1、“rREPORT No. 619DRAG OF CYLINDERS OF SIMPLE SHAPESBy W. F. LINDSEYSUMMARYIn order to determine the effect of shape, compressi-bility, and Reynolds Number on the drag and criticalspeed Jor simple Jorms, the drag Jorces On models of varioussimple geometric cross sections were measured in theN. A. C. A
2、. 11-inch hlgh-speed wind tunnel.The models were circular, semitubular, elliptical, square,and triangular (isosceles) cylinders. They were tested overa speed range from 5 percent of the speed of sound to avalue in excess oJ the critical speed, corresponding, for eachmodel, approximately to a tenfold
3、 Reynolds Number range,which extended from a minimum o 840 for the smallestmodel to a maximum of 310,O00 for the largest model.INTRODUCTIONThe aerodynamic drag of simple forms was one of theearliest subjects of aerodynamic research. Althoughnumerous investigations have been conducted, dragdata for m
4、any forms, especially as affected by ReynoldsNumber and compressibility, are incomplete or havenever been obtained. In accordance with a suggestionmade at one of the annual engineering conferences,tests to investigate the variation of drag for varioussimple forms with Reynolds Number were considered
5、for the variable-density wind tunnel. There was avail-able, however, a large amount of data on the drag offundamental shapes that had been obtained underconditions involving rather large and uncertain tur-bulence effects. It was therefore considered preferableto transfer the investigation to the l 1
6、-inch high-speedtunnel, where disturbing turbulence effects were muchsmaller and where new information could be obtainedconcerning compressibility effects.Previous investigations of the drag of simple formshave included the effects of Reynolds Number on thedrag of circular cylinders (references 1 an
7、d 2), theeffect of compressibility on the drag of circular cylinders(reference 3), the variation of drag with angle of attackfor square cylinders (reference 4), the drag of flatplates normal to the wind (reference 4), and tests ofelliptical cylinders of various fineness ratios. Testresults, however,
8、 were not available for either triangularor semitubular cylinders, nor were any previous in-vestigations available that included the effects of com-pressibility on the drag characteristics of any of theseforms, except the circular cylinder (reference 3).The present investigation, comprising measurem
9、entsof the drag of cylinders ha_fing various cross sections,was conducted over a range extending from 5 percentof the speed of sound to a speed above the value atwhich the compressibility burble occurred. This speedrange corresponded, for each model, approximately to atenfold Reynolds Number range,
10、which extendedfrom 840 to 8,400 for the smallest model and from31,000 to 310,000 for the largest model.The experiments were conducted from 1933 to 1936in the N. A. C. A. 11-inch high-speed wind tunnel.APPARATUS AND METHODSThe N. A. C. A. l 1-inch high-speed wind tunnel,in which the tests were made,
11、is an induction-typeclosed-throat tunnel having a circular air passage.The tunnel is equipped with a balance, which is of thethree-component, photorecording, spring type. Thebalance was designed for testing airfoils at speedsfrom approximately 35 percent of the velocity of soundto a speed approachin
12、g the velocity of sound. Adetailed description of the tunnel and of the photo-recording balance is given in reference 5.For some of the tests reported herein, the photo-recording balance was not sufficiently sensitive tomeasure the drag, and an auxiliary drag balance wastherefore used. This balance
13、was of the pendulumtype and was designed to measure very small dragforces on small models at low speeds. The forceswere measured by visual observation of the movementof a beam. Three balance sensitivities were used;a 1-inch deflection equaled 0.01 pound, 0.10 pound,or 1.0 pound. By the variation of
14、the sensitivityand by the addition of counterweights, forces weremeasured from a minimum of 0.001 pound to a maxi-mum of 10 pounds. One of the features incorporatedin the construction of the balance was a means forapplying tension to the model in order to overcomevibration difficulties encountered w
15、ith some of themodels in portions of the speed range.169Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-170 REPORT NO. 619-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSThe models tested were (a) circular, (b) semitubular(c) elliptical, (d) square, and
16、(e) triangular (isosceles)cylinders. The shapes and the dimensions of the crosssections are shown in figure 1. Because of the small sizeof the models and the relatively large forces involvedthe models were constructed of steel. The surfaces wer(highly polished, and the edges of the semitubular, thes
17、quare, and the triangular cylinders were sharp.W/nod/,-echonfor c_ = 0 /32“ /16“ /8“o o 0- _.-0_r _)“ SemitubuloF(-s_r e =50 ._J-Tt r =.0.96_.-o R= t/8“8:1Circular Elhco/Majoraxis.92“ D ,Square/8“ I,/4“ facei4I-1 i_ - I/4 ?x7 +7-o-V7-t-.HI 1bi-i-I-110 .1 .Z .3 .4 .5 .6FIGURE9.-Variation in C_owith V
18、/V. for the square cyinders._8_4.SZ.O_1.6o_ L-e- -_ +I I I i_, _., ,i-_“:., ,r iI I I13 _ .7 a 5I I i I I I _v_h_ol I,ne2!-ILLI .t L_inlersecfs curve / /ltz,?+ill il -1z_ i0 _, _ 3 # 5 s 78 i0 _l?eynoldm NumberFI6_RE O.-Variation in CD e with _eynods Number for the square eyinders.Square cylinder.-T
19、he results of the drag tests at thevarious angles of attack for the square cylinders arepresented in figures 9 and 10. These results indicatethat the drag coefficient is smaller when a diagonal isparallel to the wind (a-45) than when the face of themodel is normal to the wind (a=0). The total dragof
20、 models of the same size, however, is smaller ata=0 than at a=45 .Figure 10 indicates that there is but little ReynoldsNumber effect on the drag coefficient of the modelswith a diagonal parallel to the wind. Inasmuch asthe flow probably separates at the sharp edges for allvalues of the Reynolds Numb
21、er, the pressure dragcoefficient tends to remain constant and is such alarge part of the total drag coefficient that the effectof Reynolds Number is relatively small.For the square cylinders, face normal to the wind(a-0 in fig. 10), at the higher values of ReynoldsNumber, the drag coefficient is pra
22、ctically constantand approximates that of a flat plate set normal to thewind. At the lower values of the Reynolds Number,however, the drag coefficient appears to decrease withdecreasing Reynolds Number; incomplete separationat the forward edges possibly causes this change._4 I_LI II“, / / “ul , pex
23、Anqle of oltocl(. I IoLLL._ l . ;ex _ _1“III on qle, , d,d_g. I 1_“ _I_ _ _ d_. |0 L l 1/80_ -_I_. . _3olJ,-I ,i I I I II fT I i111/I0 .I .2 .3 .4 .5 .6 .7 .8r/gFmva_ ll.-Variation In C% with VV, for the triangularcylinders.II I l ! I t I me_e_ cu,-_e I!lli_1.2 _, IIl 1 l-I I_ I I , , i_Ap( _- - _:
24、i-_,_,/, _,d_p. Ililii It!i I |! IIs . _,_oVHq-t-q_IL_-!Ltl iit_7-I,_ _I_._J IJl LJ b iik _11_-q, ?,t-HTIP,-I-FI-,_ - Iltt I/tl I1Reynolds Number+_III/OsFIGURE 12.-Variation in C# 0 with Reynolds Number for the triangular cyinders.Within the Reynolds Number range investigated,no sudden changes in fl
25、ow were indicated by the resultsof the tests at any of the angles of attack.The compressibility effects for models with a diag-onal parallel to the wind (a=45 in figs. 9 and 10)appear to be independent of Reynolds Number withinthe range investigated. This result is in general agree-ment with the res
26、ults of the tests of circular cylinders.Triangular eylinder.-The effect of the apex angle onthe drag coefficient of triangular (isosceles) cylinders isProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-174 REPORTNO.619-NATIONALADVISORYCOMMITTEEFORAERONA
27、UTICSshownin figure11. Astheapexangleisincreasedandwitheitherapexorbaseto thewind,thedragcoefficientincreagesandapproaches that of a flat plate normal tothe wind, as is to be expected since the model tends tobecome a flat plate as the apex angle approaches 180 .With the base of the triangular cylind
28、er to the _nd,there is no appreciable effect on the drag coefficientfrom increasing the apex angle above a value of 60%With the apex to the wind, however, there is a continu-ous increase in drag coefficient with increase in apexangle above 30 .Reynolds Number has but little effect on the dragcoeffic
29、ient of models having triangular cross sections(fig. 12). The same characteristic is shown by theresults from tests of models having square cross sectionwith the diagonal parallel to the wind (fig. 10).The compressibility effects (figs. 11 and 12) appearto be independent of apex angle and are the sa
30、me forangles of attack of 0 (apex to the wind) and of 180 (base normal to the wind). The compressibility effectsfor both triangular (isosceles) cylinders and for squarecylinders with a diagonal parallel to the wind direction(a-45 ) are approximately the same.0 20 4? 0 80 lOG 120 /40 160 180Angle o o
31、t/ac/, a, deg.FmURE 13.-Variation in C_ 0 with a for the triangular cylinder having an apex angleof 30 . Area=altitudeXspan.The test results of figure 13 show the variation indrag coefficient, based on a constant area (product ofaltitude and effective span), with angle of attack foreach of several v
32、alues of the speed ratio VIVa. Eachcurve indicates, for a particular value of the speed ratioV/Vo, the variation in total drag for a triangular crosssection having an apex angle of 30 . The maximumdrag occurs when one of the long sides is normal to thewind, the condition corresponding to an angle of
33、 attackof 75 .The results indicate abrupt changes in the flowpattern within certain ranges of angle of attack, asevidenced by the sudden changes in drag coefficient.It is of interest to note that, at or near these criticalangles of attack, one of the long sides of the modelbecomes either parallel or
34、 perpendicular to the directionof the wind, as illustrated by figure 13.The variation in drag coefficient with the speed ratiofor several representative angles of attack is presentedin figure 14 to show the compressibility effects. Appar-ently the compressibility effects are greater at or nearthe cr
35、itical angle-of-attack ranges, as indicated bysteeper slopes of the curves in figure 14 and by thevertical displacement of the curves in figure 13._-i I I lI I I I A, gI oPoHo *,I III?. 4 _ i_ de,o. -+_4_ l_I_L_/o_ /zbl /35 /szl /8Ol/8o /.6_/.Z.40 .l .2 .3 .4 .5 .6 7 .0FIGURE 14,-Variation in Coo wi
36、th VV, for the triangular cylinder having an apexangleof30 . Areaffialdtudespan.The variation in lift coefficient with angle of attackis shown in figure 15 for three values of the speed ratio,V/_. The results show that sudden variations in thelift coefficient occur in the same critical angle-of-atta
37、ckranges in which the drag coefficient changes, a furtherindication that there are abrupt changes in the flowpattern. The variation in lift coefficient with V/I_for angles of attack within the critical angle-of-attackrange is presented in figure 16.An extrapolation of the drag coefficient of triangu
38、larcylinders having various apex angles with the base tothe wind is presented in figure 17, in which the dragcoefficient is plotted against the ratio of altitude tobase h/b for each of several values of the speed ratio,VIVa. As h/b approaches zero, the triangular sectionapproaches an infinitely thin
39、 flat plate set normal tothe wind. Thus, the extrapolation of the results oftests of models having triangular cross sections to avalue of h/b=O should give a good estimate of thedrag coefficient for flat plates of infinite aspect ratioset normal to the wind. The drag coefficient, obtainedfrom this e
40、xtrapolation, decreases slightly with increasein Reynolds Number. At equal Reynolds Numbersbased on width normal to the stream, the extrapolatedresults are in good agreement with values from Germantests conducted over limited Reynolds Number andspeed ranges (reference 4).Provided by IHSNot for Resal
41、eNo reproduction or networking permitted without license from IHS-,-,-fDRAG OF CYLINDERS OF SIMPLE SHAPES 175Effect of shape on drag.-Figure 18 illustrates therelative drag of all the models and shows the generaleffect of shape on the drag coefficient. The dragcoefficient, based on frontal area for
42、all the models, isplotted against the speed ratio, VIVa. The sizes of“ q_L II“_ _i _L x ;5 .r L , tl_A _A ,-_ j -I I iJ - _-i “5-.8 -I_ - _ _ 1_0 20 40 60 80 /00 /20 /40 /60 /80Angle of a/ac/, _,de_7.FIGURE15.-Variation in CL with a for the triangular cylinder having an apex angleof 30 . Areaffialti
43、tudespan.,6_o,TZc;L_II ?+-F4+-W135 h. - - i _-:_. .4 -_,Y- I !1!t-/60 ./ .2 .3 .4 .5 .8 .7 .e_r/r_FmvaE 16.-Varlatlon In CL with V/V, for the triangular cylinder having an al_zangleof30 . Area=altitudeXspan.the models were consistent in that the frontal areaswere approximately equal. The drag coeffi
44、cient ofthe N. A. C. A. 0012-63 airfoil (reference 10) is includedfor comparison.The agreement in drag coefficient between thesemitubular cylinder with convex surface to the wind(a=0 ) and the circular cylinder is reasonably closeand is to be expected in this Reynolds Number rangebecause separation
45、occurs in front of the central plane.At values of the Reynolds Number above the criticalvalue, however, a greater difference in drag coefficientfor the two forms is to be expected because the separa-tion occurs back of the central plane for the circular:o -_ -_ L - . /S Ix - _0EE-_- fo_ 0 - .4 .8 /.
46、-2 /.6 2.0 Z.4Rofio of o/f/tude fo bo_e, _/bFIGURE 17.-Extrapolation for Cv o of flat plates normal to the wind._ o_,:_i _E/.8,_ I V . _._ .sF-I._o LI._ _0L- ._1 _ J -I I L ) -_j r I-F-i-I-_Z_- C=4c_ q/e-s=_t _ i I- _._ .z .a ., ._ .s ._ eFIGURE 18.-Effect of shape on Cv_.cylinder and at the central
47、 plane for the semitubularcylinder.Similarly, the drag coefficient of the triangularcylinder having a 90 apex angle with the apex to thewind is only slightly less than the drag coefficient ofthe square cylinder with a diagonal parallel to thewind. This condition of approximately equal dragcoefficien
48、ts is to be expected because the point ofseparation is fixed for both forms at the sharp edges.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-176 REPORT NO. 619-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSIn general, the data show that, except for the squarecylinder _qth a face normal to the _ind, the higher-dragbodies have, in general, less rapid rise in drag coefficientat the higher speeds.CONCLUSIONSI. The compressibility effects appear to be inde-pendent of Reynolds Number for ranges wher
