Tests with geometrically similar models of the VICTORY ship

MEDDELANDEN

FRAN

STATENS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)

Nr 40 GOTBBORG 1957

TESTS WITH GEOMETRICALLY

SIMILAR MODELS OF THE

VICTORY SHIP

BY

HANS LINDGREN AND E. BJARNE

GUMPERT5 FORLAG GOTEBORG

1. Introduction

The desirability of being able to make a consistent comparison

between experimental results obtained in different model experimental tanks led to a large number of towing tank establishments throughout

the world carrying out careful tests on models of the Victory ship

prior to the Seventh International Conference on

Ship Hydrodynamics in Scandinavia in 1954. A summary

of the test results obtained by the various establishments is given in [1]1).

The Swedish State Shipbuilding Experimental

Tank (SSPA) contributed to this comparison by carrying out tests

on a model in the scale of 1: 24.

Among the Decisions and Recommendations put forward by the

Seventh International Conference on Ship Hydrodynamics [1] were the following:

Each establishment should re-examine its experimental technique in the light of the Victory ship comparative tests.

Each establishment should consider self-propulsion test by altern-ative methods. Particular attention should be given to accuracy of model propeller construction as well as experiment technique to

ensure the refinement of accuracy necessary for the investigation of the small scale effects concerned.

In carrying out self-propulsion experiments for research purposes the thrust loading should be extended over the range between model

and ship self-propulsion for at least two speeds of advance.

Since completing the above mentioned tests with a model in the scale of 1: 24, new more modern apparatus for measuring propeller thrust and torque have been brought into use at SSPA. In view of this innovation and the above recommendations, it was decided at SSPA that a new 1/24th scale model should be made and tested.

Since it was also considered desirable to make a further study of the wall-effect in the tank, the plans were extended to include tests with

a family of five geometrically similar models of different sizes. 1) Numbers in brackets refer to the list of references on p. 25.

Both resistance tests and self-propulsion tests with this family of

models have now been completed. This report deals mainly with the results of the resistance tests. The results of the Self-ptopulsion tests

are briefly summarized in Appendix 1, but it is expected that it will be possible to give a more detailed study of these and the results of the open water propeller tests at the 1957 International Towing

Tank Conference.

Tests with similar faMilies of models have been carried out both at NSMB, Wageningen, and at NFL, Teddington, and the results were published [2, 3] while the SSPA tests were in progress. HUGHES has made a comparative analysis of these tests [3] and he has also evolved a method of determining the slope of the friction line with the aid of results of resistance tests on a family of models carried out in different experimental tanks [4]. This method is illustrated in

Appendix 2.

2: Symbols

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

the Sixth International Conference of Ship Tank

Super-intendents as a tentative standard.

Am midShip section area

AT = cross section area of tank 17213V3

( 3, Metric knots and HP) PE

F213 V3

(m3, Metric knots and HP) .P,s

= total resistance coefficient

e- /2 S.V2 .

C = viscous resistance coefficient

CFIDCFS = friction resistance coefficient ,according to IlunnEs' basic line and SCHOENHERR'S mean line, respectively

n, p = form influence factors

= rate of revolution (revs, per unit time)

length on waterline PE = effective power

Ps = shaft power (at tail end of shaft)

1? =- resistance (total)

V L

Br, REYNOLDS number

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

= propeller thrust

T

= thrtist deduction factor V = speed

wake fraction (TALoie)

V = volumetric displacement

(102.0

= density of water {_{004.5 kg sec. 2 / rn4 for sea water)}kg sec.2/m4 for fresh water)

= kinematic viscosity of water') PE

= = propulsive efficiency PS

Further symbols are defined where they appear. Units and Conversion Factors

Metric units are used throughout,

1 metre = 3.281 ft. (recipr. 0.3048)

1 metric ton = 1000 kg = 0.984 British tons ( recipr. 1.016) 1 metric knot = 1852 m/hour = 0.999 British knots (recipr. 1.001)

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

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

3. Ship Models Tested

The models represented a Victory ship, the main particulars of

which are given in Table 1.

5

') For v; see [5] p. 6-7.

Table 1

Length on waterline, L = 135.31 m

Length between perpendiculars, Lpp = 133.05 m Breadth, B = 18.90 m

Draught, T = 8.53 m Wetted surface area, S =- 3698 1112 Displacement, V 14745 m3 LIB = 7.16 LppIB = 7.04 BIT = 2.22 LIV113 = 5.52 V

0676

LB T V (5PP = 0.687 Lpp B T Am 13 =0.990 V =0.683 AML

Longitudinal centre of buoyancy

= 0.18 % of Lpp forvvard of Lppl2 Half angle of entrance on waterline

= 12 degrees

Models Nos. 590 and 743-A

Fig. 1 b

Front of Rudder Post

(looking aft)

Model No. 743

Rudder and Aperture

-"A

Body Plan Models NW. 743, 753, 754, 755, 778 707,8

111111111111

111111141=Wormii

111111111111111111

111,11111M

6°11111 MEM

111111k

/401111111111111

,111111111MIF

MAI

1 MI I NM VW/30EN

VIL.11111111/11/AW

'

114\111Wv__

111 0 80 Fig. '2

Six models, in all, have been tested. The oldest of these, Model No.

590 (scale 1: 24) was tested in 1953 and was used in the original

comparison between different towing tank establishments. As stated

in the Introduction, it was considered desirable, for several reasons, to repeat these experiments and a new model (No. 743-A) in the scale of 1: 24 was therefore made.

Models Nos. 590 and 743-A were each fitted with a contra-stern

and a contra rudder as shown in Fig. 1 a and as fitted on the fullscale ship. It was however considered that models of such special form were not entirely suitable for the investigations in question and the

contra-stern and contra-rudder were therefore replaced by a normally shaped stern and a normal, symmetrical rudder, as shown in Fig. 1 b. Figs. 2 and 3 show the body plan and end contours of the thus modified Victory ship.

In addition to the two 1/24th scale models, four other models in

the scales 1: 17, 1: 20, 1: 28 and 1: 32 were made and tested. The main particulars of all the different models are given in Table 2.

7 M. 4 WI. 40 WI. 36 WL 32 LWL 28 WL 24 WI. 20 WI. 16 WI. /2 WI. 8

Models Nos. 743,753,754,755,778

WL 8

WL 4

All the models were made of paraffin wax and were fitted with a 1 mm tripwire round a section 5 % of -Epp abaft the FP.

The models were fitted with rudders in all these experiments. The Victory ship models, which were subjected to resistance tests at NE'L [2] and NS111113 [3], were without rudders and the NPL and NSMB

._ Units Model Scale 1:17 1:20 1:24 1:28 1:32 Model No ... 755 754 743 753 778 L ... . .. .. .. .. m 7.959 6.766 5.638 4.833 4.228 Lpp m 7.826 6.653 5.544 4.752 4.158 V ma 3.001 1.843 1.067 0.672 . 0.450

S ... ... .

m2 12.80 9.25 6.42 4.72 3.61 Blockage, Am/AT % 1.12 0.81 0.56 0.41 0.32 161 AR l50 ₁₀ 0 FR Fig. 3 Table 2

9 tests also differed from the SSPA tests in the draught at which the

models were run. Therefore, for the purpose of enabling comparisons between the various series of tests, the SSPA programme was extended by running two of the models, Nos. 743 and 755, whithout rudder and

at a draught corresponding to that employed at NSMB and NFL.

These experiments are further discussed in Appendix 2.

4. Tests and Results

Resistance tests were carried out over a wide speed range with all the models. A special pendulum apparatus, which is described in [5], was used for measuring small values of resistance (up to about 1 kg.).

The normal GEBERS' type resistance dynamometer was used for

measuring greater forces.

Comprehensive self-propulsion tests with varied thrust loading were

also carried out with the four larger models and the propellers were similarly tested in open water. As mentioned in the Introduction, the results of these experiments are being analysed separately and

will be presented at the Eighth International Towing

Tank Conf er en c e. The results of the normal self-propulsion tests carried out in accordance with SSPA practice with the friction

correction based on FROTIDE'S friction coefficients, are summarised in Appendix 1.

Results of Resistance Tests

The primary results of the resistance tests with Models Nos. 743,

753-755 and 778 are given in tabular form in Appendix 3.

An analysis of the results shows that at very low speeds there is considerable scatter, presumably due to insufficient turbulence

stimulation and inaccuracies of measurement. In subsequent

develop-ment of the results, therefore, all records obtained at speeds lower than that corresponding to a Reynolds number of 4.5 x 106 for the largest model have been ignored. The corresponding limit for the

smallest model was set at 2.4 x 106 and for the intermediate models

the limits were linearly interpolated. These limits were chosen empirically.

The results are illustrated in Fig. 4.

In order to facilitate a

comparison of the results, the resistance values have been corrected

50

45

35

Model Resistance Coefficients

Mod. No. 743 (1:24) Mod. No. 753 (1:28) Mod. No. 778 (1:32) dv Mod. No. 754 (1:20) Mod. Nb. 755 (1:17) Fig. 4 0 o 'C . . .

'

vs0 .., ...a 0. o .

..0/ 0

_...

'

..- 0. d d 30 -I- 1 I_----I_ _ I I 11_ I I 5 6 7 8 9 10 11 12 13 14 15 16 .17 18

Ship Speed ,V, in knots

Models Nos, Dynamometer Signum

_755,743,778 -Pendulum Apparatus 755,743,778 . _ Normal 0 754,753 Pendulum Apparatus 754,753 Normal

8000 7000 -- 6000 5000 a. 4000 0 sa- 3000 4. 4. al 2000 1000 0

Resistance Test Results according to Froude

700 600 500 400 300 200 100 0 11 . --Model --- Model Model No. 755 No. 754 No. 743 No. 753 No. 778 ..C/ .... (1:17) (1:20) (1:24) (1:28) (1:32) ."-`:::". ,

i

// 1/ / / / .6.

---

--Model -- Model -- :-..7.

,

--- - .,... --...._ / 4. \ P E .:`

/

../.

ruilliii II 12 13 14 15 16 /7 /8

Ship Speed,V, In knots

Fig. 5

was chosen because many of the tests were carried out at 15.3° C.

and the corrections were thereby minimised. The corrections, which are of secondary importance, were based on a friction line somewhat

steeper than the SCHOENHERR line (ScnoENHERR +17 % form

I-0 5000 4000 ct ₃₀₀₀ 4. '8000 7000 6000 2000 1000 0 700 600 500 400 300 200 '/00 0

1) _{The frictional reistance has been calculated uing the formuine decided upon} at the Tank Superintendents Conference in Paris in 1935

-Model Model Model Ne.743 No. 743-A No. 590 With Contra-Stern and Contra-Rudder o o

-ii.

ii Li ii - -II /2 13 /4 15 /6 '7 /8 .5bhp Speed,V,in knots Fig. 6

Fig. 5 shows values of effective power and C1 calculated by the conventional method on the FROtTDE basis1) from the results of resistance tests with Models Nos. 743, 753-755 and 778. These curves have been derived from the measured values obtained in Test

.13

in Fig. 4. The differences between the curves amount to as much as 5 or 6 % and thus can hardly be attributed to inaccuracies of measurement but rather to defects in the method of calculation.

Fig. 6 gives the results of similar calculations for Models Nos. 590

and 743-A (both with contra-sterns and contra-rudders) and Model No. 743. The agreement between the results obtained with the old model (No. 590) and the new model (No. 743-A) is good and the effect of the alterations to the stern-frame and rudder (No. 743) was

neglig-ible.

A more detailed analysis of the experimental results follows in

Section 5.

5. Analysis of the Test Results

General

The resistance of a ship or a ship model in water is normally divided.

into a wave-making component, which is assumed to conform, to

FROUDE'S well law of comparisons, and a frictional component. The frictional component can in turn be divided into two parts,

of which one is taken as being equal to the resistance of an infinitely thin flat plate of the same length and wetted surface area as the ship

or model. The other part represents the form effect.

The questions of the correct formulation of the plate friction line and the character of the form effect have promoted considerable' discussion during recent years. The FROUDE formulation for skin friction which is employed at many experimental establishments is

now, considered out of date. Furthermore, the FEMME procedure of

relating the form effect to the wave-making resistance coefficient,

which assumes that it follows the law of comparisons, is considered

not wholly correct. Several proposals for alternative solutions to the problem are being discussed at the moment.

The main purpose of this 'analysis of the tests with Victory ship models was to derive a formulation giving the best correlation on converting the various experimental results to full scale. Unfor-tunately, however, it is not possible in an analysis of this type, to disregard the blockage effect of the tank. (The blockage is defined .

as the relation between the midship section area of the model Am

and the cross section area of the tank AT). Unsatisfactory correlation may be due to errors in the asiumed skin friction coefficients, incorrect calculation of the form effect and blockage effect. These various

4e, vAl lepow a.) ETz leptw c ' (ei::,) Ls

-1....0 trIZ 'ON iapoiv

.17 -... rof . Q., Cc FL; 1:3 0 Q1:1) SSZ '0A/ _lepoki (0Z11) _I Al lapow e Fig. 7

family of models in only one tank. iliTGEfES, however, has suggested a method of separating the blockage effect from the others, and thus obtaining the correct slope of the three-dimensional friction line, by

in

15 comparing the results of tests with a family of models carried out in

tanks of different cross section area [4]. An attempt to apply this Method is shown in Appendix 2. Unfortunately, though, errors of measurement, small differences in the shape and sutface of the models, turbulence stimulation and other differences between the different tanks have combined to produce so great an effect that no positive

conclusions can be drawn from this analysis.

The resistance coefficient, CT, for each model is plotted on a base

of REYNOLDS number, R, in Fig. 7. Points of equal speed in knots

have been marked on the curves. The friction line proposed by

HUGHES for two-dimensional flow, represented by the equation

CFH = 0.066 ( 2.03 + log R0-2

...

(1)

and SCHOENHERR'S well-known mean line, expressed by the formula

0.242

= log (lin CFs) . . ...

. ...

(2)

C FS are both shown in Fig. 7.

In the following, an attempt will be made to determine which of

three different methods suggested for calculating the frictional

resis-tance gives the best correlation, i. e. most closely approaches the ideal of giving the same prediction for ship resistance independent

of the scale of the model used as a basis.

LANDWEBER [6] has proposed that the total viscous resistance

coefficient, C v (the three-dimensional friction line), should be expressed

as

Cv = CF

ne

F p ₍₃₎

where the constants n and p are independent of REYNOLDS number. Three suggested simplifications of (3) were examined, namely:

C v _{C FS ± P} (4)

C v = C Fs ± 72C Fs. . .. . . ... ... . .. . ..

. .. . ... . ... . ...

(5) where C Fs is as used in equation (2)

Cv = CF.& 11-1_{FH (6)}

where CFH is given by equation (1).

Alternative C represents the line with the most slope and alternative

A that with the least slope of the proposed formulations (apart from

4 -3 2 0 -2 dcrsio4

Model Resistance Coefficient Difference Curves

Model No.743 Model No.753

I I

111.

I I I

6 7 8 9 10 11 12 13 /4 /5 16 17

Ship Speed , V , ih knots Model No. 778 -4 Model No. 755

. ...

IiIii

Fig. 8 Alt. C Alt. B - - - Alt. A 1:32 1:28 1:24 1:20 1:17

Hypotheses on the slope of the friction line can be examined by

calculating the differences in CT values obtained at equal values of FROUDE number in experiments with models of different scales.

Fig. 8 has been derived by calculating the differences, d C2, (see

Fig. 7), for the various models, relative to Model No. 743, at constant ship's speed (i. e. at constant values of FROUDE number). The values

of d CT obtained experimentally were thus compared with values

of LI CT calculated on the basis of the above three hypotheses. The

constant n was assumed to hate a value of 0.17 (see Fig. 9) and the

value of k was taken at 0.27 as proposed by HUGHES [4].

As is evident from Fig. 8, it is difficult to conclude that any of the

hypotheses A C is the correct one. At high speeds, there is conside-rable divergence from all the lines," which indicates that blockage effect is present. The result is analogous with that shown by HUGHES. Since the blockage effect is shown to be dependent upon speed,

an attempt has been made to determine the best slope for the friction line at different speeds. For this purpose a low speed range, covering the non-wave-making range, and a normal speed range were examined. In view of the reasonable blockage values, the blockage effect can

probably be neglected in the non-wavemaking speed range.

0.15 000

0.10

0.05

Percentage Addition to Schoenherr Mean Line

according to Granville

Test points. in the range 2.5 - 4.5 x 106 00 Fig. .9.: 17 /8.7 (cc..) 2 0 0.05 0.10 ais 0.40 0.35 0.30 0.25 0.20

Resistance Coefficient, C,../O4

.

45

6:4

6.5

Model Resistance inthe- Low Speed Range

-I.

6.6

Log R n

19

Low Speed Range

A number of attempts have been made to determine, by means of model tests in the non-wave-making speed range, the correct

friction line for three-dimensional bodies. It has been shown possible (within reasonable limits) to derive points on the friction line in this

manner but it is considerably more difficult to obtain the slope of

the friction line by means of such experiments on account of the very limited speed range which can be used for the analysis. At low speeds

it is difficult to prevent laminar flow and at the higher speeds the

resistance begins to be affected by wave-making

On the basis of results of tests in the non wave-making speed range given in [7], GRANVILLE [8] derived a curve for the form influence factor n in equation (5). This curve is shown in Fig. 9. A number of new tests in the non wave-making range havebeen carried out at SSPA. The SSPA results (obtainedin the range = 2.5-4.0 X x 106) have been plotted in Fig. 9 and show reasonably good agree-ment with the curve.

It was considered that it might also be possible toverify the correct slope of the friction line by means of tests with geometrically similar

models. In Fig. 10, all the experimental spots obtained at speeds

below the equivalent of 8 knots, (apart from those obtained at extre-mely low REYNOLDS numbers, which were ignored in accordance with the principle mentioned earlier) have been plotted on a base of

REYNOLDS number.

The line with the most slope, alternative C (HUGHES), gives the

best agreement in the speed range considered, but all the friction lines given by the above hypotheses A C (equ. 4-6) appear to be too flat. An attempt was made to derive a new line by the least squares method, but the wide scatter of the spots adversely affected

its reliability. It was also apparent that the line largely, depends on

the number of points included in the calculations, i. e. on the speed

range which could be taken as the non-wave-making range for each model.

Normal Speed Range

In the normal speed range, 11-18 knots, the slope of the hypo-thetical lines can be verified by calculating the differences between the CT values obtained from model tests and lines drawn through suitable points parallel to the alternative friction lines. The point

Difference between Model Resistance 'Coefficients.

and Lines parallel to Alt.' C (Hughes)

Ship Speed, V = 11 knots V = 13 knots V 5,15 knots = 17 knots V18 knots 0.3 o.4 0.5 0.6 0.7 0.8 89 0.0 1.1 12 Am/AT in% Fig. 11

of CT and R,, for the different models at constant FRouDEnumber (i. e. constant ship's speed). Only the hypotheses A and C (see above) were considered, since these represented the extremes of slope.

Fig. 11 shows the differences obtained relative to the friction line given by alternative C (HtrarrEs), while Fig. 12 shows the differences.

relative to the line given by alternative A (ScnoENHERR). _The

differences are expressed as percentages of the imaginary parallel friction lines.

It is evident from these diagrams that alternative A gives the best correlation. Except at the extreme speeds, 17 and 18 knots, the differences do not exceed ± 1 %. Thus, in the normal speed _range, the method satisfied the requirements that the same prediction of

ship resistance should be obtained regardless of the model scale. Fig. 13 shows the absolute differences in CT for alternative A.

Difference betweeri Model Resistance -Coefficients

and tines parallel to Alt. A (Schoenherr)

Ship Speed, --- V = /1 knots --- V = /3 knots V=15 knots =17 knots V=18 knots I I I I 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Am/AT in % Fig. 12

At high speeds (17-18 knots) the slope of the difference lines

indicates a blockage effect.

As shown by Fig. 11, all the difference lines based on alternative C (HuoREs) are sloped. The slope of the lines increases with increasing speed and this indicates that there is blockage effect even at the lower speeds.

Fig. 14 shows theFEand C, curves calculated on the basis of

hypo-, thesis A (ScRoENRERR). In this casehypo-, a roughness allowance of 0.0004 was added to all the values of resistance coefficient CT. The divergence between the curves is clearly less than in Fig. 5 (FRouDE).

6. Summary

Resistance tests covering a wide range of speeds have been carried out with five geometrically similar Victory ship models.

The:experi-mental results have been described and analysed mainly with a view

to verifying different theories about the form of the friction line for

Difference heti...teen Model Resistance Coefficients

and Lines parallel to Alt. A

- - _ . Ship Speed, V = II knots V=13 knots V15 knots =17 knots V =18 knots

The follovving conclusions may be drawn from' the experimental results:

1. The requirement that the same prediction of ship resistance should be obtained whatever the scale, of the model, is best satisfied

Alternative

hypotheses

3-Dimensional Line

C y

Composition of Line

Plate Line CF Form Allowance A . ... .. . B CV= CFS ± P CV= CFS + nCFS C, = CFH-4- kCFH SCHOENHERR SCHOENHERR HUGHES Constant Percentage Percentage - I -0.3 0.4 0.5 04 0.7 08 0.9 1.0 1.1 1.2 Am

/

Ar in% Fig. 13

ship-shaped bodies and alsoih order to investigate the question of

blockage effect in experiments With large models.

In connection with the form of the friction line, hypotheses A C

8000 7000 6000 5000 a: -c 4000 0 -3000 4.1 2000 1000 0

Resistance Test Results atcording to Schoenherr

93 700 600 500 400 300 100 ---__ '----.-77-.* --- +:...

---

---Model No. Model No. Model No. Model No. Model No. 755 (1:17) 754 (1:20) 743 (1:24) 753 , (I:28) 778 (I:32) 1/ i: Iti

li

I , 1

---

---- ---. ... , _{__}

ii

. .

\\

. .

\\*:-\\

\ -_ 111111111 II 12 /3 /4 15 /6 /7 /8

Ship Speed , V , in knots

Fig. 14

in the normal speed range (11-18 knots) by hypothesis A (SCHOEN-HERR ± constant form allowance).

If hypothesis A is accepted, the blockage effect only becomes

noticeable at very high speeds (about 18 knots).

One fact.which does not support acceptance of hypothesis A

is that in the non-wave-making speed range, the slope of a mean line

drawn: through the experimental points is such that it most nearly coincides With a line based on hypothesis C (HuGHE§). It is diffiCult,

however, to be certain about this since the experimental points are considerably scattered in the low speed range.

4. If hypothesis C is correct, the results are influenced by blockage

effect over the whole speed range. The good correlation given by hypothesis A must then be explained by supposing the error in the slope of the friction line to be largely balanced by blockage effect. Finally, it can be said that there seems to be little possibility of

obtaining a correct solution to the combined problem of three

dimen-sional friction line form effect blockage effect by means of experiments with geometrically similar models. However, the

pro-posed *image» method of VAN LAMMEREN, VAN MANEN and LAP [2] and the previously mentioned HUGHES method of using the

experi-mental results from tanks of different cross section may prove valuable in obtaining a definite solution to the problem.

It seems that it will be a considerable time before any such solution

is found and the experimental results discussed herein indicate that

until that time it would be resonable to use SCHOENHERR'S mean line

with a constant form allowance. This means that the form allowance, in accordance with the FROUDE procedure, can be included with the

wave-making resistance in a residual resistance component which obeysFROUDE'S law of comparisons. The advantages of this method

are:

It is based on a friction line giving one value at any value of

REYNOLDS number (unlike FROUDE'S friction lines).

It is simple to use and involves no knowledge of the absolute value of the form addition in the non-wave-making speed range

(unlike HUGHES' method).

With models of the sizes normally employed, it appears as if the

blockage effect can within practical limits be ignored (unlike with HUGHES' method).

The methoa has been used with good results for many years at a large number of experimental establishments, where empirical carection factors (for roughness etc.) have also been worked out. One disadvantage of this method is that if, as suggested by some investigators, it is based on too flat a friction line. (compare also HUGHES' _{line), the calculated resistance will be too high in the case} of the smooth ship. The empirically deduced roughness addition is

25

'7. Acknowledgement

- The Authors wish to express their thanks to Dr. HANS EDSTRAND,

Directorof the Swedish State Shipbuilding

Experi-mental Tan k, who initiated these experiments and contributed

much valuable advice.

Thanks are also due to the staff of the Tank for all their assistance and to Mr. P. D. FRASER-SMITH, who translated the paper from the Swedish.

8. List of References

NoapsTro3m, H. F. EDSTRA:ND, HANS: »Seventh International Conference on Ship

HydrOdynamics», Publication No 34 of the Swedish State Shipbuilding Experimental Tank, Gothenburg, 1954.

yAN LA.T.rimaror, W. P. A., VAN MANEN, J. D., LAP, A. J. W.: »Scale Effect

Ex-'perirnents on Victory Ships and Models. Part I», Trans. INA, 1955. HUGHES, G: »Viscous and Interference Effects Deduced from NSMB and NPL

Victory Model Tests, Trans. INA, 1956.

HUGHES, G.: *The Effect of Model and Tank Size in Two Series of Resistance Tests», Trans. INA, 1956.

NoRnsratim, H. F., EDSTRAND, HANS: ,Model Tests With Turbulence Producing Deyices», Publication No. 18 of the Swedish State Shipbuilding Experimental

Tank, Gothenburg, 1951.

LANDWEBER, L.: »Sixth International Conference of Ship Tank Superintendents»,

Comments on Subject 2 Skin Friction, Published by SNAME, 1953.

NORDSTROM, H. F., EDSTRAND, HANS, LINDGREN, Hs: DOH the Influence of Form upon the Skin Friction Resistance», Publication No 31 of the Swedish

State Shipbuilding Experimental Tank, Gothenburg, 1954.

GRANVII,LE, P. S.: *The Viscous Resistance of Surface Vessels and the Skin Friction of Flat Plates», Trans. SNAME, 1956.

Self-Propulsion Tests

Self-propulsion tests with different degrees of thrust loading were

carried out with all the models and open water tests were similarly carried out with the model propellers. The results of these tests are being analysed separately and, as previously mentioned, will be

presented at the 1957 International Towing Tank Conference. The results of the self-propulsion tests with Models Nos. 755 (1: 17), 754 (1: 20), 743 (1: 24) and 753 (1: 28) are summarised here in Fig: 15. These curves have been derived in accordance- with the practice normally adopted at SSPA, i. e. from self-propulsion tests carried out according to the so called Continental method (GEBERs), the

skin friction correction, based on the FROUDE frictional coefficients.

being applied as a towing force.

No corrections for scale effects, air resistance, hull condition etc. have been applied in converting the measured values to ship scale. Wake fractions have been calculated in the usual way, using the

propeller as a wake integrator. Values of wake fraction were worked out on the basis of thrust identity, with the aid of curves of the results

from the open water propeller tests.

The main particulars of the propellers used in these tests were as follows (in ship scale):

Number of blades --- 4

Diameter D = 6.25 m

Pitch P = 6.98 M. (max)

90 Q." Qs" 80 " 70 e-E 6 " 40 G c 0 ee. La' t: 30 " 032 20 7 10

Self-Propulsion Test Results . according to Froude

Model No. 755 (1:17) 7-"-- Model No. 754 (1:20) Model No. 743 (1:24) Model No. 753 (1:28) 10000 9000 8000 7000 6000 5000 4000 3000 2000 t000 0 91 12 11 13 ..14 15 16 /7 18

Ship Speed, V, in knots

Comparison with Other Victory Series

Experiments with geometrically similar Victory models have been

carried out both at NSMB, Wageningen and at NPL, Teddington. In these experiments the models were run without rudders and at a draught which differed to some extent from that used at SSPA. In order therefore to be able to compare the various results, two

of the SSPA models (Nos. 743 and 755) were run without rudders and

at a draught corresponding to 8:69 m (displacement = 15 019 m3). As may be seen from Fig. 16, the resistance coefficients calculated from the results of these new tests showed only insignificant differences compared with those obtained earlier. In the case of Model No. 743 (1: 24) the differences appear to be accidental in character, while the

resistance coefficients for Model No. 755 are generally, though insignificantly, increased in the new tests. In spite of these small

differences, the experimental results obtained previously have been

used in the comparison with the NSMB and NPL results.

In experiments with families of similar models in testing tanks of

different cross section area the resistance coefficients obtained at the same FRouDE _{number and :the same blockage but at different} REYNOLDS numbers can be compared. The differences between these resistance coefficients and those derived at the appropriate

REYNOLDS number from the correct »three-dimensional» friction line

should be the same within practical limits Various hypotheses regarding the correct slope of the friction line can thus be investigated by means of such comparisons. This method was proposed byHUGHES, who explains its theoretical basis in [4].

An attempt has been made at SSPA to apply the HUGHES_method

to the Victory model series. The corrected experimental results

from NSMB and NPL, as tabulated in [3] were used for this purpose.

In the case of the NPL results, only those obtained from the tests in No 2 tank, where plates were employed as turbulence stimulators,

were considered. The SSPA results were corrected for tripwire

C x104_-r -so 45 40 35 30

0 Mod. No. 743 (Ship Displ. =15019 m3) 1 without

mod. No.755 (Ship Displ. =15019 m3) Rudder

^

Model No. 743, with Rudder (1:24) Corresponding to Ship Displacement 14745 m3 I I i 16 17 18 8' 9 10 11 I? 13 14 IS

Ship Speed, V, in knots

Fig. 16

Model No. 755, with Rudder

(1:17)

The assumed friction line was of the form proposed by HUGHES see also eqU. (6)), namely

Cv = (1 + k)CFH

Where CFH follows the HUCIRES basic line, equ. (1). Various values

of k were tried, viz. 0, 0.10 and 0.27 (corresponding, according to HUGHES, to r = 1.00, 1.10 and 1.27), representing different slopes of the friction line. Using k = 0 gives a line of approximately the same slope as alternative A, while k = 0.27 gives a line similar to

alternative C (see Section 5).

Figs.. 17-19 show the differences, A CT, between the values of resistance coefficient, C, obtained experimentally at the various

establishments and the C. values calculated from the above equation. The correct slope of the friction line, according to HUGHES, is that

which gives the best agreement between the A CT curves derived from the various tanks at the same speed. A comparison between Figs. 17-19 indicates that the closest agreement is achieved with

a k value of about 0.10 (Fig. 18).

Since the cross sectional areas of the NSMB and SSPA tanks are

of the same order, there is less possibility of drawing definite conclu-sions from a comparison between results obtained at these establish-ments than from a comparison between NPL and SSPA values.

In Fig. 20, the differences between the above mentioned ACT

curves from SSPA and NPL are plotted to a base of k at three different blockage values (AM/AT = 0.50, 0.70 and 0.90 %). In this case, the

k-value corresponding to the best friction line is indicated by the

intersection of the A CT-difference lines with the k-axis Geherally. this k-value lies between 0.10 and 0.20, i. e. lower than the value of

0.27 proposed by HUGHES. However, there is appreciable scatter and presumably the results are influenced to some degree by errors

of measurement, small differences in model form and surface

4crrio` 17 16 15 14 10 -

-k --- 0 o /3 knots

LICi= 0 when C 1.00 0.066 (-2.034- looP,)-]

II knots Am/AT in % Fig. 17 /7 knots NSMB SSPA NPL Tank No.2 I - t 1.30 1.50 1.70 31 13 12 ses 15 knots 0.90 1.10 9

III

I I t -0.30 0.50 0.70

/4 11 10 15 knots 8 1t=0.10 knots - -- _NSMB SISPA NPL rank No.2 11 knots \ \

_._e-CICT = 0 when Ct = 1.10 La066(-203+logRj2_7'

I I I I I . I I I I I I I 1 0.30 0.50 0.70 0.90 1.10 1.30 1.50 1.70 AM/AT in % Fig. 18 13 12 9 ""'" 7 6

.0 cr. io4 /0 8 7 6 5 3 2 0 \ Ic = 0.27 17 knots 15 knots 11 knots NSMB 0 _SSPA - -cc- - - NPL Tank No.2 = 0 when Cr r 1.27L-0.066 (-2.034-1o. gRn)g

...-,

I 'I I I I 1 1 I

--I

0.30 0.50 0:70 0.90 1.10 1.30 1.50 1.70 AM/AT in % Fig. 19 3

0.5 0.5 0 0.5 L /Ar= 0.50 %

0.10\ 0.20

0.30 N

_\\

N NN 11 knots _ 13 knots /5 knots 7_ knots Mean line \40 /0 \ 0.20 0.30

\

_\

\ N N N N I N 0.20 030 N k NN \N N 6.10 S. Nsx AM/AT 0.70 % = 0.90 °A.

Fig. 20. Differences bettVeen A Cr values for results from SSPA and NPL as taken

Appendix 3

Model No. 755 Scale 1:17

Series 6 Normal Dynamometer co >c V 10 -6 . Rn .R 104 T co 0 r: a> m/sec. kg E 0 II 0> ,4 0.626 4.217 0.94 36.75

z E

0.665 4.480 1.08 37.41 0.710 4.783 1.22 37.07 g" i 0.755 5.086 1.40 37.63 0.804 5.417 1.58 37.44 A 0.835 5.625 1.70 37.35 0.712 4.785 1.23 37.18 0.801 5.383 1.56 37.24 0.866 5.820 1.82 37.18 -0.909 6.108 1.97 36.52 Fo H 0.948 6.371 2.14 36.48 0.996 6.693 2.38 36.75 ;2 4DCD aiS 1.047 7.036 2.61 36.48 42 - 1.080 7.258 2.77 36.40 c .> II _{1.122 7.540 2.97 36.14}

t

1.164 7.822 1 3.19 36.06 1.208 8.118 3.41 35.80

i

1.253 8.420 . 3.68 35.91 2 1.296 8.709 3.96 36.11 q 1.330 8.938 4.12 35.68 1.370 9.206 4.37 35.66 1.411 9.482 4.63 35.62 1.457 9.791 1 4.99 36.00 1.505 10.11 5.35 36.19 Series 1 Normal Dynamometer T' 10 = Rn R 104 CT m/sec. kg 1.372 9.641 4.36 35.50 1.495 10.51 5.20 35.65 c.c >>.> c> c> 1.562 1.624 10.98 11.41 5.78 6.36 36.29 36.95 1.686 11.85 6.85 36.91 0 ..., 1.754- 12.33 7.39 36.80 4 2 II 1.813 12.74 7.86 36.63 1.875 13.18 8.42 36.69 E -g 2 1.934 13.59 9.10 37.27 a> d 1 2.003 2.063 14.08 14.50 10.04 10.82 38.33 38.94 A 2.122 14.91 11.71 39.83 2.182 15.33 12.94 41.64 2.234 15.70 14.51 44.54 2.008 14.11 10.09 38.33 1.847 12.98 8.18 36.74 1.598 11.23 6.08 36.48 1.649 11.59 6.54 36.84 Series 9 Pendulum Apparatus V 10 -6 Rn R 104

r

m/sec. kg 0.112 0.7870 0.037 45.35 az c..,) co 0.158 0212 1.110 1.490 0.074 0.123 45.35 37.76 - 0.255 1.792 0.179 42.19 ..0 0.310 2.178 0.263 41.93 '2 II 0.356 2.502 0.341 41.23 0 6.'E 0.409 2.874 0.437 40.02 71 i 0.455 3.197 0.541 40.05 0.502 3.528 0.647 39.33 ce 0.556 3.907 0.793 39.31 A 0.602 4.230 0.950 40.15 0.658 4.624 1.099 38.88 0.709 4.982 1.285 39.16 0.585 4.111 0.893 39.99 0.532 3.738 0.730 39.53

Series 7 Normal Dynamometer V 10 .-6 R,, R 104 CT misec. , kg 0.568 3.245 0.58 38.14 0.624 3.565 0.71 38.67 0.677 3.868 0.83 38.41 0.750 4.285 1.00 37.71 0.793 4.530 1.14 38.45 10 ,.., 0.839 0.879 4.793 5.022 1:28 1.39 38.56 3816 0.919 5.250 1.50 37.67 2 "" E. II 0.957 0.999 5.467 5.707 1.63 1.78 37.75 37.84 2 ci.. A E 1.040 5.942 1.92 37.63 1.082 6.181 2.06 37.31 41" i 1.107 6.324 2.14 37.05 Sse 1.151 6.576 2.33 37.29 A _{1.189 6.793 2.45 36.76} 1.233 7.044 2.65 36.97 1.273 7.273 2.84 37.16 1.299 7.421 2.95 37.10 1.340 7.655 3.16 37.31 1.377 7.867 3.31 37.03 1.130 6.456 2.20 36.54 1.169 6.678 2.41 37.39 0.725 4.142 0.95 38.33 0.777 4.439 1.08 37.94 Series 2 Nornaal Dynamometer V 10 -6 Rn R 104 - Cr misec. kg 1.268 8.156 2.81 37.08 co c..) xa az ° 1.377 1.433 8.857 9.217 3.34 3.60 37.37 37.20 1.497 9.629 4.00 37.86 a II I-D 1.548 9.957 4.28 37.88 4 1.610 10.36 4.65 38.05 ez, § 1.668 10.73 4.90 37.35 01 4> 0 k' 1.729 11.12 5.34 37.90 1.781 11.46 5.69 38.05

P '

1.842 11.85 6.29 39.32 1.899 12.21 6.78 39.87 1.958 12.59 7.42 41.04 2.011 12.93 8.20 43.01 2.068 13.30 9.40 46.62 Series 10 Pendulum Apparatus V 10 -6 Rry, R 104 - CT misec. kg 0.289 1.754 0.155 39.37 = 0.339 2.057 0.214 39.49 a3 ce .-. a 0.395 0.443 0.489 2.397 2.688 2.967 0.294 0.360 0.442 39.98 38.92 39.22 ?.i) II .e.-. 4 0.543 3.295 0.551 39.64 ..,' E 0.592 .3.592 0.666 40.30 0.643 3.902 0.778 39.92 cq 0.693 4.205 0.896 39.58 d 5 A 0.748 0.802 4.539 4.867 1.041 1.175 39.47 38.75 0.850 5.158 1.324 38.88 0.474 2.876 0.418 39.45 0.371 2.251 ' 0.257 39.62 _ _. 0.248 1.505 0.122 42.08

Model No, 743 Scale. 1:24 Series 8 Pendulum Apparatus cc, co -. 0 V 10 - 6 Rn .R 104 T o) _. Jo ce rn/sec. kg § '--> II 0.315 2.451 0.376 43.31 E 0.564 2;685 0.449 43.12 .8 -E cee s ... el 0.597 0.628 2.842 2.939 0.498 0550 42.66 42.60 4 0.666 3.170 0.606 41.73 0.624 2.970 0.535 41.96 co c: 0 0.679 0.737 3.232 3.503 0.636 0.731 42.15 41.11 "" 6 0.775 3.689 0.809 41.14

i

0.810 3.856 0.891 41.47 1 ji 0.842 4.008 0.972 41.87 0.883 4.203 1.024. 40.10 E .0 la 0.908 4.322 1.083 40.13

4 t

0.954 4.541 1.193 40.04 o. ,.,..1 0.994 4.731 1.286 39.76 It A 1.032 4.912 1.372 39.34 0.944 4.493 1.166 39.95 0.843 4.013 0.949 40.77 0.711 3.384 0.679 41.02 Series 3 Normal Dynamometer . V 10 ---.° Rn1 R 104 ' CT m/sec. kg 1.143 5.883 1.63 38.11 1.253 6.449 L97 38.33 cL., r..) 1.305 6.717 2.14 38.39 2 6 1.365 7.026 2.39 39.18 1.420 7.309 2.61 39.55 g II 1-z 1.468. 7.556 2.80 39.67 1.522 7.834 2.96 39.03 r- a) eq -E 1.578. 8.122 3.20 39.24 s 412 1.627 8.374 3.45 39.79 4 1.678 8.637 3.75 40.68 1.733 8.920 4.09 41.60 1.791 9.218 4.48 42.66 1.841 9.476 4.98 44.86 1.893 9.743 5.65 48.16 1.706 8.781 3.95 41.44 1.763 9.074 4.28 42.05 1.808 9.306 4.64 43.34 Series 11 Pendulum Apparatus V 10 - 6 ' R , R 104 - CT m/see. kg co 0.300 1.521 0.120 40.71 E c..) 0.336 1.703 0.153 41.38 O ,s ,6 0.393 1.992 0.214 42.33 "" 0.439 2.225 0.266 42:15 Y II 0.488 2.474 0.335 42.97. ,.,z E g 0_-0 eq vz 4.' 0.538 0.594 0.638 2.727 3.011 3.234 0.407 0.490 0.561 42.94 42.42 42.08 3 s.63 0 P- 0.695 3.523 0.660 41.72 A 0.804 4.075 0.854 40.34 0.895 4.537 1.039 39.61 0.966 4.897 1.205 39.43 1.037 5.257 1.370 38.91 0.743 3.766 0.736 ,_ 40.71

Series 12 Pendulum Apparatus V 10 -° R, R 104 . Cr *sec. kg 0.287 1.247 0.089 45.02 Qz 0.392 1.703 0.159 42.98 61 C-) 0.443 1.925 0.206 43.65 0.488 2.120 0.247 43.11 0.540 2.346 0.306 43.61 _...1 II 0.590 2.564 0.362 43.23 0.642 2.789 0.431 43.48 -P E 4) en 691 3.002 0.499 43.44 N 0.743 3.228 0.561 42.24 -2 43 ce 0.795 3.454 0.636 41.82 A _{0.849 3.689 0.723 41.69} 0.903 3.924 0.804 40.99 0.999 4.341 0.988 41.15 1.105 . 4.801 1.181 40.20 1.188 5.162 1.370 40.36 0.950 4.128 0.888 40.90 Series 4 Normal Dynarnorneter V 10 -6 Rn R 104 . C2, misec. kg' co up. 0 1.062 4.722 1.08 39.78 4 0 eD 1.166 5.184 1.31 40.03 ...S' ci. L216 5.406 1.43 40.20 E 7 P 1.269_1.311 5.642_5.829 1.58_1.70 40.78_41.11 .5 g 1.363 6.060 1.84 41.15 1.408 6.260 1.94 40.70 s et- 1.460 6.491 2.07 40.36 1.514 6.731 2.26 40.99 L551 6.896 2.40 41.49 1.605 7.136 2.63 42.44 1.655 7.358 2.83 42.94 1.705 7.580 3.18 45.48 1.745 7.758 3.49 47.64

Model No. 778 Seale 1:32 Series 5 Normal Dynamometer V 10 -6 . Rn R 104 CT m/sec: kg va 0.998 3.620, 0.75 40.89 Lz F L090 3.953 0.91 41.59 a) , 4 1.177 4.269 1.07 41.95 ii 7 1.228 4.454 1.1a 42.49 1.268 4.599 1.24 41.87 g 1.322 4.795 1.34 41.63 ..c2_{.,z w} 1.370 4.969 1.45 41.95 fa 1.413 5.125 1.56 42.42 s '. 1.463 5.306 L68 42.63 a 1.502 5.448 1.78 42.84 1.552 5.629 1.95 43.96 1.592 5.774 2.12 45.43 1.642 5.956 2.41 48.54 1.142 4.142 0.99 41.22 0.998 3.620 0.75 40.89 Series 13 Pendulum Apparatus V 10 - '3 Rn R 10° CT rn/sec. kg 0.200 0.7216 0.034 45.61 co uz 0.296 1.068 0.073 44.94 co 0.401 1.447 0.126 42.55 ,..,.c..) 0.495 1.786 0.196 43.44 2 6 0.547 1.974 0.240 43.55 0.596 2.150 0.292 44.64 II 0.646 2.331 0.337 43.85 0.. ..p 5 0.701 2.529 0.399 44.09 4 a) eu t 0.748 2.699 0.458 44.45 0 .9 0.798 2.879 0.500 42.64 1 '11 0.847 3.056 0.565 42.77 A 0.901 3.251 0.621 41.54 0.949 3.424 0.682 41.12 0.993 3.583 0.758 41.75 1.105 3.987 0.953 42.38 1.046 3.774 0.841 41.74 1.206 4.351 1.147 42.82 1.303 4.701 1.324 42.34 0.446 1.609 0.153 41.77