Systematic tests with ship models with δpp = 0.675 - Part I: Influence of shape of sections. Part II: Influence of shape waterlines. Part II: Influence of main dimensions and centre of buoyancy

MEDDELANDEN

FRAN

STAThNS SKEPPSPROVNINOSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SUIPBUILDINO EXPERIMENTAL TANK)

Nr 39 QOTEBORO ₁₉₅₇

SYSTEMATIC TESTS

WITH SHIP MODELS WITH

= 0.675

PART I: INFLUENCE OF SH4PE OF SECTIONS

BY

E. FREIMANIS AND _{HANS LINDUREN}

GUMPERTS FORLAG

GUTEBORO 1957

1. Introduction

A large number of systematic model expe

out at the Swedish State Ship

mental Tank during recent years. Va

of conventional form and others of more or

thus been studied systematically and their

been analysed.

The majority of this work has been devo

ships (with block coefficients of 0.625 and le

On the other hand, the large group of carg tons deadweight with block coefficients

hitherto been the subject of a comprehensive

at this tank.

The authors have accordingly planned an

for the purpose of filling this gap in our e

gramme comprises a detailed investigation

and the waterline form most suitable fro of view, and also experiments designed t

influences of fullness, position of L. C. B.

the propulsive qualities of cargo ships wi

about 0.675.

The first part of the above programme investigation of the most suitable shape of completed and the experimental results are For the experiments in question, four fb body models, with sections varyiig in for Extreme U, were made. Each fore-body h each of the after-bodies in turn so that a to

combinations have been tested.

All the model-scale experimental results

the scale of a ship having a displacement speed, fully loaded, of 16-16.5 knots. TI

have also been expressed in dimensionless for

can readily be derived for ships of similai

ments have been carried

uilding

Experi-ous types of ship, some less extreme form, have ropulsive qualities have ed to fine-formed cargo s), tankers and coasters.

ships of 5,000-10,000 about 0.675 has not

systematic investigation xperimental programme

pirical data. The pro-f the shape opro-f sections the propulsion 'point evaluate the separate nd main dimensions on h block coefficients of which consists of an

sections, has now been

given in this report. e-body and four

after-from 'Extreme V to s been combined with

al of 16 different model

ave been converted to f 9750 in3 and a trial e experimental results

as so that power curves.

4

displacement. In the case of one of the model versions, a calculation

of this type has been carried out on the basis of a displacement of

4992 m3. Self -propulsion tests in which the applied friction correction

corresponded to this displacement, have also been carried out with

this model.

2. Symbols, Units and Methods of CalculatiOn

The symbols have been chosen in accordance with the nomenclature adopted by

the Sixth International Conference of Ship Tank

Superin-t e n d e n Superin-t a as a Superin-tenSuperin-taSuperin-tive sSuperin-tandard.

Ship Dimensions

L length on waterline

Lpp = length between pependiculars

B = breadth on waterline T = draught

AM = immersed midship section area

Aw = load waterline area

S wetted surface area V = volumetric displacement

A = weight displacement; Br. tons in sea water

= distance of L. C. B. forward of midships (Lpp/2) 1/2 CE = half angle of entrance on LWL

1/2 = half angle at station 0 on LWL Propeller Dimensions

D = propeller diameter

P = propeller pitch

I 'cDt A0 = propeller disc area

=

---= developed blade area = blade width at 0.7 D12

Kinematic and Dynamic Symbols and Ratios

V = speed

VE = speed of advance

R = resistance T propeller thrust

Q = propeller torque

a = rate of revolution (revs, per unit time)

= effective power

V - VE

w = - wake fraction (TAYLOR)

V

TR

£ = - thrust deduction factor

T -.

((102.0kg sec.2/m' for fre water)

= density of water

- 1 (104.5. kg sec.2/m4 for sea water) v = kinematic viscosity of water

C1 = P' V3/PE (m3, Metr. knots and HP)

= 427.1 _{4213 1,73} (Br. HP, tons and knots)

-C. = V' V3/P8 (m3, Metr. knots and HP)

= 427.1 (Br. HP, tons and knots)

4213 V3

F5

= vi

= Fioiios number, displacement

= vi 1Ii = FROtFDE number, length

v/i/i = speed-length ratio (knots, feet)

1

B5 = - REYNOLDS number f r propellers

3,

Coefficients and Ratios.

= block coefficients

= load waterline coefficient

LB

= midship section coefficient

= prismatic coefficients (horizo. tal)

= prismatic coefficient (vertical)

= length-breadth ratio a app L B V LBT V Lp B T

_I

AM L V AM Lpp Aw T I. 5 AM BT V

6 B = breadth-draught ratio L - = length-displacement ratio = L. C. B. forward of Lpp/2 as % of Lpp = pitch ratio

= disc area ratio

J7i13 Lpp P D AD A0 = --- = propulsive efficiency 1 ?1ff

'w

hull efficiency

Units and Conversion Factors

1 metre = 3.281 ft. (recipr; 0.3048)

1 metric ton = 1000 kg 0.984 British tofls (recipr. 1.016)

1 metric knot = 1852 rn/hour = 0.999 British knots (recipr. 1.001)

1 metric HP = 75 m kg/sec. = 0.986 British HP (recipr. 1.014)

For g (acceleration due to gravity) the value 9.81 rn/sOc.2 has been used.

Methods of CalcuLation

The model-scale results from the resistance tests have been converted to the scale

of the full-sized ships in the conventional way in accordance with FP.OUDE'S method.

The frictional resistance has been calculated using the formulae decided upon at the

Tank Superintendents' Conference in Peas in 1935. No length

correction has been employed.

All the sOif-propulsion experiments were carried out according to the so called Continental method (GEBEBS) with the skin friction correction applied as a towing

force. The results have been converted to full scale in the conventional manner. KQ 2r T KT Thn2 = thrust coefficient KQ = -- = torque coefficient VE

J

= = advance coefficient KT J

In converting the measured values to ship scale, n

air resistance, hull condition etc. have been applied, s concerned with comparisons between the different ye

Wake fractions have been calculated in the usual

wake integrator. Values of wake fraction were work

thrust identity and on the basis of torque identity, wit

results from the open water propeller tests; A mea

obtained was then taken in each Case. This method the normal practice at the Tank.

3. Ship Models Test: d

As stated iii the Introduction, four for -body models and four after-body models, with sections varring i form from Extreme V to Etreme J, were made for these experim nts. AU the hall-models were made of paraffin wax and could be c upled together jn pairs so that a total of 16 model conbinations c uld be tested.

The various model combinations and thei: numbers are tabulated

below, the basic models being underlined.

Table 1

7 corrections for scale effects, ce the experiments were only sions of the models.

ay, using the propeller as a d out, both on the basis of

the aid of the curves of the

between the two values so

calculating wake fraction is

Model No. Fore Body fter Body

710 Extreme V xtrernc V 711 Extreme V oderate V -712 Extreme V oderate U 713 Extreme V xtrème U 714 Moderate V xtreme V 715 Moderate V oderate V 716 Moderate V odarate U 717 Moderate V I xtreme U 718 Moderate U xtreme V 719 Moderate U oderate V. 720 Moderate U oderate U 721 Moderate U xtrerne U 722 Extreme U xtreme V 723 Extreme T Oderate V -724 - Extreme U oderate U 725 Extreme U xteme U

-- -- Model No.7/0 (Ex/reme V I

- Mde/ No. 7/5 (ufcderc/e vi

Model No. 7O (,-m II)

Model 1k/a 725 (Exex, LI)

10

The body plans of all the fore- and after-bodies are given in Fig.

(see alsO Figs. 3-6) and it will be seen that the forms were related

in such a way that the transverse ditances between the body sections

of the different forms (e. g. the distances a, b, c and d respectively) were equal at any one waterline, while the sectional areas below

the load waterline were the same for each form.

The sectiopl area curve alid the stem and stern contours, which were common to all the models, are shown in Fig. 2, togetherwith

the load waterline for the different forms.

All the model combinations had the same fullness, principal

dimensions and L. C. B. position. The main particulars of the models

converted to full scale, are as follows:

-Model scale = 1: 20 BIT 2.40

L = 123.00 rn = 0.658

= 120.00 m = 0.675

B

= 17.00 m

0.984

T = 7.083

0

= 0.669

J7 _{= 9750 m3}

t/Lpp = -0.75%

V13 = 5.76 Length of parallel middle body

L/B 7.24

= 12% of

The waterline angles of the different fore-body and after-body models varied as shown in Fig. 2. The wetted surface areas of the

16 different combinations varied between 2839 m2 (Model No. 710)

and 2861 m2 (Model No 725), including rudder. More complete

particulars of the four basic models, Nos. 710, 715. 720 and 725, are to be found in Table 4 (Appendix II). Figs. 3-6 show the body

plans of these basic forms.

Offset tables for all the fore- and after-bodies are given with the body plans. The body plan of any of the other forms tested can be derived by combining one of the four fore-bodies with one of the after-bodies (see Table 1). Intermediate forms can, of course, be

obtained by interpolation.

All the models were tested with a 1 mm tripwie fitted at Station 19. Models Nos. 710 and 725 were also tested without a tripwire. The tripwire was found to increase the resistance by about 3.0 .%

t7oo'e/ No.7/0

11H

AV1ia

LI_1WT_Ii

LI_V

k_

III

IW

-iW1V_,Ail11

1

Ii

LM Fig. 3. 11

Stations Waterline Offsets in % of Half-Breadth

WL1/2 WL1 WL2 WL3 WL4LWL WL6 WL7 WL8 -1/2

-

--- 2.32 21.97 34.41 41.32 0 (A. P.)

-

- -

-

- 20.94 40.85 52.48 58.26 1 3.25 378 6.26 12.87 29.52 50.59 66.35 74.61 78.40 2 738 11.21 21.97 38.25 56.4 71.77 81.83 81.31 90.08 3 14.52 25.21 45.87 63.75 76.6 85.41 91.08 94.51 96.34 4 29.05 46.99 70.25 82.71 S9.8 94.12 96.52 98.05 99.01 5 51.06 70.54 87.07 93.98 97.1 98.59 99.12 99.53 100 6 73.32 87.07 96.34 99.00 99. 100 100 100 100 7 87.43 9552 99.71 100 100 100 100 100 100 8 93.63 98.59 100 100 100 100 100 ioo 100 9-11 95M8 99.36 100 100 100. 100 100 100 100 12 93.47 98.30 lOG 100 100. 100 100 100 100 13 86.00 93.87 98.9.4 100 100 100 100 100 100 14 71.05 83.85 94.34 98.06 99. 6 99.30 99.71 100 IQO la oO 47 6733 8320 9027 93 8 90 a3 97 11 9824 9906 16 29.60 46.17V 65.15 75.47 81. 8 85.65 89.16 91.98 94.40 17 1621 2700 437 o01 62 0 6871 7418 7890 8320 18 8.26 13.39 2335 32.42 40.1 47.30 53.84 60.14 65.98 19 2.35 4.54 8.44 12.80 17.13 24.00 30.13 36.55 42.81 20 (F.P.) .. -V - ).18 3.95 7.91 12.98

gI

AIWA

LI_11_MMMIII

1V_111

IIt1NI! DIII

AMMFi

P/ode! No. 720 o Fig. 5. WL 5 8L 13

Stations Waterline Offsets in % of Half-Breadth

No. WL1/2 WL1WL2 WL3WL- LWLWL6 WL7WL8 -1/2

-

-

-

-

2.34 18.59 31.34 39.61 0 (A. P.)

-

-

16.55 35.60 48.87 56.41 1 9.40 10.13 10.29 12.22 21::6 41.65 59.73 71.00 77.10 2 18.28 22.04 26.48 33.79 46.4 62.51 75.88 84.43 89.20 3 2997 37.46 4730, 56.94 67. 1 78.04 86.81 92.71 95.96 4 44.71 55.64 68O6 76.33 83. 6 89.10 93.93 97.24 98.97 5 61.59 7341 84.03 89.64 93. 0 9&08 98.03 99.30 99.88 6 77.40 86.78 94.11 97.08 98.- 7 99.38 99.73 99.97 100 7 88.31 94.78 98.73 99.65 99.7 100 100 100 100 S 93.83 98.47 99.97 100 1OQ 100 100 100 100 9-11 95.08 99.36 100 100 100 100 100 100 100 12 93.31 98.26 100 100 100 100 100 100 100 13 86.79 94.34 98.98 99.53 99. 3 99.53 99.65 99.80 99.92 14 75.15 86.45 94.34 96.21 96. 6 96.63 97.04 97.85 98.86 15 58.91 73.30 8392 87;04 88. 3 88.79 90.05 92.19 95.28 16 40.73 55.35, .67.61 71.91 73. 1 75.30 77.43 81.39 87.18 17 24.60 36.25 48.00 52;70 55; 8 57.26 60.10 65.45 73.55 18 12.01 19.31 28.17 32.29 34. 9 37.26 40.40 46.35 55.17 19 2.35 6.11 11.01 13.68 15. 7 17.58 20.73 25.97 33.67 20 (F. P.)

-

-

-

1.18 2.85 5.61 10.04

14 It

$At

I

k%AIftIi

tI.

miii

iL

lii

VIIU U111

7

.IUIIWIJ

flode/ No. 725 r- o Fig. 6.

Stations Waterline Offsets in % of Half-Breadth

No. - WL 1/2 WL 1 WL 2 WL 3 WL4 LWL WL 6 WL 7 WL S -1/2

- -

-

-

2.35 16.91 29.80 38.75 0 (A. P.)

- -

- 14.35 32.97 47.06 55.48 1 12.48 13.31 12.31 11.89 18.02 37.18 56.42 69.20 76.45 2 23.3 27.45 28.74 31.57 41.11 57.88 72.91 82.98 88.76 3 3.70 43.58 48.00 5353 62.78 74;35 84.68 91.81 95.77 4 52.53 59.95 66.97 73.14 79.80 86.59 92.64 96.83 98.94 5 66.85 74.85 82.51 87.46 91.52 94.83 97.47 99.18 99.83 6 79.45 86.64 92.99 96.12 97.94 99.06 99.59 .99.94 100 7 88.76 94.40 98.24 9947 99.94 100 100 100 100 8 93.93 98.41 99.94 100 100. 100 100 100 100

9-li

95.08 9936 100 100 100 100 100 100 .100 12 93.23 98.24 100 100 100 100 100 100 100 13 87.17 94.58 99.00 99.30 99.30 99.30 99.47 99.71 99.88 14 77 21 87 76 94 34 95 30 9 30 9& 30 95 71 96 77 98 30 15 63.13 7627 84.27 85.41 85.41 85.41 88.52 89.17 93.40 16 46 30 59 90 68 85 70 12 70 12 70 12 71 55 76 10 8357 17 28.80 40.87 50.12 51.53. 51.53 51.53 53.06 58.72 68.73 18 13 89 22 26 3057 32 24 32 24 32 24 33 68 3946 49 77 19 2.35 6.89 12.31 14.13 14.25 14.35 1602 20.67 29.09 20 (F. P.)

-

- - -

-

1.18 2.29 4.47 8.54

Poe//e' A/a. 558

#;nen,,ths ,fl ma,

Fig. 7.

4. Propeller Data and Open Water Propeller Tests

A suitable model propeller, No. P538, was chosen from the Tank

stock for use in the self-propulsion tests. Tiis propeller ran at about 110 r. p. m .at a speed Of 16.5 knots

The main particulars of propeller No. P538 (in. ship's scale) are as

follows:

15

Model scale

- 1:. 20

F/D = 0.95

Number of blades = 4 AD/AO = 47 %

D

= 500 m

Rake - 9;1 degrees

P (mean) = 4.75 m

16

5

a

a

Pro1oe//e, Na. 5iô

kteriemp /4.5C

'7 9.O8r/. A's, 2.2-24/0'

rn

___-- i

_{_}

V

_{a, a.' a., a as}

_a;

_{a a a.. to}

Fig. 8.. 90 .'O C0 40 Jo 20 /0 a

Open water propeller tests were carried out over a range of loading corresponding to 0-100 %. slip. The results are given in Fig. 8 in the usual dimensionless form, i. e., KT, KQ and as

functions of J. The results were used in calculating the wake fraction values in the sell-propulsion tests. Fig. 8 also shows the

limits between which the REYNOLDS number varied during the open water tests.

5. Resistance. and Self-Propulsion Tests

All the resistance and sell-propulsion tests were carried out in

still water. The resistance tests in most cases covered a speed range

of 13-18 knots, but with some of the more interesting models the speed range was extended to 18.5 knots..

1.20 1.00 60 70 C// C2A 60 50 40 SO /0 0

--t

0M Q) w 9000 6000 7000 6000 5000 00 3000 2000 /000 0

-_: =

A

jF1I

.-,

__f/

'Jr

V'

.-V!.

A

-

---:

', -r/

11_-

---'--

--

-=-...

t1cd7i'A//eri,.

-- ¼ 7/ 72' 72. (x/rL' Moa'V ,ToaW ExIt-LI Ex/rV

,dV

MadO ExIt-LI

----

---.-/5 /4 /5 /7. Ship Speed. V.,hk '4. 2 _{Fig. 9.}

I

a!,

0.!! 013 -. D.25 '6 L -I- I i I I I I 050 0.55 ,frV/iP"s' 0.60 I 1 I .1 I 065 a70 a 0.80 v/ Fig. 10.

-z'iT 7ir-Ilod/Vo 725

---N

---

24 7/0

.. ____

_{___ 20} -.'

_N\

7/6

7. \\

_{I \\\\}

-.-

ii

"\N

\\ - \ ..-

_7/&\\

j%\\

- /fodNa ,'pe8cc, I#er&'c,

7/0 Ex/rerne V

\\

\

_\

\\

7/4 ,lodere/e 1' fx/pen,e V '. 7/5 _"

1'"e''1

\

7/6 " flodero, uJ 7/7 £r/remeh'

\ \\ \\\

7/8 er/eL/ Extreme V 7/9 " ,7ode,v&VI 7i0 L'

\ \\

72/ " Ex/remeII 7!! Extreme/i Extreme V 725 ,7adero/e V 724 - tfode,e/e U 725 Ex/reine U

-

I

III

1111-/5 '5 76 i,?7 k,701& au ala

C2 500 450 a50 I. I H 0'5 070 /5 I I 0.5 a-0 I I. I 0.75 Fig. 11. aoa

v//t

5 b4,441

7

7

r7.

-7/0 -7/! -.---. f're B0dbI: 1&freme ,%'der tfoderatell .tx/remeL' V V I I

-

-N I I l I IC i' iii *170/5 /7 020 0.22 025

20

The self-propulsion tests in general covered the speed range 14-18 knots, but some models were tested over the speed range

13-18.5 knots.

All the experimental results are given in Tables 5-8 in Appendix II.

The results obtained with the four basic models, Nos. 710

(Extreme V), 715 (Moderate V), 720 (Moderate U) and 725 (Extreme U)

are shown diagrammatically in Fig. 9. In addition to the effective power, PE, and the shaft power, P8, the power coefficients C'1 =

I7' V3 172 _V3

and C2 - and the propulsive coefficients w, t, , FE

and have been plotted against a base of ship's speed, V.

The values of C1 and C2 for all the models are compared in Figs.

10 and 11 respectively. Crves have been plotted against speed, V, and the speed ratios F _v nL and V/VL.

Values of the wake fraction, w, the thrust deduction factor, t, the propulsive efficiency, , and the hull efficiency _, for all the

forms are given in Figs. 12-15.

In addition to the resistance and self-propulsion tests, a series of experiments was carried out with two of the models (Nos. 710 and 725) for the purpose of measuringthe radial wake distribution, w?,

by means of blade wheels. These experiments are dealt with further in Appendix 1.

6. Experimental Results

Resistance Tests

The shape of the sections has a considerable hifluence on the resistance and effective power, as is shown by Fig. 10. At a speed of 16 knots, the difference in C1, and hence in the effective power, between the best and the worst form is about 18 %. This is also ifiustrated by Fig. 16, in which, among other comparisons, the PE

and C1 values for Models Nos. 723 and 713 are plotted; these models

were shown to be the best and worst respectively over the greater part of the speed range from the aspect of resistance.

The upper diagrams in Figs. 17-20 show three-dimensional comparisons between C1 values at 14, 15, 16 and 17 knots. At all speeds, the U-formed fore-body and the V-formed after-body tend to be the best combination from resistance point of view.

55 Jo 35 30 25 eo 25 20 25 20 /1 __.__;y'_ 7/, 7/9 Z'l ModA 7/5 7/5 7/7 7,' 7/4 720 722 /4 /5

,

Ex/reme V

I /foderc/e V . -Yode,-,1 1/ IEx/reme I /7 V, ,, ,1770/S /5 0.20 0.25 I I I_ i i i I I I 0.50 055 0.60

/

i-I

i I I I i i I i_I I -I 0. 5 070 0.75 0.85 -Pig. 12. 25 7/0

/'re

odg: #ooro/e V

Fore o4: tfoo'epa/e L/

35

72/ .30

Pore 800ji: fx/rene /

55

725

-30

724

w

I

25 20 /5 25 20 /5 25 20 '5 25 20 /5 /3

Tore Boo fx/ren,e V

Tore Bad9. /7odera'e V

7,7

-Pore 8ody Moderate L/

Fore Body: Extreme LI

7d5 0. 2 Moderate V -After Badg I

me V

-Moderate/f Exñmc LI 0.25 /7 in /070/5 /8 I i I t I I 0.5 a?! 080 085 Fig. 13.

-- 72/_.--

--5--

-

-.----5-.

7/59 i%'d,Va 7/0 7/2

---7L5 722 724 /,' /5 /4 I I I 0.c0 0.55 I I aso

iZpe Bocy: Extpe,-ne 1' I p. 050 0.55 .4fter4o4' Ex/reme

/adera/è V

-Moe,-./eL/ Extreme LI 025 F,. I

00 c7- v/L'

75 70 C5 :,dep/e LI

-_1

_{I - -} 72/ 720

-7/9 ----S.---7/8

/'t-e 5o/: EX/reDe LI

725

'N

723 'S

722

'-I

ia

/25 a

Pore Body: fx/re,7e V

7/5

--7/0

Pore 506 : Moo','/e V

Pore Body Mode,/e hi

----020

Añr Ba

ftheme .V -

Mode',,te V--

_{/,de,v/e 1/}

£a*eme LI /7 rn*,7ac /8 0.25

c-I T

ala

ass

I I I I I

Li

05

070 075 Qo0 085 V/'Z Fig. 15. 72/ '/5 1/8 720 -7/9 185 7/6 "V

/re

Boo'y:fic/reme 1/

125 7Z5 129 1/5 724 1/8 --S 7?!--185 1t1 /edNa 7/,. '5 /4 /5

I'

7, 1s. 1/5

--1/0

-7/1 125 120 1/5 1/0 zac

C2 500 500 /00 0 /5 '5 .1

Ii

a,J Q20 0.2/ 0.22 ?2JPr,L.i,/vyr 25 I I- I I i I I -I 1 I 1 I I.

a5o *55 '- v/vy V" a'o

I I I I I I I I i I I I a 5 ax' a 7F - a V/ Fig. 16. /fl#t'?C/'S /,7 25

I-C ModN'.Z?3 E'r/r //ladV

4-7/0Lbv/pV

-5h'f/ /bi'er, Pg

-Eñc/,ve Powe, P, dVa

4Iofr

7/0 £V £XbV 7/f Ex/,V £v/rU 723

£rfrU /V

7/5 &bU KX/rIJ

Afte, Boo'y cz & 5 A joo cz -

_{Ad\ \\}

V/5/rno/s

I

\

= Cz I -500 150 - I v

28

Afte,

30

The great advantage of the V-formed after-body disappears under

self-propulsion conditions, as is shown by the other diagrams On

the other hand, the good qualities of the U-formed fore-body are also evident in the self-propulsion test results.

The photographs (Fig. 21) show a comparison between the wave systems around the two extreme forebody forms at 16 knots .The

superiority of the U-formed fore-body (No. 725) over the V-formed fore-body (No. 710) can clearly be seen.

In Figs. 17-20, the speeds are also given in dimensionless form V

m terms of F =

and the effective power is given in terms igV

V2!3 'V3

of C1',= . The diagrams can thus be employed in deriving the

FE

effective power curve for a ship with a displacement other than the designed displacement of 9750 m3 and with a form which can be interpolated m the family of tested forms Fig 22 can be used for converting values of F

to speed in knots.

A correction for

variations in length is given in the. next section. (Table 2).

SelJ-Poputsion Tests

As with' the resistance, the shape of the sections also has a considerable effect in the shaft power, and this is illustrated by

Fig. 11.

In addition to the best and worst resistance models; the best

and worst self-propulsion models (Nos. 725 and 710) are compared

on the basis of Ps and G2 values in Fig. 16. At 16 knots, the difference in the required power amounts to about 15 %.

The lower diagrams in Figs. 17-20 compare the C2 values of the

different forms at 1.4, 15, 16 and 17 knots. As mentioned previously, the U-formed fore'body maintains its advantage under self-propulsion

conditions. On the other hand, in spite of the V-formed after-body having better resistance qualities, the U formed after body gives better propulsive conditions; thus,, in comparisons between ships with the same fore-bodies, a ship with a U-formed after-body requires less shaft power.. This relationship is further disO'üsëd in the next sectiOn of the paper.

In the same way as that' mentioned above for determining effective

power, a curve of shaft power against speed can be derived for any ship whose form can be interpolated between the tested forms. The

32 Di.'p/dc emenl 1? /n in 5000 I Iiiiiinuui'uiiiuiuli 1k

I

ILUILIIIHII 1IIIiIIIIIIIiuIIIIIiIlUlI

giiiiiIiiIiiIiiiiiiiiHIiIiiIS

1IIflllUIIIIHhi!IIIIiiIIUllhIIi!II

II

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IHIkiIIHIIUIIiIhiIIilIIIIlHIIH

a o

050

a'0

070 P/s Fig. 22. V2!3 V3

-valu

of C2 -

is read from the lower diagrams in Figs. Ps

17-20; then for the displacement in qustion, V is derived from

. (see Fig.. 22) and Ps from C2.

The C1 and C2 values are only valid for the length and displacement

for which they are cicWated, i. e., in this- case 120 m and 9750 m3 respectively. The table below gives the factors which may be used to correct the C1 values for 120 m to the corresponding values for

L

Table 2

Model scale = 1: 16 = 98.40 m

-

96.00 m

The resistance functions FE and C1

way from the original model resistance could, however, have been derived wi

the C1 values for a ship of 120 m le Fig. 10) and applying the above men values of shaft power, P, and of C2 propulsion test, in which the friction

full sãale displacement of 4992 m3.

close agreement (differences up to using the C2 values for a ship 120

applying the correction factors give

3

B 13.60 m

T = 5.667 m

33

were calculated in the usual test results. The same values

sufficient accuracy by using

gth (for instance as given in ioned correction factors. The

were derived from a new self-correction corresponded to the

he same results, but with less bout 1.5 %), 'are obtained by in length (see Fig. 11) and in Table 2.

Ship Length

Linm C1 (actual ehip length) C1 (L = 120 m)

90 0.980 95 0.984 100 . 0.987 105 0.991 110 O.99. 115 0.99 120 1.001 125 1.00 130 1.00; 135 1.00.

The same correction factors can be a plied to the C2 values, but

somewhat greater errors will -be introdu ed.

Fig. 23 shows the values of _E,

P,

and C2 for Model No. 720 (Moderate U) calculated on the, basis of a displacement of 4992 m3.

The values are also given in Table 9 (A pendix II). A displacement of about 5000 rh3 is also usual for thj type of ship. The uneven

value of 4992 m3 was chosen because _{t corresponded to a model}

scale of l 16, The other corresponding particulars' (in full scale) are

-34

41% 80

a

Hoof ,,, ?O (,'Yoo'ero/e 1); P ?7?in'

I I_ I I I- I I a15 0.50 055 0'a I I I I I I I I I I I I I

Ii

as

0.70 075 aoo 0.85 a.9.0 Fig. 23. a .1 I I I I Ic7z.-v/qr 025

Propulsive Coefficients, Wake Fractions a d Thrust Deduction Factors

The values of wake fraction, w,

t

propulsive efficiency, , and hull efficienc 12-15. The values for each group of m

body are compared in the same diagram.

The wake fraction is governed largely

body, while the form of the fore-body has

This fact is illustrated also in Fig. 24 w after-body and fore-body form on the

thrust deduction factor, t, at 16 knots. Th

of all the speeds in the investigated rang 12-15, speed has little effect on the val factor, t, as shown by Fig 24, is largel of the fore- and after-bodies.

As mentioned previously, the V-formed after-bodies are superior

from a resistance point of view. But on ccount of the wake fraction being considerably higher with the U-fo med after bodies, the hull

_1t

efficiency, _{H =}

_1w'

_{and the pr.pulsive}

_{efficiency, j, are}

correspondingly higher for the forms wit shaft power required for these forms is t

fOr the forms with V-shaped after-bodi also been observed in the case of tanke

In addition to determining the wake from the self-propulsion and open wat special tests were carried out with th

No. 710 (Extreme V) and No. 725 (Ext

wake distribution was measured by m tests are described further in Appen

As stated in the Introduction, the form the first stage in an extensive have planned. The next stage in this to determine the most suitable water]

35

st deduction factor, t,

, are given in Figs. dels with the same fore-y the form of the

after-omparatively little effect. ch shows the influence of

ake fraction, w, and the

s diagram is representative since, as shown by Figs.

es. The thrust deduction independent of the form

U-shaped after bodies; the erefore generally lower than

s. A similar tendency has

forms.')

fraction in the normal way r test results, a number of two most extreme forms, eme U), in which the radial ans of blade wheels. These

I.

experiments described above rogramme which the authors.

Drogramme is a series of tests.

ne shape and Model No. 720

') See Experiments with Tanker Model8 IV, Hs LINDOREN, Publication No.. 36 of the Swedish State Shipbuilding Experimental Tank, Göteborg, 1956.

w

I

I,,? 40 35 30 25 20 /5 5 0 36

S/o Speed. V /6kt'o/s;

= £2563

Al/er' 5oa'y Fig. 24.

Wke fr

_____;___

-.---

.--

---

-\

för'e I Extreme /lcderoie Madera/eU

V - -

_{V -.}

L Extremeu L c)

7. Acknowledge

The experiments described herein wer

from the Hugo Hammar Found

Research, thellugo Hammar

ternational Maritime Rese

Lundgren Foundation for

The authors wish to express their grati the funds for these grants.

The authors alsO wish to extend the

STRAND, Director of the S w e d i s h

Experimental Tank, for his

staff of the Tank for all their assistanc Thanks are also due to Mr. P. I). the paper from the Swedish

is to be employed as the parent form for t has given good results and for practical r

models with extremely U-formed fore-bo

that the latter, in some cases, have bette

-j

37 e variations. This model

asons is preferred to the es, in spite of the fact

propulsive qualities.

ent

made possible by grants

tion for Maritime

oundation for

In-rch and the Martina

aritime Research.

ude to the Committees of

thanks to Dr HANS

ED-tate Shipbuilding

aluable advice and to the

APPENDIX I

Wake Distribution

In association with the investigations described above, some experiments are being carried out at the Tank for the purpose of

determining the effect of variation in pitch distribution on the propulsive efficiency with different after-body forms. It was there-fore of interest to determine the radial wake distribution behind

the different after-body forms.

The wake distributions behind Model No. 710 (Extreme V) and Model No. 725 (Extreme U) were determined in a number of tests

by means of blade wheels.

Seven different blade wheels (each with fOur blades) were used in these tests. The wheels were positioned so that the blade centres were in a plane perpendicular to the shaft axis andintersecting with

the generator line of Propeller No. P538 at 0.7 R (where R D/2).

All the tests were carried out at a speed corresponding to 16 knots. The experimental results are shown in Fig. 25, the wake fractions,

Wr, as measured by blade wheels, being plotted as a fiuiction of the

radius r The diagram also include curves of the product w r. The curves have been extrapolated to r = 0.

As Fig. 25 shows, the two models gave wake distributions of different character. In the case of Model No. 710. (Extreme V) the wake distribution falls rapidly from about 50 % at the propeller. boss to about 20 % at r = 0.5 R and then remains fairly constant over the outer radii. In the case of Model No. 725 (Extreme U),

on the other hand, the wake fraction varies more or less linearly from

- about 60 % at the boss to about 15 % at the propeller blade tips.

In order to determine whether this difference in wake distribution

is of importance in the choice of pitch distribution, it is proposed

to carry out some further self-propulsion tests with propellers having different pitch distributions.

The wake fractions calculated from the results of the

self-propul-sion and open water tests and those determined by means of blade

as

a4

as

a

-0.-c

I o

ac .azc

,co' ,'

Roois,

Fig. 25.

fractions obtained from the blade w

calculated in two ways as follows: Firstly, W r dr w1=

--(R2---R)

B

fW

r 0 and secondly, w2 -2 /50 /75 /5 50 in

eel measurements have been

here R0 = boss radius

40

Table 3

It will be observed that the values of w1 are appreciably lower than those of. w, while there is fairly close agreement between w2

and w.

Speed Model

Method

Propeller Blade Wheels

knots No.

w0/ w1 0/ _{w0 %}

710 (Extreme V) 94.3 203 22.6

16 _{725 (Extreme U)}

Suffix f and a denote forebody aid afterbody respectively.

1) Rudder area excluded Rudder area = 30 m2

APPENDIX II, TABLES

Table 4 Model o. 710 Extr. V 715 Mod. V 720 Mod. U 725 Extr. U m 123.00 12300 123.00 123.00 Lp m 120.00 12000 120.00 120.00 B m 17.00 17.I0 17.00 17.00 T m 7.083 7.0:3 7.083 7.083 V m2 9750 .97 0 9750 9750 4767 477 4767 4767 m3 4983 49::3 4983 4983 Aw 1677 163 1589 1545 Aw, m2 790 76 740 715 Aw5 in2 887 8.8 849 830 Sl) in2 2809 216 2823 2831 in2 1367 1 72 137.7 1383 8a1) AM m2 1442 118.50 144, 1 8.50 1446 118.50 1448 118.50 L/B

-

7235 7 235 7.235 7.235 BIT

-

2.400 2.400 2.400 2.400

-

5.76 .76 5.76 5.76 t/Lpp % -0.75 0.75 -0.75 -0.75 1/2 CCE degrees 18.5 4.6 11.0 8.0 1/2 _A degrees 26.8 4.2 21.6 19.0

-

0.802 1.781 0.760 0.739

-

0.775 1.750 0.725 0.701

-

0.828 1.810 0.793 0.775

-

0.984 0.984 0.984 0.984 c5

-

0.658 . 0.658 0.658 0.658 61

-

0.660 . 0.660 0.660 0.660 6a.

-

0.657 0.657 0.657 0.657 6pp

-

0.675 0.675 0.675 0.675 0.669 . 0.669 0.669 0.669 J'Jpp

-

0.686 0.686 0.686 0.686 0.821 0.843 0.866 0.891

-

0.852 0.880 0.910 0.941

-

0.793 0.811 0.829 0.848

') = Residuary resistance = Frictional resistance

Table 5. Displacement, 17 = 9750 m3

Resistance Tests Self-Propulsion Tests

V R

R')

E C1 t n P C2 PE = t w

__

RE PS kziots tons HP

/

_- .. HP

/ /

_{0 0 0}

(rnetr.) (metr.)

-

(metr.) / >'

r/mln.

(metr.) / /

/0 /0 /o

13 18.46 0.400 1646 609 0.689 85.2 2219 452 0.928 74.2 19.9 259 14 21.44 0.420 2059 608 0.690 92.6 2877 435 0.964 71.6 22.4 25.9 15 25.50 0.489 2623 587 0.715 100.6 3680 418 1.004 7L3 223 24.7 ' 15.5 27.79 0.529 2954 575 0.730 104.6 4145 410 1.023 71.3 21.7 24.5 16 30.15 0.565 3307 565 0.742 108.4 4613 405 1.036 71.7 21.3 24.3

-

16.5 32.82 0.611 3715 552 0.760 112.0 5135 399 1.051 72.3 20.6 24.6 17 36.13 0.679 4213 532 0.789 116.7 5877 381 1.101 71.7 20.2 24.3 17.5 40.99 . 0.807 4919 497 0.844 122.3 697 351 1.195 70.5 21.0 25.2 18 48.94 1.049 6045 440 0.953 129.9 87Ui 305 1.375 69.3 20.7 26.0 18.5 60.74 1.419 7708 375 1.119 139.8 11335 255 1.645 68.0 19.9 26.1 13 18.70 0.417 1667 602 0.697 14 21.99 0.456 2112 593 0.707 90.6 2749 455 0.922 76.8 19.7 28.8 15 25.63 0.496 2637 584 0.718 97.9 3468 444 0.945 76.0 19.9 28.0 155 27.67 0.521 2941 578 0.726 102.0 3935 432 0.971 74.7 21.0 27.8 16 30.1S 0.565 3311 564. 0.744 106.0 4449 420 0.999 74.4 21.0 27.9 16.5 32.68 0.603 3700 554 0.757 110.2 5020, 408 1.028 73.7 21.2 27.5 0 17 36;32 0.687 4234 530 0.792 115.2 5770 389 1.078 73.4 19.9 26.9 17.5 41.90 0.846 5028 486 0.863 121.2 .6932 353 1.188 72.5 20.4 27.7 18 49.77 1.082 6146 433 0.969 128.6 8560 311 1.349 71.8 20.7 28.3 13 19.48 0.475 1737 577 0.727 14 22.78 0.507 2187 572 0.733 89.9 2795 448 0.936 78.2 21.1 32.3 15 26.75 0.560 2752 560 0.749 973 3539 435 0.964 77.8 21.0 31.5 15.5 28.87 0.586 3069 554 0.757 101.5 4057 419 1.001 75.6 21.8 31.2 16 31.23 0.619 3426 546 0.768 105.5 4491 416 1.008 76.3 21.3 30.0 18.5 33.90 0.61 3837 534 0.786 108.7 4882 420 0.999 78.6 19.4 30.0 0 - 17 37.37 0.734 4357 515 0.815 113.1 5629 398 1.054 77.4 19.5 30.6 17.5 42.88 0.887 5145 475 0.883 119.8 6935 353 1.188 74.2 21.4 31.3 18 51.81 1.166 6399 416 1.008 128.6 8837 301 1.394 72.4 20.7 30.9 13 20.12 0.523 1794 559 0.750 14 23.68 0.565 2274 551 0.761 88.5 2766 453 O;926 82.2 19.1 35.8 15 27.57 0.607 2837 543 0.773 95.9 3507 439 0.956 80.9 19.4 34.7 0 15.5 29.62 0.626 3149 540 0.777 99.9 3967 429 0.978 79.4 21.1 34.5 Z 16 32.15 0.665 3527 530 0.792 103.8 4485 417 L006 78.6 '20.6 34.5 1&5 35.15 0.721 3979 515 0.815 107.3 4951 414 1.013 80.4 18.8.34.2 17 39.20 0.518 4571 490 0.856 112.2 5730 391 1.073 .79.8 18.4 34.1 17.5 45.04 0.981 . 5405 453 0.926 119.0 7018 349 1.202 77.0 19.9 34.5 18 54.40 1.273 8718 396 1.059 127.5 8900 299 1.403 75.5 19.4 34.7 18.5 66.11 1.628 8389 344 1.219 V 1ots (metr.) 13 14 15 15.5 16 16.5 17 17.5 18 - 18;5 19 V 0.193 0.207 0.222 0.230 0.237 0.244 0.252 0.259 0.267 0.274 0.281 flL = VyL V 0.462 0.498 0.533 0.551 0.569 0.586 0.604 0.622 0.640 0.657 0.675 = Vg 7113

v/i/i

0.647 0.696 0.746 0.771 0.796 0.821 0.846 0.871 0.595 0.920 0.945

1) RR = Residuary resistance = Frictional resistance

Table 6. Displacement, V = 9750 m3

Resistance Tests Self-Propulsion Tests

V R RR') _E C1 cj _s

C2 J

= - t

E _w

knots

(metr.) (metr.)tons

-

(metr.)HP

/

/

-"

. r/m _(metr.)HP

/ I,/

/' /

0 /0 0 /o 0 /o 13 18.52 0.402 1651 608 0.690 I 14 21.48 0.420 2062 607 0.691 9.3 2841 441 0.951 72.6 20.6 25.6

..

15 24.94 0.454 2567 600 0.699 10.2 3563 432 0.971 72.0 20.4 23.5 o Z 15.5₁₆ 27.15_29.42 0.491_0.524 2886 589_{3227 579} 0.712_0.725 10 .1 3964 429 0.978 72.8 20.4 25.4 10 .9 4442 421 0.996 72.6 20.3 25.2 16.5 31.83 0.559 3603 569 0.737 11I;9 4978 412 1.018 72.4 20.3 25.1 O _{17 35.05 0.626 4087 549 0.764 11..4 5684 394 1.065 71.9 20.6 25.1} 17.5 40.80, 0.795 4896 500 0.839 12 .4 6819 359 1.169 71.8 20.5 25.9 18 49.57 1.072 6122 435. 0.964 1'.5 8628 309 1358 71.0 19.7 26.4 13 18.73 0.417 1671 600 0.699 :3.6 2129 471 0.891 78.5 16.9 28.2 14 21.69 0.433 2083 601 0.698 '0.8 2717 461 0.910 76.7 19.1 27.6 .. 15 24.99 0.456 2571 599 0.700 '7.9 3430 449 0.934 75.0 20.4 273 15.5 26.94 0.479 2864 594 0.706 1111.3 3797 448 0.936 75.4 20.6 27.5 Z 16 29.05 0.504 3186 587 0.715 115.1 4266. 438 0.958 74.7 20.7 27.4 16.5 31.46 0.540 3561 576 0.728 119.3 4815 426 0.985 74.0 21.1 26.9 . 17 34.76 0.612 4053 553 0.759 114.0 5565. 403 1.041 72.8 21.4 27.1 17.5 40.34 0.774 4841 505 0.831 1 0.1 6669 , 367 1.143 72.6 21.0 27.4 18 48.61 1.030 6004 443 . 0.947 128.3 8556 311 1.349 70.2 21.5 28.2 18.5 60.56 1.406 7685 376 1.116 38.4 11238 257 1.632 68.4 20.9 28.7 13 18.65 0.409 1663 603. 0.696 14 21.93 0.448 2106 594 0.706 89.2 2709 462 0.908 7.7 20.9 32.0 15 25.47 0.483 2621 588. 0.713 966 3440 448 0.936 76.2 22.3 31.4 15.5 27.43 0.504 2915 583 0.720 00.2 3846 442 0.949 75.8 22.6 31.2 Z _{- 16 29.77 0.541 3266 572 0.733 04.0 4291 436 0.962} 76.1 21.6 30.6 16.5 32.60 0.595 3690 556 0.754 I 07.6 4712 435 0.964 78.3 19.2 30.0 17 36.56 0.694 4262 526 0.798 12.5 5467' 410 1.023 78.0 18.9 30.3 17.5 43.12 0.895 5174 473 0.887 119.4 6796 360 1.165 76.1 19.3 30.9 18 52.78 1.203 6519 408 1.028 127.5 8606 309 1.358 75.7 18.1 31.6 13 19.46 0.470 1735 578 0.726 14 22.91 0.511 2200 569 0.737 87.4 2621 478 0.878 83.9 18.3 35.5 ' _{.j 15 26.70 0.553 2747 561 0.748 94.8 3333 462 0.908} 82.4 19.2 34.5 15.5 28.73 0.574 3054 557 0.753 98.4 347 454 0.924 .81.5 19.8 35.0 Z _{16 3091 0.599 3391 551 0.761 102.4 4211 444 0.945 80.5 20J 343} 165 33.74 0.649 3819 537 0.781 106.4 4733 433 0.969 80.7 20.0 33.8 17 37.69 0.745 4395 510 0.823 111.1 5481 409 L026 80.2 19.6 34J 175 44.34 0947 5321 460 0.912 118.3 6807 359 1.169 78.2 20.4 34.3 18 53.92 1.249 6659 400 1.049 126.3 8579 310 1.353 77.6 18.4 34.7 V 13 14 15 15.5 16 16.5 17 17.5 18 18.5 19 V 0.193 0.207 0.222 0.230 0.2 7 0.244 0.252 0.259 0.267 0.274 0.281 FflL JIgL . V 0.462 0.498 0.533 0.551 0.5 9 0.586 0.604 0.622 0.640 0.657 0.675 v 147 V" 0.647 0.696 - 0.746 0.771 0. 96 0.821 0.846 0.871 0.895 0.920 0.945

Table 7. Displacement, V = 9750 in3

1) _{RR = Residuary resistance}

= Frictional resistance

Resistance Tests Self Propulsion Tests

R')

FE

V B

---

E C1

tj

P8 C2

P W

knots tons HP

/

. HP

/ /

, ,

/o

(met.].) (metr.)

-

(metr.) / r/mln.

(met.r.) / ,/

/

13 17.98 0.358 1603 626 0.670 14 20.78 0.372 1995 628 0.668 92.8 2840 441 0.951 70.2 23.2 24.4 O . ₁₅ 15.5 24.01 0.397, 25.88 0.419 2470 2751 623 618 0.673 0.679 99.7 103.1 3543 435 3930 433 0.964 0.969 69.7 24.1 70.0 23.4 24.8 24.9 Z _{16 28.07- 0.452 3080 607} 0.691 106.7 4357. 429 0.978 70.7 22.4 .24.6 16.5 30.74 0.503 3480 589 0.712 110.7 4893 419 1.001 71.1 21.9 24.6 o 17 34.37 0.592 4008 559 0.750 115.8 5668 396 1.059 70.7 22.8 24.5 17.5 40.62 0.784 4874 502 0.836 122.5 6989 350 1.199 69.7 21.9 25.0 18 50.04 1.088 6180 431 0.973 130.1 8831 301 1.394 70.0.20.1 26.5 13 18.23 0.377 1625 617 0.680 14 21.02 0.386 2018 620 0.677 .91.5 2775 451 0.930 72.7 23.7 2.7.2 15 24.23 0.409 2494 611 0.680 97.9 3356 459 0.914 743 22.2 26.6 15.5 26.02 0.425 2766 615 0.682 101.5 3741 454 0.924 73.9 22.2 26.4 Z 16 28.21 0.458 3094 604 0.695 105.3 4214 444 0.945 73.4 22.5 26.5 16.5 31.03 0.516 3512 584 0.718 109.6 4830 424 0.989 72.7 22.6 26.6' 17 35.15 0.621 4098 547 0.767 114.0 5519 406 1.033 743 20.2 267 17.5 41.63 0.827 4996 490 0.856 120.7 6787 360 1.165 73.6 18.6 26.8 18 51.71 1.156 6386 417 1.006 129.7 8859 .300 1.398 72.1 19.2 27. 13 18.40 0.388 1640 612 0.685 81.8 2016 498 0.842 81.3 18.7 30.7 14 2l.62 0.425 2076 603 0.696 89.2 2658 471 0.891 78.1 21.1 31.1 15 24.70 0.435 2541 606 0.692 96.4 3384 455 0.922 75.1 23.1 30.9 15 5 26 58 0 455 2825 602 0 697 100 2 3763 452 0928 75 1 23 2 29 9 16 2&86 0.491 3166 590 0.711 104.0 4211; 444 0.945 75.2 22.6 29.6 16.5 31.86 0.556 3607 568 0.739 108.0 4764 430 0.976 75.7 21.7 29.8 17 36.24 0.676 4226 531 . 0.790 113.1 5547 404 1.038 76.2 20.2 29.6 17.5 '43.31 0.899 5197 471 0.891 119.8 6765 362 1.159 76.8 18.2 29.6 18 53.40 1.225 6595 404 1.038 128.6 .8846 301 1.394 74.6 -18.4 31.1 18.5 66.92 1.652 8492 340 1.234 138.6 11583 250 1.68 73.3 16.4 31.5 13 19.26 '0.452 1718 584 0.718 80.9 2048 490 0.856 83.9 195 35.0

-

14 22.31 0.469 2142 585 0.717 88.3 2663 470 0.893 80.4 21.4 34.3 15 25.69 0.492 2644 '582 0.721 95.5 3392 454 0.924 77.9 23.0 33.7 15.5 27.65 '0.513 2939 578 0.726 98.8 3752 453 0.926 78.3 223 33.6 16 29.92 0.544 3282 569 0.737 102.4 4203 445 0.943 78.1 22.2 33.8 16.5 2.91 0.606 3726 550 0.763 106.9 4806 427 0.982 77.5 22.1 33.4 17 36.95 0.708 4309 520 0.807 112.2 5663 396 1.059 76.1 22.4 33.3 17.;5 4369 0.915 5242 467 0.898 119.2 6997 350 1.199 74.9 22.1 .34.0 18 54.34 1.263 6711 397 1.0 127.9 8948 298 1.408 75.0 19.9 34.4 18.5 67.85 1.887 8610 336 1.249 138.4 11837 244 1.719 72.7 18.9 34.3 v 13 14 15 15.5 16 '. 16.5 17 17.5 18 18.5 19 V nL ' 0.193 0.207 0.222 0.230 0.237 0.244 0.252 .0.259 0.267 0.274 0.281 VYL V

En =

.' 0.462 0.498 0.533 0.551 0.569 0.586 0.604 0.622 0640 0.657 0.675 v/ ' 0.647 0.696 0.746 0.771 0.796 0.821 0.846 0.871 0.895 0.920 0.945

Table 8. Displacement, 17/= 9750 rn3

1) RR = Residuary resistance RF = Frictional resistance

Resistance Tests Sélf-Propulsibn Tests

-B1)

V B R C1

3

n P8 C2

= - t

w

RF E PS

knots tons

HP /

U1

/ /

0' 0

(rnetr.) (metr.)

-

(rnetr.) /

,-

r rn/

(metr.) / /

0 '0 ii

/

13 17.83 0.344 1590 631 0.665 8- .6 2232 449 0.934 71.2 22.3 25.0 14 20.72 0365 1990 629 0.667 9 .1 2762 453 0926 72.0 21.3 24.6 15 23.88 0.387 2458 627 0.669 9:.8 3383 455 0.922 72.7 20.9 24.1 155 25.62 0.401 2723 624 0672 10 .2 3777 450 0.932 72.1 21.1 24.5 16 27.73.- 0.432 3042 614 0.683 i0..2 4271 438 0.958 71.2 21:5 24.3

-

16.5 30.40 0.484 3441 596 0.704 1 0.5 4868 421 0.996 70.7 21.8 24.6 17 34.45 0.592 4017 58 0.752 1 5.2 5617 399 1.051 71.5 21.0 25.0 , 175 18 42.09 0.845 53.32 1.220 5051 6585 484 404 0.867 1.038 12.5 11.9 70679332 346 285 1.212 1.472 71.5 70.6 19.4 18.4 25.5 26.5 18.5 66.59 1.637 8450 342 1.227 1 2.4 12359 234 1.793 68.4 18.0 27.3 13 17.87 0.347 1594 629 0.667 > _{14 20.58 0.354 1976 634 0662 9.0 2514 498 0842 78.6 17.7 27.9} 15 23.46 0.362 2414 638 0.658 95.9 3160 487 0.861 76.4 20.3 27.8 15.5 25.08 0371 2666 638 0.858 99.7 3552 479 0.876 75.1 21.4 27.5 Z _{16 27.18 0.402} .. 2982 627 0.669 04.0 4032, 464 0.904 74.0 21.6 26.7 16.5 30.17 0.471 3415 600 0.699 08.0 4595.- 446 0.941 74.3 20.5 27.1 - 1 34.78. 0.606 4055 553 0.759 13.6 5507 407 1.031 73.6 20.6 27.3 17.5 41.75 -0.828 5010 488 0.860 21.2 6998 350 1.199 71.6 21.3 28.2 18 52.15 1.170 6440 413 1.016 130.1 9051 294 1.427 71.2 19.8 28.7 13 18.11 0.363 1614 621 0.876 14 20.74 0.364 1991 629 0.667 87.9 2518 49 0.844 79.1 20.7 31.4 15 23.88 0.384 2457 627 0.669 95.0 3149 489 0.858 78.0 21.3 30.2 15.5 25.67 0.402 2728 623 0.673 988 3541 480 0.874 77.0 2L9 29.5 Z 16 27.85 0.436 3055 612 0.685 102.6 3988. 469 0.894 76.6 21.9 29.7 165 31.01 0.511 3510 584 0.718 106.9 4534 452 0.928 77.4 20.4 293 17 35.46 0.637 4135 542 0.774 112;9 5557 403 1.041 74.4 22.4 30.2 17.5 42.52 0.861 5102 479 0.876 121.0 7114 344 1.219 71.7 23230.4 18 53.58 1.228 6617 402 1.044 129.9 9161 291 1.442 72.2 20.6 30.7 13' 19.03 0.432 i697 591 0.710 80.3 2002 501 0.83 84.8 168 350 14 22.17 0.457 2129 588 0.713 86.8 2504 500 0.839 85.0 16.8 34.3 15 25.24 0.463 2597 593 0.707 93.7 3147 489 0.858 82.5 18.8 33.9 15.5 26.88 0.467 2857 595 0.70 97.3 3529 482 O.870 81.0 20.8 33.8 16 29.16 0.502 3198 584 0.7]: 101.1 3999 467 0.898 800 21.1 34.1

-

16.5 32.48 0.582 3677 558 0.75W 105.8 4614. 444 0.945 79.7 20.5 33.8 17 37.60 0.734 4384 511 0.82 111.1 5456 411 1.021 80.4 19.0 33.6 - 17.5 45.41 0.986 5449 449 093t 119.6 7094 345 L216 / 76.8 20.4 33.9 18 56.23 L336. 6945 383 1.09 129.7 9417 283 1.482 737 20.8 34.0 18.5 70.90 1.802 8997 321 1.30/7 140.6 12365 234 1.793. 72.8 18.4 33.5 (rnetr.) 13 14 15 15.5 11 16.5 17 17.5 18 18.5 19 V 0.193 0.207 0.222 0.230 0 237 0.244 0.252 0259 0.267 0.274 0281 = VYL V -0.462 0.498 0.533 0.551 .569 0.586 0.604 0.622 0.640 -0.657 0.675 F. = /gV1/3 0.647 0.696 0.46 0.771 p.796 0.821 0846 0.871 0.895 0.920 0.945

46

Table 9. Displacement, V = 4992 m3

Resistance Tests' Sell-Propulsion Tests

V R _E Cl _{I_)} n _P C2

c)

= -

w

knots tons HP

/ 7

. HP

/

(metr.) (metr.)

(metr.) / 7

r/nnn.

(rnetr.) / ,7

0 /0 _%

p 11 8.49 640 608 0.690 86.3 772 504 0.832 82.9 18.4 31.2 12 10.29 847 596 0.704 95.0 1038 486 0.863 81.6 19.1 31.1 - 13 12.14 1082 593 0.707 104.3 1370 468 0.896 79.0 20.5 30.0 13.5 13.05 1208 595 0.705 109.0 1563 460 0.912 77.3 22.1 29.4 Z _{14 14.16 1360 589 0.712 113.5 1784 449 0.934 76.2 23.2 29.8} 14.5 15.59 1551 574 0.731 118.5 2048 435 0.964 75.7 22.6 29.6 15 17.61 1812 544 0.771 124.5 2416 408 1.028 75.0 22.5 29.8 15.5 21.04 2237 486 0.863 132.5 3014 361 1.162 74.2 21.7 30.2 o 16 26.35 2891 414 1.013 141.8 3847 311 1.349 75.1 18.7 30.9

Appendix I. Wake Distribution

Appendix II. Tables

Contents

Page

Introduction 3

Symbols, Units and Methods of Calcul.tion 4

Ship Models Tested . 7

Propeller Data and Open Water PropI er Tests 15

Resistance and Self-Propulsion Tests . . . 16

Experimental Results 20

Acknowledgement . 37

38

MEDDELAND :N

F RAN

STATENS SKEPPSPROV INUSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SIHPBU DING EXPERIMENTAL TANK)

Nt 41 OOTEBORO 1957

SYSTEMATIC ESTS

WITH SHIP MOD LS WITH

o=O.6 5

PART II: INFLUENCE OF SHA' E OF WATERLINES

BY

E. FREIMANIS AND HA S LINDOREN

GUMPERTS FORLAG

GUTEBORG 1957

ent size.

1. Introductio

Cargo ships of 5000-10000 tons displcement, with block

coeffi-ciènts of about 0.675, are the subject of Ia programme of systematic model experiments planned by the authois. By means of these model

experiments, which have been

or wll be carried out at the

Sw.edish State Shipbuilding Experimental T-ank,

it is intended to study the influence of section and waterline form, L. C. B. positin and main dimensions n the resistance and

propul-sive qualities.

The first part of the programme, w ch consisted of an

investiga-tion of the most suitable secinvestiga-tion shape, was described in publicainvestiga-tion

No. 39 of the Swedish State Ship uilding Experimental Tank,

*Systematic Tests with Ship Models ith 3p = 0.675, Part 1* by E. FRET1WANIS and HANS LINDGREN.

The second part of the programme which is concerned with the

influence of waterline form, has now een completed and the

experi-mental results are given in this repor

A model from the previous series, No. 720, was selected as the parent form. Three new forebody f rms having different types of

waterline, were developed and teste in conjunction with the

after-body of Model No. 720.

All the experimental results have been converted to the scale of a ship having a displacement of n13 and a trial speed of 16-16.5 knots. The results have also teen expressed in dimensionless form in order to facilitate their ap i cation to similar ships of

differ-2. Symbols, Units and Methods of Calculation

The symbols have been chosen in accordance with the nomenclature adopted by

the Sixth International Conference of Ship Tank Superiri.

t e n d e n t s as a tentative standard.

Ship Dimensions

L = length on waterline

Lpp = length between perpendiculars

B = breadth on waterline

T = draught

AM = immersed midship section area

A w = load waterline area

S wetted surface area

V = volumetric displacement

A _{= weight displacement; Br. tons in sea water}

= distance of L. C. B. forward of midships (Lpp/2)

1/2 'E = half angle of entrance on LWL

/2 cmaz = maximum half angle on L WL of forebody

1/, o = half angle at station 0 on LWL

ProeUer Dimensions D = propeller diameter

P = propeller pitch

I izD'

A0 = propeller disc area

-AD = developed blade area

1 = blade width at 0.7 D/2

Kinematic and Dynamic Symbols and Ratios

V = speed

V5 = speed of advance

R resistance

T = propeller thrust

Q = propeller torque

n rate of revolution (revs, per unit time)

= effective power

P8 = shaft power (at tail end of shaft)

V - V

w

-

= wake fraction (TAYL0n) V

TR

-

= thrust deduction factor

T

= density of water 1(102.0 kg sec.'/m4 for fresh water)

v = kinematic viscosity of water

C1 = V2'3 V3/PE(m3, Metr. knots and HP)

= 427.1 E (Br. HP, tons and knots)

LI213 V

-C2 = V2I3 V3/P8 (rn3, Metr. knots and HP)

tj) = 427.1 (Br. HP, tons and knots)

A2'3 V3

-F5 . = vi = FRoUDE number, displace

= vi 1J = FROUDE number, length

vf fi = speed-length ratio (knots, feet)

1 /V + (O.7yDn)2

B5 = - = REYNOLDS n ber for propellers V

Coefficients and Ratios

V

= - load waterline coefficient

LB

AM

- midship section coefficie BT

V

AM L

V = prismatic coefficien horizontal)

'2PP _{AM Lpp}

V

AT

- prismatic coefficien (vertical) L

= length-breadth ratio

B

= breadth-draught ratio

L

Vi,a = length-displacement ratio

Lpp = L. C. B. forward of Lpp/2 as of Lpp 5 11 oPP = LBT V = block coefficients Lp1 BT

'7

= propeller efficiency in open water P

D pitch ratio AD

disc area ratiO A0 T

-

= thrust coefficient D4 n2 KQ = = torque coefficient 9D5 ni VE

J

= -=- = advance coefficient Dn KT J KQ 2t PB = - propulsive éfficiOncr PS

lt

= hull efficiency

1w

Units and Conversion FactOrs

1 metre = 3.281 ft. (récipr. 0.3048)

1 metric ton = 1000 kg = 0.984 British tons (recipr 1.018) 1 metric knot = 1852 rn/bohr = 0 999 British knots (recipr 1 001)

1 metric HP = 75 m kg/sec. = 0.986 British HP (recipr. 1.014)

For g (acceleration due to gravity) the value 9.81 m/sec2 has been used.

Methods of Calculation

The model-sOale rOults from the resistance tests have heen converted to the scale of the full-sized ships in the conventional way in accordance with FRotDx's method. The frictional resistance has been calculated using the formulae decided upon at the

Ship Tank Superintendents' Conference in Paris in

1935. No length corrCctioñ has been employed.

All the self-propulsion experiments were carried out according to the so-called Continental method (GEnERa) with the skm friction correction applied as a towing

force The results- have been converted to full scale in the conventional manner. In converting the measured values to ship scale, no corrections for scale effects, air resistance hull condition etc have been applied since the experiments were only concerned with comparisons between the different versions of the models.

Wake fractions have been calculated in the usual way using the ptopeller as a wake integrator; Values of wake fraction were worked out, both on the basis of

thrust- identity axid on the basis of torque identitr, with the aid Of the cuives of the

results from the open water propeller tests. A mean between the two values so

obtained was then taken in each case This method of calculating wake fraction is the normal practise at the Tank.

Load Waterlines

Fig. 1.

3. Ship Models Tested

It was, considered that Model No.

parent form. This model, which in P

tigation) was classified as moderate within the speed range in question.

ferred to the extremely U-formed the latter showed somewhat better

Three new forebody forms, with developed from the parent form. forebodies are shown in Fig. 1. As

Model No. 762 had the smallest ha

S-formed waterline while Model No.

of 16.5° and a convex waterline.

Model No. 720 had a slightly S-for

a straight waterline. The water

models. Since the sectional area cu (see Fig.. 3) the shape of sections

was U-formed in the most forwa and V-formed aft of station 16¼ this relationship was reversed. T Fig. 2.

20 could be employed as the. rt I (shape of sections

inves-in form, gave good results

or various reasons, it was

pre-odel, in spite of the fact that

opulsive qualities.

ferent waterline shapes, were

he load water]iiies of the four ay be seen from this diagram,

angle of entrance (8.4°) and an. 764 had a half angle of entrance

Of the two intermediate forms,

ed waterline and Model No. 763

e areas were equal for all the

e was common to all the models

as varied so that Model No. 762 d part (forward of station 16¼) In the case of Model No. 764, is is shown in the body plans in 740 in2-cOfl5t. 725 4qo8 II., - - - - /-foo'e/ 1o. 762 Model No. 720 //.0 Model / 753 /3.8

'N

-. -.-.- Model Mo. 764 /6..5 '0 / I / /7 /8 /9 /00 90 80 '0 60 50 40 so 20 /0 .0

-8

A

'w

Al

-II

R 0 0 e b

10

All the four models had the same dimensions, fullness and L. C. B.

position. The main particulars, in ship scale, were as follows: Model scale = 1: .20 L

=123.00 m

6 = 0.658 = 120.00 m = 0.675 B

= 17.00 m

= 0.984 T

= 7.083 m

= 0.760 V = 9750 in3

=0.669

L/V"3 = 5.76

= 0.75 %

L/B = 7.24 Length of parallel middle body

BIT = 2.40

= 12

0/ _of

The stem and stern contours, sectional area curve and load water-lines of the four models are given in Fig. 3.

More complete particulars of the models are to be found in Table 1

(Appendix).

Figs. 4-7 show separate body plans and offset tables for each model. Intermediate forms can of course be obtained by

interpola-tion.

All the models were tested with a 1 mm tripwire fitted at station 19.

4. Propeller Data and Open Water Propeller Tests

Propeller No. P 538, which was used in the shape of sections investigations, was also used in the present tests.

The main particulars of this propeller (in full scale) are as follows:

Model scale

= 1: 20

Number of blades = 4 P/D = 0.95

D = 5.00 m AD/Ao = 47 %

P (mean) = 4.75 m Rake = 9.1 degrees

The outline of the propeller and the open water test results are shown in Figs. 7 and 8 of publication No. 39.

Model No 762

'a-E -4

LWL.

For afterbody, see parent mod1, Fig. 5.

F

11

Stations Waterline Offs ts in % of Half Breadth

No. WL1/2 WL1 WL2 W 3 WL4 LWL WL6 WL7 WL8 10-11 95.08 99.36 100 10 100 100 100 100 100 12 92.87 98.10 100 1 0 100 100 100 100 100 13 85.68 94.27 99.56 1 0 1OO 100 100 100 100 14 72.67 85.85 95.31 779 98.31 98.41 98.83 99.37 99.71 15 55.94 72.20 84.41 8.14 89.79 90.74 92.07 93.91 96.37 16 39.15 54.41 67.41 2.10 74.60 76.34 78.34 82.18 87.71 17 24.73 36.32 48.30 2.66 55.10 56.65 58.99 64.26 72.63 18 12.37 19.97 29.07 32.41 33.99 35.30 37.66 43.65 53.21 19 2.35 6.81 12.08 14.00 14.53 15.42 17.94 23.27 31.68 20

-

-

-

-

1.18 2.39 4.94 9.28

Model No. 720

fa- /L0

"Ii

--I

6 LWL!

'-:

JJWL5

Fig. 5.

Stations Waterline Offsets in % of Half-Breadth

No. _{WL 1/2 WL I WL 2 WL 3 WL 4 LWL WL 6 WL 7 WL 8} 0 (A. P.)

- - -

_{- 16.55 35.60 48.87 56.41} 1 9.40 10.13 10.29 12.22 21.86 41.65 59.73 71.00 77.10 2 18.28 22.04 26.48 33.79 46.21 62.51 75.88 84.43 89.20 3 29.97 37.46 47.30 56.94 67.41 78.04 86.81 92.71 95.96 4 44.71 55.64 68.06 76.33 83.16 89.10 93.93 97.24 98.97 5 61.59 73.41 84.03 89.64 93.40 96.08 98.03 99.30 99.88 6 77.40 86.78 94.11 97.08 98.57 99.38 99.73 99.97 100 7 88.31 94.78 98.73 99.65 99.97 100 100 100 100 8 93.83 98.47 99.9 100 100 100 100 100 100 9-11 95.08 99.36 100 100 100 100 100 100 100 12 93.31 98.26 100 100. 100 100 100 100 100 13 86.9 94.34 98.98 99.53 99.53 99.53 99.65 99.80 99.92 14 75.15 86.45 9434 96.21 96.56 96.63 97.04 97.85 98.86 15 58.91 73.30 83.92 87.04 88.13 88.79 90.05 92.19 95.28 16 40.73 55.35 67.61 71.91 73.91 75.30 77.43 81.39 87.18 17 24.60 36.25 48.00 52.70 55.28 57.26 60.10 65.45 73.55 18 12.01 19.31 28.17 32.29 34.89 37.26 40.40 4&35 55.17 19 2.35 6.11 11.01 13.68 15.47 17.58 20.73 25.97 33.67 20 (F. P.)

-

-

-

-

_{1.18 2.85 5.61 10.04}

Model Na 763 - /38°

LWL.

For afterbody, see parent mode1 Fig. 5.

Fig./ 6.

Lv'L 5

13

Stations Waterline Offes in % of Half-Breadth

No. WL 1/2 WL 1 WL 2 WL WL 4 LWL WL 6 WL l WL 8 10-11 95.08 99.36 100 100/ 100 100 100 100 100 12 93.74 98.43 99.91 99.2 99.92 99.92 99.92 99.94 100 13 87.90 94.48 98.40 9873 98.73 98.73 98.86 99.17 99.61 14 77.64 87.05 93.38 9464 94.80 94.84 95.25 96.33 98.01 15 61.87 74.39 83.43 8593 86.47 86.84 88.03 90.47 94.20 16 42.31 56.30 67.81 711.72 73.21 74.25 7&51 80.60 86.65 17 24.48 36.05 47.71 5.73 55.47 57.87 61.20 66.64 74.48 18 11.66 18.65 27.26 3.18 35.80 39.22 43.14 49.06 57.12 19 2.35 5.41 9.94 1.37 16.41 19.73 23.52 28.68 35.66 20

-

-

-

_{J -}

-

1.18 3.31 6.28 10.79

14

Model Na7641 - /650

LWL

For, afterbody, see parent model, Fig. 5. Fig. 7.

WL 5

Stations Waterline Offsets in % of Hall-Breadth

No. WL 1/2 WLl WL2 WL 3 WL 4 LWL WL 6 WL 7 WL 8 10-11 95.08 99.36 100 100 100 100 100 100 100 12 94.18 98.59 99.83 99.83 99.83 99.83 99.83 99.88 100 13 89.00 94.41 97.83 97.94 97.94 97.94 98.06 98.53 99.30 14 80.12 87.65 92.41 93.06 93.06 93.06 93.47 94.83 97.18 is 64.83 75.47 82.94 84.83 84.83 84.88 86.00 88.77 93.12 16 43.88 57.24 68.00 71.53 72.53 7321 75.59 79.83 86.12 17 24.35 36.12 47.41 52.77 55.65 58.47 62.30 67.83 75.41 18 11.29 18.00 26.35 32.06 36.71 41.18 45.88 51.77 59.06 19 2.35 4.71 8.88 13.06 17.35 21.88 26.29 31.35 37.65 20 -- --

-

1.18 3.76 6.94 11.53

5. Results of Resistance and SIf-Propulsion Tests

All the tests were carried out in still "ater. The resistance tests covered a speed range of. 13-18 knots nd the self-propulsion tests

a range of 14-18 knots.. All the exper mental results are given in

Table 2 (Appendix). Resistance Tests

The results of the resistance tests are shown in Figs. 8 an4 9. In Fig. 8, E and C1 are plotted as funcIions of ship's speed and the speed ratios

F

and V/IlL.

Fig. 9 contains cross curves of C. plotted against. Model No. (angle of entrance) at constant values of speed.

It is evident from these diagrams thalt all the models are equivalent

at a speed of about 17 knots, but at /lower speeds, i. e. the normal speed range, the form with the snallest angle of entrance (and S-formed waterline) is the best. The form having the greatest angle

of entrance was likewise the worst, tle difference in resistance at 15 knots being about 6 %. The photogr4hs (Fig. 10) show a comparison

between the wave systems around th two extreme fore-body forms at 16 knots.

At the higher speeds, the relatioiship is reversed and the form

with the greatest angle of. entrance ave the least resistance. Self-Propulsion Tests

-As may be seen from Table 2 Appendix) the fore-body form has no dscermble influence on the vake fractions and thrust deduc tion factors: The differences obtai/ned appear to be accidental in

character.

The values of F8, C2 and are /plotted in Fig. 11 against speed

and the speed ratios. The fore-body/ form appears to have little effect

on the propulsive efficiency, so that the shaft power curves are arranged in much the same manxbr as the resistance curves. The

difference between the power value of the best and the worst models

is about 6.3 % at 15 knots.

In Fig. 12, cross curves of C are plotted against Model No. (angle of entrance) at constant v lues of speed.

700 600 500 400 300 200 /00 0 16 /3 /4 /5 /6 /7 /8 V 6, knots I. I i i i I I -045 - 050 055 0.60 i5,p-V/g I I i i i I I I I Q65 0.70 0.75 080 0.85 190 i4V Fig. 8. 9000

b-iHP

8000 7000 6000 5000 4000 3000 2000 /000 0

Model No. 762

8.4°

Model No. 720

/

1.00

Model No.

763 /3.8°

Model No. 7t54

/65°

-6% - Jill

liii

0.25 Ii I liii 020

2

q/33

/ £ a4° ,,O. /

i8°

1/2 _E /65° Fig. /9 CI 600 550 500 450 400 17 6

I

06

iii

0622

U

720 763

,e/ Ma

764

18

Model No. 762 ('/2E = 8.4°), V = 16 knots.

Model No. 764 (1/2 E = 16.5°), V = 16 knots.

in % 80 70 300 200 /00 5 Fig. 11. 19

inHP

9000 000 000 000 000 000 000 000

I

1

.1/

-

---JT

-W

Model No. 762 tTode/ No. 720 Model No. 763 MOdel No. 764 8.40 /1.0 II

/7'

7 /3.8° /6.5° -- 1 I I I

Ii

I /4 /5. /6 I /7 V in knois /8

lililliHil

025 L-V/YZ 0.50 Q55 I

I

I i i 060 -V 97' 0 I I I 0.70 0.75 065 V/P'T ago

20

c2

-Ce 450 400 350 300 763 ."ft1 /)b

74

8.4° /1°

I8°

fr'2 _E Fig. 12. /65 0586 0604 /75 0622 /8 kno.'s 0640

As stated in the Introduction, the e form the second stage in an extensive authors. With the investigations now important form variations that can be the qualities of a normal, arbitrary s among the total 19 different ship for this programme is to investigate the ef dimensions. Model No. 720 wifi aga form for this series of experiments.

6. Acknowled ement

The experiments described herein

fromthe Hugo Hammar Fou

Research and the Hugo Ha

International Maritime

to express their gratitude to the Co

grants.

The authors also wish to extend

STRAND, Director of the S w e d i s

Experimental Tank, for

staff of the Tank for all their assis Thanks are also due to Mr. P. the paper from the Swedish.

21

periments described above

rogramme, planned by the

ompleted, most of the more

ade have been studied and p form can be interpolated s tested. The next stage in ect of variations in the main be employed as the parent

ere made possible by grants

datjon for Maritime

mar Foundation for

e s e a r c h. The authors wish

mittees of the funds for these

heir thanks to Dr. HANS ED-,

State Shipbuilding

is valuable advice and to the ance.

22

') Rudder area included Rudder area = 30 in2

APPENDIX

Table 1

Suffix / and a denote forebody and afterbody respectively.

Model No. 762 720 763 764 L in 123.00 123.00 123.00 123.00 Lpp m 120.00 120.00 120.00 120.00 B in 17.00 17.00 17.00 17.00 T m 7.083 7.083 7.083 7.083 rn3 9750 9750 9750 9750 rn3 4767 4767 4767 4767 V0 rn3 4983 4983 4983 .4983 Aw in2 1589 1589 1589 1589 Awl rn2 740 740 740 740 Awa in2 849 849 849 849 8') in2 2851 2853 2855 2857 81 in 1375 1377 1379 1381 8a') m2 1476 1476 1476 1476 AM m2 118.50 118.50 118.50 118.50 L/B

-

7.235 7.235 7.235 7.235 BIT

-

2.400 2.400 2.400 2.400

-

5.76 5.76 5.76 5.76 t/Lpp % -0.75 -0.75 -0.75 -0.75 1/2 E degrees 8.4 11.0 13.8 16.5 1/2 'maz degrees 17 16.5 15.7 16.5 1/2 cA degrees 21.6 21.6 21.6 21.6

-

0.760 0.760 0.760 0.760

-

0.725 0.725 0.725 0.725

-

0.793 0.793 0.793 0.793 p.

-

0.984 0.984 0.984 0.984

-

0.658 0.658 0.658 0.658

-

0.660 0.660 0.660 0.660

-

0.657 0.657 0.657 0.657

-

0.675 0.675 0.875 0.675

-

0.669 0.669 0.669 0.689 pp

-

0.686 0.686 0.686 0.686

-

0.866 0.866 0.866 0.866

-

0.910 0.910 0.910 0.910 Va

-

0.829 0.829 0.829 0.829

Table 2

23

Resistance Tests Self-Propulsion Tests

V R

BR,-..

_FE C1 fl S C2 ,-.

= -

E

P8 W

-knots tons HP

/

. HP

/ /

_,

(metr.) (metr.)

-

/

r/

metr.) / /

'

/'o /0

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