Document
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
TECHNICAL NOTE No. 1192 .
CHARTS SHOWING RELATIONS AMONG PRIMARY AERODYNAMIC VARIABLES FOR HELICOPTER-PERFORMANCE ESTIMATION By Herbert W. Talkin Langley Memorial Aeronautical Laboratory Langley Field, Va.
~AmCHILD AlprpAt:T PROPERTI s: £PARTME:Ni.
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Washington February 1947 , I - ..
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NPTIONAL ADVISORY COMMITTEE FOB AERONAUTICS TECHNIC AL NOTE No . 1192 CHARTS SHOWING RELATIONS Al-'lONG PPIMlillY }\ERODYNNlIC V ABIA13LES FOP HELICOPTER - PEPFOHMA.J.~CE ESTIMJ._TION By Herbort 'vI . Talkin SUNI'-1.tffiY In oJ:der to fucilitate solutiono of the genaral p ro blem of helicopte:c selectiun, the aerodynamic performance of rotors i s presen t.ed in the fOlm of cha.,.ts shcwing relat i o ns be t ween primary deSign and }?el-:'orrnance variables . By t~le use of co n vent:.ional helicopter thevry , certain varia"bles are plotted and ocher variable s are considered fixed . Charts constructr:ld in such a marmer s hm1 typical results , t~'ends J anet limi ts of he l i.cop 'v er performance .
Perform311ce concii tiona conside::."ed. include hoverins , h ori zon tal fli ght , climb , and ceiling . Special problems discussed in cl ud e ve:':'tical climb !:llld the use of rotor - speed - reduct i on gears for hoverinG_ IN rrR OUJCTION TI1e general pr o bl em of helicopte~ design may be conveniently br oken dOml in to that of ob taining sui table compromises. among -she requil'ements imposed by considerations of structu.res , Vibration , and aerod:J'1l8.Y.'lics . The object of the present paper is to p :i:ov ide assistance fur o btaining solutions for the part of the deSign problem relating to ae:r'odynamics . These 801u tions are presented in t he fOl'Ill of g:.> aphical charts showing t he trends and diffel"Emces in performance wi th changes in values of t he aerod yn ami c design vaY'iables .
The charts herein al'e sJ'1lv hesi zed from the elemen tar y char ts of l·efel'ence 1 by the choice 0" typical values for certain design va::' iab les and by plotHng the relations among t h e renaining variables. The quanti t y held fixed for mos t of ~he plo r-s is an N ACA TN No . 1192 e.ve ra ge lift. · dr ag r at io f or t he rotor- b lad e sect io ns. Char ts ar~ pl o tt ed f or ea ch p erf orm; :. ncc charucteris t i<..; 011 Goordina t es of the pr i ma ry par a meter s p ow~r lo a clin ;.:; en d c.isk 10aclin [;, . Correlation b etioTe en the p er fo r .h3.!lce lnclic..,toa. by th e charts ::md tho performa n ce th a t may be reaHzed in pradi.ce is Gh~'..efly d epe ndent 011 a kn o wled ge of t he pr of i l e-ora r,: coefficient of the blade tUlder flight condi tj .o ns .
T he det~rrnillation ~ f thi:s coefficient is not a F,rt of the present paper , i.,Thich is r estr2.ctcd t o O!10'dnS the rel D tl o ns among the ot her aerodynmnic v::JriEl'bles and. the veriation of these relat10ns va th l'ot or - bl nd .e - el e.mont lift coeffi cient and. rotor - blad.o -olGIYlEmt pr of ile - UrF.l g c oe ffi dent.
The i;l cc ur acy and ap::?lieabil:i. ty of results obtained from tho charts are subject to the foll0·,,'inr.:-; condi t:i.ons 8n(. l~ .m:i. t a t: o ns : ( 1 ) 'l 'he char t a are constructocl from thooretically derived relationshi1Js . Althoug..\} ad.::quate o:cp6rimont .-:! 1 data c.re uIl, 8v3i lable f or r1 0 tai l ed cl1eckine;: no def:Lnito dJ.s crc],)a ncios 119YO been observed in ex:i.stine da ta such 8fl :'~'Jf()renco 2 . The theory is cons5.derod fully sutisf -;cto ry for tho stu y of ·tr0nds £lnd of d .iffe r enco s
in p orformance va th ch::m '- ;6 :in a.esi L' .n. ' rho se cpo of tho pros en t
pDpel" d oe s not include <:. 11 the aorod,y n Elraic infor.mc,tion no oded for actwJlly soloctj.n 8 optimum. ae ro clynemic (J.(jsi{::rJ.s hocclUSO the rotor - blsde ave r age ef'(octivo profilo-araC coeffi-:::i.ont 0 is h,)ld.
constant . Thus for C8Sf)S in vrhich t!1C vohl.O of 5 'liould ,,ral"Y 'Idth [:< desi[7l variGble, this Yarj.'-ltion is not shown .
( 2) ''clw pOi-TOr used in tho :p o;ro l' - loC\ctin5 ]~(:: r a m 0 ter is tha t de li vered to t ho liftin c, rotor . Transm :tssi on l o ss o s, Gngino coolin c; povlor : tail r 0 tor l)(lvTOr, or othor a u..'Ciliary poucr l' o quj.ro - ments . rL- not includocl . In th o l101icoptor of ref e~onco 2: for o:x.o.mplo) thoso auxiliary lossos SlCcrOG(lto some 15 porcent .
( 3) T ho charts L! :9ply i:5.roctly t o ho li copt o rs 'trl th a sin g lo lj.ftinG rotor comprisod. or throe blod.os . When coun:lJer-l'ote.ting r o tors are u8~d, :pal''!:. of th o rotational o ncr .TJ m a y DC cOEsidorod r C inm'oci from th o slipstr f .:am . The rotc:tiOllGl energy in the 1vako of a si:lglo rotor, as 'l-1ell ns tho ir cluced.-i'lm, effect of tho blad e tip; 'IflB.y bo estiJ:nated from rof erence 1; 0:::: ,;h is Go n e rally less thLn 1 percent of tho rotor pOi-T Or . Hi th Jll'..lltiplo non c 08y.2.Cll r oto rs > the holic l" pter porfor"..aancc In.:'1Y 'be 1:1PPl'Oxilll..ated by calculating OQch rotcr imlep o nc.ontly '~ri th 1 ts p:coportionato p ert 0:1 the e;coss vioight and. th o fusel " go dr q~ . This .~pp r oxim a t~L on ' ·lO uld . n OG lcct the inducecl int o rference bot'\JOen }:'otors; '\-7hich d.o:?onds on tho Geomo tricnl arr::mgomont.
(1~) Cc ,rtain fa ct ors tend to r e ci.uc o tho performance of holi - copters . f-unonc; th e so a rc blado deforn 1':lt ion undor load, r o tor ------ ---~ ---- -----~~ --~~- ----~-----~-- --~- --- ~ ~ --- .- NACA TN No . 1192 coning, ant hub interference . With careful design} these factor's c.an be made small or constant and need . not therefore influence tho study of perforlll8nce trends ~n th desic;n char-ges .
Derviations of the charts are explained in the append1x .
SfMBOLS .C' • A rotor - a.i8k area} square .J..eG'G b mmber of '01a<108 in rot or dis~:: c blade hord, feet C fusel a~e dra g coefficient alone; fliGht path> exclusive of D.p .L I f rotor blades; besed on rotor-disk area
A ( Cn - I
f \ A ,.
rot0r - blade - element profile - drag coefficient r o tor-blad e -element lift coefficJent c~
thrust coefficient ('--~-~ \
pA(OR) C) F
pm·:er-loading pa rameter foJ.~ 311..y flight path ('~\/~ P ')
1 •. tT Po ,V ., Increase in F due to finite-blade number increase in F du.s to slipstream r ota tion f ft;.selo.se 8CJ.uivalent flat - plate aroa b ased on Ull~ . t dra g L/D lift-G.J:ag ratio P rotor p01 .;rc r, horsepm;el~ R rotor-disk radiUS, feet r ro(15 us to ·3 point on rot or bl a de , feet T r o tor thrust, assumed oQual to 'rT, pOU:.'1<iB NACA TN No. 1192 v induced ax:l.aJ. velocity in rotor cl.isk, feet per aecond
v velocity of hel:tcopter eJ.o ng its flight p~1th, feet per
second unless otl:erl ·D.a e :i.ndic;atecl rate of climb in for,vard flight, feet per second. 1LlllOSS otherwise indir..:ntecl gt'oss ,\.;ei :It of helicopter mtnus fuselage lift, pounds Vl/A di sk l08cting power loading
WIP
radj.us rgtio ('~J\
1< y helicopter
velocit" uarameter (v '. /~ P ')
u - \ ~ ,.! Po
hel:i.copter rate-of -fol"vlard-climb pBrQmeter val1.1 .. e of Yh for mini1'l1.1In Fh Ybest y rotor tip-speed parameter t rotor- blade ever-agG effecti va prof'ile-dr ag coefficient v A.=- OR jJ, tip - speed ratio; that is, ratio of ~l o rizont al veloc1 ty of
heEcol'ter to rotational til' speed o~ r o tor G" ~~ "~:)
p mass density of oil' at altitude, slUG per cu bic foot mass density of air at s on 16vel, 0.002378 olug ~er cubic foot I::; Nt,\CA TN No . 1192 .-' (\1 , ax») dx
(
(il
J)
a 0<luivalcnt rota!' so_idity t~ x dx
I
O'~ I I \iO x (L~
\"
'0
r
.vlhe::-G ax == ~c~\
7tR i
/
rotor :::nsv.lar velocity) ra(1.::'on8 per second QR rot:2tiona2. tip speeC'.., feet por :cJccond Subscrir,rcs: a at alti"ti1.ldc f due t~ fuselaGe Cr8S 11 for hO!'izontsl fli Ght 1 induced
o at sea levol
v fOl~ vertiic",l fliBht
x for the r::di'J£l rutio (; == x)
6 due tJ b13do profilo drag rnaz lliQ:d1:'-~ min mtnjmum PRCBLEH Oli' EELICOiTETi SELECTION LIelic'Jptor selection 'pill be considered to mean the selection of values for the aerocl;yncrnic desie,n variables that would most nearly obtein a desired performance . Pr3cticaJ. consicieratioI2s rC<lu.:i.re a lmo llecte::;e of the usef1J~ load 8ssocieted '\Vi th Q £i ven performancc) Qnd the useful load is in turn influenced by such NACA TN No . 1192 variables a.s structwal efficiency and engine eCOnOl ]1Y . Data for t.he cV31uation of these vari2.b} e3 are not av·'11a"oJ.e a t the pres ent time bec a u se the valu es of t~1e v 61'lables are deter:'J1:tned primm - il y by considerdtiol'ls of ' ibration, safety] control, ana. comfort , r c.· <'h er th an effi ci eric~r conaideration.s .
In view of s uch cO:1sio.er at i on s the problem of helicopter selection for lJlE\Xim.'..Ill useful l oa d is not cOlll::.ic e:,:,ed. a t the pr osen ·c time to 'be r educibJe to the f'o:rrn of useful performance s electi on ch3rts . Aerod:v:nG1llic per:Lorm~nce ch arts, hOvTOver , t o S]lOVi tr ends 'H i th variat:i.oLs i::-. ·.~ .:e :pl':!.li1 a:cy desigl v3riablGs 3 re pr esen t e dj the import ance of blade and fuseJuge drag is al so c~6monst r 3 t6d. A basi s for an :2.ntell:i.sent 8P:9roach to the select i on of balanced designs is tl rw provid.od in aeco ro anes ,lith th e bost ava il ab l o c ::1 g tn eer in g a.eta . 'i'ne probltY-TIS of r-'mge 2nd endu:::' 211ce a re asso - ciat ed 1-1i th the enf,.i.ne - fuGl econ~Dly and_ arc not directly com :id.ere d herein .
SP ECD\GI~~ SELECTION CK~TS H ol i co_ ';;o r p er forInEmce is first illustreted. :tor n conv c Lt:' .o n al des:!.gn . J!'igTtre 1 8hOl-18 C' .. ; ·.l~VOs i':)l ~ comd:, an t vahles of hm':1 zont:::l cloci ty V pl ct · ceC!. on cco:;.~d::'nate s of' pOvtC1' 10 2 : L::"LS 1",iI? agcins t h dj . sk J.oading 1{ /A :for helicopt~rs ,, :i tll the f'ol lo vJ2.ng d.esign sp ec ifi ca ti o ns : Rotor -disk racH us , R, f oe t . . . . .
19 .0 Eql_'.i va lont r o tor solidity, (J • • • • • 0 . 056
T:'.p-spcod parameter ~t" "R \%~~) .. · 320
Rot Clr - bkdo Ln r eraC;G ef fe ctiv e profilo-dr3g coefncient, 5 0 . 012 Fus e12Ge equh; - ale nt flat - plato ar ea, f, square f8 et 10 .0 Al ti tude • . • . . . . . • • . • . . . • . • Soa lev el Air dCl1.si t y , PO; 81u'3: p er c ubic f t ot • . • • • . 0 .002378 Th o ro roma:i.n as do si Gn v3riables for this caso, t. ·l::>rof", rc, 'vi , P, [lnd Vh , a n;y -livro of 'i'hich d etermi ne tho third a:1(l t:1US de fine a J?Elrticular helicopter .
All eniTolopo of tho constant velocity cur yes ( fig . 1 ) r e pres e nts tho maximum. p Ovior lo n din( ; that c:m be sustein od in fliGht at o ptirl1 .. 1D1 speed . This onvo lopo is label e d (v!/P)max in th o figuros .
NACA TN No . 1192 The max:i.mum power loadtng th.?t can be suotained at zero velocity is shown by the short (lashed line E!nd is la1)0lod !10voring .
I f tllS 3ttainment of msxim:;rru pO'ver loa din.::; .Tere the only object of the design of helico:;?ters Tili th t~le constants of figure J, the f~~~e voulcl S'.lf1.Eest th'3 use of 3S 101'[ a disk loading a3 pos8:~ble .
Figure 1 ShO'vTS that the pover loading can be incre.::sed as the (i) . sri: loadine; is decreasod . For a given helicopter pO.Ter] the rotor s'Lze increases YI .. tl! decreased Qsk loading and, the:c'efore ) the rotor weir;h:t 5.ncreases . A COnl:91'ornise betw'een rotor wei6ht nnd incref'sed povmr loadins i-TOuld give an optil"lun;. disk loadil g . Since informa - tion on the vari3tion of rotor wei ~ ht wIth size ano. solid1-'cy is unavailf'lbJ.e ) this optiItrLl!ll is not sho'Wn .
The curves of const3nt velocity Bive an optiITLrr! disk loading to obtain mJx:Un.ul!l. pOI.;er loading . This optir:llli."'.l is obtained i;Twn the i.!.lduced drJ-S balances the ::;>rofile draG . l-l.t 10 'or disk loadinc the profile dra] is too hig.~, ihereas 3.t hiOJ.3r t:tisk loading tho indncec. drag is the determi:::linG factor . The v81ue of this optimum is rycatly dependent u.rO~1. the pro lIe dr2;; ett a inablc in flight .
DecreSlSinf:) the profile draB docreElDo8 the opt:X~1,1:m disk loadinc .
For 10v7 forward speeds tho induced. drag is so i2!(po r tant that the o:pt1rn.um. occurs bel011 a d::i . sk lo n dine; of 1/2 p01md ~S~: square foot .
Since th€) diok eres voule. bo e~rcmely larGe in this r aneo of disk loadin .1 these optim.ums t; re not shmm .
o C"LU"'res of IUay.imlIl1 rate 0 ' 1" clImb are ShOiill i n figure 2 and, for comparison, the hovarinG and the maximum. pm·lOr. loading curve s from figure 1 . Curves of constant service ceilin G ( rate of climb) 100 ft/min) arc shm.'Il :i.. n figLTC 3; aloo Oh01-ill are tho hoveriu3 anci t he maximum pmvcr-lo a din.:; curves from fig-meo 1. Tho curves of sorvice ceilin G are bas ed on constant rotor revolutions per minute
"n th rot er pOl'Tor proportional to the donsl ty . The pOvlOr - loading
scale is for the sea - level conctition .
Conclusi o ns dravlIl from fiQll'cS 1 to 3 aro subJoct t o tho constant valuGs arbitrarily assL:;ned to Cf ) 5, Yt R , or f .
Attention i s called to the fact tput the Mach num.bor at the tip of the adv"ncing 'blade 'Hill affect tho value of OJ 3:!.SO, t _~e L.i&cor values of the tip - speed r Cl tio !J. enc o ur..tered at tllu hIghe r for.lard speec:..s :may be impractical fr om considor . JtiollS of stability and control. F or thGGO and other rOesons it is necessary to con3ider changes that ID.8.y occur as the fixed qucntiti0s 2:0 va:d8d . Fer this purpose. , ethor types of charts ar c int~('oduccd .
N ACA TN No . 1192 The types of charts pr~sented are 8ummarized in t2ble I .
The gene.raliz!'3(l chal't.'3 are t:1e rl) ot c O:"'J,,'3ct b1.'t in t:)'JinO f.'ospe cto the le3;:lt, cOIli"nl.ent to us c ·oeca-;".f'3 t:!<;,-".- sho', relf:r~i'JDEl ':ll :10!lS complex rar:'met ()}:'S . The :fc ' ··JI~ r .. l()~d:'..r1E C.l ol:-loCtG..i.D S chart;'l are I!J.Ol"O Ci'i.l'.::.c t r Or.hlng . In c:~·\_e r to f3Ci '.itnte <':'i3C\13~d-Jll of the p'll·cff!let::r: s hse(i., tho elomcl1f31'y (les~[:1.1 '''2~~i.::~):;'es t::; b9 seJected
tE'G liutcd in ·~~) l e ::C. S:_J~)(~ifi-.;etian (f tl10 elere.eT~.t3.ry clesien
v3riubl..;s oS8c:H-s::'3.11S· a.ot3J"T,i~16S the holicopter aerodYl , amie p erfo::t::ndnce > ,,~. teh IllDY bE. e~0?ressE.d. in -G0rrt:.8 c f the elementary pel'for::"'l::u:ee V:: j.-id · ~' l o8 l~ et c-a 5n tlJ.ble Ill. 'l'l~e lm:'[;o Ij.Uliioor of the dasi()1 ': a:riG! bles aff0ctin::; ho Hcop· ~or pc:::-i'oI'l..nance complicates the dirl;ct U'?:rh i cal prcscntation 0:: the offects .
Tho pr o blem C8n bo simplifiod 0y the usc of fund~ 1onta l p o. ramet ..;rs oach representi:!e; a si S ific c;. nt - cup of va riables .
From tho analyc:i s of refer o nce 1 tho fmdzrncntal dOEien pClrametcrs of table IV 2r o obtainod . Tho corrosponding p8rformanco parameters arc g iv on in tablo V.
A com:p 3. ris on of tabl es II .slne. IV shovlS t hat uso of the funda- me ntal d. esi~ p a rameters r ocli.lce s the mlII1 bc r of v[;ri a blcs :;rom sev on t o fonr, but althou&"l this reduction e~(;atly simplifio s grcph::'cal pres ont.;:.ti :: m it cor:r-os')ondinGly campl i.eatos tto in t o r- p:::- Gtotlon of the G!'3})!J. . A compror:u80 "betuecD. the o).. -t:::-om os of tho
oloment'1:ry and the f :Ildam. ol": t3l dC8i gn V[ :r i Jb l c s ma:r bo b asc d on
u se of the famUar J?<. r amoter s pm,;or 1-: x:. 0..i112; end cli::lk laac.inG .
T hi 8 conpror.li se, howevor, ruducos the, !lv:n:..bcr of 7arie: bles by only ono .
Goneyalizod Se lection Charts A gO Eo raliz:Ja. solection chart is shown in fieure l~ . Th o siGt1ific ;J nco of tho chart is best explninorl by a briof description of its d. c rj.votion . A flulcr doriv ation for all figures is givon in tho Cl)pondix .
On a simple grsph o nly three variacles C2n bo shovm . The f o ur f1.r..1.c5.:::r"lOLG.ll (tooi en par:J11otors (ta -::. :;' e IV) plus 0 a nd a p ()r£'or::a3':'~0 parD.Lloto~c nwk0 e t ot,q l of Gix:, Cf)r..soqu.GC1tl~ tnrec va:ria~l r c, rnst bo 1'i::eo. . As e xplained in tho !lIi: b:'J~,-,-ctlo n, " conn tuc';:' '/~l~orJ h CV0 b0cn c.ss2.cned tr , 0 , T=10 n;'1). ~ of 0 for a [ :j.v eD ;:'1:1i8 is a.o~l)l""~llnefi by th o <.lV01~f':SO c'::'fcc"(;ivc rotoX'-blt:dc - el o mcnt lift coef. 'icicnt .. v{hieh is in tl:.rn cicpellclcnt on tho o NACA TN No . 1192 / Y h Thus, tip - sj;)eed ratio fJ, = -'" [lnd the quantity Y t t"\-iO of these three Q.unntities determine the third. 2nd., in gene ral ..
en optimun c omhinatio :l v/ilJ. exist fer e3er.. pcrforrr.znce re~uireI:lent .
The investigation of this optim1.1I!l. is not hOvTElvor' :part· of tho pr e sent p ~l} "er . }t'or the p:cese nt purpose the vulue of ~L is fixed.
at 0 . 3 8:lQ the valut.: of crYt2, . at 5'7 !.o. As computed frem sec-
tion 89 of referense 1 this value of crYt2 corresponc.s to 3n c:!.ve:;.'agc e:'f'ecti VEl l~otor-blau.e-elemen·lJ lif J lj coefficient of approy.i.· matoJ.y O . 4J.j. in {lOVer in £: ..
In fiGure l!. curves of constant CDfh are plott0o.
on a lo g'3.r itbEic 8c[;~~of' the ~ec1procal of the .po\-Ter-lo~ding
1. W hi PO ' • ' " •
plu'ameter := - 'VI ~ -- agcnnst tho nOTlZOll1jcl-V010Cl ty F . PAp
r--
. I !\ P .
par8lD.etor Y ~ V V 'w p; for 0 == 0 . 012. The condition
h h v crY -. '5740 .relates the ::,olidity to and thorefoY."G t .- .t.t . . ' to Yh "by the ctu"re of cr Bgcinst shmm j.n tho 10l'lOr part of tho fi S '1il'O •
' . r;:- - ' -
Curves of ~ - = ~~ 'I Jl! Po . aga inst Y = Ill? V~ E~ . for hovorin g
t Fh P A p . iiT Po are aJ. so ehovm ini'i g1. tr0 4 and cover : three conditi0l'ls, namoly ., Ul"ltv.'i sted r 0 ct n n G ula:1.~ blades with 0 = O. Ol~ . end l)...'1iform llsk loading -w:i . th 0:: 0 .OJ2 'D nd " 0 ;", 0.006 . The l)O\ .7o r r6~ui:red. fo UJlt,,:isted blades is only a.bo ut 4 perccnt h:::'&l1er tha~l the optill'ltJJ:.l that is obtained. vii th lli'1-i . form disk lood:'n g . Unless . othcnds0 stGt-.Jd., uniform disk lo a din g is used throu,91o:tt tt.G pro sent p apo r .
T ho effect of 0 on the power roquired f or hoycriClG is lar GO ; hOi 'TOVC1~, tho effect of 0 is ab01.lt 41 percent Jeator for 1.1:: 0 . 3 th an for h ove rin g, in accordance \Ji th equ u tion 23 of :::'oforc!lce l.
T~1is effect is sh o ,;·;n 'by figure 5 .. which ':Ls s'i:nilar to figure 4 but 1dti1 0 = 0 . 006 .inS)':'C8G. of 0:: 0 . 012 .
The restriction of fi[;U!'e 4 to th o c o n<1.i tion ~v -= .0 . '3 f'iJ.:os y -·h th e l~elation between Yt a nd Yh in. th:lt p,= - but incrcasin3 \.1 7 ' ~t NACA TN No. 1192
haB comparatively little effect on the curves of 1 "!. J"!. Po
Fh - PAp p in the neighborhood
against Y = V - - for constant
h h W Po
~
fi gure 6 in ,·;hi ch of ~ ~ ~~~_.This fact is illustrated by
1 v.! Iw Po
- ::: ..- \1-- -- is plotted again st I..L for CD.r.o ::: 0.01 for ti ·;O .1.h Fh P ~ A P velucs of 8 wIth Y ::: 75.
h Figures 7 ana. 8 sho'T curVGS of constant values of the maximum rate-of -for-vlarcl-cli mb parcmeter Y for helicOl)te:-cs of figtU"es 4 c and 5, that is, for 0 ::: 0.012 and 0::: 0.006, respectively .
Besia . es yielding the maximum rate of climb in fOl~YRi3:'d flight V c: feet per second , th ese c urves permit calculations of the service ceiling, For example: if the service ceiling is Qefi ned as correspondin g to the value of piPe for '"hich the rate of climb
is 100 feet 'Oer minut0, then Vc::: ~06-? = ~" Fr01"l. the value of Y
c ~, 0 3 correspondinG to a ny point on the fib~e, the value of plpo me.y then be calculated for a given value of the disk load.ing W/A.
W Iw Po ~--o-
Figure 9 shm ·;s cm-ves of -- ~ -\/-- 8{3sinst Y =OR\/-::'-'- F h P V Apt ~ H Po for representative values of Y , for tw'o values of the fusel age v vertical dra g coefficient (CDfv = 0 and 0.1) J ana . for 6::: 0 . 012 .
The solidity corresponds to aYt2 ~ ~-- . ::: 5740 . Th o figure Shovffi POC T the small effect of fuselage ve rtical drag coofficient all the po~er required for vo rti cal climb. Thus for CDf :.: 0 . 1 the fU.8e1 age v equival~nt flat-plate erea in vertical climb is 10 percent of the rotor - disk a rea, and et Yv::: 30 t his largo fuselage dJ:'ag increases
by only 8 perc en t the pov!er requirod, The valuo Yy = 30 corre-
sponds to a rate of vertical climb of 2700 foot por minute at soa
V (- fA p-)
lev el for A == 2.25. \ Yv = V'V~V Po
The o ffect of 0 in vertical climb is similar to i ts ef fect in hovering} ,mich is illustrated in fig\~o 4.
NAeA TN No. 1192 The last of the g,ene rnlizecl charts is for the rate-of·-forvrer - cl:.!.mb p"'rameter Y shown plotted in f'igure 10 3sainst the cUf- c fere ce F - Fh bet"reen the pO "Ter- loadinf\ paraIlleter available Qnd that reo.t:ired for horizont:;:,l fliGht at climbin g speed. Curves for several "i.'slues of the velocity parameter ir.. clirlb Y e.re 81101 ·: n .
This ficur' 3 is t~e same as f1gure 6 of r3ference 1.
FiG'UJ:' 0 S 4 to 10 contain ell tl18 8nsential nerodynami.c ~ . nfol"m: ~ tio:!. .:1 thin the scops of the present pe.:pe:c~. 11hon the o.i3k 10adir:'3 has been sol:':)ctecl, theso ftgures show uirectly the relations amonG
power l 03d5.ng W/p, r otational tip 8:geecl OR , and horizontel
vclocit~" VIP P0l1er-Loc:din3 Dlak-LoadinG Charts Th e effect of the a. isk 10 a o.i::13 is best s1i')";Jn by charts in
.,hi ch r Ip,- is one of t.ho coordinatos . The (: .iru : loc:dine; Tik'1.y bo
v [, ried by independent ch-:mges in either tJ '.e rotor - blad.e - olomont 2. ift coefnciont ; tho solio.ity, o:c the tip speed . T~le <lisle load.-:'ng 1,,<1S varied by ch.:mging the tip spoed in fj. G __ ~us 1 to 3.
/l.li'10ne the remaintng variabloG in these fi g ur0s the fuselagG equiva10!lt flct - p1r.lte [jj,'ca f 1-188 held. con3tant ,mel th o tip - speoa.
r Ct t:Lo I-L 1-7as allo"liuQ to vary . I n the ChE'rt8 QG6iT'..nins 'YJith :fi tSu ro 11 tho d:tsk 10Beling io a::.>ui!1 varied by che.ngine; th o t:.p speod. but the v.::;luo of I-L is held. constant llh.~le the :fuscl~G e cq'lU v alent flat -pl ute aroa is var:!.ecl . It is to bo o:""1l octOl!. thet consi<1. ') ra- tiona of minimum l)rofil.e-draG loss anit consideratior::s of stability and control at maximum speed ,·;ill tond to dotermino i;,n optiDum value of !J. .
As h a s been po:i.nted out) the usc of olor:lOnt3r;r variablos in charts i:::lcroElses tho Ilmnber of variables and. tl:oroforo tho mJ.niuor 0-:: cilClrts as compared vi th charts bas e d on fun<lam. '::J :''lt.:,l :;?Elramotors .
Ir:: tho Gencrali z ed ch3r-ts) fiE:,Ul~es 4 to 10, aduq,u:.to silllplific8tion
:as achi070d by fi~~ing the values of \J., D, CDfh' Cn ' and vYt2
fv In the chc:rts presontod as fiGures 11 to 16: the:.. v[ , luo of (J also is fixvd at 0 . 056 and the a ltitude is reatrictcd to soe lovol. In ac.d1tion, the fusol &::, o dr(lg _8 o xpressed i!1 torms of th.) r2tio f/F! .
FigLl.!'C 11 811mIs curvo s for eonstcnt V'31U8S of f Ip at B CEl
leval on tho coord:'natos of w/p 8cai.nst I'TI', for I-t == 0 . 3
and 0 == 0 . 012. A1so shov1l1 are tho hovorins c').1"\"o: CUl~ves of !JUJy.imU!il !'DtO of climb in for;la;;'~<.l f'lig..'1t; and 'Cb0 !'oc¢,on in which tho blado tip staJJ .s in h:i . gh spood . Tip st( ! ll Hns not found t.o occur for the maximum rates of cltmb showll in tho fi:juro8 t3n(l yfu3 d etormine d b~" stall at l1l.:'.Y.imum horizontel yolocitYJ as cxpl,':inod
J
~~CA TN No . 192 in th e appeLd:ix. Tho stalls sho.m. sho1."8.o. be :::- ega :c t..eo. a s a :::-efo1' - ence con c tition only, inasmuch as the ac t ual st'lLl :lepel (16 u pon the particnlaT a~.I'foil sections used . The rnxiLl1.'::l veIocl ty 1.'"a:!..~:!.eS ,·rl th W/ A and. i.... 81:"0\.;].1 by the llorizo:ltal scale ct t:le top of tr:e ,,¥,a ~~ll . 'rhG rel '1tioD. betvmen the ma:x:L.1.um velocity R nd the disk loading i 8 fi xed by, '3!!l.O~ l g other thi:l.gs, the choice 0= s o lio.i t:1" because the v81ues of ay and Yh/Yt have also bee n fixed .
t For hi ghe:::, e:peeds ,· rith a given d..-i..sk l oz din g, it -.m 11.d. t herefore b<;; necessary to e:rr.:plo;j" a higher va11A.0 of Y .
t Tho most di::::-ect applic3-Cio:l 0; ftr.:Ul~e 11 is as follo,{s : Let it be de s~_red to fi.nd hOi,T gl~oss voiSht vClries '.ritll G.isk J.oadin()
for a :;i v;:m Gncine with rotor pov~er P • T~'!e C1.U'-O£l of c c' nstant J: Ip
in the fi2;1.1re are tl -..en equiva l ent to C :;J:'V vD of constan t f and
the scale of 1~ /p :: .s prorortj.onel to the [y"03S i'!Oif,:ht "J . The
l-'igura then . sL.o\.;s hOv1 fOl~ a Gi veIl f' tho {?'OGS 1'roiS~lt docreas~s ,n th in c re ,., slng disk 10ad.::"nl3 "hile t;,.u l1"..DY , irmm speed. inc:coascs .
Inasmu ch ns tlL o se rol :::t ionsh::'ps c: :~ e d Ol)O nd.Cl1t on tho val1.:.os selected. for tho fixed q,unnti ties, tho fi : -::c;d que.n ti ti GC are ch:m3cd on 31.lb sG'lue nt f:"g1.U" cs (f ie:;s . 12 t o 16) so t hat the influo~co o:C a ll th o s i[!n:!.fi(;Qnt decign v ,:: riables rrmy bo s t:'1. c5cd . Th e solection of tho vah _3 s to be us ed for tho fiY-cd 'luanti ties is dopend(m-c.
on deta o utsido the scopo of tho pres~nt pape!' .
I n order t o compa ro tho char ts for d.::"fforcnt V.:: 11.10 8 of 0 , figure 12 is made simil a r t o fi ()'Ure 11 but ,ii th h~lf tho bl ack proLUe - dl"ag coofl'icient; th~t is, 0::: 0.006. Fi S1.U'os 13 a~ Ci. 14 apply
to ° ,-:: 0 . 012 and B::: 0 .0 06.. r os poct.ivel~·) fo r !J, == 0 . 2; an d
fi3UT.J8 15 :?::ld 16; to B '" 0 . 012 a nd 5::: 0 . 00 6, r es po c tiv ely , for !J,::: 0 . 4 . In i' i gu.r es 13 and 14, thG roGion of st a ll lies balm.; n p0\- 70 1.' l03d.ing of 5 an d is n ot sh01;n .
I n fi C :m~os 11 to 1 6 those holico!ltars ropresontod by C'L'Tves ab07C: th o hove r i n g curve have inoufficient pO\,ro r to novv r fr oo of tr..o grolL'1d offoct .7 hj _le thoso repr o sent od b;;- C'J.TV OS uol o ,,- the hovorin G curvo roC].uiro noro p01.,ror fer hig..~-[Jp ooa_ fll;;ht th un fo r o hov e ri nG. ' rho first (7'O Up of holicopto::s 103;:)0 th o ch i ef 8.L7 n t,Of.;C of a holi ,.,o ptor, that is .. th e a bility t o hover; wh or ea s th () second fP:'oup possossos mo r o pevrel ~ than rO 'l uirod for h:)verL1'::; .
1 'iguro 17 shows tho pO\'icr - loadin~; disk - l.oadiLC charact or - istics of holicop t o rs possossin~ !) o 1{ or just su:ffici on t to hovor f or conCi tions of 0 ". 0 . 012 a nd a:l?p roxim atoly conote nt c 7" th a t is , a Yl~ " 5740 . In order to avo id th e coni'usion of ::l1.uu or ou s curvos, only limitinc curvos 8:::'C GhO~~l in the fiGUro; th a t is, th o ____ ~ __ ____ -'J NACA TN No . 1192 fuselage drag coeff- tilTO solid.-line curves C:efine the extrames of f, fh n cient e:x;pressed in terms of en d t he
-. = 0 . 01 and == 0 . 25
p p dashed cu:. .... Tes are fo:-c li:ni ting values of () of 0 . 02 and 0 . 18, yespecti vely . The constant solJdi ty Cllrren are elso curves of L~:pproxi!Da~oly cop-stent service ceilinG, yaryin,;; f:.--om 10) 000 to 23,000 feet . Similarly , the CUl~V6C of constant flp 31 'e also curves of constant rotutional tip speed . JR vuryin g frw. 325 to 850 feet :per sec e ndj ineamuch as the VE lUG of jJ. has been fixed at 0. 3. tl " .ese Cl.U'VOS :Jr8 also cur7BS of conotant horizont31
yeloci:i:iy Vh v~rying fr om Go to 175 JYI.ile~ por llOtU' . ?articu.lc.rly
notable 3.n t!1.is craph is the smell va::..~j.atiorl ill :p01-:e:~ lOL.dineS reaul tiuG froID. vi}.:-ci&tions in () or f /p .
For ::g:-et:te l' dotall, the I)3rt of figlu'8 17 bounded by th e :cectan gle is erp::mded in figtJ.r0 18 ana. C1)Xves for int cl"'1uod:i .e te values are inclmled also . In nodi tio!', CurV3S of 1U2::im:'Ill. rato of climb in forwerd. flight Vc a:'o shcmn . Date ",TO fo:' DOe. loyal in figures 17 and 18 ; also tho value of p. i:'3 0 . 3 only L111ie11 E:pood since in c1:i.mb a nd 3t service cG11ing tho Sl)eed. of th o heJicopter is th a t corrospon6.ins to tho Ii1~n=~mum r a t e of cl:tmb .
In gonoTnl, vElrious roquirom:mts 1,1.11 mako unclooira'ble t 10 sel ection of helicoptors to fulfill tho reQuir ements of figures 17 and 16. Tho fibUTC8 u re of intcroet chiofly for shov,'ing tho rel£ . tions amon:,:; t.ho desir.:;n and perforI!1al:.cG va:;:ia- olos of a r.lass of helicopters tha t may be rO§arded 80 a ste.n~rd for comparison '\<Iith special d' 3s i[g1s.
The foro going st£"!toments, as woll a s those in cO~T),ection liith most of the oth~ r fi GUTes: c.pply to the same con ition for 5 in hover1n g a s in hi::;11 speed . Since 5 is the rotor- bJadc QVer£l,go effocti vo profj_le-drag coefficiont, the value of 5 will in e:;8::loral chanr~o \·ri"th ~1ach munbor and with tho tip - speed l'atio .1. .
In order to illustnr:- o tho chaIlge with IJ-, the valuos of 5 in hoverinG and high spoed were calculated for ()Yt , C orres:pond in::; t o e. lift - drag ratio LjD for jJ. = 0 . 3,. find for tho thr')e s:1rf011 sections of r eforenco 3. Tho curves ai' tho airfoil sectioI'! profilo - draG characteristics are plottod in fi;Sv1TO 19, end the mothod. used for c21culation is exp13.inod in the appcndiY: in the d.iscussion of fiGure 22 . Tho values obtained for 6 at \..1::: 0 and at \-L:::: 0 . 3 aro liste-d In the folloY7inG table: NACA TR No . 11 92 .. l.irfoil ' ....
Smooth Smooth TIOUj.l " NAC..\. Z~()15 conventional NACA 3- II-13 . 5
Flisl . lt . "~
cond.:i.tJ. on ........
--~--4---------l---- --;--- - li o':e rj.ll ~
I
0 .oc37 0 . 0 1?6 0 . 0045 (!J.::eO ) -
!
Iii 91 speecl
(IJJ = O. ~ )
I
____ _ __ -L.
The cra g co ei' :':icion t in t~e hovcrj,:J.g c O !l (li ti on i.s CNl st snt tlll'onghou t the entire r ( ' ::; 01' c "'0le ; i·,hor ol:s in the h:i.t:h -t ;pee cl ccndi t.ion, th e dI· ·::l3 coefficiont v?t~ies irlth the p)si tion of t :18 01-..0..0 d:'.x r in s th3 cycle sin ce the re1 8 ti vo VG loci ty of' the oi:1':o il section and. the air is onstantl;,r chan(:,~ng . The aV6r ::lt}3 offocti ve profile-clr:tG coefficien t :.: or the ontir0 cyt:J.e , tLe:.~ofo:;.'e, ~s de·::;ermi."1ed ';:,:.r un ir..te...;rated e7era.:.:;e of t he c.r Ctt!, COt)::'fi8iecl'G tlll'ouf.~out the cyc le .
For this rons on tho shnpo3 of the Ijft a: 1Q profilG - dI'ac C 'lXves a:::'foct t:! le ~vo r ·3.iJE; "alue fo r tho hich-speed concH tion . Tho fo~e JO iCl g table G.emonstr:;tc3 th 'l t the averr;:.e ef: ::'octi vo l)) 'of:tle - dra G c ooi' :t'icient for the onti re cycle rna;\,- oe either higher or Im·/er in the hig,.'1 - 3peo<3. concii 'Gion than in th e hovc:i:'inS conell t :L on, d.o:tJondi:1G on t~ e :o. i:L'f' o i;. s ect::o n characteristics . Th e e_1.0ctD of vcr;yin g 0 mEy b e cs ti:m a"cod. by couparin~ fi gu:.'es t~ a nd 7 for 0 0: 0 . 012 'I v:ith fi (~ " _ U '0 3 5 a nd 8 for 0 :..: 0 . 006 .
V e_:; ~~ cal...£l :'~~ . - !. fm 'i special p:.~oblom3 arc of int e rest . I t Is ')f t en n ecessary to 112VO D.7~· j.1IJb le a dofinit o rat e of "\"·o}.'ticr::l climb . Vo l'ti ca1 cl:lnD D1_".!'r be o"Jtainod oi thor o;r r oduc in ~; t}lU gr03s 'I7Oi '3-lJ.t of Cin v ::<istin c; holicopter or D~r d.esi{)1.in....; for vo' '' · :-ical climb . Fil,-..ro 20 S}10 W!3 tho rat.o of v Gl' ti cel cl:i.m.b th L, t m ay bo oota) . ned ot decreasing th o yOSG 'i{ci·jlt of B h o licop tor possossi:lg p01V0r ,just su!~fic.;icC1t -:'0 hov)r . C0ns~.a.0r a hclIcoptor thet has zorn l~3te of cliJub lor a dls l: lo ading cf ~: . 5 . If th0 cross lm1 01 t :ls reduced. 20 percont, t~o d,is~ r loud.in:::; w ou ld Do 2 IJ01mds p or sq.''.1 3 ro foot of dj. s k e.rOA ~m d. ~ vho resultinG r a to of climb may bo re a d fr om fiJUl" 'o 20 as 850 ~ 00 t :POI' ninute . (Road, thu f:!. :?- LU~O at V!
20 :,)(;rcont r o duct:t on of gos s ,loi j1t on the curvo of "A. = 2 . ) Th o fi Gt u.rG includ.es S(;7 (; r 31 CLD.'7es for CD." == 0 . 1 to 8hm! th o small 1. y NACA TN No . 1192 15 effect on the vertical rate of clLmb of such a large value for the vertic::!l drag coefficient.
When Yel~tical climb is an essential characte ristic of per- form . mee, designing fo:::, vortical clim.b may be decirnble, v:hich can be done by designing for hovoring at some grea ter . .,L ~o SS w'eight than "till be used. and reducing the gt:'oss -ITeieht to obtain the required vertical climb, 8S f,riven bj" firru:re 20 . Ii' the helico:pter is t o be ope r ated ah;ays Flt tr,-e red uced gl.'oss iVei@1t, the solidity should. be a.ecreased in the S8lli8 proportion as the gross ;{eight to obtain the origi . nally chosen value of OYt • Hovering .- Figure 21 shows curves of constant tip o:peod. for hoverIn g on-·t'he :povrer-load.i.ng disk-londing coordinates crossed by curVGS of constant solidity . It is clear from the fiG~~e that increasin3 the soli(li·~y and decre.'3sing the tip speed. is a relati vely :l.neffecti ve Lleans of increasin3 the p0i-i''3r loading as compared with decreC!sin5 tha disk lOElding . The e:'fect or rotor- blade Q\"erago effective profile-drag coofficio::J.t is inclicc:tecl by
t ie tip-spoed curve of 300 foet per socond for 5 = 0 . 006 as
com:pared .lith that for 0 = 0 . 012 .
Rotor - spoed-reductiocl gears . - 'Jlho pOi'lOr required for hover-ing with a helicopterdesignod to o:peTate at a lnaxilnl.1.In ave r age lift- drag ratio in high speed can be reduced by the usc o~ a roto~ speed-:~(;duction gear . Th o hiGh lift coofficients and corresponding hieh drag cooff':'cionts occu.rring at the tip of tho retreating l)lado in hi[;"l speed. aro absent in hovoring . Maximum 2 vera ge lift-cJ:'Q&; rG,tio of th e blado sections OCCl.1.rs a t a higher lift
coefficient in hovering (\.1::: 0) than at hij.1 ..:opec d (p .. = 0 . 3)
w"ith th e result that a 1 0'YTC r rotational speed. is desirable j.n hoverins. The opt imum. gear ratio and. th e r OS1;tltinS a dv a nt nJ<'" depend on tho chaJ'acteristics of the airfoj.l soctions usod. In figure 22 the greatest p~rcentage decrease in the pOi':cr r Cluirod.
for hovoring, resulting from tho usc of El rot or -spoed-reduction GeJr , is plotted. against the eq,uivalont rotor sol.:i.c.ity for tho threo airfoj .l soctions of ficuro 19. CaJ_culations for tho figuro arc oxplainetl in tho append.ix. The :r.-oqu.irod goal' r." _, ties O:ld.
maJdllH.l!ll avora~:;o lift-clrag re . tios ::ire shown by tho curves . It is obsorved that tho POV10r saving rosulti113 from the uso of a Gear shift is Greatly d.epencl.ont llpO:1. the shapo of tllo C1.l.rVO of ai rf oil soction chcract rintics but tenets to be larGest for high - drEiB lovT-solidity bl8dcs .
NACA TN No . 1192 COIJCLUDTHG RJ1:MARKS Th,) rolatio:'18 !Dong the prinl.QY'y aerod;·:'"13t1ic y,:u'iab10s affe-:;ti:.1G helico:pt6:~ p'3rf0r:m:mCG h:J.ve bEJon presented. ir.. the fon: 0::' gl.~2"P~1:1 '~Ql Ch'::ll'tS . Tren"l.s in the variation 0-:': l)e!'form':mce F:: th the v"'rtcti0n of :prires:cy v~riobl(>s CCln bo ob·:ei":ed. 1':;.'01:" tho Ch:ll't3 .
Se l ectect V[~J UOE: of some 0:' tl10 vc.rif!blos, Buch u:; :,:,otor - bJcd.e BYerCiG8 E:ffe.ctiv'3 p:rof:;_::'e - d.!'a(~ caefl'icient, tip-s]?:Jod ].'[,:;). 0, e<::,.1.l1'ic.lp!/-:, roter 8ol:'<lity; e~6_ 80 f\Jrth, "ero 11.SE>:.'i. t:) cover 6 1''"'ngo of V£:J.1).08 cxpocted to be CnC01.m·jerQd. :i.n :i=Jl'eGOntl - c_ay anG. i't:.tm.~t, hclico-pte:ro . Fo:::''l (:'i "on helico}) tor, th·')so vclues"re lmm·;n 2.~d., ther<.:fol'o, the P! ' Opo:::.~ c!:':ll·ts 1."'2";[ b<.1 831cc·i~.Gc. i'rC-'Ll i,·I.ieh tl-.G CO!'l',(;t perfor.':18r:-~0 t::.~enc.s DfiY [)6 obtE.inod. . J.f ,':'9-'Gctor CCCll:-C~cy is dc:.:;::'r.:;o., tha cO.13tr 'ctian cf charts for o::act 7o.1n(;s of the lmolo7!1 variables if) possj.bLl .
LWlg}.e:f H0no'~i~'l Ae1'nnav.tical L[lbo::.~[.tory N:::.tion&:L Aclvi8·.)ry CO:r.!C1itt.)o for Ac -:::- o ...3utico I,;;:nc.;.l'-W Fiold, Vr.:. ~ septemoer 3, 1946 ~ .. _-- - - - NACA TN No. 1192 APPENDIX MJill.1I-IODS FOR CONSTRUCTION OF C""rlARTS '1'he figures vere constructed (In tho basia of the equations and. charts of reference L Since helie ' 11ter perforw.ence (:'ependa up on ],J.an;;~ variables, some of thea8 veri£) 0. 18S must be .;i ven roprecen-cative fixed values ia o~:,6.er t 'J f~h c n;- p0Tforru.;c nce t2'eno.s :i.n a r;r"1:phicaJ. form. Each ch3:::,t is made- .for c.ertain fixed quanti tics] vlhich are listed in the a.ascriptions of the figures give:. ill the ~1'08ent eppcnclix. The conGtruct :~ _ o n of each figure for the ~)reGent paper is dGscribed. in soquor.ce and I!28ny of tho quest:'ons that arise :i:l1. tho a:n.al~r8:la of the fi c m"es a re thus clc.rified.
Figtll'0 ~.' - Fixed '1.U8nt~ ties for fieu.ro 1 aro 88 fol10' 7S : Altitud :) . Sea lovel 0.012 0.056 R, ft . 19
f, sq ft . . . . 10
b V . • 0, 10, 20, 50, 75, 100, 150, 2Q~ h From the definit:i.ons of tho p51"'am.eters, it follows that ,·:hon 1 W \7 Po the value of .- --\ -- - correspond.in to a. gtven value of o }i' p ,j it p h 'i
r --- -
IA 0 = V 1- -_ ; ..
G kno"t-il1. . curves of constcnt horizontal veloc:lt:r h .j \'., Po r i r lllA;)" be 9:'.'Y'~ ,k'-:' (' tJ. a ;c J.6S 0:,": }?') F C.r l 03 i .r>.g Hlp agaj nst disk locc inc .. ;/.~ f():,:, c "'l..y alt:;:~r'J!.e :<:or which tho ratio plpO is knovm.
From CClut:-i,jJ.cn (2:'~) 0:: :i.~ofGl'E'nce 1 F_ D Tho q1.1.Q~J.titios that must be mow t o calculat e Gach term ore as follo"i-m: J7 NP~CA TN No . 1192
r Term Qr.£lnt ~.ty
l-------+--------- - -i Y.l.
0 ,
"
.,."
~ .
- l11' It is thus seen tr..:::t t.le six s.uanti ties needeo. to calG1J.13te FlL are 0, 'J. Yt, Yh, CD.,,) . Gnd D. Fiye of t.,."wse (J.uantitie3 ( a ..
.I·h 5, Yt, Y , and. '.:l) are gj:ven dtrectly b;y the stuted con<lit:l.o ns h for f1.gv.re 1. The 7alue of Cnfh is calcu13tecl fro:.n its de:!:':n.:.tion .J.
10 . 0 := 0 . 00882
O!1e curve of Fh 8g<.:inst vilA cal.: nOi 'T be calcul;::ced from the
cha:::- ts of refere~1ce IJ end fr'om this curve Clre ol:;tCl:!.necl tl~e concta~t - 7elocity curves of fiCLrre 1 .
I n I'l siJ-:lilar I!KmnOr the hovering curve of fi8U'o 1 is plotted .
From e~uation (45) of refere!1ce 1
F F..!
v -v -- --- ----~~---- - ~~--------------- ~ --~----~--~--- ~ -- ~ --- -- __ r -- ___ - __ --~_ - ~ NACA TN No. 1192 19 The pov!er~loading pa r ameter for hoverinG is considered a limi tine case of that for vertical climb (Fv wIth Y -70) . The quantities v required to calculate F v a re !J, 5, Y , Y ' and b . All are t v gi ven by the stated conditions for the figure. For Y ~ 0, v Fi -= 0.0264 for uniform 108el distribution. The v al ue of FiT iT is 0.Q3 92 ~ correspondin g to which the hovering c'.ll've is dra1,-1Il in fi S 'ure 1.
Fi~Ie 2 . - Figure 2 shows curves of maximum rate of climb superi.mposed for comparison on the hovering curve of figure l.
The necessary cel c uJ_stions are bassd. on fiG'Jre 6 of reference 1, which is reproduced hereins figvre 10. The rate - of-forward - climb parameter Y is react ham. fi g ure 10 for Imo-wn values of Y c ancl F - Fh. For the maximUIll ra.te of' cl:1m"b, use is made of the miniml1D. valUE! of Fh or Fmin corresponding to e. . best value of or Y gi ven by fi.gure 7 of reference 1 in torms of !J, 5, best Y , a nd CD..,., all of ,.;h:l.Qh are lmo'Vtn . In the present example, t .I.h Fruin::: 0.0235 a nd the corresponding C'..Lt'Ve of 1J/P against W/A is plotted in !'i g1.lres 1 to 3 as the curve Ior {Vl/P)max' Figure 3. - Figure 3 ehOWE curves of const a nt s e rvice c0111.."'18
(60 Vc = 100 ft/min) superimposed on th e hovorin g and maximum
povrer-loadin g curvos from figure 1. These c urves a ro bas ed on the cond1tion th El t the rotor driving po-vmr is proportional to the air d ensity because of the engine charecterietics. The devel o pment of th o equa ti on for th e curves follows.
The quantiti s consld~rod fixed for figur e 3 a re a s follov:S: . . . . . . . . . . .
• 0 . 056 • 0 .012 . . .
• • 320
. . . . . . . . . . . . . . . . . . . • 0 .00882
. . . . . . .
• 3 Th e maximu.m rat o of climb occurs for Y:: Y . For tho beet
condi tions at sel] level (~o = 1) the value of Y obtained
b est from figure 7 of r efe rence 1 is 1~6. 7 and do es not change signifi- cantly \.-1 th altitude. The pOvTer-loading parllllletor for the maximum 20 t>IA.CA TN No . 11 92 rate of clim1J :s Gi von h;)· cq1.ntion ( 1,8) of rei'e::'on ce 1, which is Q',?pr')::ima tel:;
v = 550{~J.' F ~
~c . \. - ::nin} and !lOnco
I J. ~-~
\ ).- ~-. == (1) ~~ Vl Po r~ 2nd at pltHucle At sec. level §c ::::
\J1: ' po - E
de;).s::.ty reti o . the rot or c-X'i -.,:I.ng p01ier i s 11:,:,oP()~'ti 'Inal to the Fa::, Y ,.~ 1!·;5 :r, the corresponc':'nrj value of F ( CGll~d ~mi~' best ~- ) is calcill..~te( from the sum -. Ti'. .;. Frat -:- Fb - ~~l as h~s been e:q;>19ined for Ph in COill1ect::'on ~.-:i.. th f;i. ,:; u.:re 1. Th3 p,-u'cmoter tM.t vc:.ries ~d t:t al'~i t J,c.o in thG }?resont e:;6Ii1rle)
- v n- [,A';-- n ~ 1 t' I.. T.l "" rlh
n~e 'J, ~t. ;:; "~.l.{V"! P~ QIl.ect.s on Y !WlJOr...:1S l' 'md .t'l'ot . L_a e_fect of Y on li'rot is nec;2.iG.-i"ule in GOI:llxlrison wlth F il1) t m Qnd 1":::) Is then the onl~r term CGlw:i.n C em r:pprccie.Jlo ch9.n~ .e in
the va 1'J.e of J!'min 'Id th clti tud.e . In orcLurco i'incl.. Fo, us e 1s
rode of 8'l'..l::Jtion (2 3) 0::' rcfereJ.18e 1 NACA TN No . 1192 fro:t:l ,.:hich, for the specified constants; At sea level;
FO = 0 . 0 235 and, therefore, at altitude
n:Ln
r- rp '-'. I P 3/ 2 -1
0 .
Fe . -i.ll - 0 . 0235 .' 0 . 0130 1 \1- · + 0. 9J.1- ) i· · 0 . 0130
I- ~ Po \. Po ./ -.J
.'. 0 . 0012 ,~' 0 . on8 (E-\3/
,:. 0 . 0105
V Po + \'P
o)
Rence, from e<luation ( 1) Sol vin ;; for· P A! ,..-1 ves ~ , b
? Po r ( Po~3/2 Po .. _, rw
0 . 010
- =: -- + 1 5 \-- + 0 . 0012 - - . '. 0 . 0118 \1-
( 2)
loT 330p L P P .J t j;'
NACA TN No . 1192 CorrespondinG to each altitude is 8 ratio p/PO' 8!1d from eC).uation ( 2) :·_s obtained.::! curve of ~l/P a.::;ainst YI/A . Curves fvr standard dens1ty altitude are shown in figure 3.
~-.:~.su~~J.: .- The quantities cons:idered fixed. in fiQ.IT8 4 aro 0 . 3 0.012 0 . 02, 0 . 03 . O~ 0 . 005, 0 . 01, exp1:-:!:i..nod frr figure 1, the six ql~utit~es needed to solve As "fi'
for are a
a, , Y , Yh~ CD~' ano. b . For each value
-h t .1.h of 8 cC've of l/.r?h ae,ainst Yh o~~ Y is defined by the CDf t h c onstants for tIle fi';Ul~e . For eXarJ.ple, a value of a correspo nd_ s t o each yalue of Y oelectcd. in sccordancG v.rl th the civen condi- t rA; '.
h
tion o"Y == 5740 . ( Grar of a aGainst Y .." OR \\1- _. is given
t t
"H Po
in fig . ~.) Thus all Quantities re~nil'e(l for "'1'6 are lm01:J.1..
Likewise, a value of Yh corresponcs to ouch value of Y in t acsordance with the reletion Yh ·= \J.Y 0 . 3 Y , thus all the t t qU1:mti ties needad for Fh !:; r0 knO>7!l . In figux e 1:. tho reciprocal vl of that is, been plotted to m::.ke the Yerticel scale ]?ro:portional to the f3mi3.ia_ quantity vi IF.
Calculations for the hoveri!1G curves shov1!l in n gure l~ are
simil ar to thoso expl~i:le(1. in cO!1Il6ction "r1th fir;~1Te L For each v alue of Y selecte~, a is ottqin6d~ as in tho case of hori - t j L
zontal flig.,.~t; from tho relation ay - == 57 !.O . C:::l.cl'..la·~ions of Fa
t
Fore mad.e for both is '"" 0 .012 D.llCL a = 0.006; thus, the t110
hovering curves shm:n in fiGU..re 4· arc produeeeL As e:x;plai:led for figure 1, the v21ue of tr.e ind1-1.ccd. pOi\Ter- loaetinc; :parameter in veJ.~t1cf!1 fliCht Flv i.leect3ct to calculate 1 o 8 )1)_lios to hoverin . i·711on Y --~ 0 7ho valu13 of F, varies iii th x ~ v ' ~v tho blade shape; the Im'TOst ynlue occurrinc; -;rlth bl::td.es shaped. fo r uniform. axiol -inflov:-yol oci ty d.istribution . Such clistribut;ions NACA TN No . 1192 ~3 :cequ:lro a ta!)ered and/or t'ldsted b18de. ror uIlt1-::i.sted rect imc.,'ular bl ac los the vahLe of Fiv is ap:-9l'oximately 6 pel~Ce!lt higher. In the pl~eGent calculation the min:i...m.um value of Fi = 0 . 0264 j.B y generally used.. boca; se it serves as a cO:"1venj.ent reference. The !lOverin t; C1,',r've in f:).[1_u~e 1 ShovTS o: aly abot :. t l.~ percent dHfe:c'en:)e in 1'; /p for the tyro extrem.e cases.
Fi [ ;ure 5 . - It'igtu"e 5 is sirl1 .. l8 :- : to fitP .. '.:'o 4 6:x:cep-t:; that 0 hes a-=i21uo-o:f' 0,006 instead of C JH2 .
4 except the Ficure 6 .- Figure 6 ~S sim:!.l.:lr to fieure <luantity IJ. J.c the varisble r3'(,her \·:hich is fixed at 7 5.
thr:m Yh)
Curv€'s of conot 61! t 5 = 0.012 flnd 5 = 0.006 [i Te shmm for
C <. = 0 . 010.
D III Fi o w'es 7 ane. 8 , - Tho c Q lcuJ .. '::lt~ons m~dc for f:!. g 1U~es 7 and 8 a re si:..nlbr to those' made for fi .g.. u~e 2 .
FiQJ.l~e 9 . - FigrTe 9 :I.nclud e s) in adcUtion to the hoverin :.s curve-for 5 '"' 0 . 012 of figLU'o 4, cU.:cves for vertic::;] .. fli:;ht for t\~O valuos of CDf and for values of the rot0-0:l -v e rti cal-climb v pE1r"lIUetor up to Yv:::: 30 . The calcu.lations for tlli.s figu..re differ from tl10 se for hover inc ocly in obtaininG Fiv for the g i-ren valles of Gofv and Y from figure 5 of ref er ence 1 .
v Figure 10. - FiBLL"~010 is a reproduction of fj,~;t)..rG 6 of r efer - onc e y-:----- Figure 11. - }i'i.Gure 11 a":'ffors from the Bel:er~lize d fieure 4 tn substitution of co notant f/P for CDf, an d in selection of !l the valuos Y.I- :;: 320, and :;: 1 .
v By deftni tion, fh P
.I~ p- (Wf~ fo
--
=
p VI
~Vl Po \A, P
fh :;: - ,oF
~' ~1!
p h A p A
24 NACA TN No . 1192
p For -- .. =- 1
Po
By mee.ns of 8C}.1'..ation (3), rolr.ts in fi <31.. 'Xe 11 m.':ly "be c81c1.i~Tt.ed from pointe on tl:e ~r(Enate Y+ == 320 of :fi 0 Ul~e ~!. .
'J Calcr>J.st:ono f or the Cu:rV0EJ of constan-c rete of climb are similer to those for f~cure 2 . The nE)cess a r~r 'l'J.antH:'es a .. G 3no. Y are all lcnO Yl1.. ano. to ee ell set 0:' values of YT /?, 11/! ... , t and fh/P there coc.>responcls a v e. l'J.CI of Cn " in accordance wit.h f - .!.l eQ.uation ( 3) .
The boundary of the regicn of stall is calcul'1tecl on the basts of figure 8 .)f roi''.J:renC0 1. The nL'lU~O 811ov7S that ~'()r the aS81L71.led.
r) vC'lue of aY c.. == 5710, st111ing of the bltH.le t:lps :':13Y be expect8d.
t when the value of tho ql'.antity 'A/p_ :i..s neer 0 . 5 for ~~ == 0 . 3 ,;:i.til ~ C'orresponcL··. nc to a section lift cO ' 3fficient of approxi - mately 1.5 . From. t.lG 101-TOr pert of the OF1!llEJ fi t:, UTG it is seen that vr.i.th y, == 96 tho valuG o·p CDf is about 0 . 03 . By me 'l 11.S • h of tIl' 0 vclue an0.. o i' e'luetion ( 3), tho stalling l~e c ion is definod.
i _ fi ,'). U'e 11 .
}f':LG'1..l.YOS 12 ~00 16 . - F:::'Crros 12 to 16 ero cons ·::'ructed. s1milc.rly to fie,ure-n:- - but iiith d.ifforeI:.t fixed valt'.o8 of 0 or [J. .
Fi [,uro 17 . - The co ndition that the hF)lico2?ter 8 all fly at its D" .a :, ::'.lntiL i-- speed 'Hi til the samo po-:1e:r as reql;.:t: ' ~ed. 1'01' } oV01"'inc3 restricts solutions to tho points of :;.ntersoction of cm-yes of constant CDf' .. rlth the hoverine curyo :in f:l.g"LU'e .1;_ . From these l:nteX'sect~ons tho curVGS of consta.:J.t f II? of fLn;reG 17 are _ 1/ ~ p obtained ;)y use of t113 rolation botlreel. 0-r. [. ncl fh/ (og.uc: - ~.uf.h tioD. ( 3)), which .. ms cler::'ved for f:L.:-:;uro 1J. c·d. by t'8e of the hovering CtU'VG of ;:i .Sv.rc 4 for uniform o.i8lc 10 rld.:L:c..S vith 0 == 0 . 012 .
The j,ntorfJect".ons in f:l.f,uxe 4 also detorminG v ~ 1u()s of' Yh encl, -'hich nro ::1180 cm:O-vGS of conatnnt G? in fiQL 0 17 because \-L is conGt:- nt . The c-m:'VGS of NACA TN No . 1192 25 constCl1.t flp are found to be nearly coincid.ent with the curves of' cor.stant Vh or of constflnt ~R . Curves of constant sen-ice ceiling v!ere calculated by the method described ~'or f5_ gure 3, the proper v elues of the constant qU2ntitj . os being usee ..
!i G ure _ l~ . - Tho calculations for the curves I)f' fi[1:UX'e 18 are expleined for fiGure 17, except that the CUI'V63 f r") l' constant rate of climb are obtained by calcv~ Cl ti o ns of the type described for figure 2 but .:i th the eppropri!1te constants .
Fig~e J9 . - FiesIJ.re 19 is nd~p-c6d from fiS ,ul'G 1 of roference 3 .
Ficure . 20. - By ' reduction in the 0'08S ,- might of a hovering helicopte:rJ-:p.oV1ej~ rnz.y be :made a' : ei18ble f or a Tate 0:;: vertical climb . For the hoverin G cond.i tion,. Flv h"ls a valt~e of 0 . 0264 .
From the defi:r...i tion F.j :::: " ·V
it fol10i-TS that if the gross Voig.lt vr is reducecl - oy 6W th en
0 . 0264 By means of fiBUTe 5 of reference 1, values of Y may be rend v for ImoiVn values of Fi and CDT' on the aSSlTlllpt:ton that tho v -v pO',ler a1;)sor'ued in blado profile drag docs no t vary ;' !ith rate of vertical climb . Th c se Cluenti tj.es dC:'ino cv.rvcs of const r ot HIll..
and constant CDf on coordinates of Vv 8 3 uinst &, rj\'i .
v
Fi f, tu~e 21 . - C1.U'V0S of constant tip 8::,Jeed r.L on coorc.inates
of H7p agains t v.T IA e.re plottod. ~n fiGure 21 from the seneralizod
NACA TN No . 1192 hoyerin g cur- ve of fi011'e 4 for lmif o rm disk loadin g . For the cOl1ctit,ion crY ,-:: 57 '0, the curves of constant 0' a re siro.ilerly t obt ained .
F:1 , gure 22 . - In the construction of fiGure 22 arb itr ary vAl'--les of O'Yt 2 ';-;; ' -selecteo, . The correspond~,n G valueE:: of 5 are (;81 - cu_lated 1:y the J.:'lethod of reference 1 fo:::, one of the curves in fi [;u 1:'o 19. By th:'s method, the vo.luo of ;) :10 the const~nt dr:3.g coefficient th &t lrou.lct ~lbso rb th o sw-ue po"er as th'3 clraG coeffic::'ont i-i~1ich v3ries in 3ccorclX1ce with t:b.e Cl::;,'ves 0;;:' airfoi l sec ti on ch&r - <) ,..., 8cteristics . Then, froI11 a plot of C'oY "- 'c[;2i 1fJt O' YtC: the t coordinates of tho minilnUIll ar e read . The values of 5 and of C5Yt2 are thus c..etermined for IllD:X:i."UUlT. ave r r:Ge lift - tlra;:; r at i o . Th:i.s proc edure ts c, rried out for h ove rin e; ( : :. =-: 0) Gnd for hiGh speed ( p, == 0 , 3) . For fixed 7allles of 0' t1.1e r atio or the tip- speed paramoters is -che required Genr ratio . The values of 5 and. C5Yt 2 thus obtained. for hoverinG, vhon tiDed. to c alcula t e th e value of F v :.. or eny s81ectecl v31u e of 0', nl a] be consiclered to gi vo tho hoverin l)erfo r m.ancG i-rhen a rotor - speect -r ed uctj_on gea r is b employeJ_ . In order to fineL the performance whon a (,)ear i.e no t usecl, the value of 5 18 culcu.lated for hovering, th e optiml11u value of O' 1' t f or hi [', 'h speed being sed . The ratl0 0:' tl :e pOi-lcr-loading :p al~aT!lote rs f or verl:ScGl flight r epresents the ro.tio of the pO";7or required for hovGrinc "rj,th un d vrlthout th o gear .
REFERENCES 1 . Talkin, H er bert W .: Charts for Helicopte r -P e rforma n ce Estima - tj , Ol1 . NACA ACR No. L5E04, 1 945 .
2. Gust afso n, F . B., and Gessow J Alfred: Effect of Rotor--Tip Speed on He licopter Hovering Performance and Maximum FO rYrard Speed. NACA ARR No. L6A16 , 1946.
3 . Gustafson, F. B . : Effect on Helicopter Performance of Hodi - fications in Profile-Drag Characteristics of Rotor - Bla de Airfoil Sectio~. NACA ACR No . L4H0 5 , 1944 .
NACA TN No . .1,192 TP"BLE I SUUlIJftRY OF CHARTS C )1 .., FigtU~e C0nc.iti0n .
. ' c. ~ Generalized, charts ~
.---
~, Horizon'val fliGht cUl<.1.. hoyerins to 6 .
Vertical climb and, hoveri.ni]; Rate of climb and. ceiHn.g 8, 10 7, I --.,..---+.- charts Powel'-load1.n~ tUsk-loadinG , ,-
-
Horiz o ntal fl iGh t) climb , nnd hoverin g 11 to 16 Vertical climb .:m d hovering 21 Helicopters that will hover 18 17)
-
Speci~ \ l-p'\..lrpose Ch2j.~tS Vertical clmb by means of reduction 20 "might Effect of rotor-speed.-reo . nction gears on hovering 22 :Nft.TIONAL ADVISORY Cm , lMlTTEE FOR A'h:ROl'TAUPICS NACA TN No. 11 92 TABLE II ELEMEl\lTARY DESIGN VARIABLES Symbol Definition ").
Ro tor-d isk area -'" .I.
Fuselage equivalent flat-plate area I p Rotor pOi-.er
Gross .might of helicopter rn.:i.nuB fuselage lift w
(J Equi valent rotor B olia .i ty Mass densit y of air p Rotor anb~~ar ve lo city r!~ TP.BLE III ELEMENT.A.RY PEP.FOPJilllliCE V ARL'\BLES Definition S:J'!Ubol Maximum rate of climb in forwa rd . fli &~ t Vc
I
Maxlmum horizontal velocity V h Ra te of vertical climb ( for hoverins, Vv == 0 ) Vv Coiling (e xpressed in terms of density rat io)
p/Po
NAT I ONAL ADV I SORY COMMJ:rTKj!; FOR .IlliROriAUT IC S NACA TN No . 1192 T ABI..E TI T FUl'IDl-ilVIEl'rrJlL DESIGN PAHAlfEt.rJ!:HS ~-------~ - -------------- - ------------r------------
,----------
Defin5_ ti on S;r~bol For:r.r j~ :" POvTer - l 8(. . 1n3 p'11'8mote:: F
,--
.'\ P
Tip - s]?eed parwmeter
\J - --
V itT Po
rrel~copter drag coefficient baoeu
en"
.;.JI
on rotor - disk riA
area Equi v3lent rotor solidH;: ," cr TlffiLE V Definition Sy"ib01 Fo r mula Ma):Dn-~ velocity parcmeter y V / ' p -
\ g Po
' ,I Haximutl'l A P rate-oi' - fo r ." mrd
- clinb parameter -
Vc
r--
- c
I
\ 1{ p; r Rate - of-ve~tical - climb lx,rameter Y
r
Vv ~- P
v
I
\ I'; ; ; I Horizontal i~- - velocity ?-"larameter y V h h
V w Po
I
- N.i\TIQI.: . .'\L ADV I SO RY COMHITT1:., "; ~OR j;..EI~OHAur I CS • NACA TN No . 1192 F ig . 1 1 ++ .
L NATIONAL ADVISORY COMMITTEE FOR AERONA,,":'ICS :~ !+ ~ ; f./: It ~
I nr i
::i:-r: ~ ~+ r tf f:j:,~ 4.:tj: _ 2 3 ! ~ "'"'-
5 6
Disk loading, W/A, lb/sq ft Fi gure 1.- Specialized selection chart for horizontal flight an d hovering. p = 0.002378 slug per cubic foot; 6 = 0.012; o ~ 0.056; Y = 320; R = 19.0 feet; f = 10.0 square feet.
t Fig. 2 NACA TN No. 1192 - .
~ ,
M -
1- • i .
'"' L -H '-i- ... .J.< ~ ...., ~ h- r :+,+ H++ ± . ~ ~ ..... '-. H- i l~ 1 -'-tl" '"t+
' "'"
.
n i- ~ T .. ~ ... ,
/ali Ii} ~ ~ 4:. ~ ~
~£t
-
60 ~ ~
> ' t- - L
t; ... f- - '
~ .. ..... -:±t
0- ~ . S i:':r I .f.; -;- ,r
r r - b ~
\ '-'
. -
..
~ - - ..
+ H r i-!
.: ~ . tJ±;. "I .. C4
t\' ~
fr ~ r - 4 } ~ ~ ..
.,. ~ ...
\ ~1 ir/J1
, ,..
50 r,j -
+i -':It ' r' "F": ~ ++ I: ~ P >- lj: -.
~ - 1i ~1- - ,tt H~" - .J- i ~,.. f-.
- ,- Ht -
~" I
~ r. -,
\
..i- +. ~
... .... +~ 4 -H
t+t- t+
-
\ ~.., t:.. f+
1- ..
+- -H- b r
b\
-
, .c-L .
t- h- rl \ r r t~ Ff -t+ + r c '"
"i
1: '"
-
f :'-'- ' '\ ,
i: i-h f-.-.-
c- - ..
-+ ~ I'" .: \ ,r; f; ~ : f-i I L.
~
f\. "
\ 'lOO - .
~ ~' ., Fl ' -.
\' I:-
-
~ I ++~ ' ~ H-- r rt , ..
~ -' i. TI JJ I )J l- ~ :-q -,
l it ,-, 'i:ri -h- ~
.. " .--
_ t+ NATIONAL ADVISORY ~ n- '..
H ; , r-......
1~T: ......
+I.. COMMITTEE 'FOA AERONAUT ICS 1-: -t-t.i -I:: b , "'-.
~
I tt
"'-.
,tl· y "" ;....~ ~ , < - +--.-!. f-.+..,:: -..:+. 1-;- , ~~ ........
)0...
Ie po
.......... :;:~ ~~ - .........
--.... -
"-
- ~ '-'" , --.;., , .
-
I"-- ~ ~ ,7 -tl-L r--."
£' ,- ;f T
"-... mt I-
--.
-
~
r-
-- -- ..........
'"-- I f-- :-- ~ t4t- >-
-
-r' ~- "- W , - ....
l!c ~ c , '~ t"
-
-
- -
,-
-
10 -
4 H .J..j.
i- l nn .
, 1.t'1 I-< - ..
, -
I i i
I i ! I
_ _ ,k
o
)f-.~ +--~l' ''
1 , - -.
' .
o 1 2
4 5 3 6
Disk loading, W/A, lb/sq ft Figure 2.- Maximum rate of climb for the conditions of figure 1.
Fig. 4 NACA TN No. 1192 Y = OR;'! ...e..
t W Po _ !illl1 hoo 500 ~ - - - - Uniform disk loading -~ -- - -- Untwisted rectangular blades =
Horizontal i'l1ght, 0 = 0.012 =-
IT 10G -J·~ - 1 60 -- 80 100 120 160 Yh = VhJ!...e..
w Po .2 j -
1 \
I ~ , , t NATIONAL ADVISORY f'\..
r- COMMITTEE FOR AERONAUTICS ~ .1
I'----
1-- ___ -...
r--
-
-
o . . .
20 0 300 400 500
Y = rlRJ~ *0
t
Figure 4.- Generaliz e d perrormance ~ h art ror horizo n tal
.') rUght and ho ver ing . f-.I. = 0. 3; I) = 0. 01 2; O'Y t'- = 5740 .
NACA TN No. 1192 Fig. 3
~
r-t ..
~
~
..
~o
If
....
'0 CIS r-t ,..
II
• 0 -' -
~ NATIONAL ADVISORY COMMITTEE FOR AERONAUT ICS
o
o 1 2
4 5
Disk loading, Wi!, lb/sq tt
Figure ~ •• Service ceiling tor the conditions ot £igure 1.
NACA TN No. 1192 Fig. 5 Horizontal flight Hovering with dj.sk l.oadj.ng 1-<
~
;;:11l.
II r-III%.~ .2 .,.1 ~ fL l-'
f j
- . . J: it ~L
if: ~
~ S f ::' t I - ~ , I ~ " .;-.,. ...
t .- c.,.
" NATIONAL ADVISORY
h
~ t--
~
-.., COMMITTEE FOR AERONAUTICS -;:r- ±\:f H-
=sf
>-
b .1 ,..,.
...- . --
,..
Yf: -' '"
K
r--
"" -, t- W ~ '-t
nrJ t--s
-
- J ..., ~ , cJ o , _ ~ ~ J = L-,: ~ -' ir .': -~ '--" '-- -- - - 200 .300 400 500
Y = ORV,!:. .1L
t w Po Fi g ur e 5 .- Gener a li zed p er f orm an c e ch a rt f or Bo rizo n t a l fli ght a nd hov e rin g. ~: 0. 3; 0 : 0.0 06 ; aYt~ = 5 740.
NACA TN No. 1192 Fig. 6
2 0 o
J.5
37.5
< - -r:-rr l ....
- -cr r --
--
_J:-
- '
-f- -- 1 ~ , \.
T
..... - -
- c: .....
...--i- ' -j
I
1 y.: ~ ,- ' 7 ./ ~ -. -+- I " , f
,.,/! '1 -
I j - l I -q+ ''=1:.
t V J-.-,~ - ,-+- -+-,
40 h-
/ 1 , I- I ~ ; I
.' p
~ -
k ~ f.< >-; 1 \ - - - - h-
I n f't hI-. 1/ ~ - "
- ~ '-\- . - - " ~;
! T
--" 1 -
~ -
. _ I-t
:E
- -, '~ ~ ~-: ~ Y -: J ,..
.- f ' !- - '++ ;:;: I !
I - I ~ - I .
I Y I
'-' -'-j- -i-j' V f ,
I
..l ,~ J m '~~ ~ ' -,- .....
I I /
-+ ~ f+-' ;:-",:
! .0 12 V -
I I
- .~ II F-' -I.t -, H
i ~
-
.... , - -!- I "
A
'-'- - .
I I : i I T, ,- - T'- I '"+-- ,, ~ d
I
j " ~
-rm -
~ ,- ~ f T '''1f- - J..
; i
i T t- 't
->.1 ' t-h- - I I ,
t- t H-
I .
10 L
-
NATIONAL ADVISORY
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crY 2 =
Figur e 6.- Variation of 5740; 1:. with ~.
t Fh CD = 0.01.
Y = 75; h fh NACA TN No. 1192 Fig. 7 Yt = onV! ..E..
w Po
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2QQ 300 400
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rll~ I 60 80 100 140
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NATIONAL ADVISORY y.
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h - h W Po COMMITTEE FOR AEAONAlfTlCS
Figure 7.- Generalized performance chart for maximum rate of
climb for the conditions of figure 4. 6 = 0.012. (V
h 1s the maximum speed i.e. for Y = 0.)
l c Fig. 8 NACA TN No. 11 92 200 UOO 500 ;00 100 _ ~k
~
l!=tp..
;0 II , I r-t~ 10 I.
, 80 160 40 100 120 NAT IONAL ADVISORY COMM ITT EE FOR AERONAUTICS
Yh : VhJ~ fc
Figure 8.- Generalized performance chart for maximum rate of
climb for the conditi on s of figure 5. 6 = 0.006. (V
h
is the maximum speed, i.e. for Y = 0. )
c Fig. 9 NACA TN No . 1192 100 400 500 600 3 00
Figure 9.- Generalized per~ormance chart ~or con-
stant values o~ ehe rate-o~-vertical-climb para- meter Y at sea level. 6 = 0.012; OYt2 = 5740.
v Fig. 10 NACA TN No. 1192 t: + 50.
: - \-; , ~ c I -i: ~ ';9 , :++ fUh +
-.:1:;: m.[¥I t+t
-, h ~ - , u \ . ~ l 'i:--I±!±± _ - ~lo. - 2
.02 .o.b
0 .0.4- • .1
F - Fh Figure 10.- Chart for finding the rate-of-forward-c1imb para- meter Yc.
Fig. 11 NACA TN No. 1192 Speed, mph
o 120
rip
- - Vo - - - - Hovering ~ .0 r-i
""
..
p..
~ ADVISORY ..
AERONAUTICS
~
'd Qj r-i ~ «> ~ p..
10 tf±ttllitttttttltltM ••
• 5 .6 .8 1.0 1.5 2.0 3.0 4,.0 5.0 6.0 Disk loading, W/4, lb/sq tt Figure 11. - Power-loading disk-loading pe . rtormanc~ charl~ tor sea level. iJ. = 0.3; 6 = 0.012; 0 = 0.056; oyt = 57,+0.
NACA TN No. 1192 Fig. 12 Speed_ mph tip - - Vc
+t=m+t=~~tmmttti ,, _ _ _ _ Hovering f#++H-HffiHH!!I!!I
.5 .6 1.5 2.0 3.0 4.0 5.0 loading, W/A, lb/sq ft Figure 12.- Power-lo ad ing disk-loading performa~ce chart for sea level. ~ = 0.3; 0 = 0.006; ~ = 0.056; ~Yt = 5740.
N~TIONAL ADVISORY COMMITTEE FOR AERONAUTICS NACA TN No. 1192 Fig. 13 Speed, mph 70 HO 90 100 .1 0 f/p Vo
--
Hovering
... - - -
III ....
..
Po< ~20 OJ - l ~ t
~~!f'~
, ., tt l ~ 'lid!
'\ · gi
m ~ I ~\ttF; w- .
f'l; , 'llll'ttu -r ,
rut
2.0 3.0 6.0
1.0 4.0 5.0
Disk loading, w/A, lb/s q ft Figure 13.- Power-loa d ing disk-loading performance chart fo r sea lev e l.
~ = 0.2; 5 = 0.012; a = 0.056; OYt = 5740.
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ~
~ o 8 ~ ~ o . I--' I--' (() C0
f'Ij 1--'- I--' ~ .
(J'Cl ~ AERONAUTICS ADVISORY FOR sea 6.0 tor )0 NATIONAL
rip Vc Hovering
5740.
COMMITTEE 5.0 chart
-
-
..
C1Yt2::
( rt
-
--
4.0 Ib/sq perrormance 0.056; Q C1:: w/A, mph 3.0 Speed, 0.006; disk-loading loading, 7.0 0:: Disk I I 0.2;
=
Power-loading I.L 2.0 .
14.-
r-
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, 4' .
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level.
Figure
1.5
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~
""- NACA TN No. 1192 Fig. 15 Speed~ mph 60 80 100 70 120 140 160 laO 60 ' tip Va Hovering
- - - -
.8 1.0 2.0 3.0 4.0 5.0
.5 .6 NATIONAL ADVISORY Disk loading, W/A, lb/sq ft COMMITTEE FOR AERONAUTICS F i g ure 15.- Po w er-loadi ng disk-loading performance chart for sea level.
~ = 0. 4 j 5 = 0.012; a = 0.056j crYt2 = 5740.
Fig . 16 NACA TN No. 1192 Speed, mph
rip
Vo Hovering
~
.0 M ..
p..
~ ..
~ oM '0 DVISORY aj COMM 0 AERONAUTICS I M H (!)
~ p..
.8 1.0
.5 .6
Disk loading, W / A, I b/sq ft Figure 16.- Power-loading disk-loading p erformance ch art for sea level. ~ ~ 0.4; 0 = 0.006; a = 0.056; aYt = 5740.
NACA TN No. 1192 Fig. 17
~\
r- fh
\\
28 - • 0.25
P I
\\ ~R • 325 fps
\ I \ V • 66 mpt
V
h L- I \
1\
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r- I
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~
\ rt Service ceiling· 10,000 Po L-
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t-- 0 R • 850 fps V • 175 mph h
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1\
C1 • 0.02
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- I I • 23,000 f't Service ceiliIlg <- NATIONAL ADVISORY COMMITTEE fOR AERONAUTICS I I I 1 ~ o
o 1 6
Disk loading, W/A, 1b/sq ft Figure 17.- Power-loading disk-loading performance chart for sea level for helicopters with power just sufficient to hover.
~ = 0.3; 6 = 0.012; OYt = 5740.
NACA TN No. 1192 Fig. 18 Vh - ....- Vo ~;;p fI and aWT1c.
~
~ ..
Po ~ ' ..
W
:t1
II
.s
,..
•
• 0
Po
a.o 2.2 2.4 2.6 2.8
Disk loading, W/A, Ib/sq ft Figure 18.- Enlarged power-loading disk-loading performance chart for sea level for helicopters with power just sufficient to hover.
~ = 0.3; 0 = 0.012; aY = 5740.
t Fig. 19 NACA TN No. 1192 :j: Airfoil aection Conyentional (rough) .12 - - - - HiCA ~-B-l~.5 (amooth) - HAC. 2~015 (smooth) ~ I - I - , ~:j: )- ' 'd .10 - u I ,- ..
- ~ ,
•
- +.
...t , R+ ...t .08 '-4 , :'-tI ~ , ,- T ' -
• -
0 'h-H- " - w- ~ ~ Qf r , ' -' ~
.06
i l±. r I r 'W t) : ~' - M - ~- -., tri -t ,-r -t '-4 - ~ ~J ~ I P- -
± t
- ; s:: .04 tri -: ~ () l: ,-+ «l rIl -v t .02 , ..j H ., '.- , ~ -- '-h-' E H-l
Figure 19.- Airfoil section profile-drag coet-
ricient cd against section lift coef- o ticient Ct for the airfoil sections of figure 1 from reference 3.
NACA TN No. 11 92 Fig . 20
3000 . t I:ti: " f iJ:t!:m
t- r lw l ..
'1 ++ :!:'".
T ~ 2 000 =t :t "1 ..
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1 500 - ; +i :j+ -,' -~ -rt- ~ -h- +1- ~ +' :j:. -, '~ ' '::-: -t +J~- +, ~¥~ 11- 8.1- ;:;~-
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h J:ttm + h: I 1 1+ - -I t.-. t+ NATIONAL ADVISORY It,.-
.... lJit: y
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it :-
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=- I~ I L~-++ I.J..J ti:j It': 1 + ;:l± tt :t t ~ <-U-l. I..~ 1..l.J.l.
20 50 0 10 30 Reduction of gross weight, AW/W, percent Figure 20.- Rate of vertical climb obtainable by reduction in gross weight of helicopters with power just sufficient to hover.
NACA TN No, 1192 Fig. 21 :: ~ " .
~ ~
OR, e = 0.012
OR,
e = 0.006
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, n; p ~';rt IrATIONAl.. ADVISORY 5: COMMITTEE FOR AERONAUTICS I e:. ' l q q f 4i; I Ii l ;~:h+
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o 1 5 Disk loading, W/A, lb/sq ft Figure 21.- Power-loading disk-loading performance chart f'or hovering hel i copters at sea level with aYt2 = 5740.
Fig. 22 NACA TN No. 1192
~ H ~- H rn l __ 1#
T
41rtol1 •• et1on --'1
., i.
Conventional (rough) ~
~15
ileA 3-H-13.5 (smooth) ~
- - - -
~ ., RACA 2301 (limooth) ~
. -
~
+ ' I t++ H+t+ -m
If-;- '-' ill _ __ ..
:, '_. ~ ~
~ r ~
t
,:a.
WLO
....t I-t- H -i-'.
~ f-' : ~ s::1 ....t ., II .,
•
~ () ., i-+ Q - h· f:l: '1+
'1 FtH
0 , ;". ~!-4 .. !4 _ ,- ! ~ .20
.05 .10 .15
Solidity, a
Figure 22.- Decrease in the power required ror hovering by use or a rotor-speed-reductlon gear.