Model tests on four-bladed controllable pitch propellers

PAPERS

OF

SHIP RESEARCH INSTITUTE

Model Tests

on FourBladed

ControllablePitch Propelleres

by Atsuo YAzAKI

March 1964

Ship Research Institute

Lab.

y. ScheepsbouwkuncJe

Technische Hogeschoa

Model Tests

on Four-Bladed Controllable-Pitch Propellers

by

Atsuo YAZAKI

Summary

This paper consists of two parts. In Part I, the results of the tank tests of a systematic series of Modified AU-type four-bladed controllablepitch prope-'1er models and the design and calculation diagrams of the series are given. In part II, the results of the tank tests on a high speed cargo liner equipped with four-bladed controllablepitch propeller are described.

Part I

Open Water Test Series and Design Diagrams of Four- Bladed Controllable-Pitch Propellers Cl) Introduction

The author reported the design diagrams of the three-bladed controll-able-pitch propellers at the 20th meeting of the T. T. R. I. in 1960. (2) Further to the work, the author conducted a systematic testing work with A U-type four-bladed controllable-pitch propeller models in the Experiment Tank of Ship Propulsion Division.

In this paper, the author presents the results of the open water test series and some design diagrams.

Model Propellers and Open Water Tests

Model propellers used here are made of alminium alloy and they have _a diameter of 0.25m. Their principal particulars are given in Table 1. 1.

As given in Table 1. 1, they have two groups of _{the area ratio which}

are 0.40 and 0.55, and the author calls the former AU-CP 4-40 and the

latter AU-CP 4-55.

Model propellers shown in Fig. 1. 1 are built up with the four blades and a hub to change the setting angle of the blades. The blades are fixed to the

-1-hub by the set-screws (A) which are fitted on the fore and aft sides of the hub. Therefore, it is able to adjust the blades to a given setting position by rotating the blades to the ahead or astern direction and fixing them by the set-screws (A).

Open water tests were carried out in the No. 2 Experiment Tank accord-ing to the ordinary practice of Ship Propulsion Division.

For fixing the net thrust, the correction for the resistance of the screw hub at various speed of advance was applied for the measured thrust.

The Reynolds number Rn of the tests is shown in Table 1. 1.

The tests were conducted at various angular blades settings, that is, the blades were rotated by 5 degree intervals to increase or decrease the pitch.

(3) Tests Results

The results of the tests for each propeller are shown in Figs. 1. 2. to 1. 7. The J, KT, K0 and i are defined as follows;

VA T Q JKT

1=

_nD'

_{KT= pn2D''}

K0-

_pn2D6' ìo _2irK0

where VA; speed of advance of the propeller, n; number of revolutions of

the propeller, D; diameter of the propeller, T; net thrust with idle thrust

deducted, Q; the measured torque, and p; density of the tank water.

And O in these figures denotes the adjusting angle of the blades from the initial setting angle, therefore O=O0 _{means the initial setting condition of}

the blades of each propeller.

Positive sign of J and KT corresponds to the propeller in ahead running and negative sign to the propeller in astern running. Negative value of KQ, which is found in the case of large positive and negative J value, shows that the propeller is rotated by the current.

When the effective pitch is adjusted to nearly zero, curves of K0 show the singular characteristics. And, in curves of KT, remarkale discontinuity comes out at a certain fixed speed. Under this fixed speed of advance, the waves induced are in front of the propeller, but when speed of advance

becomes higher than this fixed speed, the waves are left behind the pro-peller, so remarkable discontinuity in curves of K will be found at this fixed

speed.

2-Such discontinuity in the curves of K is also found when the propeller is still in astern running under the positive propeller thrust.

Values of KT, K0 and read from these figures are tabulated in Tables 1. 2 to 1. 7.

(4) Design Diagrams

Fig. 1. 8 shows the / Bp type design diagrams for the propeller of the expanded area ratio 0.40, say AU-CP 4-40, and Fig. 1. 9 those of the expand-ed area ratio 0.55, say AU-CP 4-55. The metric units are used, and the density of sea water is assumed as 104.51 kg sec2/m4.

It is possible to determine such a principal dimension as diameter and pitch ratio of the four-bladed controllable-pitch propellers, applying these diagrams at the initial stage of design.

And, another some types of diagrams which are convenient for calculating the performances of the propellers when their blades setting angle is adjusted, are successively introduced. Some diagrams are shown in Figs. 1. 10 to 1. 15.

Symbols in these diagrams are as follows;

q'; thrust in tons, P; delivered horse power in PS, and 1 PS is 75 kg rn/sec. D; diameter in meter, V; speed of advance in knots, Nc; Nl 00. and N is

number of revolutions of propeller per minute.

Table 1. 1 ControllablePitch Propeller Models

3-MODEL PROPELLER NO. 1363 1364 1365 1366 1367 1368

DIAMETER(m), D 0.250 0.250

BOSS RATIO, diD 0.30 0.30

PITCH [INITIAL] (m), H 0.250 0.200 0.150 0.250 0.200 0.150

PITCH RATIO [INITIAL], HID 1.00 0.80 0.60 1.00 0.80 0.60

EXP. AREA RATIO,aE 0.40 0.55

BLADE THICKNESS RATIO, t0/D 0.050 0.050

MEAN BLADE WIDTH RATIO, BID 0.224 0.308

MAX. BLADE WIDTH RATIO, BID 0.265 0.364 FORM OF BLADE SECTION Aerofoil (MAU) Aerofoil (MAU)

NUMBER OF BLADES, Z 4 4

ANGLE OF RAKE O O

REVOLUTION (r.p.$), n 12.0 12.0

TEMP.OF WATER (°C), r 7.7-24.0 7.7-24.0

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4- BLADED CONTROLLABLE PITCH PROPELLER

Type

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Boss Ratio

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f

Fig. 1.8

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design diagram

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Part II

Tank Tests on a High Speed Cargo Ship with Four-Bladed Controllable-Pitch Propeller

Introduction

Although number of the ships with the controllable-pitch propeller is

gradually increasing, there is yet very few useful! data which is applicable

to the estimation of propulsive performances of these ships. Its reason is

based upon the more complicated propulsive conditions of these ships as compared with the ships of the fixed-pitch propeller. So, to investigate the propulsive performances of the ships with the cotrollable-pitch propeller, the author conducted the detailed tank experiments on a cargo liner model with a four-bladed controllable-pitch propeller.

Model Ship and Model Propeller

Model ship used here is M. S. No. 1384, which is 6.00m in length between parpendiculars and made of wood. This model is one of the parent models

applied to the tank test series of the high speed cargo liner by Ship Research Association of Japan. Lines of this model are shown in Fig. 2. 1, and

principal particulars are given in Table 2. 1. As the corresponding actual

ship is assumed to have the length of 150m and to be installed with the

main engine of 20,000 SHP at 118 RPM.

Model propeller used is M. P. No. 1366, which is one of the model pro-pellers of AU-CP 4 series given in Part 1, and its principal particulars are reproduced in Table 2. 2. This model propeller is nearly similar

in the

re-lation of the diameter and pitch to the model propeller No. 1357 which is applied to the tank test series by Ship Research Association of Japan and also shown in Table 2. 2.

Tank Experimens and Results

Tank experiments were perfomed at No. 2 Experiment Tank of Ship

Propulsion Division.

As the load condition tested, the full load condition shown in Table 2. 1 is used throughout the experiments. Resistance, self-propulsion and propeller

-behind tests are conducted under the various test conditons given in Table 2. 3. In this Table, (i denotes the adjusting angle from the initial blades settings at which the pitch ratio of the propeller is unity, and the plus sign of _{means the blades are rotated towards the high pitch position and the} minus sign means the blades are rotated towards the low or reverse pitch position. Rotation of the propeller

_{is denoted by n, and plus sign of}

_n means the rotatin to the right and minus sign that to the left.

Resistance Tests

Resistance of the model ship with all appendages is measured in _{the "go} ahead" and "go astern' conditions. As turbulent stimulator,

_{a row of the}

trapezoid studs of 1 mm height is equipped at 10mm intervals _{on the S. S.} No. 9- in the "go ahead" condition and on the S.S. No. -- in the "go astern" condition. In the astern tests, the resistance of the model without _{the studs} is also measured, but any differences beiween the measured resistance of the model with the studs and without the studs could _{not be found.}

Results of resistance tests are given in Fig. 2. 2 in the non-dimensional form as follows; RR TR TFS V V2 RFS s u2

where, r is the residual resistance coefficient, _{TFS is the frictional resistance} coefficient for the ship, RR is the residual resistance, is the frictional resistance of the ship, is the displacement, S is the wetted surface of the ship, and y is the speed. The ITTC 1957 model-ship correlation line is used in calculating the frictional resistance.

In Fig. 2. 9, it is shown that the resistance _{in astern running is much} larger than the resistance in ahead running.

Self-propulsion Tests

Self-propulsion tests are conducted under various angular settings, say every

5 degree from +5° to 40° of O. Propeller rotation

_{is kept to the right,}

therefore, when the setting angle of the blades is reduced _{so much that the} propeller may produce the negative thrust, the model _{ship runs astern. So,} the self-propulsion tests are carried out for both _{ahead and astern running.}

In the self-propulsion tests in astern running, the model without the studs is used for fear that the studs should affect intricately the self-propulsion factors such as the wake fraction and the thrust deduction coefficient.

Frictional resistance corrections that are used at the self-propulsion tests are introduced from the ITTC 1957 model-ship correlation line.

Self-propulsion factors, that is, the wake fraction WT, the thrust deduction coefficient t and the relative rotative efficiency for the "go ahead"

condi-tion are given in Fig. 2. 3. The full lines in this figure show the mean

velues of self-propulsion factors when 6 is zero. When there are no negative values of pitch of the propeller blades, that is, when the setting angle O is under 5° over - 15° in these tests, self-propuls5on factors are not affected by the dimensions of the setting angle, and they are likely represented by the full lines obtained for O of zero. But, in a case of the large adjusting angle, for example, in a case of O being -20°, the negative values of pitch are found in a outer region of the blades as shown in Fig. 2. 7, and values of the thrust deduction coefficient and the wake fraction are decreised. It seems that the reason for these phenomena is as follows; when the blades setting angle is rotated to the negative direction so largely, negative value of the pitch appears in the outer region of the propeller and positive value appears in the inner region, therefore, water stream induced by the propeller is contra-directional in the outer and inner region of the propeller disc, resulting in decrease of the apparent resistance and the analyzed wake fraction of the

model.

Such phenomena about the self-propulsion factors associated with the setting angle of the relatively large negative value, also appear in the tests in astern running.

However, the values of relative rotative efficiency were not affected by adjustment of the setting angle.

In Fig. 2. 4, the propulsive efficiencies in ahead running are shown by every 5 degree of O. With reducing 6, the values of propulsive efficiencies

become gradually small because of the decrease of the propeller efficiency. Self-propulsion factors derived from the self-propulsion tests in astern running are shown in Fig. 2. 5. As will be found from this figure, with decreasedpitch settings the negative pitch occupies greater part of the radius than the positive pitch, therefore, the values of the wake fraction and the thrust deduction

-coefficient increases with the decrease of O-value.

Analytical results from the self-propulsion tests, in which the propeller rotation is to the left, are also shown for reference in the dotted lines in this figure. It is found from this figure that the values of the wake fraction and the thrust deduction coefficient obtained from the tests with the controllable-pitch propeller are gradually approaching, with decrease of 6-value, to the

values obtained from the fixed-pitch propeller of the left rotation. The relative rotative efficiency is also nearly constant in this case.

In Fig. 2. 5, the propulsive efficiencies for the astern running are shown. (C) _{Propeller Behind Tests}

In propeller behind tests, number of revolutions of the prepeller _{are kept} constant of 9.83 per second, which corresponds to 118 RPM for the ship, and the model ship is fixed to the towing carriage at the full load draft, and thrust, torque and number of revolutions of the propeller _{are measured by} the Geiher's type dynamometer settled in the model ship at various ahead and astern speed.

As same as the self-propulsion tests, the propeller behind tests are perfomed under various angular blades settings.

Results of the tests in ahead running _{are plotted in Fig. 2. 3 in the form} of the self-propulsion factors. From this figure, it is found, the values of the wake fraction and the relative rotative efficiency of the tests are nearly same as the values obtained from the self-propulsion tests. However, when the blades are rotated to the extreme low pitch, the positive and negative pitch appear in the radial pitch distribution at the same time and the values of wake fraction are decreased. This phenomenon is found in the case of O

being -25° and _200.

Results of the tests in astern running are plotted in Fig. 2. 5 in the form of the self propulsion factors, and it is shown that these factors coincide fairly well with the results from the self-propulsion tests. But, when both of the positive and negative pitch appear in the radial pitch distribution, and

the model ship goes astern in spite of the positive thrust of the propeller,

that is, in the case of O being -20° and - 25°, there is no systematic varia-tion in the values of the wake fracvaria-tion by the astern setting angle.

Open characteristic curves of M. P. No. 1366 at the left-rotation are given in Fig. 2. 8, and they are used for analyzing the self-propulsion tests and

the propeller behind tests in astern running.

(D) Delivered Horse Powet, Torque and Thrust for the Ship

The propeller revolutions and the delivered horse power for the ship derived from the model tests are shown in Fig. 2. 9.

In Fig. 2. 10, the thrust, the torque and the total resistance of the ship

are given. Nomenclatures used here are as follows: Nsthe revolutions per minutes for the ship propeller DHP= the delivered horse power in PS

Q = the torque in kg-m T= the thrust in kg

R=the total resistance in kg Vs=the ship speed in knots

Symbols with subscript B in Fig. 2.10 denote the variables obtained from the propeller behind tests assuming the propeller revolutions are 118 RPM.

In calculating these values scale effect of the self-propulsion factors between the model and the ship are neglected, and the ITTC 1957 model-ship corre-lation line is used in computing the frictional resistance.

In Figs. 2. 9 and 2. 10, the fine curves of delivered horse power, torque and thrust are calculated from the results of the open water tests of M. P. No. 1366 assuming the revolutions of the propeller being 118 RPM, the wake fraction being 0.29 for ahead running and the wake fraction zero for astern running. It is found that the bold curves obtained from the tests and the fine curves derived from the calculations give the same tendencies.

From Figs. 2. 9 and 2. 10, the follows will he discussed:

Values of the delivered horse power needed for a given speed are lower in handling the propeller under constant pitch and variable revolutions than in handling under constant revolutions and variable angular settings

of the blades. Therefore, from the point of the horse power needed at a

given speed it is not favourable to keep the revolutions constant in either case of ahead and astern running.

When the ship is still in advance under the negative propeller thrust, remarkable discontinuity in the thrust curves T11 appears at a certain speed. There are forward waves induced by the propeller around the stern of the

ship under a certain advance speed, but when the ship goes over such a speed, the waves are fled afterward, and, therefore, at a certain speed of

-r,

advance, say a critica] speed of advance, remarkable discontinuity in the thrust curves will be appeared.

These phenomena are found at the values of & of -30°. -35° and -40°

respectively

The same phenomena as mentioned above were already recognized in the open water characteristics of the controllable-pitch propel]er M. P. No. 1366. which were given in part E.

When the ship is still in astern running under the positive propeller thrust, there is remarkable discontinuity in the thrust curves TB at a certain speed. This phenomenon is also considered from the reason similar to in

paragraph (b).

These discontinuities are found at the values of O of -25° and -20° in

Fig. 2. 10.

When the ship still in ahead running under the negative propeller thrust and the ship is still in astern running under the positive propller

thrust, the values of the torque and the delivered horse power of the ship at the relatively low speed are nearly constant at a given setting angle, but with increasing the speed these values rapidly grow up.

It is possible from Figs. 2. 9 and 2. 10 to estimate the operating

performances of the ship at the ahead and astern settings and the procedures of this estimation will be given in another chapter.

Dead pull forces produced by the torque at normal rating which is 118,000kg-m in this ship are 177 tons in the controllable-pitch propeller of O of -8° and of RPM of 118, but are 137 tons in the fixed-pitch propeller of designed pitch and of RPM of 79. Also, at any speed of the ship, the controlla-ble-pitch propeller adjusted in a favourable blades settings will produce more powerfull tow rope pull than in the fixed-pitch propeller.

Even if resistance of the ship increase by 20% or 30% during

navigation because of the high waves and the strong winds, amount of

adjustment of the blades setting angle needed for utilyzing the full power of engine is rather small, so it is probably not worth investigating _the

automatic pitch controll system under free running at sea.

(4) Problems Related to the Operation of Controllable-Pitch Propeller From the point of manoeuvering, powering and designing of the ship with

controllable-pitch propeller, it is considered to be important to investigate the problems related to the operation of the controllable-pitch propeller.

(A) Time to stop the ship

Equation of the ship motion in free route is given in Equation (2. 1)

dvs

m

dr

=TB(1-1)R

where, m=the ship mass with added mass included

vsthe ship speed

r = the time

IB=the thrust of propeller R= the resistance of ship

t =the thrust deduction coefficient

Keeping the direction of rotation and number of revolutions constant, and giving the time condition of pitch adjustment, Equation (2. 1) will be solved by applying the progressive approaching method to Fig. 2. 10. But, in applying

the above method it will be assumed that the characteristics of the propeller are steady during the operation.

An example of calculation of the stopping performance is given under the following conditions.

Conditions;

Initial conditions;

V5; 22.05 knots. which corresponds to the speed at the norma] rating Ns; 118 RPM, which is corresponding to the revolutions at the normal

rating

DHP; 19,600 PS, which is corresponding to the power at the normal rating 0; 0, which is corresponding to design setting angle

Pitch operating conditins;

Linear adjustment of angular settings from 8=00 to 0= 4Qc during 10

seconds

The calculation under above conditions is

carried out step by step as

given in Table 2. 4 typically, and thus the curve A showing ihe relation

between the time and ship speed is obtained as Fig. 2. 11. From the curve

A, it is found, it takes 169 seconds for the ship from 22.05 knots to stop. In the above calculations, it is assumed that the added mass of the ship is

10% of the mass of the ship, and the thrust curves TB at the adjusting

27

angle of from -25° to 40° are represented by the mean lines of the

chain ((1= -25°-j -35°) and bold full lines (0= _400) in Fig. 2. 12, neglect-ing the discontinuities in the thrust curves.

Co-ordinate of Fig. 2. 11, y, is measured so that the speed of 22.05 knots becomes unity.

Nomenclatures in Table 2. 4 will be guessed from the following Equation.

rn

-ma=TB(1-t)-R=TB'-R

The relation between the ship speed VS, the adjusting angle O and the thrust TB during the operation is shown with a bold full line ìn Fig. 2. 12.

Equation (2. 1) is also solved by using the approximate analytical method given by Dr. F. Kito.

By Dr. F. Kito, Equation (2. 1) is re-stated in the following form.

L+Gv2_Bn2p(1_E

_{: j-o}

(2. 2)

where, v== V/V0. n=N/N0, p=P/P0, G=R/mV0

B= p (1 - t) NØ2D2PQ C/rn V0, E= i - GB. r = the time v= the ship speed N= the number of revolutions, P= the effective pitch of pi opellei V0=the ship peeJ in steady free route

N0=number of the revolutions in steady free route P. = the effective pitch of propeller in steady free route

R=the resistance of ship

m = the mass of ship with added mass inciudea D=the diameter of propeller

p=the density of watei

t = the thrust deduction fraction

C=the constani iii the following Equation

CTT/pNZD2PL(1_

) (2. 3)

CT= the propeller thrust coefficient

T=the hrust, VA=the advance speed of propeller

Solution of Equation (2. 2) is given for the period [rom finishment of the blades adjustment to the stop of the ship as follows;

m1e" + ßem2

where, m1, m2 are the roots of the next Equation;

m2+ l_Em +

_1-E0

(2. 5)

and, p' is the coefficient given in the next relation;

p' = P01)

ß is the final effective pitch after finishment of the blades adjusiment, and

e = G

v0-m1

y0 is the coefficient given in the following relation;

V'=v0 V0

where V' is the speed just after finishment of the blades adjustment. From the Equation (2. 4), the time T0 which is necessary for stopping after finishment of the pitch operation is given as follows;

T0- _{log (}

v-m

m2

) (2. 6)

G(m-m2)

v0-m2 m1

When m, and m2 are complex number, Equation (2. 6) re-stated as follows; i

(tanP__tan'

b

)

(2. 7) bG a a+v0 where, i E

_b-

_a2"112

1-E'

- l-E

)

Therefore, if time for the pitch adjustment is t0, total time T needed for stopping from the beginning of pitch adjustment is obtained from the follow-ing Equation;

T=t0+ T0

Dr. F. Kito gives the relation by which y0 in the previous Equations could be obtained, but in this worked example, it will be permitted approxi-mately to solve Equation (2. 6) or (2. 7) assuming that y0 is unity.

Dr. F. Kito assumed that the coefficient C in Equation (2. 3) is constant throughout the various angular settings of the blades but in M. P. No. 1366 C varies with values of (1 as shown in Fig. 2. 13.

At such large ship as this worked example, time needed for stopping after finishment of the pitch adjustment is far longer than pitch-adjusting-time, therefore, the value of C which is corresponding to the propeller

characteris-tics after the adjustment, that is, the propeller characterischaracteris-tics of (1 of _400

-must be applied for solving the Equations, and then the relation between the time and the ship speed is derived as curve B in Fig. 2. 11.

From Fig. 2. 11 it is found that time needed for stopping is 155 seconds

in curve B and 169 seconds in curve A. Therefore, it is possible to use

successfully the approximate analytical calculation method which does not require the tank experiments.

Applying the previous method to the astern condition, the relation between

the astern speed and the time is also introduced, and the time which is

necessary for reaching the steady astern condition will be also calculated. Curve B in Fig. 2. 14 shows the relation between the time and the ship speed from normal advance speed (22.05 knots) to the normal astern speed

( 13.2 knots) via zero speed under the same adjusting conditions. From the figure, it is found that it takes in total 480 seconds from the normal advance speed to the normal astern speed. in these calculations, C-values for the propeller of O of 40° are also used, and the added mass is assumed as 10% of the ship mass.

Motion of the ship from the zero speed to the normal astern speed is re-stated by introducing - y' for y, and G' for G, and zero for y0 in Equations

(2. 4), (2. 6) and (2. 7). That is;

0m1

-V' -

+ßm2emoe em1 + ßem2 m2 log ( m m2+v' ₎ (2. 9) G(m1m2) m2 m1+v

where, -V' is y for the astern speed, and G' is G for the astern condition

When m1 and m2 are complex numbers, Equation (2. 10) must be applied. tan

a2+b2-av' (2. 10)

Therefore, total time needed for the motion from the normal advance

condition to the normal astern condition is given by I + T0 +T0'.

It is also possible to apply the above method to analysis of the ship motion under various angular settings.

(B) Torque and thrust variation during astern adjustment from the normal ahead speed

The variations on the time of the effective pitch, the slip ratio, the torque and the thrust corresponding to curve A in Fig. 2. 11 are graphically shown in Fig. 2. 15. Notations in the figures are followings;

P is PIP0, s is the slip ratio, T is the thrust, T0 is the thrust at the ahead design value, Q is the torque, and Q0 is the torque at the design value. Curve

of TITO was introduced from the thrust curve Tß in Fig. 2. 12 which was applied for the calculation of curve A, and curve of Q/QO was estimated from Fig. 2. 9.

An outline of the performances of the propeller during astern adjustment from the normal ahead speed is understood from Fig. 2. 15.

I' pitch adjustment by curve P in Fig. 2. 15 is given under the constant revolutions, the slip ratio begins to decrease rapidly and turns to infinitive via discontinous region, then gradually decreases and finaly reaches unity at the stop of the ship. The thrust begins to decrease rapidly in negative value_over the absolute ahead design value, then gradually increases keeping the negative value. The torque also begins to decrease, then i urns to increase over the ahead design value, and reaches the ahead design value. But, these descriptions are explanative, so in the actual case it is probable that the curve of TITO will have a discontinuity at a certain speed and the revolutions of _propeller will be increased in the region of extremely low torque.

(C) _{Graphical representation of speed, thrust and horse power variations} after pitch adjustment finishes

As shown in section (1), motion of the ship is mainly determined by the ship motion after finishment of pitch adjustment because the mass of the

ship is so large but the time under pitch adjustment is very short. So, it is

more convenient to use the following plain graphical method instead of solving rather complicated Equations mentioned previously when we presume the varia-tion of the ship speed and the horse power after finishment of pitch _operation.

For this purpose Fig. 2. 16 is prepared.

Fig. 2. 16 is derived from the following considerations Equation (2. 1) is re-stated as follows;

r=nzrV2 dv

R )

J u1 (1 t)(TB

In the above Equation, let

-

31

and to simplify calcutions, putting (1 t) outside of the integration sign of the Equation (2. 11), then the Equation is re-stated in the next form.

dv (2. 12)

i-t

y, Te-T

Equation (2. 12) will be integrated graphically at each given angular settings by using Fig. 2. 9, and if the time is presented in the form of ' instead of (1 - t) r, it will be possible to obtain the speed.time relations after finishment of pitch adjustment under various angular settings as Fig. 2. 16.

In performing graphical integration of Equation (2. 12), values of the thrust TB shown in Fig. 2. 9, are used, but in the region where the data from the propeller behind tests are not enough, the data of open water test of M. P. No. 1366 are used for make up a lack of data.

Abscisa of Fig. 2. 16 is the ship speed in knots and ordinate is the thrust in tons. Contours of horse power corresponding to a normal rating (20,000 SH

P), three-fourth, two-fourth and one fourth of the normal rating are also

obtained from Fig. 2. 8 and are shown in dash-lines in this figure. These horse powers are calculated at the constant revolutions of propeller of 118 per minutes and the diameter of the propeller of 6. 25m for the actual ship.

From Fig. 2. 16 it is possible to analyse or investigate the following problems

easily.

(a) Relations among the time, the speed and the horse power when the setting angle is changed from the design value (6 = 00) to a given value of f at the normal ahead speed.

For example, supposing the time for pitch adjustment is 5 seconds, and u1 is

-20°, and the speed drop during pitch adjustment will be neglected the rela-tion between the ship speed and the time will be obtained from tracing on a contour of O of -20° from the point of -r = O on the right part of the figure And, it is known, it takes more than 5 minutes to reach the terminal speed of 8.5 knots in this example. As the thrust deduction coefficient at O of -20° is nearly zero in this example, so it is possible to consider that r' nearly equals to r. As another example, supposing the time for pitch adjustment is 10 seconds and 00 is _350, it takes about 4 minutes to stop the ship, and about 12 minutes to reach at the normal astern speed of 9.3 knots.

The shaft horse power corresponding to a given pitch adjustment is obtai-ned from integrating the contours of the horse power in this figure.

Moreover, using Fig. 2. 16, it is found that the worked example in section

(1)

is not suitable because the horse power needed exceeds the normal

rating of main engine.

Relation among the pitch adjustment, ship speed and the horse

power from the stop to the normal ahead speed.

For example, even for such a case where angular setting is changed, step

by step, from 0 at the zero speed of the ship to 02 after a seconds, to 02

after a2 seconds and so on, the relation among the angular settings, the ship speed and the horse power will be able to be estimated from this figure. In

this case, it is also possible to find their approximate relation when pitch

adjustment is not discrete but continuous. Furthermore, it is possible to choice the suitable pitch adjustment with which the output of the main engine does not exceed the design value.

When the angular Eettings are changed from negative to positive, relation among the time, the speed and the horse power will be also found by using the similar consideration as section (a) and (b).

Cd) This figure is also applicable to how to determine the best pitch

adjustment for manoeuvring the ship from a normal free route to another condition. Therefore, if the ship with controllable-pitch propeller is equipped with such chart as Fig. 2. 16, operation and manoeuvring of the ship would become easier and more reliable.

For instance, supposing the permission of 10% overload of horse power will be practicable, it is possible to attain the designed ahead speed from the stop in about 6 minutes at the pitch adjustment as in Table 2. 5 (A), but if the pitch adjustment as in Table 2. 5 (B) is applied, it takes about 7 minutes. And at adjustment (A), the horse power is nearly constant during adjusting, but at adjustment (B) it varies by about 40%.

(5) Conclusins

Main conclusions obtained in part II are as follows;

(a) Self-propulsion factors in ahead running are nearly constant in the small change of blades setting angle. Therefore, even if there were no datum about the ship with the controllable-pitch propeller the variation of the speed

-and the horse power will be easily estimated from the data on the ship with the fixed-pitch propeller.

(b) _{When the setting angle is adjusted to large negative value, both of} the positive and negative pitch appears in the same blades, and as the results

the self-propulsion factors vary with the values of the angular settings

considerably.

Cc) When the ship goes ahead under the negative propeller thrust, _{or when}

she goes astern under the positive thrust, discontinuity in the curves of the propeller characteristics appears at a certain critical speed.

To keep number of the revolutions constant by adjusting the blades settings is not preferable in the point of the horse power for a given ahead and astern speed.

On the backing performance, horse power for a given speed is generally higher in the controllable-pitch propeller a constant number of revolutions than in the fixed-pitch propeller of reverse-rotation. Its main reason is that

the efficiency of the propeller of reverse-rotation is generally higher than that of the controllable-pitch propeller having the corresponding pitch settings.

The backing performance may be improved by several means. One of these is to employ blades sections which are symmetrical or nearly symmetrical about the cord, and another is to use a varying radial pitch distribution for the ahead design condition with the pitch reduced at the inner sections.

The varying radial pitch distribution as mentioned above has another advan-tage that the blades sections near the hub now have a positive ahead pitch and the complicated variation in the self-propulsion factors will be reduced appreciably when the blades are rotated in the reverse position.

By using a diagram as Fig. 2. 16, it is possible to estimate the pro-pulsive or manoeuvring performances of the ship with the controllable-pitch propeller easily, and then to choose the appropriate pitch adjustment for a given manoeuvring condition.

On the free route performance of this high speed cargo liner with the controllable-pitch propeller and the same ship with the fixed-pitch propeller, as would be expected from the open-water characteristic curves and self-pro-pulsion tests, the delivered horse power required is practically identical up to over a design speed. Therefore, for practical purpose it can be concluded

propeller installed in the same high speed cargo liner is nearly the same. (h) lt is permissible that the results from these tank tests and analysis will be generally applicable to a similar kind of this high speed cargo liner.

Acknowlegements

The author wishes to acknowlege the valuable co-operation and assistance of Mr. Einosuke Kuramochi, Mr. Yoshiro Kawakami and the staff of our Institute who jointly carried out the experiments and the performance

calcula-tions. He also wishes to acknowlege the Mitsubishi Nippon Heavy Industry Co. Ltd., because most of the work reported in Part I was carried out under the sponsorship of that Company.

To cover the wider region of the area ratio of the propeller, AU-CP 4-70 series which have a area ratio of 0. 70 are now programmed, so the results and the design diagrams of the series will be presented in the near future.

References

A. Yazaki, E. Kuramochi & T. Osaki, Design Diagrams of Four-Bladed Controllable-Pich Propellers, Journal of Zosen Kyokai, Vol. 112, Nov.

1962

A. Yazaki, Design Diagrams of Three-Bladed Controllable-Pitch Prope-llers, Nov. 1960 (In Japanese)

K. Tsuchida & A. Yazaki, Design Diagrams of Three-Bladed Controll-able-Pitch Propellers, Report of TTR1, No. 57, 1963

A. Yazaki, E. Kuramochi & H. Kadoi, Tank Tests on a High Speed Cargo Boat with Four-Bladed Controllable-Pitch Propeller, Journal of Seibu Zosen Kai, No. 26, Sept. 1963 (In Japanese)

F. Kito, Analysis on the Slip Variation under the Operation of the Con-trollable-Pitch Propeller, Monthly of Zosen Kyokai, No. 365, Feb. 1960

(In Japanese)

F. Kito, Relation between the Pitch Operation Time and the Time

necessary for the Stoping of the Ship, Monthly of Zosen Kyokai, No. 373, Oct. 1960 (In Japanese)

-Table 2. 1 M. S. No. 1384

Vd=Speed of Ship (kt)

vs (mis)

R= Resistance (ton) Ts=Thrust (ton)

(1-t) = Thrust Deduction Coefficient

Table 2. 2 M. P. No. 1366 & M. P. No. 1357

a=Acceleration (mis2) r=Time (sec.) Ts' T.s (1-t) M. P. No. 1366 No. 1357M. P. Diameter (m) 0. 250 0. 256 Boss Ratio 0. 300 0. 200 Pitch Ratio 1. 000 0. 938

Exp. Area Ratio 0. 550 0. 650

Blade Thickness Ratio 0. 050 0. 050

No. of Blades 4 5

Section Profile MAU MAU

(m) 6.00 B (m) 0.857 a (m) 0. 357 CB 0. 575 GP 0.602 CM 0. 956 Lcß (%) +1.89 V (m3) 1. 0572 S (my) 6. 720 0=-50 Vs' vs JVS R Ts (1-t) Ts' Ts'-R a ¿ft V 22.05 11.33 0 91.0 54.0 0.81 44.0 -47.0 -.025 0 0 22.00 11.30 -0.03 90.0 55.0 « 44.5 -44.5 -.024 1.3 1.3 21.90 11.25 -0.05 88.5 55.5 « 45.0 -43.5 -.023 2.2 3.5 21.80 11.20 -0.05 87.0 56.0 « 45.5 -41.5 -.022 2.4 5.9 0=-100 22.00 11.30 0 90.0 -3.0 0.81 -2.5 -92.5 -.049 0 1.3 21.90 11.25 -0.05 88.5 -2.0 « -1.6 -90.1 -.047 1.1 2.4 21.80 11.20 -0.05 87.0 -1.0 « -0.8 -87.8 -.046 1.1 3.5 21.70 11.15 -0.05 85.0 0 « 0 -85.0 -.045 1.1 4.6 -Resistance Test Table 2. 3 -Go Ahead Test Conditions (With Studs)

-Go Astern (With & Without Studs)

-Go Astern _{(0=0°), (-n)}

-Self-Propulsion Test _{-Go Ahead}

-Go Astern (0=+5°, 0°, -5°, -10°, (0= -40°, -35°, -30°) -15°. -20°), (+n) (+n) -Go Ahead (0=0°, -5°, -10°, -15°, -20°, -25°, -30°, -35°, -40°), (+n)

-Propeller Behind Test

-Go Astern (0=-40°, -35°, -30°, -25°, -20°), (+n)

4/?

0.010

Table 2. 5 Worked Example of Operation

Fig. 2. 1 Body Plan & Stem and Stern Contour of M. S. No. 1384

Fig. 2.2 Resistance test (M. S. 1384)

37

-A B Time (1 Time O Osec

7

Osec

7'

20

6

120

3

40

5

160 0 60

4

80

3

100

2

160 0

i

o 05 o 0.10 rR .- s-- .-.- . o 0.20

G-

_r &or

P

D 0.15 0.25 0.Q 0.005 TR

10

0.005

£ 1.0 LO 4-1.2 0.8 1.2 0.8 0.7 0.6

0.6-t0

4 s o

Fig. 2. 3 Self-propulsion test and propeller behind test (Go ahead)

-

20

¡ I t J n I f I I

OJO 0.15 0.20 0.25 0.30

FROUDE NO., Fn

Fig. 2.4 Propuslive coefficient (Go ahead)

- I 5

lt

I - WT

s

8 +5 o. -5 -iO' -15' -20' -25' -30 -35

Silt Prop. Test X O D V Q

Behind list s A Y + 4 e o. + 50

I 0

5.

s o aO-,_o e _{Q UD} X o 0.15 Fn 0.20 0.05 0,10 0.25 0.30

I

1.0 0.4 0.3 0.2 o

0. I

-*:Left Handed Turning

1.2

I.0-LA 0.8 o -30

l-t

Fn

Fig. 2.5 Self-propulsion test and propeller behind test (Go astern)

0.5-e= 00( Left Handed Turning)

-30°

e _4Q0 _350 t I I -0.10 -0.15 Fn

Fig. 2. 6 Propulsive coefficient (Go astern)

39

--0.20

e 00* _{-20° -25' -30° -35° -40°} Self Prop.Test X _{o o} Behind Test + A U 8 4-. i 0.8 o -5--. 0.61-.I X -'--X x - -x- - -<-Xx _300 IWT 1.0 -40° 0 + 6 0.9 A:? _%---

--»---_ - -

_{- ) -X-ç}

--0.8 -0.10 -0,15 -0.20

o -0.05 0 -al 1--0,2 -010 -03 0.4 -0.5 0. 0.7 0.3 t/R I0 0.3 -1.5 -(0 -05 0 0.5 .0 HID o o IS 2.0

Fig. 2. 7 Radial pitch distribution (ei; adjusting angle of blades, H/D; pitch ratio)

0,5 0.4 0.3 o P.-0.2 0.l o

411

Ii.i

PI....

Model Propeller NO. 365 Pitch ratio, H/D .00

Reverse rotation

o 05 1.0

J

7-k L5 o-\ 4

'

-15 -(0 -5 0 5

0

(8RPM 1

7')

o.

(Go ASTERN)4VS-- (GOAHEAO)

(knoi)

41

-,o.

\,

15 20 25

(N: number of revolutions of propeller per minute. DHP; delivered horse power in PS.

Fig. 2. 12 Stopping curve calculated through Table 2. 4

loo 200

T (s.c.

Fig. 2. 11 Stopping curves; Curve A, result of calculation through Table 2. 4, Curve B, result of calculation by Dr. Kito's procedure.

os 0.4' 0 02 _o e o o O -IO -20 -30 -40 e(°)

Fig. 2. 13 Relation between P0IC and O derived from open water test of M. P. No. 1366

Number of revolutions of propeller and delivered horse powercurves

0

zzT

/

b 'S

2O

1GO ASTERN) VSAlGo AHEAD)

Fig. 2. 10 Resistance, thrust and torque curves (R; resistance, T; thrust, Q; torque)

-I. a do '--J.c 2.0 t.o ,

Fig. 2. 14 Stopping curve calculated Fig. 2.15 Backing of propeller;

by Dr. Ritos procedure T; thrust, Q; torque,

S; slip ratio, P; effective pitch ratio, r; time

200 150 ¡00 50 (f)O -50 '5 -/5 -io -5 0 .5 /0

SPEED OP SHIP (knots), Vs

Fig. 2.16 Performance curves of the ship with C. P. P. CM. S. No.1384xM. P. No. 1366)

T; thrust, t; thrust deduction fraction, r & r' time in second. O; twisting angle

of the blades

43

-/5 20 25 Ds

i,jvj1Iu.

ìL<

_r

4ií.'!NiifájA

¡IIIU1IIN

41!Pq/

r

'II'

lii