1、 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT No. 460THE CHARACTERISTICS OF78 RELATED AIRFOIL SECTIONS FROM TESTSIN THE VARIABLE-DENSITY WIND
2、TUNNELBy EASTMAN N. JACOBS, KENNETH E. WARDand ROBERT M. PINKERTONLangley Memorial Aeronautical LaboratoryREPRINT OF REPORT No. 460, ORIGINALLY PUBLISHED NOVEMBER 193327077 0-36-1 1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COM
3、MITTEE FOR AERONAUTICSNAVY BUILDING, WASHINGTON, D.C.(An independent Government establishment, created by act of Congress approved March 3,1915, for the supervision and direction of theselentificstudy of the problems of flight. Its membership was increased to 15 by act approved March 2, 1929 (Public
4、, No. 908, 70th Congress). It eonsistaof members who are appointed by the President, all of whom serve se, such without compensation.)JOSEPH S. AMEs, Ph.D., Chairman,President, Johns Hopkins University, Baltimore, Md.DAVID W. TAYLOR, D. Eng., Vice Chairman,Washington, D.C.CHARLES G. ABBOT, Sc.D.,Sec
5、retary, Smithsonian Institution, Washington, D.C.LYMAN J. BRIGGS, Ph.D.,Director, Bureau of Standards, Washington, D.C.ARTHUR B. COOK, Captain, United States Navy,Assistant Chief, Bureau of Aeronautics, Navy Department, Washington, D.C.WILLIAM F. DURAND, Ph.D.,Professor Emeritus of Mechanical Engine
6、ering, Stanford University, California.BENJAMIN D. FOULOIS, Major General, United States Army,Chief of Air Corps, War Department, Washington, D.C.HARRY F. GUGGENHEIM, M.A.,Port Washington, Long Island, New York.ERNEST J. KING, Rear Admiral, United States Navy,Chief, Bureau of Aeronautics, Navy Depar
7、tment, Washington, D.C.CHARLES A. LINDBERGH, LL.D.,New York City.WILLIAM P. MACCRACKEN, Jr., Ph.B.,Washington, D.C.CHARLES F. MARVIN, Sc.D.,Chief, United States Weather Bureau, Washington, D.C.HENRY C. PRATT, Brigadier General, United States Army.Chief, Matriel Division, Air Corps, Wright Field, Day
8、ton, Ohio.EDWARD P. WARNER, M.S.,Editor “Aviation,“ New York City.ORVILLE WRIGHT, Sc.D.,Dayton, Ohio.GEORGE W. LEWIs, Director of Aeronautical Research.JOHN F. VICTORY, Secretary.HENRY J. E. REID, Engineer in Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.JOHN J. IDE, Technical
9、Assistant in Europe, Paris, Franed.EXECUTIVE COMMITTEEJOSEPH S. AMEs, Chairman.DAVID W. TAYLOR, Vice Chairman.CHARLES G. ABBOT. WILLIAM P. MACCRACKEN, Jr.LYMAN J. BRIGGS. CHARLES F. MARVIN.ARTHUR B. COOK. HENRY C. PRATT.BENJAMIN D. Fo ULOIS. EDWARD P. WARNER.ERNEST J. KING. ORVILLE WRIGHT.CHARLES A.
10、 LINDBERGH.JOHN F. VICTORY, Secretary.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-EREPORT No. 460THE CHARACTERISTICS OF 78 RELATED AIRFOIL SECTIONS FROM TESTS IN THEVARIABLE-DENSITY RIND TUNNELBy EASTMAN N. JACOBS, KENNETH E. WARD, and ROBERT M.
11、PINKERTONREPRINT OF REPORT No. 460, ORIGINALLY PUBLISHED NOVEMBER 1939SUMMARYAn investigation of a large group of related airfoilswas made in the N.A.C.A. variable-density wind tunnelat a large value of the Reynolds Number. The tests weremade to provide data that may be directly employed for aration
12、al choice of the most suitable airfoil section for agiven application. The variation of the aerodynamiccharacteristics with variations in thickness and mean-lineform were therefore systematically studied.The related airfoil profiles for this investigation weredeveloped by combining certain profile t
13、hickness forms,obtained by varying the maximum thickness of a basicdistribution, with certain mean lines, obtained by varyingthe length and the position of the maximum mean-lineordinate. A number of values of these shape variableswere used to derive a family of airfoils. For the purposesof this inve
14、stigation the construction and tests were limitedto 68 airfoils of this family. In addition to these, severalsupplementary airfoils have been, included in order tostudy the effects of certain other changes in the form of themean line and in the thickness distribution.The results are presented in the
15、 standard ,graphic formrepresenting the airfoil characteristics for infinite aspectratio and for aspect ratio 6. A table is also given bymeans of which the important characteristics of all theairfoils may be conveniently compared. The variation ofthe aerodynamic characteristics with changes in shape
16、 isshown by additional curves and tables. A comparisonis made, where possible, with thin-airfoil theory, asummary of which is presented in an appendix.INTRODUCTIONThe forms of the airfoil sections that are in commonuse today are, directly or indirectly, the result ofinvestigations made at Gottingen
17、of a large number ofairfoils. Previously, airfoils such as the R.A.F. 15and the U.S.A. 27, developed from airfoil profilesinvestigated in England, were widely used. All theseinvestigations, however, were made at low values ofthe Reynolds Number; therefore, the airfoils developedmay not be the optimu
18、m ones for full-scale application.More recently a number of airfoils have been tested inthe variable-density wind tunnel at values of theReynolds Number approaching those of flight (refer-ence 1) but, with the exception of the M-series and aseries of propeller sections, the airfoils have not beensys
19、tematically derived in such a way that the resultscould be satisfactorily correlated.The design of an efficient airplane entails the carefulbalancing of many conflicting requirements. Thisstatement is particularly true of the choice of the wing.Without a knowledge of the variations of the aerody-nam
20、ic characteristics of the airfoil sections with thevariations of shape that affect the weight of the struc-ture, the designer cannot reach a satisfactory balancebetween the many conflicting requirements.The purpose of the investigation reported herein wasto obtain the characteristics at a large valu
21、e of theReynolds Number of a wide variety of related airfoils.The benefits of such a systematic investigation areevident. The results will greatly facilitate the choiceof the most satisfactory airfoil for a given applicationand should eliminate much routine airfoil testing.Finally, because the resul
22、ts may be correlated toindicate the trends of the aerodynamic characteristicswith changes of shape, they may point the way to thedesign of new shapes having better characteristics.Airfoil profiles may be considered as made up of cer-tain profile-thickness forms disposed about certainmean lines. The
23、major shape variables then becometwo, the thickness form and the mean-line form. Thethickness form is of particular importance from astructural standpoint. On the other hand, the form ofthe mean line determines almost independently someof the most important aerodynamic properties of theairfoil secti
24、on, e.g., the angle of zero lift and thepitching-moment characteristics.The related airfoil profiles for this investigation werederived by changing systematically these shape vari-ables. The symmetrical profiles were defined in termsof a basic thickness variation, symmetrical airfoils ofvarying thic
25、kness being obtained by the applicationof factors to the basic ordinates. The cambered pro-files were then developed by combining these thicknessforms with various mean lines. The mean lines wereobtained by varying the camber and by varying theshape of the mean line to alter the position of themaxim
26、um mean-line ordinate. The maximum ordinateProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSof the mean line 2s referred to throughout this report as thecamber of the airfoil and the position of the ma
27、ximumordinate of the mean line as the position of the camber.An airfoil, produced as described above, is designated bya number of four digits: the first indicates the camber inpercent of the chord; the second, the position of the camberin tenths of the chord from the leading edge; and the lasttwo, t
28、he maximum thickness in percent of the chord.Thus the N.A.C.A. 2315 airfoil has a maximum camberof 2 percent of the chord at a position 0.3 of the chordfrom the leading edge, and a maximum thickness of 15percent of the chord; the N.A.C.A. 0012 airfoil is asymmetrical airfoil having a maximum thickne
29、ss of 12percent of the chord.In addition to the systematic series of airfoils,several supplementary airfoils have been included inorder to study the effects of a few changes in the formof the mean line and in the thickness distribution.Preliminary results which have been published in-clude those for
30、 12 symmetrical N.A.C.A. airfoils, the00 series (reference 2) and other sections having differ-ent nose shapes (reference 3); and those for 42 cam-bered airfoils, the 43 and 63 series (reference 4), the 45and 65 series (reference 5), the 44 and 64 series (refer-ence 6), and the 24 series (reference
31、7).If the chord is taken along the x axis from 0 to 1,the ordinates y are given by an equation of the formf y = ad x + ax + a2x2 + a3x + a4x4The equation was adjusted to give the desired shapeby imposing the following conditions to determine theconstants:(1) Maximum ordinate 0.1 at 0.3 chordx=0.3 y=
32、0.1dy/dx = 0(2) Ordinate at trailing edgex=1 y=0.002(3)Trailing-edge anglex=1 dy/dx= 0.234(4) Nose shapeX=0.1 y = 0.078The following equation satisfying approximately theabove-mentioned conditions represents a profile havinga thickness of approximately 20 percent of the chord.t y = 0.29690.1/ 0.1260
33、0x 0.35160x2 + 028430x3 0.10150x4. / - olo a - N. A. C. A. familyt_erO e+ Clark Yo Gdtt. 398/0 ./; .2 .4 .5 .6 .7 .8 .9 /.Ov = 0.29690 Arx_- 0.12600 x -0.35160x +0.28430 x -0.10150xBasic ordinates of N.A.C.A. family airfoils (percent of chord)5.0Ord_.I O 1 31 -157 4.3581 5.9261 7.0001 10.80511 that
34、isy,=6- t (0.29690.1/x-0.12600x-0.35160x2+0,28430e-0.10150x)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CHARACTERISTICS OF AIRFOIL SECTIONS FROM TESTS IN VARIABLE-DENSITY WIND TUNNELwhere t is the maximum thickness. The leading-edgeradius is foun
35、d to bear 2 0 20 ae) = .IotaWhen the mean lines of certain airfoils in commonuse were reduced to the same maximum ordinate andcompared it was found that their shapes were quitedifferent. It was observed, however, that the rangeof shapes could be well covered by assuming somesimple shape and varying
36、the maximum ordinate andits position along the chord. The mean line was,therefore, arbitrarily defined by two parabolic equa-tions of the formyo= be+ bix+ b2 X2where the leading end of the mean line is at the originand the trailing end is on the x axis at x=1. Thevalues of the constants for both equ
37、ations were thenexpressed in terms of the above variables; namely,(1) Mean-line extremitiesX=0 y=0X=1 y=0(2) Maximum ordinate of mean linex=p (position of maximum ordinate)andyr=(1 p)2 (1-2P)+2Px-el(aft of maximum ordinate)The method of combining the thickness forms withthe mean-line forms is best d
38、escribed by means of thediagram in figure 2. The line joining the extremitiesof the mean line is chosen as the chord. Referring tothe diagram, the ordinate yt of the thickness form ismeasured along the perpendicular to the mean linefrom a point on the mean line at the station along thechord correspo
39、nding to the value of x for which ytwascomputed. The resulting upper and lower surfacepoints are then designated: -Stations x and x,Ordinates y and ytwhere the subscripts u and l refer to upper and lowersurfaces, respectively. In addition to these symbols,the symbol 0 is employed to designate the an
40、gle be-tween the tangent to the mean line and the x axis.This angle is given by6 = tan-1 dxy Oa lxa. ya B=Ion- dx./0- 9 yt v Mean /insP1Chordp xOr /xt, yt/ x = x - y, sine Yu Y + yt cos B-./OL Rodius fhrough end of chord xt = x + y, sin a yt = yt - yt cos e/.00Sample calculations for derivation of N
41、.A.C.A. 6821z v, ue tan a sin v aos a y, sin e y. cos a z, v. x, m0 0 0 10.40000 0.37140 0.92840 0 0 0 00.01250.30000.03314.105030.00489.06000.383330.357930.9337510.0118600.03094.105030.00084.30000.0.03683.165030.01438.30000-0.02805-.04503.am1 .07988.0221 .048980 -.07347-.17143 -.07327-.16897 .99731
42、.98662 -.00585-.0037 .07906.00218 .805851.00037 .12863.0218 .59415.99963 -.0307-.0218Slope of radius through and of chord.FIGURE 2.-Method of calculating ordinates of N.A.C.A. cambered airfoils.yo=m(maximum ordinate)dye/dx = 0The resulting equations defining the mean line thenbecameMyr = p2 I2Px - e
43、l(forward of maximum ordinate)The following formulas for calculating the ordinatesmay now be derived from the diagram:xa =x-y, sin 6ya =y,+y, cos 0x l =x+yt sin 0y t =yr -y, cos 0Sample calculations are given in figure 2. The centerfor the leading-edge radius is placed on the tangent tothe mean line
44、 at the leading edge.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-06-GX09001Z-O550-018C -L00252206 2306 24062209 2309 2409 2212_ 2312 24122215 X3152218 2318 2418C_ _ _.1 -2421-2,506 2606 27062509 2609 27092612 -27122615 -8 2618 2918-4206 4306 4406
45、 4506 4606 47064209 4309 4409 4509 4609 47099212 4312 4412 4512 4612 47124215 4315 4415 4515 4615 47154218 4318 4418 4518 4618 47184221 4321 4421 4521 4621 97216206 6306 6406 6506 6606 67066209 6309 6409 6509 6609 67096212 6312 6412 6512 6612 67126218 6318 6418 6518 6618 -67186221 6321 6421 6521 662
46、1 6721REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSA family of related airfoils was derived in the mannerdescribed. Seven values of the maximum thickness,0.06, 0.09, 0.12, 0.15, 0.18, 0.21, and 0.25; four valuesof the camber, 0.00, 0.02, 0.04, and 0.06; and six valuesof the position of the camb
47、er, 0.2, 0.3, 0.4, 0.5, 0.6, and0.7 were used to derive the related sections of thisfamily. The profiles of the airfoils derived are showncollectively in figure 3.For the purposes of this investigation the construc-tion and tests were limited to 68 of the airfoils. Tablesof ordinates at the standard
48、 stations are given in thefigures presenting the aerodynamic characteristics.These ordinates were obtained graphically from thecomputed ordinates for all but the symmetrical sec-models, which are made of duralumin, have a chordof 5 inches and a span of 30 inches. They were con-structed from the comp
49、uted ordinates by the methoddescribed in reference 8.Routine measurements of lift, drag, and pitchingmoment about a point on the chord one quarter of thechord behind its forward end were made at a ReynoldsNumber of approximately 3,000,000 (tank pressure,approximately 20 atmospheres). Groups of airfoilswere first tested to study th
