Systematic tests with models of cargo vessels with δpp = 0.575

FRAN

STATENS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK),

,Nr 16 GOTEBORG ₁₉₅₀

SYSTEMATIC TESTS WITH MODELS

OF CARGO VESSELS

WITH

_= 0.575

BY

F. NORDSTROM

4-Lorvlik410, c;)

rq/loscW'

GUMPERTS AB GOTEBORG H.

Manuscript delivered April 1950

GOTEBORG 1950

In two previous papers') for convenience referred to in the

following as Pub!. 10 and Pub!. 14 the author gave an account of

some systematic tests with eleven models of fast cargo vessels with a

block coefficient of 0.625. The present paper _{may be considered as}

dealing with a continuation of those earlier, tests. Ten further models have now been tested, all with a block coefficient of 0.575.

Resistance tests were carried out with all models and self-propulsion

tests were also made with four of them.

The aim of the investigations was to study the influence upon the

resistance of the following factors:

length (Series A 1.: Models 353, 354, 355 and 356) L. C. B. (Series B 1: Models 357, 358, 355 and 359)

breadth-draught ratio (Series C 1: Models 382, 358, 383 and :3,84),

In each series, the author started with _{a normal form, from which}

the other models in the series were developed systematically. Thus the author. has tried to follow the principle of *one variable at a time*.

The parent form for all the models (Model No 354) may be

considered as corresponding, in the conventional meaning,

_{to a}

practical ship form. As for the developed forms, the chief aim _has

been to study the effect of the above mentioned factors upon

resistance and the question of whether the developed models can be

said to represent practical ship forms has been given only secondary

consideration.

1) H. F. NORDSTROM: Some Systematic Tests with Models of Fast Cargo _Vessel.

Publication No_ JO of the Swedish State Shipbuilding Experimental Tank, Goteborg

1948.

H. F. NOICDSTROMr Further Tests with Models of Fast Cargo Vessels_ Publica:

4

The principal data for the ship forms investigated are given in

Table 1. For comparison, the data for the previous series A, B

and C in Publ. 10 are also given in Table 1, since the results from

those series will be compared in the following withthe latest results.

The investigations have been carried out at t he S w e di s h

State Shipbuilding Experimental

Tank in

Gote-borg and were made possible by a grant from

Hugo Ha

m-mar's Foundation for Maritime

Research.

2.

Symbols and Units

The same symbols as those employed in Publ. 10 and Publ. 14

have been used in the present paper. They may, however, be

confined in this case to the following: Ship Dimensions

length on waterline

---- length between perpendiculars

B = breadth

T -= draught

immersed midship section area

wetted surface area (= mean girth x L)

V

volumetric displacement

A =_- weight displacement: Br. tons in sea water

-= distance of L. C. B. forward of midships (442)

0 = half angle of entrance on waterline

Propeller Dimensions

D = propeller diameter

H = face pitch (mean)

Dimensional Coefficients and Ratios

V

L.B.T

= block coefficients

V

L.B.T

6pp

13 --- = midship section coefficient

0

0

V

92 L prismatic coefficient

1/3 --- length-displacement ratio

Li

(LI100)3 displacement-length ratio; Br. tons, feet

= L. C. B. forward of Lpp/2 as % of LP,, Kinematic and Dynamic Symbols

speed in general

V ship's speed in Metr. knots

frictional resistance

R. residuary resistance

R1+ R. = total resistance

propeller thrust

angular velocity (revs, per unit time)

N, effective (towing) power

N, delivered power at tail end of shaft

wake fraction (TAYLOR)

= thrust deduction factor

Kinematic and Dynamic Coefficients and Ratios

=

= FROUDE'S number, displacement

FL

=

= FROUDE'S number, length

VAIL = speed-length ratio; Br. knots, feet

72/3 V3/N1; m3, Metr. knots and HP

C2 72/3 V3/N2; m3, Metr. knots and HP

427.1 .371/42'3 V3; Br. HP, tons and knots

Metric units have been employed in all the calculations. For g (= acceleration due to gravity) the value of 9.81 m/sec.2 has been

used. For the convenience of readers more familiar with British

units, the results in the tables are also given in such units. The

relevant conversion factors are to be found in Publ. 10, p. 6.

T

=

=

.6

I.

Resistance Tests

1 Methods of Calculation

The model results were converted to the scale of the full-sized ships in the conventional way according to FROUDE'S method. The frictional resistance was calculated using the formulae decided upon

at the Tank Superintendents' Conference in Paris

in 1935. For the details, the reader is referred to p. 7 in Publ. 10. No length correction has been employed since the length of the ship in every case was about 120 m ( 400 feet).

Since the object of the investigations was, in the first place, to 'make a comparison between different forms, no correction has been

made for roughness, scale effect, etc.

In Publ. 10, a comparison was given 'between the results obtained according to FEMME and SCHOENHERR respectively. Such a com-parison, however, has been considered unnecessary in the present paper

4. Models Tested

As stated above, ten models were tested (Table 1),. All were made

of paraffin wax and were designed to represent single-screw ships.

The models were run naked, that is without appendages such as

rudder, stern frame sole piece, propeller boss and bilge keels. No turbulence stimulating devices were employed in the main tests, although Models Nos. 353 and 356 were also tested with a 1 mm tripwire fitted at station No. 19. Allowing for the resistance of the tripwire, the results with and without tripwire practically coincided. The model scale was assumed to be 1/20. The displacement was the same in all tests and on this scale was equivalent to 8308 m3. The results were calculated on this basis and all data in the following tables and figures refer to the full-sized ships, at this displacement,

By presenting the results in dimensionless or quasi-dimensionless form,

they can, however, be used more, generally.

All runs were made in smooth water within a speed range

cor-responding to 16-22 knots. As the normal speed for the ships in question can be assumed to be about 18-19 knots, the models

were, quite intentionally, rather overdriven. Altogether about 240 runs were made,

Table IL I Model No. L =--1.025.- Lipp L LI LPP = o --: -4 -ce , ;--- .--1 ----j B I B --B-T L_PP

s

VII.3 (L/100)3 L_PP B

.

1___ m %, % m

-

2 -I, . .3 6 a, _:.. II' al ,.., ...a II "0 -4

-Series A. Variation of Length

I 301 113.78 1 5.46 1 175.1 111 -7.5 _,

-1

17.6761 2.4 6.230 2601 302 123.00 1, 5.91 _j 138.6 120,

0 - ir-1

_{17.000 2.4 7.059 2704} 303 304 132.23 141.45 1 6.35 1 6.79 1 111.6 I 91.1 129 138 +7.5 +15 I -1 116.3961 -1 115.853 2.4 2.4 7.868 8.705 2804 2900

Series B Vax ation of L. B. C.

-305 306 132.23 132.23 I 6.35 6.35 111.6 111.6 129 129

---...--,--,--3

-2

16.396; 2.416.396 2.4 7.868-7.868 2800 2802 303 132.23 6.35 111.6 129 _{1 -1 116.396 2.4 7.868 2804} I 307 308 132.23 132.23 6.35 6.35 111.6 111.6 , 129 129 I 0 +1 116.396 1 16.396 2.4 2.4 7.868 7.868 2806 2808, Series C. Variation of BIT

309 132.23 [ 6.35 111.6 129 1 -2 j 15.6981 2.2 1 8.218 1Z807 306 132.23 6.35 111.6 129 1

. -2

16.3961 2.4 1 7.368 j 2302 310 311 132.23 132.23 .6.35 6.35 111.6 111.6 129 129

7 -2

-

-

; -2

17.0661 2.6 17.7101 2.8 1 7.559 1 7.984 1 2787 2797 --te, 1 ' lei I:r, c v.-74 t T5 .r... ..4., .,:.... 1,, cg 6 ...5. 1172 4 II T.:, > p44 1 I

, _{Series A la Variation of Length}

353 116.85 5.77 j 148.7 114 ,1 -5 '1-1.5 17.441 2.4 6.536 2532 354 123.00 6.07 127.5 120 1 o 1 -1.5 17.000 2.4 7.059 25981 355 356 1 129.15 135.30 6.38 , 6.68 110.1 95.8 126 132 +5 I 1 +10 -1.5-1.5 16.59016.208 2.4 2.4 7.595 8.144 2662 2725 Series B 1. _{Variation of L. B. C.} 357 1 358 1 129.15 129.15 6.38 6.38 110.1 110.1 126 1 126 11-3.5 116.5901 2.4 1 -2.5 116.5901 2.4 7.595 7.595 2659 2661 355 129.15 j 16.38 110.1 126 _

-

1 -1.5 1 16.5901 2.4 7.595 2662 359 129.15 6.38 110.1 126 1 1 ___0.5 1 16.5901 2.4 _7.595 .2664

-Series C 1. Variation of BIT

2.1 382 129.15 6.38 110.1 126 -2.5 .115.5181 8.120 2660 358 129.15 6.33 110.1 126 ' -2.5 1 16.5901 2.4 7.595 2661 383 1 384 129.15 6.33 129.15 6.38 110.1 110.1 126 1 15 J -2.5 -2.5 18.54817.596 2.7 3,0 7.161 6j93 2632 2628

-

1 I I I I

8

Parent form (Model No. 3.54)

The model numbered 354 in Table 1 was chosen as the parent

form for the whole model family. It was taken from the statistical

material available at the Tank and could be expected to have good

qualities from a resistance point of view. In order to facilitate a

comparison between the results in this paper and those given in

the two previous publications, the body plan and lines were specially

chosen as being very similar to those of the parent form (Model No. 302) in the earlier investigations. The normal trial trip speed

for this type would be about 18 knots.

The main data are as follows:

L = 123.00 m /9' --- 950

L, = 120.00 m

a --- 0.561 B = 17.00 m 6np = 0.575 T = 7.083 in 13 -= 0.960

0

= 115.60 m2 99 = 0.584

7

= 8308 m2

L/713 = 6.07

tIL = 1.5 %

No parallel body

X at station No. 9 1/4

Figs. 1, 2 and 3 show the body plan, lines and profile, and sectional

area curve respectively, the scale in each case corresponding to

= 8308 m3. Dimensionless scales are also given, viz.

length/7"

and area/723, by means of which the drawings can be used for

displacements other than 8308 m3. Other systems of units can also

be employed.

5. Series A 1.

Influence of Length

The same principle as that used for Series A in Publ. 10 was

adopted in this case for studying the influence of length. Thus,

all longitudinal dimensions of the parent form, No. 354, were

multiplied by a constant factor a and all transverse and vertical

dimensions by 1/Vii. By altering the parent form in this manner,

the displacement remains unchanged. The same applies to the

following coefficients and ratios:

block coefficient

load waterline coefficient midship section coefficient

111

NO354

I f I

r

NA

11111 1111111EIWANIVEL

11/10/111.

HIT

iltell

ik

i

m

il

_II

II LI 11 kkIllrik

_{1111.1111 1111}

irla

INIMMI

It

Was mal31

MIL ml I kall INIkterif

If

-00.5' 2 5, 4 0.Qs o./ 0,2 0t3 Fig, 1

11:ent form

9 041 /ea? o 4e.w/h unit V prismatic coefficient breadth-draught ratio tILpp

On the other hand, L/7113 is altered in_{the proportion a, LIB and}

LIT in the proportion a3/2, S in, the proportion all2 and tan 0 in the proportion a-312.

Three new ship forms were derived from Model No. a54 according

to this principle. The following values _{were chosen for a:'}

a 0.95 1 _{1.05 1.10}

Model No. 353 I 354 355 356

-The principal data for the forms so obtained are given in Table 1. The results of the resistance tests are shown in Table 2 and Fig. 4

and are set down in various other forms _{in the subsequent figures.}

WL 5

BL

8

2

5 /0 _0,5 20 30 40 NO.354 60 3 Fig. 2 70 80 4 90 100 110 tenoth.,_, unit_ 20 12001 ._0"1.. 5, © Mil MEM "1111111111111111111111111 MIME MIMI WEI 11111=11111111111MIIMMIll 11111111111111111111111MINEM MIS MOM MOM mumpirmilliMiliallIMMIIIIIIIIMIIIIIIIIMIIIMIIMBI MININIIIIIMEN MIME 11=11111111111=1=111.111111111111111111111111MIMIIIMMIIIIIIIMISEILiWIIMIMININ

MIIIIIIIIIIMI MEM

ill

MIMI

IIIIMIII1111111

MOM IMMIIIIIIMIIIMMIMAI IIIMMIIIIINNI

Mil

MEM MIME !MIMI

NEM MINIM MIMI MIMI

111.111111111111111 IMMO Mai EMI 0 // 12 8 9 Ef . .13 MA= 111=11111111111111M1 MEM MIMI 19111111=1111111111111111111111=11111111111MMIIMME 111.1.11111111111111 11111=111

1111111111111=111111INIIIMINEMINIMMIIMMINIIIIIMINIMMIIIIII MIME

MENIIIIIIIIIINIMMINIIIIIMMINIIMMIIMIIIIMIIIIIINNW--14

MUM MIME MEM

15

MIME MOM MEM

MINI11111111111111111111111MIEN1111111

16

NM= NEM IMNIMIII

IIIIMIIIIII

Mil =MI

INNOMMIIININIZEIwy

17 18 NM= 19 -_ _ MINIMINEEMB INIIIIIII MEM /I= _AMIE

1

0 1 2 3 4 6 7

Sectional-Area Curie ₀ 2 4 6 70 60 50 40 30 20 3 8 0.3 130 _/0 0 -E 0 /0 /2 /4 /6 /8 20 /0 5 0 5 /0 20 30 40 50 60 0.5 0 0.5 2 .7 Length-unitII Fig. 3 N0,354

V 10-3 io-3 10-3 V F v FL -.,-VL RI Ra, R N, N, C,

0

Knots Knots I HP HP ,

/

/ °

(Metr.)

-

___. (Br.)Feet Kgs Kgs Kgs _(Metr.) . (Br )

/

/ /

/

No. 353 (L/V1/3 = 5.77) 16 0.584 0.243 0.816 17.19 7.10 24.30 2665 2629 630 0.666 17 0.621 0.258 0.867 19.20 9.74 28.94 3375 3329 597 0.703 18 0.657 0.273 0.918 21.32 15.01 36.33 4486 4425 533 0.787 19 0.694 0.289 0.969 23.53 22.18 45.71 5956 5875 473 0.887 20 0.730 0.304 1.020 25.84 28.38 54.21 7438 7337 441 0.951 21 0.767 0.319 1.072 28.24 33.03 61.27 8823 8703 431 0.973 No. 354 (L/V1/3 ---- 6.07) 16 0.584 0.237 0.796 17.63 7.04 24.66 2706 2669 621 0.676 17 0.621 0.252 0.846 19.69 8.68 28.37 3308 3263 609 0.689 18 0.657 0.267 0.896 21.86 12.62 34.48 4258 4200 562 0.746 19 0.694 0.281 0.945 24.12 18.86 42.99 5601 5525 502 0.836 20 0.730 0.296 0.995 26.49 26.18 52.67 7227 7129 454 0.924 21 0.767 0.311 1.045 28.96 30.89 59.85 8618 8501 441 0.951 No. 355 (LIVits = 6.38) 16 0.584 0.231 0.777 18.05 6.58 24.63 2702 2665 622 0.674 17 0.621 0.246 0.825 20.16 7.11 27.27 3180 3137 634 0.662 18 0.657 0.260 0.874 22.38 9.70 32.07 3961 3907 604 0.695 19 0.694 0.275 0.922 24.70 15.65 40.35 5257 5186 535 0.784 20 0.730 0.289 0.971 27.12 22.26 49.38 6775 6683 484 0.867 21 0.767 0.304 1.019 29.65 27.98 57.63 8298 8185 458 0.916 No. 356 (L/V113 = 6.68) 16 0.584 0.226 0.759 18.47 5.33 23.79 2610 2575 644 0.651 17 0.621 0.240 0.806 20.62 6.07 26.69 3112 3070 647 0.648 18 0.657 0.254 0.854 22.89 8.03 30.92 3819 3767 626 0.670 19 0.694 0.268 0.901 25.27 12.05 37.32 4863 4797 579 0.725 20 0.730 0.282 0.949 27.75 18.54 46.28 6350 6264 517 0.811 21 0.767 0.297 0.996 30.33 24.04 54.37 7829 7723 485 0.865 12 Table 2

Series A 1. Resistance Tests

V = 8308 ins BIT = 2.4 (57, = 0.575 tILap = -1.5 °,,0

-Heir. 1-1P N,

In Fig. 5, the results are shown in the form of C, as a function

of L/71/3 (or L since V is constant) at constant values of speed

(for V --- 8308 m3). At the same time the corresponding values of F, are given, by means of which the diagram has wider application. In Fig. 6, the curves from Fig. 5 are compared with corresponding curves obtained by interpolation at the same values of F from the

results with Series A in Publ. 10. This diagram shows that the

tendency for the demand for increased length is not so pronounced

for Series A 1 ((5pp = 0.575) as for Series A (= 0.625); it should,

however, be remembered that there is a slight difference in the value

of t1L between the two series. At given values of L,7 and V

(i. e. given values of L/7" and F,), the curves represent the inverse values of N, for the two ship-form series. The diagram shows the advantage of decreased 6, especially at overdriven speeds. In this case, as can be seen from the curves of B/L shown in the figure, an

increased value of B follows from a decreased pp.

In Fig. 7, the results are given in another form, namely C, as a function of Fv, the values for Series A being read from Fig. 6. Like Fig. 6, at given values of L, V and V the diagram indicates direct the relation between the values of N, (inversely proportional) for

ENO

,

Series A 1 .., woo _..-- NO 355 NO. 354 NO. 356 .." ./ ..-NO. 355

- - - -

.4,-. -8000 C..5-hI71

/

.00 ;L.::7 7. _ = ___ 7, r-.7 ____ _ _...

-.41116.

6000 600 500

-lnrdlIllaIlliiii

11/11/1all

400 ₄₀₀₀ -.--' --- --4-500 r-",-='"*."':-2000 200 ,00 n _fl I' /7 18 /9 20 21 22 V in knots (Heir) Fig. 4 ii

14 Cl 600 500 400 500 ZOO Series A 1 /7 Knots /8 19 20 21 F. 5

the different forms in question. The same could not, however, have

been said if FL (or Vil/f) had been chosen as base instead of F.

For this reason Fv has been used throughout these investigations.

A diagram has also been given in Fig. 7 by means of which the

speed scales for displacements between 7000 and 10000 m3 can be

drawn.

6. Series B 1. Influence of L. C. B.

The influence of the position of L. C. B. upon the resistance can

be studied in many ways. In this case, the same method as that

adopted for Series B in Publ. 10 has been employed. Thus, using a normal form as a basis, new forms are developed in which the shapes of the body sections are unchanged, while the spacing of

the sections is adjusted so as to give the desired shift of L. C.B.

and yet maintain the original length and displacement.

With such a modification of the normal form, the following

coefficients and ratios remain unchanged:

100 0 607 6.38 6.68 5.77 L /17W 1/6.35 123.00 129./5 V= /35.30 L in rn '/4. /20 /26 =8508 ms /52 Lpp in in 353 554 355 556 NO. 0.61/ --0.657 I 767

500 400 300 200 /00 60 353 354 545 302 303 Fig. 6 block coefficient

midship section coefficient prismatic coefficient LI7113

LIB

LIT

Small alterations take place in load waterline coefficient, S and 0.

There are various methods of adjusting the spacing of the _sections

in the above manner. The rule employed in the present investigations,

however, was the same as that used for Series B and described in

Publ. 10.

Three new ship forms were developed according to this_principle,

using Model No. 355 in Series A 1 as the normal form. The following values were chosen for tILpp:

jNormal form I 7.0 'Node/ No. F V knots17 M'. 8308 901/ 0.62/ 0.657 0694 0.730 0.767 /7 /8 /9 20 2/ /714 /8.15 /9.27 20.26 2/.29

Al

B/L a's o.10 0.05 0 Series Al Series A di. 1/4 0.575 -Z5% o.sas -tor. - c ----1 1 i 1 1 1 ' I I 1 1 1 1 1 IlLpp

3.5

2.5

1.5

0.5

Model No. 357 358 355 359 5.0 55 Series A/ series 301 C, 600

'5

33'6 304 A % --k -I

-16 700 C, 600 500 400 300 200 /00 7000 8000 9000 /0000 Fig. 7

The principal data for the ship forms so derived are shown in

Table 1.

The results of the resistance tests are given

in Table 3 and

Fig. 8.

In Fig. 9, the results are shown in the form of C, as a function

of tIL at constant values of F. (Since V and L are constant, the

curves also represent constant values of FL or Vi}/L.) As can be

seen, the optimum values of C, at the various values of Fv (or V)

lie at tiLpp

2.5 %.

For comparison, the corresponding curves from the results with Series B in Publ. 10 are also shown at the same values of Fv (by

interpolation). The difference in character between the two sets of

curves is rather surprising.

L/v'/' 6.49 t,aa' 6.38 6.1,7 6701- S.77 3308 m"---- 9031 ,, --_

' ,

-III

.."1,11111111...---714weirrirm

SEMMINI 11111111111111111

-1111MKE,

111111111111111

---_ _ . : ---..." ___. _____ -, Al Series A 6-, OAP 0.575 -/.5X 0.625 -/.0% 60 0.65 0.70 0.75 F. 1111%

som-immomimimmiliumiiiiiiraill

IlfS'il WM

2°,4E=

=gm wari

mom

MEI

0

Table ,3"

Series B 1. Resistance Tests

V = 8308 nas BIT = 2.4 5pp =- 0.575 L/V113 = 6.38 V io-3 10-3 lo-3 I , 47 Fv FL .172 Bi _{R R} Nx N1 ' Cl 1 --- ' - -- - _, Knots Knots Kg s-1 Kgs I HP Kgs ' HP

/ /

(Metr.) 1 , Feet (Metr.)

(Br.) / /

No. 357 (t/L,i = -3.5 %) 1 16 17 0.584 0.621 0.231 0.246 0.777 0.825 I 18.03 20.14 5.99 I 7.27 24.02 27.41 2635 3195 II 2599 , I 3152 1 638 631 0.658 0.665 18 0.657 0.260 0.874 22.35 10.02 32.38 3998 3944 598 0.702 19 0.694 I 0.275 0.922 24.67 15.74 40.41 5265 5193 534 0.786 J 20 0.730 0.289 0.971 27.09 24.08 51.17 7021 6926 1 467 0.898 21 0.767 1 0.304 1.019 29.62 30.13 59.75 8604 8487 442 0.949 .i d i No. 358 ( /Lpp. = -2.5 % 1 j 0.584 0.231 0.777 18.04 5.56 23.60 2589 2554 649 I 0.646 177 d 0.621 0.246 0.825 9-0.15 I 6.84 96.99 314 3104 640 9.655 58 0.657 0.260 0.874 92.37 9.18 31.55 3896 3843 614 'Il 0.683 I 19, 0.694 0.275 0.922 24.69 14.73 39.42 5136 5066 548 I 0.766 20 0.730 0.289 9.971 27.11 21.84 48.95 6716 6625 489 0.858 I 21 0.767 0.304 1.019 29.63 'I 27.24 56.87 8189 8078 464 0.904 I No. 355 ( /L = -1.5 % 16 . 1 0.584 0.231 0.777 18.05 6.58 24.63 2702 2665 622 0.674 17 0.621 0.246 0.825 20.16 7.11 27.27 3180 3137 , 634 0.662 18 0.657 0.260 0.874 22.38 9.70 32.07 3961 3907 I 604 0.695 19 0.694 0.275 0.922 H 24.70 15.65 40.35 5257 5186 535 0.784 20 0.730 0.289 0.971 27.12 22.26 49,38 6775 6683 484 0.867 21 0.767 0.304 1.019 29.65 .27.98 57.63 8298 8185 458 0.916 No. 359 (G/Lpp --- -0.5 %) 16 1 0.584 0.231 0.777 18.06 5.66 23.72 2602 2567 I 646 0.649 17. 0.621 0.246 0.825 20.17 7.42 27.60 3218 3174 626 0.670 18 0.657 0.260 0.874 22.39 10.41 32.81 4052 3997 590 0.711 19 0.694 0.275 0.922 24.71 15.95 40.67 5299 I 5227 I 531 0.790 20 0.730 0.289 0.971 , 27.14 23.30 50.44 6921 6827 474 0.885 21. 0.767 0.304 1 1:019 29:67 28.53 58.19 8380 8266 453 0.996

-1,8 700 C, 500 400 500 Fig, 9. iYetr. HP /V, /0000 8000, 6000 4000 2000' 1 > II (S 700 600 Op - - -- NO.NO. NO. 357 350 355 359

IMMI

EN

- -

NO.

Wall

ffie

MI

ill

- "211eAibliC-...._ -

MI

Prill

_{liiiiiirialia}

--40 00 200 loo Pil I 1 _ 1 I I I ,

11

1 0. 2/ - - I 1 11117=1°2111.1111rEallill

isIMMEEHEINgeatzzonl

=AMIN=

ME=

-Mila

0.730 as __.... , 1 _ 1H .. Series 81 Series B CCPP 0.575 0.625 --;---.---- 1-in %. No. 307 -/0 -3.5 357 0 358 306 .359 355 303 /7 18 /9 tnknots1/Notr.) Fig. 8 /6 2 02 200 /00 0 /A,,, 20 1/ 600 305

Fig 10 /0000 8000 6000 4000 2000 7.

Series C I. Influence of B/T

The influence of the ratio breadth/draught was studied by means of the same principle as that employed for Series C in Publ. 10.

Based on a normal form, new forms were developed by multiplying all transverse dimensions by a constant a, while dividing all vertical dimensions by the same constant. Thus the length, the sectional areas and the sectional area curves and therefore also the displace-ment and the position of L. C. B. remain unaltered.

The following coefficients are also unchanged: block coefficient

load waterline coefficient midship section coefficient prismatic coefficient

L/7;3

On the other hand, LIB and LIT are altered. S is also changed to some extent and tan i9 is altered in the proportion a.

Three new forms were developed according to this principle using Model No. 358 in Series B 1 as the normal form. The following values were chosen for

BIT:-Metr. HP N, r> CC 700

- - - -

NO. NO. 382 558 383 584 ri-NO. --- - NO. _.,...-,,,,1"" -r 1 SOO 400 , ___, _{C/ 1} 15 ...--' ..," MEM SOO ZOO /00 ...-1-/6 /7 /0 /9 20 PI PP V in knots (Me/r.)

-20

Table 4

Series C 1. Resistance Tests

V = 8308 m3 6pp = 0.575 L/V1/3 = 6.38 tILpp = -2.5 % V 10-3 10-3 10-3 V Fv FL IlL Ri R iv R N, N, C. Knots

-

___ Knots (Br.) Kgs Kgs Kgs HP HP

/ '

/

(Metr.) _Feat (Metr.)

(Br.) / /

No. 382 (BIT = 2.1) 16 0.584 0.231 0.777 18.04 5.89 23.93 I 2625 2589 640 0.655 17 0.621 0.246 0.825 20.15 7.22 27.37 3191 3148 631 0.665 18 0.657 0.260 0.874 22.36 9.21 31.57 3899 3846 613 0.684 19 0.694 0.275 0.922 24.68 14.97 39.65 5166 5096 545 0.770 20 0.730 0.289 0.971 27.10 22.38 49.48 6789 6697 483 0.869 21 0.767 0.304 1.019 29.63 27.99 57.61 8296 8183 458 0.916 No. 358 (BIT = 2.4) 16 0.584 0.231 0.777 18.04 5.56 23.60 2589 2554 649 0.646 17 0.621 0.246 0.825 20.15 6.84 26.99 3147 3104 640 0.655 18 0.657 0.260 0.874 22.37 9.18 31.55 3896 3843 614 0.683 19 0.694 0.275 0.922 24.69 14.73 39.42 5136 5066 548 0.766 20 0.730 0.289 0.971 27.11 21.84 48.95 6716 6625 489 0.858 21 0.767 0.304 1.019 29.63 27.24 56.87 8189 8078 464 0.904 No. 383 (BIT = 2.7) 16 0.584 0.231 0.777 17.85 6.79 24.64 2703 2666 622 0.674 17 0.621 0.246 0.825 19.93 8.48 28.41 3313 3268 608 0.690 18 0.657 0.260 0.874 22.13 10.49 32.62 4029 3974 594 0.706 19 0.694 0.275 0.922 24.42 16.29 40.71 5304 5232 531 0.790 20 0.730 0.289 0.971 26.82 23.24 50.05 6867 6774 478 0.878 21 0.767 0.304 1.019 29.32 29.54 58.85 8474 8359 448 0.936 No. 384 (BIT = 3.0) 16 0.584 0.231 0.777 17.82 7.41 25.23 2768 2730 607 0.691 17 0.621 0.246 0.825 19.90 8.94 28.84 3363 3317 599 0.700 18 0.657 0.260 0.874 22.09 11.20 33.30 4112 4056 582 0.721 19 0.694 0.275 0.922 24.38 15.94 40.32 5254 5183 536 0.783 20 0.730 0.289 0.971 26.78 23.05 49.83 6837 6744 480 0.874 21 0.767 0.304 1.019 29.27 28.54 57.81 8324 8211 456 0.920 II .

BIT a 0.935 Model No,. 382 .400 300 200 t/00 24 358 306 2.4 1 358 Normal formi, 26 28 383 340 3// Fig. 11 30 B/T 304}No.

The main data for the forms so derived are given in Table 1. The results of the resistance tests are given in Table 4 and Fig. 10. In Fig. 11, the results are presented in the form of C, as a function

of BIT at constant values of F. (Since

7

and L are constant, the

curves also represent constant values of FL or VAIL.) The optimum

values of C, at different values of II,

occur at BIT 2.3. For

comparison, the corresponding curves from the results with Series C in Publ. 10 are included (obtained by interpolation). The difference in character between the two sets of curves is obvious,.

0.62/ ...

-

---1 EINIMMENIMIN. 110 -II ,I , I 1 , Series C7 Series C CrP7, 0.575j-M7. 0.625 i/Lfr, 5 7. 2 0 7;

----IL 1 I II_ 9.7 - 3.0 1.061 1.118 383 384 0 2/ 2:2 382 309 700 C, 600 500 0.657 0.694S.

II.

Self-Propulsion Tests

8.

Object of the Tests

The object of the Series B 1 investigations was to study, purely from a resistance point of view, the effect of shift of L. C. B. on

the ship types in question. There is reason to expect, however,

that by moving the L. C. B. aft and consequently filling out the

after body, the conclusions drawn from the resistance test results will be modified to some extent when account is taken of the results from the self-propulsion tests.

As in Publ. 14, therefore, the aim of the self-propulsion tests was to investigate further the effect of shift of L. C. B. upon ship per-formance. To that end, self-propulsion tests were carried out with the models used in Series B 1.

Methods of Calculation

The self-propulsion tests were conducted according to the »Con-tinental Method*, i. e. with a towrope force applied to the model equal to the skin friction correction for the ship reduced to model scale at each speed. The towrope force was calculated from the formula given on p. 4 of Publ. 14, which is based on values decided

at the Tank Superintendents' Conference in Paris

in

1935.

The primary results obtained from the models were transferred to ship scale according to the conventional methods and all data

below refer to the actual ships. No corrections were made for

roughness, scale effect, etc.

Models and Propeller

mentioned above, self-propulsion tests were carried out with the models used in Series B 1, i. e. Models Nos. 357, 358, 355 and

359 with L. C. B. positions 3.5 %, 2.5 '3/0, 1.5 % and 0.5

% respectively. The principal data for these models can be found in Table 1.

The models were fitted with rudders and shaft bossinas but no

bilge keels. The stern arrangement was similar to that shown in

10.

Fig. 1 in Publ. 14. The same rudder was used for all models and

the propeller was placed in the same position in relation to the

leading edge of the rudder in each case.

No turbulence stimulating devices _{were used in the main tests.}

Models Nos. 357 and 359, however, _{were also tested with a 1 mm}

tripwire fitted at station No. 19, but no indication of laminar flow

was observed.

The displacement was the same for all tests and, assuming a

model scale of 1/20, was equivalent to 8308 m3. The results have been calculated on this basis, but since they are also presented in

dimensionless or quasi-dimensionless form they can be used more

generally in the vicinity of the mentioned displacement.

Altogether, about 100 runs _{were made within a speed range}

corresponding to 16-22 knots and all tests were carried out in

smooth water.

Since the investigations were to be regarded as comparative, the

same propeller, P 338, was used for all models. This propeller _was

also used in the investigations described in Publ. 14. Particulars

of the propeller are to be found in Fig. 2, Publ. _{14, and the results}

from the open-water tests in Fig 3, Publ. 14. _{The main dimensions}

of the model propeller were: _{D = 230 mm and H = 210 mm}

(mean).

The wake fraction was calculated in the usual manner and used in studying the influence of L. C. B. position upon the wake.

11. _Results

The main results are shown in Fig. 12 and Table 5.

In Fig. 13, the results are given in the form of C, as a function

of tILpp at constant speed values (corresponding to 7 8308 m3)

and, since 7 and L are constant, the _{curves also refer to constant}

values of 1.1,, and constant values of FL or VIVL. The »curves » are

drawn as straight lines between the observed _values.

For comparison, Fig. 13 also includes the corresponding C, curves obtained from the resistance tests with the same models (Fig. 9).

It will be noted that the C2 _{curves are not so regular as the C,}

curves.

This is due to the

_{appearance of humps and hollows}

(especially marked in the case of Nos. 358 and 355) in the N2- V

curves (Fig. _{12) which are not noticeable in the}

_{N,V curves}

inter-24

Table 5

Series B 1. Self-Propulsion Tests

V = 8308 m. BIT = 2.4 opp =- 0.575 L/V113 = 6.38

Without rudder, skeg or boss; from Table 3.

V 10-3 10-3 N,

V

I',

FL

-.-

R1) T Nil) C11) N, n

q

t w

Knots Knots HP HP

(Metr.) (Br.)_Feet

Kgs Kgs

(Metr.) (Metr.) r/min.

% % %

No. 357 (tIL" = -3.5 %) 16 0.584 0.231 0.777 24.02 29.85 2635 638 3468 117.4 484 76.0 19.5 25.9 17 0.621 0.246 0.825 27.41 34.11 3195 631 4209 125.4 479 75.9 19.6 25.3 18 0.657 0.260 0.874 32.38 39.93 3998 598 5299 135.5 451 75.4 18.9 23.8 19 0.694 0.275 0.922 40.41 49.04 5265 534 6984 146.7 403 75.4 17.6 24.1 20 0.730 0.289 0.971 51.17 61.99 7021 467 9601 161.7 342 73.1 17.5 22.41 21 0.767 0.304 1.019 59.75 72.41 8604 442 11986 173.1 317 71.8 17.5 22.0 No. 358 (t L,,, = -2.5 A) 16 0.584 0.231 0.777 23.60 29.93 2589 649 3529 118.7 476 73.4 21.1 24.3 17 0.621 0.246 0.825 26.99 33.46 3147 640 4205 126.1 479 74.8 19.3 23.9 18 0.657 0.260 0.874 31.55 39.69 3896 614 5370 136.6 445 72.6 20.5 22.5 19 0.694 0.275 0.922 39.42 48.38 5136 548 6990 147.6 403 73.5 18.5 22.6 20 0.730 0.289 0.971 48.95 58.96 6716 489 9059 159.7 362 74.1 17.0 22.4 21 0.767 0.304 1.019 56,87 69.54 8189 464 11400 171.7 333 71.8 18.2 21.2 No. 355 (t/Lp, = -1.5 %) 16 0.584 0.231 0.777 24.63 28.70 2702 622 3361 117.6 500 80.4 14.2 23.8 17 0.621 0.246 0.825 27.27 34.11 3180 634 4320 128.3 466 73.6 20.1 21.5 18 0.657 0.260 0.874 32.07 38.95 3961 604 5211 135.9 459 76.0 17.7 22.3 19 0.694 0.275 0.922 40.35 48.63 5257 535 7031 148.7 400 74.8 17.0 21.4 20 0.730 0.289 0.971 49.38 58.79 6775 484 9014 160.1 364 75.2 16.0 21.3 21 0.767 0.304 1.019 57.63 69.04 8298 458 11254 171.7 338 73.7 16.5 20.5 No. 359 (tIL,,p = -0.5 A) 16 0.584 0.231 0.777 23.72 29.03 2602 646 3559 119.2 472 73.1 18.31 23.3 17 0.621 0.246 0.825 27.60 33.46 3218 626 4412 128.6 457 72.9 17.5 21.5 18 0.657 0.260 0.874 32.81 38.87 4052 590 5434 137.1 440 74.6 15.6 21.6 19 0.694 0.275 0.922 40.67 48.30 5299 531 7197 148.9 391 73.6 15.8 21.5 20 0.730 0.289 0.971 50.44 59.78 6921 474 9481 161.4 346 73.0 15.6 21.6 21 0.767 0.304 1.019 58.19 69.45 8380 453 11693 172.6 325 71.7 16.2 20.7 -.

Mein HP N2 F Series 81 u

Imo

UP-/

. z ,... ,noc , I 1000

.

4000 /000 357 NO. 3 f 8

nu

C NO. 3 SS 3 S 9

BM

1111111111111 j PilL11111111111111 1 , ,a

11/11/111E

111111V)Edilin ao _

Tibiamisi-sia

IIIM

-1 I , , ,I 0

rm-1 ____ _._ .- --- MMie=i eNt 1

1

II I 1 1 1 I - - [ -.17 .10 /9 20 ₁₂

V ill knots (Mein)

Fig. 12

action between propeller and model 'and are, often observed in self-propulsion tests when the speed intervals are very small. Since the relation between the C2 and C, curves is equal to the corresponding

value of N1/N2 at each speed (i. e. C2/C, N1/N2), these values are

shown in Fig. 13 (from Table 5). The latter curves give a clear

indication of the irregularity of the C, curves.

The C, curves can scarcely be said to confirm the conclusion drawn

from the resistance test results, namely that t/L values of about

% give optimum results. Rather, they indicate that the most

favourable values lie between 2.5 % and 1.5 % for the ship

types in question.

In Table 5 and Fig. 14 are shown the calculated valnes of wake fraction (w) and thrust deduction factor (t). The values of w were calculated in the usual way using Fig. 3 in Publ. 14, a mean being taken between wg, .(based upon thrust) and wQ. (based upon torque),..

SOO 4.00 -100 200 /00 0 2

=

2.5

300 200 2.5 20 /5 Fig. 13 AVV: 3/4 75 70 -0.5 1'4,14 359 No. Fig. 14

As might be foreseen, Fig. 14 shows that w increases as the after

body becomes fuller. The same tendency, though not so marked,

can be observed in the case of t. It should be remembered, however, that the calculation of t is based on the subtraction of two quantities of the same order and therefore the values of t are always a little

doubtful. CorPes,o 17-83o6 /7 /6 /9 knots V

_r

r

/7 0.62/ 0.24,6 0.825 /B 0.657 0.260 0.874 /9 0694 0275 0922 20 0.730 0.269 0.97/ 2/ 0767 0304 1019 -3.5 357 .75." -15 355 -05 1,4, % 359 No -/5 -2.5 -3.5 355 358 357 26 C, ci 600 500 400 /00 0 -2.5

12. _{Acknowledgment}

The author wishes to express his gratitude for the grant made

from Hugo Hammar's Foundation for Maritime

Research which enabled the investigations to be made. The

author also wishes to thank the staff of the Swedish State

Shipbuilding Experimental Tank in Goteborg,

espe-cially Mr. E. FREIMANIS and Mr. H. LINDGREN, for all their assistance.

Thanks are also due to Mr. DACRE FRASER-SMITH, B. Sc., who has