A/AcA-L'/^ y NATIONAL ADVISORy COMMITTEE FOR AERONAUTICS WARTIMK REPORT \ , ORIGINALLY ISSUED March 19^5 as Confidential Bulletin L5C09 NOTE ON COMPKESSIBrLITY" EFFECTS ON DOWNWASH AT THE TAIL AT SOBCEITICAL SPEEDS By Jack N. Nielsen and Harold H. Sveterg Langley Memorial Aeronautical Laboratory f, / Langley Field, Va. NACA 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 order to expedite general distribution. ^-19 DOCUMENTS DEPARTMENT Digitized by tlie Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/noteoncompressibOOIang 3c. I 75^/ NACA C3 No. L50 0'^ CONFIDSTTTIAL NATIOIiAL ADVISORY COMMITTEE POfl AI:;R0MAUTICS CONPIDEKTIAL BULLETIN IICTE OI'I COMPRESSIBILITY ^IFPIiCTS ON DOV/MASH AT THE TAIL AT SU3CRTTICAL SPEEDS By Jack N. Nielsen and Harolc. F. Sweberg SUMMARY Calculations have been riiade to show the iriagnitude of the coiapresslbilitv effects on the downwash at the tall at subcritical speeds. Experir.iental results of tests of two airplane models are included to give some verifi- catioxi of the theory. The calculations shov/ed that the effects of corapressi- bility on the span load distribution along the wing and on the downv;ash angle at the tall are small for constant values of the lift coefficient. The experimental results confiru'ed th-ese calculations. INTRODUCTION A rational solution for the problem of longitudinal stability at high speeds requires a j.nom'ledge of the effects of compressibility on the downv/ash in the region of the horizontal tail surface. Studies of this problem for speeds belov; the critical have been reported by Husk in ref'erence 1 and by Goldstein and Yor'ng in reference 2. In reference 1 the dov^nwash at the tail is assumed to be unaffected b^?- Increases in Hach number for constant values of the lift coefficient. In reference 2, on the basin of the Glauert-Prandtl theory, the dovifnwash is found to decrease slightly witlx increases in "••lach numiber for constant values of the lift coefficient and span loading. No experimental verif icaticns of the conclu- sions stated in these reports are given. The present paper presents theoretical calculations, based on the methods of reference 2, to show the rragnitiide of the com.presslbility effects o'a downv/ash and gives some experimental verification of the theory. Calculations COKFILENTIaL CONFIDENTIAL FACA GB No. L5C09 have been made to obtain the span load distributions along the v;ing and the average downwash angles at the tail of a typical pursuit airplane for a range of lift coefficient and lic.ch niimber . Wind-tunnel tept data showing the effect of coiupressibillty on the avera.r;-e downwash angles at the tail have also been included for two airplane models. SYLIBOLS Ct airolane lift coefficient (horizontal tail removed ) c^,^ basic section lift coefficient (C-r = 0^ c^ additional section lift coefficient a Mq free -stream Mach number c chord b wing span y distance outboard along span from wing center line X distance from wing quarter-chord line to elevator hin':^e line e downwash angle, degrees a angle of attack, degrees a/ =:ooN. airplane angle of attack for zero angle of \ t /■ attack of tail, degrees 1^ angle of incidence of stabilizer relative to airplane reference line THEORETICAL CALCULATIGIS The effects of compressibility on the downwash at the tail may be considered the result of two factors r CONFIDENTIAL NACA CB No. L5G09 GOliyiDENTIAL the change in span loading along the wing and the change in downv/ash for a given span loading. Methods for calcu- lating' both these changes are given in reference 2 In which the Glauert-Prandtl theory of compressible floxv is used. According to reference 2, the span loading for any Mach nuiiioer n:ay be approximated by using the slope of the lift ciirve for compressible flov>r in the equation of the lifting-line theory (reference 3). The downwash at a distance x behind the lifting line may now be determined by the methods of reference [j. for incompressible flow except that the distance of the tail behind the lifting x/^h - Mo^ line is increased by the ratio 1/vl - ^o"^ • In order to show the magnitude of the coinpressibility effects, calculations have been made in vvhlch the afore- mentioned methods are used to determine the span loading along the wing and the resultant downwash at the tail of a high-speed pursuit airplane. The distributions of tvfist and chord along the v/ing shown in figure 1, which corre- spond approxim.ately to the distributions for a modern pursuit airplane, v/ere used for bhe calculations. The twist at the inboard sections is xxsed to Increase the critical speed of the wing-fuselage juncture. S - Q a n load d i s t r i bu t ion.- The load distribution along the span has been determined in two parts. The first part, v.rhich is due to wing twist, is the load distri- bution at zero lift and is referred to as the basic load distribution. This distribution has been calculated by the -v.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 ^;).(j"]/\/i - Mq per radian. Basic load distributions along tlie wing span are given in figure 2 for Mach nuinbers of s.nd O.o. Although th.e slope of the section lift curve for Mq = 0.3 Is increased 66 percent over that for Mq = 0, the ordi- nates of the basic-load-distribution 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. Tlie second part of the load distribution is that due to the untwisted wing operating at a given lift coeffi- cient and is referred to as the additional load distribution. CONFIDENTIAL ll- CONFIDENTIAL NACA CB No. L5G09 This distribution has been taken from reference 6 fore, a lift coefficient of 1.0 and is shown plotted in figure 5 for /'ach mijnbers of and 0.6. 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 will normally be small, as in the present case. The additional load distribution for lift coefficients other than 1.0 nay be obtained sivaply by nultiplying the ordlnates in figiu-e 5 'by the lift 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 given lift coefficient will also be changed very little by coir.pressiblllty. Span load distributions for elliptical wings of approximately zero aerodynamic tv;ist given in refez^ence 7 S-^id calculated from, experimental section-lift-curve slopes shov/ very small changes with Mach number up to the critical speed, Dov/nwa sh at tail .- By using the compressible-f lov/ span load distributions, calculations have been made by the method of reference i|. of the average downwash across the tail span for a range of lift coefficient and IJach number. For these calculations, the angle of attack for zero lift V'las assiTKied to be independent of Mach number and the distance-of the tail behind the lifting line was taken as 0.95^A'l - Mq . The downv/ash angles were calculated at three points along the tail semaspan and the results were averaged to obtain the average dov:n#ash angle at the tail. These results are shov;n in figure ];. . The variations of dov\?nwaEh angle v;ith ?';ach number for constant values of lift coefficient (fig. )+) are small. For low values cf the lift coefficient, the changes in downwash angle with Mach nur.iber are inappre- ciable except at very high values of t}ie Iv'ach niunber (above about Mq - O.7). At the high lilt coefficients, the downwash decreased slightly with increasing ?.!ach number up to a Mach number of about 0.7. At r.!ach numbers CONFIDENTIAL NACA CB No, L5C09 CONFIDENTIAL 3 higher than about O.7, the downwash angle decreases more rapidly than at the lower Mach nurabers. 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 niLmber, 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 vortlcity inboard than an elliptical wing, the effect tends to cause a reduction in downwash; for a rectangular wing, which has proportion- ately m.ore trailing vortlcity 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 downv;ash angle with T'lach 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 niomber because of the Increase in the slope of the lift curve and, as a result, the angle of attack of the tall 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 pltching- 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 lift-curve slopes will occur that also causes a shift of the neutral point. EXPERIMENTAL RESULTS An analysis has been made of wind-tunnel test data obtained at high >'ach numbers to verify experimentally the theory and calculations presented in the preceding section. The data were obtained from tests of com.plete CONFIDENTIAL 6 CONFIDENTIAL NACA CB No. L5C09 models cf the P-5IB and XP-58 airplanes in the Anes 16-foot high-speed wind tunnel. Downv/ash angles were computed from the results of pitching-moment measurements with the horizontal tail set at several angles of inci- dence and with the horizontal tail removed. The inter- section of the pitching-moment curves for this model with the tail on and with the tall off gave the airplane angle of attack for which the tail angle of attack is zero. The dov/nwash angles were then computed from the relation e = a /rr. -no\ -1- 1 a(at=0O) -■- It where °./'aj-=0°"') ■^'''' ^'^^ airplane angle of attack for zero tail angle of attack and i^ is the stabilizer incidence, relative to the airplane reference axis. Inasmuch as the wind-tunnel test data were corrected by inoom.pressible-f low methods, it was necessary to Investigate the effect of compressibility on the wind- tunnel wall corrections. The effect of the tunnel walls is to ca^■lse an Increment of upwash at the v;ing and an additional increment of upwash at the tail. These incre- ments necessitate a correction to the airplane angle of attack and tail-on pitching-moment coefficient. Goldstein and Young f reference 2) showed that the correction to the airplane angle of attack is unchanged for compressible flow biit that the correction to the tail-on pitching- moment coefficient m.ust be adjusted for compressibility. This adjustment Is made by assuming that the tail is at a distance y^A/^ - Mq^ instead of a distance x behind the wing quarter-chord line. The variation of the downvvash angle with L'ach number for several values of the lift coefficient is given in figure 5 for the P-5IB airplane model. In order to show the limits of the subcritlcal region and also to facili- tate the use of the data given in figure 5> curves of lift coefficient against Mach number for several angles of attack are given in figure 6. Similar dov;nwash and lift data are presented in figures 7 S-'id 8 for the XP-58 airplane m.odel. For both airplane miodels some downwash exists at zero lift fbetv;een 1° and 2°). No definite reason can be given for this a^oparent discrepancy; it may CONFIDENTIAL NACA CB No. L5C09 CONFIDENTIAL result, however, from either the v.'lng twist or inaccu- racies in the tail settings, or from both. Althovxgh the absolute magnitude of the downwash angles may be in error the variation of the downwash anr^le with Mach number is considered accurate. The results plotted in figures 5 s-^^ 7 show that at low lilt coefficients, which correspond to high-speed fli^l^t, the chanre in downv^fash an£:le v/ith Hach number is negli.vible . At the high lift coefficients, some change in the downwash angle v/ith Llach nimber occurs. This change is ?mall for the case of the P-5IE airplane model but aviiounts to about 0.5° for the XP-5o airplane model. The e::perimental results, in general, agree with the theor^r in that the variation of downwash angle with Mach ntomber at constant lift coefficient is relatively small. ■OCHJW'kS^ AT STTP^]RCRI':?'ICAL SPr.3DS Although the present paper is primarily concerned v/ith the downv;ash at subcritical speeds, a few remarks regarding the dov/nwash at supercritical speeds should be made. Evidence is available freferences 7 s^'^ 8) which shows that large changes in span leading may occur at ' supercritical speeds. The changes in span loading may ca-usG appreciable changes in the dov/mvash at the tall. If flow breakdovm due to shock occurs first at the inboard wing sections because of their thickness or because of wing-fuselage interference, there v,-ill be a shift of the load outboard and a consequent reduction in the downwash at the tail. Unfortunately, these effects are not well understood because theory has not been developed and wind-tui:nel test data are insufficient at supercritical speed.': lor which conditions the wind-tunnel tare and interference corrections are not well understood at present . CONCLUDING Rii:?:ARKS Theoretical calculations have shown that the effect of compressibility at subcritical speeds on the span load distribution along the wing and on the downwash angle at the tail is small for constant values of the lift coef- ficient. Experimental resiilts of the downv/ash variation CONFIDENTIAL CONFIDENTIAL NACA C3 No. L5CO9 v/lth ?'ach nijmber for two airplane models confirmed these calculations. At supercritical speeds, however, large changes in the sp>in loading and in the dov/nwa&h for constant v-^lues of the lift coefficient may occur. Langley L'^emorial Aeronar.tical Laboratory National Advisory CoiruTiittee for Aeronautics Langley Field, Va. REPERENCI 1. Kusk, D, I.: Compressible Flow behind a Wing, Air- craft Engineering, vol. XIV, no. I60, June 19li2, p. 160. 2. Goldstein, S., and Young, A. D.i The Linear Pertur- bation Theory of Compressible Plow, with Applica- tions to rtind-Tunncl Interference, R. cz M. No. I909, British A,R.C., 19lf5 . 5. Gle.uert, H.s The Elements of Aerofoil and Airscrew Theory. Gainbridgc Univ, Press, I926, p. I59 . [|., Silverstein, Abe, and Katzoff, S,» Design Charts for Predicting Downwash Angles and Wake Chsracteristics behind Plain and P'laDped Vilngs , NACA Reo, No. 6I4.8, 1959. 5. Pearson, N. A.: Span Load Distribution for Tapered Wings with Partial-Span Flaps, NACA Rep, No. 'yS^j, 1 o 7, r" 6. Anderson, Raymond P.; Determination of tiie Charac- teristics of Tapered ".Vings . U:\Ca Rep, No. 572, 1956. 7. Boshar, John: The Determination of Span Load Distribu- tion at Nigh cpocds by Use of High-Speed .-ind- Tunnel Section Data. NACA ACR No. ['.B22, iglii;, 8. V;hitcom.b, Richard T.; The Relation between Spanwlse Variations in the Critical Kach r'uir.ber and' Spanv/ise Load Distributions. NAG:i CB No. LI4.LO7, 19144, CONFIDENTIAL NACA CB No. L5C09 Fig. 1 A /^ ■ — —1 < 1— 1 E-i Z Cd Q 1—1 •z. o u 4 / / / / 1 y -■ £ / / O LlJ 1 / s / ^ / / / y / / / / / 1 / ^ / / / / / / / / / / / L / ^""^ ^- L ••««- t / --^ / ^^ § -5 § o C) O o ^t «0 M .'^ ^ o -J < ^ f— I I) o E-" »o o> Cd ^ ' Q ■->* \ — t <^ •z. J^ Q ^ « o o ^13 ^ R tl ^^ ^1 o 5^ ^ ^,^ s C3 ^ to 55 ^ ^b ^ 1 s; <:> b <>. ^ ri but ion n /oad/n O '^^ ^X c: i59p ' ^SIMJ_ ^. NACA CB No. L5C09 CONFIDENTIAL Fig. 2 0» o 03 -2 -4 -6 Mach number, Mo • /A x'^ ^■v ^0 r ^ \ ^ / V J // J / / / t 1 f NAl COMMIT lONAL A EEFOR )V1S0RY eONAU ICS .6 Spanwfse station, -r± .<9 /.o 2. CONFIDENTIAL Figure Z~ Effect of t^ach number on the basic span load distribution. NACA CB NO. L5C09 CONFIDENTIAL Fig. 3 100 90 ^80 •5 70 •^60 o 40 ^30 20 10 /lach number , Mr. N^ ' "^ .8 kN ^ \ >\ \ \ \, \ \ \ \\ \\ \ \\ \\ A \\ \\ 1 c NATIO )MMITTE NAL AD\ : roR A£ ISORY ^ONAUTI IS .2 .4 .6 .8 ^ 1.0 Spanfv/se station , -^ confidential Fiqure 3- £ffect of Mach number on the add if tonal span load distribution. NACA CB NO. L5C09 CONFIDENTIAL Fig. -^ 4 ^ C3 o -I c, L ■ 0.8- .6 ^ — A ■ H- -^ .2 ~- ( NATII OMMITTI NAL AD £ FOR A nSORY iRONAUT cs .2 .3 .4 .6 Mach number ,Mq .7 .8 CONFIDENTIAL Fiqure 4-- Calculated variation of the downvjash angle with Mach number for constant value's of the lift coefficient. NACA CB NO. L5C09 CONFIDENTIAL Fig. to 7 Cl 18 6 ^ - \ .6. 5 -— - -^ J .4 ■^ 4 2 3 "*'**»«^ Z ~^ 1 COMMI iTIONAL FTEE FOI ADVISOir AEROM/ liTICS n :3 .4 .5 .6 .7 .8 Mach number ,M^ confidential Figure J.- Experimental variation of the downv^a^h angle with Mach number for constant values of the lift coefficienf. P-5IB airplane model. NACA CB NO. L5C09 CONFIDENTIAL Fig. 6 .8 <^ o O O .4 -2 'A (T ^de.n 1 7 ^ A f ^ \ — - — - *t \ z ^ ■^ . „^ ■ ■2 ■ 4 "■"^ NATIONAL COMM HEE FO ADVISOF iAEROM i lUTICS .4 .5 .6 .7 /^ach number jMq .8 FiCfUre 6. CONFIDENTIAL Variation of I iff coeffic/eni v^ifh Mach number for the PS/ 8 airplane model. NACA CB No. L5C09 CONFIDENTIAL Fig. 7 w C3 <: c ^L ^^ ^ 0.6 _ .4 .2 NA COMMIT lONAL i FEE FOR iDVISORY AERONAl TICS .4 .5 .6 Mach number y Mq .8 CONFIDENTIAL Figure 7.- Experimental v^ar/afion of the downvjorsh anq/e \^ith Mach number for constant values of the lift coefficient. XP-Sd airplane model. NACA CB NO. L5C09 CONFIDENTIAL Fig. 8 .6 -2 (7, ^deo 1 COM» ATIONAL inEEFC ADVISOI R AEROW \UTICS 7 ^ . 4 J \ \ \ Z \ ■■\ > k \ N \ -2 A N \ \ .6 .7 ,<9 Mach number ^Mq CONFIDENTIAL ricfure 6.- Variation of hfi coefficient \^ith Mach number for t'he XP-SQ airplane model. UNIVERSITY OF FLORipA 3 1262 08104 977 6 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE LIBRARY P.O. 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