturer, the MDO analysis shows that the SBW still demonstrates major improvements over the cantilever wing configuration. A significant reduction in TOGW was found, but the greatest virtue of the SBW is the improved fuel consumption and smaller engine size. These results indicate that the SBW will cost less, limit pollutant discharge and reduce noise pollution for urban airports. Advantages of the SBW increase with range, suggesting that this configuration may be ideal for larger, long-range transports. The special design of the strut-braced wing necessitated the development of a wing sizing module suitable to fully exploit the benefits of this structural configuration. After validation with existing aircraft like the , the module was used for wing sizing and structural weight computation of the SBW. The great potential of the outlined wing sizing procedure lies in the consideration of jig twist, strut moment, wing flexibility, and flexible wing spanload. Consideration of the actual in-flight maneuver loads not only increases the accuracy in wing sizing but also gives the potential for further weight savings. This is especially important within a multidisciplinary design environment where due to synergistic interaction even small weight savings in one component are very likely to result in further weight reductions for other components. Further benefits of the SBW are expected to become apparent in future studies. The cooperative relationship with LMAS focused on adding realism to the SBW design effort for direct comparisons with the cantilever design. Realism often takes the form of weight penalties and expanded performance analysis, which inevitably detracts from SBW theoretical potential. Presently, efforts are underway to identify technologies and strut/truss arrangements to exploit the strengths of the strut. Limiting the SBW design arrangements so that the aircraft takes the appearance of a cantilever wing may not be the most appropriate approach to realize the full potential of the SBW. The SBW is likely to have a more favorable reaction from the public than other configurations, especially for those who suffer from a fear of flying. Affirmative passenger and aircrew acceptance is probable because other than the addition of a visually innocuous strut and a high wing, there is little to distinguish the SBW from the existing airliner fleet. Radical appearances of the blended-wingbody, joined wing, or other candidate configurations may cause apprehension in many flying patrons. ACKNOWLEDGMENTS This project is funded by NASA Langley Research Grant NAG Part of the work was done under subcontract from Lockheed Martin Aeronautical Systems in Marietta, Georgia. NASA deserves much credit for having the vision to pursue bold yet promising technologies with the hope of revolutionizing air transportation. Lockheed Martin Aeronautical Systems provided valuable contributions in data, design methods and advice. REFERENCES 1. Pfenninger, W., Design Considerations of Large Subsonic Long Range Transport Airplanes with Low Drag Boundary Layer Suction, Northrop Aircraft, Inc., Report NAI (BLC-67), November Gunston, B., Giants of the Sky: The Biggest Aeroplanes of All Time, Patrick Stephens Limited, Wellingborough, UK, pp Kulfan, R.M., and Vachal, J.D., Wing Planform Geometry Effects on Large Subsonic Military Transport Airplanes, Boeing Commercial Airplane Company, AFFDL-TR-78-16, February Jobe, C.E., Kulfan, R.M., and Vachal, J.D., Wing Planforms for Large Military Transports, AIAA , Turriziani, R.V., Lovell, W.A., Martin, G.L., Price, J.E., Swanson, E.E., and Washburn, G.F., Preliminary Design Characteristics of a Subsonic Business Jet Consept Employing an Aspect Ratio 25 Strut-Braced Wing, NASA CR , October Smith, P.M., DeYoung, J., Lovell, W.A., Price, J.E., and Washburn, G.F., A Study of High-Altitude Manned Research Aircraft Employing Strut-Braced Wings of High-Aspect Ratio, NASA CR , February, Grasmeyer, J.M., Naghshineh_Pour, A., Tetrault, P.- A., Grossman, B., Haftka, R.T., Kapania, R.K., Mason, W.H., Schetz, J.A., Multidisciplinary Design Optimization of a Strut-Braced Wing Aircraft with Tip- Mounted Engines, MAD , Grasmeyer, J.M., Multidisciplinary Design Optimization of a Strut-Braced Wing Aircraft, MS Thesis, Virginia Polytechnic Institute & State University, April Martin, K.C., Kopec, B.A., A Structural and Aerodynamic Investigation of a Strut-Braced Wing Transport Aircraft Concept, NAS , November Vanderplaats Research & Development, Inc., DOT User s Manual, Version 4.20, Colorado Springs, CO, Gundlach, J.F., Multidisciplinary Design Optimization and Industry Review of a 2010 Strut-Braced Wing Transonic Transport, MAD ,

13 12. Hoerner, S.F., Fluid Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance, published by Mrs. Hoerner, Current address: P.O. Box 65283, Vancouver, WA Pirzadeh, S., Structured Background Grids for Generation of Unstructured Grids by Advancing-Front Method, AIAA Journal, Vol. 31, February 1993, pp Frink, N.T., Pirzadeh, S., and Parikh, P., An Unstructured-Grid Software System for Solving Complex Aerodynamic Problems, NASA CP-3291, May Frink, N.T., Parikh, P., and Pirzadeh, S., A Fast Upwind Solver for the Euler Equations on Three- Dimensional Unstructured Meshes, AIAA , McCullers, L.A., FLOPS User s Guide, Release Text file included with the FLOPS code. 17. Naghshineh-Pour, A.H., Kapania, R., Haftka, R., Preliminary Structural Analysis of a Strut-Braced Wing, VPI-AOE-256, June Torenbeek, E., "Development and Application of a Comprehensive, Design Sensitive Weight Prediction Method for Wing Structures of Transport Category Aircraft," Delft University of Technology, Report LR- 693, Sept Roskam, J., Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, Roskam Aviation and Engineering Corp., Lawrence, KS, Grasmeyer, J.M., Stability and Control Derivative Estimation and Engine-Out Analysis, VPI-AOE-254, January Mattingly, J.D., Heiser, W.H., and Daley, D.H., Aircraft Engine Design, AIAA, Washington, D.C., Roskam, J., and Lan, C.-T. E., Airplane Aerodynamics and Performance, DARCorporation, Lawrence, KS, CONTACT Dr. Frank H. Gern Multidisciplinary Analysis and Design (MAD) Center for Advanced Vehicles Department of Aerospace and Ocean Engineering Virginia Polytechnic Institute and State University Blacksburg, VA , USA Phone: (540) Fax: (540) fgern@aoe.vt.edu 11