o:..42z!.zL4,z&&#’T’EC-HNiCALNOTES
NAKOITALADVISORYC~l.~[1TTEEPOPAMONAUTIw .
No.132.
THEINLXEASEIN DIMENSIONSOF AIRPLANES-
‘KUGHT,AREA,ANDLOADINGOF WINGS.
By E. Everling.
FromTechnischeBerickte,Volume111,Part2.
March,1923,
--— —- — ——- — -—
https://ntrs.nasa.gov/search.jsp?R=19930080940 2018-09-18T04:40:41+00:00Z
NATIONALADVISORYCXMMITTEEFORAERONAUTICS.
TECHNICALNOTENO.132.
THEIN~”ASEINDI?4JZNSIONSOF AIRPLANES-
WEIGHT,AREA,ANDLOADINGOF WINGS.*
By E. Everling.
Synopsis. .
Thepercentage..-weight of thewing relative to thetotal
weightof theairplane(cw= 100Ww/@J) and theweightof the
wingperunitarea (Ww,kg/ma) ofactualairplanesarerepre-
sentedin theirrelationto thewingarea (Sm2) andto thewing
loading (W/S,kg/m2) - theinfluenceof thelatterwillalsobe
dealtwiththeoretically.
1.
2.
3.
4.
5.
lt is concludedthat:-
Theweightperuaitareainczeas>s~.~~~t”lywiththewi~.g
a~ea,
Thepercentageweight of thewing increases at a greater.
rate.
Theweightof thewingperunit-areaincreasesratherrapiCi-
ly as thewingloadingincreases.
On thecontrary,thepercentageweightof thewingdecreases
muchmorerapidly. .
Thereareconsiderabledeviationsfromtheselaws,particu-
larlythatunder(1},andtheexceptionsarenotconfined
to s~ecialty~esof airplanes, .,* FromTechnischeBerichteVol.,111,Part2..(1918).
,,., . . -. ..
6,
II,
age
-2u-
Theresultsof thetheoreticalandpractimlconsiderations
regardingtheinfluenceof thewingloadingon theweight
of thewingare inagreement.
Thisinvestigationsupplemetitsthe~reviousreport(T.B.vol.
~0.2) in thatitpartlyexplainsthevariationsinthepercent-
weightof thewings,thereconsidered,in theirrelationto the
dimensionsof theairplane,particularly,by showingtheinfluence
of the‘wingloading,andin thatit dealsfurtherwiththequestion
of theweightof thewingsperunito-farea,
variationintheWeightof theWings..
Whenapportioningthe~ei~t of theairplaneintoitsmain
componentparts(T.B,VO1.11,Part3,pp.563and 579),withc%h~r
considerationsitwasascertainedthat‘thecombinedweightof the
structure(wings,tailunit,fuselage,landinggearetc.)varied ‘
‘withthedimensionsas wellas withthewingloading, but thatthe
actualrelatio~existingwerenot completely illustrativeof the
slightvariationof theweight of the‘wingswiththedimensionsof
theairplanesan-dwiththewingloading,whichwasindicatedOnly
in thefirstreport,(T.B. Vol.IX,Part2,p.279)butwhichwas “
clearlyevidentfromthetablegiving
includedin thatreport.
In thefollowingportionof this
weightof theotherpartsof thewing
and theirrelationto
Thesizeof
ingweight
thesizeof the
theairplane
(Wkg).
detailsofactualairplanes
treatise,thepercentage
structurewillbe dealtwith ‘
airplanewillbe demonstrated
willagainbe indicatedby thetotalfL~-
-3-
Table 1.
DistributionofWeightwithloadimzandcoefficientsforvarioustvpesofairplanes.
1
No.
2
1234
;?8
1:1112
ii15161?1819
%22
;:252627
%30
1
31323334Z5*SeeT.B.‘
Typeoair-,;@lane
EaDa
%.DcDd
..%DgDhSEVa
B&)DkBa
3E(II)Ca
EccCdCeCMCgChCiCkclCmCncoCpCq
%
-
3
No.informer.T~bleI.
1
:5789
::13
;:18192021222425
%’28293031323334353637 ;38 ~3s’4041.I1.11,
I14Totalflyinweigh
w
kg
5355?8604632780841e4588790190894-79549901026204010401071113012181256128613001315332213352346134613501353135914751520154615612585
‘art8,
5
ctxn-binedwt.ofstrue%ureTc
kg
206174181207245219252254ZB2256336300350326331349273325517332360392409402369327394458403459404430420462440
PP.5~
6
lpt*ofwing
Ww
kg
6262
&1058412511312599112123154143146153110135211140146164167180163150150212156174192171189192192-571.
7
wt.oftail
T/t
kg
910
:;151517163215
%
::16
%21231816
%22211522
%23161923
%
8
wt.
offuse-lage
Ff
kg
625044686060566555721518782
::8260
1:$807084100110::
13111016012088118102122m’?
9 I 10
Wt,ofacces-sories
wt. of
landinggear
kg I kgI
3122
T52!52511203027
2:3633623640431144560607028454229501680566843
::
4230302940
E4050434546445946443852 .69496864
:;5658626654625254636872
-4-.
TableI (Cent)
Distributionofmei~htwithloadjngand ~effi~ientsforVarfOUStYPes ofairplanes.
No.
36
%3940414243444546474849
::52
::5!5565?58
596061626364
6566
+‘2
Type ofair-plane
Ct
%
:$J%%GaGb
%GeGfGgGhGiGkRaRbRcRdDrar)?
Sopwith:[email protected],e
DmDnDrbDoDpSpadSVIIDqDr
3
!Jo.in~ormefiFableI
4243
%46495051
::55
$59606163646667Dra~*__****6
.---—----10
(Db)14
.eredas
4
Totalflyingweight
w
kg
16181620163916431668200327852975302430333250341!53618361836483795102031146012953L3035571616690
697738745763838857
860923
-iiEGKC
5
Gozri-bined::;$
ture‘V*
kg
4594994234314446359887428621216100284210101092112211884638495053505223
●
-r&m
6
wt.d.wing
W*
kg
1882041961’78200401541330466440395400430496506638io?o!050!350:358i9?135
861159810614399
122140
‘N%. Wt●
of oftailfuse-
J.ag.e
w~ Wf
kg kg
22 14521 12832 8822 13032 1054954 1%42 9018 25250 47061 26642 11060 37021 33921 35946 18236512704001450400145040(3”1450
9 I 10
wt.ofacces-sories
wa
kg
wt. ofandinggear
4262364742
%1?o251601351604068
1%140250250123
76183110101
R130110168168190793800900900
t**Armorcons~
. —..***ParenthesesaretakenfromTableI of thefirstreport,T.B.V:; ~~
No.2,p.286.***~ashesindicatenewtypes.
\
-5- “
TableI (Contd.) . ..Distributionof weightwithloadingand coefficientsforVariOUS
1 I 2
TType’ofair-
No. plane
Ii
6?68697071
72?374757677
Z
::82638455&6e788
%91
;;
95
9697
BCDSD-tCy
Sopwith2-se@Qj
AaCzBdBeBfCaC$CyC5CEcc
%cl.CK.CA**Cw
%JcG1GmGn
HandleyPageIReRf
@pes ofairplanes.
3
No.informerTableI
--
(R)
:;
-—
(~)
---—--—-
(X)
(;;)
(Q)
(;;)(CL)
(::)
(g)545662
[Ra)Rd)
4
Totalflyin{weigh-
W
kg
940~950961975989
103510431069108111501222123812641313132013441349135214961630164216861730183118762785317134005900
756010000
**’Wingareas,e~c., supersed
TCom– Wt.bined ofwt.of wingstruc-
Wc VfwL
*12012590
’115
“126120175175212190
I 178183
I
156165153228155206180202218214214200545375450867
---Ii&previous(3.Z
——
7
wt.ofbail
%kg
a.
8
wt.offuse-lage
Wf
kg
It
I
——
9 10 .>--”.-
wt. m; GI.”:of landingacces– g=r ___,series
Wa Wi ‘
=-k=
,
I
.-
.
‘.
-b-
TableI (Contd.)
T.—
No,,
1234
:7
:10
‘111213
::161718‘192021
%
%
%2829303132333435
2
Typeo~air–plane
EaDaEbIlb
%DeDfDgDhSEVaDiBE(I)DkBaBE(II;Ga
~bC(3CdCeCfCgcl-l.%c1CmCncoCpcqCr-C!s
* SeeT.13.V
c.
3~ho.i]for-mer*Tabl1
$45“?891112131516181920212224252627
;:303132333435363738’394041
11
cc=
100WCF-%
38.530.030.032.731,426.Q29.828.632.428.235.531.535.431.831.833.525.528.842.426.428.130.131.130.427.724.329.233.929.833,?27.428.227.229.627.’7
= Cw+ct+cf+
13
Ct
100--??~F-$
Cf
100Wf+w~w
%
15
11.7 1,710.7 1.711.6 1.613.0 2.113.4 2.010.0 1.814.8 2.1
I12i8 1.713.9 3.610.9 1.711.8 2.412.9 1.715.5 3*414.0 1.214.0 1.514,7”3*310.3‘2.311.9 1.91~.3 1.911.2 1.411.5 1,2
I12,6 1.612.7.1.413.6!1.612.2\l.611.211.111.211;625.7!1.511=5’1;212.8/1.7
I13.1 1.11142 1.2
I12.2 l.5-12.3 1.712.1[1,5
1
,pP.56S-5?
17.312.511.913.110.910<17.99.69,410.916.612.112=o10.911.911.39.310.417.59.910.111.0124910.59.77.711.811.913.114.79.712.3
1?::9.6-
7.,8.5.14.94.55,14.15.04.55.54.74.74.8
:?4.44.23.64.6
:;;5.3
::;4.74.24.34.64.84.04.53.53.5
2;:4,5
.
16
Wingarea
s
~2-14*o16,715.914.223.”623.620.520,925.822.922.822.836.426:041.736.424.032.442.52?.634.436.935.737,436.138.228.640.637.640.438.634.242.842.843.4
Z1.JL..
138.2 4.46,34.6 3.72 m38,0~ 4.4044.5.5.78
~;:j ;::
4~14!514234.9!,4,8439.6~4,32 .41.514,9241.81,5.4027.2!4.2239.515.5124,913.50~~.~i~,G’3
34:9 4:17
128.? 4.9745.5 5.0837.41.4.2435.2I4.4436,8I 4.6735.3 4.8237.5 4:5135.2 3.9247.1 5.2533.’25,2236.0 4.1533*6 4.3138.2 4J9944.6 5.0136.1~4.41
I37*3 4,5936.5,4.43
-?-
TableI (Contd,)
cc = ~+ct+cf+ct
1 2 3111112113114 15
WinelWin~1-?l;l.s:area load-
1Wt.per ,
ing un.it
stiz
.-
. s<No
3637383940414243444546474849.505152
~:55565758
596051626364
6566
Typeoair-plane
area.I&w/sw/s
kg/Z@
40.242,438:448.339.139.4“37● 940.235.638.541,049.746,742,743*o38.030.734*!539.039.232.634.931.4,
kg/m2
42 28.443 30.8
25,9:: 26.246 26.649” 32.750 35.551 24.952 28.553 40.1I55 30.9
24.6z
{
27.930.
% 30.861 31.3
11.6ICtCuCvCwCxJa**GaGb(2C::
GfGg
%
2RbRCRdDraD~
SopwithtriplanDrnDnDrbDo%SpadSVIIDqDr
40;2:38.242,734.042.750.873.574*o84.878.779,268.7??’.584,884.899.8532.0!32,O532.0\32,Oly.5:17.‘722.0
4.”685.344,595.234.687.89?.364.465.505.’594.995.825*55
1.3111.72.0 7,61.3 10.81.9 8.82.5 5.41,9 7.6L 4 8.711:2;
15*414*512.2I11.711,9I 10.6 9,2
1.6 20.81.9 12*31,2 7.91.7111.3
13.713.916.820.3
0.6 11.30,6 11.71=2 8.33.6 13.8
5.855.976.396.236,17?.087.084.835.49& 14
17,918.”1I I3.5 14.8
3.1 13,13*1 12.1
14.815.819,6 t6 ‘i
II--
—.---
10
L 14 .,
12.315.6’13.213.917.111.5
18.?17.117.217.122.320.5
3?.443.243.4$4.639.841.8
4.606.725.706.206.424.831-14*2
1!5.2/16.922.2
50.9il.6
?.22’6.30
,
-e-
TableI (Contd,)
6765697071
72
::757677I 78’798081828384E5&6878E89~~:;939495~6
97
cc = Cw+ c~+ Cf +-q
2
Typeofair-p-lane
BcDsDtCy
;opwith>seate~AaCzBdBeBfcclCP”m06“ccclCnC8CLCKCA*eCvCvJbJcG1Gm
3
—-
(5;}--17
--
(ij)
--,—--—
(i;)
(R)
(:~)—
[)Ckc1
(%)
($)
L(k-l 56Iandley 62PageRe (Ra)Rf (Rd
100 100WC w~T r
I 9.211.6
12.211.5“
I16.416.2
I18.41!5.5
I14.414.5
i-
11.912.5
,11.4
i ~F:~3..3.7
-
11:012*312.912.411*710.719.611.813,2:-14.7i
I16.1,
16 17 18
IiWing Win%
‘Wingarea Ioa Wt.re.c
irlg unit ~
I Iareas w/s phfsIn2”I kg/r?lkg/xn2
32.2 29.2 5=1920.9 45.5 5.7423.9 40.2 5-2925.8 3?.8 3.4931,6 31.3 3.62.30.223.440.640.627.140.537.535.034.435.?
34,3’4.18 ,I44.6 5.1426.3 4.3126.6i4.3142.4‘Y+8230.3 4.69_ I33.014.7436.2!5.22
I38.2 4.54 ,37.0,4.62 ~
37.1 36.3;4.12 :35.9,3?.6’:.3434.4 39.3 4.5141.3I36.2 4.9&34,0 48.015,3034.0148.315.9442.7‘39.5 5*IG““’I40.7 42.6 5.2742.? 43.0 5.0237.2 50.5 5.3.573.5[37.9 7.4275.0 42.3 5.0075.6 44.9 5.95152 38.& 5.Ee
233 [32.4 5,.21264 37.? ~mgs
I I
- :-.. -
,9-
As in T.E.Vol.11,PartZ, itwasshownt’hattheweightof
themtngwasapproxi~telyproportionalto theflyingweight,that
is to say,thattlepercentageweightof thewingsbeingpracti-
callyconstant,we cantaketheareaof thesupportingsurface
(Sm2) as an indicationof thesizeof theairplane,andthewing
loading(W/S,kg/m2$ as a relationbetweenthesizeandthe
weight,and considertheeevalUesas independentvariables.
Themeasureof theweightof thewingis”againconsideredaS
therelationbetweentheweightof thewing (Ww,kg)andthetotal .
flyingweight,Or thepercentageweightof thewingcomponent
(Cw= 100Ww/Y@) and,also,fromthepointof viewof thewing
weightperunitarea*(Ww/S,kg/m2) thisbeinga criterionof the
lightnessof theconstruction.
Weightof theWingsinActual‘Airplanes.
Datarespectingthesefourvalues,fora 5erieSofa@wl air- ‘
planesaregivenin columns4, 5, 12,16,17,18 of Table1. They
differonlyveryslightlyfromthevaluesin theprevioustables;
in oneplace,however,severalsmallerrorshavebeen”rectified,
althoughthesedidnotaffecttheconclusionspreviouslyreached..
Themutualrelationbetweenthetwoindependentandthetwodepend-
entvariablesis representedgraphicallyinFigs.1-4.
In thefirstplae, it shouldbe notedthatthewingloadirigs
underc-onsideratio~varymainlybet’ween25and 50kg/ma.nhilethe
x Theexpression‘Iwifigweightperunitarea’iisusedinthesame -senseas the‘~ingloadingr’or “weightperHP1]. .
.
,—.
. lQ-.-“!
areasof thewings(owingto thegreaternumberof smallairplanes
of whichdata‘wereobtainableandthemarkeddifferencesin the
dimensionsof thevarioustypes)lieprincipallybetween16 and43
m’,a fewbeingabout80m=,andsomeabout330m2;butbetween
thesegroupsthereareonlya fewisolatedvaluesand,therefore,
widegapsexist.Thevaluesplottedon thediagramsarealso
widelysoattered,especiallythoserelatingto thesmallertypes.
Thisappearstobe duenotonlyto thelargernumberof thesmall-
er typesbutalsoto thefactthatthelargertypesaremorestand-
ardized.
Generally,
weightperunit
boththepercentageweightof thewingsandthe
areaincreasewithincreasingarea,theformer
morethanthelatter;as thefo~er variesfrom-l@in smallair-
Flanesto 18%inthelargetypes,whiletheweightperunitarea
variesfrom4 to 6 kg/maonly. An outstandingexceptionto these
valuesisaffordedby theJ-typeairplane,whichwasreferredto
in thefirstreport
It representsa new
ages;andit isnow
considerably,as is
Flanebeingsimilar
.on aca)untof itsextraordinarilyheavywings.
typepossessingcertainaerodynamicadvant-
possibleto reducetheweightof thesewings
shownby the Cz No.73in Table1, thisair-
inconstructionto theJ-”typeairplane.The
otherparticularlyhighvaluesbelongto oldertypes.On theother
hand,ina light G-machinethewingsareonly9.#Pof thetotal
weight,whilein thefirstreportthelowestvaluetabulatedwas
11.17,applyingtoa G-typeairplane.
Thetendencywithincreasingwingloadingispartlyin the
-1.1-
Oppositedirectionto theabove;thepercentageweightof thewing
COmpOnentagainincr~a~esveryconsiderably,buttheweightof the
wingperunitareadecreasesat a morerapidrate. Theexceptions
to thisare,practically,confinedto thosetypesofairplanesZe-
ferredto in theprecedingparagraph,
To summarize,approximateaverage
follows:
TableII.
valuesmaybe laiddownas
Avera~evaluesofpercentageweightof wingcomponentandwingwei~htperWlitarea.
?Jirigloading I Weightperunitarea Percentageweightofwingunit.
kg/m2 I kg/m2 ‘%I
25 i30 i35404550
I
546
Conclusions,
Therelationsthusestablishedarenotunexpected,as a super-
ficialexaminationof thedatagivenwouldleadoneto suppose
thattheweightof thewingwillincreasewithincreasingarea
(thatis,withincressingspan), and that,undercertainconditions,
thedecreaseof thewingloadingwhichnecessarilyfollows,will
lightenthewing. As, inaddition,theweightof thewinghasnow
-12-.
beenrepresentedas a percentageof thetotalweightandin its
relationto thewingarea,itwastobe expectedthat,within-
cr-~,se.dwingloading,forrea.sonEof st~e~,gth,in thefirstpl~.ce,
thevalue Ww/S wouldincrease,whilethepercentagemeightof
thewingcomponentWOUM decrease, because the weightof thering
increasesin this@se moreslowly than the toml weight.
Theserelationscanbe moreaccurate~-yappreciatedifwe im-
aginean airpknewithitslineardimensionsdoubled.First,let
thewingloading
chester~sTheo.q
thetotalweight
creasedto eight
remainunchanged.Then,inagreementwithLan-
as shownin thefirstrepor,t,the
arequadrupled,theweightof the
timestheirformervalue,,and, as
wingareaand
wingsis in-
thezl,therate
of increaseof tineweightof thewings-isas thetotalloadraised“ ,
to thepowerof 1.5?whilethestrength.ofthewingsremainsun-
‘ changed.Accordinglyjthewingareaandthetotalweightincr~se.
as thesquare;theweightof thewing,as thecube;and thewing
weightperunitareajandalsothepercentageweightof thewing
component,as thefirstpower,of thespan. ..,
Consequently,thepercentageweightof thewingsandthawing
weightperunitareamustalwaysincreasemoreslowlythanthein-
creasein thesquarerootof thewingarea;thatis>withincreas-
ingwingareathecurvesshowingtherelat,ionbetweenwingweight
perunitareaandthewingsurfaceandthepercentagewingweight
andwingsurfacewillassumea parabolicform,as shownin Figs.
1 and 2,withthe S ltneas axisof theparabola,thecurvesrj.s-
ing fromleftto rightandopento theright.
-13-
Nowin the’firstreportit was shown regardingLanchester~s
conclusion,thattheweightof thewingisproportionalto the
totalweightraisedto thepowerof l+,mustbe replacedby the
conditionbasedonactualpractice;thattheweightof thewingis
approximatelyproportionalto thetotalweight,sinceitaverages
about14fiof thetotalweight.Accordingly,as seenpreviously
in column11 of Table1 inT,B.Vol.11,Part2,p.286jtheper-
centageweightof thewingcomponentmust,be virtuallyconstant,
or onlyincreaseslightlywithincreasingsizeof theairplane.
Further,theweightperunitarea,also,withconstanttiingload-
ing,hasalmosta constantvalue,or increasesveryslowlywith
an increaseinthesizeof theairplane,Boththeseconclusions
are inagreementwithFigs.1 and2;
As to the”relationbetweenthepercentageweightof thewing
componentand thewej.ghtperunitareaand tb~wj.ngloading(Figs.
3 and4),it ispossibletoarriveat a similarconclusionwith
rathermorecertainty,since in thiscasethedifferenttypes
Of airplanesarequitevaried,andwiththegreatdifferencesin
the constructionrepresented,emphasizethedivergencebetween
LanchesterlsTheoryand’actualpractice.. ‘
Nowletitbe assumedtmt thewingloadingof anyairplane
is increased,say,to
the$otalweight,and
talweight,however,
doubleitsfirstvalueby firstincreasing-
secondlyby reducitigthewingarea. Theto= .
mustnotbe allowedtobecomeproportional
to thecubeof thedimensionsas in thesecircumstancesthecon-
ditionsin regardtostrengtharethereuponvaried.
-14- .
Itisnecessaryhereto give more a,tterit”ionto theforces
andthecrosssectionalareasOf theparts;to thebendingand
resistancemoments;to thebucklinglengthandthemomentsof in-
ertia;anditmustbe ensUredthatthebreakingstressremains
constant,so thatthesameconstructionalmaterialsmaybe used,
Further,as in practicewe havetodealwithrathersmall
variationsin thewing Icading, varying between about25and 50
kg/m2,(thatis,thewingloadingmaybe doubled)andas theper-
centageweightof thewing c~ponent only varies between10and.‘2%, theclosedistinctiondrawnin thefirstreport,betweenthe
totalweightandtheloadCarriedby thewingsat therC)OtS(ap-
proximatelyequalto W’- Ww) maybe neglectedin considering
thefollcwingcalculations;andto compensatein some wayfor
this,thepartsof theairplanewhicharedirectlysupFortedb.Y-
thewings,suchas,fueltanks, partcf theweightof theengine,
etc., arenot takenintoacmunt.
Duringtheinvestigations,it shouldbe rememberedthat,
variouspartsof thewingstructurearesubjectindividually
the
to
differentkindsof stress- to simpletension,simplebucklingcr
purebending,-combinedbucklingandbendingor surtacetension,
becauseeachcreatesa Mffexentvariationin thedimensionsazii
weights.Therelationbetweentheweightsof thevariousparts
whichareincludedin thewingstructureto thetotalweightof thet
~ings,is shownby thefollowingdatatakenfroman earlierarticle:)(EverlingandGaule.Einzel- gewichtevonFlugzeugflugeln- T.B.
Vol.I,p.298)..
35-
.
Table111.
I IProDortiomKindof stress
PuretensionorcompressionBuckling
Rending
~om~ine~bend.ing& buck-1ing
Surfaceten–sion
Total
Parts of-struc-ural
weight
1.0.10Cables,Fit-tingsxStruts,in- 0.15eludingin–terrdlstruts.Ribs& lead– 0.25ing& trailingedgesSpars 0.30
Fabric,Fit-I O,20’tings*~ , ~
i
Combined .1.00meightofstructure
Stress (kg/~2), foraForceF (kg)or]fomentM (cmkg)
F/S S=Cross”section-al area,cm2
FZ2/1, Z=Bucklinglength,ch.
M/R R=Mornentof re-sistance,cm?
F/S+I!/R,I=Momentof in–ertia,cm4
F/t? t=Thickness,cm
On thisbasis,the
wingandtheweightper
variationof thepercentageweightof the
unitof areawiththedoublingof thewing..”
loadingwillnowbe investigated,itbeingbroughtabout,in the
firstplace,by doublingthetotalload. Thisdoublestheforces
on thestrutsincludedin thestructureandthebendingmoments
on thespars,resultingfromthegreaterloadin thebaysalong* Onlypartof theweightof thefittings;theremainderis d~.-videdamongtheothermembersas thefittingsaresometimesundercomplexstresses.** In buckling, the basis of comparisonisnotthe~CtUalstressbuta numericalquantitywhichiS inverselyProportionalto thefacto~of safetyfora bucklingload. (Inthecaseof theultimatetensilestrengththisqmntitywouldcorrespondwiththetension.”Thesurfacetensionstresscontainsanotherfactor,whichisnotconsideredhere.)
-16-.
thespars( andthedisplacementof thenodalpoints). .
As,inac~or~nceviththelastcol~.wmos TableIII>,the
stresseson thesparsareproducedthroughlateralflexuredueto
bucklingandbending,andas,fortheirsafetywhensubjectto
bucklingandbendingloads,theratioof thelongitudinalforces
to thecrosssectionalareapIUS the ratio of thenaximumbending
momentto themomentof resistanceof the moss-section,isa
measureof theirbreakingstrength;andsincethenumeratorsare
doubled,thedenominatorsmust,at least,be doubledalso. This
is thesamewhenthe cross-sectionalareaof thespars- and
hencetheirweight- isdoubled,for thenthe,momentsof resistance
autom.a~icallyincreasein a higherratio,namely,23= times,with
a geometricallysimilarincreaseof thecross-sectionto t=icethearea,
In the
theweights
same~ay,theoross-sectionalarea,and,therefore,
Of tensionmembers,- forexamFle,thewirebracing,-
mUstbe doubled;whiletheribswhichareonlysubjecttobeading
momegtrendereda twofoldincreasein themomentof resistanceof
thecross-sectionnecessary,andthesubjectionof thestrutsto
a bucklingloadwhichalsonecessitatesa likeincrease(twofold)
Of themomentof inertiaof thesectionin bothcaseswitha cor-
respondinggeometricallyeimilarincreasein thecross-sectional
area- thatis,increaseinweightin tke caseof theribsand
thestrutsof 22’3and 21’2respectively,
Further,withtwicethewingloading,thecoveringfabric
mustbe 21” timesas thick,thatis,theweightmustbe increasedto 2“2 timesitsoriginalvalue.
-17-
Hence,thetotalinoreaseinweight”willbe such’thatthefin-
al ~eightwillliesorne~herebetweentwiceand~~-timestheorigi-
nalweight.Thus,thecoefficientof increasedsizeandthepro-
portio~lincreasein theweightsof thevariouspartsof the
‘-ings,accordingto Table111,
2 (0.01+ 0.30)+ 22=X 0.25’
=0,80+0.40
approximately.
amountsto
+ 2’P(0.15+ 0.20)=
+ 0.49= 1.69= .#’76= 231A
If the~ingloadingwereincreased1.5times,insteadofas .
abovetheresultwouldbe -
0.60+ 0.33+ 0,43= 1.36=1.5G-45= (1.5)W4
that is,virtuallythe
Thus,by doubling
same power.
thetotalload,inorderto doublethe.wing
loading,thepercentageweightof thewingsbecomes0.85andthe
weightof thewings1.7timestheoriginalvalue.
Next,letthewingloadingbe increasedby diminishingthe
wingareaandtheappertaining.structureforexample,by half.
Thespan,chord,andthicknessof thewingcanthusbe decreased
in theratio l/J5 anda bendingloadon thesparsandribsis
multipliedby ~T perunitlength.
Theloadingin thebaysbetweenthestrutsremainsconstant,>
as do alsothelongitudinalforceson allstructuralmemberssub-
jectto endloading;whilethebendingmomentson thespars are
decreasedin thesameratioas thelengthsof thebays,namely.
-18-
3/J:Y Themomentsof resistanceof thesparsmay>tMrsf@re,he
decreased;butsincetheirsectionmustremaiqconstmttheir
weightcm. only be decreasedin thesameratioas thereductionin
iheirlength,nmely, 1/p Themembersundertensionm~.yalc-~
be lightenedinthesameratio.
On theotherhand,thememberssubjectedtobuckling,onac-,.—-
countof the l/~2 zeductionin theirlength,mayretaintheor=
iginalfactorof
inertia,Hence,
may be decreased
will,therefGre~
safetywithonlyone-halftheoriginalmomentof
theircrosssectionalar~fiandalsotheirlength
intheproportionof 1//-2: =.dtheirweight
be reducedbya half.
As regardsthememberssubjectto purebending,themoment—
of resistancerequiredis only 1//2 of thatorig~nal~yr.ecessa-
ry so thatthesectioncanbe reducedby (#~3 , andtheirweight5)6
()willthereforebe only 12/ or approximatelyonlyhalftheor-
iginalvalue (astheribsneednotbe @aced.::2olos.etogethe~),-.
on accountof thelengthbeingreducedby i> , .2*
Finallythefabriccoveringcanbe re.csi tohalftheweight,
as theoriginalthicknessmustbe maintained,~ecauseit takesthe
sameloadonhalfthearea.
Thus,accordingto Table
weightishere:-
111,thecoefficientof reductionin
*Z (CL1O+ 0.30)+3(O.15+ 0.25+ 0.20)=0.28+0.30
= 0.58= z-~’g = ~-4/5
If,insteadof 2 we take1.5we shallobtainthefollowingin-
steadof theabove
0.33+ 0.40= 0.43= 1.5-0’== 1.5-4’5.
Thatis,virtually,thesamepower.
Thus,by halvingthewingarea,in orderto double
loading,thepercentageweightof thewingsbecomes0.6
weightof thewings1.2of theoriginalvalue.
TableXV givestheresultof thisinvesti.@tion.
Thegeometricmeanof thetwomodifications,which
thewing
andthe
corresponds
to a doublewingloadingproducedby a simultaneousincreaseof
thetotal
It hasan
loadanda decreaseof thewingarea,isalsogiven.
approximatevalueof about l/K and fi-respecti.vely.
TableIV.
Variationof therelativeweightof thewingunitandtheweightperunitofarea,
%ithtwicethewingloading
BY doublingthetotalload
By halvingthewingarea
Geometricmeanof thetwovalues
Empiricalcoefficienta;;;;~~ to,..——
Relative Teightperunitweightofwing.
Varyin theproportion:-
of area.
O.85
o*58
0.70
1.69
1.17
1,41
- 20 ..
Thepercentageweightof thewing,thus,decreasesinprac-
ticeinalmostexactlythesameproportionwithan increasein the.
wingloadingas thatobtainedby theroughcalculationTh~eagree-
mentin thecaseof theweightof thewingperunitareaisalso
verygood.,
Theestablishmentof theempiri~lcoefficientsfromthe
availabledatais certainlysomewhatarbitraryowingto therather
‘widedifferencesbetweenthevarious types;and thesamemightbe
saidof thechoiceof thegeometricmean. However,theempirical-
coefficientslie,inany case,inpractice,withinthelimitsof
thevariationswhichresultfromdoublingthe
area,
Thepreviousdivergenciesbetweentheory
shownin thefirstreport,,giveplacehereto,
ment,althoughthisagreement,it is true,is
by”thegreatdiversityin thedatafromwhich
loador halvingthe
andpractice,as
comprehensivea.grce-
somewhatobscured
it is derived,caus-
edby thedifferencesin thetypesandtheconstructionembodied
thereinandothercontributorycauses.
v. Analysisof theStructurefromthepointof viewof theVari-ationin theWeightof Components-withthesizeof theAirplane.
synopsis.
In consideringthedivisionof thecombinedweight
of a “numberof actualairplanesintoitsfourcomponent
in the case
parts:the
fuselageandaccessories,thetailunit(stabilizer,fin,rudder
andelevator)thewingunitand t,helandinggear(includingthe..
.
—
-21-
+.ai~skid,theaveragepercentageWeightof eachunitcanbe..taksn
as li, 2, 13,and !5frespectivelyof tinetotalweight,and 36, 6,
43and15%respectivelyof thecombinedweight.
The;eightsof thevariouspsztsof thexingunitin thecase
ofaveragetypesofairplanes,arestrikinglysimilar.Theper-
centageweightof thefuselage,however,slightlydecreasesas the
dimensionsof theairplaneincrease,andthoseof thetailunit
andlandinggearunitbecomeparticularlyimportantin thecaseof
thegiantairplanesused
theconditionsinregard
tionwhicharespecified.
fortheinvestigation,prtly owingto
to strength,stability,sizeand instruc-
Analysisof theStructure.
Thepreviousanalysis of thetotalloadedweightof theair-
plane(T.B.Vol.11,Part3,pp.563-579)as to com”binedengine -
andpropellerunitweightandusefulload(fuelandcargo)showed
thatthepercentageof thecombinedweightof thestructure(fus-
elage,wings,tailunit,landinggear,etc.) inczeased~na certain
ratiowithincreasingdimensionsof theair@ane. On theother
hand,itwasshownin thefirstreport(T.B.VO1.11,Part2,p.2’79)
thattheweightof thewingcontributedonlyina smalldegreeto
thisincrease,and thefourthreport(firstpartof thisreport,.
Table1) thevariationsin theweightof thewingweree~lained “
by the.variationinthewingloading.“
Wemustnowcarrytheinvestigationfurtherandascertainto
whatextenttheothercomponent~rts contributeto theincrease
.
-22-
of thecombinedweight.Forthispurpose,theodmbinedstructural
rei~htwhichisalwaystakenas a proportionof thetotalweight,
is splitup intoitscomponentparts,andtheirrelationto thedi-
mensionsof theairplaneconsideredfixstfromthe;ointof view
of datarelatingtoactualairplanes and then from general consid-
erations.
Therequiredda- havebeengi~n alreadyinTable1 of this
report.In columns
COIUi’3.nS11 -15 the
iouscomponentsare
5 - 10 thestructuralweightsaregivenandin
cnrr’espondin.gvaluesof theweightsof thevar-
shownas percentagesof thetotalflyingweight.
Thestmctureis,analyzedaccordingto theconstructionspeci-
ficationsintotheweightsof fuselageWf, supportingsurface
(wings) Ww, tailunit(fins,stabilizer, :ele~atorsandrudders)
Wt, Landinggearunit(inclusiveof tailskid) l?~,andfuselage
accessoriesWa. Since,in theconstructionspecifications,the
“reightofmost of theaccessoriesis included in theweightof the<
fUselage,theproportionatevaluesof thetwohavebeenaddedto-
getherformingthetotal (Wf+ Wa). ‘
TheComnonentWeights.andtheirde~endenceuronthesizeoftheAirrlane.
In thediagramthesepercentageweightsof thecomponentsof
thestructureweightareplottedas ordinatesagainstthesizeof ‘
theairplane(whichis representedthereby theflyingweight W) -
(Fig,5), Theirsumg“ivesthepercentagecombinedstructural
weight cc = 100we/w. As theweightof thewingshasalreadybeen
thoroughlyinvest-igated,it is of littleimportancehere,so that
-23-
hhccTtes fronbottontotopis
1) Tailunit(stabilizer,fin,rudder,elevator),ct = 100~tt~~‘*
~) Fuselage,includingaccessories,cf= 100 [Wf+ Wa).
5) Wingcomponent(wingsandailerons),C,N= 100 ~w/~.
42) Landinggear(landinggear and’tail skid), Cl = 100 ~1/~.
so thatthetwovaiues,.thevariationsintheweightofwhichmust
alsobe followedfromgeneralconsiderationsarethelowestand can
bemoreclearlyseen. The~ercentageweightof thetailunitis,
infact,verysmall,about1.7%;andshows,withfewexceptions}
onlyslightvariations from themeanvalueso thatthepercentage
Wei@tof thefuselageFlotted”aboveit,generallybeginaboutthe
samelevelandthepositionof the circledenotingtheupperl~it
indicatestheweightof thefuselage.
Id ‘4”
No. TypesofINo, Flyingweight
airplanes- of~pes From TO
~f kg I kg
i
1 Rotaryengine 4 535 ~32\ singleseatex ~~
2 V&rticalengin~9 780 I 1026singleseatet
~
!3 Light2-seater ~4 C-typeairplan2: t 1~~ I ~~85 J-typeairplan 1 2003 20036 G-typeairplan
31: 2785 3795
7 R–typeairplan 10203 13035e MeanofalltY~55 556i13035
I i
5 6 [7 819. .
I IPercentageof flyingweightCom- Wt. ??t.~wt. lit,bined of :of of larid--stru~wing tailfuse-ing :ture t lage
i CT I Ctgear
.~ ~ $ $ ~ ;1
33 ~ 12 : 2! 14 5;1 i31 I I.13 2 11 5’.. -..
I36 I 15 3 13 529. “11 ~ 4’...38 ::/: l; f’:
141; i:317:: .19,31 13~2~115
-24-
TableV (Cont.)
AverageValuesof theVariousUnitsofAirplanes.
1 I 2
. No. Typesofairplanes
1
2
34567
RotaryenginesingleseaterVerticalengine
single seaterLight2-seaterC-typeairplaneJ-typeairplaneG-typeairplaneR-typeairplane
3
No.oftypes
10 ‘ 13 12 113I
Percentageof combinedstructural~eight.
100 t 100 100 ,100 ‘“I
Cw ~ Ct Icf.. ,2—. — —
I cfJ t cc cc
%1% ~. ;I
4 36I
5 42 17
9 42 6’ 36 16
4 43 ? 37 1323 43 5 37 i5 —1 63 8 17 1210 46 4
I36 14
4 44 8 31 17) , 1
8 .Meanof alltypes55I 43’ 6. 36 15 ““”!
It can be-seen still more clearlyinthediagramthanin Table
1, thatthevariationin thevaluesis comparativelysmallandit
appearsjustifiablethattheaveragevaluesbe takenfortheper-
centagecombinedstructuralweightfortheseparatetypesofair-
plane(TableV), Th’erelationbetwea theweightsof thecompo–
nentsandthecombinedweightpresentsstillgreateruniformity
thantheaveragevalues;accordingtothe
of thecombinedstructurecontributeina
crease in thestructuralweight. ‘
Themainexceptionis thetailunit,
tableallcomponentpvts
similarmannerto thein-
theweightofwhichis
comparativelysmallerin largeairplanesthaninsmallertypes;bUt
‘.Thichincreases,however,in giantairplanestoaboutdoublethe
-25- .
originalvalue.
Thepercentageweightof thefuselageon thecontrarydecreases.
withincreasingflyingweightfrom42@of theccmbinedstructural
weightin lightsingle-seaters,to 31Xin giantairplanes,whiiein
medium-sized airplanes it is about 36- 37%excludingtheJ-type
airplanes,thepeculiaritiesofwhi~ havealreadybeenalludedto, “-
Finally,thepercentageweightof thelandinggearunitinre- ‘
lationto thetotalloadedweightreachesthemaximumin giantair-
planes;inallothqrtypes,on thecontrary,thelandinggearunit
percentageis lighter,incomparisonto thestructuralweight.
Conclusions, —.-
In order,firstof all,toappreciatethevariationsin the ,
weightof thetailunit,itmustbe rememberedthatsome W– .airplanes,(namely,thosehavinga c valueof 0.6,;seeTable1)—.havea verylongfuselageanda comparativelysmalltailunit,and
thaton thecontrary,thetailunitsof tks 3.t.pe airplanes .-whicharelargerinproportionto thewing=.7-’.‘Z necessitate
thespecialreinforcementof thestructure,thusincreasingthe
weight.
Here,as in thefirstreport,accordingto LanchesterIsTheory,
we mightalsoconsidertherelationbetweenthe‘weightof thetail
unit,andthetotalweight,wingarea andwingloading,by a de–
tailedexaminationof thestressesproducedinthevariousmembers,
as wasmadein thecaseof thewingunit,butthisishardlyworth
whilein viewof thefactthattheweightof thetailunitis>at&most,only3%bf thetotalweight.
-26-
?lithcomparativelyheavyfuselagesitmoulcibe an advantage
to estimatetheincreaseofweight,forinstance,whenall linear’
dimensionsaredoubledwhilethewingloadingremainsconstant.
In thatcase,thewingareaandthetotalweightarequadru-
pled,therightingmomentsdueto thetailunitandtransmitted
throughthefuselage,becomeseighttimesas greatas do alsothe
bendingmomentsuponthe fuselage (consideredas a cantilever);
themomentof resistanceof thefuselagemusttherefore,be in-
creasedeighttimes,and thistakesplaceautomaticallywhenall
thelineardimensionsaredoubled.Theweight6f the
however,increaseseighttimes,thatis,as thetotal
to thepowerof 1.5,exactlythesame result as given
reportfortheweightof the‘~ings.Theinfluenceof
of thefuselageitselfUpOnthetotalloadandon the
.-
fuselage; .
weightraised
inthefirst‘
theweight
bendingmo– “-
~LentsmaYbe neglected.Accordingly,thepercentagemeightof the
fuselagemustincreasewithincreasing.totalweightas thesquare
rootof thetotalweight.In reality,however,theratioof the
~eightof thefuselageto totalweightremainsconstant,andthe
ratioto the.struotureweightis improved
Thiscanbe explainedss in thecaseof theweightsof the
wings,by thevariationof thestaticrequirements>in’regardto
localstrengthandthefactorof safetyin thestructure,andfur-
ther,owingto thepossibilitywitha tailunitof largerar~a,
andtherefore,of greaterweight,of constructinga shorterand
thuslighterfuselage;or,in otherwords,owingto thefactthat
theassumptionof a similarincreaseof dimensions,whenapplied
toa differenttypeof constructionno longerholdsgood.
. .-
-27-.
Finally,it is obviousthatinquitelargeairplanesas also..in lightfastairFlanes,thelandinggearmustbe proportionately
heavier,althoughinthiscase,thedifferenceswithvarioustypes
ofairplanesaresmall.
Thus, it is seenttiatthevariouscomponentscontributefair--.lY evenlyto thepercentagevariationsin thecombinedstructural
weight,which,’as shownin thesecondreport,in recentC– andQ-airplanes,is lessthan3@; but inR-typeairplanes,is @ of
thetotalweight. ~,
Translatedby theNationalAdvisoryCommitteeforAeronautics.
da)F+L’34=v-i
El
8
6
o
20
al
i%’~M0CY
%4
0
40
Fig.1
80 120 :60 200 240 280 320
~vv”v’iuiu.—–:-+.:.----+- -’– .-+- — ---,*
I , ; : r ‘] T---i----”-++-.—.-----—L*+..“ . . ..–– ---I II ‘I_ ~Y;--~7””:.T---: ,,;-...1 . . . . . .. . . . . .
r- -!- -:-””- ;- “ “, _._}. - J_. , {.. .-!.. -.! .__ L.._’t ●I,s.——.+-- — .
:- t, i ~ ~-“- “~- .-~ -- -—— ~.- t ~.-— — L ._Q_ ‘ ‘ ~1 I
----J--+---*-”Lt i~j’1:~< 1,
-!, - i—-—:—.—— -_+ 4------- .-*— .S..h -.. .- ... ;—_ .-—; -—f
w ~l!!’i[------ -.—L ... -—- L__;_+.-..}-...-+..[...+.,;-——
I - .&.--!-.A___d_ i. . . . h,* -4- .. -—-; -—
i! !* ~;;i;ll
● -r+----i-l::I-------4 ...,. .--- 4—— ——*-. .-J--!,~ t I!, i. 1 i;~
,. +... ~. ..-- .7-—;--- .. _—.: .-.:: :I 1
,’4.
iti! ;---”7-- i -_:. 3.. . ; .;--: ~ -: .--+- ,-—. .— . .. .. .
} !-. ... —.- ... . +- --—
i “1~.._:_
1:1 ~-q+- ~ ---● I::. ~:~~
——40
Fig.2
80 120 160 200 240 280 320Wingarea,rn2
.
Fig.3
fI
,,,
z —+—— —+ —-.--i--- * —Q !, ,:
A
+~
..4~ ..—; —- ~ .- .&-._.: ,-. : __
&o;!!0
1=----- .——l —
;*2.~. .-. . -
0-
24 ZS 32 36 40 44 48 52Wingloading,kg/m2
Fig.4
50
0
,
—---o --i’-~+----- ~P
-,.---.—-. .Ie
“-—
-. ___
..-
.—_-.”
.+-1
—I 1 11
i
iol_-P——. ;g– -4 L -- --}1---—..
f-+1” ~ ,4 I o> I il
.--—4 +- :-!- ~,?-1-- –
0 1000 2000~ 3000 !000 10C!CO11000\12000 I;Coo‘TotalairplaneweightW~kg,
Fig,5 Analysis of ,componentweights of the airplane in thel.r relation to theoombinetiweigh%,
,,
I
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