Further tests with models of coasters

MEDDELANDEN

FRAN

STATENS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)

Nr 35

_GOTEBORG

₁₉₅₅

FURTHER TESTS WITH MODELS

OF COASTERS

BY

HANS LINDGREN AND AXEL 0. WARHOLM

GUMPERTS FORLAG

GOTEBORG

1. Introduction

An earlier publication of the Swedish St ate

Shipbuild-ing Experimental Tank, viz. No. 24 Tests with Models

of

Coasters,

describes a series

of experiments carried out with

systematically varied models

of

coasters.

These investigations

comprised resistance tests with a family of seventeen models in

which the length-breadth and breadth-draught ratios, the block

coefficient and the longitudinal position of the centre of buoyancy

were systematically varied. The dimensions, coefficients and ratios

for the different models are given herein in Table I.

The results

of the above tests were expressed in terms of

dimensionless ratios and they thus make it possible to calculate the

resistance of similar forms and other forms of the coaster type.

The present pa,per deals with a systematic investigation of the

propulsive qualities of coasters. Four models with the same block

coefficient

(a = 0.65)

but

different 'breadth and

length-displacement ratios were tested at both full load and light draughts.

The form coefficients and ratios of the models were the same as in

Series A: 2 of the earlier tests (see Table I). The models in question

were selected as being, in the authors' opinion, those most interesting

to study from the aspect of their propulsive characteristics.

Self-propulsion tests have been carried out with each model using

four different propellers in turn, in order to determine the effect

of propeller revolutions on the propulsive characteristics.

The primary results of the model tests have all been worked out

for ships of the same displacement, namely V = 816 m3 at load

draught on an even keel and V = 408 m3 at light draught with a

trim by the stern. The range of revolutions covered by the four

V = 816 m3 No. .L

L"

B T

S

L

4

L

B B T 6 6pp t P13 (14100)3

L

_PP 2 %

Series A: 1.

Varying LIB, 6 = 0.60

318 46.22 45.19 8.404 3.502 494 4.95 23 5.5 2.4 0.600 0.614 388 51.67 50.52 7.949 3.313 522 5.53 168.9 6.5 2.4 0.600 0.614 0

390 56.84 55.57 7.578 3.158 549 6.08 127.1 7.5 2.4 0.600 0.614 0 Series A: 2.

Varying LIE, 6 = 0.65

313 39.3-7 38.49 8.748 3.645 458 4.21 382.7

45

2.4 0.650 0.665 0

314 45.00 44.00 8.182 3.409 489 4.82 255.0 5.5 2.4 0.650 0.665 0

315 50.31 49.19 7.740 3.225 517 5.38 183.4 6.5 2.4 0.650 0.665 0 342 55.33 54.10 7.377 3.074 543 5.92 137.7 7.5 2.4 0.650 0.665

'Series A: 3.

Varying LIB, 6 = 0.70

_{_}

319 43.90 42.92

7.901 3.326

486 4.70 275.1 5.5 2.4 0.700 0.716 0 389 49.08 47.99 7.550 3.147 515 5.25 197.4 6.5 2.4 0.700 0.716 0

391 53.98 52.78 7.197 2.999 540 5.78 151.0 7.5 2.4 0.700 0.716 0

Series B. Varying BIT

316 42.35 41.41 I 7.700 3.850 480 4.53 307.2 5.5 2.0 0.650 0.665 343 43.72 42.75 7.949 3.613 482 4.68 278.6 5.5 2.2 0.650 0.665 0

314 45.00 44.00 8.182 3.409 489 4.82 255.0 5.5 2.4 0.650 0.665 0

317 47.38 46.33 8.615 3.077 501 5.07 219.1 5.5 2.8 0.650 0.665 0 Series C: 1.

Varying 6, LIB = 5.5

'

318 46.22 45.19 8.404 3.502 494 4.95 235.5 5.5 2.4 0.600 0.614 314 45.00 44.00 8.182 3.409 489 4.82 255.0 5.5 2.4 0.650 0.665 319 43.90 42.92 7.982 3.326 486 4.70 275.1 5.5 2.4 0.700 0.716 0 344 42.91 41.96 7.802 3.251 482 4.59 295.3 5.5 2.4

0.7j

Series C: 2.

Varying 6, LIB -= 6.5

388 51.67 50.52 7.949 3.313 522 5.53' 168.9 6.5 2.4 0.600 0.614 0 315 50.31 49.19 7.740 3.225 517 5.38 183.4 6.5 2.4 0.650 0.665 0

389 49.08 47.99 7.550 3.147 515 5.25 197.4 . 6.5 2.4 0.700 0.716 0

Series C: 3. Varying 6, LIB = 7.5

390 56.84 55.57 7.578 3.158 549 6.08 127.1 7.5 2.4 0.600 0.614 0

342 55.33 54.10 7.377 3.074 543 5.92 137.7 7.5 2.4 0.650 0.665 0 391 53.98 52.78 7.197 2.999 540 5.74 151.0 7.5 2.4 0.700 0.716 0

Series D. Varying tILpp

'

320 45.00 44.00 8.182 3.409 489 4.82 255.0 5.5 2.4 0.650

0.665 +1

314 45.00 44.00 8.182 3.409 489 4.82 255.0 5.5 2.4 0.650 0.665 0 321 45.00 44.00 8.182 3.409 489 4.82 255.0 5.5 2.4 0.650

0.665 -1

322_{_} 45.00 _ 44.00 8.182 3.409 489 4.82 255.0 5.5 2.4 0.650 0.665 2 .

Propeller Dimensions

= propeller diameter

= propeller pitch

A0

= propeller disc area

(

D2)

4

Ad

= developed blade area

1

= blade width at 0.7 D/2

= maximum blade thickness referred to centre of propeller

Kinematic and Dynamic Symbols and Ratios

= speed in general

ve

= speed of advance

V

= ship's speed in Metric knots

= resistance

T

= propeller thrust

Q

= propeller torque

= rate of revolution (revs, per unit time)

Pe effective power

P8

= shaft power (at tail end of shaft)

v ve

wake fraction (TAYLOR)

T R

_{thrust deduction factor}

= density of water

/

(102.0 kg sec.2/m4 for fresh water)

(104.5 kg sec.2/m4 for sea water)

5

2. Symbols, Units and Methods of Calculation

The symbols have been chosen in accordance with the recommendations made by

the Sixth International Conference of Ship Tank

Super-indendents.

Ship Dimensions

= length on waterline

Lpp

= length between perpendiculars

B

= breadth on waterline

T

= draught

Am = immersed midship section area

S.

= wetted surface area (including wetted surface area of rudder and bossing)

V

= volumetric displacement

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

1/2 ate = half angle of entrance on waterline

= kiderhatiU itilcoitity of Water

C,

=- PI3 V3/P6 (m3, Metr. knots and HP)

C2 = V2/3 Val?, (m3, 1Vietr. knots and HP)

Fn rvi 1JT7= FEMME number, displacement

FILL

=

vi gL

FRO17DE number, length

-Vve2 (0.7 n D n)

REYNOLDS number for propellers

Dimensionless Coefficients and Ratios

V' 6PP Lpp

LB -'T

1 17 T

= block coefficients

midship section coefficient

prismatic coefficient

= lengthbreadth ratio

= breadth-draught ratio

= length-displacement ratio

-1,1

-= L. C. B. forward of Lpp/2 as % of Lpp

Lpp

= pitch ratio

Ad

= disc area ratio

A,

= blade thickness ratio

K2'

thrust coefficient

D4 n2 x(;)

=

= torque coefficient

e D5 n2 ye

=

= advance coefficient

Dn Am

=

_BT

V

KT

_{propeller efficiency in open water}

KQ 2 n

Pe

=

= propulsive efficiency

P,

Suffix m denotes model. The ship is referred to if no suffix is used.

Units and Conversion Factors

Metric units are throughout.

For g (acceleration due to gravity) the value 9.81 m/sec.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 FROUDE'S method.

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

Tank Superintendents' Conference in Paris in 1935. No length

correction has been employed.

All the self-propulsion experiments were carried out according to the so called

Continental method (GEBEas)') With the skin-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 propeller as a

wake integrator. Values of wake fraction were worked out, both on the basis of

thrust identity and on the basis of torque identity, with the aid of the curves 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 practice at the Tank.

3. Ship Models Tested

Four paraffin wax models were employed in these tests.

The

parent model, No. 618, was made in the scale 1 : 9 and was similar

in every respect to Model No. 314, referred to in Publ. No. 24. The

dimensionless form coefficients and ratios of the other models, as

mentioned in the Introduction, were the same as those of the

corres-ponding models of Series A: 2 (see Table I).

') See Congres International des Direeteurs des Bassin,s, Paris, 1935.

1 metre

= 3.281 ft.

1 metric ton

= 1000 kg

= 0.984 British tons

1 metric knot = 1852 m/hour = 0.999 British knots

1 metric HP = 75 m kg/sec. = 0.986 British HP

In order to enable tests to be carried out using the same propellers

on each of the different models, the draught (and breadth) of each

model was made the same, i. e., the variations in length-displacement

ratio and length-breadth ratio were achieved by corresponding

variations in length. This meant that each model had a different

displacement. Thus, as in the earlier tests described in Publ. No 24,

in converting the results to the scale of a ship having a displacement

of 816 m3 at full load draught, it was necessary to assume a different

scale for each model. The various model scales together with all

the ship data are given in Table II.

This table also includes the

data for the different forms at light draught (V = 408 m3).

Table II

Units

Ship Models

Model No.

-

617 618 619 620 Model Scale

-

1: 9.622

1: 9

1 :8.514 1 : 8.115 17 = 816 n-13 17

L

m 39.3.7 45.00 50.31 55.33 w PP 38.49 44.00 49.19 54.10

B .... ... .

... . . .

m 8.748 8.182 7.740 7.377 a, A _LIB

-

3.645_4.50 3.409_5.50 3.225_6.50 3.074_7.50

BIT ... .

.

-

2.40 2.40 2.40 2.40 .0

4

ao

S

m2 465 495 522 548 g

LIV"

4.21 4.82 5.38 5.92 0.650 0.650 0.650 0.650 -ci o

# ... ...

-

0.971 0.971 0.971 0.971 .5 92

-

0.670 0.670 0.670 0.670

t/Lpp ... ...

% 0 0 o o '12 0,e degrees 25.9 21.7 18.6 16.3 z r...

4 Di

V = 408 m3

,

./.., . .. . .. . T (forward) m m 36.82 1.184 42.23 1.107 47.31 1.047 52.11 0.998 = as 0 :., ....c

T (aft)

m 2.790 2.610 2.469 2.353

T (mean)

in 1.987 1.859 1.758 1.676 no 4.21 5.16 6.11 7.06 ',...4 .E BIT 4.40 4.40 4.40 4.40 E-4

s

m2 330 351 370 387 LIV"3

-

4.96 5.70 6.38 7.03

LW L Model No. 618 0.05 0.1 0.2 0.3 0.4 0.5 0;6 Length-unit (1111111111. 1/3 V Fig. 1.

The ships were systematically related in such a way that any one

of the forms could be obtained from the parent form by multiplying

all the longitudinal dimensions by a constant factor and dividing

all the transverse and vertical dimensions by the square root of the

same constant factor. This means that the block coefficient,

water-plane area coefficient, midship area coefficient, prismatic coefficient

and breadth-draught ratio were the same for all the ships of the

family.

Fig. 1 shows the body plan and Fig. 2 the waterlines and profile

of the parent form (corresponding to Model No. 618). As explained

above, the body plans, waterlines and profiles of the other forms in

the series were obtained by multiplying all the longitudinal dimensions

by a factor a and dividing all the transverse and vertical dimensions

by V a. The values of the factor a for the various forms are given

below.

IL

9

n

IIIIIIIMINA

111111=11EIVAPINII

NI

111111MMIMIIIIIIIMMI

IMIMMIFIFIFMMIll

11111111MIE

11WWL.111ME

18

NII

11111111111WINIIIIIIM

itt1BILILWMAWAVAN

6,fk

aligalrAIIIIIIIIIIIIIA17As

Parent form

Model No.

617

618

619

620

a

0.875

1

1.117

1.230

0.5 1 2. 3 4 m It Iv11 /.111 9 8 7 6 4 3 2

MIIRMIIIIIIIIMMEMEIM MMIMIIIMMMIIPAFM,

WIN111116141-IiI1111=11IMIIN

IMMIIMIIIINIMINIMIIMIPIMIIIPIM/

WAINVANIIIMIMEMMIIMINIMIN1IMMIIMIENIMINE.11111111/AMEMMIAMF

1411L.' _mINIMIIIIIMI11111111IMMIIIIIi1MEMWMA41MIN'

I

1

Mlia11111111=MMINIMMI11111111M1=1111MINMWAIIIWIEW

IMMENIO11111111111111111INIMMEINNIIMMIIIIIMINIMMMIIMIIMMIIIW

INIIIMMIENIIIMM

I1111%1IMPAINIIIPMEMII

_MEI=

-Wow_ mown=

9. 7 5 3 / 1 1 o 6 05 /0 /5' 20 2 Model No. 618 Fig. 2. 25 30 35 3. 4 I '3 5

7 9

40 Length-unit pg3

-

-iAVYMIWIMP-0P--/MMItIrdM=

ff/MMIR3=-0=im

-111.- b.\

..7A_%7-1111Aib... 2 6 10 12 14 16 18 20

Sectional-Area Curves

Fig. 3.

30 Model No. 617 Model No. 618 Model No. 619 Model No. 620 N

N.

0 2 18 4 6 8 10 12 14 16 20 25 20 15 10 5 10 15 20 21.5m 1 Length-unit

130.5

05 1 v

.0inipdsions in bin)

Fig. 4.

In order to increase the scope of application of the diagrams and

facilitate the design of similar formed ships of different displacements,

dimensionless scales in terms of the unit of length divided by

I71/3

have been added to Figs. 1 and 2. The length, breadth and draught

of any similar ship with a displacement of say Vz can be derived

by multiplying the values read from the dimensionless scales by

171/3.

Fig. 3 shows the sectional area curves for the family of ship forms

employed in this series of tests.

Each of the models was fitted with a rudder and propeller shaft

bossing (see Fig.

5).

In the resistance tests, the propeller was replaced

by a dummy boss and cone. A 1 mm. tripwire was employed in all

the tests.

4. Propeller Data and Open Water Propeller Tests

Each of the models was tested in ebnjunction with four different

propellers, P616P619. These propellers were designed

SO

that,

with a ship of the parent form, a range of revolutions of about 190

to 370 r/min would be covered at a speed of 11 knots. Data for

the various propellers in the scales appropriate to the four ships in

question are given in Table III.

All the propellers were 3-bladed and conventionally designed as

regards blade form, shape of sections and pitch distribution. The

outline

of propeller No. P616 (dimensioned. assuming the model

Propeller. No.P6I6

Top of Aperture Atilatrom Pitch ...166-8 R11215 .2 1094 j 396\ 911

=11111311IME1

729 e62±-1411 547 ,,,,,,,,,,,,,,,,,,,,, 365

mommisvimr,

203

_.L._

Y

scale 1

: 9) is shown in Fig. 4. The other propellers were similarly

shaped, but varied in diameter and piteh according to Table III.

The relative positions of the propellers in the aperture were the

same in each model and are illustrated in Fig. 5. This diagram also

shows the form of the rudder.

The propellers were all tested in open water and the results are

given in dimensionless form in Fig. 6.

5. Resistance and Self-Propulsion Tests

Resistance and self-propulsion tests with all the models were

carried out in smooth water both at the full load even-keel draught

(V = 816 m3) and at light draught with a trim by the stern (V =

408 m3) (see Table II).

1) Mean pitch.

Table

13 Ship Model Pr o-peller Model

Dm Model

scale

D 13')

PID

Num-her of Blades

Ad/A, (ID Rake

No. No. mm ram mm % % degrees

P616 270.0 2598 1948 0.750 P617 237.0 2280 1540 0.675 617 _{P618 212.0} 1 : 9.622 2040 1295 0.635 45 4.8 7.50 P619 192.0 1847 1127 0.610 P616 270.0 2430 1823 0.750 P617 237.0 2133 1440 0.675 618 P618 212.0 1- 9 ' 1908 1211 0.635 3 45 4.8 7.50 P619 192.0 1728 1054 0.610 P616 270.0 2299 1724 0.750 P617 237.0 2018 1362 0.675 619 P618 212.0 1: 8.514 1805 1146 0.635 3 45 4.8 7.50 P619 192.0 1635 997 0.610 P616 270.0 2191 1643 0.750 P617 237.0 1923 1298 0.675 620 P618 212.0 1 : 8.115 1720- 1092 0.635 3 45 4.8 7.50 P619 192.0 1558 950 0.610

Model

No. 617

Model

No. 618

Model

No. 619

Model

No. 620

N.

Dimensions for ship in

corresponding to model scale 1:9

Fig. 5.

Resistance Testa

Resistance tests were Carried out at, load draught over a speed

range corresponding to 7

12.5 knots and at light draught over

a speed range corresponding to 8

13.5 knots. The experimental

results are shown in diagraminatic form in FigS. 7 and 8 and are

Propeller No. P616 Propeller No. P617 Propeller No. P618 Propeller No. P619

( 3-bladed)

Ill

pi

11!

if/

:I! 17/ LWL Alr

AV%

1125

10 Kr

100 K0.

Propeller No. P616 Propeller No. P617 Propeller No. P6I8 Propeller No. P619 Re 6-60.105 Rn77 5,9 -6,3-105 Re 4,7-4,9.105 Re 3,8-4,0-105 15 70 60 50 30 20 10

h.._

.

Al

tat

-

-.4111111*111

giNgegm

.

iiME

01

\ \ \

E",

r"

-

il

74mi=

,..b[MM

\

\

\

1

1

.

ss

IL,

ME

it.,,..741

...

_...,,,i

.,.

I

ra

_ms.s.,.

s,..",

,

sr,1 I Ns :

Ili,

02 0 3 04 05 0.6 07 08 09

/0

v D n Fig. 6.

given numerically in Table VXII (Appendix). The results obtained

at load draught have been converted to another form in Section 8

(Fig. 19).

As mentioned in Section 3, all the models were fitted with 1 mm

tripwires. This was not the case in the tests described in the earlier

paper on coasters (Publ. No 24). Over the range of speeds in question

3-4 % greater resistance was recorded in the new tests in the case

of the three longest models, while the difference amounted to about

7 % at normal speeds and 10 % at low speeds in the case of the

shortest model (No. 617). These differences can be partly attributed

to the rudders and shaft bossings which were not fitted in the earlier

experiments. On the other hand, some of the discrepancies,

particul-arly in the case of the shortest model, must be due to the earlier

models (without tripwires) being affected to some extent by laminar

flow over the fore-body.

600 500 400 300 200 100 0

Ship Speed, V, in knots

, . 0.40 0.45

0.50055

0.60 0.65

F -

_{nr 6-p73}

Fig. 7.

0.70

---Model

=trIbmJ tven Keel

"..

.c

No. 617 0=

4,50

900

Model No., 618

L/I3= 5,50

Model No. 619

LA=

6,50

- 800

°

Model No.

620 .

L/8= 7,50

700

I

--

I

600

IFA

500 .

.au

/

Mir

400

/

i

,

/ \

lis 's

\

,s

\ /

\

. 300 ,

rAf'7111

/

_h.

200 ... ... .. ...-... ....-:-:.--- ..z.. 100 .1,...t:.,____500,._;,:::-'''' F1111-1

Hi

0 7 8 10 It -

12 --1.3

C.) 800 700 600 500 400 00 00 00

17

,lf

= 4(lei MJ

_{trim by the -tern}

----Model No.677

L/B-- 4,21

Model No. 618

L/8-- 8,16

II

. Model No. 619

L/8=6,11

Model No. 620 L/8=7,06

..,

A41

500 . GOO

NB

300

IBUF N,,,,N' /11

./

'''.

-

' IIIII1M111

./

MINIM

POO _=-

-.----0 iliiIIIII

8 10 11 12 13

Ship Speed ,V , in knots

I , I I , I

0.45 0:50 0.5-5 0.60 0.65 0.70 0.75 0.80 0.85

F

_{n17 073}

=V.

Fig. 8.

Self-Propulsion Tests

As stated in Section 4, self-propulsion tests were carried out using

four different propellers in conjunction with each of the four models.

The results obtained from the tests at full load draught

are given

in Figs. 9-12 where the shaft power, P,, revolutions, n, and the

9 10 11

Ship Speed ,V , in knots

Fig. 9.

0.40 0.45 0.50 0.55 aiei 045 0.70

F v

nI7 073

0

Propeller No. P6I6

ii

III/

_gooiar

if

PrOpeller No. P6I7

Ii!

-

moo

1 II

i11

L.

=

Propeller No. P6I8

Propeller No. P6I9 ,

800

/

700 ....- ,.. I _ ..-n _---../

/

_,...'

/

yi

Ill

- 500

MINI

lj

_ SOO - - 11 100 400 WO

A

!,,ii

MEE_=_-:30C 20C

.0

_ -,-.

pp,,

_ ----.-' 7=,

'

100 _

-

WO

- .-0 1111111.11

Model No. 617 LA-4,50

17.---816 m3 Even Keel

_z

300

Model No. 618 LA=5,50

l7F: 816 m3 Even Keel

7 a 9 10 11

Ship Speed,V , in knots

0.40 045 0.50 0.55 am F ..

,--

v n? ye 1/3 Fig. 10. 0.65 0.70 0 0 -400 19 . . /. i , _. .s. ct

Propeller No. P6I6

--

/

_ll 110

Propeller NO. P6I7

.

/

ilt

/ .

ill

/

ii _ioi . ,

tg

.i

__

_ _

Propeller NO. P6I8

.---_

Propeller No. P619

/

'90

/

z.

/.

,

4, .1

,

,1 801 1 ../.

.

1 70(

/

-n _..-'''... . ...----:..--

---III .lif

1

60( .0/ 500

piril

50( 400 ,A ₄₀₍ 11016W11,11 300

-

C274_

16..

-30( 200 WO,

--

M EM

..,

20( 100 -

Elill

.. -- -0 11111111I 300 200 166 0

.19

Model No. 619

L/8=6,50

V=8/6m3

Even Keel

1.1 0.40 0.45 0.55 0.60 0.65 0.70 F ine

VI 3

Fig. 11. 0

Propeller No P6/6

No. P617 No. P618 No. P6I9

1111

t .,.c I

/

!/

ci:n Imo 1000 900 Propeller Propeller

-- - . - - -

Propeller

1111

mir,

//,

111111111=111111

...

..__ 600

_

111111di

11111

FA

_T-71r/

;AL300 200 100

o-01.,"

poppr-

iff

_

-41.1.111111

-,._. ._ 7 9

Ship Speed ,V, in knots

400 300 200 100 CX-' 500 4.00 30 20

Model No 620 1/. 8=7,50

'# 816%113 Even Keel 6:40 0.45 0.50 . 0.55

F =

^7 V9P0

Fig. 12. 0.60 0.65 0.70

900

-00 0 21

Propeller No. P6I6

No. P6I7 No. P6I8 No. P6I9

---Propeller

Propeller

Propeller

IIIII

/

/

/

/

/

/

.

1111111111,

1

.

A

----.111E

,

I

500 . /1 400

Iftgliall

.

/

300 POO 100

Ihrdli

..,'

111111.4

,

,

..,

_\,

-_

_

Val

_

_

8 9 10 1/ 12 13

Ship Speed, V, in knots

600 400 00 - 300 00

-00 266

00

-00 - /-00

00

-00 - 0

coefficient C, have been plotted as functions of ship speed, V,

and

FROITDE number, F,,..

The corresponding results obtained at the smaller draught (V =

408 m3)

are shown in

Figs. 13-16.

The diagrams give an

indication of the way in which the propeller revolutions influence

the shaft horse-power required for the different ships. It should,

however, be borne in mind that a direct comparison of

the

experi-mental results for the different ships does not give a true picture

of the situation, for the reason that while the same propellers were

used for all the model hulls, they were in fact designed for the parent

form and were not therefore so suitable for the other models. This

problem is dealt with at greater length in Section 6. where the

analysis

of the experimental results is fully discussed.

In Tables V XII (Appendix), the values of the shaft

horse-power,

revolutions and C, are given, together with those of the

propulsive

factors

n,

w and t at different speeds and

values of FROUDE number

(F.

and FL). The wake fraction, w, and the thrust

deduction

factor, t, are dealt with further in Section 8.

6. Correction of the Self-Propulsion Test Results to

Enable

Comparisons between the Different Models

As stated in Section 4, the same propellers were used

for each of

the four ship models. The propellers were designed

for the parent

ship, corresponding to Model No. 618. A direct

comparison of the

measured values of shaft horse-power, revolutions and speed for any

two ships is not therefore entirely fair, since

the propellers were

more suitable for one ship

than for the other. However, in order to

take account of this situation as far as possible, all the

experimental

results have been corrected in the manner described

below.

The method adopted was to maintain the diameter

and speed

constant and adjust the pitch until, in a Bp

6 diagram (see Fig.

17), the Bp values based on the corrected experimental values of

Ve, P, and n intersected with the a-values (involving n in addition

to D and Ve) on the line representing optimum

diameter. It was

assumed here that the wake fraction, w, and the thrust

deduction

factor,

t, were independent of revolutions and power (within the

tta.

8 9 10 11

Ship Speqd ,V , in knots

. 1 , 0.45 0.50 0,55 0.60 0.65

F =

v n0 irgfri73 Fig. 13. 12 0.70 0.75 0.80 23 . Propeller No. P616

/.

/

.

ce 100 Propeller No. P617

_/

/

.. 90l

/

-

-- -

Propeller No. P618 Propeller No. P619 80C

-/

/

00 00 500

El

r,./,

--.

_//PP

n

,

-...--

1

ill

. $00 A

MINE

400 300

VA

00 200

litral

41&4.M

200

--_

_

PS

ERIE

100 100

_

0

IIIIIIIII

- 0

Model No. 617 LA=4,21 7= 408 m3

Tr.

Trim by the Stern

z

0 - 400

300

200

Model No. 618 118=5,16

17408m3

Trim by the Stern

- 400 300 200 100 0 Propeller No. P616 No. P617 No.P618 No. P619

f

x

.c BOO Propeller

Propeller

Propeller

III

.,

-.

id

₆₀₀ 500

ilin',"/Fr

/

i

A

griA

IlhE206

iiis

_,

_

_

_

400 306 ,00 0 -....,. ...,

_

,_,..iiii

_

9 10 11 12 13

Ship Speed V, in hnois

, 0.45 0.50 0.55 0.60 0.55 0.70 0.75 0.80 . F v

n17 Iliff3

Fig. 14. Q." 400 300 2.00 100

Model ,No. 6 19 L/8= 6,11

F. 408 m3

Trim by the Stern

IL

700

-00 0

400

300 25 Propeller No. P616 No. P617 No. P6/8 No. P6I9

,

,

Propeller

Propeller

Propeller

./

.-/

/

/

/

,

.

..-

-

.

.

..-

,

..-- . n

Ell/

El

ig

.,

,

rattik

___

111111111 =. 9 10 /2 13

Ship Speed ,V, in knots

. I I 0.45 0.50 0.55 0.60 0.65 0.70 0.75 aeo

F -

v

gp/3

Fig. 15. 00 00 00

-0-

00

00

-oo 0 500 400 300 200 /00

500 400 30o .200 100 0

Model No. 620 L/8=7,06 F. 408 m3

Trim by the Stern

Propeller No. P6I6

Fig. 16.

400

300

--

Propeller-No. P6I7

--

=

Pr-opener NQ. P6/8

--- Propeller No:

P6I9

/

/

F._

c

goo 400 30C 20C 100

//.

/

/

.

/

.. ..

..

_./

.

.

... ,

--

.----

.

.11111

..

.

-..1-.

.

.

.

.

n

---

-

__;.--- ..

,11

IV

11.---./ll

-

_MN

Illiw. I

id

-...k.

.,

'

i

radii

IIMP'

1-I11 I111-1

_

_

7 9 10 1 i 12

Ship Speed ,V, in knots

-0,45 0.50 0.55 0.60 045 0.70- 0.75 0.80

F - V

200

P/D 1.0 0.9 7: 0.8

(V=8

knots) l'--___

0 n P5 8 =

PeZ5

.10 15 20 25 30 Fig. 17.

also assumed that no correction to the relative rotative efficiency

was required.

The correction is illustrated schematically in Fig. 17, which shows

in principle part of a B

6-diagram (see Trans. North East Coast

Inst. of Eng. and Shipb:, Vol. 67, Open Water Test Series with Modern

Propeller Forms, by Prof. L. TRoon).

The experimental values are marked by open rings (only two

series, representing the extreme cases, are shown in -Fig. 17) while

the solid spots rdark the corresponding values after correction to the

optimum line.

It will be seen from the diagram that the correction applied to

the shaft horse-power, P,, is small. Moreover, the relation between

the corrected and uncorrected values of P,, by reason of the

above-mentioned assumptions, is similar to the relation between the open

water efficiency in the uncorrected case and the corresponding

corrected value. On the other hand, as is also evident from Fig. 17,

(the

correction to S =

n D

V,

considerably greater.

The values given in Table IV typify the relative magnitudes of

the various corrections and it will be observed that the correction

cr nD

'

. _{n in r/ min: ; Ps in HP .;} V,

0 in Jeer; o test results _{corrected results}

%

/

,

/

\,,,.

/

/

',,,,=

\

/

,,e.

/

,e

,,.

v

, .

_{\ 'T,}

/

so

%0

/

, .J.

/\

, \'-e \.,,e

\ /

/ \ C8 Xe , ' , , O .

\

/

\

t V'

'

97.

/ \

it, \

/

%

\

/

\

\

L"

/

/

s ,

/

\ /

A , CI.

/ \

%

/

N

/

/ \

%

'

_, e.. A/ ;Is

/

b

/

_ Models No. 620cL _i

_{z /}

.4'

0.5

% I I - 1 I O. OS A o

\\

/

\ /

ModelYNo. 517 / (V ,11,5 knots) 0c)/ 15%

s>/

5K

U'leQf

z

and hence to

the revolutions is

s,;"/ ,

I

35 40 50 60 70 80 90 100 110 120 130 140

27

V =V(1w) in knots.

Table IV

Model No. 618. Ship Speed V = 11 knots.

to the revolutions (and pitch) is large in comparison with power

correction.

The corrected results can thus be taken to represent the values

which would be obtained with each combination of model, propeller

diameter and speed,

if

the open-water optimum propeller was

employed in each case.

The implications of the test results, after being corrected in the

manner described above, are discussed in Section 8.

7. Dimensionless Presentation of the Results

The curves of C, and C2 plotted against F

are given in

Figs. 7-16, can be used for converting the results to apply to similar

ships of other displacements. Another dimensionless method of

presentation, analogous with that adopted in Publ. No

24,

is

employed in Section 8. In the second method, the effective and shaft

horse powers are made dimensionless by expressing them in terms

of Pe/ g g312 V 716 and Ps le g312 v7/6 respectively. The revolutions are

Vviia

in

expressed

terms 60 n , with n, V and g in consistent units,

9

while the speed is given in terms of the dimensionless FROUDE

number, F n r -= vlfg 171/3.

In order to simplify the use of the

diagrams, curves are given in Fig. 18 which can be employed for

re-converting the values of the dimensionless expressions and the

term 60

nV

into power in horse-power, speed in knots and

vi/3

9

revolutions in r/min.

It should be observed that the diagrams are based on results

applying to a displacement of 816 m3 (only those results obtained

Propeller No. P616

Uncorrected Corrected Increase

Propeller diam.

D m 2.43 2.43

Pitch.

P

m 1.82 1.64

9.9

Revolutions

n

r/rnin. 194.0 207.7 7.1

20 19 18 17 /6 15

EMI

1.1,111,1 1000 (Pe or P8) e Y31217716 Vg

pis

60'n _

pis

Expressions to

be

evaluated

using consistent

units

e g3I2 17716 75x 1000 1 V

viisig

Values to be

read from the

abbve curves

at

the

dis-placement in

question o 3600 g_ V P113

= V in knots

1852

P, or Pg in HP (Metr.)

in rimin.

/60 120 -'do 80 -1.25 140 -1,20 1.15 1.10 1.05 29 4019 600 800 1000 1200 Displacement P' in m3

Fig. 18. Diagram for use in converting the values of the expressions employed in

Figs. 19-24 to P, and P, in HP, V in knots and n in rirnin

The method is

indicated below.

Cri

180

60 - 1.00 = /04.49 irg sec2 g=981 m/sec2

40 - 0.95

Model ND. 617 'L/B=4.5 9 8 7 1

F

a

=1

-

ass

il/g p

1/3 Consistent throughout Units used. 1 .

III

ir,41

iiim----

_iiiimmi

NA.64

Ell

sr"

iiiiii

M

_

_

__ -.-._ 0.62 0.60

LI.

----'"

___

si

1,,

_...

0.58

-'

----.

---

_ _

--215011111111jimim

4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80

L/71/3

Fig. 19.

in the tests run at load draught have been used here). Therefore,

in converting the results to a displacement which differs widely

from this figure, some degree of error will be inevitable, due to the

fact that the frictional resistance does not obey the law of

compari-sons. As far as resistance and effective horse-power are

concerned,

it can be

' 13.own by calculation that at normal speeds the error

involved is less than 1 % for displacements between 400 m3 and

1200 m3.

In the self-propulsion

tests,

a frictional resistance correction

(applied as a towing force) appropriate to the displacement of 816 m3

was employed, and therefore the results can not be directly

applied

Model No. 618 Model No. .6/9 Model No. 620

12 10 E:". e-, a 1;:?) 14.."

§6

2 0

Model No.6I7

L/B=4,5

"ts 31 -A': 0 0 (0 --.. tO 1 \ 9... Co Q. ..._ , '?) CZ 0.62 ' Q _/ 1.- /

/

/ / I

/

I

/

v I

/

i .../...

.---=:10.60-F-

/

nv ,,v g F f1,3 1 1 __...---

/

11

I

/

1

/

i i

/

0.58

/ i

/

, i

,/

I

/

....,-./0.56

ii----1---4--

/

111111110

0.54

. Consistent Units used

..,

A.4_,.stent throughout

.,

0.46 0 100 200 300 400 500 600

60n1

71/3

Fig. 20.

to ships of other displacements. For this reason, further tests with

Model No. 618 were carried out using the frictional resistance

corrections corresponding to similar ships having displacements of

400

m3 and 1200 th.P. The differences between the values of

revolu-tions and power obtained in this way and those calculated on the

basis of the assumption that the dimensionless curves also apply to

these displacements Were insignificant (less than 1 %) in the case

of the greater displacement. At the smaller displacement (400 m3)

10 8

Model No.618

L/8=5,5

300 Fig. -21,

60n/

-g

and 2 % in revolttions, thus showing that the »dimenSionless» curves

should be employed with caution when calculating the power etc.

for ships Whose displacements differ widely from 816 m3.

8. Analysis of the Test Restilts

Resistance Tests

A comparison between the various models on the basis of resistance

(at a displacement of 816 m3) is made in Fig. 19. The dimensionless

parameters of this diagram have been explained in Section 7 and,

by using Fig. 18, the results can be readily transposed in terms of

Q

...---4---, 1 i 1 i

--r-/

/

//

all

I

1 I 0.62

--1---1

0.61)=F

-n17 -I/ 3

//0:58

..

10.56

0.54 Consistent throUghout Units used

.A

IiNiii

iiiialWir

-.../__Y7C.046 -100 . 200 400 500 600

I0 ".4 1:=4. c-) 6 4:11 ca.." 2

Model No. 6/9

L/86,5

33

o o 40 o N (C.-a.

q

.,_ - cci 0.66

a

.._

/

.

/

/

_/

/

_-10.64 /

I.

/

_/

./

v , 0.62 -

F

/ .

/

n17 vg

p

/

-- --/-

0.60

/

_{_-/----1}

Consistent Units used

-,4 ---;

_--eo.46 -.,-- - -7 throughout

---1--1 100 200 300 400 500 600

60nirt; 73

Fig. 22.

power in horse-power and speed in knots for any required

displace-ment.

It is apparent from Fig. 19 that L/

V"3

(and

LIB)

has a considerable

influence on the resistance, particularly at high speeds.

Self-Propulsion Tests

In the conaparison discussed below, all the self-proptilsion. teSt

results (obtained at a displacement corresponding to ,816

m3) hay:Et,

been corrected in accordance with the method described in Section 6.

and expressed in dimensionless form as explained in Section 7.

Figs. 20-23 show the shaft power (in dimensionless form) plotted

v

F1/3

against revolutions in the form 60 n = for different values of

8 2 0

Model No.620

L/3=7,5

... l. 0 k

l

0 t., co

.

lc ."% k: 0" c.. N .... to 0 c. cla ili Q.

..

§

0)

.

co .1 'S0.66 ...

i

,,-,

/

i-- -

---1-,

- _...:0.6

- -- ./

.

AMMO

0.50

---

0.46

AZ=Zral:

.fiEnriganig

0.62 58- F

,

' n17 v 9 I 3 -0 100 200 300 400 500 600 60

n1/7-27

Fig. 23.

FROIIDE number, Env.

The values of

shaft horse-power and

revolutions corresponding to the dimensionless expressions can be

readily obtained by means of the curves in Fig. 18.

A comparison between the different ships on a basis of the required

shaft 'horse-power at various speeds and revolutions is illustrated in

Fig. 24. The curves therein are in fact cross curves to those in Figs.

20-23.

The influence of revolutions on the required shaft horse-power

can be seen in Fig. 25, where a percentage comparison is given. The

curve is based on the average values for all the models and speeds

and, since the scatter of spots is considerable, it should

only be

employed for approximate estimations.

Wake Fractions and Thrust Deduction Factors

As mentioned in Section 5, the calculated wake fractions and

thrust

deduction factors are given

in

the Appendix (Tables V XII).

length-1000 P P93/27 7/6 11 to 4 2 9 5

35

0 11,.

1.\\

NV

I

' \

n

V v

7-

400

.350

300

200

No. 62

9

Nil,,_

-_ 1

L\

II

_

Model No. 618 _{Model No. 619 Model}

, Model No. 6/7

V'

L/8=4.5 I L/8=5.5 L/B=65 L/8= Z. 1 K.

\

\ '

111

i\\\IL

\\\.\

_N\

111

I

Consistent Units used throughout I i

11611.1.

i

.,

immum

.

._

, fi, =0.50 I I I i I 4 440 4.60 4.80 5.00 5.20 VP 113 Fig. 24. 5.40 5.60 5.80

I I I

300 250 1/ ii1/3 300

60 n

Fig. 25.

breadth ratio, LIB (or L/17113), and the propeller diameter

influence

both the wake and the thrust deduction.

An increase in speed causes a decrease in the wake fraction for

all the models at both fully loaded and light draughts.

The effect

of speed on the thrust deduction factor, on the other hand, is not

so clearly defined. At load draught, no definite tendency can be

discerned in the values for the two intermediate models (Nos. 618

and 619); in the case of the shortest model (No. 617), the thrust

deduction factor decreases with increasing speed

and in the case of

the longest model (No. 620) it has a tendency to

increase with

in-creasing speed. At light draught,

the thrust deduction factor in each

case is either constant or increases

with increasing speed.

A further investigation into the influence of length

breadthratio,

LIB, and propeller diameter (DIT) on wake fraction and thrust

deduction factor at load draught has also been undertaken.

In order

to avoid the effects of variations in the

recorded values due to

inaccuracy of measurement, in this instance the average values of

3

L/B

Fig. 26.

wake fraction and thrust deduction factor over the whole speed

range were calculated for each combination of model and propeller.

Fig. 26 shows the family of curves obtained from the mean values

of the wake fraction. It will be seen that both L/13 and DIT have

a considerable influence on the wake, and that the wake fraction

decreases as these two parameters increase.

A somewhat similar though less regular tendency is discernible in

the case of the thrust deduction factor (Fig. 27). It can, however,

be said that the thrust deduction factor tends to decrease with

increasing LIB, except within the range LIB -= 5.5

6.5 where it

remains more or less constant.

7

37

4CI 35 30 25

-DIT =0.507

-DIT =0.560 DIT =0.626 D/T = 0.7 Ia

25 15

\

ss\

Propeller No. P516; D/T =0.713 Propeller

No. P6/7; D/T

=0.626 Propeller No. P6/8; D/T =0.560 Propeller No. P619; D/T=0.507

%

1

.

/

_

-.. 6,5 7.5 L/t3 Fig. 27.

9. Acknowledgement

The authors wish to thank Mr. E. FREDIANIS, who carried out the

necessary design work and Mr. C. C. M. SCHNEIDERS who was

responsible for a large part of the calculations. Thanks are also due

to Mr. DACRE FRASER-SMITH, B. Sc., who has translated the paper

from the Swedish.

Appendix

Table V

39

Resistance Tests

Sell-Propulsion Tests

V I Fn L Ps 17 R '

P,

C1

T

P8

n

w t I c2 n

knots

tons

I

HP

/

tons

HP

(Mar.)

(Metr.) I (Metr.) /

(Metr.) (Metr.) rimill.

% 1/ 04

7 0.183 0.376 1.277

61.3 489

1.717 81.9 '

101.9 32.4 25.6 366 74.8

7.5 0.196 0.403 1.475

75.9 485

2.000 103

109.3 33.2 26.3 358 73.7

8 0.209 " 0.430 1.708

93.7 477

2.310 126

117.0 33.0 26.1 355 74.4

r...-. 8.5 0.223 0.457 1.974 115 466 2.648 153

125.1 32.3 25.5 351 75.2

CDco = p., 0 9 9.5 0.236 0.249 0.484 0.510 2.292 2.763 141 180 451 416 3.068 3.698 187 241 133.2 143.8 32.9 32.8 25.3 25.3 340 311 75.4 74.7 1 10 0.262 0.537 3.551 2,44 358 4.702 331

157.0 33.4 24.5 264 73.7

4 :0

10.5 0.275 0.564 4.939 356 284 6.437 495

176.4 33.0 23.3 204 71.9

11 0.288 0.591 6.807 514 226 8.556 731

197.3 32.6 20.4 159 70.3

11.5 0.301 0.618 8.337 658 202 10.82 1027

218.6 31.4 22.9 129 64.1

12 0.314 0.645 9.799 807 187 12.5 0.327 0.672 11.206 961 177 7 0.183 0.376 1.277

61.3 489

1.707 79.5

131.2 35.9 25.2 377 77.1

7.5 0.196 0.403 1.475

75.9 485

1.963 101

141.2 35.9 24.9 365 75.1

1

8 0.209 0.430 1.708

93.7 477

2.255 124

151.5 35.6 24.3 361 75.6

co t... _8.5

0.3

_{0.457 1.974 115 466 2.584 154}

_{162.5 35.2 23.6 348 74.7}

CO 0 CO _{9 0.236 0.484 2.292 141 451 3.022 192}

_{174.1 35.1 24.2 332 73.4}

II

i N

o-,

9.5 0.249 0.510 2.763 180 416 3.671 248

188.0 35.4 24.7 302 72.6

11. 0 cl' 10 0.262 0.537 3.551 244 358 4.648 340

206.3 35.5 23.6 257 71.8

4 1

10.5 0.275 0:564 4.939 356 284 6.300 514

232.8 35.0 21.6 197 69.3

o

X 11 0.288 0.591 6.807 514 226 8.446 774

263.1 33.7 19.4 150 66.4

ko 11.5 0.301 0.618 8.337 658 202 10.72 1090

291.8 32.9 22.2 122 60.4

4

_{12 0.314 0.645 9.799 807 187} II 12.5 0.327 0.672 11.206 961 ₁₇₁ Z1 6:1 7 0.183 0.376 1.277

61.3 489

1.717 83.5

160.6 38.7 25.6 359 73.4

7.5 0.196 0.403 1.475

75.9 485

1.981 104

172.8 38.4 25.5 35473.0

8 0.209 0.430 1.708

93.7 477

2.264 127

185.4 37.3 24.6 352

r- CO _{8.5 0.223 0.457 1.974 115 466 2.602 156 198.3 37.3 24.1 344 73.7} PI 9 0.236 0.484 2.292 141 451 3.031 193

212.5 37.3 24.4 330 73.1

713

i

9.5 0.249 6.510 2.763 ₁₈₀ 416 _{3.634 248}

228.9 37.8 24.0 302 72.6

o

_2-

10 0.262 0.537 3.551 244 358 4.684 349

252.4 38.4 24.2 250 69.9

41 0 X 10.5 0.275 0.564 4.939 356 284 6.529 549

290.8 36.2 24.4 184 64.8

a. 11 0.288 0.591 6.807 514 226 8.537 813

328.2 34.1 20.3 143 63.2

.4 m 11.5 0.301 0.618 8.337 658 202 10.65 1124

362.4 32.9 21.7 118 58.5

12 0.314 0.645 9.799 807 187 12.5 0.327 0.672 11.206 961 177 7 0.183 0.376 1.277

61.3 489

1.717 83.4

191.5 41.4 25.6 359 73.5

7.5 0.196 0.403 1.475

75.9 485

1.981 105

206.3 4L5 25.5 351 72.3

8 0.209 0.430 1.708

93.7 477

2.264 130

221.8 40.5 24.6 344 72.1

=

Co .. 8.5 0.223 0.457 1.914 115 466 2.602 159 237.9 39.3 24.1 337 72.3 CDCO _{9 0.236 0.484 2.292 141 451 3.031 201}

_{254.7 40.3 24.4 317 70.1}

Ti)124 o..--. 9.5 0.249 0.510 2.763 180 416 3.634 258

275.0 40.9 24.0 29069.8

0 4

10 0.262 0.537 3.551 244 358 4.684 363

303.7 42.6 24.2 241 67.2

41 0 X 10.5₁₁ 0.275_0.288 0.564_0.591 4.939_6.807 356₅₁₄ 284 6.529 573

348.8 42.1 24.4 176 62.1

226 8.537 862

394.6 41.1 20.3 135 59.6

11.5 0.301 0.618 8.337 658 202 10.65 1211 438.5 39.8 21.7 110 54.3 12 0.314 0.645 9.799 807 187 12.5 0.321 0.672 11.206 961 177

Table TT

Resistance Tests

Self-Propulsion Tests

V

F, L

F n p,

R

Pe C1

T

P8

n

w t C2 n

knots

tons

HP

/

tons

HP

.

imin

(Metr.)

-

-

(Metr.)

(Metr.) /

(Metr.) (Metr.) /0

/o / %

7 0.171 0.376 1.116

53.6 559

1.420 69.2

108.7 30.9 21.4 433 77.5

8 0.196 0.430 L497

82.1 545

1.898 106

126.0 29.5 21.1 422 77.5

oo 8.5 0.208 0.457 1.730 101 531 2.227 134

135.0 29.8 22.3 400 75.4

CD CO 9 0.220 0.484 1.989 123 518 2.578 163

144.0 29.8 22.8 391 75.5

1 CLi 9.5 0.233 0.510 2.282 149 502 2.944 198

153.3 29.6 22.5 378 75.3

o ..,0

4 5

10 10.5 0.245 0.257 0.531 0.564 2.649 3.228 182 480 232 436 3.340 4.050 238 305 163.0 175.3 28.8 20.7 29.0 20.3 367 331 76.5 76.1 X 11 0.269 0.591 4.608 325 358 5.410 447

194.0 30.0 21.2 260 72.7

11.5 0.282 0.618 6.018 475 280 7.547 687

219.0 29.2 20.3 193 69.1

12 0.294 0.645 8.197 675 224 10.16 1300

245.3 29.5 19.3 147 65.5

12.5 0.306 0.672 10.336 886 192 7 0.171 0.376 1.116

53.6 559

1.367 66.5

140.0 32.8 18.4 450 80.6

8 0.196 0.430 1.497

82.1 545

1.861 105

162.3 32.5 19.6 426 78.2

co II 1--et ZE,' 78, 44 8.5 9 9.5 0.208 0.220 0.233 0.457 0.484 0.610 1.730 1.989 2.282 101 123 149 531 518 502 2.167 2.488 2.632 128 157 193 174.0 185.6 197.6 32.1 32.0 32.3 20.2 20.1 19.4 419 405 388 78.9 78.3 77.2 10 0.245 0.537 2.649 182 480 3.228 235

210.0 32.0 17.9 372 77.4

o

..0

4 0

X 10.5 11 11.5 0.257 0.269 0.282 0.564 0.691 0.618 3.226 4.308 6.018 232 325 475 436 358 280 3.923 5.283 7.494 307 449 711 227.3 253.3 289.0 31.9 31.9 31.7 17.7 18.5 19.7 329 259 187 75.6 72.4 66.8 Id _{12 0.294 0.645 8.197 675 224 10.16 1089 328.0 30.0 19.3 139 62.0} II 12.5 0.306 0.672 10.336 886 192 04 ;---1 7 0.171 0.376 1.116

53.6 559

1.390 66.5

171.0 34.5 19.7 450 80.6

8 0.196 0.430 1.497 82.1 545 1.816 101

196.0 34.6 17.6 443 81.3

8.5 0.208 0.457 1.730 101 531 2.062 123

209.3 33.7 16.1 436 82.1

9 0.220 0.484 1.989 123 518 2.384 152

223.6 34.2 16.6 419 80.9

G _, a) A 40, a) 1:471:, 9.5 10 10.5 0.233 0.245 0.257 0.510 0.537 0.564 2.282 2.649 3.228 149 182 232 502 480 436 2.817 3.310 4.154 194 247 332 241.3 261.0 284.0 33.6 31.8 32.7 19.0 20.0 22.3 386 76.8 354 73.7 305 69.9 A

P-ii

11 0.269 0.591 4.308 325 358 5.417 473

314.6 32.9 20.5 24668.7

cs4 _11.5 0.282 0.618 6.018 475 280 7.330 723

355.0 33.3 17.9 184 65.7

:E m 12 0.294 0.645 8.197 675 224 9.938 1112

404.6 31.5 17.5 136 60.7

12.5 0.306 0.672 10.336 886 192 7 0.171 0.376 1.116

53.6 559

1.337 69.3

201.6 39.8 16.5 432 77.3

8 0.196 0.430 1.497

82.1 545

1.853 109

234.6 39.1 19.2 410 75.3

co 8.5 0.208 0.457 1.730 101 531 2.130 135

252.3 37.8 18.8 397 74.8

0 CO 9 0.220 0.484 1.989 123 518 2.443 164

270.3 36.8 18.6 388 75.0

9.5 0.233 0.510 2.282 149 502 2.832 200

290.9 35.4 19.4 374 74.5

a.-.

o c

10 0.245 0.537 2.649 182 480 3.303 249

310.6 35.5 19.8 351 73.1

4 .81 X 10.5 11 0.257 0.269 0.564 0.591 3.228 4.308 232 325 436 358 4.027 5.342 333 487 337.3 375.3 36.4 37.8 19.8 19.4 304 69.7 239 66.7 11.5 0.282 0.618 6.018 475 280 7.330 762

430.6 36.3 17.9 174 62.3

12 0.294 0.645 8.197 675 224 9.938 1154 489.3 35.3 17.5 131 58.5 12.5 0.306 0.672 10.336 886 192

Table VLF

41

Resistance Tests

Self-Propulsion Tests

V

FL

FThv

R

I Pe C1

T

P.

71 w

t

_{Cy n}

knots

(Metr.)

-tons

(Metr.) I

- HP

I (Metr.)

/

. /

tons

(Metr.) - HP (Metr.) , . rimin" 0, ic) 0, ic)

/ CY0

7 0.162 0.376 1.015

50.5 593

8 0.185 0.430 1.419

77.9 574

1.784 103

135.7 28.8 20.5 434 75.6

8.5 0.197 0.457 L628

94.9 565

2043. 126

145.0 28.7 20.3 426 75.3

,.. 4 o .CO 9 0208. 0.484 1.865 115 554 2.315 151

154.2 28.2 19.4 422 76.2

71) N 9.5 0.220 0.510 2.106 137 546 2.600 180. _ 163.8_ _

27.3 19.0 416 76.1

al

o _

10 0.232 0.537 2.383 163 536 2.967 216

173.7 27.4 19.7 404 75.5

4

10.5 0.243 0.564 2.728 196 - 516 3.435 265

185.1 27.4 20.6 382 74.0

11 0.255 0.591 3.189 241 482 4.093 336

198.8 26.8 22.1 346 71.7

11.5 0.266 0.618 4.123 325 . 409 5.383 473

218.6 27.0 23.4 281 68.7

12 0.278 0.645 5.712 470 321 7.180 686

241.9 27.4 20.4 220 68.5

12.5 0.290 0.672 7.673 658 259 9.236 971

267.0 27.5 16.9 176 67.8

7 0.162 0.376 1.015

50.5 593

-1

8 0.185 ' 0.430 1.419

77.9 574

1.746 102

175.8 31.3 18.7 438 76.4

to ... 8.5 0.197 0.457 1.628

94.9 565

2.012 125

187.8 31.1 19.1 429 75.9

o ez 9 0.208 0.484 1.865 115 554 2.284 151

200.5 30.3 18.3 422 76.2

To' 9.5 0.220 0.510 2.106 137 548 2.581 182

213.5 29.7 18.4 411 75.3

o 12 10 0.232 0.537 2.383 163 536 2.929 217

226.9 28.7 18.6 402 75.1

4 6. 10.5 0.243 0.564 2.728 196 516 3.365 264

240.9 28.8 18.9 383 74.2

o

vz 11 11.5 0.255 0.266 0.591 0.618 3.189 4.123 241 325 482 409 3.960 5.206

333 .257.7

470 .283.8

29.2 29.8 19.5 20.8 349 283 72.4 69.1

ti

12 9.278 0.645 5.712 470 321 7.085

710. '319.1 29.3 19.4 213 66.2

II 12.5 0.290 0.672 7.673 658 259 9.394

1067 '358.5 29.0 18,3

160 61.7 0:1 N 7 0.162 0.376 1.015

50.5 593

8 0.185 0.430 1.419

77.9 574

1.721 102

213.8 32.8 17.5 438 76.4

to 8.5 0.197 0.457 1.628

94.9 565

2.012

127 230M 32.2 19.1 422 74.7

9 0.208 0.484 1.865 115 554 2.309 156

246.1 31.9 19.2 408 73.7

78

A 4

o 9.5 0,220 0.510 2.106 137 546 2.613 189

262.2 31.2 19.4 396 72.5

TD. Ts fa,g 2 -Es P" 10 10.5 0.232 0.243 0.537 0.564 2.3832.728 163 196 536 516 2.967 3.391 228 278.3 276 295.4 31.2 31.4 19.619.7 383 366 71.5 71.0 A A 11 0.255 0.591 3.189 241 482 3.979 345

316.0 31.3 19.9 337 69.9

.o.. 11.5 0.266 0.618 4.123 325 409 5.080 475

346.1 32.3 18.8 280 68.4

.O u2 12 0.278 0.645 5.712 470 321 6.927 723

392.0 30.5 17.5 209 65.0

12.5 0.290 0.672 7.673 658_ 259 9.394 1110

445.5 29.8 18.3 154 59.3

7 0.162 0.376 1.015

50.5 593

8 0.185 0.430 1.419

77.9 574

1.721 108 256.7 35.8 17.5 '414 72.1 et 8.5 0.197 0.457 1.628

94.9 565

2.012 133

275.2 35.9 19.1 403 71.4

CD CO 9 0.208

0.44

1.865 115 554 2.309 161

294.0 35.3 19.2 395 71.4

Tli III 9.5 0.220 0.510 2.106 137 546 2.613 193 312.5 34.6 19.4 -388 71.0 ci..., o .2 pr:: 4 10 10.5 0.232 0.243 0.537 0.564 2.383 2.728 163 196 536 516 2.967 3.391 231 331.0 283 353.3 34.9 34.5 19.7 19.6 378 357 70.6 69.3 11 0.255 0.591 3.189 241 482 3.979 357

379.4 34.0 19.9 325 67.5

11.5 0.266 0.618 4.123 325 409 5.080 501

418.8 34.6 18.8 265 64.9

12 9.278 0.645 5.712 470 321 6.927 753

472.9 34.1 17.5 200 62.4

12.5 0.290 0.672 7.673 658 259 9.394 1136

538.0 32.3 18.3 150 57.9

T able VIII

Resistance Tests

Self-Propulsion Teats

V Pn L

Fnr

R

P,

CI T

P,

n

w t C2 n

knots

(Metr.) tons (Metr.)

HP

(Metr.)

/

/

tons (Metr.)

HP

(Metr.) , . ri 0//0 /0

/ 0/0

7 0.155 0.376 1.029

49.4 606

8 0.177 0.430 1.375

75.4 593

1.621 95.2

144.6 26.4 15.2 470 79.2

8.5 0.188 0.457 1.571

91.6 585

1.884 119

155.1 26.0 16.6 451 77.0

co 9 0.199 0.484 1.786 110 576 2.153 144

165.3 25.9 17.0 442 76.4

= p.., a,73 2 1:1-1 0 9.5 10 10.5 11 0.210 0.221 0.232 0.243 0.510 0.537 0.564 0.591 2.032 2.294 2.617 2.982 132 157 188 225 567 556 538 516 2.432 2.750 3.166 3.659 173 206 251 308 175.9 186.0 197.6 211.0 25.3 25.1 25.2 24.4 16.4 16.6 17.3 18.5 433 424 403 377 76.3 76.2 74.9 73.1 11.5 0.254 0.618 3.388 267 497 4.273 379

225.0 23.9 26.7 350 70.4

12 0.265 0.645 4.175 344 439 5.188 488

241.1 24.5 19.5 309 70.5

12.5 0.276 0.672 5.618 482 354 6.891 704

266.1 25.4 18.5 242 68.5

13 0.287 6.699 7.497 669 287 , 7 0.155 0.376 1.029

49.4 606

ch 8 0.177 0.430 1.375

75.4 593

1.594 95.9

187.1 29.5 13.7 466 78.6

8.5 0.188 0.457 1.571

91.6 585

1.852 119

200.8 29.2 15.2 451 77.0

co _{r- 9 0.199 0.484 1.786 110 576 2.120 146}

_{214.8 28.4 15.8 436 75.3}

a° CD co _{9.5 0.210} 0.510 2.032 132 567 2.405 177

228.5 28.0 15.5 423 74.6

II 1 .

i 44

n..-. o ,g 10 10.5 0.221 0.232 0.537 0.564 2.294 2.617 157 188 556 538 2.717 3.101 211 250 242.2 255.9 27.9 27.9 15.6 15.6 414 404 74.4 75.2

4 0

11 0.243 0.591 2.982 225 516 3.544 303

272.0 27.4 15.9 383 74.3

o

_to 11.5 12 0.254 0.265 0.618 0.645 3.388 4.175 267 344 497 439 4.103 5.127 372 501 290.6 315.9 26.5 26.9 17.4 18.6 357 301 71.8 68.7 r-: _{12.5 0.276 0.672 5.618 482} 354 6.815 723

350.3 27.3 17.6 236 66.7

II al 13 0.287 0.699 7.497 669 287 )---4. 7 0.155 0.376 1.029

49.4 606

8 0.177 0.430 1.375

75.4 593

1.654 103

231.7 30.7 16.9 434 73.2

8.5 0.188 0.457 1.571

91.6 585

1.901 125

247.8 30.3 17.4 429 73.3'

=

cc

,

co,.., 9 0.199 0.484 1.786 110 579 2.158 150

264.0 29.5 17.2 42473.3

= c., 9.5 0.210 0.510 2.032 132 567 556 2.421 2.717 179 214 280.1 296.6 28.9 28.7 16.1 15.6 418 73.7 408 73.4 Iii c4,_. 2 .,4, 10 10.5 0.221 0.232 0.537 0.564 2.294 2.617 157 188 538 3.079 256

313.8 29.2 15.0 395 73.4

X 4-4 5 11 0.243 0.591 2.982 225 516 3.539 312 334.5 28.5 15.7 3-72 72.1 Oc 11.5 0.254 0.618 3.388 267 497 4.158 388

357.3 28.3 18.5 342 68.8

.4..." m 12 0.265 0.645 4.175 344 439 5.073 511

386.8 28.3 17.7 295 67.3

12.5 0.276 0.672 5.618 482 354 6.738 748

432.1 28.2 16.6 228 64.4

13 0.287 0.699 7.497 669 287 7 0.155 0.376 1.029

49.4 606

8 0.177 0.430 1.375

75.4 593

1.654 104

274.5 35.3 16.9 430 72.5

8.5 0.188 0.457 1.571

91.6 585

1.901 128

294.5 34.7 17.4 419 71.6

co 9 0.199 0.484 1.786 110 579 2.158 155

314.5 33.7 17.2 411 71.0

ai CC) _{9.5 0.210 0.510} 2.032 132 567 2.421 187

334.5 32.8 16.1 400 70.6

i PI

0,-0 0,-0

1010.5 0.221 0.232 0.537 0.564 2.294 2.617 157 188 556 538 2.717 3.079 222 267 354.5 375.6 32.3 32.5

15.6 393 70.7

15.0 379 70.4

1.1 RI ts4 0 11 0.243 0.591 2.982 225 516 3.539 326

399.4 32.8 15.7 356 69.0

X _{11.5 0.254 0.618 3.388 267 497 4.158 405}

_{427.9 32.5 18.5 328 65.9}

12 0.265 0.645 4.175 344 436 5.073 543

467.2 31.8 17.7 278 63.4

12.5 0.276 0.672 5.618 482 354 6.738 798

. 525.1 30.4 16.6. 214 60.4

13 0.287 0.699 7.497 669 287

Table IX

43

'

Resistance Tests

Self-Propulsion Tests

V

FnL

Fnp

R Pe C,

T

Pe 1

n

i o t C2 n

knots

(Metr.)

-

-

(Met r )tons

HP

(Metr )

/

/

tons

HP

, i

(Metr.) (Metr.) rim ri*

w lc' 0, /0

/

/

0/ . 8 0.217 0.482 1.342

73.6 383

1.698 92.6

106.4 36.4 21.0 304 79.5

8.8 0.230 0.513 1.531

89.3 378

1.945 110

113.5 35.7 21.3 307 81.2

9 6.244 0.543 1.773 109 368 2.237 132

120.9 35.5 20.7 304 82.6

co 9.5 0.257 0.573 2.114 138 342 2.657 165

129.6 35.4 20.4 286 83.6

15 G = 0.1₀ 10_10.5 0.211_0.284 0.603_0.633 2.590 3.403 178 245 309 260 3.315 4.365 218 309 140.9 155.1 34:8 35.4 21.9 22.0 252 206 '81.7 79.3 i.. In 11 0.298 6.663 4.313 325 225 5.506 429 171.2 33.6 21.7 171 75.8 tsI 0 11.5 0.311 0.694 5.223 412 203 6.666 559

185.7 32.7 21.6 150 73.7

X _{12 0.325 0.724 5.975 492 193 7.716 691}

_{198.6 31.9 22.6 138 71.2}

12.5 0.338 0.754 6.698 574 187 8.656 828

210.5 30.8 22.6 130 69.3

13. 0.352 0.784 7.526 671 180 13.5 0.365 0.814 8.619 798 170 ,..2 8 8.5 0.217 0.230 0.482 0.513 1.342 1.531 73.6 89.3 383 378 1.698 1.948 86.0 197 134.8 145.1 40.9 40.0 21.0 21.3 328 316 85.6 83.5 ao © -$4

in-..-.

9 9.5 0.244 0.257 0.543 0.573 1.773 2.114 109 138 368 342 2.237 2.657 132 166 155.7 166.7 39.0 39.6 20.7 20.4 304 284 82.6 83.1 0 CO 10 0.271 0.603 2.590 178 309 3.242 219

182.8 37:5 20.1 251 81.3

o 10.5 0.284 0.633 3.403 248 260 4.200 306

202.5 36.1 19.0 208 80.1

2 -ci 11 0,298 0.663 4.313 325 225 5.387 427

222.8 36.5 19.9 171 76.1

11.5 0.911 0.694 5.223 412 203 6.538 567 242.8 35.4 20.1 148 72.7 X 12 0.325 0.724 5.975 492 199 7.542 696

259.5 34.2 20.8 137 70.7

CA .1.1 12.5 13 0.338 0.352 0.754 0.784 6.698 7.526 574 671 187 180 8.528 835

275.3 33.4 21.5 129 68.7

II 13.5 _{0.365 0.814 8.619 798 170} Pq 8 0.217 0.482 1.342

73.6 383

1.644 84.8

161.2 45.3 18.4 332 86.8

;:-.--8.5 0.230 0.513 1.531

89.3 378

. 1.890 103

173.5 43.5 19.0 328 86.7

9 0.244 0.543 1.773 109 368 2.191 129 186.3 42.4 19.1 311 84.5

r.

CO on t+ " o CO 9.5 10 0.257 0.271 0.573 0.603 2.114 2.590 138

'1/8

309342 2.611 ,9.214 162 217 200.2 218.3 43.3 43.2 19.0 19.4 291 254 85.2 82.0 in T, Po 10.5 0.284 6.633 3.403 245 260 4.145 298

240.2 43.4 17.9 214 82.2

o

0 0

11 0.298 0.663 4.313 325 225 5.351 434 270.8 40.1 19.4 189 74.9 11.5 0.311 0.694 5.223 412 203 6.611 593

300.2 37.0 21.0 141 69.5

...e 12 0.325 0.724 5.975 492 193 7.643 736

32L4 36.3 21.8 129 66.8

u2 12.5 0.338 0.754 6.698 574 187 8.437 857

337.9 35.7 20.6 125 67.0

13 0.352 0.784 7.526 671 180 13.5 6.365 0.814 8.619 798 170 8 0.217 0.482 1.342

73.6 383

1.644 84.4

191.2 48.4 18.4 334 87.2

8.5 0.230 0.513 1.531

89.3 378

1.890 106

206.7 47.1 19.0 319 84.2

9 0.244 0.543 1.773 109 368 2.191 133 _{222.1 46.5 19.1 302 82.0} co,

t G

109.5 0.257 0.271 0.573 0.603 2.114 2.590 138 178 342 309 2.611 3.214 163 218 237.6 258.6 47.3 47.8 19.0 19.4 289 252 84.7 81.7 ta.- 10.5 0.284 0.633 3.403 248 260 4.145 318 291.1 46.0 17.9 200 77.0 o ,c4 11 0.298 0.663 4.313 325 225 5.305 456 326.9 43.3 18.7 161 71.3

4 5

_X 11.5 0.311 0.694 5.223 412 203 6465 614 359.2 41.6 19.2 136 67.1 12 0.325 0.724 5.975 492 193 7.460 758

385.6 40.0 19.9 125 64.9

12.5 0.338 0.754 6.698 574 187 8.364 895

407.5 39.2 19.9 120 64.1

13 0.352 0.784 7.526 671 180 13.5 0.365 0.814 8.619 798 170

Table X

Resistance Tests

Self-Propulsion Tests

V Fn L Fn v R _Pe C1 T .P8

n

w t C2 n

knots

(Metr.) ---tons (Metr.) (Metr.)

HP

./

/

tons (1VIetr.)

HP

(Metr.) r'

/min. % %

/.,

/

0/° 8 0.202 0.482 1.143

62.7 449

1.427 80.2

115i.32.9 19.9 351 78.2

8.5 0.215 0.513 1.314

76.6 441

1.651 97.0

123.7 32.4 20.4 348 79.0

.9 0.227 0.543 1.484

91.6 438

1.868 116

132.0 31.3 20.6 346 79.0

co 9.5 0.240 0.573 1.666 109 433 2.107 138

140.0 30,9 20.9 342 79.0

CD CD 10 0.253 0.603 1.915 131 420 2.384 165

148.0 31.1 19.7 333 79.4

P.,=.

o 4

10.5 11 0.265 0.278 0.633 0.663 2.273 2.915 164 220 388 333 2.951 3.803 214 294 159.3 174.3 31.3 31.1 23.0 23.3 298 249 76.6 74.8

41 .

11.5 0.290 0.694 3.732 294 285 4.812 400

1903. 30.5 22.4 209 73.5

12 0.303 0.724 4.541 374 254 5.858 525

207.0 28.8 22.5 181 71.2

12.5 0.316 0.754 5.311 455 236 6.800 650

221.3 27.7 21.9 165 70.6

13 0.328 0.784 5.981 533 227 13.5 0.341 0.814 6.605 612 221 8 0.202 0.482 1.143

62.7 449

-1.405 74.9

146.7 36.9 18.6 376 83.7

8.5 0.215 0.513 1.314

76.6 441

1.606 90.7

156.3 36.3 18.2 372 84.5

co

o

t- . 9 9.5 0.227 0.240 0.543 0.573 1A84 1.666 91.6 109 438 433 1.808 2.055 110 132 166./ 177.6 36.1 35.2 17.9 18.9 365 357 83.3 82.6 T.,,-1 CD CO 10 0.253 0.603 1.915 131 420 2.354 162

189.6 34.6 18.6 340 80.9

II i P.i _{10.5 0.265} 0.633 2.273 164 388 2.877 208

204.0 31.1 21.0 306 78.8

2 -o 4.1 o 11 11.5 0.278 0.290 0.663 0.694 2.915 3.732 220 294 333 285 3.654 4.707 284 398 223.0 246.6 34.8 33.6 20.2 20.7 258 210 77.5 73.9 co ..., - 12 12.5 0.303 6.316 0.724 0.754 4.541 5.311 374 455 254 236 5.798 6.740 536 669 270.3 290.6 31.8 29.7 21.7 21.2 177 _161 69.8 68.0 16 _{13 0.328 0.784 5.981 533}

_22/

II 13.5 0.341 0.814 6.605 612 221 PO ;4- 8 0.202 0.482 1.143

62.7 449

1.382 73.6

177.0 39.0 17.3 383 85.2

8.5 0.215 0.513 1.314

76.6 441

1.592 89.8

188.6 39.3 17.5 376 85.3

9 0.227 0.543 1.484

91.6 438

1.801 110

201.3 38.5 17.6 365 83.3

co _{9.5 0.240 0.573 1.666} 109 433 2.047 133

214.3 38.3 18.6 355 82.0

a) co 10 0.253 0.603 1.915 131 420 2.346 162

229.0 37.4 18.4 340 80.9

To rci 0 76 P-1

0,-0 CD 10.5 11 0.265 0.278 0.633 0.663 2.273 2.915 164 220 388 333 2.839 3.676 209 296 247.3 274.0 37.3 36.2 19.9 20.7

105 18.5

247 74.3 11.5 0.290 0.694 3.732 294 285 4.722 414

303.3 35.2 21.0 202 71.0

A 12 0.303 0.724 4.541 374 254 5.768 554 331.6 33.8 21.3 172 67.5 ..c m 12.5 0.316 0.754 5.311 455 236 6.725 690

356.0 32.7 21.0 15665.9

13 0.328 0.784 5.981 533 227 13.5 0.341 0.814 6.605 612 221 8 0.202 0.482 1.143

62.7 449

1.337 73.6

207.3 43.4 14.5 383 85.2

8.5 0.215 0.513 1.314

76.6 441

1.569 90.7

222.6 43.3 16.3 372 84.5

9 0.227 0.543 1.484

91.6 438

1.801 111

238.0 42.9 17.6 361 82.5

oc 9.5 0.240 0.573 1.666 109 433 2.047 134

253.6 42.4 18.6 352 81.3

m cM 10 0.253 0.603 1.915 131 420 2.309 163 269.3 42.4 17.1 337 80.4 i r11 10.5 0.265 0.633 2.273 164 388 2.765 209

290.0 42.7 17.8 305 78.5

o c0 14 rtl 4.1 o 11 11.5 0.278 0.290 0.663 0.694 2.915 3.732 220 294 333 285 3.579 4.610 295 420 323.3 360.0 41.0 39.8 18.6 19.0 248 74.6 199 70.0 12 0.303 0.724 4.541 374 254 5.738 573

398.6 37.3 20.9 166 65.3

12.5 0.316 0.754 5.311 455 236 6.710 721

428.0 36.4 20.8 149 63.1

13 0.328 0.784 5.981 533 227 13.5 0.341 0.814 6.605 612 221