1、,.- -4I-1.The assumption is made that the component of mamentum normal to the sur-face is lost and the tangential ccmponent is unchanged. This yields apressure coefficientwhich depends only on the local slope. This simpleanalysis neglects the centrifugal forces due to body curvature. Equationswhich
2、take into account the centrifugal forces were presented by Busemann. ._ . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(reference 3) and were later rederived in reference 6. It has beensuggestedthat either the Newtonian impact theory alone or with
3、 centrifugalforces consideredmight be applied at finite Mach nmibers with reasonableaccuracywhen the shock wave lies close to the body. Newtonian theorydoes not predict the variation of pressure coefficientwith Mach numberbut simply predicts the lhiting value for verj high Mach number.PROCEDURE AND
4、SCOPEThe investigation i.ncled three body shapes, the cone, the tsngentogive,l and a modified nose of an optimum body (fig. 1). The forepartof a Haack optimum closed body defined byr/r- = -(%921”4was used as modified by the addition of a cone tangent at x/1 = 0.05.The cone was used to replace the bl
5、unt nose h order to make it possibleto apply the theories being investigated. For convenience,this modifiedbody will be referred to as the optimum body in this report.The theories were applied to various combinations of fineness ratioandkch number. The following tables list the conditions investigat
6、edfor each theory:Linearized and Second-OrderTheories.- Cones OgivesZ/d es Z/d es 2/d 5.715 o 1.958 2.836 100 5.0 6 3.05.422 3 1.5?: 1.866 150 1.38.492 2.0 ; ;:3;10.146 3.0 2.8092.836 100 1.5 3.634 : 2.03.0 1.374 200 1.34.0 1.72.02.U31A tangent ogive is a pointed convex surface of revolution generat
7、edbyrotation of a circular arc, the tangent at the maximum radius beingpsrallel to the axis of symmetry.c- _ . _ _ Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA TN 2764Tangent-ConeMethod (Total-headratio applied each way)Itimum bodies Ogives
8、 IConical-shoOptimum bodiesc-ExpansionTheoryOgivesIZ/d3612236 Tk Z/d1.5 942 1.52 3366Newtonian TheoryConesZ/d5.7152.836es %50 3.0;:8.49210.14610 1.53.04.05.05.422Z/d 68 L.866 150 1.32.03.03.634L374 20 1.51.72.02.443MO9.06.03.06.012. o3.06.0Ogives-Z/d3612241.52%;:26.03.06.06.02:12. oThe accuracy of t
9、he methods was determinedby comp=ing both thenressure distribution and the integratedpressure drag obtained by thechosen methods with those obtained from standard solutions. Standardvalues or conee were obtained from tables of solutions to the theory ofTaylor and Maccol-1(for example, reference 3).
10、Solutions calcated byuse of the method of characteristicswhich took into account the variation .of entropy in the flow field were used as standards for curved bodies.Some of the characteristic solutions used were those presented reference 7 or were obtained from the cross plots in that reference._.
11、- _ . -_Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACA TN 2764 7The validity of using pressure distributions from characteristic solu-tions as standardshas been establishedby the close correlation of someavailable expertientalpressure data wit
12、h pressure distributions deter-mined by the method of characteristics. The error in integrating thecharacteristic solutionsto obtain pressure drag is esthated to beabout 2 percent.In applying the linearized and second-ordertheories, the appronatetangency condition and.the exact isentropic equatiorrf
13、or convertingvelocity to pressure were used, as was done in reference 2. In thecalculationsusing conical-shock-expansiontheory the vertex solutionwasobtained from reference 3 rather than from the appro-te equations ofreference 4. Both the simple Newtonian impact forces givingandthe = 2 Sinethe expre
14、ssion including centrifugal forces were used in calculatingpressure distributions over the bodies investigated.RESULTS AND DISCUSSIONThe results of this investigationsre correlated on the basis of thehypersonic similarityparameter, the ratio of free-streamMach number tobody fineness ratio. The hyper
15、sonic similarityrule which was derived forslender bodies in hypersonic flow (reference8) has been shuwn to holdover a wide range of Mach nurribersand fineness ratios, but is not validfor low Mach nunibers(.?0.- -. -Provided by IHSNot for ResaleNo reproduction or networking permitted without license
16、from IHS-,-,-MACATN 27& 19Ermrin dmgMethod of chomcterr”ti”hso Li7eorized tiemy - 14% Second-oder theay oD.+. NNv- .-/ L.- 0 Zo 40 60 80 /(wLongitudinal cootiinote, percent hngfhFigure 5. Gompurison of pressun? dishibtiions determined byvarious methods on a tangent ogive at K,B 0.936, I/d* 3,&u 2.80
17、9.-. . .- - . ._. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Error in&gMethod of chan?cteritiiTangentixme meb?odCOl HA%) +1 2 %Tangen#conemethod(vezfexH/H.) - ICawbal-sbockexpansim tieory - 9Wwtonian theory -208y .* .20 40 60 80 /00Longifuuinol
18、cooroinute, percent IengfhFigure 6. Gompurison of pressure o%tvhdions determined by vuriousmethods on u tingenf ogive at K= L I/ds 3, M. z 3._. . - -. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA ITT27+ 21.8o14,Error in dmgMethodof chorvcter
19、isticsLirized thecny -12%Second-amter theoq -4Tangenf-mnerpettvd (local H& +1 2Tongent-conemethd (vertexHrnO)- IConical-shock-expansiontieocv -29120 40I t60 80 /00Longitudinal cootdinal?, percent lengthfigure Z Gomporison of pressure disfribufion determined byvarious methods ODo fungenf ogive ut KS
20、1, I/d= 2, A 2._. .- . - - -.- .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-22 mm m 27kGrorin dugAL-ihodof cbonrcterkiim- - Tangenf.cone mew coIH/ ) +12 %-A- Tangent-conemetlvd (wxIY&) -12. . Coni&-sho&xwnsion theay -12- - Newtonian /beefy -/ 77
21、t8,1t8-/=5=20 40 60 80 /00Longituohl coordinate, percent lengthFigure 8. Comparison of pnwsum distributionsby different methods on u modified optimumK=j, /d= 3, =3.determinedbody of. . ._a_ ._Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,IIIIJi,.
22、“YQ. .“i(.Error in dragMethod of characteristicsTangentione methd (1OCOI H/H. ) + 8%Tangent-cone n%?tiod (vertex W& ) -39Conicol- shock-expansion theory +/IWwfonian theory -6Newtonian phs centrifugal forces1 I I20 80 I&wLongifud?”wordh fe, pt%enf A-e 9 Comkt?n of pressure dmWbu?%ns defm?lned byd%?i%
23、wf metiods on a Amgent ogk? of KS 2, Ma 3, MO = 6,-5”P“Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.8.6*.4.2o 20 40 60 80Longitudinal coordinate, rcent lengthFigure 0.- Ctmporison of pressure oistributlons determined byvurious methods on u hngent
24、 ogive of K= 2, I/d= L5, MO=3./00. . . . - . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-IIIIIII(III)S)hvlaY/ty poramete KFigure Il. Accurucy of various uppvximate methods in inhgmted pressure drag.GProvided by IHSNot for ResaleNo reproduction o
25、r networking permitted without license from IHS-,-,-.26.08, Qa.06.04.0200 Seoond- ordertheorya75 Conibol-shock-expansiontheoryx Mefhodof churuckrisfics.1 3 4 5I6Much number, MORgure /2.-Exumple of hterpohto for drug inefficienton tungenf ogive, 14=3.MU.WW .84-52 - 1(WJ - - . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
