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,- -; ..- -- REPORT 947
THE DEVELOPMENT OF CAMBERED AIRFOIL SECTIONS
HAVING FAVORABLE LIFT CHARACTERISTICS
AT SUPERCRITICAL MACH NUMBERS
By DONALD J. GRAHAM Ames Aeronautical Laboratory Moffett Field, Calif.
National Advisory Committee for Aeronautics
Headquarters, 1724 F Street NW., Washington 25, D. C.
Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific study of the problems of flight (U. S. Code, title 50, sec. 151). Its membership was incrrased from 12 to 15 by act approved March 2, 1929, and to 17 by a.ct approved May 25, 1948.
The members are appointed by the President, and serve RS such without compensstion.
JEROME C. HUA-SAKER, SC. D., Massachusetts Institute of Technology, Cl~cknzan ALEXANDER WETMORE, SC. D., Secretary, Smithsonian Institution, Trite Chui~man HON. JOHN R. ALISON, Assistant Secretary of Commerce. DONALD L. PUTT, Major General, Unit,ed States Air Force, Director of Research and Development, Office of the Chief of DETLEV W. BRONK, PH. D., President, Johns Hopkins University.
Staff, MatBriel.
KARL T. COMPTON, PH. D., Chairman, Research and Development JOHN D. PRICE, Vice Admiral, United States Navy, Vice Chief of Board, Department of Defense.
Naval Operations.
E D W A R D U. CONDON, Pn. D., Director, National Bureau of ARTHUR E. RAYMOND, SC. D., Vice President, Engineering, Standards.
Douglas Aircraft Co., Inc.
JAMES H. DOOLITTLE, SC. D., Vice President, Shell Union Oil FRANCIS W. REICHELDERFER, SC. D., Chief, United States Corp.
Weather Bureau.
R. M. HAZEN, B. S., Director of Engineering, Allison Division, HON. DELOS W. RENTZEL, Administrator of Civil Aeronautics, General Motors Corp.
Department of Commerce.
WILLIAM LITTLE~~OOD, M. E., Vice President, Engineering, HOYT S. VANDENBERG, General, Chief of Staff, United States Air American Airlines, Inc.
Force.
THEODORE C. LONNQUEST, Rear Admiral, United States Navy, THEODORE P. WRIGHT, SC. D., Vice President for Research, Cornell University.
Deputy and Assistant Chief of the Bureau of Aeronautics.
HUGH L. DRYDEN, PH. D., Diredo? JOHN F. VICTORY, LL. RI., Executive Secretaqj E. H. CHAMBERLIN, Executive Oficer JOHN W. CROIVLEY, JR., B. S., Associate Director for Research HENRY J. REID, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va.
SMITH J. DJCFRAXCE, B. S., Director, Ames Aeronautical Laboratory, Moffett Field, Calif.
EDWARD R. SHARP, SC. D., Director, Lewis Flight Propulsion Laboratory, Cleveland Airport, Cleve!antl, Ohio TECHNICAL CO>II\IITTEES OPERATING PROBLEMS AERODYh‘ AMICS INDUSTRY CoSSULTING POM~ER PI.AXTS FOR AIRCRAFT AIRCRAFT COSSTRUCTION Coordination oj Resemch Needs oj Military and Ciuii Aviation PI eparation cf Reseal ch Prop anss Allocation of Problems Prevent.ion oj Duplication Com-iderntion of Iwenfions LEI~IS FLIGHT PROPULSIOS L.monA*roI<Y AlIES ~\ERONAuTICAL LARORATORY LAX(:I,EY AER~KAUTICAL LABORATORY Cleveland Airport, Clewland, Ohio Jloffett Field, Calif.
Langley Field, Va.
Conduct, mtler. uniJietl conlrol, for all ngerhcies of scientijic research on the jumlameutnl problems of fli,qhl OFFICE OF .%EROSATJTICAL INTELLIGENCE \Vashington, D. C.
Collecti,)??, clnsstjicntiou, compilation, arid dissemination 01 scie4jic au11 technical informntion on ne,-onn uiics II
REPORT 947
THE DEVELOPMENT OF CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE LIFT
CHARACTERISTICS AT SUPERCRITICAL MACH NUMBERS
By DONALD J. GRAHAM SUMMARY these characteristics 011 airplanes employing such wing sections is to alter, respectively, the longitudinal trim and the Several groups of new airfoil sections, designated as the longitudinal stability and controllability in such a manncl NACA B-series, are derived analytically to have lift character- as to promote serious airplane diving attitudes, recovery istics at supercritical Mach numbers which are favorable in the from which may bc rstrcmcly difficult with normal controls.
sense that the abrupt loss qf Lift, characteristic of the usual airfoil (SW rcfcrcncc 1.) On light highly mancuvcrablc aircraft, section at Mach numbers above the critical, is avoided. Aero- thcsc clinrac~tc~ristics can 1)~ avoidctl or satisfactorily coped dynamic characteristics dpterminerl -from two-rlim~nsional with by tlicl use of symmctriral airfoil sections and special wind-tunnel tests at Much numbers u,p to approximately 0.9 c~olltl~ols.
N(lithcr of thc~ means is atlvisablc for large are presen.terl -for each qf the derived ai7;foils.
0i)mparison s hclavily loatl~l aircraft, l~owcvc~r; the first, bccauscb in this are made between. the characteristics of these airfoils and thP (‘ asc tlit> airfoil must of necaessity carry some design lift, and corresponding characteristics qf represen.tatire NA(‘ A G-series tlic s~ond, bc~causc~,as is stntctl ill rc~frrcncc 1, the trim airfoils.
changes occur so abruptly that the aircraft would bc sub- The experimental results con~firtn the design expectations in jrctctl to tlangc~rously high accclcrations before the controls demonstrating for the NACA B-series airfoils either no varia- could bc Icsct . The logical means for avoiding the trim tion, or an increase-from the low-speed rlesign value, in the lift and stability changcls on large airplanrs is the employment of coe$icient at a constad atzgle of attack with increasing Mach airfoil srctions having no atlvcrsc cliangcs with l\lacali num- number above the cGtica1. It was not *found possible to im- bcr of the nnglc of attack for tlitl tlcsign lift COc~fic~ic~ilt and prove th.e variation with Mach number of the slope (if the lift of the slope of the lift curve. The tlcvclopmcnt of airfoils curve for these airfoils above that -for the NACA 6-series having suc~li c,lial.actcl,istic,s at supcrcritical ;\Iach nrim‘ bcr9 airfoils. The drag characteristics of the new airfoils are some- has accordingly l)c~~nmntlc tlio subject of an intcxnsivo s~nrcli.
what inferior to th.ose of the NA(‘ A 6-series with. respect to Although it has not yet been found possiblr to control the divergence with Mach n.umber, but the pitching-tnoment variation with ,\lacli numbcr of the lift-ciirvc slop?, a means characteristics are more .favorable *for the thinner nrw sections for achieving a favorable variation with ~lach numbrr of the in demonstrating some&at smaller variations of ?noment lift of a positively cambrrctl airfoil at the design attitude coe$icient with both angle qf attack and Mach number.
has hccn concc4vcld by H. Julian Allen of thr Amrs Acro- The effect on the aerodynamic characteristics at high Mach nautical Laboratory. This principle has been employed to numbers of re,moving the cusp -from the trailing-edge regions tlcrivc analytically a new group of airfoil sections, des;gn.lted of two IO-percent-chord-thick NACA &series airfoils is de- the KACA S-scrics. The aerodynamic characteristics of termined to be negligible.
thcsc airfoils have been tlctc~rmined cxpcrimentally in th:> The use of a negatively deflected plain flap at supercritical Ames I- by :3$foot high-spcctl wind tunnel, and thr results Mach numbers on an NACA B-series airfoil is indicated to have, in most cases, confirmed the dcsign expectations. An be a feasible and prom,ising means -for obtain.ing on demand the account of the airfoil drvclopmcnt, analytical and cxperi- favorable variation with Mach number of the lift coe$icient mental, is the subjtct of thr present report.
at a given angle of attack, characteristic of the NACA B-series airfoils, while retaining at all other times the superior drag AIRFOIL DEVELOPMENT characteristics of the NACA B-series type qf airfoil.
It was observed early in the course of investigations of com- pressibility rffects on airfoil characteristics that the initial INTRODUCTION loss in lift (sometimes termed the “shock stall”) experienced The usual positively cambered airfoil sections exhibit two at supercritical Mach numbers was associated with the forma- particularly undesirable characteristics at supcrcritical Mach tion of a compression shock wave on the upper surfacc of an airfoil before the critical Mach number of the lower surface numbers. The angle of attack corresponding to the design lift coefficient increases rapidly with increasing Mach num- had been excceclecl. It has been concluclecl that the loss in lift results from an effective change in the airfoil camber oc- ber above that for lift divergence, and the lift-curve slope decreases sharply at these Mach numbers. The effects of casioned by a suddenly thickened boundary layer behind the
2 REPORT 947-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
portions of the NACA a=0.3, 0.5, and 1.0 mean lines. (See shock wave on the upper surface while the boundary layer on the lower surface remains sensibly unchanged. Previous reference 3.) The ordinates of the mean camber line were adjusted to produce the desired design lift coefficient.
research has been aimed at continuously increasing the Mach The actual airfoil shape was then obtained by combining the base number of occurrence of the compression shock so as to delay the shock stall. In the present development the upper- profile with the mean camber line, using the methods of references 2 and 3.
surface shock wave is accepted, but the associated loss in In the manner described three airfoil sections were derived airfoil lift is forestalled by inducing a corresponding shock, with different respective upper- and lower-surface minimum- with accompanying boundary-layer growth, to occur on the pressure positions so located as to permit the effects of a lower surface.
variation of the severity of the lower-surface pressure re- It was reasoned that if the flow over both surfaces could be kept similar at supercritical Mach numbers the net lift covery to bc observed. The airfoils were designatecl as of an airfoil could be maintained at an approximately follows : constant design value. To effect this result the respective NACA 835A216 rVACA 8368216 minimum pressures on the upper and lower surfaces would Because the drag characterktics at NACA 847A216 have to bc equal.
supercritical Mach numbers moulcl be adversely affected by The shapes and velocity distributions for these airfoils are simultanous occurrence of compression shocks on the illustrated in figure 1.
respective surfaces, it would be desirable to obtain the The numbering system for these airfoils is identical with highest possible airfoil critical Mach number. It was that given in reference 3 for the NACA 7-series airfoils ancl is further realized that, to produce a. positive lift force on the summarized as follows : airfoil at supercritical kfach numbers under this condition, 1st digit- Airfoil series number the position of minimum pressure would have to be located 2nd &$-Position of minimum pressure on upper surface farther aft on the lower surface than on the upper surface.
in tenths of chord from leading edge The respective upper- and lower- surface minimum pressures Srd digit- Position of minimum pressure on lower surface being equal, a more severe adverse pressure gradient would in tenths of chord from leading eclgc thus be imposed aft of the minimum pressure position on Letter- Serial letter distinguishing airfoils having the the lower surface, forcing a greater thickening of the bound- same thickness, design lift coefficient and ary layer on this surface at Mach numbers above the minimum pressure positions but different critical. The effect of the thickened lower-surface boundary camber or thickness distributions layer should compensate, to a degree depending upon the 4th diyit -Design lift coefficient in tenths respective upper- and lower-surface velocity distributions, 5th end 6th digits-Thickness-chord ratio in hundredths for the upper-surface boundary-layer growth and result in Tests of the initial three airfoils revealed variations in lift.
either no change or an effectively positive change in the coefficient with 5lach number in the vicinity of t.he design airfoil camber at Mach numbers above the critical. It, lift coefficient which at supercritical 5lach numbers differed was therefore concluded that, by suitably choosing the in important aspects from the type of variation normally velocity distributions over the upper and lower surfaces, observed for airfoil sections. The lift coefficient at a constant airfoil sections could be designed to have, at a given angle angle of at tack increased marlicdlr with increasing Jlach of attack, an approximately constant or an increased lift at number above that for normal lift divergence as contrasted supercritical Mach numbers.
with the usually noted opposite variation. Instead of Following this lint of reasoning, an initial group of three decreasing with increasing Mach number above that for KACA S-series airfoil sections, 16-percent-chord-thick, hav- normal lift divergence, the lift coefficient at a constant angle ing different respective positions of minimum pressure (or of attack increased markeclly with SIach number. This maximum local vtIocity) on the upper and lower surfaces was The sections were clmivccl in essentially result confirmed the design expectations to a greater degree designed and tested.
than anticipated, and indicated that great difficulty would the same manner as were the later families of SACA airfoils bc experienced iu trimmin g an airplane using such wing by combining mean camber lines with basic thickness forms sections at any but positive lift coefficients at supcrcritical to produce a desired velocity distribution. Velocity clistribu- ,\lach numbers, an important safety feature for large tions were selected to provide the desired aerodynamic heavi1.v loaded aircraft. This charact,eristic was unfortu- characteristics at supercritical Mach numbers, and the airfoil nately accompanied by erratic and, from t.he standpoint of shapes corresponding to these distributions were determined airplane controllability, undesirable variations with Mach by the method of reference 2.
number of the slopes of the lift curves.
The first airfoil was proportioned to have equal upper- and The desired type of supercritical speed lift characteristic lower-surface minimum pressures occurring at 30 and 50 having been realized, efforts were dircctecl toward the deriva- percent of the chord, respectively. The base profile was tion of thinner sections with modified camber so as to produce obtained by combining proper fractions of the thickness less powerful lift changes at supercritical l\lach numbers. A forms of the KACA 63- and 65-series airfoils and the “double- A mean camber line satisfying group of lo-percent-chord-thick profiles was accordingly roof” profiles of rcftrencc 2.
derived from the NACA 836A216 airfoil, this section among the condition of equal minimum pressures for the upper n.ncl those tested having the most favorable characteristics at low lower surfaces was determined by combining suitable pro- CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTERISTICS AT SUPERCRITICAL M A C H N U M B E R S NACA 8478110 and moderate lift coefficients. This second group of airfoil NACA 847BllO sections was composed of the following: NACA 847CllO NACA 8368110 NACA 836BllO The NACA 847AllO airfoil was derived from the NACA NACA 836CllO 8478216 airfoil by reducing the base-profile ordinates of the NACA 836DllO latter in the ratio of fifteen-sixteenths times the quotient, The NACA 8368110 airfoil was scaled down in thickness resulting from the division of the ordinates of the NACA from the NACA 8368216 airfoil and the camber-line ordi- 66-010 airfoil by the ordinates for the NACA 662-015 air- nates were adjusted to give a design lift coefficient of 0.1.
foil, and by reducing the camber-line ordinates and slopes in Tests of this airfoil disclosed the need for modification of both the ratio 10 :16. The NACA 847BllO airfoil was obtained the thickness and the camber distribution, the gain in lift at by combining the sum of one-half of the base-profile ordi- supcrcritical Mach numbers still being greater than desirable nates of the NACA 8478110 airfoil and one-half of those It was reasoned that, by decreasing the negative lift carried for the NACA 64-010 airfoil with the mean camber line over the rear portion of the airfoil at subcritical Mach consisting of equal proportions of the slopes and ordinates numbers, the change in the tot,al lift of the airfoil at super- of the mean line for the NACA 847AllO airfoil and of the crit.ical Mach numbers would be reduced. The NACA The NACA 847CllO airfoil con- uniform load mean line.
836BllO airfoil was designed to effect t.his result by modifying sists of the NACA 847BllO airfoil with the cusp removed both t,hc mean camber line and the thickness distribution of from the trailing-edge region of the latter by substituting the NACA 836AllO arifoil. The mean camber line for the straight lines for the portion of the profile from approxi- former was obtained as the sum of equal proportions of the mately the 80-percent-chord posit.ion to the trailing edge.
ordinates and slopes of the mean lint for the latter airfoil, The ordinates of all of the airfoils investigated are given in and of a uniform load (a= 1 .O) mean line. The upper- and tables I to X. The shapes and theoretical velocity distri- lower-surface minimum pressures were maintained approsi- butions for all but the NACA 836CllO and 847CllO airfoils matcly equal by adding to one-half of the base profile orcli- (which cliffcr but slightly from the NACA 836BllO and nates of the NACA 836AllO airfoil, one-half of those for the 847BllO airfoils, respectively) arc illustrated in figure 1.
XACA 66-010 airfoil. The resulting changes in profile and It is to be noted that ncgativc deflections of a plain trailing- vc1ocit.y distribution may be not.ecl from an csamination of edge flap on an ordinary airfoil section would produce lower- parts (d) and (e) of figure 1.
surface velocity distributions approaching in character the The NACA 836CllO airfoil was clcsigned to invcstigatc tbc distribution previously described for the new type of airfoil effect on the supcrcritical speed aerodynamic characteristics The results of section with the reflescd mean camber line.
of the NACA 836BllO airfoil of removing the cusp from the an investigation (also conducted in the Ames l- by 3j&foot rear portion of the profile. The former differs from the NACA high-speed wind tunnel) of an NACA 65-210 airfoil with a 836BllO airfoil only iu that. the profile is linear over 20-percent-chord negatively deflected Aap accordingly are approximately the last two-tenths of the chord.
presented and comparccl in the present report with those for Tests of the NACA 836BllO airfoil inclicatcd that the the NACA 8-series profiles.
profile modification from the NACA 8368110 airfoil x-as cffectivc in reducing the magnitude of the lift-cocfficicnt SYMBOLS increase at supercritical Mach numbers in the vicinity of the mcan-line designation, fraction of chord from a design lift coefficient. Further improvement was still felt leading edge over which design load is uniform to be desirable, however, particularly in the slope of the lift airfoil section lift-curve slope, per degree curve at lift coefficients greater than the design value. A chord, feet decrease in the severity of the pressure recovery over t,he section drag coefficient lower surface (by decreasing the negative pressure peak) section lift coefficient was indicated as a possible corrcctivc measure. To test clcsign section lift coefficient this hypothesis, the NACA 836Dl 10 airfoil was derived by section moment coefficient about quarter-chord combining the thickness form obtained as the sum of equal point proportions of the NACA 8368010 and 63-010 profiles with The 134 Mach number the mean camber line of the NACA 836BllO airfoil.
V free-stream velocity, feet per second clifference between t,he NACA 836BllO and 836DllO airfoils local velocity, feet per second u may be seen from figure 1 to be principally in the magnitude X distance along chord, feet of the lower-surface minimum pressure.
clistance perpendicular to chord, feet To invest,igate t,he possibility of realizing improved char- Y section angle of attack, degrees acteristics from more rearward minimum-pressure positions a0 section angle of attack corresponding to design on both surfaces, three additional lo-percent-chord-thick au, lift coefficient, degrees sections were derived from the NACA 847A216 airfoil and flap deflection, degrees were designatecl as follows: 6, 4 REPORT 947-XATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 3‘ c (a) S.4C:\ 835.43lCi airfoil. (h) NAP.4 83SA210airfoil -8 .8 u 7, V ‘ J .6 0 ./ .2 .3 .4 .5 .6 -7 .8 .S lo s C (11) SIC’ .4 8X.41 10 ;lirfoil (cl SACA 81i:\Zlti xirfoil.
.8
ttt j i
i i
u
s V .6 .6 (f) SACA 836DllO airfoil.
(d SAC.4 830R110 nirfoil.
FIGUI:E I.-Theoretical velocity distributions and profiles for the XiSC.4 8.swirs ai!‘ foik.
CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTERISTICS AT SUPERCRITICAL M A C H N U M B E R S .8 .8 + + .6 .6 .4 .2 I I i I ! ! I I ! ! ! I I U-41 1 1 1 1 1 I 1 1 1 1 1 1 1 ) ( 1 1 1 7 .8 .9 I. 0 .I .2 .3 .4 .5 .6 0 0 .I .2 3 4 .5 .6 .7 8 .S LO .z c c (g) NACA 8478110 airfoil.
(h) NACA 847BllO airfoil.
FICWIE I.-Continued.
FIGURE I.-Concludrd.
RESULTS AND DISCUSSION APPARATUS AND TESTS Section aerodynamic charac%cristics in coefficient form are The tests wcrc made in the Ames l- by 3j&foot high-speed prcscntcd as functions of ,\Iach number in figures 3 to 47 wind tunnrl, a low-turbulence, two-dimensional-flow wind for the NACA &series airfoils, two representative NACA tunnel.
B-series airfoils, and the XACA 65-210 airfoil with a 20- The airfoil models wcrc accurately constructed of alumi- percent-chord plain trailing-rdgr flap neutral and negatively num alloy and wcrc of B-inch chord and 12-inch span. The dcflcrted through 6’ . All the characteristics are shown models rompletcly spanned the narrow dimension of the corrected for tunnel-wall interference by the methods of tunnel test section. Two-dimensional flow was assurrd reference 4. The dashed portions of the airfoil characteristics through t.ht use of sponge-rubber gaskets (to prevent end curves serve to indicate the extent of possibly unreliable leakage) compressed between the model ends and the tunnel data obtained in the close vicinity of J’ lach numbers for walls.
which the flow in the tunnel test se&o11 was choked, that is, Measurements of lift, drag, and quarter-chord pitching for which the ,Ilach number of unity was attained locally moment were made as nearly simultaneously as possible at across the test srction.
1Iach numbers ranging from 0.3 to as high as 0.9 for each of the airfoils at. angles of att.ack increasing by 2’ incrrmcnts CHARACTERISTICS OF INITIAL THREE AIRFOILS from -6” t,o a maximum of 12’ . The Reynolds number It is scrn from figures 3, 4, and 5 that the respective var- variation with Slarh number for the tests is cxprcssrcl iations with ,Ilach number of the lift coefficient at constant graphically in figure 2.
angles of attack for the KACA 835A216, 8368216, and Lift and pitching moments were evaluated by a method 8478216 airfoils differ markedly from the variations gener- similar to that described in reference 3 from integrations ally observed for ordinary airfoil sections.
An abrupt in- of the pressure reactions on the floor and ceiling of the tunnel crease of large magnitude occurs in the lift coefficient at of the forces on the airfoils. Drag values were determined angles of attack within the normally useful range at Mach from wake-survey measurements made with a rake of total- numbers above those for lift divergence in place of the cus- head tubes.
tomary decrease in lift coefficient. The difl’ erence in char- acteristics is emphasized in figure 6 which illustrates the variation with Mach number of the angle of attack required to maintain the design lift coefficient of 0.2 for each of these KACA S-series airfoils, and for the NACA 65,-215, a=0.5 airfoil (see reference 5), a representative NACA g-series airfoil.
The explanation for the radical lift characteristics of the new airfoils is to be found in an examination of the theoretical low-speed velocity distributions of figure 1. At Mach numbers above the critical the strong adverse pressure gradient aft of the minimum-pressure position on the lower Froum Z.-The variation of Reynolds number with Mach number for tests of B-inch-chord airfoil mcdels in the Ames I- by 3%foot high-speed wind tunnel. surface promotes a rapid thickening and separation of the REPORT 94’ 7--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
I I I I I I I I I I
.3 .4 .5 .6 .7 .8 .9 I.0 Mach number, M FIGURE 3.-‘ rho variation of section lift coefficient with Mach number at various angles of :6 .2 .3 .4 .5 attack for the NSCA 835.421G airfoil. .6 .7 .8 -9 I.0 Mach number, &f FIGURE 4.-‘ L’ hc variation of section lift coefficient with Mach number at various angles of attack fur the NACA 836A216 airfoil.
, / I I I ( I I I I I I / NACA 835APf6 __----__ do. 836A2f6 - --- do. 847A2l6 -_-- do. 65, - 215. - .5 .6 .7 .9 I.0 .2 .3 .4 .8 Mach number. M Moth number, M FIOUHE G.-‘ l’ hc variatirm with 3Iocb number of the scctim angle ofattack for R lift coefficient FIGURE 5.-‘ l%e variation of section lift coefficient with Mach number at various angles of of 0.2 for the S.4CA 835A?lC, 83ti.4216,847A21Gand GET215. a=O.5, airfoils.
attnck for t,hc SACa 84i.421B airfoil.
CAMBERED hIRFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTliRISTICS AT SUPERCRITICAL M A C H N U M B E R S ’ -7 boundary layer from this surface, resulting in the loss of an in the scnsc that the lift coefficient incrcascs with ltfach uum- extensive portion of the negative lift carried over that part ber rather than dccreascs, is so violent for these three airfoils of the airfoil immediately aft of the lower-surface minimum- as to cause very erratic and undesirable variations in the slope pressure position. The increasing extent of the separation of the lift curve at the higher Mach numbers. (See fig. 7.)
on the lower surface with increasing Mach number produces The variation of the angle of attack necessary to maintain the increasingly positive variation of lift coefficient at con- the design lift coefficient of 0.2, although in the direction stant angles of attack observed in figures 3, 4, and 5.
to promote safety at high Mach numbers for an airplane The variation with Mach number of the lift coefficient at employing such airfoils as”wing sections, has already been low positive and negative angles of attack, although favorable observed in figure 6 to be undesirably large. For these reasons it was concluded that the first airfoils were cambered x.24 too severely and that a modified amount of camber as well as a change in the distribution would produce less drastic Q changes in the lift coefficient with increasing Mach number.
..20 ‘ =.
The drag characteristics of the three airfoils (figs. 8, 9, and t.
lo), as was expected, are much inferior to those of the NACA .I6 6-series airfoils, as represented in reference 5 by the NACA d 65*-215, a=0.5 and NACA 66,2-215, a=0.6 airfoils, with respect to divergence with increasing 3lach number at low g I2 9’ VI and moderate angles of attack despite allowance for the small tliflerencct in thickness of thr airfoils.
L 08 The variation of pitching-mornc~ll~ cocfficaicnt with ;2lacb 2’ number for the NACA 835A216, 8368216, and 847A216 t airfoils, shown in figures 11, 12, and 13, respectively, is ;=.04 consistent with the variation of lift c~ocfficicnt. The moment corffcicnts vary from positive values at low LIncb nunlbcrs whcrc ncgativc lift is carried over the rrurwartl portion of .3 .4 .5 .6 .7 .8 .9 /. 0 fw’ och number, M the airfoil to ncgativc values at high ,\Inc:h numbers whcrc FIGURE 7.-The rwintion with Mach numhcr of the section lift-curve slope at thr design lift this ncgntivc lift is lost.
corficicnt for the NACA S5.~21G,83FA21G,847AZlti and 051-215,a=0.5, &irfoils.
.22 .I6 .06 I I I I I I I I I II I I I I I I II I I I I II I .2 .3 .4 .5 .6 7 .8 .Q I.0 .?2 .3 .4 .5 .6 .7 .8 .S I.0 Mach number, M Mach number, M FIQURE 8.-The variation of section drag coefficient with Mach number at various angles cf FIGURE S.-The variation of section drag coefecient with Mach number at various angles of attack for the NACA 835A216 airfoil. attack for the NAOA 836A21Bairfoil.
870720-50-2
8 REPORT 947-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
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CAMBERED AI.RFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTERISTICS AT SUPERCRITICAL M A C H N U M B E R S CHARACTERISTICS OF THE N A C A 836-110 AIRFOILS for the NACA 836AllO airfoil. At angles of attack apprcci- ably above ancl below the ideal angle, the lift-coefficient NACA 836AllO.-Because current design trends indicat,e thinner wing sections for high Mach number applications, variation resembles that observed for the NACA 6-series it was considered desira.ble to further t.he investigat,ion on type of section. (See figs. 18 and 42 for the NACA 64-110 a.irfoil sections of lo-percent-chord maximum thickness. and 65-2 10 airfoils.)
The effect of halving the amount of camber and decreasing A considerable increase in the slope of the lift curve at the the profile thickness of the NACA 8368216 airfoil may be design lift coefficient is observed in figure 19 for the NACA seen from an examination of the characteristics of the NACA 836BllO airfoil over that of the NACA 8368110 airfoil for The variation with 8368110 airfoil. Mach numbers between 0.75 and 0.85.
The variation of lift, coefficient with Mach number for Mach number of this parameter for the former airfoil is closely comparable to that for the NACA 64-lip airfoil.
this airfoil (fig. 14) is much less drastic at supercritical Mach numbers than that noted in figure 3 for the NACA 8368216 From figure 20, it can be seen that the variation with Mach number of the angle of attack necessary to maintain the airfoil. The lift-curve-slope variation wit.h Mach number is considerably improved for the NACA 8368110 airfoil (cf., clesign lift coefficient for the NACA 836BllO airfoil is greatly reducecl from that observed for the NACA 836AllO &foil.
figs. 7 and 19), and the angle of attack required to maintain the lift cocfflcicnt at the design value (cf., figs. 6 and 20) is The drag characteristics of the NACA 836BllO airfoil corrcspontlinglg retluccd for the thinner lower-cambered (fig. 22), although considerably improved over those of the profile. The 1atfCr variation is still unticsirably large, NACA 8368110 section, are still inferior with respect to llowcvc~I~.
divergence with 5lach number in the vicinity of the design lift coefficient. to thoscl of the NACA 65-210 airfoil when The tlificrc~nccs in thr lift c~llnJ.ac.tc~t.isti~s of the NACA 836Al 10 airfoil and the NACA 64-l 10 airfoil, as rcprcscnta- compared on the basis of equal lift coefhcicnts for the two aiJ*foils.
tivc of the best NACA 6-sclrics sclcLtionsfor high l\lnc>h num- bar nppliczntions, may t)c s(l(91 from a comparison of fg77~~3 The variation in pitching-moment coefficient with Marli 14 ant1 18 to lit in the varktions of lift cocfficic~nt with Alach number (fig. 27) for thr NACA 836BllO airfoil closc~1.v JlllrnlWJ~al s1nall posilivcb nntl Jl(‘ @ t ivc ZJIl&9 of at tack. The appJxoachcs that for the SACA 65-210 airfoil, as a result tlc~paJI71rc of thr c~lJaracteristics of the forincr airfoil froni of the camber modification from that of the NACA 836AllO tliosc usually obsc~~vctl for airfoil sectioJls at siipclrcritical airfoil.
~Iac~li Jiun~bc~rs is Jnorc~ strikirigly ill7istratctl in figiirc 20, NACA 836CllO.--This airfoil section was testctl to dctcr- tlcpic~ting tlJ7‘variation with LIaclJ number of the angle of mine the cflect on the arrotl~~namic chamctcristics of the at tack rcquirc~tl to maiJitniJi tlic tlcxsign lift corffic~icnt of 0. I KACA 836BllO airfoil of removing the cusp from the trailing- for thr NACA 836-I 10 and 64-1 10 airfoil sections.
edge region of the airfoil. Comparison of the resptctivP The drag arid pitclling-nioJii7~17t c~liaractcristics of the variations with AInch Jiumbcr of lift, drag, and pitcliing- NACA 64-1 10 airfoil sc>ctioJJat high ,\lnch numbc~*s being moment c~oefficicnts (figs. 16, 23, and 28, respectively) fol 7~11nvailnbl~~ nt tli(t prc3c~JJt writing, tlic3c cliarnctcristics foJ* tlrc KACA 836Cl 10 airfoil with the cborrcspontling variations tllcb NACA 8:16Al 10 airfoil m77st 1~ c~ompnrc~l with tl1osc for for the KACA 88GBllO airfoil rrvcals no significant tliffcr- tl1c NACA 65-210 airfoil :IS tlJ(t 11c>stmost rc~prc~scntntivc~ cn(‘ cs in tli(‘ cliaractcrist its of tlic two sections.
profile of the NACA A-sc>ricbs airfoils availabl7~. The drag NACA 836DllO.--The NAC;2 836DllO airfoil was clesign(~d c*hamc~tcristics of tlJ7‘NACA 886A110 airfoil (fig. 21) corn- to investigate the rffcct of both dccrcnsing tlic amount part unfavornbly with those of the NACA 65-210 n.irfoil of ncgat ivc design lift from that of the NACA (fig. 25), particiJlaJ*ly at the a.nglcs of attack corresponding 8368110 airfoil aJld raising the lomcr-surface critical Mach to the loner lift cocfficicJ1ts.
Divergcncc not only occurs number above that of the upper surface (note theoretical carlicr for thr former, but the drag cocfficicnts at a given lift vc1ocit.y distribution, fig. 1) in an at,tempt to obtain a more coeffirient are higher.
favorable variation with Mach number of the slope of the From figures 26 and 30, rcspectivcly, the pitching-moment lift curve. Figure 17 indicates the NACA 836DllO airfoil coefficients for the NACA 8368110 airfoil, in addition to to be the most promising of those yet discussed, virtually being more positive, exhibit a generally smaller variation no variation with Mach number being manifest in the lift with Mach number than do those for the NACA 65-210 coefficient near the design value. This characteristic is rc- airfoil.
fleeted in the small variation with h4ach number in the angle of attack required to maintain the clesign lift coefficient of NACA 836BllO:-The NACA 836BllO airfoil was clcrived 0.1. (See fig. 20.) With reference again to figure 17, the from the NACA 8368110 airfoil in such a manner as to reclucc of lift coefficient at variation with Mach number the negative lift on the after portion of the airfoil at suh- constant angles of attack other than that CorrespoJlding to critical Mach numbers at the tlrsign lift attitude a~~1 to the design lift coefficient, indicated lift-curve slopes closely rclain the approsimately equal critical AInch n7uJnbers of the resembling those of the NACA 6-series airfoils as represented upper arid lower surfaces. The rffect of these profile mocli- in figure 18.
fications on the lift-coefficient variation with Mach number is shown by a compkson of figures 14 ancl 15. The varia- Escept at the higher lift coefficients, no improvement in tion in the vicinit,y of the design lift coefficient is seen to be drag characteristics from those of the NACA 836BllO airfoil small for the NACA 836BllO airfoil as compared with that resulted from this profile modification.
10 REPORT 947~NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
I The variation with Mach number in the pitching-moment profile. From this and the similar result observed in the coefficients of the NACA 836D110 airfoil (fig. 29) does not case of the NACA 836-110 airfoils it is concluded that for differ noteworthily from those for the other airfoils of the lo-percent-chord-thick airfoils of this type of section the series.
aerodynamic characteristics are not materially affected by CHARACTERISTICS OF THE NACA 847-110 AIRFOILS removal of the cusp from the after portion of the profile.
It is to be noted that in the case of both the NACA NACA 847AllO:-The NACA 847AllO airfoil was derived 836-110 and the NACA 847-110 airfoil developments the from the NACA 8478216 section by decreasing the thickness sections having the most favorable lift characteristics are and the camber-line ordinat,es in the same manner as was those for which the negative portion of the design lift is done in the case of the NACA 836AllO airfoil. The lift- small and for which t,he minimum pressure is somewhat coefficient variation with Mach number (fig. 31) closely lower on the upper surface than on the lower surface of the resembles t.hat for the latter airfoil. The variation with airfoil. The latter result. is in contraclict,ion to the design ;\Iach number of t.he angle of attack required to maintain the design lift coefficient (fig. 35) is similar to that observed assumption that the upprr- and lower-surface prcssurc peaks should be equal. Although it was not. found possible for the NACA 8368110 airfoil (fig. 20).
to improve the lift-curve-slope variation with Mach number The variation in drag coefficient with 1Iach number (fig.
for these airfoils over that characteristic of the NACA 36) is more favorable for the NACA 8478110 airfoil than B-series airfoils, the IZ’ ACA 836DllO and 84713110 profiles for the NACA 836AllO a.irfoil from the standpoint of divcr- are inclicatcd to be the equal of the XACA 6-series type in gencc with J,lach number at angles of attack in the vicinity this respect. The drag characteristics of the best NACA of t.hc ideal angle.
S-series airfoils thus far derived are not as favorable as The pitching-moment-coefficient variation with hlach those of XACA B-series airfoils in that the drag-divergence number for the NACA 8478110 airfoil (fig. 39) is similar to Mach numbers are lower for comparable lift coefficients in that for the NACA 836AllO Grfoil, but the moment co- the vicinity of the design lift coefficients. The pitching- efficients are of smaller magnitude.
moment characteristics of the more promising airfoils of the NACA 847BllO.-The lift characteristics of this airfoil, SACA 8-series arc, if anything, superior to those of the tlevelopcd from the NACA 847A110 airfoil 1~~decreasing the ncgativc contribution to the &sign lift distribution and by SACA 6-scrics in that the variations of moment coefficient with i\ilach number arc gcncrally smaller for the former.
tlecrcasing the lower-surface prcssurc peak below that of the upper surface, arc seen from figure 32 to be considerably CHARACTERISTICS OF AN AIRFOIL WITH A NEGATIVELY DEFLECTED FLAP improved over those of the latter uirfoil. As in the case of From an examination of the lift characteristics of an the NACA 836DllO section: the variation with ,\lach num- NACA 65-210 airfoil section with a 20-percent-chord plain ber of the lift coeflkient in the vicinity of the design value is trailing-edge flap, a marked similarity was noted between the indicated to be very small, and yet. a reasonn.bly satisfactory (See fig. 34.) The variation variation with Mach number of the lift coefficient at various lift-curve slope is retained.
with ;\Iach number of the angle of at tack for mnintcnance of angles of attack for a small negative flap deflection and the characteristics previously observed for the SACA S-series t.hc tlrsign lift cocfficicnt (fig. 35) is as favorable as that airfoils. It n-oulcl bc very desirable to be able, by negatively observed for the NACA 836Dl IO airfoil. A marl~ctl im- provement. in tlic variation of drag coefficient with ,\Iach deflecting a plain flap, to effectively reflex t,hc camber of a wing section on an airplane in flight from the uniform load number at zero lift is notctl from a comparison of figures 36 type at subcritical SIa,ch numbers to something approaching and :37 for the NACA 84783 10 and 847B110 airfoils, respcc- that of an SACA S-series profile at supercritical Mach num- tivrly. For this condition the drag-coefficient varint.ion of bers. To permit an appraisal of the characteristics of an the latter airfoil is superior to that, of the NACA 836DllO airfoil with a ncgativcly deflected flap at high Slach numbers, airfoil. The superiority is considerably reduced at thr design the aerodynamic characteristics of the NACA 65-210 section lift. coefficient and disappcurs at the higher lift coefficients.
The variation in pitching-momenl- coefficient with ;\Inch with a 20-percent-chord plain flap undcflectcd, and nega- tively clcflectcd 6”, arc presented in figures 42, 25, and 30 and number for the NACA 847BllO airfoil (fig. 40) is obscrvcd in figures 43, 46, and 47, rcspectivcly, for comparison with to bc very small in thr vi&nit>- of the tlcsipn lift cocfFicicnt those of the SACA S-scrits airfoils invcstigatcd.
and parallels the chnractcristics of the NACA 836DllO The simila.rit,y between the rcspcctivc variations with airfoil in this respect.
;\Iach number in the lift corfficicnt at a constant angle of NACA 847CllO.-This airfoil was designed to invcstigntr attack for the SACA 65-210 airfoil with the flap deflected further the effects on the characteristics at high subsonic -6’ and the NACA 836DllO and 847B110 airfoils is readily Mach numbers of removing the cusp from the trailing-edge.
Lpparent from a comparison of figures 43, 17, and 32.
region of an airfoil. From figures 33,34, 35, 37, 38,40, and 41, l’ hc lift characteristics of the three airfoils are further com- t,he characteristics of the resulting airfoil are seetl to bc essentially the same as those of the cusped SACA 847BllO jared in figures 44 and 45 depicting tlie rcspectivc variations CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE L FT CHARACTERISTICS AT SUPERCRITICAL MACH NUMBERS 11 i with Mach number in the lift-curve slope and the angle of\. angle of attack, characteristic of the NACA g-series airfoils, attack required to maintain the lift coefficient of 0.1. The and yet retaining at all other times the superior drag charac- similarity between the latter characteristics for the airfoil teristics of the NACA g-series airfoils.
with the negatively deflected flap and the two NACA S-series airfoils is unmistakable.
The drag characteristics of the flapped airfoil (fig. 46) are AMES AERONAUTICAL LABORATORY, similar to those of the NACA 836DllO and 847BllO airfoils.
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS, The pitching-moment characteristics of the three airfoils MOFFETT FIELD, CALIF.; Sept. 22, 1948.
(figs. 47, 29, and 40) also bear a close resemblance to one another.
REFERENCES The principle of reflesing the camber lint by negatively deflecting plain training-cage flaps on NACA 6-series airfoils 1. Hood, Manly J., and Allen, H. Julian: The Problem of Longitudinal Stability and Control at High Speeds. NACA Rep. 767, 1943.
at supercritical Mach numbers to produce favorable varia- tions in lift coefficient with increasing Mach number on the 2. Allen, H. Julian: General Theory of airfoil Sections Having Arbi- trary Shape or Pressure Distribution. NACA Rep. 833, 1945.
strength of the results contained herein has already found 3. Abbott, Ira H., von Doenhoff, Albert E., and Stivers, Louis S., Jr.: important application (in an expedient sense) on scvcral Summary of Airfoil Data. NACA Rep. 824, 1945.
high-speed airplanes and merits further investigation.
4. Allen, H. Julian, and Vincenti, Walter G.: Wall Intcrferencc in a Two-Dimensional-Flow Wind Tunnel With Consideration of the CONCLUDING REMARKS Effect of Compressibility. SACA Rep. 782, 1944.
A nrw group of airfoil scctious, tlrsignatc~tl the SRCR 5. Graham, Donald J., Nitzberg, Gerald E., and Olsen, Robert N.: 8-serks, has bccbn tlcvclopccl having favorable lift chnrac- A Systematic Investigation of Pressrrre Distributions at High tcristics at supercritical J\lach numbers. Through the USCof Speccls Over Five Rcpre.sent,ative SAGA Low-Drag and Conven- ncgativc camber over a portion of thcl airfoil chord it has tional Airfoil Sections. NA(:A Iten. 832, 1945.
proved possible to hold tll(a lift cocfficknt of the IWW type of I. 2 nirfoil approsimatcly constant at some design vuluc~ with incrcnsing 11~11 number to at least 0.9 ,\lach number, the o&=-6” v01=4~- limit of the prcsrnt investigation. By suitably choosing the camber and thickness distributions for Lhc airfoils, a particu- lar variation with Mach numhrr of tdie angle of attarli rc~quircd to maintain a given &sign lift rorfficient can he obtainecl. No means has bcrn found for improving the lift- curve-slope characteristics of the NACA 8-scrics airfoils .6 bcyontl those of thr SACA 6-scrics srctions. Although some caontrol can be cscr&etl over the drag ant1 pitching-moment characteristics of the former airfoil sections without atlvrrscly affecting the lift rharactcristics, it is gcnrrally nrcrssnry t,o ~ccpt drag cQliaractcristirs somcwliat poorer with rcsprct to tlivergcnce with Mach number than those of the NACA G- series airfoils presently usccl for high Slash number applica- tions. The pitching-moment characteristics of the NACA 8-serirs airfoils are generally more favorable than those of the NACA 6-series airfoils in that the variations of pitching- moment coefficient with Mach number and angle of attack at supercritical Mach numbers are somewhat smaller for the former.
Flat-sided profiles may bc used in place of the cuspcd .6 trailing-edge profiles on IO-pcrccnt-chord-thick NACA 8- series airfoils without significantly altering the aerodynamic characteristics of the airfoils at supercritical Mach numbers.
-.8 The lift characteristics of the NACA g-series airfoils at supercritical Mach numbers can be approximated with NACA B-series airfoils through the use of negatively deflected .5 .6 .7 .8 .9 I. 0 plain trailing-edge flaps. This application appears to be a Mach number, M promising means for obtaining on demand the favorable FIOURE 14.-The variation of section lift coefficient with Mach number at various an&s of variation with Mach number of the lift coefficient at a given attack for the NACA 636AllO airfoil.
12 REPORT 947-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ~a=-2” w=8” j I.0 -Da= 0” dd~fo-~ Qd= e” VCL-0.6’ i----1 r I I -A- I.2 voi=4” 0 CL=-6” .a a=-4O Ad= 6” 0 a--Z” ~a= 8” =/o o L.
r7
I
.8 .6 .6 d I i l‘ trl 1 i- .4 s G 2 .2 b s 0 C .?
E -.2 u3 -.6 -.8 -I.0 -/.Oi I I I I I I I I I I .3 .4 .5 .6 7 .2 .3 .4 .5 .6 .7 .8 .9 I.0 .2 .8 .s I.0 __ Mach number, M CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTERISTICS AT SUPERCRITICAL M A C H N U M B E R S 13 I.2 I I I I I o or=-6” a ct= 2” ocA=4°1 I I I I iA l/O .?
c .04LL_I-.-U.-L. i
.2 .3 .4 .5 Mach number, A4 cr, I’ lr,rm 19.-‘ 1’ 21~ rariation with Mach number of the section lift-curve slope nt the design lift corfficirnt for the KACA 83GA110,83Fl3110.d3GCl10,83GDllO and the 64-110 airfoils.
-.6 -.6 I L I I I / I I I I m -.8 .2 .3 .4 .5 .6 .7 .8 .s I.0 .I8 --.- ;. I I I I I II h ua- L Mach number, M vci= 4” aa= 6” ,’ ; I Ill,\ V W = 8” “A”
I I I I
0”
-I--!
*^ .I4 .E ” 5 .I2 .06 -31 ’ I I I I .2 I .3 I I .4 .5 .6 .7 .8 .9 I. 0 Moth number, M Mach number, M Frnun~ 20.-The variation with Mach numhcr 01 the srction angle 01 attack ior a lilt corlf.
F~cum 21.-The vnristion cf scctian drag coefficient with Mach numbs at various snelcs of cient ofO.1 for the NACA 830A110, 836B110, 83GCllO. 836DllO and 64-110 airfoils.
attack for the NACA 836AllO airfoil.
REPORT 9 4 ‘ i--NATIONAL ADVISO RY COMMITTEE FOR AERONAUTICS 14 - .22 .20 0 or--r 0 a=-2” Da= 0” .I8 Q cr= 2 ” vof=‘ 4 ’ . NZ RO I I I I .06 A / .04 ’ I !
.2 .3 .4 .5 .6 .7 - .- .8 .S I.0 Much number; M Mach number, M FIGURE 22.-The \-aviation of section drag coefficient with Mach number at various nrlglcs of FIGURE U-The variation of section drag coefficient with Mach number at various angles of attack for the NACA 836BllO airfoil.
attack for the NACA 8 3 6 C 1 1 0airIoi1.
.20 r2
. I8 , I I I I ! I
’ ’ A
.2 .3- .4 .5 .9 I.0 .6 .7 .8 .9 I.0 .5 .6 7 3 .4 Mach number, M Mach number, k .V FIGUKE 24.-The variation of section drag coefficient n-ith Mach number at various ~nglcs ol FIGURE 25.-The mrintion of section drag coefficient with Mach number nt various angles of attack for the KBCA ESGDllO airfoil. attack for tbc NACA 65-210 airfoil.
CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTERISTICS AT SUPERCRITICAL M A C H N U M B E R S 15 .5
Tl-r-!
.4 .4 h .-l--R0 ti t.3 Y -I.” c .2 .Y Y, $ .I I.
-.4Lllllllil1111”11 .2 .3 .4 .5 .6 .7 .8 .9 I.0 Mach number, M FICUIIE 27.-The yilriati!)n of swlion quarter-chord moment corfficirnt with Mach nunlbcr at various angles of attack for the NACA 8360110 airfoil.
0 .4
i i i i i i i i i
I
Moth number, M Moth number, M .- .- ’ F W U R E 29.-The variation of scction quarter-chord moment crwfficicnt with Mach number FI~UKE 28.-The varintion of section quartrr-chord momrnt coefficient with Mach number at various angles of attack for the NACA 83GDllO airfoil.
at various angles of attack for the NACA 83GCllO airfoil.
--
llllllllll lllll UIU u u UIIIU u ~IIWI lllll I II
REPORT 9 4 7--NATIONAL ADVISORY CO~MMTI’ TEE FOR AERONAUTICS .4 .3 1 ~a’ =-6’ FIGURE :jO.-The variation of section quarter-chord momrnt coeficicnt with Mach numhrr at various ar~glrs al attack lor the NACA F5-210 airfoil.
oa=-6” vci= 4” I I ,od=-4” Ad= 6” I I I Ct=-4” A cc-2’ 9 ac= 0’ d (y= 2’ v .8 -.6
: 8
-. 8
L 1
I I I I I I I I I
-1.0 Bi I HLLLi
-LO
7 3 :4 .5 .6 .7 .8 .9 t. 0
.- .2 .3 A .5 .6 .7 .8 .9 LO Mach number, M Mach number, &f ~~T:CRE32.-The rwiation al srctiou lift cnrfficient with XIach number at !wious nngles Ot FIGURE 31.-The variation ofsccticn lift cceficicnt with Mach numhcr at ~~ariOUS allgl(Y?of attack for the NACA 84iBllO airfoil.
attack for tho NACA 847.4110airfoil.
CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTERISTICS AT SUPERCRITICAL M A C H N U M B E R S 17 --- : s ’ 5 5 ’ -NACA 847A//O Much number, M FIGI’ I~E 34.-‘ l’ hr vnriation with Mach numhrr of the swl.im lift-currr slolx at thr drsign lifl wcfliciont for the NACA 847Al10, 847Bll0, 847CllO and 64-110 ah’ foils.
.I8 .2 .3 .4 .5 .6 .7 .8 .G .I6 .06 .2 .3 .4 .5 .6 .7 .8 .9 LO .3 .4 .5 .6 .7 .8 .9 LO Much number, M Moth number; M FIGURE 35.-The rari?tim with Mach number of thr sccti-m angle of attnrk for a lift cocffi- FIGURE X6.-The variation of srction drag coefficient with Mach number at various angles of cicnt ofO.1 Ior the NACA 847AllO. 84iRll0, 847Cl10, and 64-110 nirfoils. attack lor the NACA 847Al10 nirfoil.
18 REPORT 947-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS P C % ’ 4 ” I I I I A AQ!= 6 ” vci= B” If?
.6 .5 .6 .7 Mach number, -iU - Mach number, M FIGURE 37.-The variation of section drag coefficient with Mach number at various angles of FIGURE 38.-The variation ofscction drag coefficient with Mach number at various angles of attack foolthe NACA 847BllO airfoil.
attack for the NACB 847CllO airfoil.
FIGURE 39.-The variation of section quarter-chord moment cocilicient with Mach number at various angles of attack [or the NACA 84i.4110 airfcil.
CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTERISTICS AT SUPERCRITICAL M A C H N U M B E R S I i I I I I-1 .3 .4 .5 .6 .7 .8 .9 I.0 Mach number, M FIGURE 40.-The vnriation of section quarter-chord moment weflicienl with Mach number -.3 2 .3 nt. various angles of attack for the NACA 847BllO airfoil. .4 .5 .6 .7 .8 .9 10 ,.- Moth number, M FIOL~RE 41 .-The variation of sccti,,n quar tcr-chord moment coefficient with Mach numhrr at various anglrs of attack for the NAC A 847CllO airfoil.
.4 .5 .6 .7 23 .9 LO - .5 .6 .7 “3 .9 I.0 Mach number, M Mach number. M FIOURE 4?.-The vsrintion of section lift coefficient with Mach number nt various nnglw of P m u m 43.-The wristion of section lift coefficient with Mach number at wricus nnalcs of attack for the NACA 65-210 airfoil with a 20.percent-chord plain flap. 6,,0”.
attack for the NACA 135-210 nit foil with R 20-percent-chord plain flap. 6(,-V.
w - ~- REPORT 9 4i-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS I I I I I .; I , / c I I O-II .8 .9 I.0 2 .2 .3 A .5 .6 .7 Much number, M FXURE 45.-The variation with Mach nomher of the anplr of tlttack for a lift cocfiicient of FWURE 44.-‘ l’ hc variation with Mach numhrrof thr section lift-curve slopcat a lift coefficirnt q.1 for ttlr N.4C.4 0.5210 (a,= -I?), 83GI~llO and 84iBllO airfoils.
cf 0.1 for the NAC.4 W-210 (a~=-GO), WDIIO and R47BllO airfoils.
I8 .I6 ./4
II
0" FIC.UILE4G.-The variatim of srcti.m drag rocfiicicnt nith Rfach numhcr at rariws anglrs of attack for the N.4C.4 fk-210 airf ,il with R 20-prwmt-chord plain flap. &,.-Go.
CAMBERED AIRFOIL SECTIONS HAVING FAVORABLE LIFT CHARACTERISTICS AT SUPERCRITICAL M A C H N U M B E R S ‘ I’ AHLK III.--(:OORnINATES FOR THE TABLE I.-‘ ZOOK~INATES FOR THE TABLE II.--COORnINATES FOR THE W A C A 836A216 AIRFOIL NACA 847A216 AIRFOIL NACA 8358216 AIRFOIL [Stations and ordinates given in prrcent ot nirfoil chord1 (Stations and ordinntes giron in percent of airfoil chord1 [Stations and ordinates given in percent of airfoil chord Lower surface Lower surfme Upper surrnce Lower swfacc Upper SurIace
I
_- _- ----.- Ordinate Station Ordinate Ordinate Station Station Ordinate Ordinate Station Ordinate Station ---- ------ ----- _.- __---- 0 0 0 0 0 0 0 0 0 0 0 0 -. 949 ,280 .720 .670 .697 -.927 1.090 -.890 ,303 1.145 .321 -1.108 -1.692 ,501 :: :ii ,998 ,950 .970 1.342 -1.054 530 1.402 .5M 1.538 1.494 -1.314 ,962 1.873 -1.292 1:006 I.790 1.470 1.734 1.030 1:: ;g 2.176 2.824 2.732 2.768 2.677 2.474 2.232 2.541 2. 268 -2.294 1;: 3’ ;; 4.673 3.830 5.327 1;: 3’ ;: 5.207 3.591 4.735 3.680 4.793 -2.732 :: ;t: -2.852 4.738 7.808 4.580 7.658 4.453 -2.979 7.266 2 E 10.286 lO.lb4 -3.354 5.490 5.162 -3.528 9.816 5.344 10.099 EE 1;: A:; 14.801 6.692 15.199 14.9ti6 15. 05.5 -4.276 6.264 -4.554 14.945 15:034 -4.464 19.908 -5.139 19.905 7.006 20.095 t: 3":: 19.814 7.036 -5.506 20.094 20.186 -5.079 24.973 24.721 -5.96" 25.027 -G.405 25.279 7.904 24.631 7.523 25.369 -5.G70 2 2: 29.830 29.411 29.467 -6.742 30.170 -7.246 30.533 8.134 30.589 -6.244 34.220 -7.484 35,352 8.968 34.648 34.168 ;: 2; -8.023 35.780 8.004 35.832 -6.810 39.100 -X.186 4O.f 05 8.920 39.395 -8.748 40.900 7.620 39.119 7.154 40.881 44.175 44.426 44.090 45.825 8.556 6.@37 -9.203 45.910 i.085 45.574 1;:;;; 1;: $4 49.178 50. 931 7.962 49.099 49.7txi 6.189 -9.239 50.822 G.453 50.234 54.375 -9.533 55. so9 7.226 54.091 -8.X12 55.625 5.769 55. 033 5.666 54. 967 1;: :;; 59.214 5tJ.089 -9.469 IO.78 i 6. 408 5.123 -8.037 co.311 5.067 60.222 59.778 -8.697 ('5.5 'I 64.439 6.5.32.5 65.088 --R. 934 5.545 4.567 -7.027 64.912 4.374 g: g; -8.409 70.373 -7.855 70.189 4.697 69.811 3. 703 70.336 4.010 -5.831 ti9.62i ', -7.525 75.440 -6.450 74.7.x 3.873 75.239 3.436 -4.552 74.5tx 3.100 75.287 74.713 -6.050 80.207 80. :395 -4.873 79.569 3.110 80.431 2.834 -3.246 79.605 2.515 79.793 -4.201 86. 2li5 85.3“5 85.117 -3. 239 84. f:35 2.3ri7 2.205 -1.989 84.735 1.945 84. 883 -2.404 !lO. 127 -1.688 89.79” l.PO2 90.210 1.34!!
90. 047 1.510 -.878 89.8i3 89. oti3 -.740 1)s.019 - ,433 94.652 ,820 95.048 ,821 94.981 iO7 94.9YI -.072 95.049 100.000 100.""0 0 100.000 0 IO". 000 0 0 100.000 0' 100.000 L. E. l?l’ lills: 1.121 I,. E. ladius: 1.183 I,. I?. Indills: I.242 sopr trrouptl I,. I’ ..: 0.220 Slope through L. E.: 0.191 Slope through L. IX.: 0.208 TABI,IS V.-(‘ OORnISATES FOR THF: ‘ I‘ AHI,F: VI.-COORDISATES FOR ‘ THI<: TARLIS IV.-~:OORI>ISATl~:S FOR ‘ I’ HI‘ : SAC’ A 836BllO AIRFOIL i\;ACA 836CllO AIRFOIL SA(‘ A 836A110 AIRFOIL [Stations and ordiwltrs given in percent 01 sirioil cl~ordl [Stations and ordiwtes given in prrccnt ofai!‘ ioil chord] [Stations and ordinatrs ~ivcn in pcrccnt 01 uirloil chord] Loacr surrnrr
I
Station Ordinntr Ordinate Station Station Station Station Ordinate _ _- ..-
I-
0 0 0 0 0 0 0 0 0 0 0 0 --.64:( --.5w ,481 -. A43 .3i1 ,371 ,734 ,481 .42(i .575 iO0 --.li72 062 : ;;i i24 -.765 600 GO" .x31 : 801 ,724 I: 3:; I:215 1:oi5 1: % 1.215 -.Rl,i I.145 1.143 -. 943 1: 075 1.331; I. 110 1. 580 2.4.54 - 1. 238 -1.238 2. 302 1.5&O 2.454 -1.078 2.378 2.302 2.585 1.5iX -1.679 -1.480 2.228 4.954 -1.679 4.ROS 4.8rJR 2.2n2 2.22R 4.954 4.881 5. 07fi -2. m5 7. 403 --1.X1" i. :x02 2. 750 7.403 -2. 035 7.321 7.321 7. 5 '3 2.818 2.750 .3.195 'J.OfiH -2.347 -2.347 Y. RR" :3.I95 I). 908 -2.117 9. YOY 9. 850 IO.045 :3.29; -2. I'80 3. 902 14.9!11 -2.889 -2.889 14.925 14.925 3. 902 14.991 14.958 14.99T 4.033 -3.356 -3.217 4.428 20.019 -3.358 20.015 20.015 19.940 4.5'54 4.428 20.019 20. "Ii 25.053 -3.768 25.125 25. 053 -3. i:32 25.089 a. Hex -3.768 25.12s 24.8 iY 4.917 4. 808 5. 053 :30.101 -4.144 -4.144 30.2ii 5. 053 30.101 -4.22.; 30. I89 30.2ii 29.i72 5.072 -4.4x5 5. 1.53 :35.147 -4.495 3.5.425 :35.425 5.153 35.147 --;: ;y :35.281i 34.677 8. O O Y -4.ii!I 40.16i ,' 5.12x 40. 16; -4.7iY 40.501 40.501 39.F32 4.788 5.128 40.334 45.1m -4.993 -4.993 45.516 5. 001 45.168 -5. 554 45.342 5.001 45.510 44.mi 4.475 4.794 50. 140 -5.123 -5 123 .55:y;y 4.W 50. 140 -5.670 50.308 "5;;"7;; 49. IiM 4.108 -5.145 -6.047 4.519 55.119 -5. 145 3.699 4.519 55. 119 55,255 54.721 -5.017 -6,025 tio.113 4. 1x0 60. 04,5 -5.017 60. is1 60. 181 59.847 3.279 4.180 GO.045 64.919 -4.GDO 64. !lG:i 64.949 -5.7oi (i4.95ti 3.7R4 -4.690 (i4.9lx c.5.02.i 2.836 3. 784 X.326 fig. 90.5 -4. 134 -4.134 69.781 3. 326 69.905 -5.052 69.843 09.781 70.144 2.465 -3.423 2.828 i4.802 -3. 423 74.740 i4.740 2.928 74.892 i4.816 75.174 2.033 1:: 1;; -2.RiO 79.903 2.282 79.002 -2.617 79.76i 79.765 1.722 2. 335 76.835 80.157 84.931 -1.771 -1.907 8&.X42 1.844 84.934 -2.145 84.888 1.707 84.845 85.107 1.345 -1.171 1.110 89. 983 -.956 89.925 89.929 1.325 UY.96i -1.144 89.945 90.052 ,035 -, 499 94.994 --.X18 525 94.993 -.280 94.991 94.991 493 .i45 94.992 95. ooi 0 100.000 0 0' 160.no” 0 100.M m 100.O O Q 100.000 0 100.000 L. E. radius: 0.659 I,. E. radius: 0.659 L. E. radius: 0.4!)8 Slope through L. E.: 0.095 Slope through I,. E.: 0.095 Slope through L. E.: 0.110 - REPORT 9 4 7”ATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TABLE VII.-COORDINATES FOR THE TABLE VIII.-COORDINATES FOR THE NACA 836DllO AIRFOIL NACA 8478110 AIRFOIL [Station and ordinates given in prrccnt of airfoil chord] [Station and ordinntcs given in percent of airfoil chord] upper surflxc Lo\\.er surface Upper surface LO\\W surrace __-------- ------- ~.
Station Ordinate Station Ordinate Station Ordinate Station 0rdinat.e ~-_~---~-- -- -- --__ ---- 0 0 0 0 0 0 0 0 ,443 ,769 -.678 .429 ,738 2:: -.628 1: 681 16R 1.204 ,937 1.315 :s”:; -1.004 -. 808 ,669 --.740 1.157 1: Y E 1.343 -. 915 2.396 1.652 2.604 -1.194 2.400 1.694 2. 564 -1.352 4.896 2.324 5.104 -1.556 4.8QR 2.406 5.070 -1.858 7.406 2.959 7.560 -2.244 7.403 2.857 i. 59i -1.853 9.913 3.422 10.041 -2.574 9.912 3. 298 10.088 -2.112 14.942 4.135 15.014 -3.122 14.938 4.010 15.062 -2.572 19.977 4.650 19.981 -3.578 19.970 4. 563 20.030 -2.991 25.008 4.975 24.992 -3.375 25. 010 5.004 24.942 -3.964 30.053 5.267 29.947 -3.735 30.071 5.204 ~9.891 -4.295 35.124 .5.238 34. 840 -4.5io 35. 110 5.437 34.890 -4.075 40.149 R. 119 39.817 -4.770 40.190 5.454 39.810 -4.398 45.155 4.884 44.815 -4.876 45.259 5.29i 44.741 -4.697 sn. 139 4.558 49. 833 -4.887 50. 293 5.001 49.7Oi -4.959 55.114 4.160 54.862 -4. 786 55.2X6 4.620 54.714 -5.172 GO. 051 3. 709 59.929 -,.547 60.248 4.188 59. i5? -5 298 64.995 3.251 (64.99: -4.157 65.li8 3. i29 64.822 -5.305 69.941 2. 33 70.047 -3. GO1 iO.060 3.246 69.940 -5.102 i4.932 2.325 75.058 -2.920 i4.923 2.i53 75.077 -4.579 79.941 1.84i 80.051 79.859 2.236 x0.141 -3.706 84.964 1.366 85.032 1:: :g 84.880 1.697 85.120 -2.645 89.985 ,885 90.013 --.7.12 89.930 1.134 90.070 -1.53F 95.001 427 94.999 -. 182 94.984 ,548 95.016 -.508 100.000 0' 100.000 0 100.000 0 100.000 0 L. E. radius: 0.618 I,. E. radius: 0.590 Plo[x through L. E.: 0.096 Slope through I,. E.: 0.104 TABLE IS.-COORDISATES FOR ‘ l’ H15 TABLE S.-COORDISATES FOR THE SAC’ A 847BllO AIRFOIL KACA 847CllO AIRFOII, [Stntions and ordinates given in percent of airfoil chord] [Stations and ordinntcs given in percent ofnirioil chord] - - Station Ordinntc Stntion Ordin:\lc Station Ordinate ___-- ---__ - 0 0 0 0 0 0 0 0 .443 ,555 -. ill ;$ ,445 ,792 ,555 --.ill Ii88 : ,812 -. 84i .I%8 . Yli4 ,812 -.&Li 1. 1iY 1.239 1.321 -1.055 1. 1iY 1. 23Y 1.321 -1.055 2.420 1. i23 2.580 -1.400 2.420 1. i23 2.580 -1.400 4.918 2.413 5.082 -1.8il 4.918 2.413 5.082 -1. Sil 7.421 2.94i 7.57y -2. 233 i. 421 2.Y4i 7.5iY -2. 233 9.926 3. 390 10.074 -2. 53i 9.926 :3.x90 10.074 -2.5% 14.942 4.095 1.5.058 -3.038 14.Y42 ;: ;I; 15.058 -3.038 20.03s -3.44'4 19.962 4.F31 20.038 19.962 24.985 5. 031 25.015 1;: 'ii 24. Y85 5. &l 25. 01.5 -:3. 734 3o.m 5.30~ 29.089 -4. A5i 30.011 5. ROY ZY.YnY -4.05; :35.044 S, 467 :34. Y5G -4.2i6 35.044 5. 46i 34. 956 -4. 2X1 2: 2 5.4YO 5.346 3Y. 44. 913 8X -4. -4.49x 426 40. oar 5 4Y(l 39. Yl:< -4.426 45.124 s. 346 44.8X -4.498 50.141 S.Oi2 49.X59 -4.49y 50. 141 .5.072 49.85!1 -4.49Y 55. 1:x 4. iO.5 54. 863 -4.433 55.1xi 4. i05 54. xw -4.433 (in. 119 4.973 59. xx1 -4.293 GO. 119 4. 273 59.88i -4.293 3.Ton 6*4. Y13 -4.OGY 65. nxi :3.7Qli 64. Y13 -4.06Y GS. OXi ill. 03i 3. 280 GY. Q W -3. i22 Xl. 03i 3. 2m 09. YliX -3. i22 i4.982 2. i41 i5.018 -3.2oi i4.QX2 2.741 i5.018 4: 2; is.957 2. Ii9 80. 043 -2.51i iY. Y5i 2.210 80.043 84.9ti5 I.6OF 85. 03.5 -1. i44 X4.963 I. il6 X5. O X -1.853 89.982 1.033 90.018 -. 9X NY. STY 1.218 90.021 -1.161 94.999 .4ii Y5.001 -_ 299 94.QY8 95. on2 --.5OA n 100.000 0 100.000 0 100.000 100.000 L. E. mdius: 0.693 I,. E. radius: O.fiYX Slopr throul’ h L. E.: 0.080 Slopr through L. E.: O.080 ,i., - -_ .-- <, ‘ . -:- ; ..,-:. :.,. .,‘ . .-.,, ,.. 7.y-j;;.:’ )---- -, ..-.> ;;;T.- _. :’ ,. -., .- ; --,