1、REPORT No. 267DRAG OF WINGS WITH ENI) PLATESBy PAUL E. EIEMKELangley Memorial Aeronautical Laboratory?51Provided 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-,-,-
2、REPORT No. 267DRAG OF WINGS WITH END PLATESBy PAUL E. HEUKF.SUMMARYIn this report a jorrnula jor calculating the induced drag of naultiplanes with end plates isdericed. ?%e frictional drag of the end plates is also calculated approximately. It is shown thatthe reduction of the induced drag, when end
3、 plates are used, is .st.iciently large to increase tfieeficiency of the un”ng.Curres .s7iowing the reduction of drag for monoplanes and biplanes are constructed; the in$uenceoj gap-chord ratio, aspect ratio, and height of end plate are dkerrnintd for typical cases. T%emethod of obtaining the reduct
4、ion of drag for a multilane is described.(comparisons are made of caktdated and e.rperimental reswlts obtained in ux”nd tunnel testswith airjoik of various aspect ratios and end plates of rarious sizes. The agreement Mveen cal-culated and experimental resuk is good.Analysis of i%e experimental resuk
5、t shows that the shape and section of the end plates areimports nt.INTR%DECTIOXThe end pIates which are deaIt with in this report are fins or shieIds -which are atkwlwdto the tips of airfoils; the plane of the fln is perpendimdar to the span of the airfoil. The purposeof this dwiee is to ser=reas a
6、barrier to the flow aIo the span and around the tips of the airfoil.This flow in a vertical plane containing the span is usually ded the transverse flow. By .obstructing this transverse flaw- its kinetic energy is diminished and as a consequence theinduced drag of the airfoil is thereby reduced.From
7、 -wind t.unneI tests made at Gottingen (Reference I) and at the Ik the influence of such major factors as gap-chord ratio, aspect ratio, and heightof end plates is determined. In aU cases the frictional drag of the end pIates is considered in -calculating the tot al drag.253Provided by IHSNot for Re
8、saleNo reproduction or networking permitted without license from IHS-,-,-254 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSINDUCED DR.4G OF A MULTIPLANE WITH END PLATESThe longitudinal projection of the muItiplane consists of equal, parallel st.raightilines.The same projection of the end plates
9、will aIso be considered as straight lines whose directionsare at right-angles to the projection of the multilane elements.The induced angle of attack and consequently the induced drag depend upon the induceddowmwash. It is sui%cienti theh for the purpose in hand to consider the transverse flow in av
10、ertical plane at right angles to the air stream.This two-dimensional transverse flow may be determined in severaI ways. In this reportit has been obtained by using the method of conforrna transformation. The rectilinear polygonbounding the longitudinal projection of the wings and end plates is trans
11、formed into a singlestraight line. The flow around such a line is well known.Let the plane of khe lines with end pieces be the ylane of a complex variable z as shownin Figure 1. The mid-point of the system of lines is at the origin and the direction of the lines iL?IIcB/ flEp-w bA- .J- d_., respecti
12、vely, Thetransformation is then found in the form ,=adz-iY”(2)where a is a real constant.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-DR4G OF WINGS WITH E21C!3PLATES 25.5We may integrate (2) by substitut a Z (uO) +2 (a + P, u and ,fIconstants. (4)
13、Using (4) and the correspondence given in the tabIe we hae the following equations: %2 (%)+-2(CL%)+f?=h+ib 5); K-Z (WJ+l?=h+m (6)f (E+i.ZK)Z (w) z (Wa) co.z (cd,);iv=/3h= ; (K) z (0,)h Kz (WJF= K Z (JO)+ fi (9)(10) .(12)-.Provided by IHSNot for ResaleNo reproduction or networking permitted without l
14、icense from IHS-,-,-256 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSThe transverse fiow around the Iines with end pieces is parallel to the red axis at infinit,yin the z-plane, the direction of flow at infinity being in the direction of the posiive x-axis. Thepotential function for this flow i
15、s more easiIy expressed_.in terms of t. It. is O,= pi + i+, = a lt,where 17is the velocity of the flow in the z-plane at a great distance from the origin.If we superimpose on this flow one whose potential_function is Q, = _- w-e shall have thepotential function for he fIowr set up by the motion of t
16、he lines in a fluid otherwise at rest.The Iines will move in the direction of the positive real axis in the z-plane with a constantvelocity Y.To find the kinetic energy we evaluate the integralThe path of integration, L, is the cmpIete boundary of the wing,_ P is the reaI part of (a U Ts),“ga K+*) -
17、“1By using again the reIatioa 1 PC8= Z (w) as wxJI as equations (10) and (11), we haveT=; p P 45 (K+ K-/) 2E _ and 5 show the results of the Gotthgen tests, for aspect ratio 8/3, in theform of polar curves. In each case except for end plate 3, Figure 4, the reduction of drag wascomputed from formuhi
18、 (19) using the appropriate value of aspect ratio, ratio of length of endplate to span and area of end plates. In the case of end plate 3, since the end of the wing wasonly partially shielded, an average height of the plate, over the chord, was used, The valueof CL which gave the best ameement for t
19、he frictional drag of the end dates is 0.0140.Cls.04.03.0.02AC m II-.0 -/.o /.2 1.4CLThis alculated reucfion of drag was th in one the coefficient is 0.014, and in the other 0.008.The agreement between calculated and observed reductions of drag in the American testssuggests using an end plate of giv
20、en area in the best possible way. Since the use of the entireheight of the trapezoidal end plate (fig. 6) in the formula gave calculated results agreeing veryProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-DRAG OF WINGS WITH END PlL4TES 2592.42016CL1
21、2.8.4 xperimenf Q 1 1- TheoryII IlrllH“ll l-1 -:1FIG. 3.PoIar cumes of G6ttimzen tesss showhx reduction of dragdue to end plztes 2 d 3. Aspect ra;io SE2.42.0/6c.2.8.40rfue to end plates 3 7. Asset raio, SIB.tIIEndpfde .4 .5.E_xperinen# O Ier 1 7“ ,I“IIJLI12 It.8G.,I I I f 11111 f c=” FIG. r3.-PoIm c
22、rimes of h-. ctrord=6. Clap/chord=Ml. Dragcoefficient, C%=O.01.05,. . *O4.03ACn.02.0!Q-.0/-.02.- . .- - 0.20 . !26 0.8 To .2 1.4 _CLFIG. 12.Bip1ancswith end plates. t7fdcu1ztcdrerlucthmofdr8g, D,plotted against lift coefficientfor various vrducsof MU. 21-height O(end plate. 2G=getp. Spankhord=: fwhi
23、ch is the value previously found.The expression for reduction of drag is derived in a manner quite simiIar to that used forthe monopIane. Ke find.6 =span of biplane. -c=chord.(7. = lift coefEcient.d. = area of the equivalent air stream of a biplane without end plates.AX, = area of the equivalent air
24、 stream of a biplane with end pIates.C,= drag coefficient of end plates.= h L/h=1, , , 6 and, as in FigWe , the aue (JF= .O1 was used as it represents w average VahIe of =.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-262 REPORT XATIONAL ADVISORY C
25、OMMITTEE FOR AERONAUTICS.The curves Wustrate how properties of end pIates affect biplanes of various proportions.The increase of drag at lower values. of (7Lis considerably less than iisfor larger vaIues ofgap/chord while the reduction of dragj especially when larger plates arc used, is reIat.ively
26、large.The reduction of drag persists at the higher values of (7Lfor plates which are quite large,so large as to be useless in practice.The method us.e.din calculating the effect of end plates for bipIanes may be used for multi-planes. Formula (22) would differ only as far as z is concerned. This qua
27、ntity may be ca-lculated, bowel-er (Reference 7), and the reductions of drag for muItipIanes may be calculatedin precisely the same manner as that just described and carried out for biplanes.ONf2LUS10NSCalculations show that the induced drag of monopIa.nes and multiplanes may be decreasedby attachin
28、g end plates to the ends of the wing. The frictiona drag of the end plates may becalculated approximately. The reduction of the induced drag exceeds the additional frictionaldrag due to the end pIates at all but small values of the lift. For given dimensiom of wingsand end pIates the reduction of dr
29、ag Iess the frictional drag of the end pIates varies directlyas the square of the absolute lift coefficieui. The aerage reduction of drag increases as theaspect ratio decreases. Calculations and experiments agree quite satisfacorily for single wings -equipped with end plates.Wind tunnel tests show t
30、hat the coefficient used. in calculating the frictional drg of theend plates may be reduced materially by fairing the end plates. The shape of the end platodetermines to some extent the reduction of induced-drag. Further tests would be necessaryto find end plates of good shape and having at the same
31、 time a low drag cofficient.Recent experiments hay-e shown that Inutih higher lift coefficients can be obtained thanhas been the case up to now with the conventional ahfoils. Since Jhe reduction of drag due .LOend plates is much greater at the higher vaIues of t,be lift coefficient) the use of end p
32、latestogether with the use of means for increasing the bf yin resuldig a gateriaI improvement of.-the efficiency of the present-day airplane.LANGLEY MEMORIAL ZEONAUTICAL LABORATORY,ATIOAAL .LDVISORY COMMITTEE FOR ilERONAUTICS,LANGLEY FIELD, JrA., Janzary .20, 1927.REFERENCES1. N.AGEL, F.: I?lugel mi
33、t seitlichen Scheiben. “ Vorlautige Mftteflungen der Aerodynamkehen Versuchsan-stalt zu (lottingen,” No. 2, July, 1924.2. REID, E. G.: The Effect of Shielding the Tips of Airfoils. N. A. C. A. Technical Report IYo. 201, 1925,3. LAMBH.: Hydrodynamics-Fifth edition, 1924.4. PRAXDTL,L.: Applications of
34、 modern Hydrodynamics to Aeronautics. N. .4. C. A. Technical Report No.116, 1925.5. HIPPE+LEY,R. L.: Smithsonian Mathematical Formulae and TaMes of Elliptic Functions. SmithsonianMiscellaneous Collections. Volume 74, NTO.1, 1922. _6. Tragfliigel Theorie, zweite Mitteilung. (Nachrichten der Koniglich
35、cn Geselischaft der Wissenschaftcn zuGottingen. Mathematisehe-Phy sikalische, 1919.)7. PR.WDTL,L.: Induced Drag of Multiplanes. X. A. C. A. TechnicaI Note No. 182, 1924.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-DR4G OF “GS WITH EN-D PLATESTABLE
36、 IValues of R and 2h;% for given values of 0.R=(area of the equivalent air stream of a monoplane)/(area of the equirdentwith end plates).2h/b=(height of end pIate)/(span of wing).0 degrees707580858S0.0173.0311.0:93. 0/21.0996.133.173-222,. z;.433.541. 6s61:;fL 7s2.170.971.948.909.877.844. Soo. 51. 1
37、04.653. go. a62. 50s.452.395.323.261.227NageIsformula263air stream of a monoplane-1Per centdifference+0. 33.52L i62.05L 782.503.473.833.80 3-773.563.743.15TABLE 11OBSERVED .4ND CALCUL.4TED REDUCTION OF DRAGTests made at Langley Memorial Aeronautical Laboratory. Monoplane, 4 by 24 inches; wingsection
38、, N. .4. C. A. 731o.;3:4.5.6CD (disk end plates)Observed I CakulatedIO. 0026I0. 00210- ooo. 00196. 0013 . 00159. 0003+. 0005+. 0012+. 0023+. 003s. 00095. 00005+. 00110+. 00250.00412+. 0064 .00604+. 0093 -00826+. 01s0 .01060.0.974.951.925.895.859. g22.t. /31.678.633-532.527=46S.401.321.252-217D. Cmo+. 0162 o-.-E.1J_.,-+:0011300105000s000390001s00092001s3oo28900413005530070sI 0. 18 3-50. 83. 63+. 11 1.00. S2. 54L 21+. 83+ 10.10. ,. :.- .- =-,.,-.,.,-., . -.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
