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Ttk&&........ ....=fw’@x ‘~7 TECHNICALNOTES
. . . . .
NATIONAIIADVISORYCOWITTEEFORAERONAUTICS.
No.247
t’I O km rfdtlrnm-j to
ihe fifes of thfi ~~flgl~y ,
Mtmorial AeronauticalFOR REEEZEi&MXWatory ,.
WashingtonScptemb.er,>926
.. .
.—
a-. J
.
●
NATIGNAL
Summary
in ordertobegiaressarchon thedragofairshipsitwas
firstnecessarytor,akea logicaldigestof therepGrtedpast
performancesanddatagivenon decelerationtestsfora large
numberofairships.TY=tthesedata~a:rbecomea~~ailablefor
airshipdes~.gnersina compactformis thepurposeof thisr-
port,as wellas to sezve as thebasis on w’~ichtheauthoris
continuinghisresearches,yhic”nmill‘DegivenlaterinPartII
(TechnicalNoteHo.24S).
Thisdirestas givenhereinPartZ was,begunin Sqtember,........
1923,and‘rorkedon intermittentlyuntilDecember,1325.
Theoutstaildingresultsareas follows:
1. In genexal,themaximumspeedofmostairshipswas.re– _
portefla-oout5 per centhigherthanobte.insdin thisreport.
9U* Totalmaximumhorsepowerwaszeportedinmanycases
higherandina fewcaseslower,thanobtainedin thisreport= r
3. Propulsivecoefficientsat =ximum speed&are in Wn-
erallowert-banthereportedvalues.Coefficient“C’fis con-
N.A.C~A.TechnicalNoteNo.247%
stantandthepropellerefficiency
mum speedthatthepropulsivecoeffi
2
1111E is reducedas at maxi-
cient 1!K!!fallsoff.~.- Itwasfurthernotedthatseveralshipsof widelydif–
fere~tdesigns‘tednearlythesamedragcoefficientforthe.
vholeship. However,thisis lookeduponas a coincidencein
thecaseswherethetypeof hull,cars,andsurfacesdiffered
midely.
5. That
aboutfifteen
ler‘@dshout
in gene~alan idlingprcpellerwasfoundto lhave
squarefeetareaof dragwhilea stoppedpropel-
sixsquarefeeta~eaof .:ra.g.Thiswasfcundby
workingouttheareaofd=agfromtheshipisperformanceand
comparingitwith.theareaofd~agas cbtainedon thedecelera-
tiontestwitheitherstoppedor idlingpropellersas thecase
wasreported.In somecasesthisdifferenceofareaworkedout
tobe 8 or9 sq=re feetperpropeller,but withcertaint~~es :.of enSinesit ispossiblethatall engineswerenot stoppedbut
thatoneor twowereleftidlingduringthedecelerationtests.
Appliedvaluesofprincipledataand resultsare givenin ‘
TableZ andFig.3.
Introduction
At thebeginningof theresearch- “TheDragofAirships!’-
it was immediatelydiscoveredthattherewasmuchconflicting
dataon recordconcerningany givenparticularship. Dccelera-W %iontests had ‘Deenperformedon someship6,yettheresultsof
Y.A.C.A.TechnicalNoteNo.247 3
.
●
#-
thesetestsdidnotalwaysagreewiththatheldon exactlysimi-
larships.Thereportednm.ximumspeeds,propellerefficiencies,
andmaximum horsepowermauldgivea dragcoefficientthatdif- --
feredwidelyfromthatreportedor foundon thedeceleration
-tests.Or,again,usingthedragcos:ficientfm.rkiondeceler-
ationteststogetherwiththemaximumhorsepowerand reported
maximumspeedwouldinmanycasesgivea propellerefficiency
thatuashighlyimprobable.
A digestby Lipkfs enpiricalmetho~of digestinginconsist-
entd~.tawasappliedto thefoliomfigquantitiessmaxinurnspeed,
maximumtotalhorsepowerjprop-~lsivecoefficicnhat uaxjmum
speed,propc;llerefficienc}-at maximumspee~,areaofdrag
(poner02), anddrapcoefficientforthe-wholeship. This~S
donenotml.yfoxthedatacor.ct?i~i.ng %ch individwdlshipbut
takingintoaccountthsre”!.c.tionbetv”ccrzshipson thetwoquan–
titiesofdragcocfficientend-propCIZ.QTefficicncyUPOnwhich.manyquantitiesd.~,ended.Thenethodof hou thisrelationwas
obtainedisexplain~lfull-yin thee~~lanationof Lipkais method
as givenlaterin thisrepozt.
The reasonsforundertakingthisproblemwasprimarilyto
digesttheresultsalr~adycbtainedin flighton full-sized
shipsso tll’.tt-heres’fitscouldbe usedforfurtherresmrch ..
norkas will be givenlaterinPartII (TethnicalNoteNo.248).
Thescopeof theworkextendsovernearlyall theZeppelin
shipstogetherwithfivctypesof nonrigidairships.Themethod
N.A.c.Ac TechnicalNoteNo.247 ~%
usedisLipka~sempiricalmethodofdigestinginconsistentdata
and is explainedas follows:
Themethodchosenfor~hedigestionof inconsistentdata —
is theinventionof thelateProfessorJosephLipka. It isde-
scribedas the‘Imethodof selectedpoints”iriProfessorLiplka!s
book“GraphicalandMechanicalComputation.ilThisnethodis
fran’kly.axpirical,andhasnot iherigidmathematicaljustifi-
cationof the
ious,and‘has
datavhichis
be givenmore
metkodof leastsq~res,but it is farlesslabor-
thegrec.tadvantageforthepresentproblemthat
kQowntobe especiallyceliablecanarbitrarily
weightthanotherdataof lesscertainaccuracy.
Lip~*Gmethoddoesnotalnaysgiveresultsconverging
to consistency.If thesumof theerxorsisverylarge,each
aPProx~ationS~OWS~cr~sing di~er~cncefromConsistentval– .
Ucs,showingt-hatthedatais toounreliabletobe considered.
Explq.nationof LipkalsEmpiricalMethod
fortheDigestof InconsistentData
Lipkalsempirical~ethodofmakinginconsistentdatacon–
sistentniththetheoreticalmathematicalrelationt-hatexists.
As a stipleexample,Case1:
A rectar@eactuallyexistsas inFig.1. T1--l4
An observerz~nsuresside~[a!landrepo~ts5.1 a=5d=20
k. —[1 If 1! II !Ib!
* N.A.C”A” TechnicalNoteNo.247 5
Thesereportedvalueshavebeenmeasuredperhapsby differ-J entobserversat differenttinesand theaccuracy-of theirdata
isnotknownas yet;forthepurposeof research,letus thers- .foreassumethat ab = A nustholdtrueto four(4)signifi~nt
figures. Thisisanalogousto thereporteddataconcerninga .-..singleairship.Yetwithairships,thereportedvaluesof drag
coefficient,horsepower,naximunspeed,propellerefficiencies
at naximuii speed,andpropulsivecoefficientareinterconnected
by rmthemc-ticalrelationsandwouldonlyserveto complicate
the explanationof ther.lethod.The relationbetweendifferent
ships‘;rill be later explainedanalogoustousingtwo rectangles.
. Reportedvalues :AssumeA andb correct,then a = ~ = 5.146● ,b.
a. 5.1 ,IAssumeA anda co~rect,then b = ~ = 3.943
b = 3.9 .,+ A= 20.11 : Assumea andb correct,then A = ab =.. 5.1X 3.9= 19.89
,b!
Thesemlues of a,b, andA are theMt approximation:
1stapproximation:Reporteda =’ 5.1●
a = 5.146 ~ 1stapprox.a = ~b= 3.943 : 2:10.246A = 19.89 : 54123= 1stmeanvalueofa
Reportedb = 3.901stapprox.b = 3.S43
2: 7.8433.922= 1stmeanvalueofb
ReportedA = 20.111stapprox.A = 19.89—.
2:40,0020.GO= 1st mean valueofA
-kN.A.~”A-TechnicalNoteNo.247 6
Testforconsistencyab = 5.123X 3.922= 20.092= A, calculated“4 value. -.
lstneanvalueof A.. .O . . ..-. =20>00.092
..-.
Consistentto onlythreesignificantfigures.
Nowconsidertheseraear~valuesas newreportedvaluesandcon–
tinuetheprocessto thesecondapproximation.
Similartonetho&of firstapproximation:
.
i’
a = 1staeanA = 20s001st meanb 3.922= a, 2d approx.= 5.099
A = {Z.stmeana) (lstmeanb) = 5.123X 3.922= 20.092= A,2d appro~.
(Checlzfor consisten~y,A= 5.099X 3*903= 190901*)
Lastncanvalue
2d approx.“
2d m@n II
Xeanvalue=
b =2dlXea?lA=2d meana
A = (2C!meana)
La,stmeanvalue
3d aqprox.‘~
3d,aem 1!
20.0465.Ill= 3.922= b, 3d “
(2dmeanb) = 5*111 X 3.908
a b A5.111 3.908 20.046
5.129 3.922 19.9737
5.120 3*~15 20.0098
= 19.9737= A,3d approx.
N.A.c.A” TechnicalEoteYo.247 7
b= 3&meanA = 20.oG98= 3 908= b 4tn ‘f3dmeana ~“ >
A= (3dmeana) (3dme-anb) = 5.120X 3.93.5= 20.0448= A,4thap-prox=(Checkfor consistency, 5.111X 3.9C?8= 19.9738.)
a b ALastmean value 5.120 3.915 20,C098
4thapprox.II 5.111 3.308 20,0448
4thmean ~’ 5.115 3,932 20.0273
4thmeanA s 2~:~~;3= 5.119a= —— = a, 5thapprox.4thmeanb
~thmeanA 20.@273_b _— = 3.915= a, 5th “= 4thmeana 5.115
A= (4thmeana) (4thnem b) =‘5-Z15X 3=912= 2°~~~9~~r~~.20.040s.) —‘Checkfor consistency( 5.119x 3.215=
a b ALastm~.nvalue 5.115 3.912 20SW73
5thapprox.“ 5“119 3*915 20.0998
5thmean l! 5.117 3.914 20*o1185
~t~m-n A = 20.01E15a = 5.114= 6thapprox., a= 5ihmeanb 3.914
.
– 5t~.tieanA= 2~.~1~5b— —— = 3.912= 6thapprox~,b5tnmeana ● “
A= (5thmeana) (5th‘-n b) = 5=217x 30g1& ::;:;:,=A
(Checkfor consistency,5.114X 3=912= 20.0059=)
a b ALastman value 5●117 3.914 20.0185
6thayprox.“ 5.114 3.912 20.0279,m
6thmean 1’ 5.1155 3.913 20.0237
N.A.C-ADTec~fi .NOteNo. 247
. GthmeanA . 20._o&3zs 5.1170= a, 7thapp~ox=a ~thmeanb 3.913
6thm-n ~ = 20.02S7= 3.9143= b, 7~~ 1!b= 6thman b
5a~~55,20.olw=
A = (6th~ealla) (6thmeanb) = 5“1155x 3‘913A:7thapp~~x.
(Checkfor cmsistency,5.117X 3.9143=20.0294.)
a b A
5.1162 3.91S6 20.0203Last~lean~a~ue
8thapproxa“ ~.1155 3.s131 20.02276
The
—-
8thman “ E.1M8 5.9134 20.02153
gthappro~=
8thmean~ = ~~og~152= 3.9136= “o,9th1!
-D= 8thmesaa —50~158 ..”.20.02017=
A= (8thneana) (athn-n b, = 50Z1W ‘“3“g1~ ‘gthapprox.
(Checkforconsis~~ency,5.1161X 3.S136=20,0~236.)
Consistencyexiststo four(4}sigaifigantfi~resm
desixedvaluesarethentakenfromthe9thapproxtiationas
= 5.116;b = 3=914;..A.f0210ws: a .= 20.02;
as check,ab = A = 5.116X 3.914= 20.0240.
.-
Case 2.
Nowletus consideras
exist,as fOllol.vs:
h~=4I
al=6 Al = 24
I-J
247 9
exampletworectanglesw-nichactuall~;-.
Fig.2
I\A2= 19.5Ii
.-
a2=5
It }sknown(letus say)thathumanendeavortriedtomakeside
bz = sideb2.“Thisisanalogousto twotypesof shipsbuilt
sayin thesameyear,withr.o apparentadvancementin theartof
. propellerLesignc~~passcd to -t-heshipsjustbeforeandjust
afterthebuildingof tkese twoships. It thenis safeto say &_thatthese-two ships-wouldh~veas faza.sis knownthesanepro-
4pellerefficiencies.Cr.thisrelationthatside b~ = sideb=
thefollowingwillbe workedout:
Therepcrt6dvaluesare .
istrectangle 2d rectangle Mathermticalrelationsin thiscase
bz = 3.95 ba = 3=99 al’02= .42
~z= 6.08 a2 = 4.94 a2b2 = Aa.A~ = 24.95 A. = 19.80 h~ = b2
f/
—
.
4
.
N..\.C’1~*Tcc.ki@l~OtcNo.247 10
ered
Asstiingconsistencyto threesignificantfiguresis consid-
sufficient.?roceedLsimilsrlyto Case1.
b+= Igoac)——- = 4..OG8= b=,4.94 1st !l
Al = ZI ‘~ = 6.08X 3.95= 24.016= AZ, Istapprox.
ITOWuonsitie~therelationbl = bz :
-b1> 1sta-pprox.= 3.955 -.
b H 1[29 = 4.~Q8 ,-..
+-
(ZT.anvalue j CELI. = 3.982tobe a~:eragedintothemeanvalues.
Lestman (inthiscasereporteddata):.21 bl L$-l % % 4?
Lastnean 6.08 3.95 24.05 4*94 3.99. 19.80
1stapprox. 6.CM8 3.955 24.016 4.952 4,008 19.710
(c.eanval’le)cal. 3.982 3.382
1stman value 6.084 3.962 24.033 4.951 3.993 19.755
It is tobe notedthattheasmmptionthat ~ = k based.
on hunanendeavoris givenequalweightwithreporteddataand
hencee-ntersthe~eanvalueonlyonce,havingthusone-ttiirdef-,“
feet on themeanvaluesof bl andbz* However,if (inthecase
N.A.C.A.TechnicalNoteNo.247 11w
O.fships)2 certaindata,sayaE3obtainedfromdeceleration
.-
-tests
4 is acsucd.to be highlycorrect,thiscanbe givengreaterweight __
by averagingit ona weightedmeanprinciple.On shipswherethe _
decelerationdatalookedreasona’oleit wasgiventhreetinesthe
weightof otherrepel-tcdvaluesandwasaveragedin on eachap-
proximation,therebyforcingthedependentvariablesto closely
conforuto theactualdecelerationtest. To continuethecase
at hand-
Checkforconsistency:
(a,,1stapprox.)(3:, 1stapprox.)R 6.038X3.355y 2~a078
(%, II II )(%, 1’ “ ) = 4.962X4.008 = 19.887
Cornpared,,againstthemeanvalues;f
Z4*033
19.755
1stmeanAl ~4,033= 6.065 = al, 2d approx=
lst’meanbl= 3-962. ...
1stmeanAl ~~.033—= 3.950== 6.084
bl, 2d 11l.stneanal
(lst r~ean al)(lst mean bl)= 6.084 X 3.9:2 = 24.1048=I,.2d~pprox.
IstmeanAs 19.755= 4.947= aa, 2d approx= “
1stmeanbz = 3.993
1st neailAa 19.7!55— = 3.990= bz, 2d “
1stmeanaa = 4=951 ....
(lstmeana~)(lstmeanba)= 4.951X 3.S93= 19.7693= --AZ,2d ELpprOX-
4N.A.C.A.TechuicalNoteNo.247 12
4Checkforcons.istencj~; . . ,. .,
(al,2d approx.)(b.,2d approx.),=At=6.065X 3-?~W3-956~,
(aa,2d 1’ )(52,2d “ ) = Jlz=4.947X 3.990=19.738=,.
as comparedab=instAl = 24=10~8 b~,2d approx.= 3m950
AZ = 19.7693 ba,2d 1’ = 3.990mean= 3.970
bl k ba-‘1 -1 a~ &Lastman 6.:84 3.962 24.G33 4.951 3.993 19.755.
2d a-pprox.6.065 5.950 24.1048 4.947 3.990 19.7693
Mmulvalueofbl&& 3.970 5.970
2d ncan 6.074 3.961 24.0689 .4.949 3.984 19s7622
.2dmeanAl 24.0689: 6 ~764
al=-.2CLrmanal = 3.951 “= cl> 3d approx.
.
bl = 2d EleanAI= 24.0G59= 3096~6= bl 3d II2dneanal ?.074 > ..
Al = (2dmeanal)(25ntiznbl).= 6.074X 3.961= 24.0591= Al,3d ZLppTOys
2d meanAZ%!=
= 19.7622= 496032d neanba
= aa, 3d approx.3.984 “
bz =2dmeanAa = 19.7622‘= 3.9931= ba, 3d IIZd tieanaa 4.949
A= (2dmeanaa)(2dmeanb,)= 4.949X3,984= 19.7168=A~,3d appr~x,Checkfor~onsistency: .. .. ..
(al,3d approx.)(b~, 3d approx.)=A1=6.0764X3.9626=24.0783
(%, “ “ )(~, I* II )=A2=4.9603X3.9931=19.8069.+
as comparetlaLaMst
13
Al = 24.0591
4Aa ==19.7168.
b1>2d approx.= 3.9626
b 11 II2> = 3.9931
mean = 3.9??8al bz A3 % bz AZ
Lastmean 5.(j74 3.961 24. om9 4.9’49 S.984 19. ‘7622
3d approx. ~.0764 309&6 24,05314>9603 3<993 19.7168
meanvaluebl & ba 3.9778 3.Z778 ‘ “3dmean 6.0752 3.9571 24.~5404.9546 3.9$34919.7395
X!.meanAl 24.~64~% ‘>- = 6.~558= al,
= 3.9671 4thapprox.OQ meanbl
bl = 3dmeanAl = 24.0640= 3.9510 = bl,b.~7~2 4th “Sdmeanal ‘“ .,
AZ = (W. meanaa)(Zdmeanb,)==4.9546X3.9849=19 .7436 = A.,4thapp~~x.
bheckfor consistency: .,.
(al,~thapprox.)(b.,4thapprox.)=AZ=6.0658X3.9610=24.0266(a2, II II )(ba, “ “ )=A,=4.9535x3.984&13.7347
acj apjainst.i .“ .-
A1 = 24 ●1009.,,
....~<1 ...,
.. -----
N..4.C..!!..TechnicalNoteHo.247* 14
It isseenthctrect2nqle1{0.2 hasreachedconsistencyto
4 threesignificantfigure~as specified,whicharefor engineer-
ingpurpo~es.-—.
aa= 4.95 b 3.S3‘Az13.7,“
Forch~ck4.95X 3,98= ~9.71310
Thw thevalueof ba = 3.98 canbe averagedintothenext
approxtiatim,thesa~eas theweanof bl and ba wasformer–
ly. Theilextapproximationneedonlybe carriedouton rectangle
No. 1.-
Thus:
Lastaean = 6.0752 3.96’71
4thapprox.= 6.0658 3.9610
ba = 3.98
~thn~an = 6.0?’25 3.9649
al = A 4th ~e~n _ 24.~~25 = 6.0670b 4thK,e~- 3.9594
24.0825
= ~1> 5thapprox.
Al = (4thneana:)(4ti~meanbl)= 6.0705x3.9694=24.0962=Aa,5thap rox.
7Checkfor consistency(al, 5thapprox.)(bl,5thapprox.-=6.067X3.9671=24.068.
It is seen‘~hatrectangleNo. 1 ti2sreaclmd.consistencyto three
“ significantfig’~resas specifiedwhichareforengineeringpur- _
poses.
al = 6.07 bl ==3.37 Al = 24.09 cr 24.1for3 figurer
2hGCk6.07x 3.97= 24.C979r
.
“
*
i?.A.C.A.TechnicalNoteNo.247 “ 15
It isherewelltonotethatalthoughhumanendeavortried
tomake bl = bz itwasso tempered.by thereportedvaluesof
1)~and ba thattheyneverdid
finalvaluesbl = 3.97 and bz
So itcanbe seenthateven
thatthepropellerefficiencyof
anothez,theydo notnecessarily
quiteequaleachothez.ThUS
= 3.99.
thoughan assumptionwasmade
oneshipis equal to t-atof,in thefinalvaluesequaleach
otherunlessthereporteddataagreescloseenoughtomakeit —Soo
● The interconnectingquantitiesbetweenshipswhereno data
we~availablewerepropellerefficaciesanddragcoefficients.
Thedataobtainedby directobserr~tionaremaximumspeed
andhorsepower;dragcoefficient(withdeador $dlingpropellers
as wasthecaseat thegivendecelerationtest).
Thedatacalculatedfromobserveddataaredragcoefficient
withengines‘havingnoprcpellczdrag,propellerefficiency,
maximumspeedandpropulsive
Thedataobtainedwhere
wereto consi&eras reported
betweentheshipsbuiltjust
finenessratio,typeof cars
coefficient.
no decelerationtesthadbeenrun
dataa dragcoefficientthatlay .beforeandafterwithdue regardtO.
and surfaces,contoursof hull,etc.
Thisassumeddragcoefficientwasforcedby IJipka~smethodto
varyifnecessaryto accommodatethedragcoefficientas calcu-
latedfronmaximumspeed,hors~~owerandpropellerefficiency
or fromareaof drag. Likewise,in shipswherepropellereffic’i- ,
,. .
N.A.C.A.TechnicalNoteHo.247 16.
.
*
endywasnotknownby anydata,it wasassumedas betweenthe
shipson eithersideof it. Thiscouldnotbe muchin error.as
propellerefficiencyat maximumspeedwasalmosta centinucus
fw.no’tiion. Thenagaintheareaofdragas foundfor shipson’
whichdecelerationtestMd beenrun,wasseentobe nearlya
centinuousfunctionfmm onedesignto anothez.So wherercport-
C3datancrcnissing(twocasesonly)tncsca~sumptionswere
made,
Greatweightwas given to thedxagcoefficientsandpropel-
ler efficienciesas obtainedfroman actualknowndeceleration
test. Thiswasdoneby averagingthisobserveddatain oneach
successivemeanvalue;therebyforcfilgthe conflictingreported
datato conformto thedecelerationtestdata. In sonecases
twodecelerationtcctso: thesaneshipwerefoundand theydif- .
feredindragcoefficientandpropellerefficiencies.Insuch
casesan averagevaluewasusedforthe initialreporteddata= . _.
Afterthefifthapproxirntiontherelativevalueof ~ch q~n~itY ._._
comparedto thesamevalueof shipson eachsideof itwasnain-
taincdby avora.gingin thisinterpolatedvalueofdragcoeffici-
entandpropellerefficiency.Thesetwoquantitiesdetcrnincd
all therestforeachindividualshipso gavetwicethen~ber . ..
of calculatedvaluesforquantities.Thus, ona particularship
a valueofdragcoefficientwouldbe arrivedat fromthedata
pertainingto thatparticularship’andanothervalueof itsdrag
co~ffici.ent~O~l&be arrivedat by its relation to theship~S
. ~~~~.C*A.TechnicalNote?iOo247
1!ita~-:Gllon eachsideof it,whichanounts
i portedobserveddata(givinggreatweight
17
to this:digestall re-
todecelerationtests}
forfiveapproximations,thencalculatetherelativevaluesof
sinilarquantitiesbetweeneaohitenin succession.Thenon each
successiveapproximation,averagein to itsmeanthe interpolated
valuesofdragcoefficientsandpropellerefficiencies.Thusthe .—relativevaluesof quantitieswouldhavenearlythemme relation
betweenshipsas foundto existon thefifthapproximationand
wouldbe foundto existin thefinalanafiysis.
BodyofReport
.
Preliminarycalculationsof data,and empixicaldigestof
reportedanddecelerationtestdatato obtzinconsistentvalues
of allnecessaryquantities.
*Liplatsenpiricalnethodwasused. Thismethod,as ex-
plainedin theintroduction,gi~e~consistentresultsby chang-
ingvaluestlmtlieoffther.eanby arbitrarilyuoving(byaver-
aging)theulmlfwayto thatMeanandthencalculatingthede-
.
~ pendentvariables.ThisJmsdoneforsixdependentquantities:
r:laxitnu.1airs~eed,horsepowerat naximumspeed,propulsivecoef-
ficientat~aximumspeed,-nropellerefficiencyat naximumspe~sd,
areaof drag,andwholeship’sdragcoefficient.
Itwa~foundthatthedatathoughtreliableoftenr~oved
slightlyas itwasnotalwaysconsistent.
N.A.CDA.Tcchni.calNoteNO.247 18.
4
.
Prclininaryapproxiuat~cc.lculationsweremadeon therela–
tivetotaldLr~g of eachship,itsapproximateskinfriction,re-
sistanceof thebarehull,etc. Thiswasdonepurelyto geta
convenientarrangementof theships,andnotintendedtobe the
basisfo~thesubdivisionof a ship;s dragintoitscomponent
parts,asbarehullresistanceand skinfrictionare onlyvery
approxtitc. Part11 (TechnicalNoteNo.248)dealsentirely
witht“ncsubdivisionof thedragofairships. -.—
ThequantityS = IIcharacteristiclength[’withpoweronand
poweroff, was carriedalongthroughthreeapproximations
primarilyto givea moreaccuratestart tothesystemofapprox- ._
imatione.
Consistentres-~ltswereobtainedin elevenapproximations —
whenrtostquantitiesshcmd a rapidlyconvergingscriosof their.
differenceswiththepreviousapproxizz.ation,andthedifferences
yet tobe sosaallas-toshowsucha mall rmclericalthan.=in
thedepcndontquantitiest’hatthoIiaitsof theseserieswere
takenas thefinalconsistentvalues.Thefinalvalueswere
thencheckedagainst
tions (SeeTablesI
Thejustifice,tion
eachotkcrby theforiulasof theirrcl&-
toVIIIgivenat theendof report).
Asstmptions
forth~relationsbetweenshipsisbased
Theartofpropellerdesi~nforairships ._L
s-nowcdnearlya continuousfunctionoverthetime. The!propel-.
. U-A.C.A,Teclhni.calNoteNo.247 19
lerefficienciesgaveseveralpointson thisfunction.It then
“+ was safetoassumethatthepropellerefficiencyof a shipon
.whichno decelerationdataoouldbe foundwasbetween-Thatob- -----
tainedon theshipsbeforeand theshipsafter. Thisassumed
propellerefficiencywasgivenequalweightwithreported(not
decelerationtestdata)dataon thefirstapproximateion. The
samewasdoneforwholeship?sdragcocfficienton theships
no decelerationtestc ‘hadbeenran,taklinginto.accounttype
hull,volue, typeof cars,surfaces,etc., and so,in fact,
becamean
thefirst
Each
interpolatedvalueof thedragcoefficientforuse
approximation.
where
of
it
on
ship$s datawerethenrunindependentlyof otherships
forfivcapproximations,giving~reaterweighttodeceleration
tcstdatawhe~eavailchlc.At theendof thefifthapproxima-
tionthevaluesof C and E werecomparedto theitemson each
sideof itandthisrelativepositionwaskeptby averagingin
these.,newinterpolatedvaluesonalltheapproximationsthat
follom.
—
. 1{.A.C.A.TechnicalNoteNo. 247 20
Sym’bOlsand DefinitionsUsedinPazt14 d
L,
= Lengthof shipin feet.
w = Airspeedinft./3ec.
umax.= Ai~speedat fullthrottleall engines.
A = Kaximm crosF sectional Zreain sq.ft.
—.
k = Cylindricalcocfficient..
x= EiGtar.ce fromnosetomax+imumdiareeter in feet.. x Alt30usedto indicatet-ypeof seriesas in X,~,~.....O.
—.r Uaxifi.umrcbtl,iuaof hullinfeet.
e = Zccentriaityofnoseellipse.b.4~ = Tot~lsurf~ceazeaof h-ullin sq.ft.
S.F.= SkinfriCtiGn.
Kp = Approx.dragcoef. 1duetopresmredifference.U~e&or~yin fir~t
Ks = l! 11 II II II skin :Ziction●
1
approxi-r.ations.
K = II II. II II 11 hl.11~.
K= Fropulsivecoefficientinl.z.st approximationsandfinalfiumarie~.
PO = PullTatedhorsepower.
T = A ternt’hatapproache~propellerefficiencyE.● .-.
E = Propellerefficiencyforwi~oleship.
.
. R.A. C*A.TechnicalNoteNo.,247 21
Emax.= propellerefficiencywith Wmax.and~~max”
* P = Densityof theair;consistentlyusedas a constantof.00237sWgs/c-u>ft.
I$J . Tfi&ualvolume
s= Characteristic
Sp = II
in.cuoft.
lengthinfeet.II with poweron in feet,.
A= .4rcaof draginSq.ft.
~p ~ H II II with pcnvezon infeet.
c = D~a&,coefficientof wholeshipinabsoluteunits.
Note.-Subscriptnumeralsdenotethem],a’aezof theapproximation.
Pximcs(as K’,K\’,W’)” “ II II 1! H
in thefirstfewapproximations. —
Wherethereareanyapproximationsona sheet,thewhole
6heetislabeled“Prelim.tnary Calculations%”Thisisto
preventmisuseof thisarticle.
FinalresultsofPartI aresummarizedonPage3.
* }T.A.C.A,TechnicalNoteNo.247
Formulas
●
HP. P )( ?~ol.2’3V3available= cx~ 550z
HP.r =
E
K
Ap
Ap
c.
c
●
c
K
Ap
Horsepowerusefulinlineof fliglht.
-HP.* SD-d
‘available =Q HP.available2/3 2/3
Propulsivecoeff.= ~ = 2E(1”01-) = p V3(VQ1Ap 550+.r
Areaof dragwithpoweron (sq.ft.).
Draginpounds P = slups/’cu.ft.p ~2 v = ft.,?sec. .
2 Ap = Sq.ft.
Dragcoefficiei~t(absoluteunits).
gr~,g “iIl -p CKl?ds.=K; vyvol.)2”3
T?M= virtialvolumein cu,ft.. Vol,+ N.3
ST) (r = max. radiusof crosssection).Sp = characteristiclength,poweron (ft.).
.—
.-.
. .2VM
‘poweroff= ‘powerofffoundfrondecelerationcurve..● ‘poweroff
—
Ap - Aponeroff= Areaofdrag,dueto idlepropellers.
P = .00237 slugs/cu.ft.(Allforegoingdatabasedon theu standarddensityof air.)
. N.A.C.A.
v
D
.HF.*
T~chnicalNoteNo, 247
Formulas(Cont.)
Velocity;alr,speed.inft./see.
HP.X2X55-OXE (HI?.= Max.EP.available.)c g (701.)2i3 (E = PzopoEff.at v~ax.
andEP.max.).,.,.,,... . .
w ft./see.D = pounds
@t=d-o &- ‘s=characteristicieng~fl);
-t‘poweroff= *_ ~ (7Tom slopeof$ plotted
V. -J . L t duringdecele~~%;;fi~est.)
.
Conclusion
.
●
.
1—-* Theconsistentvaluesobtainedin thebody
portandgivenagainin theSummarymustbe usedin
24
●
of thisre–
theligiltOf
themethodby whichtheywereobtained.ThilS, itmustbe real– —
izcdt“=tthenet errozsen rcpoctcddatacomparedtowhatactu-
allyexists,arepm-xitedaroundand that~rrorsin deceleration
testdataarelikmjsepro–rzztc~arounduntilconsistencyis ob-
tained.It cantkenbe saidthatthe~alueshereinobtainedare
theprobablerelat:vevaluesandttus:ordcsigmand research
purposescanbe c~rl~~d~r~d as a digestof past
decelerationdata.
?d. partII (T.1~.IYo.24S)dealswiththe
performance
subdivision
Emd
of
theDragofAirshipsandthisworkpresents(bytheauthor)the
pointofpreliminarycalculationsanda first VL curvefor
fullsizeb~l”eairshipb.ullsc
3. Therangeofapplicationof thedataobtainedinPartI
—
—
c~mnotIogicaIlybe appliedto ilewdesignsthatarenotnarlY
similartoairshipsfromwhichthosedatawereobtained.Ho’i7-
Cvcr> on thejud~entof thedesi.~.er,certainq~ntitiessuch .+
as d~~gcocfftcientandpropellerefficiencymaybe usedfor
shipsoflargervolumes,theaccuracyof theresultswilllarge-
ly dependon theassumptions~,ade.Part11 (?.N.No.248)en-
deavorstodevisea methodof calculatingquantitiesconcernin~
a newdesign.
K..4.C.A+TechnicalNoteNo. 247-
“\References
● N.A.C.A.TechnicalMemorandumNo.237*’-by FriedrichStahl,November,1923.
N.A,C...4.TechnicalReportNo.117- I’TheAirships!!by MaxM. Lti.nk,1S21.
N.A.CaA,Technical~e~ortNo.184- “The
25
“RigidAirships”
Dragof Zeppelin ..—-
Aerod~@amicForcesinAirshipEullsi’by KaxM. M-uk,1924. - -.
N.A*C.A.TechnicalNoteito.194-‘;AMethodofDeterminingtheDimensions~ndHorse-powerofan AirshipforanyGivenPerformance1~by G. P. Burgess,1924.
BureauofAeronautics(U.S.Navy)DcsigmMemosNos.30,41,~~,44and47,by C.p. ~~~~ess. .
VariousPapersby Prandtl,Furmanj31asiusandS’@nton. ..
U.S.NavyBu. Cl.&’R.BulletinITo.101,Dec.1919.
llThcRigidAirship,ZR-3[[by C.P. Burgess,publishedin. JournalA.S.N~tis,~ovembe~,1924.
ReportsonAirshipUodels,by ~iffel,1918.
ClassroomNotesfrcxnProfessorsE. P. Warnerand Lipka,Kass. Instituteof
Inadditiontodataand
‘s ‘followingdataobtainedfrom*
Tcchnolo~.
formulastaken
Germanscurces
fromtheabove,the
sireconsidered.
(Wheredataformorethanoneshipin an itemww given,theav-
erageis tabulatedhere.)
*
* N..’,A.A.Technical 26
AdditionalReportedDataI 1
9 i Air Dist.max.Prop.Prop.1DragIter~VolurlcOyd.from Coef.Eff\ I.Coef.
Nose I] at. .
~ length I~.ax., Cu.ft. Klz C*
a; 17● 50 16~361
9 I 572000 25.80 20 I
I28I.05610 I 23.62 16 33 ~.C4411 ! 25.00 19 66 ;.G71121 24.61 ~ 2613 ! 22.40 ; i9
59 1.052. 57 1.048
14 I858000, 22.19 24 55 I.J055
24I
I9 30.80 i 59 65 .02025 2400000I 24.40 56 65 ●020
Remarks —
Forr.ulaC = ~ doe= .notalwaysholdtruewiththisdata.
Cn thisiteu,datastatesskinfric$ion= 82%hulldrag. —.—
Ingenexalthisdataconflictswiththatgivenin therefer-ences. It is thusconsideredas reporteddata.
A statement‘intheabovereporteddata,thatskinfriction~constantX V-*047=fiefhulldrag(~he~eV=\-oUme of hull)isnotconsistentwithCiatareported,for.ita22.
*FOTwholeship,
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