Resistance and propulsion of a high speed single screw cargo liner design

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,

Kti-Ltit S

REPORT No. 141 S

May 1970

(S2/135)

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT

LEEGHWATERSTRAAT 5, DELFT

RESISTANCE AND PROPULSION OF A HIGH-SPEED

SINGLE-SCREW CARGO LINER DESIGN

by

IR. J. J. MUNTJEWERF

Netherlands Ship Model Basin

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Gedurende het laatste decennium is een duidelijke tendens naar hogere ontwerpsnelheden waar te nemen, terwijI de lengte van het beschouwde type vraehtschepen beperkt is tot ca. 165 m in ver-band met beschikbare kadelengten.

Dit heeft tot gevolg dat de snelheidsgraad V/VL = 1,0, waar beneden het overgrote deel der handelsschepen vaart, spoedig zal worden overschreden.

Reeds nu worden voor het thans gebruikelijke type vracht-schip met L = 150à 160 m en V. = 20à 21 knoop de gegevens voor de ontwerpregels ontleend aan de rand van het bekende

informatiegebied.

Uit een literatuurstudie betreffende de factoren die van primair belang beschouwd worden voor de weerstand en voortstuwing van dit soort snelle schepen met V/A/L > 1,0 bleek, dat andere dan de tot nu toe gebruikte parameters bij het scheepsontwerp een belangrijke rol gaan spelen. Onder andere is voor het bepalen van de weerstand bekend dat, in tegenstelling tot de geldende regel beneden V/ /L 1,0 de prismatische coefficient Cp voor minimum restweerstand boven deze waarde toeneemt.

Heden is de belangrijkste informatiebron de Taylor Standard Serie. Deze serie omvat geen variatie van de grootspantcoeffi-cient Cx, welke een belangrijke grootheid voor dit soort snelle

schepen blijkt te zijn.

Het onderzoek (uitgevoerd door het Nederlands Scheeps-bouwkundig Proefstation te Wageningen). had primair tot doel de invloed van Cx bij constant deplacement en blokcoefficient na te gaan voor een snelheidsgebied overeenkomende met 22-30 knoop respectievelijk 0,95

< V/t/L < 1,30 bij een

enkel-schroefmodel. Gezien het snelheidsgebied werd toepassing van een scheepsvorm met bulbsteven noodzakelijk geacht.

De bereikte resultaten tonen aan dat in het beschouwde snel-heidsgebied de waarde van Cx een belangrijke invloed heeft op de weerstand en het voortstuwingsvermogen en dat de optimum-waarde lager is dan in de regel wordt aanbevolen.

De met lage Cx gepaard gaande grotere Cp kan voor vracht-schepen een gunstige invloed hebben op de stuwage factor en mogelijk ook een beter gedrag in zeegang tot gevolg hebben.

Uiteraard is met deze in beperkte serie uitgevoerde proeven geen volledige aanvulling van de nog blank zijnde delen der ont-werpdiagrammen te geven. Aangetoond wordt dat parameters die bij de met lage snelheden varende schepen minder belangrijk waren, nu belangrijk zijn.

HET NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

During the last decade a clear tendency is to observe to higher design-speeds, while the length of the type of cargoliners con-sidered is restricted to about 165 m because of available

quay-lengths.

As a consequence the speed-length ratio V/i/L =- 1.0 below which the bulk of the merchant ships is operating, will be passed. The existing design-rules in use today for the type of cargoship with a length L = 150 to 160 m and speed V, = 20 to 21 knots are based on data at the border of the area with well-known in-formation.

From a survey dealing with the factors considered to be of prime importance for the resistance and propulsion of very fast ships with a speed-length ratio above V/A/L 1.0, it appeared that their design is ruled by other parameters than those impor-tant for ships with a speed-length ratio below V/ t/ L = 1.0. For instance for determining the resistance it is known that in con-tradiction to the practised rules below V/ \ L = 1.0 the pris-matic coefficient Cp for minimum residuary resistance increases above this value.

At present the main source of information being used is the Taylor Standard Series which does not include a variation of the largest-section coefficient Cy. It is to be accepted that the in-fluence of this parameter is an important quality for very fast

ships.

Primarily the investigations by Netherlands Ship Model Basin at Wageningen reported here aimed to check the influence of Cx at constant displacement and block-coefficient over a speed-range corresponding to 22-30 knots respectively 0,95 < V/A/L < 1.30 of a singlescrew shipmodel. Regarding the speed-range it was thought to be necessary to select a shiphull with bulbous bow.

The results obtained show that in the speed-range concerned the value of Cx has an important influence upon resistance and

propulsion power and that the optimum value is lower than normally recommended.

At constant block-coefficient CB the high Cp values corre-sponding to low Cx values may have a favourable influence, for instance on the stowing factor of cargo ships and may possibly give a better seakeeping behaviour.

Of course these small series of tests do not give a full comple-ment of the blind spots of the design diagrams. It is shown here that parameters which were of smaller importance to ships operating at low speeds, are now becoming more important.

THE NETHERLANDS SHIP RESEARCH CENTRE TNO

VOORWOORD

PREFACE

=

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List of symbols,.

. .

Summary

.

Page

,A '1 2

Introduction

. .

, ...

Hull form design conditions

, 7

3 4 5

Hull ,characteristics and model particulars

Propeller design and stern arrangement

,.

Method of extrapolation_

, , . ;, 11 11

12

7

8 ModeLexperiiiient results

,

Discussion on resistance test results

,

Discussion on propulsion test results .

16 19'

9 Concluding remarks

..

19 References Y.

,

e. e, .1, .Appendix o o ,

PP,.

tie .to re it s t v., t y 21 6 7 7 6 20

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LIST OF SYMBOLS

Ship geometry

A

Section area

Ax

Maximum section area

Breadth moulded

CB

Block coefficient on LBP

Cx

Largest-section coefficient

Cp

Longitudinal prismatic coefficient

CPA

Prismatic coefficient, after body

Cpp

Prismatic coefficient, fore body

Cwp

Designed load waterline coefficient

fBT

Taylor sectional area coefficient for bow size

iE

Half angle of entrance

Length of ship between perpendiculars

LCB

Longitudinal centre of buoyancy

Taylor tangent to the area curve

Draft moulded

Displacement weight in salt water in metric tons

42 Displacement weight in salt water in long tons

V

Displacement volume moulded

Propeller geometry

AB

Expanded blade _area

Ao

Disc area

A,.

Projected blade area

Diameter of propeller

Propeller pitch

Number of blades,

Resistance and propulsion coefficients

PE

425.455

Froude resistance Coefficient

422/3V3

J = VAInD

11Q = Qlen2D5 KT -= T/Qn2D4 "is PD PE

Q

= (TR)IT

V VIVL VA

= (V= VA)/V.

B PE/PDi

/7H = (1 -,t)/(1

=4)

no,

Advance coefficient of propeller

Torque coefficient

Thrust coefficient

Propeller revolutions per minute

Delivered power at propeller in metric_ HP

Effective power in Metric HP

Torque

Total resistance.

Thrust deduction fraction

Thrust

Ship speed in knots

Speed-length ratio, with V in knots and L in feet

Speed of advance of propeller

Taylor wake fraction

Propeller efficiency behind ship

Propulsive efficiency

Hull efficiency

Propeller efficiency in open water

Relative rotative efficiency

R,

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1

Introduction

At present the fastest single-screw cargo liners

in

operation or under construction have been laid out for

a design speed-length ratio VI,IL below about 1.05.

For these ships sufficient design information is available

to determine reasonable optimum lines from a point of

view of resistance and propulsion. In general it will

further be possible to keep their design speed below

the range of rapidly increasing resistances, i.e. below

the hydrodynamic boundary speed.

In the speed range above VI,IL = 1.05 even the

finest and most slender ships will be operating in a

range of rapidly increasing resistances. Especially in

the range of VI,IL = 1.10 to 1.50 not much

informa-tion is available for the determinainforma-tion of the required

power.

It may be quite possible that in the near future the

cargo liners, serving those areas where the ship length

is restricted to about 165 m, will have to sail at speeds

in the range above VI,IL = 1.05. To gather some

information for the design of these ships the following

research was carried out at the instigation of the

Netherlands Ship Research Centre.

2

Hull form design conditions

Since for the present investigations it was decided to

carry out a restricted test programme, it was necessary

to eliminate as many variations in the hull form

para-meters as possible. A survey of the available published

experimental and theoretical research on ships

oper-ating at speeds above VI,IL = 1.05 was therefore

made to determine those aspects where further

in-vestigations might be needed for design purposes. The

results of this study were given in [1] and its

conclu-sions will be summarized below.

It was found, that in addition to the parameters

RESISTANCE AND PROPULSION OF A

HIGH-SPEED SINGLE-SCREW CARGO LINER DESIGN

by

IR. J. J. MUNTJEWERF

Summary

This report describes the hydrodynamic design of a single-screw cargo liner intended to operate at speeds in the range

above V/A/L = 1.0

The ship considered is of the 20,000 m3 displacement-volume type with a length of 160 m and a maximum loaded draft of 9.15 m. The selection of the main form characteristics and the motivation for testing models with different largest-section coefficients is given. Three models were designed and tested for resistance and powering performance.

The test results are presented and discussed.

speed-length ratio

displacement-length ratio

zi/(0.01L)3,

the

prismatic

coefficient

Cp and the

breadth-draft ratio

BIT

which largely determine the

resistance of slow ships, it is also necessary for fast

ships to take into account the largest-section

coeffi-cient Cx and the detailed shape of the ship's lines

especially in the fore body.

Of the parameters mentioned the breadth-draft

ratio

BIT

happens to be the least important from a

point of view of resistance and it was decided to leave

this ratio out of consideration for the present

investi-gation.

The importance of the displacement-length ratio

z1/(0.01L)3 on the total resistance per ton increases

rapidly at speed-length ratios above VlyIL = 1.3. In

600 500 400 o 300 200 100

Fig. I. The relationship between total resistance and displace-ment-length ratio at constant speed-length ratios

A = 15.000 tons CB = 0.586 cp .0.63 = 3.75

I

5

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30 40 50 60 70 80 10 OILP 90 no 110 120 130 IGO 150

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8

the speed range corresponding to 1.0 < VI,../L< 1.3 the

influence of z1/(0.01L)3 on the total resistance per ton is

relatively small and can well be determined from

ex-isting data. To illustrate these remarks figure 1 from [1]

is included in this report.

The influence of the prismatic coefficient Cp is large.

Optimum Cp values for various speed-length ratios

can be found in [2] and [3]. They are given in figure 2.

gations. These calculations showed, that at 30 knots

(VIVL = 1.3) an effective power PE of 70,000 to

80,000 hp should already be expected. Even for the

most futuristic projects this justifies the decision to

limit the speeds below VI,IL = 1.3.

This limitation means a considerable simplification

of the work to be carried out, since at speeds below

VIVL = 1.3, the influence of the displacement-length

ratio z1/(0.01L)3 can also be disregarded, so that only

the influence of the prismatic coefficient Cp and the

largest-section coefficient Cx remain to be investigated.

Since the influence of Cp can be estimated from the

well-known Taylor Series [9], [10] it was decided to

carry out an initial test programme with 3 models

having

different

largest-section-coefficients

Ca., to

determine the influence of Cx on the power

require-ments.

Because only very little information is available on

the propulsive coefficients of very fast cargo ships, it

was considered of interest to carry out propulsion

tests as well as resistance tests [6],

[8]. The decision

to carry out propulsion tests implied some further

restrictions to the speed range to be used for the tests.

Preliminary calculations showed that

with

about

40,000 SHP a speed of about 26 knots could be

ob-tained. However, to increase the speed to 28 knots a

required power of about 65,000 SHP should already

be expected.

For a single-screw version the maximum power to

be accommodated was limited to 40,000 SHP. The

speed range of interest for the propulsion tests with a

propeller designed for 40,000 SHP at 26 knots will be

for speeds up to 27 knots. If later higher powers should

be investigated in the speed range above 27 knots, then

contrarotating or overlapping propeller arrangements

should be considered.

Finally it was decided to carry out the resistance

tests over the speed range of 22-30 knots (0.95 <

< 1.30) and the propulsion tests over the range of

22-27 knots (0.95 < VIVL < 1.17). The design speed

was settled at 26 knots or VI,IL = 1.13. For the speed

range mentioned the available information [2], [3], [4]

and [5] indicated that the choice of the following main

particulars would give the best chance to arrive at an

optimal design:

Prismatic coefficient

Cp

= 0.57

Bulbous bow area coefficient

fB,

0.10

Taylor tangent to the area curve

t

=1.10

Angle of entrance of CWL in degrees

= 7.5

Load waterline coefficient

Cwp = 0.68

Position of longitudinal centre of

buoyancy in percent of L aft

of -1-L

LCB = 2

0.85 o so 005 E 0.70 065 g BO 100 095 coo 080 neo am cp Cr 60 040 500 ILO 160 580 1/I1T

Fig. 2. Optimum C p and CT values according to Saunders

The largest-section coefficient Cx has no influence on

the total resistance per ton at speed-length ratios below

about VI,IL = 0.80. Above VI,IL = 1.5 the

influ-ence of Cx, however, is quite discernible. Not much is

known about this influence in the speed range

be-tween VI,IL = 0.9 and VIVI. = 1.5. Optimum Cx

values as suggested in [2] and [3] are shown in figure 2.

The parameters to determine the optimum general

shape of the fore body can be determined from the

data given in [2], [3], [4] and [5]. It is also possible to

design the optimum fore body lines by applying the

wave resistance theory such as described in [6]. Since,

however, the assumption on which the theory is based,

namely, that the viscosity effect is negligible, seems to

be rather doubtful [7], this theory was not used for

the delineation of the fore body lines. It is felt that for

the time being the empiric approach by using the

available design

information based on systematic

experimental results may lead to a better overall

design from a point of view of minimum total power

required.

The influence of most of the parameters mentioned

is rather speed dependent. To restrict the number of

important variables to the minimum, it is therefore

necessary to limit the speed range to be considered for

an experimental programme as much as possible.

For the type of ship in question, i.e. the single screw

cargo liner of 20,000 m3 displacement volume with a

length between perpendiculars of 160 m and a maximum

draft of 9.15 m, some preliminary resistance calculations

were carried out to find reasonable limits for the speed

range to be considered for the experimental

investi-VAIL

=

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Or AP

1 L.,..iiirargi

meaquiriall

onuorfoni

weiwerbre A

ft-m.6.1/J/

_Ad

Fig. 3.

Bodyplan of model no. 3415 with Cx = 0.93

anint.m7111"firiffirel

MINIAMIN

wwii

MalittENNE

Fig. 4.

Bodyplan of model No. 3416 with C.- 0.97

Or AP 3 M 16 20= FP II I II X 20= FP 15 17 18 2 17 18

(9)

5

Amorm

atiammilYnni

ME: WHOM

MEMNON

mitemosta

Fig. 5.

Bodytilan of model No, 3417 with Cx

0.89 q 9 IS /2 13j STATIONS Fig. 6,

curves of the models

14 15 11, 1, 18 19 ,20 1,0 08 as A/Ak, 021 _ _ ____= _

P

_PF

r

_., _ 1 _ 346 -i ... ... _N.. 1 _,.

MODE MODE MODEL

... 3416 3417

-,--IS

_. ,, i , , , 1 4;1 AP 2 3 5 14 if /5 16 7 .18 qs 20;, PP 2 3 6 7 Sectional area 0.4

(10)

The largest-section coefficient ex recommended was

found to be 0.93 and with this Cx the block coefficient

ev becomes 0.53. This block coefficient is considered

to be about the lowest acceptable value for attaining

suitable cargovolnme for a cargo vessel and for that

reason it was decided to fix the block coefficient at

this value for the present investigation.

Displacement, length, draft and block coefficient

having been determined all main dimensions of the

ship are

fixed.

With V = 20,000 rn3, L = 160 m,

T = 9.15 m and C B = 0.53, the breadth B = 25.81 m.

With these basic dimensions it was decided to test the

following ex modifications at constant C B, resulting

in the mentioned ep variations:

,p

The resistance per ton of the version with Cx = 0.93,

and Cp = 0.57 can directly be compared to the Taylor

Series, because this series also had Cx = 0.93. The

versions, with ex = 0.97 and Cx = 0.89 can be

com-pared to the Taylor Series equivalents having Cp=0.55

and C,, = 0.59 respectively. The relative differences

between the actual models and their Taylor equivalents

with 'constant ex = 0.93 will demonstrate the

in-fluence of Cx on resistance.

31

Hull characteristics and model particulars

Starting from the above-mentioned main dimensions

and principal characteristics the models 3415 (ex =

= 0.93), 3416 (e,,, = 0.97) and

3417 (Cx = 0.89) were

designed. 'The hull characteristics of these models are

Mentioned in table 1. The lines of the models are given

in figure 3 (model 3415), figure 4 (model 3416) and

figure 5 (model 3417). The sectional area curves, of the

models at 100% displacement are given in figure 6.

The models were made of paraffin wax to a scale of

1/28..

PITCH 01 STRIBUTION

00 PERCENT

Table 1. Geometrical particulars of the single screw cargo liner designs

Fig. 7.. Particulars of propeller No. 4121

Turbulence ,sfldation was obtained by studs

in

accordance with ITTC recommendations.

No bilge keels, were fitted to the models. During

the resistance tests the rudder was not fitted to the

models

-4

Propeller design and stern arrangement

Using the results of a first resistance test with model

3415 at 100% displacement, those of a short propulsion

I

4 k

1116111.1111111, 0.8 : 0.7 0.6 11

alt

MI11111"

IMMIIIIIIIIIIIIIF

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WINISSIF

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4.111111_11111111111.

921

_Vi---,,,,W

1/

wd/

Wetted surface without rudder' 4749 4769 4749

Wetted surface with rudder 4814 4833 4813

LCI3 in percent of L aft of 2.0 2.0

CB 0.529 10.530 0.529 Cp 0.569 0.547 0.594 CX 0.930 970 0.890 CPA 0.632 0.611 0.656 CPP 0.506, 0.482 0.533 Cwp 0.661 01.652 0.675 fST 0.10 0.10 0.10 iE deg.. 7.5 6.5 8.0 1.10 1.10 1.10 .A20.0 hLY 139.5 LIB 6.20 BIT 2.82 70% displacement T forward 6.53 6.46 6.59

Taft

7.14 7.07 7.20, V m2, metric tons 14000 14350 14000 14350, 14000 14350 Wetted surface Without rudder in3 3866 3874 3879

Wetted surface with rudder m2 3926 3932 3983

Model No.. 3415 3416 3417

Cx

0.93 0.97 0.899 100% displacement 111 160.00 Wetted length 163.53 25.81 T (level trim) 9.15 V m3 20000 ,metric tons long tons 20197

ex = 0.97

= 055

C x = 0.93

ep = 0.57

lex = 0.89

ep = 0.59

PROPELLER No. 412I D= 63 00 mm AE

/

= 0.9211 44,/A,,, 711 P0.7RD = 0989. Z 4

=

1.0 R R 100.6 0 7.0 20500 C,,

(11)

12

Fig. 9. Stern arrangement of model 3415

blems as much as possible. The stern arrangement of

model 3415 is shown in figure 9.

5

Method of extrapolation

The model test results were extrapolated according to

the two dimensional Froude method, since most of

the material available at present at the N.S.M.B.

which could be used for comparison in this programme

is on Froude basis. To assist in conversions to other

extrapolation methods an overload test was carried

out at a speed of 26 knots with model 3415 at 100%

displacement.

The calculation of PE is according to R. E. Froude's

frictional data, corrected for 150 centigrade standard

temperature.

The results of the self-propulsion tests refer to the

self-propulsion point of ship. These results are directly

calculated from measured model values without any

allowance for appendages not present in the model,

nor for wind and sea, so values for the ship are for

tank conditions. The towrope force applied to the

self-propelled model was equal to the skin friction

correction of R. E. Froude, reduced to model scale.

The number of revolutions of the ship's screw are

given for tank conditions, without correction for

dif-ferences between the wake values of ship and model

and without any allowance.

6

Model experiment results

With each of the models 3415, 3416 and 3417 resistance

tests and self-propulsion tests were carried out at 100%

displacement with level trim and at 70% displacement

with 2 feet trim by the stern.

With model 3415 an overload test was carried out at

26 knots for the 100% displacement condition. The

results are given in figure 12.

For the propeller design a radial wake distribution

test with vane wheels was carried out and for propeller

model 4121, used for the propulsion tests, the open

water characteristics were determined.

The results of these tests have been presented in

ta-bular form in the appendix in tables A.I up to and

including A.18.

In graphical form the results of the resistance and

propulsion tests are presented in figures 10 and 11 for

the

100% and

the 70% displacement condition

respectively over the speed range of 22-27 knots. In

figure 14 the results of the resistance tests at 100%

displacement are given over

the

speed range of

22-30 knots. The overload test results are given in

figure 12, the radial wake distribution in figure 8

and the open water characteristics of propeller 4121

in figure 13.

060

030

RADIAL WAKE DISTRIBUTION 3415 SPEED 26 KNOTS DRAFT 91S m 0,

14

0 30 0.20 OW NOTE. THE WAKE VOLUME IS AS INTEGRATED CURVE IS CORRECTED IN ACCORDANCE BY THE WITH PROPELLER SO THAT THE THE EFFECTIVE MEAN WAKE C13 0.4 as 06 OAS 0.9 LO

Fig. 8. Radial wake distribution used for the propeller design

test with a stock propeller model and those of a radial

wake distribution test, one propeller was designed for

the whole series of models. This propeller (model no.

4121) was designed to absorb 40,000 SHP at 150 rpm

at a speed of about 26 knots, using zero correlation

allowance on the Froude extrapolated values.

For sufficient immersion at 70% displacement and

for sufficient clearance at the top the propeller

dia-meter was limited to 6300 mm, which is only about

2 per cent. too small for optimum performance. The

strength calculations were made for

copper-nickel-aluminium bronze. The propeller calculations

were

carried out using the vortex theory standard

sub-routine programmes available at the N.S.M.B.

com-puter centre. The particulars of propeller 4121 are

given in figure 7. The radial wake distribution used

for the propeller design is shown in figure 8.

The propeller aperture was designed to give

ade-quate clearance between blades and hull and between

blades and rudder to avoid excessive vibration

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60000_ 50000_ 40000_ P 0 PE 3000a_ 20000_ 10000

_

0 160_ 14O_ 120_ 100

_

100 MODEL MODEL MODEL 3415 3416 C 3417 C 0/0 DISPLACEMENT ---- ...--...-"'

/

....---/

/

I

/

_0.80 11.0 _0.70 _0.60 Cx = 0.93 x :0.97 :0.89

/

PD/

/

1.10 riR _0.70

rlo

_0.60 _0.50

PP"11111111111111

Mai

RO

V

, 41 J 0.70_ 0.65 _0.30 W _0.20 0.20_

t

0.10

_

t 22 23 24 25 26 27 SPEED IN KNOT

Fig. 10. Results of the resistance and propulsion tests at 100% displacement

(13)

14 27 - --1 MODEL

_3415'ICX

:0.93 ' _ 50000 MODEL 34116 C xi0.97 150_

-=--MODEL 3417

C: 0.8-9

X . -no .,..1 70°/a 'DISPLACEMENT . -n

s..----, 1 , I L.or000H i-po..L

/

_0130

/

H . -

/

_0.70 .

FTL

....,

no

30000 ,_ 1.10

i.

/

aso 1 P la

rift

I it. OOLI 1

/

--,_

-

--....

I - .. P_ ,E

../

n.0 ../. ;43.70 ' 20000

7 r

0. 60 1 0.75..

₁

0

J

/

r-0.'501 - I 0.70 - _ . 1

.--/

....-"" 10000 _.. O.65_ _1.0.3Ia

..7=__,,,,...

I _020' I

0 .., an_

1 f

t

___ 1 1 IF __, _ _ __ 22 23 ,25 26 SPEED, IN KNOTS

Fig. 11, Results of he resistance and propulsion tests at 70% displacement

/

(14)

Fig., 12. Overload test results of model 3415

MODEL, 3415 DRAFT =9.15. rn SPEED: 26 KNOTS

I 160 i 70 i 14&3 I 1 I 500.00, i

ns

14_01

q

1 .1 . , 1 1 P 01 41261 i 1 .1 40000 PDt

p

E 300100,

ii

! , - It .1 , 20000L_ _200 1 IT 182.82 t , IR T 150 0.201 IR T 1001 1 I

t

0.101 - 2cii

k OVERLOAD [ I.N °hi

_116 0

.10

ON BASE OF P E IN TA NKCONOITION 0.673 155.73 0.148 +20

(15)

Discussion on resistance test results

From figures. 10 and 11 it follows directly, that the

total resistance decreases with decreasing Cx values at

speeds above 24 knots or VIV L = 1J05. The largest

difference is found in passing from Cx = 0.97 to 0 93,

but from Cx

0.93 to 0.89 the improvement in.

Table 2. Percentages PE and PD, taking at each speed the results of model 3415 (Cx = 0.93) as 100 per cent.

Fig. 13. Open water characteristics of propeller No. 4121

resistance is ritual

less pronounced. In the spee

range below VI.IL = 1.05 the differences between the

three models are practically negligible at 100%

dis-placement. However, at the design speed of 26 knots

,(VI\IL = 1.13) the gain in resistance at 100% displace!

inent by reducing Cx from 0.97 to 0.93 amounts

al-ready up to 7 per cent.. and by reducing Cx from 0.97

-o.e, j I 0.7 ; o.ie , .s 1 0 4 =-°' 0.3 1 0.2 1' Y 1:1,1 1

a

Y 11

D

0 -I: It ^ , 1 10 Ko ., II I. II ,

j o

0.117--- 02 1 0.3 OA 0.5 0.6 . 0.7 t 0.8

-I

0.9 1 1.0 it Seed in knots 100% displacement 70% displacement

model 3416 (Cx = 0.97) model 3417 (Cx = 0.89) model 3416 (Cx = 0.97) model 3417 (Cx = 0.89)

PE PD PE PD PE PD PE PD' 22 102.8 104.0 106.2 104.6 105.6 107.3 98.2 102.5 23 103.2 105.2 101.7 105.2 108.3 109.8 100.7 103.0 24 103.9 106.7 101.4 104.3 110.5 111.1 100.4 101.5 25 105.4 108.4 99.2 101.8 113.3 112.3 98.1 98.6 26 108.1 110.9 97.2 99.1 115.2 113.9 95.3 95.5 27 110.2 115.4 96.5 98,9 115.9 114.7 93.1 92.1 28. 108.9 93.7 114.7 92.5 29 111.8 93.2 113.2 91.7 30 111.2 92.0 113.6 91.8 - ,

S to

0.9, a 8 0.7 0.6 0.5 0.4 0.3 0.2 16 7

=

0.1 0

(16)

to 0.89 even up to 10 NI. cent. At 70% displacement

these gains amount up to 14 and 17 per cent.

respective-ly. A comparison of the resistance of the models at

other speeds can be found in table 2.

In the. direct comparison of the three models the

effects of the largest-section coefficient reduction and

the inherent prismatic coefficient increase for the given

'Nock coefficient of course are combined. To separate

these effects a reasonable assessment seems comparing

the resistance of each of the models with that of a

corn-1 900010 MODEL 3415 MODEL 3416 MODEL" 3417

qx

7.0.93 Cx ..: 0.97 C

_{x ,}

'0.89 100 010 DISPLACEMENT 1 80101 1

/

I 1 70000 1 - _ I I 600110_ ___ t 50 I I 5000'0 1.00.

-400001 0.50 1

Pr

E ' 30000 I -I 20(101:1

-In00

110 1 I

'P /P

_E _E TAYLII-", 1.00' . ph, I ... .-.... ., PE / PE TAYLOR 1 0.9 0 ... - ... I 0 SO 1 22 23 24 25 SPEED IN KNOTS I I 'I 2,6. 27 28 I Ii 29 it 30 Ma_ 0.95 1,00 105 1 t ti 7i10 1.15, 1.20 1 - i _ _ ir _ 1.25 t1 130 , 1.2 4.1. 4.8 5.0 52 5.4 15.6 5.8

Fig. 14. Froude resistance coefficients, effective powers and effective power ratios of the Models at 100% displacement

/

v7

/

. I I I I I I 1..6

(17)

18

parable Taylor form with the same prismatic

coeil-cient Cp, displacement-length ratio z1/(0.01L)3 and

beam-to draft ratio BIT. The ratio of these resistances

PEIPETay lor

is given for each model together with its

and PE values in figure 14 for the 100% displacement

condition;

PE_Taylor

values. ary.given in figure 15.

Figure 14 shows, that foi

Model

3415 with C, = 0.93

total resistance

at the design speed of 26 knots

(1/1,./L = 1.13) is only 92 per cent. of that of the

com-parable Taylor form. At 27 knots (V1.:1 = 1.17) the

ratio PEIPE

Tay lo;

0.88 which compares very well

with the data given in table 2, column 3

off('

The _PEIPE Taylot

ratios of model 3417 with C=0.97

lie about 10 per cent. above and those of model 3416

with C, = 0.89 about 10 per cent. below the values of

model 3415 in

the speed range. of 22 to' 26 knots

(0.95 <

L < 1.13). Above 26 knots the differences

become gradually smaller, but all over the speed

ranee the

smallest CA.

gives the best performance in

comparison with

the Taylor

equivalent. The

PEI

PETay lor

curves in figure 14 clearly show the importance

of an appropriate selection of C. especially in the

ranee 0.95 <

< 1.13.

This apparently

is in

contradiction with the *Conclusion found above from

MODEL MODEL

/

3415 3416

--innnnn MODEL 100% .

/

3417 DISPLACEMENT 90000

/

_/

80000 70000

/

/60000

/

50000

P

TAYLOR E 40000 PE TAYLOR

/

-**<,

...,-..----/-7 30000 ..../.." ..../--20000 10000

...---"----..../

0 22 23 24 25 26 27 28 29 30 SPEED IN KNOTS

Fig. 15. Effective powers of the models at 100% displacement accordingto Taylor

(18)

a direct comparison of the PE values of the three

models, viz., that at speeds below V1,11, = 1.05 the

differences between the PE values are negligible.

How-ever, in the direct comparison

of

the PE values the

combined effects

of C.

and Cp are present, which

cancel each other in the speed range mentioned. (see

the PE

Taylor

curves in figure 15 which demonstrate the

influence of C, at constant C).

Summarizing it can be concluded, that for the type

of

ship used for the investigation, C, has a considerable

effect on total resistance over the whole speed range

tested, viz. 0.95 < V1,11- < 1.30 and especially over

the lower part of this range, viz. 0.95 < VI\IL < 1.15.

Further it can be concluded

,

that at constant

pris-matic coefficient the lowest C, value will give the best

results allover the speed range 0.95 <

< 1.30.

The optimum C, value lies below C, = 0.89 and it

would therefore be of interest to extend the present

programme with some more modifications to

deter-mine the optimum C, value.

The amelioration to be expected from a reduction

of C, can be estimated for any speed by taking from

figure 14 the ratios of the P IP

_{- E} _Taylor

values shown for

the C, values of the tested models.

It should finally be remarked, that the optimum C,

value for the type of ship considered is much lower

over the speed range 0.95 <

< 1.15 than

sug-gested by Saunders in figure 2.

8

Discussion on propulsion test results

The results of the propulsion tests as giver' in figures

10 and II clearly show, that the conclusions derived

from the resistance tests are valid for the self-propelled

models as well. The largest-section coefficient Cx or

the distribution of the displacement over the length of

the ship with fixed longitudinal centre of buoyancy

does not influence the propulsion coefficients

notice-ably. There are, of course, small differences in the

components of the propulsive coefficients due to the

fact, that the propeller was more heavily loaded

be-hind model 3416 (C, = 0.97) with the highest PE

values than behind the other models, resulting in lower

advance coefficients J and open water efficiencies 170

and higher wake values if

for model 3416. This is

apparent at both displacement conditions. Due to the

higher propeller loading the thrust deduction fraction

t also seems to be relatively higher for the model 3416

with C, = 0.97 than for the other models.

Of the models 3415 (Cx = 0.93) and 3417 (C, =0.89)

with practically equal PE values, the model 3417 with

the fullest afterbody waterline endings has the highest

t

values. The J, go and w values of the models 3415

and 3417 are equal, which proves that the mean

nom-inal wake is practically not influenced by the variation

in the distribution of the displacement.

The relative rotative efficiencies 11R are the same for

the three models at the 100% displacement condition.

At the 70% displacement the lip values vary more.

Possibly due to the closer proximity of the propeller

to the water surface.

The combined effect of all the above differences in

the components of the propulsive coefficients results in

a slightly higher total propulsive efficiency for model

3415 (C, = 0.93) in the 100% displacement condition

than for the other models. At 70% displacement the

total efficiencies of the three models are practically

equal.

Although the above shows that the effects of the

variations tested are small from a propulsion point of

view, it should be noted, that at 100% displacement the

required power P0 is definitely the lowest for model

3415 (C, = 0.93) for speeds up to 26 knots (V1,1 L =

= 1.13) and only slightly higher than that of model

3417 (C, = 0.89) at speeds above 26 knots. At the

design speed of 26 knots the models 3415 (C, = 0.93)

and 3417 (C, = 0.89) require about the same P0 and

both models require about 11 percent less power than

model 3416 (C, = 0.97). Finally the power required

at different speeds is given for models 3416 and 3417

in percentages of the power required for model 3415 in

table 2. This table clearly shows the gains to be

ex-pected from a reduction of C, at constant CD.

9

Concluding remarks

The present investigations have shown, that at

con-stant block coefficient CB, the model with the lowest

largest-section coefficient C, has the lowest effective

power PE over the speed range 0.95< VI,/L< 1.30,

both at 100% and at 70% displacement. The propulsion

tests showed, that the above is also valid for minimum

required power P, except at 100% displacement at

speeds below VI\IL = 1.15, where the model with

Cx = 0.93 is definitely the best in respect of P.

Elimination of the variation of the prismatic

coef-E, ETay lor

ratios of

ficient by taking into account the P IP

the models has shown that for the type of ship

con-sidered, C, has a noticeable effect especially over the

range 0.95 <

< 1.15. The optimum Cx value

seems to be much smaller than suggested elsewhere.

=

(19)

20

References

WAHAB, R., Notes on the resistance of very fast cargo ships.

Report No. 66-114-HST of the N.S.M.B.

jiNfialft Principles of naval architecture. Published by

the S.N.A.M.E., New York, 1967.

SAUNDERS, H. E., Hydrodynamics in ship design. Published

by the S.N.A.M.E., New York, 1957.

LINDBLAD, A., On the design of lines for merchant ships. Transactions of Chalmers University of Technology Nr. 240,

1961.

TAYLOR, D. W., I nfuence of the bulbous bow on resistance.

Marine Engineering and Shipping Age, September 1923. PEEN, PAO C. and J. STROM-TEJSEN, A hull form design procedure for high-speed displacement ships. Trans. S.N.A.M.E. June, 1968.

Steele, B. N. and G. B. Pearce, Experimental determination of the distribution of skin friction on a model of a high speed liner. Quart. Trans. R.I.N.A. 110, No. 1, Jan. 1968.

SILVERLEAF, A. and J. DAWSON, Hydrodynamic design of

merchant ships for high speed operation. Trans. R.I.N.A. 1966.

GERTLER, M., A reanalysis of the original test data for the Taylor Standard Series, D.T.M.B.Report 806, March 1954. TAYLOR, D. W., Speed and power of ships. Third Edition,

United States Maritime Commission, 1943. ,3.

4.

,5.

(20)

APPENDIX

(21)

22

Table A 1.

Resistance test results

Test No. 25874

Model condition,: without rudder. Studs as turbulence stimulator.

on F.P. = 9.15

m Draft moulded on A.P. = 9.15 in

I mean = 9.15 m

Table A 2.

Resistance test results

Test No. 25844

Model condition: without rudder. Studs as turbulence stimulator.

on F.P. = 6.530 m

Draft moulded

on A.P. = 7.140 m

I mean = 6.835 m

Displacement volume V = 14000 na3 Temperature tank water t = 16.2 centigrade

VsVM

RTM ED RT in PE PE friet PE wave

in knots in m see-' in g in g metric tons metric metric metric

(

1

J

5s

)

F, =

A, Vm.825 f ' M

/10.0875 = Ship speed in knots

Vm = Model speed in m see-' RTm = Measured model resistance

FE = Skin friction correction from model to ship RT = Total resistance of ship

PE = Effective HP in salt water under tank condition for ship

Ss = Wetted surface ship Sm = Wetted surface model

Ship model No. 3415 Scale ratio A = 28 Frictional coefficients: for ship

fs = 0.13999

for model fm = 0.16878

f

= fm{ 1 +0.0043 (15°-ru,)}

Ship model No. 3415 Scale ratio A = 28 Frictional coefficients:

for ship L = 0.14023

for model fm = 0.16986 f' m = fm{1 +0.0043 (15°40}

Specific gravity tank water y = 1.000 Specific gravity sea water yi = 1.025

ce

CALCULATION OF EHP ACCORDING TO R. E. FROUDE'S FRICTIONAL DATA:

meir

= 0.006859

-I

Vs RTm -0.002039y ,

vs2-825(;.0 y1 A3.5 .0875

_fs)

_Vm(RTm-FD) y 75

= 427.1

42/3P E brit 42/3- v 3

ce

S P E metr = 1.025 V

British HP =

₇₆75

metric HP

Note: The PE values stated are corrected to 150 centigrade standard temperature. Model and ship dimensions are moulded.

22 2.1389 4880 1268 81.27 12264 7025 5239 513 0.829 221 2.1875 5120 1322 85.46 13189 7485 5704 510 0.834 23 2.2361 5390 1376 90.32 14249 7965 6284 504 0.844 231 2.2847 5680 1431 95.61 15411 8464 6947 497 0.856 24 2,3333 6015 1487 101.88 16772 8982 7790 487 0.874 241 2.3819 6395 1544 109.15 18343 9527 8821 473 0.899 25 2.4305 6810 1602 117.19 20095 10080 10015 459 0.927 251 2.4791 7290 1661 126.66 22154 10660 11494 442 0.962 26 2.5278 7855 1721 138.02 24615 11261 13354 422 1.008 261 2.5764 8485 1781 150.85 27420 11884 15536 401 1.061 27 2.6250 9210 1843 165.76 30700 12528 18172 379 1.123 271 2.6736 10040 1906 183.02 34524 13195 21329 356 1.195 28 2.7222 10990 1970 202.96 38980 13884 25096 333 1.277 281 2.7708 12105 2034 226.61 44299 14595 29704 309 1.377 29 2.8194 13360 2100 253.36 50398 15331 35067 286 1.487 291 2.8680 14760 2166 283.38 57341 16089 41252 264 1.612 30 2.9166 16215 2234 314.59 64734 16872 47862 246 1.729 Displacement volume V = 19999 m3 Temperature tank water f. = 16.2 centigrade

Specific gravity tank water y = 1.000 Specific gravity sea water yi = 1.025

Vs in knots Vm in m sec-' RTm in g ED, in g

Er in

metric tons PEmetric metric PE wavemetric C,,

-,-, __ 2.1389 5630 1536 92.12 13901 8615 5286 574 0.741

//;

2.1875 5930 1601 97.41 15033 9179 5854 568 0.749 23 2.2361 6250 1666 103.14 16273 9768 6505 560 0.760 231 2.2847 6600 1733 109.51 17653 10379 7274 551 0.772 24 2.3333 6995 1801 116.87 19239 11015 8224 538 0.791 241 2.3819 7425 1870 124.99 21005 11676 9329 524 0.812 25 2.4305 7895 1940 133.99 22977 12362 10615 509 0.836 251 2.4791 8410 2011 143.98 25184 13073 12111 493 0.863 26 2.5278 9005 2084 155.73 27773 13810 13963 474 0.897 261 2.5764 9690 2158 169.48 30807 14574 16233 452 0.941 27 2.6250 10575 2233 187.70 34763 15363 19400 424 1.003 271 2.6736 11735 2309 212.09 40008 16181 23827 389 1.094 28 2.7222 13070 2386 240.40 46171 17026 29145 356 1.195 281 2.7708 14495 2464 270.71 52921 17898 35023 328 1.297 29 2.8194 16080 2543 304.60 60590 18801 41789 301 1.413 291 2.8680 18115 2624 348.56 70531 19730 50801 273 1.558 30 2.9166 20280 2706 395.43 81370 20690 60680 249 1.709

=

1'

(22)

on F.P. = 9.15

m

Draft moulded on A.P. = 9.15 m

mean = 9.15 m

Displacement volume V = 20029 tri3 Temperature tank water t,= 16.3- centigrade

PE met,. = 0.006859 71- A' Vs- RTAi

0.002039y,

FD

sm.

vA41(

.825

f,

fs

)

20.0875

Vs = Ship speed in knots Vm = Model speed in m sec' RTm = Measured model resistance

FD = Skin friction correction from model to ship RT = Total resistance of ship

Ss

= Wetted surface ship Sm = Wetted surface model

Frictional coefficients: for ship

f, = 0.13999

for model fm = 0.16878 I'm = fut 1 +0.0043 (15'401

Specific gravity tank water y = 1.000 Specific gravity sea water y, = 1.025

CALCULATION OF EHP ACCORDING TO R. E. FROUDE'S FRICTIONAL DATA: 71 A3.5

vs2.825(A0.0875.f' -fs)

.17 D

M, TM -

Fp) y 75

Pr k

4,7.1

A221.1. v53 4213- v3 Ce 1 s PE me, , = 1.025 V

British HP = 75 metric HP

₇₆

Note: The PE values stated are corrected to 15= centigrade standard temperature. Model and ship dimensions are moulded

Table A 4.

Resistance test results

Test No. 26220

Ship model No. 3416

Model condition: without rudder. Studs as turbulence stimulator. Scale ratio = 28 Frictional coefficients:

on F.P. = 6.460 m

Draft moulded

on A.P. = 7.070 m

I mean

= 6.760 m

for ship

f, = 0.14024

flu = f'm{l +0.0043 (15'4)}

Displacement volume V = 13970 rn'' Specific gravity tank water = 1.000

Temperature tank water tw = 16.7 centigrade Specific gravity sea water ;), = 1.025

Vs Vm RT111 FD in knots in m sec-1- in g in g RT in metric tons PE _{PE frict} _{PE wave} ce

metric metric metric

2.1389 5080 1265 85.84 12954 7040 5914 485 0.877 221 2.1875 5385 1318 91.51 14123 7501 6622 476 0.894 23 2.2361 5720 1372 97.83 15435 7982 7453 465 0.915 231 2.2847 6080 1427 104.70 16876 8482 8394 453 0.939 24 2.3333 6485 1483 112.55 18528 9002 9526 440 0.967 /41 2.3819 6965 1539 122.09 20518 9542 10976 423 .006 /5 2.4305 7500 1597 132.82 22777

10/02/2675

405 .051 25/ 2.4791 8100 1656 145.00 25362 10683 14679 386 .102 26 2.5278 8780 1716 158.95 28347 11285 17062 366 .162 261 2.5764 9540 1777 174.68 31751 11910 19841 346 .229 27 2.6250 10380 1838 192.20 35596 12555 23041 326 .305 271 2.6736 11300 1901 211.49 39893 13223 26670 307 .386 28 2.7222 12310 1964 232.80 47711 13914 30797 290 .467 281 2.7708 13460 2029 257.21 50282 14627 35655 271 .570 29 2.8194 14840 2094 286.80 57049 15364 41685 252 .688 291 2.8680 16450 2161 321.52 65058 16124 48934 233 .826 30 2.9166 18110 2228 357.36 73537 16908 56629 217 .961 vs in knots 1/114 in m sec ' RTm in g FD in g RT in

metric tons PEmetric

PE triet metric PE wave metric C,, 22 2.1389 5750 1541 94.71 14292 8651 5641 559 0.761 221 2.1875 6070 1605 100.47 15505 9218 6287 551 0.772 23 2.2361 6400 1671 106.41 16787 9808 6978 543 0.784 231 2.2847 6785 1738 113.56 18305 10423 7882 532 0.800 24 2.3333 7200 1806 121.37 19980 11061 8919 519 0.820 241 2.3819 7680 1875 130.62 21951 11725 10226 502 0.848 25 2.4305 8220 1946 141.17 24208 12414 11794 484 0.879 251 2.4791 8850 2017 153.75 26892

13/28/3764

462 0.921 26 2.5278 9575 2090 168.42 30036 13868 16168 439 0.969 261 2.5764 10430 2164 185.99 33808 14635 19173 413 1.030 27 2.6250 11430 2239 206.81 38300 15428 22872 385 1.105

27.12.6736

12615 2316 231.74 43712 16249 27463 357 1.192 28 2.72/2 14030 2393 261.84 50289 17098 33191 327 1.301 281 2.7708 15710 2471 297.89 58234 17974 40260 298 1.428 29 2.8194 17685 2551 340.53 67737 18880 48857 270 1.576 291 2.8680 19835 2632 387.08 78326 19813 58513 246 1.729 30 2.9166 22260 2714 439.80 90502 20777 69725 224 1.899

=

-=

y

(23)

24

Table A 6.

Resistance test results

Model condition: without rudder. Studs

on F.P. = 6.595 m

Draft moulded )

on A.P. = 7.205 m

I mean = 6.90 m

Test No. 25872

as turbulence stimulator.

CALCULATION OF EHP ACCORDING TO R. E. FROUDE'S FRICTIONAL DATA:

PE nietr 0.006859 -Y1-3* Vs- RTm- 0.002039y,- Ss- Vs2.825(A_._rt .875

-J)

Y I 13.5

-

v

y 75

ED = y

Vm1.8 2

5(

f'

fs

20.0875 Vs = Ship speed in knots

Vm = Model speed in m sec-1 RTm = Measured model resistance

FD = Skin friction correction from model to ship RT = Total resistance of ship

Ss = Wetted surface ship Sm = Wetted surface model

Note: The PE values stated are corrected to 15° centigrade standard temperature. Model and ship dimensions are moulded.

0 = 427.1

P Et

A2213 Vs3 42/3 3

=

S PE metr

A = 1.025 V

75

British HP =

₇₆

metric HP

Ship model No. 3417 Scale radito A = 28

Frictional coefficients:

for ship L = 0.13995

= fm{1 +0.0043 (15°4)}

Table A 5.

Resistance test results

Test No. 25871

Model condition: without rudder. Studs as turbulence stimulator.

on F.P. = 9.15

m

Draft moulded 1 _{on A.P. = 9.15}

m mean

=9.15 m

Ship model No. 3417 Scale ratio A = 28 Frictional coefficients: for ship j's = 0.13999 for model fm = 0.16878 I'm = fm{1 +0.0043 (15°42)}

Displacement volume V = 19989 m3 _{Specific gravity tank water y = 1.000}

Temperature tank water t, = 16.2 centigrade Specific gravity sea water yi = 1.025 v, in knots Vm in m sec-t k TMin g FD

in g

RT in metric tons PE PE friet PE wave

metric metric _metric Ce

22 2.1389 5640 1536 92.34 13935 8615 5320 572 0.744 221 2.1875 5975 1601 98.42 15190 9179 6011 561 0.758 23 2.2361 6330 1666 104.94 16557 9768 6789 550 0.774 231 2.2847 6700 1733 111.76 18015 10379 7636 539 0.789 24 2.3333 7070 1801 118.56 19517 11015 8502 530 0.803 241 2.3819 7445 1870 125.44 21081 11676 9405 522 0.815 25 2.4305 7845 1940 132.87 22784 12362 10422 513 0.829 251 2.4791 8285 2011 141.17 24692 13073 11619 503 0.846 26 2.5278 8810 2084 151.34 26991 13810 13181 488 0.872 261- 2.5764 9465 2158 164.41 29886 14574 15312 466 0.913 27 2.6250 10285 2233 181.18 33555 15363 18192 439 0.969 27- 2.6736 11270 2309 201.63 38034 16181 21853 409 1.040 28 2.7222 12395 2386 225.21 43254 17026 26228 380 1.120 281 2.7708 13665 2464 252.03 49270 17898 31372 352 1.209 29 2.8194 15155 2543 283.78 56449 18801 37648 324 1.313 29- 2.8680 16910 2624 321.45 65044 19730 45314 296 1.437 30 2.9166 18875 2706 363.82 74865 20690 54175 270 1.576 Displacement volume V Temperature tank water t

= 13992 ma = 16.2 centigrade

Specific gravity tank water y = 1.000 Specific gravity sea water

yi = 1.025

Vs. in knots VM in m sec ' RTIII in g ED in g RT in metric tons PE Pk: frict metric metric PE wave metric 221 2.1389 4800 125/ 79.83 12047 7035 5012 522 0.815 22-1 2.1875 5090 1304 85.19 13147 7496 5651 511 0.833 23 2.2361 5400 1358 90.95 14348 7976 6372 501 0.849 231 2.2847 5705 1412 96.60 15571 8476 7095 492 0.865 24 2.3333 6015 1467 102.33 16847 8995 7852 484 0.879 241 2.3819 6330 1524 108,14 18173 9535 8638 478 0.890 25 2.4305 6690 1581 114.96 19713 10094 9619 468 0.909 251- 2.4791 7085 1639 122.54 21433 10675 10758 457 0.931 26 2.5278 7545 1698 131.56 23464 11277 12187 442 0.962 261 2.5764 8070 1758 142.03 25817 11901 13916 426 0.999 27 2.6250 8680 1819 154.38 28591 12545 16046 406 1.048 271 2.6736 9420 1881 169.64 31998 13213 18785 384 1.108 28 2.7222 10285 1944 187.68 36046 13903 22143 359 1.185 281 2.7708 11275 2008 208.52 40763 14615 26148 335 1.270 29 2.8194 12400 2073 232.37 46222 15352 30870 311 1.368 291 2.8680 13675 2138 259.59 52528 16111 36417 288 1.477 30 2.9166 15045 2205 288.91 59451 16895 42556 268 1.588

=

t Ce

(24)

Table A 7.

Propulsion test results

Test No. 26491

Model condition: Studs as turbulence stimulator.

on F.P. =9.15 m

mean = 9.15 m

Displacement volume V = 19999 rn3

Table A 8.

Propulsion test results

Test No. 26536

on F.P. = 6.530 m

Draft moulded

on A.P. = 7.140 m

I mean = 6.835 m Displacement volume V - 14000 in3

" v

1 S

Admiralty constant =

PD metr

British HP =

₇₆

metric HP

Ship model No. 3415 Propeller model No. 4121 Scale ratio A = 28

Skin friction correction FD from model to ship is according to Froude's constants

PD = delivered HP at propeller. PE = effective HP.

ns = RPM of the ship's screw under the below conditions, not corrected for difference between the wake of ship and model, without any allowance.

.4

_{= Displacement weight in salt water, in metric tons}

Note: Results of self-propulsion tests as stated above refer to the self-propulsion point of ship.

The results are calculated direct from measured model values without any allowance for appendages not present in the model, wind and sea; so values for ship are for tank conditions, corrected for salt water (y, = 1.025) and 15° centigrade.

Model and ship dimensions are moulded. Ship Speed in knots Vs PD metric PE metric Iii,

= Ps/Pp

Admiralty constant Revolutions per minute ns Resistance RT in metric tons Thrust T in

metric tons t = (T-RT)IT

22 20181 13901 0.689 395 119.3 92.12 109.24 0.157

22

15033 0.687 390 122.5 97.41 115.32 0.155 23 23734 16273 0.686 384 125.6 103.14 122.07 0.155

23i

25863 17653 0.683 376 128.9 109.51 129.27 0.153 24 28194 19239 0.682 367 132.4 116.87 137.82 0.152 24:1 30822 21005 0.681 357 136.1 124.99 147.27 0.151 25 33849 22977 0.679 346 139.9 133.99 157.62 0.150 25,1 37252 25184 0.676 333 143.9 143.98 169.32 0.150 26 41261 27773 0.673 319 148.3 155.73 182.82 0.148 26.1 45817 30807 0.672 304 152.8 169.48 198.12 0.145 27 51191 34763 0.679 288 157.7 187.70 216.80 0.134 Ship Speed in knots Vs PD

metric PEmetric rip - PE/PD

Admiralty constant Revolutions per minute ns Resistance RT in metric tons Thrust Tin

22 16664 12264 0.736 377 112.8 81.27 96.30 0.156

22/18/02

13189 0.729 372 115.9 85.46 101.93 0.162 23 19757 14249 0.721 364 119.1 90.32 108.23 0.165 231 21650 15411 0.712 354 122.6 95.61 114.98 0.168 24 23801 16772 0.705 343 126.1 101.88 122.63 0.169 241 26338 18343 0.696 330 130.0 109.15 131.18 0.168 25 29141 20095 0.690 317 134.1 117.19 141.08 0.169 25 32391 22154 0.684 302 138.4 126.66 152.11 0.167 26 36360 24615 0.677 285 143.1 138.02 165.83 0.168 261 41125 27420 0.667 267 148.2 150.85 181.81 0.170 27 46839 30700 0.655 248 153.7 165.76 200.71 0.174

=

t 21877

=

(25)

26

Table A 9.

Propulsion test results

Test No. 26503

on F.P. =9.15 m

Draft moulded ) on A.P. = 9.15 m I mean = 9.15 m

Displacement volume V = 20029 in'

e2,' v3

S

Admiralty constant =

PD metr

British HP

= -75

metric HP

7 6

The results are calculated direct from measured model values without any allowance for appendages not present in the model, wind and sea; so values for ship are for tank conditions, corrected for salt water (y, 1.025) and 15° centigrade.

Model and ship dimensions are moulded.

Ship model No. 3416 Propeller model No. 4121 Scale ratio A. = 28

Skin friction correction Pp from model to ship is according to Froude's constants

= Displacement weight in salt water, in metric tons

Ship Speed in knots Vs

PD metric

PE

metric r/o = FE/PD

Admiralty constant Revolutions per minute ns Resistance RT in metric tons Thrust Tin metric tons t = (T-RT),T 22 17887 12954 0.724 351 113.8 85.84 102.83 0.165 221 19710 14123 0.717 341 117.2 91.51 110.37 0.171 23 21696 15435 0.711 331 120.6 97.83 118.13 0.172 231 24006 16876 0.703 319 124.2 104.70 126.46 0.172 24 26441 18528 0.701 308 127.9 112.55 135.34 0.168 241 29433 20518 0.697 295 132.0 122.09 145.69 0.162 25 32712 22777 0.696 282 136.3 132,82 157.39 0.156 251 36691 75362 0.691 266 141.1 145.00 171.35 0.154 26 41420 28347 0.684 250 146.5 158.95 187.55 0.152 261 47091 31751 0.674 233 152.1 174.68 206.56 0.154 27 53734 35596 0.662 216 158.2 192.20 229.06 0.161 Ship Speed in knots Vs PD metric PE metric = PEIPD Admiralty constant Revolutions per minute ns Resistance RT in metric tons Thrust Tin metric tons t = (T-RT)/T 22 20993 14292 0.681 380 119.9 94.71 114.87 0.176 221 22917 15505 0.677 373 123.3 100.47 121.51 0.173 23 25029 16787 0.671 364 126.5 106.41 128.71 0.173 231 27406 18305 0.668 355 129.9 113.56 137.26 0.173 24 30089 19980 0.664 344 133.5 121.37 146.59 0.172

24/33/83

21951 0.662 332 137.3 130.62 157.51 0.171 25 36695 24208 0.660 319 141.3 141.17 169.55 0.167 251 40823 26892 0.659 305 145.8 153.75 183.83 0.164 26 45741 30036 0.657 288 150.7 168.42 200.48 0.160 261 51637 33808 0.655 270 156.1 185.99 220.62 0.157 17 ₅₉₀₉₉ ₃₈₃₀₀ _0.649 ₂₅₀ 162.4 206.81 245.04 0.156

Table A 10.

Propulsion test results

Test No. 26504

Model condition: Studs as turbulence stimulator. Ship model No. 3416

on F.P. = 6.460 m

Propeller model No. 4121

Draft moulded

on A.P. = 7.070 m

Scale ratio A = 28

I mean = 6.760 m Skin friction correction FD from model to

Displacement volume V = 13970 m3 ship is according to Froude's constants

A

=

(26)

Table A 11.

Propulsion test results

Test No. 26507

on F.P. = 9.15

m

I mean = 9.15 m Displacement volume V = 19989 m3

Admiralty constant -

1j2, /3 Vs3

P0

metr 75

British HP =

₇₆

metric HP

Skin friction correction ED from model to ship is according to Froude's constants

A = Displacement weight in salt water, in metric tons

The results are calculated direct from measured model values without any allowance for appendages not present in the model, wind and sea ; so values for ship are for tank conditions, corrected for salt water (yi = 1.025) and 15 centigrade.

Model and ship dimensions are moulded. Ship Speed in knots Vs PD metric PE metric = PEIPD Admiralty constant Revolutions per minute ns Resistance RT in metric tons Thrust Tin

metric tons I = (T-RT)IT

22

21/09/3935

0.660 378 120.3 92.34 112.96 0.183 221 22987 15190 0.661 371 123.5 98.42 120.16 0.181 23 24971 16557 0.663 365 126.7 104.94 127.58 0.177

23/27/48

18015 0.664 358 130.1 111.76 135.01 0.172 24 29414 19517 0.664 352 133.3 118.56 143.43 0.173 241 31837 21081 0.662 346 136.7 125.44 150.53 0.167 25 34459 22784 0.661 340 140.1 132.87 159.31 0.166 251 37450 24692 0.659 332 143.8 141.17 168.76 0.163 26 40907 26991 0.660 322 147.9 151.34 180.23 0.160 261 45231 29886 0.661 308 152.1 164.41 194.63 0.155 27 50625 33555 0.663 291 157.0 181.18 212.63 0.148 Ship Speed in knots Vs PD metric pE metric = PE/PD Admiralty constant Revolutions per minute ns Resistance RT in metric tons Thrust T in

27 17084 12047 0.705 368 113.1 79.83 96.30 0.171 221 18648 13147 0.705 361 116.2 85.19 102.38 0.168 23 20354 14348 0.705 353 119.4 90.95 108.68 0.163

23/22/76

15571 0.702 345 122.8 96.60 115.21 0.162 24 24153 16847 0.698 338 126.1 102.33 122.41 0.164 241 26302 18173 0.691 330 129.7 108.14 130.06 0.169 25 28739 19713 0.686 321 133.3 114.96 138.38 0.169 251 31500 21433 0.680 311 137.1 122.54 147.83 0.171 26 34735 23464 0.676 299 141.1 131.56 158.63 0.171 261 38551 25817 0.670 285 145.6 142.03 171.01 0.169 27 43150 28591 0.663 769 150.6 154.38 186.08 0.170

Table A 12.

Propulsion test results

Test No. 26508

Model condition: Studs as turbulence stimulator Ship model No. 3417

on F.P. = 6.595 m

Propeller model No. 4121

Draft moulded ; on A.P. = 7.205 m

Scale ratio A = 28

I mean

= 6.900 m

_{Skin friction correction FD from model to}

Displacement volume V = 13992 m3 ship is according to Froude's constants

=

(27)

28

Table A 13,

Slip, wake and thrust deduction

Open water test No. 8514 B.

Model condition: Studs as turbulence stimulator. on F.P. = 9.15 m

Draft moulded on A.P. = 9.15 m I. mean = 9.15 m

Note: The values have been calculated with the mean J-values of those based on KT and KQ.

Table A 14.

Slip, wake and thrust deduction

Open water test No. 8514 B

Model condition: Studs as turbulence stimulator, on F.P. = 6.530 m

mean = 6.835 m

Propulsion test No. 26491

Propulsion test No. 2.6536

Ship model No. 3415, Propeller model No. 4121 Scale ratio A = 28'

Note:, Ithe values have been calculated with the mean J-values of those based on KT and IC0. Ship. speed in knots vs Thrust HP PT True slip SR Apparent slip SA W' Taylor Hull efficiency jig Efficiency behind ship 718 Open water efficiency 110 niill1;G

J = VA*

22.0 11015 .267 +.033 +.242 .156 1.114 .661 .641 .1032 .725 22.5 23.0 23.5 11985 13040 14215 .267 .269 .271 +.038 +.043 +.050 +.238 +.236 +.233 .162 .165 .168 1.100 1.093 1.085 .662 .660 .657 .641 .640 .639 1.033 1.032 1.027 .724 .722 .720' h I 1 24.0 15521 .275 +.057 +.231 .169 1.081 .652 .638 1.023 .717 24.5 17032 .279

+066

+.227 .168 1.077 .647 .636 1.017 .713 Ill 25.0 18786 .283 +.076 +.223 .169 1.070 .645 .634 1.016 .709 25.5 20762 .288 +.087 +.220 .167 1.067 .641 0632 1.014 .704 26.0 23164 .295 +.100 +.217 .168 1.062 .637 .629 1.013 ..697 26.5 25942 .304 +.114 +.215 ..170 1.1057 .631 .624 1.011 ..688 27.0 29249 .315 +.129 +.213 .174 1.050 .624 .619 1.010 ,.677 Ship speed in knots Vs Thrust HP PT True slip SR Apparent slip SA Taylor t Hull efficiency nH Efficiency behind ship 1B Open, water efficiency qo 11B1I10

J = V

Do 22.0 22.5 13090 14171 .274 .275. +.086 +.090. +.206 +.204 .157 .155 1.062 1.061 .649, .648' .638 .637 1.017 1.016 .717 .717 23.0 15329 .278 +.093 +.204 .155 1.062 .646 .636 1.015 314 23.5 16595 .281 +.097 +.204 .153 1.064 .642 .635 .1010 311 24.0 18084 .284 +.102 +.203 .152 1.064 .641 .634 1.012 308 24.5 19736 .288 +.108 +.203 .151 1.065 .640 .632 1.014 .703 25.0, 25.5 26.0 21577 23645 26078 .293 .299 .305 +.114 +.122 +.131 +.202 +.202 +.200 .1150 .150, 348 1.065 1.065 1.065 .637 :635 .632 .630 .627 .624 1.013 1.013 1.013 .699 .693 .687 11'111 26.5 27.0 28804 32046 .313 .323 +.141 +.151 +.200 +.202 .145 .134 1.069 1.085 .629 .626 .620 .614 1.015 1.019 .679 .670, 1 I

(28)

Table A 15.

Slip, wake and thrust deduction

Propulsion test No. 26503

Table A 16.

Slip, wake and thrust deduction

Propulsion test No. 26504

Ship speed in knots Vs. Thrust HP PT True slip SR Apparent slip $A w Taylor Hull efficiency 11 II Efficiency behind ship ,18 Open water efficiency rIG 11B1,10 .1 = VAInD 22.0 13576 .288 +.091 +.217 .176 1.052 .647 .632 1.023 .704 22.5 14747 .289 +.096 +.214 .173 1.052 .644 .631 1.019 .703 23.0 15914 .294 +.099 +.216 .173 1.055 .636 .629 1.010 .698 23.5 17338 .298 +.104 +.216 .173 1.055 .633 .627 1.008 .694 24.0 18870 .303 +.109 +.218 .172 1.059 .677 .625 1.004 .689 24.5 20660 .310 +.116 +.219 .171 1.062 .623 .621 1.002 .682 25.0 22653 .317 +.123 +.221 .167 1.069 .617 .618 1.000 .675 25.5 25103 .323 +.133 +.219 .164 1.071 .615 .614 1.002 .669 26.0 27957 .331 +.145 +.218 .160 1.074 .611 .609 1.003 .661 26.5 31413 .341 +.159 +.217 .157 1.076 .608 .604 1.008 .651 27.0 35721 .351 +.176 +.213 .156 1.072 .604 .597 1.012 .641 Ship speed in knots Vs Thrust HP PT True slip SR Apparent slip SA w Taylor r Hull efficiency 'In Efficiency behind ship ,1B Open water efficiency 110 '1E010 J = VAInD 22.0 11550 .287 +.041 +.256 .165 LI?? .646 .633 1.021 .705 22.5 12690 .291 +.048 +.255 .171 1.113 .644 .631 1.021 .701 23.0 13900 .295 +.055 +.254 .172 1.110 .641 .629 1.019 .697 23.5 15209 .300 +.062 +.254 .172 1.110 .634 .626 1.012 .692 24.0 16675 .304 +.070 +.252 .168 1.112 .631 .624 1.010 .688 24.5 18379 .309 +.080 +.249 .162 1.116 .624 .621 1.005 .683 25.0 20374 .314 +.09l +.245 .156 1.118 .623 .619 1.006 .678 25.5 22763 .320 +.105 +.240 .154 1.114 .620 .616 .1008 .672 26.0 25619 .326 +.120 +.234 .152 1.107 .619 .612 1.010 .666 26.5 28933 .335 +.136 +.229 .154 1.098 .614 .608 1.011 .658 27.0 32961 .343 -1-154 +.223 .161 1.080 .613 .602 1.018 .650

Open water test No. 8514 B Ship model No. 3416

Model condition: Studs as turbulance stimulator. Propeller model No. 4121

on F.P. = 9.15 m Scale ratio A = 28

Draft moulded on A.P. = 9.15 m mean = 9.15 m

Open water testNo.8514 B Ship model No. 3416

Model condition: Studs as turbulence stimulator. Propeller modelNo.4121

( on F.P. = 6.460 m

Scale ratio A = 28

Draft moulded ), on A.P. = 7.070 m I mean - 6.760 m

(29)

-30

Table A 17.

Slip, wake and thrust deduction

on F.P. - 9.15 m

Draft moulded on A.P. 9.15 m mean = 9.15 m

Table A 18.

Slip, wake and thrust deduction

I on F.P. = 6.595 m

Draft moulded on A.P. = 7.205 m I mean = 6.900 m

Propulsion test No. 26507

Propulsion test No. 26508

Ship model No. 3417 Propeller model No. 4121 Scale ratio /1 = 28

gni Ship speed in knots Vs. Thrust HP PT True slip Sn Apparent slip SA Taylor Hull efficiency riff Efficiency behind ship qe Open water efficiency

17o ,781rIo J = VAInD

22.0 13486 .283 _+.094 +.209 .183 1.033 .639 .634 1.007 .709 22.5 14680 .285 +.097 +.208 .181 1.035 .639 .633 1.009 .706 23.0 15912 .289 +.100 +.209 .177 1.041 .637 .631 1.009 .703 23.5 17234 .291 +.105 +.208 .172 1.046 .635 .631 1.007 .701 24.0 18581 .293 +.108 +.208 .173 1.044 .632 .629 1.004 .699 24.5 20068 .295 +.112 +.207 .167 1.050 .630 .628 1.003 .697 25.0 21699 .298

+116

+.206 .166 1.050 .630 .627 1.004 .694 25.5 23504 .300 +.121 +.204 .163 1.051 .628 .626 1.003 .692 26.0 25683 .304 +.129 +.201 .160 1.051 .628 .624 1.006 .688 26.5 28215 .311 +.137 +.203 .155 1.060 .624 .620 1.006 .681 27.0 31374 .321 +.148 +.203 .148 1.069 .620 .615 1.007 .671 Ship speed in knots Vs Thrust HP PT True slip SR Apparent slip SA Taylor Hull efficiency lH Efficiency behind ship 1113 Open water efficiency lb qaMo J= VAInD 22.0 11002 .270 +.036 +.243 .171 1.095 .644 .640 1.007 .722 22.5 11966 .273 +.040 +.243 .168 1.099 .642 .638 1.005 .719 23.0 13027 .275 +.045 +.240 .163 1.102 .640 .638 1.004 .717 23.5 14188 .276 +.052 +.236 .162 1.097 .640 .637 1.004 .716 24.0 15410 .279 +.057 +.235 .164 1.093 .638 .636 1.003 .713 24.5 16827 .279 +.064 +.230 .169 1.079 .640 .636 1.006 .712 25.0 18336 .282 +.071 +.227 .169 1.075 .638 .635 1.005 .710 25.5 20014 .286 +.078 +.226 .171 1.071 .635 .633 1.004 .706 26.0 21973 .291 +.087 +.223 .171 1.067 .633 .631 1.003 .701 26.5 24251 .296 +.098 -1-.220 .169 1.065 .629 .628 1.002 .696 27.0 27052 .302 +.111 +.215 .170 1.057 .627 .625 1.003 .690