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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WAIRTIMEI REPORT ORIGINALLY ISSUED March 1915 as Confidential Bulletin L5C09 NOTE ON COMPRESSIBILITY EFFECTS ON DOWNWASH AT THE TAIL AT SUBTRITICAL SPEEDS By Jack N. Nielsan and Harold E. Sveberg Langley Memorial Aeronautical Langley Field, Va. Laboratory WASHINGTON NACA WARTIME REPORTS are reprints of papers originally Issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre viously held under a security status but are now unclassified. Some of these reports were not tech nically edited. All have been reproduced without change In crder to expedite general distribution. I19 DOCUMENTS DEPARTMENT 49^ V Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/noteoncompressib001ang NA.?A CS IN. L50?' CO'N!IDENTIAL fTATICiOAL ADVISORY CO.MT:II'T: FOR AiRO'!AUTICS CONPIDE;ITI..L BULLETIN .iCT' Cr COo'prESSIBILITY IFr CTS C.! DC ,i7' VASP AT THE TAIl AT SUYlTTTCAI. SEEDS Py Jac' U. Nielsen and T'arc,!, W. S weber.r SU ""'AY C,]oculations have ben r.iaie to sh.ow the marnitlide of ths, coi,'press_..bility effects on t do'.'.:'~sh a. t the tail at sutcritical rpeed.s. .x'rin:ental 'esu ts of tests of two sii.plane models are included to .ive some verifi cation. of the theory. TlIe calculations rhowea tt. ; t tbe effect 01o co.n'Dressi bilit;. on the span l':,od distr'.ibut icn ailon: the *;irg and on the downv.ash angle at the tail ,are s,'ll for constant values of the lift coefficient. The exn erimenta results confirmed these calculations. I YTR ODUCTTIOi A rational solution for the problem of lon.Titudirnal stability at hih speeds requires a ;.owledre of the effects of comoiessibilit.r on t'v: o'.in.:as in the recion of the horizontal tail surfltce. StiirLes of this r ro':lem for speeds below the critical have e;en re Dorted by euek in rec rence I and by Coldstein and Yrje.nr ir reference 2. In reference 1 the downrw,.ash at the tail is ..tumrd to be unaffected ? by increas s in "ach nurrber fr cona .nt valu. of the lift coefficient. In reference 2, cn the basis of the 1IauertPranrdtl t heory, the dc'wnwashh is found to decrease slightly with increases in .ci nunbcr for constant values of the lift coefficient. and span loadin:. !'o experimental verificiaticnSr of the conclu sions stated in these reports ar. civen. The present paper presents t.h.orietical calculations, based on the methods of reference ., to show the magnitude of the ccmrpressibility effects on downvwash and gives some experimental verification of the theory. Calculations COIFI]TEI'!TDIAL NACA CB No. L5CO9 have been made to obtain the s p.n load distributions along the vwinr and the average downwash angles at the tail of a typical pursuit airplane for a rnje of lift coefficient anF cch number. PWindtunnel test data showing the effect of compressibility on the average downwash anrles at the tail have also been included for two airplane models. SYMBOLS CL airplane lift coefficient (horizontal tail removed) cla a(tOo) basic section lift coefficient (CL = 0) additional section lift coefficient freestream Mach number chord wing span distance outboard along span from wing center line distance from wing quarterchord line to elevator hinge line downwash angle, degrees angle of attack, degrees airplane angle of attack for zero an.leo of attack of tail, derees it angle of incidence of stabilizer relative to airplane reference line THECT, CAL CALCUIATI01S The effects of co.p'ressibility on the downwash at the tail ma' be consilde:.,d the result of two factors? C flN~TP)~UTIAL C Or' IPE TOTAL NTACA CB No. L5CO the change in span loading along the wing and the change in downw,,ash for a given span loading. Methods for calcu latin; both these changes are given in reference 2 in which the GlauertPrandtl theory of compressible flow is used. According to reference 2, the span loading for any Mach number may be approximated by using the slope of the lift curve for compressible flow in the equation of the liftingline theory (reference 5). The downwash at a distance x behind the lifting line may now be determined by the methods of reference 4 for incompressible flow except that the distance of the tail behind the lifting line is increased by the ratio M1/1 Mo * In order to show the magnitud of the coioprssibility effects, calculations have been i'lade in ,ohich the afore mentioned methods are used to detcr.mine the span loading along the wing and the resultant do'nv.ash at the tail of a hit:hspeed pursuit airplane. The distributions of twist andc hord along the wing shown in figure 1, which corre sponi approximately to the distrIbutions for a modern pursuit airplane, were used for ,m'. calculations. The twist st the inboard sections is usad to increase the critical. sn.ed of the wingfusela'e juncture. Scan load distribution. Thec load distribution along the su. an has teen determined in two parts. The first part, which i due to wing twist, is the load distri bution at zero lift and is referred to as the basic load distri''.utlon. This distribution 'has been calculated by the ethod of reference 5 using ten harmonics for the circulation because of the sharp break in the wing twist distribution. For these calculations, the slope of the section lift curve was taken as L.67 /I o2 per radian. Basic load distributions along the wing sran are given in figure 2 for Mach nuunbers of 0 End 0.8. Although the slope of the section lift curve for MT = 0.8 is increased 66 percent over that for .oQ = 0, the ordi nates of the basicloaddistribution curve show an average increase of only about 20 percent; that is, the effect of the increased slope of the section lift curve is dimin ished to a large extent as a result of the small span within which the twist is effected. The second part of the load distribution is that due to the untwisted wing operating at a riven lift coeffi cient and is referred to as the additional load distribution. CONFIDENTIAL C0PTL':TIAL NACA CB 'To. L5o09 This distribution has been taken from reference 6 for,a lift coefficient of 1.0 and is shown plotted in figure 3 for ach numbers of 0 and 0.8. The additional load distribution is seen to be almost unaffected by com pressibility. This result depends on the wing plan form. For an elliptical wing, the additional load distribution remains elliptical regardless of the slope of the section lift curve. For other than elliptical wings, increasing the slope of the section lift curve causes the additional load distribution to become more nearly elliptical but the effect "'ill normally be small, as in the present case. The additional load distribution for lift coefficients other than 1.0 may be obtained si'aply by ntultiplying the ordinates in figure 5 by the i t coefficient. Since the total load distribution is obtained by adding the addi tional load distribution to the basic load distribution, it may be concluded that below the critical speed the total load distribution for a lven lift coefficient will also be changed very little by compressibility. Span load distributions for elliptical wings of approximately zero aerodynamic twist given in reference 7 and calculated from experimental sectionliftcurve slopes show very small changes with Mach number up to the critical speed. Downwash at tail. By using the comrpressibleflow span load distributions, calculations have been made by the method of reference 4 of the averaie downwash across the tail span for a range of lift coefficient and Mach number. For these calculations, the angle of attack for zero lift was assumed to be indenpndent of .Tach number and the distance.of the tail behind the liftin7l line was taken as 0.95;/V1 o The downwash angles were calculated at three points aonr the tail semispan and the results were averaged to ..?iQ.n the average downnash .ingle at the tail. Thi.se results are shown in figure ;. The variations of downwash un:le with !Yach number for constant values of lift coefficient (fig. i) are small. For low values of the lift coefficient, the c':anjes in downg.as:h angle with '.ch number are inappre ciable except at very "hih values of the Mach number (abova about Mo = 0.7). At the lrb lift coefficients, the dowmnvash decreased zlijhtly with increairng Mach nu'bJr up to a :?ch number of a:o.t 0.7. At Mach numbers SCTFnDE' TIAL NACA CB No. L5C09 CONFIDENTIAL 5 higher than about 0.7, the downwash angle decreases more rapidly than at the lower Mach numbers. The decrease in downwash angle with Mach number for constant lift coefficient results from two effects: (1) the distance from the lifting line to the tail, used for the downwash computations, increases with increasing Mach number, and (2) the tail moves farther above the wake since, for a given lift coefficient, the angle of attack decreases as the Mach number increases. It has already been remarked that increasing Mach number causes the span load distribution to become more elliptical. For a highly tapered wing, which has pro portionately more trailing vorticity inboard than an elliptical wing, the effect tends to cause a reduction in downwash; for a rectangular wing, which has proportion ately more trailing vorticity outboard, the effect tends to cause an increase in downwash. In either case, as for the load distribution itself, computations show that the effect is small. Although the change in downwash angle with Yach number for constant lift coefficient has been shown to be small, it does not follow that the change in the longi tudinal stability characteristics will be small. In particular, the angle of attack of the wing for a given lift coefficient will decrease with increasing Mach number because of the increase in the slope of the lift curve and, as a result, the angle of attack of the tail for the same lift coefficient will decrease a corresponding amount. This decrease in tail angle of attack for a given lift coefficient will cause an increase in airplane pitching moment coefficient and a rearward shift of the neutral point, Because of the different aspect ratios of the wing and tail, furthermore, a disproportionate increase in the wing and tail liftcurve slopes will occur that also causes a shift of the neutral point. EXPERIMENTAL RESULTS An analysis has been made of windtunnel test data obtained at high M'ach numbers to verify experimentally the theory and calculations presented in the preceding section. The data were obtained from tests of complete CONFIDENTIAL NACA CB No. L5C09 models of the P51B and XP58 airplanes in the Ames 16foot highspeed wind tunnel. Dovwjnash angles were computed from the results of pitchingmoment measurements with the horizontal tail set at several angles of inci dence and with the horizontal tail removed. The inter section of the pitchingmoment curves for this model with the tail on and with the tail off gave the airplane angle of attack for which the tail angle of attack is zero. The downwash angles were then computed from the relation a = (att=00) + it where a(at=Oo) is the airplane angle of attack for zero tail angle of attack and it is the stabilizer incidence, relative to the airplane reference axis. Inasmuch as the windtunnel test data were corrected by incompressibleflow methods, it was necessary to investigate the effect of compressibility on the wind tunnel wall corrections. The effect of the tunnel walls is to cause an increment of upwash at the wing and an additional increment of upwash at the tail. These incre ments necessitate a correction to the airplane angle of attack and tailon pitchingmoment coefficient. Goldstein and Young (reference 2) showed that the correction to the airplane angle of attack is unchanged for compressible flow but that the correction to the tailon pitching moment coefficient must be adjusted for compressibility. This adjustment is made by assuming that the tail is at a distance x/l M02 instead of a distance x behind the wing quarterchord line. The variation of the downwash angle with Mach number for several values of the lift coefficient is given in fi. ure 5 for the P511 airplane model. In order to show the limits of the subcritical region and also to facili tate the use of the data given in figure 5, curves of lift coefficient against P'acli number for several angles of attack are given in figure 6. Similar downwash and lift data are presented in fi ur,s 7 and 8 for the XP58 airplane rodel. For both airplane r;odels some downwash exists at z,:ro lift (between 10 and 20). No definite reason can be given for this apparent discrepancy; it may COIUPID'IUTIAL CONFIDEI'TIAL IIACA CB No. L5C09 result, however, from either the wing twist or inaccu racies in the tail settings, or from both. Although the absolute magnitude of the downwash angles may be in error, the v,riation of the dcwnwash anle with OTach number is considered accurate. 'Tie results plotted in figures 5 ,nd 7 show that at low lilt coefficients, which correspond to highspeed fli.ghit, the change in downwash anLgle with Mach number is neg.li_ible. At the hit.h lift coefficients, some change in the do'vnvash angle cith Iach number occurs. This change i.*F small for the cast of the P51E airplane model but a'ou.nts to about 0.50 for the XF5 airplane model. The c: ncrimental results, in ,,nral, agree with the theory in that the variation of deo~*'.,ash angle with 1rach number pt constant lift coefficient ic relatively small. AT 'Tr.s AT CTTP':CRImICAL SP'DS Although the present pa,.'pe.r is primarily concerned with the dJownwash at subcritical sr,,dr, a few remarks regarding the downwash at s'uper'p.critical speeds should be made. Evidence ir available referencess 7 and 8) which shows that larce changes in rnan lcarding ,may occur at supercritical speeds. The chanr:cs in span loading may cause anpreciable changes in th iownw'.ash at the tail. If flow breakdown due to shock occurs first at the inboard win, sections because of their thickne.rf or because of wingfusel.age interference, there '..ill be a shift of the load outboard and a con.a'seiuent reduction in the downwash at the teil. Unfortunately, these effects are not well understood because theory has noc been developed and windtui.nnel test data are insufficient at supercritical speeds for which conditions the '.':indtunnel tare and interference corrections are not 'ell understood at present. CONCLUDI''TG rE'AE IS Theoretical calculations have shown that the effect of compressibility at subcritical speeds on the span load distribution alonr the wing and on the downwsh angle at the tail is small for constant values of the lift coef ficient. ZExpeeimental results o.' the downwash variation CONFIDENT IAL CONFIDENTIAL NACA CB 1%o. L5C09 with MIach number for two airplane models confirmed these calculations. At supercritical speeds, however, large changes in the span loading and in the owv;nwvash for constant values of the lift coefficient may occur. Langley e :orial Aeronautical Laboratory .tional Advsory Committee for A.ronautics Langley Field, Va. 1. Husk, D. I.: Compressible Flow behind a Wing. Air craft Engineering, vol. XIV, no. 160, June 1942, p. 160. 2. Goldstein, S., and Young, A. D.: The Linear Pertur bation Theory of Compressible Flow, with Applica tions to idindTunncl Interference. R. & M 1. l. 1909, British A.R.C., 1943. 5, Glausrt, H.: The Elements of Aerofoil and Airscrew Theory. Cambridge Univ. Press, 1926, p. 139. 4. Silverstein, Abe, and Katzoff, S.: Design Charts for Predicting Downwash Angles and .a!e Characteristics behind Plain and Flapped wings. HACA Rep. No. 648, 1959. 5. Pearson, H. A.: Span Load Distribution for Tapered Wings with PartialSpan Flps. NACA Rep. No. 535, 1937. 6. Anderson, 3'S.,ni F.: Determination of the Charac teristics of Tapered Wings. 1ACA Rep. ir'. 572, 1956. 7. Doshar, John: The Dtcormination of Span Load Distribu tion at High Specds by Use of HighSoecd iindru.niiel Section Data. :.CA AiC h. iB22, 1944. 8. Whitcomb, Richard T.: The elationn between Spanwise Variations in the Critical ]Kach 1.:'.r and Spanv'ise Load Distributions. i.". CB Ui. L4L07, 1944. CO1FTIDLE;TIAL CONFIDENTIAL NACA CB No. L5C09 4 CM, IV  ^ T  z / / *II 3 b,c J O I i z~4 (~J 0 Fig. 1 '0 O q.) r0 0 i.JcZ 0 lb )ZI Is t8 NACA CB No. L5C09 6 2o 2 6 Spanwise station DNTAL bi CONFIDENTIAL Figure Z. Effect of Mach number on the basic span load distribution. Mach number, M. 0 NA IISORY COMMIT FORONAU C 2 .Z .4 .6 .9 1X0 CONFIDENTIAL Fig. 2 NACA CB No. L5C09 /00 90 0 70 Q '60 b50 40 30 20 /10 .4 Spanwise .6 .8 station , /0 CONFIDENTIAL Figure J. Effect of Mach number on the additional span load distribution. 7lach number /1o 0  0 .8 NATI A. AD ISORY C MMIfI ro A ONAUnIls ^^^1    ]      ^   ^^' __ __ ___ ___ ___ S __ ___ ___ ___ ___ ___ ^<\ ____ ~ ~ ~ ~ ~ ~ ~ AI ___L A___ ISORY^^ __ __ ___ ___ _ C)MR O \ 0AT 0L 0 Fig. 3 CONFIDENTIAL NACA CB No. L5C09 .3 .4 Mach number .5 .6 .7 .8 7 'V0 CONFIDENTIAL Figure 4. Calculated variation of the down wash anqle with Mach number for constant values of the lift coefficient. .c,_  .6  08       ._..._ ,..._ .._ .6     _ ^ .. 4.  0 AMI RM IA MSORY IOM 'ITIE FOR A ROMAUT S CONFIDENTIAL Fig. 4 NACA CB No. L5C09 c>, 0b ^J I) o Mach number /0 CONFIDENTIAL Figure J. Experimental variation of the downwash anqle with Mach number for constant values of the liff coefficient. P5/8 airplane model Fig. 5 CONFIDENTIAL NACA CB No. L5C09 () 1. q) 4U, 0 .2 .4 ..9 .5 lMach .6 .7 number ,/ N CONFIDENTIAL Figure 6. Variation of lift coefficient with Mach number for the P5/B airplane model. I I.Hn A A 7 ___4 WTIONAL ADVISOF I COMM TTEE FO AERON UTS "7" CONFIDENTIAL Fig. 6 f ? NACA CB No. L5C09 0 L .3 .4 .5 .6 .7 .8 Mach number /0 CONFIDENTIAL Figure 7 Experimental variation of the downwash angle with Mach number for constant values of the lift coefficient. XP58 airplane model. Fig. 7 CONFIDENTIAL NACA CB No. L5C09 2 L .3 .4 .5 .6 .7 Mach number IO CONFIDENTIAL Fiqure 8. Variation of liff coefficient with Afach number for the XP58 airplane model. CONFIDENTIAL Fig. 8 f I !i >* f f. UNIVERSITY OF FLORIDA 3 1262 08104 977 6 *I Ul i RIFYG OF FLOR;DA FC:LJUMENTS tlEPARTMEkiT 1 .:\ rj..FSTON SCIEBICE LIBRARY 'O. .OX 117011 C.A.J'VlILLE, FL 326117011 USA I; 