26TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES

WING DESIGN OF SUPERSONIC TRANSPORT BY A MULTI-POINT OPTIMIZATION METHOD

Kentaro HIGUCHI*, Zhong LEI** and Kenichi RINOIE* *Department of Aeronautics and Astronautics, The University of Tokyo, Tokyo, 113-8656, JAPAN **Aviation Program Group, Japan Aerospace Exploration Agency, Tokyo, 181-0015, JAPAN

Keywords: Supersonic Transport, Multi-Point Optimization, Low Fidelity Method

Abstract CL lift coefficient I moment of inertia, m4 One of the difficulties in the aerodynamic design x I polar moment of inertia, m4 of a supersonic transport is the wing design P L/D lift-to-drag ratio considering both supersonic and low-speed M bending moment, Nm performance. The wing with large sweepback x M twisting moment, Nm angle and low aspect ratio is often used to y S wing area, ft2 reduce wave drag at supersonic cruise, but it W T/W thrust-to-weight ratio also results in poor performance at low speeds W maximum take-off weight, lb such as take-off and landing conditions. TO x chordwise coordinate measured from the Therefore, a large area is required for the wing aircraft nose, ft to generate enough lift and, consequently x chordwise coordinate measured from the reduce the take-off and landing field length. On W wing apex, ft the other hand, this also leads to an increase in y spanwise coordinate orthogonal to x, aircraft weight and uneconomical flight. The measured from the wing center-line, ft purpose of this research is to propose a multi- z coordinate orthogonal to the x-y plane, ft point design method which can obtain a compromised solution of wings for a supersonic α angle of attack, degree transport, by using low fidelity methods such as δ flap deflection angle, degree a combination of the Quasi-Vortex-Lattice Method and the Leading-edge Suction Analogy Subscripts for high-lift device design at low-speeds, and le leading-edge the supersonic linear theory at supersonic te trailing-edge speeds. The multi-point design method proposed in this paper is applied to a conceptual design of a supersonic regional jet. Results show that 1 Introduction the multi-point design can improve aircraft performance by reducing the wing area and Recently, there is a high interest in the next thus the aircraft weight, and suggests a generation Supersonic Transport (SST). guideline towards the optimization of wings in Researches to make the next generation the conceptual design phases. supersonic transport (SST) a reality are being carried out all over the world. The supersonic business aircraft concept has been studied [1, 2] Nomenclature and the HISAC project[1] lead by Dassault AR wing aspect ratio Aviation, focuses on noise reduction and NOx emission. In Japan, the former National CD drag coefficient Aerospace Laboratory of Japan (NAL) which is CDi induced drag coefficient

1 Kentaro HIGUCHI, Zhong LEI, and Kenichi RINOIE

now the Japan Aerospace Exploration Agency performance at both supersonic cruise condition (JAXA) successfully launched a scaled and take-off / landing and satisfies structure supersonic experimental airplane in Australia in constraints. For the optimization of wing 2005[4], and validated computational design planform at supersonic cruise condition, methods as well as retrieving flight data. estimation of aerodynamic performance and Presently, JAXA is promoting the Silent structural analysis are integrated in an automatic Supersonic Technology Demonstrator (S3TD) design process, which is driven by genetic project[5] which puts emphasis on low sonic algorithm methods implanted in a boom, noise reduction, and integration of commercially-available software iSIGHT-FD advanced demonstration system. (Engenious Software Inc.). Also, low fidelity One of the factors which make the methods are used to reduce computational cost, aerodynamic design of the SST difficult is the which will be useful when considering wing aerodynamic design. Usually, to reduce preliminary design where many cases or wave drag at supersonic cruise, wings with configurations must be put into consideration. highly-swept leading edge and low aspect ratio In this paper, the calculation methods for wing are adopted. However, this type of wing is low speed and supersonic flight conditions will known to have poor aerodynamic performance be described. The Quasi-Vortex-Lattice Method at low speeds and can possibly put the designers [6] coupled with the Leading-Edge Suction into the following cycle. The wing area will Analogy [7] (QVLM-SA) will be used as the have to be large enough to generate lift for take- calculation method for low speed aerodynamics, off and landing within the required runway and a Supersonic Linear Theory (SLT) proposed length. In the meantime, a large wing area by Carlson [8] will be employed for calculations associates with large additional profile drag and at supersonic cruise conditions. Some numerical wave drag at cruise conditions, and inevitably tests using QVLM-SA will be conducted and make worsen the cruise performance; bad cruise compared with corresponding wind-tunnel performance consumes more fuel, thus increase experiments to validate the method. Results weight; in turn, the increased fuel requires a show that QVLM-SA can well estimate the larger wing area. On the other hand, qualitative effects of flaps. Since, the supersonic improvement of the aerodynamic performance linear theory (SLT) has been used to design the and reduction of weight can reduce engine scaled supersonic experimental airplane at the power setting and therefore community noise. National Aerospace Laboratory of Japan, it can So, to avoid this problem in the design of a wing be said that the applicability is already validated. for the SST, it is desirable to use a multi-point Furthermore, as an example, the multi-point design method which takes into account both design method will be applied to the conceptual supersonic and low speed performance. design of a supersonic regional jet (SSRJ). Compared with high fidelity methods, such as computational fluid dynamics which is used currently in many aerodynamic designs with 2 Analytical Methodology large computational cost, a low fidelity method will be useful for multi-point design and 2.1 Calculation Method for Low-Speed conceptual design phases where large numbers Aerodynamics of calculation cases are required. Therefore the objective of this study is to develop a tool to The method for low-speed aerodynamic design wings for the SST considering both calculation was developed by coupling the supersonic and low speed performance. classical Quasi-Vortex-Lattice Method (QVLM) This study combines optimization of wing with the Leading-Edge Suction Analogy planform at supersonic cruise conditions with (LESA). In this paper, this method is called high-lift device design at low-speeds, and is QVLM-SA[9]. Wings with large leading-edge intended to investigate possibility of a wing sweep angles used for a SST are known to form which has less weight, better aerodynamic leading-edge separation vortices, which

2 WING DESIGN OF SUPERSONIC TRANSPORT BY A MULTI-POINT OPTIMIZATION METHOD generate additional lift and drag. LESA is a were obtained by integrating the aerodynamic simple method to estimate the vortex forces, by load and the weight of wing structure [11]. The assuming that the amount of vortex suction wing weight was estimated by [12]. To account acting normally on the wing surface is equal to for the rigidity of the wing section, the bending the amount of leading-edge suction acting moment was divided by the moment of inertia normally on the leading-edge to the upper of cross-sectional area Ix, and the twisting surface. The potential forces are calculated by moment was divided by the polar moment of QVLM which divides the wing into trapezoidal inertia of cross-sectional area IP. or triangular regions, and distributes vortex segments and control points for each region. 2.4 A Multi-Point Design Method The vortex suction forces are calculated using the leading-edge suction calculated in the The flow of the multi-point design of SST process by LESA. Details of the QVLM-SA wings is shown in Fig. 1. In the first phase, the calculation are described in [9]. wing planform will be optimized using iSIGHT- FD. Each planform is warped by the Carlson’s method to minimize the induced drag at a 2.2 Calculation Method for Supersonic specified lift coefficient. Then, the fuselage and Aerodynamics the tail are designed as will be explained in The Supersonic Linear Theory (SLT) was section 4.2.3. Afterwards, the high-lift devices employed to calculate supersonic aerodynamics. will be designed at a low speed condition by the Wing camber and twist (warp) are designed to use of QVLM-SA. It will now be possible to reduce the lift-induced-drag by Carlson’s evaluate the take-off and landing performance. method[8] based on the SLT. Although the SLT If the take-off and landing performances (see is a low fidelity method, its capability has been section 4.2.4) meet the requirements, it will be verified in the past. Also SLT has been applied considered whether the wing area can be in the aerodynamic design of the scaled reduced for weight reduction. In the second supersonic experimental (NEXST)[10] and the phase, the wing planform with the modified usability of the method has been confirmed. wing area will be re-optimized, and the design process will repeated, until the take-off and 2.3 The Optimization of Wing Planform landing performance is fulfilled. It must be noted that, the weight and The above SLT was used with a commercially parasite drag are estimated by empirical available optimization software iSIGHT-FD to methods used in traditional conceptual design optimize the wing planform at supersonic [12, 13], and the accuracy is generally not very speeds. NCGA (Neighbor Cultivation Genetic accurate. Therefore, in this study, we just intend Algorithm) embedded inside iSIGHT-FD was to analyze the design and provide useful used for multi-objective optimization by setting information for the wing at the preliminary several objective functions in the design process. design phase. Minimization of induced drag will be the primary objective of wing planform optimization. However without the constraint of 3 Verification of the Calculation Methods structural considerations, it is known that a wing planform with a large aspect ratio has better 3.1 QVLM-SA aerodynamic performance. To obtain realistic solutions, the pressure distribution calculated by To verify the applicability of QVLM-SA, SLT was integrated on the wing to calculate the calculation was compared with a wind tunnel bending and twisting moments (around the test conducted at the former National Aerospace quarter location of the mean aerodynamic Laboratory of Japan (presently JAXA)[14]. The chord), which were taken as other objectives in geometry of the wind tunnel test model is the optimization. The bending moment and shown in Fig. 2. The model consists of a twisting moment acting on wing cross sections cranked- arrow wing planform, an 3 Kentaro HIGUCHI, Zhong LEI, and Kenichi RINOIE

axisymmetrical body, inboard and outboard segmented leading- and trailing edge flaps at leading-edge flaps (LEF), and trailing-edge Mach number of 0.25. Reference 18 flaps (TEF). The camber and twist of the main investigated 70°/49° cranked arrow wing with wing was designed by Carlson’s method based leading- and trailing flaps at Mach number of on the supersonic linear theory. Measurements 0.205. Comparison of experiment and were carried out for various flap deflection calculation show that, at low angles of attack, combinations. For simplicity, the flap deflection the calculation results agree well with configurations will be named Sxxyyzz, where experiment for configurations with and without “xx”, “yy”, and “zz” represent the inboard LEF, flap deflection (Fig. 5). The qualitative flap outboard LEF, and the TEF, respectively. effects were also well estimated when leading- Details of the wing model are described in [15]. and trailing-edge flaps are deflected differently The Reynold's number based on the wing's (Fig. 6). Therefore, it can be concluded that mean aerodynamic chord was 9.45x105. QVLM-SA is capable of estimating Figure 3. compares lift coefficient CL and aerodynamic forces for arbitrary wing and flap drag coefficient CD of the experimental and the planform. computational results for configurations S00000, S000010, S301200, and S301210. An empirical 3.2 Supersonic Linear Theory (SLT) method suggested in [16] was used to estimate fuselage aerodynamic characteristics. To Carlson’s warp design method can be used to account for the skin friction drag, the minimum reduce lift-induced drag at supersonic speeds. drag calculated from the experimental results of Some preliminary calculations were tested using the baseline S000000 configuration was added iSIGHT-FD. The optimization method used is to the drag coefficients in all calculations. Also, Multi-Island Genetic Algorithm (MIGA), and a since the main wing has a warped wing section, parametric study was carried out using the 20,000 individuals calculated during the the CL at α=0° will not be zero. Therefore the angles of attack in the calculation were offset by optimization. Seven design parameters which 1° according to the experiment. It can be seen define the wing planform are shown in Fig. 7. that experiment and calculation well agree with The calculation conditions are as follows. each other up to a moderate angle of attack of z M1.6 z S =1,883 ft2 10°. However, discrepancy can be seen at high W z Design cruise C = 0.1 angles of attack due to vortex breakdown L z Number of islands 15 observed in the experiment. The non-linear z Number of individuals per island 15 effect due to vortex breakdown cannot be z Number of generations 100 simulated by QVLM-SA. The wing area and design C was set To investigate effect of flap on the L referring to the supersonic regional jet proposed aerodynamic performance, the lift and drag at JAXA, which will be introduced later. increment (ΔC , ΔC ) compared to the baseline L D Figure 8 shows some preliminary S000000 configuration was calculated. Fig. 4. calculation results. This figure shows induced shows the ΔCL-α and ΔCD-α curves of the drag versus bending moment (Fig.8(a)) and experiment and calculation. Though the induced drag versus twisting moment (Fig.8(b)) calculation results do not agree exactly with the for different wing aspect ratios AR. In Fig. 8(a), experiment, the overall patterns of the results the calculated individuals are scattered in a are generally well reproduced. So it can be said graph with the induced drag as the vertical axis that QVLM-SA can estimate the qualitative and the bending moment as the horizontal axis. effects of flap. In Fig. 8(b), the twisting moment is used as the Furthermore, validation was carried out for horizontal axis. It can be observed from the other wind tunnel tests conducted at NASA [17, graphs that there is a tradeoff between 18], to verify that QVLM-SA can be applied to aerodynamic and structural characteristics in various types of wing planforms. Reference [17] front of the solutions. When the wing has an tested a highly swept arrow wing with 4 WING DESIGN OF SUPERSONIC TRANSPORT BY A MULTI-POINT OPTIMIZATION METHOD aerodynamic advantage (small drag), the moment (Type 3). Planforms of the selected structural load will become large. three wings are shown in Fig.9(c). The details of warped wing sections of Type 2 are shown in Fig. 10 as an example, and its aerodynamic 4 A Design Example of a Supersonic characteristics are shown in Fig. 11. This figure Regional Jet shows an example of a warp designed wing and its characteristics. By comparing the polar- 4.1 The Baseline curves of a flat plate wing and a warped wing (Fig.11(d)), it can be seen that the warped wing The reduction of sonic boom is one of the most can reduce drag at some specified lift important problems for SST research. It is very coefficients. difficult to reduce the level of sonic boom to an acceptable value by current technology due to 4.2.2 High-lift Device Design and Performance the large payload and range of the SST. Estimation at Low Speed Therefore, a suitable goal for the present SST QVLM-SA was used to design high-lift devices technology may be considered as a small scale and estimate the aerodynamic performance at aircraft with less weight and less challenging take-off and landing conditions. Three leading- from a low-boom perspective. Thus a edge flaps shapes with different area were supersonic regional jet (SSRJ) was chosen as a considered. The three leading-edge flaps are design example of the proposed multi-point named Flap A, B, C, where Flap A is the flap design method. The design requirements and with smallest area, and Flap C is the flap with basic parameters of the SSRJ proposed by largest area. The outboard leading-edge flap is JAXA[19] were used as the baseline. The tapered and its chord length is 10% (Flap A), design requirements of this SSRJ are twin 20% (Flap B) and 30% (Flap C) of the local engines, 50 passengers, 3500nm range and wing chord length. The inboard leading-edge cruise speed of M1.6. The basic parameters such flap is not tapered and its chord length is the same as the wing chord length at the wing kink as a wing area SW and maximum take-off weight location. Both the leading- and trailing-edge WTO determined by the conceptual design study [19] are shown in Table 1. These parameters are flaps are deflected by 10° downward when the used as the starting point of present multi-point angle is measured parallel to the free stream. optimizations. The take-off and landing field The drag increment ΔCD to the clean condition length requirement in this paper was set to 7,000 (no flap deflection) were calculated. The results ft to make possible the use of conventional for Type 2 are shown in Fig. 12. It can be seen regional airports. that the flap shape with the largest area has the smallest ΔCD. Due to the structural constraints, 4.2 Phase One Design Flap B was selected. 4.2.3 Design of Tail-planes and the Area-Rule 4.2.1 Optimization of Wing Planform at Fuselage Supersonic Cruise Condition Next, other components such as tail-planes and Wing planform optimization using iSIGHT-FD the fuselage were designed. The tail planes were was carried out at the supersonic cruise designed empirically based on past SST data condition of M1.6 and CL=0.1 and at the same [20]. Fuselage diameter and length were optimization conditions as described in section selected preliminary to be 7ft and 123ft, 3.2. The Pareto solution is shown in Fig. 9. The respectively, based on the consideration of cabin axes in this figure are the same as in Fig.8. volume. According to the linear area rule theory, Among all solutions which have drag less than the area-ruled configurations with the same 25 cts (drag counts, 1 ct=0.0001), three typical longitudinal distribution of cross-sectional area candidates were chosen: the planforms with the have the same wave drag for supersonic flows. smallest drag (Type 1), the smallest bending The fuselage was then modified to have an moment (Type 2), and the smallest twisting equivalent cross-sectional area distribution of 5 Kentaro HIGUCHI, Zhong LEI, and Kenichi RINOIE

Sears-Haack body, which has the minimum weight ratio T/W indicated in Table 4 are the wave drag at supersonic conditions. Since the necessary value to make an 8% climb at 250 kts. shapes of the main wing and tail planes have When comparing the T/W of the three cases, been designed, the necessary area distribution of Case 3 has the smallest T/W. This is due to the the fuselage can be obtained by subtracting the large L/D achieved by the use of the leading- area distributions of the wing and tail planes. In edge flap. A small T/W will result in reduction this design, the Sears-Haack Body area of engine noise, thus more environmental distribution was achieved by a T-tail layout (Fig. compatibility. Therefore, the flap deflection for 13 for Type 2). Rear mount engine layout was configurations must be carefully considered to also helpful to achieve the desired cross determine the BFL. In this design example, only sectional area distribution. Longitudinal stability the advantage of BFL was taken into account. A analysis was carried out by estimating locations tolerance against the requirement of 7,000ft of center of gravity, wing aerodynamic center, suggests the possibility to reduce the wing area and tail-plane positions. It indicated a trim point further at phase two optimization. without the use of elevators at supersonic cruise conditions. 4.3 Phase Two Design -Towards 4.2.4 Performance Comparisons of the Three Optimization Planform Types Type 2 which has an advantage in structure, i.e. The cruise performance of the designed aircraft minimum bending moment Mx, was chosen to are compared in Table 2. Since the three wing carry out the next design cycle as was shown in planform configurations selected have small Fig. 1. The wing area was reduced to lessen the difference in induced drag and all other tolerance against the take-off field requirement. components are common, only small differences For simplicity, the wing planform was kept the were seen in cruise performance. same as that used in the first phase, and the The take-off performance was calculated weight reduction due to wing area reduction was for three flap deflection cases by the method considered (Since the cruise CL will differ from described in Ref. [21], which solved aircraft that of the first phase due to reduction of aircraft static force equation to estimate the take-off and weight, to obtain the true optimum, wing landing performance. Three flap deflection planform optimization using the new conditions cases considered are as follows. is needed). Configurations and weights of all • Case 1: no flap is deflected other components were also kept the same as • Case 2: only the trailing-edge flap is those of the first phase. The profile drag was deflected by 10° reduced because of the reduction of wing area, • Case 3: both leading- and trailing- edge but the lift induced drag was increased. On the flaps are deflected by 10° other hand, the necessary CL was increased, Flap deflection angles were determined by which actually increased the L/D. The conducting parametric studies of different flap maximum weight of the aircraft was 133,500 lbs, deflection angles. The take-off field length which was lighter than the initial baseline. This (TOFL) and balanced field length (BFL) are weight was estimated by taking into account the compared in Table 3. It can be seen that Case 2 fuel consumption using the mission fuel fraction has the smallest BFL for every configuration. method [13]. The BFL was increased and the Though the LEF increases L/D by reducing the tolerance against the requirement became vortex lift and drag, the reduced lift will result smaller. The comparison of performance of the in an increase in lift-off speed. Therefore, the first and second phase configurations are shown case which generates the most lift (Case 2) will in Table 5, and the aircraft configuration is have the smallest lift-off speed and thus the shown in Fig. 14. Since there is still a tolerance smallest BFL. However, when considering the against the BFL requirement, a possibility is left climb performance after take-off, the for further improvement. advantages will be different. The thrust-to-

6 WING DESIGN OF SUPERSONIC TRANSPORT BY A MULTI-POINT OPTIMIZATION METHOD

5 Some Limitations and Challenges obtained by this method will not be a reliable optimum. So, the proposed method should be It can be said from the above design example used as a guideline which will indicate a that, the multi-point design method presented in direction of optimization. this paper can consider both low-speed and supersonic flight conditions; furthermore, it is possible to improve cruise performance, reduce 6 Conclusions wing area and thus aircraft weight. However In this paper, a multi-point design method for there remain some limitations in the design. the SST which considers both low-speed and Firstly, the wing planform optimization was supersonic performance was proposed. carried out to minimize only the lift-induced (1) A low fidelity method to estimate low-speed drag, but when considering the cruise aerodynamic performance was developed by performance of the entire aircraft, wave and coupling the Quasi-Vortex-Lattice Method parasite drag must be included in the drag and the Leading-Edge Suction Analogy minimization because the wave drag might (QVLM-SA). The calculation results of cancel out the advantage of induced drag. QVLM-SA were compared with wind- Secondly, this multi-point design does not take tunnel test results, and comparisons show into account the level of sonic boom. The sonic that the QVLM-SA can reproduce the boom is one of the large problems to realize the experiment well at low angles of attack. SST, and a SST without installing low sonic Also flap effects were compared between boom technologies will most likely not be experiment and calculation, and the results certified to fly over land. show that QVLM-SA is capable of Nevertheless, it is not easy to bring wave estimating effects of flaps qualitatively. drag, parasite drag and sonic boom into this (2) By using the supersonic linear theory and optimization design process. These factors the Carlson’s warp design method with a depend strongly on the entire aircraft commercially-available software iSIGHT- configuration, and in order to optimize the tail- FD, wing planforms were optimized at plane design and trim analysis will need to be supersonic cruise conditions. Structural automated. In the current situation, tail-plane characteristics were also calculated to avoid planform design / positioning and Area-Rule structurally-unrealistic wing shapes. fuselage design are done manually, while Preliminary calculations were carried out analyzing the longitudinal stability. There are using iSIGHT-FD and results showed that many parameters to be determined, and it is up there was a trade-off between aerodynamic to the designer to decide whether the aircraft performance and structure. configuration is acceptable. For these reasons, (3) A multi-point design process was proposed. further research will be needed for a complete It employs wing optimization at supersonic automatic design process, which is necessary for speeds and high-lift device design at low- integrated design optimization. speeds. The example design of a SSRJ Also, the trim drag is not considered in the showed that by the use of this design proposed method, because there are difficulties process, it is possible to design a supersonic in obtaining the aerodynamic pitching moment aircraft with less weight and improved due to the leading-edge separation vortex. It is aerodynamic performance required to assume the location of the vortex. Trim drag will possibly reduce the L/D and the performance. Acknowledgement Furthermore, the weight estimation method used in this study is based on empirical and low- The authors would like to thank Dr. Yoshida of fidelity methods. Therefore, a thorough the Japan Aerospace Exploration Agency for his optimization of wing area, thus aircraft weight beneficial advice and assistance in is impossible. In other words, the optimum computational matters and SST design.

7 Kentaro HIGUCHI, Zhong LEI, and Kenichi RINOIE

References Edges for Supersonic Transport Configuration," Journal Aircraft, Vol.41, No.4, pp.829-838, 2004. [1] Aronstein, D.C. and Schueler, K.L., "Two Supersonic [16] Jorgensen, L. H., “Prediction of Static Aerodynamic Business Aircraft Conceptual Designs With and Characteristics for Space-Shuttle-Like and Other Without Sonic Boom Constraint," Journal of Aircraft, Bodies at Angles of Attack from 0° to 180°,” NASA Vol.42, No.9, 2005, pp.775-786. TN D-6996, 1973. [2] Henne, P., "Case for Small Supersonic Civil [17] Quinto, P. F., Paulson, J. W. Jr., “Flap Effectiveness Aircraft," Journal of Aircraft, Vol.42, No.9, 2005, on Subsonic Longitudinal Aerodynamic pp.765-774. Characteristics of a Modified Arrow Wing,” NASA [3] “HISAC, Environmentally Friendly High Speed TM-84582, 1983. Aircraft Project,” http://www.hisacproject.com/ [18] Coe, P. L., Jr., Kjelgaard, S. O., and Gentry, G. L., Jr., [retrieved 28 April 2008]. “Low-Speed Aerodynamic Characteristics of a [4] Onuki, T., Hirako, K. and Sakata, K., “National Highly Swept, Untwisted, Uncambered Arrow Experimental Supersonic Transport Project,” the 25th Wing,” NASA TP-2176, 1983. Congress of the International Council of the [19] Horinouchi. S., “Future of the Next Generation Aeronautical Sciences, ICAS 2006-1.4.1, Hamburg, Supersonic Airplane (in Japanese),” Journal for 2006. Japan Society of Fluid Mechanics, Vol.25, pp. 337- [5] Murakami, A., “Silent Supersonic Technology 344, 2006. Demonstration Program,” the 25th Congress of the [20] Roskam, J., Airplane Design Part II: Preliminary International Council of the Aeronautical Sciences, Configuration Design and Integration of the ICAS 2006-1.4.2, Hamburg, 2006. Propulsion System, DAR Corporation, Lawrence, [6] Lan, C. E., “A Quasi-Vortex-Lattice Method in Thin Kansas, 1997. Wing Theory,” Journal of Aircraft, Vol.11, No.9, [21] Miyata, K. and Rinoie, K., "Estimation of Take-off 1974, pp. 518-527. Performance for Supersonic Transport with [7] Polhamus, E. C., “A Concept of the Vortex Lift of Leading-edge Vortex Flaps and Trailing-edge Flaps Sharp-Edge Delta Wings Based on a Leading-Edge (in Japanese)," Journal of the Japan Society for Suction Analogy,” NASA TN D-3767, 1966. Aeronautical and Space Sciences, Vol.51, No.593, [8] Carlson, H. W., and Miller, D. S., “Numerical pp.327-329, 2003 Methods for the Design and Analysis of Wings at Supersonic Speeds,” NASA TN D-7731, 1974. [9] Higuchi K., Rinoie, K., Lei, Z., and Kwak D., “A Appendix A Optimization Algorithm Low Fidelity Method for Flap Aerodynamic Design of a Cranked- Arrow Wing,” 25th AIAA Applied Two types of genetic algorithms (GA) were Aerodynamics Conference, AIAA Paper 2007-4178, used in this paper. One is the Multi-Island Miami, 2007. Genetic Algorithm (MIGA), and the other is the [10] Yoshida, K., “Overview of NAL’s Program Including Neighbor Cultivation Genetic Algorithm the Aerodynamic Design of the Scaled Supersonic Airplane,” held at the VKI, RTO Educational Notes 4, (NCGA). These optimization methods are 15-1~16, 1998. included in the commercially available [11] Kanno, Y., Iwasaki, K., “Stuctural Weight Estimation optimization software iSIGHT-FD. for Winged Vehicles (in Japanese),” National MIGA distributes the individuals to Aerospace Laboratory Technical Report, NAL TR- different groups (islands) and genetic search is 1351, 1997. performed on the islands independently. [12] Harloff, G. J., and Berkowitz, B. M., “HASA― However, at some probability individuals will Hypersonic Aerospace Sizing Analysis for the migrate to other islands. This method was Preliminary Design of Aerospace Vehicles,” NASA CR-182226, 1988. developed to avoid localized solutions as well as [13] Raymer, D. P., Aircraft Design: A Conceptual improving performance. Approach (AIAA education series) Second Edition, NCGA is a powerful multi-objective American Institute of Aeronautics and Astronautics, genetic algorithm which uses neighborhood Inc., Washington, D.C., 1992. crossover. To obtain a Pareto solution in a [14] Kwak, D., Miyata, K., Noguchi, M., Sunada, Y. and multi-objective optimization, the algorithm will Rinoie, K., “Experimental Investigation of High Lift need to search globally to obtain a broad range Device for SST (in Japanese),” National Aerospace Laboratory Technical Report, NAL TR-1450, 2002. of solutions. On the other hand, a local search [15] Rinoie, K., Miyata, K., Kwak, D.Y. and Noguchi, M., must be done to ensure the solutions are "Studies on Vortex Flaps with Rounded Leading- accurate. There are common techniques for a

8 WING DESIGN OF SUPERSONIC TRANSPORT BY A MULTI-POINT OPTIMIZATION METHOD global search which is used among many Copyright Statement algorithms. However, these algorithms cannot The authors confirm that they, and/or their company or perform sufficient local search. NCGA uses institution, hold copyright on all of the original material crossovers between individuals which are close included in their paper. They also confirm they have in the objective function space to carry out a obtained permission, from the copyright holder of any sufficient local search. third party material included in their paper, to publish it as part of their paper. The authors grant full permission for the publication and distribution of their paper as part of the ICAS2008 proceedings or as individual off-prints from the proceedings.

Table 1. Basic parameters of JAXA’s SSRJ[19]. Table 4. Comparison of L/D and necessary T/W for an 8%, 250 Wing area 1,883 ft2 kt climb Maximum weight 144,000 lb for the three planform types and three flap deflection cases. Thrust per engine 31,000 lb Type 1 Type 2 Type 3 Case 1 Design CL 0.1 L/D 5.60 5.29 5.20

T/W 0.258 0.268 0.272 Table 2. Comparison of drag and L/D at supersonic cruise Case 2 for the three planform types. Type 1 Type 2 Type 3 L/D 6.52 6.13 5.95 T/W 0.233 0.243 0.248 Induced drag 0.00226 0.00248 0.00250 Case 3 Wave drag 0.00392 0.00363 0.00357 L/D 10.1 8.97 8.66 Parasite drag 0.00750 0.00744 0.00745 T/W 0.179 0.191 0.195 Total 0.0136 0.01355 0.01347 Table 5. Comparison of characteristics of phase 1 and 2 Cruise lift-to- configurations. drag ratio 7.30 7.38 7.40 Phase One Phase Two CL=0.1 Maximum weight [lb] 144,000 133,500 Wing weight [lb] 8,958 7,578 Table 3. Comparison of take-off field length for the three Wing area [ft2] 1,883 1,530 planform types and three flap deflection cases. Cruise CL 0.1 0.11 Type 1 Type 2 Type 3 Induced drag 0.00248 0.00300 Case 1 Wave drag 0.00363 0.00379 TOFL 5495 5884 6072 Parasite drag 0.00744 0.00689 BFL 6562 7051 7290 L/D 7.38 8.04 Case 2 TOFL 4698 4972 5181 Balanced field length [ft] 5934 6391 BFL 5591 5934 6196 Necessary Thrust for climb [lb] 27515 25220 Case 3 Landing Field Length [ft] 4241 4896 TOFL 5246 5562 5819 BFL 6275 6675 7005

9 Kentaro HIGUCHI, Zhong LEI, and Kenichi RINOIE

Initial value of WTO and SW

Wing Planform Optimization at Supersonic Cruise Conditions

Parasite Drag High-lift Area Rule Design Estimation using Device Design of Fuselage Conventional at Low-speeds Estimation Methods Fig. 2. NAL Wind-tunnel Test Model Dimensions (unit: mm). Landing Weight Estimation 1 Experiment CL Presented Method

Take-off/ Landing D C 0.6 , Performance Estimation L Estimate new C CD weight using new wing area 0.2 Are the requirements no -5 0 5 10 15 20 α,deg satisfied? -0.2 Phase 1 (a) S000000 1 C yes Experiment L Phase 2 Presented Method D

Can the wing area yes C 0.6 , L C be made smaller? CD

0.2 no Optimized S and W -5 0 5 10 15 20 W TO α,deg -0.2 (b) S000010 Fig. 1. Multi-point Design Method. 1 Experiment CL Presented Method D

C 0.6 , L C

CD 0.2

-5 0 5 10 15 20 α,deg -0.2 (c) S301200 1 Experiment CL Presented Method D

C 0.6 , L C

CD 0.2

-5 0 5 10 15 20 α,deg -0.2 (d) S301210 Fig. 3. Comparison of experiment and calculation for S000000, S000010, S301200, and S301210.

10 WING DESIGN OF SUPERSONIC TRANSPORT BY A MULTI-POINT OPTIMIZATION METHOD

0.15 S000010 0.15 S000010 L L

C S150510 C S150510 Δ S301210 Δ S301210

0.1 0.1

0.05 0.05 -5 0 5 10 15 20 -5 0 5 10 15 20 α,deg α,deg

(a) ΔCL-α (Experiment) (b) ΔCL-α (QVLM-SA) 0.05 0.05 D D C C Δ Δ

-5 0 5 10 15 20 -5 0 5 10 15 20 α,deg α,deg

S000010 S000010 S150510 S150510 -0.05 S301210 -0.05 S301210

(c) ΔCD-α (Experiment) (d) ΔCD-α (QVLM-SA) Fig. 4. Lift and drag increments (ΔCL, ΔCD) of S000010, S150510, S301210.

1.6 1.6 Experiment Experiment 1.4 1.4 QVLM-SA QVLM-SA C 1.2 1.2 L

C L C L,C D 1 C L,C D 1 0.8 0.8 0.6 0.6 C D 0.4 C D 0.4 0.2 0.2 0 0 -5 0 5 10 15 20 -5 0 5 10 15 20 -0.2 α , deg -0.2
, deg (a) without flap deflections (b) δle= 10deg (6 segments) δte=20deg (3 segments) Fig. 5. Comparison of experiment by Quinto et al.and calculation (QVLM-SA).

δle=30, δte=0 δle=30, δte=0
C L 0.25
C L 0.25 δle=30, δte=10 δle=30, δte=10 0.2 δle=30, δte=20 0.2 δle=30, δte=20 δle=30, δte=30 δle=30, δte=30 0.15 0.15

0.1 0.1

0.05 0.05

0 0 -5 0 5 10 15 -5 0 5 10 15 -0.05
, deg -0.05
, deg -0.1 -0.1 (a) ΔCL-α (Experiment) (b) ΔCL-α (Calculation) Fig. 6. Comparison of experiment by Coe al.and calculation (QVLM-SA).

11 Kentaro HIGUCHI, Zhong LEI, and Kenichi RINOIE

Λ LE2 AR Λ TE2

Λ TE1 η LE

Λ LE1 η TE

Fig. 7. Design parameters of the cranked arrow wing.

(a) Induced drag versus bending moment. (b) Induced drag versus twisting moment. Fig. 8. Results of the preliminary iSIGHT-FD calculation.

0.0035 0.0035

0.003 0.003 Type 2 0.0025 0.0025 C Di C Di 0.002 Type 3 0.002 Type 3 Type 2 Type 1 Type 1 0.0015 0.0015

0.001 0.001

0.0005 0.0005

0 0 0 1000 2000 3000 4000 5000 6000 0 -20 -40 -60 -80 M I x / x M y /I p (a) Induced drag versus bending moment. (b) Induced drag versus twisting moment.

10 10 10

5 Type 1 5 Type 2 5 Type 3

0 0 0 0 4 8 1216202428 0 4 8 1216202428 0481216202428

-5 -5 -5

-10 -10 -10 (c) Selected three wing planforms Fig. 9. Pareto solution of the optimization calculation.

12 WING DESIGN OF SUPERSONIC TRANSPORT BY A MULTI-POINT OPTIMIZATION METHOD

xxw, ft 7 -1 0 5 10 15 20 25 6 -3 5

-5 4

-7 3 , ft , ft y 2 z -9 1 -11 0

-13 -1

-15 -2 Fig. 10. Warped wing section of Type 2.

0.4 0.06

Flat plate wing 0.3 0.05 C D Warped wing C L 0.04 0.2 0.03 0.1 Flat plate wing Warped wing 0.02 0 0.01 -4.0 -2.0 0.0 2.0 4.0 6.0 α , deg -0.1 0 -4.0 -2.0 0.0 2.0 4.0 6.0 -0.2 α , deg

(a) CL-α curve (b) CD-α curve 0.4 0.4 0.3 C Flat plate wing M 0.3 0.2 Warped wing C L 0.1 0.2 0 -4.0 -2.0 0.0 2.0 4.0 6.0 -0.1 0.1 Flat plate wing α , deg -0.2 Warped wing 0 -0.3 0 0.01 0.02 0.03 0.04 0.05 -0.4 -0.1 C D -0.5 -0.6 -0.2

(c) CM-α curve (d) CL- CD curve Fig. 11. Aerodynamic characteristics of Type 2.

13 Kentaro HIGUCHI, Zhong LEI, and Kenichi RINOIE

0.02 70 Flap A

60 Flap B Flap C 0 50 0 0.2 0.4 0.6 0.8 C L 40 -0.02 y , ft 30 -0.04 20

Flap A 10 Δ⎠CCDD -0.06 Flap B 0 Flap C 0 20406080 x , ft -0.08 xw, ft (b) ΔCD versus CL curve. (a) Leading-edge flap shapes. Fig. 12 . Comparison of leading-edge flap shapes for wing planform Type 2.

40

MAC

20

0 0 20 40 60 80 100 120 140 x , ft

Forward Aft C.G. C.G. -20

-40 , ft y,z

-60

-80 Fig. 13. Result of Area-Rule fuselage design for Type 2.

14 WING DESIGN OF SUPERSONIC TRANSPORT BY A MULTI-POINT OPTIMIZATION METHOD

40

20

0 0 20 40 60 80 100 120 140 x , ft

-20

-40 , ft y,z

-60

-80 Fig. 14. Second phase configuration of Type 2.

15