1、i,1! ij “_iiI /I/.I1, zk2OSTAi “ “ itt /t_ “7 _ v “t TTHE AE_O,_ NAMIC _“_F(,RC_,a: C_:_ .: AIRSHIP tT_TT.t.q : By ,5IAX _L _.IUNKNoti.ce- , .i /( , .q: _hla _ -_ v , be Protected by Co:r,rL:h1“,L,. , : . ) - L,.“._._OD_ED BY. NATIONAL TECHNICAL .“ INFORMATION SERVICE :.I.,_ OPI_RTtANT Of COMMERCE_R
2、IN_ILD, VA, 22161= . ., (:; WASItINGTON_OYERb:MEN_“ PRI.NTII_G OIlIC_;192_1ik .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NOTICETHIS DOCUMENT HAS BEEN REPRODUCEDFROM THE BEST COPY FURNISHED US BYTHE SPONSORING AGENCY. ALTHOUGH ITIS RECOGNIZED TH
3、AT CERTAIN PORTIONSARE ILLEGIBLE, IT IS BEING RELEASEDIN THE INTEREST OF MAKING AVAILABLEAS MUCH INFORMATION AS POSSIBLE.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“!REPORT No. 184TItE AERODYNAMIC FORCESAIRSHIP HULLSBy MAX M. MUNKNational Adviso
4、ry Committeefor Acrol, auticsON-“ :-TZ=-I:. L :-T“I ;T“-7 674_-2I-q Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-INDEX.I. (_E_I-IAL PICt)I_-HtrIES ,x)F .+%EILODY,_AMIC |“L(,I%V:4,Pe,ge.I. VclociLy I._,telittal 52 Air l,res,qure . 63. Khtetic enerl
5、=y aml it_omenlum . TILE At;ILODfNA.%IC :OIP, IHS ON :VlllLCllllP ULT,.,4.4. ,q(lal_hi. lilo(h_ri “. 95. I“,:ular p:lll . 12tl. ll._trilnith_i_ of lhc ,g.(,rod)i,.alilie Iorl,t_ . “ 1_7. (oiril_,ll._oli with :l model i_l . 5lIT. ,_(i_.IH PR.IICTIIAL (!ONCLUsIO.k.S. llelnctrk on the required ,_ize ,f
6、/he lhi,_ . 70. The iiir_hil_ in cinlllar It_hi . l,_i0. Aerod)iliiniiv lo!_ t,. c_ll ;ill aii._hll II)inl thioill_h gll._l)“ air 3Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ivAERONAUTICAL SYMI3OLS.1. FI_t_DAMENTAL AND DERIVED UNITS.iI/Length.Ti
7、me .Force Metric. English.Symbol.Unit. Symbol. UrAt. Symbol.ltmotor .second weight, of one kilogram .In,see.kg.foot (or mile) .eecond (or h_ur) .weight of one pound ft. (or w.i.).see.(orhr,).lb.Power. P kg.m/sec Sp ed m/ o hor. o o,vormi/l_r . M. P. If.Weight, W= m:z.Standard acceleration of gravity
8、,g = 0.S06m/sec? = 32.172 ft/scc2IVMass, m=-gDensity (mass per unit volume), pStandard density of dry air, 0.12-t7 (kg.-m.-see.) at 15.6C. and 760 ram. =0.00237 (lb.-ft.-see.)2. GENERAL SYMBOLS, ETC.Specific wcight, of “standard“ air, 1.223 kg/,n, z_- 0.07635 lb/ft. *Momcnt of inc:tia, roT:-_ (indlc
9、ato axi: of theradius of gyration, 76 by proper sub_crlpg.Area, S; wing area, Sw, ctc.Gap, GSpan, _; chord length, c.Aspect ratio = b/cDistance flom c. g. to _,Icvator dnge,f.Coeflicicnt of visco_ityN_:, _3. AERODYNAMICAL SYMIOI,g.True airspeed, VDynamic (or impact) pressure, q=2 pLLift, L; absolute
10、 coeiIicient_ CL=_:_$_Drag, D; absolute coefficient C,;_, D-Cross-wind force, C; al)solut,o eocfliclentCResultant force, R(Note that thcsn coefficients are twicelargo as the old cocfllcients L, De.)_sDihedral angle, */nolds Numbcr=p-v t, where l is ,: linear di-P.e)r“m.ension.e. g., for a model airf
11、oil 3 in. chord, 100 a:ifhr.,normal prcssure,0C: 255,000 and at 15.t _C,230,000 ;or for a mo,lcl of I0 cm. chord, 40 m/see.,cerrc_pondiug r;umbers aro 299,000 and270,000.Ccntcr of pressure ocmcicnt (ratio of distancoof C. P. from leading edge to chord length),v,.Angle of setting of wings (relative t
12、o thrust Angle of stabilizer setting with reference toline), i, lowcr wing. (it-/,) =;7Angle of stabilizer setting with reference to Angle of attack, athrust li=c it Angle of dowwwasl,PrecedingpageblankProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
13、REPORT No, 184.TIlE AERODYNAMIC FORCLS ON AIRSIIIP HULLS.By ,Max ,lXl_.,-_,SUMMARi.This report describes the new method for making eomputati,m_ ire connection _:ith tilestudy of rigid airships, which w_s used in the investigation of Navys ZR-I by the specialsubeommit, tce ,)f the Yati(m_ ._,(Ivisory
14、 Commil, tee for Aeronautics appa_-tcd for thi._ purpose.It presents the general the,)ry of (,lle Mz forces on aiship hulls of (he t.l_e mentiom, d, and a:iattempt has been made it) (levelop the results from the very fundamcntc;_ o.r mceh_nie_, will:-out reference to some of lh(, )node)i highly deve
15、loped concepti()ns, _Gich may ),t yet bethoroughly know) () a reuler uninitiated into modern nezodynmnics, nat which m_y perhapsfor all times :em_in restrie(.ed I,o a small nuniber of sp(:einlists.I. GENERAl, I)ROPERTIES OF AERODYNAMIC FLOWS|1. Th(, studonl ,.)f the motion of solids in air will find
16、 advantage h fitst neglecting theviscosity )rod compressibility of the latter. The influence of these tw., properties of air arcbetter stu,lied )fter the stmlont has become thoroughly familiar with tee simplified pr._tlem.The results are then t,() be e()rreeted and modified; but in most cases the;x
17、remain sut,._tantiallyv,llid.Accordingly I l)ezin with the di._eussion of the _eneral properties of aerodynamic flowsproduced by the motion of one or more solid hudies within a perfect C“.fid otherwise at rest.In order to be ahle to apply the genera| laws of mechanics to fluid motim I.suppose th,.,
18、air tobe divided into partiele,_ so small that the differences of velocity at diffe_dlt points of one par-ticle can he neglected. This is always possible, as sudden ehanges of velocity do not nceurin actual flows nor in the kiml of llows dealt with at present. The term “flow“ denotes theentire distr
19、ibution of velc, eity in erich case.With aClodynamie th)v,_ external volume forces (that is, farces uniMmly distrihutcd o_erthe. volume) do m,t occur. The only farce of this character which could t,e supposed to influ-ence the flow is gravity. 11 is neutralized by the decrease of prcs,.ure _:i:h inc
20、reasing altitude,_n,I both gravity and pressure decrease c,qn 1,e omitted without iT_ju_y to the. rcsnl,. Thisdoes not nefor 1o aerostatic forces sueli ns t l_e buoyancy of an airship, b_;t. the aelost_tio forcesare not a subject of this paper.The only f()rce satin V O)l a particle is therefore the
21、resultant, of th, f,_r_.es ex_,rted by the)i, li_cent partMes. .ks the, fluid is supposed t, be nortviscous, it Ca:l n:)t )lan.sure, orrather tlle nc_+ltive gnldient. ._.nyslendy di,_t,il,u/i,m of pressurehns a =radirnt. at o._r.b p,ir_t,but. it“ a distrib,ti,n .i“ force., t-, of _,tll,u“ vectors) i
22、s given, it, is _-t. aluays possible to asst,1,a quantity such ih,t thc f()re(,s are it.,; gradient.We dl:nt,tc the (lc,l.-il.v ,f air 1)y n: that is, the nt:_ss per ttnit vq)itmt(, a.-_.umt,d t,) 1)c t,n-staut, dr re;iv dem,l, ihc small v,lmn, of ;i pavtieh, t,f .dr. Tht, m;_:s ,f thi: p,rllch, i_
23、thoupdr. The t. ,if“ tile v,h,.ity I“ ,ff till-; littrticle puallel t,+ .r,y, lind z may lie den,ted19by it, 1, ,givr the c.mp-nents fi.“the t_wthcr,irecti_nr-.The_e integr_Aswill hltel“ be trlln-:fi,rmed t, nlakr t.llrnl lit for il(.tual ct,n_put+ition of tile energy i/rid theliionl elll tim.Ii is
24、stnlt, liine._, iiseful I_ consider very largo forrt, s, lll_.-;:l!/es, ,i“ vllhlnit, ftd(cs actili 7duriil 7 Ii time thnlcnt dt ;_, Ihat their I)illdutt. ,iy this lilii( ehitiOll lie,ll+-, lifo calh, “ilupiilive.“ ._iiltillliel by the tinie eh.n,ienl tiler illO eillled inllllllsos: ,_rtlensit.y ,t
25、inlllul,_e liOi unil lirCil or tlnit, vohirno iI,-. tho eli.,.;(,lililV lr_2. ilh,r thesr 7Ollel/ll d0iiniion: illld exI)ilinlltitnl. % I prumed t_ hloproduvcd 1,_ the iu.tit,n t,f bt, its _ll;_co cu- dUlin_ li very sh_,ittime inlorval ,1; _,nl.v, dUlirig wllic,i l.ho ,?hangos of the l)il(:c c(llllJ
26、/+lit_t,s, id“ thr llnrlich.,: Cllll lit;neffh,vlecilie_ riP( Iillilt. The f, lrres i:iid plt, sSllle-;, ,veve.l. are .:npi),:od t:j,-, h _l thtat dlliirig_, l,lir short int.orviil (inil.r vllanTes ill v,!i,l),nents n or potential llows gives a potential lowagain, it is thus dem,mslrated thai all ae
27、rodynnmic flows are p(ttenti,d flows.It. can huth(.r lie sh,)wn that, for euch m(,li(m (if the he,lies immer:_ed in the fluid, tuqoexists only ,he 1)otcntia /low. l:m“ the intcg!nl () app)ietl to a slro,m line (that is, a linealways parallel h) the velocity) has always the same sign of the integranl
28、, and henee (an m,tbecome zert). lence a str(am line can not. le ch)se(l, as othe.rwise the integral (t;) would ;.ivctwo different i)()tenlinls f()r tim same p()int, or ditrcr(,nt impulsive prt,ssmes, wliich is not 1)o:;-sible. On the t(,ntrary, ea(h stream line begins and ends at. the surface t)f o
29、ne of the immers,dhi,dies. Now suppose that two potential tlows txist fro“ one moti,n of the he(lies. Thenreverse one , f them 1)y (hanging lh(, sign ,f the potential an(l sul(rl)oSe il, on tim idher. Theresulting fh,w is chnra(rl(nized lly all lmdies being at rest. .,tit llell no stre;tlrl lille Ca
30、ll /It%illtit their surf:we, and tt,n(.e tim h)w has no stream, lines tit all altd the two originttl ilf tJ)e ,-_pn(e c,)4,rdim)l(,s,and so is t,he acceleration (If it parlicl(;. Each comptment of the _wc_.h, rali(,n, s_ly di“ ires to_)bt expressed 1)y the h)cal rate uf chttllgt2, of the velocity co
31、mponent at . certain pt)itlt -_,_ alldProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-by the veh)cily c_,jnP(,m, ni:,n,l th,.i:l,mll d(,riv_tixe:_ lhendve_. Thin is ,h,ac by the equa-tiond, t.),- /.)“ _“ b,ilt = bt _ v b.r-i )b;t:- _b (9) .7For durin
32、_ th(, unit (,f lil_l(_ lt,_, t)_lrli(le vh)m.k, es its c()()rdim, t,s hv , ),. _md ,i,. r(,_pectively,nnd therrf()r_, r(a(hes _t rrgir)n wh(,re the ;,hcil.y is larger by u_._, etc. increase (Ifvelocity has t() I)e ,d(led to th( rate ,)f chang(, per unit time (,l“the veloeily at one l)artirtdnrp(.)i
33、ni.The gemral l)rin,il)les of me(hani(s. )_pl)lied to a par(.ich, .f unit vMume, give thereforrb,I b, 1d, _1, u._: vb_-, ,v6-; Ofdt = _t _ -: =- , -;_/ : . , (_t)Nul)stitut, ing (,gu)tti(m (7) in tlm h_st e(luntion , we have_rts sut)erpo.-ed. “!he first t)_r_.,bl,.-t)_/._s tiu, part ()f lhe inessme
34、lmihling up )r chnnging the l:_tential flow. It, is zero i_ tl_olh)w is steady; rind, is, ifb+0-_=o . (_:3)Thr second part:_ 1._p!f the l)rosuro m,erssnry t() mainlain ,nd keep u I) t.he steady potrnti_d fl()w. It depends only()n the vel,)citv _md th, n._itv of the ilui(I. lho greater the vthcitr th
35、i, smalhn“ tt,e pres_ _re.It is s.metim(,.,ressurr :,.ct,s I?erm:hcntly without chan;:ini:.the Ih,w, nml h(,nce with()ut than,m_ its kinetir (nergr. It tMh)ws tt_eref(,re tlmt tilt: Bofm)uillis pressure (14) n(ting nn the surface of a lnoving 1),)(_ cu_). not pt, rfornt or tonsure(:any m(,rh:mia is
36、zero.3. ,“:,ome iml),)rlant f(,rmulas ft,ll,n_ from the ;(,l)lefi.)ll(s that tho m,unenitun imparted I_) (h:, II,:,v armm,I a h,ly m,:vingtn_nslatorv is par,rib to the Jrmli,)l_ ()f the t)odv. Sitwe _his m,_u.ntum is )rot)()rti,nnl t,) lhevehcity, the ,4feet of the air (,n the m,)ti(m ()f th(. body
37、in this (lir,(.tion is then _aken care ()f byimparting b) the 1)()1)“ an apl)aren_ ad(litimml m_ss If the vel,)dty i: n()t ae(uhra)(.(t, m) forceis noce_;s:r: t, maintr_in thv m,ti,n. “lhr h()dv (,xl)crion(.(.s n,_ d:,_, whi(h i., pla_).,:il,h, ,s e,lissip_(i,)n ,f ent.rgy is ,.-sumc(I. . sin)ihn“ t
38、hing may hal)pu_ wilh a rot,ring body, wht,reProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“l;lll:; AEROT)YNAMIC FtJl_dI:,S ON AIIISI.ilP ttl;irs. 9then the body seems to possess an apparent additiollttl moment oTmf the lira, produced by the movir:
39、gbody in the lluid othelavise at rest.II. TIlE AERODYNAMIC FOIICI2S ON AIRStllP IISLLS.,t. An important b,an(,h of theoretical aerodynamics deals with moments on bodies m,v-ing through the air while producing a polent.ial tlow. Wings prodw, c atlow difrerent from apotential llow, in the strict, mean
40、ing of the word. The wings haw therefore to l,e excludedfront the following discussion.Consider litst bodies m(,ving slr:_ight and with constant veloeilg V tllr,mgh air ext,:mlingin. all direeli,ns t,) inlinitv. Tl,ere can not then be a drag, as th,.l.inetic energy of tit; flowremains COllelallt ali
41、a no dissipation of energy is supposed to lake iplaee. Nor van tl)ere t,. t,67 tsd-24-2Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 RI;P(JIFI NATIONAl, AI,flN_RY t;bt31!FFEI.; l“Ol_ ,tI;R(I:,AIJTIC.g.,/ Ilifl. in CtlllfOl1111ilrV with tlle rema
42、rks jt,_t, made. ilencc lhe k, pressmres can at, best producaa resultant, pure c,*uple _t foree_ ar re._ult:mt nmment. The,nngnitudc and ,lirecli,m of ,.,ismoment will depend ,n the magnitude ,_f the eel.city 1“ and m the po.dtion of the hod 5“ rda-tivc t, the direction ,f its moti-n. With :L change
43、 ,f veloci_ all pr,.ssures measured from a._uitable stnnd:_rd, change pr,port.ianaI t* the square of the vdtmily, as tollows fr,ml equnt ,1(1,1). Ih, nce the resultant moment is likewise praportitmal t,_ti, r square of the velt;cily. Inaddition it. will depend on.the pc,siLi,m of the hody relative t
44、., the direction of motion. hestudy t,f this latter retation is the chief sulet of this seethm. At each different positiml c_fthe Imdy relative to the motion the llow produced is different, in ;sacral aud s is the m,_menlum,ff the fhm-, posse._sing different components in the direction of md at righ
45、t angles I,_ tile dixce-t.i,n of motion, l_y no means, however, san the relation l_,_,veen the lnomel_tlm-t and Lhedireclion of motion be quite arbitrarily prescribed. The lime dee to the straight motion inany direction can t)e obtained by tilt ._uperposition ,)f three fhxvs produced by the m,_tiot,
46、s irtthree particular directions. That restricts the possibilities eoadderably. Bug that is not:. all.the moments san not even arbitrarily be prescribed in thrat directions. I shall preser, tlyshow that On,re are additional restrictions based (m the primiple of conservation of energygild ll|(_lllell
47、 tllln.Let. there bc a component af the m,!nentum lateral to fit, motion, equal to l:al), wh,.rt:a dmmtes the. density of the air. Sines the l,ody is advancing, this lateral component of themomentum has emltinually t_, be annihilated at its momentary,msitlon and to be created an,.win its next positi
48、on, occupied a ngment later, This process nguires a resultant moment,M= It_ TZp (17)about au ttxis at. right angles to tilt, direction of moti(m and to t;ie monu,ntum. It: other wor h_wever, if the m,tion of lheimmersed solid is rerersed, for then tire entire flow is revcr.s,_,t. lhcrcfore each pair of dirce-
