Systematic experiments with models of fast coasters

(1)

IRCH!EF

&e,44,4é- )ifrl

SKIPSMODELLTANKEN1 NORGES TEKNISKE HØGSKOLE,TRONDHEIM.

NORWEGIAN SHIP MODEL EXPERIMENT

T,Lb(, v

Schpbo1

THE TECHNICAL UNIVERSIrv OF NOR WAYTedThe

SYSTEMATIC EXPRIMENTS WIÎH

MODELS OF FAST 'COASTERS

BY.

HARALD BZØRN HANSEN

NORWEGIAN SHtP' MODEL EXPERIMENT TANK PUBLICATION NQ 44

(2)

BY

HARALD BJÖRN HANSEN.

TABLE OF CONTENTS. - Page

1. INTRODUCTION

2

2 SYMBOLS AND UNITS

2

Ship Dimensions .2

Propeller Dimensions 2

Kinemátic and Dynamic Symbols arid Ratios 3

Dimensionless Coefficleilts and Ratios 3

Units and Conversion Factors .

. L4.

TANK AND CARRIAGE PARTICULARS 4,

METHODS OF CALCULATION

4

5 SHIP MODES TESTED

f

. 4,

PRESENTATION OF SHIP RESISTANCE-DATA . .5

METHODS OF DEVELOPING NEW FORMS 5

GROUP A Variation in Formof the Sections 5

GROUP B. Variation in Breadth - Draught Ratio 5

GROUP C Variation iñ Longitudinal Position of Centre of Buoyancy 6

GROUP D. Variátion in Prismatic Coefficient

6

GROUP E. Variation in Length - Displacement Ratio 7

GROUP F. Vâriation in Bulbous Bow 7

. PART I.

Towing Tests on DLWL. Presentation of Ship Particulars and Results. Analysis of the Results.

GROUP A. Variation in Form of the Sections

GROUP B. Variation in Breadth - Draught Ratio 11

GROUP C. Variation in Longitudinal Position fCentré Of Buoyancy

13

GROUP D. Variation in Prismatic Coefficient

14

GROUP E. Variation in Length - DisplacementRatió

17

GROUP F. Variation in Bulbous Bow 19

9. PART II.

Towing Tests on WLI. Presentation of Ship Particulars and Results.

Analysio of the Results. 21

GROUP A. Variation in Fort of the Sections.

21

GROUP,B. Variation in Breadth - Draught Ratiò 2

GROUP C.. Vriation in Longitudinal Position f Cèntré of Búòyancy 2

GROUP D. Variètion in Prismatic Coefficient

27

GROUP E Variation In Length - Displacement RatiO,

29

GROUP F. Variation in Bulbous Bow .. 30

lo. PART III.

Propeller Data and Open Water Propeller Tests.

Self - Propulsive Tests on DLWL. Presentation and Analysis of the Results. 32

GROUP A Variation in Form of the Sections 35

GROUP L Variation in Breadth - Draught Ratio . 37

GROUP C. Variation in Longitudinal Position of Centre of Buoyancy 39

GROUP D. Variation in Prismatic Coefficient 41

GROUP E. Variation. in Length - Displace's nt Ratio

43

GROUP F. Variation in Bulbous Bow .

. 45

47

11. ACKNOWLEDGEMENTS

APPENDIX 1. Line Drawings

47

(3)

2

-1.. INTRODUCTION.

At the Norwegian Ship Model Experiment Tank several tests

_with

models of coasters have been carried out.

Publication No. 4, "Some Systematic Form Variations of Fast Coasters and the Influence of these Variations on Resistance and Propulsice Results" by Andreas Haáland, describes some tests with models of a particular type of vessel, employed to carry passengers, post and cargo. in the local traffic on thé Norwegian coast. _{As thelocal shorter routes} are not always sheltered, these vessels have to hé really seaworthy.

Another publications viz. No. 13, by Arme Voll and Harald Walderhaug:ÑTowing.. and Pro-pulsive Tèsts with Modèls of Fast Coasters and Whalers", deals with model experiments of smaller vessels with greater speed-length ratio, designed for the local traffic in the sheltered Norwegian fjords.

The present publication describes experiments carried

_{out with models of vessels that.}

are relatively larger and traffic the long sea routes along the Norwegian cast

_from

Oslo to Kirkenes, a distance of more than 1450 nautical

miles.

For this type of vessel vm'y little of published data were available for the designer, both regarding the different factors Influencing the resistance and data for calculating it. _{The material for determening the wake fractions and thrust deduction coefficients} were also insufficient.

The publication consists of six. groups with the object of

_examining

the effect of vary-ing.the following;

Fore 0g the sections. Breadth - draught ratio.

Longitudinal posltionof centre of buoyancy.

D Prismatic coefficient.

L Length - displacement ratio.

F. Bulbous bow.

The influence of these variations, on resistance - and propulsive results for designer's load waterline, are investigatéd over a Speed range from 11 - 1H knots or a speed-length ratio from 0,70 -

1,15.

Resistance tests are also carried out on a trim waterline, corresponding to 2/3 of the displacement on load waterline. _{Thé speed interval, being the}

_same.

While Group A consists of fiSc models, the other groups consist of four models each.

One

is the parent form, and the other three models are in different

ways developed from that

form.

The lines of the

parent form and the choice of variations werè decided in conjunction

With the leading ship-owners of the coastal traffic in Norway.

2 SYMBOLS AND UNITS.

The syrnbols. chosen are in accordance

with

those used at

_{the Norwegian Ship Model}

Experimént Tank and at Norwegian ship yards.

A. Ship Dimensions.

L,.. .

a

Length on waterline.

n

Length on designer's load waterline.

LE % Length

of entrance in

_%

of

LWL

measured on

DLWL.

LR %

Length

of

run in

%

of

DLWL measured on DLWL

m Length between perpendiculars,

p

'and.

FP

.3 m

Breadth on waterlihe.

d m

Draught.

Rise of floor

AM

n

Immersed

maximum

section area.

Ac n2

Immersed midship section area (at ¿.j)/2).

AL,, in2 Area of

waterplane.

f

n2 Area of bulbows bow at .

n2 _{Wetted sürface area (excluded wetted surface area of rudder and}

bossing).

V n3 _{Volume' of displacement (forébody}

_v.

_, _afterbody

L7 ) 4 tons Displacement. (metric tons).

O-4(a % Longitudinal position of centre of buoyancy from

_LWL/2,

in % of LDLw,

( A

aft of _JLWL

/2,

E

förward

_of'LD,b

/2).

Half angle ox entrance on .DLWL .

B. Propeller Dimensions.

D m

Propeller diameter.

p

_{Propeller pitch.}

F

n2 Propeller disk areal

lT/i, .0

).

(4)

C. Kinematic and Dynamic Symbols and Râtios.

y

knots Speed of ship ( metric knots).

knots Speed of advance (metric knots).

m

seca

Speed of advance.

kg Resistance.

r

kg Propeller thrust.

Q

m kg Propeller torcue.

-per min Revolutions.

a per sec Revolutions.

EH?

Effecti-ve horsepower (metric horsepower). Froude wake fraction.

________

Taylor wake fraction.

1'

r-R

_r

Thrust deduction coefficient.

Ç' kg sec2m4 Density of water

lo2,o

for esh water.

lo4,6

for salt water. ' kg m Specific weight of water.

boo for fresh water.

lo26

for salt ..-water.

g

m

sec2

Acceleration due to gravity 9,81.

©

426,4.8

?

Coefficient of resistance.

cftl/2

Speed - length ratio.

.j Speed - displacement ratio.

D. Dimensionless Coefficients and Ratios.

C

_A

_LSd

ç' Block coefficient.

CM

Ad

Maximum section coefficient.

..8

Midship section coefficIent.

4,

Prismatic coefficient.

Prismatic coefficient of forebody.

Prismatic coefficient of afterbody.

'q- _{Waterline coefficient.}

CI,,

L.a

Bulbous bow.

Wetted surface area coefficient.

Length - displacement ratio.

Length - breadth ratio.

8

-i-Breadth - draught ratio.

L

Pitch ratio.

-p

Expanded blade area ratio.

Thrust coefficient

Toraue coefficient.

Advance coefficient.

} Index O for open water.

'ç

6

(5)

Tank: Towing Carriage: 70 7H

Z,r

-4--

ç

_{Propeller efficiency in open wàter.}

r

-Q0

Propeller efficièncy behind hull. .Ç

2Y

Relative rotative efficiency. (

7

when

2:

Hull efficiency.

Ç-

X0

r

Total propulsive efficiency.

E. Units and Conversion Factors.

As metric units are used throughout the following conversion, factors are given:

1 metre i metric ton i metric knot i metric HP 3,281 feet

boo

kg _-1 1852

mhour

75

kg n seca

3. TANK AND CARRIAGE PARTICULARS.

The main data are as follows:

Length overall: Breadth:

Depth of water: Maximum speed: Minimum speed:

o,94 British tons

0,999 British knots o,986 British HP

17oo

in io;5 in 5,5 m 8;oo in sed o,o5 n sec 4. METHODS OF CALCULATION.

The results ei the towing tests arepresented as () -values, corrected to a standard

temperature of 150 Celsius. These areconvetted from model scale results to the scale

of the full sizod ship in the conventional way in accordance with Froude's method and

by the aid of Frude's skin friction.

According to the lecision made at the Tank Superintendents Conference in Paris 1935, the wetted surface area Ias been calculated frOm the measured half - girths without

any correction du to obliquity. The wetted surface area of rudder and bossings are

not included. -

-The self - propuls5on tests were carried out according tó the Continental Metho4 with the skin - friction correction applied as a towing force.

This force is calct:lated from the resistance tests ànd it includes a standard lo % in-crease in the ship rcsistance, thus abolishing the favourable conditions in the tank, and bringing the resistance in accordance with trial trip conditions.

Wake fractions are :alculated in the usual way with the propeller as a wake integrator. Values of wake fraction are worked óut on the basis of thrust identity with the aid of the results from the open water propeller tests.

5. SHIP MODELS TESTED.

In the tests described 2L models were employed, all made of a mixture of wax, consisting of paraffin, ceresin ar bees - wax. The scale used was 1/14. - Principal dimensions and coefficients for the ships, corresponding to the models tested, are given in tables when dealing with the towing tests of each group.

In all groups the deveiopment of new forms were made i-n such a way that the original form is retained as far as possible. The length on DLWL is kept constant for ali models. The methods used In designing new forms will-be given later.

The resisLnce- and propulsive tests were carried out over a speed range from about

1,5 -. 2,5 n sec1 corresponding to il . 18 knpts for ship djmensions. Thus the Reynolds number a 150 Cfor mo4el is between 6,8 lcPand 11,3 b0, and for ship between

3,4 io and 5,6 iou. - - - -

-As a turbulence producing device a i mm trip - wire was fitted, placed at section 9 1/2, 5 % of the waterline length from FP. The tripwire was fixed by means of small staples, and care was taken to secure contact with the hull ail around the girth. The hull

re-sistance is not corrected for the rere-sistance of the tripwire and no correction is

given for the laminar flow ahead of the stimulator.

-Each model was fitted with rudder and propeller shaft bossing. For the resistance tests the propeller was replaced by a dummy böse and cone.

(6)

6. PRESENTATION OF SHIP - RESISTANCE DATA. As mentioned before

thè

ts of the towin

tests are presented as ship

©

-values. According to H. Lackenby

4J"

the ternis In e , when neglecting the arbitrary

rwxnerical

coefficients, Can be rearranged as follows:

y2

/(v)2

(I)

When

©

is plotted to a base of ,

it is clear that the ordiafltes of the different

óurves plotted, for a particular value of speed_disPlacement ratio, will be directly

Pro-portional to P/ . Thus the order of

superiority of the ships will be measured by the

resistance per unit of.displaceflleflt, which is

obvioUSlY a good criterion of resistance

performance.

To Investigate the base of comparison when

©

is plotted to a speed - parameter of the

form ¡'/z' , (Z) can be

rearranged in the following way:

R

z

/y2

g_

/74

____

Y/

L

a

/(P31U1

(2)

From this it will be seen that a plotting of on

/oe

will only show a true

compari-son on a - baSis provided that the length

-displacement ratio

L/4

is constant for all the ships being compared.

Fòr the towing - tests carried out on DLWL the shit

©

-values are plotted to a base of

the ship - speed in knots, and since the length is the same for

aIl ships, a

correspond-Ing scale for 't/OE is given. When the displacements are

kept constant a third scale

of v/4'% is added.

For the groups where the displacement s varied, a diagram,

showing

©

to a base of is given. The length on DLWL is. however, kept constant.

For a trim waterline orrespondIflg to 2/3 of the

displacement On DLWL, the

waterline-lengths and disrlacements are varying. The

©

-values are therfore plotted to a

ship-speed in knots only. The corresponding values of p'/" and

p'/ are, however, given in

tables.

7. METHÓDS OF DEVELOPING NEW FORMS.

GROUP A. Variation in Form of the Sections.

Three basic models were manufactured for these tests,

one having U - form sections, Model

No. 354, the second V -form sections, Model No. 353, and the

third middelform sections

(M - form), Model No. 352.

Models No. 352 and No. 353 were first

designed, and Fig. 1 illustrateS how sections for

the two models were used to obtain sections

for the U - forii, Model No. 35 4, according to a method described in "Experiments with Tanker Models I". 3J

The lines of the afterbodY had to be slightly changed near the end, but the

midship -

sec-tions were kept coñstaflt for all models.

The models had the same sectional area curves, given in Appendix 1. This, together with the constant midship

section, made it

possible to part the models at Section 5 and join together the different mOdel - halves.

Denoting the forebody by F and the afterhCdY by A. the nine possible combinations are given

in

Table 1, paged.

GROUP B. Variation in Breadth - Draught Ratio.

The parent form used in this, and the following grous, is

Model

No. 353 F - 354 A. That is a model with V - form sections In the forebody and U - form sections in

the afterbodY, being a

compromise between seaworthiness and propulsive efficiency.

The other three models of the group viz. No. 385, No.

386 and

No. 387, are all based on the same lines - plan as the parent model. Other breadth - draught ratios are produced by multi-Fig.l. Sketch showing

the method of obtaining new forms when two

sec-dons with the same area

to DLWL are known

i) H.Lackenby: "On the Presentation of Ship

-Resistance Data", Quarterly

Transactions

of the Institution of Naval Architects, 1954, Volume 96.

Harald Björn Hansen: 'Sam.nenligfliflg av motstandsdata for skip",

Teknisk Ukëblad,

Nr. lo 1955.

H.Edstrand, E.Freimanis and H.Lindgrefl "Experiments with Tanker Models I". Publication No. 23 of the Swedish State Shipbuilding

(7)

plying all transverse dimensions by a constant, whilst dividing all vertical dimensions by the saine constant. With the same length, the displacéments will be the same for all models,,but the breadth - draught ratio will vary with the square of the constant.

GROUP C. Variation in Longitudinal Position of Centre of Buoyancy. Models No.

392, No. 393

and No

investigations. The new forms were designed by a method, keeping the body sections con-stant in shape, but altered in position, to give the desired variation of the centre of

b.i-oyancy at constant displace-ment.

The method used is given in a publication by H.Lackenby.l)

In.Fig. 2 the full line ABC re- A

presents the complete sectional area curve for the basis ship and the dotted line the derived

curve having the new position of longitudinal centre of buoyancy.

ao

.90

r

2D

/9

0 =

394, based on Model No.

₃₅₃

F -

354

A, were used for the

1) H.Lackenby: "On the Systematic Geometa rical Variations of Ship Fòrms". Transactions of the Institution of Naval Architects,

1950,

Volume 92.

di

-

dx'

y'

-6-The sectional .rea curves thus obtained are given in Fig.

_3.

As the models have no paralleli middle. - body, the

Fig.

_3.

Sectional á:'eà curvas for Group C.

Vari-ation in longitudiai position of centre

of buoyancy.

of the models with increasing nrismatic

dent decreases.

The new positions of he sections are fixed by the centre of buoyancy constant.

According to H. Lackenby it is convenient to consider the twô halves óf the sec-tional area curve separately. Referring to Fig.

4,

the full lime ABC represents the curve of areas of the basis ship for one half of the body, which is considered as being one unit long, and the maximum ordinate of the area curve also equal to unity. All.horizontal dimensions are therefore fractions of the half length and the area under the curve ABC is nu-merically equal to the prismatic coeffi-cient of the half - body.

coefficient,

e

Fig. 2. Method of varying the longitudinal buoyancy at constant displacement.

C

centre of

Let

Ï

the position of longitudinal centre of buoyancy in the original forth,

d2

the required change in longitudinal centre of buoyancy,

9

the pòsition of the vertical centroid of the original area above the base. The new sectional, area curve is then derived by turning each ordinate through the same

angle Ø given by

turning of the area curve will change the area of the midship section. Thus the prismatic coefficient

c,. will vary with C . The

prismatic coefficient defined

with C, will, however, remain

constant as it is given for maxi-mum section area, which is not

changed in size, only in position.

GROUP D. Variation in Prismatic Coefficient.

Models

No. 396

_{No. 397}

and No.

39

are derived from Model

No.

353 F - 354.

A in a manner similar

to that used for the forms in group C. The sections in the fore- and after - body are, how-ever, here moved towards the ends and towards midships when the

coeffi-airs of keepin& the position of the

----____

/2'/'

Iur

-394

riu

-Fig.

4.

Method of varying the nriamatic coefficient when the longitudi-nal position of centre of buoy-ancy is constant.

(8)

I

X

o

Fig.

_5.

Sectional area curves for Group D. Vari-ation in prismatic coefficient.

In this group, whiöh consists of Models No. 407, No. 4o and No.

4o9, all transverse and vertical dimensions of Model No.

353 F

-354 A are multiplied by the same constant.

By keeping the lengths unchanged, the displacements are varied, but the breadth - draught ratios re-main constant.

The sectional area curves are shown in Fig.

6.

GROUP F. Variation in.Bu.bous Bow. As the parent form of these experi-ments, Model No. 353 F -

351,. A, on

account of the fullness and- length,

must be characterised as "over

-driven" .above

V/a. =

.5 -

.90,

Let SCO = the required change in prismatic coefficient, the change in forebody prismatic coefficient, the change in afterbody prismatic coefficient,

2

= the distance of LCB in the basis

ship from midships expressed as a frac-tion of the half length (positive forward of midships, negative aft), the distance of the centroid of the original forebody curve from midships,

= the distance of the centroid of the original afterbody curve

from midships,

the fractional distance from midships of the centroid of the added "sliver" of area represented by

C-i7 the fractional distance from midships of the ceñtroid of the added "sliver"

of area represented by cCpg

The levers

h,-

and

h

of the added "slivers" of area are

calculated first, so that

changes in the prismatic coefficients of the bodies, ¡Cp. and

éCp,7 , can be

deter-mined. The exact value is given by the following equation:

¿'F =

-c,,.a,c,)

#

_{[/-2Cpp(i-i)J}

For moderate changes in Cp , experience shows that the second term is negligible

com-pared with the first, and a very good approximation to 4 is given simply by

The shift of sections in each body is then given by

1x=

(i-x)

-Sx,

éCpfi

_(ix)

/ - Cp,g

By this method the length is the same for all models, but the displacements are varied as shown in Fig. 5.

GROUP E. Variation in Length - Displacement Ratio.

i -4 a

Fig. 6. Sectional area curves for Croup E. Variation in length - di

h,

4=

Ç,1 (i-2,)

/- Cpp

Cpi (i-)

/-;,9

The expression for éCp,c

and 6C,,9

can be calculated

by

(7,)

60 i,o

--

I

__ 354A

1.

1°' - - . . ₃ _3& I

ii.p1aIIaI

.iii==UlII

IIllr--iUIVA -

--IuII

2 ¡4e (h,ç -1)

/4c. 3'hg 2 ¡Cp

C», 'i)

(9)

-8-one might expect a reduction in resistance by adding a bulbous bow.

Two graduating students from The Technical University of Norway, Mr. Stian Mr. Clay Tröim carried out these experiments, and three models were made,

(353 F - 354

AIA, No.

(353

F -

354

A)B, and No.

(353 F - 354

A)c.

The bulbous bow is desòribed by the sectional area curve by the following

=

Thus 6 is the ratio between the area at the forward perpendicular and the

midship section in %.

The sectional area curves are given on page

49.

8.

PART I.

Towing Tests on DLWL. Presentation of Ship Particulars and Results. Analysis of the Results.

GROUP A. Váriation in Form of the Sections.

TABLE 1. SHIP PARTICULARS FOR DLWL. GROUP A. VARIATION IN FORM OF THE SECTIONS. area at the

MODEL NO.

35

- 33

1,

352

F-353 A

352F-

_{354 A}

353 F-

352 A

353 F..

354 A

354 F-

352 A

353 A

4 F-¿

72,450

72,45o

72,450

72,45o

72,450

72,45e

72,450

11,582

U,582

11,582

d

4,9oo

4,900

4,9oo

.075

.o75

.075

.ò75

.075

2396

275 2475

2475

C0

_.982

982 .982

.982

982 .982

.982

982 .982

.982

.92

.982

.583

.604

6o4

.6o4

6o4.

.6o4

.604

Cp

.594

.584

.725

.745

.710

.734

.727

.736

.730

.717

.726

5,87

5,83

5,90

5,84

5,89

5,86

5,88

5,86

1-/ra

_5,414

5 414

5,414

5 414

5 14

5 414

5 414.

15

15,5

14,5

15 15

15,5

14,5

.6F

36,o

36;o

36,0

36;o

36,0

36,o

36,0

36,o

37,5

37 5

37,5

37 5

1-l.a

6,255

6,25

6;255

6,255

6,25

2,364

2.364 2,364

2,364

Erichsen and Models No. expression:

(10)

TABLE

2. SHIP

(EJ -

VALUES FOR DLWL. GROUP A. VARIATION IN FORM OF THE SECTIONS. 1.5 IA

'a-w

352 353-352A 9 B 7

-9-is la 13 _{SA1OFSPEDflIKNOTS} 16 17 16 I

'

ALOVflC lbO ihs

lo

- 15

oo

W

5O 5 400 42.5

--

4O

475 SpO

SCM..E

Fig.

7. Ship © - values.

DLWL. Group A. Variation in forTs of

the sections. --

© FOR MODEL NO

-Y/

₃₅₂

₃₅₃

354 352 F- 352 F- 353 F- 353 F- 354

F- 354 F..

V

_«iZ'

353 A

354 A

352 A

354. A

352 A

353

A 11

11,5

12 12 5

±3

13 5

14

145

15

15 5

16-16,5

17 17,5

.18

713 .746

.778

811 .843

.876

.9o8

.941

;973

1;oo5

].;o38

1,o7o

1,1o3

1,135

1.168 2,991

3,127

3,263

3,399

3,535

3;671

3,807

3,942

4,o78

4,214

4,350

4,486

4,622

4,758

4.894

766 .779

.784

786 .8o1

.839

.915

l,o12

1,o95

1;151

1;172

1;176

i;186

1,216

1311

773 .783

.788

796 .809

.839

.925

1,o4o

1;141

1;Zol

1;221

1;235

1,257

1,297

1.359 .770

772 .77].

772 .784

.816

.883

.98o

1,o61

1;llo

1;124

1,121

1,147

1,215

1.310

765

.7714.

.776

.774

.790

.831

.9o5

1;oo6

1;o94

1;144

..,172

1,182

i;].84.

1,222

1.316

764 .777

.786

792 .797

.826

.892

967 1;o41

1,107

1,142

1;152

1;165

1,2o5

1.304

767 .782

.791

785

.795

.851

942 i,o36

1;112

1,174

1,213

1,228

1,236

1,271

.1.340

778 .784

.783

788 .8oIi

.832

886 .999

1,o78

1;].4o

].;].76

1,192

l,2oo

1,234

1.3oo

762 .770

.77°

775 .789

.818

.875

.966

].;o59

1;llo

1,126

1,135

1,149

1,187

1.275 .744

.755

.767

770 .772

.811

.898

.987

],o68

1,131

1;154

1,152

1,163

1,2o1

1.287

(11)

1.6 1,5 .9 t 1, IP

FCRBODY: V-FORM AFTERBODY V-FORM

: UFORM :

-355

- 3F-355A

354F3$M

s

FCREBODV. V-FORM, AFTERBV: U-FORM

:ÇQq_._...

U FORM, :

-.9 .8 .7 8 7 't lo -85 - 9O .95 IpO 1p5 110 SC LE OFVftC'

CLE/8"

4:25

4 *5

Fig. .

Shjp ® - valués.

_DLWL. _{Group A.}

Variation in form of the sections.

13 t4 15

SCALE OF SPEW IN KNOTS

-- i I i t 70 .75 8O -85 90 95 - 1,00 SCALE OF v,4Ç I i i - - I I OO 3,25 3,50 4,00 y SCALEOF v/s' j I & 1,10 1,15 20

4:,5--

0O

Fig. 9.

Ship © - values.

DLWL. Group A. Variation in form of the sections.

16 17 18

I'

SCALE OF SPEED IN KNOTS

I --- I- j

(12)

DLWL. Group A.

GROUP B. Variation in Breadth - Draught Ratio.

TABLE

_3.

SHIP PARTICULARS FOR DLWL. GROUP B. VARIATION IN BREADTH - DRAUGHT RATIO.

TABLE 4. SHIP - VALtJES FOR DLWL. GROUP B. VARIATION IN BREADTH DRAUGHT RATIO.

i'

r

FOR MODEL NO.

i'/4'/o 385

353 F-

386

387

11 .713

2,991

.777

.778

.795

.798

11,5

.746

3,127

.778

.784

8o2

.809

12 .778

3,263

.776

.783

.8o6

.813

12,5

.811

3,399

.778

.788

.812

.823

13 .84.3

3,535

.788

.8o4

.828

.838

13,5

.876

3,671

.822

.832

.866

.877

14 .9o8

3,807

906 .886

.931

.943

3.4,5

.941

3,942

l.o22

.999

1.018

1.027

15

.973

4,o78

1.118 1.o72

:.1o4

1.1o8

15,5

1.005 4,214

1,164

l,l4o

1,157

1,172

16

1,o38

4,350

1,178

1,176

1,186

1,2o5

16,5

1,o7o

4,4.86

1,176

1,192

1,208

1,222

17 l,1o3

4,622

1,185

l,2oo

1,236

1,251

17,5

1,135

4,758

1,220

1,234 1,288

1,310

18 1,168

4,894 1,3o

l,3oo

1,37o

1,4o6

MODEL ÑÖ. 385

353 F-

386 38

354 A

L

_72,450

72,450

72,650

72,450

3 _11,o32

_11,582

1216l

12,468

d

_5,144

4,900

4,667

4,550

.o79

.o75

.o71

.070

7 ₂₃₉₆

2396

2475

C

.982

4v

.982

.583

Cp-

.6o4

6oL4.

.6o4

6o4

¿p

.594

.94

.594

C,,,

.594

C,,

w

.584

.730

.584

.730

.584

.730

.584

.730

®

5,89

5,87

5,84

5,83

44(

(°e

.5

15,0

414 5 414

15,5

5 43.4

7,o

5

17,5

414.

o-4h

.6F

.

.6F

36;o

36,o

36;o

36,o

L&

37 5

37,5

i

6,57

6,255

5,958

5,811

(13)

15 13

01,2

-j

411 u

UI IP .9

8

.7 .7 1$ 1,5 1,3

012 b'

1,l 1,0

s

.8

-12-1,

i

r

14 -1S

SCALE OF SPEED IN KNOTS 16

-:

385 - - :SS3F-354A

----: 386

387 frj. SCALE OF V CALE OF

Fig. 11. Ship C -values. DLWL. Group B. Variation in breadt - draught ratio.

2

21 2,4

SCALE OF B/d

Fig. 12.

_{Ship ©}

_{values as a function of breadth - draught} ratio. DLWL. Group B.

(14)

TABLE

5.

SHIP PARTICULARS FOR DLWL. GROUP C. VARIATION IN LONGITUDINAL POSITIOÑ OF CENTRE OF BUOYANCY. .1.6 15

©

4 8

li

-SCALE 0F SPEED IN KNOTS

.i 7S 8) 4

9

l,O

105

i.O 115 O

SCALE OF- v//C'

GROUP C. Variation in Longitudinal Position of Centre of Buoyancy.

Fig. 13.

Ship © - values.

DLWL. Group position of centre of buoyancy.

TABLE

6.

SHIP - VALUES FOR DLWL. GROUP C. VARIATION IN LONGITUDINAL POSITION OF CENTRE OF BUOYANCY.

C. Variatior in lorgitudinal

I"'

392

393

353 F- 391f 11

.713

2,991

.825

.791

.778

11,5

.746

3,127

.855

.809

.784

.783

12 .778

3,263

.884

.825

.783

.788

12,5

.811

3,399

.9o5

.839

.788

.798

13 .843

3,535

.925

.850

.8o4

.82e

13,5

.876

3,671

.957

.878

.832

.873

14 .908

3,8o7 l,o2o

.946

.886

.

.965

14,5

.941

3,942 1,123

1,o65

.999

1,o81

15

.973

4,078 1,222

1,149

l,o78

1,179

15,5

1,005

4,214 1,295

1,186

1,140

1,259

16 1,o38

4,35° 1,344

1,194

1,176

1,314

16 5

1,070

4,486 1,367

1,195

1,192

1,347

17 1,1o3

4,622

Ï,371

1,199

l,2oo

1,371

17 5

1,135

4,758 1,374

1,229

1,234

1,414

18

1,168

4,894 1,420

1,3o3

1,300

1,46

MODEL NO. 392

393 353 F-

394

354A

L

72,45o

72,450

-

11,582

11,52

11,582

í

4,900

.o75

.075

.o75

V

₂₃₉₆

2396

275

2475

2475 C

.94

.972

.982

.976

CM

.982

4

c

.583

.588

.583

.596

.583

.6o4

.583

6o7

Cp

.611

600 .594

.597

4w

.5911. E-o3

.594

.590

.594

.584

.594

.579

.724

.727

.730

.734

5,83

5,84

5,86

5,87

L/

_{5 414}

5414

5 414

7.e

15,5

17,5

2,9A

1,6A

.6F

2,oF

'-E

43,5

L.o,5

36,o

32,o

-

3o,5

32,5

37,5

42,5

L/

6,255

..6/af

2,364

/

¡

Ii

---

--

I

L

--iL.----

--.-.--

392 393 :353F-354A 394

-i_

5 o.

LE OF

450

(15)

14

-Fig. 14. Ship ® -. values as a function of longitudinal position

of centre of buoyancy. DLWL. Group C.

ROUP D.

Variation in Prismatic Coefficient.

TABLE 7. SHIP PARTICULARS FOR DLWL. GROUP D. VARIATION IN PRISMATIC COEFFICIENT.

MODEL NO. 396 353 F- 397 398

354A

¿ _72,45o _72,45o _72,450 72,450

3

11,582 11,582 11,582 11,582

d

4,9oo 4,9oo 4,900 4,9oo

R .o75 .075 .o75 .075 2271 2396 2516 2635 2316 2475 2599 2722 .982 .982 .982 .982 C _.982 _.982 _.982 .982 .552 .583 .612 .641 4.c .571 .6o4 .633 .663 .562 .594 .623 .653 .562 594 .623 .653 .553 .584. .613 .64.3

C ..7o6 .73o .756 .78o

®

5,92 5,86 5,79 5,74

Z/

_5,512 5,414 5,327 5,245 "-e 14,7 15,5 16,9 19,6 .6F .6F .6F .6F 39,o 36,o 34,5 33,5 39,o 37,5 36,2 35,3

½ 6,255

6,255 6,255 6,255 2,364 2,364 2,364 2,364

(16)

TABLE

8.

SHIP - VALUES FOR DLWL. GROUP D. VARIATION IN PRISMATIC COEFFICIENT. 15 16 'D .0 6 .7 '1 is

I

/

L

/

SCALE C4SPEEI) II ICITS 'I

/

r,--S96

---t 507

1-,

.---

.a' 10 SCALE OF *4Ç

-Fig.

15.

Ship - values. DLWL. Group D. Variation In prismatic coefficient.

"

MODEL NO. 396 MODEL NO.

53

F-351f A

MODEL NO.

397

MODEL NO.

398 V"

_/

Ø

v/I4 ®

R/

_®

R

¡'/

®

il

11 5-12

12 5

13 13 5

14.

-14 5

15

15 5

16

16 5

17 17,5

18 .713

.746

.778

.811

.81+3

.876

.9o8

.94].

.973

1,005

1,o38

1,o7o

1,1o3

1,135

1.168 3,o18

3,155

3,292

3,129

-3,566

3,703

3,841

3,978

4,115

4,252

4,389

4,526

4,664

4,8o1

4.938 .745

.762

.768

.777

.791

.811

.81+o

.874

.910

.942

.965

.984

1,o22

1,113

1274

2,319

2,593

2,845

3,123

3,439

3,8o2

4,235

4,727

5,266

5,822

6,355

6,893

7,597

8,768

lo621

2,991

3;127

3,263

3,399

3,535

3,671

3,8o7

3,942

4,078

4,214

4,35°

4,486

4,622

4,758

4.894 .778

.784

.783

.788

.8o4

.832

.886

.999

1,o78

1,140

1,176

1,192

1,200

1,234

13oo

2,385

2,626

2,856

3,119

3,4.42

3,84.1

4,399

5,32o

6,144

6,938

7,627

8,22o

8;785

9,573

lo.67o

2,967

3,lol

3,236

3,371

3,5o6

3,64].

3,776

3,910

4,o45

4,180

4,315

4,450

4,585

4,72o

4.854. .77o

.779

.784

.790

.8o5

.847

.9L7

l,lol

1,258

1,372

1,437

1,467

1,483

1,494

1,546

2,317

2,562

2,807

3,o69

3,383

3,838

4,616

5,757

7,o39

8,198

9,148

9,931

lo,659

11,377

12,454

2,94.4

3,o78

3,211

3,345

3,479

3,613

3,747

3,881

4,o14

4,148

4,282

4,416

6,55o

4,683

6.817 .834

.850

.861+

.882

.911

.964

1,o63

1,24.9

1,46].

1,670

1,831

1,895

1,912

1.909 2,4.70

2,752

3,o45

3,373

3,769

4,3o].

5,100

6,427

8,o45

9,821

11,473

12,628

13,520

14,242

14.817

(17)

1,9 1.8 1.7 1.5 .9 .7

-

16

-/

sçAL-oF C

Fig. 17.

_Ship®

- values ae a function of prismatic coeffiöient.

DLWL. Group D.

iii

HP2iUi

pvriiuii

11

iiiii

__II.w

_UP!

a-

-___

riIi.ìI1

O 56 57 -58 3 3,8 4p 4.2 4,4 46 4.8 5,0 SCALE

Fig. 16.

Ship Ø - values.

DLWL. Group D. Variation in pris-matic coefficient.

(18)

TABLE 9. SHIP PARTICULARS FOR DLWL. GROUP E. VARIATION IN LENGTH - DISPLAC'1ENT RATIO.

TABLE lo. SHII OEj

-

VALUES FOR DLWL. GROUP E. VARIATION IN LENGTH - DISPLACEMENT

RATIO. V 11 11 5 12 12 5 13 13,5 14 14,5 15 15,5 16 16,5 17 17,5 18 .713 746 .778 811 .843 876 .9o8 .941 .973 1,005 1,o38 1, o7o l,1o3 1,135 1,168 MODEL NO. 4o7 353

F-354A

408 4o9

¿ 72;45o 72;45o 72,45o 72,45o

lo,394 11,582 12,473 13,443

d

_4,900 5,277

.o67 .075 .o81 .o87

'7' _1929. 2396 2778 3227

1993 2475 2869 3333

.982 .982 .982 .982

.583 .583 .583 .583

.6o4 .6o4 .6o4 .6o4

Cp .594 .594 .594 .594 .594 .594 .594 .594 .584 .584 .584 .584 .736 .730 .730 .730 6,o7 5,86 5,71 5,57 5,82o 5,414 5,154 4,903 14,0 15,5 16,5 18,0 .6F

6F

.6F .6F 36,0 36,o 36,0 36,o

375

37,5

375

zj 6,9+0

6,25

5,809 /d 2,364 2,364 2,364 2,364

MODEL NO. 4o7 MODEL NO. 353

F-354A

MODEL NO. 408 MODEL NO. 409

/()R/akV«b®R/&

'//©/

7J®R/

3,lol 3,242 3;383 3,524 3,665 3,8o5 3,946 4;o87 4,228 4,369 4,510 14,651 4,792 4,933 5,074 .755 .762 .763 .766 .782 .827 .894 97o 1,o49 1,104 1,126 1,131 1,140 1,174 1,224 2;485 2;74]. 2;989 3,256 3,595 4,loo 4;766 5,547 6,420 7,214 7,841 8,375 8,961 9,779

1o,3

2;991 3,127 3;263 3,399 3,535 3,671 3,8o7 3,942 4,o78 4,214 4,350 4,486 4,622 ,758 4,894 .778 .784 .78

.7&

..o&i. .832 .886 .999 1,o78 1,14o 1,176 1,192 1,2oo 1,234 1.3oo 2,385 2;626 2,856 3;119 3,L.42 3;841 4,399 5,32o 6,144 6,938 7,627 8,22o 8,785 9,573 lo,67o 2;918 3,o51 3;183 3,316 3,449 3,581 3,714 3,847 3,979 4,112 4,245 4,377 4,510 14,643 4,775 .797

8o8

.816 .826 .849 .891 .959

i,o8

1,141 1,2o2 1,223 1,235 1,251 1,297 1,373 2,324 2,575 2,832 3,110 3,458 3,913 4,53° .5,310 6,187 6,960 7,51.5 8,1o3 8,713 9,573 lo,72o

2;26

2,992 3,122 3,252 3,382 3,512 3,64.2 3,772 3,9o2 4,032 4,162 !+,292 14,422 1,552 4,683 .817 .831 .832 .836 .853 .895 .969 1,o71 1,147 1,198 1,228 1,257 1,290 1,337 1,421 2,284 2,539 2,768 3;o17 3,330 3,768 4,387 5,2o2 5,962 6,649 7,262 7,9o5 8,612 9,458 lo,635

(19)

1,4 1,2 9 1! I I 13

SCfD??KN5

16 17 -- IB

353F-353A

'pp

409

Fig. 19. Ship - values. DLWL. Group-E. Variation in length

-displa ement ratio.

-?0 .75 - 80 90

sc.i

v/dr

1,00 1,05 1,10 1,15 1,20

Fig. 18. Ship - values. DLWL. Group E. Variation in length -displacement ratio.

2,8 3,0 3,2

34

36 3,8 4,0 4,4 4,6

(20)

Fig. 2o. Ship

® -

values, as a function of length - displacement ratio. DLWL. Group E.

GROUP F. Variation in Bulbous Bow.

TABLE 11. SHIP PARTICULARS FOR DLWL. GROUP F. VARIATIONS IN BULBOUS BOW.

MODEL NO.

353F-354 A (353

F-354

A)A (353 F-354 Â)B (353 F-. 354 A)C

4

72,450

72,4.5o

72,45o

- 11,582 11,582 11,582 11,582

d

4,900 4,9oo 4,900 4,900

.075

.o75

c .o75 .o75

2396 2422 2434 2447 2475 2502 2515 2528 .982 .982 .982 .982 .982 .982 .982

.982

.583 .589 .592

.595

c

6o4

.616 .622 .628

.594

.600

.6o3

6o6

¿,

.594

.584

600 .584.

.6o3

.584

6o6

.584

.730

5,87

5,95

5,96

/v 5,414 5 395 5 ,387 5 377

I49

15 5 15.5 15,5 15 5

.F

.9F

1,3F

1,F

36,o

36,0

36,o 36,o

37,5

¿/a

6,255

6;255

2,364.

2,364

(21)

TABLE

12.

SHIP ® - VALUES FOR DLWL. GROUP F. _{VARIATION IN BULBOUS BOW.} 1,5

7.

353V- 354A (553F- 354A) A (353F- 354A) B

-

(353F354A)c

2o

-¿I MODEL NO.

353 F-354 A

MODEL NO.

₍₃₅₃

F-354. A)A MODEL

_{NO. (353}

F-354 A)B

MODEL NO.

(353 F..

354 ?B

Y &

12 .77;

,2.3 7

2,;

.

3,257

.2;

3,002

3,254

.;32

3,012

3,25o

;37

3,o23

12,5

₁₃

.811

_.843

3,399

_3,535

.788

_.8o4

_3,442

3,119

3,393

.832

3,273

3,390

.834

3,276

3,386

.836

3,276

3,528

.836

3,557

3,525

.835

3,548

3,52].

.835

3,54o

13,5

.876

3,671

.832

3,84].

3,664

.859

3,942

3,661

.849

3,890

3,657

.847

3,871

14 .9o8

3,8o7

.886

4,399

3,800

.915

4,516

3,76

.896

4,415

3,792

.897

4,410

14,5

₁₅

.941

3,942

.999

5,32o

3,935

.996

₂₇₃

3,932

.964

5,o96

3,927

.967

5,o99

.973

4,o78 1,o78

6,144

4,071 1,073

6,o79

4,o68 1,o4o

5,883

4,o63 1,037

5,852

15,5 1,005

_{16 1,038}

4,214 1,14o

6,938

4,207 1,129

6,829

4,203 1,107

6,686

4,198 1,o88

6,555

4,350 1,176

7,627

4,343 1,152

7,426

_{4,339 1,142 7;5o 4,334 1,118}

_7,178

16 5 l,o7o

_{17 1,1o3}

4,486 1,192

_{4,622 1;2oo .8,785}

8;22o

4,478 1,157

7;931

4,474 1,148

7,857

4;469 1,136

7,757

4,614 1,163

8,463

4,610 1,154

8,384

4,6o5 1,162

8;422

17 5

18

1,168

1,135

4,758 1;234

_{4,894 1,3oo lo,67o}

9,573

4,75o 1,2o4

_{4,885 1,281 lo,4So}

9,284

4,745 1,18o

_{4,881 1,247 lo,157}

9,o85

_{4,875 1,240 lo,o76}

4,710 1,193

9,163

18.5 1,2o1

_{5,o21 1,392 11,996}

_{5,017 1,362 11,719}

_{5,oll 1,341 11,511}

11 12 13 14 15 16 IB

I I I I I I I I

--10 -75 -80 -85 90 .95 WO 1,05 1,10 1,15 1,20

-Fig.

21. _Ship

_(Z3

-

_values. DLWL. Group F. Variation in bulbous bow. 1,3

r

IP 9 8 .7

(22)

-_IB KNOTS 17 KNOTS 16 KNOTS 15 KNOTS 14KNOTS f 3JKNOTS 4 6 8

SCALE OF % BULBOUS BOW

Fig. 22. Ship ® - values as a functión of % bulbous bow. DLWL. Group F.

9. PARTII.

Towing Tests on WL I. Presentation of Ship Particulars and Results. Analysis of the Results.

GROUP A. Variation in Form of the Sections.

TABLE 13. SHIP PARTICULARS FOR WL I. GROUP A. VARIATION IN FORM OF THE SECTIONS.

I

r

'T L 10 MODEL NO

32

353 35L 352 F-353 A 352 F-' 354 A 353 F-352 A 353 F-354 A 354 F-352 A 354 F-353 A L, B

4 4«

¿/'/i e-4'a

¿«/A

BId 69,290 11;582 4,313 3,486 2,659 1597 165o .974 .571 .586 .684 6,o5 5,927 l,SA 5,983

3322

69,160 11,582 4,31i 3,512 2,713 1597 1650 .976 .568. .582 .7o5 6,o6 5 916 i,4A 5,971 3. 298 69,4.lo 11,582 4,314 3,460 2,606 1597 165o .972 .574 .591 .678 6,oß 5,938 1,3A . 5,993 347 ,3 69,22o 11,582 4,312 3;5oo

2688

f597 1650 .975 .569 .584 .695 6,o4 5,921 l,3A 5,977 3 3o9 69,3oo 11,582 4,313 3,483 2,653 .1597 165o .974 .571 .586 .678 6,o7 5,928 114A 5,983 3 325 69,18° 11,582 4,311 3,5o8 2,7o5 1597 1656 .976' .568 .582 .694 6,o3 5,918 1,6A 5,973 3,3o2 69,170 11,582 4,311 3,510 2,7o9 1597 165o .976 .568 .582 .688 6,o8 5,917 1 6A 5,472 3,3oo 69,390 11,582 4,314 3,465 2 616 1597 1650 .972 .573 .590 .684 6,o9 5,936 1 4A

5,9l

3,33

69,280 11,582 4,312 3,488 2,664 1597

150

.974 .571 .586 .695 6,12 5,926 l,2A 5,982 3,321 u., O

(23)

TABLE 14.

GROUP A.

VARIATIONI'N FORM OF THE SECTIONS.

MODEL NO.

352

353 354

352 F-353 A

352 F-354 A

353 F-352 A

353 F-354 A

54 F-352 A

354 F-353 A

I,

v/w®

v

©

11 3,2oo

.730

.782

.730

.786

.730

.793

.730

.757

.729

.765

.730

.So].

.73o

.793

.729

.777

.730

.756

11,5

12 3,345

3,491

.763 .796

.777 .778

.763

.797

.788 .79].

.763 .796

.8o1

.8o4

.763

.796

.764

.768

.763 .796

.779

.788

.763 .797

.818 .832

.763 .797

.793 .798

.762

.795

.780 .782

.763

.796

.765 .768

12,5

3,636

.829

.783

.83o

.79°

.829

.8o7

.83o

.774

.829

.793

.83o

.834

.83o

.8o1

.828

.789

.829

.768

13 3 782

.862

.8o2

.863

8o2

.862

.826

.863

.787

.862

.811

.863

.842

.863

.818

.862

.8o5

.862

.78e

13,5

3:927

.895

.84o

.896

.843

.896

.852

.896

.819

.895

.841

.896

.868

.896

.855

.895

.84o

.895

.816

14 4 o73

.929

.893

.929

.905

.929

.896

.929

.881

.928

.891

.929

.912

.929

.9o8

.928

.902

.929

.883

14,5

4218

.962

.950

.963

.958

.962

.975

.962

.948

.962

.955

.962

.957

.963

.962

.961

.962

.936

15

4,364

.995

.993

.996

.998

.995 1,o27

.995

.996

.995 1,006

.996

.998

.996 1,007

.994 1,006

.995

.983

15 5

4,509

1,o28 1,o15

1,029 1,o23

1,o28 1,o9

1,029 1,o17

1,o28 1,035

].,o29 1,o36

1,o29 1,032

1,o27 1,o32

1,o28 1,o12

16

4,654

1,o61 1,027

1,o62 1,o37

1,o62 1,o i

1,o62 1,o28

1,o61 1,o46

1,o62 1,o6o

1,o62 1,o47

i,o6o 1,049

].,o61 1,o28

16 5

4,800

1,o94 1,o33

1,095 1,o6o

1,o95 1,o78

1,095 l,o52

1,o94 1,o7o

1,o95 1,o73

1,o95 1,o69

1,o94 1,o66

1,o94 1,o37

17

4,945

1,127 1,o67

1,129 1,loo

1,128 1,124

1,128 1,loo

1,127 1,119

1,128 1,o98

1,129 1,115

1,127 1,1o7

1,128 1,071

17 5

5091

1,161 1,172

1,162 1,18o

1,161 1,214

1,161 1,181

1,161 1,213

1,162 1,158

1,162 1,2o6

1,16o 1,185

1,161 1,153

Is

5;236

1,194 1,36o

1,195 1,311

1,194 1,366

1,194 1,316

1,194 1,351

1,195 1,3o6

1,195 1,376

1,193 1,3o7

1,194 1,275

(24)

1,6 1,3 III 8 7 FCRODY: V-FORM, P1-FORM, U-FORM ArTERRODV: P1-FORM.

-352

---:3S3F.55A

..-:354F-55U

14 15 16

Fig. 23.

Ship ® - values.

WL I. Group A. Variation in form of the sections.

Fig. 24 Ship ( - values. WL I. Group A. Variation in form

of the sections. 1,5 1,4 1,2 1,0

9

8 - -FOBODY VFORM, FORM, M-FORM, AFTERBOOV: V-FORM.

-/

---:

U

-:

-- -. :

-.-/

- -353 -552F-353A

---:354F-35M

-16

Il

11 12 13 14 1 13 12 IT 18

(25)

16 1,5 1,4 1,3 1.0 9 7 Ç0RBW1'

V--.,-:

t

U-

--FORM, AFTERBODY: U-FORM

FQRM.. --FORM, :

I

34

:352V- 354A :353V - 354A 3

li

-

24 -12. 13 14

SCALE 0F SPEED IN KNOTS

Fig. 25.

WL I. Group A. Variation In form of the sections.

GROUP B. _{Variation in Breadth - Draught Ratio.}

TABLE 15. _{SHIP PARTICULARS FOR WL I.} _{GROUP B.} VARIATION IN BREADTH - DRAUGHT RATIO.

I? 1

MODEL NO.

- 385 353 F- 386 - 387

354A

69,17o 69;17o 69;17o 69,17o

3

_11;o32 _11,582 _12,161 _12;468

4,472 4,311 4;o57 3,956

4 3;688 3,510 3;343 3,262

d,, 2 845 2 7o9 2 582 2 517

7 1597 1597 1597 ±597

4

_165o _165o _165o

165o .976 .976 .976 .976 4B .568 .568 .568 .568 .582 .582 .582 .582 .688 .688 688 .688 6,oI

6o8

615

618 L/,

5,917

5,17

O-'./

1 6A i 6A 1 6A 1 64

"/2

6,7o

5,72

5,88

3/a

2,991 3,300 3,638 3,822

(26)

1,6 1.5 1.4 13 7 16 SCALE OF SPEED IN KNOTS

385 353F- 354A

386

387

ii

12

TABLE 16. SHIP - VALUES FOR WL I. GROUP B. VARIATION IN BREADTH - DRAUGHT RATIO.

Fig. 26.

WL I. roup B. Variation in breadth

-draught

ratio. y

v/7

- MODEL NO. V,/4'/6

35

_F

386

387

11 .730

3,200

.783

.793

.821

.835

11,5

.763

3,345

.783

.791

.823

.833

12 .797

3,491

.781

.798

.826

.834

12 5

.830

3,636

.786

8o1

.835

.841

13 .863

3,782

.8o7

.818

.855

.857

13 5

.896

3,927

.849

.855

.888

.890

11.

.929

4,o73

.909

.908

.934

.938

14 5

.963

4,218

.961

.962

.981

.992

15

.996

4,364

1,00l

1,007

1,019

1,039

15 5

16 1,029

l,o62

4,509

4,654

1,o26

1,o38

1,o32

1,o47

1,o71

l,o71

l,1o2

16 5

1,o95

4,800

1,o57

1,o69

1,1o9

1,138

17 1,129

4,945

1,1o3

1,115

1,1'7o

l;186

17,5

(27)

26

-GROUP C. _{Variation in Longitudinal Position of Ceñtre of Buoyancy.}

TABLE 17. SHIP PARTICULARS FOR WL I. GROUP C.

VARIATION IN LONGITUDINAL POSITION OF CENTRE OF BUOYANCY.

TABLE 18. SHIP ® - VALUES FOR WL I. GROUP C.

VARIATION IN LONGITUDINAL POSITION OF CENTRE OF BUOYANCY.

MODEL NO. -392 393 353 F-354 A 394 WL

2

69,24o11,582 69,210 ].1,582 69,17o 11,582 69,14o 11,582

d

d 4,313 3,487 2,661 4,312 3,496 2,68o 4,311 3,510 .2,7o9 4,310 3,519 2,728

4

1597165o 1597 165o 165o1597 1597 165o .938 .968 .976 .981 '-a .571 .57o .568 _.567 .6o9 .589 .582. .578 .679 .684 .688 _.7oo

6.,o'3 6,o5 6,o8

6p9

L/,'/,

5 923 ,8A 5 920 ¿,3A 5 917 l,6A 5,914 o,1F 4v/B 5,978 5,976 5,972 5,97° 3,321 3,313 _.3,3oo _3,291 y MODEL NO. - 392 393 353. F-354 A .394 11 3,2oo 730 ₈₆₃ 730 852 730 793 730 792 11,5 3,345 .763

.92

.76,3 .869 .763 .793 .763 .792 12 3,491 .796 .919 .796 .883 .797 .796 .797 .793

12,5 3,636 .83o .943 .83o .894 .83o .Sol .830 .8o2

13 3,782 .63. .969 .863 .910 .863 .818 863 .831

13 5 3,927

.96

1,o16 .'96 94o .896 .855 .896 .882

14

4073

.929 l,o88 .929 .992 .929

9o8

.929 .945

14,5 4,218 .962 1,164 .962 1,o55 .963 .962 .963 l,o12

15 4,364 .995 1,231 .995 1,1o3 .996 1,007 .996 l,o69

15,5 4,5o9 1,029 _1,28? _1,o29 1,134 l,o29 l,o32 1,029 1,1o7 16 4,654 1,o62 1,331 l,o62 1,156 l,o62 1,o47 ì,o62 1;131 16,5 4,800 1,095 1,39? 1,095 1,187 1,o95 l,o69 1,o95 1,162 17 4,945 1,128 1,467 1,128 1,248 1,129 1,115 1,129 1,215 17,5 5,091 1,161 1,563 ,l61 1,344 1,162 1,2o6 1,16? 1,299 18 5.236 1.194 1.689 1.194 1.4.90 1.195 1.376 1.195 1.431

(28)

1,6 9 .7

7

392. 393 -- - _353F-354A 394 1I 12 13 - 14 15 16

Fig. 27.

Ship ® - values.

WL I. Group C. VariatiOn in longitudinal oositiori of centre of buoyancy.

GROUP D. Variation in Prismatic Coefflcieñt.

TABLE 19. SRI P PARTICULARS FOR WL i. GROUP D. VARIATION IN PRISMATIC COEFFICIENT.

17 MODEL NO. 396 353 F- 397 398

354A

£WL _69,100 _69,170 _69,24o _69,310 11,582.

11582

11,582 11,582 d, d, 4,310 3,520 4,311 3,5].o 4,312 3,500 4,312 3,490

4

2,730 2,7o9 2,6$8. 2,668 P' 1514 1597 1677 1757 1564 165o 1732 1815 .976 .976 .976 .976 .537 .568 .597 627 4° .550 .582 .612 642 Lw .666 .688 .721 .749

®

6,o9 6,o8 6,o6 6,o5

4',á 6 017 5 917 5. 828 5 742

Q-17$ 1,5A i,6Ä 1,7A 1,8A

'-"/a 5,966 5,972 5,978 5,984

(29)

TABLE

2o.

SHIP ®

VALUES FOR WL

I.

GROUP D. VARIATION IN PRISMATIC COEFFICIENT. 1UUL NU. V

396 353 F-354 A

397

398 v/'4

'/

V/

'4

®

,

,/

P'4

®

v/

'/

®

11

.731

3,229

.778

2;773

.73o

3,2oo

.793

2,776

.730

3,174

.816

2;811

;729

3,15o

.881

2,988

11 5

12

125

13

.764

.797

.830

.863

3,375

3,522 3,669

3,816

.78°

.783

.790

.800

3;o38

3.321 3;636

3;982

.763 .797 .83o .863

3,345

3,491 3,636 3,782

.793

.798

.81

.818

3,026

3,324 3,621 3,999

.763

.796

;83o 863

3;319

3;463 3;6o7

3;751

.828

.835

.832 .85o

3;118

3,423 3,701 4;o90

.763

.796 .829

.862

3,293 3,436 3,579 3;722

.899

.921 .943

972 3,332

3,715

4,130 4,6o4

135

16 14. 5

15

.897 .930 .963

3,962

4,1o9

4,256

.814

.829 .841

4,369 4,786 5;208

.896

.929 .963

3,927 4,073 4,218

.855

.908 .962

4,5o8

5,149 5,85].

.896

.929 .962

3,896 6,o4o 6,184

.899

.977

1;o59

4,665

5;452

6;339

.895

.928

962 3,865

4;oo8 4,152

1,009

1;o71

1,2o9

5;154

5;884

7,125

15,5

.996

1,o3o

4,403

4,549

.85o

.862

5,633

6,loo

.996

_1,o29

4,364

6,509

1,007 1;o32

6,555 7,173

995 1,o29

4;329

4,673

1;155

1,217

7,399

8,324

;995

1;o28

4,295

4,438

1,362

1,468

8,590 9,886

16 16,5

1,o63 1;o96

4,696

6,843

.881 .923

6,643 7,401

1,o62 1,095

6,654 6,800

1,o47 1,069

7;754 ß,42o

1,o62 1,095

4;617

4,761

].;248

1,269

9;o96

9;836

1;o61 1,o94

4,581

4,724

ì,532

1;561

lo,993

11,912

17 1,129

6,990

1,oll

8,6o6

1,129

4,945

1,115

9,322

1;128

4;906

1,3oo

lo,696

1,127

4,867

1,575

12,76o

17,5

1,162

5,136

1,138

lo,265

1,162

5,091

1,2o6

10,685

1,161

5,o5o

1,375

11,989

1,161

5,oll

1,585

13,6o6

18

1.196 5,283

1,315

12,549

1,195

5,236

1,376

l2,490

1,194

5,194

1,611

14,86o

1,194

5.154 1,600

14.53o

(30)

1,3

i

)

TABLE 22. SHIP ® - VALUES FOR WL I. GROUP E. VARIATION IN LENGTH - DISPLACEMENT RATIO.

/

I

/

,1 /

/

./.

'i

/

,,'

//

.'

/

---y

V

----

--

_353F-396 V 397 398 354A

-

--- Ic 16 17 18 MODEL NO.

4o7 353 F-354 A 4o8 4o9

.2 lo,39469,17o 69,17o 11,582 69,170 12,473 69,170 13,443 3,869 4,311 4,643 5,004 3,150 3,510 3,78o 4,074 2,431 2,709 2,917 3,144 7

4

12861328 1597. 165o 1852 1913 2151 2222 Ca .976.568 .976 .568 .976 .568 .976 .568

Cv

.582.688 .582 V 688 .582 .688 .582 .688 6,3o ¿,o8 5 93 5,78

/V'6

6 36o 5 917

5,33

5 358

I

6A

I,6A

. l,6A I,6A

"/3

6,55

,972 5,546 5,145 /d, 3,3oö 3,300 3,3oo 3,300 MODEL NO. V V ,, . F- A o8 o 11 .730 3,31: .7.3 2,-71 3,200 .793 2,77. 3,122 .;34 2,779 3,o45 .850 2,695 11 5 1.2 .763 .797 3,469 3,619 .765 .77° 3,146 3,448 3,345 3,491 .793 .798 3,o34 3,324 3,264 3,4o6 .84o .843 3,o59 3,343 3,183 3,322 .852 .853 2,952 3,218 12 5 13 .83o .863 3,770 3,921 .776 .790 3,771 4,152 3,636 3,782 .8o1 .818 3,621 3,999 3,548 3,690 .851 .87o 3,662 4,o49 3,4.6o 3,599 .862 .881 3,529 3,9o1 13,5 14 14,5 15 15,5 16 16,5 17 .896 .929 .963 .996 1,029 l,o62 l,o95 1,129 4,o72 4,223 4,374 4,524 4,675 4,826 4,977 5,128 .824 .879 .931 .963 .982 .996 1,o15 1,o6o 4,67o 5,358 6,o88 6,739 7,337 7,930 8,594 9,527 3,927 4,073 4,218 4,364 4,5o9 4,654 4,800 4,945 .855 -.908 .962 1,007 1,o32 1,o47 1,o69 1,115 4,5o8 5,149 5,851 6,555 7,173 7,754 S,42o 9,322 3,832 3,974 4,115 4,257 4,399 4,541 4,683 4,825 .9o5 .956 1,o14 1,o63 1,o88 l,1o5 1,135 1,191 4,542 5,16o 5,871 6,587 7,199 7,791 ,510 9,479 3,737 3,876 4,o14 4,152 4,291 4,429 1,568 4,7o6 .913 .967 1,025 1,o69 l,o96 1,121 1,168 1,242 4,36o 4,966 5,646 6,3o2 6,899 7,519 8,331 9,404 17,5 18 1,162 1,195 5,278 5,429 1,138 1,259 Io,839 12,686 5,091 5,236 1,206 1,376 lo,685 12,490 4,967 5,1o9 1,292 1,446 lo,397 12,903 4,844 4,983 1,370 1,623 lo,993 13,28o 11

SCALE OF SPEED l KNOTS

Fig. 28. Ship ( - values. WLI. Group D. Variation in prismatic

coefficient.

TABLE 21. SHIP PARTICULARS FOR WL I. GROUP E. VARIATION IN LENGTH - DISPLACEMENT RATIO.