Some systematic tests with models of fast cargo vessels

(1)

MEDDELAN DEN

FRAN

STATENS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)

Nr 10 GOTEBORG 1948

SOME SYSTEMATIC TESTS

WITH MODELS OF

FAST CARGO VESSELS

BY

H. F. NORDSTROM

GUMPERTS AB GOTEBORG

(2)

GUTEBORG 1948

(3)

1.

_Introduction

The development of cargo ships during the past ten or twenty years has steadily tended towards higher speeds. Especially is this so in Scandinavia. For ships of more normal speeds _{it can be said that} designers have rich sources of material to draw upon, based both on full scale trial trip results and on model tests. Systematic _model tests have not, however, kept pace with ship developments so that when it comes to a question of relatively fast cargo ships the designer

has rather to grope forward in the dark. _{Here, obviously, is an}

important field of work for the model tester. _{These present model} tests are designed to make a contribution towards _{the dimensioning} of cargo vessels of relatively high speeds. In _{these investigations} the author has started from _{a chosen parent form which itself could} be expected to have good qualities from _{a resistance point of view.} The development from the parent form of the other forms was made with the object of examining the effect of the_{following variations:}

Effect of length (Nos. 301, 302, 303 and 304)

Effect of the longitudinal position of the _{centre of buoyancy} (Nos. 305, 306, 303, 307 and 308)

Effect of the ratio breadth/draught (Nos. _{309, 306, 310 and 311)} Principal data for the ship forms investigated are given in Table 1.

The investigations have been carried

_{out at The Swedish}

State Shipbuilding Experimental

_{Tank in}

Gote-borg and were made possible by

_{a grant from Hugo Hamma r's}

Foundation f or Maritime

_Research.

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4 MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALTNR 10

2.

Symbols and Units

Dimensions of Ship

= length on waterline

Lpp length between perpendiculars

breadth -= draught

0

immersed midship section area

wetted surface mean girth x L) volumetric displacement

weight displacement

= distance ofcentre of buoyancy forward of amidships

(Lpp/2)

= half

angle of entrance on waterline.

Dimensionless and Quasi-dimensionless Coefficients

°PP L -7B T 1

I-Lpp B T

block coefficient

0

fi

B T

midship section area coefficient

V

0 = prismatic coefficient

=

length-displacement coefficient vi,r3

(LI100)

displacement-length ratio; British tons, feet

3

(The relationship between and

V I (L/100)3

shown in Appendix 2)

100t/Lpp = centre ofbuoyancy forward of Lpp/2 in %of Lp,

is

V

L

(5)

Dynamic Symbols

= speed in general

V _{speed in knots (Metric or British; 1 Metric knot}

=

0.9994 British knot)

-8/ _{= frictional resistance}

R. residuary resistance

R =-7 R ± _{total resistance}

N effective power. (towing power

Dimensionless and Quasi-dimensionless, Dynamic Coefficients

FL

gL roude's number, length

.v

Froude'S number, displacement yg 7113

C'

IL F. NORDSTROM, SOME SYSTEMATIC TESTS ETC. 5

Apeed-length ratio; British kriats, feet V (The relationship between FL and

in Appendix 3, and also the relationship _between FL and Fy at different values of L/7113)

\743 V3

- (m3, Metric knots, Metric HP)

0

= 427.1

d213 Va (British HP, British tons, British

knots)

(The relationship between Q and .(:) is shown in Appendix 4) Rf frictional coefficient e- /2 Sv3

v

is shown

=

V

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6 MEDDELANDEN FRAN STATENS SREPPSFROVNINGSANSTALT NR 10

General Symbols

specific weight of water (dimensionless) weight of water per unit of volume

= density of water kinematic viscosity

acceleration due to gravity temperature in °C

a linear ratio, ship to model index for model

index for ship Conversion Factors

In all calculations Metric units have been employed. The following conversion factors have been used when passing from Metric to

British units:

1 metre = 3.281 feet (1 foot = 0.3048 metre)

1 metric knot = 1852 m/hour = 0.9994 British knot (1 Br. knot = 6080 feet/hour = 1.0006 Metric knot)

[From a practical point of view: 1 Metric knot = 1 Br. knot] 1 Metric ton = 1000 kgs = weight of 1 m3 of pure water = 0.984

Br. ton

(1 Br. ton = 1.016 Metric ton)

1 Metric HP = 75 m kg/s = 0.986 Br. HP

(1 Br. HP = 550 foot pounds/s = 1.014 Metric HP) Values of y and g employed

The following values of 2, and g have been

used:

1.000 for tank water (w 1000 kg/m3) = 1.025 for sea water (w, = 1025 kg/m3)

--- 9.81 m/s'

w 1102.0 kg s2/m4 for tank water

=

104.5 kg s2/m4 for sea water "S

No consideration has been given to the variation of y and with temperature.

t,.

=

g

(7)

The results with the models were converted to the scale of the full-sized ships in the conventional way according to FROUDE'S method. For calculation of the frictional resistance, the following formulae were used.

For the ship:

Rfs = As Ss 1.825 (1)

where

H. F. NORDSTROM, SOME SYSTEMATIC TESTS ETC. 7

3.

Methods of Calculation

0.258 )

(0.1392

+

2.68 + L,

y, = 1.025, L, in rn, Ss in m2 and vs in m/s. The temperature of the sea water was taken at 15° C.

For the model:

Rim --- Am_8m_{v L825} ₍₃₎

where

0.258

11_0.0043

(t-]

5)1

[0.1392 ±

2.68 (4)

= 1.000, L. i1 m, S. in m2 and vm in m/s. The temperature t of the tank water is expressed in °C.

The formulae agree with those decided

_{upon at the Tank}

Superintendents' Conference in Paris in 1935 (see:

Congres international des clirecteurs de bassins, 1935, pp. 192, 201 and 209) except that the factor y has been added. The author stated at that time that the formula for 2 in metric units in the Report did not correspond with the same formula written in British units. (The German version on p. 192 appears to be in error.) Agreement is arrived at, however, at least as regards sea water if, as above, the factor y is included. This question is also considered on p. 418 of Trans. S. N. A. M. E. 1939.

On transferring the model results to the full scale ships, when R10 -=ysly. a3Run, the formulae used were:

1 'Rs

=

78a3

R.

0.29737, (A.a0.0875- 28) S, V825 (2) (5)

=

. .

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8 MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALT NR 10

and

v,

N,- 75 0.006859 R, V,

where R is in kgs, S in m2, V in Metr. knots (v in m/s) and N in Metr. HP.

No length correction has been made since the length remains in the range about 120 m (--- 400 feet).

The American Towing Tank Conference

(ATTC)

decided in 1947 to use SCHOENHERR'S formula for the calculation of

frictional resistance, with an addition for full size vessels of a roughness

allowance of +0.0004 to the cf value which the formula gives.

SCHOENHERR'S formula, as is well known, has the form

0.242v L)

log

(Ci (7)

Cf

where cf is the resistance coefficient in the general formula for

frictional resistance

Rf Cf (8)

In Appendix 1 a comparison is given between the results obtained

by the two methods of calculation. Reference may also be made to

Figs. 5, 10 and 13.

4. Models Tested

Eleven models were used in the tests. All were made of paraffin wax and were designed to represent single-screw ships. The models were quite naked, that is without appendages such as rudder, stern

frame sole piece, propeller boss and bilge keels. No turbulence produc-ing devices were used. The scale used was1/20. In all tests the

displa-cement was the same and equivalent to 9031 m3. The results are cal-culated on this basis. By also presenting the resultsin 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 15-21 knots. Altogether about 400 runs were made. (6)

log

. ...

(9)

H. F. NORDSTROM, SOME SYSTEMATIC TESTS ETC. Table 1.

V = 9031 m.

Parent Form (No. 302)

The model numbered 302 in Table 1 was used as the parent form.

It was taken from the statistical material available at T h e

Swedish

State

Shipbuilding

Experimental

Tank in Goteborg. The normal speed under favourable trial trip conditions for this ship type would be about 17 knots.

The main data are as

follows:-No. L L Li Lpp ,..,1

,

P. 1.4

.

. :,. 100 t B B T L_PP

_,

.PP S vl /3 (L/100)3 _B m

-

_{_--} _- m % % m m2

Series A. Variation of Length

301 113.78 5.46 175.1 I 111 -7.5 -1 117.6761 2.4 I 6.2801 0.625 2601 302 123.00 I 5.91 138.6 I 120 0 -1 117.000 2.4 7.059 1 0.625 2704 303 304 132.23 141.45 6.35 6.79 111.6 91.1 129 138 +7.5 +15

-1

16.39615.853 2.4 2.4 7.868 8.705 0.625 0.625 2804 2900 Series B. Variation of Longitudinal Position of Centre of Buoyancy

305 132.23 306 132.23 1 6.35 6.35 111.6 111.6 129 129 +7.,5 +7.5 ---. 3

-2

16.39616.396 2.4 2.4 7.868 7.868 0.625 0.625 2800 2802 303 132.23 I 6.35 111.6 129 +7.5

-1

16.396 2.4 7.868 0.625 2804 307 132.23) 6.35 308 132.23 1 6.35 111.6 111.6 129 129 +7.5 +7.5 0 +1 16.396 16.396 2.4 2.4 7.868 7.868 0.625 2806 0.625 2808 Series C. Variation of Breadth/Draught

309 132.23 6.35 111.6 129 +7.5 -2 115.698 2.2 8.218 0.625 I 2807 306 132.23 6.35 J 111.6 129 +7.5 -2 (16.396 2.4 7.868 0.625 2802 310 132.23 311 132.23 6.35 6.35 111.6 111.6 129 I 129 J +7.5 +7.5

-2

17.066 17.710 2.6 2.8 7.559 7.284 0.625 0.625 2787 2797 123.00 m 0 --- 10.5° Lpp --_--- 120.00 m o 0.610 17.00 m _°PP _{-= 0.625} 7.083 m _{= 0.970}

0

116.80m2 --= 0.629

V

r=9031 m3 100 tILp,

- 1 °A

v1/3 = 5.91 I L B

=

L

(10)

-0 MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALT NR 10

Fig. 1.

5.

Series A. Influence of Length

In general, increased speed demands increased length. The

influence of length can be studied in many different ways. An alteration of length, while maintaining constant displacement, naturally involves the alteration of other dimensions and coefficients. It is important that these alterations are such that they do not run counter to the effect of the increase of length.

In order so far as possible to obtain only the effect of length Figs. 1 and 2 show the body plan, lines and profile. The scales correspond to V = 9031 m3. Dimensionless scales are also given,

length

vl

viz. 3 By the use of these the drawings can be used for

displacements other than 9031 m3. We can thus use different systems of units, e. g. m, m3 or feet, feet3 and so on.

III

11 NITAIVAIVIA

IIMIXIL

N° 3°2

MIIIIIIII

20

II

til,

MIL

EMI\

inn= mvl I

IINiggli

NMI J

LOW101011,11118

kb

._"q drr__.w- -!",,

0 05 / 2 4 5 6 7 8 9 / /77 0 ,005 0,2 03 04 as Lenath-uni, 7 6 WL 5 4 3 2

(11)

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NIMEMIIIIMII IMMO MINIM 1111=1.11MI NMI IIIIIMI MIMI MINIM

EMU INIIIM MIMI 1111111111111! MIME

1-3 Vi 4 tn a

mow

====.111111=11111MIIIIIIIIMIMIM

Willi MIME MEM MEM 11111MNI

MEM = . 3 4 5 7 13-9 II /2 / /4-it /7 NO. 302 50 2 Fig, 8I? 3.°' 100 /2o ,n Length-unit v0 -Li (I2 --A.-'%-.,... 41111. -I-/0 Jo 20 0.5 -g2 a /8 2. 70 40 20

(12)

12 MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALTNR 10

alteration

the investigations have been made as follows.

On departing from the above defined parent form new individual forms have been developed by multiplying all the longitudinal dimensions by a constant factor a and at the same time multiplying all transverse and vertical dimensions by another constant b. If we then take b = the displacement will remain unaltered.

V a

It may be established without difficulty

that with such an

alteration of the parent form, the following coefficients, among

others, will remain unchanged:

Block coefficient

Load waterline coefficient Midship section coefficient Prismatic coefficient and

Breadth the ratio

Draught

The body plan will be unaltered in form, i. e. the body plan of

the parent form may be used if a different

scale is employed. The sectional area curve of the parent form may also be used but with different scales. The longitudinal position

of the centre of

(

100 t

buoyancy expressed as a percentage of Lpp _Lipp will therefore be

unaltered. On the other hand is altered in the proportion

'

a' and in the proportion a", S in the proportion

a112 and tan 8 in the proportion a32.

Resistance tests on a series derived in such a way from a parent form would appear to be suitable for obtaining for the ship type in question a clear picture of the effect on resistance of alteration of length at constant displacement.

The following values were chosen for a: Parent form

a 0.925 1 1.075 1.15

No. 301 302 303 304

1

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,t :Sec-bowl-Are& Curves .." ,- ..-I/ --,-/.

,(,'i

/1

...-r

/

1 , -I . .- ..- ...-/. i ...- ,-1,-: 2 70 60 I

tv

2 4 40 JO 1 -- i 0.3 1-130 r._ Ir---! I I 1 ' NO. _501 302 303 504 _s.N., .1. N , , so T,, ".. .1 ,,,,..,.... 1 '',1 0 7:1 1-3 0: 0 4 0-3 4 :143 Cs) 1-3 ---ra , .1. iI _i ! ! ! H ---6 cui,.. 0.2.7 _7, 0.1--- ''' E .. . (3 -.'c .4 i 1 I :"... -... I \ i . i i i ,i I

NO. NO. _NO.

`:-...

\N

'.`, 5`...", I". I \ I I. 'N I I 1 _I___I. _i_ 1-1 a 10 /0 1 12 /4 /0 20 JO -16 /8 20 40 50 60 70 177 0.5 0 0.5 L017019-7-Und V 0 Fig. 1! LI/ 1-3 7 10 5 0 6 50 20

(14)

14 MEDDELANDEN FRAN STATENS SKEPPSPROVNI4GSANSTALT NR 1 0. Table 2. Series A V = 9031 00 BIT = 2.4 SOO 111.pp = -1 % F v = FL= 1 10-3 I i0-3 10-3 - _ V I v v

y

Ri Rw 11 , 1? N N ' C ,

0,

il g v1/3 1/ 971 Knots ' Knots HP HP (Metr. )' - -(Br.) Feet Kgs Kgs Kgs _(Metr.) _(Br.) No. 301 15 0.540' 0.231 1 0.776 15.70 7.64 23:34 2402 I 2369 609 0.68911 16 0.576 0.246 0.828 17.66 9.39 27.05 2967 2927 599 0.700 17 0.612 0.262 0.879 19.73 14.49 34.22 3990 3936 534 0.786 .18 0.648 0.277 0.931 21.90 98.79 50.68 6259 6174 404 1.038 19 0.684 0.293 0.983 24.17 46.45 70.61 9-'O1 9076 323 1.299 1 20 0.720 0.308 1.035 26,54 60.91 87.45 11998 11835 989 1.452 No.. 302, 15 0.540 0.222 0.746 16.31 6.34 22.65 2331 2299 628 0.668 161 0.5,7,6 0.237 0.796 18.35 7.67 26.02 2854 2815 622 '0,674 171 6.612 . 0.252 0.846 20.49 10.22 30.72 3581 3532 595 0.7051 18 0.648 0.267 I 0.896 22.75 17.85 40.60 5014 4946 504 0.83 ?I 19 0.684 0.281 I a 945 25.11 31.88 56.99 7426 7325 ' 401 1.046 20 0.720 0.296 l' 0.995 27.57 48.45 76.02 10430 10288 333 1.260 No. 303 15 0.540 0.214 0.720 16.89 5.52 22.41 ' 2306 2275 635 0.661 I 16 0.576 l 0,228 0.768 19.00 6.92 25.92 I 2843 2804 625 0.671 17 0.612 0.243 9.816 21.22 8.31 29.03 3443 3396 619 0.678 18 II 0.648 0.257 0,864 23.56 12.23 35.79 4419 4359 ' 572 0.733 19 0.684 0.271 ' 0.912 26.00 20.66 46.66 6079 5996 489 0.846 20 I 0.720 0.286 0.960 28.55 34.001 62.55 8582 8465 404 1:038i No. 304 15 1 0.540 I '0.207 0.696 r17.46 4.28 21.73 2236 22061 655 0.640 16 ' 0.576 0.221 0.742 19.64 5.51 25.14 2758 2720 644 0.651 17 0:612 0.235 0.789 21.93 6,81 28.74 '3351 3305 636 0.660, 18 0:648 0.249 0.835 24.35 8.59 32.93 ii 4067 4012 622 0.674 1 19 0.684 0.262 0.881 26.87 13.31 40.18 5235 5164 568 0.739 20. 0.720 0.276 0.928 29.51 24.33 53.84 7387 7287 470 0.893

(15)

-H. F. NORDSTROM, SOME SYSTEMATIC TESTS ETC.

In Table 1 the principal data are given for the forms so obtained. Fig. 3 shows the sectional area curves. The scales given refer to

V

9031 m3. At the same time dimensionless scales are included,

length area

namely _1/3 and \72"

The results of the resistance tests are given in Table 2 and Fig. 4. It should be unnecessary to state that the second decimal in the columns for R in the Table is very doubtful, and that the same applies to the fourth figure in the columns for N.

In Fig. 5 the results are shown in the form of C as a function of 7,3 (or L, as 7 is constant) at constant values of speed (for

_V

=-9031 m3). At the same time the corresponding value of FROUDE'S .number, Fv, is given, with the use of which the curves have wider application. The dotted curves refer to the results when the cal-culation for frictional resistance is carried out by SCHOENHERR'S

formula, according to the decision of the ATTC; (see further in

Appendix 1). _{The fairness of the curves may be considered relatively}

good when one considers unavoidable experimental errors and that graphical methods had to be used for parts of the calculations.

Metr N /4000 ,. ?...

,

6 700 Series A 0 J

NITENEMINIE

IM

SIM

//

MINISE

MEINIMII

ENMIINIII

MIMI

---

NO JO, NO. 302 NO. 3 NO. 304 600 0

INEINNININNIE

0 0 .5

MI li WialliTlian

4 00

MESIMIN-i--- MEM

-,.ala MillINIENTIIIIMMINNIUMI

3 0 0 20o I 0 0 -0 t /5 /6 /7 /9 20 2/ V n Knots (Metr) Fig. 4. / 2 0 0 0 if5.9, 0 0 0 0 8000 6000 4000 2000

=

(16)

16 MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALT NR 10 V Yg (7 //3 / 7 Kno7's /8 600 500 400 300 200 /00 0 /9 20 tsci cr) ni 6.73

L v

/38 L in m Fig.

In Fig. 5 it is the curves for speeds of 17 and 18 knots which have the greatest interest. The figure shows, as expected, the demand for increased length with rising speed.

6.

Series 11:

Influence of Longitudinal Position of

Centre of Buoyancy

It is generally known that the longitudinal position of the centre of buoyancy plays an important part in the question of ship resistance.

Studies of the effect of the longitudinal position of the centre of buoyancy may be made in various ways. It is important, as in

304 No. O.6/2

plp10.

imprataggi,

.41agg

.

POW-.dada

6 48 -.WO

00

_ .

add

AdailliCeldliall

I 0.720

II/

. -,1 1 5.46 5.9/ 6.35 /// /20 129 (F=9031 m3) 30/ 302 303 5.

(17)

H. F. NORDSTROM, SOME SYSTEMATIC TESTS ETC. 17 Series A, that alterations are made in such a way that the original form is retained as far as possible. At the same time the displacement and the length should remain unaltered. This can be attained as follows. 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 altered in such a way that the displacement is unaltered while the desired alteration of the longitudinal position of the centre of buoyancy is effected. The spacing of the sections in the fore and after bodies will therefore differ from each other. For example, if a movement aft of the centre of buoyancy is desired, the spacing of the sections in the after body will be reduced and of those in the fore body will be increased from the spacing in the original form. The spacing of the individual sections from each other will also differ in each body.

It is easily seen that with such an alteration of the original form

the following coefficients and ratios, among others, will be unaffected: Block coefficient

Midship section coefficient Prismatic coefficient

L/7/3

LIB LIT

On the other hand there are small alterations in the load waterline coefficient, S and 8.

The rule for alteration of the spacing of sections which the author finally decided upon is given in Fig. 6. The full line curve represents the sectional area curve for the normal form, and the dotted curve

that for the altered form; in this case the longitudinal centre of buoyancy is moved aft. Shift in a longitudinal direction thus takes place by a linear rule. Obviously the displacement will be unchanged with this alteration.

4/2

Fig. 6.

(18)

(19)

100 IY 40 SO 60 70m i - --.L__ _ $ H 2 3Length-und o 0 14 tt w Fig. 7, 20 !21 4 CI) Lrj 4 rj 0 02 :1-. "Q -1 Sechbnal-Area ,o,.., n ;ii P,,,; . curves . ,, zi. ,z,..

4 A

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(20)

PIv = i FL= V 10-3 1 10-3 .10-3 V v I N IV C

V

L RI Rw R I 1/g v1/3 1/gL Knots Knots - HP HP (Metr.)

.-

(Br.)Feet Kgs Kgs , Kgs .(Metr.) 1 (Br.) L No. 305 15 ; 0.540 0.214 0.720 16.87 I 5.59 22.46 2311 2280 633 0M63 1 16 I 0.576 0.228 0.768 18.97 7.48 26.46 2902 2863 612 0.685 17 0.612 , 0.243 i 0.816 21.19 9.44 30.64 3572 3523 597 0.703 18 1 0.648 I , 0.257 I 0.864 I I 93.52 11.89 35.41 4373 4314 578 0.726. [ 19 0.684 0.271 0.912 25.96 19.17 45.13 5880 5800 506 0.829 20 1 0.720 0.286 0.960 28.51 32.59 61.10 . 8383 8269 414 1.013 No. 306 1 15 I 0-540 0.214 0.720 J 16.88 5.69 22.57 ; 2329 2290 630 0.665 16 0.576 0.228 1 0.768 18.99 7.08 26.07 2860 2821 621 0.676 17 0.619 .1 0.243 0.816 21.21 8.54 29.75 3469 3422 614 0.683 18 I 0.648 0.257 0.864 23.54 11.31 34.84 4303 4244 588 0.713 19 0.684 0.271 0.912 25.98 19.97 45.95 5987 5906 497 0.844 20 0.720 0.286 0.960 28.53 33.22 61.75 8472 8357 409 1.026 - _{No. 303} ----15 0.540 0.214 . 0.720 16.89 5.52 22.41 2306 2275 635 0.661 16 0.576 0.228" 0.768 19.00 6.92 24.92 2843 2804 625 0.671 17 I 0.612 0.243 0.816 21.22 1 8.31 29.53 3443 3396 919 0.678 18 0.648 0.257 0.864 23.56 I 12.23 35.79 4419 4359 572 0.733 19 10.684 0.271 0.912 26.00. 20.66 46.66 '6079 591)6 489 0.846 20 0.720 0.286 0.960 28.55 34.00 62.55 8582 8465 404- 1.038 1 No. 307 15 , 0.540 , 0.214 0.720 16.90 5.31 22.21 2285 2954 641 0.654 16 0.576 I 0.228 0.768 19.01 6.53 25.55 2803 2765 634 0.662 -17- 1 0.612 0.243 , 0.816 21.24 8.90 30.14 3514 I 3466 606 0.692 18 0.648 1 0.257 0 864 93.57 13.96 37.54 4636 4573. 546 0.768 19 0.684 I 0.271 0.912 26.02 22.79 48.81 6360 I 6274 468 0.896 20 0.720 0.286 0.960 28.57 37.28 64.85 9034 8911 384 1.092 No. 308 15 0.540 0.214 0.720 16.91 5.18 22.09 2273 2242 H 644 0.651 16 0.576 l 0.228 0.768 19.03 6.89 25.92, 2843 2804 625 0.671 17 0.612 1 I 0.243 0.816 , 21.25 11.54 32.80 3824 , 3772 557 0.753 .1 18 0.648 0.2.47 1 I 0.864 23.59 16.52 40.11 4953 I 4886 511 0.821 19 1 0.684 0.271 0.912 26.04 27.23 53.26 6940 I 6846 435 0.964 20 0.720 0.286 0.9601 28.59 1 43.92 72.51 9948 9813 349 1.202

20 MEDDELANDEN FRAN STATES SKEPPSPROVNINGSANSTALT NR 1,0

Table 3..

Series B V = 9031 m3 L/V113 = 6.35 BIT 2.4

(21)

H. F. NORDSTROM, SOME SYSTEMATIC TESTS; ETC._ Nasosi / /../i

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NO. 3031 / / NO. 308 -1/2. 20 11 I , ,

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wail400 L.,_, SOO 300 : ?00 I 1 1 1, 1

1

,00i- 1 1 1 ' 1 1 1 1 1

-o ,' ' _ 1 ; 1, /6 /7 /8 ./Q 20 2/ -V in Knots (Melt) 9. 10.5440342, 0 0.5 / 2 4 5 6. 8 9 /0177 o aos 02 OJ 0.4 OS Le/7071/7-unil'' -4; /2000 ioodb 000 doa N /4000

/

NO. 307 /5 Fig. 0/ 4000 000

(22)

22 MEDDELAND EN FRAN STATENS SKEPPSPROVNDTGSANSTALT NR 10

F._

v °

Vg7'

0.6/2 600 0.64a _ _ --- - - _ Fig. H).

The object of the Series B investigations was to study, purely

from a resistance point of view, the effect of longitudinal shift of the centre of buoyancy on the ship type in question. The author fully realises, of course, that the results obtained are by no means

the last word on this subject.

The author hopes in the near

future to be able to complete the tests by making trials with self-propelled models, which would certainly modify the results.

/7Kno45

500-400 300 200 /00 0 19 a 11, 20 - 0. 684 0.720 _

--3 305 -2

-

/ 0 +1 306 303 307 303 /00 V40i, No.

(23)

IL F. NORDSTRoM, SOME SYSTEMATIC TESTS ETC. 23

Breadth

7.

Series C. Influence of Ratio

Draught

In Series A and B the ships have been considered purely from a resistance point of view, ignoring important practical points such as stability and seaworthiness, suitability from a constructional standpoint and so on. It may then be advantageous for the ship type in question to investigate the effect on the resistance of the

breadth

ratio,

_draught this ratio, at least to a certain degree, may

be said to be a measure of stability.

In such an investigation also, the alteration of the chosen normal form should be such that

breadth

the ratio _draught is, as far as possible, the only changing factor

which affects the resistance. This has been effected as follows. 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. It is obvious that by this change the sectional areas will be unaltered. It follows, then, that the

sectional area curve will be unaltered and consequently the longitudinal

position of the centre of buoyancy. The method has the unimportant result that the bilge circle of the normal form will become an ellips.

The following coefficients are unchanged:

Block coefficient

Load waterline coefficient Midship section coefficient Prismatic coefficient

L/7/3

On the contrary LIB and LIT are, of course, altered. S is also altered somewhat and tan # is altered in the proportion a.

In this way three new individual forms were developed from No.

hoot

1

306 as the normal form. Design No. 306

2 % was

chosen as the basis on account of the results obtained in Series B. The following values of BIT were chosen:

Normal form

BIT 2.9 2.4 2.6 2.8

a 0.957 1 1.041 1.080

(24)

24.MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALT NR 10 iESethom, Fig. 111-B/T NO. .369 2.2 NO. 306 2.4 NO. 3/0 2.6 NO. 31/ 2.8 H) -II

In Table 1 the main data are given for the forms so derived. In Fig. 11 the midship sections are shown. The sectional area curve is found in Fig. 7 (No. 306).

The results of the resistance tests are shown in Table 4 and Fig. 12.

.MetrHP N a . ! Z . ,.5erie5 C 309 306 3/0 NO.

in

WOO I NO. mo.

MIIII

11,21

6000 ,s,' N 700 - - -

Mill

,Ailid I 1 I 600 KO mi

MI

liniiiMill

I f 600C '

iiiiiIPMEIMMI

I I 1 400C 400 I

ill

30° 111111112111111 1 . 11111M

IIII

I I 1

Ill

1.1

1 ,

1

1 . 1 .

I

1 11 2oo< ,, 15 %6 /7 18 /9 2/ V in Knots (Me7`r) Fig- 12.

In Fig. 13 the results are produced in the form of a values at constant speed values (for V = 9031 m3) or at constant values of

-F. The base is the ratio BIT.

WL

(25)

H. F. NORDSTROM, SOME SYSTEMATIC TESTS ETC. 25 Table 4. Series C V = 9031 m3 L/ V 113 = 6.35 100 (Lpp = -2 % V

F, =

v FL= v V 10-3 RI 10-3 Rio 10-3 R N N C

0

11 L

yg V1/3 ,,--

v g L Knots Knots HP HP

(Metr.)

-

(Br.)_Feet Kgs Kgs Kgs (Metr.) (Br.)

No. 309 15 0.540 0.214 0.720 16.91 4.71 21.62 2225 2195 658 0.638 16 0.576 0.228 0.768 19.02 6.54 25.56 2804 2766 633 0.663 17 0.612 0.243 0.816 21.25 7.71 28.95 3376 3330 631 0.665 18 0.648 0.257 0.864 23.58 10.59 34.17 4220 4163 599 0.700 19 0.684 0.271 0.912 26.03 18.96 44.98 5861 5781 508 0.826 20 0.720 0.286 0.960 28.58 34.46 63.04 8649 8531 401 1.046 No. 306 15 0.540 0.214 0.720 16.88 5.69 22.57 2322 2290 630 0.665 16 0.576 0.228 0.768 18.99 7.08 26.07 2860 2821 621 0.676 17 0.612 0.243 0.816 21.21 8.54 29.75 3469 3422 614 0.683 18 0.648 0.257 0.864 23.54 11.31 34.84 4303 4244 588 0.713 19 0.684 0.271 0.912 25.98 19.97 45.95 5987 5906 497 0.844 20 0.720 0.286 0.960 28.53 33.22 61.75 8472 8357 409 1.026 No. 310 15 0.540 0.214 0.720 16.79 5.70 22.48 2313 2282 633 0.663 16 0.576 0.228 0.768 18.89 6.87 25.75 2825 2787 629 0.667 ] 7 0.612 0.243 0.816 21.09 8.53 29.62 3454 3407 617 0.680 18 0.648 0.257 0.864 23.41 11.24 34.65 4280 4222 591 0.710 19 0.684 0.271 0.912 25.84 18.55 44.39 5784 5705 514 0.816 20 0.720 0.286 0.960 28.38 31.75 60.13 8250 8138 420 0.999 No. 311 15 0.540 0.214 0.720 16.85 6.05 22.90 2356 2324 621 0.676 16 0.576 0.228 0.768 18.95 7.36 26.32 2887 2848 615 0.682 17 0.612 0.243 0.816 21.17 9.32 30.49 3555 3507 599 0.700 18 0.648 0.257 0.864 23.50 12.09 35.58 4395 4335 575 0.730 19 0.684 0.271 0.912 25.93 19.28 45.21 5891 5811 505 0.831 20 0.720 0.286 0.960 28.48 32.37 60.85 8348 8234 416 1.008 :1

(26)

v

V fc, 171/3

Fig. 13.

At normal speeds BIT = 2.4-2.6 are most suitable from a

resistance point of view (if no consideration is given to BIT values

below 2.4). If the speed is forced up somewhat above the normal

value BIT 2.6 gives the best results.

8.

Acknowledgment

The author wishes to express his gratitude for the grant made

from Hugo Hammar's Foundation f or Maritime

Resear c h which enabled the investigations to be made. The author also wishes to express his thanks to the staff of T he S wedish

100 0 22 24 2o

2.8

3/7-.309 306 3/0 3/1. No. C 600 500 400 300 200

(27)

State Shipbuilding Experimental Tank in

Gote-borg for all their assistance. Thanks are also due to Mr. H. J. ADAms who on this, as on previous occasions, has assisted the author in translating the paper from Swedish to English.

Appendix 1

Comparison between Sehoenherr" and "Froude"

The calculation of frictional resistance for model and ship in the present investigation has, as stated, been carried out with the use of formulae (1) and (3), i. e. according to the decision of the Tank Superintendents in Paris in 1935. For the sake of brevity this is hereafter called "Froude". At the

same time the frictional resistance has also been calculated according to the

rule adopted in 1947 by The American Towing Tank

Con-f erence, involving the use oCon-f SCHOENHERR'S formula (7) but with a

roughness allowance of +0.0004 for the ship. This will hereafter be called

"SCHOENHERR'".

In connection with this it may be of interest directly to compare formulae

(1) and (3) with SCHOENFIERR'S_{cf values. Formulae (1) and (3) can seemingly}

be arranged byREYNOLDS' Rule in the following way:

Formula (1) has the form

0.258 )

= (0.1392+ S v1-8"

2.68 + L where the units are in m, secs and kgs.

Introducing

e g

= =

1000 1000

the formula can be written

( R1 \ g 0.258 \ L "75

v LI

0175 =

e/2 S v2) 500 0.1392 + 2.68 + L/ v I v

This applies to ships at 15° C.

In a similar manner for models formula (3) may be converted to:

0.258 L 10.175 v L 0.175

(10)

= [1-0.0043 (t 15)] (0.1392 +

500 2.68 + v v

As is seen the ci formulae so obtained are not dimensionless. They_{are not}

v L

functions of only REYNOLDS' number , as REYNOLDS' rule requires, but

also of L and v (and t). The formulae are also restricted to the system of

units used in the original formulae, i. e. in this case m and secs (and °C).

(9) .

(28)

28 MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALT NR 10 0.00. is Mode/ , 1 N :1 V \ I 1_{\ 1} \ ' ==---=---- NO 301 NO 302 _ ?..5. -1 Shoenherr NO 303 NO 304 line ?0' 5 -2oicr7 Ship ,o.oao4

_i_

1 ,. ..._ ca.. h 1 I I 1 , o.5.107 /107 1.5407 0.7 /0' 0,9 0.9 1-10"9 -/.1-- 1.2 1 1410 Reynolds'Number 4,1-Fig. 14.

In Fig. 14 cj, according to "Schoenherr", is shown as a function of

REY-v L

IsTOLDS' number , where L = length on WL. For better comparison a linear scale has been chosen for ci instead of a logarithmic scale, as usually employed. The

v L

scales for are also linear but are not the same for model and ship. The

values of are taken from Report 576 (Second Edition) from t h e, D. W.

Taylor

odel Basin.

Values of c1 have been calculated for Series A (Nos. 301, 302, 303 and 304) according to formula (10) for the models and according to formula (9) for the corresponding full size ships. In these calculations the values of v have been

taken from the above mentioned report, viz:

for Models (fresh eater), t 13°C, v = 1.205 x 10-6 m2/s, for Ships (sea Water),,, t 15° C, v = 1.190X10--,6 m2/s.

As seen from Fig. 14, the cl values for the models according to "Fronde" are somewhat higher than those according to "Schoenherr", which means that

the residuary resistance Bv, will be less according to "Froude" than according

to "Schoenherr". On the other hand for the full size ships "Froude" gives a

somewhat lower cf value than "Schoenherr"..

I

(29)

H. F. NORDSTROM, SOME SYSTEMATIC TESTS ETC. 29 Table 5. From Series A V Effective Power 10-3 N "Schoenherr" _Mean "Froude" "Froude" "Schoenherr" Metr. Knots Metr. HP No. 301 15 2.40 2.42 1.0075 16 2.97 3.03 1.0212 17 3.99 4.07 1.0201 18 6.26 6.37 1.0177 1.017 19 9.20 9.31 1.0151 20 12.00 12.21 1.0177 No. 302 15 2.33 2.37 1.0167 16 2.85 2.94 1.0301 17 3.58 3.69 1.0304 18 5.01 5.14 1.0251 1.023 19 7.43 7.56 1.0180 20 10.43 10.59 1.0153 No. 303 15 2.31 2.35 1.0191 16 2.84 2.91 1.0236 17 3.44 3.55 1.0311 18 4.42 4.53 1.0251 1.026 19 6.08 6.26 1.0298 20 8.58 8.82 1.0277 No. 304 15 2.24 2.30 1.0286 16 2.76 2.82 1.0225 17 3.35 3.45 1.0295 18 4.07 4.21 1.0352 1.028 19 5.24 5.39 1.0296 20 7.39 7.57 1.0248

(30)

In Table 5 a comparison is given between the results of the calculations

of effective power according to "Fronde" and "Schoenherr" for Nos. 301, 302, 303 and 304 (Series A): see also Fig. 5. As seen from the Table "Schoenhere'

gives a value about 2.5 % higher than "Fronde". The average of the ratio

"Schoenherr"

(see also Fig. 13)

It is generally known that results according to "Froude" give too low values when compared with results of full-scale trials. Such comparisons, however,

are often impossible to make due to the trial trip not having been made at a draught corresponding to that of the model test. Further, the trial trip result

must often be considered uncertain, due to difficulties in determining exactly

the engine power, engine efficiency, shaft friction, & c. Full scale towing

tests or thrust and torque measurements are seldom available.

The most important reason for lack of agreement between model tests and trial trip results is that "Fronde" does not take sufficient account of the roughness of the ship. One reason for adopting "Schoenherr" appears to have been, among others, to find a remedy for this. In the author's opinion, however, a roughness allowance of 0.0004 is not sufficient. A somewhat

higher value, say about 0.0006, is suggested as being preferable. This applies

to cargo vessels of the type now dealt with. Further, it is assumed that the model tests are carried out with models of length about 6 to 7 m (20 to 23 feet).

In connection with the foregoing it may be mentioned that the Tank in

Goteborg is accustomed to evade the problem of model test against t r i al tri p result in a practical way as follows:

On the basis of experience gained, clients are recommended to make an

addition of 10-12 % to the Tank estimate of the S. H. P. (obtained from self propulsion tests according to the Continental method). The values so obtained

are considered likely to correspond to full scale trial trip results in fine weather. This applies when the model has been tested without bilge keels.

In cases where the model has been fitted with bilge keels the addition may be

reduced to 8-10 %. At the same time an increase of 2-21/4 % to the Tank estimate of revolutions is recommended. The given additions are most

applicable to cargo vessels with all-welded hulls. The question is, of course,

of such a nature that each case must be treated separately. shows a tendency to increase with

"Froude"

calculations carried out for Series B (constant length)

average values:

length of ship. Similar

give the following

No. 305 306 303 307 308

Mean 1.023 1.025 1.026

(see also Fig. 10)

and for Series C (constant length):

1.019 1.022

No. 309 306 310 311

Mean 1.028 1.025 1.026 1.023

(31)

-It

k

, , A 28560

-..._

1 IMI6,

111. (L/00

..

{/Y --I=

- [L/17 (//= 1.025 ) "3 ]3 ' ...44

III

, __ -8 a-tS, 6 5 /00 / 50 209 (L/ioo)J Fig: 15, 9

(32)

MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALT NR 10

Appendix 2

Relationship between and

V1/3 (L/100)3

L ZI

In order to permit a conversion from to or vice-versa a

V1/3 (L/100)3

graphical representation of the relationship between them is given in Fig. 15.

Since is non-dimensional any system of units may be used, e. g. m, V1,3

LI

or ft, ft3 & c. In the case of , on the other hand, one is restricted (L/100)3

to British tons for 4 and to feet for L. Since 4 always refers to sea water

weight of sea water

an assumption must be made of the ratio . As stated

weight of pure water

previously this ratio has been taken as 1.025. With this assumption the relationship between the two quantities will be

[1

28560

(LI100)3 [L/ V'!3]3

Appendix 3

Relationship between and FL and between FL and

Between Froude's numbers F, = and FL =_ r_ there exists

V g V1/3 V gL

the relationship

F,

=1/- L

V1;3 FL

At constant values of L/V1/3, F, is therefore a linear function of FL. In Fig. 16 this function is shown graphically for a few normal values of L/V1I3. Side by side with the scale for FL is given a scale for the corresponding value of

V

based on the relationship

yL

= 3.359

yL

where is taken as 9.81 m/s2 (= 32.19 ft/s3). V 32 L m3 . =

(33)

MU

SUMO a

SIIIIIIPININ

snessulass

,..annuannollei-_ANIMPAUVENrdill

PrininiMMIEN-IMINISMENNEr

ILPINNWSINDP"""

Il

ralinegaro

111141881102"-0.,

oni

Q.,

MEW

ORM=

a

0i4 0.8

(34)

34 MEDDELANDEN FRAN STATENS SKEPPSPROVNINGSANSTALT NE 1.1j

Appendix 4 Relationship between C and 0

V213 V3 .

Both C _ and 0 = 427.1 are what wasp formerly

A213 vs

termed quasi-dimensionless. They are fixed by agreed units. Further itshould be

stated they are understood to apply to sea-water (N in C, and N and

d in0).

[In the Goteborg Tank it is not unusual to carry out tests for vessels

intended for the Baltic. For the Baltic y is usually taken as 1.015, equivalent

to e= 103.5 kg s2/m4. To make C independent of type of water it is usual,

in the Goteborg Tank to define C as follows:

C V213 T73' 104.5 Fig. 17.

(/=

0.4/9.5

, I C /.025) , 7 1 1 1 1 II I 1 ii II _ 05 /.5 2 .0 4-00 C.. .300 2 /00 ZOO 600 500 = 0 /0

(35)

Since 104.5 is the value of e for normal sea water the factor _for

104.5

such water. For other values of e the factor has a value differing from 1.

This, however, is compensated for by calculating N with the same e value (see formula 5).]

If as formerly y is taken 1.025 for sea water the relationship between C and 0 will be

419.5

This relationship is shown graphically in Fig. 17. =