Propulsive performance in still water of high speed cargo ships with methodically varied form coefficients

PROPULSIVE PERFORMANCE IN STILL WATER

OF

HIGH SPEED CARGO SHIPS

WITH

METHODICALLY VARIED FORM COEFFICIENTS

by

A. Akre

Norwegian Ship Model Experiment Tank Publication No. 110

May 1972

-BbIiotheek van de

Ondera

'ing der

.s.ouwkunde

Tech ...ut...- .eschool, Deift

UMEN TA TIE

DATUM:

TECNISCE

VERSTT

Laboratorium voor

Norwegian Ship Model Experiment Tank

Scheepshydromechanica

Archief

-III--Page.

TABLE OF CONTENTS.

PREFACE.

_V

NOTATION.

VI

LIST OF FIGURES.

XIII

LIST OF TABLES.

xv

SUMI"IARY.

_xix

MAIN REPORT.

1

1. The Models.

a. Parent model.

b. Constant conditions for the test series,

1 i i

c.

d.

Test series 1.

Variation of LDUL/B and B/T.

Test series 2.

Variation of longitudinal

2

e.

centre of buoyancy.

Test series 3.

Variation of block

2

coefficient.

3

f. Propellers of the test series.

3

2. The Tests.

₆

a. General test conditions.

6

b. Towing tests.

₆

c. Open water tests.

6

d. Self-propulsion

tests.

6

3. Preparation of Test Results.

₇

a. Resistance data for each ship model.

7

b. Results of open water tests.

9

o. Results of self-propulsion tests.

₁₀

4. Discussion.

_ii

a. General rerarks.

₁₁

-IV-Page.

Variation of longitudinal centre of

buoyancy.

15

Variation of block coefficient.

15

5. Conclusions.

16

G.

APPENDIX.

1. Model Documentation.

18

Tables and figures for the description of

ships and ship models.

18

Propeller particulars and design.

29

Methods for variation of geornetr4cal

parameters.

31

2. Test Results for Each Model.

37

Tables and figures.

37

Calculation manner ar.d example.

68

Testing facilities and procedure.

81

3. Polynomials with Georetrical Parameters as

Independent Variables.

83

Principle of development and restrictions

of use.

83

Tables of polynomial coefficients.

87

4. Test Results Prepared for Discussion of Parameter

Influence on Resistance and Propulsion Qualities.

93

Contours of CTV and FM as functions of LDWL/B

and B/T.

93

Diagrams for CTV and F1 as functions of

(LCB)LDWL and CB(LDWL).

A.

PREFACE.

-V-The present report presents the results of systematical

towing and self-propulsion tests of high speed cargo ships in still

water.

The tests are carried out at The Norwegian Ship Model

Experiment Tank in Trondheim, and are financed by the Royal

Norwegian Council for Scientific and Industrial Research.

In

addition, corresponding results of tes in waves exist.

The bodyplan of the parent model is designed according

to specifications worked out by

. temporary committee.

The rembeis

of the committee represented Norwegian ship-yards, shipownes and

institutions of ship research.

One of the principal tasks of the committee was to work

out specifications for a fast cargo shi

which is economically

optimal with respect to both easy cargo handling and propulsion

power requirement.

The desigi d L 1ca2e ship, to which the parent model

corresponds, is of 11500 tonnes dead weight.

The total hold

capacity is 1130000 ft.3

(31980 m3), the total length 564.3 ft.

(172 m) and the service speed 21 knots.

The committee concludes that the proposed ship design

possibly favours the hydrodynamic requirements on cost of the

requirement of economical cargo handling.

Possibly one might vary

the form coefficients even more in a direction which is favourable

for the cargo handling.

Results from methodical experiments for the

required combination of form coefficient values did not exist,

and the committee recommends such experiments to be carried out.

The use of the present methodical experiment results,

for prediction of the propulsion power of a ship with

orm

coefficients within the coefficient ranges, which the experiments

cover, will be dealt with in another report.

-VI-B.

NOTATION.

Comment:

The subscript s means fuliscale quantities and rn means

model quantities. A more detailed list of definitions

and equations is given in G 2.b, page 68.

1.

Units and Physical Constants.

Unit of length: meter (m) ,

(l/l000)m = 1 millimeter (mm)

Unit of force (and weight) :

kilopond (kp)

1000 kp = i metric ton-force (tonne),

1.016047 tonnes = i english ton-force (ton).

Comment:

The connection with the SI (former MKSA)

unit system:

i kp = 9.80665 Newton (N).

Unit of time:

second (sec) ,

60 sec = 1 minute (mm)

Unit of revolution rate:

revolutions per sec (rps)

revolutions per min (rpm)

Unit of energy:

kilopond-meter

(kpm).

Unit of power:

75 kpm per sec = 1 metric horsepower

(Hp(m)).

Unit of speed:

metres per sec (rn/sec),

0.5144 rn/sec = 1 knot.

Unit of temperature:

degree centigrade.

(°C)

g

Acceleration due to gravity.

(m/sec2)

Kinematic viscosity of water.

(rn2/sec)

p

I4ass density of water.

(kp sec2/m)

-VII-

B

Unit

Geometry of Propeller.

AE

Expanded blade area.

(m2)

A0

Disc area.

a

Distance between designed center line of model

propeller blade and station 0.

(mm)

D

Diameter of propeller.

(m)

d

Boss diameter.

P

Propeller pitch.

Comment:

The value of r is often used as

sub-script, e.c. P

0.7

P/D

Pitch ratio at r = 0.7

R

Radius of propeller.

r

The distance between center line of propeller

boss and any one of the propeller blade sections,

expressed as fraction of R.

Z

Number of blades of the propeller.

z

Vertical position of model propeller.

(nun)

Geometry of Ship.

a.

Dimensios.

Area of waterplane.

(rr)

Area of maximum transverse section.

The laroest molded breadth nf the

hnd'

below

Unit

KM

Distance between metacenter and molded baseline.

(rn)

L

Length of ship in general.

LDWL

Length of designed load waterline.

LLWL

Length of load waterline in general.

Length between perpendiculars.

S

Wetted surface, excluding appendages, such as

shell plating, rudder etc.

(m2)

SR

Wetted surface of rudder.

T

Molded draft at LDWL/2.

(m)

V

Molded displacement volume, excluding

appen-dages, such as shell plating, rudder etc.

(m3)

Comment:

If the subscript DWL is used,

designed load waterline is the load line.

A

Molded displacement weight, A = V(pg)/l000

(tonnes)

Trim

The difference between the heights of load

waterline above molded baseline, at station O

and station 20, respectively, expressed in per

cent of LDWL.

Positive trim when the heigth at

station 20 is smallest (trim by the stern).

X

Model scale.

X = L /L

s

m

b.

Form coefficients.

Comment:

Meaning of additional subscripts

for the symbols of form coefficients.

Subscriot LDWL:

L = L

-Subscript LL:

_{L = LLUL.}

Definitions

CB

Block coefficient in general.

V/(B T L)

Prismatic coefficient in general.

_CB/CX

Waterline coefficient in general.

Aw/(B L)

C

Maximum transverse section coefficient.

_{Ax/(B T)}

B/T

Breadth-draft ratio.

(LCB)

The distance between longitudinal centre

of buoyancy and L/2, expressed in per cent

of L.

(LCB) is positive forward of L/2

and negative aft.

L/B

Length-breadth ratio in general.

LDWL/B

The length-breadth ratio based on

LLWL/B

The length-breadth ratio based on

_LLWL.

L/B

The length-breadth ratio based on

Wetted surface coefficient.

S

4.

Ship in Motion.

a.

Speed.

F

Froude's number.

Speed-displacement coefficient.

F

nV

Froude's speed-displacement coefficient.

V/4T/(gV'1)

V

Speed.

(Unit: m/sec)

v/ /g LD

-X-

B

Definitions.

b.

Resistance.

Froude's resistance coefficient.

_RT/(L\

= (l25/)RT/(½pV2V2/3) = (l25/)CTv.

CA

Incremental resistance coefficient for

model-ship correlation.

RA/ (½pV2S)

CF

Specific frictional resistance coefficient.

RF/(½pV2S)

Comment:

The coefficient calculated

according to the ITTC-1957 model-ship

correlation line: C=O.O75/(lo

R-2)2.

CRy

Residuary resistance-displacement

coefficient.

RR/ (½pv2

y2ì'3 ) =

=CTV

-r,

m

mFm

Froude's residuary resistance coefficient.

RR/(A®2)

=

CTV

Total resistance-displacerent coefficient.

RT/(½pV2V2/3)

Comment:

1'

_'TVs

₌

+

(C

+C ).

'-1s

Fs

A

Froude's frictional resistance

coefficient.

_RF/(A®

2)

Comment:

The coefficient calculated

according to the method of Froude and

Baker: F = O® (FVT)°'75

O

The "O"-values of Froude's method.

Comment:

O is a function of the

skin-friction coefficients of Froude.

Effective power.

(unit: Hp(m))

RA

:lodel ship correlation allowance. (unit: kp)

RF

Frictional resistance.

RR

Residuary resistance.

(unit: kp)

R.

Total resistance.

T

c.

Propulsion.

Cornnient:

The subscript O means test

results in open water, the subscript B means

test results of the propeller behind ship.

FD

External tow force in a

self-propulsion test.

(unit: kp)

FM

Overall factor of merit.

CTV/(nHxnR)

J

Advance coefficient of propeller.

_{VA/(n D)}

Comment:

Both by thrust and torque

identity is

KQ

Torque coefficient of propeller.

Q/(pn2D5)

KT

Thrust coefficient.

T/(pn2D)

n

Rate of revolutions.

(unit: rps)

Delivered power at propeller. (unit:Hp(m)).

21TQn/75

Thrust power.

(unit:Hp(m))

_TVA/75

Q

Torque of propeller.

(unit: kpm)

T

Thrust of propeller.

(unit: kp)

t

Thrust deduction fraction.

_{((TB_RT)/TB)}

VA

Speed of advance of propeller. (unit:m/sec)

Definitions.

w

T

Taylor's wake fraction determined from

thrust identity.

= l-(J/(V/(n3D))).

Definitions.

n5

Propeller efficiency behind ship.

_{TBDB =}

= KTBJ/(2'iTKQB).

nD

Propulsive efficiency.

EDB

=

1H

R

Hull efficiency.

((l_t)/(l_wT))

Propeller efficiency in open water.

_{o=ToDo =}

= KT0J/(2ITKQ0).

Relative rotative efficiency.

ns/no =

= (KTB/KTQ) (KQO/KQB).

Comment:

Thrust identity is used in the

report.

KTB=KTOF which gives: nR=(KQoQB).

d.

Speed influence on draft:

Sinkage.

The change in vertical position

,

expressed

in per cent of T, of a point on the vertical

center-plane of the ship, when the speed

in-creases from zero speed to actual speed.

Reference level is smooth water surface.

The sinkage is positive when the position

of the point is highest at zero speed.

Appendix, section

2.

Fig.lO. OPEN WATER CHARACTERISTICS.

₆₇

Appendix, section 4.

Figures 11 - 24. Contours of

_{CTV and FM.}

_{Test series 1.}

_{94 - 107}

Full load condition.

Model scale 1/30.

-XIII-Page.

C.

LIST OF FIGURES.

Main report.

Fig. 1. THE BODYPLAN AND THE BOW AND STERN PROFILES

OF THE PARENT MODEL.

4

Fig. 2. SECTIONAL AREA CURVE AND PRINCIPAL

PARTICULARS OF THE PARENT MODEL.

4

Fig.

3.

SCHEME FOR THE VARIATION OF GEOMETRICAL

PARAMETERS IN TEST SERIES 1. (Parameter area).

₅

Fig. 4. SCHEME FOR THE VARIATION OF GEOMETRICAL

Appendix, section 1.

Fig.

5.

PROPELLER AND RUDDER LOCATION.

₂₇

Fig.

6.

SECTIONAL AREA CURVES.

28

Fig.

7.

PARTICULARS OF THE PROPELLERS.

₃₀

Fig. 8. THE METHOD FOR THE VARIATION OF

_CB.

₃₅

Fig. 9. THE METHOD FOR THE VARIATION OF (LCB).

₃₆

PARAMETERS IN TEST SERIES

2

AND

_3.

5

Page.

Figures 25 - 32. Contours of CTV.

Test series 1.

108 - 115

Half load condition.

Model scale 1/30.

Fig.33. CTV AND FM AS FUNCTIONS OF

LONGITUDINAL CENTRE OF BUOYANCY.

Test series 2.

116

Full load condition.

Model scale 1/30.

Fig.34. CTV AS FUNCTION OF LONGITUDINAL

CENTRE OF BUOYANCY.

117

Half load condition.

Model scale 1/30.

Fig.35. CTV AND FM AS FUNCTIONS OF BLOCK

COEFFICIENT.

Test series 3.

118

Full load condition.

Model scale 1/30.

Fig.36. CTV AS FUNCTION OF BLOCK

COEFFICIENT.

I, ti

il

117

Half load condition.

Model scale 1/30.

Appendix, section 2.

Table lOa. RESISTANCE DATA FOR PARENT MODEL.

MODEL NO. 788.

38

Table lOb. PROPULSION DATA FOR PARENT MODEL.

39

Table lOc. COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS FOR PARENT MODEL.

tI II II

₃₉

Table lla. RESISTANCE DATA.

MODEL NO. 844.

Test series 1.

40

Table llb. PROPULSION DATA.

MODEL NO. 844.

lt

41

Table lic. COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 844.

't

41

Page.

D.

LIST OF TABLES.

Table 12a. RESISTANCE DATA.

MODEL

C. 817.

42

Appendix, section 1.

Table

1.

PARTICULARS OF THE MODELS.

19

Table

2.

DIMENSIONS OF SHIPS FOR THREE MODEL SCALES.

20

Table

3.

OFFSETS OF THE PARENT MODEL.

MODEL NO. 788.

21

Table

4.

OFFSETS OF MODEL NO. 820.

Test series 2.

22

Table

5.

OFFSETS OF MODEL NO. 821.

It It

23

Table

6.

OFFSETS OF MODEL NO. 822.

Test series 3.

24

Table

7.

OFFSETS OF MODEL NO. 823.

It It

25

Table

8.

OFFSETS OF THE MODELS IN TEST SERIES 1.

26

Table

9.

PROPELLER NUMBER, PITCH AND LOCATION IN THE

Page.

Table 12b. PROPULSION DATA.

MODEL NO. 817.

Test series 1.

43

Table

Table

Table

12c.

13a.

13b.

COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 817.

RESISTANCE DATA.

MODEL NO. 816.

PROPULSION DATA.

MODEL NO. 816.

ti it t, it it t, t, ii

43

44

45

Table

Table

Table

13c.

14a.

14b.

COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 816.

RESISTANCE DATA.

MODEL NO. 852.

PROPULSION DATA.

MODEL NO. 852.

it i, it ti ti it it il

45

46

47

Table l4c. COEFFICIENTS OF PROPELLER LOAD

Table 15a.

Table 15b.

Table l5c.

Table 16a.

Table 16b.

Table 16c.

Table l7a.

Table 17b.

POLYNOMIALS.

MODEL NO. 852.

RESISTANCE DATA.

MODEL NO. 845.

PROPULSION DATA.

MODEL NO. 845.

COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 845.

RESISTANCE DATA.

MODEL NO. 819.

PROPULSION DATA.

MODEL NO. 819.

COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 819.

RESISTANCE DATA.

MODEL NO. 818.

PROPULSION DATA.

MODEL NO. 818.

ti It it It it it ti ti ti t, t, 't

i'

ti t, ti ii

ii

ti

47

48

49

49

50

51

51

52

53

Table

Table

17c.

18a.

COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 818.

RESISTANCE DATA.

MODEL NO. 854.

ii t'

ti ti

53

-XVII-

D

Paae.

Table l8b. PROPULSION DATA.

MODEL NO. 854.

Test series 1.

55

Table l8c. COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 854.

Table 19a. RESISTANCE DATA.

MODEL NO. 853.

J, it it ti II

55

56

Table 19b. PROPULSION DATA.

MODEL NO. 853.

Ji It il

57

Table 19c. COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 853.

'J It Ji

57

Table 20a. RESISTANCE DATA.

MODEL NO. 820.

Test series 2

58

Table 20b. PROPULSION DATA.

MODEL NO. 820.

" it it

₅₉

Table 20c. COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 820.

Table 2la. RESISTANCE DATA.

MODEL NO. 821.

it It it JI i,

'I

59

60

Table 21b. PROPULSION DATA.

MODEL NO. 821.

It It II

61

Table 2lc. COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 821.

iI ti

61

Table 22a. RESISTANCE DATA.

MODEL NO. 822.

Test series 3

62

Table 22b. PROPULSION DATA.

MODEL NO. 822.

it ti

63

Table 22c. COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 822.

ti Ii

63

Table 23a. RESISTANCE DATA.

MODEL NO. 823.

Table 23b. PROPULSION DATA.

MODEL NO. 823.

I, Ji JJ Ii ti

64

65

Table 23c. COEFFICIENTS OF PROPELLER LOAD

POLYNOMIALS.

MODEL NO. 823.

it

65

-XVIII-

D

Page.

Appendix, section 3.

Table 25.

COEFFICIENTS OF THE RESISTANCE

AND PROPULSION POLYNOMIALS FOR

VARIATION OF (LCB) AND CB.

Test series 2 and 3.

90

Table 26.

COEFFICIENTS OF THE CONTOUR

POLYNOMIALS.

Test series 1.

92

E.

SUMMARY.

Methodical experiments are carried out with three series

of ship models.

The parent ship is a fast cargo ship, designed for

economically optimal cargo handling and transport.

The designed

full load displacement is approximately 20200 tonnes and the

corre-sponding deadweight is 11500 tonnes.

Nominal values of the form

coefficients are:

_{CB(LDwL)=O.56l Cp(LDWL)=O.5771 CX=0.97, (LCB)LDWL}

=1.0 per cent, LDWL/B=6.64 and B/T=2.94l.

The shape of sections is

a moderate U-form.

Service speed is 21 knots.

The LDWL of the parent

model is 5533.3 mm, which corresponds to a model scale of 1/30.

Test series 1 consists of 9 models plus the parent model.

LDWL/B and B/T are varied in this series and the variation ranges

are 5.8 - 7.0 and 2.7 - 3.2, respectively.

(LCB)LDWL is varied in test series 2, and the series

con-sists of two models in addition to the parent model.

The variation

range is from 0.2 to 1.8 per cent of LDWL.

In test series 3, CB(LDWL) is varied and the variation

range is 0.535 - 0.585.

The series consists of two models in addition

to the parent model.

Towing and self-propulsion tests are carried out for a

speed range which corresponds approximately to a fullscale speed

range of 15 - 26 knots at model scale 1/30.

The towing tests are

carried out for full load condition and half load condition.

The

half load displacement is 70 per cent of the full load displacement.

Two propellers of the controllable pitch type were

de-signed for the test series.

The designs were based on data from

wake tests and from short preliminary propulsion tests with

_{a stock}

propeller.

Self-propulsion tests were carried out only for full load

condition, but in a way which permits independent choice of model

scale, model-ship correlation allowance, etc., after the finishing

of the model tests.

In the report these tests are called propeller

load tests.

The presentation of the resistance and propulsion data

is made by means

tables.

Fuliscale values are given for three

model scales, which correspond to the full load displacements of

approximately 10000, 19750 and 50000 m3, respectively.

The

full-scale values are calculated according to the ITTC-1957 model-ship

-XX-

E

correlation line, and the model-ship correlation allowance is zero.

In addition to the data based on the ITTC-l957 model-ship

corre-lation line, the residuary resistance coefficient of Froude is given.

Furthermore, the basic propulsion data WT

1

and n

are given in separate tables, by means of polynomial coefficients.

The corresponding polynomials are called propeller load polynomials,

in which the propeller thrust is independent variable.

The speed

condition is constant for each set of polynomial coefficients.

An example of calculation of propeller power, based on the above

mentioned tables, is shown.

The influence of the varied form coefficients on

resistance and propulsion data, is given by means of polynomials.

Sets of polynomial coefficients are given in tables, and each set

belongs to a constant speed condition.

LDWL/B and B/T are independent variables in the

poiy-nomials which are named contour polypoiy-nomials.

In the polynomials

which are named resistance and propulsion polynomials, CB(LDWL) and

(LCB)LDWLI respectively, are the independent variables.

The contour polynomials and the resistance and propulsion

polynomials are used to draw graphical representations of the total

resistance-displacement coefficient (CTV) and the overall factor of

merit (FM) as functions of the above mentioned form coefficients.

A discussion is carried out on base of these graphical

representations.

The discussion concerns the influence of form

coefficients, and in particular the possibility of using greater

B/T and block coefficient values and smaller LDWL/B-values than

those of the parent model, without serious increases of propeller

power.

According to the test results, an increase of B/T of at

least about 9 per cent is possible without more than about one per

cent power increase.

The mentioned values concern the service speed

condition, and the LDTL/E-value of the parent model.

But a

corre-sponding tendency exists for other speed conditions and LDWL/B_

values.

Noticeable decrease of the LDWL/B or increase of the

block coefficient without serious increase of power is probably not

possible according to the test results.

F.

4AIN REPORT.

1.

The Models.

Parent model.

The parent ship is designed for a full load displacement

in sea water of 20236 tonnes and a service speed of 21 knots.

is 160 metres, and the draft to designed load waterline is 8.5

metres.

The principal dimensions are given in the top part of Table

2, page 20, the part marked model scale: 1/30.

The value of

for

full load displacement and service speed is 0.6635.

The model was made to the scale 1/30 and model No. is

788.

Bodyplane, profiles of bow and stern, sectional area curve and

principal particulars are given in Figures 1 and 2.

The rest of the

particulars are given in Table 1, page 19, and the offsets are given

in Table 3, page

21.

The length of designed load waterline is used

as base for the stations, and also for the form coefficients,

originally.

But the form coefficients are given also on base of

The designed load waterline is used as load waterline for

full load condition.

In addition, a load condition with a

displace-ment of about 70 per cent of the full load displacedisplace-ment is used.

This load condition is called half load condition, and the trim is

one per cent of LDWL.

The definition of trim is given in Notation,

page VIII.

The size and location of the rudder are given in Fig. 1,

page 4.

Constant conditions for test series.

The variation of the parameters LDWL/E, B/T,

_(LCB)LDWL

and CB(LDL) are carried out for constant full load displacement,

constant maxirium section coefficient (Cx) and constant shape of the

sections.

Only one of the mentioned parameters is varied at a time,

and the others are kept constant.

The nominal displacement of the models for half load

condition is 0.512 m3, which corresponds to 70 per cent of nominal

-1--2-

Fl

displacement for full load condition.

The trim for half load

con-dition is i per cent of LD7L.

The models were made of paraffin wax.

The same rudder

was used for all models, and the distance between rudder and stern

tube was kept constant.

The longitudinal locations of rudders are

given in Fig. 5 and Table 9, pages 27 and 26.

Test series 1.

Variation of LDWL/B and B/T.

Nine models were made for this series in addition to the

parent model.

In Fig. 3, page

5, the variation scheme and the No.

of each model are given.

Particulars of the models are given in

Table i, page 19, and principal dimensions of the corresponding

ships in Table 2, page

20.

Offsets of the models are given by means of the conversion

coefficients in Table 8, page 26, and the offsets of the parent model

in Table 3, page 21.

The sectional area curves are equal to the

curve of the parent model.

In Appendix, section 1.c, page 31, the calculation of

the conversion coefficients is shown.

The influence of LDWL/E and B/T on

is presented by

means of ten terms polynomials.

The polynomial coefficients for

full load condition and half load condition are given in Table 26,

page 92.

In Appendix, section 3.a, page

83, the polynomial is

described.

In the report this polynomial is called contour

poly-nomial.

Test series 2.

Variation of longitudinal centre of buoyancy.

The test series consists of two models, model No. 820

and No. 821, in addition to the parent model.

The variation scheme

is shown in Fig. 4, pace 5.

Offsets of the two models are given in Tables 4 and 5,

pages 22 and 23, and particulars in Table i, page 19.

Principal

dimensions of the corresponding ships are qiven in Table 2, page 20.

-3--

Fi

In addition, the variation method is shown in Appendix, section 1.c,

page 32.

The influence of longitudinal centre of buoyancy on

is presented by means of three terms polynomials.

The polynomial

coefficients for full load and half load condition are civen in

Table 25, page 90.

The polynomial is described in Appendix, section

3.a, page 83.

Test series 3.

Variation of block coefficient.

The test series consists of two models, model No. 822 and

No. 823, in addition to the parent model.

The variation scheme is

shown in Fig. 4, page 5.

Offsets of the two models are given in Tables 6 and 7,

pages 24 and 25, and particulars in Table 1, page 19.

Principal

dimensions of thecorrespondincj ships are given in Table 2, page 20.

The method for variation of C3 is shown in Appendix, section l.c,

page 33.

The influence of block coefficient on

is presented in

the same way as described in the previous section concerning

in-fluence of longitudinal centre of buoyancy, and the polynomial

coefficients are given in the same table, Table 25.

Propellers of the test series.

Two propellers of the controllable pitch type were

de-signed for the test series, propeller No. 708 and No. 710.

The

particulars of the propellers are given in Fig. 7, page 30.

The

propeller No. and the pitch ratio for each ship model are given in

Table 9, page 26.

The proe1ler designs were based on data from wake tests

and from short preliminary propulsion tests with a stock propeller.

A short description of the mentioned tests and the design of the

Principol particutors. LDWL/B r 6640 (LCB)LL r 0.9961 per cent

r693$

CLDIJ

r 0.5598 r OE5771

Reference: Table No. 1,

Full load cendition

Measures in millimetres

FIG. 1. THE BODYPLANE AND THE BOW AND STERN POFILES OF THE PARENT MODEL, MODEL NO 788. FIG. 2 SECTIONAL AREA CURVE AND PRINCIPAL PARTICULARS OF THE PARENT MODEL

Vertical centerplane rop of model. Per cent of A5 ded baseline

0 ½

1 1½ 2 3 1. 5 6 7 8 9 lO 11 12 13 11. 15 16 17 18 18½ 19 19½ 20 11WL. Knuckle-Line

2/

ule-12WL. iOW \ Corner of transom. 1 /2 9W L 163 i 8WL. 8WL 7WL.

¡17W

L s... 45

¡.4I

6WL

ORg.

'

4WL

It

J

IJ6wL.

4WL.

IlIIr4

I

mituilrl

.. . 3WL. rn

8

iii

2WL. . 2WL. _____

L4L

a

185 2 19 191/2 20 B 833.3 mm LD 5533.3 Lpp 5333.3 T r283.3 S 5.1891. m2 SR r 0.0668 V r 0.7312 m3 BIT r 2.941

7.0 6.0 0.59 0.57 0.56 0.55 0.54 0.53

FIG. 3.

SCHEME FOR THE VARIATION OF GEOMETRICAL PARAMETERS

IN TEST SERIES 1. (The parameter area).

Na 822 _{C8 =0.585} 1.0

(LCB)L

per cerrt1.5 5.8 Na 820 No. 788 No. No.

V

823 CB= 0.535 Mod 1.8

eis of test series 3:

821

e

No. 851.

n

No. 816 No. 853

E

N 819

No.788

n

No.818

n

No.852

E

No.

n

817 No.81.5

n

No. 844

Li

2.6 2. 2.8 2.9 B 3.0 31 32 3.3 T

FIG. 4.

SCHEME FOR THE VARIATION OF GEOMETRICAL PARAMETERS

IN TEST SERIES 2 AND 3.

Na B8, the parent model:

Models of test series 2:

No. 788

the parent model:

s

Models of the test

series 1.

6.61. 6.2

5-

Fi

LL

B 6.5 058 CB([JJWL}

02

0.5

-6-

F

2.

The Tests.

General test conditions.

All models were fitted with trip wire at station 19.

Except from rudder the models had no appendages.

Speed range was

1.4 - 2.5 rn/sec which corresponds to about 15 - 26 knots for the

model scale 1/30, and to a F

-ranqe of about 0.48 - 0.82 for full

load condition.

Information about the testing facilities and procedure

and about the accuracy of measurements is given in Appendix,

section 2.c.

Towing tests.

Towing tests are carried out for two load conditions,

full load condition and half load condition.

In addition to the

measurements of the resistance and the speed, the sinkages of the

model at station 20 and station O were measured.

Definition of the

sinkage is given in section B.4.d.

A propeller boss of correct weight

in water replaced the propeller during the towing tests.

Open water tests.

The open water tests were carried out with three pitch

values for each propeller, design pitch, P/D = 0.80 and P/D = 0.90,

respectively.

A revolution rate of 13 rps was used, which

corresponds to approximately 140 rpm for the fuliscale propellers

and model scale 1/30.

Self-propulsion tests.

-7-

F2

permitted choice of propeller load at constant speed, after the

finishing of the tests.

The possiblility then exists of using

in-dependent model scale, inin-dependent sea temperature, inin-dependent

model-ship correlation allowance, etc. for the calculation of

full-scale data.

The self-propulsion tests were carried out for full load

condition, only.

Three different functions for the external tow

force (FD) were used for each model, making three sets of test runs.

Expressed as fractions of RTm the three FD-functions are

approximate-ly 0.1, 0.35 and 0.55, respectiveapproximate-ly.

In the report these tests are

called propeller load tests.

For the parent model a fourth such set of test runs was

carried out, using a FD-function of approximately -0.1 RT.

The

corresponding (RTm_FD)_function is then approximately 1.1 RT.

For each ship model the propeller was adjusted to a pitch

which probably would give 140 rpm for the fuliscale propeller at

the model scale 1/30 and the fuliscale speed of 21 knots.

The

propeller No. and pitch ratio are given in Table 9, page 26, for

each ship model.

In connection with the self-propulsion tests of each

model, the resistance was checked by means of separate towing test

runs.

Three runs were carried out immediately before, and the same

number immediately after the self-propulsion tests.

_{The Fnvalues}

0.55, 0.65 and 0.75 were used.

When calculating the thrust

de-duction fraction (t), the results of these towing tests were used

together with the ordinary towing tests.

3.

Preparation of Test Results.

a.

Resistance data for each ship model.

The ITTC-1957 model-ship correlation line is used for the

calculation of resistance coefficients from the measurement data.

Temperature corrections to 15°C in sea water and in fresh water for

the ships and the models, respectively, are made.

The resistance data are given in Tables 10 - 23, table

-8-

_{F3 a}

chosen as basis representation for the resistance, and the

speed-displacement coefficient (Fv) for the speed.

In addition, the

Froude's number (F) and the speed in rn/sec and knots for model

and ship, respectively, are given.

The displacement of the actual

load condition is used when calculating the resistance-displacement

coefficients and the speed-displacement coefficient, and the length of

actual load waterline is used when calculating Froude's number.

CTV

was faired by means of a manual curve fitting process.

The Froude's residuary resistance coefficient

is

also given.

The temperature correction of the ITTC-1957 model-ship

correlation line was used when calculating it, as it was calculated

from the temperature corrected model values of CTV.

No model-ship correlation allowance was used when

calcu-lating the fullscale values.

Consequently the incremental resistance

coefficient for model-ship correlation (CA) is zero.

This is in

accordance with ITTC-recommendations for test series of ship models.

Total resistance-displacement coefficient for ship:

CTVS = CRv+()s(CFs+CA) =

For actual resistance calculations the value 0.0004 for

CA is often used.

Furthermore, the calculation of fullscale values was

based on wetted surface without appendages, not even rudder.

Two model scales were used, in addition to the original

model scale, 1/30.

The model scale 23.9 corresponds to a full load

displacement of approximately 10000 m3, which may be used as

standard displacement for presentation of test data, according to

ITTC-recommendations.

The model scale 40.9 corresponds to a full load

displace-ment of approximately 50000 m3.

Fuliscale speed, CTV

and effective

horsepower

are given for the three mentioned model scales.

The sinkages of the models in motion are given as

per-centage of T.

T is the draft at LDWL/2 and for the actual load

condition.

Definition of the sinkage is given in section B.4.d.

The choice of F

-values in the tables has been made in

nV

such a way that 1irear interpolations between the speed values give

sufficient accuracy.

In Appendix, section 2.b, page 68, the

calcu-lation of fuliscale resistance data is described and a calcucalcu-lation

-9-

F3

example based on the above mentioned table series a, is shown.

The influence of form coefficients on

resistance-displacement coefficients is presented by means of polynomials.

Such polynomials are made for CTV and CRV and the form coefficients

are independent variables.

Only the CTVS which belongs to model

scale 1/30, is used.

The polynomials are given by means of sets of

polynomial coefficients.

Each set belongs to a constant speed value.

The contour polynomials are based on data from test

series 1 (variation of LDWL/B and B/T, Tables lOa - 19a) and consist

of ten terms.

The polynomial coefficients (A1 - A10) are given in

Table 26, page 92.

The contour polynomials for

are used to draw

the contours in the Figures 11, 13, 15, 17, 19, 21, 23 and 25

- 32,

pages 94 - 115.

The resistance polynomials based on data from test series

2 (variation of (LCB), Tables lOa, 20a and 21a) and test series 3

(variation of CB, Tables lOa, 22a and 23a) consist of three terms.

The polynomial coefficients are given in Table 25, page 90.

In

addition to the sets of polynomial coefficients (a0

_{- a»}

for CRV and

CTV

corresponding sets for the ratio CRy/CRy

,

are given.

a re n t

0RV parent

is the values of the parent model, model No. 788.

The

diagrams in the Figures 33 - 36 are drawn by means of the polynomials

for CTV.

In Appendix, section 3.a, page 83, a more detailed

description of the polynomials are given, and also the restrictions

of use.

b.

Results of open water tests.

Torque and thrust coefficients were calculated from the

test results, and the open water characteristics for three propeller

pitch ratios are shown in Fig. 10, page 67.

In addition extracts of

the open water characteristics are given in Table 24,

page 66.

Open

water characteristics for other pitch ratios have been obtained by

means of interpolations between the values in the mentioned table.

The interpolations were made by means of manually drawn parabolas.

-10-

F 3

c.

Results of self-propulsion tests.

As explained in section F 2 d, three different functions

for the external tow force (FD) were used for each model, making

three different sets of test runs.

For each of the mentioned run sets, WT

t and

have

been calculated according to thrust identity and plotted in a diagram

as functions of F. In the same diagram the measured revolution

rate of the model propeller (n) and the difference between total

resistance of model and external tow force (RTm_FD) have been plotted

The plotted functions have been faired by means of a

manual curve fitting process, and subsequently, values of each

function have been read at constant F

-values.

The F

-values are

nV

nV

equal to those in the resistance tables for full load condition.

Three sets of such corresponding values then exist for

each model and constant value of Fn1 covering approximately the

(R

-F )-range from 0.45 R

to 0.90 R

.

On base of these values

Tm

D

Tm

Tm

a computer calculated the coefficients of the polynomial:

y = C1+C2(R

-F )+C (R

-F

)2

_y

represents WTI t1

and n.

Tm

D

Tm

D

The polynomial is in the report named propeller load

polynomial and the coefficients are given in Tables 10 - 23, table

series c, pages 38 - 65.

Each set of polynomial coefficients

(C1 - C3) belongs to a constant speed value.

As mentioned in section F 2 d, a fourth function for the

external tow force was used in a separate set of test runs for model

No. 788.

The corresponding (RTm_FD)_function is approximately

1.1 RT.

The above mentioned polynomials for model No. 788 fit with

sufficient accuracy for this fourth set of values.

Probably greater

values of (R

-F

)

than 0.9 R

may be used for the other models also

Tm

D

Tm

The propeller load polynomials are used for the calculatio:

of the propulsion data which are given in Tables 10 - 23, table

series b.

The conditions are the same as for the resistance data of

full load condition in table series a, previously mentioned.

Only

_WTI

D'

n and F

are given for the model scales

23.9 and 40.9.

But by using CTV and

from the table series a, one

may easily calculate

a.

General remarks.

The discussion concerns the influence of the varied form

coefficients, LD,7L/B, B/T,

_{CE and (LCE3) on the resistance and}

-li-

F 3

nR = CTV(lwT)/((lt)FM)

_D

= PE/nD

,

no = (nD FM)/CTV

In Appendix, section 2 b, page 68, the calculation of propulsion data

on base of the resistance data in table series a and the propeller

load polynomials in table series c is described, and a calculation

example is shown.

The influence of form coefficients on propulsion data is

presented by means of the same types of polynomials as used for the

presentation of the influence on the resistance-displacement

coefficients.

_{Polynomials for WT}

1

and FM have been made, and

the form coefficients are independent variables.

The polynomials

are given by means of sets of polynomial coefficients, and each set

belongs to a constant speed value and to model scale 1/30.

As

mentioned before, a more detailed description of the polynomials is

given in Appendix, section 3 a.

The contour polynomials are based on the data from test

series 1

(Tables lOb - 19b), and the polynomial coefficients

(A1 - A10) are given in Table 26, page 92.

The polynomials for FM

have been used to draw the contours in Figures 12, 14, 16, 18, 20,

22 and 24, pages 95 - 107.

The propulsion polynomials are based on data from test

series 2

(Tables lOb, 20b and 2lb) and test series 3

(Tables lOb,

22b and 23b).

_{The polynomial coefficients are given in Table 25,}

page

90.

In addition to the sets of polynomial coefficients (a0

-a2) for WT,

1 _n

and FM, corresponding sets of polynomial coefficients

for the ratios w /w

,

t/t

and n /n

are given.

T

T parent

parent

R

R parent

w

,

t

and n

are the values of the parent model.

T parent

parent

R parent

The diagrams in Figures 33 and 35, pages 116 and 118,

are drawn by

means of the polynomials for FM.

-12-

F4

propulsion qualities of the ship hull.

Fuliscale data for the model

scale 1/30 were used for this comparison.

The total resistance-displacement coefficient (CTV) was

chosen to represent the resistance results, and the overall factor

of merit (FM) to represent the delivered power at propeller

The propeller efficiency in open water (no) is not included in FM,

and consequently one may assume the influence of the propeller

it-self to be nearly eliminated.

CTV and FM are presented graphically as

functions of the

above mentioned form parameters, for the following constant values

of the speed-displacement coefficient (Fg):

0.50, 0.55, 0.60, 0.65,

0.70, 0.75 and 0.80.

For the half load condition, also F

=0.85 is

nV

used.

As previously mentioned, service speed condition of the parent

ship (model scale 1/30) corresponds to F=O.663S.

Consequently

the F_va1ue 0.65 for full load condition is especially important,

concerning the comparison.

The discussion of FM and CTV has been performed parallelly

for each speed condition or group of speed conditions, even if FM is.

considered to be the most important quantity.

The possible

in-fluence of the form coefficients on the quantity

x nR) is then

more easy to discuss.

The values of (11H

>

are in a way an

expression of the working conditions of the propeller behind the

ship.

When (flu

X

decreases, the working conditions are assumed

to grow worse.

b.

Variation of L/B and B/T.

Contours of CTV and FM as functions of LDWL/B and B/T for

full load condition are shown in Figures 11 - 24, pages 94 - 107.

The influence of B/T on CTV and FM for LDTL/B-values less

than about 6.0, is not discussed, owing to the restrictions of use

which are mentioned in Appendix, section 3 a, page 83.

It is

difficult to define any general tendency for the B/T-influence

through the whole speed range.

Eut the influence is not great and

is mostly smallest for CTV.

Starting with the two smallest Fva1ues (Figures 11

-13-

F 4 b

smallest for the high values of LDL/T.

The tendency is, however,

that a minimum point for both CTV and FM exists at B/T of about

3.0.

If B/T decreases from this minimum point, the increase in

_CTV

and FM is a little larger than if B/T increases from the same point.

Furthermore the figures show that the influence is

great-est on FM, which means that the quantity

x

_{decreases both}

when B/T increases and decreases from the B/T-value 3.0.

The above mentioned tendencies of influence exist also for

the F

-value 0.65, and concerning F

,

for F

=0.60 in addition

M

nV

(Figures 16, 17 and 18)

.

The tendency is mostly stronger than in

Figures 11 - 14.

The exception is CTV for Fv=O.6O (Fig. 15)

.

For this

F7-va1ue1 CTV decreases for increasing B/T through the whole

B/T-range, except for LDWL/B-values in the neighbourhood of 6.1.

As previously mentioned, the contours for

_{F=0.65 are}

especially important.

In the corresponding figures (Figures 17 and

18) one may for instance take a closer look at the B/T-variation

_for

the LDWL/B-value 6.64 (the LDWL/B-value of the parent model)

.

A

variation of B/T with the value 0.2 (about 6.5

per cent) to each

side of the minimum point B/T=3.0, gives the following approximate

percentage increases in comparison to the minimum value:

CTV increases with 1.4 per cent on both sides of the minimum point.

The corresponding values for FM are i per cent for the variation

on the upper side of B/T=3.0 and 3 per cent on the lower.

Consequently the power increase is less if one increases B/T from

the minimum point value, than if one decreases it from

the same

value.

The mentioned tendencies at the

_{LDL/5-value of 6.64,}

become stronger for smaller values of

_L

_,T/B.

_{According to these}

D w

results, one may increase B/T to the value 3.2 without

any serious

increase of power, provided LDWL/B is greater than 6.1.

If the service speed is increased,

one really may save

power by increasinq B/T, according to the F\4-contours in Figures

20, 22 and 24.

_{The exceptions are LDWL/B-values in the}

neighbour-hood of 6.1.

For these L

/B-values

¡

F

is constant or slichtly

DWu

M

increasing if B/T is increased from 3.0 to 3.2.

_{The influence on}

Cri

(Figures 19, 21 and 23)

is far less, but for the Fn7_values

0.70 and 0.80, tne same tendency excists

_{as for}

-14-

F4b

the F

-values 0.70, 0.75 and 0.80 as it did for the F

-values

nV

nV

0.50, 0.55, 0.60 and 0.65, previously discussed.

The mentioned

quantity mostly decreases when B/T is decreased from the value 3.0.

And this tendency is moré clear for the contours which belong to the

F

-values 0.70, 0.75 and 0.80.

nV

At the end of the discussion concerning the B/T-influence

on CTV and FM of full load condition, one may draw the following

conclusion:

It is possible to increase B/T to greater values than that

of the parent model (B/T = 2.941) through almost the whole speed

range, without any serious power increase.

The restrictions of use which are mentioned above, concern

also the LDWL/B-variation.

Consequently the general discussion of

the LDWL/B-influence on CTV and FM concerns mainly the LDwL/B

range 6.0 to 7.2, except when the whole L/B-range

is mentioned.

The main tendency through the whole speed range is

in-creasing CTV and FM for dein-creasing LDWL/B.

The rate of increase of

TV

and FM is smaller for the L/B-range 6.5 - 7.0 than for LDWL/B_

values less than 6.5.

Furthermore the increase is mostly smaller at

B/T-values of about 3.0 than in the rest of the B/T-range.

As mentioned before, the contours which belong to FO.65

are especially important.

A closer look at the variation of LDWL/B

for the constant B/T-value 2.941 (the value of the parent model)

gives the following results:

If LDWL/B decreases from 7.0 to 5.8 (about 20 per cent

decrease), CTV increases about 15 per cent.

The corresponding value

of increase for F1 is about 16 per cent.

The increase is great, but

of about the same size for both quantities.

Consequently the

corresponding decrease of the quantity

x

is small.

The discussion of the LDWL/B-influence on CTV and FM for

full load condition may end with the following conclusion:

If one

wants to decrease LDWL/B, increased power is the consequence.

In

most of the cases, the rate of increase grows as LDWL/B vary from

greater values to smaller.

Contours of CTV for half load condition are given in

Figures 25 - 32, pages 108 - 115.

E/T and LD\7L/B of full load

condition are used in the figures.

The restrictions of B/T

-15-

F 4

and LDTL/B which are used for the discussion

of the contours for

full load condition,

are used for the half load condition also.

The influence of B/T on CTV is small through the whole

speed range.

For F-values greater than 0.60, CTV mainly

in-creases slightly if B/T dein-creases.

And the increase is greatest for

the highest values of LDWL/B.

The service speed (21 knots at model scale 1/30)

corre-sponds to F=0.7O4 for half load condition.

Consequently the

contours in Fig. 29 (Fv=0.7O) are especially important.

The

in-fluence of B/T on CTV is especially small.

For the B/T-range 2.94

to 3.2 CTV is approximately constant, except for LDWL/B-values in

the neighbourhood of 6.1.

The tendency of influence of LDWL/B on CTV is

approxi-mately the same as for full load condition.

Variation of longitudinal centre of buoyancy.

In Fig. 33, page 116, CTV and FM as functions of

_(LCB)LDWL

are shown for full load condition.

The influence of (LCB)LDWL

C

and FM is small.

The average variation of CTV and FM through the

_{(LCB)LDWL_}

range from 0.2 to 1.8 per cent of

is about 3 per cent.

_CTV

and FM mostly increase if the longitudinal centre of buoyancy

moves

towards the fore end of the ship.

For the greatest F-values.

CTV and FM are approximately

constant through the whole (LCB)-range.

A

corresponding diagram for half load condition is shown

in Fig. 34, page 117.

CTV is shown as function of the (LCB)LD7L

which belongs to full load condition.

The influence of (LCB)LDWL

on CTV for half load condition is smaller than the corresponding

influence on CTV for full load condition.

Variation of block coefficient.

-16-

F4d

of

E(LDWL)

in Fig. 35, page 118.

The increase of CTV and F

is

mostly great for increasing CB(LD) ,

if this form coefficient is

greater than 0.56.

The increase is greatest at the constant

values 0.75 and 0.80.

Minimum values of CT

and FM excist at CB(LDWL) of about

0.55 for the constant F

-values 0.55, 0.60 and 0.65.

The increase

nV

cf F1 is mostly greater than the corresponding increase of CTV.

Consequently the quantity

X

decreases if CB(LDWL) is

in-creasing for CB(LDL) values greater than 0.56.

A closer look at the CTV function for the constant

F-value 0.65, gives the following information:

If CB(LDWL)

in-creases from 0.55 to 0.59 (about 7 per cent increase),CTV inin-creases

about 13 per cent and FM about 24 per cent.

It is obvious that for the service speed condition (Fv

about 0.65), the choice of CB(LD7L) for the parent ship is correct.

A moderate decrease of CB(LDWL) will cause no noticeable decrease of

power, but an increase of CB(LDWL) will increase the power.

If the

service speed is increased to greater F_va1ues, one may save power

by decreasing the Cß(LDwL).

A corresponding diacram for half load condition is given

in Fig. 36, page 117.

CTV is shown as function of the CB(LDWL)

which belongs to full load condition.

As mentioned before, the CTV function for the constant

Fnv_value 0.70, is especially important concerning half load

con-dition.

Minimum values of CTV for service speed exist at a CB(LDwL)

value of about 0.55 both for half load condition and full load

con-dition.

For great increases of service speed, one will save power

by decreasing Cß(LDWL).

5.

Conclusions.

In the previous sections the influence of form coefficients

ori resistance and on delivered power at propeller were discussed on

l2ase of the test results, and some conclusions were made.

The influence of B/T is not oreat, but a B/T-value of

aaut 3.0

ives rinirurn values of propeller power for the speed range

ui

to the service steed.

-17-

F 5

The main tendency for the influence of LD,L/E is

in-creasing propeller power for dein-creasing LDlL/B.

And mostly the

in-crease of propeller power is great.

Variations of the longitudinal centre of buoyancy within

the tested range, cause only small variations of the propeller power,

and the variations are smallest for the highest speed values.

Increase of CB(LDWL) to greater values than about 0.56,

causes increased propeller power.

The increase is mostly great.

If

the speed is higher than the service speed, the same tendency exists

for values smaller than 0.56 also.

In particular, the power variations caused by changes of

the form coefficients of the parent ship, were examined.

The

following conclusions mainly concern service speed:

Great increase

of B/T is possible without serious increase of propeller

power.

But noticeable increases of block coefficient or decreases of

_LDWL/B

probably cause serious increases of propeller power.

_{The mentioned}

changes of the form coefficients of the parent ship are assumed to be

favourable for the cargo handling.

Concerning the results of the propeller loa

tests, some

conclusions may be drawn. The influence of propeller loa-9 on the

quantities wTI t and

is not great for these test series.

The

tendency is a small decrease of the mentioned quantities for

in-creasing propeller load.

The decrease vary a little through the

-18-G.

APPENDIX.

1.

Model Documentation.

a.

Tables and figures for the description of ships and ship models..,

Particulars for the models and ships:

Tables 1 - 2.

Comment:

In addition to the particulars for each model and

ship, the schemed nominal particulars are given.

Offsets of the models:

Tables 3 - 8.

Reference:

Fig. i page 4.

Comment:

Offsets are given in millimetres.

Offsets of the

models in test series i (variation of LDWL/B and B/T) are

given by means of the offsets of the parent model in Table

3 and the conversion coefficients in Table 8.

Conversion

coefficients times offsets of the parent model give offsets

of the particular model.

Propeller and rudder location on the ship models:

Table 9 and Fig. 5.

Reference:

Fig.l.

The propeller No. and propeller pitch ratio used on each ship

model:

Table 9.

Sectional area curves:

Fig. 6.

Comment:

For the test series 3

(variation of CB), the actual

distance between station O and station 20 (LDWL) is not equal

for all the models, and is reduced to different scales in

Fig. 6.

At the top of the sectional area curve of this series LDWL

of the models are given as fractions of

of the parent

model.

The sectional area curves of test series 1 are given in Fig.

1.

Also in this figure, different scales are used when

Test series Parent_form Series 1. Series 2. Series 3. Model No. 788 844 317 816 852 845 819 818 854 853 820 821 822 823 o o 0 C g ! !

LD/B

6.64 5.80 6.20 7.00 6.20 6.64 7.00 6.64 B/T 2.941 2.700 3.200 2.700 3.200 2.700 3.200 2.941 Im3) 0.7316 I(LCB)LD

1.000 per cent of

_{L0w1 from LD/2}

0.2000 1.8000 1.000

CB(LDWL) 0.560 0.585 0.535

L0 litan) 5533.3 5060.0 5286.6 5731.3 5136.7 5436.6 5378.7 5690.7 5573.3 5896.7 5533.3 5533.3 5453.4 5618.3

B (zum) 833.3 871.3 852.6 818.7 828.6 877.0 810.0 857.0 796.0 842.3 833.3 833.3 821.3 846.0

T (jmti) 283.3 296.3 290.0 278.3 307.0 274.0 300.0 267.8 294.6 263.3 283.3 283.3 279.2 287.6

Trim 0.0 per Cent of LDWL

;i (mm) 313.4 327.8 321.2 305.5 309.4 329.0 302.4 321.6 297.5 316.8 310.3 308.4 309.2 313.3 s Im2) 5.1894 4.9679 5.0802 5.2869 5.0051 5.1570 5.1233 5.2803 5.2189 5.3730 5.1830 5.1987 5.1455 5.2585 y (m3) 0.7312 0.7312 0.7316 0.7324 0.7307 0.7305 0.7328 0.7321 0.7320 0.7317 0.7308 0.7322 0.7313 0.7325

LD/B

6.6400 5.8072 6.2002 7.0001 6.1987 6.1992 6.6403 6.6400 7.0017 7.0004 6.6400 6.6400 6.6400 6.6410 B/T 2.9410 2.9404 2.9402 2.9413 2.6992 3.2007 2.7000 3.2002 2.7014 3.1987 2.9410 2.9410 2.9416 2.9416 CB)LDWL) 0.5598 0.5597 0.5597 0.5609 0.5592 0.5592 0.5607 0.5605 0.5601 0.5595 0.5594 0.5605 0.5848 0.5358 Cp(LDWL) 0.5771 0.5770 0.5767 0.5778 0.5769 0.5769 0.5781 0.5776 0.5776 0.5770 0.5767 0.5778 0.6031 0.5522 (LCB) per LDWL cent 0.9961 0.9969 1.0070 0.9952 0.9925 0.9901 1.0101 0.9904 0.9857 0.9930 0.2107 1.7966 1.0030 0.9978 C 0.9700 0.9700 0.9706 0.9707 0.9693 0.9694 0.9699 0.9704 0.9697 0.9696 0.9700 0.9700 0.9697 0.9703 6.3938 6.1209 6.2572 6.5069 6.1697 6.3578 6.3033 6.5004 6.4254 6.6171 6.3882 6.3994 6.3393 6.4713

L/B

6.4002 5.6136 5.9851 6.7403 5.9894 5.9783 6.4060 6.3947 6.7471 6.7348 6.4002 6.4002 6.4029 6.3980 CB)Lpp) 0.5808 0.5791 0.5798 0.5825 0.5788 0.5798 0.5812 0.5821 0.5812 0.5816 0.5804 0.5815 0.6065 0.5562 Cp(Lpp) 0.5988 0.5970 0.5974 0.6001 0.5971 0.5981 0.5992 0.5999 0.5994 0.5998 0.5984 0.5994 0.6254 0.5732 (LCB)_LPP per cent -0.842 -0.695 -0.757 -0.896 -0.725 -0.820 -0.782 -0.891 -0.863 -0.942 -1.656 -0.011 -0.811 -0.864 0.6626 0.6624 0.6624 0.6627 0.6626 0.6629 0.6630 0.6632 0.6627 0.6625 0.6584 0.6663 0.6836 0.6418 (mm) 5333.3 4891.1 5102.9 5518.3 4962.8 5243.0 5188.9 5480.3 5370.7 5672.7 5333.3 5333.3 5258.7 5412.7 o -'0 LL (mm) 5111.8 4674.5 4884.0 5294.0 4745.0 5022.5 4964.8 5257.0 5148.0 5447.0 5111.8 5111.8 5036.0 5188.8 B (mm) 833.3 871.3 852.6 818.7 828.6 877.0 810.0 857.0 796.0 842.3 833.3 833.3 821.3 846.0 T (mm) 207.6 217.1 212.7 203.6 224.9 200.8 219.6 196.1 215.8 192.8 207.4 207.4 204.5 210.6

Trim 1.000 per cent of

S (is2) 4.2140 4.0337 4.1213 4.2852 4.0394 4.2145 4.1309 4.3068 4.2134 4.3869 4.2121 4.2120 4.2068 4.2300 V (mi) 0.5118 0.5127 0.5127 0.5107 0.5122 0.5125 0.5117 0.5117 0.5124 0.5120 0.5138 0.5112 0.5133 0.5113 B/T 4.0140 4.0134 4.0085 4.0211 3.6843 4.3675 3.6885 4.3702 3.6886 4.3688 4.0178 4.0178 4.0161 4.0171 0.5788 0.5798 0.5789 0.5787 0.5793 0.5794 0.5794 0.5792 0.5794 0.5788 0.5816 0.5786 0.6069 0.5531 Cp)LWL) 0.6052 0.6066 0.6058 0.6051 0.6057 0.6064 0.6063 0.6062 0.6058 0.6053 0.6082 0.6050 0.6350 0.5781 )LCB)LwL 0.4470 0.6280 0.5040 0.4310 0.6440 0.4360 0.5526 0.3374 0.5150 0.2610 -0.378 1.2767 0.4050 0.5772 0.9563 0.9558 0.9556 0.9564 0.9564 0.9555 0.9557 0.9555 0.9564 0.9562 0.9563 0.9563 0.9558 0.9568 6.5860 6.2970 6.4337 6.7070 6.3100 6.5810 6.4570 6.7320 6.5800 6.8545 6.5652 6.5882 6.5620 6.6153 CB(Lpp) 0.5547 0.5542 0.5540 0.5552 0.5538 0.5551 0.5544 0.5556 0.5554 0.5558 0.5574 0.5546 0.5812 0.5302 Cp)Lpp) 0.5800 0.5798 0.5797 0.5805 0.5790 0.5810 0.5801 0.5815 0.5807 0.5813 0.5829 0.5799 0.6081 0.5541 )LCB)pp t -1.411 -1.077 -1.278 -1.482 -1.086 -1.394 -1.449 -1.569 -1.352 -1.703 -2.267 -0.551 -1.431 -1.300

-19-

Gla