1、REPORT No.289FORCES ON ELLIPTIC CYLINDERS IN UNIFORMAIR STREAM “By A. F. ZA13M, 1+. IL SMITH, and F. A. LOUDENAerodynamical Laboratory, Bureau of Construction and Repairted States Navy215.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IH
2、SNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT NO. 289FORCES ON ELLIPTIC CYLILNDER IN UNIFORM AIR STREAMBy A. F. ZAHM, R. H. SMITH, and F. .4. LOUDENTM repor presents thefineness ratios, conducted inthe tests was to investigatenormally has an elliptic sect
3、ion with a fineness ratio of 4.0; ako to learn whether a reduction inINTRODUCTIONresuIts of wind tunnel tests on four elliptic cylinders with variousthe NTavy Aerodynamic Laboratory, Washington. The object ofthe characteristics of sections suitable for streamline wire whichfineness-ratio would esult
4、 in improe-ment; ako to determine the pressure = “distribution on the model of fineness g.ratio 4-. iFour elliptic cylinders w-ith fine- +ness ratios of 2.5, 3.o, 3.5, and 4.o zwere made and then tested in the 8 “b 8 foot tunnel; first, for cross-wind ;force, drag, and yawing moment. at30 miIes an h
5、our and arious angles gof yaw-; next for drag at 0 pitch and .200 yaw and Yarious wind speeds; thenfor end effect on the smallest and FLG.l.ElIiptic cylinder 2 by 5 inches momted with end pIeteslargest models; and lastly for pressure distribution over the surface of the largest model at 0pitch and 0
6、 yaw and various wind speeds. In alI tests, the lengLh of the model -wastransverseto the current. The results are given for standard air density, p= .002378 slug per cubic foot.This account is a slightIy revised form of Report 3T0. 315, prepared for the Bureau of Aero-nautics, July 13, 1926, and by
7、it submitted for publication to the ATationa.l Advisory Committeefor Aeronautics. A summary of conclusions is givert at the end of the text.DESCRIPTION OF MODELSThe four elliptic cylinders, the smallest of which is shown in Figure 1, and profles of whichare shown in Figure 10, were each 62 inches lo
8、ng and 2 inches thick; their widths were .5, 6, 7,and 8 inches. The specified offsets are given in TabIe 1 and for each case can be derived from theequation of an eIIipse. All of the cylinders were of laminated pine, varnished, and then rerifiedby apphcation of their construction templates. After th
9、e tests, howeer, a few measurements ofoffsets taken on the plane table indicated that the modek were slightly unsymmetrical. The2 by 8 inch cyIinder had detachable end segments to fill up the space between the floor and ceilingof the tunnel during the pressure distribution test.In a second test seri
10、es adjoining end plates, Figure 1, w-ere used to detertie the end effecton two of the cy!inders. They were made from fairly plane galvanized-iron plate and measured24 by 24 inches.In Figure 2 the pressure colIector is shown inserted as a center segment in the 2 by 8 inchmodel. It w-as made of bronze
11、 accurate to 0.001 inch in the offsets. Its dimensions and the loca-tion of its 16 holes are given in Figure 3. The pressure leads, one running from a hole in the noseand the other successively from each surface hole, were each connected with -inch tubingwhich ran lengthwise through the strut to a m
12、anometer outside the tunnel.492*2915 217Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-218 REPORT NATION.4L ADVISORY COMMITTEE FOR AERON.4UT1CSMETHOD OF TESTINGTO measure the forces and yawing moment, each cylinder was mounted, without end plates,at
13、 its center on the two-prong fork, Figure 1, extending from the shank of the tri-dimensiondbalance described h reference 1. The angle of yaw was varied from 6 to 20 by 2 inter-vals, the wind speed was held at 30 miles an hour, and the cross-wind force, drag, and yawingmoment were simultaneously meas
14、ured on the cylinderand exposed portion of the holder; then on the holderalone with the cylinder detached but not removed.The difference u-as taken as the true force or momentcomponent. The precision of such measurements isgiven in Reference 2. The drag measurements withthe cylinders at 0 pitch and
15、0 yaw were taken inthe. same way; the wind speed being varied from 20to 60 miles an hour by 10 mile intervals.To determine the end effect of the smallest andlargest cylinders, the plates were mounted at the endsof the model as shown in Figure 1, and the cross-windFIG. 2.Pressure collector inserted i
16、n 2 by 8 inch eIliptic force and drag were measured at intervals of 4 yaw.cylinder The measurements were repeated without the plates.The percentage difference applied to the original force data gave values for the infinite cylinder.The pressure distribution measurements were made on the 2 by 8 inch
17、cylinder, which wasmounted vertically in the tunnel with extension end segments accurately in line and with thepressure collector inserted in the middle of its span. The difference of pressure between thenose and each of the holes aft of the nose wasdetermined successively. To do this all thesurface
18、 holes were plugged except one whichwas joined to one pressure lead, while thenose hole was joined to the other lead. Thewind speed was then varied from 20 to 70miles an hour, by 10 mile intervals, andthe cliffere.ntial pressure was measured onan alcohol .rnanometer having a 1 to 10slope. These meas
19、urements could be read inaH cases to within O.OO5 inch vertical ofalcohol, Thus the point pressure could bedetermined to about one-haIf of 1 per centfor speeds above 40 miles a-n hour; to withinless than 2 percent for the lower speeds. Theair speed was held constant to within one-haIf of 1 per cent.
20、RESULTS. OF FORCE AND MOMENTMEASUREMENTSThe cross-wind force and drag on the62-inch cylinders at various angles of yaware given in Tables II and IX together withtQ, 7:., -Q,., Nj,. , J:,”.:.,.: .,. . .FIG. 3.Bronze pressore collector for elliptic cylinder 2 by 8inches, fineness ratio 4their coeffici
21、ents which are the respective forces divided by pV12 times the frontal area S, T1being feet=per second. The coefficients are plotted in Figures 4 and 6.The cross-wind coefficient * increases positively at negative yaw and negatively at positiveyaw as the fineness ratio is increased from 2.5 to 4.0.
22、The fact that the force is not zero atzero yaw is probably due to the models being slightly unsymmetrical. The maximum coeffi-cient is 4.28 for the 2 by 8 inch cylinder.iTOexpessthese cross-wind coefficients as lift coefficients, muftiply them by frontal area/chord. plane area.Provided by IHSNot for
23、 ResaleNo reproduction or networking permitted without license from IHS-,-,-FORCES ON ELLIPTIC CYLLNDERSFIG. 4.EfIiptic clinders of varions fimess ratim. Lmgth of cyIinder 62inches, models at O“pitch, sir speed 30 M. P. Ef.LY UMFOR31 .41R STREA31 2193“0:1111”1 111(llll.1 I !2.0 L+ Jb X4,; /.0 t t, I
24、I 1111Qd o Ill 1111.c beyond 130 yaw, the greater the fineness ratio the greaterthe drag coefficient.The yawing moment about the N-axis is presented in Table IV; the resulting lines of forceand the center of pressure travel are shown in Figures 9 and 10. As the fineness ratio of thecylinder increase
25、s the center of pressure moves slightly aft.:The ratio of the forces C/D, is given in Table .5 and the graphs are given in Figure 8. The2 by 8 inch cylinder is superior for angles of yaw up to 16. (2D max. for this cylinder is 12at 8 yaw.Tables VI and VII give the force measurements on the smallest
26、and largest mode with andwithout end plates, the percentage difference and the coefficients for the infinite cylinder;Figures 5 and 7 compare the coefficients of the finite and infinite cylinders. The cross-wiadforce coefficient is increased positively at negative yaw and negatively at positive yaw
27、whenthe cylinder becomes endless. The drag coefficient for the infinite cylinder is less than forthe finite. aWith the cyhnders at 0 pitch and yawl the resistance and corresponding coefficients forvarious speeds are given in Table VIII and plotted in Figure 11. IIere the resistance of the 62-inch cy
28、linder was taken to be substantially the same as for a 62-inch segment of an infinitecylinder, as the increment due to end effect was small arndcould not be measured. On comparingthe four struts, it is seen that at high speeds the drag coefficient is not lowered by increase offineness ratio; at-spee
29、ds of 50 and 60 miles an hour, the models with fineness ratios of 3.0 and.3.5 have a lower cefficient than the 2 by 8 inch model.RESULTS OF PRESSURE DISTRIBUTION MEASUREMENTSThe differential pressure measurements made on the 2 by 8 inch cylinder are presented inTable IX, and their conversion from in
30、ches of alcohol on a 1 to 10 slope to vertical inches ofwater is ako given. Table X gives the point pressure at the se-eral holes found by subtractingthe differential pressure from the nose pressure. These data are plotted in Iigures 12 and 13.Table XI gives the point pressure in terms of the nose p
31、ressure.One sees from Figure 12 that for this strut shape the point pressure at alI used speedsdecreases from full impact P V* at the nose to zero at a distance of 2.1 per cent of the cylinder.width from the nose; the maximum suction occurs at about three-eighths of the width from theleading edge an
32、d is equal to about .6 the nose pressure. For speeds of 40 to 70 niles an hourthere is another point of zero pressure near the trailing edge and a positive pressure aft of that;for the lower speeds, a slight suction is still evident at the trailing edge. Figure 13 shows thatthe pressure at each hole
33、 varies nearly as the square of the velocity.The graphs of the faired values of the point pressure, multiplied by (70/ V)z to make themconlparable are shown in Figure 14= The integrals of each pressure graph, giving the elementsof the pressure drag and the summation of these or the resultant pressur
34、e-drag, are given inTable 12 and plotted in Figure 15. N7ith them are shown the total drag and the rwdtantfriction. The order of graphic integration here used to find the force J pdy over the variousportions of the surface of tk l-foot-long center Segment of the cylinder is detailed in thediagrams o
35、f Figure 17.It is seen that-the downstream push and the upstream suction vary as P. The upstreampush is zero at low speeds since the pressure did not become positive near the trailing edge of themodel at these speeds. The difference between the total downstream and upstream pressureforces, which is
36、the pressure drag, is seen to increase up to a speed of 35 miIes an hour and thendecrease. The difference between the curves of total drag and pressure drag, giving the frictionaldrag, varies as V“ where n.= 1.97.Provided by IHSNot for ResaleNo reproduction or networking permitted without license fr
37、om IHS-,-,-FORCES ON ELLIPTIC CYLIXDERS Hi UNIFORM AIR STREAM 221.Angieofyuq FFIG. 8.Elfiptic cylinders of various dneness ratia Leh of cylinder 62inches, modek at 0 pitch, air speed 30 M. P. H.FIG, 10.Center of preasme at various angles of yaw, of elliptic eyliuders of various dne-ness ratios. Leng
38、th of cyIinder 62 inches, modefs at 0 pitch,”o2.5, Ii I-J . l:7-“L ,; iili iii ! I I ! I f I I t I 1,.,.! ( !.501 ,! 1.,. ., I,“.-,L l*!llll.J. Jll.J!llli 1 !i 11 11)111 ,.,. . . . . .Y , , 1FIQ. 1I.Elliptic cylinders W various fineness ratios. Modelsat 0 pitch and 0 yaw .11111/,+1 2 5Disfanefr0rn4n
39、oseinhches6 7 8.07 v I I I I I I I 1 I ./ I I I/1 )111,06 ! ! ! I I I I I 4/1/?-oQ.;. i-i / ; iII , 1 ( I.04 I I I I I I / I I,r+dil! I I I I I I i II I I I LJI 1 I t t I I I I I I I I III I 1 1/ I I I I I I I I II 1111 Ill.!.031 ! ! ! 1/ I I I I I$ / 1 I ( I I I I I I II 1-111111i i/i I! I Ill I I
40、I I I 1 I 1111111r-.02.0/ 1 I 1 ! I 1 I I I I 1 I I I f I I I 1 120 30Dga710- Vokfesofp a71 9-Va/uesofDYfrom measure - compufed frommen+s of40M8M. .3 pressures p, OFIG. 16.Elliptic cylinder 2 by S inches. Graphs indicate theoretics values. p= l;pdy(a+b)2y/k+(a3bf)g where unit pressure=p Yi2. D,=2be
41、shown, Reference 3, that tke zonal pressure drag is upstream on the fore part; downstream onthe rear part; zero on the whole. The model in Figure 16 exhibits these properties except thatthe resultant pressure drag, owing to viscosity, is not quite zero.AL 40 miles an hour the drag coefficient of the
42、 2 by 8 inch elliptic strut; at zero yaw and withfree ends, is about 2.5 times that previously found for the best Navy strut, as given in Reference 4.REFERENCESReference 1.A. F. Zahm, “The Six-Component Wind Balance.” N. A. C. A. TechnicalReport No. 146, 1922.Reference 2.Aercmautics Staff, “Air Forc
43、e and Center of Pressure of M-80 Airfoil.” C. . : 4379 .4999CII = Drag coefficient= 2D/pV,S.D= Net (model without holder) drag impounds.IS= Frontal area of cylinder =O.8611 sq. ft.1, = Air speed =44 ft./see.p= Air density =0,002378 slug/cu. ft.EIIiptic cylinder. Various fineness ratioTABLE IVNET MEA
44、SURED Y.4WNG MOMEXT ABuUT N=AXIS ZOF MODEL EIOLDER IN POUND-INCHES AT 30 M. P. ILModelat 0 pitch!Angle of yaw(degrees)I 2.56-4- “z-o-+2_4_6_8-lo- _:-:12-. _._-. .-lo._ .-_.-!lo-_ -_.-_!18-+20-_ -_!-_!2. 738 3.2953. 8213. 7942. .546. 640+; ;4;5:2447.1909.21811.33612.963+.1. 69fjFinen ratio3.0 3:109 3
45、.3293. 5193. 161 L 601$ ;5;5:3817.86010.30612.37614.88216.837+ 18, 5903.5 4.% 3. 2.587433857727634356444337528772856728633215I1-4.0 ,-. 5.8075. 1354, 0292. 346+ 2883.5147.09210.31114.40618.246 /21828 2.:? + 18.732 i1 N=axis is 6.91 inches above chord of cylinder for all fineness ratios, and 2.26 inc
46、hes aft of nosefor finenessraLio=2.O; 2.72 inches aft of nose for fineness ratio=3.O; 3,35 inches aft of nose for fineuess ratio =3.5; 3.84inches aft of nose for fineness ratio=4.O.-, =.,. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-FORCES ON EL
47、LIPTIC! CYLIiiDERS 1A UNIFORM AIR STREAMIHIWc Cyltik. I-arimrs Enenes ratioTABLE VCID AT 30 M. P. H. FOR 62 INCH LONG CYLINDERSModel at 0 pitchI Fineness ratioAngk of 6W (degrees)! 14 3“0 b-la,6-_.-. -l +8. 12 +9. 2s + 10.3 I ,+-104 !4-6.76 7. n-?I t3.63 +3. 95 +: I 8 - - 7. 75 7. 65 2. 73En,ptm cli
48、nder. Fineness ratio =2.5 and 4.0TABLE VICROSS-D FORCE WITH AXO WITHOUT END PLATES AT 30 M. P. E., PERCENTAGEDIFFEREk”CE. AND COEFFICIENT FOR LNFINITE C!YL12KDERModel at 0 pitchCross-wind force on 62JIrck cyhnder j(pounds) Cross-wind force coefhcient (abso-lute)!.ngle ofFaw (degrees) I %:;,ITithout end With end 1 Finite cylinder Inlirdte cyekpIates C platesC C.=2 Cprls.( Table z) cc+
