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Cecil H. (Cecil Hobart) Peabody.

Propellers online

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to the first, we have

Zi 4 : L 2 *::di 3 :d 2 3 ::Wi : W 2 ;
so that



For sake of comparison we may reduce to a common denom-
inator and it appears that, while the theory of similitude makes
the power increase as the J-f power of the displacement, it demands
that the weight of the engine shall increase as the If power; on
the other hand, constant piston speed makes the engine weight
increase as the H power of the displacement.

This discussion applies only to the engine and not to the
boilers, the weight of which for a given type may be expected to
be proportional to the power.

In the development of marine engineering improvements in
construction and design have much reduced weight of types of
engines so that the conclusions just given will apply only to a
given type and period.

Internal Propulsion. A motor or an engine in a vessel can propel
it only by acting on the water in which it floats, and must impress
a stern ward velocity on the water affected. Suppose that the
propeller acts on W pounds and imparts to it an acceleration of



INTERNAL PROPULSION 105

a feet per second. Then the force which is exerted on the water
will be equal to the mass multiplied by the acceleration, or,

Wa

g '

where g is the acceleration due to gravity.

If the ship has. a speed of v feet per second, the work done
per second will be

Wav
g

The kinetic energy imparted to the stream of water set in
motion will be

Wa 2



per second. The total work is the sum of the two amounts, while
the first part is the useful work. Consequently, the efficiency may
be considered to be

Wav



g

If this is to be applied to the propulsion of a ship by a propeller
we may transform the expression for efficiency as follows:




prs



' r 2 pr(i-s 1 ) "a(i-Ji)

This transformation is made with the assumption that the
acceleration of the water in feet per second is

prs + 6o



106 PEOPELLERS

while the speed of the ship is



in feet per second; p and r are the pitch and revolutions of the
propeller while 5 and si are the real and apparent slips.

Example. If the real slip is 0.25 while the apparent slip is
o.io, the efficiency by the above equation is

e = = 0.88.



This is to be considered as a limit neglecting friction and other
resistances. If a factor 0.8 be allowed for resistances the efficiency
would appear to be

0.88X0.8=0.7

which is not unusual for high grade propellers. This method may
be applied where direct information is lacking, to ship propellers
or aeroplane propellers. For the latter s and Si are probably
equal.

The form of equation (22) on page 80 may be justified by a
special application of this method. In the first place the acceler-
ation imparted to the water, may be assumed to be proportional to

sV a

where 5 is the real slip and V a is the velocity of advance of the
propeller, the latter being taken as proportional to the speed of
the ship. The mass of the water acted on may be made propor-
tional to the area of the disk swept by the propeller blades and
to the speed of advance, that is, to

d 2 V a .

The thrust of the propeller may therefore be made propor-
tional to the product of the preceding quantities, that is, to

sd 2 Va 2 .



INTERNAL PROPULSION 107

The power may therefore be made proportional to this product
and to the speed of the ship, or for the latter we may again sub-
stitute the speed of advance. Then



1000



where A is a factor depending on the pitch-ratio, the real slip,
and the form of the propeller; the factor 1000 is introduced to
control the decimal point of A .

To show that this last equation conforms to the theory of
similitude we may make V a proportional to the square root of
the length, whence as d is itself a linear dimension,

S.H.P.oc ?/ = /*,
as shown on page 100.



109



TABLES



TABLES



111



FOUR-BLADED PROPELLERS.

PROJECTED AREA RATIO = O.28. THICKNESS RATIO = O.

Point off one place for D, two for R, Three for e.



6

II

PH


REAL CLIP.




0.06


0.08


O.IO


0.12


0.14


0.16


0.18


O.20


0.22


0.24


0.26


0.28


0.30


0.32


0-34


O.60


R


467


478


491


54


5i8


534


55<>


568


















D


639


642


645


649


652


655


660


666


















c


5*4


5 J 7


5 J 9


521


S 2 -


5 2 3


524


524
















0.65


R


421


43 2


444


458


472


488


54


521


538


557


576












D


620


622


624


627


630


633


636


640


645


650


655












e


533


536


539


54i


542


542


543


543


542


542


540










O.yO


R


39 1


403


4i5


428


441


455


469


483


498


5*5


533


55 1


57








D


608


609


611


613


615


617


620


623


626


629


632


636


641








e


55<


558


560


56i


562


562


562


56i


560


558


556


553


550






-75


R


365


376


388


400


412


425


438


452


466


482


499


5i6


535


556


578




D


596


597


598


600


602


604


606


608


610


612


615


619


623


627


6 3 I




e


568


574


578


58o


58i


58i


58o


578


576


574


570


566


56i


556


55


0.80


R


339


349


360


372


385


398


412


426


440


45 6


472


488


506


526


548




D


584


585


586


587


588


59


59-


594


596


599


602


605


608


611


6l 4




e


584


59


594


595


59^


595


593


59 1


589


586


582


577


572


567


562


0.90


R


301


310


3 J 9


3 2 9


340


352


365


378


39 2


406


422


438


456


476


495




D


566


566


566


566


567


568


5 6 9


57


572


574


576


578


58i


584


588




e


607


611


615


618


615


620


618


616


612


608


604


598


592


585


578


I. 00


R


272


280


288


297


307


3*7


3 2 9


342


355


368


38i


395


411


429


449




D


55


55


55


55


55


55


55


55 T


55 2


553


555


557


559


56i


563




e


628


632


635


637


6 3


638


636


633


630


626


621


616


609


601


592


i .10


R


250


257


264


271


280


290


300


312


325


339


353


368


383


399


416




D


536


536


535


535


535


535


53^


536


537


538


539


540


54i


543


545




e


649


652


653


654


655


654


65-


649


645


6 39


633


626


618


610


600


1.20


R


227


234


241


248


256


266


277


289


301


3*3


326


340


354


368


384




D


5 21


521


521


520


520


520


5 co


5 21


521


522


522


523


525


527


529




e


654


669


673


676


678


677


674


670


663


656


647


638


629


620


611


I. 3


R


209


2^5


222


?29


236


245


254


265


276


288


300


312


325


339


354




D


505


54


504


S4


54


54


54


5S


55


506


507


508


59


5 10


5 12




e


672


679


68 3


685


686


687


685


682


676


669


660


650


640


630


621


1.40


R


*95


200


206


2IC


219


226


235


245


255


266


278


291


34


3i7


332




D


494


493


492


491


490


49


490


49


491


49 2


493


494


496


498


500




e


680


685


689


692


694


695


694


691


686


678


669


659


649


6 39


628


1.50


R


182


187


193


199


206


213


221


230


239


250


261


272


284


296


309




D


481


480


479


478


477


477


477


477


478


478


479


480


482


484


486




e


683


690


694


697


699


700


698


6 95


691


684


676


668


658


648


638


I. 60


R


170


175


181


I8 7


194


201


208


217


226


235


245


2 55


266


278


290




D


47i


470


469


468


467


467


466


466


466


466


467


468


469


470


47 1




e


678


685


691


696


699


700


699


697


694


689


682


673


663


653


643


I. 80


R


*53


158


164


170


176


I8 3


189


197


205


214


223


232


242


252


263




D


453


45 2


45i


45


449


448


447


446


445


445


445


446


447


448


449




e


671


681


688


692


696


698


697


6 95


692


688


681


673


664


654


644


2.00


R


140


145


151


156


162


169


176


183


190


198


206


215


224


234


245




D


439


437


43 6


435


434


433


43 2


43 1


43


430


43


429


429


429


43




e


668


676


683


688


691


692


692


691


688


683


676


669


660


650


640



112 TABLES

FOUR-B LADED PROPELLERS.

PROJECTED AREA RATIO = 0.36. THICKNESS RATIO = O.o6.

Point off one place for D, two for R, three for e



1


REAL SLIP.




0.06


0.08


0.10


0.12


0.14


0.16


0.18


0.20


O.22


0.24


0.26


0.28


0.30


0.32


0.34


0.60


R


439


455


47 1


487


53


5 J 9


535


55*


5 68


586














D


668


669


670


6 7 I


673


675


677


679


681


685














e


522


5 2 3


522


520


5i6


5 11


506


501


494


487












0.65


R


406


420


434


449


464


480


496


5 12


529


547


565












D


653


653


654


6 54


655


656


657


6 59


66 1


664


667












e


543


546


548


548


547


545


54i


537


532


527


522










0.70


R


376


389


402


416


43


445


461


477


494


5 12


532


553


574








D


637


637


638


638


638


6 39


640


642


644


646


649


652


655








e


560


564


567


5 6 9


568


566


563


560


556


SS 2


548


543


538






-75


R


35


362


374


387


400


414


429


445


462


480


498


5 J 7


537


559






D


624


624


623


623


623


624


62s


626


627


629


631


633


636


639






e


575


58i


584


586


586


584


581


578


574


57


565


560


555


548




0.80


R


328


340


352


3 6 4


376


389


403


417


432


447


463


481


SGI


523


547




D


610


610


610


609


609


609


610


610


611


1612


614


616


618


621


624




e


589


595


599


601


60 1


600


598


595


592


588


584


578


57i


5 6 4


555


0.90


R


290


300


3 11


322


334


346


358


37 1


385


399


414


430


447


465


486




D


598


598


597


597


596


596


596


596


596


596


597


598


600


602


604




e


611


617


621


622


623


622


621


619


616


613


608


602


595


588


580


I.OO


R


260


269


279


290


301


312


324


336


349


362


375


389


404


420


437




D


57


5 6 9


567


S66


566


567


565


565


565


565


S66


566


567


568


568




e


639


643


646


648


649


648


646


643


639


634


629


622


614


605


597


I. 10


R


237


245


253


263


274


285


296


37


3*9


33i


344


358


472


387


403




D


553


55 2


55 1


550


549


548


547


546


546


546


546


546


547


547


548




e


652


658


662


666


666


665


662


6 59


654


648


641


634


627


619


609


1. 20


R


216


223


231


240


25


260


271


282


293


35


3*7


33


344


358


373




D


538


536


534


53 2


S3 1


53


530


529


529


528


528


5^8


5 2 9


53


53 1




e


66 1


668


674


677


679


6 79


676


672


668


66 1


653


645


636


627


617


1.30


R


200


206


213


221


230


239


249


260


271


282


294


307


320


334


348




D


523


521


5*9


518


5 1 ?


5i6


SiS


5 T 4


5i3


5 12


5 12


5 12


5"


5i3


5 J 4




e


670


677


681


684


685


685


684


682


677


670


662


653


644


633


622


1.40


R


182


198


J 95


207


215


224


233


243


2 53


264


276


288


300


3*3


326




D


5 11


59


57


55


53


5 01


499


498


497


496


496


496


496


497


499




e


679


684


688


691


692


692


691


688


683


676


668


658


648


6 39


629


1.50


R


*75


181


1 88


195


203


211


219


228


237


247


258


269


281


294


308




D


qoo


497


495


493


491


489


487


485


484


483


483


482


482


483


483




e


682


690


6 95


698


699


698


696


692


686


680


672


662


652


642


632


1. 60


R


166


172


178


185


192


199


206


2I 5


22^


234


244


255


267


280


293




D


49


486


483


482


479


477


475


474


472


47 1


470


469


469


469


470




e


683


691


696


699


701


701


699


6 95


690


682


674


664


654


642


631


1. 80


R


148


J 54


160


167


J 74


181


1 88


196


205


215


225


235


246


257


268




D


4.71


467


464


461


458


455


453


45i


45


4i8


447


446


445


445


446




e


671


680


688


6 95


698


697


696


693


687


678


669


658


648


638


627


2.00


R


I3 1


137


143


J 5


157


164


172


180


188


197


206


215


225


235


246




D


452


448


444


441


438


435


433


43i


429


427


426


425


424


423


423


! e 644


658


669


676


681


684


683


680


677


671


663


655


646


635


624



TABLES



113



FOUR-BLADED PROPELLERS.

PROJECTED AREA RATIO = 0.48. THICKNESS RATIO = 0.05.

Point off one Place for D, two for R, three for e.



o d




REAL SLIP.




0.06


O.o8


O.IO


0.12


0.14


0.16


0.18


O.2O


0.22


0.24


0.26


0.28


0.30


0.32


0.34


O.6O


R


397


4 IO


424


440


456


473


492


5"


530


55


57












D


716


714


712


711


709


707


7<>5


704


73


701


700












e


5i3


519


524


528


53


53i


531


53


529


528


524










0.65


R


37


383


396


411


427


444


463


482


5 01


52i


541


563










D


696


6 93


691


689


687


686


68s


684


683


682


681


680










e


5 2 9


537


542


546


548


549


548


546


544


54i


538


533








O.^O


R


345


358


372


487


402


418


435


452


47


49


5 10


53 1


SS 2


575






D


676


6 73


671


670


669


668


666


665


664


663


662


662


66 1


660






e


54i


550


557


501


564


566


5 6 4


562


560


556


55i


545


539


53i




o-75


R


323


335


348


302


376


392


408


425


443


462


481


501


522


543


565




D


6 59


656


654


6 5 2


650


649


648


647


646


645


645


645


644


644


644




e


559


566


572


576


578


58o


58o


578


574


5 6 9


563


556


549


540


531


0.80


R


300


312


324


337


35i


466


482


400


418


437


456


475


495


5i6


538




D


643


640


637


634


632


631


630


630


630


630


629


629


629


630


630




e


572


580


586


5o


593


594


594


59i


588


583


577


570


56i


SS 2


541


0.90


R


269


280


291


302


3 J 3


327


343


359


375


39 1


407


424


443


464


485




D


618


614


610


607


605


603


601


600


599


598


598


598


599


600


600




e


600


609


616


620


622


622


620


616


611


606


599


592


583


573


56i


I. 00


R


243


253


264


275


286


297


310


324


339


354


369


386


4>3


422


441




D


598


593


589


586


583


580


577


575


573


572


572


57 1


57 1


572


573




e


613


623


631


636


638


639


639


637


633


628


619


610


600


59


5 8o


I. 10


R


220


230


240


2 5 1


262


273


284


296


308


321


336


352


369


386


403




D


580


574


5 6 9


566


563


560


557


554


SS 2


55


549


548


548


548


548




e


625


637


645


651


654


656


654


651


648


642


634


626


616


606


6 95


1.20


R


200


209


220


231


242


253


264


2 75


286


298


312


327


343


359


375




D


56i


557


552


548


544


54i


539


537


535


534


532


53 1


53 1


53


530




e


629


643


653


6 59


663


665


663


659


654


649


641


633


624


613


602


1.30


R


184


193


2O2


212


223


234


245


256


267


279


291


304


320


336


35 2




D


548


542


538


533


528


524


522


520


5i8


S J 7


5i6


5*5


5 X 4


5*3


5 12




e


636


648


658


664


668


668


666


663


658


652


646


637


627


616


605


I .40


R


171


179


188


198


208


219


229


240


250


261


273


285


298


3*3


3*9




D


535


529


523


S J 7


5*4


5 10


57


54


502


500


499


498


497


497


496




e


632


646


658


666


670


670


669


666


66 1


655


648


640


630


618


606


!-5


R


J 59


167


176


1 86


196


205


214


224


234


244


254


266


280


2 95


310




D


522


5i5


510


505


500


496


492


489


488


486


484


482


481


480


479




e


623


640


653


664


669


671


670


667


663


656


648


639


628


617


606


1. 60


R


!5


158


167


176


186


J 95


204


213


222


231


241


2 5 1


265


279


293




D


5 12


55


498


49 2


488


484


480


477


474


472


470


468


467


466


466




e


613


631


644


655


662


665


664


662


658


652


645


637


626


616


603


1. 80


R


*33


142


151


159


168


176


185


194


202


211


219


230


242


254


267




D


493


48S


478


472


466


462


459


45 6


453


45 x


449


447


445


444


443




e


586


606


621


632


641


646


648


647


644


640


634


625


616


606


595


2 .OO


R


121


128


136


145


153


1611 169


177


186


J 95


204


214


224


235


246




D


476


467


459


453


448


444


440


436


433


43 1


429


428 427


426


426




e


501


583


601


614


622


627


630


630


628


624


618


611 602


592


582

































114



TABLES



FOUR-BLADED PROPELLERS.

PROJECTED AREA RATIO = O.6o. THICKNESS RATIO = 0.04.

Point off one place for D, two for R, three for e.



6

P


REAL SLIP.




0.06


0.08


O.IO


0.12


0.14


0.16


0.18


0.20


0.22


0.24


0.26


0.28


0.30


1

0.32 1 0.-J4


O.6o


R


377


39 2


408


424


441


458


475


492


5 11


53


55 1


575










D


75


746


742


738


735


732


729


727


725


723


722


722










e


49


496


499


501


501


499


497


493


488


481


473


463








0.65


R


347


362


377


392


408


424


441


458


477


497


5 J 7


539


563








D


724


719


7 J 5


712


709


706


73


701


700


699


699


698


698








e


502


508


5 J 3


5^


5i8


5 J 9


5*7


513


508


502


493


483


47 1






0.70


R


326


339


353


367


382


397


4i3


43


448


467


487


508


53 1


555






D


704


699


694


689


686


683


681


679


677


676


675


675


675


675






e


5i6


522


528


53 2


534


535


534


53 2


5 2 7


522


513


504


492


478




-75


R


35


3i8


33 1


445


459


374


39


406


423


441


460


480


500


522


547




D


686


680


674


670


666


663


660


658


656


655


654


654


654


654


S4




e


525


535


541


545


548


55


550


548


544


539


53 1


523


5 12


500


487


0.80


R


286


299


312


325


339


354


37


386


403


420


437


456


476


497


520




D


669


662


657


653


649


646


644


642


640


639


638


637


636


636


636




e


535


545


553


558


562


564


565


564


56i


556


548


540


53i


520


508


0.90


R


2 55


268


281


294


307


321


335


35


365


38o


395


412


43 1


450


470




D


639


631


628


62C


621


617


613


610


608


606


605


604


604


603


603




e


544


562


573


681


587


59


590


588


585


580


574


566


557


547


536


I.OO


R


231


243


2 55


268


281


294


307


320


334


349


364


379


396


4i3


43 r




D


614


609


604


599


595


59 1


588


586


584


582


580


578


577


576


575




e


553


572


586


597


603


606


608


607


605


600


594


585


576


566


555


I. 10


R


211


222


234


246


258


270


282


294


308


322


336


35 1


366


382


399




D


59 2


587


572


578


574


57


566


563


560


558


556


554


553


552


55 1




e


556


577


594


606


614


618


621


621


618


613


606


597


588


578


566


1. 20


R


192


203


214


225


236


248


260


272


285


298


312


326


34i


357


373




D


574


567


562


557


SS 2


548


545


54i


539


537


535


534


533


532


53i




e


556


578


596


607


618


621


624


624


621


616


611


605


595


585


574


1.30


R


177


188


199


2IO


220


231


242


253


264


277


290


303


316


33i


347




D


557


55


544


539


535


530


526


523


520


5i8


5i6


5 X 4


5*3


5 12


i 5I1




e


554


57i


597


608


615


620


623


624


622


617


611


605


596


586


577


1.40


R


166


176


186


196


206


216


226


236


247


259


271


283


295


310


326




D


543


536


529


524


5*9


5*5


5 11


57


54


5 01


499


497


495


494


493




e


549


579


599


611


617


623


622


621


618


614


6 10


604


597


589


579


1.50


R


*55


165


174


184


194


203


213


223


234


245


256


267


280


294


309




D


53


523


5*7


5 10


55


500


496


493


49


487


484


482


480


479


478




e


539


57i


594


608


616


619


619


618


615


610


605


599


592


583


574


1. 60


R


*45


J 54


163


J 73


183


192


202


212


221


231


241


253


266


279


293




D


5 J 8


5 IX


54


498


49 2


488


484


4 80


477


474


47 1


469


467


466


4 6 5




e


524


558


582


596


605


611


612


611


608


605


600


593


586


578


57


1. 80


R


130


139


148


156


l6 5


J 73


182


191


201


2IT


221


233


245


257


269




D


5 01


493


485


478


472


466


462


459


456


453


450


448


446


445


444




e


502


540


561


576


584


589


59 1


59 1


589


586


582


576


568


56i


553


2.OO


R


118


126


135


J 43


J 5 2


160


168


176


I8<;


T 95


2O^


215


227


238


250




D


485


476


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