NASA NACA-TR-1050-1951 Formulas for the supersonic loading lift and drag of flat swept-back wings with leading edges behind the Mach lines《在马赫线后带有前缘的平坦后掠机翼超音速荷载 升力和阻力的公式》.pdf
《NASA NACA-TR-1050-1951 Formulas for the supersonic loading lift and drag of flat swept-back wings with leading edges behind the Mach lines《在马赫线后带有前缘的平坦后掠机翼超音速荷载 升力和阻力的公式》.pdf》由会员分享,可在线阅读,更多相关《NASA NACA-TR-1050-1951 Formulas for the supersonic loading lift and drag of flat swept-back wings with leading edges behind the Mach lines《在马赫线后带有前缘的平坦后掠机翼超音速荷载 升力和阻力的公式》.pdf(41页珍藏版)》请在麦多课文档分享上搜索。
1、REPORT 1050commssuMMmY -INTRODUCTION-_-, _IMETHOD OF THE SUPERPOSITION OF CONICALFLOWS_-_-_-_-_-_-M lines from the ledns- md trefM-edgew-= md m tiePS-.and (d). The case (fig. 1 (a) in vrhich,the Mach numberand aspect ratio are so low that interaction takes place betmeen the tip flow fields will not
2、be treated. An approxi- mate solution to this probkn may be found in referenoe 3. -Whaa a wing with a subsonic leading edge is to be studied,considerable simplification of the probkm may be achieved “-by making” use of the solutions, aaiIable in refermw 41147Provided by IHSNot for ResaleNo reproduct
3、ion or networking permitted without license from IHS-,-,-.1148 REPORT 1050-NAiMONAL ADVISORYCOMMITTEEFOR .4EROItAW1CSand other sources, for the infinite triangular wing.1 Fromthese solutions the aerodynamic characteristics of a varietyof swept-back plan forms can be calculated by the use ofthe super
4、position principle of linearized theory to cancelany lift,beyond the.specified wing boundaries. Two methodsof cmcellat ion have been developed:”on-e,presented in refer-ence 5, uses supersonic doublets and is general enough toapply to curved boundaries; the other, originally due toBusemann (reference
5、 6), canceIs by means of the super-position of conical flow fields. In the present report theccnical-ffow method is used, since it appeaxs to offer someadvantages for the straight-sided plan forms underconsicleration,particularly in determining the integrated lift.The material prwented in this repor
6、t is largely drawnfrom references 7, 8, and 9, with some simplifications sug-gested by practical experience. In particular, the formulasfor the total lift have been reworked tQ substitute, withno increase in computational labor, a combined iprimary”and “secondary” correction for each .of the tprimar
7、y” cor-rections in reference 7. Also, the formulas containing ellipticintegrals have beeu rewritten to tie full advantage ofavailable tables. As in the preceding papers, the final for-mulas W be derived for unyawed wings with tips parallelto the stream, but the application of the general methodand t
8、he basic SOIUtione to other plan forms and problemswill be appnrent. Some numerical examples will be includedin order to show the magnitude of the effects discussed andto summarize the. method. .A table summarizing theformulas is also included.IMETHOD OF THE SUPERPOSITION OF CONICALFLows _A couical
9、flow field is oue in which the velocity componentsu, ,and win heStreamjcro-gt.ramand vertic directions,respect.ively, are constant in magnitude along any ray fromthe foremost point, or apex, of the field. Such flows arefound as solutions of the linearized potential equation forsup) s and any point x
10、,y has the conical coordinate(4)x-m/9sin the field with apex at 8.Other symbols referring to”angular locations -ml -1 0 f m“a m9kwldM the second side is-the extension of a ray from apmO of the wing. Between the leading edge (a=m) and theleading-edge filach line (a= 1), no division of the field isnec
11、e=ary since the lift density is constant in that region,If a sector with apex at A and angle tan- is used to cancelthis unifomn lift, then the remaining superposed fields mustbe used where aa, u=O(5) When t=a 1, u=u=w=O.The solution of the e.upelsonicflow equation satisfying theabove boundary condit
12、ions has been derived in refrrencc 4.3In”the W lane, tlestreamwise component of the velocity isu= kr,p. : cos- , a+t+2af -.t=a (10The sigi refer to the upper and lower surfaces, respectivcly.In fimi.re 5, the eswmtial features of the solution arcshown. - At the top is a detail view of the wing sido
13、cdgo andshows the boundary conditions. In tho center is a typicalplot of the argument of the inywee cosine in equation (10),against ta. mere this quantity is less thtin 1 (i. e.,Otz and t.O)aLeoding-edge con-ecfion - YvOblique troiling-edge correc?im -Symme fric fraifing-edge comecffon - J(a)20 40 6
14、0 80 100Disfance from leading edge, percenf chod(a%tion A-A f3u m-O.4; ?ni.0,6,.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-FORBJITAS FOR THE f31WERS0.NICLOADIXGOF FLAT SWEPT-BACKTVES-G-sWITH LEADIXG EDGES BEHISD MACHLINES 1:63 .=B# Findfoadinq -
15、fLeading-edge correction - Y%ymmefric fraiing-edge correc%-r -1 I 1 I 120 40 “80 80 100Disfunce fmm Ieudinq edie. percenf chord(a) Seetfm A-A BIIjcFO.60i5432B%Ic-I-2- Corecfion forKuf fa condition (estimo+ed)fA - Triongulor-winq loading/Finulfoodng -“Leading-edge correchim -, OMique fraihnq-edqe cwr
16、eciion-2 .Symmefric fraiiing-edge correcfhn -”r r I 1 20 40 80 m 1-00 .Disf ante from leading edge, percenf chord .(b)*dIon B-B Pra-OJWFICmEE IS.Lond dfstribntfons c.ahdated by the aInk8LEowK zm?thd for two streemwfse sm!thns of m mrknpered Z m-O.L .11, fsdhg aIong a mowed inverse cosine curve from
17、thedue of the error at the trailing edge to ZWO, w-M zerosIope, at the boundary of the region afEected. Vilth tbieboundary (the llach line from the point x2,y2), it is possibleto draw a. satisfactory estimate (dotted curve) of the correc-tion needixl to brirg the pressure once more to zero at thetra
18、iling edge.The untapered wing -with the same sweep (m=O.4) rehit.iveto the Xheh lines is show in iigure 18, with the load dis-tributions cslcukted at the same stations.Four section lift distributions are pre;ented (fig. 19 for?n=o.% Ak =0.15 only the rear 60 percent is influencedcoby the subsonic tr
19、ailing edge. The reflection of this infhenceat- the leadiug edge alters the pressure over the rear 40 per-cent of the sectiom At section B-B, the leading- andtrailing-edge interaction afEecta the entire section. A furtherreflection of this effect at the trailing edge must be estimated.At section C!-
20、C the iufhmnce of cancellation of the leading-edge correction at the trailg edge extends over the -ivholeof the chord and any estimate of its magnitude Todd beneceasariIy arbitrary. AIao, B cond pair of reflectionsmust be taken into account. The final pressure dktributionhas therefore been dravrn as
21、 a band within which the truecurve may be shown to lie. Its height is the error introducedat the trailing edge by the firstt leading-edge correction,except very near the leading edge,.where an infinite negative “-correction is ?mowu to be introduced by the second leaSymme +ricfroiling-edge, .a-corre
22、cfion -”) 1 1 I 1 !20 ongr- wing 1000ingF“Leading-edge corm iion -ObJique +iling-edge correction-.b) 1 I 1 I t20 40 60 80 /00Llkfance from” leading edge, percen f chord/ -Trianguior - wing 100ding!.Symmetric froifing-eoge,d) corfj-k”/ 1 II 120 I. .40 60 80 /00=.tonce from Ieocfingedge, percen t“”cho
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- NASANACATR10501951FORMULASFORTHESUPERSONICLOADINGLIFTANDDRAGOFFLATSWEPTBACKWINGSWITHLEADINGEDGESBEHINDTHEMACHLINES
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