1、x ,INASA Technical Paper 1020Theoretical Parametric Studyof the Relative Advantagesof Winglets and Wing-Tip ExtensionsZCASE F_ LCOPYHarry H. Heyson, Gregory D. Riebe,and Cynthia L. FultonSEPTEMBER 1977Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-P
2、rovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NASA Technical Paper 1020Theoretical Parametric Studyof the Relative Advantagesof Winglets and Wing-Tip ExtensionsHarry H. Heyson, Gregory D. Riebe,and Cynthia L. FultonLangley Research CenterHampton, Vi
3、rginiaN/Lq/XNational Aeronauticsand Space AdministrationScientific and TechnicalInformation Office1977Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SU
4、MMARYThis study provides confirmation, for a wide range of wings, of the recommendationsof Richard T. Whitcomb in NASA Technical Note D-8260. For identical increases in bend-ing moment, a winglet provides a greater gain in induced efficiency than a tip extension.Winglet toe-in angle allows design tr
5、ades between efficiency and root moment. A wingletshows the greatest benefit when the wing loads are heavy near the tip. Washout dimin-ishes the benefit of either tip modification, and the gain in induced efficiency becomes afunction of lift coefficient; thus, heavy wing loadings obtain the greatest
6、 benefit from awinglet, and low-speed performance is enhanced even more than cruise performance.Both induced efficiency and bending moment increase with winglet length and outwardcant. The benefit of a winglet relative to a tip extension is greatest for a nearly verti-cal winglet. Root bending momen
7、t is proportional to the minimum weight of bendingmaterial required in the wing; thus, it is a valid index of the impact of tip modificationson a new wing design.INTRODUCTIONThe current high cost and, at times, limited availability of fuel have led to anextensive examination of possible ways to cons
8、erve aircraft fuel by increasing aircraftefficiency. The most obvious means of increasing efficiency, or lift-drag ratio, is toreduce induced drag by an increase in aspect ratio. On the other hand, any of severaltypes of tip modification, generically referred to as end plates, could be appended to t
9、hetip of the wing.End plates have been recognized for years (for example, ref. 1) as a means ofincreasing the effective aspect ratio of a wing. Numerous experimental investigationsof end-plate effects are summarized in references 2 and 3. These studies concentratedon the simplest form of end plate,
10、large-chord flat surfaces, where the associatedincreases in parasite drag largely offset the reduction in induced drag.Examination of the basis for end-plate induced efficiency (ref. 1) reveals that theonly requirement is to produce a suitable distribution of vorticity in the far wake. Asimple flat
11、plate is not an efficient means of producing the appropriate vorticity distri-bution. A highly optimized narrow-chord surface can produce the same, or greater,gain in induced efficiency at a far smaller cost in weight, parasite drag, and compress-ibility drag. This concept has been pioneered by Rich
12、ard T. Whitcomb (refs. 4 and 5).Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-The improvement in overall performance over a simple end plate is so great that thesemodern surfaces are referred to as winglets to distinguish them from the older concep
13、ts.Recent experimental tests (refs. 4 to 9) demonstrate that winglets could signifi-cantly improve the efficiency of transport aircraft, and reference 4, in particular,presents general rules for the design of such winglets. For other designs, such as thespan-loaded aircraft of references 10 to 12, t
14、he application of winglets is envisioned onaircraft which differ radically from current transport aircraft. As yet, no sufficientlygeneral study is available to provide guidance in the design of winglets for such aircraft.Aerodynamic efficiency cannot be isolated from its impact on the overall aircr
15、aftconfiguration. Aerodynamic gains from either span extensions or winglets are accom-panied by increased loads and increased wing weight. Since similar aerodynamicimprovements can be obtained in either manner, the final choice will be largely deter-mined by loads and weight.This study examines a br
16、oad range of wings and explores the effects caused byvarying aspect ratio, taper ratio, and washout. The relative gain in induced efficiencyis presented as a function of the relative penalty in wing-root bending moment, which, inturn, is shown to be proportional to the minimum weight of material req
17、uired to resistthe aerodynamic bending moments imposed on the wing. The results of this study areintended to illustrate trends and not to provide design charts; thus, in order to reducethe number of variables to a manageable level, certain obvious features of practicalwings are omitted. The wing and
18、 winglet have no camber; thus, all angles should bemeasured from zero lift. The wing has 30 leading-edge sweep. The winglet has alength which is a constant percentage of the wing span, is untwisted and of constant chord,and is canted outward 15 . The tip extensions are assumed to be simple linear co
19、ntin-uations of the wing. The flow is assumed to be incompressible. A brief examination ofthe effect of varying these values is made for one set of wings with a taper ratio of 0.5and 5 washout.No attempt is made to examine theoretically optimum span-load distributions. Theentire approach is based up
20、on calculating the efficiencies and root moments of an arbi-trarily selected set of wings with and without winglets and wing-tip extensions.SYMBOLSA aspect ratio of unmodified wing, b2/Sspan of unmodified wingc local wing chordProvided by IHSNot for ResaleNo reproduction or networking permitted with
21、out license from IHS-,-,-CD, iC LCnC rctDieFNghkLM lMrqSinduced drag coefficient, Di/qSlift coefficient, L/qSlocal normal-force coefficient,root chordFN/qctip chord of unmodified winginduced dragpotential-flow induced efficiency factor,local normal force per unit spanCL2/yACD_iacceleration due to gr
22、avitylocal mean vertical distance between cover plates of wing boxwinglet toe-in angle, measured normal to plane of winglet, positive withleading edge inward, degconstant of proportionalityliftlength, normal to span, of wing-box cover plateslocal bending momentbending moment at root (or center) of w
23、ingdynamic pressurearea of unmodified wingeffective thickness of wing-box cover platesProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-W minimum weight of wing bending materialdistance along span measured from center lineYcYtFlateral location of cente
24、r of lift of wing panelvalue of y at wing tipcirculationwinglet cant angle, measured positiveoutward from vertical,degAbApercentage increase in wing spanleading-edge sweep angle, positive rearward, degtaper ratio of unmodified wing, ct/c rp densitylocal stressSubs cripts:design stressw wingletwith w
25、ith tip extension or wingletwithout without tip extension or wingletBASIC CONSIDERATIONSComputer ProgramThe computer program used for this study is a modified form of the North AmericanRockwell unified vortex lattice (NARUVL) program (ref. 13). The modifications consistedof a faster matrix solution
26、routine and a substantially improved routine for far-wakeProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-calculation of the induceddrag. In addition, routines were addedto calculate root bend-ing moment,bending-momentdistribution, anda factor proport
27、ional to the minimumweight of bendingmaterial. This program was chosenbecauseit is relatively rapidand sufficiently accurate for parametric studies.The NARUVL program satisfies the linearized boundaryconditions with the localairfoil slopes. Airfoil thickness andout-of-plane displacementsdue to cambe
28、r areignored. Displacementsdueto dihedral are retained. Noviscous effects are included;that is, there are no friction drag and no separation or stall. Induceddrag is calculatedin the Trefftz plane. Subsoniccompressibility is treated as a Prandtl-Glauert stretchingof ordinates; thus, supercritical re
29、gions are not represented accurately.In the present study, the unmodifiedwing is always represented by 200singular-ities, 10 chordwise and20 spanwise. Whenthe wing tip is extended,the total number ofsingularities is increased by a proportionately larger number of spanwisestations.Winglets are repres
30、ented by an additional 50 singularities on the winglet, 5 chordwiseand 10 spanwise. Both wings and winglets have no camber. As a rough approximationto the effect of camber, angles of attack and toe-in angles can be considered to bemeasured from zero lift. The flow is assumed to be incompressible, th
31、at is, at zeroMach number.The input variable in the NARUVL program is angle of attack rather than liftcoefficient. The present results for constant lift coefficient were obtained by two pro-gram executions: once to obtain lift coefficient as a function of angle of attack and then,using these results
32、, to obtain values for the desired lift coefficients.The effects of tip extensions and winglets are presented in the form of dimension-less ratios to the corresponding values for the unmodified wing at the same lift coeffi-cient and Mach number. All coefficients are computed by using the aspect rati
33、o and areaof the unmodified wings; thus, the change in efficiency factor represents the total reduc-tion in induced drag. This form of presentation yields an immediate rough estimate ofthe overall effect of modifying a given wing.Standard WingsTypical standard wing planforms considered in this study
34、 are illustrated in figure 1.Leading-edge sweep is fixed at 30 , and three taper ratios (1.0, 0.5, and 0.25) are con-sidered. Five aspect ratios (4, 6, 8, 10, and 12) and three linear washouts (0 , 5,and 10 ) are considered. The ranges of taper ratio, aspect ratio, and washout are signif-icantly gre
35、ater than the ranges encountered in current design practice. Certain of thesevariables are altered subsequently to examine the relative magnitude of their effects.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Tip ExtensionsFigure l also illustrates
36、the tipextensions (5,10, and 15 percent) thatare con-sidered herein. In each case, the tipextension isa simple linearextrapolationofthegeometric characteristicsofthe basic wing. Inthismanner, taper ratio decreases, andwashout increases, as the wing is extended. Despite these changes inthe resultingw
37、ing,the extended wings are described herein interms of the taper and washout of the originalunmodified wing.Standard WingletsThe typical standard winglet configuration studied in this paper is shown in fig-ure 2. The winglet has no geometric twist since, as noted in reference 4, the basic wingflow f
38、ield already introduces a significant aerodynamic twist. For simplicity, the winglethas no taper. The winglet chord is always one-half of the wing tip chord and its trailingedge is coincident with the trailing edge of the wing. The winglet leading-edge sweep ischosen to be 45 . In its own plane, the
39、 length of the winglet is chosen to be 15 percentof the wing semispan and it is canted outward 15 . These values are fairly representa-tive of the winglets used in references 4 to 9. The angle of incidence, or toe-in, withwhich the winglet is attached to the wing is varied from -4 to 4 in increments
40、 of 2.Variation of Standard ParametersThe simple winglet design used herein is merely intended to illustrate trends. Itis not intended to represent a practical design. A briefer study, using only wings witha taper ratio of 0.5 and 5 washout, was made in which a number of parameters werevaried indepe
41、ndently. These cases include: a Mach number of 0.8; wing leading-edgesweep of 0 with both swept and unswept winglets; winglet length of 0.3 wing semispan;winglet cant angles from -15 to 90o; winglet sweep angles of 0 and -45o; and a wingletwith taper ratio of 0.5 and an area reduction of 25 percent.
42、 These results are presentedafter the results for the standard wing-winglet combinations.RESULTS AND DISCUSSIONIn the current study, winglets and tip extensions of arbitrary configuration areaffixed to the standard wings. The interplay of the additional surfaces and the wingdetermines the load distr
43、ibution, the induced efficiency, and the root moment. Thisprocedure is in contrast to that of reference 14 where the wing and the modificationsthereof are required to have an optimum load distribution. In that procedure, all thestandard wing and winglet combinations would have identical induced effi
44、ciencies and rootbending moments because they all have the same trace in the far wake (fig. 2(c). TheProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-present approachalso differs from that of reference 15,where the wing was assumedtobefixed, but the w
45、inglet twist (which includes toe-in angle)was optimized in eachcasefor minimum induceddrag at onelift coefficient. Not only doesthe procedure of refer-ence15tend to obscure the full effect of changesin winglet design, but it also negatesthe possibility of examining the offloadedwinglets recommendedb
46、y reference 4.StandardWingsEfficiency and lateral centroid of pressure.- The efficiency factors of the standardwings are shown as a function of the nondimensional lateral centroid of pressure in fig-ures 3 to 5. It is helpful to examine these results in terms of basic and additional loaddistribution
47、s (ref. 16). The basic load distribution is the distribution at zero lift, iscaused by twist, and is a function of both twist and taper. The additional load distributionis that caused by angle of attack. It is a function of taper and is unaffected by twist. Thecomplete load distribution is a linear
48、superposition, at any angle of attack, of the basicand additional load distributions.With no washout, the basic load distribution is zero; all the loading is caused by theadditional load distribution. Therefore, the nondimensional load distribution, the effi-ciency factor, and the centroid of load (fig. 3) are independent of lift coefficient. It hasbeen shown by Glauert (ref. 17) that a taper ratio of about 0.5 results in the best effi-ciency factor (approximately 0.99) for untwisted unswept wings. The increased tip load-ing associated with sweep alters this result. Indeed, figu
