1、REPORT 1386INVESTIGATION OF THE DRAG OF VARIOUS AXIALLY SYMMETRIC NOSE SHAPES OF FINENESSRATIO 3 FOR MACH NUMBERS FROM 1.24 TO 7.4 _By _l)alcD _,. PF:ItKf,_, I,f.;LAXt)H. JORCIEN_I.;N, and,_Mo_ (L _oM_ri.:itSUMMARY/)rag m_a._umme,t._ har_ l)_,ll made at =ero a,gle q atlach:l.r a ._,_._ ;_ ,o.,v ,dml
2、._,_, 7l rood,4, in-r a ._erh_,q/hf.,i._,he,i-(all g b/uated cortex uere (t/.vo abtai.ed. 7tie .l(Ich tl#llft#ll atldl;eynohl,_ numDr ranges (_ the te._! wt.re 1.2_ to 7.uI atve a.llach nl,mb_r lilil(k. (l(f._) iitieikhl_ ;111(I I,(_hiiid II. J()lg_,IIs(,ll, 1!i,2, :lll(l t_l(, I(l“,(,:l) lli _.ligl
3、l_ll;ill_llilii _)21113 t)_, 7iIlll)ii (. 71)liillICl“ _ir_|I irJi(_ a., Stark, 19D2.52G597 G(I “,0 23 1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1232 REPORT t386 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSintegral equation as the basis for the
4、se derivations, theapparently uimecessary ,eL simplifying assumption ofzmo slope of the meridian at the base itas been inposed.This restriction is pointed out, by Ward in reference 5,wherein lle shows that his more genera| expression for wavedrag reduces to that obtained by yon I(firmfin for the spe
5、(ialcase of a )o(13 having zero slope at, (he)as(. In a lat(,rpaper (ref. 6) Ferrari developed _).minimum drag nose shapefor a given hnglh and diameter which has a finite slope oftle Ill)rid)an at, the )as(:. For the high supersonic Nlachnutnber raDge, minimum drag shapes based upon Newtonslaw of rc
6、sistamc have been derived l)y Eggers, Itcsnikoff,and Dennis (v(,f. 71). These shal)eS differ appreciably fromcomparable optimum shapes fi)v low supersonic Nla(hnumbers, although the theoretical optimum shapes i. bothinstances have blunt noses when the length is fixe(i a.d sharpnoses when the h,ngth
7、is allowed (o vary.Due (o the basic assumptions in (he derivation of th(,K_hrm:m integral eq_,ation, it may be expected that timshapes result ing fiom the use of this equal)on arc theoreticallyoptimum from a minimum drag standl)oin( only for largefineness ratios and low supm.sonic Math numbers. It)
8、con-trast, l!w shapes resulting from the Newtonian theory maybe expected to be optimum only tit high supe)sonic Mathmmfl)ers. Iowevcr, fi)r low fineness ralio shapes at moder-ate Math mmfl)ers, it is impossibh, to say q priori which of(h(: (heoretically opt immn shapes will have the lesser wavedrag,
9、 or in fact if (:iwr of Abe t twories is capldle of predictingthe east-(lrag protile. One of (he purposes of the presentinvestigation is, th(refore, 1o coral)are the experin,_n(aldrags of these t he(wet)tally opt)reran slmpcs and of ot her morecommon profih,s for an intermediate fitwness ratio over
10、awide Math m, mbev range. To this end n sezies of /inencssratio 3 models of these theoretically optimum shapes havebeen tested in the Math mHnber range from 1,24 to 3.67.SYMBOLSA model base tlrea, sq iu.(_, total drag (o(ti(ie)l(, ttal-(l!_agqA(“he fotedra_ (,o(qIici(,)tt bets(,() () It+is(: ttJt,a,
11、t(!al ,hn_ !)+!s2: ,it_gqA,)(%, for)drag cot,filch,at based on volume t() tI)c !_ l)ow(w,total drag I)_s(, drngq I2:“0._iv(, (z_ig(+w w_Ivc (ha_ (o(qihi(,nl, - - q:ld h(,misl)lw.(, (li.me(,v, it).1) mo(M bast. (li)mwt(.r.iK simib)vi(y /)ara)ne(,r, 1,)L mod(l hq)_(b in.11/tp_pptp_q1Rl“.VOLT0free-stre
12、am .Math lllllnb(Tpressure (oeflir wnying (he test section Nach number.For (he tests in (he supersonic free-flight tunnel (,he ntod(,lswet(, launched front a smooth-bore 2()mn-t gun, and w(,vesupl)or(,ed in the gun )y plastie sabots. Separation of (h(,model from the sabot was achieved by a muzzle co
13、nstri(tio)lwhich r(,tarded the sabot and allowed the model to provc(,lh) fiee flight throtl the test section of the wind t.)m(,I.A move JOf_ivq,n h,n_lh and I)_l_(,di:_met(,t.lh( measnr(,d t()lal (ha F _ll(1 Imse )r(,_sm_ drag. Ieca, useof tim Ol)er_tting (hara(hwisli(,s of tim Immel_, il was nol)os
14、sihlc Io nminlain a (onshlnl lllO(- llilllliill_ (Ifltxt-, in llw .me_ _qll)ersl)nic free ili_ht wiml tram.l,A_r- otf operohon J r i- / I J8hmgitu(limfl pressure distril)ution al each :I( in(r(,m_,nt iu(iremnfcr0ntial an_h, was ()l)l_ti_,(l. The r.,sullin_ )ressm_,(,lfli(i_lHS al (tuh lonFitudimfl s
15、llilimlw,r(, :_vlraF(d I.othtii_ I1., valu(,s lW,s_,nte(l.Free-flight wind tunnel.- Wilh nn air Ibm lhrough lhewi.d Immcl, M_h m_ml)_,rs varMl fr()m .2 to 4.9, (hpm_d-ing on the model hmnchi_g velo(4|y. lt_i_ (.n(tiliml isrcfl,rr_,d to as “air off.“ l%nohls nulnh.(,r vari(,.i lim,.rl_ith hlach mmfl)
16、(,r from 1.0(10 6 h)3.3(I() _, as shown i_lligme 3. Wilh air flow (shdlislu,d in lh,wi.d tum(,l,rcl(wr(d h) as “air on,“ the (oml)incd v(,lo(iti_,s of lh( modealul Na(h numl(,r 2 fir stream, wilh the rldu(cd Sl)(,.d ()ts.un(I in tin, h,s( _(,(qio h l)rovid(,d lesl, Ma(.h numbers from3,8 to 7.4. In l
17、ifts regi(m of testing, llevnohls WUllll)er Wash(hl al)l)roxim_llely at 4(10 l)v controlling h,sl-s(,(lionstatic l)r(,ssurc. In llddition, some mod(,ls win(, tested a!al)lW(_xim;_le .(._his mmd)(,s of 3:4 1iF al .Xlach mml)(,r 6.Drag eo,_,llhi(,n( was obtained by r(,(rding tl., lim(,-dislan(.c histo
18、ry of (he ttighl of tim mod_,l wih the aid of a(hr()nograph _u.l fern sha,(lov.graph slalim_s al 5-fool inter-vals along tin, test se(tion. From thes. (labs., d_c(hrdio.was (.Oml)uted qnd (,).v(,rh(l to drag (oeflieicnt. Thisrel)orL inch(h,s only lhc data from mod!s which ha(I maxi-mum observed angl
19、es of attack of less Ibm 3 , sin(,r over tlt(,cnglh of (m(h mo(M t(,._te(l was less (ha)/ 0.01 f(w allt(,sI Math numl)(ws. lh(_ tnwertahlty in lhe Nla(h numl)erit a given point in flu, st, l(_llJtl iS 0.0(I;).lh(+ Inagnitu(h“ of the er(+(nI and the tnaximtmt deviation“+vtIS -I p(qc(qICTHEORETICAl, C
20、ONSII)ERATIONSWAVE DRAGWith the excel)lion of som(_ of the very bluntest, lnot(,_st)t( a ssutnl)tion thal (h( pressure on the cotd(mlsmfa(e _outl l)e the ,+)_m(as on a )oit)ted (.one of 11)( Still(,SOl)C. lh,n(, the l)rtssur( (1,ag n was o)tait_(+er. An alqwoxinml( expression forwhich is ._utticienl
21、ly accurate for the drll_ e_;limales is,+_ tan -_L2 (L/D) _ (,/I)2 t:+,)FOREI)RAG:llhlt_ of the foreJh_t.t,_,have |)t,(,n (mLculut( I)5“ the a(hlit iunof the (_st.inu_te(l or th(,oreti(al way(, drag and the t:teorcti(aa In (lh_ alq+li(at i,)_ (_fthis nlcthod a firsl-on(hl sohll iq)tLis tle(t“:q:lt i
22、y c)t)t:tine :it 0 :trig(, of al ta(.k.2L3,1.6Q 1.2Ea;d4C-,4oP tel tube pressure ,rot, ti ut_.lrlcompressrble pcre_hz rl_* ,_r, _2- _.wtont(rl ff_nor,. “ “ _COS “ r_t? .4 ._ .R i.OD_stonce lrorn 1he nose, A“(c) Model 6p, D- 1.00l“_(; uzt ,: I. ( on cht(|ed.skin-friction drag. _ince the sMn-friction
23、drag for laminar-boundaryAa.yer flow c.t_tributes so liHle to the foredrag, theinclusion of the small effeels of body shape and compressi-bility on 0_e sMn-friction drag was not considered justified.Therefore, the lamimu-sMn-fri(tion drag coefficients were cal-culated by the lasius fo,-mula for fiat
24、-plate incompressibh,boundt,y-layer flow (ref. 13). For the cstinmtes of the skin-frier,ion drag for hubuhml-l)oundary-htyer tlow, the bodyshape effects were neglected, but the effect of compressililitvwas ewduated by means of lhe Jnterpolalion formula of ref-erence 14 which is based ll)Oll ttlI ext
25、en(h,d Frank| andVoishel amllysis,RESULTS AND DISCUSSIONIIEI_IiSPHERICALLY BLUNTED (:ONESPressure distributions.-The pressure-distribution datael)Lathed for m_dels 4p, 5p, aml 6t) at Nach numbersbct.ween 1.5 and 3.8 arc shown in figure 4. The data arereferred to the free-stream N_leh numlwr ahead of
26、 thenormal shock wave at. the nose of ea(h model. Althoughthese Nlach numbers were approximately the same for eachmodel, they differed slightly bectutse of the differences inpositions of the models within the test s,etion. For eachof the models, the pressure coefficient at the nose agreeswilh lhe pi
27、lot-l)rCssure l_hpnieally hhmtvqcim(, ullllh.l 5_ at _.arJlnl,_ 3.a(:h ilUlllhers.(d) M ;LO(;(e) M 3.1;7I:iRure (k ( :om.huh,d.(See tig,. 4.1 AI firs! gh_me il mighl _q)l)t4tr Ihat this waxu_ouhl w _ssmi_lled with a regioll .t St,lmVtlted lmv on1 theIH,misl)hericnl lip, with sul)sequenl ne_ttl_l(.hn
28、lvult a(,i,on_-imnivd hy n sl.wl,: wnve. lowever. Ihe sehlimell picluressh.w no pvidvl.e of tt.w Selmrulion. Additiomdl3. il is_l)l)eUenl from the sehlim(,n pictur(,s tirol this shl_, wa_edm,s m_! extmul frmn the outer thin down to thi, bodysuzl_ce but a,pl)p_lr_ lo lw dittuse_l ne._r lira _uuf_tcv.
29、 lh_,_eohservation_ h_td t_, lhe speeuhttiol_ tirol lhe migin ,f thewave musl he _ssocialed with llw Ir_msonic or mix.,t t3l)eof lhnv whivh ocm_rs in the vicinily of the nose of the hodsTIw me,_lmnism hv _hich the compression wave is Imm_,dI1l_13 _:,( IltllCh 111( S_llllp lls lhtll _lisvuss,4t in ze
30、lmm_,._, 1“, forIhe lv.o-dinwnsiomd Ibm“ nruund n shnrlnmv, ed douhh-wedVe_irf(filst4lion,xithdetnchl4l hnw wn;l,. It isl,l,lh,ve(Illmt tlw xv_x-_, z(,sults from u conh.scenc_f ,.x,4_.: COmlWe_-sim_ v_ux*p;relle,led loln th(, holly s,url_tcp. (lhp _.xist_,ii_._,c,f (hv COml)rCssi,m_ region is cmlirm
31、(,_l t:,3 flu l)nvsul( ,-distribution daln.) Th,se x_nxes uptmrm_tly origilmlv aseXlmnsi_.nw_tv_,_lrmn Ow b.d; sm.l,w.,dmcnslzenvnfromlhIsmilepoinl. A.simlicnle_linllwsl.a,lvh,llwseeXlmIi(.nwnves whMl Irnvel nhmv clmr:wlerisliclin_,sare r_,lh.cl.,dfrom Ih(, s.nic line ,_n(l the bow ;nv(, as COml)r(,
32、s, si(m x,.-_tv(,swhich n.r, in turn zetheted from Ihe body surf_im,. TI.,r(,lh4ti(m ,_1 lilesevqtcelolsfrom lh(b()(v surfn(.vI)(qtllS ill:4ll(h I1 Illllllll(l llll lh( (oaes(p 1o fOllll II ,_l()(l _. tAI|V(,The d(l)(nd(,lwv.f this l)h(,umm,.nmn.n ln)lh the fi(4,-slr(,nln31n(hnun_l)(,r:imlth(im.lilm
33、lioul,)fthe l)odvsurfacejust dt)xvltslre._ul_ (_( lhp l)Oml of tnngmwy of the h(,mi-,idwreProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-INVESTIGATION OF THE I)H, AG OF VAItIfIUS AXIAI.I/t“ SYMMETRIC NOSE SIfAPES OF FINENESS RAIO 3 239ores/ _ _ - xp
34、onsion I_OCh /I t -_ -Compression_ lir, esI/with the afterbody is demonstrated by tile followi.g obser-vnii(ms. For Ihe henlispheri(.ally I_hmied (,(rues, n(,ilherlht, sho(k wave nov lhe region of i(X)lllpleSSlOII O11 thOhodv surfa(e wits found for Math mmd)ers ahovt, :_.06.The (isal)lWaVan(t, of th
35、is shock wave and region of com-I)rtssim_ results from lh( combiualioll of Ihe movcmt,nt oflilt bow wave close| to tilt, body sm fneo and the small up-stream movt, m(,nt of Ihi soni(, poiul with increasino MnehIlUlUb(q. rht,st_ (,hangcs rcduce the extent t)f the ntixedIh)w region so Ilmt ft)r Maeh m
36、uubt,vs alloy(, apprt_ximahqy3 nu)sl (If llte eOml)re,.;stm wavelets refletied from theso.it line and bow way(, ure incident upon lh0 body surfat.ein Ih, t,xpansimi region between tilt, sonic )oinl and thepoint of tltll_tiltt3_ of tht! hemisphere with the afterbody andh(,nce ave (_alw(qed. The impor
37、tance of thc inclination ofthe t)t.ly surfltcc in tlw region of th(, reflections is indicatedI)y the fa,.t thai, “tllhough tlu, 1)rt,ssure-distribution dahlfor m,l,h.l 6p (fig. 4(9) sh,w thnI al the lowest l(,st %hwhuumt)er IJ,we oxisis _ reffion of recompzession just dow.-slve_nl from lhe juncture
38、of the h,misphere and cylimlri(.nafl_wb.(ly, the tmlg.Jlutle of the reeompt(ssion is very smallltil(I does not r(!sull in a st,eond.try shock wiwe thuI elln bed(,tech.(I i. the sehliere, l)ictures.Drag. The vnrialiot/ of drag chmting fay a. fineness ratio 8 body results in anincrement in wave drag c
39、oefIicienl of (1.(152,corrcsl)ondinff|0 111 ill(lOllSP Jlt l)leS._llll dlllg of more than 300 pereenl.The eslimaled xvavc dril_ roMl%ienls for lhc d/l)-0.3(IFlb:_74“ r T 1%o._b1,_:,.17,Io_ItE 1-t 8,3.14xl0e k_j_,_oJ2 r-r_-,Wd :i l lJ-_i-q-x:_.,_,o:_.+20 ._ .2 .3 4 .5d_luntress, _r3Cri :rl,mto Fcredr
40、agc_ Wove drag Drew,-, d_srr rn,ael,Estlm,3_e- Wove drug-Foredrag eshmoted _ave draq+ R!UStU5 ominor skin fricf_onF,Nged symbolsd(m,: tL, ,EP - I.I 7x i( ! : .-0 I 2 .5 .4 5_3 u,f_lnetS, ,_Fi(:c_aE 8.-VariaUon of foredrag coefficient with bhmtness forLhemisphere-cone series, con_tanl -/_:3.Provided
41、by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-INVESTIGATIONOFTHEDRAGOFVARIOUSAXIALLYSYMMETRICNOSE SHAPES OF FINENESS RATIO 3 1241aud 0.50 models at, Math munbers of 3.06 and 1.96 are invery good agreement with the wave drag determined fromthe pressure distr
42、ibution models (see fig. S). Similarly theagreement between tit( experimental foredrag and the esti-nmted foredrag based upon tho estinmtod wave drag plushmfinar imompressible skin-fri(_lion drag is very good forMath numbers 1.96, 3.06, and 3.67. For the tests at theseNla(,h mmd)ers the s(hlieren l)
43、ietures taken during lilt, testsitldieated that the boundary layer was completely lnnlinarover each of the models. An int(,restil_g effect of 1)ody shapeupon boundary-layer transition is indicated by the resultsof the tests at 5l- 1.44 and 1.24. Fronl the sehlieren pictures_md the foredrag data it w
44、as evident, that lurbulent bound-ary-layer flow existo( on part of the conical afterbodies oflho diD=0.30 and diD=0.50 bodies for the higher R(,ynoIdsmlmber at .I=-:1.44 and 1.24. In contrast, the t)oun(ar3-b_)er fh)w w_ls laminar oww the entire surf_we of the conefor Ihe identical test (.onditions.
45、 I. is t)eliov(,d lhat thedittvlOnee betwoeu the results for the con( and th(_ bhmtbodies results largely from the (qle(_ts of the differen(_es inI_o(ly pressure distributions. For the (one the pressure iscollstallt along the Slllfaee all( tlereore neutral insofar itsits effect on the boundary-layer
46、 flow is earn:elnod. For |)oththe bhmt l)odii,s at the low Maeh mmlbers, the pressuregradient in the streamwise direction is positive just down-stroanl from lhe point of tangeney of the nose with theconical section (see fig. 4) and hence reads to thiuken theboutl(lary lay_w and promote t ransitiol_.
47、 Both the sehlierenpictures and the force n|easurements indicate that for thehigh Reynohls numl)ers the boundary layer is tmbulent overa lnu(h greater portion of the surfaci; of the blunter of thetwo bodies. This result is in agreement with what might be(,xpceled on the basis of the differences in t
48、he pressure distri-Imtions for the two models. Although the adverse gradientsfro“ both the diD=0.30 and diD=0.50 models start at/,ssen-tially the same longitudinal station along the maiMs, andinitially are of apl)roxinlat.ely equal magnit,ude, the adversegradient for the t)hmter nip(M, diD=0.50, extends overmost (if the conical
