resistence and propulsion of ships_wf_durand
TRANSCRIPT
8/11/2019 Resistence and Propulsion of Ships_WF_Durand
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The resistance and propulsion of ships. By William F. Durand ...
Durand, William Frederick, 1859-1958.
New York, J. Wiley & sons; [etc., etc.] 1898.
http://hdl.handle.net/2027/uc2.ark:/13960/t2p55g95d
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R A R Y '
T O F C A L I F O R N I A
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E A N D PR O P U L S I O N
.DU R A N D
lo MarineC onstruction
.
O N .
S A N D.
Y & S O N S .
A PMA N & H A L L , L I M T D.
P u b l i c D o m a i n
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DU R A N D .
U M MO N D E L K C T O T P R K A N DI ' R I N T R . N E W Y O R K .
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w en t o r t hi r t y e a r s t he l i te r at u re
eandPropulsiono shipshas
uableandimportantaddit ions. Of thef ew
edinthisperiod thoseo thehighest
rictede itherinscopeorinmodeo
spart how e er the importantaddi-
ebeenpublishedonl inthetransac-
dscienti icsocieties orinthetechnica l
specia larticlesarefarf rompro id-
o thetrendo modernthoughtand
ntworkhasbeenundertakenin the
a ie ldo use ulnessf oraconnected
ns i e e p o si t io n o t h e su b e c t f r o m t he
gineeringstandpoint.
ndinlargemeasureonthee tant
ect andtheauthorwouldheree press
entstothosewhoha epreceded
an placesspecialobligationsareclue
iontogi especialre erencesat
papersorsources.W iththe
egenera ll iteratureo thesub ect
considerableamounto original
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E .
illcontributesomewhattowhat-
a luethew ork asaw holema possess.
madeo ca lculusandmechanicsinthe
su b e c t t h e na t ur e o t h e tr e at m en t
hesepow er ulau il ia ries. A tthesame
tantresultsandconsiderationsbearing
generaltermsandf romthedescrip-
l loperationsin o l edintheactua l
rereducedtosimplee pressionin
mathematica lprocesses. I tw il lthusbe
ss i on o t h e pa r ts i n o l i n g hi g he r
bta inaf a irl connectedideao most
mthedescripti estandpo int andtoappl
orpurposeso design.
o suchmethodsthepurposehas
ahsa longw hichthestudentma pro-
omtheinit ia lcondit ionstothedesired
themethodinsuchaw a assha llcon-
ntapplicationo engineeringj udg-
nthedesigno screw-prope llers
numbero contro ll ingconditionsis
epurposehasbeentopresentamodeo
importantcontrollingconditions
ormulae andinw hichthedetermina-
a lueso theserepresentati esb
n estimate orassumptionisforcedupon
udentinsuchaw a astoca lla teach
cto engineeringj udgment.
ho d ma d i f e r f r o m ot h er s i t i s
erieso operationsinsuchw a asto
o aconsiderablenumbero re lati e l
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ullandf reeapplicationateachstepo
cedentasma beathand. S uch
eradaptedtothediscipline o the
o thetra ineddesigner andit is
ormerratherthanf orthe latterthatsucha
tthesametimeit seemsnot
orthetra ineddesignerthesplitt ingupo
tothe irseparatef actorsiso tenan
andonewhichw illthemorereadil
ethodstorapidl changingprece-
design.
si eandtheneedo homo-
dthew ork inman respectslesscom-
ightha ew ished andman
tsespeciall inpuretheor ha e
otice . A spresented thew ork repre-
ecturesonR esistanceandPropulsion
r t o st u de n ts o C o r n e ll U n i e r si t i n t he
nstruction andman f eaturesbothin
deo treatmentha ebeenintroduced
eriencethusobta inedindea lingw ith
N I V E R S I T , I TH A C A , N . Y .
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E .
G
a m li n es , 1 6
onsiderations, 28
pl I mmersedP lanesMo ingNormaltoThemsel es32
p l I m me r se d P la n es M o i n g O b l i u e l t o t he i r
esistance40
Ship- ormedB odies49
theQ uantit ies/ andw f orS k in- resistance52
n D ue t o t he M o ti o n o a S h i p- o r me d B o d t h ro u gh t h e
a T r ai n o W a e s 8 9
choesintheTrans erseandDi ergentS y stemso
sistance95
s ta n ce i n G en e ra l t o th e D en s it o t h e L i u i d 10 6
perimentsonF ourModels106
esistanceDueto I rregularMo ement108
sistanceduetoR oughWater109
sistanceduetoS ha llow Waterortothe I n luenceo
sistanceduetoS lopeo C urrents119
esistanceduetoC hangeso Trim120
ilge-k ee lsonR esistance123
o u l B o t to m o n R e s is t an c e 12 7
sistanceB eginstoR apidl I ncrease127
parisonoro K inematicSim ilitude128
eL aw o C omparison142
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.
ntheTheorieso R esistance145
orR esistance146
hodso DeterminingtheR esistanceo S hip- ormed
nce151
.
N .
o theProblem157
ls i e E l e me n t 15 9
ingtoS crew Propellers169
no theElemento aS crew Propeller172
no theE ntirePrope ller177
ew Propellerv iew edf romtheStandpo into theWater
e lerationImparted195
Treatedf romtheStandpo into 37198
ulsion. 203
crewPropellerswithGuide-blades205
I .
E T WE E N S H I P A N DPR O P L L E R .
theW ak e, 208
f e r en t K i n d s o S l i p o M e an S l i p a n d o M e a n P it c h 21 1
b li u it o S t r e am a nd o S h a t o n th e A c ti on o a S c r e w
e W a ke a n d it s V a r i a bi l it o n t he E q u a t i on s o 3 6 2 24
esistanceduetoA ctiono P ropeller229
w ernecessar f orP ropulsion230
9
rentS lip. . . . . 240
.
D S I GN .
de lEx perimentsw ithA ctua lP rope llers243
erDesign261
sR elatingtotheC hoiceo V a luesintheE q uations
andtotheQuestiono N umberandL ocation
sA f f ectingtheO perationo S crew Propellers292
ono theL aw o C omparisontoPrope llerDesign300
ropeller-blades303
crew Propeller, 310
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H I P ,
C K
W portheWork A bsorbedb thePropeller, 327
8
o r A u i l ia r ie s 3 36
a m pl e 3 38
aw o C omparison340
placementC oe f icient343
dship-sectionC oe f icient347
i n g W e lt e d S u r a c e 34 7
nstants349
p ar i so n w he n t he S h i ps a r e N o t E x a c tl S i m i l ar 3 5 0
C omparison355
onso aDisplacementS peedPow erSur ace357
eL aw o C omparisontoShow theGenera lR e lation
a r r i n g C a p ac i t f o r a G i e n S p e e d 35 9
.
.
iono theObser ationstobeMade367
da l I n l u en c e 37 1
hePurposeo O bta iningaC ontinuousR elationbe-
o l ut i on s a n d Po w er 3 7 5
SpeedPow erandR e o lutionsf oraL ongdistance
ithS tandardi edS crew 383
A cce lerationandR etardationonTria l-tripData386
e R e u i re d t o E f f e c t a C h a ng e o S p e ed 3 8 7
l siso Tria lData397
ogarithmicC ross-sectionPaper407
ellerData414
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R Y N O T R E L A T N G TO U N I T O F
T .
t ando f orceingeneral usedin
hepoundandtheton the latter
s . I t w i l l a lw a s b e s o un d er s to o d in t h e
arethef ootpersecond thef ootper
The latter w hileo tenusedinthe
s r ea l l a s p ee d o r v e l oc i t . A s
a y D e pa r tm en t i t i s a sp e ed o
heB rit ishA dmiralt k notisaspeed
Thedistance6080. 27f t. isthe length
naspherew hoseareae ua lsthato the
thwhich weareconcernedinthe
S . andB rit ishA dmiralt k notsma
theUnitedS tatesthestatute
r e u e nt l e m pl o e d i n th e me a su r em e nt
hek not andtheshortorlegaltono
easuremento displacementandw eightin
nesareusua ll re erredtotheminute
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E A N D PR O PU L S I O N O F S H I P .
E .
D A S .
d r os t at i cs i t i s s ho w n f o r a b od
mersedina li uidandatrestre lati e
hehori ontalresultanto a llf o rces
thebod isz ero andthatthev ertica l
i gh t o t h e bo d . I f , h o we e r t h er e
eenthe li uidandthebod , the
e uil ibriumnolongerho ld andw e
ceactingbetw eenthe li uidandthebod
posethemo ement andthustend
elocit tozero . Thisf orcew hichw e
reonecalledintoe istenceb the
a lha ebothahori onta landa
elatter w hilegenerall omitted
ma inspecia lcasesreachanamount
Thee istenceo sucharesist ing
m at e l t o t he r e la t i e m ot i on m a b e
ate l asarisingf romachangeinthe
thesur acef orcesactingonthe
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C E A N D PR O PU L S I O N O F S H I P .
ore lati emotionbetw eenbod and
f orcesarew holl normalpressuresand
hat asabo enoted thehori ontal
hev erticalresultante ua lstheweight.
ses howe er thesur acef orces
nbothamountandcharacter.The
eorless changedinamountanddis-
dition tangentia lforcesw hichw ere
hebod w asatrestarenow calledinto
uencethehori onta lresultantisno
r ta i n am o un t R , t h e e u a l o w h ic h m us t
nthedirectiono motioni uni orm
wconditionsisto bemaintained.
tantmust o course stille ualthe
how e er ma beconsideredasmade
duetothemotion andtheothertothe
theportionimmersed. Thesumo
ew eight. Hencew heninmotionthe
lnotingenera lbethesameeitherin
orthecondit iono rest.
ono thesur acef orcesmust
hef o llowingcondit ions:
ormanddimensions
i m me r se d p or t io n .
r o w e t te d s ur a c e.
ot i on .
e locit betw eenthebod and
concerned it ise identthatw ema
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E . 3
romtwostandpointsaccordingaswe
standthebod mo ingthroughit
the li uidf low ingpastit . The
ler smethod andthe latterasL a-
hodhascerta inad antages anditw ill
iew thephenomenainpart a tleast
econstitutiono theresist ingforce
s a s a s um ma t io n o v a r i n g f o r c es
andtheelementso thesur aceas
theotherhandconsideringthewater
thisdisturbance inthedistribution
uidf orcesacerta inserieso phenomena
iththe locationo thebod re lati e to
u i d. T he s e we w i ll b r ie l e a mi n e.
estcasew ew illsupposethebod
f arbe low thesur acethatthedis-
cpressurebecomeinappreciablenear
esultsthattherearenosur acee f ects
. I , r ep re se nt t he b od i n q u es ti on c on -
uidf low ingb . N ow considering
c le s o w a te r i t i s f o u n d b e p e ri e nc e
peso motionma bedistinguished.
rabledistancef romthebod
ndistinguishable f romstraightlines.
d w esha llf indthatthepathsbecome
daroundthebod asshow natL MN.
a lspaceratherthanplanecur es.
the bod themorepronounced
a llthesepathsthedistinguishingf eature
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C E A N D PR O PU L S I O N O F S H I P .
l o wi n g f o r m a nd t h e ab s en c e o a n t h in g
ooping. Suchcur esarek now nas
tillnearerthebod , how e er w e
o r m i s b lu n t or r o un d ed a s e ri e s o l a rg e
mingl f o rmedatornearthestern.
in ol emucho thewatere tending
somelitt ledistancesternw ard. Thew ater
sobef oundtobemo inginamore
egularmanner.Theseeddieswith
enthemconstitutetheso-called
peedsa lso andw ithabluntorbroad
m a b e f o u n d i n ad d it i on j u s t f o r w ar d o
w aterinw hichthemotionisnot
th. A ga in atthesidesandbetw een
eam- linesandthebod w eshallf inda
d ingw aterinw hichthe loopsandspira l
thew holeconstitutingare lati e l thin
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E .
nintothemostv io lentcon usionas
sparticles. Thee tento thedisturb-
f romthebod outwardtothewater
thstream- linemotion. Thecharacter-
mo t io n o t h e wa t er i n o l e d i n th e se
t c. i s t he r e o r e it s i r re g ul a ri t a n d co m -
edf romthesmoothnessandsimplicit
ed . T he v o l um e s K E F a n d A B C a r e
uidprow andstern. Thef ormer
inappreciable incomparisonw iththe
water" isalsosometimesappliedto
s in o l e d .
t he p a th o t h e pa r ti c le s b R u l e r s
ion. Thisw illbesimpl themotiono
hesurroundingbod o w aterconsid-
utl ingparticles suchasthose
M N , w e s h al l h a e n o w si m pl a m o e -
bod mo esb . Thepathsout
thesame andtheparticledoesnot
returnto itsstarting-po int. If w enow
ingtowardG thepatho aparticle
s om e s uc h c ur e a s L R S . T h is i s a
heparticlebe ingmo edoutf romL and
w it h ou t f i n a l v e l o c it w he r e it t h er e o r e
n o l edintheeddiesandw hirls
r e en t ir e l i n de i n it e a n d co n si s t o
ralsandloops.Theparticle isnot
o a t o ne p o in t a nd a s d e i n i t el l e t a t
a becarriedw iththebod some
ithacertainv e locit andenerg , the
matel becomingdissipatedasheat.
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C E A N D PR O PU L S I O N O F S H I P .
especia lrestrict ionre latingtothe
andletussupposethemotiontotak e
aceo the li uid. Thenormaldis-
t icpressurenearthesur acew illnow be
naddit ionalresult changeso e le ation
ta inserieso w a es. A s w eshall
i n o l e d i n th e se w a e s i s pa r tl
edw ithinthes stem andpartl
ost.
eralconsiderationo resistance
a approachitsestimationf romtw o
e m a s e ek t o s tu d t h e am o un t a nd
nce inthedistributedli uidf orcesact-
ace. ( 2 W ema seek tok now the
w eenthebod andthe li uid through
terasmani estedinthev ariousw a s
tteristhepo into v iew usua ll
ointitseemsnaturalto chargea
cetoeachmani estation andthusto
roductiono thecur edstream- lines a
theeddiesatthebow andstern a
tduetotangentia lorf rict iona lf orces
.
stationsweshallproceedtotakeup
m- linemotionha epla edso
ariousv iew sw hichha ebeenheld
esow elltoshow certa inf eatureso
atw esha llf inditpro itableto f irst
deta il.
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E .
N E S .
dgenera ldescriptiono w hatis
ewema re ertotheprecedingsection.
i n e a st r ea m- t ub e o r tu b e o f l o w. L e t
b e a n c l os e d cu r e i n a p la n e pe r pe n di c ul a r
K . L e t t hi s c ur e b e l oc a te d a t a
t h at t h e st r ea m -l i ne s P U V > e t c. a r e at
L . Theparticlescomprisedinthe
instantw ill inthe irpassagepastA B ,
thsw hichb the irsummationw illf o rm
uchisca lledatubeo f low . F rom
articleo w aterw hichisw ithinthetube
a inw ithinit andnoothersw illenter.
e a t u be o v a r i n g se c ti o n in w h ic h
houghitsw allsw ereo a f rict ionless
o thegeometrica lboundar speci ied.
erta inamounto w aterf i l l ingthe
be w ef indthemotionpara lle ltoKL .
assA B thedirectionandvelocit o
tthe lattera lwa sinsuchw a asto
tl f ull. A f terpassingbe ondA B
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
w il lapproachKL , andf ina ll a ta
il lagainbecomeparalle lto it. Suppos-
ndit ionstoremainunchanged the
stream- linesw illremainconstant and
willbenov aria tionf romonemoment
owsthatthecondit ionsf orstead
d r od n a mi c s ar e f u l i l le d a n d he n ce
suchmotionaredirectl applicableto
tinthetube. A ssumingf orthe
s h d r od n a mi c al l p e r e c t t h at i s
s du e t o v i s c os i t t h e e u a ti o n f o r
unitarea
e a f i e d da tu m ;
chstream-line ca lledthetota l
head;
head.
onstantf oreachlineor inde initel
ble f romonetoanother ma beconsid-
e l op t h e f u n d am en t al e u a ti o ns o h d r o-
assumethestudentf amilia rw iththemorw ithinreach
e su b e c t.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
i lable f orthef low o the li uidw ill
a tak ennormaltothestream- lines. A t
rf romA B thisw illbearightsection
d o A B , h o we e r w h e r e th e s tr e am -
theorthogona lsectionw illbecur edor
J . Theareao thisw illbegreater
ctionatMN, andhencethea erage
low mustbegreater. Thise f ectw ill
nearthebod w herethechangein
sw epassonto /thestream- linesare
so the largetube andhencethe
orf low w illbetherightsectiono the
A B . H encethea eragecross-
f low mustbe less' herethanatthe
e thedi f erencew illbemorepro-
thanf arremo edf romit. Sim ilarl
o rthogona lsectionw illbecur edandthe
cr e as e d a s a t H J .
t ha t i n an t u be o f l o w in w h ic h
narea opposite indirection andin
e f ecto the interna lpressuresiso
resde eloped
transportthe
hate er.
an closed
g . 3 n o m at t er
aria tiono
itf i l led
i s co u s li u i d
notangentia lf orce
ewallso thepipe. Thecondit ions
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
thosef oraclosedtubeo f low
upposethe li uidw ithinthistube
otiono f low aroundthetube. There
e r i se t o a d is s ip a ti o n o e n er g t h e
initel . Wek now f rommechanics
case
emand
ultant
ethepipe
uchis
eenb
rewere
orcew e
lowingF lG- 4-
omearesistance. Suchper ormance
t on t h e v e l o ci t o t h e li u i d a n d
rkwithoutthee penditureo
etobecircularincontourando
n F i g . 4 .
ct i on o p i pe
ntour
u i d = 62 . 5 f o r f r e sh a n d 64 f o r s al t
o r ce d u e to l i u i d.
n smallelementisardO , andthe
ga lf orce is
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
B b e 2 0 . L e t 6 b e th e a ng l e
e lement. Thenthecomponento d
ef orthetotalresultanta longOC
df romO towardC ma bee uili-
ngentialtensionsatA andB . L eteach
/ . Th e n we h a e
etothe mo emento theli uidin
w otangentia ltensionsattheendso the
sare independento itslengthand
v . Thisisa lsoe identl trueno
ro thecontour orw hetherit is
n pipe closedincontourornot
ni ormareaandcur edinthearco
u e to t h e f l o w o t h e li u i d th r ou g h th i s
uldbebalancedb twotangential
t h e ar c e a ch e u a l to c r a * - ~ g .
pipeo an irregularcontourand
ig. 5. LettheendsA andDbeo the
nan directionre lati e toeachother.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . 13
o e t o f l o w t h ro u gh t h e pi p e. R e u i re d
o theinternalpressures.
p le t ed b m e an s o a p i pe A F E D
ndmadeupo circulararcsA F andD
. Theni acirculationissetupin
hatthev e locit iesatA andDare
theconditionsinA B C Dw illremain
ow asabo ethattheentireresultantiso
d u e to t h e li u i d in A F a n d D a r e
satthee tremitieso thosearcseach
g . Th e e f e c t du e t o th e s tr a ig h t pa r t
tensionsatF andE w illba lanceeach
entireresultanto thef orcesinthe
ourw esha llha ethee ua ltangentia l
/ 3 = D N a t A a n d D . N o w s i nc e t he
o r t h e e nt i re c o nt o ur i s b al a nc e d i t f o l lo ws
heli uidinA B C D mustberepre-
se ua landoppositetoA MandDN.
mustrepresentindirection po into
ttheresultanto thef orcesduetothe
C D F i g . 6 b e ac ur e d pi pe o
na l a re a b u t wi t h it s e nd s A a n d E e u a l
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
ndinthesameline. A ppl ingthe
o llowsthattheresultantw illbethato
n d E S e u a l an d o pp o si t e in d i re c ti o n
nce insuchcasetheresultantiso
tomo ethepipe inan direction
cetendingtomo eit inthedirection
stablishthe init ialproposit ionrelati e
ubeo f low . I nthemostgeneral
atthetw oends w hilepara lle l a re
ne.Theprecedingtreatmentstill
ndw eshallha ef orsuchcasetheresultant
ua landopposite f orcesnotinthesame
rmingacouple.
g . 7 b e a b o d a b o ut w h ic h t he l i u i d
a lf orcesinstream-linepaths. L et
ataninde initedepthsothatsur ace
e. Wew ishtoshow thatthetota lf orce
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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b thestream- linesiso . This
de r in g P Q R S a t u be o f l o w en t ir e l
w ithitsstra ightendse ua linarea
ndinthesameline ando v ariable
Df orminganinterna lboundar . The
ethenapplies andtheresultanto
nterna lboundar A C B Dw illbeo .
S ma beconsideredasmadeupo
smalltubesf oreacho w hichthe
p le . I t i s e as i l s e en h o we e r t h at
thesecouplesw ill f o rthew holetube
orml distributedo ertheendsPR
theentireresultantw illbeo .
ma alsobereachedb con-
tntf orcew erecommunicatedf romthe
mi g ht o b ta i n wo r k b a l l o wi n g A B t o m o e
meresistance. B y thesupposit iono
gentialf orcebetw eenA B andthe
e p la c e wi t ho u t a f e c ti n g th e v e l o c it o
thouttangentia lf orcetheve locit o
bea f ected. H encew eshould
penditureo energ , andthesup-
ult arethere oreinadmissible.
oteaf urtherresulto there lation-
e ge n er a l e u a ti o n o h d r od n a mi c s
substantiall constantandv to
epressurewillcorrespondingl
mitf oracertainv e locit w esha llha e
e l s m al l i nc r ea s e o v e l oc i t w o ul d l ea d
anegati epressureortensioninthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O PU L S I O N O F S H I P .
actuall rea li ed andtheresult
breakingupo thestreamintominute
es. Thee istenceo suchturbu-
impl apre iouscondit ioninwhich
c tow ardaninde initedecrease inthe
beconsideredasitsh drod namica l
ctua lcasethestreambecomesunstead
hepressurebecomesactua ll reduced
sa lw a smuchreducedascomparedwith
f low . A furtherresulto thegreat
sua ll f oundinthegi ingupb the
hitho ldsinso lution. Thea irthus
ormo smallbubblesmingledw ith
oam ory east appearancew hich
sphenomenon.
F S TR E A M- I N E S .
otethere lationo stream- linestothe
ncew asPro . R ank ine. Hisin esti-
aminationo the irgenera lproperties
f ormsf orshipswhich underthespecial
uldgi e f orthere lati emotiono
am-linepaths.W ewillnowshow
ngstream- linesf orv ariousspecialcases
nk ineandotherin estigatorssincehis
rroundabod areingeneral
ert ieso suchlineso doublecur a-
attheirin estigationisaw ork o much
o. M an h e lp u l a nd i n st r uc t i e s u gg e s-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . I /
b e d er i e d f r o m a s t ud o p l an e w at e r-
noticewillberestricted.
ph sica lcondit ionw hichwouldgi e
od partl immersedina li uidonthe
rigidf rict ionlessplane. L etasim ilar
ndersideo thebod . Thenlet
p la n es m o e p a st t h e bo d o r v i c e
o e r e la t i e t o t he l i u i d. T h e re l at i e
bod ma thenbeconsideredastaking
inedinhori onta lplanes. A tthe
heplanesapproachedv er near the
thatportionconta inedbetw eenthem.
eina thinhori ontalsheetinplane
mechanicsthatforsuchw ater-l ines
on i > s u ch t h at
=
ng y = ^ - .
cit inan directionistherate o
tioninadirectionperpendiculartothe
show nthatthisf unctionisconstantf or
ndthatitma there orebeconsidered
uationtosuchline. I t isl ik ewise
oran one line isproportionaltothe
betw eensuchlineandsomeoneline
eo re erence.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
tusassumetw oplanesasabo e
n d v e r n e ar . A t a g i e n p oi n t le t
uni ormrate. S uchapo into
urce. I nsuchcasethe li uidw ill
adiatingf romthesource. Sim ilarl
dli uidabstractedatauni ormrate.
ractionisca lledasink . I nsuchcase
wl l mo e
ging
he p o in t
e e r en c e
low is
amount
ther
t h e a ng l e
a n d an l i ne O P .
A andO Pisthatcorrespondingto
n ce w e h a e
calledthestrengtho thesourceor
dromechanicsthatthefunction$ f or
sink sandsourcesissimpl thea lgebra ic
unctions consideringi/ > f orasourceas
. H e n c e f o r s u ch a s s t em i n g en e ra l
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
u a l st r en g th w e h a e
e u a l st r en g th w e h a e
implecombinationtheactua lstream-
oundb a constructionduetoMa w ell
.
e tradiatinglinesbedraw natangular
oa- -2 r. Thenthenumbero l ines
oaH -2n. Takean po intP.
atb goingacrosstheq uadrilateral
ndanotherpo intf orw hich^ isincreasedb
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
n d 6 d e c re a se d b t h e e u a l an g le Q O ^ S .
a e ( 6 1 - - # 2 ) o t h e sa m ev a l ue a s a t P.
po intsononeo thestream- lines
rces<9 and( 9a. I tf o llowsthatthe
orthesesourcesw illbeobta inedb
edlinesdiagonall acrosstheseries
rmedb the intersectionso theradiating
2 . S i m il a rl i t m a b e s ee n t ha t f o r Q
# t # a ) a r e th e s am e a n d he n ce t h at
neo thestream- linesf orasource
n l i ke m a nn e r t h en t h e se r ie s o s t re a m-
t asit istermed w illbef oundb
ilineardiagonalsintheother direc-
q uadrilaterals.Theseconstruc-
gs. 10and11 andit isreadil seen
cur esarearcso circles.
eralthatf ora llcaseso combination
s i nk s a nd s o ur c es o r t he i r e u i a l en t s t h e
tream- linescouldbefoundgeometricall
f o r t he t w o co m po n en t s s t em s a n d
scontinuousl diagona ltotheseries
s f o r m ed . I n t h is w a t h e re s ul t o a
umbero sink sandsourcesma be
he l a bo r i n o l e d i s v e r g r ea t w he n
ourinnumber.
ourcesarenota llo thesame
esamemethodho lds.
asaspecialcasetheresulto
ourceandacontinuousstreamwith
atterma beconsideredasapart
asourceo in initestrengthsituatedat
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . 2
a . Thegeometrica lmethodf orthe
sult ingstream- lines stemise actl
andcomesunderthegeneralrule o
e. I t isi l lustratedinF ig. 12. The
romO arereplacedeachb acur ed
thiss stemo cur edlinesspring-
e l e ct e d li n es o t h e un i o r ml f l o wi n g
enthatthe lineA B C separatesone
omtheother a lsothatthere isnof low
e andhencethatitseparatesthe
hesourceO f romthatorigina ll inthe
d en t t ha t i i n st e ad o t h e so u rc e O
eam- lines w eshouldsubstituteaf rict ion-
e t e nd i ng a w a i n d e i n i t el , t h e l i ne s o t h e
a e e a c tl t h e sa m e f o r m wh i ch t h e
thecombinationo thesourceand
ormstreamincombinationwitha
a e t h e r e su l t o F i g . 13 . I n t h is c a se
introducedatO andw ithdrawnat
wa i n de i n it e l , b u t is c o n i n ed t o t he
e li n e A B C , a n d th a t a s b e o r e t h is
dthusintroducedandw ithdraw n f rom
ream. Hencea lso i , insteado the
shouldintroduceathinf la tso lidw ithf ric-
. . . , theresult ings stemo stream-
eamw ouldbethesameasthathere
mandthedoublet.
ma i n t hi s w a a r ri e a t t he
esduetoaf rict ionlesssolido certain
orml f low ingstream.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
snot howe er suitablef orthe
a n d it i s o nl b a n e t e ns i on o t h e
sforship-shapedf ormsma be
sionin o l estheappropria techoice
andsinkssuchthatthe resultingline
lose l asma bedesiredresemblea
mostgeneralmethodo e f ectingthis
M r. D . W . T a l o r w hi c h we m a
a s f o l l o ws :
mo separatesourcesandsink s
urce-and-sinklineornarrowslot
li u idisintroduced andthroughthe
sw ithdraw n. Thevaria tiono
orrespondstoadi f erence inw idth
o strengthma berepresented
B C , F i g . 14 w h er e O B r e pr e se n ts
P thesink portion thestrength
ortiona ltotheordinateo A B C .
PC must bee ual elsethetotal
ithdrawnwouldnotbethesame.
graphicalrepresentationandinte-
ut e o N a a l A r c h i te c ts v o l . x x x v . p . 3 85 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
currentf unctionore uationf orthe
ngtosuchasink-and-sourceline and
c ha ra ct er o A B C , F i g . 14 t o v a r t he
n g c on t ou r A B C . . . , F i g . 13 s o a s
eddegreeo sim ilarit toagi en
am-linesbeingknown itisa
b t h e he l p o t h e e u a ti o n f o r s t e ad
hecorrespondingdistributiono pressure .
15.A B C
o thehori-
d producing
inesasshown.
O Y 1
o erthe
ntedb the
r e la t i e
m il ar l t he d e e c t
tsma be
e s u ch a s F G .
sa longtheF lG- I 5-
ss o s p ee d i s re p re s en t ed b t h e cu r e H I
es s ur e b J K . A t a c o n s id e ra b le d i st a nc e
a luesallapproachinde inite l nearto
dthevaria tionsthere rombecome
sindicatedb thediagram.
cialcondit ionsassumedinthetreat-
thetotalresultantf orcebetw eenthe
so theresistancetothemotiono the
w illa lsobeo. The in estigationo
oreo importance inthedetermina-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
ance inan gi encase butratheras
umptionso planestream-linesandno
enthesur aceandthe li uid w hat
etosmoothandeas stream- lines and
actuall i u idw oulde periencethe
e
i uidisq uite f ree insteado be ing
gidplanes.Thisintroducesinto the
ne s e s pe c ia l l n e ar t h e su r a c e p r o o u nd
ndicationsrece i edf romplanestream-
aution andonl so f arascompari-
e perimenta lin estigationma seem
u r th e r 14 o n w a e - r e si s ta n ce .
G N E R A L C O N S I D R A T O N S .
icationo thegenera lprinciples
tchaptertotheresistanceo ships it
a tf orthepresentw etak eno
uenceduetothepresenceo aprope ll ing
chwehereconsideris theactual
resistancewhichtheship would
asb tow ingthroughthew ateratthe
icationsduetothepresenceo a
willbeconsideredin45.
t h er e o r e t h e g e ne r al p r ob l em o t h e
immersedbod inanactua ll i u id as
ncew esha lle aminethesub ectunder
sistance. The li uidbe ingno longer
nterna lshearingstresses thestream- line
c t li u i d wi l l no t b e q u i t e re a li e d a n d
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
ese linesintheactua ll i u idw ill in o l e
f r o m th e b od . T h is i n o l e s t he
tantf orcebetw eenthe li uidandthe
la t i e m ot i on o t h e tw o o r i n t he
tiono the latter. Thisgi esthef irst
nceasabo e.
s ta n ce . W e c o me n e t t o t he w a te r i n o l e d
tern. A sa lread noted thisdoes
- linepaths. I t isthrowninto irregular
h e en e rg o w h ic h i n th e a ct u al l i u i d is
ntoheat. Thew aterin o l edinthis
o er remainthesame butgradua ll
gino new particlesandthee pulsion
sli uidprowandsternwill gi e
a c on s ta n t dr a in o e n er g f r o m th e m o i n g
t o w h ic h i s ma n i e s te d a s a re s is t an c e to t h e
stheseconditemasabo e.
k i n o r F r i c t io n al R e s i s ta n ce . W e t a ke
i n g wa t er p r od u ce d b t h e ac t io n o t h e
eenthesur aceandthe li uid. These
re lationtothemotiono thebod
theedd resistancesocalled. The ir
dra insenerg f romthebod , and
tancetothemo ement. Thisgi es
ta nc e. F i n al l w e ha e t he wa e s s te ms
n themotiono a bod nearthesur-
s remark edinI andasw esha ll later
o l e d i n th e se s s t em s i s no t r et a in e d
constantl be ingpropagatedawa and
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N DPR O PU L S I O N O F S H I P .
thew a es stemsre uires there-
p l o e ne rg f r om t he m o i n g bo d , a nd
uscases gi esrisetoaresistancetothe
ourthitemasabo e.
t in t h e mo s t ge n er a l v i e w ( i a n d ( 4
esma beconsideredastheresult
lnesnearthesur ace andhence inits
nce(i m ightbeconsideredasincluding
h er ec la ss i i e d h ow e e r w em ea nb ( i t he
ntenanceo thes stemo stream-
rmedw erethebod mo edw iththe
initedepthbelow thesur ace. The
e- ormationisthentak encareo
c a se ( i i s v e r s ma ll s in ce w it h th e v e lo ci -
w aterbeha esnearl asanon-
ia rl ( 2 a n d ( 3 m i gh t w it h p ro p ri e t b e
nce sincebothitemsarisef romthe
emso eddies. S incetheirimmediate
w e er it iscon enienttoconsiderthem
( 2 isf re uentl termedthehead-
sometimesconsideredaso tw oparts
ances thef ormerbe ingduetothe
nthe li uidprow andthe lattertothe
g li u i d st e rn . I n a sm u ch a s t he c a nn o t
er w esha llusetheonetermf orboth.
f ormthisissosmallastobe
nothercases asinthemotiono the
r-blade bilge-k eelinoscil lat ion etc.
itemso theresistancetothemotion
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 31
o r m we a r e th e re o r e co n ce r ne d c hi e l
eresistance.
( 4 oro ( i , ( 2 , and( 4 iso ten
tance.Thistermhas re erenceto
p-resistancewhichrecogni esbuttw o
k in r e si s ta n ce .
a nc e i n cl u di n g ( 4 , a b o e a n d al l o th e r
s i i e d un d er ( a .
tenthatthisclassi icationo resist-
ariouse f ectsproducedonthew ater
more logica lmodeo subdi ision
tngf romthebod andconsidering
mmersedsur ace issub ectedtoacer-
rcema beresol edintotwocom-
l theothernormal. Thisisentire l
f ectsnomatterf romw hatcause
theothermethodo subdi isionit
gtudina lcomponentso thetangentia l
the irsummationthesur aceorf rict iona l
ngitudinalcomponentso thenormal
the irsummationtheremainingorresid-
on d in g t o ( i , ( 2 , a n d ( 4 , o r w i t h sh i p-
ntire l to ( 4 . Thissubdi isionis
an supposit ionw ithregardtothe
r andisthemostdirectorimmediateas-
. Thetw opartsma betermed
stances.
we m a t a ke o t h e su b di i s io n o
gedtogotoe perimentalin estigation
in ormationasto itsamount. Wepro-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D PR O P U L S I O N O F S H I P .
othedescriptiono thevariouse perimental
othediscussiono theresultsw hichma
m.
C E O F D E P Y I M M R S E D P A N E S MO V I N G
T E M E L V E S .
g. i issupposedtobereducedtoaplane
otion theresultw il lbeas stemo
omew hatasinF ig. 16 thoughthe
tw eenthetw oisnotf i ednorsode i-
db aroughdiagrammaticrepresen-
egi es. Thetangentia lresistance
entia lf orce isatrightanglestothe
sdoesnotmeanthat theactual
to thecharactero thesur ace but
angentia lf orcesha eno longitudina l
thesur acew illpresumabl
stream-linef ormationandtheamountand
row andstern sothatultimate l itw il l
theresistance. V iew edimmediatel ,
nce isduew holl to theeddiesand
ectli uid. Ex perimentshow sthat
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 33
sema beappro imatel e pressed
h e f o r m
inpounds
t
u i d 62 . 5 f o r f r e sh a n d 64 f o r s al t
gr a i t = 3 2 .2 f t . ;
f e e t
e e t pe r s ec o nd .
2 g i s v e r c o mm o nl p u t e u a l to i .
a tionbecomes
f icientf whichha ebeendeter-
ha ev ariedwide l . Thisisdoubtless
he perimentsha ebeencarriedon
r e r s un d er d i f e r en t c on d it i on s n o ta b l a s
e d e pt h o i m me r si o n a n d ac t ua l v e l o ci -
ecthasnotbeene aminedw ith
esstoshow satis actoril thegenera lre la -
thethreeconditions area immer-
nf actthere isconsiderabledoubtasto
asestrict l asthearea w earenotsure
s h ou l d f o r a l l v e l o ci t ie s b e 2 a n d th e
ingimmersionisnotsatis actoril k nown.
re toe presstheresultso e periments
n g co n di t io n s b t h e si m pl e f o r mu l a ab o e
e uenceso a lldi f erencesbetweenthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D PR O P U L S I O N O F S H I P .
w ma w ithj ustice leadtow ide l
o r t hi s c oe f i c ie n t.
perimentsw erethoseb C o l.
theGreenlandDock sinL ondonbetw een
n s u a re f e e t v i n f e e t pe r
nd s t h e me a n v a l ue o / d ed u ce d f r o m
bouti. i .
perimentsonplanesabout3f t.
unitsameanva lueo about1. 7.
o about3. 28f t. persecond
intainedstationar inamo ingstream
86 . F o r a s t a ti o na r l i u i d an d m o i n g
t he s a me h e f o u nd f = 1 . 43 . I f i n
idmo edsteadil andw ithouteddiesor
ndinthesecondcasethe li uidw as
e lati espeedbeingthesameineach
houldbe thesame.Thediscrepanc
di f icult o mak ingsatis actor
a n v e l oc i t o a f l o wi n g st r ea m a n d
ndi f erence ine f ectbetweena
andwithturbulence.
e l s e p e ri m en t s in t h e ri e r L o i r e
etiron. 98f t. highb 1. 31f t. long
e. 66f t. o watero ertheupper
a l u e o f = . 1 . 6 . Th e ma i m um v e l oc i t
.25f t. persecond.
. R . E . F roudehasdeterminedthis
ndit ionsw hichinsurethehighestdegree
rac . Theresult ingva lueagreesv er
ag e o B e a u o ' s v a l ue s m en t io n ed
uti. i .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 35
e r ge n ce f r o m al l t he v a l ue s a bo e
heresultso e perimentsonbilge-
itthisf ormulao resistancetothese
i c i en t v a r i n g f r o m 5 o r 6 t o1 5 o r 16 .
r ia b il i t , a s we l l as i t s gr e at d i e r ge n ce f r o m
icatesthatweha ehere in o l edsome
epresentedb thef ormula and
enhithertounsuspected.I tis
mentsunderthedirectiono R . E .
w hich it ise pected w illthrow light
o no t e th a t i t h e im m er s io n i s su f i -
ucethesur acedisturbancetoanegligible
w illbepracticall independento an
pth. Thisisreadil seenf romthefact
notf romthepressure w hicho
depth butratherf romadi f erence
chpressure andthatthisispracti-
depthso longassur acedisturbance is
ema v iew theresistanceasdueto
thestream- lineandedd s stems
umdepthabo ementionedthe
sewillbeconstant theenerg absorbed
ewilllikewiseremainthe same.
neoutb B eau o ' se periments.
at accordingtoourde init ion head-
due totheedd andstream-line
e immersiono thebod sogreatthat
renegligible . I t isnottheresistancedueto
dedd f ormationi nearthesur ace
hew a e- resistanceasw ell. I nthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
ore tangentia lresistancebeingabsent w e
n thetotalresistanceasthe plane
easduetotheresistancearisingf rom
n a n e p er i me nt t he re o re i t he
ce theresistanceactuall measuredw ill
ad-resistanceproperandwa e-making
e r s li gh t wa e m a i n o l e c on -
ecia ll i itslengthisgreat. H ence
a c e e f e c ts m a c o un t f o r m u c h in t h e
h e e p l an a ti o n o m u ch o t h e v a r i a-
h e co e f i c ie n t f n o t ed a b o e m a b e
ations.Theactualamountmeasured
ance. I f the immersionisnotsu f icient
sturbances thenthistota lresistance
tothew a e- ormation. Thismust
nditionnotrepresentedintheformula
ee latera lso w a e- resistancev ariesw ith
amuchhigherinde than2. The
re orew holl unsuitedtorepresentthe
n andan attempttomakeitrepresent
ichthew a e-mak ingportionma be
willnatura ll leadtow ide l di ergent
caseo bilge-k eelsthesur acedisturb-
nsiderableamount anditseemslik el that
isduetothew a e-mak inge f ects
ittheabo ef ormulatothe
orenatura ll leadtoava lueo /
romitsv a luef orhead- resistancea lone.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
C E O F D E P Y I M M R S E D P A N E S MO V I N G
Y TO T H E I R N O R M A L .
eado standingatrightanglestothe
sinclinedatanangle6 w eha earesult
ig. 17. I nsuchcasethef orce in
B a s d et e rm i ne d b J o e ss e l s e p e ri -
e f o r m ul a
nt ortheresistanceinthe line
o r e
0
ee pla ined thenomenclatureo thissectionis
epreceding.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
o ' s r e su l ts w e ma p u t ap p ro i -
. ( 6
m. F roudealsoagreedingi ing
tthecondit iono ourin ormation
f r o m sa t is a c to r , a n d f u r th e r e p e ri -
mntsw erea lsodirectedtow ardthe
ationo thecentero thes stemo
nobli ueplane.Theresultswere
plane inthedirectiono motion
hecentero pressuref romtheleading
s i n # / . .. . .( 8
speeds o to4. 25f t. persecond
ependento theve locit .
g. 17 it isk now nthatthestream
w i ll d i i d e an d p as s a ro u nd a p a rt b C
tB K betheplanew hichseparatesone
romtheother. ThenL ordR a le igh
erminedb thef o llowingproportion:
co s 3- ( n B ) s in B
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
identl lessthani bothstreams
ction asw hentheplane ismo ed
k betheratiobetw eenthetangential
ThenC otterill* hasshow nthat
ono theserelationsisshown
cingedd resistanceb anappro-
m f o r a s h ip - sh a pe d b od a n d th e a o i d-
Q I N D GR E E S
allsur acesnormaltothedirectiono
nchangeso directioninthesur ace
us a p pe a rs a s s ho w n b T a l o r f f o r a
e I n s t i tu t e o N a a l A r c h i te c ts v o l . x x . p . 1 52 .
d S c r e wP r op u ls i on " p . 2 7.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N DPR O PU L S I O N O F S H I P .
0k nots usingtheresultso 7 f or
hattheresistanceo ones uaref oot
w ndirectionisabout770timesas
meareae posedtotangentia lorskin-
isconnectionthati the lineso a .
orherspeed large unstableeddiesare
stern suddenl shi t ingaboutf rom
randcausingsuddenanduns m-
al resistanceandintheaction o
ingsuchshipsver di f iculttosteer.
L O R S K I N R E S I S T A N C E .
mo resistancehasbeenre erredto
orthedeterminationo itsamount
e a u o , T id ma n a nd W m . F r ou de .
the latterarethemostrecentande -
ontentw ithabrie resumeo theresults.
sboardsT3inchthick 19inches
e r en t l en g th s f r o m 4 t o 5 0 f e e t w er e c o e r ed
sandtowedlengthwiseinatank o
peedandresistancebeingcare ull meas-
aratus.
theresultso thee perimentsthe
pposedtovar accordingtothe
inpounds
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
f e e t
e e t pe r s ec o nd o r k no t s a c co r di n g to
e perimentalresultsisshow ninthe
O WI N GR E S U L T O F E X P R I M N T O N
S TA N C E .
c e or D i st a nc e f r o m C u t w a te r .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
dertestmo essurroundedb a
e t h e ma i nt e na n ce o t h e en e rg o
esistanceunderconsideration.The
boardisconstantl enteringw ateratrest .
comeincontactwith wateralread
ar d e nd a n d po s se s si n g t h er e o r e t o a
thisedd ingmotion. I ntheseeddies
ew ater-particlesne ttheboardis
s o t h e wa t er b e in g i n o l e d a n d wi t h a
accordingtothe lengtho t imethe
andtotheothercircumstanceso thesur-
o llowsthattheedd ingmotionw illbe
edasw egof romthebow a t.
ardnearthef orw ardendad ancing
l meetamuchgreaterresistance
ednearthea terend andentering
ssessesinlargemeasuretheedd ing
detailthecharactero thee ua-
stanceasgi enabo e especia ll asto
uantit iesin o l edandthecircum-
iment.
kenasthearea withoutmodi ication
sabo ethatthe lengthf actoro area
ce s o t ha t w e ma c o ns i de r s o f a r a s
a nt i ti e s o t h e f o r m ul a i s co n ce r ne d A t o
h. Supposenow thatw eha egi en
R f o r a ra ng e o v a l u es o q u a l it , l en gt h
a luew illgi easinglee uation
k now ns/ andn. Thesema beboth
po int andnotk now ingonw hatthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
consideran tw oe uationsassimul-
hemforthedeterminationo / andn.
outothercondit ionstherelationso /
eso thee perimentare indetermi-
assumptionmustthere orebemadein
otherdeterminedinaccordancethere-
v a l u es o R f o r f i e d q u al it , a nd
eeds itseemsmostnatura ltoassume
ra llsuchva lueso R , andtothen
withthis assumption.Thisis
gthat/ isdependentonq ualit and
nto speed. Wema a lsoconsider
o i d in g f o r e f e c ts d u e to c h an g es o t e m-
l i u i d. I t m a a l so b e we l l to n o te
a n d in f a c t th e e nt i re e u a ti o n i s c on -
thedeptho immersion.
dependento speedvariation it
eamounttakenastheunito speed.
:I nthef ormula gi ev av alueI .
R -r-A .H ence/= themeanv alue
o o t at t h e un i t sp e ed .
husknown itma besubstituted
o ns r e pr e se n ti n g th e v a l u es o a t v a r -
a lueso ; / thusdetermined. I t isseen
m a v a r w i th t h e sp e ed a n d th e w i ll
a rt icularv a lueo / used.
lldependonlength q ua lit o
andtemperature w hilenw illdependon
onspeedandtheotherv ariouscon-
iplestotheresultso F roude s
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
i n d in g e ne r al f o r a g i e n q u a l i t , t h at f
engthata decreasingrate:also
ua lit inthew a w eshouldnatura ll
nsideritsrelationto thethree
ua lit , length andspeed. Wef irst
noscaleo q ua lit , a lthoughthere is
nbe ingingenera llargerf orroughthan
F o r l e n gt h w e f i n d b c o mp a ri n g th e
a lit andspeed thattherelationo n
riablew iththeq ua lit . Theresults
n F i g . 1 9 .I n ( a a n d ( b f o r v a r n i sh
t h er e i s a f a l l i ng o f , a t f i r st m a rk ed
sthe lengtho 50f eetisapproached.
s a nd t h e v a l ue i s p ra c ti c al l c o ns t an t a n d v e r
o r m ed i um s a nd . C u r i ou s l , a l so t h e
r e gr e at e r th a n th o se f o r ( d .
dis muchlesssimpleorregular.
graphicall thev aria tionso nw ith
litiesasabo e. F orcon enience indea l-
ble 500f t. perminutew aschosenas
commentonthecur esisunneces-
t ed t h at t h e w er e d er i e d b m e th o ds
hecur espublishedintheB rit ish
abo ere erredto.
orlargehigh-speedshipsin ol es
tions:
an d n f o r a n p r op o se d q u a l i t o s u r-
r o m 2 to 5 0 f t . i n le n gt h a n d mo i n g at
tinB rit ishA ssociationR eportsfor1874 o w hich
artialresume.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
00f t. perminute . R e uiredappropria te
aps600f t. in lengthandmo ingat
E E T.
tsperhouror2000to2500f t. per
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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C E A N D P R O PU L S I O N O F S H I P
00
E T P R M N U T
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E .
seiseither toassume/ andnas
be ondthema imumlengthandspeed
e ri m en t al d a ta o r t o at t em p t an e t r a-
mits o the lawsgo erningthe irvaria -
mnta lrange. Thee tremeuncerta int
pe c ia l l a s r eg a rd s t he v a r i a ti o n o n i s
c u r e s o F i g . 19 e t e nd e d b j u d g-
sasgreatasthema imumthere
i g . 20 t o s pe e ds t h re e o r f o u r t im e s as
egi en. Theuseo suchmethods
u s ti i e d b t h e l a ck o m o re e t e nd e d
alcomputationde initeva luesmust
ed. I tmustberemembered how e er^
orlargeshipsathighspeedsisamatter
rt a in t . T h us i n t he t a bl e s f o r f g i e n
thef iguresinthethirdsigni icant
i gn i i c an c e wh a te e r . S i m il a rl f o r n
or1. 829asusedma perhapsanswer
butitmustnotbef orgottenthatno
tof iguresinthethirdplaceo
mportanceto thoseinthesecond
a r e ma r k th a t a di f e r en c e o I
w il lcausef orusua lspeedsadi f erence
r ce n t in t h e v a l ue o v n , s o t ha t s uc h a n
isnotgreaterthanthattow hichw e
gineeringwork.Thisdiscussion
ow hatane tente trapolationisnecessar
uteskin- resistance andhow greatis
endede perimenta lin estigation.
deaso M. R isbecasgi enina
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C E A N D PR O P U L S I O N O F S H I P .
interest. Thisauthorconsidersthat
methatf undamenta ll sk in-resist-
t d oe s t he e n er g o e d d i n g wa t er w i ll
uareo thespeed andtow ritethe
sthentobe determinedinaccordance
data andisconsideredasincluding
p e rt u rb a ti o n " t h e v a l u e o w h ic h
n g v a l u es o n i n t he m or e u su a l mo d e o
bit o suchatreatmento the
ousf romtheprecedingdiscussiono
ntit iesinthee uationtothecondit ions
e h a e s i m p l t o f i n d f o r t h e v a r i ou s
l e ng t h a n d sp e ed t h e q u o ti e nt
ntstheq uotient/ asaf unctiono
a ch q u a li t o s u r a c e o t h e sp e ed v ,
h e c o mp l e i t o t h e re s ul t in g e u a -
o thee actnatureo theparam-
f e c te d b t h ei r e t e ns i on t o l en g th s
ndthoseconta inedinthefundamenta l
onablew hetheran ad antageistobe
d e o c o n s id e ra t io n . I t i s h o we e r o
blemodeo consideringtherela-
othecharacterist icso thee periment.
s o c i at i on T e ch n i u e M ar i ti m e v o l . v . p . 4 5.
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C E A N D PR O P U L S I O N O F S H I P .
e perimentso W m. F roudeon
touseforA theactua lw ettedsur ace
deri edf romhisresultsandgi eninTable
tendedtocorrespondtothisva lueo thearea.
t h e re d uc e d su r a c e is f r e u e nt l u s ed
edsur acema bederi edb
nasshow ninthetheor o statica l
r b t h e us e o o n e o t h e f o l l ow i ng
ateformulae:
a c e in s u a re f e e t
s-
t
n t o f i n en e ss .
enotationletusput
romtable
h ip s e ct i on ;
n t o f i n en e ss .
o N a a l A r c h i te c ts a n d Ma r in e E n g i n ee r s v o l .
ut e o N a a l A r c h i te c ts v o l . x x x v i . p . 72 .
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E .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D PR O P U L S I O N O F S H I P .
erdegreeo accurac weha e
aeha ethead antageo simplicit ,
curate itserrorsbe ingusua ll less
c e we h a e f r o m th e f o o t - no t e
asbe orew eha ethef o llowing
n5andS r:
L U E S O F T H E Q U A N T T E S / A N D nF O R
S TA N C E .
umo thepractica lv a luesw hich
v ariousauthorit iesforthecoe f icient
n
unds
d su r a c e in s u a re f e e t
erhour
o N a a l A r c h i te c ts a n d Ma r in e E n g i n ee r s v o l .
p . 13 8 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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E .
H O WI N GF R O U D ' S E X P R I M N TA L V A L U E S .
ce .
ce .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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s s
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E A N D PR O PU L S I O N O P S H I P .
.
R S H I P B A S E DO N T D MA N ' S E X P R I M N T .
R .
a n d
athing.
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/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
or/gi enintheabo etablesare
ntso F roudeandT idman. A s other
mentionthef o llowing:
eva lue/ = . 0167f orrough-sawn
orsmooth-planedw ood. Thesame
orf ine" grass" ormarinegrowth/
rom. 048to . 062. F orcleancopperthe
andf orf resh-pa intedironthev a lue. 01.
t usedb Pro .R ankine.These
so usua llength oratleasto er50
esultsgi eninarecentpaperb
n s tr u ct o r H i c hb o rn f a r e o i n te r es t . F r o m
aperthef o llowingtabularpresentation
how sthepercentageincreaseo total
ttomo erthatw ithclean reck onedon
eshoulde pect thattheterm
i n de i n it e a n d ma m e an a l mo s t an c o n-
ance issensibl increased. In the
tablethetotalresistanceo theB enning-
n d Du d eb o ut T h eo r ie d u N a i r e v o l . in . p . 37 6 .
e o N a a l A r c h i te c ts a n d Ma r in e E n g i ne e rs v o l .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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C E A N D PR O P U L S I O N O F S H I P .
mesthatw henclean. A t the low
nsw eremade mosto theresistance
sothatw hiletheabo ef iguresre er
eratiosf orthesk in- resistancew illnot
t h ou g h sl i gh t l g r ea t er .
sinthestrongestmannerthe
acleanbottomespeciall f o reconomi-
peeds andf orthepossibleatta in-
eeds.
esub ecto w a e- resistancew eshall
tonabrie accounto thecommonl
a e-motioninli uids w ithastatement
results butw ithoutthedeta ilso the
ment.
n a sa t is a c to r m a nn e r th e i n l u en c e
somework ingtheor astothe ir
sre uired. I tmustbeunderstood
ottobev iew edasf ina ltruthinitse l ,
entmethodo correlatingasnearl as
ts ando deducingb appropria te
ef o llowingw orksma beconsultedb those in-
pbuilding TheoreticalandPractica l. L ondon
S y s t em o M o de r n N a a l A r c h i te c tu r e " v o l . i . L o n -
n ic a a r ti c le W a e .
orieduN a ire v o l. in. Paris 1892.
S . N a a l I n s ti t ut e 1 88 3 p . 2 23 . A n n a po l is .
ansactions1847.
o litana articleT idesandWa es.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E .
probablenatureande tento the
bee amined. Themostsimpleo the
ndis thatknownasthetrochoidal.
snamef romthetrochoid whichisthe
o w a e s r es u lt i ng f r o m th i s mo d e o
on. Thetrochoidma bede inedas
F i g 2 1 w hi ch r e o l e s un i o rm l
c h ce n te r i ts e l m o e s u ni o r ml a l on g
n t h is c a se i O m o e s u ni o r ml
d O P r e o l e s u ni o r ml c o un t er - cl o ck wi s e
w illresult. F orcomparisonthere is
nuso ido e ua llengthandheight
etw eenthetw oisindicatedb theshaded
bede inedasthe locuso apo intin
w hichcirclerollsuni orml a longa
22letacircleo radiusO Q ro ll
A B . L etPbethetracing-po int.
illbeacur eC PD , andtheidentit
w ocur esinF igs. 21and22is
etracing-po intP isonthecircum erence
ecomesthecommonc clo idasa
choid. I f thepo intpassesbe ondQ,
ti l lca lledatrochoid. Thespeci ic
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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A N C E A N DPR O PU L S I O N O F S H I P .
ndcurtate-trochoidaregi ento
r e s . I t i s o n l w i th t h e f o r m er a s
twearehere concerned.
sarever nearl trocho ida larebut
ghamoderate l hea y sw ellinca lm
timea terthesubsidenceo the
e istence q uiteclose l con orms
da l w a e i s m or e o e r t h e t p e -
edb mathematica lmeans andisthere-
orpurposeso theoreticalin estigation.
atrochoidalwa ein ol esthe
g i e n wa e a ll p ar ti cl es r e o l e i n f i e d
ertica lplanespara lle lto thedirectiono
thelineso crestsandhollows
ngularve locit andindirectionwith
crest.
a e r o w a t er o r ig i na l l h o r i o n ta l t he
entersareonthesamehori onta l
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E . 59
creasewithincreaseo depthaccord-
er.'
o rigina ll inthesamev ertica lare
se.
r a c e la e r o p a rt i cl e s an d a ll s u c-
al h o ri o n ta l w il l t ak e t he f o r m o
continua ll decreasingalt itudesaccord-
singradii. I t f urtherresultsthata ll
ho llow sf orsuccessi e la ersw ill l ie
e andhencethata llw a e- lengthsf or
a lsubsur acesw illbee ua l andthat
pagationf ora llmustbethesame.
awa ema beillustratedin
presentsasectiono acertainpor-
dedb hori onta landv erticalplanes
hownin dottedlines.Thef ull
ockso waterwhenthrowninto
o n ta l p la n es o 1 2 e t c. f o r s ti l l
e thrownintothetrocho ida lsur aces
rrespondingcircularorbitsareshownon
P u b l i c D o m a i n
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C E A N D PR O P U L S I O N O F S H I P .
entersareseentobeele atedabo ethe
planesb successi e l decreasing
mthesur acedownw ard. Toa o id
mthe circularorbitsareelsewhere
o l edinthef igurema bev iew ed
onts. Thusw ema considerthe
ote asthew a eprogresses thechange
tan onepo int. O raga inw ema
umnso waterbetween.thedistorted
/ e t c. a n d no t e th a t as t h e wa e p r og r es s es
dbroadenandthenlengthenand
mew a ingtoandf row iththeperiod
larblock o sti l lw aterisrepresented
o rt e d bl o ck a n d th e s uc c es s i e f o r ms
blocksisthrow nma beseenb f o l-
distortedq uadrilateralsbetweenthe
ochoida lsur acesf orthew a e.
a e m a a c tu a ll e i s t in a l i u i d it
drod namiccondit ions. Theseare:
rsur acethepressuremustbeconstant
ce. ( 2 Thatthe li uidcannot
mpressionduringtheprocesso
secondit ionsma bemadetofurnish
thandthev e locit o propagation
asingradiio thecircularorbits.
e e t
i n f e e t pe r s ec o nd
cle :
t ;
P u b l i c D o m a i n
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C E A N D PR O P U L S I O N O F S H I P .
characterist icso w a e-motionasw eare
urtherserieso resultsfo llow ing
ed.
mslopeo an trochoidcorresponds
n b
s l op e t h en
5
w a e = 2 r .
tintersectsthev erticalthrough
gcircleattheconstantdistanceR
o r e al w a s a t t he p o in t o c o nt a ct o t h e
nwhichit rolls.
choidalsubsur aceisconstantand
edeptho thecorrespondingplane
t h e li n e o c e n t er s
c e or b it
epthz-
l e.
P u b l i c D o m a i n
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a t h i t r u s t . o r g / a c c e
s s
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C E .
resto awa eislessthan that
sti l lw aterintheratio
e inthehollow o aw a eisgreater
ldepthinstil lw aterintheratio
ta n t f o r c e du e t o gr a i t a n d to
tsa longthenormaland
aneouscentero
rcleasspeci ied
t O A = R . T h en i
t isrepresentedb
e to c e nt r i u g al f o r ce w i ll
adiusOP andthe
P .
p a rt i cl e
i t = 3 2. 2 ;
t \ / - ;
presentedb A P .
8
er s f o r a n t r oc h oi d al s u r a c e or
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 05
e S y s t em s . Gi e n t wo t r oc h oi d al
paralle lcrests mo inginthesame
suchacombinationgeometrica ll ,
roduceaserieso groupso w a es
a imumo he ightw heretwocrests
mumwherecrestandhollowcombine.
eculminatesinaw a eo ma imumalti-
smalldisturbancebetw eeenthesuc-
beshownthatsuchgeometrical
i lthenecessar h drod namica l
orecannote istpermanentl asacom-
hoida ls stems. Theactua lresulto the
es stemsistoproduceamoreorless
em w ithcharacterist icsre lati e tow hich
eometrica lcombinationo trocho ida ls s-
asappro imations. Wedof ind
binationso w a es stemsagree ingina ll
tcsw iththosegi enb thegeometri-
edto anditthere oreseemsf a irtouse
basisf orthe e aminationo such
in.
assumethatthetw oseriesareo
b ut o d i f e re nt l en gt hs Z , a nd Z a . Th en
onwillgi earesultas indicatedin
thephasesareopposite andtheva lues
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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s s
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C E A N D PR O P U L S I O N O F S H I P .
resultantdisturbance iso andw eha e
ca ll undisturbedw ater. A tapo int
thephasesarethesameandthetw o
g i i ng a wa e o h ei gh t 2/ , t he m a i m um
s. Thegroupf romA toC isthen
d t o th e r ig h t an d l e t a s f a r a s th e g i e n
g th A C i s g i e n b t h e e u a ti o n
o p r op a ga t io n o t h e re s ul t an t g ro u p as
p r op a ga t io n o t h e co m po n en t o
propagationo thecomponento
^ i n v a l u e t he l e ng t h o t h e gr o up A C
locit w il lapproachmoreandmore
ato thecomponents. A t the limit
lengthw ouldbecomeinde initeandthe
meonehal thato thecomponents.
oupisthee pressiono acerta indistribu-
s co n si d er e d th a t th e v e l o c it o p r op a ga -
hesameasthato thegroup.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
ecialcaseo tw otrocho ida l
r en t a lt i tu d es b u t o e u a l le n gt h s an d t he r e-
o ci t ie s .
notetheorbitcenterf oragi ensur-
ectedb eithercomponent. Strict l
renot
t t he d i f e r -
disusua ll
eninstant
notethephase-
component and
o the
O B
tdi f er-
thetw o
= rtand
combination
sw illresult inatrocho ida ls stemo
t h at o i t s co m po n en t s a n d o s u r a c e
andw ithphaserelationshipsw ithits
t h e an g le s C O A a n d C O B . I n o t he r
o gr a m O A C B i s m ad e t o re o l e u n i-
l e th e l at t er m o e s u ni o r ml a l on g x ,
opriatetothe wa e-lengthtaken
acethecontouro thef irstcom-
h e se c on d a n d C t h a t o t h e re s ul t an t .
di f erencebetweensimilarpo ints
GO theangularv e locit , V the linear
eradiuso thero llingcircle . Thenthe
e di f e r en c e A O i s g i e n b
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D PR O P U L S I O N O F S H I P .
- 7 i n a ng u la r m ea s ur e
ee s .
C w e de r i e f o r t he a l ti t ud e o t h e
u l i l me n t wh i ch t h e id e al t h eo r -
ma besa idingenera l andw ithout
at so f arasobser ationscanbemade
racterist icsare inf a iragreementw ith
omtheor . Theagreementisb no
nf actdi f ersincerta inparticularsin
hebelie thatatrul trocho ida lwa e
rmetw ith. O ntheotherhandtheagree-
closetoseemingl w arranttheuseo the
s s o t h e na a l a rc h it e ct a t l ea s t in s o
w ithw a esindeepwater.
s i e s o w a e s t he f o l lo wi n g
:
t ionitma bef a irl concludedthat
0to1500f eetarever rare l metw ith
ndf oracceptingreportso e cep-
gthapproaching3000f eet. Thecorre-
e15to17secondsf orthef irst
econdsf orthe last.
ee idence ismuchmorecon lict-
w e r t h at f r o m 40 t o 4 5 f e e t i s ab o ut
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E .
w hichcanbeacceptedasre liable and
sef iguresaremetw ithbutrarel .
m a b e t ak e n as t h e or d in a r l i mi t . I t
e er thattheseheightsre latetoa
esascontemplatedb thetheor , and
tsarisingf romtheinter erenceand
e r en t s s t em s .
he ightto length it isf ound
thincreaseo length. Thehighest
ppeartobeaboutI : 6 suchbeingf ound
el shortw a es. Morecommonl the
I : 25. Thecorrespondingva lueso
narerespecti e l about32 15
s. Whenw ecometow a esin
asnearl ascanbedetermined the
obeell iptica lw iththe longera is
omeetthisdeparturef romthetro -
so-ca lledell ip-
water
Thisidea l
ra t ed a s f o l -
F i g . 27
or i o n ta l
l on g X w i th o ut
line
theverti-F lG-27-
ertica landthroughA ahori-
rsectonthee ll ipseatP . LetO B
t o t he l e t . T he n t he l o cu s o t h e po i nt P
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D PR O P U L S I O N O F S H I P .
mo emento thee ll ipsea longO X
w illbeanell iptica ltrocho id. C omparing
lt ingf romthecircleasabase as
merisseento lieslightl w ithinthe latter
o llow andsteepercrest thesedi f er-
onouncedasthedi f erencebetw een
llipse isgreater
rochoid
Trocho id
ionthef eatureo especia linterest
r op a ga t io n . F o r t hi s t he f o l lo wi n g e -
ed:
n f e e t pe r s ec o nd
s a t su r a c e
i t = 3 2 .2 .
comparisonwith( i , thatthe
ow - wa t er w a e i s l es s t ha n t ha t o a d e ep -
a llength aconclusionborneoutb
e wa t er . T he n w he n 2 nd ~ - L i s
hat
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
the idea lwa es stemthus
a n d se e mi n gl c a nn o t b e m ad e t o f u l i l t he
tionsnecessar to itsactua le istenceas
r e e n t h o we e r s u ch f o r m o
ossibl , acloseappro imationtow hat
nordoesitseriousl inter erew ithits
o imatework ingtheor o sha llow -water
on. Thew a esthusf arconsidered
initeseries andrepresenttheresult
ddisturbance. Thet pica lw a eo
ncharacter andrepresentstheresult
nF ig. 29letA B beatroughorcanal
argere lati eto itsbreadthanddepth. L et
partit ionmo ablew ithinthecana l
. I f n o w C D b e mo e d r ap i dl f r o m
terw illbecomeatf irstbank edupinf ront
e t ar d ed a n d f i n a l l b r ou g ht t o r es t a t
d -u p w at e r wi l l le a e C ] D l a n d tr a e l o n as a
e n ti r el a b o e t h e g e ne r al l e e l o t h e
catedinthediagram. Suchaw a eis
atthepartit ionw asatC lDland
t he n b e mo e d f r o m C , D t o C D .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
depressionw illbef ormede isting
a lle e lo thesur ace. Thisho llow
n amannersimilartothe crest
d . S u c h a wa e i s c al l ed n e ga t i e .
a a l so b e f o r m e d b p l un g in g i nt o t he
ecanalablock w hichw illoccup the
r b t h e su d de n i nt r od u ct i on o a c e rt a in
uidintotheendo thetrough.
w a e m a b e f o r m e d b w i th d ra w in g a
wi n g a s b a l i t i ng - pu mp a c e rt a in
r op e rl f o r me d a re q u i te p e rm a ne n t
ir e n er g a n d f o r m b e t e rn a l f r i c t io n
o r c es . I n o t pr o pe r l f o r me d t he w a e
rregularseries thememberso
hdi f erentv e locities sothatthe
dandtheformdisappears. The
chlesspermanentthantheposit i e and
eitsintegrit f o rashortt imeonl .
mento an sheeto particlessit-
laneseemstobethesame. The
saccordingto itsdistancef romthe
andseemstobev er nearl proportiona l
o an particleseemstobev er
asshownatA GO inF ig. 30. I tthere-
etothepassageo thew a e a particle
hasbeentransportedandle tatO ;
lparticlesinthetrans erseplaneo A w ill
dinaltranslation andw illbe le tin
tainingO. C aremustbeheretaken
motiono theparticleandthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E ,
hile theparticlemo esthrough
e w a e - o r m wi l l mo e f o r wa r d it s w a e -
i g . 29 .
uro awa eo translationma be
llowingconstruction:
pserepresentingthepatho asur ace
b e t he d e pt h o t h e ca n al . T he n l a o f
tr uc t th e si nu so id A E F . N e t l a o f t o
n th i s cu r e a s A , c g e t c. d i st a nc e s
e t c. o r t he i n te r ce p ts b e tw e en t h e el l i ps e a nd
o in t s O y d z , e t c. t h us d e te r mi n ed
ntouro the idea lw a eo translation
tionsassumed.
o p r op a ga t io n ;
henatrest;
a b o e s t i l l -w a te r l e e l ;
O F , F i g . 30 ;
A O . F i g . 30
constitutingw a e:
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
le o w a e .
k ( 18
s m al l w e ha e
note ceedk . Onreachingthis
t h e wa e b r ea k s at t h e cr e st . H e n c e as a
w e ha e
e l s m al l
w e h a e
a e s t h e en e rg i s o ne - ha l k i ne t ic
theentireamountbe ing
\ ( 2 4
c en te ro g ra i t o w a e a bo e th e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
E L A T O N B E TW E E N Z , T A N D V F O R
L WA V E S .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
.
E V A R I A T O N O F PR E S S U R E V E R T C A L L Y DO W N -
C R E S T A N D H O L L O W O F A W A V E .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
B E TW E E N W A V E S I N S H A L L O W A N D D E P W A T R .
iiesf orS ha llow WaterandC orresponding
ter.
n
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O PU L S I O N O F S H I P .
to these init ia lorfundamenta l
er muchmodi iedb propagationand
mbinationo the ire lementar results.
o we e r t h e di s tr i bu t io n o n o rm al p r es s ur e
theshipw illbemuchchangedf romthat
staticcondit ions suchchangeresult-
romf orw arda t. Thisresultantw ill
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
creasede penditureo energ
meitw ill j uste ua ltheenerg necessar
hes stemo w a esandstream- lines.
edtothemodi iedstream- lines stem
enaasasu f icientinit ia lcausef or
e s w e m a e a m in e t he i r ac t ua l c ha r ac -
detail.
a n d 33 a r e sh o wn w a e p a tt e rn s a s
. F roudeforthev ariouscasesmen-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
indicatedtw oq uitedistinctvarieties
d is t ri b ut i on :
crestsperpendiculartothe lineo motion
rseseries
re s ts o b li u e t o th e l in e o m o ti o n c o n -
di ergentseries.
A V E S Y S T M MA D B Y D F F E R E N T V E S S E L S
P E D .
e C r e s t s in d ic a te d b s h ad i ng .
H
rsewa esaredistributedalongthe
ship andma beconsideredasagroup
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . 81
sdescribedin10. Thespeedo the
esameasthato theship andhence
ocrestcorrespondsclose l to that
oda lw a etra e lingatthesamespeed
lwa sf oundatornearthebow and
beconsideredasthe init ia lresulto
n de n c i n t hi s r eg i on . T o a o i d c o n u -
romthediagram andonl themore
tionsconstitutingthedi ergentcrests
e pla inlater how e er theenerg
sdra inedaw a sternw ardre lati eto
is e t o a se r ie s o s e co n da r w a e s o r
ed theprimar anditsechoesthus
w hole.
hip thecrestsandhollowsshow
omthebow gradua ll decreasingin
tr a ns e r se l a n d th u s in o l e m o re
aduall decreasingenerg . I f the
thatthew a esha eb thisprocess
nappreciable thenitw il lbef ound
t willbegeneratednearthestern
b thesameprocesso sternw ardpropa-
il lg i erisetoasternserieso
pressureamidshipswillbeso
tedo ersogreatadistancethat
usua ll bescarce l noticeable . If
a lle lbod w eha etheusualf orm w e
crestatthebow andstern anda
c to f ormaprimar ho llow amid-
thew a esthusf ormedw illbepropa-
ore thusgi ingrisetoechoesandto
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
markedinit ia ls stems. These
ce andthew holewillf o rmacomplete
ho llow so si eanddistribution
tero thevariouscomponents. A s
cit duetothestream- linemotionare
de o s u ch w a e s w il l b e sm a ll a n d at
arescarce l noticeable. A sthe increase
s is m o re o e r q u i te g r ad u al t h e co r re -
lusua ll beslight andacorrespond-
mentinthecombinedseries. I nman
thighspeedsandw hentheelementso
l thecombinedseriesma show a
ow amidships.
tseries weha ethecon iguration
o l ingineachcaseaninit ia l
edoneithersideo thebow. These
heprimar resulto certaintendencies
re ert. Thesamedraino energ
dobtainshereaswiththetrans-
asw esha lle pla in theresult istheseries
arrangedinsk ew orimbricatedorder
eso erlappingliketheshingleso a
l ai n t he f o r ma t io n o t h e pr i ma r
b o w. W e h a e a l re a d e p l ai n ed t h e
hetrans ersecrestatthebow. This
m al l a lt i tu d e a n d e t e nd s o e r a c on s id -
hespeedandtotherateo v aria -
thestream- lines. R e erringtoF ig. 34
stiono thecontourorle e ll inesfor
e lw hichwouldresultf romtheinit ia l
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . 83
thecondit ionsf romf orw arda t.
issupposedtolie onthesur aceo the
dEF arehumpsorcrests andC Disa
wthetendencieswhichleadto the
hew aterthroughoutA B becomev er
, thef orw ardendo thesur aceo
heshipandthe li uid. A sa result
stthesur aceo thebow atA a
w allo w ater. Thisma beconsid-
geratedmani estationo thegenera l
gi erisetothehumpasaw hole .
see inthiswallthesimpleresulto
a c e A r a pi d l t h ro u gh t h e wa t er o r v i c e
to placinganobli uef aceA ina
m.
specia le le ationo w aterisdue
thesamegenera lcauseastheremaindero
mustbeconsideredasaparto this
, y e t i t is e l e a t ed s o d e i n it e l a b o e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
maindero thehump thatimmediate l
ationundergoingpropagationsomewhat
t r an s la t io n . Mo r e e a c tl o r m or e
iew thispropagationasaresulto the
pressure inthew aterinthisneighbor-
testquiteneartheship and
egoslightl outward. Thew ater
tura ll y ie ldina lldirectionsinw hich
ce itw il ly ie ldupwardandout-
isetoaninitia le le ationo w aterand
nthe directiono themostrapid
Thisatf irstw illbenearl normalto
eo theship.
l estotheshipandconsiderthe
R elati etotheshipthe init ialpropa-
hedirectionO P sensibl perpen-
g . 35 . L e t v b e t h e v e l o c it . T h en i a t
amcouldbesuddenl arrested the
rmingthee le ationA B w ouldbe
hv elocit v . I ntheactua lcase
ationtakesplacenotintostil lwater but
wardwithitsnaturalstream-line
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . 5
m at e l p a ra l le l t o A Q . T h e el e a t io n o
llha etw ov elocit iesone v , a long
w a longOQ . H encetheactua lpropagation
thesetw o anditsdirectionO R w ill
Q s u ch t h at t a n f t = v w . A l s o
mak eanangley w iththedirectiono
f t =
beconsideredasdependingonthe
r es s ur e f r o m A Q o u tw a rd o r o n th e
hesur aceo theshipinthisne ighbor-
raportiono thev e locit o
ee le ationA B consideredasa
an s la t io n . I n a s mu c h h o w e e r a s t he
reseemstobethe importantf actorin
mspre erabletore erthew hole
onandpropagation tothisgeneral
ee identthatv wil l increaseand
cit o theshipaccordingtoa law too
e pression.
elocit alongthestream-lines.I t
lessthanu thev e locit o the
o t h e f l o w a s a wh o le . F o r f i n e sh i ps
t s v a l u e ca n no t d i f e r w id e l f r o m
a l u es o a t h is w o ul d g i e t o o sm a ll a
tany abo e itisseenthat the
n di n g on s p ee d i s th e r at i o v - - w . B o t h
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
e s e en d e pe n d on t h e sp e ed o t h e sh i p
a ltosupposethatv l ik ew ma v er
w i th u y t h e sp e ed o t h e sh i p. I n s u ch
h it y t w i ll r e ma i n v e r n e ar l t h e sa m e
hishasbeenf ounde perimenta ll to
ecia ll f o rf ineshipsatmoderateand
f u l l sh i ps t h e v a l ue o y s e em s t o
hespeed indicatingthatf orsuch
orerapidl thanw . B e ore lea ingthis
a b e w el l t o sh o w th e me t ho d o f i n di n g
n a f o r t h e bo w . I n F i g . 36 l e t
reck onedplusa t. Theni a
t h e cu r e A B w e h a e
y
t an c td = - - I d = .
l
o r t he m ea n v e r t i ca l l , w e ha e
= a r ea o h al - se ct io n A C - T - z . .
w =
C
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
m a b e t ak e n at 1 0 t o 15 p e r ce n t o
oc i ti e s o t h e sh i p th e w at e r in t h e el e a -
i n st e ad o f o r mi n g a si m pl e s ha r pl - m ar k ed
The generalresultwillbethe
s t he b r ea k in g i s si m pl e u i a l en t t o po u r-
ngA B , andthedistributionandrate
pressurew illbesuchastogi ethesame
tionasabo edescribed.
dthepropagationo asingle instan-
w aterA B andtheconsiderationsonw hich
w ene tobser ethatasthepropaga-
ormingthee le ationatan one
e succeededb anotherlik ee le ation
a continualele ationpropagated
ngthedirectionO R . A sthee le a-
, how e er thecresttendstobroadenand
inall becomesinsensible.Toward
nma changesomewhat duetothe
denciesatthatpointon theinitial
hesideo theshipisle t themost
surew illbedirectedmorenearl trans-
a t t o wa r d th e h ol l ow a mi d sh i ps . I n c o n-
o ge t he r w it h t he c h an g ed v a l ue o w t h e
aroundsomewhattowardthestern.
hedecreasinga lt itude thischangeis
edthede elopmento theprimar
ge n t s s t em o w a e s a t th e b ow . A
ormedatthesternthroughtheactiono
nthiscasethe initialwallor
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
w aterisf ormedunderthesternandis
theoutl ingw ater w hich dueto
othestream-linemotionin this
mew hatlow erve locit thanatthe
ia ldirectiono propagationo the
besomewhata to thedirectionf or
hestern y ettheothercomponent
wtheresultingdirectionis notf ar
ends. A thighspeedsinsteado the
ormedagainstthesideo theshipit
astern. I nthiscasethetw ostreams
deo theshipcombinedw iththat
ma beconsideredasmeetingand
ele ationalongthe lineA B , F ig. 37.
ns ersel outwardoneachsideinto
esriseasbe oretothetwodi ergent
Q . A t c e rt a in s p ee d s an d wi t h ce r ta i n
a e i s v e r p r on o un c ed t a ki n g th e f o r m
w aterslopingaw a inaf an-shaped
decreasinginalt itude. A tsti l lh igher
desstil lf a rtherasternandusua ll
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . 9
ronounced.E speciall isthisthe
a ter-bod w hichappro imatestoa
ow nandedgenearthewatersur aceat
ndonmostmoderntorpedo-boatsandman
dthef ormationo theprimar
ou s s er i es o w a e s i n o l e d i n th e
it ist imetotak eupthequestiono
rg a lread re erredto.
G A T O N O F A TR A I N O F W A V E S .
ie l consideredin10.W e
oredeta iltheconse uenceso the
nF ig. 38letthefull l inerepresent
w hichC marksthecenterandprincipa l
ecrestsone ithersidegradua ll
the becomenegligible.Then
ntw iththeor showsthatsuchacon-
ropagatedw ithonl aboutoneha l
i nd i i du al w a e s A , B , C , e tc . N o w th e
econsideredasthee pressiono a
nerg , andhencetheve locit o the
edasthev e locit w ithw hichthe
asdistinguishedf romthevelocit o
t m u st b e c on s id e re d t h er e o r e t h at
a lcharactertheenerg ispropagatedat
l o c it o t h e wa e s t he m se l e s . V i e wi n
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D PR O PU L S I O N O F S H I P .
andpo int le tuse aminethepropaga-
w a e s i n F i g . 3 8. T h ew a e C r e pr e -
berispropagatedf orwardwitha
t m o e s f o r wa r d ho w e e r i t l e a e s
erg , andhencegradua ll decreasesin
erthema imummembero the
sle tbehindisabsorbedb B , w hich
dbecomesa teracertaintimethe
tandhencethenew centero the
themeantimehasgonef romC toC ^
bro thegroup assuch hasgone
l at te r e i d e nt l f i e s th e v e lo ci t o t he
tinualpropagationo theindi-
a rd w h il e r el a ti e t o t he w a e s t he i n di -
epropagatedbackward.Thegroup
r e th e d i f e r en c e be t we e n th e se t wo . I t
dua lwa easA tra e lsa longthrough
onsuccessi e l thecharacterist icso
a n d f i n a l l d i n g ou t a t th e f o r w a rd
rrisesatthea teredge andthusthe
aga in w ema considerthatthe lead-
l dw indlinganddisappearingf orlack
th e l e a e b e hi n d w h il e t he f o l lo w in g
b t h e ac c es s o e n er g w h ic h t he a s
T hu s i v i s t h e v e l o ci t o t h e wa e s
e l oc i t o t h e gr o up a n d o t h e en e rg i s
e t o t he g r ou p t he v e l o c i t o t h e
r d a n d o t h e e n er g o . R e l at i e t o t he
t h e gr o up a n d o t h e e ne r g i s v / 2
g r ou p v e l o c it o a t r ai n o w a e s
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . gi
actproo supposestrocho ida l
ularpathsforthemotiono theparti-
asew herethew a esv ar in
circumstancesthegroup cannotbe
nt e enneglectingv iscousdegradation.
er ation.A gain inshallowwater
appro imatel e ll iptica l thegroup-
n o ne h a l t h e wa e - e l oc i t , a n d he n ce
istransmittedatav e locit greater
t h e in d i i d ua l wa e s . I n t h e e t r em e
eo translationinw hichthegroup
ndi idua l thev e locit o onebeing
eother. I nsuchcase then theenerg
cit e ua ltothato the indi idual
N O F T H E E C H O E S I N TH E T R A N S V E R S E A N D
Y S T M O F W A V E S .
bowtrans ersewa e weseethat
necessaril k eeppacew iththeship.
er thatit isconstitutedappro imate l as
senerg w illbecontinua ll dra iningto
etoasuccessi eserieso echoes.
lspreadingsidewa ssoonloseall
becomenegligible.
rgents stem wef indinthe
heenerg re lati e totheshipcom-
nalpropagationpeculiarto this
aiono theo erlappingorskew arrange-
ma considerthatthesedi ergent
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . 93
v i r tu e o e n e r g d r a wn f r o m th e s hi p b et w ee n
e rw i se r e la t i e t o t he s h ip a n d th e c on -
r c r es t A B , e n er g i s c on s ta n tl d r ai n -
rda longO Q theresultbe inga
outwardinsuchmannerastogi erise
appingcrest- l inesasshown.
ondecho isformed andsoonuntil
andv iscousdegradationthea lt itude
kemannerthestern serieso
g i e r i se t o a s im i la r s er i es o e c ho e s.
erredtoF igs. 32and33inil lustra -
ernw hosef ormationw eha eattempted
now calla ttentiontocerta inf urther
aiono theprimar bow andstern
sthebow di ergentw a esaref ormed
asthespeedincreases theirmeanloca-
thera t. A tlow speedsthestern
o r me d o n th e q u a r t er a n d di e r ge
inF ig. 32. A sthespeedincreases
gether andf ina ll coa lesce intoanelon-
preadingaw a inV shape asa lread
erseprimar wa esha ethe
gitudinall asthedi ergentpri-
eha ea lread po intedout the latter
gerationso thegenera lprimar e le a-
mar bowandsternwa es
thespeed.A tmoderateorhigh
sideredasslightl greaterthanthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D PR O P U L S I O N O F S H I P .
a a ilabledata isnotsu f icientto
theamounto e cess butit isusua ll
ercento the length.
tso thew a e- lengthsf orthe
ref oundtobeincloseaccordw iththe
rocho ida lw a eo thesamespeedas
n b f o rm ul a 1 0 ( i . I t m a t h er e o re
b e periencethatthew a e- length
resisinsatis actor agreementw ithw hat
ngthemasaserieso trochoida lw a es
theship. I nconse uence itseems
rthew a eso thiss stemsuchf urther
aw a esasma becon enientf orthe ir
stemthecase issomew hatdi f erent.
arastheircon igurationisconcerned tra el
ci t o t h e sh i p. I f y i s t he a n gl e o
udina l how e er thecomponento
tothecrest- l inewillbeusiny . N ow
atthewa e-lengthinthisdirection
hthato anatura ltrocho idalw a e
s i n y . I t f o l lo w s th a t in a s e ns e w e ma
smadeupo a serieso bitso tro -
e locit usiny anda lengthcorres-
hw esha llha e
romcresttocrestona longitudina l
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 95
s t em w e ha e l i ke wi s e
engtho thetrans erseseriesshould
nf orthedi ergentseries. Thisis
ms re erencetow hichshow sthatthe
a llf a rtherandf artherasternrelati e to
hile thedi f erencema notbeso
hef ormulaeabo e thetendenc is
heerrorso thef ormulaema natura ll
er ectmannerinw hichsuchw a es
characterist ics.
I N G R E S I S T A N C E .
e d th e f o r m a ti o n o t h e v a r i ou s w a e
motiono ashipthroughthew ater
inethe irre lationtoresistance.
s erses stem weha eseenthat
e s i s r e la t i e t o t he s h ip c o ns t an t l
esametimetheenerg o the
sbemainta inedconstant. Hencethis
nw ardmustbemadeupb energ
p andit issimpl thetransmissiono
esrisetothisparto thew a eresist-
t iono energ w hichf a llsasternre la-
endonthegeometrica lcharactero
stnotbeconsideredthattheratio1/ 2
a n ap p ro i m at i on w h ic h h o we e r
srati epurposes. Hence letusassume
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D PR O P U L S I O N O F S H I P .
isnatura ll propagatedw iththe
h al m us t b e ma d e up f r o m th e s hi p . I t
er tw ow a e- lengthsruntheshipmust
ce s sa r t o t he f o r ma t io n o o n e wa e .
o t he wa e L t he w a e - le ng th a nd
s maintenance.Thensinceresist-
oneorenerg transmitteddi idedb
e
w ouldho ldf orthee lemento resist-
e di e r ge n t wa e s a t th e b ow E b e in g
ongitudina lw a e- lengthf orthis
ew ork whichisdoneb theship
mainta iningtheses stemso
t t o ad d in g o ne n e ww a e t o e ac h s s t em
e- lengthstra e led. Sim ilarconsiderations
duetothesternw a es stems.
onsideredthebow andsternw a e
dualaspect. Weha enow toconsider
thef ormeruponthe latter.
s o f a r a s t h e di e r ge n t s s t em i s c on -
uence ispossible sincethesew a es
e l a n d co m e in c o nt a ct w i th t h e sh i p at t h e
t h e sh i p is v e r l o ng f o r h er s p ee d
a longmiddlebod , thebow trans erse
gligiblebe orereachingthestern so
r od u ce i t s in d i i d ua l e f e c t. I n t h e
er thebow trans erses stemw illnot
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
aredb thetimeitreachesthestern
edatthispo intacombinations stem
aindero thebow s stemandthe
heentirewa es stemsma becon-
ow trans erseanddi ergents stems
e r ge n t s s t em p o ss i bl m o di i e d b
stem plusthato thesterncombina-
tparto the latterw hichisrece i ed
m. F orthetrans erses stemsalonethe
a l to t h e su m o t h e en e rg o t h e st e rn
sthe losso energ inthebow s stem
tancebetw eenthenatura lbow and
discussedin13 andletA bethe
w ema tak easthato atrocho ida lw a e
t he s hi p. L e t L = n - - a .T he n a is
sternprimar crestf orw ardtothe
w s stem. Hencea-= -^ isthephase
2 a - ~ i s t he p h as e d i f e r en c e an g le .
ud e o t h e bo w wa e k h ^ t h e r em ai n in g
stemw henitreachesthestern and/ / 3
hesternw a e. Thenre erringto
atthecombinations stemw illbetro -
i i , i t i s s e en t h at t h e en e rg o a
hmeasureda longthecrestispropor-
t h e wa e - le n gt h b t h e s u a re o t h e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
breadthtrans erse l a tthebow .
inite since// graduall decreasesaswe
r d. W e m a , h o we e r c o ns i de r h
uareso thea lt itudesf orabreadth
risinga llo thew a ew hoseele ation
thebow primar w a ew illthen
^ . L etB andhdenotesim ilarq uan-
ons stematthestern. Thenthe
ombinationwa ew illbeproportiona lto
t h e la t te r h o we e r p r op o rt i on a l to
d er i e d f r o m th e b ow s s t em . H e n c e th e e ne r g
a intenanceo thew holes stem andto
pinrunningadistance2A , ispropor-
B ^ / P/ V ^ A . N o w as su mi ng t ha t B l
same substitutingf ortheva lueo / /
sult proportionaltotheworkdone
mingaresistanceR m throughadistance
i cos ^
, ' + h + z k h i c os -B . . .( i
e - ma k in g l en g th o s h ip i n w hi c h a s
sua ll 1. 05to i.io . Thensw illconsist
multipleso A w itharemaindera .
A ) c os ( 2 n a- = - A ) . A l so A = 2 n * ~ - g
= - A g s ~ v 1 g m ~ v 1 , a nd h en ce
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
put
presenttheresistanceduetothenatura l
m o t h e f o r m / / V , a n d t h at d u e to t h e
a s i mi l ar t e rm / V . T h e n f r o m th e
t f o llowsthatw eshouldlikew iserepresent
hecombinedseriesb ane pression
icincharacter themeanv alue
) B v \ T o i l lu s tr a te t h e v a r i at i on f r o m th i s
26
os ^ l a id o f f r om O X a s a i s.
ermw ema re ertoF ig. 40. We
eva lueso thee pression
mericalv a lues-o theterms
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
eedstheamounto w a e- resist-
sef luctuationsareentirel imper-
sincreased how e er apo intis
e- resistancef ormsanimportantpart
andw heree idenceso sucha
tsamountarepla inl indicated. This
showingtheresidua lresistance-
O T
R E S I DU A L R E S I S TA N C E
e e r al d r a t s a s de t er m in e d b M r . R . E .
h e di e r ge n t se r ie s w e ma t a ke l i ke -
portiona ltothe length breadth and
t e o N a a l A r c h i te c ts v o l . x x i l . p. 2 2 0.
nc he s o k ee l.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E . I O I
. H e n c e // B , a n d A d e n ot i ng i n
erist icsasabo e w eshouldha ef or
,
g t he a b o e p r in c ip l es w e ma r e e r
rimentso Mr. F roudeonthe in luence
middlebod onw a e-mak ingresistance.
he in estigation aninit ia lmodelw as
ip160f eetlong. S uccessi e
d ebod representing20f eetinlength
otal lengthrepresented500f eet.
tv ariousspeedsandtheresistance
alresistancebeingthencomputed
sidualresistancewasconsideredas
i nt e na n ce o t h e wa e s s t em s . I n
graphicall the in ormationw as
a b o e A A r e pr e se n ts t h e re s id u al r e si s t-
a s r mr k ed f o r v a r i n g v a l u es o L
. S im ilarl thecorrespondingline
rict iona lresistanceatthesamespeed
ships theordinatesinthiscasebeing
llowingpo intsindicatedb this
r e si d ua l r es i st a nc e s ho w p la i nl a
e lengtho eachperiodordistancef rom
te o N a a l A r c hi te ct s v o l . X V I I I . p .7 7.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
mbeingappro imate l constantatan
eperiodorspacingbetw eenma ima
E I N TO N S
E I N TO N S
, 1 .1 I I |
E I N TO N S R E S I S TA N C E I N TO N S
creases theva luebeingf oundto
s u a re o t h e sp e ed .
thevaria tionincreasesasthespeed
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 1 03
thevaria tiondecreasesasthe length
isduetothe rapidl increasingim-
ak ingresistance ingenera l a terpassing
somoredirectl to thev a lueo k
sw iththespeed. Thedecreaseo ( 4
k as L i n cr e as e s. I f L w er e s u f i -
dbeno inter erence andhenceno
ariationintheresistance.
rmula( 2 wema f urthere amine
andB tothespeed.
emotioninhori onta lplanesand
h e su r a c e we h a e d e no t in g t he
) S ee 2( i
nef oraslightchangeinve locit
eu w hereerepresentsacerta inf rac-
init ia lv e locit , thepressure incre-
n gi enpo intwillv ar asthe
i t . I n a c tu a l wa e - li n e mo t io n a t
ationwillcorrespondnearl to the
andhencew eshouldf indtheva lueso
p r op o rt i on a l to * . A t h i g h er s p ee d s th e
per ect anditseemsprobablethat
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
suref oragi enpercentageo speed
esomew hatmoreslowl thanasthe
A s s u mi n g h o we e r i n g en e ra l t hi s
asbe orerepresenttheresistancedueto
n wa e s b / / V a n d / V . W e
sin(3
a s be e n us u al l a s su me d t ha t B i s
t a t v a r i n g sp e ed s a n d th a t it m a b e
proportionaltothelineardimensions
caseweshouldha e
atitshouldbeconsideredratheras
n d he n ce w i th & 2 . I n s u ch c a se w e s ho u ld
rectl o thedimensionso the
tsacombinationo thesetwotermsin
ncreasesB w illbecomemoreand
alueo R w . I tma benotedthat
s e u i a l en t t o
donthedimensionso theshipandn
4 to 6.
s s oc i at i on T e ch n i u e Ma r it i me v o l . v . p . 5 2.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
oldwithregardtothe resistance
s t em e a ch m e mb e r o w h ic h m a b e
rm
uchterms accordingasthe law is
d. Hencew ema considerthatin
tota lwa e-mak ingresistancew ill
s o me i n de b e tw e en 4 a n d 6 o r a s a su m
rintermediatee ponents. Theprob-
so PandQ w ithincreasingspeed
retak enasconstant decreasethee ponents
es t h e w o ul d o th e rw i se h a e a n d th u s
satef orthe increase ine ponentdue
etermB .
we er o thetotalwa e-making
dto thedimensionso theshipis
besatis actoril determinedf romthe
emstobeground how e er f orthe
asesitshow sahigherrateo v aria tion
e e p o ne n t 4. S e e al s o 26 . F o r t h e
w earethrow nback onmoreempirical
s im p l t o e p r es s a s ne a rl a s m a b e t he
. Suchf ormulaew illbefoundin29.
dataf rommodele perimentsw e
mate l f o rasatis actor determination
a n d ( 2 o r i n ot h er l i ke f o r mu l ae s h ow n
esuitabletothepurpose inv iew .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
O F R E S I S TA N C E I N G N E R A L TO T H E
TH E L I Q U I D .
andskin-resistanceperunitarea
e ns i t o t h e li u i d en t er s a s a f a c t or .
n si t m u st b e a f a c t o r o t h e en e rg o
partso theresistance andhenceresist-
ar w iththedensit . Thev aria tion
i e n s hi p w it h c ha n ge o d e ns i t o t h e
i n l ar g e me a su r e o f s e t b t h e op p os i te l
m me r se d b od o s h ip . A s b e t we e n
edi f erence isslight andisusua ll
ecaseo modele perimentsorver
densit ieso f reshandsa ltw aterare
ioo i. o : 1.032 orlessaccuratel in
E X P R I M N T O N F O U R MO D L S .
epublishedapaper show ingthe
tsonthecomparati eresistanceo
o thesamedisplacementbuto certain
o r m. T h es e m od e ls w e re c a ll e d A , B , C , D
rkara.Thedimensionscorrespond-
w ereasf o llows:
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . I O /
oreanda terbodieso B , C , andD
os e o A b e p a ns i on l o ng i tu d in a ll ,
v e r ti c al l a s r e u i re d . Th e f o r e a n d a t e r
ethere orethesameratioso fullness
asthoseo A , andtheresult ing
ncema there orebeconsideredasdue
epresenceorabsenceo thepara lle lmiddle
mari edb sa ingthatatall
ssresistancethanA orD. A s
he latterha ingthe lessw ettedsur ace
sbetw eenA andD the latter
tedsur ace hadatthespeedstried
d greaterresistance thoughatthe
onso thetw oresistance-cur esw ere
ersection andlowerv a luesf orA f or
highspeedsB andC changedplaces
alerw a e- resistanceduetoB ' sgreater
gmore in luentia la tsuchspeedsthanits
. A ta llspeedsA hadlessresistance
ertheresistancebeganto increase
otsandf orthe latteratabout14
i e l rapidincrease inresistance
t19k nots w hile fornospeedupto
enc noticeablewithB .
ingenera lthatresistancew illbe
o a p a ra l le l m id d le b o d t h e f o r e a nd
andedsoastoobtainashipo thesame
llelm iddlebod , e eni theratioB
w hatincreased.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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C E A N D P R O PU L S I O N O F S H I P .
T O N O F R E S I S T A N C E DU E TO I R R E G U L A R
rimentall ina llcaseso bodies
t h at a c e rt a in a mo u nt o w a te r i s
hebod andmustbeconsideredas
nitsmotion especia ll inan rapid
celerationsandretardations-This
s ma bef rom15to20percento
eship. I tf o llowsthattheresistance
bethatduesimpl to themasso
hecombinedmasso shipandw ater.
stberememberedthatduringretar-
f o r t is g i e n o ut . I t i s h o we e r a
reenerg isre uiredtomaintaina
ement theve locit oscil la t ingabout
a t t he s a me u n i o r m v a l ue o t h e
use ingenera lR v ariesw ithuaccord-
anI , andbecause insuchcasethe
uchpow erso uisgreaterthanthemean
u ch p o we r . Th i s is r e ad i l v e r i i e d f o r
ashipin irregularmotionbutat
ore ingenera lbegreaterthani
emadeuni ormatthe?ameamount.
opulsionemplo edusuall in ol e
tion andthesema bemoreorless
teso w ind current t ide deptho
ua ll f a orableconditionsit isnot
o R duetothiscause isimportant
nde planationareo interest.
P u b l i c D o m a i n
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C E A N D P R O PU L S I O N O F S H I P .
se uentdecrease inthe irregularit ieso
E O F R E S I S T A N C E DU E TO S H A L L O W W A T R
F L U E N C E O F B A N K S A N D S H O A L S .
tthattheresistanceo a shipor
e d is v e r m u ch i n cr e as e d b s h al l ow
m it o b a nk s a s i n th e n a i g at i on o
s. Theprimar causeo thise cess
f oundinthedisturbedstream- line
thedecreasedcross-sectionw ithin
stbecontained therearisesan
ormandinthew a econ iguration
ngeneralisv er muche agger-
dit ioninopendeepw ater andthenet
considerable increase intheamounto
hemaintenanceo thecon igurationo the
spondingincreasein theresistance.
ireastothe lim itsw ithinw hichthese
ablesigni icance.
iono shallownesso water theother
ed w eha ea largenumbero
nw hichthe increaseo resistancedue
lessclearl shown.
o llowinginstance:
eraging9f athomsmade20
P . Thew a ephenomenaweremost
w aterf rom22to36f athomsw ith
was21.5 knots.
S . S . N e w Y o r k bo th w a s o e r a
l A r c h i te c tu r e 1 8 9 4 p . 4 67 .
P u b l i c D o m a i n
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E . I l l
oundthatatthesamepointeachw a
terw aschartedas37f athomsthe
slightl , w hile thesteam-pressurebecame
ertheremaindero thecoursew as
msdeeperthanatthispo int. Themean
a e-motioninshallowwaterha e
sthereshow nthatthepathso the
ainsteado circular thee ll ipse
waterbecomesshallower.N owit
so longasthedepthissu f i-
correspondingtothespeedo the
itstrocho ida lformandconstitution
stancewill result.Thepropriet
morethanaroughl appro imatere la -
stioned sincew edonotk now thatthe
b theshipismorethanroughl tro -
T a bl e V , i t a pp e ar s t ha t i t h e
thew a e- lengththedi f erencebetw een
esw ouldbeq uitenegligible . This
0 ( i t o t he f o l lo wi n g ta b le :
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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C E A N D P R O PU L S I O N O F S H I P .
aw nf romastud o thedistribu-
dercerta inidea lcircumstances D. W.
tadeptho watere ualtotentimes
mit andthatnosensible increase
obemetw ithso longasthedepthis
hedra t.
theN ewY ork i reliable indi-
e tendstoaconsiderabl greater
dra t orthantheamountgi enb
ontisonethatcannotbesettled
en t s a ti s a c to r il e t e nd e d da t a o w h i ch
nse istingincanals weha e
uetothebottom buta lsothatdue
edingatoncetoa representati e
brie l thephenomenaattendingpropul-
hthecross-sectiona larea isonl some
thato thegreatestsectiono theship.
ratespeedsthebow wa eisq uite
rlesstrans erse l oneachsideora
andf o llowedamidshipsorasternb
llow . F o llowingasternisatra ino
r o w h i c h mo e s w it h t he v e l o c it o t h e
aw holemo esata lesserv e locit , as
w ertheboatmo esthemoreare
notedinconnectionwithmotion
speedincreasesthemorede initel
e ontherearedgeo aw a easin
epronounceddoestheserieso f o llow-
sthespeedo theboatapproaches
ut e o N a a l A r c h i te c ts v o l . x x x v i . p . 23 4 .
P u b l i c D o m a i n
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E . 1 13
propagationo apermanentw a e
g h t h e wa e s b eg i n to t a ke o n mo r e
sicso w a eso translation. The
eaterproportiono energ andthe
dshorter. Theresistance how e er
etotherapidl growingsi eo the
uentl increaseddemandf orenerg .
crit ica lv e locit o rpassesslightl
o w a escontractstoasinglemember
crestamidshipsorwiththeboat
w ardslope. Theresistancethendecreases
wedalongatthisspeedw ithamuch
pow erthanj ustbe ore . Thecauseo
law o resistance isfoundinthe
hew a e. Thenecessar energ to
litar w a eha ingbeene pended
enplacedinthemostf a orableposi-
a e t h e ma i nt e na n ce o t h e wa e a n d
oatma beobta inedatacomparati e l
diture . Theresistanceforthemostpart
anceo thew a einanimper ect
reasedtendenciestow arddegradationdue
sandbottom.
w ingresultso e perimentsmade
e ll t h e pi o ne e r o e p e ri m en t al i n e s ti g at i on
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
p e ed i n
r.
ondit ionsobta incannot how e er
edincana ls duechie l to thew ear
romthewasho thew a e andthe
peedsnecessar f ordepthso w ater
e e t.
herconcernedastothee f ecto the
sistanceat moderatespeeds and
obetw eenthesectiono thecanaland
rthatthe increase inresistancema
oragenera ldiscussiono thesepoints
h a e h o we e r c e rt a in p a rt i al r e su l ts
esthef o llowingf ormulaasrepre-
serieso e perimentsmadeb himon
c an S o c ie t o C i i l E n g i n ee r s v o l . i . p . 9 9.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E . 115
rsecond
c a na l t o th a t o b o at .
m2to3 f eetpersecond orf rom
ur sv ariedf rom2870to3090
pt h o w a t er f r o m 7 to 8 f e e t d r a t o
t displacementf rom260to310tons.
case o thegeneralf ormulapro-
u s s e ll a n d Du B u a t f o r r es i st a nc e i n a
.
nstantstobedeterminedb e peri-
a l ue s o r v y a n d s ar e m an i e s tl t o o
ationo theseresultstoconditions
r o m th o se c o e r ed b t h e e p e r i me n ts .
noneinstancew herer= 3aspeed
nw asreducedwiththesamepow erto
ono thesamepaperGordonstates
w herer10 aspeedo tenmiles
o7.
o llowingresultscitedb Po lla rd
sentedb a f ormula
i ng s o I n s ti t ut i on o C i i l E n g i n ee r s L o n do n
0 .
v o l . i n . p. 4 5 8.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E A N D PR O PU L S I O N O F S H I P .
hesamesigni icanceasabo eandf is
e e ds p e r S e c on d o
shasconductede tensi e
e theresultso w hichha ebeenmade
mongtheman interestingfeatures
thef o llowingma bementioned:
towingontheS eine.The
thestreamtothe immersedsectiono
orw hichtheresultsshouldbe presum-
m th o se f o r a r at i o in d e i n i t e l l a rg e . Th e
ble I, f romw hichitappearsthatthe
tSpeedsperMinuteo
nto thelengthwithinthelimits
mplo ed. Thesamethreeboats
ntheB ourgogneC analatspeeds
h I n t er n at i on a l C o n gr e ss o n I n l an d N a i g at i on 1 8 94 .
ieR obinson P roceedingsI nstituteMechanica lE ngi-
P u b l i c D o m a i n
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E .
tso 49. 2f eetperminute f rom
inute w iththesameresultas
ependenceo resistanceonlength.
spropositionmustb nomeansbe
periments thoughthereseemsreason
duetothepeculiarf ormo cana l-boats
re lati e l smallin luenceonthe
sw ithparticularsasinTable I I w ere
cana l w ithresultsasgi enin
R S O F B O A T .
t
.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E A N D PR O PU L S I O N O F S H I P .
a lsomadeinvariousw aterw a so
e e t lo n g 1 6 . 4 f e e t wi d e a n d o t h e
aregi eninTable IV .
N N E I N D F F E R E N TW A T R WA Y S .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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s s
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E .
mitiesislessandlessuse ultoreduceresist-
iono cana ltoboatisless. I t is
ntma bereachedw heretheresistance
mewhatnarrow andfullf o rmthanf oran
de uallength butw ithf ineendsand
andhencewitha greaterconstric-
ss-sectionf orstream- linemotion.
E O F R E S I S TA N C E D U E TO S L O P O F C U R R E N T .
w herethecurrentisnoticeablethere
pgrade andaresultingv ertical
ment. Thetota lenerg e pended
there ore include inaddit iontothat
methew ater- resistance anamountDb
ementandbisthetota lchangein
dduringthe inter a linq uestion. Thecorre-
tura ll Dsina= Da w herea isthe
wa ssmall. Natura ll theamounto
esistance insuchacase isusua ll
reachsuchanamountastopre entthe
erethespeedo thecurrentisconsider-
blespeedo theshipinsmoothw ater.
m a r e ac h a v a l u e o f r o m .0 0 1 to
edsthesmooth-waterresistance
o D o r e e n l es s s o t ha t i t is r e ad i l
eresistancema reachanamount
nwiththatf orsuchspeedsunder
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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A N C E A N D PR O PU L S I O N O F S H I P .
C E O N R E S I S T A N C E DU E T O C H A N G S O F T R I M .
ancew eha ethusf arconsideredonl
nt . I t i s q u i t e e i d en t h o we e r i
a inedinherstatica ltrimanddra t
ateratan gi enspeed thatthe1
geso pressurew ouldingenera l
l lasahori onta lcomponent. I nman
ighspeeds itbecomesimportanttotak e
i s t e nc e o t h is v e r ti c al f o r ce . C o n s id e re d
tant itusua ll actsthroughapo int
al c e nt e r o b u o a n c . I n t h e ac t ua l
reetoy ie ldtothisf orce shew illchange
ewhatmorethanthe sternsinks
acementb asmallamount. A t
modi ications especia ll thechange
r noticeable. A tsti l lh igherspeeds
-pf ormo a terbod mentionedin
tthetrimma begintogoback
thoughthedisplacementwillprob-
sewiththe increaseo speed.
v iew w ema considerthatthe
s pe c ia l l a t h ig h s pe e ds g i e s r is e t o a
thattheboatnatura ll accommodatesitsel
tcso thiss stem. In genera lat
mw ill in o l eaho llow underornear
thebow thusplacingtheboaton
a eandnatura ll gi ingrisetothe
s ta n ce i s g i e n b W h i t e o m e as u re -
l A r c h i te c tu r e p . 4 7 0 .
P u b l i c D o m a i n
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E . 1 21
ow onatorpedo-boatabout80f eetlong
s. Thechangeo trimw asaboutone-
lengthorf ort inchesbetweenbow and
w atersur acef orw ardthebow raised
oot w hilere lati e tothesur acea tit
hes. Theremaindero thechangein
thechangeinthe le e lo thew ater
f ormation.
enaattendingthemotiono aso lid
geo trimando displacementcannotat
bstractmathematics. The in estiga-
anceo modelsandsuchcomparati e
se ina idingto f ormanestimateo the
e inan gi encase.
changeo trimonresistanceisprob-
isaresultandnotacauseo
tma beacauseo amodi icationo
thedi f erencew hichitma cause in
e r se d b od . W i t h u su a l f o r m s th e i n l u -
ngeso thischaracterasusua ll occur
portant. I t isprobablethattheprin-
achangeo trim isduetodecreased
ropulsi eapparatusratherthantoactua l
seconsiderationsitma bepo inted
belie ethatf ore tremel high
th suchasareatta inedb some
aunches andnotabl b recent
do-boatdestro ers thecoe f icientsin
stancewhichho ldf orlargershipsandfor
dergoconsiderablechange.A
P u b l i c D o m a i n
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C E A N D P R O PU L S I O N O F S H I P .
eresultsf orlow erspeedstosuch
othere orea llow able andthevarious
sticso empirica lf ormulaef orresist-
eterminedb directe periment
orunderotherscomparablewith
dspeedso 28to31k notsha e
o f rom180to200f eet. The
isshowntov ar w itha lowerinde
tespeeds as e . g. 18to24k nots and
holeseemstoindicate ageneral
ationo theresistancetotheattendant
angeinre lationshipw ema look to
ent andconse uentl inw ettedsur-
ng e d lo c at i on o t h e wa e s s t em r e la t i e
tv er highspeedsshow thatunder
ase inwettedsur acema beq uite
ataare lack ingto furnishasatis actor
n gi encase.
ceo aboatina canalwhenit
hatitcanbef orcedo erontothe
t h e pr i ma r w a e h a s al r ea d b e en
tedthatthesecondit ionscanbe
butweknowthatas thespeed
thebow primar w a ef a llsf arther
andphotographstakenunderthesecondit ions
hangeo trimseemtoshowthatat
hightheboatisf orcedatleastpartl
P u b l i c D o m a i n
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C E A N D P R O PU L S I O N O F S H I P .
coe f icientfortheshipasaw hole is
theshipwithoutthek eels sothat
ota larea isgreater thecoe f icient
tisbutslightl increased. Thereason
a e r ag e c oe f i c ie n t ma b e r ea d il s e en
s o c l i nd r ic a l f o r m m o i n g a i a ll
nebesmoothand theotherdeepl
longitudina ll botho thesame
w illtendtosetinmotionac linder
esamediameter andw iththechannelled
w i ll b e s o e f e c ti e t h at a t a nd n e ar
ne lsthere lati ev e locit o thesur-
bev er slight andhencetheresist-
e c oe f i c ie n t o s u r a c e re s is t an c e f o r
w illthere orebe lessthanf orthe
eismuchgreater thetota l sur ace
asedin aproportionaldegree.
erimentsonthemodelo theS ardegna
theshipf rom16to21k notsanincrease
to5percentincreasingw ithspeed or
rease inspeedf rompracticall nothing
ent. Thesee perimentsseemedto
increaseinthe resistancedueto
peedso about18k notsupw ard. I t
tthisw asdueinlargemeasuretoa
speedsandtoadisturbanceo the
irtueo w hichthek eelsbecameplaced
low andthuso f eredacerta inamount
O c t . 1 8 95 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E .
S TA N C E .
onso ashipinmotionare o
air- resistance. Thisf romtheirregularit
a irandthegreatirregularit o thesur-
r d i f i c ul t o c o m pu t at i on . E x c e pt i n
e l o c i t o t h e wi n d h o we e r t h is
redo greatimportance andusua ll no
teits amount.F romdataobtained
na iritappearsthattheresistancema
f o r m ul a
s t h e pr o e c te d a re a o t h e su r a c e
ctionbeingmadeonaplaneperpendicular
ion. F oranunriggedshipthisis
g s im p l t h e ar e a o a n e nd v i e w o t h e
ew ater. Wheretheshipisriggedthe
er inde inite andnoestimatecanbe
mp a ra t i e m e th o ds f o r w hi c h u n o r tu -
o d a ta a a i la b le i s i ns u f i c i en t . W m .
ethatinthecaseo theGre hound
ggingw asaboute ua ltothato the
er much how e er onthenature
anddoubtlessonthespeedo the
istobetak enasthe longitudina l
t i ev e locit o thew indandship.
speedo theship inaf ollowing
dinaheadw indmore.
f icient/restson e perimental
erimentso Wm. F roudeandothers
P u b l i c D o m a i n
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C E A N D P R O PU L S I O N O F S H I P .
f eet andsecondsasunitsitsv a lue
. 00 1 7 a n d wi t h po u nd s f e e t a n d
0048. Thee perimenta lva luesare
o s m al l o r mo d er a te s i e a n d th e re i s
astotheva luessuitable f oruseon
his pointaremuchneeded.
e h o un d u nr i gg e d w i th a r e la t i e
hee f ectproducedw asmeasuredb 330
k notsthisw ouldcorrespondtoabout
.5 percento thewater-resist-
ithriggingitwas assumedthat
sothatinaca lmtheshipw ould
anceo perhaps3percento her
deratespeeds orso longasthe
ssensibl asthes uareo thespeed
tionbetweentheair andwater
bl constant.F orhigherspeeds
creasemorerapidl thanthe
sothattheratioo a irtow aterresist-
speeds.
a irwesupposeaspeedo 10k nots
aheadw indo v e locit sa 30
ev = 40 andthea ir- resistancew ould
hasbe ore orunriggedabout25
resistanceandriggedabout50 percent.
ma n o t be e a c t t h e a r e s u f i c ie n tl s o
es andshow pla inl the importance
a assumeine tremecases.
antdecreaseo sa ilsandriggingon
esse lstendstodecreasethe importance
heother theconstante f ortto
P u b l i c D o m a i n
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E .
iners w ar-ships torpedo-boats etc.
all causeswhichinan manner
sstance. A ddit iona le perimentsinthis
eded. S uche perimentsmightbe
ashiptodri t inaf a irl smoothsea
thew indalone andmeasuringthe
p re l at i e t o t he w at e r an d t ha t o t h e
p. Thenf rommodele perimentsor
etotheship herresistanceatthe
k nown andthismuste ua lthatdue
heshipw iththere lati ev e locit
shipmightbemooredandsub ected
beingmeasuredb suitabled namo-
C E O F F O U L B O TTO M O N R E S I S T A N C E .
orbelie ingthattheconditiono
illessentia ll a f ectan thingbutthe
ulbottomonskin-resistancehasbeendis-
gainmentionedheresimpl tomak e
esw hichma a f ectthetota lresist-
H I C H R E S I S TA N C E B E G N S T O R A P D Y
.
eso resistanceusuall showsthatf or
tota lresistancev ariesnearl asthe
suchre lationremainingnearl constant
edatwhichtheresistancebegins
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
easemorerapidl , the inde becoming:
e w hileatsti l lh igherspeedsthe inde
sometimesapparentl toe enless.
thecur eo residua lresistanceare
peedatwhichthef irstrapidin-
chie l , nodoubt onthew a e-
heship andw hile it isnote pressible
b a n s i mp l e f o r m ul a y e t i t is
atforgenera lpurposesitma be
espeedo aw a eo lengthe ua l
ncew eshouldha e
t. Withk notsandf eetasunits bis
s ap p ro i m at e l i i n w hi c h c as e w e ha e
gi ingsimpl anindicationo
onwheretheresistancew illbeginto
herthantheactua llocationo ade inite
ememberedthatgenera ll the loca-
behigherastheratioo lengthto
stheprismaticcoe f icientisless.
F C O M PA R I S O N O R O F K I N E M A T C
.
he law o comparisontof urnishfor
om et r ic a l f o r m b ut o d i f e r en t s i e
erentspeeds are lationbetw eenthe
etw ocases. Thisin o l es asw e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
w a e-mak ingormodi iedstream- line
careshouldbehadin notingthe
onsonwhichthestatemento the law
esinaninde inite li uidmo ing
etthemotionthroughoutthese
Thatis le ttherebenodiscon-
go w a esatthesur aceorthe
wi t hi n t he b o d o t h e li u i d. T h e
ead motionw illthenappl , andde-
k w esha llha ef oran stream-
. . . .( i
a easecondbod sim ilargeomet-
tA t imeslargerina lldirections. The
enbeconsideredasamagni icationo
tioA . L etitbeplaced lik ethef irst
n it e e t e nt m o i n g pa s t it w i th s o me
hthatthestream- linedistributionsinthetw o
ll sim ilarandinthe linearratioA .
ntires stemsinthetw ocasesare
andma beconsideredasderi edthe
lineare pansionordim inutioninthe
line intheseconds stemsituated-
thef irstw eshallha e
" /
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
d il c o nc e i e o a s t re a m- l in e A C ,
eadf romsomeinde initel la rgereser-
nde initedistanceawa . This
o wa c h an g e th e n at u re o t h in g s at
ethestream- linecontinuedback toa
ocit isinappreciable . I f thestream-
m al l F w i ll b e o s m al l f i n it e a re a a n d we
mallasw echoose andhenceasv er
imensionso thereser o ir. Then
B C r e pr e se n t a st r ea m- l in e o t h e f i r s t
i m u st h o ld t h ro u gh o ut i t s le n gt h a n d we
stak ez asmeasuredf romabase-
/ wil lbesimpl thestatica lpressure
a n d/ - - a w i ll i n f e e t be e u a l to t h is
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D PR O PU L S I O N O F S H I P .
"
w eh a e
/A .
erto f ul i lthecondit ionso sim i-
os stemswemustha eaconstant
l to I / A . P u t ti n g th i s f o r n i n ( 2 w e ha e
( 4 >
i a nd ( 4 , p = A / .
ore er otherstream-line
oghouttheentireseconds stemthe
thatatcorrespondingpointsin the
herw ords themagni icationinpressure
ndtothatinlineardimension. This
oldbetweenthepressuresatcorre-
ur aceso thetw obodies because
r acesthroughoutare incontactw ith
stream- lineso F ig. I thebod is
tel immersed sothatnosur ace
theprecedinge uationsandcon-
e r f o r a n s t re a m- l in e i n a pe r e c t
r e f o r a s t r ea m -l i ne s s t em a b ou t a b od
o longastheconditionso continuit
led. Now itisduetothedistributiono
astream-lines stemthatthe
ses.H encethisresistancewillbe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 1 33
ra lo the longitudina lcomponento the
nersur aceso thestream- lines s-
thesur aceb dsandtheangle
elongitudinalb 6.Thenwe
s te m
mtheentiredistributiono pressure
andthe lineardimensionsare increasedin
cetheratiobetweencorresponding
wi l l be A a , a n d in t h e se c on d s s t em w e
* d s = V f p co s6 ds = K R m .
emsundertheconditionsweha e
weentheresistancesduetostream-line
a a lsonotethatthisisl ikew isethe
umeso thetwoimmersedbodies
splacements.
thusderi edin ol esthreecon-
re ulattentionshouldbegi en:
o geometrica lsim ilarit ;
o correspondingspeeds-
t h e la w .
orthetw os stemsbeingassumed
describedasthosewhichwill pro-
rsim ilarw a econ igurations and
ntheratioo thes uarerooto the
asedonthesecondit ions w etho
atemento the law:
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E . 13 5
dd andsk inresistance itappears
heeddiesasthee pressiono these
nceshouldnotinter ereessentiall w ith
aw tothes stemso stream- lines
e br e ak i ng o a w a e i n o l e s a d is c on -
low andinsuchcasew earenot
endthe law tothestream-lineorw a e
itsprescribedb thiscondition
considerthe law assatis actoril estab-
onsideritashighl probablethat
esthegenera lcon igurationsinthe
orrespondingspeeds sti l lbeessentia ll
sistancesin o l edw illst il lessentia ll
comparison. I tmustberemembered
s uc h m a b e t he c a se i t s v e r i i c at i on w i ll
atherthanonmathematicalreasoning.
thequestiono the law o compari-
d i f e r en t s ta n dp o in t a n d th u s to e t e nd
eapplication. I tw il lbenotedthat
gi enestablishesthe law undercerta in
esnotf o llow howe er thatthe
pplicableunderwiderconditions.To
nourattention.
hipsa llo sim ilargeometrica lf orm
on. A ssumethattheresistanceso
atv ar ingspeedsma berepresented
n co n si s ti n g o a s e ri e s o t e rm s a ll o t h e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
omet pica ldimension necessaril
series v isthespeed andA isone
ntsdependingonf ormcharacterist ics
houttheseries.S uchageneral
o r e co n si s t o a s e ri e s o t e rm s a s f o r
l 2 v 2 + C W * v * + Dlt , . . ( 6
cc es si e l t he v a l ue s I , 2 3 4 . I t
r thatnshouldbe integra l sothat
M z A 2 , . / V ' 8 , e t c. m a o c cu r. I n f a ct
e nt c o nc e rn e d n m a h a e a n v a l ue
ndthenumbero termsma be inde i-
ortheva lueso thesee ponents
termindependento speedand
e a n d v a r i n g di r ec t l a s v o l u me o r
lik e l , andw ema consider
o v a lueso n. Theupperlim it
dependento dimensionanddepending
ndicatede lsew here ithasbeen
sprobable oratleastpossible.
ow e e r i t is e i de nt l t he u pp er l im it f o r n
ibil it o atermin o l ingadecrease
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
aseo si e w hichseemsq uiteunlik e l .
ma b l h a e a n v a l ue b e tw e en o a n d 6
simpl asanillustrationo thekind
dinsuchane uation w enoteag-a int-hat
c a r e f o r m c on s ta n ts a n d re m ai n u nc h an g ed
f amil o ships. We assumethen
toe presstheresistancef an ship
speedb substitutingintheappropria te
r m c on s ta n ts A , B , C , e t c. a n d th e
d v . F o r a n o th er t p e o f o rm t he re
rserieso f ormconstantsw iththe ir
e p o ne n ts f o r / a nd z / n o t ne c es s ar i l t h e
n f o r t h e f i r s t t p e .
hesameshipatvar ingspeedsthis
possibil it o representingtheresist-
termsin o l ingthevariablev w ith
w h ol e o r f r a c t io n al w h il e f o r d i f e r en t
w eshouldha etheresistance
t e rm s i n o l i n g th e v a r i a bl e / w it h
ents w ho leorf ractiona l.
wthattheseassumptionsare
n o l edinthederi ationo the law
h d r od n a mi c s. T h e a d mi t a w id e
andaninde initenumbero termsinthe
b i nd i ng t h e e p o ne n ts o / a n d v o nl t o
ee ponento / plusonehal that
T a ki n g ( 5 t h er e o r e as t h e s m b ol i c
eb itsmeanstheresistanceso tw o
halinear-dimensionratioA . andat
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
en t s t h e di f e r en c e be t we e n th e v a l u es o
edandasderi edb comparison
otak eanil lustrati ecase suppose
en ce v ^ - r- v l 2 . A l s o l et t he v a l ue s o
thee ponentn1. 85. Thenthe
nceb comparisonwillbe64 w hile
e
5 3 . 64 .
showingthatb f ormulathe
sthanb comparison. I f thesk in-
eha l thetota l thisw ouldin o l ea
ut8percento thetota lresistance.
we e r e s pe c ia l l w i th r o ug h b ot t om
p o ne n t is n e ar l o r q u i t e 2 a n d th e
small. I nsuchcasesthistermwould
underthegenera llaw w iththeothers.
ormo thetermse pressingwa e-
ssedin14. I w etak ethetw o
* , w e f i n d t h at e a ch c o me s i nt o p la c e as o n e
, a n d h en c e bo t h f u l i l t he l a w o c o m-
i es o e u i a l en t e p r es s io n s f o r
tanceratiosf ortw osimilarshipsat
eha e
e _ /A y ( * , ) _ M
v - ^ i w - v -
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
e a n d ot h er s w hi c h ma b e wr i tt e n
a l en t f o r ms o t h e r a ti o s in o l e d i n th e
rresistance.
eltintheapplicationo thislaw
ceortotheresidualresistance
stingratherontheresulto e peri-
actproo necessaril in o l ingas-
f ul i l ledintheactua lcase. This
consideredasindicatingthe degreeo
a considereithertheresidualor
eo e pressionb thesumo a
m bo li e d in ( 5 .
a lin estigationrelatingtothe law
ma mentionthee perimentsre erredto
nw hichintwoseparatecasesthe
ando itscorrespondingshipw hen
hslaw w eref oundtobeinver
nt thegreatesterrorsbe ingw ithin3per
ma a lsonotethee perimental
Wm. andR . E . F roudeonthew a e-
sim ilarf ormsmo ingatcorrespond-
etoamodel o theGre houndand
rrespondingspeedswerecompared
eirsim ilarit w asf oundstrik inge en
e s s t em . I t w a s al s o f o u n d f o r t h e
o about1. 6f eetpersecondthe
we d a lm o st e a c tl t h e cu r e o s k in -
f ormula . I tw asamattero
hisspeedthemodelmo edw ithout
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 1 41
t higherspeedsthetota lresistance
dl o erthatduetosk in- resistance
o llow thepla inl v isibleaugmentation
e s s t em . Mr . R . E . F r o ud e a ls o
e-con igurationabouttw omodels
e o t h e ot h er t h e la r ge r t ra e l li n g at
smaller.Thesmallerrepresenteda
k notsperhour andthe largeraship
tsperhour. Thecon igurationsthus
rad re erredtoandareshownin
theirgreatsim ilarit inpositionand
k ingl seen. In F ig. 33isa lso
rthesmallermodelatthesamespeedas
a eherethecomparisono tw ow a e
f erentsim ilarshipsatthesamespeed.
distributionrelati etothewateris
icatesthere orethatsimilarships
illproducesimilarwa e-con-
achtotheship w hile thesecond
at thesamespeedwillproduce
rw a e-con igurationsrelati e tothe
a leadtothesuggestionthat
a g i e n t p e o s h ip i s i n l ar g e me a su r e
eo theship andsimpl dependenton
d o n sp e ed . H e n c e th e e ne r g i n o l e d
k ewisedependentonl onthesame
setheresistance. I t istheseconsidera-
ll l im itw hichgi esB v * asthef ormo
esistance in14. I noneimportant
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
thew a epatterncannotbe independento
hisf eature isthecompositestern
ldependsontherelati eposit ionso
eprimar bow andsternw a es
ntherelationbetweenthewa e-
peed. Hence inpart a tleast
emustdependonthedimensions and
a perhapsin o l etermsinbothv *
suggestedin14.
O N O F T H E L A W O F C O M PA R I S O N .
e tw o s im i la r s hi p s b 5 a n d 5 a . I f t h e
sumedtoappl to theentireresist-
ormsimpleproportionsase pressedb
o rm s in 2 6 ( 7 a nd ( 8 . T he g i e n i n-
aril in o l ethreeterms:
5 a at a g i e n s pe ed
tatthisspeed
5aatacorrespondingspeed.
isthenreadil f oundf romthepro-
hicalrepresentationo theresist-
ingspeeds. Wenow w ishtoshow that
a lsobeconsideredasadiagramo resist-
ps thespeedandresistancesca les
ed.
ordinateasA B gi esthe
s p ee d v = O A . S u p po s e no w we h a e
inlineardimension.Thenata speed
lbeW? . H ence i thescalesareso
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
henew sca ledenotes4/ U / andA B
onew illproperl correspondtotheother
ldingf orotherpoints w esha llha e
amo theresistanceo thenew ship
enotethattoe f ectthischangethe
ngunitspeedmustbedi idedb A * ,
esentingunito resistancemust
A c u r e o t hi s ch ar ac te r t he re o re b
thescaleswillrepresentgraphicall
m i l , t h e r e si s ta n ce o a n s h ip a t a n
determinedb theorigina ldataand
t h e sc a le s .
e t O P , F i g .4 6 d en ot et he cu r e o t ot al
n s hi p 5 a t v a r i n g sp e ed s . L e t t h e
tedaccordingtothemethodso 8.
o m O P t d o wn w ar d a t th e v a r i ou s s pe e ds a s C B
ur eO Q asthegraphicalrepresenta-
sstance w hilethe interceptbetw een
ow thev a lueo thesk in- resistance. The
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
enb OQ isthentreateddirectl b
e itherb proportion orb achange
e pla ined. Onthe lattersupposit ionO Q
dasrepresentingtoappropriatescales
thesecondship52atv ar ing
tanceo 53beingthusfound the
omputedasin8b anappropriate
nts.Thetwobeingaddedthe entire
ed.F orgraphicall representing
5 w ema proceedasf o llows: The
istanceo 5aha ingbeencomputed
epresentationtoasca leX stimesas
t . L a t he se o f f r om O Q , u si ng a
saslargeasthatfor5 . Theresultw il l
resentingtothesechangedsca lesthetota l
f i n s t ea d o t h e s h ip 5 w e h a e a m o d e l
onsaree actl sim ilar andw ema
asagenerale planationo the
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E . 1 45
theresultso amodele perimentw ith
ts.
R E M A R K S O N TH E TH E O R I E S O F R E S I S T A N C E .
onstreatingonthe resistanceo
dentthatpuretheor isq uiteunableto
ecessar to theso lutiono an gi en
tiono theor asatpresente isting
ato pro idingameanstoas s-
phenomenaattendingthemotiono a
roughthew ater ando establishingthe
comparisono theresultso onevesse l
inorderthate perimentaldatama
rpurposeso predictionanddesign.
rkedthattheso-ca lled" f ormo
bstractsensehasf orthedesigner
. I t i s o c o ur s e tr u e f o r a n o n e
n t c h ar a ct e r o s u r a c e s t at e o t h e
t h at t h er e m us t b e so me f o r m o l e as t
somef ormthanw hichnonecano f er
orm how e er w il ldoubtlesschange
thef ourf undamentalcharacterist ics
uestiono resistancemusta lw a sbe
e t , s t re n gt h a n d ca r r i n g ca p ac i t ,
specialconditions.Thepurposeis
g i e n c as e t o pr o du c e a f o r m o l e as t
tratheraf ormw hichsha llthemost
hese era lqua li icationsinthepar-
orb thecircumstanceso the
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
R M U L A F O R R E S I S T A N C E .
mu l ae w hi c h ha e b e en p r op o se d f o r t h e
esistancew esha llmentionbutfew .
tisusua ll pow erratherthanresist-
thoughw iththenecessar assump-
h e on e ma b e d er i e d f r o m th e o th e r. I n
iono pow erw illbediscussed and
rmulaeandmethodswillbegi enf orits
w hich b in erseprocesses theresist-
i desired.
tons
ecoe f icientsthecoe f icient
dmira lt coe f icient.
ee plainedin46and 62 and
e f o r m ul a i s si m pl d e ri e d f r o m th e
rmulaf orpow er ande ceptw hereused
son ase pla inedin62 itsresults
edasroughl appro imate.
ducedf romnumerouse perimentson
ow ingformula o w hichthef irstterm
ndthesecondterm theskinresist-
u i te s m oo t h t h e e p o ne n t o v i n
emade1. 85insteado 2.
c h i f s ma sc hi ne 1 88 6 v o l. I I . p .5 79 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E .
eet andknots.B isbeam L >
m i ds h ip s e ct i on ; S , w e tt e d su r a c e w h il e
etak enf romthef o llowingtable using
ientasargument:
thisf ormulama bee pectedto
e pt f o r v e r l o ng f i n e sh i ps i n w hi c h
ewhattoolarge.
orspeedsuptothat f orwhichz / in
w a e-mak inglengthisnotmorethan
wng:
esthesk inresistanceandthesecond
ak ing. Theunitsarepoundsf orR ,
etandk notsf ortheotherq uantit ies. Dis
o N a a l A r c h i te c ts a n d Ma r in e E n g i n ee r s v o l .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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s s
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C E A N D P R O PU L S I O N O F S H I P .
en gt h s s ur a ce f t t he c oe f i ci en t o s ki n-
8 9 andbtheblock coe f icient.
ma a l so m en t io n C a l e r t s
tanceo sectionso propeller-bladesor
m mo i n g at a s l ig h t ob l i u i t t o t he
e e t p er s e co n d
t ;
on
pendingon0 asindicatedb the
N TA L M TH O D O F D T R M N I N G TH E
E O F S H I P - O R M D B O D E S .
tanceha ebeenmadeinaf ew cases
r t he m o st p a rt h o we e r s u ch e p e ri -
dtomodelsusua ll f rom8to15f eet
se l s ha e b e en u s ed t h e h a e b e en
t e o N a a l A r c h i te c ts v o l . x x v n i . p. 3 0 3.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
racing-point thelatterbeingcar-
ngthewater-l ineso thevesse lw hose
d. I nthisw a successi ew ater- l ines
ersuccessi ehe ightsonthesur ace
thecross-sectionsattheendo the
eso steps the innercornerso
edesired.Theoutercornersarethen
b hand-too lsuntilthe innerangleo
lbare l remains. Thesur ace isthen
andisread f orthetrials.
mentconsistso atankorcanal some
0 o r 12 f e e t de e p a n d f r o m 3 00 t o 4 00
ningonra ilsspansthiscana land
pparatusforho ldingthemodeland
ariousspeedsattained.The
electricalcontactsatknowndistances
throughthere o lutionso thetruck -
tso theentiredetermination includ-
namometerpulls changeso trimand
all registeredonadrumdri enb con-
els.Themodelsaretakenhold
h e a r e f r e e t o as s um e wh a te e r d ra t
econdit ionsf rommomenttomoment.
ecia lmeasurementsb photograph and
eo thew a es stemsproduced.
e f ecto thepropelleronresistance
edcarr ingthepropellerconnected
uchw a thatitma bedri enatan
o lutionsperminute . Thepropeller
entire l independento themodelis
operpositionasterno themodel
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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E . $
usteduntilthetota lthrustde e loped
edresistanceo themodel. Thecon-
thosewhichwoulde istwerethe
thisthrustdri ingthemodelatthe
sono theresistancethusf oundw ith
pellershowstheincreasedue tothe
ustheper ormanceo model
estigated andthusmostv a luable in or-
signo f ull- si edpropellersma be
ersweshallre erlaterin49.
R E S I S TA N C E .
ettheresistancef ormotionlongi-
e d b R ^ = A ^ v * , a n d th a t f o r m o ti o n
= A ^ J 1 . Th en i t he a ct ua l mo ti on o a
cit uinadirectionmak inganangle8
hecomponentso theve locit lon-
erse l w il lbeucos6andusin6.
thecorrespondingcomponentso
e A j ? c o s 6 a n d A j ? s i n 2 0 t h e
being
c os 4 6+ A ; si n4 0 . .
irectionwiththelongitudinal
t a n
beconsideredasgi ingarough
c tu a l v a l u es . T he s e r e h o we e r
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
onso principa linterestw hicharethe
pplicationo thistota lf orceR .
abilit o routewhenthev esselis
b a t o w - li n e. I n F i g . 47 f o r a c er t ai n
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E .
l e t T b e t he d i re c ti o n o R , a n d
theappliedtowingf orce . LetM
ointo applicationo theresistance.
hedsomewhereintheline S T.
plicationistow ardTf romM it isreadil
e lopedb an slighty aw orde iation
cionO V w ouldgi erisetoamoment
ptothisdirection andtotheful i l-
o rigina ll assumed U nderthese
t h er e wi l l b es t ab i li t o r o ut e . I f , o n t he
ewereattachedbe ondMtow ardS ,
w w ouldtendtostil lf urtherincrease
therew ouldhencebeinstabilit o route
parto thevesse ltosw ingaboutand
w ard. F oreachv a lueo thedirec-
identl beapo intM andtheco llection
bledirectionsw illgi ea locus asshow n
er l itt lee perimentaldatare lating
cteristicso thislocus. C erta ingenera l
r m a b e r ea c he d a s f o l l o ws :
lineSTmusttouchthe locusatM.
a ll therew illbebutonesuchpointf or
O V , i t f o l lo ws t h at S T c a n to u ch t h e
ncew illbetangentto itatM. H ence
elopeo theserieso l inesST.
oesselre lati e tothe locationo the
rplanes 6 itseemsreasonableto
orlongitudinalmotionwillbeat
hatastheangle isv arieditwil lsomew hat
e it h er s i de t h us g i i n g a cu s p at t h is
wouldbe likecuspsatB , thecenter
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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C E A N D P R O PU L S I O N O F S H I P .
ndatC andD thecentersformotion
thee actangledependingontheamount
we e n th e f o r e a n d a t e r bo d ie s o t h e sh i p.
maindero the locustobeasindi-
there orean po into attachment
thetow -rope theanglebetw eenthe
tabil it o routewillbedetermined
romthispo inttotheen elope.
rsuchtangentsingeneral according
wthouttheen elope. Obser ation
w h ic h o ne i s a pp l ic a bl e t o an g i e n
theanglebetweenthekeelandthe
# the inclinationo thedirectiono
h sica lreasontobelie ethatthe latter
thek eelandthedirectiono thetow-
e indicationso ( 2 f orv er
b u t we m a w el l d ou b t th e e a c tn e ss o
itw hereoneo thecomponentv e loci-
e m a e p e ct t h er e o r e t h a t t he r e la -
somewhatasindicatedinF ig.
( a 0 a n d a ar e p lo t te d i n re c ta n -
a l ue o ( a 0 i s ( - - b e tw ee n O
p ro i m at e l b e tw ee n o a nd 9 0 a n d ( )
B . F o r a = o 1 8 0 an d s om e an g le
cideand( a6 w illbeo asindi-
o r e t h e in o r ma t io n e p r es s ed b t h es e t wo
n problemin o l ingtherelation
ttachmento atow -rope itsdirection
ue a n d th e d ir e ct i on o t h e mo t io n i s
o r tu n at e l w e h a e n o s u c h ac c ur a te
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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E .
ntati ecases andinlieutheproblem
edb tria landerror. Gu ouhas.
A N G E a
imentf ora launchthatthepo intA la -
e lengthf orw ardo thecenter.
odiagramsabo ewilldependon
, andinthesecondplaceonthefo l-
rthetrimb thesternthegreater
eenthef orw ardanda terbodies andthe
cebetw eenthebranchesA C andC B o
a t a s a wh o le r e la t i e t o t he s h ip a l so
ated.
o u nd b e p e ri m en t t ha t w he n v i n -
slightl . Thisindicatesthatthetrans-
esistance increasesmorerapidl thanthe
o a isnotthere ore independento
s e u a ti o ns .
tiono therudderiscapableo
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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TA N C E A N D PR O PU L S I O N O f S H I P .
ctero theen elopeo F ig. 47b
obli uef orceatthesternandb
m-linemotion. I tf o llowsthatw ithin
eandabsoluteva lueso 6andama
theappropriateuseo thehelm.
shipswhenmooredb singlecable
ow edb single lineorbridle are
thepractica lapplicationo these
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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C E A N D P R O PU L S I O N O F S H I P .
rdcomponent therewillresultonthe
af orw ardcomponent suchreaction
apropulsi ethrust. Thef undamen-
are there ore thatachangeo
ucedinmatterb anagentattached
chchangemustha easternward
case wateristhematteractedon
ngeo momentumisproduced.A
h o we e r b e g i e n b a g u n f i r i n g
sternorb abo throwingapplesor
ion asw ellasb themeansf ound
alpropulsion.
ondmethodo v iew ingathrust.
i n C h a p te r I t h a t no b o d c a n b e
dw ithoute periencingaresistance.
epa iro bodiesmadeo theshipand
d andletusattempttoproducere la -
o i n g t h e la t te r r el a ti e t o t he f o r me r
easternwardcomponent. Such
sistancew hich asw ek now is
thedistributeds stemo pressures
actingonthesur aceo themo ing
llreacta longthe lineo re lati e
oreha eaf orw ardcomponent and
ie ldapropulsi ethrust. I tresults
heshipandthato thepropeller both
motiono thef ormer orw hatisthe
ineo motiono thes stemasa
l. Wesha llne te aminegeometrica ll
onthissecondmodeo v iew .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N .
A P R O PU L S I V E E L E M N T.
r e pr e se n t th e s hi p a nd C t h e el e me n t
an bod soconnectedwiththeship
sa longa lineA B w ithav e locit v .
ssaril hori ontal butma ha ean
ssimpl de inedasmak inganangle6
. A saresulto thismotiono C
a v e l o c it u a l on g L H . I n t h e us u al
= w asthedirectionandamounto
etothesurroundingbod o sti l lw ater.
K , rememberingthatitsdirectionin
b L H andA B . Whiletheactual
lo n g C J , l e t it s f o r m be s u ch t h at t h e
emo distributedf orcesactingonits
e line inspaceC R , mak inganangley
nc l in a ti o n o C R t o A B b / / a nd t o
anddenotetheva lueo thisresultant
F i g . 49 i s d ra wn a s t ho u gh a l l th e
ntalplane. A snotedabo e suchis
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
e b u t wi t h th e a ng l es A , / / y , a n d
t h e st a te me n t o t h e co n i g ur a ti o n is
emotiono C alongA B will
j w a n d f o r t h e to t al w o rk p e r o r m e d b
sha llha e
R v c o s/ /( i
ustw esha llha ethe longitudina l
tanceo ship; ( 2
ontheship
R u c o sA ( 3
eo motiono C relati eto
andf orthew ork thuse pendedw e
= R w co sy ( 4
,
o s\ ~ \ - wc os y . . .. ( 5 .
bederi eddirectl f romthetriangle
i c ie n c . I n t h e re m ai n in g c ha p te r s o
re uentoccasiontousetheterm
s ge n er a l se n se i t i s si m pl t h e ra t io o
e nt o r o t h e us e u l r es u lt r e ce i e d
cessar to itsattainment. Thef un-
u st b e c ar e u l l k e pt i n m in d f o r i a
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N .
tosa w hatistheuse ulreturn or
re i s n o am b ig u it a n d we h a e f o r
- w co s y '
e th r ee v e l oc t ie s v c o s // u c o s A ,
e c ti o ns o t h e v e l oc i ti e s v , u a n d z e /
lresistanceC R , andthatthee f icienc
t h e tw o pr o e c ti o ns o u a n d v a l on g
etthef oregoinge uationsre lateto
a c e o C i n s t ea d o t h e wh o le b o d , o r
dertheelementasa smallplane.
g.50.I nthisdiagram asbe ore we
notnecessaril inoneplane.The
ereberepresentedb itstw ocomponents
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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N C E A N D PR O PU L S I O N O F S H I P .
ntialtotheplane.Denotethe
ongitudina lb aandtothe lineA C
nationso Q tothesamelinesare
r es pe ct i e l . W e h a e t h en f o r th e
.... ( 7
o R a l on g A C
t + Q s in f t . . . . . ( 8
u l w or k
& , . .. .( 9
mf t v , . . .. ( 1 0
u
~ : ^ r . . . .( I I )
) f f ) z /
ha e
s ec a
entsupportedonasmoothun ie ld-
d b U V . T h en w h en i t h as m o e d
amedistanceA N asbe ore theship
^ a n d th e e le m en t t o C ^ I n s u ch c a se
dedisthatontheship. Henceemust
1 2 v t a t a n d f t r e ma i n th e s am e w h i le
s e c a . O r i n o t he r w or d s v c o s f t s e c o
pw ouldha ei C w eresupported
gsur ace. Thisisreadil seen
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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N .
F ig. 50areconsideredinone
plicationo spherica ltrigonometr is
ica lproo .
eenthev elocit v cosf tseca andthe
lledtheslip. Thisw edenoteb 5
c o s /3 s e c a b s . H e n c e we h a e
,
ti n g v a l ue o t h e e f i c i en c w h en t h e
eo.
eresultsthusf arde e lopedare
an supposit ionre latingtoPorQ or
c h th e v a r ; a n d f u r t he r t h at t h e
( n o r ( 1 2 i s p ur e l a g e om e tr i ca l
lC ases. ( a S upposethee lementa
edirectiono motionandmo edin
andhencenormalto itse l . I nthis
esonthee lementba lance andR is
c e o t h e tw o n or m al f o r ce s o n e on t h e
heback. R e erringtoF ig. 49 w e
o a s th e v a lu e o t h e an gl es A , / , y , a nd 0 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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C E A N D P R O PU L S I O N O F S H I P .
nt b e a n s o l i d s m m et r ic a l bo d , o r a t
hatthetota lresistanceR isinthedirec-
etthe latterbe longitudina l. Thenin
r t he v a l ue o A , y u 7 a nd 6 .H e n ce
l a s f o r ( a .
e nt b e a p la n e re o l i n g ab o ut a t r an s -
otheboatasinaradialpaddle-w heel.
oatprope lledb aw heelconsistingo a
lements w ek now thatinorderto
actionthee lementsmustmo eback -
tothew ater andthati ubethe
theperipheralspeedo thepaddles
. I f v w e re e u a l to u i t i s r ea d il
ti etothewater woulddescribea
b ei n g in f a c t e a c tl a s t ho u gh t h e bo a t
aradiuse ua ltothato the
ollingwithoutslipon arigidplane
. I ntheactua lcasethemotionwillbe
reducedin diameterintheratio
w iserolledw ithoutslippingonsuch
esultthee lementw illnow tra e l
sil lustratedinF ig. 51. I nthisf igure
thehea y line andthe low erpor-
o i n t P is s h ow n b t h e cu r e P Q R S .
B , andtheslipbeingtaken at20
c ti e r a di u s O O i s 8 0 pe r c en t o O R . T h e
hthe lineC D w hichthere ore
eouscenterso thepatho the
thecentero thew heelf orsucces-
thee lementbe ingasshownb the
thecorrespondinginstantaneouscenters
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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N .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D P R O PU L S I O N O F S H I P .
rt ica ll underneathandsim ilarl
. The locationo thesecenters
posit ionthedirectiono motiono the
w ater andhenceappro imatel the
eblade. Tak ingthebladeasa
ementsl ingbetw eenthe innerand
a r i n g v a l u es o r a n d he n ce o v , a n d
f erenttrocho ida lcur es a lldeter-
b t h e co n di t io n s an d i n th e m an n er a b o e
0w eshouldha e
a e
..( 15
sas theelementpassesthrough
h o we e r b e o r e re a ch i ng t h e v e r t ic a l
noneside anda terpassingitthe
side itf o llowsthatQ itse l a lso
ethatthehori onta lcomponento Q
. H e n c e th e v a l u e o T w i ll a l wa s b e
1 5 , c o n s id e ri n g 6 as a l wa s p l us . W e
co s- Q s in f f ) u ;
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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N .
e nt b e a p la n e mo i n g as o n t he e n d o
eplaneo theoartoremaina lwa s
dil seentobesim ilartotheradial
arasthegenera le uationsgo those
a p pl h e r e a s we l l.
t b e a pl a ne a l wa s v e r ti c al a n d re o l -
e d t o th e b oa t a s i n ce r ta i n f o r m s o
els( 38 . Thepatho thee lement
lbethesameasbe ore butw esha ll
; ) - i i
s i n ;
f f ) v \
t b e as i n ( c a n d ( e t b u t so c o nn e ct e d
spassc
o the
re lati e to
ormso
el. ( S eeF ig.
ha e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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s s
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N C E A N D P R O PU L S I O N O F S H I P .
7 - n
- + Q s i n - ;
c os y w
lim itinge f iciencieso these
le-w heele lements assumingthatuand^
.Thelatterconditionisnecessar
risonpossible andisper ectl
since itmere l re uiresanad ustment
r a c e to t h e si e o r r es i st a nc e o t h e sh i p.
e uationsappl simpl a tagi en
ce sof arase f icienc goes isseento
( c . F o r ( / t he e f i c ie nc i sc on st an to ri nd e-
here orethisisthev a luef ora llpartso
hichthee lementisacting andthere-
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. 1 09
hise lementasaw hole . F orotherlik e
a r i n e r se l a s v , a n d he n ce
ia l d is t an c es f r o m th e a i s o r e o l ut i on .
f icienc is o course ameano
ues.
, h ow e e r t h e c as e is d i f e re nt . Th e
n en t ir e s tr o ke w i ll b e t he u s e u l w or k d i i d ed
rthesameperiod. H encew eshould
u n ct i on o a n d th e v e l o ci t ie s i t
ergenera le pressioncanbeobta ined
ecia lassumptionsastothef ormo P .
be lie e how e er thatundersim ilar
e ce llencew ithregardtobothlim it-
enc mightbee pectedtoremainthe
N S R E L A T N G TO S C R E W PR O P L L E R S .
esaboutanotherperpendicularto itas
ametimemo eitspo into contacta long
inthisre o l inglinewilldescribe
e lineasaw holeoran parto itw il l
ce .
f orourpresentpurposebede ined
morebladesha ingontherearor
imate l he licalsur ace suchblades
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E A N D PR O PU L S I O N O F S H I P .
onbossor centralportionthrough
eirmotiono rotationinatrans erse
ip.
ur-bladedright-handpropeller.
beright-handorle t-handaccording
thehandso aw atchwhenv iew ed
n g th e s hi p a he a d.
aceo abladeisthe rearf ace.I tis
nthewater andw hichinreturn
o pressurew hichgi esthedri ingthrust.
thef orwardside.C aremust
usionintheuseo theseterms.
ingedgeso abladearerespecti el
redges.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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. 1 71
elleristhediametero thecircle
eblades.
tancebetweentwosuccessi e
e lica lsur ace. I nanactualprope ller
stoodasstrict l re erringtoasmall
g- aceonl . Withthisunderstanding
nedasthe longitudinaldistancew hich
nw eresuchelementtow ork ona
ace asf ore amplethecorresponding
i ednut. P itchisthusseentobe
unctiono thepropeller. I tsv a lue
po i nt t o p oi n t o e r t he e n ti r e dr i i n g- a c e o r
nthe lattercasethepropellerissa id
ch . I i t i nc r ea s es a s we g o f r o m th e h ub
erence thepitchissa idto increase
ateronthef o llowingthanonthe leading
to increasea ia ll . The lattermode
impliedb thesimpletermincreasing
area orhelicoidalareao abladeis
thedri ing- ace. F orthepropellerit
su m o t h e ar e as o t h e bl a de s .
correspondingl , theareao the
erseplaneo onebladeoro a llthe
thecirclesweptb thetipso
ralbod towhichtheblades
hinturnisattachedtothesha t.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E A N D PR O PU L S I O N O F S H I P .
E A C T O N O F TH E E L E M N T O F A S C R E W
ede init ionintheprecedingsection
stlie inthesur aceo ac linder and
othedistancebetw eentw osuccessi e
e li measureda longthesameelement
s s ho w n in g e om et r t h at i t h e su r a c e
e eloped thehelica lpathbecomesa
na lo therectanglerepresentingthe
erconta iningonecon o lution. Thusin
i nd r ic a l su r a c e be c u t al o ng t h e li n e A B ,
outandf la ttened theheli A HB
C o a r e ct a ng l e A B C D F i g . 5 5 .
denotesthepitchandA D thecircum-
o d i am et e r A D F i g . 5 4 . Th e a ng l e
s c al l ed t h e pi t ch - an g le a n d th e r at i o A B - ~
ca ll ed \ . \ z p it ch -r at io .
n g so a s t o al w a s r e st o n L L a n d
atthesametimek eepingperpendicularto
ibeahelica lsur acesuchasw earenow
considerasmalle lemento thissur-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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N .
. I f thise lementactedw ithoutslip as
h en i t i s e i d en t t ha t f o r o ne r e o l ut i on
naheadadistanceA B andthe
thehelica lpathA H B . I nthe
ie ldingo thew aterthe longitudina l
o n wi l l be A B l i n st e ad o A B , w h il e
remainthe same.Theelement
erseahelica lpathA H 1B 1insteado
representedinthede elopeddiagram
T he n D = A B ^ , t he a mo un t o l on gi -
= B B l t t he a mo u nt o s l ip . T he
ntermedtheslipangle .
i g . 54 = d
r
;
.5 5 = 0 .
clatureo F ig.50 weha e
0 ;
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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N .
t a n a ;
2 7r rN t an a( i s = u
a.
5 asthegenerale pressiono P>
s A " = C E c o s a = j r /7 V c o s a.
E K .
andreducing w ef ind
a ki n g th e r el a ti e g l id i ng v e l oc i t o
, andassumingavaria tionasthe
w e ha e
A =
ependon thelengtho theele-
u r a c e a n d an g le 0 .
nddW denotef orthise lementthe
a n d th e t ot a l wo r k i n s t ea d o T W i
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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E A N D PR O PU L S I O N O F S H I P .
3 , ( 4 , weha e
( a ss in a co sa V i + ( i - - s * t an 2 a
) " ) ;
- J X / 4 < W s in 2 a' / i+ ( i - j ) 1 ta n3 a
i + t an 2 a
a ss in 2 V i + ( i - ^ ) a .t an 3 a
a ) .
t an 3 a = B \
a = C \
= E .
n 3 a.
tionsbecome
A ( a sc ot a -f C c ot * ) ; . . . ( 6
s d A ( a sB - f C ) \ . . .. ( 7
erey isav ariabledenotingthe loca-
ermso thepitch. I t isca lledthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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N .
identl thereciprocalo thepitch-
inquestion. F orthepropellerasa
a n d y w i l l be o c o ur s e t h os e o t h e
ewishtoespeciall distinguish
luesw eshalldenotethemb c^
dA \ ^ s B cot aC c ot a ;
E A C T O N O F TH E E N T R E PR O P L L E R .
s in t h e pr e ce d in g s ec t io n f o r d T d U ,
atedo erthesur aceo theblade w e
o r t h e e nt i re T U , a n d W . A s s u mi n g
berepresentedb
( asB cota-f C cota dA ; ..( i
-s f y \ a s B -/ C ) d A ; .. .. ( 2
b ( 3 , we ha e s imi lar to 35 ( 9 ,
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D PR O P U L S I O N O F S H I P .
o l edinthisintegrationw ema
, C , E , a nd d A a r e de te rm in ed b t he
pellerandb theslip. The arethere-
t i s n ot t h e sa m e h o we e r w i th a
aledconstants there isnoreason
a lueswillbethesamef ordi f erent
a c e o r f o r d i f e r en t a gg r eg a ti o ns o s u ch
chindicationsasw eha epo inttow ard
a luew ithdi f erentva lueso thetotal
t h ic k ne s s o b l ad e c o nd i ti o n o s u r-
. e lement.
icient/ itmustberememberedthat
rel asur acee f ect butratherthe
irectiono theplaneo thedri ing-
seo thicknessf romthetipsinw ard
respondingincrease inthev a lueo this
directresistanceis takeninthef orma
to n o c o ns t an c i n t he v a l u e o a
nv irtuall assumesthatthenormal
w iththesur ace. This how e er
pro imate l trueuptoacerta inpo int.
n32thetwogeneralmethodso con-
actiono ane lement. Thusf arw e
esecondoneonl . I nconsideringthe
t h is c o e f i c i en t a w e sh a ll f i n d it u s e u l
erthepropulsi eactiono thee lement
iew edf romthef irststandpoint. I n
discussiono theapplicationo
nd.
iew theactiono thee lementisto
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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, 1 79
ddirectionthe wateractedon.This
c l i nd r ic a l sh e ll o w a te r o r a di u s e u a l
o thee lement ando thickness
t. F orthepropelleritw ouldbea
w a te r o d i am e te r s en s ib l e u a l to t h at
w ithahollow coreo diametersensibl
hu b . A s w e s ha l l sh o wl a te r t h e ma i m um
dependsontheslipandon the
ono thee lementoro thepropeller.
ns i de r t he e l em e nt v e r n a rr o w a s f o r e a m pl e
- lik eblade theamounto acce leration
e lementorb thebladeasaw hole
sthanthisgeometrica lma imumabo e
obta inedw illthere orebecorre-
increasethew idtho suchablade
rstbenearl constantf oreachelement
oratimethethrustw ill increasedirectl
how e er asw eapproachacondi-
macce lerationandma imumthrust
he increase inthrustf oreachaddit iona l
lessandless orinotherw ords the
owerandslowerraterelati etothe
ha llthere oref ina ll reachaw idtho
alincrease willaddsensibl tothe
hatasw ethusincreasetheareaf rom
abladethea erageva lueo aorthe
tareaw illsteadil decrease atf irst
apidl . I te enseemspossiblethat
a terha ingpassedacertainpo int
ightbeattendedb anactualdecrease
ncreasingcon usiono thestreams
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
sepointsw illbeaga inre erredto in
to indicatethatthiscoe f icient
w iththetota larea inthegeneralmanner
l u es o 4 > d u e t o th e i n l u en c e o t h e
edgema perhapsbeq uitedi f erent
erminedgeometricall , andthe law o
t h e an g le i s a g ai n n o t q u i te e a c t.
d en t t ha t t he c o e f i c ie n t a in s te a d o
bl v ar f ordi f erentlocationsand
e el e me n t f o r d i f e r en t v a l u es o t h e sl i p
a mo u nt s o t o ta l a re a o b l ad e . I f t h er e o r e
tuseo thesee pressionsf orT U ,
d w e sh o ul d n ee d a s er i es o e p e ri m en t al
f icientsappropria tetothecircumstances
he r e is h o we e r n o s uc h s et o v a l ue s
e e n i i t w er e d es i ra b le n o d ir e ct u s e ca n
thesee pressionsintheformgi en
st how e er tonote inpassing
e aminationintothequestiono the
ueso aand/ radia ll a longtheblade.
menta ldeterminationo thev a lues
a i la b le w e h a e i n F r o ud e s e p e ri m en -
pe llers the integratedresultscorre-
, a n d e. A s w e sh a ll r e e r m or e
perimentsata laterpo int it issu f icient
edatathusobta inedgi ethe
a n d e f o r a s e ri e s o p r o p el l er s o c o ns t an t
ut e o N a a l A r c h i te c ts v o l . x x v u . p . 25 0 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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. 1 81
pitch( andhenceo v ariablev a lue j , )
w i t is e i d en t t a ki n g an o n e sl i p
theva lueso aand/ substitutedin
mu la e ( i , ( 2 , ( 4 w il l gi e t he o bs er e d
tb aprocesso tria landerroran
robabledistributionma bereached.
4 , i t i s se e n th a t e de p en d s so l el o n
hedistributiono thisratioma be
r o m th e v a l u es o e f o r v a r i o us e t e rn a l
. L i k ew i se f r o m ( i i t i s se e n th a t T
a f u n ct i on o / a n d a -T - / a n d h en c e i
m ined thedistributiono theva lueso
r o m th a t o t h e v a l ue s o T . T he v a l u e s
sf ound thev a lueso a immediate l
ngintothedetailso theoperation
tsasf o llows:
ent itwasf oundthatadistri-
n b A B , F i g . 56 w ou ld g i e b s ub -
bs er e d v a lu es o t he e f i ci en c . N e t
sshow ninC D w ould inconnection
t r f , g i e b s u bs t it u ti o n in ( i t h e
T . Theresult ingv a lueso aareshown
soclearl indicatedthatnootherdistribu-
r in g f r o m t h is i n c ha r ac t er c o ul d f u l i l t he
a l u es o / a r , a s w es h ou l d e p e ct
ntamorecomple v aria tion due
i n g wi d th o b l ad e a t di f e r en t r ad i al
ope ller andatpo intsha ingthe
ameterratioondi f erentprope llers and
notappearf romthedataathand.
ow e er w earenotsomuchcon-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D P R O PU L S I O N O F S H I P .
T O
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N .
ono theva lueso aand/ asw ith
he r w it h v a l u es o t h e in t eg r al s o ( i , ( 2 ,
ee i nt e gr a ls d e pe n d on t h e v a l ue s o y l a n d s
portions andareao theblade. Sup-
the lattere lementsconstant it is
an f i n d th e v a l u es o t h es e i nt e gr a ls f o r a
v a l u e s o y ^ a n d s w e s ha l l be a b le t o
h e th r us t u s e u l w or k a n d e f i c ie n c
enseto condit ions.
r e e r t o th e e p e ri m en t s mo s t a a i l-
n thepaperabo ere erredto-
r e su l ts o a s e ri e s o e p e ri m en t s
ttheA dmira lt E x perimentalTank
estigatingthere lationo thrustand
hratioandslip. Thepropellersw ereo
a n d we r e al l o 8 . 16 i n ch e s di a me t er a n d
J - 4 > x ' 8 2 . 2. T h e
elopedf orm as
ubtook theplace
h e el l ip s e a n d th e f o r m
thispointtogi ea
attachmentbetween
imumw idtho the
esepropellers
a lueso theslip. I t
he lim itso thee perimenttheresults
uiteclose l b thef o llowinglaws:
i p an d v a r i n g v a l u es o y l t h e t h ru s t
a n e u a t io n o t he f o r m
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D P R O PU L S I O N O F S H I P .
f i ci en c a nd v a r i ng v a l ue s o y l t he
es s ed i n t he f o r m
adeuseo toreducetheobser a-
nateminorinstrumentalandobser-
da lsoto interpo latef orintermediate
. Wherethenatureo the law seemedto
l u es w e re e t e nd e d sl i gh t l b e o n d th e
menta ldetermination.
werethenput intographical
e s o n e o w h i c h ga e T a s a f u n c t io n o
g v a l u es o t h e pi t ch - ra t io < : . T h es e c ur e s
dependento absolutedimension
r assumptionsasdiscussedin49and
theproperf unctionso an proposed
eapplicabletoan gi encase.
e s o e f i c ie n c , i t wa s f o u nd t h at b
c ti on o s f o r v a r i ng v a l ue s o j / o r < ; , a
eobta inedw hichw ereessentia ll the
a r i n g ho r i o n ta l s ca l es . I t t h er e o r e
anappropriatecho iceo hori ontalsca le
t o b ri n g al l o t h es e e f i c ie n c c u r e s i nt o
dhencetouseonefora ll. Thisf usion
i c ie n c c u r e s w as t h us o b ta i ne d b s u bs t i-
saq uantit ca lledabscissav a luesuch
( c ^ ) .
n d c l be i ng t h en g i e n a n d th e c or r e-
( O D e m g kn o wn t h e ab s ci s sa v a l ue
r o m th e c ur e t h e e f i c ie n c i s k no wn .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N .
betreatedsomew hatdi f erentl here
ertotheoriginalpaperf orf urther
tothemethodsgi enf orappl ingthese
design.
adeo aserieso e periments
T h or n c r o t a n d B a r na b . T h e
ee perimentsa lsoclose l correspond
de andasthe latterarethemore
sethemasthesourceforoure perimen-
u at io ns ( i , ( 2 , ( 3 , ( 4 i nt he
mf orapplicationtothesee perimentsw e
i n g wi d th o b l ad e a n d b l th e m a i -
s b e o r e t h e ra d iu s o a n e l em en t a nd
blades.H enceweha e
c ^ r d = 2 b dc l d .
described
2 1 4 V 1 -y - i y .( 5
< tc V c y c y * d .
t e C i i l E n g i n ee r s v o l . en p . 7 4.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
theellipticalbladestothe
erandtothema imumw idthb^ W e
orthissomef ormo re lationshipin
ractero thecontouro theblade
n o l ed. Tothisendw ere latethe
ct l t o n d - ~ 4 o r t o th e d is k a re a o
put
r .
ratio.
reao abladesuchasrepresentedin
areao thee ll ipse . Hencef orone
. 35 ^ , .
prope llerinthiscase
1 4 = -
w eha e asthemoregenera lre lation
rememberthat, = . 4^ = . 2d.
w eh a e
S ^ 1 o r A = . 35 6.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N .
dasthestandardva lueo hf or
llers.
in ( i , ( 2 , ( 3 , w e ha e
V c y c y * d \ \
a s B
.
ebracketsareseento bef unc-
so thepropellerando theslip or
d s . D en o te f o r a n g i e n c as e t he i r
L , r e s p ec t i e l . W e m u s t he r e re me m be r
tappl ingthesee uationstopro-
simpl to thepropellerso thisseries
w hi c h th e s i e p r op o rt i on a n d sh a pe o
tant andy landsw eretheonl
ma properl considerthatthev a lues
a re f u nc ti on s o t he se v a r i ab le s on l . W e
at e u se i s t o be m ad e o t h es e e u a -
c o ns i de r U a n d e. W , i d e si r ed i s
i di ng U b e a nd T b d i i di ng U b
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D P R O PU L S I O N O F S H I P ,
e ri e a c tu a l v a l u es o K b s u bs t i-
t h e v a l ue s f o u nd f r o m F r o ud e s
dthepresenceo largenumbersinour
te f o r / d a n d N , a s f o l lo w s:
in. _ N
ultingv alueo K b thetwo
af unctiono theslipsandisintended
nceo thisv ariable and/ isa f unction
tio c or^ 1, , andisintendedtorepresent
ariable .
d kl .. .. .. ( 1 4
a n a ct u al v a l ue o U a s g i e n b
s c u r e s o t h ru s t b t h e s p ee d , a n d
units w eareabletoderi ethev a lue
ctork lcorrespondingtotheparticular
s as s um e d. I f t h is b e d on e f o r a l a r ge n u m-
a n d s w e sh a ll h a e a c o rr e sp o nd i ng s e ri e s
e se w e ma n a tu r al l s e ek t o e p r es s
thevariableonw hichitdepends.
st io n ( a a b o e i t i s e i d en t t ha t
0 5
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N .
t h e se r ie s o v a l ue s o k l t he n s ho w ed
o ul d b e v e r n e ar l e p r es s ed b t h e
nd/will bef oundin50.I nthe
onthef ina lresultbecomes
, - .17 .
s i n ho r se - po we r u ni t s / , N ' t a n d d
w hi l e s an d y l a r e to b e e p r es s ed a s
/willthenbef oundtoclosel
a ll ingw ithinthe lim itso sandy l
e ri m en t s.
17 isthere oresimpl empirical
t h e e p e ri m en t s no t ed a b o e a n d
tall applicablesimpl to thepropellers
hapterI V w esha llconsiderthee ten-
opropellersingenera l.
e st io n o e f i ci en c . F r o m ( 4 i t
i s. a f u n ct io n o s a f , B , C , E , o r
r I f w e no w as su me t ha t th e in l ue nc e o t he
andf one isunimportant itw ould
p r es s i n ge n er a l e as a f u n ct i on o j ,
m er a s f i i n g th e c ha r ac t er o t h e pr o -
atureo itsuse. Thisassumptionis
blew henthecharactero thebladeas
atiohw ide l v aries andthe in lu-
e isperhapsnotunimportant. A sa
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
er le tusf irstassumethebladesa ll
a rdf ormandproportionsasusedin
nts andletusneglectthe in luencedueto
k now ingthee f icienc o themodel
n othersim ilarprope llerw illbethesame
thesamepitch-ratioandw ork ingat
tw eassumethearea- ratiohandthe
, theresultsdeterminedw illbecorre-
eS til lf romsuchindicationsaswe
hatf orslightv aria tionsinarea- ratioor
t h e e f i c i en c w o ul d b e sm al l . I n
a c t in o r ma t io n t h er e o r e w e s ha l l ta ke
p e ri m en t s as o u r st a nd a rd o e f i c ie n c ,
epartf romtheshapeandpropor-
reusedtheresultswillcorrespondingl
rac .
t h e e f i c ie n ci e s o t h e mo d el p r o-
b F r o ud e a s a f u n c ti o n o c a n d s b
ss a v a l u e " t h ro u gh t h e ag e nc o w h ic h
e s f o r a l l v a l u e s o c w e re b r ou g ht i n to
esentpurposes how e er w epre er
n a so me w ha t d i f e r en t f o r m a s
de sdiagramstheva lueso cands
an t v a l u es o e i t w as f o u nd o n p lo t ti n g
so candsf orconstantew asver
andthatthebundleo l inesradiate
masinglepo int. Theactua lcharactero a
t er m in e d is f i e d b p r op o si t io n s ( a
c o ur s e ar e a pp r o i m at e a n d no t p h s i ca l l
mtheseproposit ions it ma beshow n
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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. 1 91
tastra ightline andthatits
mp l e . B e t w e en t h e li m it s o t h e e p e r i -
hee uationrepresentsa locusw hichisver
haracterthusf oundb geometrical
ore j usti iedb thenatureo the
undamentaldiagramsarebased.
plicitl in ol edinF roude s
a c t th a t th e e f i c ie n c c u r e s f o r v a r -
meanso theabscissava lue as
bereduceda llto thesamef orm andhence
ra ll.
bo ee plainedisshownin
matef ocuso the linesisatabout
s o t ha t t he a p pr o i m at e e u a ti o n to
- 2 I = n c + 6 . 8 . T h e ac t ua l l in e s o
chmostclosel representthepoints
rginaldata anddonotthere ore
abundleemanatingf romthef ocus
r en c e is v e r s l ig h t h o we e r a n d is
hanthenecessar di f erencebetw een
u e v a l u es i n a n g i e n c as e a n d is
ni icant. Thisdiagramma becare ull
. Geometrica ll itma beregardedas
scuttingthesur acew hichw ouldrepre-
cands. A planeperpendiculartothe
b A B w o ul d c ut o u t a cu r e o
on s ta n t sl i p as a f u n ct i on o p i tc h -r a ti o w hi l e
hea iso cw ouldcutoutacur e
o r c on s ta n t pi t ch - ra t io a s a f u n c t io n o s l ip .
ninF igs. 59and60. I t isthe latter
Mr. F roude. L ook ingaga inatthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D PR O PU L S I O N O F S H I P .
sseenthatitreadil indicatesthe
r op e ll e r o s t an d ar d f o r m g i e n i ts p i tc h -
i c e v e r s a i t s ho ws t h e ra n ge o v a l ue s o
1.71.81.92.0 2.12.22.32.42.5
A M O F E F F I C I E N C Y A S A F U N C T O N O F S L I P A N DP TC H
whichan particulare f icienc ma be
f or69percentshow stherelati e
ng w h ic h t he b e st e f i c ie n c w a s f o u n d
etwolines f or68percent shows
a lueso c andsw ithinw hichthe
below 68percent. A ga in itshow spla inl
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N .
o asw eapproachsmallsl iprather
se uencethatit isbettertow ork ina
hanthatf orma imume f icienc
eruseso thediagramw illappear
mso design buttheabo ew ill
E S O F E F F I C I E N C Y .
hemainlinesa longw hichitsstud ma
satthis pointbecautionedthat
t h e e f i c i en c h e re g i e n a re p r ob a bl
t i ev a lues. U na o idableerrors
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
nto man o thequantit iesin-
n c a n d in a d di t io n s om e mo d i i c at i on s w er e
nordertoreducetheva luestoagree-
J 3
) abo e. Thenumbersheregi en
nsiderednotasabsoluteva lues butas
w hilethe indicationsastochangeo
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
norotationisproduced andwhere
narrowthatlittleorno sensible
edinthetime takentopassthrough
hatoneha l theaccelerationw illbe
t h e pr o pe l le r a nd o n e ha l i n t he r a ce a t
e r w e s h a ll h a e i n a nd a t o t h e
pressure inthe interioro theco lumn
r ce . I n t h e ac t ua l c as e t h er e o r e
ha l o theaccelerationw illbepro-
eprope ller acerta inamountw hilepass-
emaindera to thepropeller.
tthehigherthepitch- ratio themore
eversa . H encew ithpropellerso high
pectthatmosto theaccelerationw ill
o thepropeller w hilewithlow values
rtionthererece i edma bebutlittle
total.Thecolumnasa wholemust
low decrease incross-sectionasitpasses
ndtosuchdistancea tasthev e locit
w ateractedoncouldbek now nandthe
d thethrustcouldbeimmediatel
ngthespeed theuse ulw ork w ould
w ouldbethesumo theuse ul plus
thek ineticenerg impartedtothe
tingthewasteisseen todepend
actedonandonthe init ia landf ina l
learthatw ema di idetheenerg
eeparts asf o llows: ( i thatdue
v elocit ; ( 2 thatduetocircular
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N .
o r r ot a ti o n ( 3 t h at d u e to t u rb u le n ce a n d
iso coursenecessar to theproduc-
st w h il e ( 2 a n d ( 3 , t h o ug h n ot f u n da -
cannotbeentiret a o ided. Theenerg
rotationhasbeenmadethesub ecto
. F r o u d e * w ho s h ow s b c e rt a in i d ea l
luenceone f icienc w illbepractica ll
a rgeva lueso theslipandhighpitch-
aseMdenotestheamounto w ater
i tu d in a l ch a ng e o v e l oc i t , 4 2 ( 4 ,
portionaltoM andtheenerg
N o w f o r a g i e n v a lu e o M i t is r ea di l
m inimumw henMisama imumand
f o r a g i e n t hr u st t h e en e rg d u e to
sleastwhenthemassacted onis
issmall. F orhighe f icienc , there-
onpointstotheuseo largepropellers
thanthere erse.Thiscorresponds
uentontheassumptiono the
angentia lf orces. A ctua ll thee ist-
eddiesandturbulenceduetosk in- resist-
sstructura lconsiderations l im itthesi e
f i c ie n c a s a lr e ad s h ow n i n 36 .
scusstheactiono thescrew pro-
onto thepresentsection. I nthe
r n o ne o t h e te r ms h e re i n o l e d c an b e
w nquantit ies sothat asintheother
w earethrow nupone perimentf orthe
t e o N a a l A r c h i te c ts v o l . x x x m . p .2 6 5.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D PR O PU L S I O N O F S H I P .
ate erf ormulaema beproposed. We
n 3 8 a s a n il l us t ra t io n t h e tr e at m en t o
thispointo v iew .
-W H E E L T R E A T D F R O M TH E S T A N D -
bein estigatedinthesame
ew propellerin35 36. The
ceo thisinstrumento propulsion
s e em t o j u s ti y t h e n e ce s sa r w o rk a n d
nosuche perimentaldataf orthef ina l
onsasw iththescrew propeller. We
itbrie l f romthestandpo intmen-
edtomoreespecia ll in37.
thesternwardmomentumo
meanso thepaddle .
e an v e l o c i t o t h e wa t er i n f . s . ;
me a n v e l oc i t o t h e wa t er i n f . s . ;
la reao thestreama f ected;
t h e sh i p in f . s . ;
ecircledescribedb the
thepaddles( thispo intma
rantdeta ilso thevarioustheoriesw hichha e
the linesherere erredto re erencema bemadeto
pl e s o t h e A c t i on o P r op e ll e rs . B y P r o .
n s ti t ut e o N a a l A r c h i te c ts v o l . v i . p . 13 .
B lade inaS crew Propellernecessar toF orm
B y P r o . J . H . C o t te r il l . I b i d . v o l . x x . p . 15 2 .
e O p e r at i on o P r op u ls i on b D i f e r en c es i n
R . E . F r o ud e. I b id . v o l . x x x . p . 3 90 .
f e c t o t h e R a c e R o t at i on o n S c r e w- P ro p el l er E f f i -
. F r o ud e. I b i d. v o l .X X X T I . p. 26 5.
y S . W . B a r na b . L o n do n a nd N e w Y o r k.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N .
thecentero thepaddle
e o lutionsperminute .
olumeactedonperminuteandf or
- -60isthemassinpoundsactedon
ng e i n v e l oc i t p e r se c on d . H e n ce
- O
.2 =
sistance andhence sol ingf orA ,
v a l ue o ( i z / ) i s u n c er t ai n
ngR ank ine ha econsideredthat
e r or p a dd l e- wh e el = s - .
eine act butwema useitf orthe
pose. Weha e there ore
ge n er a ll a n d mo r e sa e l
o n e pa d dl e ~ A . H e n c e i w e
e pa d dl e b a w e ma p u t
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
g n we m a p r e e r ab l p u t th e e u a -
asf o llows:
D N J s . .. .. .( 3
. .. < 4
u ~ a D N ) s s i s . . .( 5
k o r I . H . P.
e h a e
-s , . .. .. ( 6
addle-wheelswhichha eper ormed
ef oundthusre latingtheareao blade
usl assumedquantit ies.
ipsma betak enf rom20to30
eatheringpaddlesf rom15to20percent.
dependontheunits chosenf orZ > ' ,
merica lcon eniencew ema tak etheseas
b onew heel
e i nf e e t - - 10 = D - + - I O ;
on s pe r mi nu te - - 1 0 = N ~ 1 0.
f r o m 2. 0 t o 2. 5 .
onef loat.Thenumbero f loats
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N .
7 f o r r a di a l wh e el s a n d f r o m . D t o
w heels. Theproportionso f loatsare
breadth.
theupperedgeatmeandra t
8thebreadth accordingastheboatis
roughw aterandtovar l itt leormuch
o ur i n st e ad o ( 4 w e s ha l l ha e
DN( \ -s
ulaetakethef ollowingdata:
eelsand500ononew heel
umed.
2 . 4
rs a 2 0 s . f t .
orebe8 X 2 .5.
DN inan proportionsuitabletothe
s e. T h us i w e ta k e N ' 4 0 w e ha e
pu t D = 15 , w e h a e N = 4 8 .4 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
ento F eatheringPaddlesI nF igs.
sualkinematicarrangementsf or
F ig. 61the link ssim ilartoA B are
nk actuatesthe le erB C andblade
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
ore
usthatin ol edintheaccel-
thew ater andpossibl inra ising
f o r s im p li c it w e ne g le c t th e l os s d ue
andsupposethe waterdischarged
eheadasthatunderwhich itenters
totalw ork
ankine sideale f icienc , since
thee f icienc underthesupposit ions
the additionallossesduetoeddies
ew ork to- -ormore anddecrease
approachingmoderateorhighspeeds
lre uirecorrespondingl la rgeva lues
b o th . Th e f i r st m e an s h ea y m ac h in e r
i c i en c . I n a n p r ac t ic a l ca s e th e
r ge a s t o re d uc e t he e f i c ie n c b e lo w th a t
edscrew propellerorpaddle-wheel.
w ouldre uiresmallv ^ andhence large
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N .
sibletorea li e inpractice andthe
e o r e n e ce s sa r il s m al l .
heremoderatespeedissu f icient
mportante lement orw hereanordi-
l iabletoracev io lentl o rbecome
eatmanoeu ringpowerisre uiredasina
m o de o p r op u ls i on m a h a e a d a n ta g es
suse. Themanoeu ringpowerisusua ll
schargeno z lessosituatedandso
ctionma bedirectedinan line and
rdirectionortrans erse l or
asonapi ot.
B I N E S O R S C R E W PR O P L L E R S W I TH
S .
wturbinema betakenasanillustra-
st peo propell ingagent. Thepropeller
b A B C , F i g . 63 w i th b l ad e s A D B
ia ll andshorterradiall thanthe
nconse uencetheinclination
s sl i gh t . A f t o t h i s i s a pr o e c ti o n
e d t o th e s hi p . Th i s co n si s ts o a p r ol o ng a -
e s p in d le - o r me d b od F G H , a c l i n-
MN, andaserieso bladesconnecting
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N DPR O P U L S I O N O F S H I P .
- ormedbod asindicatedatKG
sha easlightinclinationinthe
o thepropeller-bladesA D B .
adesis v ariable.Theproducto
pitchatE isintendedtobee ua lto
o f e e d o r t h e v e l o c it o t h e st e rn o
k una f ectedb theactiono the
there o lutionsb thepitchatD
e ualtothespeedo de li er , and
nA B C andconse uentreductioninarea
tobesuchastogi e f orthisvariable
l o w f r o m B E t o D A . T h e wa t er o n l ea -
ropellerhasaconsiderablerotar
ichit impingesonthef i edblades
nce it isbroughtgradua ll toana ia l
na ll de li ered. The longpro ection
oseo pro idingforsomethingapproach-
erlea ingtheguide-blades andto insure
hevariousstreamsw itheachotherand
theactua lw ak ease pla inedin
thatw hile inagenera lw a the inten-
thedistributiono pitchandsectiona l
heve locit ieso f eedanddischargema
e t s uc h r es u lt m u st b e f a r f r o m e a c t a n d
a r i a ti o n o p i tc h c an h a e m uc h i n l u -
tono e f icienc tothecharacter-
ise identthatthere isnoreasonf or
ddi f erence inthisf eaturebetweenthis
pr o pe l le r . I f , t h en t h er e i s an i n -
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N .
cienc itw illprobabl bef oundinthe
ngagenttotheship. Eitherthe
duetothepropellermust belessorthe
44 , orboth. Thereseemstobeno
n essentia ldi f erence inthew ake
b e f a i r l e p e ct e d th a t du e t o th e p re s su r e
enormaldirectiono w hichw illha e
therema besomereturnf orthe
duetothe actiono thepropeller.
dditionalattachmentf urnishesacon-
sistance andhence it isdoubt uli the
thanwithapropellero theusual
e oree pectaboutthesameultimate
h co n cl u si o ns a r e bo r ne o u t b e p e ri e nc e .
roundingcasingdoes howe er
a irandtheradia lescapeo the
asestheresistanceo thebladesto
ethethrust. I tresultsthatthere uisite
f romapropellero smallerdiameter
o r m e s pe c ia l l i t h e dr a t i s s ma l l
deso acommonpropellerw ouldcome
hew ater. I nsuchcasesthereseemsto
n e ss f o r p ro p el l er s o t h is c h ar a ct e r a n d
c r o t t p e h a e b e en i n st a ll e d wi t h v e r
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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I .
E T WE E N S H I P A N DPR O P L L E R .
T TU T O N O F TH E W A K E .
propulsionw eha etothispo int
enttoacti nundisturbedwater.
s f a r f r o m co r re c t a n d we h a e n o w
ecto irregularl disturbedw ateronthe
causeandnatureo thedisturbance.
asthe t picalpropellingagent
hesterninwhatistermedthew ak e
eneighborhoodissub ecttothe
ses:
o ti o n. I n 2 w e ha e s e en t h at t h e
nthew aterandtheshipislessatthe
pand theoutl ingundisturbed
etothe latterthestream- lineaction
w ard. Duetothesamegenera lcause
ati emotiono thew aterandshipis
andinw ardcomponentasitf o llowsthe
. Thisbringsitsdirectiono f low
thepropellerDuetothedi f erence
morestrongl markedw ithtwin-
screw . The in luenceo this
w illbediscussedata laterpo int. Thispart
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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B E TW E E N S H I P A N D PR O P L L E R . 2O O ,
u e nt l r e e r re d t o th e w a e - m o ti o n du e t o
e s g en e ra t ed b t h e mo t io n o t h e sh i p.
e r t o r e e r i t to s t re a m- l in e m ot i on a s a
ecto thecause. Thisnaturall in-
thewak econta inedinthef ree l - low ing
o l edinf rict iona landdead-water
orF rict iona lWak e. Thenatureo
kno theshipandthew aterhas
romw hichitappearsthatthew hole
db a la ero turbulentw aterpartak ing
orw ardmo ement. Thismotionis
hea terend andatthesternw e
blemasso w atermo ingf orw ardre la -
bod o sti l lw ater.
theresult ingcomple w ak e w e
onsiderations:
o r m o t h e s h ip i s r el a ti e l f u l l an d
hestream- linesiscorrespondingl more
o thenormalhori onta ldistribu-
heresult ingw a e-motionisa lsore la -
e ar t h e su r a c e. A s t o t h e v e l o c it o
hereseemslittlereasontoe pectan
depthf orpo intsneartheship ssur-
w i ll h o we e r r a pi d l d e cr e as e a t po i nt s
e r an d f a r t h er f r o m th e s ur a c e.
t iono w ak e- e locit , aninterest-
mentshasbeencarriedoutb G. A .
t he s t er n o a m od e l 28 f e e t lo n g an d
edcargosteamerw asf ittedaf rame
a a l A r c hi te ct s v o l . x x x i . p .6 1.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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TA N C E A N D PR O PU L S I O N O F S H I P .
dse era lvertica lw irese tending
stance belowthekeel.Thesewires
dw ithv anesandf reetosw ingtothe
noutriggere tendingintoundisturbed
.The heightsrecordedinthese
dintove locit iesb theusual
g h .
nso determiningthev elocit o
po intinthew ak eandre lati etostil l
e locit o thew ateratthispo into
lw ater. Thewak e- e locit iesthus
daspercentageso theve locit re lati e
ctiono thew akeincludingthe
ssa loneo thescrew beingf itted the
all inenearthestern-postvariedf rom
thesur acedownw ard inahori onta l
f rom64to7percentf romthestern-
ori ontall inenearthek eel f rom17
estern-postoutward. Thea erage
about 19percent.
madetodeterminetheportiono
lw ake. Tothisendathinplank o
odelwastowedatthesamespeeds.
ancesbeingf itted thew akespeedsat
e o t h e pl a nk a t d is t an c es o I , 7 1 4
o m t he f o r wa r d en d w er e f o u n d r es p ec t i e l
a n d 50 p e r ce n t o t h e s p ee d o t h e pl a nk .
ppro imate l thew ake- e locit ies
lprogressionasthe distancesf rom
arithmeticalprogression.
rations f orthedetailso w hichthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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B E T WE E N S H I P A N D PR O P L L E R . 211
onsulted theauthorconcludesthato
w ak eabout5percentw asdueto
rcenttowa e-motion orstream- line
termit andtheremaining5percent
w ise ischargedtothe in luenceo
ingw ateraboutthesternduetothe
o f o r m.
ew ake- e locit ingenera lise -
roughoutthecross-sectiono thew ake
isandothere perimentaldetermina-
ata laterpo int itappearsthatinclud-
mediatel asterno theship and
luencedb prope llers itsa erage
r o m 6 or 8 p e r ce n t to 2 0 o r 25 p e r ce n t o
e l. I ngeneralit isf oundthatthew ake
hipislongerandf uller andlessasit
orempirica le uationsre latingits
ti c s o t h e sh i p se e 5 0 ( 9 a n d ( 1 0 .
O N S O F D F F E R E N T K I N D O F S L I P O F M A N
F M A N P T C H .
that ' unlessotherwisestated a ll
edtothesurroundingbod o sti l lw ater
tsupposethew ak etobeuni orm.
h ip ;
ak e i prope llerw erenotactingand
speedu;
o w a t e r at o r j u s t f o r w ar d o t h e
w a te r d ue t o i n l u en c e o t h e pr o -
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
ut i on s = p N = s p ee d o a d a n ce
ake i therewereno
ad anceo propellerrelati etothe
a n ce o p r op e ll e r re l at i e t o t he
utit.
p r op e ll e r = S ^ ; . . . ( i
u - - ^ = S l - - = t r2 ie sl ip o p rop el ler S 2 ;
r ue s li p o p ro pe ll er 5 2 ; ( 2
w at er = 5 3 ( 3
d f o r w ar d a nd v ^ a t a n d he n ce 5 3 w i ll
o v a n d v 9 .
notedthatthesethreek indso slip
thougho coursenotindependent.
enotedthat5aand53arenotthe
e o F i g . 55 w e ma r e ad i l r e la t e
2 o r j a a s f o l lo ws :
sthattheactiono asur ace in
mttingskin- resistanceandthef orma-
essimpl achangeindirectionw ithout
andthetota lf orce interactionbetweenthe
smeasuredindirection andamount
ge inmomentum. I nthatdiagramthe
roachingtheblade withv elocit
ddirectionb E A , andaslea ing
para lle lto theblade. Thisisrepre-
ectionb mak ingK A = E A . Then
ono motionstheresultantchangeis
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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B E T WE E N S H I P A N D PR O P L L E R . 213
ndamountb E K . The longi-
isisE G andthisisthere orethe
ctl use ulinpro idingthrust.
A R i s s ma l l we m a p u t
p N c os 3 a = 5 a c o s 3 a .
e v e l oc i t S 8 i s v a r i a bl e f o r a g i e n
reasingasadecreases andthere ore increas-
ard ata llpo ints how e er be ingless
c d in g d ue t o t he I r r eg u la r it o t h e W a ke .
e
ctualwakeasdescribedin41 it
a v a r f r o m pe r ha p s o to 5 0 p er c e nt
slisusua ll f oundbetw een10and
m a v a r f r o m sa 5 o r 1 0 pe r c en t
e enmore. I tthusappearsthat
sl i p is v a r ia b le o e r t he s u r a c e o t h e
po intinthere o lutionbetweenthe
dabo e andthesema notperhapsbe
tisindeedquitepossiblethatf or
mightbeoore ennegati e w hile
mightrisepossibl tonearl 100percent.
ideao slipf orthepropellerasa
ke haslostentire l thesimplicit o
abletogi eto itw hendealingw ith
rbedwater.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
o t he w id e ra ng e o e t re me v a l ue s
hattheslipma ha e thecondit ions
a n d f o r m o st o t h e re o l ut i on a r e su c h
chnarrow errangeo f luctuation and
doubtedl donebetw eenacompara-
v aria tion. Wearethusledtothe
p. Thisadmitso de init ioninv arious
enasthearithmetica lmeanf oran
thevariousslipso thee lementscompos-
me n ta r v a l ue s a re q u i te u n e u a l in
ordingtothe irlocationandtheva lue
eemmoref a irtogi etoeachelementa
egrossworkabsorbedb it.Thus
denotetheamounto w ork absorbedb
s^ s3, etc. thecorrespondingva lueso
i i n g to e a ch e l em e nt a r s l ip a w ei g ht
ork w ema tak e itsthrustoruse-
e lementar thrustsb / , / e tc.
hodo appl ingthew eightsthusindi-
w il lbegi enbelow underthediscussion
1 2 , t he t ot al w or k o a n el em en t is e p re ss ed
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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B E TW E E N S H I P A N D PR O P L L E R . 21
geometrica lf ormo thepropellerandthe
e llerw ithvariableslipthetotal
thesummationo suche lements.
ipinsteado v ariable isconstantat
ndit ionsremainingasbe ore andthat
tionf ortotalworkW isthesame
en t l s m a b e c on s id e re d r el a ti e t o
o slipasameanore ui a lent
asde iningmeanslipastheslipat
nauni ormstreamatthesame
sw ouldabsorbthesametota lw ork as
ot al w or k as i n ( < / , t he d e i n i ti on m a b e
use ulw ork orthrust. Thisisthesame
astheslipatw hichthesamepropeller
thesamenumbero re o lutionsw ould
w ork orthesamethrustasintheactua l
encesthusf artoanentirepropellerw e
u n i o r m pi t ch o n t he d r i i n g- a c e.
ha ediscussedthevariabil it o slip
t hr o ug h ou t t he r e o l ut i on a n d ha e
it ionso meanslipasabo e. P rope llers
e h o we e r w i th p i tc h v a r i a bl e o e r t he
husisintroducedanothere lemento v aria -
slip anda lsotheneedforsome
msmeanpitchandmeanslipasappliedto
a tak eageometrica lbasisandde ine
thedistributedv a luestak eno er
e r e th e p it c h v a r i es s i mp l f r o m th e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
gedge themeano thetw ova luesat
entl tak enasthemeanpitchinsteado
nasabo e.
simplemeano thedistributed
rhapsmoreproperl gi etothepitcho
portionaltothe workwhichit
hichitde e lops. B y re erence
, i t a pp e ar s t ha t t hi s w ou l d be v e r c l os e l
othepitcho eachelementaw eight
tcaseb theproducto itsareab the
o r b t h e cu b e o i t s ra d iu s a n d in t h e
du c t o t h e ar e a b t h e s u a re o
Thef o llowingactua lcaseo a f our-
a begi enasanil lustrationo the
ducedmeanpitchin thesecond
crossthebladeswas takenatf our
e ua lto . 3 . 5 . 7 and. 9theradius
proportionaltothebreadth.The
sthenarrangedasf o llows:
mo thecolumnr bintothesum
bladethereducedmeanpitche ua lto
bladesthev a luessim ilarl f ound
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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B E TW E E N S H I P A N D PR O P L L E R . 21 J
, a n d 15 . 54 . T h is g i e s a s th e f i n al
ope llerthev a lue15.67 .
anpitchbeingthusf oundf romeithera
ade init iono meanslipf o llows
ila rtotheonegi enina llrespects
hichsha llbeuni ormando themean
ned andletthisprope llerwork ingina
samenumbero re o lutionsabsorbthe
work asthegi enpropeller. Thenthe
onsw ouldbeful i l ledw ouldbea
lp f o r t he g i e n p ro p el l er . T hi s i s e i -
a b o e f o r t he c a se o u n i o r m pi t ch .
t a ke t h e us e u l w or k o r th r us t a s th e
init iono meanslip.
gmeanpitchonapure l geometrica l
i t a d n a mi c al d e i n it i on a s f o l lo w s:
erw ork inundisturbedw aterw ith
dspeed. Lettherebeapropellero
samediameter area andshapeo
undisturbedwateratthesame
Thenthepitchat whichthelatter
esameturningmoment oratw hich
w ork asthef irst ma beconsid-
ntmeanpitcho thef ormer. S im ilarl
ebasedone ui a lentthrustsinsteado
ments.
thatthepitchthusdeterminedw ould
here o lutions andw iththere lation
dspeed sothatitcouldnotbecon-
mensiono thepropeller.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
it i on o m e an p i tc h h a i n g be e n th u s
o meanslipw ouldmostnatura ll f o llow-
e a bo e .
themeanpitchorslipo apro-
ormanceincomparisonwiththato
mpitch the in luenceo thethick nessor
i n o l e d . To t h is w e ma b r ie l
ecross-sectiono aprope llerbladeas
r el a ti e t o t he w at e r in t h e di r ec t io n o t h e
distributiono thestream- linesissuch
ssureonA B there isane cessf rom
esspronouncedde ectbetweenB
enera lrepresentedb apressureon
n g it s c en t er m u ch n e ar e r B t h an A , a n d
bladeaboutintheclockwisedirec-
t h e di r ec t io n K L i s a i a l t h er e w il l
i eorf orw ardthrust. Thatis i
disturbedwateratsuchre olutions
attheslipo thedri ing- ace iso
aslightposit i eorf orw ardthrust
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E T WE E N S H I P A N DPR O P L L E R .
thestream- linemotion andit is
dri ing- ace issti llf urtherdecreased
ti ethattheforeanda tcomponents
o r c es e a c tl b a la n ce a n d gi e a z e r o
enotedthatthisz erothrustisactuall
ponenta tduetothetangentia lf orces
ctionandedge- resistance ando a
etothenormalforcesorthosedueto
sI f , there ore thef ormercouldbe
propellerwould underthecondi-
t i l lshow aposit i e thrust anditw ould
ncreaseo negati esliptoreducethe
thenormalpressurestoz ero.
f re uentl notede perimentall , and
b ecto q uantita ti emeasurementin
ntscarriedonb theauthor.
ntl re erredtob thestatement
icknessresultsinav irtualincreaseo
e e u i a l en t p it c h be t a ke n a s ( l o n gi -
o th r us t - - ( r e o l ut i on s , t h e re s ul t w il l
edb themeasuremento thedri -
cessw ouldbestillgreatercouldthe
minated.
edvariouspossiblede init ionso
pinordertoshow thev ariet o
gi entotheseterms andtheconse-
signi icanceattendingthe irusew ithout
ebasiso de init ion. Ouruseo the
i r t ua l l a s su m e th e d e i n i t i on o m e an
Thatis w esha llassume asw illbe
N a a l A r c h i te c ts a n d Ma r in e E n g i ne e rs v o l . V .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
f ortheactua lv ariableslipma besub-
ui a lentva luef oruse inthee ua-
o thetota luse ulw ork.
o v ariablepitchitma benoted
intendedtopro idef orsome
slipo erthesur ace assumingthe
ormstream. When how e er w e
abil it o thestreamorw ake it is
attempttosecurean speci ieddistri-
f uti le andthatinan gi encasethe
uitedi f erentf romthatintended.
ts r e su l ti n g f r o m a v a r i a bl e p it c h wi l l be q u i t e
r d o ub t u l i , i n t he p r es e nt s t at e o
san thingtobega inedb introducing
esigns.Theseconclusionsseemto
ri e nc e f o r p ro p el l er s o u n i o r m pi t ch
e s i n pr a ct i ce t o b e e u a l in e f i c ie n c t o
sv ariableaccordingtovariouslaws.
nof urtherattentiontovariablepitch
w propellers butsha ll ina llcasesassume
m pi t ch o e r t he e n ti r e dr i i n g- a c e.
C E O F O B L I Q U I T O F S T R E A MA N D O F S H A F T
O N O F A S C R E W PR O P L L E R .
t h e sh a t t h e di r ec t io n o t h e st r ea m
ancearealldi f erent. Thisisi l lus-
ereA C representsthedirectionand
t h e sh i p re l at i e t o s ti l l wa t er B C t h e
hestreamre lati etothesame O F
t andOA thespeedanddirection
etotheship. Thenb thecomposi-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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B E T WE E N S H I P A N D PR O P L L E R . 221
onsitf o llowsthatB A representsthedirec-
reamre lati etotheship andB O that
tothebladeore lement. L etz > denote
streamre lati etostil lw aterasrepresented
e th e an gl e B C A b r . T he n a s in 3 3
w eenOG andthenormalON tothe
nationo z / to thenormalisthen
9 c os ( a 7 7 i s th e co mp on en t o t / in t he
andhencetheve locit inthisdirec-
ssedonthe elementb thestream
i t h er e w er e n o sl i p. T h e re s ul t o t h is i n t he
w ou l d be a v e l o c it v 9 c o s ( a r ) s e c a.
a lve locit w ithoutslipinstil l
seca . Hencedenotingthetota l
t h er e w er e n o sl i p b ' , w e s h a ll h a e
a - - v 9 co s( a r ) s ec a
9 c os ( a 7 7 ) s e c a.
w iththesha tatanangleew iththe
h e an g le f i f o r a g i e n e le me n t is c o ns t an t
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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B E TW E E N S H I P A N D PR O P L L E R . 22
hisdi f erence isreadil putinthe
teform:
r
e v a l ue s o A S a n d he n ce o A s
e su r a c e o t h e bl a de a n d he n ce t h e en t ir e
wi l l v a r f r o m po i nt t o p oi n t o e r t he
eposit iontoanotherinthere o lution.
eo slip2A S isseentoincreasewith
ev a lueo A S w illcontinuousl
o thee lementf romthehuboutw ard.
6mustbe countedisseenf romthe
ns. Theoriginf oristheprositonf or
# ; a n d s i nc e V Q i s s m al l u w i ll d e pe n d
d wi l l r ea c h it s m a i m u m v e r n e ar t h e po s i-
a imumorama imumorwhen
c e th e o p os i ti o n o i s r ea d il s e en t o b e
malisparalleltothe planedeter-
n d di r ec t io n o a d a n ce a n d in w h ic h
o ad ance lieonoppositesideso
thestarboardturningtotheright
letthesha tsinclineoutw ardf rom
su a ll f i t te d .T h en i t f o l lo ws f r o m th e
bladeo eachpropellertheslipisma i-
onand minimumnearitslowest.
ght-handpropellerandthesha tinclined
n blade isma imumw henit ishori-
heright andminimumw henhori-
he le t. Withright-andle t-hand
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
e n ot ed t he e f e ct o t he o bl i u it o t he
r in c re a se d b t h e na t ur a l ob l i u i t o t h e
e f o llow thecontouro theship thus
streamre lati etostil lw atersomew hat
. I n c li n at i on o t h e sh a t s i n th e o pp o si t e
orrectthevariabilit o theslipdue
romstructura lreasonsthisisrarel
theprecedingsectionthe in luence
thew ak eonslip andinthepresehtsec-
o b li u i t , a s su m in g t hu s f a r a u n i o r m
ningthese in luencesw esha lle i-
i e n c as e v a r i at i on s o s l i p o e r t he
tthere o lutionrangingthroughlim its
butprobabl asw ideasf romoora
or75percentormore. We sha llha e
lit notedin41 42 w ithanadded
. A s n o te d i n 41 h o we e r m o st
nbetw eennarrow erranges butdue
he s e ma b e c on s id e ra b le . I t b e co me s
importanceto in uiretow hate tent
m a b e i n a l id a te d b t h e e i s te n ce o
ip .
F TH E W A K E A N D I T V A R I A B I L I T O N T H E
O F 36.
n l u en c e o t h e v a r i ab i li t o t h e
c .
t e th e e f i c ie n ci e s o t h e v a r io u s
pre iousnomenclatureweshall
rope ller
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E T WE E N S H I P A N DPR O P L L E R .
o ^ v a r ie s b a l i ne a r la w wi t h sl i p f o r
n w e s ha l l ha e
ie n c d o es n o t ac t ua l l v a r b a l i ne a r
mosto thew ork isdonebetw eena
ge o v a r ia t io n o s l ip t h e v a r i at i on o
b e a pp r o i m at e l e p r es s ed b s u ch a l a w.
c in( 2 isthenseento bethatcorre-
pasde inedin42( & ) . Theactua l
so me w ha t l es s t ha n t ha t g i e n b ( 2 , a n d
hise uationsimpl indicatesthe
w hichnogreatlosso e f icienc
a b le s l ip v i . t h at m o st o t h e wo r k
mparati e l narrow rangeo slip
t b thee perimentso R .E .
considerthatthe latterconstitutereall
ptionsre lati e tothew ake. These
ariablewakema beconsid-
a lenttoasingleuni ormw ake andthat
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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B E T WE E N S H I P A N D PR O P L L E R . 227
n ce m a p l a b u t it s v a l u e i s be l ie e d
e e n t in d e a u lt o s u f i c ie n tl
nw earecompelledtoassumeitsin lu-
ualpoint wherethein luenceo
o w ak etouchesourmethodso
e on e f i c ie n c t o w hi c h re e r en c e ha s
parto thepresentsection.
l assumeina llcases fortheactua l
bstitutionw ithoutchangeine f icienc ,
o v e l oc i t z / , t h e a m ou n t o t h i s v e l o ci t
a l en c e o t h ru s ts a s p re i o us l e -
uv \ thespeedo ad anceo thepro-
boutthe stern.Whence
w e ha e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
t he i n l u en c e o t h e un i o r m wa k e
r u s e u l w or k a nd e f i c ie n c i n 3 6 ( 2
ttheuse ulw ork mustbeobta ined
u st b t h e sp e ed o t h e sh i p re l at i e t o
( i s ^ p N . I n a l l ot h er p l ac e s
entersintothesee pressionsitw il lbe
w esha llha e insuchcase
s ^ y \ a sB - f C ) d A ;
\ a sB + f E } d A .
illgi eanapparente f icienc .
must o course bethatf orthepropeller
Thepresenceo thew akecannot
c o t h e pr o pe l le r i ts e l , w h il e i t ma
use ulresultU . The increase inU
akeratherthantothepropeller.
e erredtoin46. F orthese
o U toW anapparentratherthan
ie n c . T h is w e ma d e no t e b e l t w hi l e
w h ic h w e wi l l de n ot e b e t w i ll h a e t h e
( 4 . H e n ce w eh a e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E T WE E N S H I P A N DPR O P L L E R .
T O N O F R E S I S T A N C E DU E T O A C T O N O F
on s id e re d t he i n l u en c e o t h e sh i p
tproduces ontheactiono the
tothe in luenceo thepropelleron
hip.
37consideredtheactiono thepro-
onto itse l ade ecto pressureand
thetotalaccelerationproduced
onreachesthepropelleritsel . This
sforthemostpartduetothecentri uga l
pntherotationo theraceb thepro-
identl begreaterastheblades
reanda t andhenceasthepitch- ratio is
pressurew ill inter ereseriousl w ith
tion.Thewaterinsteado being
ternandf ormthenatura lsternw a e
bedanddrawnaw a tothepro-
sisadiminutiono thepressure
istaboutthesterni theshipw ere
. Theresulto thisis o course
to resistancetobeo ercomeb
ncreasewhenv iewedf romthe
ancema betermedtheaugmentor
nce.
eusedasthepropellingagent a
periencedthoughitarisesf romsome-
s. Theactiono thepaddle-wheelsat
midshipsgi esrisetoaraceo w ater
etotheshipthanw ouldbethecase i
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D PR O P U L S I O N O F S H I P .
Theresult isanincreasein the
heelsa lsoundoubtedl e ercisea
thenatura lstream- linemotion and
uceanadditiona le lementintothe
nce.Theamounto augmentation
notbeenase tensi e l determined
orscrew propellers butvariouse peri-
R . E . F r o u d e a n d Me s sr s . De n n
uchdi f erinamountf romthatf or
econditions o speed.
S O F TH E P O WE R N E C E S S A R Y F O R P R O PU L S I O N .
horse-pow er
sorbedb thef rict iono theengine
a n a t ta c he d p um p s.
ppowerdeli eredtopropeller.
c es s ar t h ru s t s u pp o si n g th e s hi p t ow e d
T- -theamounto aug-
f ecti ehorse-power andTuiscalled
eratio~ iscalledthepropul-
muchmorede initel relatedto
c , h a s un o r tu n at e l r e ce i e d n o sp e ci a l
tnguishitasthecoe f icient// .
h e ap p ar e nt p r op e ll e r e f i c ie n c i s
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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B E T WE E N S H I P A N D PR O P L L E R . 231
opellere f icienc is
theultimatetesto theper ormanceo
impl asapropeller. I t isgi ena
k W p. Work inginundisturbedw ater
a = ( v u + z > ) , i t w o u ld d e e l op t h e
an a mo un t o w or k T v 5 ) =
um e ra t or o e t a b o e .
w e c on s id e r th e p ro p el l er s i mp l a s a m ea n s
ughthew ater theuse ulw ork willbe
mountwhichwouldbere uiredtotow
TheratioTu- -W pisthere ore
a lueo thepropellerasameanso
ship. I f theshipproducednow ak e
mentationo resistance thisratio
at i o e = T u v } - W p w o u ld b e t he
enthem there ore in o l esthe
hipandpropeller. Theratioe press-
termedthehulle f icienc . We
n c '
u ll e f i c ie n c X t r u e pr o pe l le r e f i c ie n c .
T T 7~ - ^ = - = .- - = ( i + 2 / ,
7 /
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
isthusseento betheproducto two
- - ( u ^ ) . T he f i r st i s t he r a ti o o
dresistance orthereciprocalo
a u gm e nt a ti o n as a b o e d e i n ed . T hi s f a c to r
. E . F roudethe" Thrust-deduction
h o we e r p r e e r t o co n si d er i t a s t he
f iciento augmentation T -T -T . The
c to r a s s ee n i s t o de c re a se t h e hu l l e f i c ie n c
t t h er e o r e im pl i es a l o ss i n e f i c ie n c
resistance.
uv 9) ( i+ w , asalread
e c t o t h i s f a c t or a s s ee n i s t o
c ie n c in t h e ra t io ( i - - w . I t t h er e o r e
cienc duetothe locationo thepropeller
ado inundisturbedw ater. Thisga in
entobeduesimpl to thega ininthespeed
i thepropellerwerew ork inginundis-
re o lutionsandtrueslip5aand
t h e sp e ed o a d a n ce w o ul d b e ( v 5 2 ) .
uetothef actthatthew ak ewateris
speak tomeetthepropeller thesame
thaspeedo ad anceugreaterthan
sp e ed o t h e wa k e v 9 . H e n ce t h e tw o sp e ed s
d uv 9 , a nd t he ir r at io i s ( i - - w , a s
t h us c o ns t it u ti n g hu l l e f i c ie n c o n e is
eotherlessthanI . H encethe
seteachother andtheproductorthe
us ua ll n ot v a r w id el f r om I . I n f a ct
b R . E . F roudeindicatethatthehull
sua ll betak enasiw ithoutsensibleerror
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
edb theaugmentationo resistance.
sassumedasthesame withor
bdb thetrueortow edresistance inthe
ecti ehorse-power
bdb thetrueortow edresistance inthe
dpower re olutions thrust andre-
ncreasethespeedf rom( uv ) to
, a n d h e nc e t he u s e u l e f e c t in t h e
soillustratedas f ollows:
e f i c ie n t ;
f i c ie n c ;
o a u gm e nt a ti o n ;
w = w a ke -r et ur n f a c to r
ediagramo F ig. 66isnotappli-
thandwithoutw ak e f orthepower
andresistancearesupposedtoremain
eedchangesf rom( uv ) tou. The
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E T WE E N S H I P A N DPR O P L L E R .
we e r t o t he p e r o r ma n ce o t h e
wake undertheconditionsthat
andresistancesha llremainconstant and
tthetw ospeeds( u^ ) andusha ll
sistance.This isusuall themost
s i s a s i t se r e s t o co n ne c t th e p ro p el l er
ith thesamepropellerinundis-
pingatthesamere o lutionsandtrueslip
a s in F i g . 67 i ll us tr at e th e e f e ct o
patconstantspeed resistance and
butv ar ingre o lutionsandpower.
F d e no t e f o r t h e sh i p wi t h wa ke t h e
6 w h il e A ^ B ^ C f ^ E ^ d e no t e si m il a r
at thesamespeedandresistance
w errepresentedb C E iso
resentedb C J E ^ Thepropeller
a l po we r A E a r e h o we e r l e ss t h an
tsB lE landA ^ E ^ Thissa ingo
o l lo w s: A s s h o w n in 3 6 ( i t h ru s t
sandwithslip. Now i therewereno
t, thenecessar thrustw ouldbe
nnumbero re o lutions. Withthe
peed utheslipbecomesincreasedto
a nd t he r e o l u ti on s ne ce ss ar t o de e lo p th e
espondingl decreased. N ow w ithcon-
momentortor ue andhencethe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
es s ur e i n th e c l i nd e rs w i ll a l l r em a in v e r
ethepropellerhorse-pow erW pand
rW willv ar v er nearl asthe
h il e t he w o rk C E w i l l e u a l " , - , , t h e
lw ork A E w illbe lessrespecti e l than
v e r n e ar l i n t he s a me r a ti o a s th a t in w h ic h
ced. I nthisw a , then it isseenthat
kemakesitpossibleto obtainthe
opulsiono theshipwitha low er
sandw ithacorrespondingl decreased
sturbedwater.
tiono theship anditskinetic
energ w hichhasbeenputinto itb the
roughthew ater. Theenerg o the
romtheengine ormoreult imate l
a s t he s o ur c e o e n er g . T h er e du c -
erandf ue l-consumption asabo e
ere orebeconsideredasareturnf romthe
a t io n o a s ma l l pa r t o t h e en e rg w h ic h
tsf ormation.
ctionwilldependonthe relation
on s a n d sl i p a n d ca n no t b e e p r es s ed i n
( 1 4 a nd ( 1 6 , h ow e e r w e ha e
' ( - 34 + . 8 5 ) ,
rmsre latingtothegeometr o the
85 5 ( I )
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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B E T WE E N S H I P A N D PR O P L L E R . 237
on sisreadil determined andf orcon-
thisonN * isshownappro imatel
n c e f o l lo w s th e e f e c t on N a n d o n
n suppose j , = . 15andw = . 133.
, s9= .25 andf rom( i abo e
esthepropulsionwithoutthewake
elopmento about24percentmore
ase.
merica li l lustrationo theana l sis
ropellerin undisturbedwater
dgi ethesamethrustasobta ined
ercentapparentslip there o lutions
se.
= 1.151
. P. b e de no te d b
. . .. . . .
pellere f icienc
e r e f i c ie n c
+ w
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
a u gm e nt a ti o n be = 1 . 16 5
P= .575
.= .669
ie n t = . 5 7 5
= . 9 88
wstheresultso certaine peri-
tchtugboat. Duringthetrials
datthethrust-block b ah draulic
theva lueso theE . H. P . w eredeter-
periments.
1 0
"
.H .P.v arieswithincreaseo
a n d th a t o E . H . P . t oI . H . P . f r o m
thepropellerw as7. 63feet and
theslipvariedf romabout1. 5to19
propulsi ecoe f icientatlow
ndslipissomew hatabnormal but
hedataorto anincreasedv alue
nc atthesepointsdoesnotappear. The
sisava luableone anditma behoped
lgi eusman moreo thesame
o r O c t o be r 1 89 7 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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B E T WE E N S H I P A N D PR O P L L E R . 239
D TH R U S T.
uentl occursinengineeringlitera-
o l l o ws :
s=
dcorrespondtoanabsenceo
en c o i . T hi s i s a wh o ll i m po s si b le
tasit isconsideredcon enientf orthe
re lationships w ew illshow itsconnection
nquantit . L etC beanengine
h e e u a t i on
2 X s t ro ke i n f e e t
ti epressurereducedtothe L .P.c lin-
nedb thee uation
dthrustandreducedmeane f ec-
adil seenthatthere isaconstantratio
cethattheonei sinconstantpro-
cew ema rememberthatthe
aq uantit proportiona ltothe
ti epressure .
nothere pressionf orthere-
e p r es s ur e . L e t A l t A A t b e t he a r ea s
l i nd e rs o a t r ip l e- e p a ns i on e n gi n e A ,
he low-pressurec linder. L et/ t, p^
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D PR O P U L S I O N O F S H I P .
e a c tu a l me a n e f e c ti e p r es s ur e s in
ene identl
nd( 4 aree identl thesame.F or
ineso an numbero stagesthe
lies.F ortriple-e pansionengines
om160to180poundsabso lute or145
e re d uc e d me a n e f e c ti e p r es s ur e i s
0poundspers uare inch.
A P PA R E N T S L I P .
ke theapparentslipslandthetrue
e. Withthede elopmento the
etrueslipremainingthesame theappa-
mepoint isreachedwherean
onsismaintained.
= s > ( i s s ) w .
b o e s 9 r e ma i ns c o ns t an t a nd w
nuousl decrease. If w reachesasu f i-
lbecomeoandthennegati e . Thecondi-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E T WE E N S H I P A N DPR O P L L E R .
ossibilit orotherwiseo aoor
1 i s s im p l a q u e st i on o t h e po s si b il i t o r
a luee ua ltoorgreaterthanthisva lue
T h er e i s no i n he r en t r ea s on w h s u ch a w ak e
wh i t s ho u ld n o t be f o r me d b t h e
ughthew ater.
h o we e r d e si r ab l e o r i nd i ca t i e
f i c ie n c . I t i n di c at e s th e e i s te n ce o
ef o llowing:
a nd c on se u en tl a l ow e f i ci en c a s
c c u r e s a s i n 3 6 .
eship- resistancecorrespondingtothe
o t h is v e l oc i t .
t h e ap p ar e nt p r op e ll e r e f i c ie n c w i ll b e
c ie n c m a n e e r th e le s s be q u i t e l ow a n d
ono displacementw illnatura ll be
e r en t w a o e p r es s in g t he c o nd i ti o n o
em a t ak e 42 ( 2 . T hu s
S a < v 9 .
asimpl ingsimpl thatthepro-
urnishingthenecessar thrustwithatrue
s t ha n t he w ak e - e l o c it v . T hi s i & -
en t t o th e c on d it i on e p r es s ed i n ( i
p r ac t ic a l me t ho d s wi l l be g i e n f o r
ul i lan gi enprogramo condit ions.
wo- I dprobabl showoornega-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
e o r e si m pl t o f i a s o ne o t h e co n di -
e u a l to o r l es s t ha n t ha t g i e n b ( i ,
assha llbedeemedappropria te. Thus
a l u eo w i s v e r c o mm on l a b ou t . i .
w . 0 9 a n d a pr o pe l le r d es i gn e d to f u l i l
hatrueslipo f rom7to9percent
oorslightl negati eapparentslip.
be v e r l a rg e a nd w a st e u l a n d a s
teundesirable . Theseresultsinactua l
theassumptiono amuchlarger
. Theirmentionissimpl introduced
entirepossibil it andsigni icanceo
o t h e ap p ar e nt s l ip . W h i le t h er e o r e
seresultsisun uestionable it is how -
atman reportedcaseso negati eslip
orso measurement especia ll inthe
tthisbe thecasewithpropellerso
chthede init iono meanpitchisneces-
racter accordingasw emak eitpurel
t a d n a mi c al b a si s b g i i n g to t h e
weightproportionaltothe thrust
w ork w hichitabsorbs. Duetothis
haractero thede init iono meanpitch
ee pressionsmeanpitchandapparent
ni icancewhichw eareabletogi e
uni ormpitch. S eea lso42.
rcesonascrew-propellerblade re-
F igs. 64and85 indicatesf urther-
asmallposit i e thrustwithasmall
uredw ithre erencetothef ace. The
, h o w e e r m u s t a lw a s b e p os i ti e .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
as t h e s u a re o t h e sp e ed o r t ha t t he
, a nd K - - L = e a r e in de pe nd en t o a ct ua l
mpl f unctionso pitch- ratioandslip.
e n c , a s a ti s a c to r g e ne r al c o rr e sp o nd -
esf ormodele perimentsandactua l
iedtob numerouscomparisons. I n
undthatthegenera lshapeo the
a s s ho w n in F i g . 60 i s c ha r ac t er i st i c o t h e
ll- si edpropellers. A ccordingtoMr.
s w e ma d e pe n d sa e l o n t he g e ne r al
i c ie n c d a ta a n d on t h e v a l ue s t he ms e l e s
w h il e a bs o lu t el t h e m a i n o l e a
ma s a e l d e pe n d on t h e e p e ri -
orrectl thegenera lcondit ionsf or
a nd h ow t he e f i ci en c w il l v a r f o r gi e n
slip w hile therema beslight
es o t h e e f i c ie n c i t s e l . I n a n c a se
presumabl small ande perienceseems
bequitesa e inusingthesedata at
othedesirablerangeo v a lueso
hinw hichtow ork inan gi encaseo
bein ol edinpassingf romthe
dpropellerareo threek inds:
meter andhence ina llo therdimensions
- r at i o h = A - . ;
e o b l ad e .
o r a ll o t h es e m ig h t be i n o l e d .
tingtoe f icienc impl onl change
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
calsim ilarit betweenthemodelandthe
emainta ined. H enceonl under
utso themodele perimentsstrict l
r ia t io n s ( 2 a n d ( 3 e n te r i n to a g r ea t er
euseo theseresultsmustbeattended
easingdegreeo accurac andcon i-
o we e r a g r ea t c on e n ie n ce i w e
o introducingw ithinmoderate lim its
, o r m or e e sp e ci a ll t h e f o r m er . N o w
tion intothedeta ilso w hichwew ill
sthatthevaria tiono e f icienc w ith
( 3 i s v e r s l ow a n d he n ce t h at w e ma
uchchangesinmoderatedegreewith-
tn g th e e f i c ie n c .
eo A Tin36 ( ii , wenotethat
clratiosandthetw ocoe f icientsaandf .
e e f e ct o c ha ng es ( i , ( 2 , a n d ( 3 o n
between/andtheskin-resistance
itw ouldseemprobablethatitw ouldbe
e c te d b c h an g e ( i , a n d he n ce t h at i t
orrectionsim ilartothatf orlength as
hedata f orsuchcorrectiondo
ndicationsasarea a ilable indicatethatit
f st i l l lessimportancearethee f ects
.
athecase isb nomeansthesame.
a irl ma , thatso longasproportionand
thetota lnormalresistancevariesasthe
o t h e sp e ed i t f o l lo w s th a t a ma b e
o change( i . I tsv aria tionw ith
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
a l li n g o o t h ru s t wi t h e c e ss i e
ustobtainablef orgi endiameter
andslipisthatcorrespondingtothef or-
edacompletecolumn; thatis aco l-
eachparthasrece i edthef ullacce ler-
etrica ll per ectaction thepropeller
. Theamounto thisma imumthrust
asfo llow s:
i t i s sh o wn t h at t h e v a l ue o t h e
sgi enb
S i c o s 2 a = / T V c os 3 a.
thetotalco lumnconsistingo a
cknessdr mo ingw iththisacceleration
ersecondX acce lerationE G.
o f e ed X E G .
ct o f e e d as r e pr e se n te d b D G
a n ce D - - t h e ac c el e ra t io n E G . T h e
a n d f o u nd i n 4 2 as s um e s th e a ng l e C A E
mptionw ema a lsoput
S 9 s in a = s ^ N s in a .
a ;
o r s 9 , w e ha e
a i s si na .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
a n d d = 2 r = p . M a ki n g th e se
g w ef ind
propellerthema imumidea lthrust
ntegrationo thise pressionbetw een
. Thisisseentobeentirel independ-
bladeorareao itssur ace. Thethrust
ema imumpossibleonthesupposi-
correspondtotheper ectactiono
heabsenceo sk in-resistance. I t is
couldbeobta inedinan actualcase no
o sur ace.
theva lueo a isconstant C ot-
e e p r es s io n f o r d T to f i n d th e
sar to f ormacompleteco lumnat
j / . T hi s w as d o ne b e u a ti n g th e t hr u st
m s im i la r t o 35 ( 6 , o m it t in g / an d
1. 7 f o r a a n d so l i n g f o r d A . S i n ce
ue i s n ot a c cu r at e f o r a a n d si n ce m o re -
inconstantbutmustf a llo f inmarked
eo area theresultsthusfoundcan
oughappro imationstothe low er
w emustgo inordertoapproachthe
ondit ion. Sof arasthese indications
e s h ow ed t h at p r op e ll e rs o o r di n ar p r o-
mpleteco lumns andhencedonot
hrustcorrespondingtothe irdiameter
t e o N a a l A r c h i te c ts v o l . x x . p . 1 52 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
n d sl i p. T h is i n st e ad o b e in g a f a u l t i s
f orit isv er surethatapropellerw ork -
thethrustw ouldbe lesse f icient
ndthrustw ere less a llo thercondit ions
arisesf romthef actthatthe last
ustbeobta inedb theaddit iono a
sur acew ithitsaccompan ing
esult inanincreaseo / re lati e to
n g lo ss i n e f i ci en c ( 3 6 ( 4 ) . H e n ce
gi ea largethrustf oritsdiame-
d re o l ut i on s t h e pr o po r ti o n o u s e u l t o
ti e l poor.
e p r es s io n f o r t h e t hr u st i n ( i .
u n ct i on o y b e tw ee n v a r i o us v a l u e s o t h e
a lueso thema imumidea lthrust
ro correspondingpitch- ratios. A
ththev a luesactua ll obta inedb e -
ndit ionso diameter pitch re o lu-
o interest.
f ectedb appro imatemethods
nb C D F ig. 68. Theseareplotted
umidea lthrustintonsf orprope llers
at100re o lutionsand20percentslip
u es o t h e pi t ch - ra t io a s g i e n o n th e a i s o
B ' mthesamediagramgi essim ilarl
hethrustasderi edf orthesamecondi-
se perimenta lmodels assuminggeomet-
r egi esthere oretheactua lthrusts
easabo e ando area- ratioh= . 36.
thesliptheresultsw ereentire l sim ilar
learl thatthepropellero usua l
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
mde elopingthema imumidea lthrust.
hrustsisshownb thecur eE F .
ia ll use ultok now the law con-
stw ithh. U n ortunate l the in or-
e r s c an t . R . E . F r o u d e gi e s a s
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
d . 6 5 . 8 65 I . I n F i g . 6 8 t he r e la -
ealma imumforpitch- ratio1. 3isseento
d o f a s t he l i ne C D . W e h a e
Q , a nd R a s e p e r im en ta l po in ts w it h C D a s
ll im itbeingslightl less. Thecon-
hevaria tiono thrustw ithhmust
as O P Q R S .
tioasimilarcur emustpass
ak ethethrustf orh. . 36asre la-
gintheupperlim itsf orpitch- ratio2
B a n d E F . W h i l e th e d at a o n wh i ch w e
eagre itseemstobeaf a irconclusion
eseva lueso thepitch-ratiow illbe
O G T w i th i n te r me d ia t e cu r e s f o r
thepitch- ratio .
adehereo thee perimentso
ttheresultso w hichindicateagenera l
conclusionsw eha ej ustdrawn.
F ig. 69itw ouldf o llow thatw ith
h- ratio thethrustincreasesnearl as
greaterv a lueo hthanw ithlow
beringthatwithpresentpracticeh
een. 35and. 45 it isseenthatare la -
ismuchmoreadmissibleonapropeller
nononeo low andthatinthe latter
n e s ti g at i on o t h e in l u en c e o t h e am o un t o s u r-
anceo screw propellersisnow beingcarriedonb the
w hi c h s o f a r a s de t er m in e d j u s ti y t h es e g en e ra l
ependentl o thee perimentalw ork . F orapre-
thew ork re erencema bemadetotheTransac-
o N a a l A r c h i te c ts a n d Ma r in e E n g i n ee r s v o l . v .
C oastI nstituteo E ngineersandShip-builders
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
tw here increaseo areaw illgi e
ncreaseo thrust. Theseconclusions
e indicationso actuale perience
ndinconnectionwiththe proper
dthatthere isver l itt lee peri-
A T O
here lationsshow ninF ig. 69 and
nattempttoe pressthea a ilable
r e e r en c e to a n i de a l ma i m um w hi c h ma
tiono thecondit ionso operationo
hegenera lnatureo thevaria tion
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
w or k a n d he n ce o t h e co e f i c ie n t a w i t h
dso changew ithwhichw ema be
romthemodeltothef ull- si edpropeller
( i a n d ( 2 . F r o m th e p re c ed i ng
thatthechangeo aw ith/ / andits
hrustanduse ulw ork ispresumabl the
ce andtheonl onef orw hichwesha ll
e rr in g to 3 6 ( 1 0 a nd ( 1 1 , i t is s ee n
ui a lenttoachangeinthev a lueo
theva lueso w hichshouldgraduall
thuscorrespondingtothedecreasing
rustw itharea. I nsteado attempting
toninK asaf unctiono pitch- ratioand
esentitsratio tothestandardva lue or
b a f a ct or m .W e h a e t he n i ns te ad o
* k lm ( 2
pendonh andpitch-ratio.I f
, a n d ( 2 b e co m es t h e sa me a s
pondingthustothegenera lcondit iono
etweenthemodelandthepropeller.
en a v a l u e f o r m m us t b e se l ec t ed h a i n g in
sindicatedinF ig. 69. I t ise ident
lueso marerepresentedb theordinates
P , e t c . H e n ce b i n sp e ct i on a v a l u e
sha llappro imatel correspondtothe
tch- ratioandh.
notedthatasheretreatedthe
ero bladesdoesnotdirectl enter.
rminedb theareaandnotb the
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
meattentionmust o course bepa id
tweenlengthandbreadth o
ethefundamenta ll contro ll ingfeature .
ndthef o llowingasa eguide:
15to .25 2bladesma beused
t he e f e c t du e t o ch a ng e ( 3 a
theblade. Thee f ectarisesherenot
b u t f r o m a c ha n ge i n t he f o r m o d A
enelementv ariessensibl asthe
a n d he n ce f o r g i e n r e o l ut i on s a s t h e
encetheentirethrustw illv ar
tiono eachelemento areamultiplied
s ra d iu s o r a s th e m om e nt o i n er t ia o t h e
s. Denotethismomentf oran
andf oranotherbladeo e ua lareabut
/ . T he n t he f o r m o b l ad e b ei n g th e o nl
enthetwopropellers weshould
eso thethrustw ouldbesensibl inthe
i nc e t he a r ea s a re e u a l i n t he r a ti o o t h e
g r a ti o n. I t s h ou l d be r e me mb e re d
simpl topro idef ortheresultso
ecoe f icientmbeingintendedtopro ide
h an g e in a r ea . A c h an g e o f o r m h o w-
geo area incerta inpartso theblade
angeintheva lueo thecoe f icient
eparture intheva lueo thethrust
othemomento inertiaors uareo
n.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
no thispo intseemsto indicate
rorshouldnotbesensibleso longasthe
goro a linf orm w hile i dist inctl
ctualgaininthrust willbesome-
atedb theratioo themomentso
rd l j u s ti i e d m o r e o e r i n e t e nd -
d a ta t o b la d es o t h is f o r m ; s o t ha t i t ma
limitationthat thebladesto
ndmethodsaretobe appliedshould
o n g or o a l f o r m a n d t ha t i t h e a r e
l w iththebroadendatthetip theuse
lbeattendedw ithmoreuncerta int .
nestimatere lati e tosuchbladeshas
eanso moredirectcomparisonare
there lationsindicatedw illprobabl
eobtainableunderthecircumstances
ef orcesandw ork in o l edbeingprob-
rthanthosegi enb theestimate. I n
icationso theseformulae madeunder
f o r t he p u rp o se o a n al z i n g th e p er -
ers the w ereappliedtoa llv arietieso
o e tremeproportion. Thegenera l
denceandtheconsistenc o theresults
hadbeenanticipated and sof aras
ated thesef ormulaeandmethods
urnishasatis actor degreeo accurac
oses.
isin luenceduetov aria tionin
ns l e t
P :~ * '
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
rationo thebladeareaaboutthe
m a b e d et e rm i ne d b a n a pp r o i m at e
Theva lueo / is e identl repre-
tradiusr. Theappro imate
n g i e n b la d e ma b e o bt a in e d in t h e
o llowingf orm re erringtothepro-
esthef ractionso theentire
sb aremeasured.Thene t
areso theseva lues. Thethirdco lumn
thebladeatthecorrespondingradia l
columngi estheproductsbr , w hich
hetrape o ida lruleassu f icientl
e inv iew . Theco lumnissummed and
sumo theendva luesissubtracted
02. Thisquantit isproportiona lto /
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
g a s i s re a di l s e en r s - ~ 1 0 w he n ce
determinedf romcolumn3b a
heomittedf actorherebeingr-7-10.
emorecon enienttousetheratio
7 . I n t h is c a se t h er e o r e w e ha e
gw eshouldf indf oran e ll iptica l
t i esi eo hub
. .. .. ( 3
4
_ = 1 . 0 4.
3 and( 4 arethesamef oran ellip-
w hatthesur ace-ratio pro idedthe
hato thepropeller. Denotetheratio
x . T h en f o r o th e r v a l u es o x t h e
o r mu l a wi l l gi e v e r c l os e l t h e v a l ue s
l ad e s in t e rm s o t h at f o r x = . 2 a s
. .. .. . ( 5
o r m p 2 ma b e f o u n d b a n i nt e gr a -
abo e andithusdetermined.
show naserieso bladeso thesame
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN . 2 $
. 2 b ut o v a r i ng f o rm w it h th ei r v a l ue s
stratetherelationo ito f ormf or
andw illa idinmak inganestimateo
thedetailedcomputation.
o re t he f a ct or i i nt o ( 2 , w e ha e
\ i klw ( 6
ck n es s o B l a d e s. O n t h i s s ub e c t bu t
a ilable . Wek now ingenera lthatan
w ill increase/ andhencedecrease
. D a ta h o we e r a r e la c ki n g f o r a
o t h e am o un t o s u ch i n l u en c e. S o
tunusualtheresultsshouldnot
ia tionduetothiscause andw eshall
hisin luence. Weshouldremember
inginthick nessso longasrigidit andthe
notsacri icedisa lwa sdesirableon
en c .
E MA R K S .
e( 6 t o ge t he r w it h t he e u a ti o ns
el a ti n g to m k a n d / a n d th e e f i c i en c
din36andshow ninF igs. 58or71
af orprope llerdesign.
cationo thesedatatoactua lcases
uschangesdesignatedundertheheadings
3 , a nd e sp ec i al l t ho se w ho se e f e ct s ar e re pr es en te d
i a n d ; ; / t h e as s um p ti o ns u s ed h a e b e en
tenth pothetical andthee perimen-
ationo theva lueso thesecoe f icients
r m e ag e r. I f , h o we e r t h e ad m is s ib l e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
, thatis tochangesindimension
shapeo bladeandarea- ratio thenmand
mpl reproduceF roude se perimenta l
aserieso propellers.Thegeneral
esultsgi enb inte ll igentuseo the
w ithsuccess ule perience indicates
edw ithahighdegreeo con idence in
tinan e entitw il lbemuchbetter
nbetw eentheresultso e periment
thedatama beca lledinq uestion or
hin o l esa lessdeta iledana l sisand
d f e r en t v a r i a bl e s in o l e d i n th e
no thecoe f icientsmandiinto
urposeo pro idingagreatere lasticit
mandarea- ratio w ithoutaseriouslosso
eundoubtedl themethodma be
encew henf ormandarea- ratioarecon-
themodelprope llers y etf or
mountinthesef eaturesthee f ectsmust
r es e nt e d b t h e c o e f i c i en t s i an d ; ; / a s
sdeparturef romre liableresultsw illbe
nan e entw herere liabledataf rom
suchcasesisnota a ilable this
urnishthemostre liableresultstobe
stances.
m o re f u l l b i l l us t ra t i e e a m pl e s
nottaketheplaceo j udgmentand
asthemethoditse l isconcerned there
itenumbero propellers eachmoreor
il l ingthecondit ionsimposed andinthe
hesef ullscopema bef oundforthe
P u b l i c D o m a i n
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C E A N D P R O PU L S I O N O F S H I P .
e n se l ec t o r as s um e t he t r ue e f i c ie n c
ork ore lsef i thetrueslipand
rdeterminethee f icienc . Then
s e f i ci en c g i e s C ^ , t he u se u l wo rk
ormula . A ga in itma arisethat
P. w e h a e t h e E . H . P . o r a ss u me t h e
ie n t a n d th u s pa s s f r o m A E t o C F d i re c t.
hulle f icienc = C tE , theuse ul
a lread noted unlessspecia lin ormation
e f i c i en c i s u su a ll t a ke n a s un i t .
mn e th e v a l u e o p N .
s. Then
eetperminute.
,
w ( l - s ) .
oranestimateo thewake
at e l t h e in o r ma t io n a a i la b le a s a b as i s
er meager. F roudeinconnectionwith
re iousl re erredtogi esaseries
o v a r io u s ch a ra c te r is t ic s a n d be o n d th i s
nisa a ilable inthegenera ll iteratureo
otheseaf ew otherk now nvalues
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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D S I G N .
sconnectedthemw iththecharacter-
mpirica lf ormulae asf o llows:
ctor
r ic a l co e f i c ie n t
o n co e f i c ie n t
f o r s in g le - sc r ew s h ip s
f o r t wi n -s c re w s hi p s.
entsimpl thea ailabledata and
ager caremustbee ercisedinthe ir
ormationisotherwiseobtainable
pr o ba b l s e r e t o g i e a f a i r ap p ro i m a-
d.F urthersuggestionsonthispoint
thersre latingtothecho iceo v a lues
nt i ti e s in o l e d w il l b e gi e n i n th e f o l -
ow w ithoutmoredela , i l lustrate
ormulae diagrams andtablesto
e ct e d f o r m f o r c on e n ie n ce t h e
chwema ha eoccasiontouse:
o N a a l A r c h i te c ts a n d Ma r in e E n g i n ee r s
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
8 ' ) ; .
r si ng le s cr ew -s hi ps ( 9
1 . I f f o r tw in -s cr ew s hi ps ; . ( 1 0
o F i g . 69 p . 2 53
putationorb j udgment
8 1 a n d 49 ( 5 .
ando 101.32^ ma alsobetakenf rom
I I , f orthev alueso slip pitch-ratio and
interpo lationf orintermediateva lues.
L U E S F O R F A C TO R k.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
A L U E S F O R F A C TO R /.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
1.71.81.92.0 2.12.22.32.42.5
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
e a m pl e l et u s t ak e
pe r c en t = 5 98 H . P . ( A B , F i g . 70 .
H . P . ( B E , F i g . 7 0 .
gi ensupposew f oundorestimated
ct. 26astheproposedva lueo the
h e n f i n d f r o m ( 6
= . 1 56 .
/ no r T V f i e d w e ma p r oc e ed a s
le c t a pi t ch - ra t io o , l e t us s a , c = 1 . 26 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P ,
s problemthatthebladesare
to . 36 sothatbothiandmare I .
a n d F i g . 71 w e th e n f i n d
X 4 00 2 = 27 21 ( C , E , F i g . 70 .
e
2 X . 1 97 X . 6 2 4
i ti o ns r e ma i n th e s am e a s ab o e e c e pt
etthearea-ratiobe.48and the
1. 03. F romF ig. 69itappears
o ut I . . H e n c e we h a e
2 X 1 . 03 X . 1 9 7 X . 6 24 X 1 . 1 ;
th e s am e d at a a s in ( a w e f i b o th
roposetof indthenecessar shape
area. Thuslet/ = 24f eetand
th t h e sa m e v a l ue o p N w e f i n d
1 .3 3 a n d we h a e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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D S I GN .
re
n g f o r t h e co m bi n ed f a c to r ( t i n w e
. 5 82
withanellipticalblade o area-ratio
ratioo .36andshapesimilarto
esiredcombinationo thetw ofeatures
theproductimsha lle ua l1. 03.
e d at a as i n ( a , l et u s f i N a t n o.
ueo pN weha e
17. 5.
ortria ladiametero 16f eet. Then
re
m a s in ( c , w e h a e
. 739
rea-ratiooraslightf i l l ingouto the
o t h e bl a de w i ll t h er e o r e f u l i l t he
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D PR O P U L S I O N O F S H I P .
consideredha ebeenimplicitl
urblades. To il lustratetheapplication
ropellerso tw oorthreebladesw ema
50 00
4 3 50
5 .0 3 .
o= 1.4
weha e
. 5 4 4 x . 9 2 =
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN . 273
tw o-bladedpropellerw ema tak ethe
6 .8
= 9. 21 .
o= i.i
weha e
- 7 3 9 X . 7 2
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
l lustrationo specia ldesignletustak e
f thedesignisbasedonthecondi-
atura ll tak ethespeedlow andthe
2 4 9
1 0 .9 1.
.2;
) ;
t en si on o F i g .7 1 ;
e
2 5 4. - 6 63
ol edma besomewhatgeneral-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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E A N D rR O PU L S l O N O F S H I P .
p l ot t ed t h e v a l u es o ' - o n p it c h-
c u r e f o r c on s ta n t v a l ue o s ^ a s
e oresimpl to tak eonthisdiagram
thegi env a lueo pitch- ratioand
o t h is p o in t r el a ti e t o t he c u r e s f o r
ow thecorrespondingva lueo s9.
takingthedatao ( a e ceptst andwt
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
npitch- ratio1. 26wef ind. 26as.
heslip correspondingtotheva lue
. B y s u bs t it u ti o n in ( 6 w e t he n f i n d
m F i g . 7 1 r a = . 6 8 .
pl e w em a t a ke t h e f o l l ow i ng d a ta
serDetroit:
eanresultsf orthetw opropellers:
enat14percent.
1 . 09 x . 6 7 7 x . 9 = * 2 5 5 "
cef indst = . 215.
1 . 09 3
= . 6 88 .
onsinthismannerin alargenumber
derthedirectiono theauthor
atdi f iculttosatis actoril determine
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
msuchana l sisa lone. Thisisnotso
inthee uationsastothef actthata
hedataw illmak eare lati e l much
o i . Thisarisesf romthefactthat
er m in e d f r o m t he q u a nt i t ( i - - w .
erateamountinthedataorinthesuit-
to ns t o t he d a ta m i gh t g i e f o r e a m pl e
en t i n th e v a l u e o ( i - - z v ) , m ak i ng
a lue1. 12w henitshouldbe i.io . This
en c e o . 0 2 in w o r a n er r or o 2 0 p er
e tr u e v a l ue . S o f a r a s or d in a r a p pl i ca -
w e er andespeciall so f arasthe
o l e d i t is t he f a ct or ( \ - - w a nd
dhencechangeso re lati e l la rge
il lha ecomparati e l smallin lu-
suchproblems. I tma bea lsomen-
theva lueso w determinedin
e n b e u a ti o ns ( 9 a n d ( 1 0 a n d
ow edinnearl a llcasesthatadi f er-
en t i n th e f r i ct i on o t h e en g in e o r m or e
s m al l a mo u nt i n t he p i tc h o t h e pr o -
i c ie n t to a c co u nt f o r t he d i f e r en c e in t h e
certa int astotherea lva lueo the
ablepitchhasbeenconsideredin42;
inmindas wellasthepossibilitieso
ementina llcases andthef urther
ngine- rict ion itw ouldappearthat
lmentiscloserthanmightnatura ll ha e
hatf orproblemso designthee uations
sedwithahighdegreeo con idence
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
correctestimateo winaproblemo
edb thef o llowinge ample:
a a b o e s u pp o se . 1 4 t o be t h e co r re c t
t itsestimatedva luebetak enas. 09. Then
a lueo s^ w esha llha e
oughasin( a , weshouldf indthe
n d i n ( a .
acceptedandthe propellerf itted
henask tw oquestions: ( i Whatw ill
cienc andw hatthepowernecessar at
6 k no t s o r ( 2 W h a t w il l b e th e r e-
wer4002isde li eredtothepropeller
speedo 16k notsatta inedw itha
2 72 1 a s i n ( a . W e t he n ha e b s ub st it ut io n
N ' ) a n d k a r e bo t h un kn o wn b u t bo t h
e s ol i n g w e h a e
158 2.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
a p r oc e ss o t r ia l a v a l u e o J 3 s u e
s o k a n d p N ' ( u s in g o c o ur s e th e
w il l gi e f o r ( p N ' ) * f c t he v a l ue 1 58 2 o r
l os e a pp r o i m at i on t o s uc h v a l u e . F o r t he
i n ( a w e ha e k = . 19 7 an d ( p N ' ) *
' ^ k 1 3 9 9. T h e v a l ue 1 5 82 r e -
a lueo s^ largerthan. 26 andoneortw o
toshow thatthedesiredresult isv er near
p f N ' ) * k 1 58 7. W e ma t ak e t he re o re .
i g . 71 ,
ults there ore there o lutions
hanthe96. 1e pected thee f icienc
007 andtherew ouldbere uired41
sbut4002H. P . de li eredtothispro-
theresult ingspeed w eha ea
ritsso lutionaresistance-cur ef orthe
rposes how e er w ema assume
i c ie n c . 0 07 a n d th a t po w er v a r ie s a s th e
sw ouldgi e f ortheratioo thepower
ue
' l . oi = 1 . 0 0 3.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
risdesignedtow ork atornearitsma i-
omef urtherdiscussiono thesepo intsw ill
wingsection.
P rope llerDesign. Thef ormulaeand
oseapplicationsareshowninthepresent
a ll resultf romthegenera lmethod
opedinthisw ork . Thesameorigina ldata
s e p er im en ts m a b e us ed i n av a r i et o
d b F r o u de * B a r na b , f C a i rd \ a nd
beenlonginusea lsobrie erand
screw-propellerdesignthanthosein-
nsiderationsdiscussedinthe present
encetosuchmethodsma herebemade.
oundf romthegi enspeeduandan
e ap p ar e nt s l ip j , ( s e e ( 4 ) . T h ev a l ue s o
ctedb j udgment.
thenbef oundf romthef ormula
tak enbetw een18000and25000.
athisise ui a lenttotak ingtheva lue
/ m ( i a s co ns ta nt o r as su mi ng i ts v a l ue
enlimitscorrespondingtothosespeci ied
ut e o N a a l A r c h i te c ts v o l . x x v n . p . 25 0 .
ono C i i lE ngineers v o l. cir. p. 74.
uteo E ngineersandShipbuildersinS cotland
o N a a l A r c h i te c ts a n d Ma r in e E n g i n ee r s v o l .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
l f o u nd b e tw ee n 2 a nd 2 . 5 w h il e f o r
cra titma f a llto f rom1. 2to2.
berelatedtothe displacementD
o u nd b e tw e en . 8 a nd I . , w h il e f o r
cra titma f a llto f rom. 6to . 8.
thedisk areatotheshiptheresult
theareaf ora llthepropellers one
t te d . Th e v a l u e ma t h en b e d i i d ed a s
ameterimmediate l f ound.
ulaebrie l re erredtointhese
e ce s sa r il a l a rg e e le m en t o j u d gm e nt ,
f oritsorderl e ercise . The
n o p ro i s io n f o r e s t i ma t in g i n de t ai l t he
aria tionsinthedi f erentcharac-
r.W iththemoredetailedmethods
nthepresentc hapter therangeo
narrowed itsapplicationissimpler
ma d e f o r t h e or d er l e s ti m at e o t h e
ngesin themoreimportantchar-
S U GG S T O N S R E L A T N G TO T H E C H O I C E
I N TH E E Q U A T O N S F O R P R OP L L E R
D TO T HE Q U E S T O N O F N U M B E R A N D
F PR O P L L E R S .
precedingsectionthe I . H. P . is
undamentaldata . Thisimplicit l
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
er e i s mu c h co n l i ct i ng t e st i mo n , t h er e
dicatingina generalwa thesuit-
p it c h- r at i os f o r s hi p s o f u l l f o r m a n d o
hipso moderateandf inef orms. The
principa ll onthee f ectduetothe
ingmorepronouncedonaf ullthanon
ow theaugmentationincreasesin
andwiththe pitch-ratio.H ence
c t is c o nc e rn e d w e s ho u ld e p e ct t h e be s t
pitch-ratioandsmalldiameter and
e u a ti o n ( i , 5 0 a r e se e n to b e
ntheotherhand w ithv er f ullships
certainamounto deadoredd -
rope llerissosmallandsonearthestern
partinthisedd , itssuppl o w ater
rgular andthee f icienc w il lbe
ased. J udged there ore f romthis
pectthebestresultsf romapropeller
hestructura larrangementsw illa llow
f icienttoreachoutthroughtheedd ing
regularstream-linemotion.S uch
terw ouldnatura ll gow ithare lati e l
ethere ore inthiscase asin
hichw eha etodea l opposingcon-
ngasmalldiameterandthe othera
lue inan gi encasewillneces-
a lanceo theseconsiderations andf or
o ourin ormation nogenera lrule
in l u en c e o a v e r f u l l st e rn
ad e t o an e t r em e c as e i n st a nc e s o w h ic h
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
r. I ncasesw herethe in low o water
theactiono thepropellerma
enearl to thato acentri uga l
w aterw itha largeradia lortrans erse
htlongitudina lacce leration andthus
butslightgaino thrust. Thede ect
o t h e pr o pe l le r w il l h o we e r p r od u ce i n
e c t on t h e hu l l a n d in t h e e t r em e c as e
belessthanthesternwardresultant
ndthusthef ina lresultantf orceonthe
erthanf orw ard. I nsuchcasetheship
atterinw hatdirectionthepropeller
ebeenreported a lthough o course
wthusualf orms.
llers.Thisq uestionisonewhich
edesiredsubdi isiono thepower the
d th e d es i re d n um b er o r e o l ut i on s o t h e
ta lpow erismorethanitseemsdesir-
sha t andthustwoormoresha ts
d. Thisw asthecasew iththeU. S .
umbiaandMinneapolis inwhichit
meo the irdesigntosubdi idethe
ortransmissiontothepropellers.
se eralreasonsf oradoptingthis
chit occupiedaprominentplacein
eneralproblem.S imilarconsidera-
cean- linersde e lopingf rom20 000to
thesecasesitseemsdesirabletotransmit
sintw ounits andi therewereno
i ision it isdoubt uli underpresent
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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TA N C E A N D PR O PU L S I O N O F S H I P .
nsuchcasesthethermod namicand
esshouldbe impro ed. Thescrew snot
r aredragged andthisincreasesthe
sua ll increases especia ll w ith
r e su l t in a l o ss o p r op u ls i e e f i -
t h er e o r e i t h as b e en f o u nd b o th i n t hi s
thattheuseo oneortw oscrew sat
lt inincreasede f icienc . I na
oalre uiredfora gi enspeedwithone
how edbutslightv aria tion andthe
nappro imatee ui a lence in
N otw ithstandingthis triple-screw sha e
troducedintothepracticeo theGerman
lase lsew here thechie reasonsbeing
a llerandlowerengines smallercastings
betterstow ageo theenginesinthe
a s t sh i ps a n d ad a n ta g es a r is i ng i n t im e
pesubdi isiono thepow erandengine-
ono single -ormultiple -screwsthere
r d i f e r en c e in p r op e ll e r e f i c ie n c a l on e
risef romabetterpossiblese lectiono
or another.With theproper
properdesignthroughoutthereis
oespecia lad antageinprope ller
pectedoneitherhand andthatthecho ice
the considerationsdiscussedabo e.
s. The locationo apropeller
no augmentationo resistance onits
donv ariousstructuralconsiderations.
heaugmentationo resistance ismorepro-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
w ithaf inef orm andwiththe
lvar inmarkeddegreew iththedis-
romthestern-post. I nsuchcasesit
pe ller i single shouldbeatadistance
tlessthanonehal ortw othirdsits
ce isdecreasedf romaboutthis
w atertothepropellerbecomesmoreand
pete thethrustde e lopedbecomes
ndtheaugmentatione f ectbecomes
ed. Withv esselso moderateand
esee f ectsare lessnotable incharacter
gle isusua ll placeddirectl a to the
distanceasthenecessar structura l
enient. I ntorpedo-boats launches
risf re uentl droppedbelow thek eel
eda to therudder. Thisfa ors
w o w atertothepropeller andtendsto
resistance.
placedinthesameplaneand
hestern-post. I nsuchcasethea erage
isk o thescrew f orw ardtotheship ssur-
anw ithasingle-screw andtheaug-
e iscorrespondingl less. I nsome
ncut throughthedead-woodoppo-
etogi eanoutletatthispo int and
romtheperiodicshock tow hichit
thebladespassingv er nearthesur-
thescrew sha ebeenlocatedindi f erent
achw ithapertures andw iththe irdisks
antagescla imedaredecreaseddistance
hagi endiametero prope ller or
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N DPR O P U L S I O N O F S H I P .
endistancebetweenthesha ts
e er w hetherthef ina lresultsaresuch
ngementf orgeneraladoption.
ecenterone isusuall more
hoseatthesides thethreesha t-
trans erseplanef ormingatriangle
ecenterpropelleris alsonaturall
seattheside andw iththisdistribution
er erencebetweenthepropellers
e f i c ie n c i n a ct i on .
borne inmindthatthef arthera
mthesterno theshipthe lessin
ntaugmentationo resistance and
lereturnf romthewak e. I t ise ident
ngasthepropellerisatasu f icientdis-
oobta inagoodf low o w aterandto
eeo augmentationtherew illbe in
itsf artherremo al f orthe lossin
e t an f u r th e r ga i n b w a o a d e cr e as e
O N D T O N S A F F E C T N G TH E O P R A T O N O F
P L L E R S .
heapplicationo thee uationso
supposesthatthepropellerhas
o w hatissometimestermed" so lid
a te r w it h ou t s en s ib l e ad m i t u r e o a i r. I t
t h e de e c t o p r es s ur e w hi c h e i s ts i n
mf low ingtoandthroughthepro-
adesintheupperparto the irpath
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
aceo thew ater andmoreespecia ll i
ur ace thata irisdraw ndownand
heresult isamoreorlessf roth or
t h e de n si t o w h ic h i s mu c h le s s th a n th a t o
cethethrustforgi enre o lutionsand
orgi enthrustthere o lutionsandslip
thercasethee f icienc isgenera ll
pso thebladescomever nearthesur-
t h e lo s s in t h ru s t an d e f i c ie n c m a
ecia ll w ithlargepitch- ratioandhigh
n de r st o od t h at a l o ss o e f i c i en c i s
a ttendantonthew ork ingo apro-
hemeref actthatthetipso theblades
oractua ll cutit . Thew holeques-
perationo thepropellerisconcerned is
utanttrueslipatw hichitw orks. I t
ossibletodesignapropellerw ithblades
tw ithsu f icientdiametersothate en
dmi tureo a irthetrueslipw ould
f orgoode f icienc .
t o k ee p d ow n t he s i e o t h e pr o pe l le r
nw aterprac . ica ll f reef romair its
osenw ithre erencetothedra to
modi iedb thepossiblechangeo
hatthetipso thebladesw illa lw a s
perienceseemsto indicatethatthe
thetipso thebladesw hennearest
be lessthanabout. 2or. 3the
er. I naddit iontothe indraughto
there isa lw a sundernormalcondit ions
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
he ldinabsorptionb thew ater .
moreorlesscompletel abouttheedges
sinconse uenceo thepartia lvacua
nts. Thisw illgi eriseuna o idabl
oaminthewak e theconse uenceso
r e be l ie e d t o be i n se n si b l s m al l .
ttheStern. Mentionhasbeenmadeo
dingsection.
inaseaw a thebladesarecon-
g th e ir d i st a nc e s f r o m t he s u r a c e or a c tu a ll -
dthere o lutionsundergocorrespond-
pse tremev ariations unlessb some
g de i c e th e s up p l o s t ea m t o th e e ng i ne
v enatthebestthere o lutions and
e u e nt l v a r t h ro u gh v e r w i de r a ng e s.
a l so b e d ue p a rt l t o t he e f e c t o t h e
w atercomposingaw a e themo e-
hecrestanda tintheho llow . Such
o thepropelleraref a orabletothe
andthustoawasteo energ andloss
h er e i s i n ad d it i on a f u r th e r lo s s in e f i c i en c
slipthroughwhichthepropeller
ndicatedb F ig. 71 thatf orthebest
dworkat orcloseaboutasingle
tinv io lentracingtheslipf orthepro-
a r f r o m pe r ha p s a ne g at i e v a l ue t o
n mo r e. H a i n g re e r en c e to F i g .
asuchw idevaria tioninthev a lueo
c a us e a s er i ou s f a l li n g o i n t he a e r -
h e r t hi n gs b e in g e u a l t h e se e f e c ts w i ll
orereadil thepropeller-bladesare-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
andhencethenearerthe aretothesur-
n or m al t r im . W e h a e h e re t h er e o r e
rgoodimmersiono thepropellers. I t
a inoneo the irad antages the ir
ssibleimmersiongreaterthanf ora
sametotalpower.
e c t du e t o V e r H i g h P r op e ll e r V e l oc i -
h a s A B , F i g . 83 i s d ra wn t h ro u gh t h e
space immediate l in itsrearisren
onaccounto thetimere uiredfor
ndthemo ingblade. A tslow
illonl e tendslightl be low the
w h il e i t h e sp e ed i s s u f i c ie n tl g r ea t i t
mo theblade be ingshapedincon-
b B C D. Thevelocit inf eetper
ndstof lowintoanopenspace is
f o r m ul a v V 2 g /i . W h e re t h e sp a ce
n F i g . 8 3 h = s i mp l t h e he a d o
ample atthebottomo aboardimmersed
1 6 w hi le i t he d ep th i s I f o ot
a ce i s s hu t o f f r o m th e a ir a n d is a
/ = theheadduetotheatmosphericpressure
r or/ / = 34f eetplusdeptho
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
casethevacuumcannotbeper ect but
randsomeairgi eno f f romthe
cethev a luesforsuchcasew illbe less
mtheheadgi enabo e w hichmust
upperorlimitingv alue.
o t h e bl a de s o a p r op e ll e r is s u f i -
entthatsuchspacesw illbeformedat
courseentirel underw ater. When
ntinan markeddegreethewater
erisfoundtobecometurbulent
continuous andw ithf urtherincrease
aninthrustisv er slight.
nin estigatedb M.N ormand
edinlocationinsteado inf reeroute .
erwasabout6.5f eetandmeanpitch
thesha tw asmainta inedatf our
rom4. 8to3. 85f eet. Thecur escon-
lutionsareasshow ninF ig. 84 in
s uareo there o lutionsN, and
ntthrust.Theregularincreaseo
hedeepestimmersionisshow nb the
htlineOD. F orthe lightestimmersion
nsthethrustw asslightl greaterthan
sion butthedi f erencew asnotlarge
s uareo there o lutionsw as
ngabout135re o lutions howe er the
rustw ithre o lutionsbeganq uick l to
thispo intontherew asbutslightincrease
so r e o l ut i on s u p to a b ou t 2 30 t h e
s s oc i at i on T e ch n i u e Ma r it i me v o l . i . p . 68 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
ined. V er neartheend howe er
e therateo increasew asslightl
tepoints.M.N ormandsuggests
andC correspondstoaperiodo
0
I L O GR A MM S .
enspaces duringw hichthe arebe ing
edw ithmoreorlessirregularit , thus
o thew ater w hilebe ondC the
ent andthe increaseo thrustw ith
erapid. Theremainingcur esgi e
orintermediate immersions.
thistothecase o v esselsin
in becausetheconditionsare
eslipismuchless theamounto w ater
ndtheactua lve locit o theblades
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
f orthesamere o lutions. I t
atinf reeroutethere o lutionsmight
trw ithoutruptureo theco lumnthan
lo c at i on .
hesephenomenaha ebeenindepend-
P a rs o ns ~ x ' a n d B a r na b f i n E n g l an d .
the lim itingcondit ionsw henca ita -
morereadil e pressedintermso
elopedperunito pro ectedbladearea
cit , andbothin estigationsf urnished
substantia ll thesamev alueo n
the immersiono thetipso the
t thepo intw herethisa erage
pro ectedbladeareaw asreached
egantoappear andonincreasingthe
enonbecamemoreorlesspronounced
ust wasgained.B arnab states
ddit iona lf ooto immersionthethrustper
ncreasedabout- pound. Theva lue
htl w ithpitch- ratio be inglessi the
in luenceduetothisf eature issosmall
l ig ible.
o r e a c co r di n g to t h es e i n e s ti g at i on s
udspers uare incho pro ectedblade
asthema imumthrustw hichcanbe
op e d a n d i m o re t h an t h is i s r e u i re d i t ca n
f i c ul t a n d a t a l os s o e f i c ie n c .
itationhaspresenteditsel moreor
nectionwiththemoderntorpedo-
t e o N a a l A r c h i te c ts v o l . x x x v i n .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
aso sim ilart peorcondit ion. In
. H. P . pro idedf oreacho tw opro-
ameterat400re o lutionsandupw ard
0k notsandupw ard. I tseemsprobable
causetroublewithf urtherincrease
inboatso thischaracter andthea ll-
uchcasesisthere oreastothebest
nsanddimensionsf orthede elop-
mthrustperunitareaw ithoutundue
c ie n c d u e to t h is c a us e . Th e o b i o us w a t o
h er e p os s ib l e i s t o pr o i d e a su f i c ie n t
adetoreducethea eragethrustbelow
dtheuseo ninepropellersonthe
thistreatmento thedi f icult .
r-blades. F romthelaw sregulating
sureo eraplanemo ingthrough' the
itf o llowsthattheouterportions
orsuchportionsasma beconsidered
a l en t t o th i n f l a t s u r a c es w i ll t e nd t o p la c e
hestreamorlineo f low . Thisw ould
ncrease
ural
eportionsor
unded
e r en t . I t i s
p e ri m en t t ha t
li uethe
ctionsisindeed
rightanglestothestream but as
the incipientmo ementisclock wise
e thef ina lposit iontow ardwhichthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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C E A N D P R O PU L S I O N O F S H I P .
ownindottedlines w ithcon e
iswillr esultinatendenc to
ip. ( C omparea lso42 F ig. 64.
enc tospringduetothe irregu-
tiono pressure thebladeasaw hole
erthe in luenceo thethrust.
paniedb aslightuntwistingo
gtow ardanincreaseo pitchandslip.
el moreimportantthantheothers
dhence inthecomple e f ecttheresult
stingo thebladew ithincreaseo
eso theusualsti f nessitdoesnot
f ectw illbesu f icienttoproducean
eper ormanceo thepropeller. I n
er w herethebladesha ebeenthinned
t h e e f e c ti e p i tc h a nd s l ip m i gh t
i bl a f e c t th e e f i c ie n c u s ua l l
T A P P I C A T O N O F T H E L A W O F C O M -
P R OP L L E R D S I G N .
odo propellerdesignindicatedinthe
spossibletoappl directl the lawso
din26. A s re uiredb thenature
m e:
eometrica lf ormandsituationw itha
measthatw hiche istsbetw eenthe
s p ee d s as d e i n ed f o r s hi p s o r l in e ar
* . Thiscondit ionw ille identl appl
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
o intsonthetw opropellers. Letr l
suchpointsonthetwopropellers and
on s . Th e n 2n r l N l a n d 2 r 7 V r a w i ll b e t he
thesepoints. Hencew eshallha e
ds
speedsthere o lutionsw illbe
r sp e ed s o r i n e r se l a s t he s u a re r o ot
ratio.
d f urther thattheseassumptions
u a l pe r ce n ta g es o s l ip e u a l v a l ue s o
u a l v a l u es o t h e f a c t o r o a u gm e nt a ti o n
de ua lmechanicale f icienciesf orthe
eassumptionso 26 thattheratio
ssar todri ethetw oshipsisA * .
assumed it isseenthatthe f ul i l
so the law o comparison consider-
oleresistance.H encetheratioo
ersemotion theratioo thethrusts
a llsim ilarcomponentso thef orces
1. Thespeed-ratio isA * . H encethe
tso use ulw ork willbeA % the
talamounts or inotherw ords the
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
dwillgi esimilarresultswith
= = 1 . 44 ^ = 1 6 k no ts A ^ , = 1 0 0.
3= displacement-ratio= 2.986 andA * =
nu = 19. 2andN z 83. 3. I t
thatthe largershipw ouldre uireapropeller
rthesmaller andw ithane penditureo
3. 3re o lutionsw oulddri e ita ta
w i th t h e sa me e f i c ie n c a s f o r t h e
isonisreall aspecialcaseo that
section.The methodb com-
eo appl ingtheresultso agi en
oneo sim ilarf ormundersim ilar
ndingspeeds whilethemethodo
dre lationsaswillpro idef orthe
tso agi enpropellertothedesign
ormundersim ilarcondit ionsbutatan
een50 ( i , andthe law o com-
b appl ingthef ormertothedesign
datao asim ilarcaseatcorrespond-
the latter w eha e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
u a ti o n U , d p a n d N a s w el l a s th e
icso thepropellertobethegi en
ombinedf actor( ik lt i i isreadil
op o se b m ea n s o t h is g e ne r al e u a ti o n
designo aprope llerf orasim ilarship
ssumingthesameslip pitch-ratio
orthepropeller thef actor( Mm w ill
s. / 3f romthelaw o comparison
7 , andsincethespeedsarecorrespond-
w il l e u al \ * ( p N ' \ . H e nc ef o rt he se co nd ca se
X ' ' ( ^ ) i .... ( 2
i t i s e i d en t t ha t
lha ethesamefactoro sim ilitude
e itsre o lutionsinthe in erseratioo
is f a c to r t h e sa m e as i d e te r mi n ed b
iscussedabo e. I notherw ords the
i , t o s uc h a c as e i n th e m an n er a b o e
ctl thesameresultsaswouldbegi en
o the law o comparisonitse l .
G TH O F PR O P L L E R - B L A D S .
rma beconsideredasabeam
heroot andloadedinav ariableand
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
f i c ie n tl p r o i d ed f o r b t h e f a c t or o
e r e e r en c e o o u r f i n a l e u a ti o n to a c tu a l
nationo theva lueo theempirica l
roduced.Thebendingmomentat
othef ace isthere ore
ngtho thesectionw herethe
nd/ thema imumthick ness. Wema
thegeometricalcharacteristicso this
a r . I n a c tu a l f o r m i t c lo s el r e -
bolicsegment.Thegenerale uation
s
uterf iber;
o m ne u tr a l a i s o s e ct i on t o s uc h f i b er
o sectionaboutneutrala is.
o emaderegardingthenatureo
e
sec =
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N DPR O P U L S I O N O F S H I P .
. 6 6 w e r ea d il s e e th a t
Q Q
ti o ( T h ru s t H . P . - = - ( I . H . P . .
k ethe inclinationattheassumedcenter
erat, j rl inordertoa llow somew hatf or
t h e bl a de s a t th e o ut e r en d . W e h a e
ereto ore weha e
I - .
in g i n ( 3 w e ha e f i n al l ,
I . H . P. V i + t - 4- 4 .8 4 , .
mpli iedb makingthef ollowing
eq uiteadmissible consideringtheun-
n o l ed:
e
si b l c o ns t an t .
n one whichwedenoteb A * ,
e a nd I . H . P .= H .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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D S I GN .
mberedthatA includesthe
a l andhence itsva luemustbetak en
itmustberemembered gi esthe
to theblade. Thef il le tb w hich
so coursee tra andisnothere
o ema betak enf romthefo llow ing
uationw itha largenumbero
how nsu f icientstrength it isfound
e l A m a b e t ak en a t f r o m 9 to 1 2 w h il e
eshouldbe increasedtof rom14to17.
eniencethesevariousitems w eha e
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C E A N D P R O PU L S I O N O F S H I P .
nchesatrooto blade;
thetableabo e;
sectionatrooto blade;
rmin. ;
s t e el
on.
S U I T A B L E F O R S C R E W -PR O P L L E R S .
alpurposeinthepresentv olumeis
nsionsandf ormo prope llers y etsome
ateria lssuitablema notbeouto place.
b r as s g u n- m et a l a n d th e v a r i o us
tironisthecheapest butbe ingre la -
ethebladesarenecessaril thickerand
ithstee lorbron e. Thestrengtha a il-
2 O O O t o 2 5 oo o I b s . pe r s u a re i n ch o
sma bebrok enshorto f b striking
suchco ll isionsare lik el tooccurit
cast- ironbladesthanstee lorbron e
demightsparemoreseriousresults
theengineandsterno theship.
r w ew ishthebladestoho ldandnotto
urposecastironisatare lati edisad-
ancastiron itsult imatestrength
propeller-bladesrangingf rom50ooo
uare incho section. Thesectionsma
nner andabettere f icienc obtainedin
thisf eature . Thesur ace isnatura ll
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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D S I GN .
castiron butw ithimpro ed
thedi f erence inthisf eature isinsig-
r al l a s m oo t he r s ur a c e a n d se e m
ealow ercoe f iciento sk in- resistance.
h andgoodcastingq ualitiesmakes
mooththinbladew ithsharpedges a ll
es f a o r ab l e to g o od e f i c ie n c . T h e
thebestbron esv ariesf rom40oooto
re incho section. Withordinar gun-
35oooI bs. pers uare incho section
lewithcommonbrassnotmorethan
houldbedependedon. Of these
nganese-bron e isprobabl moreusedthan
bettercombinationo desirablequa lit ies
f ness goodcastingq ua lities resist-
tc. C are isneededinthemanipulationo
pouringandcoolinginordertoobtain
utw ithsuchcaretheproductishomogene-
eaterre lati ecostrestrictsitsuse
ps y a c ht s a n d la u nc h es o c ea n -l i ne r s a n d
portanceo asa inginpropulsi e
eredworthobta iningataslightincrease in
peller-bladesisintheorder:bron e
hetwolatterusua ll deteriorateb
a lpitt ing thea erageli ebe ing
e t o t en y e a r s . Th e l i e o b r o n e b l ad e s is
oratleastasgreatasthato theship
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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TA N C E A N D PR O PU L S I O N O F S H I P .
F T H E S C R E W P R O P L L E R .
e latingtothegeometricalf ormo
ebeengi enin34. Weha enow
accounto theprincipa lformsw hich
sur aceo ascrew propelleringenera l
b a line/ mo ingontw ootherlinesas
a i s s tr a ig h t f o r mi n g th e a i s a n d th e
s u r a c e o a c l i nd e r o w h i ch a i s t he a i s .
eloped weha etheactualf ormo b.
orm-pitchpropellerw ithbladesatright
eadil seenthat/ isstra ightandat
hatthede elopedbisstra ightandat
erseplanesuchthatw esha llha e
thec linderinw hichbissupposed
;
' * a is ;
o r g ui d e- i ro n .
e e lopedb b.
f oundin/are asf ollows:
trightanglestoa
to a
d i n an a i a l pl a ne ;
an s e rs e pl an e.
bleincharacter.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
asf ollows:
2 isusuall suchthattheanglea t
creasesf romtheforw ardtothea ter
n o t h e su r a c e we m a a l so h a e
owhether/ changesitsangularposition
the longitudina lcomponento the
contacto / w ithbisgreaterorlessthan
o nt a ct o / w i th a t h e pi t ch w i ll v a r
hehuboutw ard. I nsuchacasepracticall
uiredonenearthehubtosuitthe
andtheotherasusua lattheouterend
hatpoint.
o thev e locit ieso thepo intso
w ithb. Thenw ema ha ethree
o he lico ida lsur acesma begener-
b a n d c th e d i f e r en t v a r i at i on s a s ab o e
h a e h o we e r o t he r f o r ms o h e li -
nnotbegeneratedb arigidline inan
m e n t io n ed . W e m a m o st r e ad i l c o nc e i e
m a de u p o t h e su m ma t io n o a n i nd e i n it e
andthusasgeneratedb av ariableguide
ndperhapsangularl andlongitudina ll as
sametimethesuccessi eshapesand
db thenatureo thepitchatthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
on s . I n t h i s w a a n f o r m o b l ad e
pitch nomatterhow comple , ma
mined andb theuseo areasonable
a ll producedinthef ormo apattern
oundr .
r t h e su r a c es o p r op e ll e rs a r e su c h as
gidline ando thegreatv ariet
rmedbutf ew arecommonl f ound
mmonpropellero uni ormpitch;
p r op e ll e r o u n i o r m pi t ch w i th s t ra i gh t e le -
heplaneo re o lution;
e s t h e p ro p el l er o u n i o r m pi t ch a s i n th e l as t b u t
d a wa f r o m th e p la n e o r e o -
e s t he p r op e ll e r o u n i o r m pi t ch w i th e l em e nt s b en t
o r e o l ut i on ;
mone panding-pitchpropeller thepitch
w ardtoa teredge.
thesev ariouscombinationsw ithc^ orcs
aria tiono pitchinan w a
eatl v ar theappearanceo apro-
ingthe locationo thepartactuall tak en
o m a h el i co i da l s ur a c e o u n i o r m
l locatingandshapingthecontour w e
whichhastheappearanceo be ingbent
re o lution andw hichoncasuale am-
t h e sa me a s t ha t g i e n b l f l c l o r
c h is b n o me a ns t h e ca s e.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
tevariet o propellersarepossible
adeanddistributiono pitch itmustbe
tsof arase perimentaloractua lresults
apositiontoselect amongthem
aterist icsasthebest andespecia ll an
h orindeedtosa thatan distribu-
uceapropellersuperiortothato uni-
siblethatsomedistributionma be
butw earenotatpresentinaposi-
rdispro ethisb e perimentaldata .
a v e r g e ne r al t e nd e nc t o c on s id e r th e
pitchasthestandardint pe. Thebent-
/ , < : h a s be e n mu c h us e d on t o r-
andsmallcra t thepresumablereasons
o ldonthew ater andadecrease in
ngaroundthetipso theblades.
en c e o a n f a n ci u l v a r i a ti o n o p i t c h
berthenatureo thew akeasdiscussed
thatrelati e toauni ormpitch
stnecessaril w ork withane cessi e l
s l ip b o th o e r i ts s u r a c e an d d ur i ng
ncerelati etoauni ormslipitmustact
correspondingl v ariable . A pro-
leaccordingtosomede inite law w ill
o rrespondingdistributedvaria tiono
iationo pitchissosmallastobeen-
egreaterw akev aria tiono slip so
thewak ew illbebutslightl di f er-
n i o r m- p it c h pr o pe l le r a n d in a n e e n t
t f r o m th a t in a u n i o r m st r ea m.
osedtoarisef romsomeparticulardistri-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
w il lthere orebew holl f anci ulor
actua lcasethevaria tiono slipcorre-
chw illnotbee enappro imatedto .
aS crewPropeller.W etakeas
caseapropellero uni ormpitch
W e m u s t h a e t h e f o l l ow i ng d e ta i ls g i e n
H ub.
orsimplicit thatthebladesareto
ndthatthe aretobes mmetrica l
b e t he a i s a nd O F a p e rp e nd i cu l ar
B istak ene ua lto theradiuso
henla ido f asinthef igure. The
w ereadil f indthemeanhal -w idth
lguidesk etchinatria lha l -
ama thenbecheck edb planimeter
usteduntil it iscorrectinamountand
or . The lengtho theroot-sectionis
thato thema imumwidth.
ndi idedintoan con enient
e as u ri n g f r o m e it h er B , C , o r O , a s m a
ue o t an a f o r a n p oi nt F i s
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
ke a p o in t E s u c h t ha t O E = p ~ - 2 n t
i e t h e co r re s po n di n g v a l u eo a . A
ra llo therpo ints sothati f romE a
ntothese era lpo intsontheradius
slinestoOB w illgi ethecorrespond-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
ke n e u a l to F G i t is e i de nt t ha t E l
G o n a l on g it u di n al p l an e a n d H I i t s
e r se p l an e . I f , t h e r e o r e F K i s m a de
e th e p ro e c te d v i e w o G a n d ma ki n g
e t w o po i nt s o n th e p ro e c te d c on t ou r o
w e ma f i n d th e e nt i re p r o e c te d
shown. Theotherpro ectionsareread-
m an n er b u t as t h e i n o l e o n l a n
egeometr , thedeta ilsneednotbehere
s e en t h at s o f a r a s th e c on t ou r i s
constructionisappro imate andnot
bementionedthatinthepro ectionon
inessuchasGG1ma betak enas
asradius andthedistancessuchas
d o f a l on g t he s e ar c s o r p ra c ti c al l a s
m me t ri c al a b ou t O B , i t m a b e l ai d
de s ir e d a n d th e n th e t wo p a rt s m us t b e pr o -
butotherw ise inthesamegenera lmanner.
esamegeneralmethodis used
ingappropria tel modi iedtosuitthe
othehub. I nan casetheblade j o ins
ta c ha b le i t s ci r cu l ar b o ss b a w e ll - ro u nd e d
omplicatedf ormanddistributiono
rinciplesma beappliedto f indthe
ceo thepro ections. I tma beob-
t h at a t b es t t he s e ar e b ut a p pr o i m at e a n d
ractica lva luetothepattern-mak eror
ono w hichhemak esdirectuse is
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
amount asw illbee pla inedata
t h e ne t s t ep i s t o la d o wn t h e
to theblade. A stra ightline MB ,
hisw illgi ethemiddle- l ine
ussections. A tthetipsuchlinemust
how n inorderto insuregoodcasting.
ssuchthick nessma betak enatabout- a
meter. F orcastironitmustbeslightl
ectionsorthick nessstripsma now
m ad e e u a l to S T a n d a ci r cu l ar o r
ghP Q , andR . Whentheouter
sinF ig. 87 suchanarcw ouldgi etoo
ecasting. Wema , there ore draw
n mak ingtheedgeo there uisite
asmoothcur etangenttothese lines
e ltoA B atthecentreD. Thismini-
f r o m as l i tt l e as 5 f o r s ma l l br o n e
eusedontorpedo-boatsandfasty achts
npropellerso la rgesi e suchasare
ntilepractice.Thesmalleranglesare
ourse placedonthebacko the
w ardo thehelico idalsur acew hichhas
ing- ace. F orthesectionsnearthe
rtainmodi icationsaresometimesmade
sderations: A B , F ig. 88 denot-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
e b t h e us u al c o ns t ru c ti o n E C = p i tc h
consideringthew aterasundisturbed
t o t he p r op e ll e r w e ha e D O a s t he d i re c -
on. Draw HJ para lle ltoDO. Then
section theback o thebladef romB
isstream andtheresultantpressure
romf orw arda t thusreducingthe
f , h o we e r t h e se c ti o n is m a de a s s ho wn
e ha e t h e ba c k me r el e p o se d t o f r i c t io n al
rectf low meetsthef aceonl , andma
creasedthrust. Thischangeinsection
aseo pitchonthedri ing- acef rom
c it o t h is c o ns t ru c ti o n h o w e e r i s
epresentingthepatho thew aterinthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN . 319
tispossiblethatsomesuchmodi ica-
herootma bead antageous w eare
chan opinionupone perimental
e r re d t o th e f a c t t h at t h e in o r ma t io n
hepattern-mak erormoulderdoesnot
metricalpro ectionstherere erredto.
necessar issimpl thef ollowing:
ndcharacteristicso thepropeller
e d f o r m o r co n to u r o t h e bl a de a s i n
i g . 8 6 t h e sh a pe a n d an g ul a r po s it i on o t h e
he f o r m o a s e ri e s o g u id e s at s u cc e ss i e
stributiono thethick ness. The
nma there orebeclassi iedunderthese
n si o ns ;
t h e bl a de
p i tc h
o thethick ness;
tchpropeller thein ormationgi en
thepro ectionA K B isa llthatisneeded
odorsweepuptheforminloam.
emethodsomedesignerspre erto la
ctiononatrans erseplane mak ingthe
n f r a ct i on o t h e di s k ar e a. S e e f o r
e pandedf ormandtheotherpro ec-
n d b t h e in e r se o t h e me t ho d s gi e n
a c op o t h e wo r ki n g dr a wi n g f o r
S . battleshipsI ndianaandMassa-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
n ormationpro idedinthesecaseso
S crew Propeller. F rom( i w e
t h er e o r e at a g i e n v a l u e o r t h e
P L L E R
I P N o2.
edetermined thepitchisk now n. S uch
necessaril theestablishmento a
aneperpendiculartothea iso the
e llerisl ingonaf loor the latterma
enthatthepropelleris soblockedup
ependiculartothef loor. Otherw isea
culartothea isasw ingingarmma
h o le t h us g i i n g a mo a b le l i ne o
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I G N .
pe llerisinplaceontheship thearm
hubortothesha tnut orso
a s t o gi e a l i ne o r e e r en c e mo a b le
ans erseplane.
ppro imatemethodw hichconsists
a l ue o r w e h a e a = 4 5 t a n
2nr. Thetrans erseplanebeing
abe elortrianglew ithangle45or
h ee t o m et a l ma b e a pp l ie d a n d th e
rappro imatel f ound.
suresw eha etodetermineata
w o si d es o a t r ia n gl e a s i n F i g . 8 9. A B
e a nd o n t he s u r a c e o a c l i nd e r o
ef aceo thebladeandonthesame
ctthe irintersection. B C ispara lle l
e A B d e e l op e d is e i d en t l
ig. 55f orthesameradiusandpitch the-
n F i g . 90 . I f , t h er e o r e w e ha e a n
is w ema b runninga lineper-
a f i edv a lueo rdeterminean
tsonthe lineA C . The lengtho A C
b a f l e i b le r u le o r b at t en o r i i t i s
e r s en s ib l f r o m th e s tr a ig h t li n e j o i n i ng
sthendeterminedasthedi f erence
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
a lue thoughw ithpropercarethe lim it
emuchless.
tiono measuringthepitchwill
w iththemeansathandandtheparticular
ase buti thef undamentalgeometrical
k eptclearl inmind suchnecessar
no d i f i c ul t .
eS lipA ngle< f > with theS lipR atios.
ws:R e erringtoF ig.55 weha e
enclaturethereused w ereadil f ind
alueso f orv ar ingv alueso y
heModi icationo Pitchduetothe
npropellerswithdetachablebladesit
def ortw istingthebladeslightl onthe
i n g th e p it c h. T h e am ou n t o m o di i -
ad i al d i st a nc e o r v a l u e o y , i s f o u nd a s
w e h a e i n g e n er a l
a
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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C E A N D P R O PU L S I O N O F S H I P .
o t w is t . Th e n e i d en t l ,
u i te s m al l t h is m a b e p ut i n t he f o r m
TT /
na " _ '
lueso / -r-/f orv ar ingv alueso /
amounto changev ariesconsider-
t p or t io n s o t h e bl a de . H e n c e i t h e pi t ch
tw isting itcannotbesoa terward.
f act trans ormedthesur acef romone
oonew ithamoreorlessirregulardistri-
o b l ad e .T h is o c o ur s e i s b n o
udicial andso longastheangleo tw ist
sone perimentall toe pectan
hergoodorbadduemerel to the irregu-
hetw istingthuspro idedf orisf orthe
he e f e c ti e o r m ea n p it c h o t h e pr o -
theabo econsiderationsindicatethat
tw istissmall w eha enoe peri-
ct ingtothismodeo obtainingsuch
w ema ask whatw illbethemean
modi ied. Thisw illdependonthe
pitchasdiscussedin42 tow hichre er-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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D S I GN .
H E S L I P A N G E 0.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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H I P .
T O R Y .
uentso thepowerwhichitis neces-
ec linderso amarineengine inorderto
speedha ebeenalread discussedin
onsiderthev arioussupposit ions
keanestimateo thetotalpower
i encase. Theseareo tw ogenera l
neralmethodsf ortheestimateo
o thenecessar constantsw hichw ill
esistance andthepowerre uired
therw iththatre uiredforthev arious
omakeuptheI . H. P . Thisa lso
t w o wa s :
ke t h e v a r i ou s a ss u mp t io n s ne c es s ar t o
ntconstituentsindi idua ll . Thisin-
ge lements: thepow erf ortheresistance
theamountin o l edintheaugmen-
t h e wa k e f a c t or t h e pr o pe l le r e f i c ie n c ;
b f rict ion. B y apropercombina-
tedb F ig. 66w ereadil w ork back to
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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H I P .
k etheassumptionsnecessar tocompute
andthenassumethepropulsi e
. H . P . - r - I . H . P. w he n ce t h e la t te r f o l -
e former andw ithoutspecia lassump-
idua le lements.
ra lmethodin o l escertainassump-
t h e e t e ns i on o t h e la w o c o mp a ri s on
er andthusenableustocomputethe
n c as e f r o m th a t ac t ua l l o b s er e d f o r
ingspeeds.
ethodsinorder.
T A T O N O F W P , O R T H E W O R K A B S O R B E D
L L E R .
mationandassumptionsre uisitef or
ha ebeendiscussedinC hapterI and
ugmentationo resistancemustbe
uidedb suchin ormationre latingto
a a ilable . UsingtheE . H. P . asa
mounto pow erthusre uiredw ill
w een10and25percent. De inite
totheamounto thisconstituento
a ll obta inableb modele perimentsas
suchappliances thetrueand
rereadil f ound.
blesomede inite in ormationbased
re lati etotheprobableamounto
ttleuse inattemptingitsindependent
ewakef actorwhasbeenalread
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
9. Withthew akef actorand
ssumed w ereadil pass ase -
F t o C f , F i g . 66 .
stimatingaugmentationandw akef actor
o ns i de r t he s h ip e f i c ie n c ( 4 6 a s i
g . 6 6 C F = C ^ E a n d p r op e ll e r po w er o r
de d b p r op el le r e f i ci en c .
gtopropellere f icienc ha e
1. Guidedb suchin ormation
eemsapplicabletothecase inhand its
asw eha eseen ma inusua lcases
ween65and69percent.
R I C T O N .
mo u nt o p o we r a bs o rb e d b f r i c-
andthec linders.
ebeginningthatthere isv er l itt le
in ormationonthesepo ints. Model
n o a a i l a t l ea s t f o r p u r po s es o
chmeasurementwouldre uireat
multaneousdeterminationo the
ndo thepowerrece i edatthepro-
a m pl e j u s t f o r w ar d o t h e pr o pe l le r t he r e
ssiond namometerwhichwould
ent thentheproducto thisb 2n
o lutionsperminutew ouldgi ethe
ropeller.S uchdeterminations
i c ul t a nd c o st l , a n d he n ce m or e o r le s s
tedto.
assumedthatthetota lpower
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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H I P .
m a b e e p r es s ed b a n e u a ti o n o t h e
ran gi enengine N isthenumber
dhN istheamountduetow hatistermed
hileW isthe I. H . P . and/ isl ik ewisea
nengine.
talf rictionalpowerma be
tearbitrar , butseemstoanswerthe
se l aspresentdatacandetermine.
attherew ille istatthevariousj o ints
certa intangentia lresistanceo w hich
sensibl independento re o lu-
resentsw hatistermedthe init ia lf ric-
t h is f a c to r i s ch i e l d u e to t h e
s t u f i n g- b o e s p i st o n- r in g s e t c. a n d
a tingandothermemberssupported
thetotalf rict ionisa lsosometimes
eadload.Theworknecessar to
antresistancew illvar directl asthe
cew illberepresentedb a termo the
rtherassumedthattheremaindero the
erubbing-sur acesw illv ar directl
o rasthemeane f ecti epressure
ssar too ercomethispartwillbe
cto meane f ecti epressureand
lpow erde eloped. Hencethispart
w illberepresentedb atermo the
ma b e e p e ct e d to v a r w i th t h e t p e
gine andw iththepresenceorabsence
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
ngeneralthef rict iono hori onta len-
to v ertica l. Thepow erabsorbed
esingeneralw iththenumbero c lin-
icationo rubbing- o ints. Thef ric-
a lsonatura ll greaterthanw henthe
tw orn. A ga in incorrectad ustment
beginningorduetowearor work-
e r i se t o e c e ss i e f r i ct i on a l lo s s. I n
islik e l tomani estitsel b hot
atsomethingis wrongatthepoints
resenceo attacheda ir-pumpsoccasions
notonl too ercomethef rict iono
sregularrunning w hichamountmustbe
. H. P . inordertoproperl obta inthat
temisnottobev iew edasa
chcasesasaconstituento thetota l
natedinorder todeterminethe
thepropeller.W ithindependent
course doesnote istasaconstituento
ngines.
peratepumpshasbeendeter-
cialandindi idualtria ls. Thepow er
rict ionhasbeendeterminedb slowl
nengineb theturningengine
o m cu r e s o r e o l ut i on a n d po w er a s
tsub-head.Thepowerabsorbedb
eenestimatedf romvariouscoe f icients
ar enginesinw hichthedi f erentquan-
measurement andf romanal seso
chthevariouse f icienciesandratios
arisonf rommodele periments.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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H I P .
t ialF rict ionf romSpeed- trialData .
n ed t h e re d uc e d me a n e f e c ti e p r es s ur e
considerthisasbalancedagainstthe
hemo emento theengine. This
consideredasthesumo tw oparts
adandtheotherduetothef rict ion
erredtothef rict iona lortangential
sandrubbing-sur acesundertw oheads:
nsandthatdueto theload corre-
df rict ion. E v identl thef rict iona l
tionalpressureonthe pistonsoran
ducedmeane f ecti epressureas
dsuchaddit iona lamountma natura ll be
onedueto init ia lf rict ionandthe
on. Wema thusconsidertheentire
ti epressureasmadeupo threeparts
etor deli eredpowerandtwodue
D en o ti n g th e se r e sp e ct i e l b / / ,
n it i al f r i ct i on a s a bo e d e i n ed i t
stantandisinf actproportiona ltothe
hile / anda lsopw illvar w iththe
e ri e s o c o rr e sp o nd i ng v a l ue s o H a n d
e b 4 7 ( 3 t he v a l ue s o / . P lo tt in g th es e
w e s ha l l ha e a c u r e a s i n F i g . 91 . N o w
/ mu s t ne c es s ar i l b e o a n d he n ce / wi l l
th e re o r e th e c ur e b e e t e nd e d ba c k b
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
t h e a i s o Y a t a p oi n t A w h i c h wi l l
on O A t o t h ev a l ue o / . T h en f o r t he
O F N *
nitia lf rict ionpow eratan numbero
e
e .
ap p ro i m at i on m a b e o v a l ue
nwith thedeterminationsrelating
cur e andthere o lutionsshould
numberatwhichtheenginecan be
ement.
esameresultusethesamedatasome-
s f o l l o ws :
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
e-pow erformulaw eha e
edonTV asanabscissaw eshallha ea
f t h is b e e t e nd e d ba c k th r ou g h O b
N
e a t O a c e rt a in i n cl i na t io n t o O X , a n d
ge o r o B O X w i ll t h er e o r e be a n
a l u e o ~ ^ - ; a n d f r o m t hi s t he c o rr e -
m a b e f o u n d . S e e a ls o 7 8 f o r a n ot h er
e init ialf rict ion.
gtoinitial f rictiongatheredin
catethatinamountitma be
n5and8percento thef ullpowero
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
w i ll b e f r o m 5 to 8 p e rc e nt o t h e/ f o r
rrespondtoava lueo f rom2to3
onthe low-pressurepistonf ortriple -
rusua lcondit ionsasabo enoted.
obedenotedb ianddenotef ull-
cents. Thenw eshouldha e
on a t f u l l l o ad h N ' = i H ' ,
ict ioningeneral= hN ' = . , w here
ma e p e ct i t o b e f o u n d be t we e n .0 5
elatemoreespecia ll to themain
r i c t io n . W e h a e a b o e s t at e d th a t
a lto thew holepowerH . I tm ight
t asproportionaltothetotal
ict ion. Thedi f erence in o l edis
gligible inv iew o thegenera luncertaint
uestion andw enatura ll pre er
o themethodasstated. Weha e
.
gtoloadf rictionindicatethat/
ar betw eennearl thesamelimitsasi
orF rict ion. C ombiningthetw oparts.
f f .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P ,
pow erandthepow erabsorbedb
f rict iononre o lutionsasanabscissa
masinF ig. 93 w heretheordinates
N
e t h e v a l ue s o t h e in i ti a l f r i c t io n
d O B t h e v a l u es o t h e lo a d f r i c t io n a n d
d O C t h e v a l u es o t h e ne t o r de l i e r ed
ddiagramser eto il lustratethe
ortanceo f rict ionatreducedspeeds.
werthef rictionistakenat 14per
dedbetw eenloadandinit ia lf rict ion.
1 0 0 w e s ho u ld t h en h a e f o r o ne -
atel one-e ighthpow eror12. 5. The
educedinthesameproportion and
e7- i-8= . 875. The init ia lf rict ion
atioo there o lutionsorappro i-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D PR O P U L S I O N O F S H I P .
sf ull-pow erva lue orto3. 5. Hencethe
75 andthepercentage4. 375-= -12. 5
tratesf orcibl thew aste ulnesso
andthe impossibil it o obta ining
icienciesunderthesecondit ions.
e o r e w e m a e p e ct t h at t h e f r i c t io n
absorbanamountl ingnotfarf rom
meanvalue. Withthebestmodern
hisf igurema f a llto12percentor
ercent w hilewitho lderenginesor
k o ad ustmentitma riseto18or
re.
dthatthedi isiono thepower
tionasindicatedinthepresentsectionis
to r a n d th e o nl e c u se f o r i ts u s e is
ecorrectana l sis. I t isnottobe
abso lute l constantata llre o lutions
a c tl w i th t h e lo a d. F u r th e r e p e ri -
muchneededonthesepoints.
U I R E D F O R A U X I L I A R I E S .
aref undamentall concerned o
rneededforpropulsion. I nasmuch
n re uentl meetw itha ir-pumpsattached
re erredto inthe lastsection anda lso
erorpow erdata includingthatre uired
il lbewelltonotebrie l thepow erw hich
a bee pectedtoabsorb.
ductioninthisamountwithin
u i l ia r m a ch i ne r h a s be e n so i m -
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
onstructionthatitscostinpower
onismuchlessthanitw asf romtento
ttheearlierperiodf rom5to8percent
e lie edtobeabsorbedb theresistance
mosto w hichwereattachedtothe
den * w rit ingf oraperiodaboutten
thef o llowingestimate basedondataderi ed
ntsteamersw ithtriple -e pansionengines:
7.8
teforthea ir-pumpo aboutI per
no t b e f a r i n e r ro r f o r t h e c as e s in o l e d
e r ce n t re u i re d f o r a l l a u i l ia r ie s
era ll w iththoseobtainedinthis
a rs a g o e s pe c ia l l i n t he e a rl v e s se l s o
. Tak ingmorerecentl theresultso
pecia ll inw ar-shipdesign w eha ethe
. P.
blow ers w eha ef ortheremaining
. 3 pe r c en t o r s li g ht l o e r I p e r
. C o a s t I n s t. E n g i n ee r s an d S h i p bu i ld e rs v o l . v n .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D PR O PU L S I O N O F S H I P .
Thechie impro ementhasbeenin
w hichtogetheraf ew y earsago
ercent w hilewiththe latestpractice
ducedtoaboutonequartero this
ge-pumpsinearlierestimatesis not
ha ingdecreasedtoa lmostanegli-
essthan. I percent. Theamount
natura ll v ariablebetweenw ide
tonthedegreeo f orceddraughtand
hetherthepow ero anattacheda ir-
oassmalla f igureasforanindepend-
e l to thef actthattheattached
sterthanthe independent andf aster
navacuum. I nconse uencethe
eater andf orsuchcasesprobabl not
ere uired.
A T V E E X A M P E .
applicationo thepreceding
ono the I . H. P . inagi encase
r thevariousva luesin o l ed.
l e t tr u e re s is t an c e = R .
= R u.
gmentationbe1.16.
I .\ 6R .
C E = i. i6R u.
i c ie n c = . 6 7.
. 1 5.
5.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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H I P . 339
= i . 6 R u ~ 1 . 1 5 =
er= B E = i.oiR u-= -.67=
r i ct i on a l lo s s le t i a nd / e a ch = . 0 7.
= \ . iR u- -.86= 1.756^.
ie n t : = -
ondtothef ollowingsubdi ision
percentages.
7
= .661
wakegain..199
t he p ro pu ls i e c oe f i c ie nt w er e to b e
shouldintheprecedinge ampledi ide
i n g\ . j t > R u a t on ce .
a a ilable f ortheestimateo the
s i n o l e d i n th e p ro c es s a bo e i t w il l
u iteassatis actor toassumethepropul-
ectl . Thisagaincanonl bedoneinte ll i-
menta ldataareathandf romsomew hat
l likeconditions.Therangeo
membered isusua ll f rom. 50to .60.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
G B Y TH E L A W O F C O M PA R I S O N .
edareasf ollows:
hattheentireresistance issub ectto
Thepropriet o thisassumptionhas
tow hichre erencema bemade.
rrorisq uitesmall andma beconsid-
mito genera luncerta int surround-
urther w ithaslightl roughened
i s ts f o r m os t o t h e ti m e t h e i n de o
orskin-resistancewillapproachthe
errorw illcorrespondingl decrease.
hatthetermsimilarise tendedto
andmachiner . Thisin o l esthe
arit betweentheshipsandbetween
obeing o course thesamef oreach.
snotnecessar f orthemachiner , but
megeneralt pe ineachcase orat
groundforassumingane ual
case.
hatthetermcorrespondingspeedsis
espeedso thepropellersrelati e to
her asw ellasthespeedso the
ter.
sha llha esim ilarpo intsonthetw o
arpathswithv elocitiesintheratio
ho wn w e s ha l l ha e a l so
A , 1 /
i ( 2 a nd ( 3 a re f u l i ll ed t ha t th e
relationtotheresistancein each
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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H I P . 341
eandapparentw illbethesamepercent
hee f icienciesw illbethesame and
nandwakef actors.I tisassumed
ere lationo thepropellertotheship
ocases.
eassumptionse identl dependson
stheapplicationo the law o com-
theshipitse l .
ecedingassumptionsitf o llowsthat
opellersat correspondingspeeds
l si e c o e f i c ie n ts .
esssa e l considerthatindepen-
me nt o ( 2 a nd ( 3 , t he p ro pu ls i e e f i ci en -
sameinthetwocases.
and2denotethetw ocases. Then
tw oresistances
peeds
osimilardimensions
he l i ne a r ra t io ;
e f i c ie n t
powers.
s er ie s o e p re ss io ns f o r 7 , - - R t
unctionso theshipando thespeeds.
n d re m em b er i ng t h at , ~ u t = y \ =
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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N C E A N D PR O P U L S I O N O F S H I P .
e ad i l f i n d th e f o l l o wi n g se r ie s o e p r es s io n s
eratiobetw eenthepow ersnecessar toprope l
ingspeeds:
x _ /. _ /A } K V _( A W/ V
7:" W \ D \ l ~- D \ l
l isto e pressionsinw hichthe law
ethusrepresentedisb nomeans
al l a re e u i a l en t a nd e u a ll c o rr e ct a n d
s pro idedthefundamenta lcondi-
. e . i theshipsaresim ilarandthespeeds
now thedata inan onecase it isasim-
v a luef orasim ilarshipatacorre-
es s io n s ha e b e en g i e n f o r c o r r e-
h a i n g gi e n o nl D l a n d D w e t ak e
1 .0 85 , = I 7 -4 -
00 X I X
a ki n g ot h er e p r es s io n s f o r ~ , t h e sa m e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
d. H encethesim ilarshipo displace-
w ouldre uire5230I . H. P .
larit betweenthetwoshipsis
e s o ur c es o e r ro r i n th e u se o t h is
nsiono the law o comparisontoskin-
possibil it o adi f erence inthepropul-
thetw ocases. Thenatureo theerror
esehasbeendiscussedabo eandin26.
ma beseenthati thespeedo the
a m pl e i s l ow o r f a r f r o m th e n or m al s p ee d
icientwillprobabl bepoor andlessthan
pectedf orthesecondshipi nearher
thepowero thef irstshipinsuch
otherthingsbe inge ua l result inan
ow erforthesecond.
er e o r e j u d gm en t m us t b e us e d as t o
sar condit ionsareful i l led andasto
tobeplacedontheva luesresult ing
m p ar i so n .
L T D S P A C E M N T C OE F F I C I E N T .
ormulaef orpow eringw hichha ebeen
ars nonehasobta inedsow ideandgenera l
l ingtheuseo theso-ca lled
entconstantorcoe f icient. Thisf ormula
nganteriortothe introductiono the
ndw esha llf indito interesttoe amine
w.
ssedb thee uation
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
ease.Theresultis thatH becomes
greaterthan3 andw eha ea
e v a l u eo K .
moderateandabundantin orma-
tngtonearl e ua lshipsatnearl the
thiscoe f icientw asreasonabl satis-
mp t io n h o we e r w a s al m os t e nt i re l a
andtherew eref ew guidingprinciplesb
de initeva luemightbedeterminedas
case.
lainthiswa hasthere oreinrecent
a or andit isw ellunderstoodthatthus
b e e p e ct e d to g i e a r o ug h a pp r o i -
lein an proposedcase.
t he r e la t io n ' o t h is f o r mu l a to t h e
eha einonecase
andZ > aaresim ilarshipsanduland
g sp e ed s . Th e n f r o m 6 1 ( i w e h a e b
w it h ( 2 , i t f o l lo ws t ha t K , * A \ = i
e t h e re o r e de r i e t h e im p or t an t r es u lt t h at
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D PR O P U L S I O N O F S H I P .
pondingspeedsha ethesameA d-
t
statemento thelawo e tended
chitw il lbee ua ll correctw ithan o
edinthe generale uationo
mentsuppliesthere oretheprinciple
h e ch o ic e o A d m ir a lt c o e f i c ie n ts a n d
ogni edandf o llowed thisf ormula
mitsf ormerconditiono re lati eunre-
hesamele e l orrathermadeiden-
tendedcomparison asa lread so
ed a b o e .
ample letustak ethef o llowing:
data isaspeed-pow ercur ef ora
ment6000. Weha enow tof indthe
shipwillcorrespondwiththef ormer.
o t he r d at a w e ma t a ke t h e ra t io
1 . 04 9 . H e n ce u = 1 8 - - 1 . 04 9 1 7. 1 6.
ncur eataspeed o 17.16 suppose
e h a e t h en D l 6 0 00 u l 1 7 .1 6
itutingthisintheA dmiralt f o rmula
o w b t h e la w o c o mp a ri s on a s a bo e
cientissuitable f orthesim ilarshipo dis-
espondingspeed18.H ence
ntheformula w ef indf orthepro-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
dareunderthesamelack o con i-
describedw henusedinthesamew a .
s " K i r k s A n a l s i s " a n ap p ro i -
acew asfoundb computingthato
withprismaticmiddlebod and
da terbodies. Theappropria teva lue
umedf romthedataa a ilable insim ilar
oreespecia ll intendedf orthe
merso moderatesi eandspeed w ith
a a ilabletoser easaguide inthe
so theconstant. Underthesecircum-
f a i rl s a ti s a c to r r e su l ts a s i nd e ed
ermethodsherediscussedw henusedin
u gm e nt e d su r a c e m et h od t h e we t te d
m mo n l t h e re d uc e d su r a c e 8 w as
rcalledthecoe f iciento augmentation.
unctiono thef ormo theshipatthe
c al l o t h e an g le s o m a i m um i n cl i na -
ater- l inesatthebow . Theareathus
augmentedsur ace. ' I tsv a lue
a b o e a n d ap p ro p ri a te v a l ue s o K ^
asinothercases.
ormulaproceededontheassump-
ancenecessar toconsiderw asthe
stthattheresistancemightbeconsidered
uareo thespeedandhencethepow er
ed ; a n d f u r t h er t h at t h e in l u en c e o t h e
o g l id i ng o r t he r e la t i e v e l o c i t o s k in
sentedb thisf unctiono theangles
disinterestingas containingan
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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H I P .
n luenceo thef ormatthebow .
u at e h ow e e r t o pr op er l p ro i de f o r
o r m in g e ne r al o r f o r v a r i n g sp e ed s . I t
e actl thesamelim itationsanderrorsas
ediscussed andre uiresthesamek ind
he p r op e r se l ec t io n o t h e co e f i c ie n t in -
ormulaetothelawo e tendedcom-
tica lw iththato thetw opre iousl
isseenthatthe area llspecia lcases
w hichtheshipisrepresentedb an
unction andthespeedhasthe
o r e th e a r e us e d as e p r es s io n s o t h e
mparisonthe w illha ethesameauthorit
resultsasan o theothere pressions
l l s uc h f o r mu l ae m a t h er e o r e be m a de
w o e tendedcomparisonb thesimple
pondingspeeds^ v illha ethesame
o r m u la f o r p ow e r.
C I A L C O N S TA N T .
orthelawo e tendedcomparisonin
r i e t o " c o ns t an t s " o r c oe f i c ie n ts
w ouldbethesamef orsim ilarshipsat
econstantsconsideredin62
ld er i e d f r o m th e f u n ct io n / ; / . O f t he
mightbefoundinasim ilarmanner
t o th o se d e ri e d f r o m t h e f u n c t io n s Du a n d
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
e b K z a n d K ^ w e h a e f o r t he c o rr e -
orpow er
psatcorrespondingspeedsthesame
nt K z b e t ak e n o r t he s a me v a l ue s o t h e
comparisonw illbef ul i l ledandthe
beusedf orthedeterminationo pow erb
samemanneraswiththosediscussed
iscusstheuseo thesev ariouscon-
geometricalsimilarit isnotcom-
F C O M PA R I S O N W H E R E T H E S H I P A R E
Y S I M L A R .
he law o comparisonhasnosigni icance
milar. Wherethe are an and
pressionsf orcorrespondingspeeds f or
w erw illgi ee actl thesameresults.
n ot p e r e c t h o we e r t h e v a r i ou s
espondingspeeds f orresistanceandf or
sameresults andw hilestrictl none
uitee identthatthe ma a llbeconsid-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
moreorlessnearaccordingtothe
andtotheparticulare pressionused.
orethatinsuchcases andhence inmost
actua lpractice it isnota ltogethera
encew hate pressionsareusedf orthere la-
andbetweenthepowersin thetwo
noteclearl thetw oquestionsin o l ed:
eenthepow ers and( U ) there lation
rthede init iono " corresponding
tothe latter w earef reetotakean
e ss io ns o 2 6 ( 7 a nd ( 8 . C o r re sp on d-
obethosef orw hichthe li uidsur-
milarshipsshall alsobesimilar.These
hew a e- ormation andthisonthe
ethanonan otheronef eature . I t
erableto f i thecorrespondingspeedsb
s andw etak ethere ore
w illdiscussthethreefunctions
t t 4 , o r t h e f u n c t io n s wh i ch g i e r i se t o t he t h re e
, K ^ a s ab o e d er i e d.
seis e ui alenttotheassumption
correspondingspeedsthepowerv aries
ns mbols
me n si o ns o t h e sh i p b L , B , / /
t b b a n d re m em b er i ng t h at u ~ L * w e
satcorrespondingspeeds
b
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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N C E A N D PR O P U L S I O N O F S H I P .
ssumemorebroadl thatresistance in
sedastheproducto somefunctiono
re o t h e sp e ed t h e us e o t h e co n st a nt
t t o th e a ss u mp t io n t ha t s uc h f u n ct i on i s B J i b .
u F u 4.
w eassumethatresistance ingenera l
eproducto somef unctiono theship
o t h e sp e ed t h e us e o t h e co n st a nt K z
ssumptionthatsuchf unctionis-= . .
uationo resistance in o l ingthe
erso thespeed letusintroducethose
i c ie n ts . W e h a e t h en
tanceinthisf ormisthusseento-
t h e co e f i c ie n t K z a s a bo e .
i n d f o r t h e f o r m o t h e ge n er a l
pondstotheuseo thecoe f icientK
r X ( 2
chcorrespondstotheuseo K ^
Q ( B hb ^ ( 3
t ha t ap pr o i ma te l ( D ) ^ ~
J * ~ 5 . W he nc e we m a w ri te ( 3 i n
Q ( B hb u ( 4
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P . 353
ere lationo thethreef unctionsto
shipandtheblock coe f icientasf o llows:
u n ct i on D u i s e u i a l en t t o L * B k b ;
essionsit isreadil seenhow the
ouldv ar incasesw herethesim ilarit isnot
atthesecondshipisre lati e l longer
ength-ratiowillbe greaterthanthe
asderi edf romtheabo ee pressions
romthef irsttothe last. V icev ersa
b ro a de r d e ep e r o r f u l l e r t h e f i r s t o
w ouldgi ethe largestv a lue andthe
ss.
standpointo thef ormulao resist-
asthough( 3 , andhencethef unction
antK ^ shouldbethemostnearl correct.
ndicate how e er thatthere isnoone
ca b le t o a ll m o de s o v a r ia t io n f r o m e a c t
icientdataare lack ingforthede initere la -
formo f unctiontothenatureo the
it .
adeo thef unctionZ # w hichis
ciall inconnectionwithaspeed-ratio
u n ct i on s D u a n d D u o r t he c o ns t an t s
berecommendedinpre erencetotheothers.
tobethemorecorrect though
thefactthatit isthew ell-k nownA dmiralt
enmuchused andsuchuse islik el tocon-
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
sontow ide l dissimilarf orms but
ormso e pressionaremostlik e l to
suchslightvaria tionsase perience
tedw ithoutsensibl a f ectingthe
asstated.
S MO D O F C O MPA R I S O N .
o displacementDlandZ > 2atspeeds
g e ne r al " c o rr e sp o nd i ng . T h en i t i s al w a s
delso di f erentdimensionsuchthat
l correspondtoDl andtheother
pleso 26w eshouldthenha ethe
hetota lresistanceso themodels
en
utiono Mechanica lEngineers 1896 p. 79.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O F S H I P .
v a l u e s as a b o e w e f i n d
2 = 5 2+ W v
a, slts t, aretobecomputedin the
propria teva luesf orthesk in- resistance
mngalsofortheshipDltheratiobetw een
. H . P .( C E - = - A E , F i g . 66 , w e c a n
nd h en ce W ^ T he v a l ue o n i s f o u nd b
andd simultaneousl f romtheendso
rmediatepoint.Thepointo sup-
ti lthebarremainsatrightanglesto
I nthiscondit iontheresistancesare
e r se r a ti o o t h e le e r -a r ms a n d he n ce a
tterw illgi ethev a lueo nasdesired.
espossibletodeterminethev a lueo W ^
t h e to t al r e si s ta n ce 5 2 + W ^ .
t h e ab o e m e th o d o t r ea t me n t l e t us
parisontoco erthetotalresistance
onl . L etthee perimentbemadeas
eo nsim ilarl determined. Thendenot-
/ , r , r v w e ha e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
n j j
comparati e nod namometric
andthee perimenta ldeterminations
mp l e. S i n c e h o we e r t h e re s ul t s ar e
bso lute itsf ie ldo use ulnessw illbe
sonwiththe usualmethodas
U S S E C T O N S O F A D S P A C E M N TS P E D
A C E .
a lserieso ships a llo thesame
a w o e t e nd e d co m pa r is o n f u r n i sh e s th e
lltheshipso suchaseries no
mentorspeed. I t isthere oree i-
w ercur ef oragi endisplacement
hespeed-powercur ef orthew hole
nappropriatemodi icationo hori ontal
p po s e f o r e a mp l e t h at w e h a e a
entDlplottedwithsca lesasf o llows:
un i t = p k no t s. O r d i n at e I l i ne a r un i t =
amecur ew illa lsorepresentthespeed-
w iththefo llow ingsca les:
un i t = p - ^ - k no t s
un it = g j r I . H . P.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
c at i on s t h er e o r e o n e cu r e w ou l d
so v a lueso pow erf orthevarious
ntandspeed.
w eenS peedandPow er. Displacementconstantf or
ontheright.
M N T
betw eenDisplacementandPow er. S peedconstantf or
ontheright.
uchaserieso v a lueswouldre uire
esentationasur aceo w hichthe
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
/ / locatedb abscissaecorresponding
Dandu. Thev arioussectionso this
aa lle lto thea eso H anduw ouldrepre-
c ur e f o r a g i e n v a l u e o D .
there oreberepresentedb a
ingsca les orw ithuni ormsca lesand
erredtoma alsobecutb planes
H andDorDandu thuscuttingout
M N T
betw eenDisplacementandS peed. Pow erconstantf or
ontheright.
ingthere lationbetweenH andDf ora
a n d th e o th e r th e r el a ti o n be t we e n D an d u
e o H . T h e v a ri ou s cu r e s o s ec ti on a re
6 a n d 97 a s t ud o t h e ge n er a l ch a ra c -
berecommended.
O N O F T H E L A W O F C O M PA R I S O N T O S H O W
L R E L A T O N B E TWE E N S I Z E A N D
C A PA C I T F O R A G V E N S P E D.
d en ot e th e cu r e o E . H . P . f o r a gi e n
acementatspeedsf rom10to20
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
modeltak enasthet pef oraseries
cementf rom5000to20oootons. Thenb
rmationtheE. H . P . f oreacho these
rm i ne d f r o m t h e gi e n c ur e a s e p l ai n ed
ngaconstantpropulsi ecoe f iciento
192C
O T
s o t h e I . H . P. m a b e s im i la r l o b ta i ne d
t h e or d in a te s o w h ic h a re e u a l to t h os e
a c o ns t an t p ro p ul s i e c o e f i c ie n t co u ld b e
O - t p e s hi p C D w ou l d be i t s cu r e o
h o we e r w i th t h e sa m em a ch i ne r a t
e p r op u ls i e c o e f i c i en t w il l v a r s o t ha t C D
rrespondtoane perimenta lcur e
n e sh i p a n d we m a m o re p r op e rl c o n-
eproportiona ltoE . H. P . L etus
f o r o u r s er i es o s i mi l ar s h ip s a l l at 2 0
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
twhichthe5OO O -tonshipw ill
Datthis speed letitbe denoted
P . f orthesimilarshipat20k notsw ill
e A B , F i g . 99 w hi c h sh o ws t h e
orthesupposedserieso ships. The
8 3 0
N T I N 1000 TO N U N I T
showspla inl thatH increasesatamuch
actinthisparticularcasetherate is
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D PR O P U L S I O N O F S H I P .
rooto thedisplacement. Ne tsuppose
andf itt ingstobe. 50o thetotaldis-
eseries. Thisratiow illv ar consid-
t peo structure andw ouldnot
esameinshipso sogreatdi f erence in
h ow e e r t he v a r ia ti on w il l no t be s u f i -
enera lnatureo there lationswhichw e
somesuchassumptionisnecessar in
cessar simpli icationintothere la -
rd i na t es t o t he l i ne O D F i g . 9 9 w i ll
ment andthosebetw eenOH andOD
etc. Tak ingthetota lw eighto
asone-ninthtonperI . H. P . or9
dcoa lat1. 8poundsperI . H. P . perhour
dassumingenoughcoa lf orase en-da s
ariationinDdue totheconsumption
r o therw ise consideringthatthemean
ipcorrespondstothev a lueso the
oundthatthew eighto machiner and
theordinatebetw eenO H andC C .
weenC C andthea iso X is
ingorearningcapacit . I tappearsthat
O - tonshipcouldbare l mak ethe
easDincreases theearningcapacit
se risingto3000tonsforZ > 16ooo
0ooo.
itroughl thattheoperatinge penses
w er thetimebeingthesame the
, re la ti e toe penses theearning
Disincreased. Thusf orD= 9000
esentedb 14400andtheearning
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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H I P .
00 0 t on s w h il e b a n i nc r ea s e o D t o
nthee pensesare increasedb
earningcapacit b 200percent.
l e t us n o te t h e v a r i at i on o c a rr i n g
helengtho v o agebeingconstant.
O T
ationthe12ooo- tonship. A B isthe
heconstantordinatebetw eenC DandE F
hto hullandf itt ings. Theordi-
dGH denotethew eighto machiner
ecreasingwiththedecrease inpow er but
eo time.Theordinatesbetween
then thetota lw eightsonthesamesuppo-
mainingordinatesbetweenGH and
io n o c a rr i n g ca p ac i t w i th s p ee d a n d ho w
ghtatthee penseo thef ormer.
orthesev ariousrelationshipsinan
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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E A N D PR O PU L S I O N O F S H I P .
onman considerationshereomitted.
heresults howe er issu f icientl
ms w hicharechie l intendedassug-
the law o comparisontothestud o
scharacter.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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.
.
T O R Y .
o atrialtripis todeterminethe
ma bemainta inedcontinuousl f o r
eI nadditiontothisfundamenta l
sirabletoobser esuchdataasbearin
ra lproblemo resistanceandpropulsion
ariouscharacterist icsma be
f erentpo intsonwhichin ormationis
ationo speedit issu f icientto
r ationso distanceandtime. We
detailthemeasuremento power
edb indicatorsintheusual
iousmeasurementsnecessar f orthe
dma v ar somew hatw iththe length
a h a e ( i a l on g co ur se a s f o r e a m-
esormore o erw hichbutonerun or
chdirection istobemade or( 2 a
n e or t w o mi l es u s ua l l t h e f o r m er o e r
a bemadeasdesired.
shbetweenthepurposeo thetrials
determinationo thespeedorpow er or
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
_ u s e # p d
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C E A N D P R O PU L S I O N O f S H I P .
eo condit ions suchasf ullpoweror
m pl e ; o r ( b t h e de t er m in a ti o n o t h e sp e ed
o v ar ingcondit ionssothatthe
eenspeedandpow erf orw idel v ar -
a bedetermined.
l m e nt i on t h e ch i e p o in t s re l at i ng t o
luencespeed andthecondit ionstobe
m u m s pe e d.
Thisshouldbeaslightaspossible
isnotindependento ( b and( c .
r acesshouldbesmooth blades
nditmustbew ellimmersed.
ncewillnotpresumabl v ar sen-
es o t r im b u t it m a r e su l t th a t a v e r
uchf ore ampleasmightbenecessar
henthedisplacementisver l ight
asetheresistancef orthegi endis-
therei salsotheaddedloss dueto
e th r us t .
houldbesmoothandf reshl pa inted.
a . Th e w in d s ho u ld b e l ig h t a n d pr e e r -
m or a l i tt l e ah e ad i n o rd e r to g i e t h e be n e i t
r tf orthebo ilers. Theseashould o
thef undamentalandsecondar
hef o llowingdataarere uisiteor
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.367
ctingthere lationo theshiptoresist-
uchas
k nown.
s id e o v e s s e l.
u nd e r wa .
w indandw a es.
w hichareobser edatthetimeo the
co theshipando thepropellerare
D C O N S I D R A T O N O F TH E O B S E R V A T O N S TO
ia lre erencetopow er w ef irst
which weareconcernedisthat
entheshipthroughthe water
erthegroundorbetweenf i edpo ints
o t idesandcurrentsmust there ore
hedistanceactua ll tra ersedthrough
tance itse l w eha etw ogenera l
satanchor andrange-mark s. The
blef ora longcourse w herethechange
w ingingtothetidew illbeo nore lati e
ourse sucherrorswouldbeinad-
o thecoursemustbemark edw itha ll
suchcaserange-mark sonshoreare
g. 101A B andC Daretw opairso
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E A N D PR O PU L S I O N O F S H I P .
rminingthetwoparallellinesA B
hensomelineE atrightanglesto
uchadistancef romtheshorethatthe
esu f icienttoa o idsensibleretardation
otheranges tw ore uisitesarethere-
e r to d e i n it e l f i t h e co u rs e a d ir e ct i on
tonisusuall k nownb compass
sirabletomark itb rangesand
sisa lsousedto indicate itsappro i-
rencetotheproperdeptho w ater.
oursethereshouldbeplent o roomf or
a iningheadw a be oreenteringtherun
sde elopedin77showthat the
r runshouldbepre erabl notless
eemsto beinagreementwith
rchiba ldDenn suggests* thattheship
uno atleastone-hal m ile and
oreenteringthecourseproper.
nationa lC ongresso MarineE ngineersandNa al
1 8 93 . P ap e r x x x i .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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.369
urseatright anglestoA B andC D
uelineasE^ ise identw ithout
swillbeshownlater thetidal
t-coursetria lma beappro imate l e lim i-
eatmento theotherdataobser ed.
nonedirectiononl suche lim ina-
dw ithasinglerunineachdirection
actoril usedw ithoutspecia ltreat-
no t ida lin luence. I t isthere ore
a emadespecia lt idalobser ations.
atsorshipsma beanchoredatinter a ls
a longthecourse andshouldmak eobser a-
tenasonce inf i teenminutesthroughout
ationsshouldpre erabl bemadeat
a to thevesse lundergo ingtria l. The
e s i mp l t h e co m po n en t o t h e ti d e in
urse orperhapspre erabl thew hole
tion. S uchobser ationsareusuall
ntor tarlraillog.Thisconsists
lscrew propeller w hichinthecaseo
edastern there o lutionsbe ingcom-
w ingcordorb othermeans toa
hecaseo av esse latanchornear
sucha logisbuo edashortdistance
ppropria tedepth andobser ations-
ecomponento thetide inthedirection
desired the logmustbemainta inedin
entirev e locit andthedirectionare
the logmustha eav aneattachedand
th e t id e . A s s h ow n b F r o ud e s
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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C E A N D PR O P U L S I O N O F S H I P .
struments i madewitha llthecare
ctiono apieceo trul scienti ic
r e li a bl e . A s u s ua l l f u r ni s he d h o we e r
ection andshouldberatedinw ater
dnearthatatw hichthe areused.
is h o we e r o l e ss i m po r ta n ce i n
whensuchinstrumentsareused to
e l oc i t o t h e sh i p it s el . I n a d di t io n
ns thetimeo passageo theshipat
thatw eha ethusatourdisposala
atf romf ourtoe ightpo intsa longthe
o bs e r a t io n s at i n te r a l s o a b ou t f i -
o letrial.
t ida lobser ationsaremadeatall
sw illnaturall bemuchless according
degreeo accurac w ithw hichthe
anceisdesired.
timecare ulobser ationwith
icientf orlong-coursetria ls. F or
bableerroro readingwiththeusual
dw atchma becomesensible . F orsatis-
t op - wa t ch e s ma b e u se d o r p re e r ab l , f o r
omef ormo chronographb w hichan
he instantcontactismadeb the
countingo re o lutionsona long-
r engine-counterisquitesu f icient.
thesamemeansma beused though
s actor accurac isatta inedb the
phicarrangement. I nWea er sspeed
P u b l i c D o m a i n
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.
apapertape isf edatauni ormspeed
ca ll contro lledpens. Oneo these
k mak esamark e er second. A nother
maker andisusedtonotethe
dlea ingthecourse. Otherpensare
w itheachmainsha tandthusregister
u c h a n i ns t ru m en t i s o c o ur s e o n l u s e d
os t o t h es e a re s e l - e p l an a to r .
bedeterminedb measuringdown
e n. T h e us e o p h ot o gr a ph f r o m a
a lsobesuggested. Thechangeo
atrestandw henunderwa ma be
o apendulumad ustedtosw ingina
O N O F T DA L I N F L U E N C E .
bser ationsmadeonashort-course
s id e re d a s f u r n i sh i ng f o r a n g i e n
lve locit , andthecorrectionconsists
radding asthecasema re uire .
w herese era lhoursma bere uired
theassumptiono a sensibl uni orm
andthemoredeta iledobser ations
becomenecessar .
hodo appl ingthecorrectionisas
, , e tc . d en ot e th e le ng th s in m in ut es o t he
a lsbetw eenpassingthepostso obser-
v v e t c. b e t he t i da l v e l o c it i es p e r mi n ut e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E A N D PR O PU L S I O N O F S H I P .
uccessi estationatthe instanto
-be ingconsideredasdenotingave locit
he s hi p. T he n \ ( v ^ - - z / , % ( v y - -
v t ) t e t c. a r e ta k en a s t he m ea n t id a l v e l oc i ti e s f o r
a ls. Thecorrespondingtidalin luences
;
will bethensimpl thealge-
alcorrections.
moreaccurate inprinciple the
ggested:
asiswellknown aree pressible
unctionso t imeanddistancef roma
tida lve locit a ttheshipatan instant
appro imatel asasinusoida lf unction
F i g . 10 2 l et t h e or d in a te s a t ( 9 P
dalv e locit iesatthesuccessi epo intso
o n a t im e ab s ci s sa . Th e n O P P Q , e t c.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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.
e inter a lsbetweenthepointso obser-
ttemptingan re inedana l siso the
ma q uiteclose l obta inacontinuous
e locit a ttheshipateachsuccessi e
u gh t h e po i nt s ^ , B , C , e t c. a s m oo t h
ndthecharacterist icso asinusoida l
a re a o t h is c u r e b e f o u n d b a p l an i me t er
negration theresultw illgi ethetotal
t ide + oraccordingtothecir-
e. Thetotalcorrectionf oundine ither
nappliedtothetota llengtho thecourse
edlength f romw hichincon unction
sdirectl f ound.
hee liminationo t idalin luencef or
specialobser ations.
hetimere uiredtomak eadouble
dewillbeso smallthatwithout
ocit ma beconsideredconstant
sethesimplemeano thetw oruns
h e tr u e me a n sp e ed t h us :
( u - v ) u + ,
is k n ow n a s th e m et h od o " c o nt i nu e d
sobeenmuchused. Thisisasf o llows:
made tw o ineachdirection gi ingappa-
t a , ? / ? / 4 . T h es e a re t r ea t ed a s s ho wn b t h e
ge
ntakenas thecorrectspeed thus
dsobser ed. Thisise ui a lentto
thirdrunsthreetimesthew eighto the
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
dthef ina lresultma bemorereadil
mu l a th a n b t h e ac t ua l f o r m a ti o n o t h e
a e r ag e s.
ag e .
s
methoddependsoncertain
brie l note.
minconstantatu. Letthetida l
s ed a s a f u n ct i on o t h e ti m e as f o l lo ws :
te ua lt imeinter a lsw hichma
ortheapparentspeedswesha llha e
b - - 4c ;
ormulaf orcontinueda erages
i nd
thetruespeedremainsconstant
en c e v a r i es a s a q u a d ra t ic f u n ct i on o t h e
P u b l i c D o m a i n
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.
e in t er a l s ar e e u a l t h is m e th o d wi l l gi e
ctua lcase how e er notoneo
neralbef ul i l led. I t isthere ore
o f o u r ru n s th u s re d uc e d is a n m o re
a erage orthanthea erageo tw o
timeinter a laspossible .
thatw henthetide isj ustonthe
er i s f r e u e nt l a f e c te d b e d di e s
w hichthoughsmallinv e locit areso
nastode y an attemptate lim ination.
t h e ti d e is a t a bo u t ha l - e bb o r h al - l o w t h e
butquiteregular. Thisresultsnatura ll
a ractero t ida lmotion asaresulto
e locit isleastw hentheve locit is
de andthechangeisgreatestw hen
ullt ideorslack w ater. I tf o llowsthat
de inedregulartida lv e locit uni orml
urse isingenera lpre erabletoslack or
pan ingeddiesandirregularities.
ea lingw ithtida lin luencesw illbe
tion.
L S F O R T H E P U R PO S E O F O B TA I N I N G A C O N -
L A T O N B E TWE E N S P E D R E V O L U T O N S ,
eenconcernedw iththeactualtrue
tre erencetothecorrespondingnum-
th e I . H . P . n ec e ss a r . F o r t h e i n e s ti -
e p e r o r ma n ce h o we e r i t i s q u i t e
icientdatato f urnishacontinuousre la-
uantities.F orthispurposethe
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P ,
uitable.Theactual conducto
erentf romthata lread described
hadecreasingserieso speedswith
tionsandpowers toanumbero
nbemainta ineduni orml b the
theproperdisposit iono thedata
plicatedthanwhenspeedalone is
odeterminenotonl thetrue
o lutionsandI . H. P . w hichcorrespond
o u nd d i f i c ul t e e n f o r a n o n e ru n
onsandpowerconstant.W ithcare
slight butatthebesttheq uestionma
roperinterpretationo thedata
e p ow er r e o l ut i on s a n d tr u e sp e ed
n d / / , 7 V a , u . 2 t h o se f o r t he s e co n d v b e in g
enasconstantf orthetw oruns. Then
urnishusw ith
+ ) ;
, - ) .
obeatthesamespeed thev aria -
w ema properl assumetheslipo
mef orboth. A saresultthetrue
l w iththere o lutions andthetrue
ndtothemeannumbero re o lu-
P u b l i c D o m a i n
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.
e ingenera l
keon theshipandon thespeed.
s pe e d is n o t la r ge w e ma s a e l t a ke
nasnegligible . I nthepresentcase
h a e
o thise uationisinthe same
a b o e a n d it m u st t h er e o r e gi e t h e
hichcorrespondstothetruemeanspeed.
eobser edpowersH land// isthen
d si d e o ( 2 a b o e . T h e e p o ne n t n
betw een3and4. A sanil lustrationlet
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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N C E A N D PR O P U L S I O N O F S H I P .
f ind
eragewouldbe3400 andasthe
uremento pow erarere lati e l f a r
erencethusresult ing andasthesev a lues
epresentav aria tiongreaterthanwouldbe
econdit ionsassumed itseemsfa irto
ew ema properl tak ethemean
N S
themeanspeed.F ortworuns
k t h er e o r e t h e me a n re o l ut i on s
pow er asa llcorresponding.
beingmadeata lowerpower
ound andsof ortheentireseries.
P u b l i c D o m a i n
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.
a e f e c t th e g en e ra l a e r ag i ng b
lows:
re o lutionsasinF ig. 103 each
dingtoadoublerun intendedtobe
. Thenaf a ircur epassingthrough
a betak enasthebestappro i-
elationbetweenre olutionsand
plotthemeano thespeedsasan
there o lutionsasanabscissa asin
husgi ingacontinuousre lationbetw een
stra ightlineOA showssim ilarl
T O N S
ntslipwereo. Hencethevertica l
andOB showsthecorrespondingloss
romthesediagramsw ema then
rdacur eshow ingthecontinuous
ndspeed.
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
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E A N D PR O PU L S I O N O F S H I P .
there lationbetw eenre o lutionsand
plottingeachseparatespeedonre o lu-
usobta iningtw ocur es onef orspeeds
peedsaga instthetide w ithpairso
ere o lutionsoneach. A meancur e
dre lationbetw eenre o lutionsand
entmodeo graphica ll determiningthe
tionsandtruespeedis thatdueto
w h ic h i s br i e l a s f o l l o ws :
erbackandf orth goingo er
o f asw ellasonthecourse sothat
eenthemiddlepo intso therunsma
s t he s p ee d s. F o r e ac h s uc c es s i e r u n th e
sedb asnearl aspossibleane ua l
serieso runsatcerta inre o lutions
herseriesw ithotherre o lutions
these isthenplotted gi ingcur es
o lutions w ithandagainstthetide.
takenasthecur eo truespeed. The
eanso anil lustrati ee amplethat
theabo econditionsw ellw ithinpracti-
dalin luencew illbee lim inatedw ith
curac f ora llpractica lpurposes.
orthismethodis thatagi en
satis actoril co eredw ithasmaller
henthe aremadeinpa irsaspre-
c. o N a a l E n gi ne er s v o l . i . p .5 87 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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.
B E TW E E N S P E D PO W E R A N D R E V O L U T O N S
-D S T A N C E TR I A L .
betocarr onsuchatriala t
actualcasetherew illnatura ll a rise
nthevariousq uantit iesin o l ed.
eanre olutionsarereadil f ound
amounto v aria tionw ema presum-
rrespondingtheoneto theother.
whichcorrespondsto suchmean
how e er there ismoreroomf oruncer-
ea serieso indicator-cardstaken
thetrial andgi ingpresumabl the
essuresinthec lindersatthe instantin
tionsarea lsotak enatthesametime
iongi esthedataf ordetermininga
tthatinstant. Themeano thesere o-
il lnotbethetruemean dueto indi idual
a n d to t h e f a c t t h at t h e a r e me r el a
ueso N , w hile thetruemeanis
inuouscountergi ingthetota lnumber
t h i s ac c ou n t t h er e o r e a n d f o r f i n di n g
mspre erabletousethemeane f ecti e
ds andthetruemeanre o lutionsf rom
hodf ordoingthiswe ma
n a n g i e n p ro p el l er i t i s re a di l s e en
themeane f ecti epressure inthe
e i n i t e l b e t w ee n t he m e an e f e c ti e
1. p. c linder( 47 , andthethrust
stanceo theship mustbev er nearl
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
e r w i de l v a r i n g co n di t io n s. W e m a
ssumethatthereducedmeane f ecti e
er nearl astheresistance. Denoting
/ > , , e t c. w e ma , w i t h a ll s i gn i i c an t
e me p r es s ib l e in t h e f o r m / = b N * j
dingthemethodoutlinedin73for
dhereusef orthef ina lmeanpressure
me a n s u a r e r oo t s o t h e v a r i ou s v a l u e s
ssureusedw iththetruemeanre o lu-
nappro imationtothecorresponding
i c an t a cc u ra c a t l ea s t so f a r a s
aathand.
ment butusuall w ithoutpractica l
su b st i tu t io n f o r 2 o a n i nd e t o b e
a le aminationo there lationbetween
dpow er.
thepow erisnotunusua ll la rge the
s u a re r o ot w i ll n o t se n si b l d i f e r f r o m
an andinsuchcase thelatterma
heamounto thevaria tion le tthree
d b 6 4 8 1 a n d 10 0 . Th e n th e s u a re
rootis81 and- thearithmeticalmeanis
essthanonepercentine cess.
ethatina llusua lcasesw ema , f or
othemeanre olutionsorspeed
a lmeano thepressures asabo e
ns. A tthesametimethesubstitu-
t h e me a n s u a r e r oo t f o r t h e a ri t hm et i -
gi eamorecorrectresult andi
ni icant the lattermethodshouldbeuse
P u b l i c D o m a i n
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.
S E TR I A L W I T H S T A N D A R D Z E D S C R E W .
a llcasesassumedthemeasuremento
tedb meansindependento theship s
long-coursetria lhasbeenusedto
e r b m e an s o w hi c h th e p ro p el l er
e n st a nd a rd i e d i s m ad e t he i n st r um en t f o r
edistance.Thisisknownas the
thod andhasbeenusedincerta in
esuggestiono theB ureauo S team
a y D e pa r tm e nt .
nthemeasuredmileand thecon-
peedandre olutionsasdiscussed
ermined. Theshipbe inginthe
sdra t trim condit iono bottom
nsmoothw aterandca lmw eather and
measma bedesired. F orthebest
hecountershouldbetak ene er ; tenor
a n e e n t th e t ot a l ti m e an d t ot a l De o l u-
ator-cardsare o course tak enat
oughouttherun.
on s ha e b ee n un i o rm o r i t he h a e
tnotouto arangew ithinw hichthe
k enassensibl constant then asin
dandthemeanre o lutionsw ill
o rmerma bedetermineddirectl
e ai d o t h e cu r e o s t an d ar d i a t io n .I f
re o lutionsarewide l v ariableandthe
w ithre o lutions thiscorrespondence
causeo theerrorandamethod
a beseenasfo llow s:
P u b l i c D o m a i n
/ h t t p : / / w w w . h
a t h i t r u s t . o r g / a c c e
s s
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E A N D PR O PU L S I O N O F S H I P .
5 b e a t im e a bs c is s a on w h ic h a re l a id o f
enumberso re o lutionsperminute
e aretaken. A smoothcur eA B
thusf oundgi esacontinuousrela -
o lutions. Thenf romthecur eo
edcorrespondingtoeachnumbero
ound. Thesebeingplottedatthesame
eC D^ showingthecontinuousre lation
TheareaO C DX be ingfoundb
imate integration theresultw il lbe
stance andthetimebeingknown
usdetermined. I now theapparent
B , F i g . 10 4 a s t ra i gh t l in e t h e cu r e s
besim ilarandthe integrationo A B w ould
easthato C D. B utthe integration
d b t h e re o l ut i on c o un t er a n d he n ce t h e
eterminedwouldwithconstantslip
rtruespeed. A ga in i there o lutions
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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.
dentthatbothA B andC Dbecome
X andtheirconstantratiow ould
d r e o l ut i on s g i e n b F i g . 1 0 4 f o r
the latter.
re n o t f u l i l le d t h at i s i r e o l ut i on s
p wi t h re o l ut i on s t h en t h e cu r e s A B
besim ilar andtheuseo thef ormer
themeanre o lutions w ouldno longer
t.
o v aria tionintheseq uantit ies
llbenegligibleandthemeanre o lutions
werhasalread beenconsidered
antageso thismethodmentionma
wing:
dalcorrectionstoconsider. Thisarises
meanso thestandardi ationthepro-
ntf ormeasuringdistance.
r' tria lisindependento thepresenceo
rse-mark ersandf ortida lobser ations.
ot i n a l id a te d b d e pa r tu r e f r o m a
oursedesiredma bef o llowedso long
smallenoughradiustogi erU etoa.
nedareconstantl k nownduringthe
a c t st a tu s o t h e sh i p re l at i e t o t he .
ce isk nownf rombeginningtoend.
menttothemachiner w hichmight
se n o t on l i n co n cl u si e b u t
ur n o v a l u ab le d at a w il l ha e n oe f e ct
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
tria lma beconsideredasendedat
completeten-minute inter a l and
onsideredsatis actor ornot atleast
va luabledataareobtained.
imitationo thismodeo tria lso
it o condit ionsbetw eenthestandard-
rtrialmustbecare ull noted. The
w iththeconditiono thebottom and
a n d co n di t io n o t h e wi n d an d s ea a n d
moothsea aretheonl conditions
described it isnecessar thatboth
tantiall undersuchconditions.
E N C E O F A C C E L E R A T O N A N D R E TA R D A T O N
I P DA T A .
s a nd p o we r o r me a n e f e c ti e p r es s ur e
luctuations the w illno longerha ethe
sforuni ormcondit ions. I f the
ses aportiono theresultantincrease
egoestowardacceleratingthemotion
meanpressure re o lutions andpow er
orthee istingspeedunderuni orm
w itharapidl decreasingpressurethe
utions andpowerw illbe lessthanf or
runi ormcondit ions.
ressureisusuall notsu f icientl
practica limportance thoughthe
stenceasadisturbingf eaturema be
in a te d b a k no w le d ge o t h e v a r -
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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.
perimentaldeterminationo w hich
o s ma l l di f i c ul t . A f u r th e r pr o bl e m
milarconsiderationsisthatconcerned
cnecessar toe f ectachangeo
eordecrease. Thisiso suchgenera l
connectionwiththe sub ect-
hapterthatw ema properl turnto
nt.
N D D S T A N C E R E Q U I R E D TO E F F E C T A
P E D.
ecti epressure inthec lindersto -be
o in t s o c u t- o f . W i t h a n f i e d
ere ore andneglectingv aria tionsdueto
turningmomentw illbeconstant and
themomentresistingthetrans erse
rA ga in assumingthatthedistribu-
thesur aceo thepropellerissensibl
urningmomentnomatterwhatthe
o llowsthatthere lationbetw eenthe
ane f ecti epressure isgeometrical
merremainsconstant sow illthe latter.
sma notbequitee act the must
n e ar t h e tr u th . S u p p os e t h er e o r e t h e
tsteamo agi enpressure isturnedon
f sinsuchposit ionthatthe irj o int
an e f e c ti e p r es s ur e s u f i c ie n t to g i e
nta intheshipataspeedo u k nots.
hipw illgraduall gatherheadwa and
ibl thespeed, , duringw hichadis-
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
tra ersed. I nthusconsideringthrust
entthatactualthrustandactua lor
towedresistancemust betaken.
sistanceatspeed^ , andingenera lR
ha ethenaconstantthruste ua l
ariableh draulicresistanceR . The
w i ll b e a n et f o r ce a a i la b le f o r t he a c ce l er a -
sta lsorememberthatacertain
reorlessclose l associatedwiththe
ndpartak eso itsaccelerationandretar-
o r e us e } * D i n st e ad o D . W e h a e
o r mu l ae o d n a mi c s R i s m ea s ur e d
npoundsmass. A s the irratio is
intheunit the ma bothbemeas-
t h er e o r e a s t he u n it s i n th i s e u a -
ds , . n d to n s. N o w r e p re s en t R i n t he g e n-
inedsothatR andDma be in
econdork notsperhour. I nthis
saril aconstant. Thisw illpro ide
ctua llaw o augmentedresistance. We
i ,
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.
w e ha e
n d ( 4
integrationw eassumecaconstant w e
dsf romstarting
i t a pp e ar s t ha t w he n u = , , b o t h t a nd
p a r e su l t o t h e f o r m o t h e
dcatesthatunderthecondit ionsassumed
oninde initel increasing butw ould
theamounturThisisthenatura land
h e de c re a si n g v a l u eo - 7 - as g i e n i n ( 3
andw hile itma beasuprisingresult
htheph sica lcondit ionsassumed. I n
a n e f e c ti e p r es s ur e i s ne e r e a c tl
ecorrespondingve locit uliscon-
outameanva lue. The importantpo int
ngorhow faritw il ltak etoac uire
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
a th e r a v e l oc i t s e ns i bl e u a l to i t a s
, o r. 999 , . Theserelationsare il lustrated
O N D
Distancef orga iningS peed.
a l u e s o ( 7 a n d ( 8 a r e pl o tt e d f o r s u c ce s ^
e w i ll n o w e p l a i n t he r e du c ti o n o t h e
suitable f orcomputation.
P u b l i c D o m a i n
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m i r al t d i sp l ac e me n t co e f i c i en t a s de i n ed
eenthethrusthorse-power
. P . Th e n we h a e
orse-pow er ton andk not.
oot-tonperminute ton andf oot
9 ) 3 '
_ 7.0 5i \ , ,
6 ou ~ V K ) U u -
g en e ra l f o r m f o r A * i n ( 2 , i t i s
- = - K . T hi s m a b e t ak e n as t h e de i n -
chthatw hensubstitutedin( 2 itw il lgi e
nsandninf eetpersecond. Sub-
c i n ( 7 a n d ( 8 w e s ho u ld t h en h a e
o nd s a nd s i n f e e t e p r es s ed i n t er m s o
persecond. Whilereta iningthe
sf or/ ands itw il lbemorecon en-
ght-handsideo thee uationsthe
sothatcommonlogarithmsma beused
dspeedma bemeasuredink nots
d. Mak ingthesesubstitutionsin( 7
ng / = i . i w e f i n d
lo g
P u b l i c D o m a i n
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N C E A N D PR O P U L S I O N O F S H I P .
2 4 0 an d K ~ e = 4 0 0 D
w e h a e
. . . .. ( 1 2
( 11 and( 12 areplottedinF ig.
r re d t o. T h e cu r e A B g i i n g th e t im e i s
notline thusshow inggeometrica ll the
thespeedtothe15k notsasa lim it.
kewisetherelationbetweentimeand
moreandmorenearl astra ightline in
peedisgradua ll appro imatedto .
evesse lgo ingaheadunderuni orm
atthe engineissuddenl
w it h f u l l m e an e f e c ti e p r es s ur e a st e rn .
a eadi f erentgeometrica lre lation
orceduetothe screwandthemean
t h an f o r m ot i on a h ea d . I n g e n er a l h o w-
i n s uc h c as e
llduetoengine andR = resistance
o r wa r d.
s i mi l ar t o ( i ,
P u b l i c D o m a i n
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thespeedatw hichthegi enmeanpressure
e ad . W e h a e t h en f o r ( 1 3
lmanner w eha e
. ( , 6
c l a n d c w e ma b e ar i n m in d t he
ns: Thecoe f icient< : islessthanthec
tonduetotheroundedback so the
uentdecreasedlongitudinalcomponent
acepressures. F oragi enmeanpres-
epullw ouldbe lessthanthethrust. A s
w o de inite in ormationislack ing
hde initedataw ew illtak ethepullas. 8
eva lueo clcorrespondstotheactua l
motionaheadwhenthe propelleris
nthelatter issendingastreamo
hestern thereb producingane cess
tinsteado ade ectasw henw orking
cetomotionaheadis there ore
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
creased ortheaugmentationma be
Theratiobetweenclandthecf or
espeedw ouldbee ua lthere oreto
tanceminusthis decrement and
usualaugmentation.Takingthe
mentaboutthesame thisratiowould
a n d we w i ll t h er e o r e ta k e c a s e u a l to c ^
e v a l u e o c w e ha e
utingthesev ariousv alues and
dh perbolictocommonloga-
og ^ i + \ ^ j J J . . ( 1 9
e s im pl
-
l v a l u es a s b e o r e w e h a e
l + ^ j j j ; . ( 2 3 )
P u b l i c D o m a i n
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.
o /ands f oran speeduaregi enin
us a d i ag r am o t h e e t i nc t io n o f o r wa r d
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E A N D PR O PU L S I O N O F S H I P .
ariesthroughoutasthes uareo the
s e i s f a r f r o m b e in g a ct u al l t h e ca s e.
bee pectedtov ar considerabl inthe
ingspeedf romrestorstoppingf romf ull
v a r ia t io n o K - ^ e w e r e kn o wn t h at i s
ono theactua lresistancew ithspeed
headandbackingthe f unda-
r ea d il b e s ol e d b a p pr o i m at e o r
di f erence intheresult how e er
uldnotchangethegeneralnature o
thesubstitutiono theconstantva lue
b e r em ar k ed h o we e r t h at i n t he s e le c -
a m ea n r at h er t h an m a i m um v a l u e
nf rom( 21 isthatthedistance in
ebroughttorestf rommotionaheadis
thespeed anddependsonl onthe
e istak enaspractica ll constant
w h theremustactua ll beaten-
huni ormit inthedistancerunma
ee ampletak enthisdistancew ould
l en gt hs . I n t h e ca se o v e r f u ll o r po or l
r w it h f o u l b o tt o m w e mi g ht h a e a n a e r ag e
ssthan240. A s anil lustration le tK =
0. Thenthedistancetra ersedinsuch
ef ourthso thatunderpre iouscon-
ha e f o r t he s a me s i e o s h ip
P u b l i c D o m a i n
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.
hthegeneralresults o thee peri-
t ishA ssociation * b w hichitwas
usuall bestoppedinf rom4to6
stanceseemedpracticall independent
therwords o thespeedatw hichthe
lltheforego ingthattheengine is
andthattheengine instantl gathersits
ack asthecasema be. Thisisnot
thatdueallow anceshouldbemadein
aresultswiththosegi enb thef ore-
r .
ra lnatureo theseresultsiscorrect
hatthe ha eanimportantbearingon
esselsandonthepropercondit ionsf or
miletrialsespeciall theimportance
ongstartinorderthattheshipma
imumspeedbe oreenteringuponthe
TR I C A L A N A L Y S I S O F T R I A L D A TA ,
temso data pow er speed and
plotthef ormeroneithero the latteras
s a s in F i g s. 1 0 8 1 0 9 o r w e ma p l ot
ingacur easinF ig. 110. The
ecur esneednoespeciale planation.
edcur ef orpurposeso comparison
us t b e re me m be r ed t h at t h e gi e n c ur e
theshipinthegi encondit iono dis-
p . 4 21 .
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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E A N D PR O PU L S I O N O F S H I P .
ndit iono bottom ando w eatherand
notbeappliedtothesameshipf ora ll
N S
tduea llowanceha ingbeenmadef or
on d it i on a s m a e i s t.
i n te r es t t o kn o wt h e in d e o t h e sp e ed
riesatan gi enspeed andsimilarl
P u b l i c D o m a i n
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.
resistancew ithspeed ore itherw ithre o-
a n q u a nt i t w h i c h ma b e e p r es s ed i n
ma determinethatat10knotsthe
beo thespeedandtheresistanceas
O N S
15 k n ot s t he p o we r m a v a r a s t he
tancethere oreasthe inde 2. 7.
m et h od s o d e ri i n g th e v a l u e o
e n v a l u e o t h e ab s ci s sa . T he n t he
oassumethe inde sensibl constant
thersideo thisv a lue sa betweenthe
e u i di s ta n t ab o e a n d be l ow x ^ T h en f r o m
eha e
P u b l i c D o m a i n
/ h t t p : / / w w w . h
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N C E A N D PR O P U L S I O N O F S H I P .
o g; r
hecur e isathandshow ingthere lation
usua ll thecase thef o llowing
ef oundmuchmorerapidandsatis-
e inge actinprinciple fora continua ll
.
aclearideao thenatureo the
hereconcerned.
t h e v a r i at i on o a n f u n ct i on y
e a t x b e v T h en l e t x b e i nc r ea s ed
chthatitsnew valuedi idedb its
er e e i s a q u a n ti t v e r s m al l c om p ar e d
achangeintheva lueo y in
n ot e b ( i + / . N o w o b i o us l
gthenatureo thee ponentm
ncerned. It w ouldthere oref o llow
eedw ere increasedipercentit
seo thepowerintheratio ( i. o i 1.
o increase isinde inite thechar-
tw il l lack mathematica ldist inctness and
a ll ledtode inemastheratioo log
- - e w he n e is i nd e i ni te l d ec re as ed .
P u b l i c D o m a i n
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.
b d a n d d , w e ha e t h en b d e i -
oremo e pansionthisbecomes
thee ponentmthusde inedis
sthe; / . o thegenera le uation
g a - - n l og x .
inthecasesw ithw hichweha e
t w edi f erentia te consideringboth
s . W e t hu s h a e
^ r - - .
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
unlessnisconstant mandnw ill
o f o llowsthatinthegenera lcasethe
h e e p r es s io n i n ( 2 , b e i n g an a p pr o i m a-
w i ll n o t sa t is y t h e f u n d am e nt a l e u a -
i t i s f o u n d e c e pt f o r a p ar t ic u la r v a l u e
s o v a l u e s th u s f o u n d wi l l no t i n
u n d am e nt a l e u a ti o n ( i f o r a n c o ns t an t
u r th e r sh o ws t h e f a c t o t h e di f e r en c e
ndnasherede ined.
masthusde ined weproceedto
eometricaldetermination.
hegraphica lrepresentationo the
bean gi enpo intcorrespondingto
t C A b e a t an g en t t o O P a t A . T h e n
P u b l i c D o m a i n
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.
C
theabscissab thesubtangent.
heonl uncerta int isthatin o l ed
c u r e . T hi s m a , h o we e r b e
a s f o l l o ws : W e m a e i d en t l a s su m e
tthecur e inthev icinit o A ma
co theseconddegree. Wethen
e uidistantf romB andnotethe
dR onthecur e . Thenb aw ell-
chcur esa linedraw nthroughA
tangenttothecur eatA .
chisessentiall di f erentincharacter
b e d e i n ed s i mp l a s t h e e p o ne n t wh i ch w i ll
u nd am en ta l e u a t io n y = a " . I t s v a lu e is
undb tak inglogarithms w hence
e en t h at t h e v a l u e o n w i ll d e pe n d on
orx , butoncethisunitde ined the
e i n it e . L e t x = I , o r t he u n it . T he n
onstanta= theordinateforx = i.
putmoregenera ll
beseentorelatesimpl tothe
po intinquestion. Wema there ore
nstantaneousvaria tion. It mustneces-
P u b l i c D o m a i n
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E A N D PR O PU L S I O N O F S H I P .
n t in o l e d w he n w e sa t h at a t a n
rta inpow ero x . O ntheotherhand
sontheentire law o v aria tionf rom
tothepo intinq uestion. I tthere ore
f ect betweenthesepo ints o the
eso m. I f the law issuchthatmiscon-
denticalas inthecommonalgebraic
betw eenmandnf orsuchcur esas
hmustnot bef orgotten.
recedingtothev ariationo power
P u b l i c D o m a i n
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.
sob ious. I nF ig. 112aregi en
i s t h e g i e n f u n da me n ta l c ur e C D i s
n e nt / / / a n d C E i s t ha t o t h e e p o ne n t
stheunit. Thesediagramsarese l -
re p a c a re u l e a m in a ti o n. E v i d e n tl
ma bemadewithre erencetothe
ur e . Thespeedandre o lutioncur e
w h ic h m a a l so i d e si r ed b e p lo t te d
F i g . 11 3 . I f O A , F i g . 10 4 w e r e a st r ai g ht
O T
udbeconstant A B w ouldbehori-
esrelatingpow ertore o lutionsand
. Practica ll thisisne erf ound
t h e sl i p wi l l v a r b u t sl i gh t l t h ro u gh a
n a me t ho d o f i n di n g th e m ea n
correspondingtothe init ia lf rict iono the
eanotherduetoWm. F roude.
b e a c u r e o m ea n p re s su r e p r op o r-
en i n 4 7 t o t he c u r e o i n di c at e d
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E A N D PR O PU L S I O N O F S H I P .
sumethatthispressurev ariesasthe
erf orspeedsbelow uv asspeedwith
w e h a e o n l t o c on t in u e B A b a
andw ithre erencetosomeat
X f u l i l li n g th e c on d it i on t h at m = n
k m= 1. 87 andtheconstruction
nimmediateresulto thegenera l
e f orthedeterminationo m. The
ws: A tA draw atangenttothecur e . .
O - = - m e re ct a p er pe nd ic ul ar C D a nd d ra w
r u n in t a ng e nt a t E t o E X a n d a t A
e l f u l i l t he c o nd i ti o ns r e u i re d f o r
pressurecur edow nward andOE w ill-
ue o / > , o r t he v a l u e f o r t he i n it i al f r i c-
eso drawingatangentatthe
heuncerta int thatthepressurev aries
indeedw ithan otherconstantinde o
resultnecessaril partak eso theuncer-
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.407
temptstoe tendagraphica llaw
e r ed b t h e ob s er a t io n s.
O N O F L O G A R I TH M C C R O S S - E C T O N PA P R .
ctionpaper thedi isionsaresim ilar
orinotherwords thedistancesf rom
tothe logarithmso thenumbers
ectionpaperruledinthisw a h
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C E A N D P R O PU L S I O N O F S H I P .
onstov ariousproblemsinna a larchi-
descriptiono themore importantma
= a H .
a - - n l o g x .
onthispaperthe abscissaand
, b u t lo g x a n d lo g y , t h e ab o e
-ntimesabscissa.
inthef orm
aightline.
suche uationw illonthispaperbe
ghtline inclinedtoX atananglewhose
ngY atapo intw hichgi esa . This
hasanumbero importantapplications
thef o llowing:
we ha e
thispaperw illgi ea locuso
nde w holeorf ractiona l todetermine
ssar todraw alineoraserieso l ines
t o X .
thispaperhasbutasingle logarith-
0 s u bd i i d ed a c co r di n g to t h e si e o
n t hi s h o we e r a n u mb e r o l i ne s
o the inde , asinglesheetma be
owerorrooto an numberf romo
ew illtakethecaseo atableo f
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.
oe pressgraphica ll the locuso
r 3 . L e t F i g . 1 1 6 d en o te a s u a re c r os s -
cscalesasdescribed.S upposethat
andtoeachotherontherightand
ie s er i es o s u ch s u a re s s im i la r l d i i d ed .
gf romones uaretoanad acent
e thattheunitbecomeso thene t
dentthatsuchaserieso s uareswould
ono theunit representa llva lueso
oandoo.
gina ls uaredi idedonthehori onta l
hev ertica linto3 thepo intso
B , C , E , F , G . Th en l in es j o in in g th es e
gramwillbeatan inclinationto
angentisf . N ow beginningatO, O E
. r f o r v a lu es o J T f r om I t o 10 . F o r
he linew ouldrunintothene tad acent
to n o t h is l i ne i c o nt i nu e d m a b e s ee n
o t ha t o B C i n t he s u a re b e o r e us .
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TA N C E A N D PR O PU L S I O N O F S H I P
nsideringtheunitsaso thene thigher
i l l gi e v a l ue s o x * f o r x b e tw e en O a n d
rlargerv a lueso x w eshouldrun
a re a b o e w i t h c ha n ge o u n it f o r / b u t
Weshouldheretra ersea linesim ilar
p r op e r ch o ic e o u n it s w e ma u s e G
w h er e x l i es b e tw e en 3 1 . 6 - - a n d 10 0 . W e
e ts uareontherightre uiring
o t h e ne t h i gh e r or d er a n d tr a e r se a
hichtak esusf ina ll to theopposite
c cle the lastlinegi ingusv a lues
tw ee n 1 00 a n d 10 0 0. F o l l o wi n g th i s t h e sa m e
sultf ornumberso succeedingorders.
thesub ectw illshow thatthe
r an v a l u eo x b et we en I a nd o om a t hu s be
romoneoranothero these lines and
b e tw e en I a n d oo , t h en l i ke wi s e f o r a n v a l ue
on o thedecimalpointisreadil
ntiontothenumbersin o l ed. A rule
ederi ed butiso l itt leaddit iona l
m it i ng v a l ue s o x f o r a n g i e n l in e
thusenablingapropercho icetobe
dinthiscase ma bereadil e -
anditw il lbefoundingeneralthat
presentedb , thecompleteseto
d i i d in g o ne s i de o t h e s u a re i n to
rts andj o iningthepo intso di i-
n a l l th e re w i ll b e ( m + n i l i ne s a n d
nX therewillbenlinescorrespond-
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C E A N D P R O PU L S I O N O F S H I P .
w i th . A s a n e u a ti o n th i s is
; * ( l og * \ l og * , ) .
a n d B d e no t e th e p oi n ts x ^ a n d x ^ ,
ghtsdenotedb y landj j / 9. Then
ualdistancesin o l edarethe
spondingquantit ies w ereadil seethat
o rA C + n C E . Th er e o r e a li ne f r o mC
ontoX w hosetangentisn. I f ,
e a n r ea d m ea ns o p as si ng f r om C , a
ecoordinatesx ly lta longanobli ue
o X atananglew hosetangentis#
alpassa longacontinuousserieso
latedtox ly lthattheproportionabo emen-
d. Toso l ean suchproportion there-
pl t o st ar t at t he g i e n po in t x l y ^ a nd
ineuntilw ereachapo intw hose
respondingordinatewillbethe desired
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.
v i c e v e r sa i w e st op a t an g i e n v a lu e o
thecorrespondingabscissawillbex^ , so
ntit iesthattheproportionisf ul i l led.
meansf ormo ingintheright
oi nt w ha te e r as , r y , , a s er ie s o e u i-
anglema beruled. Withthisa id
i m at i on t o t he p r op e r v a l u es o x ^ y ^ m a
eo theuseo thisproportion
indthecorrespondingspeedsfortw o
throotso thedisplacements.
e f indthepoint consideringone
dandtheotherasthato displacement.
lineinclinedat anangletan 1^ to
shallpassthroughacontinuousserieso
rrespondingdisplacementsand
edisplacementD w ereado f directl
v iceversa stoppingataspeed2w e
ondingdisplacementZ > 2 .
hecorrespondingspeeds w ema b
hesameprinciple f indthe I . H. P . b
t he e u at io n
onw ema tak ethedeterminationo
c ie n ts f r o m th e e u a ti o n
e in o l edma becarriedouton
v a lueo thecoe f icientsrapidl
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N DPR O P L L E R DA TA .
w i l l b e f o u n d a co l le c ti o n o d a ta
e llerper ormance. A f ew o the
arenotrepresentedinA duetothe
ta i ni n g sa t is a c to r v a l ue s o s o m e o t h e d a ta
itshouldbenotedthatthev a lueo
uiredforonepropeller andnotthat
asaw hole inthecaseo tw inortriple
etablesha ebeengatheredf rom
shearaspossible ina llcasestotheorigi-
sandderi ati eq uantit iesha e
ndependentl computedf romthefunda-
itcanhardl behopedthatamongso
rs h a e b e en a o i de d i t i s ho p ed t h at
theircharacternotsigni icant.The
c oe f i c i en t i f o r t he p r op e ll e r ha e b e en
elopedf ormso theblades andshow
m a e i s t in t h is f a c to r e e n a mo n g
generalestimationbeconsidered
n he a de d S c r e w ' , t h e le t te r s ha e t h e
ce:
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O w o N O O m c o w c oO c o r ^ r ^ I - H O O O O *
O O r ^ n 1- 1 MO O O c o c o r O i n -t - 1- 1 in c oO O O O c o
O m o u -> o i n m i n o O m t - > - oo o m m
O O c oo M O o o co o o O ~ t - O f ^ O m o in O o o
c n mQ O O O O m m mr ^ i n o o mr ^ o c a M
O O t ^ C O O " C O O ^ C X 3 C O C O C O I ~ > .O O O C O O O O Q ^ O r Dr^ ^ O ^ I ^
m O m rt N r - I H r O c oO * - i C O M O r W M r
M O O < N O m c nc or ^ mN o o O N O i -N C O
i n mo o i ^ m O w t ^ m o oc o H C O O O
- d e - O O W N N c o ^ - O O c o O ^ e n > n
O ^ ' T O N c r . r r T - M - H T - o c or ^ Tt
r ^ o o mo ro mO O O r ^ O O O O Q r ^
o c o r ^ c o o c cT ' - o O T t ^
^ ' ^ t -r ; - t-
m o < N T tc oc oc w co o ' - ^ i - w m ro
T - c o T to c o - 3- * 1 - r r M mm c o - i ^ c o c o- l -c o i- i
> n q q c > q o q r ^ q q q q q q
c 5c oc > O O O m Q v w M co oo o oc o r> - O O O O
t ^ O O ^ O < - < > - < " - O N c or ^ m rt w MO
O o or ^ c o m oo O N c o mN c o c o O O c o
o m O m 1 - r - c om c o N O t ^ O - m o
r - a 1 - 1 O m mr l -
H c o co * c o ^ t N
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N DPR O P L L E R DA TA .
O
t ^ en
n
o r. o ^ - C M e n t- i oo o o om
J " T t ~ ^ r O M o O O O r ^ * o i n oO
r ^ c o o r ^ c o r ^ c o c oc o O c o o O
m
C N O O C O C M < ~ i M O O ^ - m
n O o oc oO c o O e n O O o o O e nO
GO o o t r ^ O e n o O m ^ o
o c o
t e n e nM C M C M T - M ^ t c M r - i -
M
c o O O e ne nO O ^ n O t ~ Q
O c o O O c oen oO N O O O
- ^ j - r - i- t M en en cn en e no m i ne n
T -o oO O O O O M O O O O
M
* } c o
c O ' 3 -O O o oO f ^ T tc oc MO t ~ > '
- X 3
5 -
C M e n co C M ^ v o * n o in o * o oo o o
M C M ^ M M N o t ^ C M
. . t ' ' . t> -
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O O
ooco
i n o i n in i n
r ~ *
t ~ * a o o
m
ooo
C C
o c
C O T T
c o ri - oo
- r^ o
o TO "
O
mi n O i n N O c o oO O O o o O N T O
T T t i- r O M in O t oC a T O N O f ^ m
m in TO C O c o
mm N O O O m oo
T T O O T
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N DPR O P L L E R DA TA .
. * 3 - o O O c o r > r - r ^ M 04 c o r . 0 4 04 c o C N o C N c o C T
c > d d 3 c o co d d
O O u ~ > o ^ O t ^ r ^ o i T O O w t -+
t - ^ > - < Mi ~ 1 i- i04 r C Q U - > O C O C Q ~ ~ "
M - r " c c C O O ^ ^ t o O O mO T " " ' O ^ O * T c oc o
o c o om p C M C O O ' T c oi n t T t c o m c o c o
r^ r^ r^oc4o i0404cocococococoo-^ ' t ir
ooooo ooooooo-ioo o
O O O O O C O T t -C O r O 4 O 4 > -O 4 C 4 04 r> . l- ih -c O
O C O C O C O C O C O ' -iC O MTC O O 4TC O ' ^ -C O ( N O 4O l
c c ow o O v O O ' t t T O O T i - O M O
O O t n r- r ^ r ^ i ^ r - r ^ t ^ t - i w r ^ M M 0 00
M M r ^ o c c oc c dc D c oc o i ^ ^ c o ^ T c oc o M
MC 4W 04MMMMMMMMMM04MMM
O O O O ^ C - C ^ O O O O O O O u -i O O co
^ o ^ ^ ^ ^ - r r ^ r - ^ r ^ - r - o oo d oo co dd M
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1T
c ^ > - - -- -- -- - > - c
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t oO ( O i O r ^ r ^ . O t n co O o o t or ^ o O c o H I
I c oc oO O c oc or r ^ r ^ r ^ r O c o O O O O O
i H i O O a 6c ot oi oc oc od dd s O 0 4 co co oi " ~ '
o ^ < ^ q c o co a oc o co c s r ^ O O O O
o " } - t- f ^ C O O 4 O O O
1 ~ O O Q H ' H i ^ - i- iT - coc O O H i C O H i H I H i O l O C O
c o co t o 10 H I M H I H - H I H . C O C O O 0 4 o o O
o t ou i u ^ 1 0 ^ t r ^ r ^ r ^ r ^ i . r > * . s oo u ^ t ot o co c o co
i H i i o io t ^ t ^ t ^ r ^ t ^ r ^ r a - Tt i o io r >
H I ^ * * T O O O * O ^ O ^ s 3 O ^ O O * * c o co co co ^
M 0 4H I H I N 0 4l O i O iO i O i O t O t O to O O O T * t \ T >
C O H i ^ -r O O O aO ^ O O C O C O t O O O
* ^ * f ^ O O ^ o m o to 10 10 o O O 4 t ot ot ou > t o
dc dr ^ r ^ - i- T -i -- ' i -- v C o o o d H l H l w
O O O O O O O O O O c oc ot oc oc oO C Q
o oo O O u > * / ii oi oi oi oO O r oc oc o O O O
r^ . r- - i- - rto io to io ioioHiH icococo iri
J . , - _ -_ .
; ; ~ ' . . . c/i
I I > * ^ J
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N DP O P L L E R DA TA .
u- > o o - * - c o o
mi- iMM
O W c o co c oc o u- t n ir > i r >
oO M O O O O O O O O
t o- t li ^ o /r t
- o ^ 1- 1 - 3
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> O O O o o Mr ^ O M O O m c oc oO o o O O O
M M ' C 4C J C ^ < N | | | |
^ O o o
o i nt r im c o
- N
O r^ cocom O " -1O ^ ao\ O cocov O O ^ aoO
oo \ t ~ , \ n r t- * T - o O t ^ r ^ t ^ r ^ i ^ r ^ c o co co tH
o o o oo o
- 3- " ~ >
i-i l-l C O C O N C O C O M t H C O O O C O O O C O C O C O C O C O I ^
i o ir i r > i r
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N DPR O P L L E R DA TA .
O O u -> o
O C O C O C O C O C O C O C O C O C O C O C O v O ' O ^ -C O I -iO " ^
c o co co co co oO O
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C O C O C O C O C O C O C O C O C O C O C O C O - n-aW O J M C O C O
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M O N O t ^ r ^ o u > < O c Q c o co
O O O O r ^ i O O O
n i- i- iO O ' n O \ O i n ir > O
M i > - s dO ^ ^ T O
^ C O C O C O C O C O
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O O C O O O O v ni DM- iMM O ^ U - N C < v O O * - C O
O o o O ^ ^ - r> v r > r N O x n o t- oo r a
- O f * c oc o -t oo ^ O M O > O c o
- O ' ^ C O I ^ l -i - C O C O O O O O l -i W a
M
C J
d dd
= - 2
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ation in luenceo , ontria ldata386
entcoe f icient343
ctioncoe f icient347
9 2-
ic a l o t r ia l d at a 3 97
r e u i re d f o r p r o pu l si o n 23 0
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istanceduetoactiono propeller229
R a n k i ne s 3 4 8
r e u i re d f o r 3 3 6
2 98
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n g i n ee r in g . N a D e pa r tm e nt 3 8 3
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T O F C A L I F O R N I A L I B R A R Y
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