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Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1948-05

Investigation of methods of plotting resistance of

ships to simplify preliminary design power studies

Nicholson, William M.

Massachusetts Institute of Technology

http://hdl.handle.net/10945/6461

Lib <

U. S. Naval Pi

Monterey, California

Cambridge, Mass&chusetts,May 20, 1948.

Professor J. S. Newel],Secretary of the Faculty,Massachusetts Institute of Technology,Cambricce, Massachusetts.

Dear Sir:

In accordance with the requirements for the

degree of Master of Science in Naval construction and

Engineering, we submit herewith a thesis entitled, "In-

vestigation of Methods of Plotting Resistance of Ships

to Simplify Preliminary Design Power Studies."

Respectfully,

3IMPUK PRSLJ 3~3I3.

By

)n Wayne Hoof'omraander, U. S. Mavy Lieut. Joafniander , U.S. Navy

5., U.S. teval Academy, 19^1 B.3. . Javal Aoadetny, 19*1

->njitt»d lr> Partial Fulfillment of the

Reoulrenents for the Degree of

' R 0?- 5CISK0E IN HAVAL NHJCTl

•arc EKaisrawwo

at the

IP ITT3 INSTITUTE 0? TECHNOLOGY

1948

7"/' r

ACKNOWIEDGl'ENT

The authors wish to express their appreciation

to Professor George c. Manning for his suggestion of the

idea on which this thesis is based, and for his continued

interest in its development.

6931

TABLH OF C"ATT^T3

I Summary 1

II Introduction 3

III Procedure 4

A. Limitation of variables 4

3. Method of plotting 4

, Corrections for L, 3/H, and ro. 6

IV Results 11

V Discussion of results 29

A. Criteria 29

3. Accuracy 29

C. Advantages 29

D. Number of charts required 30

E. Conclusion 32

VI Appendix 33

A. Details of procedure 34

1. 3a»ple calculations 45

Bibliography A7

Figure Title Page

I Method of Plotting Tabulated Values of Re. 7

II Method of Platting Contours of Ro froa? 8Figure I

III Correction A for Variation of Length 14

IV "B/m Correction for Total Real stance in 15Pounds oer Ton of Displacement

V - XVII Contoure of Total Resistance Re in 16 - 28Pounds Per Ton of Di aplacement

T TT Plot of Mean Values of Rf/Rt 39

XIX Mathod of Eliminating J? as a Variable 42in the Correction for Vu

XX Method of Plotting Contours of B/h 43:orreotlon

4

I,JST OF TA9L5'3

Table Title Fac;e

I Table of Representative Characteristics 35 - 36

II Porrs for Recording Data 37

III Computation of A 40

IV Table of Calculated DesistMnce for SampleHulls by "Tiesl s curves ^nd maylor SerleB 46for Comparison

\

SYMBOLS

^ Displacement in tons

3 Ream in feet

Draft " "

L Length "

Speed in Knots

35A.X Longitudinal Coefficient -^ eHt_ .

Jl, Nearest plotted value of Jl below actual hull .

£z Nearest plotted value of Jf above actual hull.

m Midship Section Coefficient -s.ect *

gn area

-

d Displacement - length coefficient ^(L/100)5

f Ticercan's constant for frictiowal resistance.

Rr Residual resistance in pounds per ton of displ

Rf fictional

»

n n n n ti ri n

Re Total " •» w « n m «

(for mean hull B/K3.0 and L 500 ft.)

Rt Total Resistance in pounds per ton of displ.(corrected for actual hull)

x Ratio Rf/Rt

°< Lenrth correction to Rf for variation from L COO ft.

C f Correction tc Re for-B/H variation of + 1.0 froman value 3.0.

Correction to "Re for ?/h of actual hull.

A ngth correction to be applied to (Re + c)

I

This t ps aa a' b. to obi a

. concise determini reaial '•

Ion In 1 - s^^ps r p ^ fre-

crarves In c] a arr marfe and quail tat J

than exact quantitative information is r

i of inv> 3 been rei I n of tl

lor* 3 contours of resistance and elimina-

variables which have minor effects wh<

n fou >t contou tcta. s

3 d and v VlT for a . hull at various valu A

ares V to XVII) and to provide tv;o slnpL iction

lengt r) anri one for P/^ (figure IV)

•esulta accurate within 2-^'' of lor 'a

table IV) • We thus have a to1

~f wh

I

for an\ Lfic hull.

•ta maj I ' ecniced to the foil

- equatl i

= f^c * ] (1)

v/^ere 9c is obta »oin figures

C r (• • • 3.0) C and CA IT I

.

i

: ed without t

X

sac rj .ice

accur . 'able Improvement ove r tl

charts r Taylor.

ors have found use of these curves much

simpler', quicker, art5

, les? subject to errors of rfarin^ and

interpolation than the curves used in Taylor. mhey

Intended to Improve on the accuracy of Taylor's data, and

of course they will not allow for special variations In hull

MB used to Improve en the standard series such as transom

sterns an" t ulbous bows . "tie work should be very useful,

however, in any r rob] ems involving estimates of resistanc

especially in preliminary design work.

-

es1 re

a 3 hull

generally plve '

"/{T. es s(

• tcr. 1m i ed to

lentlal at 1

of b appeared ;

rminlnp real s

'

1st: In the preliminary st:x>cr-* A s

p subject cf resistance revealed only o

- a set cf curves develi

ese curvei .

art' ;] I In 1

Shi' w c f War :h 1941 , "fT fr

and plotted i absc

an ordinate of Fr. ''tils £lves

of est!-

use of 3u-

riationa

icr's curve

"Ttie Sp€M of Ships, " 1 y ; . .

I tl'

I the data used in the develops

this thesis. Tbp frictlonal resistance data was obtalr

frcr. Taylor's fi; ire 108 and the residua 1 resistance was •

Itainod from ^ylor's contours of residual resistance.

A • Limitation of Variables *

The first a -he development of the thesis

was to select the ccr.f f ic ients of form to bo Used in the

prepr! >n of curves, and to lln.it the range of these co-

Mc ients as far as practical. ^o this end, a table of

representative characteristics (Table I) was prepared,

nes of ships In actual service. For simplifi-

cation oth plotting and use it Is desirable to fix as

many variables as possible, jt was decided t>at a rr.ean

value cf Ctt] I be used, thus eliminating one interpola-

tion r evil red in Taylor's curves. A rean p/ll value c

was s« It was also dec to cover values of d frc

50 • . v/fT from .60 to 1.00, and X from .56 to .80. It

was nc • Large the effect of variation of m

t&tively it was decided to leave It out cf

4

I oris .

rt of P3

° data (

VT was :

1 e abscissa as it is always *

Llowin

ot, referre e introduction,

h ££ and -i£.

various values X ind d. 36 resistance "actors were

also tried on coordinates of Jr ror arious values

-y", but the results were not promising enough to warrant

refinement. TTse of these ratios requires computation

an^ provides little or no simplification in the number of

operations that mus t be performed to arrive at the total

i stance. After a study of these prelim in- cries it

was decided that the most promising line of effort v:as to

plot - >rs of total resistance on d ane V/yL for succes-

sive values of a. If these values cf J, are selected close

enough together it makes it possible to use the nearest

charted value of a to the actual hull being cc red with

good accuracy. If, on the other hand, it is more desirable

to limit the number of charts a smaller number of values

A should be used and the actual results obtained by inter-

polation. It was decided that intervals of »02 would be

close enough to permit approximate use without

and yet would cover the desir inge without too many

ion c it was to use a lengtl

t. an^ a wetted surface coefficient 1 .4 as

lor's -u

ancc data presented in Taylor*

e

was • 'crir for use in .

S

.

[ In tl .endlxisasa-

-" "-1 in th r

- thesis

I

irves " R

\ne se • rvea v.

! in

se cu] lsc !Tv esls note-

k ) •r- I i e ^ s

;

11 scale, t<

the me 1 • It will be noted that a li

p a c c u Y7"

•

the select eel mean coefficient

Prom t ite c a up 11 lus* -

••es I and II. ?he contours an

CVI 'er results

.

VorrFCt:lon3 f o r I,, "_'",

It Is obvious that several errors

of : and L aro present if these ccntours oJ

parie1 ills - of v. er

• in coefficients usee he re . 11

nt could be r roducJ

b correc '• - one por vs

La 1 1 oh cj

on

k. {£ xviii).

tv

FlfiUEE XLoislC CotF -A .(oZ

5-6 TO .^O I.IO 1.30

5p^eo LENGTH Goer

|S"o1

FlCiU«t£ Shou^mC r^CTViOO Of= PlotTinJG Va.l.ci«5 OF Re. \T|\»iiLATEO

F«om "Tpkyi_OE.'s "^SP£EO - FbuJER OP -SmiPS* )

Am o Mcmoo o^ TKftMSFCRKtM^ Rsimtj To Contuurs of RtSisrft^ct

1 U

Figure HE

31

jj.

yf

u

hi

1CV

*>

II

s

3

£2o

t So n

u. ur

II

V)

S

<0

u

J

LL

1

£

v7-

2.)

raph whi ch

.

correction is giveti I

on of b/k as t? - onp

e coe .

' [6 one on t]

* f ""-. ^ v - effect on wetted

o p f or less for n<

tcta] resistance is of cc small*

esr rro^erate to lar^e values of ' i

1 1 ne s s in s

t on ?r t is quite large -11

to about 10"* of the total resistance it it

essential to correct for It Lf t) *

accuracy. . cis c

an^ the final cne selected was

ion fcr several valu ^

rrec tion va 3 at|

I •

Por a

10

cce* only variable unaccounted for. ">>is

variable mi considered In the same manner as the effec k

on the wetted surface coefficient. Fere a^ain we have

"seconc 1 order" effect and it Is neglected in this developi

An examination of figure 20 in Baylor will show these effec*

B amission these second order effects is justifi'

obtal ned .

11

"irs

rT

\ e results of this study are r resented graphi-

cs 3 III thrcugr} !bes< lots provide

a quick and simple means of deterrnininp preliminary powerft

;uirer.cnts on the basis of Taylor's Standard Series.

? c s V to ""II are contours of v.c vs d and ,7 //l" Tor value

9

• of $ it to .30, a mean b/h of 3.0 and a mean length of

500 ft. b' -- re T plves the correction C 1 which, when nulti-

• plied by ( " /H - 3.0), [Wes the value C which must be adc

to T*o to correct for the actual value of R/ ::. ^if.ure III

gives the length correction, A, which, when multiplied by

CHc f c), rives the actual value or" R1 ,

Accurac; , i

' course, is the first question to

be considered in usin{$ a set of curves such as these. ,rr'

resistance ills of normal form may be determined from

"se ctri with an eyr-ected error (based en Taylor's

series) c than 2\{fL % which Is certainly closi

for prelin iar5 studreF . Pesu' r both Baylor's

set of curves over a wide ranre cV represent;,

•ills are ,' /en ftr comparison encMx (t

12

(1), aaa

i

I L ..14

9-0

] :

- 95 »

* a d

1r •

ytv/e pbtain :co r _

fl .62) v»r; '., r

ice

f-^gi x = Corr..02

*Ve ni •'

'

' on fif • TV C*

• = .14 (.75)

C

. t =

s A(1c f C) * .97 (1! - 12.4

.4

.1

12

• 75

10

12

1.4

J? and this

1 owinj

- fif. VIII •

l 12.6

obtain .75

C .10

» C 2.7

frc • IT1 ol \ .97

12.32

figure of 12.32 obtained without lnt*

tion, compare r1 to 1! . Interpolated data shows a

dlfff e of c:\. ,uite satisfactory. .The

r. here reduces I "rom Taylor's se

just es likelj *o increase the error in ether cas<

a discussed in the next sec-ion, and can b< j

c 1 <T "

.

.

,

Fir- tipf TiT"

-rl.10

-1.08

-1.06

1.20(a OVER)

UO+1.00 .90 .70 .50

SPEED LENGTH COEFFICIENT

v/tC

.200'

.300'

.400'

500'

600*700'800'

J- 1000'

1200'

LENGTHL

LENGTH CORRECTION FACTOR A

RT -A(R c +C)

Bim.N.S.-5-10-48-25

-1.04

-1.02

-1.00

- .98

- .96

- .94

- .92

CORRECTIOFACTOR

A.1

B jo

Bsn.N.S.-5-10-48-25

.70 JO JO 1.40 1.501.00 1.10 120 1.90

SPEEO LENGTH COEFFICIENT

B/H CORRECTION TO TOTAL RESISTANCE IN POUNDS PER TON OF DISPLACEMENT (C*)

TOTAL B/H CORRECTION (0= C'(B/H-3.0)

L60 1.70 1.80

190LONGITUDINAL COEFFICIENT •

. 56

\\ \

_l_

170T

n| ~A "T T[j

ISO/

j

I T[j

~i_ T Y2 ti

1*0j

~T_ T '

\

3 1 6 6 aj sN /A it /6| (ELM is :« 35 1) JH 4ol J

110 / 11 j

s, X v ^ ^U1

\ 30 9o OO ((O

/ i

j

'I j\ I

1 \\\\

90 /~1_

/T I

\ Vj

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I \\ \ \70 / i j

1 /1

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1

1

1 f~ /,I

\

i \ \ \

/ / / j1

1'/

/ i \50 /

f / / /

1

/ 1 / / / \ \30 40 70

190

170

ISO

130

110

o<a.v>

90 5

70

50

Bsn.N.S. -5-10-48-25

.80 .90 1.00 I.K) 120 1.50 1.40 1.50 L60 1.70 1.60

SPEEO LEN6TH COEFFICIENT

CONTOURS OF TOTAL RESISTANCE IN POUNDS PER TON OF DISPLACEMENT

190LONGITUDINAL COEFFICIENT-.58

r |

1

1

T 1

170 4 Trt~

150 / i

130 /

H1

/, / A f $/,7 6'*y /2/ / *| id i8 ap 25 -3Q1

110

i

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?w vj sh X ^ v.

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[A TC y oo lS°\ /Otfy //^\

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Bsn.N.S.-5-10-48-25

j60 .70 .80 .90 1.00 1.10 1.20 1.30 1.40 1.50 L60 1.70 1.80



190L0N0ITU0INAL COEFFICIENT -.60

SO j60 .TO .80 .90

Bsn.N.S.-5-10-48-25

1.00 1.10 1.20 i 50



190LON6ITU0INAL COE FFICIENT > . 6

2

J1 1

1

170 *l

ino1 1

1 XT4,)

1

,

|

....

1301

\ i L65,

*>< o«w«p

' J JLSJ «#/ si 6 I 1 / $\ I1/2/ t /4 t& » I*- 2KlQ_JJL_aolwiJl1

1 w110 / / /

^ S. S . C s™^^.

T \\

/ / / in \90 / / / / I \vA//'/ /,

1

/

'

,v,\\

\ \ \

70

t I

/ 1'

j

1

i

p \ \\/ J /

.1

|

JLi

\\ V \

50 h / / a//

1/

f-

., JL \ \\Vso £0 .70 .80 .90

Bsn.N.S.-5-10-48-2B

1.00 1.10 1.20 130



1.40 1.90 L60 1.70 1.80

190L0M«TUOINAL COEFFICIENT* 64

.90 £0 .70 .80 .90 1.00 IK) 1.20 1.30 1.40 1.50 L60 1.70 MO


CONTOURS OF TOTAL RESISTANCE IN POUNDS PER TON OF DISPLACEMENTBsn.N.S.-5-10-48-25

LONGITUDINAL COEFFICIENT •. 66

JSO 40

Bsn.N.S.-5-10-48-2B

.70 .80 .90 1.00 1.10 120 1.30



90 5

1.40 1.50 1.60 1.70 1.80

LONGITUDINAL COEFFICIENT •. 68

30

Bsn.N.S.-5-10-48-25

j60 .70 .80 .90 1.401.00 1.10 1.20 1.30


CONTOURS Of TOTAL RESISTANCE IN POUNDS PER TON OF DISPLACEMENT

1.90 160 1.70 1.80

LONGITUDINAL COEFFICIENT v70

SO BO 70 90 .90

Bsn.N.S. -5-10-48-25

1.00 I.K) 120 1.90 140 1.90 L60 1.70 1.80

9PEED LENGTH COEFFICIENT

CONTOURS OF TOTAL RESISTANCE IN POUNOS PER TON OF DISPLACEMENT

LOWSITUOINAL COEFFICIENT • .72

40 40

Bsn.N.S.-B 10-48-25

.70 80 40 1.00 I.K) 1.20 1.50 1.40 1.90 LSO 1.10 140



190LONGITUDINAL G0EFFICIEN1 •.74

|1

170|

mo \\\\

/ / / 1 \ \\ \\i\VA130 / / / / j \ \la \\ \

V J.A &N a] 5 lid t zj m /6\ J ) 35 40\ ' *5"\ 5o\ A «A<Am\ \

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%ij i A >A \

\ \

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/ /

11

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1

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\ A \tf L8o\S5\SO S. K>>\

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\

190

ITO

150 HUJ

5

ISO

no

Ein

90 5

TO

5050 MO .70 .80 .90 1.00 I.K) 120 1.30 1.40 1.50 L60 1.70 1.80


CONTOURS OF TOTAL RESISTANCE IN POUNDS PER TON OF DISPLACEMENTBsn.N.S. -5-10-48-25

190LONGITUDINAL C0EFFIGIEN1'•.T6

170 V 1

,

150

/1/

[./

7—

130

\ ,

J -f / /• I7Is/ 9/ 0/ /z. /*//< 1 :5 J0 otfft? *5\ v! A j-A 60\ ^\ A\\\

110 / [

Vj *J k - V. v. ^

\^

*CJ

/ 1\\ > \ \

90 / / ,1 v \ \1F

/

A

\ L \ IOO\

70 / \ \ v\\1'/ 1 he 'a I

\

\ AV90 / /

1 SI v.

/ 1 \ l\\ \

\\^ \

90 JO .70 .90 .90 1.00 IK) 1.20 1.30 1.40 1.90 L60 1.70 190

3PEE0 LEN6TH COEFFICIENT


190L0N9ITU0INAL COEFFICIENT • .78

.50 BO 70 .80 .90 1.00 IK) 1.20 1.30 1.40 1.90 L60 1.70 1.80

SPEEO LENGTH COEFFICIENT


LONGITUOINAL COE FFICIENT .80

JSO TO SO .90 1.00 1.10 1.20 1.30 140 1.50 1.60


CONTOURS Of TOTAL RESISTANCE IN POUNDS PER TON OF DISPLACEMENT

1.80

Bsn.N.S.-5-10-48-25

29

'scussiov __s

A • "rite- rig

"ors started cut tc find an approxinu,

met: T determining resistance for preliminaryi

"^ere arc two prlrary criteria to 1 to

resv ' r such a study: (1) Is it accurate encufrh to"

be use i? and (2) Poes 1t represent any real advantar^s I

c or :r use which make it preferable to thl ular

It Is our opinion that both of these criter

y thes» curve

•

• Accuracy

Accuracy of the charts, as mentioned under re-

sults, Is vithin the accuracy to be expected of preliminary

calculations. In fact, a tw<* percent error in the re:

is within the limits of accuracy of wany tests used to deter-

a nee- It has been said that EHF curves shou'

drawn «lth a paint brush instead o : en, and this in

a one or eve: rcent variation frcrr. Taylor's SerJ

' signs in fen Ta; ' 8 S r'T

by spec if: 1 ^e -s, such as ^ransom sterns and ous bows.

rvea are net 1 11cm for ?ucr variations 8

3 far as ""•' s Sate normally

.

I 3 for

3C

Line and accuracy of use 9.

e 1 in 1 na * 1

.

»d four-way I a t i on re -

simplicity and

this, In turn, offers crtunltiea for or. In

T IV for c --, rhen Inr. s-

crr Lea Indie an error in c ether

rake was st invariably found In the

Lona of Taylor's Series. There I v. le

saving* in tine as w«ll, especially la-

tiori3 are to be made.

D .r'fflber of Char ts Acquired

b total number of charts require eaks r or

[he 15 charts here are to be compared to 56 In

only .iy specific hull the ccr

* a nay be obtained from three or four

'.ev; chafta owing to the use of v/fL as an abac'

• char f• ad in Taylor. '"he total

charts re Dr net it is

sir'- elate between values of Jf • If it is desired

to use t) otted value of X to the hull in quest

iV'en It 1j nee ess

.ts in * be an - had t]

war: 'to b e use<: . In *

val * 'on,

" A - .

A

^¥

1.0. ;. eragc'

e .

value j J^

The -i this

IV i which fives representative

and out Interpolation for comparison to Taylor' es.

le to limit the tc of

[ 11 b-- ex ucei 1 y ace

. n and using values of K

06, h case the total numl

ic es to 7 .

e range cf values of a tc be covered is al

to b if i cation. It seetrs unlikely t;

>r a ncnnl, use, although it is pre*

ossible to go t< values of X

foi raluea cf V ^ belofo 1.00 tut this^dj

..

In cc ' ' 1 on c • er cf char 1

of an ad

the accuracy cf 1

1

A*

If v.<

A

32

I

accuracy Is not essential.

Conclusion

Is trie cplnlc the authors that these cu:

are simpler to handle lcr series. jire cer-

tal. ore condensed and t^ey are well within the ' ts of

accuracy normally expected Cor preliminary studies, "hey

re6 for use wherever they may be applicable.

AFPKNDIX

3*

Details of Procedure

\— - . . . i. . ..

As rfrnt

'

In the section on procedure a j

cf v tentative chtippcterl sties was Fade

cidr on the ranp of ccefflc lent s to be covered. Table

is • lation of a wide variety of ships In actual sc

which basis for this study. It is felt that this

lis* ' es all typos likely to be cricounte Ln nor

dec '

• ork

.

s!stc:ice ?

a from Taylor's "Speed and Fewer" wa:

r ease in plotting. Table II Is a

sample of this form. criminals are all filer* in \

>tebook. The es in any case n

ylcr's curves if d< d.

'.

i correction

In cc | le methods of

a corr It vas di

h and ' /*fT wc e the best

sen bee

. . ': ! cause an ej i

ly an

\ I

ERISTICS

35

SKI? 7 i -

;6 108 43,000 3.18 1.

-. tleship :>8 34 54,000 33 3.18 . 1.

Air, Carrier ;0 93 29 34,000 33 .21 . 1.

;iser "4 .7 .5 ir>,ooo . . .

liser .63. 24 12,700 33 2.63 • 1.

Battlocr • 5

.

31 31,700 2. 1."

^oyer 36 39.3 13 3,100 36 . ,4 1.

ort 300 3C. 11 p 00 24 3. . 1.

Mine 170 6. )0 16 . • 1.

!..inos7 2^ 32 9 850 18 . x •

r 107 17 C 108 22 . .

O 1 <*»

.

er 520 .3 . 1G,700 • 18 .

ier 1 . .7 8,900 13 2.70 142 .

Tender 300 41 12 2,400 20 ,42 1.16

Rep; :ipr 1 1Z . 19 13,000 19 3. .

i .

Lip 41 60 19 .100 17 . .

7 5 . 00 . .

41 CO 25 11, COO 19* .40 160 .

Car-- 1.8 27 < 14,200 11 . .

• .5 .7 ,200 2.05 .

. .

Tan. , , 8 .

Tan . , 16i

.

• • . 11 . .

.5 1 . . •

.)

a yz

a- v is 3 .ot#

k* bly for cargo vessels wifort lias be on mi

in or estimate loaded figures.

f

36

- , )0 17 3.00 1 . '

. k

. ^oo : . .5

Lnt D 3r. . " ,500 18 2.85

0,000 14

Sal\ ,530 17 5.00 1.

' lig 38.5 ] 1,500 16 2.70 20? 1.

37

TA3L^ II

SAI. T?0F:. JD TO RECORD

X .667/j/T o90

DATA

d Rr2.25

RrB/R 3.75

RrP/H 3.0

Rf Re

50 .3 4.3 4.05 9.6 13.

70 4.07 .7 4.39 Q.O 12.

90 4.25 4.9 4 57 7.05 11.62

110 4.35 5.1 4.73 6.4 11.13

130 4.4 .2 4.60 1 10.70

150 4.5 5.3 4.90 .5 10.40

170 4.56 5.4 4.98 10.18

190 4.6? 5.45

v/VT 1«

5.03

00

4.9 9.93

50 c>,85 .9 8.97 11.5 20.37

70 10.3 10.4 10.35 . 75 20.10

90 11. '.J 11.5 11.5 8.6 20.10

110 12, 12.2 .25 7. .05

130

1

13,1 12. 12.95 7.2 20.15

,7 13.3 13.5 6.7 on oj

170 14.

9

13 7 11.0 S.3 2r.

190 14 14.0 11.4 5.95 20.35

men /i

orrec

©< lor's

1 resistant

Ion t( anal resistanc (oC-lJ^f, a

we see that Rf = ^t(jc). C we

ha .

ec tion r ^ t ( x ) ( <* - 1

)

= ^t. f Rt(x) (« -1 )

r cte„ ; "[] t <x j

l x K-l)l

Th i o ! s r

.

Ion oi 3

.

f the on

3 t* 6

Figure: .XYIW

Puor or r^e^vs values op X

^ - R«/Rt )

•**

..i

X 2-.SL' >

*.*.fc4

*

*

a

,C | \. O

*

r

A \. o

o"6

.2.o a

1

O A 1 1 \— 1 i

' .70 *o no l.lo

vfor

i.^-o l.lo

40

Gi O CO o NJ4 o rH

o o o t>

o o ao •

•

H r-i r-i rH

LO o O to r-i r> to

oiH O

H o a£>

• • • • • • • • • • • e

rH ^ rH rH r-i , <

CO o 0) o H w to o to

o rH 1/5 to o a> GO r- o to to to

O o o o c O• 1 • • • • • • o a • • -

•H r rH i-4 rH H

rH O L) O a 0) O to rH

o + t> to H O t- t> o LO ^OJ O o o c» c> C) O•

1^1/I

•

rH•

rH• • • • • c •

£> o O rH o Ho < C> lO w £> lO to •^ to Cvi

t> o O o O Oj Ct c^

• •

H•

rH•

rH• • • • o • •

O o CO o CD OJ o •^ *-

o CM o O H H W C\i W CJ

to o o O O o a O Oo • • o • • • • • • • • •

H 1 1 1 i 1 1 1

<LO 10 o o t> ^ a> to oo rH

t—

(

L% lO n»* rH o o rH H CJ Cvl to

1—1 H o o Q o O o o O oM •

rH• "> • • • •

1

• •

1

•

1 1

•

1

•

1

w .

vA o CM o a CO <tf o to o< o 10 *-^ rH o o H w tO to

r-i o o o o O o o o• • • • • • • • • o • c» •

H 1 i 1 1 1 1 1 1

O tf H r~ to o a rH o t> to oo lO i rH o rH to to <*

o O O o o o o o• • • • • 5 •

1

•

1

• •

1

•

1

•1

•

1

o o tD O H r>

o LO O rH N LO CD

L> o o o O o o• • • • c • • • • • . • •

I

1 1 1 1 1 i 1

—r-4 t> o rH

-* to CJ to to t>

1 o O o o o o, • • • • o • • • • • •

• V 1 1 1 1 1 i 1

H rH rHr> rH

.• o oV • • • • • • • • •

J o oo oo

W to orH rH rH

41

, to i .. a si. plot of contours

variatlc resl e on c .'na + e?. of any tw<

Imary variables '

:/-^,X, or d. Plots w< ide of the vt-

tion of resistance V3 . X for erent values cf d at several

valuer, of ^ Plcts were cfede for the variation in

resistance with variation of b/K vs. v/^TT f cr different

values cf d at several values cf $ . : ther of these at-

tempts a possibility of simplification for easy usi

£. The next step in this investirat ion was to plct

variation in resistance for unit variation of p/H vs. d for

different values of jt and at different values of v//"L (see

fig. XIX). It was found that for each value of V/'-fL t:

curves for different values of J( fcVrred a compact family of

cs, H I ioh a mean ecu" drawn and thus X was

as a variable. These rean curves at differe

values oV V/^T* wer^ then combined in a single plot (

chec variation ccul^ be

n coordinates of d and ^~T~ in the sai^e mi as

the *?c contours of figures V to XVII. Thf ;d plct is

cbta it 13 ill 1

by f ips . XIX, i re-

.0)7 r"

'

"'

I

was 3 cJLe ct ' o fBlrr-

\

toB H

Figure ZESTMethod of ETuminating £ /\s ^ Variable iin

B/H Correct-ion

\.

-1

3

2

v/fc = ll0

(Curved Puci-r-Te:D Foh? Er^-H 1/aluE of £)

?- .80 p . .76

'ea/v Curve:

J'o TO 90 //o /ao as-o '7a /?o

Di5Placem eiKiT- Length Coef.d

oo90 //o /3o /60

placement Lemgth Coarr:

Curves For EA .h v^lue o^ v/vTl!

Figure ~X>

Method op Plotting B/h Cokrccticxn Comtou>

4

3

I

go no '3o

DuPLRctMCNT Length Cocf*/£=-* 00

La/ ±'><ij«<i

44

n as

r' et ' In rrection is

arl ^r values of r •

rid sub 1 ve

^ess t) . - a exception rill r• ^ as a

all negative! area on figure I

c * It is to be noted that here a^ain we have deve]

an nb correction wb'eh will not cc • 11

nna but will five poor' result r when combined with the

Ions mado in this study. As a.tated before, with

no correction for V TT it Is possible to introduce er

r °r Sxtr U .0 cr 4.0).

correction as, I :

> e 17, the max-

ssible error is reduced to Z%. It should oe em,

rcssible errors are the maximum obtained at extrt

values of the coefficients and V/fF« .

•• errors to I

. enere.l use are much leas than these figures.

*5

Sur.rle Calculations

Calculations fcr a var.'

fc *r' een made fcr comparison of t)

urves developed in this Lg, -> re ill

calcu] is are tabulated !ri fcafcle T v . ] icu

lations themsalves ar- riled in th< sis note:

46

u rH

r I

B

^ co

oO TJ

<D

OC

P<

•

.«.

0)

rH * o rHcJ :!: r> rH o

o - •

rH r-i

-pto

<L o t»- CO co^ -p 0> n CJ D- O o o

co • s • • • • • e • • • • • •

o H rH TJ«

CO rH CJ CM to

-

<L o O to o to lO O o o o o45 »5< O C) o lO o OJ to

• • • • o • • • • • • o • • •

rH rH CJ 0* rH rHO

U o o CO o O£- CO o v o CM C/ O

o • • • • • • • • o • • • •

a C) ' lO to CM OJ «4« %* r-l

H CM CJ CO LO Ol

.

CI H 01 to toAJ ci o CO o> o LO lO LQ CO to

X, • • • • • • • • o • • • • •

CO ' CJ H rH tO ^ r-l

rH OJ CJ to lO CI H

to ^ ** o o*H cm o CJ fv. o CM

to to to ts o D to to• • • • • • • • • • • • • •

to •f CJ to CO o to o o to toto C7i CJ O CJ CI CJ OJ

o

lO•

CD rr> O

CO

0) o»

lOo

m t£> c OJ to to 10 OJ to OJ CO co CO OJ r-\ H H H to to to to r-i

m *n lO to If}

• • o •

01 -* CO •tf O t> o ^ 0> o>CJ CM tO CM to CJ rH r-\ H

to• •

rH O t- CO to to rH r-i

CJ to to o {> to

a m to to o o o oj . t-\ Cj o> o £> O

to x* ^ 0- 10 "tf

•• o o o o o o oo o en

<\•> * • * •> •> • • • * •. •> » •^ »

rH r^ r-\ rH HrH r\

o

O

05

u

r<

ti

• •

uto

•

-p

•

•

47

. - —

.

—

.

arch lt: 47

b931TKcsii NicholsonN5 Investigation of methods

of plotting resistance ofships to simplify prelimin-ary design power studies.

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'

6931it Nicholson

** Investigation of methods o*plotting resistance of ships to

simplify preliminary design powerstudies.

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Moo ii

investigation of methods of plotting resistance of … the nps institutional archive theses and...

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