Aerodynamic parametric analysis of an unconventional joined-wing aircraft configuration
Javier Perez-Alvarez1, Cristina Cuerno-Rejado2 and Jose Meseguer1
Abstract In this paper, the experimental results of an unconventional joined-wing aircraft configuration are presented. The test model uses two different wings, forward and rear, both joined in tandem and forming diamond shapes both in plant and front views. The wings are joined in such a way that it is possible to change the rear wing dihedral angle values and the rear wing sweep angle values in 25 different positions that modify the relative distance and the relative height between the wings. To measure the system aerodynamic coefficients it is necessary to perform wind tunnel tests. The data presented corresponds to the lift, drag and induced drag aerodynamic coefficients, as well as the aerodynamic efficiency and the parameter for minimum required power, from the calculated values of the lift and drag time series measured by a 6-axis force and torque sensor. The results show the influence on the aerodynamic coefficients of the rear wing sweep and dihedral angles parameters. As a main result, it can be concluded that, in general terms, the lift and induced drag aerodynamic coefficients values decrease as both the distance and height between the wings increase, on the other hand, the total drag aerodynamic coefficient decreases if the distance between the wings increases, but nevertheless shows a slight tendency to increase if the height of the rear wing increases, whereas the aerodynamic efficiency and the parameter for minimum required power increase if the distance between the wings increases.
reduction in costs by using more energetically efficient Introduction systems.2 In the last 50 years, one of the major fields of innov To date, every single enhancement destined to ation in aeronautical design is the pursuit of improve improve the efficiency of aircraft has been carried ments for optimizing the aerodynamic and structural out by preserving the conventional configuration, efficiency and the weight of aircraft.1 Although the i.e. slender fuselage aircraft, mid and low wings, ver objective of improving the aerodynamic characteris tical and horizontal stabilizers attached to the tail tics, and as a result the performance of the aircraft, cone, and wing-mounted or empennage-mounted has motivated designers to use the idea of configur engines. However, it appears that technological devel ations based on high aspect ratio wings, the problems opment levels where the investment in advances of the weight of the structure, incremented by the makes up for the results are reaching their own sig increase of the required structural stiffness to accom nificant productive capacity limits. A clear example of plish the requirements entailed, have restricted the geometry to a safe design. IDR/UPM, ETSI Aeronautica y del Espacio, Universidad Politecnica de On the other hand, the rise in and instability of the Madrid, Madrid, Spain cost of petroleum and its products (to its stabilization 2DAVE, ETSI Aeronautica y del Espacio, Universidad Politecnica de in 2012) and the continued growth of the commercial Madrid, Madrid, Spain aviation market, are generating ever-increasing fuel costs. The corresponding impact on the direct operat ing costs (DOCs), producing a rise between 30% and 40%, has led to a search for innovating solutions in the design of both aircraft and propulsion that allow a this fact can be found in the recent developments of In 1979, Julian Wolkovitch,5 in collaboration with The Boeing Company, where its latest model, the J. L. Johnson, deputy director of the ACA Industries Boeing 787 Dreamliner, is designed with the aim Dynamic and Stability Department, conducted some that 50% of the primary structure, including both tests in a wind tunnel on a joined-wing aircraft con the fuselage and wings, is made of composite, which figuration for agricultural purposes. The configur results in, according to the company, using a 20% less ation, designed by the prototypes manufacturer fuel than any other aircraft of the same size in similar Elbert L. Rutan (founder of Scaled Composites, missions. Inc.), consisted of a propeller-driven aircraft with Likewise, there is a much clearer alternative that the rear wing joined to the mid span of the forward involves supporting the development of non-conven wing. tional geometric configurations,3 which are already In 1989, the designs suggested by ACA industries, considered as real options by large aeronautical com with the aid of the NASA Ames Research Center, panies. The nonconventional configuration aircraft were studied in a wind tunnel to measure the aero concept of Airbus shows what air transport could be dynamic characteristics of the joined-wing model. The like in the year 2050 or even in 2030 if the progress in tests were conducted by modifying the NASA-AD 1 existing technologies maintains its momentum. Such aircraft,6 preserving the fuselage and the engines in nonconventional configurations include extremely two different versions. high aspect ratio wings, semi-embodied engines and In early 2000, Boeing developed the SensorCraft 4 a U tail aircraft. The result is lower fuel consumption joined-wing model7,8 with the purpose of meeting and a significant reduction in pollutant gases. the needs of the U.S.A.F. for the design of an aircraft Within the abovementioned idea resides a noncon with larger and better surveillance capacities. The key ventional configuration model called the joined-wing factors that determined the design of the SensorCraft configuration aircraft. This consist of a design that aircraft were the need to keep 360° radar coverage uses a forward wing and a rear wing that are joined over the aimed zone and to widen the capacities of in tandem so that it is diamond shaped both in top the unmanned aircraft. and front views. Figure 1 shows a simplified represen At the end of the first decade of the 21st tation of this kind of configuration. century Air Force Research Laboratories (AFRL)
Figure I. Simplified representation of the joined-wing configuration. commended the research on the aerodynamic char As a conclusion, it can be established that, in gen acteristics of the joined-wing model called Houck9 eral, all the studies show in their results a significant to the Department of Aeronautics of the United reduction in the induced drag coefficient of the joined- State Air Force Academy. The model of study was wing model. However, not every single one of based on the LRLE concept (long range, long endur them suggests aerodynamic aspects as the principal ance) within the unmanned aerial systems (UAS) direct cause. The structural advantages of the environment. joined-wing model,5,18 as the reduction of weight From an aerodynamic standpoint, all research (80-90% of the weight of the conventional wing) performed on this specific configuration, in the and the reduction of deflection of the wings, due the arrangement of the lifting surfaces, presents a direct influence of the join of the forward wing and rear influence on the lift, CL, and drag, CD, coefficients of wing, give a higher aspect ratio resulting in a reduc the system.2'5,7,10 12 In general, a significant reduction tion in the induced drag. in the induced drag coefficient, CDi, is presented as On the other hand, all the previous studies agree in one of the most important advantages of the model. confirming the appearance of a significant increment The problem to reduce the induced drag of multi of the overall lift of the aircraft, presenting better planes systems (including the joined-wing configur values of the maximum lift coefficient for level ation) was discussed by Prandtl13 who provided cruise flight, hence, improvements in aerodynamic formulas for the theoretical calculus of the aero efficiency.5,19 dynamic efficiency using the general laws established This situation makes the joined-wing model a suit by Munk.14 Recent numerical investigation has able candidate for research and development in view demonstrated that the Munk's minimum induced of a future application in air transport, provided that drag theorems are also applicable to joined-wings the social obstacles that introducing such significant and generic bi-wings.15 changes in the geometry of civil aircraft imply are The Prandfl-Munk theory predicts that multi overcome. Furthermore, and in a more immediate planes systems configurations have lower induced way, this kind of configurations are perfect for the drag than conventional configurations of similar UAS field of application, where the specific charac span, total lift, and dynamic pressure. teristics of this configuration can provide a great 7,8 In this context, Prandtl stated that the main idea advantage. for the minimization of induced drag is to reduce, as In view of the foregoing, the analysis of different much as possible, the gradients of the circulation. configurations for the optimization of the model is From this idea, Wolkovitch5,16 conducted several posed as the objective, by evaluating how and in studies where the advantages by the use of multi what way different variations of geometric parameters planes systems are shown. affect the main aerodynamic characteristics of the One of the advantages, that he demonstrated, was system. that (in tandem-wing configuration) the induced drag This work is divided into three sections. In the first is less if the vertical gap between the front wing and section, a conventional test setup design is undertaken the rear wing increases. where the parameters of the test model and test equip Secondly, Wolkovitch5 confirmed with tests con ment are described. The next section shows how the ducted in a wind tunnel that the Oswald efficiency aerodynamic coefficients of the joined-wing model factor, e, was greater than the one predicted by the change as a function of the design parameters, and Prandtl-Munk biplane theory.14 in the last section of the article a final analysis is pre The analytical method of Prandtl-Munk produced sented on the basis of the results of the previous as a result that the ratio of the Oswald efficiency sections. factor, e, of the joined-wing configuration with respect to the equivalent monoplane was of the order of 17 Test setup 1.05, while the tests performed by Wolkovitch showed that the value was 1.09, ergo, 4% bigger To conduct the different tests it is necessary to con than the one predicted by the Prandtl-Munk theory. struct a physical model that allows the geometry of On the basis of his research, Wolkovitch maintained the different configurations to be adopted in a simple that the classical theory disregarded the deflection of way. The test physical model is comprised of a for the wake over the forward wing, which leads to a ward wing semi-span and rear wing semi-span reduction in the induced drag coefficient, CDU of the mock-ups, this being the basic configuration with its order of 5%, consequently resulting in the increase in geometric parameters shown in Figure 2, both in front the value of the efficiency factor. and top views. In a similar way, from the aerodynamic point of The test model geometry is completely determined view, other studies about the joined-wing model have with the geometric parameters shown in Table 1. assessed the optimal shape of the joint between In choosing the basic values of the geometric par wings9,10 in order to determine its influence on the ameters defined in Table 1, the following consider drag components (induced, pressure and friction). ations about the technical and functional aspects Figure 2. Top and front views of the simplified representation of the unconventional joined-wing aircraft configuration test model. related to the nature of the test have been kept in the purpose of this study and secondly due to the mind: geometric constraints and speed in the test chamber. • The forward wing span value and the forward wing The type of joint employed to attach both wings root chord value have been determined to avoid together is a rigid joint, which was selected when corrections by geometric blockage in the wind considering the best tradeoff between strength and tunnel test section. As it is well known, for this to stiffness21 (Figure 3). happen, the relation between the test model front Finally, when choosing the airfoil, constructive, area and the wind tunnel test section cross sectional endurance, and aerodynamic aspects were con area must be less than 7.5%.20 This relation is of sidered. The choice of a symmetric airfoil simplifies the order of 4% for the test model. the manufacturing of the wings. Relatively higher • In selecting the rear-forward span ratio parameter thickness provides greater stiffness to the assembly value, B, the studies conducted by other authors and, from the aerodynamic point of view, as have been considered, which, after analyzing differ known, relative thicknesses between 12% and ent configurations, suggest that the optimal value 15% provide a higher value of the maximum lift of this parameter is between 0.6 and O.7.4,9 coefficient. • The assigned value to the forward wing sweep angle, in general, differs from the one denned by Furthermore, the NACA 0015 airfoil shows an Smith and Stonum.6 Even though the majority of acceptable performance for low Reynolds numbers 22 authors study configurations near to 30°, in the As a result the values of the basic geometric par present work, the study of lower values was ameters for the forward and rear wings have been chosen; firstly to find more suitable situations for established and are presented in Table 2. Table 1. Geometric parameters for the test Table 2. Test model values of geometric model definition. parameters.
Parameter Definition Parameter Value
bF Forward wing span bF 1.56 m
h Forward wing taper ratio XF 0.40
Of Forward wing root chord CrF 0.158 m H>f Forward wing sweep angle *PF 15° h Forward wing dihedral angle sF 3° u Rear wing taper ratio 6 0.60 CrR Rear wing root chord bR 0.93 m
VR Rear wing sweep angle ^R 0.60
SR Rear wing dihedral angle CrR 0.09 m 6 Rear-forward span ratio V>R See Table 3 4 Distance between wings SR See Table 3 h, Height between wings
Table 3. Study configurations as a function of the rear wing
sweep angle, Rear wing sweep angle, -10 -15 -20 -25 -30 Rear wing dihedral angle, SR (°) -25 JWC, JWCI2 JWC l3 JWC, 4 JWC ls -20 JWC2I JWC22 JWC23 JWC24 JWC2S -15 JWC3, JWC32 JWC33 JWC34 JWC3S -10 JWC41 JWC42 JWC43 JWC44 JWC4S -5 JWC5I JWC52 JWC53 JWC54 JWC5S position on the turntable (mark 4, Figure 4). However, the rear wing span, bR, and rear-forward span ratio parameter, B, are constant. The variation of these parameters implies changes to the rear wing position in relation to the forward wing (Figure 5). The variation of the dihedral angle modifies the position in height of the rear wing, ht, decreasing this height if the dihedral angle decreases Figure 3. Scheme showing the rigid joint between the rear in absolute value. However, an increase in the vari wing and the forward wing. The detail shows binding by a shaft, ation of the sweep angle modifies the relative position fixed to the front wing, and attached on the rear wing by a of both wings, lt, decreasing the distance between screw. them. The height values, ht, and relative distance between wings values, lt, are expressed as follows All the study configurations are obtained by keep ing the forward wing basic geometry constant and ht = Blp cos Sp cos p — tan 4>R) + - ctR 4 (Table 3). 3 (2) For every testing configuration, each rear wing is + -crp[B(lp-l)+l] an assembly of two pieces: a basic piece (mark 3, Figure 4) and a partial rear wing (mark 2, Figure 4). where lp corresponds to the forward wing non- The junction of the forward wing (mark 1, projected semi-length, X is the forward wing taper Figure 4) with the rear wing is a fixed point, so the ratio, ctR is the rear wing tip chord, crF is the forward length of each rear wing is different in function of its wing root chord, Sp, cpp, SR, and cpR are the dihedral Configuration JWC^j Configuration JWC j ^ Figure 4. Sketch of the experimental set-up showing the junction of the forward wing (I) with the rear wing (2, 3) and fixed to the turntable (4). The figure shows two different configurations. angle and the sweep angle on the 1/4 chord line of the To measure the system aerodynamic coefficients, forward and rear wing respectively, and B is the rear- the development of tests in a wind tunnel is necessary. forward span ratio, expressed as The A9 Tunnel of the "Instituto IDR/UPM" is an open return wind tunnel with a closed test section and b_R open-circuit flow (Eiffel type). As can be seen in B (3) bP Figure 6, the A9 Tunnel is comprised of an inlet con traction (1), test section (2), and diffuser (3), which The rear wing position values (height and distance) also acts as an adapter for the drive section where are nondimensional values related to the JWC15 con the fans are (4). The test section is about 3 m long figuration position which corresponds to a dihedral with a cross section of 1.5m width and 1.8m height. angle value of SR = —25° and a sweep angle value of Before measuring the joined-wing model in the A9 ht intensity distribution, Iyx, has been considered. ht (4) h (JWCi; To determine the turbulence intensity, the velocity of the wind inside the test section, empty with no model, has been measured using a hot-wire anemom- (5) WC,; etry equipment and an adjustable traverse guides system. Using expressions (1) and (2), the dimensionless To obtain a wide spatial resolution, the velocity has height values, ht, and dimensionless distance values, been measured in 132 points contained on the cross lt, are shown in Tables 4 and 5. section of the test section, distributed in a matrix of Position of real" wing for p^^ 25 configurations ' fit/fame^ X 1.00 ////mvc15 " *H 1.00 0.30 / / >^8 / / / y\y^ / /yS s>yy^ y^ Figure 5. Drawing of the rear wing position in relation to the forward wing. 3% in the center of the test section, but is greater Table 4. Values of the dimensionless height, ht, as a function of the rear wing dihedral angle, SR (°). (>3%) near the walls (about 50 mm). Although these values are greater than the required 19 Rear wing dihedral angle, SR (°) ones for aircraft aerodynamic tests (<0.5%), they -5 -10 -15 -20 -25 are acceptable for their application in the field of UAS. ht 0.30 0.40 0.60 0.80 1.00 The normal operating altitude of UAS, in the most general case and for Class I and mini and small cate gories,23 is lower than 1500 m where the settings of the atmosphere are due to atmospheric boundary layer Table 5. Values of the dimensionless distance,/„ as a function (ABL). The ABL is caused by the interaction of the of the rear wing sweep angle, IL V?f ^ • K.i V \ ! / / / / / / / / / / / / / |§| _ ua 1 2 XT 3 4 1 0 -r ;: .;. !;:ll \——__ = Figure 6. Front and top drawing views of the A9 Tunnel: (I) contraction, (2) test section, (3) diffuser/adapter, and (4) drive section/ fans. 1500 40 ZT (1,D yr" o -J.-U-I- CO L_L1LIJJJ_ MINIM ID 1 29 CO 1420 Figure 7. Velocity points matrix for the determination of the turbulence intensity. spin for the loads measure at different angles of attack aerodynamic drag, D, and the pitching moment, My, to be studied (Figure 8). The total loads measure on acting on the model. the test model is performed by a Delta force sensor SI- The tunnel parameters to obtain the aerodynamic 330-30 of Ati Industrial Automotion with detecting forces over the test model are: ranges, in axes xT and yT directions (Figure 7), of 330 N and a resolution of 1/16 N, which makes it • Velocity of the free-stream in the tunnel: possible to calculate the aerodynamic lift, L, U = 25 m/s aerodynamic chord of the front and rear wing ensem ble, values according to b bR P (8) COS Sp COS (fp cos &R cos q>R A^(f)+A*(j) A (9) b_ (10) A where SF is the forward wing area, SR is the rear wing area, and A is the effective aspect ratio.5,24 The effective span, b, is defined as the mean of the not projected lengths of the quarter-chord lines of the forward wing and the rear wing. The effective aspect ratio, A, is a geometric relation and takes into con sideration the individual wings surface area, but it does not account for any aerodynamic coupling 4^3 between the joined wings. In addition, the associated aerodynamic coeffi Figure 8. Test model assembly diagram in the A9 Tunnel test cients, induced drag coefficient, CDi, and the aero section where the turbulence intensity contour lines distribu dynamic efficiency, E, are also determined, and tion is shown: (I) test section, (2) test model, (3) spin sensor, calculated by the expressions and (4) load sensor. c2 Cm (11) n Ae • Range of angles of attack: a = [—15°, 15°], at c intervals of l CL (12) • Measuring frequency: /= 1000 Hz CD • Measuring time: T = 120 s • Reynolds number based on front wing mean aero where e is the induced drag efficiency factor corrected dynamic chord: Re = 250000 for the Wlkovitch's joined-wing model by the effect of the forward and rear sweep angle5 and given by e = e [l +0.0435 (tan Through aerodynamic analysis, it is possible to get where et is the theoretical induced drag efficiency optimum configuration of the joined-wing model factor. This factor was estimated by Letcher25 for from the point of view of the position of the rear nonplanar wings; v-wings and diamond-wings. wing, in order to analyze the best performance and Several years after, DeYoung26 developed a general flight characteristics of a joined wing aircraft in the ized equation for arbitrary cross-sectional wing forms, preliminary design stage. including diamond box-wing and partial span Specifically, the experimental analysis is aimed at diamond box-wing,25 expressed as defining the basic aerodynamic coefficients of lift, CL, 3 2 and drag, CD, evaluated from the time series values of et\B=Q.6= 0.04H + 0.18tf + 0.1H+ 1 (14) lift, L, and drag, D, measured by force and torque sensors according to the expressions where Hj-2 6 is the dimensionless maximum height according to C (6) L qbc H- (15) bP D CD (7) qbc As can be seen in equation (13), the value of e is a function of the forward and rear wing sweep angle where q denotes the dynamic pressure, b is the effect and as can be seen with equation (14), it has a ive span,5 and c is the effective wing mean strong dependence on the height between the forward wing and the rear wing.26 This value is shown On the other hand, the graphs of the aerodynamic in Table 6. coefficients, CL, CO, and Cm are represented as a The values of the lift, CL, and drag, Co, coefficients function of the rear wing sweep angle, cpR, and the are represented in Figure 9, and the values of aero rear wing dihedral angle, SR, for different values of dynamic efficiency, E, and the factor c[ /Co for min the angle of attack, a where CL, CO, and Cm are imum required power are depicted in Figure 10, where normalized with respect to the values of the JWCi5 the variation with respect to the angle of attack, a, can configuration ones (CLU, CO15, and Coi15)- be seen. In Figure 12 the variation of the normalized lift Similarly, the variation of the lift, CL, and, C[ , coefficient, CL, is shown, where it can be seen that coefficients as a function of the drag coefficient, Co, the value is greater when the rear wing is closer to are represented in Figure 11, and the dashed line is the the front wing; this is due to the front wing causes tangent to the curve being the contact point the max downwash5 on the rear wing, and the rear wing /2 5 imum value of CL /CD, i.e. minimum required power induces upwash on the front wing. Stating that, point. These figures correspond to the JWC15 config the total lift of a joined-wing is lower than the uration, i.e. for rear wing dihedral angle SR = —25°, simple sum of the front and rear wings lifts, because and for rear wing sweep angle Rear wing dihedral angle, SR (°) This may be due to interference from the front wing -25 1.039 .044 .048 .052 1 .057 flow impinging on the rear wing. -20 1.035 .039 .043 .048 1 .053 In Figure 14 the normalized induced drag coeffi -15 1.031 .035 .039 .044 1 .048 cient value, Coi, is shown. The behavior of this -10 1.027 .031 .035 .040 1 .045 value is inversely proportional to the value of the -5 1.024 .028 .032 .037 1 .041 induced drag efficiency factor, e, which, as stated, increases as the height of the rear wing increases. o SR 25°, 0.8 W) 0.6 / 0.4 \J r 0.2 U 0 -0.2 -0.4 -0.6 0.05 -0.8, 1.0L 0 15-10-5 0 5 10 15 -15-10-5 0 5 10 15 an a[°] Figure 9. Variation of the lift, CL, and drag, CD, coefficients as a function of the angle of attack, a, for rear wing dihedral angle <5R = —25° and rear wing sweep angle 6.0 6.0 4.0 2.0 Figure 10. Variation of the aerodynamic efficiency, £, and factor CL /Co for minimum required power, as a function of the angle of attack, a, for rear wing dihedral angle <5R = —25°and rear wing sweep angle cpn = —30°. Free-stream Reynolds number Re = 250,000. fo=-25°,^ =-30° $H =-25°, Figure I I. Variation of the lift coefficient, CL, and coefficient, CL' , as function of the drag coefficient, Co, for rear wing dihedral angle <5R = —25° and rear wing sweep angle <^R = —30°. The dashed line shows the maximum CL /Co point. Free-stream Reynolds number Re = 250,000. In each figure, and for each angle of attack, the In Figure 15, the maximum value of the aero maximum and minimum values for each coefficient dynamic lift and minimum value of the drag are rep are shown, as well as the values for each coefficient resented as a function of the rear wing sweep angle of the reference configuration. and for each value of the rear wing dihedral angle. (« = 4° Cu& = 0.37) CLma, = 1.2G Ctmin = 1.00 (a = 6° CLl5 = 0.55) CLlllaj. = 1.24 CL , = 1.00 -20 1.15 %-lS 1.10 .05 -5< (a = 8° Ctl, = 0.09) U£maa = 1.23 C/.,,,,-,, = 1.00 (o = 10° CLl, = 0.79) ftm„ = 1.22 CLmil, = 1.00 ~s-15( -IOC (Q = 12° C£l0 = 0.83) CimM! = 1.21 Cr,„lh, = 1.00 (Q = 14° CL„ = 0.82) CLnar = 1.21 O, = 1.00 -25 -20 -20 6 1.15 ^-15< ^S-15C 1.10 1.10 -IOC '1.05 -5C^^^^^^^^^™*K> D ™1.05 -10 -15 -20 -25 -30 -10 -15 -20 -25 -30 rlt\ Yin Figure 12. Variation of the lift coefficient, Q, as a function of the rear wing sweep angle, -20C —10* (Q = 4° CDl5 = 0.065) CD , = 1.40 C -25 -20C -20 -25 (a = 8° CDls = 0.080) C^m„:, = 1.30 Co,,,,-,, = 0.06 (a = 10= C0u = 0.094) C^„„, = 1.27C^„,-„ = 0.90 ~25<^——Q O p —1.30 -25C^« -Q Q C^™rf> ^H 1.25 1.20 1.15 t -1? 1.10 1.05 Figure 13. Variation of the drag coefficient, Co, as a function of the rear wing sweep angle, — 8" Coh 0.02:1) C0,„m,r = 1.49 CD,„,,„ = 1.00 {o = 10° CDhs = 0.030) Cm„,„ = 1.46 CDhllhl 1.00 -25 ( 45 -25C 1.45 (a = 12° CBM, = 0.034) Cw„„,,. = 1.45 Co,™,-,, = 1.00 (a = 15° C,j„:, = 0.031) CD .,. = 1.48 CDlmh, = 1.00 •25 .45 -25' 1.45 Figure 14. Variation of the induced drag coefficient, Co,, as a function of the rear wing sweep angle, Downloaded from pig.sagepub.com at ETSI Aerouauticos - UPM on December 16, 2015 1.1 1 1 0.09 1 1 0 SR = -25° 0 <&H = -25° D SR = -20° • SR = -20° O SR = -15° O Sn = -15° V SR = -10° V ^ = -10° A 5B = -5° 0.08 . A SR = -5° . 0.07 sj 0.9 0.06 0.8 0.05 -10 -15 -20 -25 -30 10 15 20 25 30 Figure 15. Variation of the maximum lift, Cj.max, and minimum drag, Comin, coefficients as a function of the rear wing sweep angle, cpR, and the rear wing dihedral angle, <5R. Free-stream Reynolds number Re = 250,000. 10 1 1 10 -25° 0 5R = o 5fi = -25° • S = -20° SR = -20° D R o 5R = -15° i 9 ^ ^ V -10 -15 -20 -25 -30 -10 -15 -20 -25 -30 Ml0] 3/2, Figure 16. Variation of the maximum aerodynamic efficiency, £max> and maximum CL /CQ for minimum required power coefficients as a function of the rear wing sweep angle, Finally, in Figure 16 the maximum value of the aero Conclusions dynamic efficiency and maximum value of the param- ^3/Z2 eter C/ /CD for minimum required power coefficients In view of the results, it has been proven that the are represented as a function of the rear wing sweep variation in the aerodynamic coefficients is more pro angle and for each value of the rear wing dihedral nounced as the rear wing sweep angle, (SR = —5°, (pR = —10°) presents maximum values up port aircraft; a project of five Italian Universities. In: to 20% higher than the JWC15 configuration XXVII Congresso AIDAA, Roma, 2003. (8R = —25°, cpR = —30°) presents. In conclusion, the 4. Mannings R. The Future, by AIRBUS. AIRBUS lift coefficient decreases as the distance and the height Industrie, 2011. of the rear wing increase. 5. Wolkovitch J. The joined wing - An overview. / Aircraft 1986; 23: 161-178. The drag coefficient tends to be lower as the rear wing 6. Smith SC and Stonum RK. Experimental aerodynamic dihedral angle decreases and the sweep angle increases characteristics of a joined-wing research aircraft config (both in absolute value), as shown in Figure 13. In uration. NASA TM 101083, 1989. general, the JWC55 configuration (8R = —5°, 7. Nangia R, Palmer M and Tilmann C. Unconventional SF forward wing area SR rear wing area Appenc lix T time measuring time measuring turbulence intensity Notation Tv U velocity measuring b effective span Uv velocity measuring turbulence intensity bF forward wingspan (x, y, 0 mock-up coordinates system bR rear wingspan (xT, yr, zT) tunnel coordinates system B rear-forward span ratio a angles of attack c effective wing mean aerodynamic chord forward wing dihedral angle c forward wing root chord SF rF rear wing dihedral angle rear wing root chord SR CrR forward wing taper ratio rear wing tip chord Ap CtR rear wing taper ratio drag coefficient Aft cD effective aspect ratio normalized total drag coefficient value A CD forward wing aspect ratio AF Cm induced drag coefficient rear wing aspect ratio AR Cm normalized induced drag coefficient forward wing sweep angle value