resistence and propulsion of ships_wf_durand

8/11/2019 Resistence and Propulsion of Ships_WF_Durand

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i c D o m a i n

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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

P u b l i c D o m a i n

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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.


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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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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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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


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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.


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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


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_ u s e # p d



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


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s s

_ u s e # p d



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.


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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


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s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d





/ h t t p : / / w w w . h


s s

_ u s e # p d



E .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d





/ h t t p : / / w w w . h


s s

_ u s e # p d



E .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



E .

00f t. perminute . R e uiredappropria te

aps600f t. in lengthandmo ingat

E E T.

tsperhouror2000to2500f t. per


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



E .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


p . 13 8 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 ;


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




- 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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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:


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




.

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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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:


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 :


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



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

.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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

" /


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




"

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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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:


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 -


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



E . 1 41

t higherspeedsthetota lresistance

dl o erthatduetosk inresistance

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 inresistance. The


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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



/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



N .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 ;


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



. 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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



. 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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 ;


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 ,


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



, 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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



. 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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




T O


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



. 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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




ento F eatheringPaddlesI nF igs.

sualkinematicarrangementsf or

F ig. 61the link ssim ilartoA B are

nk actuatesthe le erB C andblade


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 -


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



I .


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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 -


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 /


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 )


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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^


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 :~ * '


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 /


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




, 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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



D S I GN .

A L U E S F O R F A C TO R /.


/ h t t p : / / w w w . h


s s

_ u s e # p d




1.71.81.92.0 2.12.22.32.42.5


/ h t t p : / / w w w . h


s s

_ u s e # p d



D S I GN .


/ h t t p : / / w w w . h


s s

_ u s e # p d





/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 =


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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



/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 =


/ h t t p : / / w w w . h


s s

_ u s e # p d




. 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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 inresistance.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



D S I GN .

H E S L I P A N G E 0.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 :


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 -


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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 \ =


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 inresistance

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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




onman considerationshereomitted.

heresults howe er issu f icientl

ms w hicharechie l intendedassug-

the law o comparisontothestud o

scharacter.


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d



.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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



.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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d



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-


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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.


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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:


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 -


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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-


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 ,


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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.


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 ,


/ h t t p : / / w w w . h


s s

_ u s e # p d



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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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 )


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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 .


/ h t t p : / / w w w . h


s s

_ u s e # p d




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


/ h t t p : / / w w w . h


s s

_ u s e # p d



.

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

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eha e


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o g; r

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.

aclearideao thenatureo the

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chthatitsnew valuedi idedb its

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achangeintheva lueo y in

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tw il l lack mathematica ldist inctness and

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.

b d a n d d , w e ha e t h en b d e i -

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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 - - .


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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 -

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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

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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


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C

theabscissab thesubtangent.

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n t in o l e d w he n w e sa t h at a t a 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 -

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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

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udbeconstant A B w ouldbehori-

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n a me t ho d o f i n di n g th e m ea n

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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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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

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k m= 1. 87 andtheconstruction

nimmediateresulto thegenera l

e f orthedeterminationo m. The

ws: A tA draw atangenttothecur e . .

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indeedw ithan otherconstantinde o

resultnecessaril partak eso theuncer-


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.407

temptstoe tendagraphica llaw

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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

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onstov ariousproblemsinna a larchi-

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onthispaperthe abscissaand

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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

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nX therewillbenlinescorrespond-


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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

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o rA C + n C E . Th er e o r e a li ne f r o mC

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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

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ntit iesthattheproportionisf ul i l led.

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oi nt w ha te e r as , r y , , a s er ie s o e u i-

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eo theuseo thisproportion

indthecorrespondingspeedsfortw o

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e f indthepoint consideringone

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lineinclinedat anangletan 1^ to

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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

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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

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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 *

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o m O m 1 - r - c om c o N O t ^ O - m o

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ation in luenceo , ontria ldata386

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