Analysis of gross curves of the series sixty

(1)

A N A L Y S I S

OP CROSS CURVSS OP TIE

1{S EO

Elaborated byz

L,Krystyn Kupras

Wlodzirnierz Majevski

CKO

Str.

(2)

CBKO i

Gdansk

Str

Analysis

of cross curves of

the

series 60 _1/2;

Introduct ion

T'ne theoretical forms o± single screw vessels of the series 60 arc more and. more utilized for designing ships owing to a rich informational material concerning resistance-propulsion charac-teristics being at disposal.

These foru, as

ready checked., are marked out by favourable

properties not only from

the viewpoint of the resistance and

propulsion, but

also from the viewpoint of

a

good behaviour in

the waves.

The present elaboration aims

at carr"ing

out an

analysïs of

these forms from the viewpoint of the

stability

and it will therefore

be in

the writers' opinion an additional information for the designers.

The forms themselves oÍ' the series 60 are

not described

here, because they are generfly 1cown and. a lot of literature can be foimd in this respect.

Scope of researches and method of calculation

The subject of analysis are cross curves

of

hulls of the series 60. By cross curves are meant curves showing the distance

of the line, of action of the displacement

force from the

point K iyi ng on the intarsection of

the ships' centre line

with th baso line /d.rg.1/.

Distance is called hereafter

ciia1i

t frcc lerer.

I

It was

assumed

that the displacement force lever is a function Qf the parameters:

VI _r H B

. _, V, , ,

£1

(3)

-CBKO i

Gclansk

JialysiS

of cross curves oi the series 60

Su

The nlysis of the cross curves was carried out _{systematically.} There was calculated a total o± 26 sets of cross curves for va-rions combinations of the basic parameters of the forro.

Scopes of the parameter variations were as follows: a,'. block coefficient

from 0.6 to 0.8, _{every 0.05}

b/. ratio of the depth moulded to the breadth E from 0.54 to 0.66, every 0.04

0/,

ratio of the breadth to the draught

T

B

from 2 to 2.5, every 0.5

d/. ratio of the sheer fore to the breadth from 0.15 to 0.30 , every 0.15

the sheer aft constituting the half of the sheer fore.

0/.

Oituation of the centre of displacement alongside:

J1__

for _{= 0.6}

_X

_{= 1.5 percent L}

0.5 percent L

V

_pp

pp

Ifor

= 0.7 X, = 0.5 porcent _{0.5 percent}

for

é

= 0.8

X

0.5 percent L _{1.5 percent L}

V

_pp

pp the calculations have been carried out according _{to a specially}

elaborated pro.wm by means of the Elliott

_{803 B digital co}

puter in the Central Ship Design Office No.1 _{at Gdaiísk /see} enclo-sure!. According to this programe the _{cross curves are} calculat-ed for angles of heel from

_{o( = loo}

to _{o( = 70°} every 10°, each for 6 displacements.

Basic data were ordinates of the body lines o± the series 60 which had been calculated by _{means of an other progranno;} this allowed to avoid taking the measurement _{from the body plan.}

(4)

CBKO I

Gd ans k

i

nalys is

of cross curves of the series 60

Calculations were carried out for following dimensions:

L

150m.

pp'

B =

20m.

arid for remaining parameters for the scopes as given

above1

The calculations took no account of

the

caber and influ-ence of the superstructures.

Analysis of the results of calculations.

On completion of the calculations all cross

curves

have

been

plotted. Due to the fact that the change in the block coefficient involved a chance in the scope of the displacement arid raises difficulties when comparing with the cross curves, the ratio of the draught corresponding to the given displace-ment to the moulded draught of the ship being heeled, T/Tk accepted on the horizontal scale.

The running draught T can be read off from

the

hydrosta-tic curves sheet or from the di,ram on the drawing 2 where the correlation T/Tk between the dimensionless displacement V0 and the block coefficient C3'

is siiown.

V =

o

_{L .B.Tk}

pp

So, the cross curves are shown in the form of the correlation: V

('Tk

$

XL

-

_{'B' B'}

hj

..bn.

,B,X

_V 3 4

(5)

CBKO i

Gdarsk

I

L =

150m.

pp B

S

B/T

H/B

W/B T

i

_s

=f

_o

_'

_Tk)

Analysis

of cross curves of the series 60

dimensions can

be generally expressed by:

It was

further on assumed that

the cross curves

analysis

will be carried out by

comparing with standard cross

curves,

i.e. with curves for a

ship having densions

and parameters

called standard ones

Then the displacement

force lever for a ship

having standard

The preliminary

ialysis of the results has

shown that the

expression

14/

can be written

down in the form:

+f4(,c

-

'

T'1

1 20

1J

T\

2(B

T =

+ f1

, , +

f

- ,O< .

)f3(

. k! k

because the increment for the

displacement force lever

provoked

by the change in one

parameter does not depend

practically on

other parameters.

It

sas

stated

here that:

5 =

20m.

= = 2 =

0.62

=

0.15

(6)

CBKO i

Gdansk

b=

f4

(o(

0.04 d _T 0,5

H

-0,62

or

1 does not depend practically on the abscissa X of the centre of displacement /buyoancy/

functions

fi ,

f2, f3 and f4 can be expressed as

fol-lows:

Tl

Tk) =

a(e).

hlfrk)

T

d().

h4

viere a,

b, c

and

d are linear functions.

a = _{in the whole considered scope of}

_S

w

- - 0,15

B in the whole considered scope of

0,15 -

0,58

0,04

(o(

_'T

T /see example of calculation /

in the whole considered scope _B/T

The double form of the function o () results therefrom that the acceptation of an equta]. function h3

(o(

. in the

whole considered scope of the parameter

_H/B

_{from 0.54}

to

0,66 would give a

too bi

error. This scope has been

there-= =

b().

c).

(Hl

h2(o(

h3 (o(

T 6 Str Analysis

of cross ctn'ves of the series 60

T

(7)

CBKO I

Gda,Ssk Analysis

'-4)' '- 24t zh=

fore subdivided into three compartments: from 0,54 to 0,58, from 0,58 to 0,62 and from 0,62 to

0,66.-UnJ..inear functions h1, h2 , h3 and h4 are

shown

on the

drawings 3 - 8. Drawing 3 shows the function b.1, drawing 4 shows

the function h2, drawings 5, 6 and 7 show the function h3,

cor-respondingly for the aforesaid scopes of the parameter }VB and drawing 8 shows the function h4.

Application of the results of the lysis for the preliminary calculation of the righting lever cm've.

The difference of the value

4

resulting from the in-troduction of the expressions /6/ in the formula

/5/

lies

within the limits of some centimeters. Thanks to it the results shown can serve for a quick calculation of the righting lever curve, when predes1gii1iïg, for any ships displacement. The

diagrrn. can be used for the value 1.1

k

How to make use of the diagrams, as well as the exactness of the results is illustrated by example. The results of the

calculations are scheduled in table No.1 amI plotted on drawing 10.

Example of calculation.

Principle dimensions of the ship with forms of the series 60 are as follows:

L 140 zu. = 0,6

B

19m.

= 2,24

(8)

CBKO I

Gdansk Analysis

S

= 0,67

H 11.40

W =

2,84m.

Calculate rigYitlrg lever curves for the displacement V = 10.000 in3 and Kt = 7,1 ni.

Ca.loulat ion:

Dimensionless displacement:

V 10.000

V

om the dgram

i it is read off for data: _{V0 = 0,443} _and

S0,67

. The ratio of displacement where the ship reaches

a displacement cf V = 10.000 ¿, to the moulded draught Tk= 8,5 ni,

k

= 0,7

Prom the diagram 9 it is read off for = 0,7 the value k

l for a ship having standard dinirnsions and parameters.

Prora the diagram 3 the values of the function h caused by increase in the block coefficient by the value ± 0,05 are read off for = 0,7 and mi1tiplied by:

K.

S

0,7 0,67 0,70

a

= 0,05 - -0,6

obtaining f1

f1 = h1 , a _{/see table 1, line}

_31.

Prom the diagram 4 the value h2 ¡une 4/ is read off and multiplied

by

o _LBTk _140.19.8,5 = 0,443

tt( s S SZ (15. V rte. F.u. I I 6-ZO t(U ka1 te.kn.

(9)

CBKO I

Gdansk

_{of cross curves cf the series 60}

Analysis

w

b = B

-

0,15

=

0,15 - 0,15

0,15

0,T5

Obta1rtirg

f2

=

h2

.

b

/line5/

H

Because in the example

referred to the ratio is within

0,58 and 0,62 , use

is made

of the

diagram No.6 wherefrom suitable

values h3 are read off

and nr.iltiplicd by:

H

-0,62

_{0,6 - 0,62}

o-

-0,04

-

0,04

=

-0,5

obtaining

_{5 :}

f3

=

h3

.

c

/line7/

If 0,62

<

(

0,66

,

suitable values are

read cff from the diagram 7.

However, if

0,54 (

< 0,58 suitable values are read off from the diagram 5

₍

h' '

and from the diagram

6 ( h3

f3

will

be derived from the formula:

/

f3

_{= c. h3}

-

h3

where

:

-

0,58

C

0,04

From the diagram 8

the

values h4

¡une 8/

aïe read off and multiplied by:

B

d

_-

¶2

2.24-2

0,5

=

0,5

=

0,48

(10)

CBKO i

Gdansk

_{of cross curves of the series 60}

Analysis

tr

obtaining f4

f4 = h d

/line9/

Values for the standard breadth B = 20 m and remaining parameters like for the ship exnplified:

=0.6,

=2.24,

=0.67,

0,15

is calculated according to the formula:

1 = l + f1 + f2 + f3 + f.4

¡une 10/

Values _l'« for the breadth B = 19 n. are calculated by multiplying values i

_«

by the ratio of B 19 to the atan-dard breadth B = 20 ra B = . . = i « 19 20

In ljne 14, table 1, there are -given values

_l«

calculated

by means of. a digital computer.

On drawing 10 two right1 lever curves are plotted, one calculated by means of the prograume on the digital computer, the other in a simplified way - by means of diagrams. om the comparison of the results it is seen that the exactness o! the simplified method is sufficient for the purpose of

(11)

2. Increments i caused by

the

change in by value ± 0,05

t3.

Correction f1 - b.1 a 8. h 10. Values l

for standard breadth

ni.

f'

+f +

11.

Ya1ues 1

for breadth B = 19 ni.

lo(.

j 20

112. sin

Specification

.

h3

.

c

2

Value of 8tandard cross curves

torT

0,7

Increments i

caused by the

in-crements

W by value

0,15 B Correction f1 h2 . b Increments l,,

caused by the

re-duction

from 0,62 to 0,58

B

Incrementa l

caused by the

in-crement

B

froni

2 to 2.5 T

symbO'

h

h4

3

10

4 1 36

o

_o

0,005 ₀₁₁₀₈₅ 5 2,83 0,015 -0,01 o o 0,033 0,017 30 6 4,32 0,030 -0,018 0,005 0,053

o

0,086 0,247 0,043 -0,124 0,132 0,187 0,340 0,39 0,041 0,063 0,09 0,163 0,187 1.40 2.87

-$1.33 I 2.73 4.35 5.61 6.41 6,88 4,13 5.33 6.09 6.54 5,58 0,043 -0,025 4.56 6,43 6,93 7,20 0,037 0,018 0 -0,022 - 011 0 0,117 0,20 0,262

01

0 0 0,374 0,434 0,471 -0,187 -0,217 -0,235 0,36 0,256 0,174 0,126 7,09 6.74 5.43 6.15 6,67 o

î

fi

D) I-o (D w (D $1 fi. (D w

I

40 50 60 70 7 8 9 10

(12)

f p p 1 2

34

5 6 7

8.

9

10 Ö

13. Righting levers

.

h

i

sn

0.09

0.30

0.58

0.77

0.66

0.39

0.07 O

14. lues l

calcul

â

means

t

1,2

2,72

4,18

5,36

6,14

6,59

6,76

-. I

15. Differences between suitable

values I

calculated by means

0.01

0.01 -0.05

-0.03

-0.05

-0.01

-0.02

of diaraxns and digital computer

(13)

a-CBKO i

Gdañsk

X V -Analysis

Jesignation.

L

- length between perpendiculars m

B iuoulded breadth

m

Tk - moulded draught

m

T - draught corresondig to the displacement V

m

S

-

block coefficient calculated for the moulded draught

Tk ra

H

- rnould.ed depth ra

W

-- forward sheer ¡calculated on the forward

perpendicular! w

- abscissa of the center of displacement

/from midship in forward direction

_1+!

_pp

in after direction

I-I

V - displacement corresponding to draught T - dimensionless displacement

V L

.B,T

pp

k

h1,h2,h ,h4 increments of the cross curves for the standard breadth B 20 w. caused by the change in the considered parameters:

, H B

L.,, I,

¡

_.

- displacement force lever for a ship having

dimensions and standard coefficients w

displacement force lever for a ship hav-ing the standard breadth and the remainhav-ing

parameters changed

w

- _{displacement force lever for the ship}

hay-irg assumed dimensions and parameters h - righting levers

KG - distance of the centre of gravity from

the base line

w

P - determination of the position of the centre of displacement for the ship heeled

through the angle O(

Str 12 V o w w

(14)

CBKO i

Gdatsk

_{of cross eurves of the series 60}

Analysis

B n e i o s u r o.

The Central Ship Design Office No.1 at Gdask owns a digital

computer of

TT1I0T 803

B type. This computer is a transistor machine with ferrit storage for 4096

words and ccputin

_speed

of about 1,500 additions per second,

equipped with an automatic progrm"iing system.

The Central Ship Design Office No.1 has elaborated some scores

of programes for design and economic calculations whereof the most important are:

A. Calculations combined with designing a ship.

The designing of body lines

of merchant and fishing vessels

is based on the results of

èystematic model tests

cerried

otrt iii various model tnnlc tests. The progra2res of desig'ing the body lines have been elaborated according to the follow-ing series of models z

i Series 60 ¡David

Taylor Lodel Basin,

_Washington

Series of tankers /SSPÀ-Goeteborg, Sweden

Series of

general cargo ships /SSPAJ

Stern operating trawlers

Coasters.

sic data for all these

_prograiinnes

are the ship s rincipal

dimensions, block coefficient end abscissa of the centre of displacement; as a result is obtained a table of ordinates

of body lines. The table of ordinates, recorded on

perfora-ted tape produced by the digital computer

constitu±'es a set

of basic data for further progranmes as follows:

Calculation oÍ' Bonj can scale

(15)

CBKO i

Gda,ísk

Analysis

of icss curves of the series Co

Calculation of transverse stability

Calculation of floodable length

Calculation of resistances,

Prorcnimrs No.6, 7 and S have beon also elaborated in the other version for data measured from ready-made body lines0 Por the same /nieasured/

data the following

_{prograes have}

been elaborated in addition:

Calculation of

longitudinal strength of hull.

Calculation of the dia'am of trins and that of checking the bending moment in any condition of loading.

Calculation of tank sounding tables at any ship's trim.

Viithin the designing of the fishing vessels, except for the progranne No.4 still following programmes have been car-ried out:

74. Determination of optima]. volume

of fish holds and ship's speed depending on the type of ship, propulsion, _{as wefl} as on the Liahing area.

15. Determination of optime]

principal dimensions of

_the stern operating trawlers.

Vdithin the hull construction and arrangements following

programes have

been elaborated:

1G. Calculatìon of longitudinal scantlings _{from the} vievi-point of a rninirru1 weight based on the strength

stan-dards

of Register of USSR.

Calculation of bipod. masts /Voigt's method!

Calculation Qf natural frequencies and torsional vibra-tion stresses of the shafting.

As the complement of the cycles of pro i'amrs comprising the ship designing there are in the offing the ca1culations

(16)

CBKO I

Gdassk

of optimal propellers moderately loaded ¡according to vcrte

theo-ry/, calculations of drge

stability and launching

calculations.

B. Analytical

ressing of

the hull form.

Simultaneously with the programming of the design calcula-tians work striving

for

analytically expressing the ship's huB. form has been taken up. There have been elaborated 9

_programes

allowing to find the mathematical form of hull with

a

great

exact-ness. Results of these works will find usa,ge in hyd.rodyriamic resear.. ches of hull properties, in improveElent of the lofting works, as well as preparation

for

_{the introduction of}

_numerically

_controlled

plate cutting machines.

O. O'gaiation of production.

i A p1Dgranne

fixing the monthly

_{production plan for the} ship-yare had been elaborated, which ensures, from _{one side, to put} ships into cou.isaion at the tines provided for and from

the

other side to ixtiize the productive capacity

of

_{the shipyard's} departments most uniformly.

The method simplex of linear

pro

nirrt1ig has been applied here 2. The application of the

_{PERT-method. is}

_{tested for use on a}

lar-ger scale in the organization of the shipyard 's production. The PERT-method which gets lastly

_ahead

_{throughout the world allows} to detect and provide

for

_{the "bottle necks" in the production,} as well as to provide full information about the cooperation of all the shipyard's subcontractors.

_Prograzmie

_{elaborated for the}

digital computer Elliot 803 B allows to analyse 700 various ope-rations simultaneously.

Except for the afores1 _{prograres of technical and economic} calcnlations a lot of auxiliary _{progranes in the field of}

inter-p dat

ion, approximation, matrix calculus and others has been elaborated,

Analysis

I

:"t I27 t4 a. t. Atek. hx - It 6.-2u: su lu

-

IScr'

(17)

CBKO i

6dañsk

OtL,t.t. OI .___...

Analysis of cross curves oÍ' series 60

Str.

16/a

Descrint ion of dravinjzs

Pig.2: Relation between the T ratio, d±mensionless displacement

and block efficient

2.

=f/Vo,6#/

xainple: Principal dimensions: Lpp 145 m B

= 20m

T

=7.8m

= 0.67 Dimensionless displacement: V Vo = Lpp.B.Tk

from the diagram:

m

= 0.7

Fig.3: Increments l caused by the change in from o.? to c.75 Pig.4: Increments l caused by the change in W/B from o.15 to 0.30 Pigs 5, 6, 7: Increments l ceu.sed by the change in H/B respectively

from 0.4 to 0.58, from 0.50 to 0.62 and from 0.G2 to 0.66 Fig.8: Increments l caused by the change in B/T from 2.0 to 2.5

Pig.9: Standard cross curves Fig. 10: RigtThg lever curve

values calculated on the digital computer

values ca1ci1oted in simplified way by means of diagrr

Actu1 displacement: V = 10,000 cu.ni.

(18)

r. -r

C&KO i

Gdcnsk

Str.

RYS.NR I

(19)

&

CBKO i

Gdak

Vo 1p 05

RYS. NR 2

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PE.NOTuWOC AD.UBA

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GrZGraf. 1271 12.462 10.000 kaIL- eclin.

PRZ,'AD WyPOJNc V 11Yr1AY

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Lpp i45 8 20 i

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(20)

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PRVROSTV RAP4ION 511CV WYPORU

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PRZ.VRO STH WSP(PICC2YN NIKA PEhNOTLIW'OSCI

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PRZYROSTV RArUOPJ 51kV \VYPORU SPOWODQWANE

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(21)

CBKO I

Gdcñsk

PRZVROSTV RAMION SilLY WYPORU SPOWODO\VANE PRZYROSTEM

OD WARTOSCI 0,54 DO 458

RVS.NR5

[m]

05 0,4 ¿ 03 0 I

(22)

PRZVROS1Y RAMION SWV WYPORU

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h [m] 0,6 _0$ ₀₂ 0,1

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(23)

C B K o i

Gdai4sk

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(24)

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CBKO i

GdatSsk

I1tI:_

KRZYWA

RAMION

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Lpp: 140m

9 19m

T

_85m

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1414m

2l%I.pp

97

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711m

( a. Sk. )3/2(/

(25)

W1IRY I

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(26)

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TECHNISCHE UNIVERSITEIT DELFT

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