REG NACA-RM-A9K01-1950 An analysis of the forces and pressure distribution on a wing with the leading edge swept back 37 25 degrees.pdf

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1、RESEARCH MEMORANDUM , AN ANALYSIS OF TEE FORCES AND PRESSURE DISTRIBUTION ON A WING WITTI TEE LEADING EDGE SWEPT BACK 37.25 By George G. Mwards and Frederick W. Boltz Ames Aeronautical Laboratory kEbffett Field, Calif. NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON March 30, 1950 Provided by

2、 IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-By George G. Edwards and Frederick W. Boltz SUMMARY A semispaa model of a wing with the leading edge swept back 37.25, an aspect ratio of 6.04, and a taper ratio of 0.5 was tested to ascertain the compressibility

3、effects on the forces, the momsnts, and the surface pressures. The WFng had 110 twist and the profiles normal to the quarter chord line were the mclcA 641-2l2. Lift, drag, and pitchwment data together with the chordwise distribution of static preesure at five spanwise stations are presented for Mach

4、 rimers from 0.18 to 0.94 at a conetast Reynolds nuuiber of a constant Reynolds nuniber of 1,100,000, and for Mach nunibers up to 0.90 at a Reynolds nuniber of 3,000,000. I 2,000,000. Force data are presented also for this Mach nuniber range at L An analysis of the data is made to correlate the chan

5、ges In the pressure distribution aver. the wing with the changes in the total forces. In this analysis a critical flow condition is considered to exist when the component of local VelocTty normal to the isobar equals the local s eed of sound. It is indicated that, at angles of attack between Oo asd

6、that at which the critical flow condition had occurred at the crest line of the entire wing (the crest line being defined a8 the locus of points on the wing surface at wbfch the surface is tangent to the direction of the undisturbed air stream). For this wing, having moderate sweepback, the critical

7、 flow condition was attained at the crest of the various spanwise stations witb a narrow range of lhch nunibers. 4%, the abrupt drag Increase be- at Mach nunibers slightly higher than Ar? approximate procedure for calculating the draflivergence Bkch number from lmpeed data is investigated. INTRODUCT

8、ION .i The use of the swept“wing plan form. for delaying the omet of serious compressibility effects to higher Mech rimers has received COR- I siderable theoretical and experimental study. A knowledge of the degree Provided by IHSNot for ResaleNo reproduction or networking permitted without license

9、from IHS-,-,-2 WCA RM Agm 1 to which these compressibility effects can be delapd and alleviated by King sweep is of valuein.the propr design and application of swept wings. It is important to how the Mach nuniber above which the rapid drag increase, the loss of lift, and the sudden changes in load d

10、istri- bution and longitudinal stability occur. Tbe basic theory of the swept wing was developed from consideration of the-flaw over a yawed airfoil of infinite span and has served as a very useW.guide for qualitative estimates of the benefits of wing sweep. The simple sweep theory does not, however

11、, taIoe account of many of thevariables in the flow over a swept wing of finite spm. Press- measuremsnts st high bhch nunibers correlated with measurements of forces and momants are imgortant to the extension of present swept-wing theory etnd to .a-beter erstanding of the flow phenomena involved. “

12、.- - / - . .- Ih this report, the results of such an investigation are presented for a wing having mderate sweepback. The testa were conducted in the Ames Moot pressure wimi tunnel at Mach Illmibers from 0.18 to 0.94 and a constant Reynolds number of 2,000,000. In the analysis of the data, le cp equ

13、als the local speed of sound) local pressure coefficient for incomgressible flow semispan wing area, square feet local air velocity, feet per second free-stream velocity, feet per second component of local velocity normal to the isobG, feet per second local speed of sound, feet per second speed of s

14、ound in free stream, feet per second local wing chord parallel to plane of symmtry, feet average wing chord parae1 to plane of symmetry, feet Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA RM AgKOl local static pressure, pounds per square foo

15、t free-stream static preBsure, pounds per square foot fiee-stream mc. pressure ( govo2) , po- per square foot - distance from leading edge along chord line, feet perpndiculaz distance from plan-of symnaetry “ along semispan, feet angle of attack, degrees uncorrected angle of attack, degrees “ . “ .

16、“ ratio of specific heat of air at cvtant pressure to specific heat of air at canstant volums (2 = 1.4) qle of twist with respect to root chord (positive for washin), degrees . angle of inclfnation of local velocity vector from free-stream direction, dedes - - 7- - coefficient of viscosity of air, s

17、lugs per foot-second free“stream ma88 density of air, slugs per cubic foot local angle of sweep of isobars, degrees (See fig. 1. ) An attempt is made in this report to correlate the changes in local flow conditions on a wing having 37.25O sweep of the leading edge and pmmstry and at soma distance aw

18、ay, and these pofnts are connected by a line which is free from discontinuities or abrupt changes of curv-ature. For the purpose of wing the pressure data of this report, the critical flow condition will be assumed to exist when the component of local velocity normal to the isobar equals the local s

19、ped of sound. Equation (1) and the sweep of the isobars will be used to compute the local critical pressure coefficient corresponding to this critical flow condition. The free-stream PlIach number at which the critical flow condition is attained at tt specified point on the wing xi11 be denoted by t

20、he symbol s. Drag and Lift-Divergeme Mach Numbere In general, critical flow conditions do not occur sfmltaneously at all spanwise stations on a swept wing of finite span, and the effect of the growing region of supercritfcal flow on the lift and drag forces increases progressively with Mach mmiber.

21、The drag-divergence Mach rider will be defined in this report 88 that free-atream Mach auniber at which the rate of change of drag coef- f icient with Mach nupiber at a constant angle of attack equals 0.10. This def initfon is advantageous in that the draplivergence Mach number can be determined wit

22、h fair accuracy from plots of CD against .twl aix-stream turbulence or by exper- imental scatter in the data. For similar. reasons, the lWt4imrgence Mach n defined a6 the point on the airfoil section at Khich the surface is tesgent to the direction of the undis- turbed air stream). With further incr

23、ease in the free-stream Mach nufber, the surface pressures ahead of the crest tended to increase while those to the rear continued to decrease, the latter as a result of rearward growth of the local region of sllpersonlc flow. These an unswept airfoil, it appears that the attainmnt of sonic velocity

24、 at the airfoil crest presages the rapid drag increase with further increase In the free-stream bkch lllzzaber. - pressure change6 entailed an increase in the presmre drag and, thus, for Although the analysis of the flow over a swept wing of finite span involves mre factors than does that for as uns

25、wept airfofl, it is reasonable to exgect the crest concept to be of value in correlating the pressure changes with the drag increase at high Mach numbers. The crest line will be defined a6 the locus of points on the wing at which the surface is tangent to the direction of the undisturbed a9r stream.

26、 The crest-line location has been noted on the pressure plots for the upper range of Wch nwibers. Local Mach N coordinates of sectim parallel to the free-tream direction are presented in table 11. The model, which had a semfsmsf.5 feet., was constructed of lami- nated mahogany secured to a steel spa

27、r. Pressure orifices were installed at five spanwise stations on the wtng and distributed A.m. the leading edge to the 8-e.rcent-chord points. Additianal. orificae were installed at 40 percent of the chord at intervals of about 4. inches from the root to the tip of the wing. A aketch of the plan for

28、m of the modei showing pertinent dimensions and the location of pressure orifices is shown in figure 4. A photograph of the model installation is presented in figure 5. The semispan model was mounted vertically in the wfnd tunnel with the floor of the tunnel serving as a reflection plane. The turnta

29、ble upon which the model ms“m6unted was directly connected to the force-measuring apparatus. Pressures were evaluated from photographic record6 of - multip1e-t- manometera. r. . Static 1oad.tests were conducted in order to furnish an indicatfon of the effects of the elastic properties of the model o

30、n the test results. The model was clamped in.a horizontal position and loaded with lead shot as illustrated in figure 6 The load was proportioned both spanwise and chordwise to simlate the aerodynamic load on the model, for two specific test conditions, aa determined from pressure-distribution masur

31、elents on the w-ing. Templates, were utilized to insure an accurate representation of the load. Deflections at .the leading ad the trailing edges at five spanwise stations were Illeasured with EL height gage. It was established that-for duplicated loadings the twist msasurements could be repeated wi

32、thin 10 percent.- figure 6, the upper photograph shows the model loaded to produce the deflections occurring at a corresponding to a Mach number of 0 .go at the same - Reynolds nmiber As indicated from the lift data presented in figure 8, the Mach nuniber for lift divergence ms 0.88 at an -le of att

33、ack of Oo asd decreased to 0.84 at an me of attack of 6 . The-liftcurve slope, shown in figure 10, increased with increasing Mach nuniber approximately to the libsch rider of lift divergence and decreased with further increase in Mach number. Also shown in figure 10 is the theoretical lift-curve slo

34、pe obtained from a chart of reference 8 lld corrected for compressi- bility b- the msthod of reference 9. The agreement between the theore+ ical values of lift-curve slope at zero lift coefficlent and the experS mental values is excellent up to the Mach nmiber for lfft divergence. . The pitchiwnt co

35、efficients for constant lift coefficients between 0 and 0.4 becam more negative with increasing Wch mer a8 shown Fn figure 8. As illmtrated in figure 10, the aerodynamic center at zero lift coefficient remained at about 28.5 percent of the mm aerodynamic chord in the range of Mach nuaibers from 0.18

36、 to 0.78 and then mwed aft with further increase in MEtch nmiber to 4.4 percent at a Mach a Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-t NACA RM AgKO1 ll nuniber of 0.94. With reference ta figure 7(b), it is to be noted that the location of the

37、aeroaynamic center was a function of the lift coef- ficient as lnferred from the nanlineerity of the pitchwmomnt curves, particularly at the higher Mach numbers. The effect of Mach n-r on the drag coefficient corresponding to canstant Etngles of attack is shown in figure 9. A small, nearly linear, i

38、ncrease in drag coefficient Hth increasing Wch nuniber preceded the abrupt increase in drag. The drag-divergence Mach nmhr for which (c8 presented fn figures 14 through 22 for a conatant Reynolds nuniber of 2,000,000. The figures are arranged in sequence to show the distribution of pressure at the M

39、ach nmibers and the angles of attack indicated in the following table: . Figure me of attack Mach nuniber 14 15 16 17 18 19 20 21 22 oo to 18 0.18 4O to 100 0.60 40 -10 00 10 0.18 to 0.94 20 3O 40 J All pressure data except those for a Mach nufber of.0.18 were obtained simltaneously with the force a

40、nd momnt data shown in figure 7. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-With reference to figures 14(d) and 14(e), it is noted that, at a Mach nuzdber of 0.18, stall occurred on the outer portion of the wing at an angle of attack between 14O

41、 and 160 and progessed toward the root, causing the utable trend of the pitching mmnt noted from figure 7. A similar stall characteristic may be observed in figure 15 for a Mach nuniber of Om distribUt.iOm for Mach numbers of 0.18 and 0 6. TY effect on section chord force.- To explore the effect of

42、campresaibility on pressure drag, so- of the pressure data were integrated to obtain section chord-force coeff icfents at Oo angle of attack for variaus Mach nmibers. The results must be considered of qualftative value only, since it was necessary to extrapolate the pressure data to 100 percent of t

43、he chord. In order to better indicate the varia- tion in chord force along the semispan, the section chora4orce coeffi- cients were weighted according to the local chord to obtsh the section chord-rforce par-ter Cc(C/Cav). The apamsiee distribution of section chord-force parmeter at several lhch num

44、bers is illwtrated in the upper portfon of figure 28. In the lower paxt of the figure, the section chord- force paramstem at ffve spanwise statiane are shown as functions of Mach nuniber . It is noted from figure 28 that the root seations of the wing had posttive pressure drag, while the tip section

45、s had negative pressure drag. I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. This result is Fn qualitative apeement with the theoretical predictim given in reference ll. With Fncreasfng Mach nlmiber, the region of positive pressure drag increase

46、d both in magnitude and spanwfse extent. The reason for this dlstribution of pressure drag is evident from the pressure.data of figure-29 in which the upper and the lower-surface pressures at three spanwise stations are compared for Mach riders of 0.18, 0.80, and 0.88 for the wing at Oo Etngle of at

47、tack. The crest llne on the upper surface of the wing, as previously defined, is at 40 percent of the chord for this angle of attack. Near the wing root, the surface pressures ahead of the crest were higher and behind the crest they were lower than at sections near the wing tip. The integrated effec

48、ts of these pressure differences weresuch as to cause the section chord force at the root to be higher than at the tip. With further reference to figure 28, it is noted that the effect of compressibility on the section chord-force parameter varied along the semispan. At shtions 0.15 b/2 and 0.31 b/2

49、, the section chord-force parameter at Oo angle of attack continually increased with increasing Mach nuniber. On the reminder of the winejthe section chord-force paramster decreased up to a Mach nuniber of about 0.80, thus tending to offset the increase occurring in the vicinity of the wing root. For Mach nuztibers above about 0.80, the section chord-force parameter increased wfth Mach nuniber at all ex