Experiments with tanker models IV

FRAN

STATENS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)

Nr 36 GOTEBORG 1956

EXPERIMENTS WITH TANKER

MODELS IV

BY

HANS LINDGREN

GUMPERTS FORLAG

GOTEBORG 1956

This paper describes a continuation of the experiments with tanker models which were begun in 1952 at the Swedish State

Ship-building Experimental Tank. The results obtained in

the earlier tests have been described in Experiments with Tanker

Models IIII, by HANS EDSTRAND, E FREIMANIS and HANS

LIND-GREN [1 3].1) The subjects dealt with in these earlier papers are as

follows:

Experiments with Tanker Models I [1]: The effect of the shape of fore-end sections on the performance qualities of the hull.

Experiments with Tanker Models II [2]: The influence of the length-breadth ratio LIB (and length-displacement ratio, LII7113), on the resistance and propulsive qualities.

Experiments with Tanker Models III [3]: The influence of the breadth-draught ratio, BIT, and the block coefficient, 6, on the resistance and propulsive qualities.

In the investigations described herein, the propulsive characteristics and problems were the principal points of interest. The experiments were primarily concerned with the study of the effects of systematic variation of two factors, namely:

The form of the after-body sections, which was varied from that referred to herein as extreme V-form to extreme U-form. Two intermediate forms were tested in addition to the extreme forms. The propeller dimensions, which were varied systematically to give four inter-related propellers of equal coarseness. The four model hulls were tested with each of the four propellers in turn.

4

2. Symbols, Units and Methods of Calculation

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

the Sixth International Conference of Ship Tank

Super-indendents.

Ship Dimensions

L = length on waterline

Lnp = length between perpendiculars

B = breadth on waterline

T =- draught

Am = immersed midship section area

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

V = volumetric displacement

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

112 rxe = half angle of entrance on waterline

Propeller Dimensions D = propeller diameter

P = propeller pitch

Ao ---propeller disc area (= D2) 4 Ad = developed blade area

/ = blade width at 0.7 D/2

Kinematic and Dynamic Symbols and Ratios v = speed in general

ve = speed of advance

= ship's speed in Metric knots = resistance

T propeller thrust

Q =propeller torque

n = .rate of revolution (revs, per unit time)

Pe = effective power

P8 =-- shaft power (at tail end of shaft)

vs

w wake fraction (TAYLOR)

T

t thrust deduction factor

= density of water (102.0 kg sec.2(m4 for fresh water)_{(104.5 kg sec.2/m4 for sea water)} = kinematic viscosity of water

= V213 V3/Pe (m3, Metr. knots and HP) C2 = Pia V3/P8 (m3, Metr. knots and HP)

En, r = J713 _{FROUDE number, displacement}

EnL = v/ VTL = Fpounn number, length

1 -live= (0.7 n. D n)2

Rn = REYNOLDS number for propellers

Dimensionless Coefficients and Ratios

= block coefficients

6PP

Lpp

B T midship section coefficient

V = prismatic coefficient Ant L = length-breadth ratio -= breadth-draught ratio 17113 = length-displacement ratio -= L. C. B. forward of Lpp/2 as % of Lpp Lpp = pitch ratio

= disc area ratio

A,

= blade thickness ratio

KT thrust coefficient e- D4 n2 KQ = torque coefficient e- D5 n2 ve = = advance coefficient Dm KT

J

= propeller efficiency in open water

KQ 2v P,

= = propulsive efficiency

6

Units and Conversion Factors

Metric units are used throughout.

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

Methods of Calculation

The model-scale results from the resistance tests have been converted to the scale

of the full-sized ships in the conventional way in accordance with FROUDE'S method.

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

Tank Superintendents' Conference in Paris in 1935. No length

correction has been employed.

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

Continental method (GEBETts)1) with the skin-friction correction applied as a towing

force. The results have been converted to full scale in the conventional manner

In converting the measured values to ship scale, no corrections for scale effects, air resistance, hull condition etc. have been applied, since the experiments were only concerned with comparisons between the different versions of the models.

Wake fractions have been calculated in the usual way, using the propeller as a

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

thrust identity and on the basis of torque identity, with the aid of the curves of the

results from the open water propeller tests. A mean between the two values so

obtained was then taken in each case. This method of calculating wake fraction is the normal practice at the Tank.

The parent model in these investigations, Model No. 614, was selected on the basis of earlier experience and was exactly similar to Model No. 539 in ref. [2]. Three

basic forms (Models Nos. 612, 613, and 615) were derived from the parent form and a further variation, as described in Appendix 1, was also developed.

The model results have been worked out in terms of a ship. having a displacement, V. of 22000 m3 and a designed fully loaded trial speed of about 15 knots.

The experiments were carried out at the S w e dish State Shipbuilding Experimental Tank in Goteborg and were made possible by a grant from

Hugo Hammar's Foundation for Maritime Research.

3. Ship Models Tested

The parent model, No. 614, was made of paraffin wax to the same lines as Model No. 539, ref [2]. Fig. 1 shows the body plan and end contours of this form.

Using the body plan of Model No. 614, three new forms (Models Nos. 612, 613 and 615) with after-body sections of different shape

1) See Congres International des Directeurs des Bassina, Paris, 1935, p. 86. 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)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15w

(V-22088 m3)

Fig. 1.

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were developed. These models were exactly similar forward of Sta-tion 9, but their after-bodies were systematically varied (see Fig. 2). The new models were obtained by altering the original model, No.

614.

The after-body lines of all the models were related in such a way that the transverse distances between the body sections of the different forms (e. g. the distances a and b in Fig. 2) were equal at any particular waterline, while the sectional areas below the load waterline were the same for each form. The common sectional-area curve is shown in Fig. 3.

All the models had the following common particulars (in ship

scale):

Model Scale 1 : 22.5

BIT = 2.30

L. =- 160.13 m = 0.750 = 156.43 m ory = 0.768

= 20.53 m

# = 0.993 8.92 m 99 = 0.755 V = 22000 ra3 _{= 1.0 %} L/V1/3 5.72 1/2 cc, = 24.2 degrees

LIB

=

7.80 Length of parallel middle body

= 25 % (of

The wetted surface area varied between 4952 m2 (Model No. 612)

and 4982 m2 (Model No. 615).

In this paper, the following designations have been applied to the various models, in view of their respective afterbody lines:

Model No. 612 Extreme V Model No. 613 Moderate V Model No. 614 Moderate U Model No. 615 Extreme U

This terminology may be slightly misleading unless it is understood that in no case was the form either pure U or V. since from previous

experience it is known that true U or V-forms are not very suitable. In fact, in all cases, the most aft sections in the after body conform more to a Y-form. The description »extreme» in the above designation is only used in a relative sense.

..---- Model No. 612 (Extreme V)

- - Model No. 613 (Moderate V)

Model No. 614 (Moderate U)

Model No. 615 (Extreme U)

Fig. 2.

q. of Am 100 90 80' 70, 60 50 401 30 20 10 0 0 Aflor Body Models Nos. 612-615 SectionalArea Curve Fore Body 2 3 4 5 6 7 8. 9 . .10' 11' 12 13 14 16 17 18 '19 20 I' I I I I I I I 10 20 30 40 50 60 70 80m Fig. 3.

In addition to the aforementioned models, a further version, No. 613-B, was developed. This model was a modification of Model No. 613 and is described in Appendix 1.

All models were tested with a 1 ram tripwire fitted at Station 19.

4. Propeller Models Tested

As mentioned in the Introduction, four different propeller models (P490, P467, P470 and P468) were employed in these experiments. They were selected from the Tank's stock of model propellers and had been used previously for a similar investigation [4]. Particulars of these propellers (in ship scale) are given in Table I.

The diameter and pitch of the different propellers are such that all the propellers can be regarded as being of approximately equal coarseness. However, in order to be able to make a true comparison between the results of the different self-propulsion tests, a small correction must be applied, as explained in Section 7. The pitch distribution and other features of these propellers conform exactly

with TRoosT's B. 4.40 Series [5].

Since existing propellers were used in these experiments, it was not possible to take blade strength or cavitation characteristics into consideration. A decrease in the propeller diameter should, as a rule, be accompanied by an increase in the blade area ratio, in order to maintain the same degree of safety from cavitation. But such an increase in the blade area ratio entails a decrease in the propeller

Table I

1) The pitch is not constant over the whole radius and the figures given refer to the outer sections.

-Units Propeller Model

P490 P467 1 P470 1 P468 D mm 6152 5670 5366 5186 F') rrirfl 4365 4876 5216 5472 PID 0.710 0.860 0.972 1.055 Number of blades 4 40 t/D ... .. . .. .... . . % 4.5 Rake degrees 15

12

40 50 60 70

Blade Area Ratio, Ad/AO, in 0/0

Fig. 4. The influence of the blade area ratio on the required shaft horse-power,

138, calculated for model No. 614 and propeller No. P467 at 15 knots.

efficiency and hence an increase in the required shaft horse-power. The influence of the blade area ratio on the required shaft horse-power can be estimated with the aid of TRoosT's curves [5]; Fig. 4 shows the results of such a calculation for the parent model, No. 614, and propeller P467 at 15 knots. In the experiments in question, however, the risk of cavitation was small on account of the light loading (and low revolutions) of the propellers.

In order to enable the correlation of the present experimental results with those of the earlier tests, the self-propulsion results for Model No. 614 obtained with propeller P467 are compared in Appendix II with those obtained with propeller P506, which was used previously [2].

5. Open Water Propeller Tests

Open water propeller tests, covering the range of J-values in question, were carried out in conjunction with an earlier series of tank experiments [4]. The experimental results are given in Fig. 5

in the conventional dimensionless form of KQ, .1f7, and ne as functions

of J.

Fig. 5 also shows the limits between which the REYNOLDS number varied during these tests.

6. Resistance and Self-Propulsion Tests

All the resistance and self-propulsion tests were carried out in still water.

Resistance Tests

Resistance tests were carried out with all the models over a speed range corresponding to 13.5-16 knots. About eight experimental 'spots' were obtained in each case. The experimental results for 7'." .s 6 4 .s .9 2 8 0

Fig. 5. Propeller No. P490 Rn = 2.7-2.9.105 Propeller No. P467 Rn = 2.4-2.6 105 60 50 40 30 20 10 0

.

.

.. .. . Propeller No. P470 Rn =2.3-2.5.105 Propeller No. P468 Rn --2 . -...

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Models Nos. 612-615 are shown in Fig. 6 and are given in tabular form in Appendix III.

Results of the resistance tests with the modified model, No. 613-B, are given in Appendix I.

Self-Propulsion Tests

Self-propulsion tests were carried out with Models Nos. 612-615. Each model was tested in conjunction with each of the four propellers described in Section 4. The tests covered a speed range corresponding to 13.5-16 knots with about eight experimental 'spots' in each series. The experimental results are shown in Figs. 7-11 and are tabulated

in Appendix III. In Figs. 7-10, the shaft horse-power, F8, the

revolutions, n, the wake fraction, w, and the thrust deduction factor, t, are plotted as functions of the ship's speed. In Fig. 11, the propul-sive efficiency for all the models is plotted in the same manner.

The results of the tests carried out with Model No. 613-B are

given in Appendix I. In addition, as mentioned in Section 4, a

comparison between propeller P467 and the one used in the earlier experiments, P506, is given in Appendix II.

7. Experimental Results

Resistance Tests

The influence of the shape of the after-body sections on the

resistance is clearly indicated in Fig. 6. The two models with

V-formed after body sections showed a marked superiority, from a resistance point of view, over those with more U-formed sections.

Within the speed range in question, the two V-formed models were

approximately equivalent, while Model No. 614 (moderate U -form) was about 2.5% worse and Model No. 615 (extremeU -form) about 5 % worse. The results, to a large extent, confirm earlier experience on this subject.

Self-Propulsion Tests

There was some doubt as to the best method of obtaining a true comparison between the results of the various tests with the different

,models and propellers. It was considered, however, that the most

suitable means of comparing the powers was to correct all the values obtained at each speed to the same revolutions. A suitable mean curve of revolutions was therefore constructed and the correction was. based on the following assumptions:

Model No. 612 (Extreme V) Model No. 613 (Moderate V) Model No. 614 (Moderate U) Model No. 615 (Extreme U)

7000 6000 5000 4000 3000 2000 1000 13.5 14 . 14.5 15

Ship Speed, V.inknots

Fig. 6.

16.

Model No. 612 (Extreme V)

10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 1 ---= Propeller Propeller 1 No. P490 No. P467 .---_ Propeller No. P470 ,...-. ---r. ...- ....--...,- ....--- .--- ...-_ _ _ ...--..-,... ...,.

/

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--

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-

-13.5 14 14.5 15 155 16

Ship Speed, V. in knots

Fig. 7. 120 110 100 90 40 30 20 10

Model No. 613 (Moderate V) 120 1 10000 9000 8000 7000 6000 TZ 0. 5000 .0 0. 4000 3000 2000 1000 0 16

---...

Propeller Propeller No. P490 No. P467 ...--' _

--

Propeller Propeller No. P470 No P468 ..---. ,-."..:..r.."---- -.It,' ...---. ,...-,;-' -_ _ ..--- ...--7,- ' n -

....-/./

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Ship Speed, V, in knots

Fig. 8. 110 100 90 40 30 'C 20 10

18 120 110 90 40 30 -S 20 10

Model No. 614 (Moderate U)

10000 9000 8000 .7000 6000 5000 4000 3000 2000 1000 0 L

---

Propeller - Propeller No. P490 No. P467 ..z_ -- -- Propeller Propeller n ...--- ...- ...---No. P470 No. P468 i_ ....--..>. -....,- ....--...-- --- ' ---.. - ....-- ---

..----/

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Ship Speed, V. in knots

---Propeller No. P490

- Propeller No. P467

Propeller No. P470 Propeller No. P468

Model No. 615 (Ektrerne U)

o

14.5 i5

Ship Speed, V.in knots

Fig. 10.

20 80 60 80 60 80 60 40 20 Propeller No. P490 Propeller No. P467 Propeller No. P470 Propeller No. P468

in '1. Model No. 615 (Extreme U)

Model No. 614 (Moderate U)

Model No. 613 (Moderate V)

Model No. 612 (Extreme V)

0

13.5 14 14.5 15 .

Ship Speed, V. in knots

Fig. 11.

.80 .

60

16 15.5

fa, in °1. 7 65 60 55 50 45 (Fig. 12),

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That the revolutions could be corrected without any implied alteration in the propeller diameter. (i. e. the pitch was assumed to be altered).

That with constant propeller diameter, the wake fraction, w, and the thrust deduction factor, t, are independent of the revolutions

(within the limits in question in this case).

That the relative rotative efficiency remains unaltered.

These assumptions imply that the propeller thrust, T, is independent of the revolutions at any one speed.

The efficiency curves obtained from the open water propeller tests were transformed into a series of curves at constant values of

KT

ve

J2 e D2 ve2

22. 110 100 90 Corrected Values of.h 80 1 11 I 135 14 14.5 15 15.5 16

Ship Speed, V. in knots

Fig. 13.

The open water propeller efficiency, no , corresponding to the values (

of J

v-

and -K_J2 in question, were read from the curves. Then

ve

the value of J1

corresponding to the required corrected

Dni

revolutions n1, was calculated and the efficiency n'd Was read from

KT

the curves at the same value of _J2 as before. Since, therefore,

according to the above assumptions-, the hull efficiency and relative rotative efficiency are independent of the revolutions correction, the required shaft horse-power, PI, could be derived from the expression

In ps Tioi

no

The power correction, obtained in this way, amounted to about 2 % in the case of propeller P463, while for the other propellers it did not exceed 1 %.

The curve of revolutions to which all the results were corrected is shown in Fig. 13 and the corrected powers for 14, 15 and 16 knots are given in Fig. 14. A »three dimensional* comparison between the

8000 7000 'cr 6 000 .s 0. 5000 4000 5000

Model No. 612 (Extreme V) Model No. 613 (Moderate V) Model No 614 (Moderate U) Model No. 615 (Extreme U)

Diameter, D, in mm Fig. 14. co -o -Kr o_ o r... ..cr a -,ir a 0_ \ '-'47.r...- ---,_{\ --_,} --:\ -... . 16 knots ...--,..---...--' ..._ , 15 knots _---..._ ---.. --. . 14 knots , I 1 I -. I _.--I i I I I 5500' 6000

24 10 5000 5500 6000 Diameter, D, in mm 10 612

F.WA I WA AM I

14°A

I r

613 Extr. V)

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614 ModY)

Arr A/Aprilnill.

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0 I Model No. 615 5 000 5500 6 000 (Extr.U) Diameter, D, in mm 10 14 knots

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shaft horse-powers required at 14, 15 and 16 knots is given in percentage form in Fig. 15, where all the values are compared with the shaft power required for Model No. 614 and propeller P467 at the speed in question. For each speed, there is a minimum point in the diagram, thereby indicating the most suitable combination of propeller diameter and after-body form.

In spite of the fact that the V-formed after-bodies were shown to be the most suitable from a resistance point of view, the self-propul-sion test results (see also Figs. 14 and 15) indicated that the model with moderately U-formed after-body sections required the least shaft horse-power at practically all combinations of speed and propeller diameter. The better propulsive qualities of this model (No. 614) thus more than counterbalanced the worse resistance properties.

For the purpose of investigating this relationship further, a new modified version of the model was prepared and tested. The data for this model and the experimental results obtained therewith are given in Appendix I.

The optimum propeller diameter for open water conditions can be derived in the conventional manner from, for example, TROOST'S Bp - (3-diagram [5], by using the values obtained here for wake fraction and power. Such a calculation has, in fact, been carried out, in order to determine the relationship between the optimum propeller diameter indicated by the self-propulsion tests and that obtained

from the .137, 6-diagram. It was found that the optimum propeller

diameter for open water conditions was a little over 6 m, while the optimum diameter indicated by the self-propulsion test results was about 5.7 m, depending to some extent on the after-body form and the speed, as shown by Fig. 15. The difference between these two values, about 5 %, agrees well with EDSTRAND'S findings in ref. [4]

and can be attributed to the fact that the smaller propeller works

( 1 t

at a better hull efficiency than the larger propeller.

In this connection, it may be mentioned that the comparisons between the various propellers were not strictly true for the following

reasons:

1. As stated in Section 4, no account was taken of cavitation limits

The comparisons can be regarded, therefore, as somewhat distorted,

since a decrease in the propeller diameter should, as a rule, be accompanied by an increase in the blade area ratio in order to

26 35 30 25 40 20 15 (Model No. 615) (Extreme U) (Model No. 614) (Moderate U) Fig. 1 6.

maintain the same degree of safety from cavitation. An increase in the blade area ratio, moreover, normally leads to a decrease in the propeller efficiency and hence to an increase in the shaft horse power (see Fig. 4): In this case, on the other hand, there was little risk of any cavitation.

9. In the experiments described herein, the after-body, propeller aper-ture and shaft position were not altered for each propeller because it was desired to simplify the comparisons as far as possible. In an actual design, however, if a small diameter propeller is adopted, some advantage can be derived from designing the cruiser stern

Propeller No. P490 Propeller No. P467 Propeller No. P470 'Propeller No. P468 (Model No. 613) (Moderate V) (Model .Na. 612) (Extreme V) ----., ... ... _... ..._ --...., 0 --... w ...-I _...'...l... 14 .. I '''... I ---- -- --, - ., ,_ -, _ - -.;,.. __ ,

-7=-and aperture to suit the propeller. By lowering the propeller shaft, increasing the depth of the cruiser stern correspondingly and fining the after-body lines, improved results can usually be obtained. These two features of the tests with the smaller propellers, i. e., the small blade area ratio and the unsuitable after-end design, will have had opposite effects on the relative comparisons. No corrections have been introduced to take account of them.

Wake Fractions and Thrust Deduction Factors

Wake fractions and thrust deduction factors were calculated for each series of tests and the values are given both in diagrams (Figs.

7-10) and in tables (Appendix III). In order to show clearly the

influence of propeller diameter and after-body form on the wake and thrust deduction, the results have also been plotted collectively in Fig. 16. The points through which the curves have been drawn mark the mean values of wake fraction and thrust deduction factor for each of the various model and propeller combinations.

It is evident from the curves of mean wake fraction that the wake decreases with increasing propeller diameter and also as the after-body sections are made more V-formed.

The curves of mean thrust deduction factor in Fig. 16 are rather less regular. There is, however, a discernible tendency for the thrust deduction to increase with increasing propeller diameter. Further-more, in general, the V-formed after body induces a greater thrust deduction factor than the U-forrned after-body with a propeller of the same diameter.

8. Acknowledgement

The author wishes to express his gratitude for the grant made

by Hugo Hammar's Foundation for Maritime

Research which enabled these investigations to be carried out. The author also wishes to extend his thanks to Dr. HANS ED-STRAND, Director of the Swedish State Shipbuilding Experimental

Tank, for his valuable advice in connection with these investigations and to Mr. E. FREIMANIS, for his generous assistance with the design work.

Thanks are also due to Mr. P. D. FRASER-SMITH who translated the paper from the 'Swedish.

28

9. List of References

[1-3] EDSTRAND, HANS, FREIMANIS, E., and LTNDOREN, HANS: *Experiments with

Tanker Models Publications No8. 23, 26 and 29 of the Swedish

State Shipbuilding Experimental Tank, Goteborg 1953 and 1954.

EDSTRAND, Hews: »Model Tests on the Optimum Diameter for Propellers»,

Publication No. 22 of the Swedish State Shipbuilding Experimental Tank,

Goteborg 1953.

TROOST, L.: »Open Water Test Series with Modern Propeller Forms», Trans N. E. C. I. 1951.

Appendix I Tests with a Modified Model

On comparing the experimental results obtained with Models Nos. 613 and 614, it was found that No. 613 was superior from a resist-ance point of view (Pig. 6) while No 614, when fitted with a

After Body Model No. 613 Model No 6I3-B On, - 2-2-._ I \ \ I \ i \

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Ship Speed. V. in knots

Fig. 18.

suitable propeller, required the lower shaft horse-power (Fig. 15). Thus the higher propulsive efficiency of Model No. 614 more than balanced the better resistance qualities of Model No. 613.

Model No. 613-B was therefore constructed for the purpose of discovering whether a compromise between the two forms might give still better results. The lines of Model No. 613 were used as a basis for this form, but a bulb was superimposed on the after end as shown on the body plan in Fig. 17.

The results of the tests with Model No. 613-B are compared in Fig. 18 with the experimental results obtained with Nos. 613 and 614. Propeller P467 was used in all the tests in question.

It is evident from Fig. 18 that the after end modification adopted in Model No. 613-B was sufficient to cause a considerable increase in resistance in comparison with Model No. 613. At the same time, the good propulsive qualities of Model No. 614 were not altogether, achieved, so that the final result was rather worse (i. e. the required shaft power was greater) than for Model No. 614. It should, however, be remembered that Model No. 613-B had a greater displacement (48 m3 greater in f ull scale) than the other models of the series.

Appendix H

Comparison with the Results Obtained in Corresponding Tests with Propeller P506

In the previous investigations on tanker forms carried out at the Tank, another propeller, namely No. P506, was employed (see ref.

[1] and [2]). In order to relate the two series of experiments, there-fore, the self-propulsion test results for Model No. 614 (identical with Model No. 539; see Section 3) with propellers P467 and P506 have been compared in Fig. 19. The main particulars of propeller P506 (in ship scale) are as follows:

Number of blades = 4 PID = 0.75

D = 5.78 ta Ad/A, = 48 %

= 4.33 m Rake = 10 degrees.

As shown by Fig. 19, propeller P506 was slightly inferior to

propeller P467. The difference in shaft power (maximum 3 %) can mainly be attributed to the higher revolutions and greater blade

110 90 80 60 20 9000 8000 7000 6000 5000 .s 0. 4000 3000 2000 1000 .. -- ..-..." ... ...-..- ...-..-

,

--- ..-_ _..- ...-"" ..- ..-- ..---...

/..-/

./

/

...

/

./ / /

/

/ / -.... Ps .... .., / -... .... -7 ? _ _ _ _ Model No.

_

614 (Moderate Propeller Propeller U) No. P506 No. P467 I 1 1 1 1 _ _ _

_

14 14.5 15 15.5 16

Ship Speed. V, in knots

-2

80 90 100 110 120 130 140

.n in rimin.

Fig. 20.

area ratio of propeller P506. The relatively small difference in

diameter was probably of little importance.

As mentioned previously, all the tests described herein were carried out with comparatively slow running propellers. An indication of the effect of revolutions on the required shaft horse-power can be

obtained from data such as that given in TROOST'.8 B7) a-diagram

[5], if the way in which wake fraction and thrust deduction factor vary with propeller diameter is known.

Using the values of wake fraction and thrust deduction factor derived from the tests with Model No. 614, it was possible in this way to obtain the curve shown in Fig. 20. In this case, it was assumed firstly that the wake fraction and thrust deduction factor were independent of revolutions at constant diameter and speed and secondly that for each value of revolutions the propeller diameter was the optimum for open water conditions.

32

4

.5 2 .5.

Appendix III

Resistance Tests Self-Propulaion Tests

V Fn L Fn F. R Pc Ci. T _{P8 n} I ID t c2 n

knots tons HP

/

tons HP

(Metr .)

-

-

(Metr.) (Metr.) / (Metr.). (Metr.) ca. i n .

% % / 0/0

0 E 13.5 0.175 0.419 32.13 2975 649 42.15 4014 88.7 29.6 23.8 481 74.1 .`21 4" 2 14 0,182 0.434 35.28 3388 636 46.93 4650 92.8 29.6 24.8 463 72.9 P-1,-, ra,_ cs 14.5 0.188 0.450 38.63 3842 623 51.37 5289 97.0 28.8 24.8 453 72.6 ''' so" II L' 15 0.195 0.465 42.34 4354 609 56.27 6015 101.0 29.1 24.8 441 72.4 q 15.5 0.201 0.481 46,66 4960 590 62.23 6900 105.2 29.0 25.0 424 71.9 16 0.208 0.496 52.15 5721 562 68.42 7921 109.8 28.8 23.8 406 72.2 13,5 0.175 0.419 32.13 2975 649 41.68 3930 88.3 30,1 22.9 491 75.7 a) el+ 14 14.5 0.182 0.188 0.434 0.450 35.28 38.63 3388 3842 636 623 46.12 50.55 4531 5162 92.3 96.3 30.1 29,8 23.5 23,6 475 464 74.8 74.4 o.ot 10 -. ,.., 2 -t ii P"I Aq 15 15.5 0.195 0.201 0.465 0:481 42.31 46.66 4354 4960 609 590 55.34 61.53 5869 6854 100.1 105.2 30.3 29.4 23.5 24.2 452 427 74.2 72.4 N --, co 16 0.208 0.496 52.15 5721 562 68.42 7966 110.0 29.6 23.8 404 71.8 -c- c 13.5 0.175 0.419 32.13 2-975 649 42.73 4138 89.8 31.4 24.8 467 71.9 o t ,,,, co 14 0.182 0.434 35.28 3388 636 45.77 4594 93.0 31.7 22.9 469 73.7 14.5 0.188 0.450 38.63 3842 623 49.74 5175 97.0 30.7 22.3 463 74.2 c.., '..a. ,7..., a,- hi 0 4 40- 4 II q 15 15.5 0.195 0.201 0.465 0.481 42.31 46.66 4354 4960 609 590 55.34 61.41 6024 7034 101.6 106.7 31.1 30.6 23.5 24.0 440 416 72.3 70.5 16 0.208 0.496 52.15 5721 562 67.72 8131 111.5 30.6 23.0 396 70.4 E 13.5 0.175 0.419 32.13 2975 649 42.15 4171 906 34.0 23.8. 463 71.3 t, 4 = 14 0.182 0.434 35.28 3388 636 45.42 4660 94.0 34.2 22.3 462 72.7 hi o 4 14.515 0.188 0.195 0.450 .0.465 38.63 42.31 3842 4354 623 609 49.50 54.87 ,5335 6199 98.2 103.1 33,5 33.2 22:0 22:9 449 427 72.0 70.2 4,1 0 II . 33.2 c...., 15.5 16 0.201 0.208 0.481 0.496 46.66 52.15 4960 5721 590 562 60.71 66.66 7173 8218 1079 112.6 33.3 23.1 21,8 408 391 69.1 69.6

3 4

Resistance Tests Self-Propulsion Tests

V _{Fn L} Fa V R Pe C1 T P, n w t Cy 7)

knots tons HP

/

tons HP

(Metr.)

-

-

(Metr;) (Metr.) / (Metr.) (Metr.) r/in in. /,

% / %

E 13.5 0.175 0.419 32,31 2992 645 43.78 4124 88.5 30.8 26.2 468 72.6 14 0.182 0.434 35.22 3382 637 48.22 4738 92.5 30.5 27.0 455 71.4 c,., cp ci o TS 14.5 0.188 0.450 38.22 3802 630 51.84 5286 95.9 30.6 213 453 71.9 4 .91 II 15 0.195 0.465 42.13 4335 611 56.62 5948 99.5 30.9 25.6 446 72.9 15.5 0.201 0.481 47.53 5052 579 64.21 7063 105.0 30.2 210 414 71.5 16 0.208 0.496 53.02 5816 553 71.10 8199 110.0 29.4 25.4 392 70.9 p 13.5 0.175 0.419 32.31 2992 645 43.55 4036 88.1 32.6 25.8 478 74.1 '.- --' t 4 ; . 14 0.182 0.434 35.22 3382 W37 47.52 4597 91.9 32.2 25.9 469 73.6 )... v.) caw-- )c.: o 0 14.5 15 0.188 0.195 0.450 38.22 0.465 42.13 3802 630 611 51.49 5180 95.7 31.8 25.8 462 73.4 o p., o II ,,,A 15.5 0.201 0.481 47.53 4335 5052 579 55.92 61.76 5864 6719 99.5 103.9 31.8 31.8 24.7 23.0 452 435 73.9 75.2 :::....' cz 16 0.208 0.496 53.02 5816 553 68.30 7820 109.0 31.0 22.4 411 -74.4 C0 p 13.5 0.175 0.419 32.31 2992 645 42.26 3988 88.5 33.4 23.5 484 75.0 7:' -o_{0 = p., c0}ctiL.; co 14 0.182 0.434 35.22 3382 637 46.47 4575 92.5 312 24.2 471 73.9 )ri o..t)7 14.5 15 0.188 0.195 0.450 38.22 0.465 42.13 . 3802 4335 630 611 50.79 55.69 5197 5930 96.3 100.6 33.6 33.6 24.7 24.3 461 447 73.2 73.1 cc 15,5 16 0.201 0208. 0.481 47.53 0.496 53.02 5052 5816 579, 553 61.06 66.90 6819 7785 105.2 109.6 32.8 32.9 '22.2 20.7 429 413 74.1 74.7 13.5 0.175 0.419 32.31 2992 64.5 : 42.15 4125 90.0 35.3 23.3 468 72.5 14 0.182 0.434 3122 3382 637 45.88 4639 93.8 34.8 23.2 464 72.9 15 PI-1 2 °-. Ca.-z ut 14.5 0.188 0.450 38.22 3802 630 49.85 5234 97.6 34.t 23.3 457 72.6 2 7:10 il 15 0.195 0,465 42.13 4335 611 54.87 6085 102.2 35,0 21.2 435 71.2 15.5 0.201 0.481 47.53 5052 579 61.06 7107 107.3 35.0 22.2 411' 71.1 16 0.208 0.496 53.02 5816 553 _67.72_ 8242 112.6 34.1 21.7 390 70.6

V ,,,L Fiir R Pe Ci T P8 _n /0 t C2 7)

knots I tons HP

/

tons HP

(1VIetr.) I

-

(Metr.) (Metr.). / (1VIetr.) (Igetr.) rimin. 0/0

% / 0/0

-,0 13.5 0.175 0.419 33.75 3125 618 44.01 4109 87.7 33.3 23.3 470 76.1 14 0.182 0.434 36.67 3521 612 " 47.17 4573 90.6 33.6 22.3 471 77.0 14.5 0 4) 0.188 0.450 39.91 3969 603 51.02 5136 94.2 33.4 21.8 466 77.3 15 0.195 0.465 43.23 4449 596 56.16 5835 98.2 33.2 23.0 454 76.2 2 15.5 0.201 0.481 4758 5058 578 62.46 6733 102.9 32.7 23.8 434 75.1 16 0.208 0.496 52.72 5784 556 69.35 7806 107.9 31.9 24.0 412 74.1 13.5 0.175 0.419 33.75 3125 618 43.31 , 3900 86.6 35.0 22.1 495 80.1 et-C, E 0. ..1.,c0 14 0.182 0.434 36.67 3521 612 46.82 4405 90.0 35.0 21.7 489 79.9 !i) ' rg P-I 14.5 0.188 0.450 39.91 3969 603 51.02 5008 94.0 34.8 21.8 478 79.3 ' c,`"12''' 7 ''''II 15 0.195 046'a 43 93

-

4449 ' a96 " 3616 5738 98 9

-

34 1' 23.0 462 775

A -

15.5 0.201 0.481 47.58 5058 578 62.11 6631 102.9 34.0 23.4 441 76.3 16 0.208 0.496 52.72 5784 556 68.65 7742 107.9 33.2 23.2 415 74.7 73; -1) E 13.5 t !..,- © 14 0.175 0.182 0.419 0.434 33.75 36.67 3125 3521 618 612 43.20 47.17 3990 4549 87.7 91.7 37.2 36.2 21.9 22.3 484 474 78.3 77.4

i

To Pt" g 14.5 0.188 0.450 39.91 3969 603 51.49 5190 95.7 35.9 22.5 461 76.5 15 0.195 0.465 . 43.23 4449 596 56.62 5971 100.1 35.5 23.6 444 74.5 :a ,n pt, 0..A azII 15.5 0.201 0.481 47.58 5058 578 62.46 6879 104.8 35.4 23.8 425 73.5 16 - 0.208 0.496 52.72 5784 556 68.65 7878 109.4 35.3 23.2 408 73.4 E 13.5 0.175 0.419 33.75 3125 618 42.96 4095 89.4 36.9 21.4 472 76.3 .4t 'IT, ea 14 0.182 0.434 36.67 3521 612 46.58 4607 93.0 37.0 21.3 468 76.4 c4 14.5 0.188 0.450 39.91 3969 603 50.55 5236 97.0 36.5 21.0 457 75.8 15 4..4 II r4 q 15.5 0.195 0.201 0A65 0.481 43.23 47.58 4449 5058 596 578 55.22 61.06 5995 6923 101.2 105.8 36.4 36.4 21.7 22.1 442 422 74.2 73.1 16 0.208 0.496 52.72 5784 556 67.48 7986 110.9 35.9 21.9 403 72.4

36

Resistance Tests Self-PropuLsion Tests

V F, L Fn p R 1 Pe C1 T Pe n w t C2 ri knots (Metr.)

-tons (Metr.) HP (Metr.)

/

/

tons (Metr.) HP (Metr.) r/rnin. 0/0 0/0

/

/

0/, 13.5 0.175 0.419 35.03 3244 595 ' 45.53 4100 86.8 35.5 23.1 471 79.1 14 0.182 0.434 37.93 3643 591 49.04 4581 . 90.0 35.7 22.7 470 79.5 ;Ell 'cg 14.5 0.188 0.450 41.04 4082 586 52.89 5146 93.6 35.5 22.4 465 79.3 4,24,-g ii 15 0.195 0.465 44.70 4600 576 58.02 5867 97.6 35.0 23..0 452 78.4 ,--, ..., 15.5 16 0.201 0.208 0.481 0.496 50.31 56.37 5348 6184 547 520 64.91 73.55 6807 8151 102.2 108.1 35.1 34.0 22.5 23A 430 395 78.6 75.9 13.5 0.175 0.419 35.03 3244 595 44.95 3979 86.2 37.8 22.1 485 81.5 S r-- E 14 0.182 0.434 37.93 3643 591 47.87 4389 89.2 37.9 20.8 491 83.0 7-r) P-1i:° 14.5 0.188 0.450 41.04 4082 586 51.84 4959 92.8 37.9 20.8 483 82.3 C-,-6 6 N 44 0 p,'' T II 15 15.5 0.195 0.201 0.465 0.481 44.70 50.31 4600 5348 576 547 ' 57.67 64.33 5800 6790 97.4 102.4 37.5 36.8 22.5 21.8 457 431 79.3 78.8 uo -, co 16 0.208 0.496 56.37 6184 520 71.45 7904 107.5 36.1 21.1 407 78..2 7,; g 13.5 0.175 0.419 35.03 3244 595 44.72 .4091 87.3 41.0 21.7 472 79.3 o _..527-'-'' 14 ,.,--/',,c, 0.182 0.434 37.93 3643 591 48.92 4694 91.5 40.2 22.5 459 77.6 14.5 0.188 0.450 41.04 4082 586 53.35 - 5347 95.5 39.6 23.1 448 76.3 F,-, 15 44 `g ii 15-.5 0.195 0201, 0.465 0.481 44.70 50.31 4600 5348 576 547 58.26 63.98 6083 6986 99.5 104.1 39.7 39.3 23.3 21.4 436 419 75.6 76.6 16 0.208 0.496 56.37 6184 520 70.28 8056 108.8 39.5 19.8 399 76.8 co E 13.5 0.175 0.419 35.03 3244 595 44.25 4240 89.2 41.8 20.8 455 76.5 c",',:',?, CD 14 0.182 0.434 37.93 3643 591 48.22 4840 93.4 40.5 21.3 445 75.3 7-:*u P" 4 14.5 c..,- 6 0.188 0.450 41.04 4082 586 52.54 5497 97.4 40.4 21.9 436 74.3 ' o 0 ₁₅ ''' 0.195 0.465 44.70 4600 576 57.21 6240 101.4 40.4 21.9 415 73.7 "' II ra.i 0 X q 15.5 0.201 0.481 50.31 5348 547 62.46 7086 105.6 40.5 19.5 413 75.5 16 0.208 0.496 56.37 6184 520 69.23 8211 110.9 40.0 18.6 392 75.3

Page 1. Introduction . . . .

. .... .

. . . . .

9 _{Symbols, Units and Methods of Calculation 4}

3. Ship Models Tested 6

4. Propeller Models Tested 11

5. Open Water Propeller Tests . . . 12

6. Resistance and Self-Propulsion Tests 12

-7. Experimental Results 14 8. Acknowledgement 27 9. List of References 28 Appendix I 28 Appendix II 30 Appendix III 33