The SSPA cargo liner resistance

ME DDE LANDEN FRAN

STATEN S SKEPPSPROVNINGS AN STALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)

Nr 66 GÖTEBORG 1969

THE SSPA CARGO LINER SERIES

RESISTANCE

BY

AKE WILLIAMS

LS

_'A

SCANDINAVIAN UNIVERSITY BOOKS AKADEMJFÖRLAGET-GUMPERTS GÖTEBORG

SCANDINAVIAN UNIVERSITY BOOKS

Dennwrlc: MUNKSOAARD, Copenhagen Norway: UeIVBSITETSFORLAOET, Oslo, Bergen Sweden: AKADMIFÖRLAGET-QUMPsBIs, Göteborg SVENSEA BOK'ÖRLAGET/NorStedts Bonniers, Stockholm

PRINTED IN SWEDEN DY ELANDERS BOXTRYCRERI AKTIEBOLAG 19S

Preface

In the present report results are given from a survey and reanalysis of resistance data given for cargo liners systematically tested at the Swedish State Shipbuilding Experimental Tank (SSPA). The initial model tests were carried out by H. F. NORDSTRÖM and published in 1948-1950. Most of the investigation work, however, was carried out

in the fifties by H. EDSTRAND, E. FREIMANIS and H. LINDGREN and

reported in a number of publications from SSPA.

The reason for a new preparation of the model test results is two-fold; the need of a more actual presentation of non-dimensional re-sistance data and the demands for handy-sized dimensional diagrams useful at the preliminary stages of ship design.

In a following report a similar work will be presented regarding propulsion data for the SSPA Cargo Liner Series.

1. Summary

As an introduction the serial tests for cargo liners at SSPA are reviewed. Attention is given to the selection of results suitable for further analysis. Also the choice of representative hull forms from the series is discussed. Fore/afterbody sections of "Moderate U" character are designated "standard forms".

Regarding single hull form parameters the series includes block coefficients from 0.525 to 0.75 and length/breadth ratios from 6.18 to 8.35 with a standard breadth/draft of 2.4.

The non-dimensional presentation follows the recommendations of the International Towing Tank Conference (ITTC) 1957, i.e. all fric-tional data are given on basis of Reynolds number. Conversion to effective power (EHP) for the actual ship size is performed by use of "ITTC 1957 model-ship correlation line". The dimensional

presen-tation of resistance data includes EHP as function of the ship's

speed, length, breadth, displacement, etc., all in metric units.

The standard hull forms of the series can be approximated by

mathematically defined forms, which is shown in Appendix 1. The use of analogue computer for easy derivation and drafting ofarbitrary hull forms within the actual series is exemplified in Appendix 2.

2. Introduction

It can be generally pointed out that systematic investigations of

the resistance and propulsive properties of standardized hull forms

meet the following three desires:

Simplification of the shipyard's and shipowner's first design work regarding the ship's hull.

Preliminary predictions of speed and power. Also indications of the influence upon speed and power from small deviations in main

dimensions and fullness.

Possibilities to analyse model test results for other hull forms (Is the actual hull form favourable or not and why?).

Therefore it comes quite natural that model testing institutions are performing, on behalf of their customers, serial tests for resistance and propulsion.

The first results from systematical tests connected to the present

cargo liner series were reported by NORDSTRÖM [1].') These results

are not used here as the investigated hull form

(block coefficient

0.625) was later redesigned. However, that special work is mentioned here because the way of planning, performance and utilization of the tests was guiding for the subsequent serial tests.

The earliest test results to be used in the present account are

extracted from an investigation by EDSTRAND and LINDGREN [2] concerning ship forms with a block coefficient of 0.525. Another extensive investigation has been carried out for block coefficient

0.675 by FREIMANIS and LINDGEEN [3]. Other publications by these

authors for the same hull fullness comprise hull forms differing from standard regarding fore- and afterbody sections, location of centre of buoyancy and breadth/draft ratio.

Only hull forms with standard sections ("Moderate U"), standard LCB (see Table i further on) and standard breadth/draft (=2.4) are included in the present account. Some non-dimensional data, how-ever, are given for other breadth/draft ratios (see Fig. 35 further on).

6

A "cross-over" test series including hull forms of block coefficients from 0.60 to 0.75 at constant length/breadth ratio was investigated also by FREIMANIS and LINDGREN [4]. Remaining data for other length/breadth ratios at block coefficients 0.625 and 0.725 as well as

all data for block coefficient 0.575 appear for the first time in the present report.

A plan of actual ship models is given as Fig. 1. In Table i the

geometrical data are assembled.

Table 1. Geometrical data for ship i,iocieis. Ship model No. Block coeff. 8,,.,, Length/displ. Length/breadth ratio ratio

L/"

LIB LCB in rei. to L/2 % SSPA publication No. 881 0.525 5.63 6.18 -2.00

-631 0.525 5.95 6.70 -2.00 38 632 0.525 6.26 7.24 -2.00 38 633 0.525 6.57 7.79 -2.00 38 634 0.525 6.89 8.35 -2.00 38 882 0.575 5.47 6.18 -1.85

-883 0.575 6.07 7.24 -1.85

-884 0.575 6.68 8.35 -1.85

-835 0.600 5.99 7.24 -1.70 44 857 0.625 5.32 6.18 -1.50

-858 0.625 5.61 6.70 -1.50

-833 0.625 5.91 7.24 -1.50 44 859 0.625 6.20 7.79 -1.50

-860 0.625 6.50 8.35 -1.50

-795 0.650 5.83 7.24 -1.25 44 809 0.675 5.18 6.18 -0.75 42 810 0.675 5.47 6.70 -0.75 42 720 0.675 5.76 7.24 _-0.75 42 811 0.675 6.05 7.79 -0.75 42 862 0.675 6.33 8.35 -0.75

-796 0.700 5.69 7.24 -0.10 44 846 0.725 5.06 6.18 +0.45

-847 0.725 5.34 6.70 _+0.45

-799 0.725 5.62 7.24 +0.45 44 848 0.725 5.90 7.79 +0.45

-861 0.725 6.18 8.35 +0.45

-834 0.750 5.56 7.24 +0.85 44

3. The hull forms tested

The parent hull form of block coefficient 0.675 represents, by its character and ratios of dimensions, the medium speed cargo liner of

about 10,000 tons d.w., a predominant type of dry cargo vessel

during the forties and fifties. Also to-day a number of ships are built

having these dimensions and fullness, mostly for general dry cargo

service on non-express routes where conventional cargo handling still

is used.

Other hull forms of the present series are derived from the parent mainly by use of the well-known "one minus prismatic method"

described in ref. [4].

Most of the modern dry cargo ships are now built with block coeffi-cients lower than the actual standard. Despite the fact that the cor-responding serial hull forms of such low fullness were designed many years ago they are still used frequently. A great number of newly delivered high speed cargo liners, refrigerated vessels and container

ships show up hull lines as well as resistance and propulsive properties

very similar to data presented in this report. In [5] some characteris-tics of a large modern container ship (block coefficient about 0.60, moderate speed/length ratio) are compared with a similar ship inter-polated from the present series. The agreement regarding resistance

qualities is very close.

The hull forms of the actual series are presented in detail in the referred publications from SSPA. As a survey, however, contours and body plans for block coefficients 0.525-0.725 are outlined in Figs. 2-7. The form variation method mentioned above is strictly used for the block coefficient interval 0.625-0.750. An extension of the varia-tion principles to lower fullness would mean a virtually negative parallel middle body because this is equal to zero for block coefficient 0.625. Also a maintenance of the moderate U-character in the ver-tical sections for the lowest fullness is not pracver-tically justified. There-fore the hull forms of block coefficient 0.60, 0.575 and 0.525 have been given an increasing V-character in the sections as well as lower

midship section coefficients.

General points of view regarding mathematical definition and variation of hull forms are given in Appendix 1.

6 L WL o _AP Mod. No. c5 835 a600 833 Q25 795 Q650 720 0.ô75 796 0.700 799 Q725 834. 0750

Fig. 2. Stem and stern contours.

s 4AJ 6. a000 2 :: 3% 20

8,/I-

w'

.1/

/1/f L WL pp /8 'g

LI

hifi äiA

WIEMMIII

IiIiiIIIL

I_'1IIIM1hi

_{__%IIIIIENII}

lÍI_

Fig. 3. Body plan 8,,=O525

---II--III

¡ii___

VIif,,,IIi

iktIIWffß

Itw

__IIIII

-'--I'll

_1111111111

wawIsIhiJ

KLS

Fig. 5. Body plan _=O62S

I

6111

-_Iii

Fig. 6. Body plan =O.675.

3

-Ii'

N___liii

liii

LL_

hIN_hl

11W__11111

w

Muli

-_

-

1111:

IlL

-__

_Ir:

12

Fig. 7. Body plan 3=O725

111cv;

116

____I.

__

IL___

113

il

I,x

4. Construction of ship models and resistance test procedure

All ship models in the actual series were manufactured in paraffin wax. The length of the models varied from 5.4 to 6.6 meters. For securing of turbulent flow along the hull surface a tripwire of 1 mm diameter was attached around station 19 of each model.

The tests were carried out as normal resistance tests in calm

water in the SSPA towing tank of the dimensions 240 meters length, 10 meters breadth and 5 meters depth of water.

Extrapolation of model resistance data up to any ship size is per-formed by use of the ITTC 1957 ship-model correlation line.

0.075 CF

- ('°log RN- 2)2

where

CF = frictional resistance coefficient RN = Reynolds number

The frictional resistance RF (kilopond) is derived from RF= CF l/2p8 V2

where

p =water density in kps2/m4 (102 for fresh water, 104.5 for sea

water)

S=wetted surface in m2 V=speed in rn/s

To obtain the ship effective power a standard frictional allowance

zJC (due to roughness, etc.) of 0.0004 is used. Similar to the

fric-tional resistance the residuary resistance coefficient CR is defined as RR

CR

_1/2pSV2

and is considered to be the same for model and ship. Thus the total resistance coefficient CT for the ship can be expressed as

14

and finally the ship effective power _E is calculated from

R C1/2p(O.5144 V)2S1O

0.5144 10

VSRT 75

where

Rrzrrtotal resistance in megapond V = ship speed in knots

5. Test results in non-dimensional form

The residuary resistance coefficient 0R is a convenient basic figure for a following calculation of the effective power for ships of different size. The commonly used admirality constant has a dependance of the ship length and is therefore not considered here.

Accordingly, the first part of the non-dimensional presentation of the resistance data includes a set of sheets with residuary resistance as function of Froude number, Figs. 8-17.

Due to wave interference phenomena the wave resistance will be locally increased or reduced. As the wave resistance is a predominant component of the residuary resistance, the occurrence of the corre-sponding "humps and hollows" is clearly visible in the present CR-curves. A study of the diagrams, Figs. 8-17, makes it evident that there are three narrow intervals of relative speed where the actual resistance differ from an "even curve", i.e. the approximating expo-nential function valid for the total speed interval.

The first interference phenomenon within the investigated speed range, the "ist hump", occurs around Froude number=0.20 and is relatively weak. The increase of the total resistance is of the order i-2%. The occurranee is somewhat dependent of hull fullness, FNL= 0.18 for block coefficient 0.70 and 0.21 for block coefficient 0.55.

In a speed interval corresponding to FNL=O.22-O.25 a "hollow" in the resistance curves is visible, especially for block coefficients 0.60-0.65. On the presumption that increase and decrease in resistance due to these interference phenomena are of the same order, the effect of the actual hollow upon the total resistance is up to 5%.

The "2nd hump" appears at Froude numbers around 0.29. As it is near the end of the considered speed range the strength of the

interference can be estimated only with difficulty. Even the definition of the resistance augmentation can be discussed. However, for the lowest block coefficients the expression hump may be justified and the local effect is 2-5% upon the total resistance. In Table 2 a review is given of the interference phenomena and also of the influence from hull fullness and length/displacement ratio.

.5-0.20 .25

7V

2.0 1 .5 1.0

05

CR I I I O 20 5

2.0

I.o

9Q _{C. 25 Ü3O -F}

o :1

i

w o w -I

2.G

i

_'-'---

_z

Fig. 16. Residuary resistance as function of Froude numberfor =O.725.

-25

o

Fig. 17. Residuary resistatico as function of Froude number for

26

Table. 2. "Humps and hollows" due to wave interference.

1) _{Wave interference strong but can not be estimated regarding location and}

max. strength.

In order to facilitate the derivation of residuary resistance for an arbitrary hull form of specified fullness and length! displacement ratio diagrams like Figs. 18-30 have been drawn. Residuary resistance is here given as function of fullness at constant relative speed and with

parametric values for length/displacement. Auxiliary diagrams making

it easier to carry out a following calculation of effective power are given in Figs. 31-35. It should be noted, however, that data given for wetted surface and influence from varied breadth are valid only for the present standard hull forms.

Block coeff. 3pp Length/ dispi. ratio LA1''

ist hump Hollow 2nd hump

Freude number NL Change of eff. power APE Froude number NL Change of eff. power APE Froude number NL Change of eff. power APE 0.55 7 0.21 +1% 0.25

-i%

0.29 +2% 0.55 6 0.21 +1% 0.25 -1% 0.29 +2% 0.55 5 0.21 +1% 0.25 -2% 0.29 _±3% 0.60 7 0.20 ±2% 0.25 -3% _{0.29 +4%} 0.60 6 0.20 _+2% 0.25 -4% 0.29 _+5% 0.60 5 0.20 +2% 0.25 -5% 1) 1) 0.65 6 0.19 _+2% 0.24 -3% 0.29 _+5% 0.65 5 0.19 +2% 0.24 -4% 1) 1) 0.70 6 0.18 ±1% 0.22

-"°'

_-/0 1) 1) 0.70 5 0.18 _±1% 0.22 -°-' ¡o 1) 3)

0.5

-O rn,

Fig. 22. Residuary resistance as function of fullness at Froude nurnber=O.22.

o j

5

i

O,T

2.5 2.0

í.5F

0.5 024 0Go 0.70

o=Tq1unu Op11O.IT SF1TJ[flJ JO IIOTDUflJ Sil il)itfl1SOi .TilflpST

0.5

/' /

1

/

V / / / /

//

////

L/.//5

/1 / / / //

/

--

_{/ / /7 / // /}

/1 I I 0.50 0.60 0.70

Fig. 6. Residuary resistance as function of fullness at Fronde number=O.26.

0,26 1

0.50 o.6o

Fig. 28. Residuary resistance as function of fullness at Froude number=O.28.

u

r

i I i t

O5

I I I

C.5Q o6o 07Ü

5f44. y

\ \\

V

'\

\\

\

\\

\\

htp epied iu knots N

N \

\\

g aco. or gravity (9.1

/2)

WL lath of N,

\\\\\

\\ \\

NN

N

\\\N\\

\\NNN*

2

\ \

\\

\

\

_N

_'N

N

_N

\ 'N\ N

N

N

N N 'N N N

N

N _N

N

_N N_{N N} N N N NN, c t s \\ , N, " N ' N "N N NN N 22

'\\\

N N

NSNN

N

N. ' N, X 'N N, N 'N, N N N 'N 'N "N N N 'N

'N

'",

N N _N 'N N 'N. N N N'N 'N N

_N

N,

N

N, N,,

N

N,

_"N

Fig. 31. Froude number as function of ship length and speed.

1 200 T,.,

k 2. O5O k V i :

vetted surface inc1 rudder area

'ç isp1aosient a3 length p a / T 06G

-e

-

e-4.5

-0.70

-

-1

600

100 150 200

i _{I I}

Fig. 34. The value of for different ship lengths and displacements.

V ni 5000 20000 -. i50X 10000 5000

10LCR 103CR 0.60 ( -B/T. 5 050 4

4_-_

-. 5.0

o.a)(B/ 2.4

2.5 2.0

---I i I 0.60 0.70

6. Dimensional presentation of effective power

The hull dimensions of SSPA Cargo Liner Series cover practically all ships of small and medium fullness and with displacements from 5000 to 25,000 m3. Owing to the size and fullness range the actual speed interval is 12-22 knots. Corresponding ship lengths are from 80 to 200 meters.

It seems important that the results from a systematical investiga-tion like this are made available also as handy-sized survey diagrams.

In this case it is desirable to provide an easy read-off of effective power

on basis of single geometrical coefficients, main dimensions and dis-placement in suitable units. An attempt to satisfy these demands is made in the diagrams, Figs. 36-55. Contours of effective power in metr. HP are given for varied length and displacement at constant speed, fullness and standard breadth/draft ratio (= 2.4). Wave inter-ference phenomena according to Table 2 are also indicated in these diagrams. Humps and hollows supposed to have an influence less than 2% of the total resistance are excluded.

ooe

L

15O

2 oce ooe lo ç)oo-. eoo

/ /./

,f I' p_E 200

25 u0 0 000 9o&

/

;

/:

//

B22

/

loo 5.0 5.4 5.6 6.2 7.0 400Q 4

5 eoo 10 000 5000 J= 22 !:' j / / IJ0 5.0 .4 6.2 .6 7.0 TiÓ110 1 50 WV 500 I I t 200

25$OO

-- 2G O6 15 OOÓ O55 r 20 5.0 5.8 .2 ¿.6 7.0

I.

I:

L 25 000

r

20 000

5 £0()

-5 ooe L

32

- 0.55 22 kn 5.0 5..4

5j

6.2 6,6 o 2nd. itimp

Fig. 41. Contours of effective power in HP (metr.), V=22 knots.

i 50

r 20 000 15 O0 10 000

5 o

r

-V.

2 biop 5.0 5.4 5.6 6.2 *,.6 7.0 1. J

/

JI

/

i

i

/

1/

/

,/_.

,/

;/

,11 i /1

/

I6CO 150 200 J

i

I I I

150 200

Fig. 44. Contours of effective power in HP (metr.), =O.6O, V= 16 knots.

Hollow nuwp

H25 ØO

no.60

V-20

lcnop

5.O 5.4 5.8 6.2 6.6 7.0

.1!.

Fig.46. Contours of effective power in HP (metr.), =O.6O, V=20 knots.

'SPA

I _I

1Óo _{150 200}

Fig. 47. Contours of effective power in HP (metr.), ,=OGO, V=22 knots.

1 OO 000 32O ri 14 Ist hu loo 5o 200

Fig. 48. Contours of effective power in HP (nietr.), 0.65, V= 12 knots.

5óS

62

2& 00 15 CrÙ t0 000 4 100 : huer 200

COG 15 OOG 5.0 5.4 5.B 6.2 6.6 7.0

15ì

P,, hc I 150

Eallow

ao 150 20

r

5 tXiO

B1i

.8 .2I1E6

Ìpr7

Fig. 54. Contours of effective power in HP (metr.), 8=O7O V=16 knots.

t I I

900

7. Acknowledgement

The author is indebted to Dr. HANS EDSTRAND, Director of the

Swedish

State

Shipbuilding

Experimental

T a n k, for his valuable advice and for the encouragement he has given the work Thanks are also due to the staff of the Tank, specially to Mr. L. G. JONSSON and Mr. H. OLoFssoN, for their important

Appendix 1. Mathematical representation of parent

and derived forms

The present series of ship hull forms was designed before the

proce-dures for defining ship lines analytically were used more commonly. It may therefore be interesting to investigate if the actual hull forms can be "reconstructed" by use of mathematical methods.

In order to keep a strict definition of the hull shape, it is necessary to introduce form parameters affecting the entire surface of the ship. Regarding waterline sections these may be defined by the first and second derivatives at begin and end of entrance (run), and also by

the area, which secures the over-all coincidence. These waterline

para-meters faired in the vertical direction make the draft funetions used in the SSPA method for mathematical ship lines [6].

As an example, the method is applied to the forebodies of the serial hull forms with block coefficients 0.675-0.75. The draft functions of ist order, stem contours and boundary lines between the entrance and the cylindrical midship, are shown in Fig. 56. In the present case the shape of the waterlines is then governed only by the waterline area and ist and 2nd derivatives at the stem, see Fig. 57.

Starting from the established draft functions for the parent fore-body the approximating mathematical form can be drawn using the method mentioned above. The result of such a calculation is shown in Fig. 58, the small differences between the original and mathemat-ical form are without influence upon hydrodynammathemat-ical qualities.

The use of draft functions as a "reduced" hull form makes it pos-sible to carry out systematical variations without such restrictions involved in e.g. the one minus prismatic method. It would be possible to design a strictly systematical series of hull forms where the outer forms, each favourable with regard to its fullness, have quite different characters. The well-known disadvantage, more or less serious, of the one minus prismatic method is that the outer forms of the series are given, once the parent form is established.

Studies have been performed at SSPA regarding a more

non-conditional method for creating series of ship forms [7]. Thereby the one minus prismatic method appears as a special case.

Fig. 56. SSPA Cargo Liners ,=O67SO7S Forebody draft functions of ist order.

Stem contours and boundary lines between entrance and cylindrical body.

- - - - Boundary line at side.

VI_10

,t1OCWL

Fig. 57. SSPA Cargo Liners a=O.675O.75. Forebody draft functions of 2nd

order.

AWF

=forobody waterline area.

(2ly/d).

=

i st derivative of waterline at stein.

(d2y/dx2)_== 2nd derivative of waterline at stem.

9 8 7 6 5 4 3 2 Vb b BL AWF im2)

I

I

II

2a derivata (d2y!dx2 for La derivata (dyldx), for Vattenlinjearea AWF 6.. oBiS 5 750 1BQ 200 6pp 675 . ..o .67 7.. 725

Nil

.'

1!

1(1

9 B 7 6 5 4 3 _Vb BL 5ó0 7ò0 8ôO o. i .10 (dyIdx&x o 001 0:02 (d2y1dx2)5,ml)

70

U1pu.,ghgø (rnj.r

Fig. 58. Pa ent forebocly sections. Original and mathematical hull form. - - - - Matheniatical lines.

Appendix 2. Derivation and drafting of serial hull

forms by analogue computer

In the preliminary stage of ship hull design it may be useful to draw up, in a simple way, some alternatives of hull lines from a stand-ard series. Starting from fixed main dimensions a number of prelim-inary lines drawings can he worked out with varied fullness in order to study e.g. the influence of hull form upon general arrangement, stability, etc. For rapid work an analogue computer with a connected tracing machine is most valuable. Operating procedures for this object have been worked out at SSPA [8].

Having defined the actual cargo liner series as a set of draft func-tions tlìe derivation of an intermediate hull form means an interpola-tion among the draft funcinterpola-tions. The input data to the analogue com-puter consist of the waterline geometrical parameters, mentioned in Appendix 1, derived from the interpolated draft functions. Setting of parameters are easily performed by use of the push-button operated potentiometers of the analogue computer, which also provides digital

control of entrance data.

The output signal transmitted to the drawing machine represents the waterline polynomial which can then be traced directly. In this

case there are no complications in form of required transformations to basic curve elements as when the ship lines are traced by digital

methods.

To illustrate the design method forebody waterlines and sections of block coefficients 0.67 and 0.68 (referred to the entire ship) are traced by the EAI-VARIPLOTTER connected to the SSPA

analo-gue computer system, Figs. 59-62. The waterline drawings are

pre-sented in that very shape they leave the computer, whereas in the drawings of transverse sections, Figs. 61 and 62, the sectional lines have been drawn manually on basis of half-breadth offsets plotted by the computer. The offsets are visible as small dots in the drawings. A complete drafting of transverse sections as well can be realized by use of additional components such as analogue/digital (A/D)

con-72

verters and a digital memory unit. The application of such a "hybrid computer" have been studied at SSPA. During the computation pro-cess (and the simultaneous drafting of waterlines) the hull coordinates are stored digitally via the A/D converter. By a separate procedure the memorized coordinates can be rearranged so that a following reading of the memory will give consecutive ordinates for the trans-verse sections. After a second passing through the AID converter the analogue computer is ready to trace all required transverse sections. The further development of these routines is the object for future research work at SSPA.

o o 'o ,'

¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿

I'ig. 59. Forebody waterlines S,,,=O.67 traced by EAI-VARIPLOTTER.

C) X

Fig. 60. Forebody waterlines 8=O.68 traced by EAT-VARIPLOTTER. n u' ej n o o o o o o o ¿ d o

4.) N N N o t" ('J o

Fig. 61. Forebody sections 0.67. Ha1f-breadth offsets by EAI.VARIPLOTTER.

N

N

76

-

'I '.0 .\ ,-,

O.

O ¿ N ¿

Fig. 62. Forebody sectous Half-breadth offsets by EAI-VARIPLOTTER.

C-'.0

o

o o o

References

NORDSTROM, H. F.: "Some Systematic Tests with Models of Fast Cargo Vessels", SSPA Publication lO, 1948.

EDSTRAND, H., LINDaREN, H.: "Systematic Tests with Models of Ships with S,,1,_O.525", SSPA Publication 38, 1956.

FREIMANIS, E., LINDaREN, H.: "Systematic Tests with Ship Models with 3=O.675,

Part III", SISPA Publication 42, 1958.

{4] FREIMkNIS, E., LINDaREN, H.: "Systematic Tests with Ship Models with

0.600-0.750", SSPA Publication 44, 1959.

EDSTRAND, H., WILLIAMS, A.: Discussion on "The First O.C.L. Container Ships" by M. Meek, Paper No. 1, RINA Spring Meeting, 1969.

WILLIAMS, A.: "Mathematical Representation of Ordinary Ship Forms", SSPA

Publication 55, 1964.

J0BuD, S.: "Mathematically Defined Hull Forms in Systematical Series", SSPA

General Report 25, 1967 (in Swedish).

[S] WILLIAMS, A.: "Future Design of Ship Lines by Use of Analogue and Digital Com-puters", SSPA Publication 59, 1966.

Contents

Preface ₃

Summary ₄

Introduction 5

The hull forms tested 8

Construction of ship models and resistance test procedure 13

Test results in non-dimensional form 15

Dimensional presentation of effective power 45

Acknowledgement 66

Appendix 1. Mathematical representation of parent and derived

forms 67

Appendix 2. Derivation and drafting of serial hull forms by

anal-ogue computer 71